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Multiphase Transport in Sea Turtle Nesting Beaches

presented by

Nathan Andrew Miller

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6/07 p'IClRC/DateDueindd-pj

MULTIPHASE TRANSPORT PROCESSES IN SEA TURTLE NESTING
BEACHES

By

Nathan Andrew Miller

A DISSERTATION

Submitted to
Michigan State University
in partial fulﬁllment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Zoology

2007

ABSTRACT

MULTIPHASE TRANSPORT PROCESSES IN SEA TURTLE NESTING
BEACHES

By

Nathan Andrew Miller

Sea turtle embryos develop in nest environment determined by the interaction
between their own development and the ability of the nest substrate to transport the
important commodities of heat, water, and respiratory gases. Relatively little is
known of the nest microclimates or how physical characteristics of the nest site
determine the nest environment. This study reports on the nest microclimate in
natural loggerhead turtle nests and presents a computational model which predicts
which nest and nest site characteristics most inﬂuence the nest microclirnate.

The nest p02 in loggerhead turtle nests on Sapelo Island, GA was measured
during the summer of 2006 using ﬁber-optic 02 sensors. The rate that nest p02
declined and the minimum nest p02 varied considerably between nests with some
nests exhibiting rates of decline and minimum p025 2.3 and 1.4 times greater,

respectively, than others. While the mean minimum nest p02 (13.8:t 0.21 kPa)

differed little from previous work, the p02 declined much more rapidly suggesting
that the nest p02 may be low for much longer than previously thought.

To account for this variability in nest microclirnate a three-dimensional,
computational model (Beach-MPT) was developed to predict the multiphase transport
of heat, gas, and water in and around turtle nests. The model was solved using the
ﬁnite element method to take full account of the highly heterogeneous, multilayered
beach substrate and variable clutch characteristics. Model evaluations using physical
nest models demonstrated that the model accurately predicts heat and gas transfer in
dry sand. The model less successfully predicted transport in damp sand.

Subsequent sensitivity analyses demonstrated that nest p02 and temperature
were as sensitive, if not more sensitive, to the abiotic parameters of the nest substrate
compared to the more typically measured biotic characteristics. Additional
simulations demonstrated that nest temperature and nest p02 respond differentially to
changes in the abiotic parameters. My results suggest that sea turtle nest management
and conservation must focus more that it has on abiotic nest characteristics because
processes that alter nesting substrate can dramatically alter nest environments. This
suggests that directed habitat alterations could lead to increases in nest success while
alternatively, haphazard management of nesting substrate can easily decrease nest

SUCCESS.

This dissertation is dedicated to my parents, Robert and Karen Miller for their
unwavering love and belief in me during what has been a long and sometimes

tumultuous process. This dissertation is your support manifested in print.

iv

ACKNOWLEDGEMENTS

I want to thank my advisor, Richard Hill, for his continual support, insightful
comments, and timely advice. Your assistance has improved this dissertation
immensely. I also would like to recognize the incredible support that Mandi McElroy
and Mark Dodd, from the Georgia Department of Natural Resources, provided in the
ﬁeld. The ﬁeld data is as good as it is because of them. Jon Garbisch, at the
University of Georgia Marine Institute, provided incredible logistical support,
wonderful stories about the Georgia low-country, and even taught me a bit about
small-engine repair. Financial assistance was provided by many sources and I would
like to thank the Department of Zoology, the Ecology, Evolutionary Biology, and
Behavior program, the Quantitative Biology and Modeling Initiative, and the College

of Natural Science for their support.

I am also extraordinarily grateful for the kindness and generosity of Page,
Mollie, and Julie without whom I may have faltered. Your ﬁiendship made this

possible. Thank you.

TABLE OF CONTENTS

LIST OF TABLES ....................................................................................... vii
LIST OF FIGURES ..................................................................................... x
INTRODUCTION ....................................................................................... 1
CHAPTER 1

p02 in Loggerhead sea turtle (Caretta caretta) nests
measured using novel ﬁber-optic oxygen sensors

1.1 INTRODUCTION ...................................................................... 7
1.2 METHODS ................................................................................. 13
1.2.1 Fiber-optic Oxygen Sensors .................................. 15
1.2.2 Sensor Calibration ................................................. 15
1.2.3 Schedule of Measurement ..................................... 17
1.2.4 Nest Characteristics .............................................. 17
1.2.5 Statistical Procedures ............................................ 17
1.3 RESULTS ................................................................................... 18
1.4 DISCUSSION ............................................................................. 28
CHAPTER 2

The Structure and Evaluation of a Finite Element Model
Predicting Transport Processes In and Around Sea Turtle Nests

2.1 INTRODUCTION ...................................................................... 35
2.2 Beach-MPT Model ...................................................................... 40
2.2.1 Model Geometry .............................................. 40

2.2.2 Governing Equations ........................................ 45

2.2.3 Variably-Saturated Water Flow ....................... 45

2.2.4 Boundary Conditions ........................... 46

2.2.5 Heat Transport .................................................. 50

2.2.6 Boundary Conditions ........................... 54

2.2.6 Respiratory Gas Transport ............................... 56

2.2.7 Boundary Conditions ........................... 58

2.3 Beach-MPT Evaluation Experiments .......................................... 59
2.4 METHODS ................................................................................. 61

vi

2.4.1 Mesocosm _ ...................................... 61

 

 

2.4.2 Temperature Evaluation .......... 61
2.4.3 p02 Evaluation ................................................. 62
2.4.4 Comparison to Beach-MPT predictions ........... 66
2.5 RESULTS ................................................................................... 68
2.5.1 Temperature Experiments ................................ 68
2.5.2 Oxygen Partial Pressure Experiments .............. 79
2.6 DISCUSSION ............................................................................. 86
2.6.1 Temperature Evaluation Experiments .............. 86
2.6.2 p02 Evaluation Experiments ............................ 87

CHAPTER 3
The Consequences of Nest Site Characteristics on the
Microclimates within Sea Turtle Nests: A Simulation Study

 

 

3.1 INTRODUCTION ...................................................................... 92
3.2 METHODS ................................................................................. 96
3.2.1 Sensitivity Analysis .......................................... 96
3.2.2 Consequences of Beach Renourishment and
Nest Crowding ......... ..... 96
3.2.3 Simulation of Development ............................. 98
3.3 RESULTS ................................................................................... 103
3.3.1 Sensitivity Analysis .......................................... 103
3.3.2 Consequences of Beach Nourishment and
Nest Crowding ............................................ 104
3. 3. 3 Simulation of Development ............................. 105
3 .4 DISCUSSION ........................... 118
APPENDIX I ................................................................................................. 124
APPENDIX 11 ............................................................................................... 127
APPENDD( III .............................................................................................. 145
BIBLIOGRAPHY ......................................................................................... 150

vii

LIST OF TABLES

Table 1. Summary statistics of nest which were followed to within
5 days of hatching. Sample size, range and mean values of several
important nest parameters measured during the study ............................................. 20

Table 2. Reported values of minimum pOzs in sea turtle nests.

Summary of the data available on the minimum p02 measured in

the nests of sea turtles. Means are included when they were given

or could be calculated from the data provided in each reference. In

some cases, the minimum nest p02s were obtained from ﬁgures and

as a result were approximate ..................................................................................... 31

Table 3: Constants used in the base model with values and units .............................. 44

Table 4: Dry Sand Temperature Experiment The coordinate location

of each sensor, the linear distance from each sensor to the nest, and the

maximum difference between the 95% conﬁdence intervals for the

model predictions and the dry sand mesocosm at each location. The

coordinates for each sensor location are measured in centimeters. The x

and y coordinates are measured from a single corner of the mesocosm and

the z coordinate increases from the bottom of the mesocosm to the top. The

max difference calculated as described on page 66. If the 95% conﬁdence

intervals overlap the difference is reported as zero ................................................... 73

Table 5. Damp Sand Temperature Experiment. The coordinate location

ofeach sensor,the lineardistance from eachsensortothenest, and

the maximum difference between the 95% conﬁdence intervals for the

model predictions and the damp sand mesocosm at each location. The

coordinates for each sensor location are measured in centimeters. The x and y
coordinates are measured from a single comer of the mesocosm and the

z coordinate increases from the bottom ofthe mesocosm to the top. The

max difference is calculated as described on page 66. If the 95%

onﬁdence intervals overlap the difference is reported as zero .................................. 77

viii

Table 6. Dry Sand p02 Experiments. Assessing the accuracy of the

Beach-MPT model in (a) Dry Sand p02 Experiment 1 and (b) Dry

Sand p02 Experiment 2. Provided are the linear distance (in cm)

between each sensor and the nest and the mean difference in p02. The

mean difference in p02 for each sensor was calculated as the mean

difference between the p02 predicted by the Beach-MPT model and

the actual mesocosm p02 measurement during the ﬁnal 8 or 9

measurements in each experiment (time > 75 min) .................................................. 82

Table 7: Damp Sand p02 Experiments. Provided are the coordinates

of each sensor (in cm), the linear distance from each sensor to the nest

(in cm), and the mean difference in p02. The mean difference in p02

was calculated for each sensor as the mean difference between the p02

predicted by the Beach-MP1“ model and the actual mesocosm p02

measurement after the p02 levels were roughly constant (the 8

measurements made after each experiment was run ~75 min). The x

and y coordinates are measured from a single corner of the mesocosm

and the z coordinate increases from the bottom of the mesocosm to the top ........... 85

Table 8: Consequences of the tortuosity function on p02. Provided is

the mean difference in the p02 at each sensor location during the damp

sand experiment when two different methods of calculating the sand

tortuosity (Millington and Quick (1961) or Penman (1940)) were used.

The mean difference in p02 was calculated for each sensor as the mean

difference between the p02 predicted by the Beach-MPT model and the

actual mesocosm p02 measurement after the p02 levels were roughly

constant (the 8 measurements made after each experiment was run ~75 min) ......... 90

Table 9. Parameter values used in the Beach-MPT sensitivity analyses .................. 99

Table 10. Parameter values used in Beach-MPT simulations exploring

the consequences of beach renourishment. Because beach nourishment

may lead to increased sand water content or decreased sand porosity

both situations were simulated using the parameters listed here .............................. 100

Table 11. Parameter values used 1n Beach-MPT simulations exploring
the consequences of nest crowding - .................. 101

 

ix

Table 12. Data on four nests studied at Sapelo Island (Chapter 1),
used to parameterize Beach-MPT simulations testing the model’s
ability to predict p02 changes through the entire incubation period.
During the summer of 2006 measurements of the depth to the top
and bottom of the loggerhead nests along with measurements of nest
width, sand water content, sand porosity, and nest p02 were made on
Sapelo Island, GA. Detailed methods are described in Chapter 1. The
nest depth refers to the distance from the sand surface to the top of
the nest, while nest height refers to the distance between the top and
the bottom of the nest. The nest width was measured horizontally at
the widest portion of the nest .................................................................................... 102

Table 13: Response of end-incubation nest p02 to changes in parameter

values. As part of the sensitivity analysis the model parameters were

individual assigned the values shown here. The resulting nest p02 was

recorded and used to calculate a sensitivity index (S) using equation 3.1.

Parameters with larger sensitivity indices have larger affects on the nest

p02 than parameters with smaller indices ................................................................. 106

Table 14: Response of end-incubation nest temperature to changes in

parameter values. As part of the sensitivity analysis the model parameters

were individual assigned the values shown here. The resulting nest

temperature was recorded and used to calculate a sensitivity index (S)

using equation 3.1. Parameters with larger sensitivity indices have larger

affects on the nest temperature than parameters with smaller indices ...................... 107

Table 15. Mean difference, throughout the incubation period, between
the actual nest p025 and the nest pOzs predicted by the Beach-MPT
model (shown in Figure 28)-- -- .................... 117

 

LIST OF FIGURES

Figure 1. A map of Georgia, USA, with the location Sapelo Island, GA

Illustrated ..................................................................................................

Figure 2. Diagram of 0; sensor placed in turtle nest. (a) Wiﬁle golf
ball out in half to show the 02 sensor and thermocouple inside.

(b) Diagram illustrating components of the sensor ...................................

Figure 3. Loggerhead turtle nest pOzs measured over the full course
of incubation in 20 randomly selected nests. The bold line indicates

the day of hatchling emergence ................................................................

Figure 4. p02 measured at four control (nest-free) locations at a depth
of 40 cm during the course of the study

................ 14

................ l6

................ 21

............. 22

 

Figure 5: Relationship between the date a nest was laid and the length

of incubation (Pearson correlation = -0.73, p < 0.0001) ...........................

Figure 6. Relationship between the minimum nest p02 and the length
of incubation (Pearson correlation = -0.316, p = 0.084)

................ 23

- .............. 24

 

Figure 7. Relationship between clutch size and the minimum nest p02

(Pearson correlation = 0.016, p = 0.931) ..................................................

Figure 8. Relationship between the minimum nest p02 in each nest
and the arcsin of hatching success of in that nest. A signiﬁcant
quadratic relationship was found suggesting intermediate, minimum
nest p023 are indicative of nests that will be more successful (one-way

................ 25

ANOVA testing the signiﬁcance of the regression, F230 = 4.2, p = 0.025) .............. 26

xi

Figure 9. Nest p02 following washover by a high tide. a) nest 30,

b) nest 47. The arrows approximate the time of initial tidal washover .........

Figure 10. a) Diagram of a section of insect muscle tissue with
tracheolar tubes, b) tissue section broken into many small elements

as part of the ﬁnite element method (FEM), c) FEM solution of oxygen
diffusion from tracheoles into muscle tissue. Light areas have high p02,

anddarkareasarelowerpOz ........................................................................

Figure 11. In the base-version of the Beach-MPI' model, '/4 of the nest
and surrounding sand is analyzed to reduce the computational cost.
Other geometries, including those considering the interaction among

several nests are possible ....... _ ..........

 

Figure 12. Diagram of experimental setup for 0; evaluation .......................

Figure 13: Diagram (a) and photograph (b) of a ﬁberoptic 0; sensor

mounted in syringe ...................................

 

Figure 14: Change in temperature at individual sensors during
mesocosm experiments using dry sand (0, n = 3) and predicted
change in temperature from simulation model (0, n = 3) and with
95% conﬁdence intervals (d refers to linear distance between the
sensor and nest) Figure is continued on pages 71 and 72

 

Figure 15: Relationship between a sensor’s distance from the nest
and the mean slope of the difference between model predictions and
the dry sand mesocosm measurements plotted as a function of time
(with 95% CI). Negative slopes show the model increasingly
overpredicts the mesocosm temperatures. A slope of zero shows that
the difference between the model predictions and the mesocosm

temperatures remains constant over time -- ...............

 

Figure 16. Change 1n temperature at individual sensors 3during
mesocosm experiments using wet sand (0.1 m3 H20/m3 )(0, n= 3)
and predicted change in temperature from simulation model (0, n= 3)
with 95% conﬁdence intervals. (d refers to the linear distance between

the sensor and the nest). The ﬁgure is continued on page 76 .......................

xii

............ 27

............ 38

............ 41

............ 63

............ 65

......... 7O

............ 74

............ 75

Figure 17. Relationship between a sensor’s distance from the nest
and the mean slope of the difference between model temperature
predictions and the damp sand mesocosm measurements potted as
a ﬁmction of time (with 95% Cl). Positive s10pes show that over
time the model increasingly underpredicts the mesocosm
temperature. A slope of zero shows that the difference between
the model predictions and the mesocosm temperatures remains
constant over time ........................ 78

 

Figure 18. Dry Sand p02 Experiment 1. Comparison of p02

predictions from the Beach-MPT model (0) and measurements

made in the dry sand mesocosm (0). Artiﬁcial nest internal p02

~13 kPa. (d refers to the linear distance between the sensor and

the nest) - - - - - - -- - ....................... 8O

 

Figure 19: Dry Sand p02 Experiment 2. Comparison of p02

predictions generated by the Beach-MPT model (0) and p02

measurements made in the dry sand mesocosm (O). Artiﬁcial nest

internal p02 ~13.5 kPa. (d refers to the linear distance between the

sensor and the nest) ............................................................................... 81

 

Figure 20. Comparison of p02 predictions generated by the

Beach-MPT model (C, A , D) and p02 measurements made in the

wet sand mesocosm (o, v, I). Sensor coordinates are also shown.

MeanpOz innestwas 11.4 kPa. (dreferstothelineardistancebetween

the sensor and the nest) ............................................................................................. 84

Figure 21. Vertical transect through a beach in which a 0.1 meter

radius turtle nest is positioned at 0.4-0.6 m depth. a) simulated p02

values around a nest in a natural beach (- -) and a nourished beach

(—) which holds ~3 times the water, b) simulated p02 values around
anestinanaturalbeach(- -)andanourishedbeach(—)inwhichthe

porosity is decreased by 0.05 m3/m3 or ~10%. Horizontal dashed lines

delineate the nest boundaries ............... - .......................... 108

 

xiii

Figure 22. Vertical transect through a beach in which a 0.1 meter

radius turtle nest is positioned at 04-06 m depth. Simulated p02 values

around nest in a natural beach (- -) and a nourished beach (—) in which

the water holding capacity was increased ~3 times the water and the

porosity was decreased by 0. 05 m3/m3 or ~10°/o. Horizontal dashed

lines delineate the nest boundaries ..... _ .......... - ..................... 109

 

Figure 23. Vertical transect through both a natural and a nourished

beach in which a 0.1 m radius turtle nest is positioned at 0.4-0.6 m

depth. The nourished beach holds ~3 times more water than me

natural beach. Horizontal dashed lines delineate the nest boundaries ...................... 110

Figure 24. Vertical transect through both a natural and a nourished
beachinwhicha0.1mradiusturtlenestispositionedat30H4-06m

depth. The porosity of the nomished beach rs 0. 05 m3/m3 or ~10%

lower than the porosity of the natural beach. Horizontal dashed lines

delineate the nest boundaries. To prevent overlap and aid in visualization,

a 0. 2° C displacement was added to the lines representing the nourished

beaches ......................... - ..... 11 1

 

Figure 25. Results of Beach-MPT simulation showing the p02 gradients

within and around two nearby nests. Both nests had a radius of 0.1 meter

and were centered at a depth of 0.5 meters. The solid lines represent
horizontaltransectsdrawnthroughthecenters ofeachnestatadepthof

0.5 meters. A) nests 0.3 meters apart, b) nests 0.5 meters apart, c) nests

1 meter apart Parameters used in simulations are provided in table 3 ..................... 112

Figure 26. Simulation of p02 gradients in and around a set of four,

0.1 meter diameter nests, centered at a depth of 0.5 meters. a) Three-

dimensional reference for the images shown in Figure 24b and

Figure 24c. b) p02 gradients as seen from the side. The sand surface

is the upperboundary. c)thep02 gradientsaroundthe fournestsas

viewed from above. The black dashed lines in Figure 3b are one

meter apart and in Figure 3c the dashed square is one square meter.
TheminimumpOzinallfournestswas 17.1 kPa. -- .............................. 113

 

Figure 27. Results of Beach-MPT simulation showing the p02

gradients within and around two nests in the four nest simulation.
Allnestshadaradiusof0.1meterandwerecenteredatadepthof

0.5 meters. The solid lines represent a horizontal transect drawn

throughthe centers ofeachnestatadepth of0.5 meters ......................................... 114

xiv

Figure 28. Simulated of p02 gradients in and around a set of nine,

0.1 meter diameter nests, centered at a depth of 0.5 meters. a) Three-

dimensional reference for the images shown in Figure 26b and

Figure 26c. b) p02 gradients as seen ﬁom the side. The sand

surface is the upper boundary. c) the p02 gradients around the

nine nests as viewed ﬁom above. The black dashed lines in ﬁgure
3aareonemeterapartandinﬁgure 3bthedashedsquareisone
squaremeter.TheminimumpOzwasl3.2kPainthecentralnest - - --115

 

Figure 29. Horizontal transects through the nine nest simulation

shown in ﬁgure 8 illustrating the p02 gradients in and around

three nests. a) Horizontal p02 transect through three nests along

the edge of the arrangement. b) Horizontal transect through three
nestsinthemiddleofthearrangemenLAllnestswerecenteredata

depth of 0.5 meters and both transects went through the middle of

each nest. Nest locations are shown by the cross-hatching. The
distancebetweenthenestedgeswas005 meters _ ............ 116

 

Figure 30. Comparisons of predicted (e) and actual (o) nest p023

throughout the course of nest incubation in the four nests selected

for study. In each case the model was parameterized with the ﬁeld

data shown in Table 12. The actual nest p023 were measured during

the 2006 nesting season on Sapelo Island, GA - 117

 

Images in this dissertation are presented in color

XV

INTRODUCTION

The sandy beaches of the Eastern and Gulf coasts of the United States serve as
nesting habitat for the loggerhead turtle (Caretta caretta), the green turtle (Chelom’a
mydas), the leatherback turtle (Dermochelys coriacea), the hawksbill turtle
(Eretmochyles imbricate), and the Kemp’s ridley turtle (Lepidochelys kempr). All
marine turtles are listed as endangered or critically endangered by the World
Conservation Union (IUCN), and therefore questions of habitat use and suitability are
of the utmost importance (IUCN 2004). Little is known of their lifespans, although it
is speculated that some species may require 25 -35 years to reach reproductive
maturity and they may live for 50-60 years. Once reproductively mature, female
turtles migrate to terrestrial nesting sites and deposit their eggs on sandy beaches
within ﬂask-shaped nests. A loggerhead female typically lays two to three clutches of
110-120 eggs each, every two to three years (Ackerman 1997).

Postovipositional care is absent in turtles, and as the eggs develop over the
course of 50-70 days, the nest site is an important determinant of the developmental
environment for each embryo. Laboratory work has shown that the nest environment
can have dramatic effects on the survival and phenotype of turtle embryos. Physical
characteristics of the nest environment such as temperature, moisture, and respiratory
gas pressure inﬂuence incubation length (Mrosovsky and Yntema 1980, Ackerman
1981, Drake and Spotila 2002), sex determination (Matsuzawa et a1. 2002), and
embryonic survival (Mrosovsky and Yntema 1980, Kraemer and Bell 1980, Mortimer
1990). These physical characterstics may also alter other important phenotypic traits

including body size (Tracy et a1 1978, Hewavisenthi and Parmenter 2001), growth

rate (Kam 1993, Rhen and Lang 1995), and running speed (Miller et al. 1987).
Therefore, nest site characteristics have far reaching consequences for turtle ecology,
evolution, and conservation.

Despite considerable laboratory-derived knowledge concerning the effects of
temperature, moisture, and respiratory gases on turtle embryos, and despite broad
recognition that successful marine turtle conservation is dependent on an
understanding of the clutch environment (Ackerman 1980), remarkably little is
known about the microclimates within natural turtle nests (Maloney et al. 1990). Even
less is known about how the physical characteristics of the nest site inﬂuence the nest
microclimate. As a result, an understanding of the physical processes that determine
nest environment rarely drives terrestrial management decisions (e.g., decisions about
beach nourishment, nest movement, and hatchery construction). As dune
modiﬁcation, coastal development, erosion, and rising sea levels continue to alter
sandy beaches (Titus 1998, IPCC 2001 , Titus and Richman 2001), there is a growing
need to ensure that the integrity of marine turtle nesting habitat is maintained.

Achieving balance between economically viable beaches and nesting habitat
requires a predictive understanding of the physical processes that determine the nest
environment. In the past this has been accomplished through retrospective analyses,
which attempted to correlate nest site characteristics with a measure of nest success.
In the ﬁrture what is needed are prospective analyses which use ﬁrst principles to
develop predictions of the nest microclimate. Additionally, because sea turtles are
endangered and attempts to measure the relevant parameters in situ necessarily alter

the nest environment, strictly empirical studies must be supplemented by alternative

techniques. In the past, to circumvent these challenges, researchers have used
analytical models to examine how the physical characteristics of the nesting beach
inﬂuence the nest microenvironment (Ackerman 1977). The drawback of analytical
models is that transport phenomena of interest must be represented by rudimentary,
uncoupled equations, and the habitat must be represented by simple geometry. As a
result, much of the physical and biological complexity these models are built to
explore must be ignored.

The inherent limitations of analytical models will not allow us to generate the
accurate, quantitative predictions we need. In this study I have combined disciplines
(a biological problem explored with engineering technology), models (computational
and physical models), and techniques (using computational, laboratory, and ﬁeld
studies) in an effort to improve our understanding of how the physical characteristics
of the nest site inﬂuence the nest microclimate. To this end, I have used a numerical
modeling technique, the ﬁnite element method (Kaliakin 2002, Logan 2002), which
differs in several ways from the analytical models that biologists have traditionally
used (e.g., Ackerman 1977, Seymour and Roberts 1991, Seymour and Seely 1996).
This method is widely used in engineering ﬁelds to model complex systems, but is
currently underutilized in biological ﬁelds. The method allows model parameters
(such as thermal or hydraulic conductivity or porosity) to vary realistically in both
space and time. It also permits inclusion of realistic geometries and can couple
nonlinear transport phenomena so their simultaneous operation can be understood. I
have combined this solution method with physical models of turtle nests and ﬁeld

studies of actual conditions within sea turtle nests under natural conditions. Through

this multifaceted approach I have assessed quantitatively the impact of conditions
such as nesting substrate heterogeneity, clutch metabolism, and microbial respiration
dynamics on nest microclimates and nest survival.

The environment within a sea turtle nest is determined by complex
interactions between biotic clutch characteristics and abiotic characteristics of the nest
and nest site, with important consequences for embryonic development. Several
authors have reported empirical data on the gaseous environment (Ackerman 1977 ,
Mortimer 1991, Wallace et al., 2004, Ralph et al., 2005) within artiﬁcial or hatchery
nests. All of these studies, however, used methods which required the removal of nest
air to measure the nest p02. Such methods raise serious concerns because the removal
of gases ﬁ'om the nest will induce the bulk ﬂow of gases into the nest, thereby
altering the current measurement and all subsequent measurements as well. Wallace
et al. (2004) and Ralph et al. (2005) both recognize that their methods could induce
signiﬁcant bulk ﬂow and attempted to quantify and discount the effect. They also
used methods that tended to minimize the potential for generating dramatic bulk ﬂow.
Despite these important steps concern remains over whether the previously reported
nest pOz’s represent actual nest pOz’s or include methodologically-induced artifacts.
In addition, all previous studies primarily examined nests that were relocated to
hatcheries and thus may not have represented the conditions found in nests at natural
nest sites. To quantify accurately the nest p02 in natural nests, measurements must be
made in nests at natural nest sites and be made in a manner which does not alter the

gaseous environment in the nest.

With this in mind, I describe in Chapter 1 the results of a ﬁeld study
demonstrating the robust nature of a relatively new 02 sensing technology, use of
ﬁber-optic oxygen sensors, which does not alter pOz’s or induce bulk gas transport,
and then I document for the ﬁrst time unaltered nest p02’s in loggerhead turtle nests
at natural nesting sites. The data from this study identify the undisturbed p02 levels
within sea turtle nests in natural nest locations and demonstrate the variability that
exists among nests.

Although the results presented in Chapter 1 show the considerable variability
that exists between nests in terms of p02, the reasons for this variability are unclear.
Clarifying the factors that drive this variability requires an understanding of how heat,
water, and gases move in and around a turtle nest. To describe the mechanisms that
contribute to the nest p02, nest temperature, and moisture levels I developed a
dynamic computer model using the ﬁnite element method. In Chapter 2, I begin by
brieﬂy describing the ﬁnite element method and then provide a detailed discussion of
the structure of the computational model (Beach-MultiPhase Transport, Beach-MPT),
including parameter values and governing equations. I conclude Chapter 2 by
describing the results of a series of rigorous laboratory experiments which conﬁrm
the Beach-MPT model’s ability to predict temperature, water content, and p02 under
controlled laboratory conditions. I carried out these laboratory tests because of my
recognition that whereas models are inherently simpliﬁcations of the real world
(Oreskes et al. 1994), there is a need to demonstrate that a model exhibits internal

consistency and is capable of generating accurate and useful predictions.

After demonstrating the ability of Beach-MPT to predict transport accurately
within sandy beaches (in Chapter 2), I use the model in a heuristic manner in Chapter
3 to explore how variation in nesting substrate (both natural and human-induced),
microbial respiration, nest depth, and other environmental and clutch-speciﬁc
characteristics inﬂuence nest microclimates. A series of sensitivity analyses elucidate
which model parameters most inﬂuence the nest temperature and p02. I then use the
model to explore the potential consequences of beach nourishment and nest crowding
on nest microclimates.

This dissertation broadens our understanding of the microclimate in sea turtle
nests and the biotic and abiotic factors that inﬂuence it. Combining empirical ﬁeld
studies with physical and computation models has provided new insights into how
nest microclimates are determined, what physical and biological characteristics are
most important in this detemrination, and how these characteristics may interact. This
type of understanding provides insights into the developmental environment in
natural turtle nests, suggests the consequences of human-induced changes to these

characteristics, and provides a basis for informed sea turtle conservation.

CHAPTER 1

p02 in Loggerhead sea turtle (Caretta caretta) nests measured
using novel ﬁber-optic oxygen sensors

1.1 INTRODUCTION

All sea turtles are listed as endangered or critically endangered by the World
Conservation Union (IUCN 2001), and therefore questions of habitat use and
suitability are of the utmost importance. During the nesting season loggerhead sea
turtles migrate to terrestrial nesting sites and deposit their eggs on sandy beaches
within ﬂask-shaped nests. A loggerhead female typically lays two to three clutches of
110-120 eggs each, every two to three years. Postovipositional care is absent in
turtles, and as the eggs develop over the course of 50-70 days, the features of the nest
site are important determinants of the developmental environment for each embryo.
Laboratory work has shown that the nest environment can have dramatic effects on
the survival and phenotype of turtle embryos. Physical characteristics of the nest
environment such as temperature, moisture, and respiratory gas pressure inﬂuence
incubation length (Ackerman 1981; Drake and Spotila 2002; Matsuzawa et al. 2002),
sex determination (Mrosovsky and Yntema 1980; Yntema and Mrosovsky 1980), and
embryonic survival (Kraemer and Bell 1980; Ackerman 1981; Mortimer 1990). These
physical characteristics may also alter other important phenotypic traits including

body size (Tracy et al. 1978; Hewavisenthi and Parmenter 2001), growth rate (Kam

1993; Rhen and Lang 1995), and running speed (Miller et al. 1987). Therefore, nest
site characteristics have far reaching consequences for turtle ecology, evolution, and
conservation.

Despite considerable laboratory-derived knowledge concerning the effects of
temperature, moisture, and respiratory gases on turtle embryos, and broad recognition
that successful marine turtle conservation is dependent on an understanding of the
clutch environment (Ackerman 1980), remarkably little is known about the
microclimates within natural turtle nests. Even less is known about how the physical
characteristics of the nest site inﬂuence the nest microclimate. There is every reason
to think that sand type, for instance, could affect respiratory gas pressure or other
attributes of the nest microclimate. Because of a lack of information on such effects,
however, management decisions about beach nourishment, nest relocation, and
hatchery construction are rarely driven by knowledge of the ways in which the
physical setting of nests will inﬂuence the nest environment. As dune modiﬁcation,
coastal development, erosion, and rising sea levels continue to alter sandy beaches
(Titus 1998; IPCC 2001; Titus and Richman 2001), there is an increasing need for an
understanding of the physical determinants of the environments in which turtle
nestlings develop. This is additionally important because nests which may be
threatened by waves, vehicles, or foot—trafﬁc are often relocated by managers to
“superior” locations. Without a better understanding of how the physical environment
determines the nest environment, the superiority of the new nest site is simply

speculative.

Nest temperature has been the most measured component of the sea turtle nest
microclimate, in part because of the dramatic effects of temperature on sex
determination. Nest temperature has also been the most reliably measured
component. Miniature temperature dataloggers buried within nests, for example, can
record temperature with little concern that the methods are affecting the results.

In contrast the nest oxygen partial pressure (p02) has been measured
comparatively few times. Moreover, the methods heretofore available for measuring
nest p02 have potentially altered the p02 to at least a small extent because all such
methods have required that gas ﬂow be induced in the nests. In several cases gas
samples for analysis were withdrawn from the nest through plastic tubing by syringe
(Ackerman 1977; Maloney et al. 1990; Clusella-Trullas 2000). More recently, p02
measurements were made by pumping gases ﬁom the nest, through a portable gas
analyzer, and back to the nest (Wallace et al. 2004; Ralph et al. 2005). Both methods
raise concerns because the removal of gases from the nest will invariably induce bulk
ﬂow of interstitial gases into the nest, thereby possibly altering not only the current
measurement, but all subsequent measurements as well. Wallace et al. (2004) and
Ralph et al. (2005) recognized this concern and minimized the potential for
generating bulk ﬂow during their measurements, while at the same time quantifying
the errors such ﬂow would generate.

The recent development of ﬁber optic p02 sensors has created the opportunity
for noninvasive measurement of p02. Fiber optic sensors, which do not consume 02
and require no gas movement to carry out accm'ate measurements, capitalize on the

ability of 02 to dynamically quench the ﬂuorescence of an 02 sensitive dye. A small

amount of the ﬂuorescent dye is immobilized on the tip of a ﬁber optic cable. When
blue light is transmitted down the cable, the dye is excited and ﬂuoresces. The
ﬂuorescent signal travels up the ﬁber optic cable, and the ﬂuorescence lifetime (the
length of time the dye ﬂuoresces) is measured. In the presence of 0;, molecular
collisions between the excited dye and the 02 result in an energy transfer from the
dye to the 02 molecules. This energy transfer decreases the ﬂuorescence lifetime of
the dye, and the decreased ﬂuorescence lifetime is proportional to the 02
concentration (Klimant 1995; Glud et al. 2000). Physically, a ﬁber optic 0; sensor
consists of an arbitrarily long piece of small-gauge ﬁber optic cable with the dye
immobilized on one end and the other end connected to an excitation/read-out device.
In application to sea turtle nests, the dye-treated tip is placed within a nest and the
connecting cable is threaded to the sand surface. Measurements, as earlier noted, do
not themselves alter the p02, nor do they require or induce gas movements. Installing
a cable requires manipulation of the sand, but after a cable is in position, it requires
no maintenance and can be left in place, undisturbed, indeﬁnitely.

Fiber optic 0; sensors provide the opportunity to assess directly whether p02
measured by traditional ﬂow-based methods are realistic. In the past, the potential
errors that gas ﬂow might induce could be assessed through modeling but not by
direct comparison of the data obtained with data from a non-ﬂow-based method.

Fiber optic 02 sensors also provide the opportunity to sort out paradoxes in
the literature because the potential for ﬂow-based artifacts can be eliminated ﬁom
consideration. To illustrate, Wallace et al. (2004) found no signiﬁcant relationship

between minimum nest p02 and hatching success, attributing the lack of signiﬁcance

10

to the large variability in interclutch hatching success. Ralph et al. (2005) also
reported no relationship between nest p02 and developmental success and suggested
that other environmental variables such as substrate moisture might control hatching
success. These results from ﬁeld studies of natural nests are paradoxical because
laboratory experiments have shown that under low p02, hatching success and
embryonic growth rate decrease (Ackerman 1981). Does the lack of a relationship
between minimum nest p02 and hatching success in the ﬁeld data indicate that ﬁeld
biology is different from lab biology, or is it possibly a reﬂection that the nest p02
has not been accurately or thoroughly quantiﬁed with the ﬁeld methods? Fiber optic
methods promise to address this question because they are intrinsically less likely to
induce p02 artifacts than ﬂow-based methods, and they permit especially thorough
studies because individual measurements require little labor.

The objective of this research was to develop a noninvasive means of
accurately measuring the nest p02 in loggerhead turtle nests in natural nest locations,
evaluate the extent of the change in p02 during incubation in multiple nests, and
examine the relationship between nest p02 and hatching success, incubation length,
and certain management-motivated nest relocation protocols. Given the apparent
importance of p02 for metabolism, growth rate, and hatching success in laboratory
studies (Ackerman 1981; Kam 1993), I suspect that a relationship between nest p02
and hatching success has not been detected in the ﬁeld because of the methods used
to measure nest p02. I further suspect that by accurately measuring nest p02 using a
relatively non-invasive 02 sensing technology, ﬁber-optic oxygen sensors, 1 would

ﬁnd that the minimum nest p02 alters hatching success and incubation length. Finally,

11

I suspect those nests that have been moved by managers to “superior” locations will

have higher p02s that those nests left in their initial location.

12

1.2~ METHODS

This study was conducted during the summer of 2006 on the undeveloped beaches of
Sapelo Island, a barrier island along the coast of Georgia, USA (Figure 1). The
nesting season on Sapelo Island runs ﬁ'orn late May through early August, with all
nests hatching by the middle of October. Freshly laid nests were located each
morning and randomly assigned to an in situ or relocated treatment as part of a
Georgia Department of Natural Resources (DNR) study. At in situ nests, which were
left at the sites where mothers constructed them, the sand immediately above each
nest was removed until the upper surface of the nest was located. Twelve to ﬁfteen
eggs were removed to create an opening into the center of the nest. Then an oxygen
sensor was placed in the middle of the nest, the eggs that had been removed were
replaced, and the nest was recovered with sand. Relocated nests were moved to new
locations that appeared, based on the judgment of expert managers, to be of
equivalent or better quality than the original nest site. For example, nests laid low on
the beach were moved into the primary dunes, and nests laid in the primary dunes
were relocated to equivalent sites in the dunes. Each new nest was constructed by
hand, ensuring that it was the same depth and width as the original nest. After half of
the eggs had been placed in the new nest, an oxygen sensor was placed in the middle
of the nest before the remaining eggs were added and the nest covered with sand. The
aboveground portion of ﬁber optic cable was protected in a small, plastic container,
when not being employed for data collection. At four randomly chosen locations, 02
sensors were buried at a depth of 40 cm in sand where there were no nests, to serve as

controls. Within several days, both wind and rain had thoroughly packed the

13

    

Savannah. GA

Smclo Islmd, GA

Jacksonville, FL

Figure 1. A map of Georgia, USA, with the location Sapelo Island, GA illustrated.

14

sand, and all measurements were made on naturally weathered nests. All 02 sensors
were left in place for the duration of the study.

l.2.1~ Fiber-optic Oxygen Sensors

Five meter multimode simplex optical ﬁber patchcords (Anixter, Grand Rapids, MI,
USA, 100/140, ST,ST) and the ﬂuorescent dye, Pt(II) meso-tetra(pentaﬂuorophenyl)
porphine (Frontier Scientiﬁc, Utah, USA) were employed to construct the sensors,
following the method of Klimant et al. (1995). Sensors were then mounted inside
golf-ball-sized Wiffle TM balls (Figure 2). The p02 measurements were made using a
Microx-TX3 excitation/measurement unit manufactured by Presens Precision Sensing
GmbH, Germany and the corresponding software (OxyView, version. TX3_v531).
Each sensor could be connected to the Microx-TX3 by use of a ST—type ﬁtting. A
thermocouple was arranged in tandem with each sensor, providing a measure of nest
temperature and of the temperature of the ﬂuorescent dye, necessary for calculating
p02.

1.2.2 Sensor Calibration

Each sensor was individually calibrated using a two-point calibration protocol. The
ﬁrst calibration point was the p02 of humid atmospheric air and was performed in a
ﬂask containing a moist towel. The p02 of an oxygen-free 1% sodium sulﬁte solution
served as the second calibration point. Rechecks of the calibration of numerous
sensors demonstrated that the calibration did not change over time [as also reported

by Klimant et al. 1995 and Gatti et al. (2002)].

15

 

Figure 2. Diagram of 02 sensor placed in turtle nest. (a) Wifﬂe golf ball cut in half to
show the 02 sensor and thermocouple inside. (b) Diagram illustrating components of
the sensor.

1.2.3~ Schedule of p02 Measurement

p02 measurements were made every 3 days at the same time of day
throughout incubation. After day 47 of incubation, the p02 was measured daily so as
to better quantify the nest p02 just before and just after hatching. When possible, the
nest p02 was measured for 10 days following hatchling emergence from the nest.
l.2.4~ Nest characteristics

At each nest, the depth to the top of the nest, the width of the nest cavity, the
depth of the sensor, and the number of eggs in the clutch were recorded (Table l).
The elevation of all nests above mean sea level was measured by a Georgia DNR
survey crew.

Ten days post-emergence, the number of successful hatchlings from a nest
was calculated by excavating the nest and counting the number of whole eggs,
hatchlings, and broken and torn shells in the nest cavity. The procedure was carried
out by the Georgia DNR, which used a 50% rule, whereby a shell ﬁ‘agment that
represented more than 50% of the total egg shell was counted as representing a
complete hatched egg. All smaller fragments were not considered to represent
hatched eggs. It has been shown that this practice results in a small, 6% error in the
estimation of the number of hatched eggs (Mark Dodd, GA DNR, personal
communication). The number of unhatched eggs, and the number of live and dead
hatchlings in each nest was recorded at the same time.
l.2.5~ Statistical Procedures

Differences between in situ and relocated nests were assessed using one-way

ANOVA, and all linear correlations were calculated using SPSS (ver. 14).

17

l.3~ RESULTS

F ifty-nine nests had oxygen sensors placed in them, but three sensors either
failed or broke during the measurement period. Time constraints limited the number
of nests in which p02 could be recorded for the ﬁll] duration of egg development,
ﬁom egg deposition to hatchling emergence. Of the 59 nests containing sensors, 27
were followed until hatchling emergence. An additional 8 nests were followed to
within 5 days of hatchling emergence. Two nests, numbered 30 and 47, studied
throughout development, were washed over by high spring tides several times, and
while these nests were of considerable interest, they were not included in any
summary statistics or statistical analyses involving nest p02. As a result, of the 56
nests containing working 02 sensors, 33 were used in analyses involving nest p02 and
35 were used in all other analyses, unless otherwise noted (Table 1).

The minimum nest p02 did not differ between in situ and relocated nests (one-
way AN OVA, F3 29 = 1.829, P = 0.164) though a priori, independent contrasts
demonstrated that the minimum nest p02 of the nests was signiﬁcantly different from
that of the control locations (Contrast test, df = 4.9, t = -7.56, p = 0.001). For all
subsequent analyses the nests were combined.

In the nests followed up to the date of hatching (or to within 5 days of that date), the
nest p02 declined throughout development, the rate of decline being greater during
the second half of incubation in all nests (Figure 3). The p02 also declined in all nests
that were not followed for the full duration of incubation. Control sites (those without
nests) showed much slower declines in p02, though the p02 at control sites was 2-3

kPa below atmospheric levels by the end of the measurement period (Figure 4). There

18

was a signiﬁcant relationship between the rate at which the nest p02 declined and the
minimum nest p02 (Pearson correlation = -0.837, p<0.0001). A strong negative
relationship was observed between the date that a nest was laid and the length of
incubation (Pearson correlation = -0.73, p < 0.0001, Figure 5), with nests laid later in
the season exhibiting incubation periods that were approximately 6 days shorter than
the earliest nests. There was no evidence of a signiﬁcant linear relationship between
minimum nest p02 and incubation length (Pearson correlation = -0.316, p = 0.084) or
clutch size and minimum nest p02 (Pearson correlation = 0.016, p = 0.931). However,
a signiﬁcant quadratic or hump-shaped relationship was observed between minimum
nest p02 and the arcsin of hatching success (one-way ANOVA, F250 = 4.2, p = 0.025,
Figure 8)

The two nests (30 and 47) washed over by high tides during the come
of incubation showed dramatic declines in nest p02 following the washover events,
but p02 levels began to rise within 2 days (Figure 9). Both nests suffered high
mortality with hatching success of 13.6% (16/117) and 0.0% (0/82), in nest 30 and

47, respectively.

19

Table 1. Summary statistics of nest which were followed to within 5 days of hatching.
Sample size, range and mean values of several important nest parameters measured
during the study. The minimum nest p02 of the controls was 18.5 i 0.24 kPa.

 

 

 

 

 

 

 

N Range Mean :t SE

Depth to Top of Nest (cm) 35 17.0 — 44.0 28.8 :I: 1.15

Depth of Sensor (cm) 34 27.0 - 57.0 42.8 :I: 1.43

Width of Nest Chamber (cm) 32 17.5 — 30.0 23.0 i 0.63

Hatching Success (%) 34 0.0 - 97.7 75.6 :I: 4.19

Minimum Nest p02 33 11.4 — 16.4 13.8 d: 0.21
Clutch Size 35 71-165 116i3.3

 

20

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Day of Incubation

Figure 3. Loggerhead turtle nest p02s measured over the full course of incubation in
20 randomly selected nests. The bold line indicates the day of hatchling emergence.

 

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Oxygen Partial Pressure (kPa)
63

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Figure 4. p02 measured at four control (nest-ﬂee) locations at a depth of 40 cm
during the course of the study.

22

 

 

 

 

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Figure 5: Relationship between the date a nest was laid and the length of incubation
(Pearson correlation = -0.73, p < 0.0001).

23

 

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17

Minimum Nest pO2 (kPa)

Figure 6. Relationship between the minimum nest p02 and the length of incubation
(Pearson correlation = -0.316, p = 0.084).

24

 

 

 

 

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Figure 7. Relationship between clutch size and the minimum nest p02 (Pearson
correlation = 0.016, p = 0.931).

25

 

arcsin (Hatching Success)

 

 

 

 

11 12 13 14 15 16 17
Minimum Nest p02 (kPa)

Figure 8. Relationship between the minimum nest p02 in each nest and the arcsin of
hatching success of in that nest. A signiﬁcant quadratic relationship was found
suggesting intermediate, minimum nest pOzs are indicative of nests that will be more
successful (one-way AN OVA testing the signiﬁcance of the regression, F 2 30 = 4.2, p
= 0.025).

26

8
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Oxygen Partial Pressure (kPa)
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9‘

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0 10 20 30 40 50 60 70
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Day of Incubation
Figure 9: Nest p02 following washover by a high tide. a) nest 30, b) nest 47. The
arrows approximate the time of initial tidal washover.

27

l.4~ DISCUSSION

The nest microclimate within sea turtle nests may have dramatic effects upon
embryonic survival and hatchling phenotype, and prudent conservation requires
cmeful documentation of the variability in nest conditions. I report here, for the ﬁrst
time, the use of ﬁber-optic 0; sensors in measuring 0; partial pressures in sea turtle
nests. Because these sensors do not consume 02 or induce bulk ﬂow they represent a
more certain means of measuring nest 02 levels compared to previous methods.
F iber-optic 0; sensors have been used to measure p02 in sediment boundary layers,
microbial mats, and benthic respiration in deep sea sediments (Glud et al. 1999; Gatti
et al. 2002). These sensors have also been used to quantify the p02 in amphibian eggs
(Warkentin et al. 2005) and decapod crustacean egg masses (F eméndez et al. 2002).
The present research, however, represents one of the ﬁrst uses of these sensors in a
terrestrial system and one of the longest sensor deployments (~60 days). It also
represents the ﬁrst time that undisturbed nest p02’s have been recorded for sea turtles.

I recognize that the initial placement of these sensors may signiﬁcantly alter
the nest p02. However, all sensors were placed in the nests the morning after each
nest was laid and while the nesting substrate was still disturbed from the nesting
female. Therefore, the additional disturbance at this time should have little affect on
subsequent nest p02 values. Relocated nests clearly experience additional
disturbance, but the minimum nest p02 in relocated nests did not differ ﬁ'om those
measured in in situ nests, suggesting that the additional disturbance does not have

long term consequences for nest p02.

28

Not unexpectedly, the p02 in all nests was found to decline throughout the
incubation period. The rate and extent of the decline varied considerably between
nests, however. The rate of decline was 2.3 times as great in certain nests than others,
and the minimum p02 was 1.4 times as great in certain ones than others. Whereas
previous authors found that the nest p02 did not begin to decline until the second half
of incubation (Ackerman 1977, Wallace et al. 2004), I found that the nest p02 began
declining within a few days of the nest having been laid. It is quite possible that using
techniques that withdraw nest gases during the early stages of development masked
early declines in nest p02 (possibly less sensitive techniques are able to detect
reduced nest p02 only after nest metabolism has risen to a threshold value). It is also
of interest that whereas the control (nest-ﬂee) sites used by other authors closely
approximated atmospheric pOz’s (Ackerman 1977, Wallace et al. 2004, Ralph et al.
2005), I found that the p02 at my control sites declined to a level 2-3 kPa below
atmospheric levels (Figure 4). Microbial or root respiration may account for the lower
02 levels at the control locations, though ﬁrrther studies are needed. It may be that the
control sites of other authors simply lacked microbial populations, or it may be that
the ﬁber optic method is more suited to detecting small differences than other
methods.

Despite the different measurement methods, the mean minimum nest p02
recorded in this study (13.8 i 0.21 kPa) is in general agreement with the results of
Ackerman (1977) who measured minimum nest pOz’s of 93-146 kPa in loggerhead
and green turtle nests and Maloney et al. (1990) who measured nest p02’s of 16.8-

175 kPa in several loggerhead turtle nests. These values are signiﬁcantly lower than

29

minimum pOzs measured in the nests of leatherback (Wallace et al. 2004; Ralph et al.
2005) and olive ridley turtles (Clusella-Trullas 2000) (Table 2). The differences in
minimum nest pOzs between species cannot be explained as a consequence of nest
depth because the leatherback nests were 0.75 m deep, whereas the average depth of
the loggerhead turtle nests was 0.40 m in Ackerrnan’s study and 0.29 m in this study.
Wallace et al. (2004) suggest that tidal pumping could account for the high p025 in
leatherback nests at Playa Grande, Costa Rica, but comparative studies of the
importance of tidal pumping in nests on divergent beaches have not been performed.
Wallace et al. (2004) and Ackerman (1977) both found a signiﬁcant
» relationship between clutch size and minimum nest p02, but I failed to detect this
relationship. I did ﬁnd a signiﬁcant quadratic relationship between minimum nest p02
and hatching success (Figure 8), a result which was not observed by Wallace et al.
(2004) or Ralph et al. (2005). It may be that Wallace et al. (2004) and Ralph et al.
(2005) did not consider the possibility of a quadratic relationship between minimum
nest p02 and hatching success or it may be that given their smaller sample sizes such
a relationship was not discemable. It is not possible to assess either of these
possibilities ﬁom either reference. This hump-shaped relationship is not entirely
unexpected. Those nests that exhibited dramatically low p023 would be expected to
have low hatching success. Alternatively, those nests that had much higher minimum
nest pOzs might simply be those nests in which the embryos died early in
development so the nest p02 was never drawn down. Those nests with intermediate
pOzs represent nests which contain respiring embryos as well as sufficient gas

exchange.

30

Table 2. Reported values of minimum pOzs in sea turtle nests. Summary of
the data available on the minimum p02 measured in the nests of sea turtles. Means are
included when they were given or could be calculated ﬁom the data provided in each
reference. In some cases, the minimum nest p02s were obtained from ﬁgures and as a

result were approximate.

 

 

 

 

 

 

 

 

. Nest Minimum nest p02
SW“ Number (e SE if available) “chm“
Leatherback Turtle .
(Dermochelys coriacea) 16 Mean. 18'9 i 0'28 kPa Ralph Ct al. (2005)
Leatherback Tuiﬂe 21 Mean: 18.9 a: 0.16 kPa Wallace et al. (2004)
(Dermochelys coriacea)
Olive Ridley Turtle 1 15 2 kPa CIuSCIla-Trullas
(Lepidochelys olivacea) ' (2000)
Loggerhead Turtle
(Caretta caretta) 2 16"” kPa Maloney (1990)
Loggerhead Turtle ~
(Caretta caretta) 10 14'5 kPa Ackerman (1977)
Loggerhead Turtle . .
(Caretta caretra) 34 Mean. 13.8 :t 0.2] kPa Thrs study
Green Turtle
(Chejom-a mydas) 10 ~95 kPa Ackerman (1977)

 

31

The lack of a relationship between minimum nest p02 and incubation length
was also unexpected given the critical p02 (chZ: the p02 below which metabolism is
reduced) of loggerhead embryos. Kam (1993) found that at day 22 of incubation the
chZ of loggerhead turtle embryos was 16.5 kPa and the chz increased over the
course of development to a maximum of 18.1 kPa on day 45. Embryos exposed to
p02’s lower than the chz should exhibit depressed metabolic rates, which may slow
development, increase the length of incubation, and require the greater consumption
of yolk stores in the egg. On average I found that the nest p02 dropped below 16.5
kPa by day 34. With an average incubation length of 53 days, the developing embryos
appear to spend a third of incubation below their chZ, presumably experiencing
depressed metabolic rates. If this is in fact the case, the metabolic depression did not
manifest itself in an increased incubation length. Further laboratory studies of
embryonic metabolism in sea turtles, and the consequences of temperature and pop,
on embryonic metabolism, are clearly needed. In particular, measurements of Qlos
during development would be very useful.

While there was no clear relationship between low nest p02 and incubation
length, I did ﬁnd that nests washed over by high tides suffered dramatic mortality.
The two nests subjected to tidal washover exhibited dramatic declines in nest p02
immediately following the washover event (Figure 9). Within a few days the nest p02
began to rise. Both nests had very low hatching success, suggesting the impact of
relatively short periods of reduced nest p02. The small sample size makes
generalizations difﬁcult, but it is interesting to note that the nest with more developed

embryos (nest 30) had higher hatching success than the nest containing less

32

developed embryos. This is counter to what one might expect given the increased
oxygen demand of older embryos. Additional studies in which nests are exposed to
simulated washover at different stages of development, with differing degrees of
inundation, while ethically troubling, would provide great insights into the interaction
between developmental stage and the tolerance of low pOZ’s induced by tidal
washovers. At this point, however, given the high mortality in inundated nests and the
fact that relocated and in situ nests did not differ in p02, it seems prudent to relocate
any nest constructed below the spring high tide line.

This study demonstrates that ﬁber optic oxygen sensors can be deployed for
long periods on open beaches to measure the p02 in sea turtle nests and that such
sensors provide exceptionally detailed and dependable information on incubation
environment. It also suggests that previous measurements of nest p02 using methods
that may induce bulk ﬂow may be reasonably accurate in predicting the minimum
nest p02. This study, however, indicates that a reassessment is needed of the rate and
timing of the decline in nest p02 that occurs during development. Even in relatively
dry sands of the sort on Sapelo Island, developing embryos may experience low nest
p023, with the associated depressed metabolism, for a signiﬁcant portion of their
development. In this study there was a bump shaped relationship between the nest
p02 on hatching success, though the reason for this relationship remains unclear.
While the p02 in most nests may depress metabolism, it appears unlikely to be lethal
for the majority of the embryos. This is not to say that the low p02 is inconsequential,
because it may have consequences on hatchling size or dispersal success. However,

these variables have yet to be considered in relation to nest p023 in the ﬁeld, and as a

33

result it remains difficult to predict the consequences of the low nest p02. Now that
we have a robust measurement of the nest p02, there is a clear need for additional
studies delineating how tolerant sea turtle embryos are to decreased p02 and the
consequences of low p02 in terms of survival and measures of ﬁtness (e.g., body size
or swimming speed). It is also important to recognize the considerable variability that
exists among nests, making it difﬁcult to specify the environment within a typical

loggerhead turtle nest.

34

CHAPTER 2

The Structure and Evaluation of a Finite Element Model
Predicting Transport Processes In and Around Sea Turtle Nests

2.1~ INTRODUCTION

The ﬁnite element method (FEM) is a numerical technique for obtaining approximate
solutions to complex problems. In both engineering and biological contexts there is a
need to examine such problems as the stresses imposed on an irregular shape, the
transport of gases in a non-uniforrn background, or ﬂuid ﬂow in a system of
branching tubes. For such systems it is quite simple to write out the governing
equations and even the boundary conditions, but it quickly becomes apparent that a
simple analytical solution is unavailable. When faced with this situation there are two
solutions. The ﬁrst is to make a series of simplifying assumptions and reduce the
problem to one that can be solved analytically. Several useful texts (Carslaw and
Jaeger 1986; Crank 1980) provide analytical equations for solving heat transfer and
diffusion problems involving common geometries. Analytical solutions have been
widely used in engineering and mathematics, and they have been the almost exclusive
solutions used in biology. Yet, the use of analytical solutions often ignores much of
the complexity that made the research question initially interesting. With increasing
computer processor speed, approximate numerical solutions to complex problems are

becoming a more reasonable alternative.

35

A typical ﬁnite element problem begins with a problem domain. The problem
domain might be roof joist, a brake pad, a carnivore skull, or a section of beach sand.
Within this domain there is a variable of interest, referred to as the ﬁeld variable.
When considering heat transfer the ﬁeld variable is temperature; in structural
mechanics the ﬁeld variable could be displacement. The distribution of the ﬁeld
variable in the problem domain is typically described by a set of partial differential
equations. In many cases such equations are very difﬁcult or impossible to solve
analytically. The ﬁnite element method is able to solve these problems because it
proceeds by breaking the partial differential equation into a set of more manageable
ordinary differential equations. As a result, this method produces a piecewise
approximation of the partial differential equation.

To illustrate the ﬁnite element method, consider the problem of gas transport
in insects. The internal tissues of insects are supplied with 02 through small air-ﬁlled
tubes (tracheal and tracheolar tubes) that extend from the exoskeletal surface to the

tissues. 02 then diffuses out of the tubes into the surrounding tissues. One objective
might be to predict the oxygen partial pressure (P02) in the muscle tissue given a
speciﬁed P02 in the tracheoles. Figure 8a provides a diagram of a small section of

insect muscle tissue with three tracheal tubes running through it representing the

problem domain. In this example, the tissue P02 is referred to as the ﬁeld variable

and its distribution is described by a governing equation of the form

aPQ 6 6P02 . . . . e e 0
— = — Dg — , where 08 IS the drffusron coefﬁcrent, t rs time, and x rs the
at 6x 6x

one dimensional coordinate system. At the boundaries of the tissue (outer edges of

36

the block and the tube surfaces) the ﬁeld variable (P02) is assumed known and

speciﬁed. The complex geometry of this system makes it difﬁcult to ﬁnd an analytical
solution, but a numerical solution through FEM is possible. In a ﬁnite element
analysis, the tissue block is ﬁrst broken into a large, but ﬁnite, number of parts or
elements (Figure 8b). All elements are interconnected at speciﬁc points on each
element called nodes, and each element is assigned an interpolation function, which
describes how the value of the ﬁeld variable varies in each element. The interpolation
functions can vary from simple linear ﬁrnctions to complex quadratics depending on
the complexity of the transport properties of the substance. Each element is also
assigned a set of physical characteristics (porosity, diffusion coefﬁcients). Each node

is assigned a simple form of the governing equation, which generates a set of

37

 

Figure 10. a) Diagram of a section of insect muscle tissue with tracheolar
tubes, b) tissue section broken into many small elements as part of the
ﬁnite element method (FEM), c) FEM solution of oxygen diffusion ﬁ‘om
tracheoles into muscle tissue. Light areas have high p02, and dark areas are

lower p02.

38

simultaneous equations calculating the ﬁeld variable, one for each node. Solving
these equations provides a piecewise approximation of the ﬁeld variable across the
whole structure. Values at positions not deﬁned by nodes are calculated using the
elemental interpolation functions. In the current example, solving the system of

simultaneous equations provides an approximate solution to the P02 distribution

within the entire tissue (Figure 8c). The precision of the solution can be enhanced by
dividing the tissue into more elements or by assigning more precise interpolation
ﬁtnctions to each element. By using smaller and smaller elements it is also possible to
approximate highly irregular objects without adopting a simpliﬁed approximation of
the geometry. In addition, solving the problem in parts (at the element level) allows
each element to have a different set of physical properties ﬁ'om the others, and allows
the model to accommodate systems that vary both spatially and temporally in their
physical properties.

Here I describe a computational model (Beach MultiPhase Transport, Beach-
MPT) for predicting transport processes in and around sea turtle nests, its governing
equations, and parameters. I then describe a series of four laboratory experiments
which used physical models of turtle nests to evaluate the model’s predictions of heat

and gas transfer.

39

2.2~ Beach-MPT Model:

Beach-MPT is a three-dimensional model of variably-saturated water ﬂow, heat
transfer, and gas transfer constructed using COMSOL Multiphysics (Comsol, Inc.,
Burlington MA) ﬁnite element modeling software. All transport phenomena are
coupled to one another. This means, for example, that the movement of water
inﬂuences the movement of heat and vise versa. The model solves the Richard’s
equation (Jury et al. 1991) for variably saturated water ﬂow and convection/ diffusion
equations for both heat and gas transport. The heat transport portion accounts for heat
transfer by conduction, convective heat transfer by ﬂowing water, and latent heat
transfer by water vapor. The governing gas transport equations account for mass
transfer by convection in ﬂowing water, as well as diffusion in the gas phase. The
model also takes full account of a highly heterogeneous, multilayered beach substrate.
2. 2.1~ Model Geometry:

Within Beach-MPT the geometry describing the beach and one or more turtle
nests within the beach is ﬂexible. In the current working version, the geometry
consists of '/4 of a 0.2 m diameter turtle nest centered at a depth of 0.45 m and the
surrounding sand (Figure 9). This geometry represents an average loggerhead sea
turtle nest with its immediate surroundings. By assuming that the sand characteristics
do not depend upon which side of the nest one examines I can simply examine % of
the nest and surroundings, reducing the computational cost associated with each
simulation. This geometry provides a baseline with which to compare alternative
geometries, including models in which the nest depth is either increased or decreased,

or models in which nest size or the number of nests within close proximity is varied.

40

The model’s predictions for these alternative geometries will be discussed in Chapter

3.

Depth

Turtle nest

 

 

 

 

Figure 11: In the base-version of the Beach-MPT model, '/4 of the nest and
surrounding sand is analyzed to reduce the computational cost. Other geometries,
including those considering the interaction among several nests are possible.

41

Table 2. Symbols used in the Beach-MPT model with associated units.

Arabic

AraAzaA3
C(h)
C

CT
C3,C",C’"
(J/m3K)

D. D.

1,19 1,19

Du.

constants used in calculating oxygen solubility.

speciﬁc water capacity (-)

volumetric heat capacity of the turtle nest (J / m3 K )

total volumetric heat capacity of the sand (J / m3 K )
volumetric heat capacity of gas, water, and quartz, respectively

02 dispersion coefficients

02 diffusivity in gas phase (m2 / s)

transverse and longitudinal dispersivity, respectively
water vapor diffusivity (m2 /s)

02 diffusivity in water (m2 /s)

surface boundary layer width (m)

evaporation rate in terms of pressure head (m / s)
saturation vapor pressure at the beach surface (kPa)
saturation vapor pressure in the air (kPa)

02 source or sink (kPa)

latent heat correction factor

thermal conductivity shape factors

vapor conductance at sand surface (m / s)

hydraulic pressure head (m)

relative humidity

sand-system hydraulic conductivity (m / s)
saturated hydraulic conductivity (m / 3)

total sand-system thermal conductivity (W / m K)
thermal conductivity of air (W / m K)

thermal conductivity of sand gas phase, pore water, and sand particles,
respectively (W / m K)

ﬂuid conductivity of the sand (W / m K)

0; partial pressure (kPa)

42

Q
E
(b
er

 

$95»

as: ‘m 9

5‘4on was

a,N,M,L

91>»

ﬂ
on

ya a. :1

atmospheric pressure (kPa)

Darcian water ﬂux (m / s)

magnitude of the velocity vector (m / 3)
speciﬁc humidity at sand surface (kg / kg)
speciﬁc humidity in the air (kg/kg)
universal gas constant (m3kPa/mol K)
heat source or sink

time (s)

sand temperature (K)

air temperature (K)

constant in latent heat correction
Cartesian coordinates (m)

02 solubility in water (mot/m3 kPa)

factor converting gas pressures to gas concentrations (moi / m3 kPa)
total sand porosity (m3 pore space/ m3soil)

volume ﬁaction of water-ﬁlled pore space (m3 1120/ m3)

residual water ﬁlled pore space after sand has air-dried (m3 H20/ m3)
volume ﬁaction of sand solids (m3 / m3)

volume fraction of air-ﬁlled pore space (m3 / m3)

volumetric water content at which ﬂow ceases (m3 H20/ m3)

effective saturation
van Genuchten constants for calculating K, 6,, , and C (h)

latent heat of vaporization of water (J / mol)

slope of the saturation vapor pressure function
gas transport tortuosity in water ﬁlled pores

gas transport tortuosity in air-ﬁlled pores

gas transport tortuosity in trutle nest

molar density of air (mo! / m3)

weighting ﬁaction for calculating thermal conductivity

43

Table 3: Constants used in the base model with values and units.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Term Value (units) Reference

K, 7.44155 (m/s) Schaap and Leij (1999)
19, 0.0 (m3/m3)

a, 0.49 (m3/m3)

a 2.57 Schaap and Leij (1999)
N 1.68 Schaap and Leij (1999)
L 0.5 Van Genuchten (1980)
R 8.314e'3 (m3 kPa / mol K)

d 0.005 (m) Campbell (1999)
C’" 7.44e'2 (J / m3 K) Campbell (1999)

CW 4196’ (J / m3 K) Campbell (1999)

(:8 1.256e6 (J / m3 K) Campbell (1999)

kg 0.025 (W / m K) Campbell (1999)

D, 0.0001 Bear(l979)

1), 0.005 Bear(1979)

p, 101.325 (kPa)

km 8.8 (W / m K) lncropera and DeWitt (2002)
kw 0.6 (W / m K) lncropera and Dewitt (2002)
19, 0.05 (m3/m3) Campbell et al. (1994)
u 2.0 Campbell et al. (1994)
g, 0.1 Campbell (1994)

0' 5.669768 (w / m2 K“) Krieth and Bohn (1993)

 

44

2.2.2~ Governing Equations:

2. 2.3~ Variably-saturated water ﬂow:

The governing equation for variably saturated water ﬂow in a porous medium
where the air phase does not inﬂuence water ﬂow is the Richard’s equation (Jury et
al. 1991).

c(h)%'t1=—(V-K).v(h+z)‘ c(h)=§:— (2.1)

where h is the pressure head (m), K is the hydraulic conductivity (m/s) , C (h) is
the speciﬁc water capacity, 6,, is the water content (m3/m3 ) , t is time (s) , and z is

the vertical Cartesian coordinate (m). The unsaturated soil hydraulic properties

(water content, hydraulic conductivity, and speciﬁc water capacity) are based upon
the closed-from expressions of van Genuchten (1980) shown in equations 2.2, 2.3,

and 2.4. The van Genuchten ﬁmction for water content is given by

((BT—6,)*Se+t9,) (h<0)
0T (h 20) (22)

where HT is the saturated water content (m3/m3 ), 6, is the residual water content

(m3/m3 ), Se is the effective saturation given by

Se = (1—(a*|h|)” )M

where a, N, and M are constants speciﬁc to a porous medium type.

 

° The symbol V is a gradient operator. [c.g. (V - K )is shorthand for [g + 96—”:- + 3%)]

45

The expression for hydraulic conductivity is given by van Genuchten (1980)

K. *SeL *(l‘l1‘sel/M )M )2 (h <0)

K =< (2.3)

Ks (h 2 0)

 

where, K s is the saturated hydraulic conductivity (m/s) and L is a ﬁtting parameter,

typically taken to be 0.5. The expression for speciﬁc water capacity is given by

1 (NM, (19, —6,) M
(1-M)*Se'/M *(l—SeVM)
C(h)=< (2.4)

 

 

( 1
2. 2. 4~ Boundary conditions:

The surface boundary setting can take three forms: evaporation, rainfall
(followed by rainfall inﬁltration), and ﬂooding.

Evaporation boundary condition:

The evaporative boundary is in part dependent upon the surface temperature

predicted ﬁ'om the heat transport portion of the model using a variation of Campbell

(1999)

E = —[gv *(h, *qu—qa )] (2.5)

46

where the evaporation rate (E, in m / s) is dependent upon the vapor diffusion rate
through the surface boundary layer (g, in m/ s) , the relative humidity of the sand at
the beach surface (h, ) , the saturated speciﬁc humidity of the sand at the beach
surface at the surface temperature (qu in kg / kg) , and the speciﬁc humidity of the air

(qa in kg / kg) . The variables in equation 2.5 are deﬁned in equations 2.6, 2.7, 2.8, 2.9, and

2.11.

The relative humidity is a function of the hydraulic pressure head at the beach surface

(h in m) , the molecular weight of water (M W , 0.018 kg/ mol), the beach surface

temperature (T in K), and the ideal gas constant (R, 8.314e‘3, m3 * kPa/mol*K)

(Warrick 2002).

 

9.8 * MW * h
h, = exp( R * T J (2.6)

The vapor diffusion through the surface boundary layer (g, in m / s) is a ﬁlnction of
the vapor diffusion coefﬁcient (D, in m2 /s) and the thickness of the boundary layer

(d in m) (Campbell 1999).

D
= —" 2.7
gv d ( )

The vapor diffusion coefﬁcient (D, ) is dependent upon the beach surface

temperature (Campbell 1999).

T 1.75
D, = 2.4 x 10‘5 *(——) (2.8)
293.15

47

The speciﬁc humidity at the beach surface (qu in kg / kg) , is an empirical function

of the saturated vapor pressure (esT in kPa) at the beach surface (Campbell 1999).

 

e
~ = 0622* ST 29
q" [101.325 -0.378*e.r] ( )

The saturated vapor pressure (esT in kPa) in Eq. (2.9) in turn a function of

the beach surface temperature (T in K) (Campbell 1999).

 

(2.10)

17.27“ 273—T
esT =0.611*exp ( )
36—T

The speciﬁc humidity of the air (qa in kg / kg) is calculated in much the same way

as the speciﬁc humidity of the sand q”. (Campbell 1999).

 

q, = 0622* e“ (2.11)
101.325—0.378*ea

where the saturated vapor pressure in the air (ea in kPa) in Eq (2.11) is a function of air

temperature(7;, K) (Campbell 1999).

 

(2.12)

1727* 273—T
ea =0.611"‘exp{ ( 0))

36—Ta

Rainfall boundary:
The rainfall boundary condition takes the form of a Neumann boundary condition,

ah
—K—=R
62 f

where Rf is the rainfall rate (m/s) and K is the hydraulic conductivity (m/ s).

Flooding boundary:

48

The ﬂooding boundary condition is simply a Dirichlet boundary with a speciﬁed

pressure head at the sand surface, corresponding to the depth (hf in m) of the ponded

water, h = hf.

A single simulation can have one or all of these boundaries expressed at different
times throughout the simulation so that the simulation may begin with an evaporative surface,
switch to a rainfall boundary, and then return to an evaporative boundary following the
rainfall event.

The bottom boundary is variable and can be speciﬁed depending upon speciﬁc
. . 6h
modellng goals. The bottom boundary can be specrﬁed as a ﬂux boundary, q = a (m/ s) ,

with water draining from the beach profile. The boundary can also be speciﬁed as a

permanent unmoving water table (h = 0) or a speciﬁed distance above an unmoving water

table (h < 0) . A ﬁnal possible boundary speciﬁcation is one that features a beach water table

that ﬂuctuates on a sinusoidal tidal cycle of 12 hr 50 min.

h = 0.3 * sin (-——ﬂ—)
46200*t

All other boundaries are speciﬁed as no-ﬂux or symmetry boundaries

_a_h_
ax

_ 2h.
x=0 ax

a
x=l 6y

-212.
y=0 6y

= 0
y=l

 

 

 

 

Liquid water transport is assumed to not occur within the turtle nest.

49

2. 2. 5~ Heat Transport:
Heat transport is described by a convection/conduction equation (Bird et al.
2002)

erg=-(v.K,,).vr—(v.q).cwvr+s (2.13)

where C, is the total volumetric heat capacity of the sand (J / m3 K), K H is the
thermal conductivity of the soil (W / m K), C W is the heat capacity of water

(J / m3 K ) , q is the Darcian water ﬂux (m / s , coupled with the water transport portion of

the model), T is temperature(K) , and S is a heat source term (W / m3 ).

Volumetric Heat Capacity

The volumetric heat capacity of the porous medium (CT ) is a function of the

volumetric heat capacity of the constituents of the medium and the volume ﬁaction of

each constituent (DeVries 1963).
CT =le9m +Cw61w+Cg6lg (2.14)
In equation 2.13, the C’” , C w , and C 3 are the volumetric heat capacities

(kl / m3 K) of quartz, water, and air, respectively, while 19", , 19w , and 19g are the

volume ﬁactions (m3 /m3) of sand, water, and air, respectively.

Thermal conductivity:
Within porous media, heat ﬂows through a complicated system of mineral,
water, and air paths, and the conductivity and quantity of each constituent strongly

inﬂuences the behavior of the composite mixture. In addition, a substantial quantity

50

of heat is carried by evaporation and condensation in soil pores, and these processes
are inﬂuenced by both water content and temperature. To account for this the Beach-
MPT model computes thermal conductivity as weighted sum of the conductivity of

the constituents as proposed by DeVries (1963).

_ 19,:ka + ogggkg + 6,5,1,"

2.15
” 0,5,, + Hgkg + 6mg," ( )

 

Here 6 is the volume fraction (m3 /m3 ) , 5 is the weighting fraction, and k is the

thermal conductivity (W / m K) of the constituent, and the subscripts, w, g, and m
indicate the water, gas, and mineral fractions.
The thermal conductivity of the gas phase (kg) is the sum of the thermal

conductivity of air and the apparent conductivity resulting ﬁom latent heat transport.

The complete expression is (DeVries 1963)

kg = [to +——’1A;":”:DV. (2.16)
a 0

Here k0 is the thermal conductivity of air (W / m K), ,1 is the latent heat of
vaporization of water (J / mol) , h, is the relative humidity, ,5 is the molar density of
air (mol / m3), 0, is the vapor diffusivity of soil (m2 xs), pa is total atmospheric

pressure (kPa) , and ed is the vapor pressure (kPa) . A is the slope of the saturation

vapor pressure function.

= bc esT
(o+(T—273.15))2

 

(2.17)

51

es, is the saturation vapor pressure, the constants are b = 17.502, c = 240.97, and T is
temperature (K) (Campbell 1999).

The correction factor fw in equation 2.15 accounts for water vapor movement.

Under saturated conditions when opposite sides of soil pore differ in initial
temperature water may evaporate from the warmer side, diffuse across the pore in the
air space and condense on the cooler side of the pore. The latent heat of vaporization
in this case is carried with the water across the pore. After the water condenses it can
undergo mass ﬂow back to the warmer side of the pore and evaporate again. As the
soil water content declines the return liquid ﬂow declines, as does the contribution of

latent heat to the entire heat transfer process. Campbell et al. (1994) suggest that the

fw term, if deﬁned as now written, corrects for this declining latent heat contribution.

f... =-——1—— (2.18)

“ll
1 + (5]
60
Here 19 is the volumetric water content, 60 represents the water content at which the
return ﬂow declines, and u determines how rapidly it declines. The 60 term ranges

from 0.05 for course sand to 0.25 for heavy clay. The constant u ranges from 2-6
with course materials having lower values.
The weighting factors for calculating soil conductivity depend upon the

shapes, conductivities, and volume ﬁ'actions of the constituents.

52

2 1
3:1+ga(kg/kf-1):+ :l+gc(kg/kf—l)

 

§g=

b)

 

 

 

 

5w _ 2 .+ 1 . (2.19)

— 3[l+ga(kw/kf —1)] 3[1+gc(kw/kf —1)]

 

2 1

3[1+ga(km /kf 4)] 3[l+gc(km/kf 4)]

k f is the ﬂuid conductivity for the soil and according to Campbell (1994) is

calculatedas kf =kg +fw(kW—kg). It canbeseen thatindrysoil(asfw —)0) the

ﬂuid conductivity is that of the gas phase and for a saturated soil it is the value for

water. The go and go terms are shape factors and depend on the shape of the soil

particles.

0.1 for mineral soils
g“ 0.33 for organic soils

8. =1- 2a..
Thermal characteristics of the nest:
The thermal conductivity of the nest is a composite conductivity including
both the conductivity of the air ﬁlled spaces around individual eggs and the

conductivity of the eggs themselves, km, = kai,_space

+ keggs . The fractions of the nest
volume that are air-ﬁlled pore space and occupied by eggs are calculated by assuming
the eggs are packed in the nest in a face-centered array. By this standard, eggs

constitute 74.05% of the nest volume and 25.95% of the nest volume is air space.

Given these values and assuming the thermal conductivity of each egg is the average

53

conductivity of a chicken egg (kegg = 0.45 W / m K, Polley et al. 1980) it is possible

to calculate a nest thermal conductivity.

The heat capacity of the nest is treated similarly. Assuming a turtle egg has
the speciﬁc heat of a chicken egg (3.3 kJ/kg K, Romanoff and Romanoff 1949) and
given that an average loggerhead turtle egg has a mass of 32.7 grams and a volume of
36.2 mL (density = 903.31 kg/m3, Ackerman 1997) the volumetric heat capacity of an
egg is 2.9809 x 106 kJ/m3 K. The volumetric heat capacity of air is 1.256 x 103 kJ/m3
K. For a nest in which the eggs are packed in a face-center fashion the volumetric

heat capacity is

 

 

CHn=(O-7405*2.9809x106 U )+(0.2595*1.256x103 U )

m3K m3K
The ﬁrst term accounts for the portion of the nest volume composed of eggs, while
the second term accounts for the air ﬁlled spaces.

Heat produced through the metabolism of the developing embryos is modeled
using metabolism data from the Ackerman (1981) assuming a respiratory exchange
ratio (REE) of 0.7. For example, a loggerhead turtle nest approaching the end of
incubation containing 100 eggs, has an oxygen consumption rate of ~6.661 x 10'4
moles Oz/m3 s. Assruning an REE of 0.7, a caloriﬁc coefﬁcient of 443,520 J/mole Oz,
and an egg density of the heat production of the nest is ~295 J/m3 s.
2.2.6~ Boundary conditions:

The surface boundary temperature is calculated using a sin function, which

speciﬁes the hottest portion of the day at 15:00.

7;, =310.5+12*sin(L—lrr) (2.20)
43200*t 12

54

Here t is the time (s) and the average surface temperature is 310.5 K with amplitude
of 12 degrees.
Convective heat transport at the bottom boundary takes the form of a

Neumann boundary condition and is dependent upon the results of the water ﬂow

portion of the model 26’: = —K,, - VT —(q * T). All other boundaries are speciﬁed as no-

6T 6T
ﬂow or 5 me boundaries, —— = —
ym try ax 1-0 ox

-91
x=l ay

-22:
y=0 6y

= 0
y=l

 

 

 

 

55

2.2.6~ Respiratory Gas Transport:

Gas transport in both the gas and liquid phase is described by

(16w +ﬂg)% = —(Dl,iﬂw +Di,j16w + Di,kﬂw +Dgrgﬂg)'Vp—Vq(pﬂw)+F (221)

Where ,6“, is the gas solubility in water; ,0, converts gas pressure to gas

DU"

concentration; D”, and D”, are hydrodynamic dispersion coefﬁcients; Dg is the
gas phase diffusivity; rg is the gas phase tortuosity; q is the Darcian water ﬂux
(coupled from the water ﬂow portion of the model); p is the gas partial pressure, and
F is a gas source term (Freeze and Cherry 1979).

The solubility of oxygen in water ( ﬂw, mol / m3 kPa) is temperature

dependent and expressed as:

A. =(exp(A, + 2141?)”, 111(1—36”) /(101.325*0.0224)

Here A1, A2, and A3 are constants ﬁtted by Weiss (1970). The solubility values
calculated using this equation are nearly identical to those calculated using the

equation found in Battino (1980).

The gas conversion factor ( ,Bg , mol / m3kPa) assumes ideal gas behavior and

is temperature dependent:

1

WE

where R is the universal gas constant (8.314 x 10'3 1113 kPa/ mol K) and T is the

temperature (K).

56

The hydrodynamic dispersion coefﬁcients describe the spreading of gas in

solution by mechanical mixing and molecular diffusion (Bear 1979).

 

2
(Dn)=D.5’i+Drﬂiiq—=+Dwrw (o,)=(o,,)=(o,_o,)qijly

 

 

(D )=DL1’2’—-+-DT‘IJ::z q22+DwTW (Dx)=(D:r)=(DL—Dr)q|xqqlz

are
lql

2 +
()_——— (D.)=(o.)=o.—ol
Here those functions in the form of D". represent the principal components of the
dispersion tensor and those in the form of Dy. represent the cross terms of the
dispersion tensor. BL is the longitudinal dispersivity, DT is the transverse
dispersivity, M is the magnitude of the velocity vector, q, is the Darcian water ﬂux

in the ith direction, D, is the oxygen diffusion coefﬁcient in water, and rw is the

tortuosity factor in the liquid phase.

The magnitude of the velocity vector is calculated as (Bear 1979):

M=lc+c+r)

 

The diffusion coefﬁcients both in the liquid DW and gas phases D8 are

temperature dependent and expressed as (Campbell 1999):

T 1.75
D, =2.67e—9*( )
293.15

 

 

T 1.75
D =2.15e—5*( )
8 293.15

57

The tortuosity factors for the liquid 1,, and gas phase I are expressed as

 

 

8
(Millington and Quirk 1961):
9 10/3 910/3
7w = w 2 rs = g2
6T 9T
2. 2. 7~ Boundary Conditions:

The upper surface boundary is a Dirichlet boundary with a speciﬁed oxygen
partial pressure of 21.23 kPa (approximate average atmospheric value). At the bottom
boundary, a Neumann boundary yields convective transport of dissolved gas and is
dependent upon the results of the water ﬂow portion of the model.

Gas Characteristics of the Nest:

The nest oxygen consumption rate is included as a diffuse sink term,
pararneterized by use of the same metabolism curves used to calculate nest heat
production (Ackerman 1981). Within the nest, gas transport occurs solely by
diffusion through the air-ﬁlled pore spaces between individual eggs. The pore space
is again calculated using a face-centered arrangement yielding a fractional air-ﬁlled
pore-space of 0.2495. Individual eggs are not modeled, but instead total nest
metabolism is modeled as a diffuse consumption throughout the egg-ﬁlled nest

volume. Nest gas transport is calculated as

(ﬂ8)%€-=—(Dg *TnIIBgin

The variables are deﬁned in the same manner as equation 2.21 except that r” is the

. 0.2495(‘0/3)
nest tortuosrty 1'" = _—T' .
0.2495

58

2.3~ Beach-MPT Evaluation Experiments:

Models in the biological sciences can be broken into two classes: those that
describe and those that explain (Ginzberg and Jensen 2004). Models in the ﬁrst class
are typically statistical in nature, and data are used to ﬁt the parameters in the model
through maximum likelihood or least squares procedures. These models are used to
predict or resolve basic relationships between speciﬁc variables and often exhibit
good predictive ability. These models, however, do not describe causal relationships,
but rather, describe the statistical relationships among components of a biological
system (Peck 2004).

Models in the second class attempt to explain biological phenomena. These
models represent a theory about how the components of a biological system work
causally to produce a given outcome. Additionally, this second class of model allows
researchers to run simulations and therefore, provides an in silico experimental
system (Peck 2004, McCulloch and Huber 2002). Experiments can be designed and
carried out in much the same way as in a real system, but with complete control.
Simulation experiments allow for experimentation that would otherwise be
impossible, too costly, too time consuming, or unethical in a real system (Peck 2004).
Simulation models are powerful, therefore, because they provide insight into “what
the world would look like if it worked the way we think it does” (Peck 2004).

In order for a simulation model to serve as an experimental system in which
the experimental results are accepted by the scientiﬁc community, some measure of
the model’s validity is required. To evaluate the useﬁllness of the Beach-MPT model

in predicting temperature, moisture, and oxygen gradients around sea turtle nests, I

59

have developed a set of four model evaluation experiments. Each experiment uses a
sand mesocosm containing an artiﬁcial turtle nest. Measurements of sand
temperature, water content, or oxygen partial pressure are measured around the nest
in the mesocosm. Comparing the actual measurements to those predicted by the
Beach-MPT model provides a valuable measure of the model’s usefulness and

provides a springboard for subsequent explorations using the model.

60

2.4~ METHODS:
2.4.1~ Mesocosm:

The predictions from the Beach-MPT model were evaluated in a laboratory
setting using a sand mesocosm to replicate a segment of sandy beach. The mesocosm
consisted of a 0.23 m3 (0.61 x 0.61 x 0.61 m) plywood box, with a bottom of ﬁne,
stainless steel mesh (320 mesh), and was ﬁlled with quartz sand. In all trials the
thermal conductivity of the sand solids was assumed to be that of quartz.

The bulk density of the sand was calculated ﬁ'om the mass of a known volume

of sand from the mesocosm. The porosity of the sand was calculated from the sand

bulk density
mineral density

 

bulk density as, Porosity = (1 — ). The mineral density was assumed

to be the particle density of quartz (2.65 g/cm3, Skopp 2002).
2. 4.2~ Temperature Evaluation:

Experiment 1:

The Beach-MPT model predicts the temperature gradients in the sand around
a nest based upon a set of sand and nest characteristics. These include the nest heat
output, the thermal conductivity of the sand, the porosity of the sand, the water
content of the sand, the temperature of all boundaries, and the initial sand
temperature. To evaluate the computer model, a mesocosm experiment in which all
these parameters were known was run. To replicate a developing turtle nest, a 20-cm-
diameter artiﬁcial nest was constructed ﬁom a wire mesh sphere covered in a thin
membrane. The membrane minimally impeded heat transfer while keeping the sand
from ﬁlling the nest. Within the nest heat was generated by a series of resistors (total
resistance = 12 Ohms). The heat output of the resistors was calculated using Ohm’s

61

law, and a range of heat outputs were realized by manipulating the applied DC
voltage. A 1.5-watt computer fan in the nest ensured even heat distribution. The heat
output of the fan and the resistors together represented the heat output of the nest.

The temperatures of the inner surfaces of the mesocosm and the sand surface
were measured periodically during each experiment using surface thermistors, and the
sand temperature at predetermined coordinates around the artiﬁcial nest was
measured with multiple thermocouples (30-gauge, Type-T) and logged using a
datalogging program written in LabVIEW (ver. 6.0, National Instruments, Austin,
TX). Each thermocouple recorded the temperature every 10 3 during an experiment
(which ran 4-6 h), and 10-min averages were calculated.

Experiment 2:

Using the same set-up as just described, a second experiment was conducted
with a layer of wet sand (0.1 m3 HzO/m3) placed between a depth of 20 and 40 cm in
the mesocosm.
2.4.3~ p02 Evaluation:

Experiment 1:

Figure 10 provides a diagram of the experimental set-up for the p02
experiments using a second 20-cm-diameter artiﬁcial nest covered by ﬁne, stainless
steel cloth (320 mesh) that excluded sand from the nest. The sand in these
experiments was dry. To realize a known and speciﬁc 1102 within the nest, N2 and 02
were passed at regulated ﬂow rates through a large mixing chamber and into the
hollow nest. A small fan in the nest ensured the gases remained mixed. An outlet was

provided by a length of tubing (1.5 m, 1.27 cm ID.) of sufﬁcient diameter and length

62

that it ensured atmospheric pressure within the nest and inhibited ingress of

atmospheric gas. A water manometer connected to the nest veriﬁed the pressure

 

 

 

 

 

 

  
 
  

 

 

equality during all experiments.
F lowmeter . . Water
M'x'"9 Manorneter
Chamber
Inﬂow to
nest

Large

Diameter

/ Outflow

N2 02 Tubing

 

Nest

L) d Mesocosm

Figure 12. Diagram of experimental setup for O2 evaluation.

 

 

 

 

 

 

 

 

F iber-optic Oxygen Sensors:

For monitoring p02 in the p02 evaluation experiments, ﬁber optic 02 sensors
were used. These have the advantage that they do not alter the p02 measured (Klimant
at al. 1995). The ﬁber-optic sensors were made of 5-meter lengths of multimode
simplex optical ﬁber patchcord (Anixter, Grand Rapids, MI, USA, 100/ 140, ST.ST)
coated at the active end with the ﬂuorescent dye Pt(II)meso-tetra(pentaﬂuorophenyl)
porphine (Frontier Scientiﬁc, Utah, USA) following the method of Klimant et al.

(1995). The active ends of the sensors were mounted inside syringes so that they

63

would be protected during insertion in the sand yet extended during measurements by
using the syringe plunger (Figure 11). The p02 measurements were made using a
Microx-TX3 excitation/measurement unit manufactured by Presens Precision Sensing
GmbH, Germany and the corresponding software (OxyView, version TX3_v531). A
thermocouple was arranged in tandem with each sensor to provide data on the
temperature of the ﬂuorescent dye, necessary for calculating p02.

Sensor Calibration:
Each ﬁber-optic 02 sensor was individually calibrated using a two-point calibration
protocol. The ﬁrst calibration point was the p02 of humid atmospheric air and was
performed in a ﬂask containing a moist towel. The p02 of an oxygen-free, 1% sodium
sulﬁte solution served as the second calibration point. Rechecks of the calibration of
numerous sensors demonstrated that the calibration did not change over time [as also
reported by Klimant et al. (1995) and Gatti et al. (2002)].

Sensor locations:
Each experiment employed six oxygen sensors placed at deﬁned coordinates within
the sand mesocosm. One sensor was also placed in the center of the artiﬁcial nest to
measure the nest p02. At the beginning of each experiment, an initial p02 was
recorded ﬁom each sensor. Flow from the O; and N2 tanks was then initiated (and the
fan activated) to produce an altered p02 within the model nest. Thereafter, pO2
measurements were made at the six locations in the sand every min for the ﬁrst hour

and every 10 min thereafter (for «4 hours).

64

 

 

 

 

Needle
Scmor Tlp

Plunger Optical Fiber

(a)

 

Figure 13: Diagram (a) and photograph (b) of a ﬁberoptic 02 sensor mounted
in syringe.

65

Experiment 2:
Using the identical experimental set-up a second set of experiments were conducted

with a layer of wet sand (0.1 m3 HzO/mB) placed at a depth of 20 to 40 cm in the
mesocosm.
2. 4. 4~ Comparison to Beach-MPT predictions:

Temperature:

In all experiments the model’s usefulness in predicting temperatures was
evaluated by using characteristics of the sand mesocosm as inputs for a set of Beach-
MPT simulations. Visual comparison between model predictions and mesocosm
measurements provides the ﬁrst measure of the model’s accuracy. Secondly, when
possible 95% conﬁdence intervals around the mesocosm measurements and the
model’s predictions were calculated to determine if the intervals overlapped. In cases
when the intervals did not overlap 1 determined the distance between the conﬁdence
intervals (example shown in Figure 12) and if this distance was less than 05°C the
model accuracy was considered acceptable.

To further characterize the ﬁt of the model I calculated the difference between
the time-speciﬁc model predictions and the corresponding time-speciﬁc mesocosm
measurements (mesocosm — model) and plotted the difference against time (diff/time
plots). The slope of this relationship provides an index of how well the model
predictions ﬁt the mesocosm measurements over time. A positive slope demonstrates
that over time the model increasingly underpredicted the mesocosm temperature,
while a negative slope demonstrates that over time the model increasingly
overpredicted the mesocosm temperature, and a slope of zero demonstrates no

tendency for the model’s accuracy to change over time. Only diff/time plots

66

reasonably ﬁt by linear regression were used in this analysis, so situations in which
the model initially overpredicted, then underpredicted, and then overpredicted near
the end of the experiment were not considered. Plotting the slope against the distance
between the sensor and the nest also explored whether the model’s accuracy varied
with nest proximity.

Oxygen Partial Pressure:
Around natural nests changes in p02 occur much more gradually than the rapid
changes in p02 generated in the mesocosm trials. To assess the model under the
conditions where it will be used, the model’s predictions were compared to the
mesocosm measurements after a steady-state condition was achieved. I considered a
priori an average difference of 0.5 kPa between the model prediction and the
mesocosm measurements to be excellent and a difference of 0.5 — 0.75 was

considered acceptable. Any greater difference was deemed unacceptable.

67

2.5~ RESULTS

2. 5.1 ~ Temperature Experiments:
Dry Sand Temperature Experiment:

Comparisons of the temperatures predicted by the model and those measured in the
mesocosm measurements at each sensor location are shown in Figure 11. The
temperature evaluation experiments using the dry sand mesocosm demonstrated
reasonable agreement between the mesocosm measurements and the Beach-MPT
predictions (Figure 12). The 95% conﬁdence intervals for 5 of the 20 sensor locations
showed consistent overlap. In only three cases when the 95% conﬁdence intervals did
not overlap was the difference between the intervals greater than 05° C (Table 4).
There was a signiﬁcant relationship between the mean slope of the diff/time plots and
the distance between a sensor and the nest (Pearson correlation = - 0.931,
p = 7.8 x 109). The mean slope was consistently negative, but the variation in the
mean slope decreased considerably with increasing distance from the nest (Figure
13).This suggest that nest the model is more consist at points further from the nest,
but because the total temperature change also declined with distance it may be that
the model is simply more accurate when temperature changes are small.

Damp Sand Temperature Experiment:
Experiments conducted using a 20-cm thick damp sand layer in the mesocosm
between a depth of 20 and 40 cm showed considerable agreement between Beach-
MPT model temperature predictions and mesocosm temperature measurements
(Figure 14). The temperature predicted by the model, however, always exceeded the
temperature measured in the mesocosm.The 95% conﬁdence intervals for 10 of the

13 sensor locations showed consistent overlap. At an additional location the

68

difference between the conﬁdence intervals was considered acceptable at A < 0.5° C.
The conﬁdence intervals at the last two sensor locations did not overlap and the
difference between the conﬁdence intervals was greater than 05° C (Table 5). There
was no signiﬁcant relationship between the mean slope of the diff/time plots and the
distance between the sensor and the nest though the slope was consistently positive
(Figure 15). The variation in the slope appeared to decline with distance from the
nest, again suggesting that the model may be more accurate as one moves away from
the nest (Figure 15). As one moves away from the nest the maximum change in sand
temperature declines as well, which might suggest that it is not that the model is
necessarily more accurate due to increasing distance from the nest, but is simply more

accurate when predicting smaller temperature changes.

69

Change in Temperature (°C)

O-ttowhma)

Dilute-hula:

 

 

Sensor1.d=11.2cm

0 oooeceeeeeeﬂiliili

 

 

T r

 

Sensor 2, d= 5.8 cm

 

ooessttiigiiiiiiii

0

 

 

 

Sensor 3, d = 5.0 cm

0 oarriiiiiiiiilllll

 

 

 

Sensor 5, d = 11.2 cm

0 censuseBQQQIEBSSET

 

 

“"04kaan

j

 

Sensor 7. d = 0.0 cm

 

 

 

Time (min)

70

Sensor 4. d = 5.8 cm

0 09933

rillttiiiliii

 

 

Sensor 6. d= 5.0 cm

 

Distance Between
Confidence Intervals

 

 

0 50 100 150 200

Figure 14: Change in temperature
at individual sensors during
mesocosm experiments using dry
sand (0, n = 3) and predicted
change in temperature from
simulation model (O, n = 3) and
with 95% conﬁdence intervals (d
refers to linear distance between
ﬂnasnmorandrmsO.thnes
continued on pages 71 and 72.

Change in Temperature (°C)

Figure 14, continued

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

6 Sensor9,d=0.0cm Sensor 10.d=5.0cm
5. l
:1 silllllllllllll
b: .flli scarriilifiiiiiillil
-1 - . . . a . . . T . .
6 Sensor11,d=8.0cm Sensor12.d=1.2cm
51 i
44 . 0°,a
3? 0.,311111111111
b: sooosssiitiiiiiiiiii i .iillf
.1 . . . . . T
:4 Semor13.d=o.0cm can. Sensor14.d=1.2cm
41 °°°°°°°

‘ 1“” lillil
WWW“ (illllll
o. .lll .illl
-1 . a . . - -
:lsemals'dﬂ'oa“ , Sensor16. d=11.2 cm
0: o oasssstsiiifgggggz o 062888883222333§§§
‘1 0 50 100 150 200 0 SD 100 150 200

Time (min)

71

Figure 14, continued

 

 

 

 

 

 

 

 

0.1 n.
6.1 H.
0.1 no
of! ne
o.! ne
oi. as
o3. oe
oi. as
ot. o.
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._ on = 8
d 3 d 9
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w o m o
n n
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S S
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ol ..5
a! o.e
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no .8 R. on
5 a r 5 0. w
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7. cc
4| 4|
m m
n m
e
S S

 

 

 

 

 

 

Gov oaauacoaaoh E owe—EU

100 150 200

50

 

200

Time (sec)

72

150

100

Table 4: Dry Sand Temperature Experiment. The coordinate location of each sensor,
the linear distance ﬁ'om each sensor to the nest, and the maximum difference between
the 95% conﬁdence intervals for the model predictions and the dry sand mesocosm at
each location. The coordinates for each sensor location are measured in centimeters.
The x and y coordinates are measured ﬁom a single corner of the mesocosm and the z
coordinate increases from the bottom of the mesocosm to the top. The max difference
calculated as described on page 70. If the 95% conﬁdence intervals overlap the
difference is reported as zero.

 

Sensor Coordinates (x, y, 2) Max Difference (°C)

1 0.15, 0.30, 0.15 0.07
2 0.25, 0.30, 0.15 0.13
3 0.30, 0.30, 0.15 0.00
4 0.35, 0.30, 0.15 0.00
5 0.45, 0.30, 0.15 0.07
6 0.15, 0.30, 0.30 0.43
7 0.20, 0.30, 0.30 0.69
9 0.40, 0.30, 0.30 0.57
10 0.45, 0.30, 0.30 0.00
11 0.15, 0.30, 0.40 0.11
12 0.25, 0.30, 0.45 0.36
13 0.30, 030,040 0.65
14 0.35, 0.30, 0.40 0.00
15 0.45, 0.30, 0.40 0.09
16 0.15, 0.30, 0.45 0.16
17 0.25, 0.30, 0.45 0.00
18 0.30, 0.30, 0.45 0.33
19 0.35, 0.30, 0.45 0.32
20 0.45, 0.30, 0.45 0.21

73

 

 

 

 

 

 

 

 

4.0e-5
2.0e-5 1 _ v
0.0 «—-—-j-—--——————__—_;; ....... 1: ___________

—2.0e-5 1 . 1' f
8. -4.0e-5 - .
_0 m
(D -6.0e-5 1 5 ‘-

-8.0e-5 .

“1.06.4 '4 a;

-1.2e-4 - J

-1.4e-4 . . . T , ,

0 2 4 6 8 10 12

Distance (cm)

Figure 15: Relationship between a sensor’s distance from the nest and the mean slope
of the difference between model predictions and the dry sand mesocosm
measurements plotted as a function of time (with 95% CI). Negative slopes show the
model increasingly overpredicts the mesocosm temperatures. A slope of zero shows
that the difference between the model predictions and the mesocosm temperatures
remains constant over time.

74

Change in Temperature (°C)

 

 

Sensor 1, d== 6.3 cm

    
   

   
  

l. 5'
11 ml!“
waif"

....‘.':¥ "Ill

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

OJ
-1 a . a .
o 100 200 300 400
6
5. Sensor3,d=12.0cm
4.
31
2.
1.
oi
-1 T . . .
o 100 200 300 400
6
5‘ Sensor5,d=7.0
4.
3.
2.
11
04
-1 . . .
0 100 200 300 400
6
54 Sensor7,d=6.6
4.
3.
24
1.
0.
-1 . . 1 ﬂ
0 100 200 300 400

Time (min)

75

 

Sensor 2, d = 7.7 cm

 

 

 

 

 

 

 

 

 

 

 

 

 

 

o 100 300 400
6
51 Sensor4,d=8.0
4.
3.
24
14
0+
-1 . . . .
o 100 200 300 400
6
5. Sensor6,d=2.8
4.
34
2.1
11
04
-1 . . s
o 100 200 300 400

Time (min)

Figure 16. Change in temperature at
individual sensors during mesocosm
experiments using damp sand (0.1 m3
HzO/m3) (e, n = 3) and predicted
change in temperature ﬁ'om simulation
model (0, n = 3) with 95% conﬁdence
intervals. (d refers to the linear distance
between the sensor and the nest). These
ﬁgures are continued on page 76.

Change in Temperature (°C)

Figure 16, continued.

 

 

   

 

 

 

 

 

 

 

 

   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

6 6
5‘ Sensor8,d=5.4 5‘ Sensor9,d=3.8
.. .. W
3. 3 l
21 21 #551“ II |
1. 1.
o. o.
1 -1 . .
o 100 200 300 400 o 100 200 300 400
6 6
51 5.
44 44
31 3.
2‘ 21
1. 11
01 01
.1 -1
o 100 200 300 400 o 100 200 300 400
6 6
51 Sensorl2,d=5.8 5- Sensorl3,d=7.5
4. 4.
3. 3.
2. 2-
1‘ 1‘ iii
0. o. I
-1 . . . . -1 . . . .
o 100 200 300 400 o 100 200 300 400

 

Time (min)

76

Table 5. Damp Sand Temperature Experiment. The coordinate location of each
sensor, the linear distance from each sensor to the nest, and the maximum difference
between the 95% conﬁdence intervals for the model predictions and the damp sand
mesocosm are shown at each location. The coordinates for each sensor location are
measured in centimeters. The x and y coordinates are measured from a single corner
of the mesocosm and the z coordinate increases from the bottom of the mesocosm to
the top. The max difference is calculated as described on page 65. If the 95%
conﬁdence intervals overlap the difference is reported as zero.

 

Sensor Coordinates (x, y, 2) Linear Distance Max Difference

 

to Nest (cm) (°C)
1 0.24, 0.28, 0.15 6.3 0.0
2 0.35, 0.38, 0.15 7.7 0.0
3 0.14, 0.32, 0.15 12.0 0.0
4 0.12, 0.31, 0.30 8.0 0.29
5 0.29, 0.47, 0.30 7.0 0.0
6 0.40, 0.22, 0.30 2.8 0.0
7 0.44, 0.39, 0.30 6.6 0.0
8 0.20, 0.24, 0.40 5.4 0.95
9 0.25, 0.22, 0.40 3.8 1.1
10 0.38, 0.28, 0.40 3.0 0.0
11 0.28, 0.29, 0.45 5.2 0.0
12 0.35, 0.31, 0.45 5.8 0.0
13 0.30, 0.39, 0.45 7.5 0.0

77

 

0.014
0.012 -
0.010 -‘

0.008 - o

Slope

0.004 . .. T 9 I.

0.002 -1 "' .- “' f

 

 

 

 

 

 

 

 

 

0.000 -1 —————— — — - ————————————

 

 

 

-0.002 . . r u T
Distance to nest (cm)

Figure 17: Relationship between a sensor’s distance from the nest and the mean slope
of the difference between model temperature predictions and the damp sand
mesocosm measurements potted as a function of time (with 95% CI). Positive slopes
show that over time the model increasingly underpredicts the mesocosm temperature.
A slope of zero shows that the difference between the model predictions and the
mesocosm temperatures remains constant over time.

78

2. 5.2~ Oxygen Partial Pressure Experiments:
Dry Sand p02 Experiments:

The two experiments testing the Beach-MPT model’s predictions of 0;
transport in dry sand showed close agreement between actual and predicted pOzs
(Figure 16 and Figure 17). There was reasonably good agreement during the period of
rapid p02 decline, but more importantly there was good agreement after the p02
began to stabilize (time > 75 min). During the ﬁrst experiment, four of the six sensor
locations showed excellent agreement in the average difference between the model
predictions and the mesocosm measurements, values being less than 0.5 kPa The
other two locations had a larger average difference, but were both acceptable (A <
0.75 kPa). The p02 predicted by the Beach-MPT model was always lower than the
p02 measured in the mesocosm. There was no signiﬁcant relationship between a
sensor’s distance from the nest and the accuracy of the model’s predictions (Pearson
correlation = 0.18, p = 0.73). There was no relationship between sensor location (in
terms of being below, beside, or above the nest) and the accuracy of the model’s
predictions either (Table 5).

In the second experiment, the agreement between the model and the
mesocosm was excellent at two sensor locations with the difference between the
model and the mesocosm values < 0.5 kPa (Figure 17). At the other four locations the
differences were greater than 0.5 kPa. Of these, three locations were considered
acceptable, and one was clearly unacceptable (Table 6). Again there was no
signiﬁcant relationship between sensor’s distance from the nest and the agreement
between the model predictions and the mesocosm measurements (Pearson correlation

= -0.65, p = 0.16).

79

 

 

 

 

 

 

 

 

 

 

 

 

”(5‘ Sensor 1. d= 20.0 cm
a 22.
i‘,
2 1:
8 20‘
2 3
o.
a-ml ‘
1:
a ’8
S16‘ ‘7’”888 8 a 8
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0 50 100 150 200 250
Time (min)
’1? Sensor 3. d = 5.23 cm
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9
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0 50 100 150 200 250
Time (min)
3“: 22 ‘ Sensor 5,d=7.55 cm
V o
9 o
3 0
i2" -
o. 3.
g 18‘ ‘31..
& %;°"Oee e e e
: °°°Ooo o
o 16‘ ° °
0)
i‘
O 14 . .
0 50 100 150 200 250
Time (min)

Oxygen Partial Pressure (kPa)

Oxygen Partial Pressure (kPa)

Oxygen Partial Pressure (kPa)

 

 

 

 

 

 

 

 

 

 

 

 

Sensor 2, d = 8.4 cm
22 . o
d’
20 1 Q5
'1:
18 i \'0e
8'8”: 8 8 8
16 i
14 . . . .
0 50 100 150 200 250
Time (min)
22 J Sensor 4. ct: 2.81 cm
0
O
18 l ,
e
16 1 a
8833881388 8 8 8
14 . . . . .
0 50 100 150 200 250
Time (min)
22 ‘ Sensor 6. d= 10.62 cm
in
20 4 O
J Qo‘Iee. .
‘8 *“0332.: Z 2 2
16 -
14 . . . . .
0 50 100 150 200 250
Time (min)

Figure 18. Dry Sand p02 Experiment 1. Comparison of p02 predictions ﬁ'om the
Beach-MPT model (0) and measurements made in the dry sand mesocosm (0).
Artiﬁcial nest internal p02 ~13 kPa. (d refers to linear distance between the sensor

and nest).

80

 

ml

16*

Oxygen Partial Pressure (kPa)

Sensor1.d=8.0cm
o
o
O
O
:z‘... . g . O O
0°00 o o o o o

 

 

14

 

r

0 50100150200250300350

 

18‘

16‘

Oxygen Partial Pressure (kPa)

Time(min)
Sensor 3. d= 7.1 cm
0
o
§g°0000 . . . O O
°°°oo o o 0 o

 

 

14

 

0 50 100 150 200 250 300 350
Time(min)

 

Oxygen Partial Pressure (kPa)
a;

 

Sensor5.d=11.2cm
8"883: ° '8 z 3

 

 

T

Time (min)

0 50100150200250300350

Oxygen Partial Pressure (kPa) Oxygen Partial Pressure (kPa)

Oxygen Partial Pressure (kPa)

 

16‘

 

Sensor 2. d = 8.6 cm

0..
00:... o o. O
000 O o O O O

 

14

 

0 50100150200250300350
Time(min)

 

18‘

16‘

 

Sensor4,d=11.4

[so 0‘

O.
O.
0.
O O
0.
O.
O.
0.
O.

 

14

 

O 50100150200250300350
Time(min)

 

18*

16*

 

Sensor 6. d = 5.1 cm

0

o.

R'Oooeo... o o
%

°°°°Ooooo o 0

 

14

 

0 50100150200250300350
Time(min)

Figure 19: Dry Sand p02 Experiment 2. Comparison of p02 predictions generated by
the Beach-MPT model (0) and p02 measurements made in the dry sand mesocosm
(0). Artiﬁcial nest internal p02 ~13.5 kPa (d refers to linear distance between the
sensor and nest).

81

Table 6. Dry Sand p02 Experiments. Assessing the accuracy of the Beach-MPT
model in (a) Dry Sand p02 Experiment 1 and (b) Dry Sand p02 Experiment 2.
Provided are the linear distance (in cm) between each sensor and the nest and the
mean difference in p02. The mean difference in p02 for each sensor was calculated as
the mean difference between the p02 predicted by the Beach-MPT model and the
actual mesocosm p02 measurement during the ﬁnal 8 or 9 measurements in each
experiment (time > 75 min).

 

 

 

 

(3)
Sensor Linear distance Mean difference in p02
to nest (cm) (kPa, 8 measurements)
1 20.0 0.36
2 8.4 0.23
3 5.23 0.19
4 2.81 0.27
5 7.55 0.70
6 10.62 0.61
0))
Sensor Linear distance Mean difference in p02
to nest (cm) (kPa, 9 measurements)
1 8.0 0.74
2 8.6 0.64
3 7.1 0.33
4 1 1.4 0.60
5 11.2 0.33
6 5.1 1.31

82

Damp Sand p02 Experiments
In the three experimental trials testing the accuracy of the Beach-MPT
model’s predictions of 02 transport in a mesocosm containing a 20-cm thick layer of
damp sand, there was considerable difference between the predicted and actual p02
values (Figure 18). All six sensors showed roughly the same error at the end of the
experimental period (2.0 — 3.0 kPa, Table 7). There was no relationship between a
sensor’s distance from the nest and the degree to which it differed from the model

predictions (Pearson correlation = 0.12, p = 0.82).

83

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Time (min) Time (min)

Figure 20. Comparison of p02 predictions generated by the Beach-MPT model (O, A ,
El) and p02 measurements made in the damp sand mesocosm (e, v, I). Sensor
coordinates are also shown. Mean p02 in nest was 11.4 kPa. The values in
parentheses are the sensor coordinates. The x and y coordinates are measured from a
single corner of the mesocosm and the z coordinate increases ﬁ'om the bottom of the
mesocosm to the top.

84

Table 7: Damp Sand p02Experiments. Provided are the coordinates of each sensor (in
cm),theﬁneerdistanceﬁomeachsensortothenest(incm),andthemeandifference
inp02.1‘hemeandiﬂ‘ereneeinp02wascalmﬂatedforeachsensorasthemean
difference between the p02 predicted by the Beach-MPT model and the actual
mesocosm p02 measurement after the p02 levels were roughly constant (the 8
measmementsmadeaﬁereachexperimentwasrun~75 min).Thexandycoordinates
aremeasmedﬁomasinglewrnerofthemesowsmandthezeoordinateincmases
fromthebottomofthemesocosmtothetop.

 

 

sensor (3mm ism Mean p02 difference
(x.y,z) (mpg)
to nest (cm)
1 (belowgﬁﬁ’fjim) 20.0 2.52
2 (883.831.2253 111832;: sand) 34 2.67
3 mid‘é'iiimiﬁs...) 5.23 1.9
4 (above ngszsc’lgfdgﬁsgmsmon) 2°81 2-55
5 (above ngiscig/ﬁﬁmiﬁom 7.55 3.44
6 (amgézgétg’gssm) 10.62 2.91

 

85

2.6~ DISCUSSION

Simulation models offer the opportunity to explore and test ideas by creating
an artiﬁcial, but realistic environment in which to experiment. The results generated
by simulation models must be validated under under controlled conditions. In this
study I demonstrated that the Beach-MPT model is able to accurately predict
temperature and p02 gradients that develop around artiﬁcial nests.
2.6.1~ Temperature Evaluation Experimenm:

Dry Sand

The dry sand temperature evaluation experiments demonstrated that the model
accurately predicted the temperatures at most thermocouple locations. The
correspondence was quite good, with 17 of the 20 locations exhibiting overlapping
conﬁdence intervals or conﬁdence intervals that differed by less than 05° C (Table
3). Only three locations (7, 9, and 13) had conﬁdence intervals that differed by more
than 05° C. At these three locations the thermocouples were placed in direct contact
with the nest surface and I suspect the lack of agreement at these locations is a
consequence of this. When sensors are ﬁuther from the nest and their temperature
more dependent upon heat transfer processes in the sand, the model appears to be
accurate. It is under these conditions that the model will be used, and therefore I
argue that the lack of agreement at locations 7, 9, and 13 detracts little from the
model’s overall usefulness.

Damp Sand

The damp sand evaluation experiments also showed a close correspondence

between the predicted and actual sand temperatures. Eleven of the 13 thermocouple

86

locations exhibited overlapping conﬁdence intervals or conﬁdence intervals that
differed by less than 05° C. The errors at locations 8 and 9 may be due in part to the
relatively large temperature changes at these sensor locations, with a mean change in
temperature at sensors 8 and 9 of 3.8° C and 49° C in six hours, respectively. Nest
temperature changes will not occur at such high rates in natural nests so these results
may illustrate the model’s limitations, but should not discount the model entirely. The
consistent overlap of the model predictions and mesocosm measurements suggests
that the model captures the important aspects of heat transfer and as a result is very
capable of predicting heat transfer in damp sand.
2.6.2~ Oxygen Partial Pressure Evaluation Experiments:

Dry Sand

The p02 evaluation experiments using dry sand demonstrate that that the
Beach-MPT model can accurately predict gas transport as well. Both experiments
demonstrate that the difference between the model and the mesocosm measurements
was typically acceptable and often excellent (Table 5 and Table 6). Only once was the
difference between the mesocosm measurements and the model predictions
unacceptable by the standards speciﬁed. The unacceptable result is not explained by
the sensor’s location relative to the nest, though inaccurate sensor placement is
possible. While the model is sufﬁciently accurate, it is important to note that in all
cases it overpredicted the p02 values. The consistent overprediction suggests that
there is a systematic error in some aspect of the model. This could be something as
simple as an inaccurate speciﬁcation of the sand porosity or a more ﬁrndamental error

in the structure of the governing equation for gas transport. Whatever the error, its

87

consequence appears quite small and the model is consistently accurate in predicting
gas transport in dry sand.

Damp Sand

The p02 evaluation experiments using damp sand showed much less
agreement between the model and mesocosm measurements than the other evaluation
experiments. The model consistently overpredicted the p02 in the mesocosm by 2 to 3
times. The degree to which the model and the mesocosm data differed was not a
consequence of the distance between the sensor and the nest, the fact that a sensor
was above or below the nest, or the water content of the sand layer in which the
sensor was located. It seems that the damp sand layer simply did not impede gas
transfer as much as the model predicted.

The lack of agreement suggests that there are inaccuracies in the mesocosm
experiments or the model’s gas transport equations. Alternatively the model might not
include all the parameters which are important for predicting gas transfer in damp
sand. The fact that the model accurately predicts transport processes under other
conditions suggests that the mesocosm experiments are adequately controlled and
accurate. In addition, the accurate prediction of gas transport in dry sand suggests that
the basic gas transport equations are well constructed. Given that the model
accurately predicts heat transfer in damp sand and accurately predicts gas transport in
dry sand suggests that inaccuracy stems not from inaccuracies in the water ﬂow or
gas transport portions of the model, but from the interaction of the two. The mostly
likely culprit is the tortuosity function. This function relates the amount of water-

ﬁlled pore-space to the tortuousness of the diffusion path for a given gas molecule.

88

Tortuosity is not directly measured, but there are several methods of predicting
tortuosity from measurements of other parameters including the sand water content
and the total porosity. In the original simulations, I adopted the widely used
theoretical method of calculating tortuosity from Millington and Quirk (1961), but
beyond its widespread use and general acceptance there are no additional reasons to
assume this method will accurately predict the tortuosity in the sand mesocosm. To
explore whether an alternative method of calculating tortuosity might improve the
model’s predictions, I ran the model using an alternative tortuosity function ﬁom
Penman (1940),

r = 0.660 (2.22)

where 0 is the sand water content (m3/m3 ). This method is also widely used and

mathematically much simpler than the Millington and Quirk (196]) function.

The results suggest that using the Penman tortuosity function narrows the gap
between the model’s predictions and the mesocosm measurements, but the model
remains relatively inaccurate at predicting gas transfer involving a damp sand layer
(Table 8). The damp sand evaluation experiments consistently overpredicted the p02
values, in the same manner as the dry sand experiments, but to a much greater degree.
While the errors associated with the damp sand experiments may be a direct
consequence of the model’s ability to predict transport in damp sand it is also possible
that they errors do not represent a poor ability to predict transport in damp sand, but a

reduced ability to predict transport through layered sands. The model might exhibit

89

Table 8: Consequences of the tortuosity function on p02. Provided is the mean
difference in the p02 at each sensor location dining the damp sand experiment when
two different methods of calculating the sand tortuosity (Millington and Quick (1961)
or Penman (1940)) were used. The mean difference in p02 was calculated for each
sensor as the mean difference between the p02 predicted by the Beach-MPT model
and the actual mesocosm p02 measurement after the p02 levels were roughly constant
(the 8 measurements made after each experiment was run ~75 min).

 

 

 

 

 

 

 

Sensor Mean Difference in p02 (kPa) Mean Difference in p02 (kPa)
Millington and Quick (1961) Penman (1940)

1 2.52 1.35
2 2.67 1.8

3 1.9 1.11
4 2.55 0.45
5 3.44 1 66
6 2.91 1.75

 

 

 

 

 

equally poor predictions if instead of including a damp sand layer, a layer of course
sand was added to the mesocosm. To tease apart the affects of damp sand from those
of sand layering it would be necessary to run several experiments in which the entire
mesocosm was ﬁlled with damp sand. If the model accuracy increased under such
conditions one would concluded that the model accurately predicts gas transport in
damp sand, but poorly predicts gas transport in layered sands. To date, such
experiments have not been conducted.

The errors observed in the damp sand/p02 experiments may also demonstrate

that an important real-world parameter has not been included in the model. Because

90

of the highly controlled nature of the mesocosm, it is difﬁcult to speculate what the
neglected parameters might be.

The four evaluation experiments described in this chapter suggest that the
Beach-MPT model is quite capable of predicting heat and gas transport in dry sands
and heat transport in sand proﬁles containing a damp sand layer. This is quite
impressive given that the model is based strictly upon transport principles and was
not ﬁtted or calibrated to the mesocosm. The results of the damp sand p02
experiments are less reassuring. While the model captures the general trend in sand
p02 under such conditions, it is quantitatively inaccurate in predicting gas transport in
sand proﬁles containing a damp sand layer. This suggests that in its current form the
Beach-MPT model can be use to generate quantitative predictions with regards to
heat and gas transfer under dry conditions and heat transfer under damp conditions.
However, the model should be used cautiously when attempting to predict gas
transfer in damp sands and under such conditions the model’s p02 predictions should
be viewed as capturing general trends rather than precise p02 values. Despite the
current limitations, the Beach-MPT model is clearly a new and powerful tool for
assessing the potential and very practical repercussions of habitat change on sea turtle
nests. In addition, by manipulating various nest parameters will allow researchers to
explore more theoretical consequences of clutch size, nest depth, or even nest

crowding on nest microclimates.

91

CHAPTER 3

The Consequences of Nest Site Characteristics for the
Microclimates within Sea Turtle Nests: A Simulation Study

3.1~ INTRODUCTION

The conditions within the nests of sea turtles are the expression of a complex
set of interactions among the physical characteristics of the nest site and the biotic
characteristics of the developing clutch (Maloney et al. 1990, Wallace et al. 2004).
The biotic half of this story has been reasonably well told through laboratory and ﬁeld
studies examining the effects of temperature, moisture, and respiratory gases on turtle
embryos (Tracy et al. 1978, Ackerman 1981, Kam 1993), but comparatively little is
known about the physical characteristics that inﬂuence the transport of heat, water,
and respiratory gases to the embryos (Mortimer 1990). As a consequence, our
understanding of the interaction between the physical and the biotic, and our
understanding of the nest microclimate remains incomplete.

In a recent study (Chapter 1) I found that the minimum nest p02 in loggerhead
turtle nests varies considerably among nests and is unrelated to clutch size. The lack
of relation to clutch size suggests that the variability in p02 cannot be explained by
variability in nest metabolism, but rather represents variability in the rate of 02
transport to nests at different sites. This variability could be the consequence of

differences in nest morphology (e. g., depth to the top and bottom of nest, nest width),

92

in nest temperature, sand porosity, sand water content, biotic characteristics of the
sand such as microbial populations or root densities, or tidal pumping due to nest
location.

Exploring all these possibilities empirically, while important for successful
sea turtle conservation, is unreasonable given constraints on time and money. This is
especially true given the likelihood that many of these possibilities will actually have
limited impacts on the nest p02. Simulation modeling provides the opportunity to
narrow this list of possibilities by quickly simulating, for example, the consequences
of different nest morphologies or sand porosities. Subsequent, empirical work can
then focus on the most promising areas of study.

To this end, I developed a computational model (Beach-MPT‘) which
simulates heat, water, and gas transport in and around turtle nests, and I report here on
a set of simulations which make use of this model. I begin by describing two
sensitivity analyses which investigated the relative importance of biotic and abiotic
parameters to the variability in predictions of nest p02 and nest temperature. Such
analyses suggest which parameters must be measured accurately during empirical
studies, as well as parameters that might be most sensitive to human intervention,
both positive (e.g., conservation) and negative (e.g., habitat alteration).

In my second set of simulations, I used the model to consider two scenarios
that are of signiﬁcant concern in the area of sea turtle conservation: beach
nourishment and nest crowding. Beach nourishment has arisen as a potential threat to
sea turtles in the United States because of pervasive erosion along the Atlantic and

Gulf coasts. Beach nourishment involves either pumping sand from offshore sand

93

deposits or trucking sand ﬁ'om upland areas, and then using heavy machinery to
rebuild a beach. Over the past 15 years, considerable evidence has accumulated that
nourished beaches are far different from the original beaches they replace (Meylan et
al. 1995). Water-holding capacity, porosity, thermal conductivity, and albedo have all
been shown to differ following nourishment (Steinitz et al. 1998). Empirical studies
of the implications for sea turtle nesting and nest survival have yielded mixed results.
Some studies have found that nourished beaches negatively impact nest construction
and embryonic survival (Crain et al. 1995, Trindell et al. 1998), whereas others have
found little change in nest success (Davis et al. 1999). By clarifying how the physical
characteristics of a nest site inﬂuence the nest microclimate, the Beach-MPT model
can help us develop a systematic understanding of the effects of beach nourishment
on sea turtle development.

The consequences of nest crowding, the second scenario, have long been a
concern in the construction of hatcheries. Often managers have assumed that spacing
nests at least 0.5 meter apart is sufﬁcient to eliminate nest interactions based on the
simple, single-nest model of Ackerman (1977). Whether this spacing actually
eliminates the interactions between two or more nests is unknown. The consequence
of nest crowding during arribadas (the coordinated, mass-nesting events exhibited by
olive-ridley sea turtles) or on densely nested beaches is unclear. Recent empirical
work suggests that nest crowding may inﬂuence nest microclimates (Honarvar et al.
2007). However, while the empirical work is still in its early stages, the Beach-MPT

model can be used to suggest the potential consequences of nest crowding. As

94

empirical data becomes available, comparisons with the model’s predictions will help
to clarify our understanding of the system.

I conclude with a third set of simulations which consider how well the model
might predict nest p02 changes that occur during development. The simulation
experiments I have already described focus exclusively on a few days at the end of
incubation when the embryonic metabolism is at its highest and nest conditions may
therefore be at their most extreme (highest embryonic metabolism and lowest nest
p02). Beach-MPT was originally evaluated (see Chapter 2) with a focus on those days
at the end of incubation and the model therefore would be considered most accurate
during those days. However, to explore how well the model could predict nest pOzs
over the entire developmental period, I simulated ~50 days of development and

compared the results to actual nest pOzs.

95

3.2~ METHODS
3.2.1~ Sensitivity Analysis:

To explore the relative inﬂuence that clutch metabolism, sand porosity, sand
water content, nest depth, rainfall, and sand microbial respiration have on late-
incubation nest p02 and nest temperature, two sensitivity analyses were conducted
using the Beach-MPT model. Parameters in the Beach-MPT model were individually
varied using the values shown in Table 9, and the resultant change in nest p02 or nest
temperature was recorded. For each parameter value a sensitivity index of late-

incubation nest p02 or nest temperature was calculated using the following equation,

 

 

(3.1)

 

 

 

in which R0 is the p02 or temperature predicted by the model using the original
parameter value, while RA is the p02 or temperature predicted when the original
parameter value is increased or decreased. In the denominator, P0 represents the
original parameter value and PA represents the new parameter value. S is the
sensitivity index. For simplicity of interpretation, parameters such as sand microbial
respiration, sand porosity, and sand water content, were applied uniformly throughout
the sand proﬁle and not as a function of depth. The sensitivity index provides a means
of comparing how much changes in individual parameters alter nest p02 and
temperature, when the absolute value of each parameter differs.
3.2.2~ Consequences of Beach Renourishment and Nest Crowding

To explore the consequences of beach nourishment using the Beach-MPT

model, two sets of simulations were conducted. The ﬁrst set considered the

96

consequences of the water holding capacity; nourished beaches tend to have increased
water holding capacity (Steinitz et al. 1998), and the effect of this increased capacity
on the p02 and temperature gradients in and around a turtle nest was explored. The
parameter values for these simulations are shown in Table 10. Beach nourishment
may also reduce sand porosity and this effect was explored in a second set of
simulations in which the sand porosity was reduced ~10% (Table 11). Because the
temperature results were highly sensitive to the initial temperature conditions, I
conducted the simulations with two different initial conditions. The cooler
simulations had an initial temperature gradient which ranged from 25° C at the
bottom of the proﬁle to 27° C at the surface. The warmer simulations had an initial
temperature gradient which ranged from 27° C at the bottom of the proﬁle to 37° C at
the surface. All results were presented as vertical transects through the nest and
represented conditions near the end of development.

The consequence of nest crowding on nest p02 was ﬁrst explored by including
two nests in the Beach-MPT model. In separate simulations the distance between the
nests was varied from 0.3 meters to 0.5 meters, and then 1 meter. The nest p023
resulting from each arrangement were compared to identify the potential
consequences of nest crowding. To further characterize the impacts of nest crowding,
the nest p02 values resulting from nest densities of 4 and 9 nests per square meter
were also simulated. The physical parameters used in all nest crowding simulations

are shown in Table 11.

97

3.2.3~ Simulation of Development

To simulate developmental changes, the Beach-MPT model was
independently parameterized using the physical measurements from four nests at
Sapelo Island, GA shown in Table 12. Fifty days of development were simulated for
each nest. In these simulations the nest metabolic rate was assumed to increase during

development according to the logistic equation from Ackerman (1981),

125

—0.l6(r-37.0)

 

V02 =
1+e

where V02 is the oxygen consumption rate (cm3 Oz/day) and r is the day of

incubation.

98

Table 9. Parameter values used in the Beach-MPT sensitivity analyses.

 

Parameter

Values

Comments

 

Sand Porosity
(m3/m3)

0.35, 0.40, 0.45

Typical porosity
values of beach sand
are in this range
(personal obs.)

 

Sand Water Content
(m3 H20/m3)

0.03, 0.09, 0.15

Typical beach sand
water content

(personal obs.)

 

Rainfall Rate
(cm HzO/hr for 1 hour)

0.0, 2.5

Typical rainfall
duration and rate
along Georgia coast
(GCE-LTER Data
Portal, 2006)

 

Depth to Top of Nest
(m)

0.2, 0.4, 0.6

Typical depths to the
top of turtle nests

(Chapter 1)

 

Sand Microbial Respiration
(cm3 Oz/m3s)

0.0, 0.16, 1.2

Microbial respiration
rates in beach sands
have been measured
in this range (U rban-
Malinga and
Opalinski 1999)

 

Sand Thermal Conductivity
(W/m K)

6.8, 8.8, 10.8

The thermal
conductivity of
quartz is 8.8 W/m K
(Krieth and Bohn
1993) 6.8 and 10.8
are i ~25% the
quartz value.

 

 

Clutch Size
(eggs)

 

50, 100, 150

 

Typical clutch size
values are in this
range. (Miller 1997
and this study

Chapter II

 

99

 

Table 10. Parameter values used in Beach-MPT simulations exploring the
consequences of beach renourishment. Because beach nourishment may lead to
increased sand water content or decreased sand porosity both situations were
simulated using the parameters listed here.

 

 

 

 

 

 

 

 

 

 

Increased Decreased
Sand Water .
Parameter Porosity Comments
Content Simulation
Simulation
Reasonable reduction
Sand Porosity in beach sand porosity
(1113/1113) 0.4 0.35 .followrng .
nounshment (Cram
1995).
Sand water contents
Sand Water in natural and
Content 0.1 0.03 nourished beaches are
(m3 HzO/m3) in this range. Rimkus
and Ackerman (1995)
Standard value for
Nest Metabolism 390 390 nests containing 100
(cm Oz/hour) eggs.
(Ackerman 1977)
Depth to Top of
Nest 0.4 0.4 This study, Chapter 1
(m)
Represents an average
Nest Radius 0 1 0 1 nest radius.
(111) ' ' (Ackerman 197 7, and
this study, Chapter 1)

 

100

 

Table 11. Parameter values used in Beach-MPT simulations exploring the
consequences of nest crowding.

 

 

 

 

 

 

 

Parameter Value Comments
Sand Porosity A reasonable sandy
(m3/m3) 0.4 beach porosity (This
study, Chapter 1)
Sand Water Content Linear increase from Realistic water content
(m3 H20/m3) 0.05 at upper surface gradient in a sandy
to 0.11 at bottom of beach
the proﬁle (Ackerman 1997)
Nest Metabolism Reasonable estimate of
(cm3 Ozlhour) the metabolic rate for a
390 nest containing 100
eggs.
(Ackerman 1977)
Depth to Top of Nest Average depth of
(m) 0.4 loggerhead turtle nest
(This study, Chapter 1)
Nest Radius Represents an average
(m) 0 1 nest radius.
' (Ackerman 1977, and

 

 

this study, Chapter 1)

 

101

 

Table 12. Data on four nests studied at Sapelo Island (Chapter 1), used to
pararneterize Beach-MPT simulations testing the model’s ability to predict p02
changes through the entire incubation period. During the summer of 2006
measurements of the depth to the top and bottom of the loggerhead nests along with
measurements of nest width, sand water content, sand porosity, and nest p02 were
made on Sapelo Island, GA. Detailed methods are described in Chapter 1. The nest
depth refers to the distance from the sand surface to the top of the nest, while nest
height refers to the distance between the top and the bottom of the nest. The nest
width was measured horizontally at the widest portion of the nest.

 

 

 

 

 

Clutch Mean Sand Mean SandWater Nest Nest Nest

Nest Size Porosity3 (:t S. E) Content (:h S. 3.E) Width Depth Height
(eggs) m/m3 ) (m3 H2 O/m3 ) (m) (m) (m)
10 115 “47:39-00“ “07::2-01) 0.2 0.3 0.24
11 119 0495:0307) 0045:0305) 11.21 1.17 1.33
19 111 0475301) 1.111 551,018) 11.23 1.21 1.311
23 103 0 48 $2007) 0°07 $05005) 0.26 0.3 0.33

 

102

3.3~ RESULTS
3.3.l~ Sensitivity Analysis

Late-Incubation Nest p0 2:

The sensitivity analysis demonstrates that both increases and decreases in nest
metabolism had equivalent, but opposite affects on the nest p02 (Table 13). This is
not the case with alterations in sand water content where the nest p02 is more
sensitive to increases in sand water content. The same general pattern is observed
when the porosity was varied, with the nest p02 more sensitive to decreases in
porosity. The nest p02 was relatively insensitive to rainfall or differences in rainfall
rate over the rates and duration (1 hour) simulated. Relative to the other parameters
examined, the nest p02 appeared moderately sensitive to sand microbial respiration
and nest depth, but the sensitivity did not depend on whether either parameter was
increased or decreased. Ranking the sensitivity of the nest p02 to each parameter gave
the following order from most inﬂuential to least: sand water content, nest
metabolism, sand porosity, sand microbial respiration, and rainfall.

Late-Incubation Nest Temperature:

The second sensitivity analysis showed that the nest temperature was not
nearly as sensitive to parameter variation as the nest p02 (Table 14). Increasing or
decreasing nest metabolism had equivalent, but minor affects on the nest temperature.
The nest temperature was also quite insensitive to changes in sand water content, the
rate of sand microbial respiration, and the thermal conductivity of the sand solids.
Changes in nest depth had minor affects on nest temperature, but the nest temperature

was most sensitive to variation in sand porosity. Ranking the parameters in terms of

103

their relative inﬂuence upon nest temperature from most to least inﬂuential results in
the following list: sand porosity, nest depth, nest metabolism, sand water content,
thermal conductivity of the sand solids, microbial respiration, and rainfall.

3.3.2w Consequences of Beach Nourishment and Nest Crowding

Beach Nourishment Simulations

The Beach-MPT model predicts that nests laid in nourished beaches may have
p02 values that are lower than those laid in natural beaches. In the beach nourishment
simulations which assumed that nourishment simply increased the water content of
the sand, the nest core p02 decreased ﬁ'om 17.1 kPa to 14.7 kPa, even when the nest
depth and sand porosity were held constant (Figure 19a). Alternatively, when beach
nourishment was assumed to decrease sand porosity, the nest core p02 decreased 0.5
kPa (F igure 19b). When beach nourishment was assumed to both decrease porosity
and increase sand water content (Figure 20), the nest p02 was reduced to 13.8 kPa.
Altering initial sand temperatures had no signiﬁcant effect on the response of nest
p02 to simulated beach nourishment.

Beach nourishment appears to have weaker affects on nest temperature,
though the effect of beach nourishment in part depends upon the initial sand
temperature used in the model. With cooler initial conditions the model suggests that
nests laid in nourished beaches which hold more water may be 4°C warmer in the
middle and 3° C warmer at the top of the nest compared to nests laid in natural
beaches (compare Figure 21-a to 21-c). The difference in nest temperatures between
natural and nourished beaches is largely lost if the initial sand temperature is warmer

(compare Figure 21 -b to 21-d), and in fact, the upper portion of the nest is predicted

104

to be slightly (0.5° C) warmer in the natural beach. When beach nourishment is
assumed to reduce sand porosity, beach nourishment has no affect on nest
temperatures and changes in initial sand temperature simply shift the temperature
transects to warmer values (Figure 22).

Nest Crowding Simulations

In the nest crowding simulations involving two nests, the p02 changed very
little as the distance between the nests was reduced. The nest core p02 decreased
from 17.6 kPa, to 17.3, to 17.2 kPa as the distance between the nests was reduced
from 1 meter, to 0.5 meters, to 0.3 meters, respectively (Figure 23). When four nests
were simulated in a l-m2 area of beach each nest had a core p02 of 17.1 kPa, while
the p02 between the nests was ~18.8 kPa (Figures 24 and 25). When nine nests were
packed into l-m2 (nest edges 0.05 meters apart) the p02 in each nest differed
signiﬁcantly from that found in the other nest arrangements. The nests on the comers
had core pOzs of 14.6 kPa, whereas those in the middles of the sides had core p023 of
14.0 kPa, and the nest in the middle had a core p02 of 13.2 kPa (Figures 26 and 27).
3.3.3~ Simulation of Development

Based on simulations of the four selected nests, the Beach-MPT model is
qualitatively accurate in capturing the trends in actual nest p02 throughout incubation.
Quantitatively, however, the model is routinely in error by 1-2 kPa (Table 15) and
tends to overestimate the nest p02. Nest 10 appears to be the exception with the
model underestimate the nest p02. Despite the errors the rate of p02 decline is

captured relatively well during the ﬁrst half of incubation.

105

Table 13: Response of end-incubation nest p02 to changes in parameter values. As
part of the sensitivity analysis the model parameters were individual assigned the
values shown here. The resulting nest p02 was recorded and used to calculate a
sensitivity index (S) using equation 3.1. Parameters with larger sensitivity indices
have larger affects on the nest p02 than parameters with smaller indices.

 

 

Response
Description Parameter Shift Parameter A of neat S
P03
50% Increase in 100 eggs -)
Nest Metabolism 150 eggs 50 '1 '843 0'21 5
50% Decrease in 100 eggs -)
Nest Metabolism 50 eggs '50 1'8“ 0215
1 Sand Water 0.09 m3HzO/m3 -)
Content 0.15 m3 HzO/m3 0'06 '3'369 0'294
1 Sand Water 0.09 m3 HzO/m3 —>
Content 0.03 m3 age/m3 '°°°° 2387 ”-209
. 0.40 tn3/tn3 -)
T Porosrty 0.45 m3/m3 0.05 0.351 0.160
. 0.40 tn3/tn3 ->

1 Porosrty 0.35 m3/m3 -0.05 -0.472 0.224
Moderate 0.0 cm/hr -) 2.5 -0.032 0.0019
Rainfall (1 hour) 2.5 cm/hr
1 Miami“ 0.16 cm3 02/m3s -)
Respiration 0.0 cm3 02/m3s -0.16 1.249 0.068
T Microbial 0.16 cm3 02/m3s -)
Respiration 1.2 cm3 02/m3s 1.04 -8.939 0.080

40 cm -)
1 Depth 20 cm -20 0.58 0.068

40 cm -)

1‘ Depth 60 cm 20 -0.6 0.07

106

Table 14: Response of end-incubation nest temperature to changes in parameter
values. As part of the sensitivity analysis the model parameters were individual
assigned the values shown here. The resulting nest temperature was recorded and
used to calculate a sensitivity index (S) using equation 3.1. Parameters with larger
sensitivity indices have larger affects on the nest temperature than parameters with

smaller indices.

Parameter A Response

 

 

Description Parameter Shift of nest T S
50% Increase in 100 eggs 9
Nest Metabolism 150 eggs 50 0'75 0005
50% Decrease in 100 eggs 9
Nest Metabolism 50 eggs '50 '0'74 0-005

0.09 m3 HzO/m3 ->
381:1}, am 0.15 m3 0.06 0.04 2.0 x 10“
Hzo/m3
1 Sand Water 0.09 m3 HzO/m3 -) _
Content 0.03 m3 H20/m3 0'06 '1'24 0006
3 3
T Porosity 0‘4 m h” 9;) 45 m3/m3 0.05 -003 0,24
3 3

l Porosity 0.40 m /m :35 [113/ms 4105 0.03 0.24
l Microbial 0.16 cm3 Oz/m3s 9 _4
Respiration 0.0 cm3 02/m3s -0.16 -0.09 3.0 x 10
T Microbial 0.16 cm3 02/m3s 9 _5
1 Depth 40 cm 920 cm -20 2.59 0.017
T Depth 40 cm 960 cm 20 -229 0.015
lThermal 8.8 W/m K 9 4
Conductivity 6.8 W/m K -2 -0.02 2.9 x 10
T Thermal 8.8 W/m K 9
Conductivity 10,3 W/m K 2 0.13 0.002

107

Sand
surface

 

 

 

 

1.0- a)
r r r r r r r 1
14 15 16 17 18 19 20 21

Oxygen Partial Pressure (kPa)

 

Sand
/ surface

/

 

 

 

 

 

1.0a b)
I l l l I T I I
14 15 16 17 18 19 20 21

Oxygen Partial Pressure (kPa)

Figure 21. Vertical transect through a beach in which a 0.1 meter radius turtle nest is
positioned at 0.4-0.6 m depth. a) simulated p02 values around a nest in a natural
beach (- -) and a nourished beach (—) which holds ~3 times the water, b) simulated
p02 values around a nest in a natural beach (- -) and a nourished beach (—) in which
the porosity is decreased by 0.05 n13/tn3 or ~10%. Horizontal dashed lines delineate
the nest boundaries.

 

108

Sand
/ surface

 

 

 

 

 

 

i l r I r l l r l
13 14 15 16 17 18 19 20 21

Oxygen Partial Pressure (kPa)

Figure 22. Vertical transect through a beach in which a 0.1 meter radius turtle nest is
positioned at 0.4-0.6 m depth. Simulated p02 values around nest in a natural beach (-
-) and a nourished beach (—) in which the water holding capacity was increased ~3
times the water and the porosity was decreased by 0.05 m3/m3 or ~10%. Horizontal
dashed lines delineate the nest boundaries.

109

 

 

 

 

 

 

24 28 28 30 32 34 36
Temperature (°C)

Figure 23. Vertical transect through both a natural and a nourished beach in which a
0.1 m radius turtle nest is positioned at 0.4-0.6 m depth. The nourished beach holds
~3 times more water than the natural beach. Horizontal dashed lines delineate the nest
boundaries.

a) (—) temperature gradient in a natural beach with initially cooler temperature

b) (- - -) temperature gradient in natural beach with initially warmer temperature

c) ( - - ) temperature gradient in nourished beach with initially cooler temperature

(1) (— —) temperature gradient in nourished beach with initially warmer temperature

110

 

 

Depth (m)

 

 

 

 

1' y“;
0 .8 "" ,’ :7
i ,7'7
0.9 -‘ z ,7
”/7
1.0- "
I T 7 l l l l

24 26 28 30 32 34 36
Temperature (°C)

Figure 24. Vertical transect through both a natural and a nourished beach in which a
0.1 m radius turtle nest is positioned at 0.4-0.6 m depth. The porosity of the nourished
beach is reduced by 0.05 m3/m3 (~10% lower than the porosity of the natural beach).
Horizontal dashed lines delineate the nest boundaries. To prevent overlap and aid in
visualization, a 02° C displacement was added to the lines representing the nourished

beaches.

a) (—) temperature gradient in a natural beach with initially cooler temperature
b) ( . - .) temperature gradient in natural beach with initially warmer temperature

c) (- - -) temperature gradient in nourished beach with initially cooler temperature
d) (— —) temperature gradient in nourished beach with initially warmer temperature

111

 

19.5 ‘
19.0 -

18.5 <

18.0 ‘

17.5 1 U

 

p02 at 0.5 m of Depth (kPa)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

      

 

 

 

 

 

17.01 a)
16.5 1 r t 1 W7
0.3 meter
’3 Horizontal Distance (m)
g 20.5 I
20.01
'5
3 19.51
G 19.01
“5‘
18.5<
E".
in 18.01
g 17.5‘ I
b 1
O” 17.0. ) i
9" 16.5 . 1 1 1.
0T5mete;
Horizontal Distance (m)
”a? 21.0 i i i i
3 205‘ I l : l
'5 20.0« I I I I
8‘ I I I I
3 2:1 I l l l
o .
E 18.54
V} 18.01 : | : :
o
a we : I : :
I l I i
6' "'01 C) I I I I
I l l
D-t 16.5 1 l
1.0meter
Horizontal Distance (m)

Figure 25. Results of Beach-MPT simulation showing the p02 gradients within and
around two nearby nests. Both nests had a radius of 0.1 meter and were centered at a
depth of 0.5 meters. The solid lines represent horizontal transects drawn through the
centers of each nest at a depth of 0.5 meters. A) nests 0.3 meters apart, b) nests 0.5
meters apart, c) nests 1 meter apart. Parameters used in simulations are provided in
table 3.

112

20.5

20

'19

 

 

   

‘—
2 meters

p02 (kPa)

Figure 26. Simulation of p02 gradients in and around a set of four, 0.] meter diameter
nests, centered at a depth of 0.5 meters. a) Three-dimensional reference for the
images shown in Figure 24b and Figure 24c. b) p02 gradients as seen from the side.
The sand surface is the upper boundary. c) the p02 gradients around the four nests as
viewed ﬁ'om above. The black dashed lines in Figure 3b are one meter apart and in
Figure 3c the dashed square is one square meter. The minimum p02 in all four nests
was 17.1 kPa.

113

20.0

 

19.5 -

19.0 4

————_—-
-——————-—
-———————q

———————_

   
 

18.5 1

18.0 J

17.5 4

p02 at 0.5 m depth (kPa)

17.0 ‘

 

 

_—__——_

l
l
l
I
l
l
l

 

16.5

 

 

‘-
‘

 

0.3 meter
Horizontal Distance (m)
Figure 27. Results of Beach-MPT simulation showing the p02 gradients within and
around two nests in the four nest simulation. All nests had a radius of 0.1 meter and

were centered at a depth of 0.5 meters. The solid lines represent a horizontal transect
drawn through the centers of each nest at a depth of 0.5 meters.

114

 

 

   

P02 (kP a)

  

‘— 2 meters —’

Figure 28. Simulated of p02 gradients in and around a set of nine, 0.] meter diameter
nests, centered at a depth of 0.5 meters. a) Three-dimensional reference for the
images shown in Figure 26b and Figure 26c. b) p02 gradients as seen from the side.
The sand surface is the upper boundary. c) the p02 gradients around the nine nests as
viewed from above. The black dashed lines in ﬁgure 3a are one meter apart and in
ﬁgure 3b the dashed square is one square meter. The minimum p02 was 13.2 kPa in
the central nest.

115

 

   

 

 

  
   

/////////////////////// ¢///////////
////////%//// /M/////
///////////////// ¢////////////

 

  

 

 

)
a

 

 

 

W

098765432

3.3 ease a no a 8g

. Horizontal// Distance (m')

 

   

 

 

   

/////////////////////////// //////////
///////////////////%/////%¢////
//////////////// a7//////

 

  

 

 

T

I Horizontal /Di/:tance (m)

Figure 29. Horizontal transects through the nine nest simulation shown in ﬁgure 8

)
b

 

 

 

098765432

3%: 59% e no a 8m

illustrating the p02 gradients in and around three nests. a) Horizontal p02 transect
through three nests along the edge of the arrangement. b) Horizontal transect through
three nests in the middle of the arrangement. All nests were centered at a depth of 0.5
meters and both transects went through the middle of each nest. Nest locations are
shown by the cross-hatching. The distance between the nest edges was 0.05 meters.

116

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

22 22
Nest 10 Nest11
20 20 .I
A 18 1 3 18 .
g 2
<5: "5 J (2 16
§ 14 ~ g 14 «
12 J 12
10 T V 7 10 v I v v v T
0 10 20 30 40 50 60 0 10 20 30 40 50 60
Day of Incubation Day of Incubation
22 22
Nest 19 N994 23
20 . 20 <
A , A 13 .
g 18 9:
V ‘ J
(g 16 cg 16
.5 ~
3 14 « g 14 I
12 1 12 4
1o 1 I I I I l 10 V T ﬁr V I 1
0 10 20 30 40 50 60 0 10 20 30 4O 50 60
Day 01 Incubation Day of Incubation

Figure 30. Comparisons of predicted (o) and actual (O) nest p023 throughout the
course of nest incubation in the four nests selected for study. In each case the model
was parameterized with the ﬁeld data shown in Table 12. The actual nest p023 were
measured during the 2006 nesting season on Sapelo Island, GA.

Table 15. Mean difference, throughout the incubation period, between the actual nest
p023 and the nest p028 predicted by the Beach-MPT model (shown in Figure 28).

 

Nest Mean (kPa) Range (kPa)

 

10 1.4 :t 0.25 0.1— 2.3
11 1.6 :t 0.27 0.5 — 2.9
19 1.1:I:O.13 0.6—1.9
23 2.5 :I:0.15 1.8 - 3.2

117

3.4~ DISCUSSION

Physical characteristics of the nest environment such as temperature, moisture
level, and respiratory gas pressures have been shown to inﬂuence incubation length,
sex determination, and embryonic survival (Mrosovsky and Yntema 1980,
Matsuzawa et al. 2002). These physical characteristics may also alter other important
phenotypic traits, including body size, growth rate, and running speed with the
potential for long-term consequences (Ackerman 1981, Miller et al. 1987). I recently
demonstrated that one of these characteristics, nest p02, varies considerably among
loggerhead turtle nests and that this variability was not driven by clutch size (Chapter
1). This suggests that nest site characteristics and their variation may have profound
consequences on developing turtles. Despite modest knowledge concerning the
effects of temperature, moisture, and respiratory gases upon turtle embryos, we know
remarkably little about the microclimates within natural turtle nests. Less is known
about how the physical characteristics of the nest site inﬂuence the nest microclimate.

The sensitivity analyses reported here were designed to address this area of
limited knowledge by clarifying the inﬂuence of nest and nest-site characteristics on
the nest temperature and nest p02. These analyses suggest that while nest p02 is
sensitive to changes in clutch metabolism it is equally sensitive to changes in sand
porosity and sand water content (Table 13). The fact that the model is similarly
sensitive to sand porosity and sand water content is not unexpected given that both of
these parameters affect the amount of air-ﬁlled pore space available for gas diffusion.

This ﬁnding suggests that when considering nest p02 it is important to recognize that

118

the characteristics of the substrate around the nest may be just as important as the
characteristics of the developing clutch.

There were some additional surprises in the p02 sensitivity analysis. Nest
depth, which is often considered very important in determining nest microclimate,
had a moderate affect on nest p02, but nest p02 is less sensitive to nest depth than
both porosity and water content (Table 13). Short-terrn rainfall events (1 hour, 2.5
cm/hr) were also found to have relatively little effect upon the nest p02. Presumably,
the low impact of the rainfall is because the 02 in the sand serves as a reserve supply
during the relatively short period of time that the surface sand pores approach
saturation during rain. Relatively large ﬂuctuations in respiration by sand microbial
populations were also found to have little affect on the nest p02, suggesting that
empirical quantiﬁcation of microbial populations is unnecessary to understand
variation in nest microclimates (Table 13). Taken together my sensitivity analysis
suggests that the large variability in nest p02 is mostly like due to variation in sand
porosity or sand water content, and developing more accurate means of measuring
these variables in the ﬁeld is an important goal. It also suggests that any processes,
natural or otherwise, that alter the nesting substrate will have important consequences
on nest p02.

Nest temperature was less sensitive than p02 to changes in all of the
parameters that were included in the sensitivity analysis. The nest temperature,
however, was relatively sensitive to changes in sand porosity. The sensitivity to
porosity may be a consequence of the fact that as the porosity changes, so too does

the thermal conductivity of the sand system because of the low thermal conductivity

119

of air. Relatively porous sands contain more air and therefore exhibit a lower thermal
conductivity than more densely packed sands. Changes in water content might be
expected to have a considerable affect on the nest temperature, because high water
content results in less air, and the thermal conductivity of water is far higher than air.
The potential effect of water content is not realized in practice, however. The nest
temperature was relatively insensitive to changes in water content, presumably a
consequence of the high speciﬁc heat of water which would tend to buffer
temperature changes. Changes in nest metabolism had a relatively small affect on nest
temperature, once again demonstrating that the nest microenvironment is oﬁen less a
ﬁinction of the biotic processes in the nest and more a consequence of the abiotic
characteristics of the nest site.

Given that the nest environment may often be a consequence of the physical
characteristics of the nest site, one would expect that activities such as beach
nourishment, which alter nest site characteristics, can dramatically alter the nest
environment. The Beach-MPT model predicts that nests laid in nourished beaches
may have p02 levels that are signiﬁcantly lower than those found in nests laid in
natural beaches (Figure 19 and 20). The actual reduction in nest p02 depends on
whether beach nourishment increases the sand water content, decreases the porosity,
or both. There has been some disagreement over whether beach nourishment actually
alters porosity (Ackerman 1997). My analysis, however, suggests that effects of
changes in porosity are dwarfed by the effects of changes in water holding capacity,
which is much less in doubt (Crain et al. 1995). Given that the critical p02 (cp02: the

p02 below which metabolism is reduced) of loggerhead embryos has been found to

120

be 18.] kPa during late incubation (Kam 1993) the Beach-MPT model predicts that
embryos developing in nests laid in nourished beaches may experience signiﬁcantly
depressed metabolic rates, which may slow development, and increase the length of
incubation.

Beach nourishment appears to have weaker affects on nest temperature,
though the thermal effect of beach nourishment depends upon the initial sand
temperature used in the model. When the initial sand temperature is low and beach
nourishment increases the water holding capacity of the sand, the nest temperatures
increase dramatically (Figure 21). This effect is lost if the initial sand temperature is
higher, which suggests that. the consequences of beach nourishment could vary
seasonally. Nests laid earlier in the nesting season are exposed to lower sand
temperatures, and the model suggests that these nests may be more sensitive to beach
nourishment than nests laid later in the season and exposed to warmer sand
temperatures. Such a possibility deserves attention. Both nest temperature and p02
are most affected when beach nourishment increases the water holding capacity of the
sand rather than when beach nourishment lowers porosity (F igurel9 and 22). This
suggests that care should be taken when nourishing beaches to maintain natural levels
of water holding capacity. The water holding capacity is largely the result of particle
size and packing or bulk density (Horn and Baumgartl 2002). Therefore, it is
important to ensure that the sand being used for nourishment is of a similar particle
size as that naturally found on the beach.

Nest crowding may negatively impact the nest environment for nests placed in

hatcheries, those laid naturally in heavily nested beaches, or those laid during the

121

simultaneous, mass-nesting arribadas of the olive ridley sea turtle. The Beach-MPT
model suggests that when only 2 nests are nearby, the p02 in both nests changes very
little (~ 0.5 kPa) as the distance between nests is reduced. The p02 gradient in the
sand between the nests changes much more however (~2.5 kPa). This suggests that
measuring the p02 between two nests may not provide a good measure of the
conditions within the nests. More importantly, measuring the p02 between two nests
may not provide a good measure of how much the two nests interact. In fact, it

appears that despite the fact that the p02 values in the sand between two nests

 

declines considerably as they are moved closer to one another, the nests themselves
interact minimally.

Even at a density of four nests per 1 m2 (0.3 meters between nest edges), the
p02 within each nest did not differ signiﬁcantly from the two-nest simulations in
which the nests edges were 0.3 meters apart (compare Figure 23a to Figure 25). It
was only when the nests were packed nine per square meter that the nest p02 clearly
declined. These results suggest that considerable crowding is required before the nest
p02 is negatively impacted. Therefore, while nest crowding may be a concern under
special conditions, under most conditions nests are predicted to not interact
signiﬁcantly. As more empirical work becomes available, it will be interesting to test
the validity of these predictions.

While an understanding of the developmental environment to which sea turtle
eggs are exposed clearly requires consideration of the biotic parameters within the
nest, I have demonstrated using the Beach-MPT model that often the abiotic

characteristics of the nest site may be of equal importance. Currently, most managers

122

 

measure nest parameters such as clutch size, nest depth, hatching success, or the
distance to mean high water line when assessing nest success and suitable nest
locations. My results suggest that supplementing these measurements with accurate
measurements of nest site characteristics such as sand porosity and sand water content
will improve our ability to predict which nest sites may be successful. These results
also suggest that practices that alter nesting substrate can dramatically alter nest
environments. Therefore, increasing nest success may be achieved through directed
habitat alterations. Alternatively, haphazard management of nesting substrate, could

easily decrease nest success.

123

APPENDIX I

Mesh and solver parameters used in individual Beach-MPT simulations.

Dry Sand p02 simulations

Element Number: 1 168

Degrees of Freedom: 32636

Element Type: Tetrahedral

Element Interpolation: Lagrange-Quadratic
Time Stepping: Free

Time-dependent Solver: GMRES
Preconditioner: Geometric multigrid

Damp Sand p02 Simulations

Element Number: 6586

Degrees of Freedom: 30990

Element Type: Tetrahedral

Element Interpolation: Lagrange-Quadratic
Time Stepping: Free

Time-dependent Solver: GMRES
Preconditioner: Geometric multigrid

Dry Sand Temperature Simulations

Element Number: 1496

Degrees of Freedom: 30990

Element Type: Tetrahedral

Element Interpolation: Lagrange-Quadratic
Time Stepping: Free

Time-dependent Solver: GMRES
Preconditioner: Geometric multigrid

124

Damp Sand Temperature Simulations

Element Number: 18072

Degrees of Freedom: 79617

Element Type: Tetrahedral

Element Interpolation: Lagrange-Quadratic
Time Stepping: Free

Time-dependent Solver: GMRES
Preconditioner: Geometric multigrid

Two Nests, 1 meter apart

Element Number: 4066

Degrees of Freedom: 18983

Element Type: Tetrahedral

Element Interpolation: Lagrange-Quadratic
Time Stepping: Free

Time-dependent Solver: GMRES
Preconditioner: Geometric multigrid

Two Nests, 0.5 meter apart

Element Number: 3899

Degrees of Freedom: 19063

Element Type: Tetrahedral

Element Interpolation: Lagrange-Quadratic
Time Stepping: Free

Time-dependent Solver: GMRES
Preconditioner: Geometric multigrid

Two Nests, 0.3 meter apart

Element Number: 3985

Degrees of Freedom: 19008

Element Type: Tetrahedral

Element Interpolation: Lagrange-Quadratic
Time Stepping: Free

Time-dependent Solver: GMRES
Preconditioner: Geometric multigrid

125

Four Nests

Element Number: 15345

Degrees of Freedom: 64969

Element Type: Tetrahedral

Element Interpolation: Lagrange-Quadratic
Time Stepping: Free

Time-dependent Solver: GMRES
Preconditioner: Geometric multigrid

Nine Nests

Element Number: 20248

Degrees of Freedom: 83484

Element Type: Tetrahedral

Element Interpolation: Lagrange-Quadratic
Time Stepping: Free

Time—dependent Solver: GMRES
Preconditioner: Geometric multi grid

126

APPENDIX II

A model report describing all parameters, equations, and functions were included in
the Beach-MPT model.

Model Properties

"Property 7 Value
Model name

Author

Company

Department

Reference

URL -

Saved date Jan 22, 2007 3:39:43 PM
Creation date * .Feb 4, 2006 4:03:51 PM
COMSOL we; COMSOL—3.3.0.511 "

 

File name: C:\Documents and Settings\NATHAN MILLER\My Documents\Nest
Simulations\2Nest\2Nests lmeterapartmph

Application modes and modules used in this model:

. Geoml (3D)
0 PDE, General Form
0 Convection and Conduction
o PDE, General Form

- Geom2 (2D)

127

Constants

{Name 3 Expression Value Description
ECs ' - 2.13e6
Cw ‘ 11.19e6

.Ca 1.256e3
MW 0.018
THETAF ”0.0"

N i 11.68

M l-l/N

L .5
ALPHA2.57
R 8.314e-3
Ks 7.44e-5
‘DL 0.005

DT 0.0001

d "0.005
sigma "5.6697e-8
aaaa ‘99.41””
A1” 5 51583877 ' ‘
A2 "8513076" 5
A3 "233439

a " 3.611, “ '

b ‘ "ii—5'02

c 340:9?
thetaO ‘ 0.05

ml A 12

rhea—1t w1'41 .4

frea— _ " 10.053

.kw .6
rat—5115788 _
‘ga‘WH‘l

.ge' " 1421a
{beta 2”“

(egg iii—052.3%

128

5. Geoml

Space dimensions: 3D

Independent variables: x, y, z

5.1. Expressions

5.1.1. Subdomain Expressions

“same.
'main
tauw
‘av

theta

qx
'qy -
qz
absq

CH 5‘

,, (9 91:9)3

{1 2-3
1

thetaA(10/3)¥(hp<0)(rHETAs02

_ THETAs-theta* (hp<0)

((THETAs-
THETAr)*Se+THETAr)*(hp<0)+THETAs*(hp>= ,
'0) .

* 1Ks*Se"L*(1 (1-5

Se"( 1/M))"M)"2*(hp<0)+Ks* (hp>=0)

’ le-010*_(_t——-0)-K*hpx

1K*hpy
1-K*( l +hpz)

_ ' sqrt(qx"2+qy"2+qz"2)

ALPHA*M*(THETAs-THETAr)*Se"(1fM)*(1-
Se"(1/M))"M*(hp<0)/(1-M)

2*Cs*Vols+Cw*theta+Ca*av*(hp<0)+Cw*THET 0 7405000000000001*c ;
1As*(hp>=0) egg+0. 2595*Ca

111+(ALPHA*abs(hp))AN)A( -M)

' exp(9.800000000000001*MW*hp/(R*T))*(hp<0)
0. 7
11-THETAs

{2.4673009

10.0021284875*(0100341 11301175511011 1” ‘0.0021§3(0f00341*T)01 . ;
1 75/patrn

10.4405907440999996*exp(A1+100*A2/T+A3*log

129

bg :1/(R'1'T) if 1 f ’ FI/(RI‘T)

taug av"(lO/3)*(hp<0)/THETAs"2 0.1655
M02 0. 0006661

thetaD DL*qx"2/absq+DT*(qu2+qz"2)/absq+le *tauw
xx I

thetaD DL*qy"2/absq+DT*(qu2+qz"2)/abquDw1*tauw
YY 1

thetaD DL*qz"2/absq+DT*(qu2+qy"2)/absq+Dw1*tauw -
22 1

thetaD (DETDT)*qx*qy/ab_sq -1 7

xy

thetaD '(DL-DT)*qx*qz/absq

xz 1

near) (DL-DT)*qy*qz/absq

,yz I f

IDV 2. 4e-005*(O. 00341"T)"1 .75

1Dh 2. 15e-005*(0. 00341*T)"l. 75

1amda 2501:070023611‘T

TesT * a*exp(b*(273 T)/(273-T-c))

delta b*c*esT/(-273+T+c)"2

lea .esT*hr

fw .1/(l+(theta/theta0)"(;q))

~fg ka+lamda*de1ta*hr*fw*rhoarr*Dv/(patm-ea)

kf 1kg+fw*(kw-ka) 7

epa 2/(3*(1-ga*(1 ka/kf)))+1/(3*(1-gc*(1-ka/kf)))
epa“ 2/(3*(1-ga*(1-kw/kf)))+1/(3*(1-gc*(1-kw/kf)))

,epm 2/(3*(l-ga*(1-kquartz/kf)))+1/(3*(1-gc*(1-
‘ kquartz/kf)))

Ksoil '(theta*epw*kw+av*epa*ka+VolS*epm*kquartz)/(t
'heta*epw+av*epa+VolS*epm)

kg ka+lamda*delta*hr"‘fw*rhoa1r*Dv/(patm—ea) '

Kn ’ ' .0.7Z105;K"watetl+0§2595*

I . ‘Kair
1Kair ‘ 0. 024%. 999e-005*T
{Kwate 0. 56+0. 0018*T ’

Ta 7 310. 5+12*s1n(2 3148e-005*p1*t-0 583*pi)

130

Initial 121.1 194587.21*zA4+954.09*zA3-
H20 430.48*z"2+57.807*z

THET 0.46
As

5.2. Mesh

5.2.1. Mesh Statistics

Number of degrees of freedom 18983

Number of mesh points 943
Number of elements 4066
Tetrahedral 7 i i 4066
Prism 0
1Herahedra1 0
'Nu’mberﬁ of boundary elements 1128
Triangular ’ i l 1128
Quadriiateral ’ ‘ 0

‘Nurnberof edgeelements 142
Number of vertex elements- 18
Minimum element quality 0.335
Element volume ratio 0.003 J

5.3. Application Mode: PDE, General Form (Water)
Application mode type: PDE, General Form

Application mode name: Water

5.3.]. Application Mode Properties

Property EValue

1Default element type Lagrange - Quadratic
:‘wane‘eiaansian' "on ’ ’ ‘
rang ' tram; (xyz)

”Weak constraints on"

131

5.3.2. Variables

Dependent variables: hp, hp_t
Shape functions: shlag(2,'hp')
Interior boundaries not active

5.3.3. Point Settings

Point' :1-18

'é'tyiej "10.10.11.25511
5.3.4. Edge Settings

Edge 1-30
style 7{0,{0,0,255},'sorid'}

5.3.5. Boundary Settings

’Boundaryi I1-2,4-1'4 ‘ 3

Type , Neumann boundary condition Neumarm boundary condition
”(g)" 0 ' 7 7 {in ’ "

5.3.6. Subdomain Settings

,7 i at-“

Subdomain 1

Damping/Mass coefﬁcient '(C+Se*('l'I-IETAs-THETAr))*(hp<0)-l-(THETA8-
'(da) 3 .THETAr)*(hp>=0)

Source term (1) 1 0

Icons—snares... source . *ﬁ-KirhEt-Kflmy—i-K*(hpifi)}}
gterm (ga)

1Subdomain initial value I ;1
1hp‘ '7 ‘7 ‘ 1’111itialH20.
5.4. Application Mode: Convection and Conduction (Energy)

Application mode type: Convection and Conduction

Application mode name: Energy

.132

5.4.1. Application Mode Properties

Property - V 7 Value‘ 1

Default element type Eagrdiige - Quadratic
Analysis type Stationary

Equation form Non-conservative
Frame _ Frame (xyz)

Weak constraints Off

5.4.2. Variables

Dependent variables: T
Shape functions: shlag(2,'T')
Interior boundaries active

5.4.3. Boundary Settings

Boundary ' 1-2, 5, 14-18 6-13

Type A Thermal insulation Continuity
Temperature (TO) K 0 70
Boundary 3 4

Type Temperature Temperature
Temperature (T0) .300 Ta

5.4.4. Subdomain Settings

Subdomain 1 2-3
Thermal conductivity (k) W /(m-K) Ksoil Kn
.Density (rho) 7 kg/m3 1 l
'neatzaaano (C) ’ ”kg,“ (CH ” CH
Heat source (Q) ‘ W/m3 0 800.4529
xiuelocitylu) ’m/s 7 7 ’qx 0 '
y-velocity (v) m/s ‘ qy 0
z-verCity (w) 1 ,m/s I .qz 0
Subdomain initial value} *1 23
Temperature (T) ’ W K_300-2*z 305

133

5.5. Application Mode: PDE, General Form (Gas)

Application mode type: PDE, General Form
Application mode name: Gas

5.5.1. Application Mode Properties

:Property :Value

Default element type Lagrange - Quadratic
Wave extension Off

Frame Frame (xyz)

Weak Constraints 1 Off

5.5.2. Variables

Dependent variables: p02, pO2_t
Shape functions: shlag(2,'p02')
Interior boundaries not active
5.5.3. Point Settings

Point 7 i148

style L 1040,0255};

5.5.4. Edge Settings

Edge 130
style , {0,{0,0,255},'solid'}

5.5.5. Boundary Settings

 

Boundary; {1-2,5,14518 ‘ 3

[Type 7 1 Neumann boundary condition Neumann boundary Condition
(8) 110 W 7 _ H —lqz";p02_ 1 7
1r) _ i v-poz '-p02

‘Boundary14i * "1

Type— " {onenerionndary‘canainon

.(g) _ 1". THE“;

(r) I-p02+(.2095*patm)

134

5.5.6. Subdomain Settings

Subdomain 51 1 1 2-3

Damping/ . (theta*bw+av*bg)*(bp<0)+(THETAs*bw)*(hp>= 0.2595*bg

Mass _ 0) .

coefficient

(da)

Source 0 '-1.154e-3

term (t)

1Conservati .{{- {{-

Lve ﬂux ; j(bw“’tbetanerw”'tlletany-l-bw"‘tlretanzHaug (taug*Dg1*bg)*p

source *Dgl *bg)*p02x-qx*(bw*p02);- 02x;-

term (ga) ‘ (bw*thetaDyy+bw*tbetany+bw*thetaDyz+taug (taug*Dgl *bg)*
1*Dgl*bg)*P02Y'¢IY*(bW*P02)3- 02y;-
(bw*thetaDzz+bw*tbetanz+bw*tbetaDyz+taug (taug*Dgl*bg)*p
1081*bg)*P021-¢IZ*(bW*P02)}} 0221}

Subdomain initial value 1 2-3

p02 19 19

7. Interpolation Functions

7.]. Interpolation Function: NestV02

Interpolation method: Piecewise Cubic

Data source type: Table

x i 111;)
86400 5. 812e-6
432000 109965
864000 2.4285e-5
11296000 5.31932e-5
172800011.14355e-4 .
2160000 2.3658264 .
12592000 14.55193e-4 ,
3024000 7.78374e-4 ;
3456000 .1.143016e-3:
3888000 1.447763e-3

135

4320000 £1.644808e-3
4752000 175194963
5184000 51.8047736-3

7.2. Interpolation Function: NestHeat
Interpolation method: Piecewise Cubic

Data source type: Table

x f(x)
86400 ' 25778
432000 4.875
864000 10.771
1296000 23.5922 ,
1728000 50.7186
2160000 104.929
2592000 201.887
3024000 345.224
3456000 506.95 ‘
3888000 642.111
4320000 729.505
4752000 777.025
5184000 800.4529

8. Solver Settings

Solve using a script: off

Auto select 5611er On I

Solver Time‘dependent
Solution form 1 Automatic ‘1
891111516616 5* 5 oh’ "
Xdéiaiikiﬁ ' 011‘”

136

8.1. GMRES

Solver type: Linear system solver

Parameter ‘Value
Relative tolerance LOB-6
‘F actor in error estimate 400.0 :

Maximum number of iterations 10000 ,
Number of iterations before restart 50
Preconditioning Left

8.1.1. Geometric multigrid

Solver type: Preconditioner
Parameter Value 1
Number of iterations 2
rMultigrkid cycle 7 'V-cycle

8.1.1.1. SOR

Solver type: Presmoother
Parameter Value
(Number of iterations 2

Relaxation factor (omega) 1.0

8.1.1.2. SORU

Solver type: Postsmoother
Parameter -VaIue
:Number of iterations 2 ‘
{Relaxation factor (omega) 1.0 5

8.1.1.3. UMF PACK

Solver type: Coarse solver

[Parameter 'Value '
1Drop tolerance 10.0
Pivot threshold 0.1

Memory allocation—factor 50.7

137

8.2. Time Stepping

Parameter 5 Value

jTinIes‘ 5 e 0: 86400: 172800
11616116; tolerance _ 7 0. 01 5
Absolute 1616an ‘ ‘ 0. 0010 5'

Times to store in 6616111 . h 5 Spec1ﬁ&ft1mes -
.Time steps taken by solver Free

Manual tuning of step size I {Off

Initial time step I r0.00150.
Maximum time step I 1.0 1
Maximum BDF order U 5 I ‘

Singular mass matrix Maybe
Consistent initialization of DAB systems Backward Euler 1
'Error estimation strategy Include algebraic
Allow complex numbers :Off

8.3. Advanced

Parameter

Constraint handiing manna 5

Null-space function

Assembly block size

FValue

‘ 13116161611611

Automatic 5

iUse Hermitian uanspose of constraint matrix and m Symmetry detection Off_

Use complex functions with real input

.[Stop if error due to undeﬁned operation

'Type of scaling

Manual scaling

:Row equilibration

Manual control 61“ reassembly

F_——_ __-_ -—___ -.____

iLoad constant

Constraint constant I

Mass constant

Damping (mass) constant

J acobian constant

iCbnstraint Jacobian constant

138

'Off

1011"

If .anamanc

99 9 9‘ 999.9

10. Variables

10.1. Boundary

Name 1 I 5 Description 'Expresgﬁi;

.ndﬂux_ T _Energy Normal nx _Energy * dﬂux_ T_ x :Energy+ny_ Energy"
'conductive heat dﬂux_ T _y Energy+nz_Energy*
Iﬂux, T dﬂux_ T_ 2 _Energy

ncﬂ'ux_T_Energy Normal nx _Energy* cﬂux_ T_ x Energy+ny_ Energy“
convective heat cﬂux_ T _y Energy+nz_Energy*
;ﬂux, T 1cﬂux_T_z_Energy

ntﬂux_T_Energy Normal totaI IA an _Energy * tﬂux_ T x _Energy+ny_ Energy“
1 heat ﬂux, T tﬂux_T_y_Energy+nz_Energy*
tﬂux_T_z_Energy

 

10.2. Subdomain

10.2.1. Subdomain 1

Name 5 Description Expression

abshpx:Wate lgradmp)| I sqrt(hpx"2+hpy"2:+hpz"2)
.r

abggai x_wat 1661 XI énméaix02+ga1§024gai 212)

er

grad_ T__ x _En Temperature Tx

Eergy gradient, T, x 1

E component

Edﬂux_ T_ x E Conductive E—kxx_T_Energy * Tx-kxy_T_Energy * Ty-
Energy heat ﬂux, T, kxz_T_Energy * T2

1 x component j

cﬂux_ T__ x _E EConvective Erho_T;Ener—gy_ {grilling l" T 1* u_T_Energy
nergy Eheat ﬂux, T, '
i Ex component '

.tﬂux_ T x_ E ETotal heat _ dﬂux;T_x_Ener_g_y+cﬂux_T_x_Energy

 

 

Energy Eﬂux, T, x

5 . Ecomponent

[grad_T_y_En Temperature ETy

,ergy gradient, T, y

1 component .

Edﬂux_T_y_E Conductive E-kyx_ T _Energy * Tx-kyy_ T _Energy * Ty-
gnergy heat ﬂux, T, Ekyz T Energy * Tz

cﬂux_T_y_E
nergy
tﬂux_T_y_E
nergy
grad_T_z_En
ergy
dﬂux_T_z_E
nergy
cﬂux_T_z_E
nergy
tﬂux_T_z_E
nergy
beta_T_x_En
ergy
beta_T_y_En
ergy
beta_T_z__En
ergy
grad_T_Ener
8y
dﬂux_T__Ene
rgy
cﬂux_T_Ene
rgy
tﬂux_T_Ener
gy
cellPe_T_En
ergy

y component

Convective
heat ﬂux, T,

y component

Total heat
ﬂux, T, y
component

Temperature

gradient, T, 2

component

Conductive

heat ﬂux, T, 2

component

Convective

heat ﬂux, T, 2

component
Total heat
ﬂux, T, 2
component
Convective
ﬁeld, T, x
component
Convective
ﬁeld, T, y
component
Convective
ﬁeld, T, 2
component
Temperature
gradient, T
Conductive
heat ﬂux, T
Convective
heat ﬂux, T
Total heat
ﬂux, T

Cell Peclet
number, T

Dm_T_Energ Mean

y

diffusion

rho_T_Energy * C_T_Energy * T * v_T_Energy
dﬂux_T_y_Energy+cﬂux_T_y_Energy

Tz

—kzx¢T_Energy * Tx§k2y_T_Energy * Ty-
kzz_T_Energy * Tz

rho_T_Energy * C_T_Energy * T * w_T_Energy
dﬂux_T_z_Energy+cﬂuX_T_z_Energy
rho_T_Energy * C_T_Energy * u_T_Energy
rho_T_Energy * C_T_Energy * v_T_Energy

rho_T_Energy * C_T_Energy * w_T_Energy

sqrt(grad_T_x_Ene1-gy"2+grad_T_y_Energy"2+grad_T
_z_Energy"2) E
sqrt(dﬂux_T_x_Energy"2+dﬂux_T_y__Energy"2+dﬂux
_T_z_Energy"2)

Esqrt(cﬂux_T_x_Energy"2+cﬂux__T_y_Energy"24rcﬂux_

T_z_Energy"2)
sqrt(tﬂux_T_x_Energy"2+tﬂux_T_y_Energy"2+tﬂux_ E
T_z_Energy"2)

h *

sqrt(beta T x EnergyAZ+beta_T_y_Energy"2+beta_T_

z_Energy"2)/Dm_T_Energy

‘(kxx_T_Energy * rho_T_EnergyAZ * C_T_EnergyAZ *

u_T_Energy"2+kxy_T_Energy * u_T_Energy *

140

coefﬁcient, T

res_T_Energ Equation
y Eresidual for T

res_sc_T_En Shock

ergy capturing
:residual for T

da_T_Energy Total time _ _
scale factor,
‘T

absp02x_Ga EQEHMD» '

S .
absgaEXLGas lga3x|

32
0|
-]|

glimﬁg| {HOE

'IH‘OOd—df
WHaAHHP NH“

1 -kxx_
kxz

rh
'kzx_

rho_T_Energy"? * C_T_Enengf/‘ZA: I
EV_T_Energy+kxz_T_Energy * u_T_EnergY *

rho_T_EnergyAZ * C_T_EnergyAZ *

T nergy+kyx_ T _Energy* v_ T _Energy *
_EnergyAZ * C __T _EnergyAZ *

n_ergy+kyy T E_nergy* rho_T_EnergyAZ *
nergy"2 * v_ T _Energy"2+kyz_ T _Energy*
nergy * rho_ T _EnergyAZ * C _T _EnergyAZ *
n_ergy+kzx T _Energy* w __T _Energy*

_T _EnergyAZ * C_ T _EnergyAZ *
_Energy+kzy_ T _Energy* w _T _Energy*

o_T _EnergyAZ * C __T _EnergyAZ *
__Energy+kzz T _Energy * rho_ T _EnergyAZ *
_EnergyAZ * w_ T _EnergyA2)/((rho_ T _Energy“
_E

llmg'gjlml

_Energy * u_ T ___Energy)"2+(rho T __*Energy
_:Energy v_ T _Energy)"2+(rho_ T _Energy*
nergy* w_ T _Energy)"2+eps)

T _Energy * Txx-kxy_ T _Energy * Txy-
_T_Energy * sz+Tx* rho_T_Energy*
_T_Energy * u_T_Energy—kyx_T_Energy * Tyx-
_T_Energy * Tyy-kyz_T_Energy * Tyz+Ty *
_T_Energy * C_T_Energy * v_T_Energy-

T

T

0

_Energy * sz-kzy_T_Energy * sz-

o
kzz_ _Energy * Tzz+Tz* rho_ T _*Energy

‘C_ T _Energy* w _T _Energy-Q_T_ Energy

Tx* rho_ T _Energy * C_ T _Energy* u_ T _Energy+Ty *

rho_T_Energy * C_T_Energy* v_T_Energy+Tz*
rho_T_Energy * C_T_Energy * w_T_Energy-

C_T_Energy
Dts_T_Energy * rho_T_Energy * C_T_Energy

sqrt(p02x"2-Ep02y"2+p022"2)

if '3‘1}t(‘g‘a3xA2+g.3‘yA2+g.3 2A2)

141

 

10.2.2. Subdomain 2-3

Name
abshpx_Wate
r

absga l x_Wat
er

grad_T_x_En
ergy

dﬂux_T_x_E
nergy

cﬂux_T_x_E
nergy

tﬂux_T_x_E
nergy

grad_T_y.En
ergy

dﬂux_T_y_E
nergy

cﬂux_T_y_E
nergy

tﬂux_T_y_E
nergy

grad_T_z_En
ergy

dﬂux_T_z_E
nergy

cﬂux_T_z_E
nergy

tﬂux_T_a_E

Description
lgrad(hp)l

lgalxl

Temperature
gradient, T, x
component
Conductive
heat ﬂux, T,
x component

Convective
heat ﬂux, T,
x component

Total heat
ﬂux, T, x
component

Temperature
gradient, T, y
component
Conductive
heat ﬂux, T,
y component
Convective
heat ﬂux, T,
y component
Total heat
ﬂux, T, y
component
Temperature
gradient, T, z
component

Conductive

heat ﬂux, T, 2
component
Convective
heat ﬂux, T, 2
component

Totaliheat

Expression

Tx

-kxx_T_Energy * Tx-kxy_T_Energy * Ty-
kxz_T_Energy * Tz

rho_T_Energy * C_T_Energy * T * u_T_.Energy
dﬂux_T_x_Energy+cﬂux_T_x_Energy

Ty

-kyx_T_Energy * Tx-kyy_T_Energy * Ty-
kyz_T_Energy * Tz

rho_T_Energy * C_T_Energy * T * v_T_Energy

dﬂux_T_y_Energy+cﬂux_T_y_Energy

-kzx_T_Energy * Tx-kzy_T_Energy * Ty-
kzz_T~Energy * Tz ‘

rho_T_Energy * C_T_Energy * T * w_T_Energy
dﬂ®_T;Z_Energy+cﬂux_T_z_Energy

142

nergy
beta_T_x_En
ergy
beta_T_y_En
ergy
beta_T_z_En
ergy
grad_T_Ener
8y
dﬂux_T_Ene
1' gy
cﬂux_T_Ene
rgy
tﬂux_T_Ener
gy
cellPe_T_En
ergy

ﬂux, T, 2
component
Convective
ﬁeld, T, x
component
Convective
ﬁeld, T, y
component
Convective
ﬁeld, T, 2
component

rho_T_Energy * C_T_Energy * u_T_Energy

rho~T_Energy * C_T_Energy * v_T_Energy

rho_T_Energy * C_T_Energy * w_T_Energy

Temperature sqrt(grad_T_x_Energy"2+grad_T_y__Energy"2+grad_T

gradient, T

Conductive
heat ﬂux, T

Convective
heat ﬂux, T

Total heat
ﬂux, T

Cell Peclet
number, T

Dm_T_Energ Mean

Y

diffusion

_z_Energy"2)
sqrt(dﬂux_T_x_Energy"2+dﬂux_T_y_Energy"2+dﬂux
_T_z_Energy"2)
sqrt(cﬂux_T_x_Energy"2+cﬂux_T_y_Energy"2+cﬂux_
T_z_Energy"2)
sqrt(tﬂux_T_x_Energy"2+tﬂux_T_y_Energy"2+tﬂux_r
T_2_Energy"2)

h :1:
sqrt(beta_T_x_Energy"2+beta_T_y_Energy"2+beta_T_ E
z_Energy"2)/Dm_T_Energy

(kxx_T_Energy * rho_T_Energy? * C_T_EnergyAZ *
u~T_Energy"2+kxy_T_Energy * u_T_Energy *

coefﬁcient, T rho_T_EnergyAZ * C _T _Energy"2 *

res_T_Energ Equation
residual for T Ikxz_T_Energy * sz+Tx * rho_T_Energy *

Y

v rT__Energy+kxz T _*Energy u_ T _Energy*
o_T_Energy"2 * C _T _EnergyAZ *

:T_ nergy+kyx_T_Energy* v_T_Energy *
o_T EnergyAZ * C _T _EnergyAZ *

1T“ Ene nergy+kyy_ T E_11ergy* rho_T_EnergyA2 *
__T En nergy? * v_ T _EnergyA2+kyz_ T _Energy*
_T_ En

__T E

Egl

nergy *_rho T _EnergyAZ * C _T _EnergyAZ *
nergy+kzx_ T _*Energy w_ T Energy*
_EnergyAZ * C _T _EnergyAZ *

_ nergy+kzy_ T _Energy* w_ T _*Energy

0T EnergyAZ * C_ T _Energy/‘2 *

nerg_y+kzz T Energy* rho__ T _Energy"2 *
nergy"2 * w _T _EnergyA2)/((rho_ T _Energy*
nergy **u_T_Energy)"2+(rho_T_Energy
nergy * v_T_Energy)"2+(rho_T_Energy *
nergy * w_T_Energy)"2+eps)
-kxx:T_Energy * Txx-kxy_T_Energy * Txy-

“EIEIE€<O‘==*

roT

"11

HOOHW a.
Wear—1"]:
ImImImIn-ng

143

C_T_Energy * u_T_Energy-kyx_T_Energy * Tyx-
kyy_T_Energy * Tyy-kyz_T_Energy * Tyz+Ty *
rho_T_Energy * C_T_Energy * v_T_Energy-
kzx_T_Energy * sz-kzy_T_Energy * sz-
kzz_T_Energy * Tzz+Tz * rho_T_Energy *
C_T_Energy * w_T_Energy-(LT_Energy

res_sc_T_En Shock rTx * rho_T_Energy * C_T_Energy * u_T_Energy+Ty *
ergy capturing frho_T_Energy * C_T_Energy * v_T_Energy+Tz *
residual for T rho_T_Energy * C_T_Energy * w_T_Energy-
Q_T_Energy
da_T_Energy Total time Dts_T_Energy * rho_T_Energy * C_T_Energy
scale factor,
T

absp02x_Ga |grad(p02)| sqrt(p02x"2+p02y"2+p022"2)

s
absga3x_Gas |ga3x| sqrt(ga3x’;2-Jr‘ga3y"2¥ga3qz"2)

144

APPENDIX 111

To test the basic coding of the water ﬂow equation in the Beach-MPT model, the
model calculations were compared to two simple, analytical solutions shown here.

Water Flow in 11 Saturated, Uniform Sand Column

/ Constant pressure head

1

 

 

Point2zzz=100,p2=18,H2=118 +

Sand

K9=100

cm/
day L= 100 cm

 

v

 

 

 

Pointlzzl=0,p1=0,H1=0 +

\

Open to atmosphere

Figure A. l . Uniform, saturated soil column used in the ﬁrst test demonstrating the proper
coding of the water ﬂow equation in the Beach-MPT model.

145

The ﬁrst test uses the sand column shown in Figure A1. The saturated conductivity
(K5) is assumed constant everywhere in the 100 cm long soil column and a constant

pressure head of 18 cm is applied to the upper surface. Below 1 detail how Darcy’s
law is used to calculate the hydrostatic pressure (p) at any location in the soil

column and these values are compared to the hydrostatic pressure predicted by the
Beach-MPT model.

To calculate the hydrostatic pressure at a location (2) in the sand column Darcy’s

law (Eq. A.1) is applied between the arbitrary point (z) where p is unknown and the
bottom of the column where z = 0 and p = 0 . This gives Eq A.2.

J, = —K, M (A.l)

(22 ‘21)

J, = —K, (33—2) (A2)
2

We can also apply Darcy’s law across the entire column because we know the ﬂux
(Jw) in terms of the pressure at z = L (p = b), giving equation A3.

.1, = _11, 9:22 (A3)

Setting A.2 equal to A3 and solving for p we ﬁnd that

(A.4)

 

Using equation A.4 we can calculate the hydrostatic pressure at any point (z) and
compare this to the Beach-MPT prediction.

At 2 = 40 cm, using equation A.4, the hydrostatic pressure p is 7.2 cm.

Atz = 75 cm,p = 13.5 cm.
Atz= 23 cm,p= 4.14 cm

146

Figure A.2 shows the Beach-MPT model predictions, which match those calculated
analytically.

100

 

A O) on
O O 0

Column Height (cm)

N
O

 

 

O ........
024681012141618

Hydrostatic Pressure Head (cm)
Figure A2. The hydrostatic pressure head distribution within the sand column shown
in Figure A.1 as calculated by the Beach-MPT model. The distribution matches
exactly the hydrostatic pressure head calculated analytically using Darcy’s law and
equation A.4.

 

147

Water Flow in Saturated Layered Soil

A second test of the coding of water ﬂow in Beach-MPT was performed using the
saturated, layered soil column shown in Figure A.4.

/ Constmt pressure head

 

 

 

 

 

 

 

w“ I b=10cm
Point 2: z; =100. p2=10,H2=110 5 41
Sand
K3=75 L=75cm
crn/day
_____________ V
41
Loam
L=25cm
K1=5 cm/dzy
Pointl:zl=0,p1=0.H1=0 —" \V
Opentodmosphwe

Figure A.3. Saturated, layered soil column used in the second test demonstrating the proper
coding of the water ﬂow equation in the Beach-MPT model.

A layered vertical soil column consists of 25 cm of a loam soil with a saturated
hydraulic conductivity of K1 = 5 cm/ day overlain by 75 cm of a sandy soil with a

saturated hydraulic conductivity of K2 = 25 cm / day . The top of the column has

water ponded to a constant height of 10 cm above the column, and the bottom is open
to the atmosphere. To test the coding of the water ﬂow portion of the Beach-MPT
model I calculated the hydrostatic pressure distribution in the coltunn using Darcy’s
law and compared the results to the Beach-MPT predictions.

148

To solve this problem by hand it is ﬁrst necessary to calculate an effective saturated
hydraulic conductivity for the entire column, using equation A5.

K = _E_—— (A.5)

where L J is the height of layer J and K J is the hydraulic conductivity of layer J.

_ 25+75
617-25 75
___.+—
5 25

(A.6)

Kw. 212.5 cm/day

We can use this value and apply Darcy’s law to the whole column to calculate the
ﬂux from the bottom of the column. To do this I assumed point 2 is the upper surface
ofthe column 22 = 100, p2 =10, and H2 = 110 and point 1 is the bottom boundary, 21
=0,p1=0,andH. =0.

K
Fl _—____2'IL 110—0 A.7
1“ 100( ) ( )

Flux = —l3.75 cm/day

Now that we know the bottom ﬂux we can apply Darcy’s law to portion of the
column and calculate the hydrostatic pressure at any point in the column such as the
interface between the two soil layers.

J = K M (A.8)

w l (23 _ l)
We’ll specify the interface as point 3 (H3 = p3 + 25) and the bottom of the column

remains point 1 (HI = 0 ). The equation is then written as

—13.75 = —355—(p3 +25) (A.9)

Solving for p3 gives a hydrostatic pressure head of 43.75 cm at the interface between

the two soil types. Complete agreement between the analytical solution and the
Beach-MPT model at all other locations as well.

149

This can be compared to the prediction made by the Beach-MPT model
simulating the same soil column. The results are shown in ﬁgure A.4. The Beach-
MPT model predicts the hydrostatic pressure head at the interface between the two
soil types is also 43.75 cm. The hydrostatic pressures predicted by the model matches
those calculated analytically at all other points as well.

 

 

100
E80-
3
5,60-
m
I
E40
2
o
0 20*
O a . . .

 

 

-1O 0 10 20 30 40 50

Hydrostatic Pressure Head (cm)

Figure A.4. The hydrostatic pressure head distribution within the sand column shown
in Figure A.4 as calculated by the Beach-MPT model. The distribution matches
exactly the hydrostatic pressure head calculated analytically using Darcy’s law and
equation A.9.

These two tests demonstrate that the equations for calculating soil water ﬂow have
been properly coded into the Beach-MPT model.

150

BIBLIOGRAPHY

Ackerman, RA. 1977. The respiratory gas exchange of sea turtle nests (Chelom‘a,
Coretta). Resp. Physiol. 31219-3 8.

Ackerman, RA. 1980. Physiology and ecological aspects of gas exchange by sea
turtle eggs. Am. Zool. 20:275-283.

Ackerman, RA. 1981. Growth and gas exchange of embryonic sea turtles (Chelom'a,
Coretta). Copeia 757-765.

Ackerman, RA. 1997. The nest environment and the embryonic development of sea
turtles. Pp. 83-106 in The Biology of Sea Turtles, (P.L. Lutz and IA. Musick,
eds). CRC Press, New York.

Battino, R. 1980. Oxygen and Ozone: lUPAC Solubility Data Series Vol 7. Pergamon
Press, New York.

Bear, J. 1979. Hydraulics of Groundwater. McGraw-Hill Inc, Israel.

Bird, R.B., W.E. Stewart, E.N. Lightfoot. 2002. Transport Phenomena, 2"(1 Ed. John
Wiley and Sons, New York.

Brutsaert, W. 1982. Evaporation into the atmosphere: Theory, history, and
applications. D. Reidel, Boston.

Campbell, G.S., J.D. Jungbauer, Jr., W.R. Bidlake, and RD. Hungerford. 1994.
Predicting the effect of temperature on soil thermal conductivity. Soil Sci.
158:307-313.

Campbell, GS, and J.M. Norman. 1998. An Introduction to Environmental
Biophysics, 2'“I ed. Springer Science, New York.

Carslaw, HS, and J.C. Jaeger. 1986. Conduction of Heat in Solid, 2'“I ed. Oxford
Science Pub, England.

Clusella—Trullas S. 2000. Energetics during Hatchling Dispersal and the Environment
of Natural and Hatchery Nests of the Olive Ridley Sea Turtle (Lepidochelys
olivacea) at Nancite Beach, Costa Rica. MS Thesis. Purdue University, Fort
Wayne,.lnd.

Crain, D.A., A.B. Bolten, K.A. Bjomdal. 1995. Effects of beach nourishment on sea
turtles: Review and research initiatives. Restoration Ecology 3: 95-104.

150

 

Crank, J. 1980. The Mathematic of Diffusion. Oxford Science Pub., England

de Vries, DA. 1963. Thermal properties of soils, in Physics of Plant Environment,
Van Wijk, W.R. ed. North Holland Pub., Amsterdam.

Davis, R.A., M.V. FitzGerald, J. Terry. 1999. Turtle nesting on adjacent nourished
beaches with different construction styles: Pinellas County, Florida.
J. Coastal Res. 15: 111-120.

Drake, D.L. and J .R Spotila. 2002. Thermal tolerances and the timing of sea turtle
hatchling emergence. J. Therm. Biol. 27: 71-81.

Fernandez M., L.M. Pardo and J .A. Baeza. 2002. Patterns of oxygen supply in
embryo masses of brachyuran crabs throughout development: the effect of
oxygen availability and chemical cues in determining female brooding
behavior. Mar. Ecol. Prog. Ser. 245: 181-190.

Freeze, R.A., and J .A. Cherry. 1979. Groundwater. Prentice-Hall, Inc. New Jersey.

Gatti S., T. Brey, W.E.G. Muller, O. Heilmayer and G. Holst. 2002. Oxygen
rnicrooptodes: a new tool for oxygen measurements in aquatic animal
ecology. Marine Biology 140: 1075-1085.

GCE-LTER Data Portal. 2006. UGA Marine Institute Climate Monitoring.
http://gce-ltermarsci.uga.edu/portal/ugami_climate.htm.
Downloaded 22 November 2006.

Glud RN, 1. Klimant, G. Holst, O. Kohls, V. Meyer, M. Kuhl and J .K. Gunderson.
1999. Adaptation, test and in situ measurements with 02 microopt(r)odes on
benthic landers. Deep—sea Research Part 1- Oceanographic Research Papers
46: 171-1 83.

Glud R.N., J .K. Gunderson and NB. Ramsing. 2000. Electrochemical and optical
oxygen microsensors for in situ measurements. pp. 19-73 in In situ monitering
of Aquatic Systems: Chemical Analysis and Speciation. J. Buffle and G.
Horvai eds. John Wiley and Sons.

Hewavisenthi, S. and Cl Parmenter. 2001. Inﬂuence of incubation environment on
the development of the ﬂatback turtle (Natator depressus). Copeia 668-682.

Honarvar, 8., MP. O’Conner, and J .R Spotila. 2007. Density-dependent effects on
hatching success in olive ridley sea turtles. Proceedings of SICB Annual
Meeting.

Horn, R. and T. Baumgartl. 2002. Dynamic properties of soils. Pp. 17-48 in Soil
Physics Companion (A.W. Warrick, ed.). CRC Press, New York.

151

lncropera, F .P. and DP. DeWitt. 2002. Introduction to Heat Transfer, 4'“ ed. John
Wiley and Sons, New York.

IPCC. 2001. Climate Change 2001: The Scientiﬁc Basis. Contribution of Working
Group I to the Third Assessment Report. Houghton, J .T., Y. Ding, D.J. Diggs,
M, Noguer, P.J. van der Linden, X. Dai, K. Maskell, and CA. Johnson (eds.).
Cambridge University Press. Cambridge, UK and New York, NY, USA.
88lpp.

IUCN 2004. 2004 IUCN Red List of Threatened Species. http://www.iucnrcdlist.org.
Downloaded on 2 February 2005.

Kaliakin, V.N. 2002. Introduction to Approximate Solution Techniques, Numerical
Modeling, and Finite Element Methods. Marcel Decker, Inc. New York, USA.

Kam, Y. 1993. Physiological effects of hypoxia on metabolism and growth of turtle
embryos. Resp. Physiol. 92: 127-138.

Klimant I., V. Meyer and M. Kuhl. 1995. F iber—optic oxygen microsensors, a new
tool in aquatic biology. Limnol. Oceanogr. 40: 1159-1165.

Kraemer, J. and R Bell. 1980. Rain-induced mortality of eggs and hatchlings of
loggerhead sea turtles (Caretta caretta) on the Georgia coast. Herpetologica
36: 72-77.

Krieth, F. and MS. Bohn. 1993. Principles of Heat Transfer, 5th ed. West Publishing
Co., New York.

Logan, D.L. 2002. A First Course in the Finite Element Method, 3'rd ed. Brooks/Cole,
USA.

Maloney, J .E., C. Darian-Smith, Y. Takahashi, C.J. Limpus. 1990. The environment
for development of the embryonic loggerhead turtle (Caretta caretta) in
Queensland. Copeia 378-387.

Matsuzawa, Y., K. Sato, W. Sakamoto, K.A. Bjomdal. 2002. Seasonal ﬂuctuations in
sand temperature: effects on the incubation period and mortality of loggerhead

sea turtle (Caretta caretta) pre-emergent hatchlings in Minabe, Japan. Mar.
Biol. 140:639—646.

McCulloch, AD. and G. Huber. 2002. Integrative biological modeling in silico, in ‘In

silico’ simuation of biological processes, G. Bock and J .A. Goode, eds. John
Wiley and Sons, UK.

152

 

Meylan, A., B. Schroeder, A. Mosier. 1995. Sea turtle nesting activity in the State of
Florida Florida Marine Research Publications 52:1-51.

Miller, K., G.C. Packard, MJ. Packard. 1987. Hydric conditions during incubation
inﬂuence locomotor performance of hatchling snapping turtles. J. Exp. Biol.
127:401-412.

Miller, J .D. 1997. Reproduction in sea turtles. Pp. 51-82 in The Biology of Sea
Turtles (P.L. Lutz and J .A. Musick, eds.). CRC Press, New York.

Monteith, J .M., and M.H. Unsworth. 1990. Principles of Environmental Physics.
Elsevier Limited, UK.

Mortimer, J .A. 1990. The inﬂuence of beach sand characteristics on the nesting
behavior and clutch survival of green turtles (Chelonia mydas). Copeia 802-
8 1 7.

Mrosovsky, N., C.L. Yntema. 1980. Temperature dependence of sexual
differentiation in sea turtles: implications for conservation practices. Biol.
Conserv. 18:271-280.

Oreskes, N., K. Shrader-Frechette, K. Belitz. 1994. Veriﬁcation, Validation, and
Confn'mation of Numerical Models in the Earth Sciences. Science 2632641-
645.

Peck, S.L. 2004. Simulation as experiment: a philosophical reassessment for
biological modeling. TREE 19: 530-534.

Penman, BL. 1940. Gas ad vapor movements in soil. 1. The diffusion of vapors
through porous solids. J. Agr. Sci. 30: 437-462.

Polley, S.L., Snyder, OR and Kotnour, P. 1980. A compilation of thermal properties
of foods. Food Tech. 11:76-94

Ralph C.R., R.D. Reina, B.P. Wallace, P.R. Sotherland, J.R. Spotila and F .V.
Paladino. 2005. Effect of egg location and respiratory gas concentrations on
developmental success in nests of the leatherback turtle, Dermochelys
coriacea. Aust. J. Zool. 53: 289-294.

Rhen, T., J .W. Lang. (1995). Phenotypic plasticity for growth in the common

snapping turtle: Effects of incubation temperature, clutch and their interaction.
Am. Nat. 146:726-747.

153

 

 

Rimkus, T.A., and RA. Ackerman. 1995. The impact of beach renourishment on the
hydric climate of sea turtle nesting beaches along the Atlantic coast of Florida.
Pp. 97-102 in Proceedings of the 12th Annual Workshop on Sea Turtle
Biology and Conservation (J .1. Richardson and TH. Richardson). NOAA
Technical Memorandum, Florida.

Romanoff, AL. and A.J. Romanoff. 1949. The avian egg. John Wiley and Sons, New
York.

Schaap, M.G.and F .J . Leij. 2000. Improved prediction of unsaturated hydraulic
conductivity with the Mualem-van Genuchten model. Soil Sci. Soc. Am. J.
64: 843-851.

Seymour, RS, and J .D. Roberts. 1991. Embryonic respiration and oxygen
distribution in foamy and nonfoamy egg masses of the frog Limnodynastes
tasmaniensis. Physiol. Zool. 64: 1322-1340.

Seymour, RS. and MK. Seely. 1996. The respiratory environment of the Namib
Desert Golden Mole. J. Arid Environ. 32: 453-461.

Skopp, J .M. 2002. Physical properties of primary particles, in Soil Physics
Companion, A.W. Warrick, ed. CRC Press, Boca Raton, pp 1-16.

Steinitz, M.J., M. Salmon, J. Wyneken. 1998. Beach renourishment and loggerhead
turtle reproduction: A seven year study at Jupiter Island, Florida. J. Coast.
Res. 14: 1000-1013.

Titus, J .G. 1998. Rising seas, coastal erosion, and the takings clause: How to save
wetlands and beaches without hurting property owners. Maryland Law
Review. 57: 1279-1399.

Titus, J .G. and C. Richman. 2001. Maps of lands vulnerable to sea level rise:
Modeled elevations along the US. Atlantic and Gulf coasts. Climate
Research. 18: 205-228.

Tracy, C.R., G.C. Packard, M.J. Packard. 1978. Water relations of chelonian eggs.
Physiol. Zool. 51: 378-387.

Trindell, R.N., D. Arnold, K. Moody, B. Morford. 1998. Nourished beaches and
marine turtle nesting in Florida: An evaluation of recent projects. Proc. 18th
Intemat. Symp. Sea Turt. Biol. Conserv. 217-218.

Urban-Malinga, B. and K.W. Opalinski. 1999. Vertical zonation of the total, benthic,

and abiotic oxygen consumption on a Baltic sandy beach. Oceanological
Studies 28: 85-96.

154

 

van Genuchten, M.Th. 1980. A closed-form equation for predicting the hydraulic
conductivity of unsaturated soils. Soil Sci. Soc. Am. J. 4:892-898.

Wallace B.P., P.R. Sotherland, J .R. Spotila, R.D. Reina, B.F. Franks and F.V.
Paladino. 2004. Biotic and abiotic factors affect the nest environment of

embryonic leatherback turtles, Dermochelys coriacea. Physiol. Biochem.
Zool. 77: 423-432.

Warkentin K.M., I. Gomez-Mestre and J .G. McDaniel. 2005. Development, surface
exposure, and embryo behavior affects oxygen levels in eggs of the red-eyed
treeﬁ'og, Agalychm's callidryas. Physiol. Biochem. Zool. 78: 956-966.

Weiss, RF. 1970. The solubility of nitrogen, oxygen, and argon in water and sea
water. Deep Sea Res. 17: 721-735.

Yntema CL. and N. Mrosovsky. 1980. Sexual differentiation in hatchling loggerhead

(Caretta caretta) incubated at different controlled temperatures.
Herpetologica 36: 33-36.

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