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dissertation entitled

ASSESSING AND MODELING TEE SPATIAL VARIABILITY OF SOIL
WATER REDISTRIBUTION AND WHEAT YIELD ALONG A SLOPING
LANDSCAPE presented by

AYHAN ABDALLAH AHMED SULEIHAN

has been accepted towards fulﬁllment
of the requirements for

 

DOCTOR OF PHILOSQEE! degree in _CROP_AND_SOIL SCIENCES
/ Major professor

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ASSESSING AND MODELING THE SPATIAL VARIABILITY OF SOIL WATER
REDISTRIBUTION AND WHEAT YIELD ALONG A SLOPTNG LANDSCAPE

By

AYMAN ABDALLAH AHMED SULEIMAN

A DISSERTATION

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

DOCTOR OF PHILOSOPHY
Department of Crop and Soil Sciences

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' ABSTRACT

ASSESSING AND MODELING THE SPATIAL VARIABILITY OF SOIL WATER
REDISTRIBUTION AND WHEAT YIELD ALONG A SLOPING LANDSCAPE

By

AYMAN ABDALLAH AHMED SULEIMAN

Assessing and modeling the spatial variability of soil water redistribution and crop
yield along a sloping landscape is a prerequisite for a better understanding of site-speciﬁc-
management. The objectives of this research were to (l) evaluate and improve, when
appropriate, the vertical soil water dynamics in the water balance portion of the CERES
model, (2) develop a simple functional model to simulate lateral downslope soil water ﬂow,
and (3) combine remote sensing and crop modeling to predict the spatial variability of wheat
yield grown on a sloping landscape. The daily change of soil water content (SWC) in a recent
version of the crop model CERES is estimated from the difference between the initial and
residual SWC of the water balance components multiplied by a transfer coefficient
representing the fraction of the remaining soil water that can be removed in the processes of
soil evaporation, vertical drainage and root water uptake. The transfer coefﬁcients for the
three processes is assumed to be ﬁxed for all soils. The residual SWC values depend on the
input soil properties for the SWC at air dry, drained upper limit, and lower limit of plant
availability, respectively. Testing the dependancy of the drainage and evaporation transfer
coefﬁcients on soil characteristics was done by monitoring the SWC. The drainage and
evaporation transfer coefficients were found to be soil speciﬁc and highly correlated with the

drained upper limit SWC. Reﬁnements in the drainage and second stage evaporation models

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improved their accuracy for different soils.

A functional model was developed to simulate downslope lateral soil water ﬂow based on
Darcy’s Law and equations for estimating unsaturated and saturated hydraulic conductivity.
The model requires inputs of the drained upper limit and saturated SWC, water table level,
slope, and the amount of incoming ﬂow. Soil water proﬁles and water table levels were
monitored at 15 locations along a sloping landscape to test the model. The model performed
reasonably well in estimating lateral soil water drainage. A wheat crop grown on the 6 ha
ﬁeld where lateral ﬂow was studied provided an opportunity to assess spatial variation in
yield as inﬂuenced by soil spatial variability of differences in water supply related to position
in the landscape. Remote sensing from an aircraft helped to quantify spatial variability in
leaf area index (LAI) in the ﬁeld. When this spatial variation in LAI at anthesis was input
in the CERES-Wheat model as an alternative to predicting LAI unifonnly for the whole
ﬁeld, the modeled spatial variation in yield agreed quite well with the variation in yields
monitored for the entire ﬁeld. The experiments done for this research demonstrated the need
to take both vertical and horizontal water ﬂow into account for sloping land in humid regions

in order to adequately describe causes of spatial variability in crop yields.

DEDICATION

To
Muna, my wife, for her understanding, patience, and support

Zena, my daughter, for the enjoyable time she has given us

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ACKNOWLEDGMENTS

I would like to express my appreciation and gratitude to:
Dr. Joe Ritchie, my major advisor, for his ﬁnancial support, friendship, and enlightening
guidance throughout my study at Michigan State University.
The graduate committee:
Dr. Harold Belcher, Dr. James Flore, Dr. David Lusch, and Dr. Alvin Smucker.
Dr Anwar Battikhi, University of Jordan, for his great assistance through introducing me to
Dr. Joe Ritchie.
Bary Darling, University Farms manager, and his crew for their great help throughout my
ﬁeld research.
Brian Graff, Crop Science Field Lab manager, and his staff for their great help throughout
my research.
Marc Hooper and Sharon, from Grower Service Corporation, for their help in getting the
infrared images.
Homer Nowlin group: Bruno Basso, Brian Baer, Dr. Samira Daroub, Dr. Aris Gerakis,
Dr. Alagarswamy Gopalsamy, Eirini Katsalirou, Carlos Paglis, Scott Piggott, Sharlene
Rotrnan, and Dr. Serena Stornaiuolo for their sincere friendship and assistant throughout my
stay at Michigan State University.
My parents and all my family members for their continuous care and concern.

My parents in-law, and all their family members for their invaluable gift!

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TABLE OF CONTENTS

LIST OF TABLES ..................................................... viii
LIST OF FIGURES ..................................................... ix
INTRODUCTION ...................................................... 1
References ....................................................... 6
CHAPTER ONE
ASSESSING AND MODELING SOIL WATER DISTRIBUTION UNDER
SECOND STAGE EVAPORATION .................................. 9
Introduction ...................................................... 9
Theory ......................................................... 11
Second stage evaporation ..................................... 11
Second Stage Evaporation Model in CERES Water Balance ............... 13
Materials and methods ............................................. 14
Laboratory Experiments ...................................... 14
Field Experiment ........................................... 15
Laboratory Results .......................................... 15
Effect of Water Table ........................................ 27
References ...................................................... 35
CHAPTER TWO
ASSESSING AND MODELING VERTICAL SOIL WATER DRAINAGE . . . 37
Introduction ..................................................... 37
Theory ......................................................... 39
Drainage Model in CERES Water Balance ............................ 43
Materials and Methods ............................................. 44
Laboratory Experiments ..................................... 45
Field Experiment ........................................... 45
Results and Discussion ............................................ 45
Laboratory Results .......................................... 53
Field Results .............................................. 60
Conclusions ..................................................... 67
References ...................................................... 70
CHAPTER THREE
ASSESSING AND MODELING DOWNSLOPE LATERAL SOIL WATER FLOW
ALONG A SLOPING LANDSCAPE ................................. 72
Introduction ..................................................... 72
Theory ......................................................... 73
Material and Methods ............................................. 78

vi

Data Collection . . . .‘ ........................................ 78

Site Description ............................................ 80
TDR Description ........................................... 82
Data Analysis .............................................. 84
Results and Discussion ............................................ 84
Water table ................................................ 89
Leaf Area Index ............................................ 91
Lateral downslope soil water ﬂow .............................. 95
Conclusions .................................................... 101
References ..................................................... 102
CHAPTER FOUR
ASSESSING AND MODELING THE SPATIAL VARIABILITY OF WHEAT
YIELD WITHIN A SLOPING LANDSCAPE ......................... 104
Introduction .................................................... 104
Materials and Methods ............................................ 105
Site Description ........................................... 109
Field Management ......................................... 111
Normalized Difference Vegetation Index and LAI ................ 111
Integrating CERES-WHEAT Model and Remote Sensing .......... 112
Results and Discussion ........................................... 113
Spatial Variability Along Access Tube Transect .................. 113
Model Performance Along Access Tube Transect ................. 116
Infrared Images Interpretation ................................ 1 18
Modeling Spatial Variability of Grain Yield ..................... 120
Conclusions .................................................... 127
References ..................................................... 128
SUMMARY AND CONCLUSIONS ...................................... 131
APPENDICES
Appendix A. Soil properties at access tube locations. .................... 134
Appendix B. Daily solar radiation (SR), maximum (TM) and minimum
temperature (Tmin), and Rainfall (R) for the sloping landscape .............. 137
Appendix C. List of abbreviations. .................................. 147

vii

 

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LIST OF TABLES

Table 1.1. Soil physical properties of proﬁle 1 and proﬁle 2 for soil ﬁeld in Lansing. . 16

Table 4.1. Measured and simulated grain yield near all access tube locations. ....... 117

viii

 

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LIST OF FIGURES

Figure 1.1. Daily solar radiation (SR), maximum (Tmax) and minimum (Tmin)
temperatures, and rainfall (R) from DOY 200 to 280 in 1997. .............. 17

Figure 1.2. Measured and simulated soil water content proﬁles of 60-cm columns of loam
and sandy loam soils drying during second stage evaporation. . . . ........... 18

Figure 1.3. Measured and simulated soil water content proﬁles of 60-cm columns of loam
and sandy loam soils drying during second stage evaporation. .............. 20

Figure 1.4. Relationship between a and 0d“. of 8 soils: Loamy and Sandy loam soils from
Michigan and 6 soils from D.A. Rose (1968). ........................... 21

Figure 1.7. Soil water content proﬁles of 60-cm columns of loamy and sandy loam soils
versus Boltzmann transform under second stage evaporation. .............. 25

Figure 1.8. Soil water content proﬁles at six depths of sandy loam soil proﬁle in 1997. 26
Figure 1.9. Measured, simulated (using Eq. [8] with n=-2 and a=0.63), simulated (M)
(using Eq. [8] with n=2.09 and a=0.47) soil water content of a bare soil in Lansing

ﬁeld in 1997 at six different depths. .................................. 28

Figure 1.10. Soil water content proﬁles of ISO-cm columns of loamy soil drying during
second stage evaporation. .......................................... 29

Figure 1.11. Soil water content proﬁles of ISO-cm columns of sandy loam soil drying
during second stage evaporation. ..................................... 30

Figure 1.12. Soil water content proﬁles of ISO-cm columns of loamy and sandy loam
soils versus Boltzmann transform during second stage evaporation. ......... 32

Figure 1.13. Cumulative evaporation of ISO-cm column of loamy and sandy loam soils
during second stage evaporation. ..................................... 33

Figure 2.1. Relationships between C,, C2, and C with (lno.)“n for any realistic possible
combination of 6, and 9d,“. .......................................... 46

Figure 2.2. Measured and estimated C using Eq. [20] of the international soils versus
(1nd)“n .......................................................... 48

Figure 2.3. Relationship between C and 0d,, for any possible realistic combination of 9S
and 0d,". ......................................................... 49

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Figure 2.4. Measured and estimated C using Eq. [21] of the international soil versus OMSO

Figure 2.5. Relationship between C and Q, for a soil of 9, = 0.4 cm3 cm’3 and 6d“, = 0.4
cm3 cm"3 .......................... ' .............................. 52

Figure 2.6.a. Soil water content proﬁles for a ISO-cm column of loamy soil during
drainage cycle at 3, 6, 9, 12, 15 and 25 cm depths. ....................... 54

Figure 2.6.b. Soil water content proﬁles for a 150-cm column of loamy soil during
drainage cycle at 35, 45, 55, 65, and 75 cm depths. ...................... 55

Figure 2.7.a. Soil water content proﬁles for a ISO-cm column of sandy loam soil during
drainage cycle at 3, 6, 9, 12, 15 and 25 cm depths. ....................... 56

Figure 2.7.b. Soil water content proﬁles for a ISO-cm column of sandy loam soil during
drainage cycle at 35, 45, 55, 65, and 75 cm depths. ...................... 57

Figure 2.8. Daily drainage rate of a 150-cm column of loamy soil and a ISO-cm column
of sandy loam soil. ................................................ 59

Figure 2.9. Cumulative drainage of a ISO-cm column of loamy soil and a ISO-cm column
, of sandy loam soil. ....................................... g ......... 61

Figure 2.10.a. Soil water content proﬁles for proﬁle 1 of sandy loam soil during drainage

cycle at 3, 6, 9, 12, 15, and 25 cm depths. .............................. 62
Figure 2.10.b. Soil water content proﬁles of proﬁle 1 of sandy loam soil during drainage

cycle at 35, 45, 55, 65, and 75 cm depths. .............................. 63
Figure 2.11.a. Soil water content proﬁles for proﬁle 2 of sandy loam soil during drainage

cycle at 3, 6, 9, 12, 15, and 25 cm depths. .............................. 64
Figure 2.12. Daily drainage rate of proﬁle 1 and proﬁle 2 of sandy loam soil. ....... 66

Figure 2.13. Cumulative drainage of proﬁle 1 and proﬁle 2 of sandy loam soil versus
time. ........................................................... 68

Figure 3.1. Cartesian rectangular space coordinate x and z and rotated coordinates x. and
2.. ............................................................. 75

Figure 3.2. (a) Elevation (ﬂ), slope (%), and access tube locations within the ﬁeld. (b)
relative soil surface height (cm), water table (WT) height (cm), and restricted
layer (at 150 cm depth). ............................................ 79

Figure 3.3. Daily solar radiation (MJ m'z), temperature (C°), and rainfall (mm) ﬁom DOY

 

 

 

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1 through DOY 200 in 1998. ........................................ 80

Figure 3.4. A discontinuous TDR probe (DTDRI 50) and a typical wave. ........... 83
Figure 3.5. Relationship between C and C sin y with sin y and 0d“. at representative
combinations of 0d“. and sin y. ....................................... 84
Figure 3.6. Example of a typical relationship between C,‘ and x. for a soil ........... 86
Figure 3.7. Example of a typical relationship between CI, and Qi for a soil. .......... 90

Figure 3.8. Measured and simulated change of soil water table depth (cm) from DOY
124 to 146. ...................................................... 91

Figure 3.9.a. Corrected simulated LAI at Ll through L8 from DOY 90 through 200.
............................................................... 93

Figure 3.9.b. Corrected simulated LAI at L9 through L15 from DOY 90 through 200 and
mean and standard deviation of LAI for the 15 locations. .................. 94

Figure 3.10. Mean and standard deviation of simulated daily actual (E..) and potential
(Em) evapotranspiration from DOY 124 to 146. ......................... 96

Figure 3.11. Estimated C and C sin 'y at all access tube locations. ................. 97

Figure 3.12. Measured and simulated cumulative lateral down slope (L) ﬂow at all access
tube locations from DOY 124-132, 132-140, and 140-146. ................ 99

Figure 3.13. Measured and simulated daily lateral downslope soil water ﬂow (L) at the
middleofL12andL13. 100

Figure 4.1. Elevation, contours, slope, and access tube locations within the experimental
ﬁeld. .......................................................... 107

Figure 4.2. Daily solar radiation, maximum (Tmax) and minimum (Tmin) temperature,
and rainfall from DOY 1 through 200 in 1998. ......................... 108

Figure 4.3. Infrared images were captured (from left to right) on April 4, April 28, June 4,
and July 14, 1998. ............................................... 109

Figure 4.4. Elevation, slope, and some soil properties (total nitrogen, organic matter, soil
texture, and bulk density) of the surface layer .......................... 114

Figure 4.5. Crop characteristics at harvest time (plant density, heads number, number of
grains per head, head weight, unit grain weight, grain number, and grain yield. 115

xi

 

 

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Figure 4.6. Normalized difference vegetation index (NDVI) (from left to right) on April

4, April 28, June 4, and July 14, 1998. ............................... 121
Figure 4.7. Leaf area index (LAI) (from left to right) on April 4, April 28, June 4, and
July 14, 1998. ................................................... 122
Figure 4.8. Relationship between simulated stem weight and simulated leaf area index at
anthesis. . . . .' ................................................... 123
Figure 4.9. Relationship between measured grain yield and measured seed number near
access tube locations. ............................................. 124
Figure 4.10. Measured and simulated grain yield maps. ........................ 126

xii

INTRODUCTION

ASSESSING AND MODELING THE SPATIAL VARIABILITY OF SOIL WATER
REDISTRIBUTION AND WHEAT YIELD ALONG A SLOPING LANDSCAPE

By
AYMAN ABDALLAH AHMED SULEIMAN

A model has been deﬁned as a small imitation of the real thing or as system of
postulates, data and inferences presented as a mathematical description of an entity or
state of affairs (Hanks and Ritchie, 1991). Crop models are valuable as: (i) aids in
interpreting experimental results, (ii) agronomic research tools, or (iii) agronomic grower
tools (Whisler et al., 1986). Boote et a1. (1996) proposed three primary uses or reasons for
crop modeling: research knowledge synthesis (combining Whisler’s ﬁrst two categories),
crop system decision management, and policy analysis (such as climate change and
sustainable agriculture). The genesis of such models can be traced to the arrival of
mainframe computers in the early 1960's, and their rapid growth in the past decade has
been simulated by the ubiquity of desktop computers (Monteith, 1996; Passioura, 1996).
Further advances in computer technology should facilitate the continued development and
reﬁnement of crop simulation models.

Most models used for evaluating crop production systems can be categorized as
mechanistic or functional. Mechanistic models are usually based on dynamic rate
concepts (Ritchie and Crum, 1989). They incorporate basic mechanisms of processes
such as Darcy’s Law or Fourier’s Law and the appropriate continuity equations for water
and heat ﬂux, respectively. Functional models are usually based on capacity factors and

treat processes in a more simpliﬁed manner, reducing the amount of input required. Every

model of the plant-soil-atmosphere system, whether mechanistic or functional, uses some
level of empiricism in order to reduce the need for input information. Thus it may be
somewhat difﬁcult to distinguish between mechanistic and functional models. The most
important difference between mechanistic and functional models is their usefulness as
either research or management tools. Mechanistic models are useful primarily as research
tools used to improve understanding of an integrated system, and usually are not widely
used due to their complexity. The functional models have modest input requirements
making them useful for management purposes. Because of their simplicity, functional
models are more widely used and independently validated than their mechanistic
counterparts.

Mechanistic modeling of soil water ﬂow is based on Darcy’s Law and the
Richards equation. Darcy’s Law is the basic concept for one-dimensional water ﬂow in a
homogeneous soil (Philip, 1995). However, for two or three-dimensional water ﬂow in
homogeneous soil, Richards equation may be useful. According to Youngs (1995),
Richard (1931) derived his equation from Darcy’s Law using the same two basic
parameters: hydraulic conductivity and hydraulic water potential. Richards’ equation is a
good theoretical description for the homogeneous soil water ﬂow. However, it may not be
appropriate under ﬁeld conditions. Youngs (1995) mentioned seven factors that often
make Richards’ model an inappropriate basis for computing soil-water ﬂow under ﬁeld
conditions. These factors are: the inﬂuence of the air phase on the soil water movement,
the effect of soil heterogeneity, soil swelling, soil aggregation and soil instability,
deviation from Darcy’s Law, thermal effects, and the hysteresis in soil water

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Although a well-deﬁned laboratory experiment can be a preliminary step (Rose,
1996), the real challenge is to describe the soil water ﬂow dynamics in ﬁeld conditions.
Soil in the ﬁeld is rarely homogeneous and is a dynamic system. Approximations to soil
water ﬂow problems in the ﬁeld may be used. But even if Richards’ equation is valid
under ﬁeld conditions, its use can be difﬁcult because measurements of soil hydraulic
conductivity or soil water diffusivity in the ﬁeld are time consuming and expensive
(Ahuja et al., 1993).

The CERES program, a functional model, is designed to continuously simulate
crop, soil, water and nutrient conditions under different management strategies. These
strategies may include various crop rotations, planting dates, plant populations, irrigation
and fertilizer applications, and tillage regimes. The program can simulate plant growth
and soil conditions daily (during growing seasons and fallow periods) for any time period
when weather sequences are available. This also provides a framework whereby the
interaction between different areas under different management practices can be
compared easily.

CERES consists of many subroutines which take into consideration many factors
related to the soil-plant-atmosphere continuum. One of the most important CERES
subroutines deals with water balance. The water balance subroutine in CERES is adapted
for different soils, climatic conditions, and crops. The water balance subroutine accounts
for the water coming to the proﬁle as well as to the water going out of the proﬁle. This
subroutine simulates the temporal soil water contents, evapotranspiration, drainage, and
runoff, however it does not account for soil water lateral ﬂow. Soil water lateral ﬂow is

evident in sloping landscapes and it may account for 20% of the water balance.

 

 

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Therefore accurate modeling of the soil water balance is important for efficient water
management and for simulating crop performance (Savage et al., 1996; Ritchie, 1972;
Ritchie, 1981).

The soil water balance in CERES has been built using simpliﬁed approaches that
require few soil inputs. Drained upper limit and lower limit soil water contents and
saturated hydraulic conductivity are needed to run the soil water balance in CERES. It
was found that the soil water limits as well as saturated hydraulic conductivity can be
estimated reasonably well from texture and bulk density (Ritchie et al., 1999; Suleiman
and Ritchie, 1999).

The movement of water ﬁ'om one location to another within a sloping landscape
could explain crop spatial variability. Differences in crop production within agricultural
ﬁelds vary by a factor of two to four. Applications of Global Positioning System (GPS)
and yield-sensors allow expression of such differences. Differences of yields within ﬁelds
are also obvious in many developing countries, even without access to GPS and yield
monitoring equipments (Bouma etal., 1995). Finding the reasons why yield spatial
variability occur is a primary step in the development of management procedures that can
reduce or make use of these differences (Bouma et a1. 1995). Differences in yield within a
ﬁeld is a consequence of the variability of the microenvironment.

The spatial covariance between soil and crop and its transformation as a function
of time remains largely unexplored in the agricultural science as well as their application
to soil speciﬁc framing (Nielsen et al., 1995). Some research, however, has been
conducted on soil water variability. Rosek (1994), found that soil physical properties and

the amount of soil water within a sloping landscape are largely determined by landscape

position. This is in agreement with Miller et al. (1988) ﬁndings, where a strong spatial
dependency was found between soil properties and wheat yield.

According to Miller et a1. (1988) no correlation was found between percent slope
and yield or soil properties, using the standard regression analysis, but semiveriograrns
and cross-semiveriograms showed a strong correlation among them. Geostatistics, which
is regionalized variable analysis, has been used to improve the assessment of soil and
crop attributes within site speciﬁc domains (Burrough, 1991; Mulla, 1993; Nielsen and
Alemi, 1989; Robert et al., 1993; Trangmar et al., 1985). The Geostatistics techniques in
soil speciﬁc farming have been giving a good explanation for the spatial variability and
their future is expected to be bright (Nielsen et al., 1995).

The spatial variability affects, in turn, the temporal variability. For instance, soil
erosion creates spatial variability of clay content as well as a variation of the clay content
over time at a certain spot. On the basis of that, determining the effect of time on the
variability structure is necessary as well as determining the spatial variability for
sustainable farming.

The Geographical Information System (GIS) is widely used to describe the spatial
variability and to help in decision making. The early development and commercial
success of GIS were fueled more by the need for efﬁcient spatial inventory rather than
decision making (Eastman et al., 1993). The GIS is an important tool that makes use of
remote sensing data. The combined use of remote sensing, GIS, geostatistical techniques,
and crop simulation models has the potential for improving agricultural management.
This study aimed to:

1. Evaluate the vertical soil water movement dynamics during vertical drainage

and second stage evaporation in the water balance component of CERES,

2. Develop and evaluate a simple functional model to simulate lateral downslope
soil water ﬂow along a sloping landscape, and

3. Integrate CERES-WHEAT and remote sensing in order to simulate the spatial

variability of wheat yield within a sloping landscape.

References

Ahuja, L.R., O. Wendroth, and DR. Nielsen. 1993. Relationship between initial drainage
of surface soil and average proﬁle saturated conductivity. Soil Sci Soc. Am. J.
57:19-25.

Boote, K.J., J .W. Jones, and NB. Pickering. 1996. Potential uses and limitations of crop
models. Agron. J. 88:705-716.

Bouma, J ., J. Brouwer, A. Verhagen, and H.W.G. Booltink. 1995. Site speciﬁc
management on ﬁeld level: high and low tech approaches. Kluwer Academic
Publishers in cooperation with International Potato Center. Netherlands.

Burrough, PA. 1991. Sampling design for quantifying map unit composition. p. 89-127.
In M.J. Mausbach, and LP. Wilding (ed.) Spatial variabilities of soils and
landform. SSSA Spec. Publ. No.28. Soil Sci Soc. Am., Madison, WI.

Hanks, J ., and J .T. Ritchie. 1991. Modeling plant and soil systems. Number 31 in the
series of Monograghs. Agronomy. Madison, Wisconsin, USA.

Eastman, J .R., Kyem, P.A.K., Toledano, J ., and W. Jin. 1993. Introduction: GIS and
decision making. Explorations in Geographic Information Systems Technology,
Vol 4, Geneva: Unitary European Office, p. 1-20, 93-98.

Miller, M.P., M.J. Singer, and DR. Nielsen. 1988. Spatial variability of wheat yield and
soil properties on complex hill.

Monteith, J .L. 1996. The quest for balance in crop modeling. Agron. J. 88:695-697.

Mulla, DJ. 1993. Mapping and managing spatial patterns in soil fertility and crop yield.
In P.C. Robert et al. (ed.) Proceedings of soil speciﬁc crop management: A
workshop on research and development issues. SSSA Spec. Publ. No. 28. Soil Sci
Soc. Am., Madison, WI.

Nielsen, DR, and H. Alemi. 1989. Statistical opportunities for analyzing spatial and
temporal heterogeneity of ﬁeld soils. p. 261-272. In M. Clarholm, and L.
Bergstron (ed.) Ecology of arable land-perspectives and challenges. Proc. of an
International Symposium, 9-12 June 1987, Swedish University of Agricultural
Science, Uppsala, Sweden. Kluwer Academic publishers, Dordrecht.

Nielsen, D.R., Owendroth, and MB. Parlange. 1995. Opportunities for examining on-
farm soil variability. Mausbach, and LP. Wilding (ed.) Spatial variabilities of
soils and landform. SSSA Spec. Publ. No. 28. Soil Sci Soc. Am., Madison, WI.

Passioura, J .B. 1996. Simulation models: science, snake oil, education or engineering?.

Agron. J. 88:690-694.
Philip, J .R. 1995. Desperately seeking Darcy in Dijon. Soil Sci. Soc. Am. J. 59:319-324.

Ritchie, J.T. 1972. Model for predicting evaporation from a row cr0p with incomplete
cover. USDA Soil and water Conservation Research Division, Blackland
Conservation Research Center, Temple, Texas.

Ritchie, J .T. 1981. Water dynamics in soil-plant-atmosphere. Plant Soil 58:81-96.

Ritchie, J .T., and J. Crum. 1989. Converting soil survey characterization data into
IBSNAT crop model input. p.155-167. In J. Bouma and AK. Brget (ed.) Land
Qualities in space and time. Wageningen, The Netherlands.

Ritchie, J .T., A. Gerakis, and AA. Suleiman. 1999. Estimation of soil water content
limits for water balance models from soil survey data. ASAE. (In review).

Robert, P.C., R.H. Rust and WE. Larson. 1993. Proceedings of soil speciﬁc crop

management: A workshop on research and development issues. SSSA Spec.
Publ. No. 28. Soil Sci Soc. Am., Madison, WI.

Rose, DA. 1996. The dynamics of soil water following single surface wettings. European
Journal of soil science. 47:21-31.

Rosek, M.J. 1994. Spatial and temporal soil water content changes within a sloping
landscape. Doctoral Dissertation. Crop and Soil Sciences Department. Michigan
State University, East Lansing, Michigan, USA.

Savage, M.J., J .T Ritchie, W.L. Bland, and WA. Dugas. 1996. Lower limit of soil water
availability. Agron. J. 88:644-651.

Suleiman, AA, and J.T. Ritchie. 1999. Estimating saturated hydraulic conductivity from
drained upper limit water content and bulk density. ASAE. ( In review).

Trangmar, B.B., R.S. Yost, and G. Uehara. 1985. Applications of geostatistics to spatial
studies of soil properties. Advances in Agron. 38:45-94.

Whisler, F.D., B. Acock, D.N. Baker, R.E. Fye, H.F. Hodges, J .R. Lambert, H.E.
Lemmon, J .M. McKinion, and V.R. Reddy. 1986. Crop simulation models in
agronomic systems. Adv. Agron. 40:141-208.

Youngs, E.G. 1995. Developments in the physics of inﬁltration. Soil Sci. Soc. Am. J.
59:307-313.

 

lntr

cons
(2) ti
surﬁ
rate:
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(Alcl
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198:

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196
and
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mod

 

CHAPTER ONE
ASSESSING AND MODELING SOIL WATER DISTRIBUTION UNDER SECOND

STAGE EVAPORATION

Introduction

Soil water evaporation is a large component of the water balance (Ritchie 1972).
The water evaporation ﬁ'om a soil surface (E) can be divided into two stages: (1) the
constant rate stage in which E, is limited only by the supply of energy to the surface and
(2) the falling rate stage in which water movement to the evaporation sites near the
surface is controlled by the hydraulic properties of the soil (Ritchie, 1972). The constant
rate stage of evaporation vary not only with the prevailing atmospheric environment, but
also with soil surface features such as soil surface color, aerodynamic roughness
(Mcllroy, 1984). The falling rate stage of evaporation requires an internal movement of
water to the regions where vaporization is actually occurring (near-soil surface) (Mcllroy,
1984)

Several mechanistic models have been reported in which Richard’s equation of
water ﬂow is used as a basis to calculate Es (C.W. Rose, 1968; Gardner and Gardner,
1969; van Bavel and Hillel, 1976; Hillel and Talpaz, 1977; Feddes et al., 1978; Norman
and Campbell, 1983; Hanks, 1991; Evett and Lascano, 1993; Farahani and Ahuja, 1996).
Ritchie and Johnson (1990) stated that functional models for estimation of B5 are less
evident in the literature and few evaluation have been conducted on such functional
models (Gabrielle etal., 1995).

Ritchie and Johnson (1990) showed that mechanistic and functional models may

have very similar outcomes in estimating soil evaporation even though mechanistic
models require more inputs. Mechanistic models usually require data of hourly weather
(global radiation, air temperature, rainfall/irrigation, dew point temperature, wind speed),
soil (water retention curve, K vs. 0, soil albedo vs. 0, Ksat, and porosity), and initial
values of (0 vs. depth and temperature vs. depth). Functional models require data of daily
weather (global radiation, maximum and minimum temperature, and rainfall/irrigation),
soil (soil albedo and DUL), and initial values of (0 vs. depth). Increasing interest in
regional evaporation models emphasizes the need to quantify the spatial distribution of
evaporation (Lascano and Hatﬁeld 1992). This would enhance the need for models that
require less inputs.

D.A. Rose (1968) showed that diffusivity theory explained the soil water
distribution under second stage evaporation for homogenous soils whose initial soil water
content was equal to the drained upper limit soil water content. In a study on a bare soil,
Black et a1. (1969) examined the diffusivity theory in the ﬁeld and demonstrated that E3
was function of soil diffusivity. Both of DA. Rose (1968) and Black et a1. (1969)
approved that the cumulative soil evaporation, under second stage evaporation, was
function of the square root of time. On the basis of the diffusivity theory and the
published work of both D.A. Rose (1968) and Black et al.(1969), Ritchie (1972)
developed a simple functional model to estimate Es, under second stage evaporation. This
model has been used worldwide to estimate E,, because of its validity and simplicity.

The objective of this research was to test upward soil water ﬂow dynamics and
second stage soil water evaporation model in the water balance of CERES crop

simulation model family. In many agricultural ﬁelds, especially those with restricted soil

10

 

 

 

 

la}?

CV3

W35

The

56

(7

th‘

is SI

Sec

sub:

layer in the root zone, water table may have a profound impact on second stage
evaporation, and hence the impact of water table on the rate of second stage evaporation

was assessed.

Theory

The generalized vertical ﬂow equation can be written as follows (Philip, 195 7):

07((0)
52

5’6 a( an)
at'az Dwaz "

 

(1)
where D(0) and K(0) are soil water diﬁusivity and hydraulic conductivity, respectively, 0

is soil water content, and t and z are time and distance, respectively.

Second stage evaporation
When a semi-inﬁnite soil column 2 > 0, initially at a uniform water content 9d,”,
subsequently has its surface maintained at the water content 0“, in equilibrium with the

relative humidity of the atmosphere, the initial and boundary conditions governing ﬂow

rateare:
6:0“, 220 t=0
1955:90‘, z=0 t>0

Esa<Ep t>0

ll

 

WI

161’]

cap

neg

When

where 0 is volumetric soil water content, 0d“. volumetric drained upper limit soil water
content, 955 is volumetric soil water content at the soil surface, Gad air dry voliunetric soil
water content, 2 is depth, t is time, E5, is actual soil evaporation, and Ep is potential soil
evaporation.

The solution of Eq. [1] subject to these conditions is, for all except large t,

z(6,t) = 2 int 72 (2)
n=1

where I. = zt‘“2 is the Boltzmann transform. The 1,, are all single-valued functions of 9,
and the series converges so rapidly that, except when t~ co, only the three or four leading
terms are needed to describe ﬂow problems of practical interest, e. g. inﬁltration, or
capillary rise above a water table. When gravity can be ignored (e.g. horizontal ﬂow) or
neglected without serious errors (e.g. drying a vertical column of well-structured soil with

0“, < 0i 5 0d,“) only the ﬁrst term of the series is needed and then, dropping the sub,
2 = 2(6):”2 (3)

Thus, the quantity of water lost by evaporation (Q cm) or cumulative evaporation

(EC, cm) is given by
9...; I

Q=Ec= jzd0=at/2 (4)
0'.

where

12

adv!

a = [new (5)
00d

and the evaporation rate

1 _
E: dQ/dt= 5: V20: (6)

The assumptions in the analysis are justiﬁed, and the boundary conditions are
satisﬁed when, for a given material, evaporation yields water content proﬁles invariant
with zt'm, i.e. when M0) is uniquely dependent on 0. Diffusivities controlling evaporation

are functions of water content alone (Philip, 1957; DA. Rose, 1968).

Second Stage Evaporation Model in CERES Water Balance

The change of volumetric soil water content in a day at any depth > 2 cm under
second stage evaporation can be estimated as follows:
A 0 = C (0-0“) (7)
where 0 is the volumetric soil water content at any time, C is constant function of depth
(d) as follows:
C = a d " (8)
where a and n are constants and equal to 0.63 and -2, respectively.

The change of volumetric soil water content at 1 cm depth is calculated as
follows:

C = a d “ ( 0.82 - 4.7 (0.45-9du.)") (9)

13

Air dry volumetric soil water content (Gad) is estimated as follows:
9m = 0.44 Bdulz (10)

Cumulative evaporation (15,) from soil under the following initial and boundary

conditions

9., = 0d". 2 2 0 t = 0
9V, = 93d 2 = 0 t > 0
Es,l < Ep t > 0

is estimated from Eq. [4] assuming a is a constant and equal to 3.75 mmd‘m.

Materials and methods

Laboratory and ﬁeld experiments were conducted to study the upward soil water
ﬂow dynamics during drying cycle. Besides the laboratory and ﬁeld experiments, data of
six different soils from D.A. Rose (1968) were used for comparison.
Laboratory Experiments

Two different soils from Michigan were used to measure the second stage
evaporation rate. One of the soils was obtained from Saginaw area and it was loamy soil
(25.4 % clay and 43 % sand). The second one was obtained from Lansing area and it was
sandy loam soil (9.4 % clay and 65.4 % sand). The two soils were air dried, sieved
through 2 mm screen, and then assembled into PVC columns of 60 cm height and 30 cm
diameter. Twenty cm time domain reﬂectometry probes (TDR) were installed
horizontally at depths of 3, 6, 9, 12, and 15 cm from the surface. ‘The t0p 25 cm of the
soil columns were saturated by adding water on soil surface and then the soil surface was

covered to avoid evaporation. The soil columns were allowed to drain for 10 days and

14

 

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15

In

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311

Dr:

then the soil surface was uncovered. A light source and a fan were directed toward the
soil surface of each column to ensure high potential evaporative losses. Soil water
content was monitored at the 5 depths every 15 minutes for about two months.

The two soils were also used to evaluate the effect of water table on the second
stage evaporation rate. The air dried soils were assembled into PVC columns of 150 cm
height and 30 cm diameter. Twenty cm TDR were installed horizontally at depths of 3, 6,
9, 12, 15, 25, 35, 45, 55, 65, and 75 cm ﬁom the surface. The soils were saturated from
the bottom using constant head of 150 cm. The soils were allowed to drain the excess
water for 10 days while the soil surface was covered. A light source and a fan were
directed toward the soil surface of each column at the end of drainage cycle to ensure
high potential evaporative losses. Soil water content was monitored at the eleven depths
every 20 minutes for two months.

Field Experiment

Two sets of 20-cm TDR probes were installed horizontally at depths of 3, 6, 9, 12,
15, 25, 35, 45, 55, 65 and 75 cm from the surface in a ﬂat bare ﬁeld in Lansing area on
July 10, 1997. The two sets were 3 m apart. The soil water content was monitored at all
depths every 20 minutes for a month. The soil was saturated using ponding and then the
soil surface was covered for15 days on August 15, 1997. After the drainage, the soil
surface was uncovered again for 10 days. The soils texture and bulk density are
presented in Table 1.1. Daily solar radiation, maximum and minimum temperatures, and

rainfall from day of year (DOY) 200 to 280 of 1997 are shown in Figure 1.1.

15

 

Ta

Table 1.1. Soil physical properties of proﬁle 1 and proﬁle 2 for soil ﬁeld in Lansing.

 

 

 

 

 

 

Profile 1 Profile 2
Depth Clay Sand B1' Clay Sand B
cm % g cm" % g cm‘
10 11.3 65.3 1.44 14.6 62.7 1.42
15 11.3 68.1 1.45 27.9 57.3 1.40
25 11.3 68.0 1.46 26.5 43.9 1.34
35 13.9 72.4 1.50 19.6 54.4 1.41
45 25.7 57.2 1.43 31.5 45.3 1.37
55 28.2 57.5 1.44 29.1 48.4 1.40
65 16.6 73.9 1.53 21.4 49.8 1.41
75 22.2 54.9 1.45 17.1 53.8 1.44
TB is bulk density.

16

 

 

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E 25 -
V
at :20 -
15 a
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5 -
0 , ﬂﬁ -5? l I D If Mb-
220 230 240 250 26

200 210 0 270 280

DOY

Figure 1.1. Daily solar radiation (SR), maximum (Tmax) and minimum (Tmin)
temperatures, and rainfall (R) from DOY 200 to 280 in 1997.

17

 

0.35

 

    

 

 

 

 

0.30 « -
0.25 -
'E 0.20 -
O
E
3 0.15 -
m)
0.10 -
0.05 -
0.00 M
0.20 1
”is 0.15 "
0
5 1
> 0.10
c .909 .9090
0.05 -
0.00 I I F j I I
0 10 20 30 40 50 60 70

t ((1)

Figure 1.2. Measured and simulated soil water content proﬁles of 60-cm columns of
loam and sandy loam soils drying during second stage evaporation.

18

Results and Discussion
Laboratory Results

Soil water content distribution under the second stage of evaporation was function
of depth and time (Figure 1.2). The change of soil water content decreased with
increasing depth and time (Figure 1.2). Soil water content went from 0d“. toward 0“,. The
volumetric drained upper lirnit soil water content was about 0.32 cm3 cm'3 for loamy soil
and about 0.24 cm3 cm'3 for sandy loam soil. The volumetric air dry soil water content
was about 0.05 cm3 cm’3 for loamy soil and about 0.03 cm3 cm'3 for sandy loam soil
(Figure 1.2).

The simulated soil water contents, using the water balance of CERES, were higher
than measured ones for loamy soil and lower than measured values for sandy loam soil at
all depths (Figure 1.2). The simulated water contents had trend similar to the trend found
in the measured soil water contents. The simulated water contents were function of time
and depth and the change of simulated soil water contents decreased with increasing
depth and time (Figure 1.2).

Using value of n constant equal to -1.94 instead of -2, produced simulated water
content close to the measured soil water contents for loamy soil (Figure 1.3). Similarly,
using value of 11 equal to -2.2 instead of -2, produced simulated water content close to the
measured soil water contents for sandy loam soil (Figure 1.3). This suggested that n was
soil speciﬁc, and was related to 06“,, and a was related to 0d,“.

The relationship between 0d“. and a was investigated and demonstrated in Figure
1.4. As explained in the theory, a can be obtained by solving Eq. [5]. Numerical solutions

were obtained for the loam and sandy loam soils, and the six different soils from DA.

19

 

loam

0V (cm3 cm'3)

0v (cm3 cm'3)

Figure 1.3. Measured and simulated soil water content proﬁles of 60-cm colmnns of

0.35

0.30

0.25

0.20

0.15

0.10

0.05

0.00

0.20

0.15

0.10

0.05

0.00

 

Loamy soil

   
 

M3cm'-.

 

 

 

 

 

 

. M 6 cm °
Q M 9 cm
[:1 M 12 cm
A M 15 cm
— Simulated
n" v-"
. '- * --"- " I A n Sand lo m oil
. Oil-g:-.h-=...-ol'—‘::=. - . ..~_ _- _ y a s
00. . I. -I -II II. . _
. l-n... .-.-..- I .
9 I Ii-
‘ I - i..-
0 10 20 30 40 50 60

t (d)

loamy and sandy loam soils drying during second stage evaporation.

20

 

70

 

 

Figu
Mich

 

0.6

 

  
  
   

 

 

 

a=-0.125+1.60dul 8:073
05- $1.190“ r2=0.69
3A 0.4 -
'-c
E ......
8,
:5 0.3 ~
. . DARose(l968)datapoints
0.2- ‘ o ........ Bestﬁtlinewithintucqxofzero
_ Bestﬁtline
A Sandylcnnsoil
I Irramysoil
0.1 1 I I I I
0.15 0.20 0.25 0.30 0.35 0.40 0.45
Onl(cm3cm3)

Figure 1.4. Relationship between a and 0d“. of 8 soils: Loamy and Sandy loam soils from
Michigan and 6 soils from D.A. Rose (1968).

21

 

-2.15

n = -2.22 + 0.71 9.1.1 12 = 0.99

-2.10 r

-2.05 i

-2.00 ~

-l.95 -

-l.90 -

 

-l.85 -

-1.80

 

1.1 *

a=20dul r2=0.99

1.0 a

0.9 -

0.8 -

0.6 _

0.5 ~

  
  

0.4 -
0 Five representative soils
— Best ﬁt line

   

0.3

l

 

 

0.2 j I T j I
0.15 0.20 0.25 0.30 0.35 0.40 0.45

9001 (cm3 cm'a)

 

Figure 1.5. Relationships between drained upper limit soil water content (90111) and
constants n and a.

22

Rose (1968). A linear relationship was found between a and 0dul with r2=0.73 for the best
ﬁt line and 0.69 for best ﬁt line with zero intercept (Figure 1.4) . Because no soil would
have negative 01, best ﬁt line with zero intercept is more realistic. By deﬁnition, a is
proportional to Ec and equal to Ec at the end of ﬁrst day of evaporation under second stage
evaporation. This led us to conclude that, Ec is site speciﬁc too.

The developed relationship with zero intercept between a and 9.11.1 was used to
obtain simulated values to n corresponding to ﬁve different 9.11.1- Trial and error was used
to produce n values. A value of n was accepted if the simulated BC was equal to Ec that
was calculated from the developed relationship between a and 9.11.1- A linear relationship
was found between n and 9.11.1 with 11:0.99 (Figure 1.5). The developed relationship
between 11 and 0d". can be used to improve the simulated EC.

It was noticed that any alteration of 11 should be accompanied with change of a to
preserve the diffusivity theory and keep a linear relationship between Ec and t‘”. It was
found, that a linear relationship existed between a and 9.11.1 with r2=0.99 as shown in
(Figure 1.5). When n was equal to -2, a was equal to 0.63 at 9.11.1 of 0.305 cm3 cm‘3 (Figure
1.5). The value of a was inversely related to 11 (Figure 1.5). The relationships of n with
9.101 and a with 0dul were evaluated and validated for values of 9.1.11 ranged from 0.15 to 0.45
cm3 cm'3.

Loamy soil evaporated more water than sandy loam soil (Figure 1.6). At day 1,
measured E, in Figure 6 was too low because the change of soil water content below 2 cm
was not included in computing Ec since the closest TDR probe to surface was at 3 cm.
The relationship between Ec and t"2 was linear (Figure 1.6). The simulated Ec that was

obtained by using modiﬁed values for n and a was accurate (Figure 1.6).

23

30

 

15*

Ec (mm)

10-

 

 

 

 

I ((110,)

Figure 1.6. Measured and simulated cumulative evaporation (13,) of loam and sandy loam soil
during second stage evaporation.

24

0.35

 

 

 

 

 

 

 

0.30 ~
0.25 .
(:1A
a 020 1
0
M
E
3 0.15 .
o>
0.10 -
0.05 -
0.00
.. aﬁI'v '17.”- V
0.20 -
MA _
'E 0.15
O
M
E
3 3cm
> 0.10 - 9
a: 0 12cm
' 9611
v 12011
0.05 - I 15cm
0.“) I I I I l I I
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

19(cmd'm)

Figure 1.7. Soil water content proﬁles of 60-cm columns of loamy and sandy loam soils versus
Boltzmann transform under second stage evaporation.

25

 

     
  
         
  

      
     
 

3" w ‘

      

      

 

  

       

   

1' rr I L9 1- . _v
ntﬁﬂﬁd’ﬁﬂ"“"'&lilﬂﬁﬁﬂﬁu tiff-“lume— ‘Iu-EW-ir-r
'V f "I'l'rlLrﬁLrI-llllLrllllrLrLriE:I’LL...
-__,_,_ . , _'

0.24 “ IITIIIII

   
 

 

 

 

 

   

 

 

 

MA
'5
m0 0.22 -
E
63
a; 0.20 -
0.18 -
0.16
202.0 202.5 203.0 203.5 204.0 204.5 205.0 205.5 206.0
DOY
J /
0-45 / /
0.40—
. 3cm
0 60m
035- v 9cm
v 12cm
A
r? I 15cm
5 030‘ 1:1 25 cm
E
3, 0.25-
>
o
0.20-
0.15—
0.10 1 1 1 // .
200 205 210 215 220 250 260
DOY

Figure 1.8. Soil water content proﬁles at six depths of sandy loam soil proﬁle in 1997.

26

Volumetric water contents at 3, 6, 9, 12, and 15 cm depths had the same relationship with
19 for loam and sandy loam soils for about 62 days (Figure 1.7). This is a proof that
diffusivity theory is valid for heterogenous but uniform and isotropic soil drying under
second stage evaporation and this is in agreement with D.A. Rose (1968). Soil physical-
characteristic play an important role in deﬁning the movement of soil water. Signiﬁcant
change of soil water content started at about 2.5 cm (1“2 for loamy soil and at about 2 cm
11'“2 for sandy loam soil (Figure 1.7).

Field Results

Field data, in addition to the laboratory data, were used to evaluate the second
stage evaporation module of water balance of CERES. Soil water content proﬁles were
shown at six depths (Figure 1.8). A 4-day close-up, on which daily solar radiation was >
15 MJ (1", average temperature was about 20 C°, and rainfall was 0, was selected plotted
in Figure 1.8 to show the ﬂuctuation of soil water content between day and night. It was
clear that soil water content at 3 cm depth and to less extend at 6 cm increased at night
(Figure 1.8) as result of upward soil water ﬂow at a time of zero evaporation. The driving
force of such movement is the soil hydraulic gradient.

Simulated soil water contents in the ﬁeld showed good agreement with the
measurements (Figure 1.9). The root mean square error (RMSE, cm3 cm") was 0.013,
0.013, 0.005, 0.01, 0.011 at 3, 6, 9, 12 and 15 cm depths, respectively, using Eq. [8] with

= -2 and a=0.63. Whereas, RMSE (cm3 cm‘3) was 0.014, 0.014, 0.005, 0.01, 0.012 at 3,
6, 9, 12 and 15 cm depths, respectively, using Eq. [8] with n=-2.09 and a=0.47. The
RMSE values showed that the modiﬁcation of n and a values had no improvement on the

prediction of soil water content distribution under second stage evaporation. However,

27

 

 

 

 

 

 

 

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200 205 210 215 220 225 230 235 240 ~245 250 255
DOY

Figure 1.9. Measured, simulated (using Eq. [8] with n=-2 and a=0.63),
simulated (M) (using Eq. [8] with n=2.09 and a=0.47) soil water content of a
bare soil in Lansing ﬁeld in 1997 at six different depths.

28

 

0.35 -

  

0v (cm3 cm'3)
O
8

 

 

 

 

0.30 l I j l | I I I
0 50 100 150 200 250 300 350 400 450

t(hr)

 

Figure 1.10. Soil water content proﬁles of 150-cm columns of loamy soil drying
during second stage evaporation.

29

 

0,, (cm3 cm")

 

 

 

f

 

 

Mb I... 11'“. v
" "."0’1‘: f. .3!
E h “"10 ' . '0‘»?ch
. ’ (9
m0 ‘1. 1'3” ' I 1"»+\"
\ I, ,
E . h ‘ .192"?! 09
O \‘F\~\."‘.l III
v «any. .-
> V
CD
0
O
0 24 v 55 cm
° v 65 cm
I 75 cm
0.22 1 j r m 1 r r 1

 

 

0 50 100 150 200 250 300 350 400 450
t(hr)

Figure 1.11. Soil water content proﬁles of 150-cm columns of sandy loam soil drying
during second stage evaporation.

30

the modiﬁed version of second stage evaporation model can be used since it was
produced under ideal second stage evaporation initial and boundary conditions.
Effect of Water Table

If one or more of the boundary conditions of second stage evaporation was
violated, the above relationships may not be applicable. For instance, having a shallow
water table may violate the boundary condition of semi-inﬁnite soils. Because a shallow
water table is evident in many agricultural ﬁelds, in this research the impact of a shallow
water table on the diffusivity theory under second stage evaporation was investigated.

Figure 1.10 and Figure 1.11 show volumetric soil water content at 11 depths
under evaporation for loam and sandy loam soils. The soil initial soil water content was
not uniform but rather increased from 9001 at 3 cm to about saturation at 75 cm for loamy
soil (Figure 1.10) and increased from 9.11.1 at 3 cm to about saturation at 45 cm for sandy
loam soil (Figure 1.11). Soil water content under evaporation was function of depth and
time and the change of soil water content decreased with depth and time (Figure 1.10 and
1.11).

To test the validity of diffusivity theory under such conditions, volumetric soil
water content was plotted against 1., as shown in (Figure 1.12). It was found that soil
water content at any depth for loam and sandy loam soils was going from its initial value
toward a certain soil water content higher than 0,d_ That soil water content was about 0.19

cm3-cm'3 for loamy soil and about 0.12 cm3 cm“3 for sandy loam soil. Soil water content

had different relationship with 1., at each depth when 1., 2 2 cm 01'”2 (Figure 1.12) since

initial soil water was different at different depths(Figures 1.10 and 1.11). It was

31

0.45

 

 

 

 

 

 

Loamy soil . 0 °
0.40 4 00 o o o
«o oo <> 0 .
an. 3000000 9‘ g ,0
O . 0 Ch A
A 0.35 - . 'v V. D 0.0 A‘“
Is SW00 “ A AMA A A
U
”a 0.30 - f.-
8
Q)
0.25 -
0.20 -
0.15
. 'I n
033 Sandy loam son 2‘0‘ 9 ‘0‘ ”
03
0A 0.
0.30 - 00000“ 0 O
O. Q 0
pr“ 0.27 - .*.06’. Auto A A
E . 0 AA 3 cm
'20 024 q 0 ' 0 V0 AFA 6 Gem
E ' 0 CPU ‘3 0'
3 O W0 . v 9cm
> 12 cm
. 1 - V
d: 02 I 15 cm
0 25 cm
0.18-i o 35 cm
0 45cm
0.15 - A 55 cm
A 65 cm
0.12 W I I f I I T I I . 75 cm
0 2 4 6 a 10 12 14 1e 1e 20

1.8 (cm 0"”)

Figure 1.12. Soil water content proﬁles of ISO-cm columns of loamy and sandy loam
soils versus Boltzmann transform during second stage evaporation.

32

 

 

 

 

E51546” fcrloerrysoil
a).
1351211” fcraﬁyloansoil O 0'
5% 00
E 401 .0
O
E; .
LIJ 331 O 0
m-
0 Sara/loaned
10* 0 o loarysal
O l I T l
0 1 2 3 4 5

t (01”)

Figure 1.13. Cumulative evaporation of ISO-cm column of loamy and sandy loam soils
during second stage evaporation.

33

concluded, that Boltzmann transform cannot be used since there was no single-valued
function between soil water content and M.

A linear relationship was found between Ec and t"2 for loam and sandy loam soils
(Figure 1.13). This suggested that soil evaporation was limited by soil water content and
soil characteristics. Evaporation from loamy soil was higher than that from sandy loam
soil (Figure 1.13). The slope of the best ﬁt line was 15.4 mm cl'”2 for loamy soil and 12.1
mm d“ for sandy loam soil (Figure 13). The slope of the best ﬁt line should be close to
(1. Hence, a for soils affected by shallow soil water table was about 4 time greater than a
for semi-inﬁnite soils under second stage evaporation. This led us to conclude, that the
relationships that developed for semi-inﬁnite soils were not applicable for soils affected
by shallow water table.

Conclusions

The second stage evaporation model in the water balance of CERES was
evaluated. The two constants (n and a) that used in the model were found to be soil
speciﬁc since 01 was soil speciﬁc. However, they did not vary much and were highly
correlated to 9d,“. New linear relationships between 0., n, and a with 0d“. were developed.
These relationships enabled the second stage evaporation model in the water balance of
CERES to better simulate soil water distribution and soil water evaporation for diverse
soils.

It was found that the impact of water table on second stage evaporation could not
be captured by second stage evaporation theory because soil water contents at different
depths had different relationships with Boltzmann transform. Further studies should be

conducted on modeling evaporation from soils that have shallow water table.

34

 

 

 

Refer
Black

Evett

Pam‘-

Fedc

Gab

Gar.

Ha:

Hill

Las

MCI

Nor

Phili

Ritch

Ritchi.

References
Black, T.A., W.R. Gardner, and G.W. Thurtell. 1969. The prediction of evaporation,
drainage, and soil water storage for a bare soil. Soil Sci. Soc. Am. J. 33:655-660.

Evett, SR, and R.J. Lascano. 1993. ENWATBALBAS: a mechanistic evapotranspiration
model written in compiled basic. Agron. J. 85(3):763-772.

F arahani, H.J., and LR. Ahuja. 1996. Evapotranspiration modeling of partial
canopy/residue covered ﬁelds. Trans. ASAE. Vol. 39(6):2051-2064.

Feddes, R.A., P.J. Kowalik, and H. Zaradny. 1978. Simulation of ﬁeld water use and crop
yield. PUDOC, Wageningen, Netherlands.

Gabrielle, B., S. Menasseri, and S. Houot. 1995. Analysis and ﬁeld evaluation of the
CERES models water balance component. Soil Sci. Soc. Am. J. 59: 1403-1412.

Gardner, HR, and W.R. Gardner. 1969. Relation of water application to evaporation and
storage of soil water . Soil Sci. Soc. Am. Proc. 33:192-196.

Hanks, R.J. 1991. Soil evaporation and transpiration. ASA-CSSA-SSSA, 677 S. Regoe
Rd., Madison, WI 53711, USA. Modeling plant and soil systems-Agronomy
Monograph no. 31.

Hillel, D., and H. Talpaz. 1977. Simulation of soil water dynamics in layered soils. Soil
Sci. 123254-62.

Lascano, R.J., and J .L. Hatﬁeld. 1992. Spatial variability of evaporation along two
transects of a bare soil. Soil Sci. Soc. Am. J. 56:341-346.

Mcllroy, LC. 1984. Terminology and concepts in natural evaporation. Elsevier Science
Publishers B.V., Amsterdam, Agricultural Water Management, 8:77-98.

Norman, J .M., and G.C. Campbell. 1983. Application of a plant-environment model to
problems in irrigation. p. 155-188. In D. Hillel (ed.) Advances in irrigation. Vol.
2. Academic Press, New York.

Philip, J .R. 1957. Numerical solution of equations of the diffusion type with diffusivity
concentration-dependent. 11. Aust. J. Phys., 10:29-42.

Ritchie, J .T. 1972. Model for predicting evaporation from a row crop with incomplete
cover. Water Resour. Res. 8: 1204-1213.

Ritchie, J .T., and BS. Johnson. 1990. Soil and plant factors affecting evaporation. ASA-

CSSA-SSSA, 677 South Segoe, Madison, WI 53711, USA. Irrigation of
Agricultural Crops-Agronomy Monograph no. 30:363-390.

35

Rose, C. W. 1968. Evaporation from bare soil under high radiation conditions. Trans. Int.
Congr. Soil Sci. 9‘“, Adelaide. 1:57-66.

Rose, DA. 1968. Water movement in porous materials 111. Evaporation of water from
soil. Brit. J. Phys., Ser 2, Vol. 1:1779-1791.

Van Bavel, C.H.M., and D. Hillel. 1976. Calculating potential and actual evaporation

from a bare soil surface by simulation of concurrent ﬂow of water and heat. Agric.
Meteorol. 17:453-476.

36

CHAPTER TWO

ASSESSING AND MODELING VERTICAL SOIL WATER DRAINAGE

Introduction

According to Corwin et a1. (1991), groundwater is a major source of drinking,
industrial, and agricultural water. Groundwater supplies will become even more
important resource as world demands for water grow. Acute and chronic health affects
resulting from contaminants in drinking water has brought the degradation of ground
water to public attention. Groundwater quality is a concern for health reasons, and
because of the decrease in crop productivity, which can often accompanied by the use of
poor quality irrigation water. Suitable mathematical models and appropriate values for
downward soil water ﬂow are needed to assess the impact of surface-applied
agrochemicals on the subsurface environment (V anderborght et al., 1997) and
groundwater (Corwin et al., 1991).

The ability of a soil to drain water could be critical for crop yield. Fast drainage
would be desirable to avoid long-term saturation conditions. On the other hand, water can
be taken by plants while drainage out of the root zone is occurring. Many productive
agricultural soils drain slowly, providing a potentially signiﬁcant quantity of water for
plant use before gravity induced drainage stops (Ritchie, 1998). So accurate modeling of
soil water drainage is needed for prediction of crop yield as well as for water use
efficiency.

Preferential ﬂow paths are formed in soils by biological, chemical and physical

37

processes and their interactions. Their inﬂuence is usually reﬂected in reduced travel time
through the soil, increased solute concentrations in drainage water, or deeper penetration
of chemicals into the soil proﬁle, than predicted by conventional ﬂow theory. Preferential
ﬂow maybe considered the main contributor to solute transport (Montas et al., 1997).
Corwin et al. (1991) developed a functional model to account for the bypass ﬂow. Such
model is beyond our scope in this work since total daily drainage is the main concern of
this study and preferential ﬂow makes more difference when the time step is minutes or
hours.

It was found that the drainage model in CERES has to be calibrated in order to
give good estimates of soil water drainage (Gabrielle et al., 1995; Gerakis and Ritchie,
1998). Although a procedure was introduced to determine the drainage coefﬁcient (the
fraction of drainable soil water that can be drained in a day) that is used in CERES
drainage model based on soil porosity (Ritchie et al., 1986), Gerakis and Ritchie (1998)
and Ritchie (1998) suggested that the drainage coefficient can be assumed constant for
different soils in the drainage model.

A theoretical basis for the drainage coefﬁcient was lacking in the literature. An
effort has been made to ﬁll that gap by introducing a theoretical basis for the drainage
coefficient. A theory was introduced on the basis of Darcy’s Law, the assumption of a
unit gradient for a drainage cycle, and the validity of Brooks and Corey (1964) equation
for unsaturated hydraulic conductivity estimation. Two new methods were developed to
estimate the drainage coefﬁcient from drained upper limit and saturated water content.
The link between the drainage coefﬁcient and soil physical properties enables the

drainage model to take into account the spatial variability of the drainage coefﬁcient.

38

The objective of this study was to link the downward soil water ﬂow dynamics
and drainage model in the water balance of the CERES family models to the vertical
drainage theory and establish a relationship between the drainage coefﬁcient and drained
upper limit soil water content. Ritchie et al. (1999) demonstrated that drained upper limit

soil water content can be estimated reasonably well from texture and bulk density.

Theory
Darcy’s equation works well in describing soil water ﬂow during drainage for
homogenous soils with uniform initial soil water content (Youngs, 195 7a,b). It can be

written as follows (Philip, 1957):

q = mfg) (1)

where q is the soil water ﬂux (cm d"), K(0) is soil water hydraulic conductivity (cm (1"),
0 is soil water content, and ah/az is the hydraulic gradient. The hydraulic gradient maybe
assumed I for saturated soil water ﬂow or for soil water ﬂow in drainage cycle. Based on
such assumption, the soil water ﬂow can be described as follows (Black et al., 1969;

Gabrielle et al., 1995):
q = K09)

(2)
When a layer of soil of 1 cm thickness, initially at a uniform water content 0,. has

its surface covered, the initial and boundary conditions governing ﬂow rate are

39

E5 = 0 t 2 0
0 = 08 z 2 0 t = 0
05>0>0dul 220 t>0
where z is depth, t is time , and E5 is soil evaporation.
The change of soil water content in 1 day (d0) under the above initial and

boundary conditions can be described as:

dz dz
0119— = C 19 - 6l — 3
dt 1( 5 did ) dt ( )
where Cl is the fraction of drainable soil water that can be drained from the soil layer in

the ﬁrst day (d").

By combining Eq. [2] and Eq. [3] Cl can be described as follows:

= K19)

I (as ’ 6am) (4)

where K.(0) is the 1“t day hydraulic conductivity. A harmonic mean can be used to

estimate K,(0) as follows:

2K(0.)K.
W) = K(a)+ K

S

 

(5)

where 0I is soil water content after 1 day of drainage and Ks is saturated hydraulic
conductivity.

The unsaturated hydraulic conductivity at any 0 can be estimated using the

40

following equation (Brooks and Corey, 1964; Brutsaert, 1967; Corey, 1977; Corey et al.,

1965; Mualem, 1976; Mualem, 1978; Schuh and Cline, 1990):

 

9- 6, "
j

K(6l)= K16? a

where 0r is residual soil water content and can be assumed equal to 0d“, in drainage cycle
(Suleiman and Ritchie, 1999; Ahuja et al., 1984; Ahuja et al., 1993), and n is a constant
that depends on the soil pores distribution (Corey et al., 1965) and the amount of work
per unit volume of soil required to drain a saturated soil to the wilting point (Mualem,
1978) (the lower limit for drainage cycle is drained upper limit and not the wilting point,
and the energy needed to drain saturated soil to the wilting point is substantially greater
than to drain saturated soil to drained upper limit soil water content). According to

Suleiman and Ritchie (1999), K5 can be estimated as follows:

 

6: ’ 6cm! 2
K = 37 —— (7)
gdul
By combining Eq. [4], Eq. [5], Eq. [6], and Eq. [7], Cl can be calculated as
follows:
1— C "
1 = a ( I) (8)

where 0. can be written as:

41

a = 74%] (9)
adulz

Using the same procedure, C2 (the fraction of drainable soil water that can be

drained from the soil layer in the second day) can be calculated as follows:

(1— C,)""(1— Cl — C,(1— C,))"
(1—C,)"+(1—C,—C,(1-C,))"

 

C2 = a (10)

Estimating n from other soil properties would be helpful since it is impossible to
determine its value or even its range from purely theoretical basis (Mualem, 1978). Schuh

and Cline (1990) showed that n can be estimated from percent of sand (ps) as follows:

n = 47.61exp(— 0.026;»)

(11)

Eq. [11] gives high values of n and such high values of n is only found when
measurements are taken at low saturation with a capillary tension of several atmosphere
(Mualem, 1978). What is relevant for drainage cycle of n values are those measured when
soil matric potential is between 0 and -50 kPa since that would cover any drainage cycle.
It was noticed that n values that are measured at low saturation with a capillary tension
of several atmosphere is about 4 times greater than that for those measured at the drainage
range on data published in Mualem (1978). Eq. [11] was used to estimate n for all the

soils of Ratliff et a1. (1983) data set and then the estimated 11 values were divided by 4 to

42

estimate n values relevant to a drainage cycle. Then, a linear relationship between 11 and

0dul was developed as follows:

n = 3+ 2026],“, (12)

The initial water content can vary in the ﬁeld and it may never be equal to 05. It is
clear from Eq. [8] and Eq. [10] that C (drainage coefﬁcient) is dependent on initial soil
water content. An average C for each soil can be introduced to be used at any initial soil
water content. The C can be calculated from C1 and C2 in the condition that the soil
water content at the end of day 2 is identical whether Cl was used for day 1 drainage and
C2 for day 2 drainage or that C was used for day l and day 2. Assuming the initial soil
water content, 0,, soil water content after 2 d of drainage, 02, and drained upper limit soil

water content, 0d,], C can be calculated as follows:

0. = 9. - Cx (61- 6'...) (13)

where 0l is soil water content after 1 day of drainage.

62 = 61 " C" (61 " 66a!) (14)

By substituting Eq. [13] in Eq. [14] 02 can bedescribed using 03 as follows:

62 = 6, — 2x Cx (6 — 6d,,)+ C2 x (6,— 61M)

S

(15)
C can be calculated using the quadratic formula as follows:
—(2 x (9,, — a.» — ((26... - 6.»: - 4(6. - 606. — a...)

C = (16)
2(63 " 6:114!)

 

 

43

Drainage Model in CERES Water Balance

According to Ritchie (1998), redistribution of water in the soil proﬁle and
drainage out of the root zone are calculated using a functional model developed from
ﬁeld drainage information. For soil water redistribution during inﬁltration water is moved
downward from the top soil layer to lower layers in a cascading approach. Drainage from
a layer takes place only when 0 (soil water content) is between 0sat (0.92 of saturated soil
water content) and 0d,, (drained upper limit soil water content).

The change of volumetric soil water content in a day at any depth under drainage

is calculated as follows:

A 6: C(6— 6d,”) (17)

where C is a constant equal to 0.55 (Ritchie, 1998).

Materials and Methods

Laboratory and ﬁeld experiments were conducted to study the downward soil
water flow and drainage during a drainage cycle. In addition to the laboratory and ﬁeld
experiments, data from Reichardt and Nielsen (1984) were used to evaluate the drainage
coefficient in the drainage model in the water balance of CERES. Their data set include a
dozen soils of diverse taxonomy, from Belgium, Brazil, Chile, Cyprus, Japan,
Madagascar, Niger, Palestine, Senegal, Syria, and Thailand (Reichardt and Nielsen,
1984). Although complete drainage cycles were done on these soils, only saturated soil
water content, initial soil water content, ﬁnal soil water content (drained upper limit soil

water content), and soil water content aﬁer 2 days of drainage were available. These soil

44

water contents were needed to estimate the drainage coefficient for each soil. Data from
Ratliff et a1. (1983) were used to produce a relationship between n (deﬁned in the theory)
and 0“,. Sand content (ranges from 0.9 to 97.5 cm3 cm’3) and drained upper limit soil

' water content (ranges from 0.068 to 0.45 cm3 cm‘3) were available for each of the 388
soils in Ratliff et al. (1983) data set. Drained upper limit, for these soils, was measured in

the ﬁeld aﬁer drainage a cycle.

Laboratory Experiments

Two different soils were used to study the soil water distribution under a drainage
cycle. One of the soils was obtained from Saginaw area, Michigan and it was loamy soil
(25.4 % clay and 43 % sand ). The second one was obtained from Lansing area, Michigan
and it was sandy loam soil (9.4 % clay and 65.4 % sand). The two soils were air dried,
sieved through 2 mm screen, and then assembled into PVC columns with height of 150
cm and diameter of 30 cm. Twenty cm time domain reﬂectometry probes (TDR) were
installed horizontally at depths of 3, 6, 9, 12, 15, 25, 35, 45, 55, 65, and 75 cm. The soils
were saturated from the bottom using a constant head of 150 cm. The soils were allowed
to drain for 10 days while the soil surface was covered to prevent evaporation ﬁ'om the
soil surface. Soil water content was monitored at all depths every 20 minutes during the
drainage cycle.
Field Experiment

Two sets of 20-cm TDR probes were installed horizontally at depths of 3, 6, 9, 12,
15, 25, 35, 45, 55, 65, and 75 cm from the surface in a bare soil in the Lansing area on

July 10, 1997. The two sets were 3 m apart. The soil was saturated using ponding and

45

then the soil surface was covered for15 days on August 15, 1997. The soil water content

was monitored at all depths every 20 min during the drainage cycle.

Results and Discussion

Trial and error procedure was used to solve Eq. [8] and Eq. [10] in order to ﬁnd
C, and C2 at representative combination of 0s and 0d,“. These values of C, and C2 were
used then to solve for C using Eq. [13] through Eq. [16]. Linear Relationships between
C,, C,, and C with (1nd)“n were developed (Figure 2.1). These relationships (Eq. [18], Eq.
[19], and Eq. [20]) can be used to estimate C,, C,, and C directly from 0, and 0,“, instead
of using trial and error to solve for them. All of C,, C,, and C are dependent on 05 and to
greater extent on 0,“, because a is function of both 05 and 0d,“, whereas, 11 is function of
0d,”. The reason that C2 is lower than C, is that average soil water hydraulic conductivity
during the 2"d day of drainage is lower than that during the 1St day of drainage. The
drainage coefﬁcient, C is greater than arithmetic mean of C, and C, as can be seen in
Figure 2.1. The ratio of C to C, was 68% for soils with 0d“, equal to 0.07 cm3 cm", and
0.83 for soils with 0,“, equal to 0.42 cm3 cm'3. An average ratio of C to C, was about 0.75.
The root mean square error (RMSE) of the estimation of C using Eq. [20] was 0.144
while it was 0.253 assuming a constant value of 0.55 (Ritchie, 1998) for the international
soils (Figure 2.2). The international C values showed clear dependence on the
independent variable, (1nd)" “, (Figure 2.2). Some of the error was due error measurement
and some resulted from using Eq. [12] to estimate n because Eq. [12] estimates an
average value of n at each 0d,". Overall, Eq. [20] is a better estimate of C instead of using

a constant of 0.55 for different soils.

46

1.0
09~
0,8- Eq[1qg=064x-061

07: ErmC=097x-082
06-

 

Eq [18] c1 =1.c2x- 075

    
  

O 051

 

 

 

Figure 2.1. Relationships between C,, C2, and C with (1nd)"u for any realistic possible
combination of 0s and 0d“,

47

It is possible to approximate C from 0,“, only since C is highly dependent on 0,“,
(Figure 2.3). A quadratic polynomial relationship was developed to estimate C from 0,“,
(Figure 2.3). The deviation of points from Eq. [21] line is due to the difference between 05
and 0d“, The deviation from Eq. [21] line is greater at lower 0d,, and minimum at high 0d,“.
However, maximum deviation from the line is about 10% at any 0d,“. The advantage of
using Eq. [21] over Eq. [20] in modeling soil water drainage is that the independent
variable in Eq. [21] (0“,) is available while the independent variable in Eq. [20] (Lna)”n is
to be calculated from 08 and 0d,“.

TheRMSE of the estimation of C using Eq. [21] for the international soils was
0.136 (Figure 2.4). The 0.55 line overestimated all the points of soils that have 0,“, of 0.22
cm3 cm'3 or greater. For instance a heavy soil with 0d,, of 0.4 would drain on average 20-
25% of its drainable water not 55% in a day (Figure 2.4).On the other hand, a light soil
with 0d,, of 0.05 would drain on average 70-75% of its drainable water not 55% in a day
(Figure 2.4). Although Eq. [21] it was developed to simplify the estimation of C, Eq. [21]
outperformed Eq. [20] in the case of international data soils. This led us to conclude that
Eq. [21] can also be used to estimate C for different soils in the water balance of CERES
instead of assuming constant value of C of 0.55. To account for the impact of incoming
water flow (Q,) on the change of soil water content of a certain layer during drainage, a

generic relationship between C and Q, can be introduced as follow:

C: a+bln(Q,+¢e) (22)

where ¢, (cm3 cm'3) is soil effective porosity and equal to 05 - 0d,“. Having in mind that

(1) when Q, = 0, C has to be equal to the original C and (2) when Q, = K,, C is O, a and b

48

 

 

 

 

 

0.9«
8
0.8
0.7
0.6-
o 0.5-
0.4~
0.3-
0.21 . ,' ........ 0.55UneRMSE=0.253
01‘ '. . —Eq[20]LineHVISE=O.144
' 0
0.0 1 T I T 1 1 I
1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8

Figure 2.2. Measured and estimated C using Eq. [20] of the international soils versus
(may/n.

49

I

 

 

0.8
0.7 « Eq. [21] C=2%x2-262x+0.85
0.6 -
0.5 -

o 0.4 ~

0.3 1

 

0.2 1

0.1 - A C
— BestﬁtlinefaC ,

 

 

0.0 ,
OLE 0.10 0.15, 0.20 0.25 0.30 0.35 0.40 0.45

0d, (cm3 cm3)

 

1 I 1 1 I I

Figure 2.3. Relationship between C and 0,“, for any possible realistic combination of 0s
and 90m-

50

1.0

 

 

 

 

 

0.9« '
0.8-
0.7-
0.6-
o 0.5-
0.4-
0.3-
0-2] O Datapourts . ..
_ Eq. [21]RMSE=0.136 0
0-11 -------- 0.55UneRMSE=0.253 ' ' n
0.0 1 T T 1 1 1 1 I
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45

0d,, (01113 cm“)

Figure 2.4. Measured and estimated C using Eq. [21] of the international soil versus 0d,“.

51

can be deﬁned as follows:

a = —b 1n(1<,)
and (23)
b = C

 

To explain Eq. [22] and Eq. [23], let us assume that a saturated soil layer has 05 =
0.4 cm3 cm'3 and 0,", = 0.2 cm3 cm'3. Using Eq. [21], C was found to be 0.44 and using
Eq. [23], a was found to be 0.324 and b was found to be -0.075. Assuming that Q, ranged
from 0 cm d‘l to 100 cm (1", applying Eq. [22] C against Q, was plotted and shown in
Figure 2.5. It was clear that C was equal to the original C when Qi was 0 and C was equal
to 0 when Qi was equal to K, (37 cm (1"). When Qi was greater than K, (37 cm d“) C is
assumed to be 0 and only Ks (37 cm d") of water can pass through the soil layer.
Laboratory Results

A revision of the deﬁnition of drainable soil water had to be done to explain the
laboratory results. Deﬁning the drainable soil water as the difference between 0, (initial
soil water content) and 0,“, (as in Eq. [17]) is correct if the ﬁnal soil water content (0,)
after a drainage cycle is equal to 0d,, However, if 0, aﬁer drainage cycle is greater than
0,“, , the drainable soil water content has to be deﬁned as the difference between 0, and 0,
and not the difference between 0, and 0d,“. The deviation of 0, from 9.11.1 for a soil layer

usually happens when that layer is affected by a water table. Zacharias and Bohne (1997)

52

0.45 3

 

0.40 1
0.35 1 '
0.30 1 °

0.25 — g

0.20 - '
015- 0

0.10 -

 

 

0
0
0....
0
005“ ..'0000
0....
0

(1m 1 1 1 1 I t m—
0 5 10 15 20 25 30 35 4O

Q(cmd1)

 

Figure 2.5. Relationship between C and Q, for a soil of 0s = 0.4 cm3 cm'3 and 0,“, = 0.4
cm3 cm

53

introduced a procedure to determine 0, in such a case. In this study, the actual measured 0,
was used at each soil depth instead of 0,“, in deﬁning the drainable soil water. Final soil
water content at 3, 6, 9, 12, 15, and 25 cm depths of loamy soil and sandy loam soil could
be considered equal to 0,“, (Figure 2.6.a, Figure 2.6.b, Figure 2.7.a, and Figure 2.7.b).
Whereas, 0, at 35, 45, 55, 65, and 75 cm depths of loamy soil and sandy loam soil were
greater than 0,", assuming that both soils were uniform and each soil had only one 0,“, for
all depths (Figure 2.6.a, Figure 2.6.b, Figure 2.7.a, and Figure 2.7.b).

When 0, is greater than 0d,”, using Eq. [4] to deﬁne C and Eq. [20] or Eq. [21] to
estimate C is irrelevant because the change of hydraulic conductivity in a day will be less
than if 0, was equal to 0d,”. An approximation was developed to estimate C at any 0f as

follows:
C: C+ (0.85— c)(1— H)

(24)

where H ranges from O to 1 and can be deﬁned as follows:

(25)
(as — 6d)

[{==

Using Eq. [21] and Eq. [24], C was 0.57, 0.51, 0.62, 0.39, and 0.51at depths of
35, 45, 55, 65, and 75 cm, respectively, for loamy soil and it was 0.66, 0.79, 0.79, 0.72,
and 0.79 at depths of 35, 45, 55, 65, and 75 cm, respectively, for sandy loam soil. There
was no signiﬁcant improvement in estimating the daily soil water contents during

drainage cycle of loam and sandy loam soils by using these values of C for loamy soil

54

0.46
0.45

0.44 1
0.43 1

0.42

V

9 (cm3 cm“)

0.38

0.45 -
0.44 ,
0.43 «
0.42 <
0.41 «
0.40 ,

V

0 (cm’ cm°)

0.39
0.38
0.45
0.44
0.43
0.42
0.41

V

9 (cm3 cm“)

0.40 1
0.39 1

0.38

0.41 1
0.40 1
0.39 1

 

3cm

 

6cm

 

 

 

9cm

 

 

 

 

 

 

 

 

Figure 2.6.a. Soil water content proﬁles for a 150-cm column of loamy soil during
drainage cycle at 3, 6, 9, 12, 15 and 25 cm depths.

55

 

046

0.45 «
0.44 <
0.43 ,
0.42 -
0.41 -
0.40 «
0.39 -

9' (cm’ cm")

038

0.45 <
0.44 «
0.43 <

0 (cm8 cm")

V

0A01
0391

038

0451
0A41

9 (cm3 cm")

V

038

 

 

450m

 

 

0A21
0411

 

 

 

650m

 

 

0A31
0A21
0A11
0A01
0391

 

750m

 

 

1w)

10

10

Figure 2.6.b. Soil water content proﬁles for a ISO-cm column of loamy soil during
drainage cycle at 35, 45, 55, 65, and 75 cm depths.

56

 

038‘ 3cm ‘ 60m
0&1
0.3411

0&1

0&1

0,, ( 01113 cm’)

 

 

 

0381

 

0&1

0341

0&1

0&1

0,, (cm3 cm")

031

 

 

0v (em3 out")
p
a

 

‘ ------- Smlaed using Cd055
,— smaedts‘ngczmaadc

 

 

 

 

 

 

I,

0 1 2 3 4 5 6 7 8 9 100 1 2 3 4 5 6 7 8 9 10

l
l
1

Figure 2.7.a. Soil water content proﬁles for a ISO-cm column of sandy loam soil during
drainage cycle at 3, 6, 9, 12, 15 and 25 cm depths.

57

 

031 ﬁg“ ‘ XL 450“

051

 

0:4
032- ‘ ).

0:0 1

6,, (cm3 cm")

081
051
0241 1

0381 L 550m «
O o
. . A A J

0151

 

 

0341

0&1

 

0, (cm’ cm")

031 1

0241

(13+ \\ 750“ O 1 2 3 4 5 6 7 8 9 1O
. . . A A A A

031

 

 

 

 

 

0341
0:21

030,

9,,(001’ 01114)

0.81

0 mm
025, SmlaedusinngOSS
— Smiaadtsirgdalaedc

0211

 

 

 

Figure 2.7.b. Soil water content proﬁles for a 150-cm column of sandy loam soil during
drainage cycle at 35, 45, 55, 65, and 75 cm depths.

58

and sandy loam soil over using C of 0.55 for both soils (Figure 2.6.a, F ig.2.6.b, Figure
2.7.a, and Figure 2.7.b).

Using the calculated C for loamy and sandy loam soils gave better estimates of 1“
day drainage rate than using C of 0.55 (Figure 2.8). The measured lSt day drainage rate
was about 10 mm cl“l for loamy soil and about 22 mm d’1 for sandy loam soil (Figure 2.8).
The measured 1St day drainage rate for sandy loam soil was about double of that for
loamy soil partially because C was higher for sandy loam soil than that for loamy soil
and mainly because the drainable soil water for sandy loam soil was about twice that for
loamy soil. There were no signiﬁcant differences in estimating the drainage rate of loam
and sandy loam soils on other days between the different models (Figure 2.8). The over
all estimate of the drainage rate was reasonably accurate on all days of the drainage cycle
for the different models.

Measured and simulated cumulative soil water drainage at the end of a drainage
cycle was about 20 mm for loamy soil and 36 mm for sandy loam soil (Figure 2.9).
Measured and estimated cumulative soil water drainage at the end of a drainage cycle for
loam and sandy loam soils was essentially equal regardless of what C was used, because
measured and estimated cumulative soil water drainage at the end of a drainage cycle was
equal to the drainable soil water. Knowing and using the right 0, was important in
deﬁning the drainable soil water and as result in estimating the cumulative soil water

drainage.

59

24

 

Loamy soil

Drainge Rate (mm d")
S

 

0 i . . ...... . A

 

Sandy loam soil

 

 

 

 

20 '1
7'0
E 16 1‘
E
3
g 12 '1
0
DD
2 8
E
Q
4 -1
0
0 l 2 3 4 5 6 7 8 9

t(d)

Figure 2.8. Daily drainage rate of a 150-cm column of loamy soil and a 150-cm column of
sandy loam soil.

60

Field Results

Equation[20] was used to estimate C of proﬁle 1 and proﬁle 2 in Lansing area.
The calculated C was 0.48. The daily soil water contents were estimated better for proﬁle
1 using C of 0.48 than using C of 0.55 at 6, 9, 15, 25, 35, 45, 55, and 65 cm depths
(Figure 2.10.a, Figure 2.10.b). The daily soil water contents were estimated better for
proﬁle 2 using C of0.48 than using C of0.55 at 3, 6, 15, 25, 35, 45, 55, 65, and 75 cm
depths (Figure 2.11.a, Figure 2.11.b). These results showed that using 0.55
underestimated the soil water contents. The maximum negative difference between
simulated and measured soil water content was about 0.02 cm3 cm'3.

Using C of 0.48 for proﬁle 1 and proﬁle 2 gave better estimate of 1“t day drainage
rate than using C of 0.55 (Figure 2.12). There was no signiﬁcant difference in estimating
the drainage rate of proﬁle 1 and proﬁle 2 on other days between the different models
(Figure 2.12). The over all estimate of the drainage rate was reasonably accurate on all
days of the drainage cycle for the different models. Measured and simulated cumulative
soil water drainage at the end of a drainage cycle was about 104 mm for proﬁle 1 and
about 99 mm for proﬁle 2 (Figure 2.13). Measured and estimated cumulative soil water
drainage at the end of a drainage cycle for proﬁle 1 and proﬁle 2 was essentially equal
regardless of what value was used of C because measured and estimated cumulative soil
water drainage at the end of a drainage cycle was equal to the drainable soil water. Using
C of 0.55 overestimated the cumulative soil water drainage during the ﬁrst 4 days during

a drainage cycle (Figure 2.13).

61

 

 

 

 

 

    

 

 

 

 

Loamy soil
as -
’E‘
g 30 -
0:
c»
g 25-
O O
.3 2°- 11
E
3
E 15-
3
0
10 -
5
Sandy loam soil #sﬁ c 4.5
35 1
E
g 30 -
m
a:
10
.E 25 1
S
O ‘9
m 20 1
.g
S;
g 15 - A Collected drained water
3 0 Measured
0 ....... Simulated using C 010.55
10 1 Simulated using calculated C
5 r r r v I If I I
0 1 2 3 4 5 6 7 8 9

t ((1)
Figure 2.9. Cumulative drainage of a ISO-cm column of loamy soil and a 150-cm column
of sandy loam soil.

62

 

00

03m 30m , 60m

0,, ( m3 cm")
9
8

 

 

9,, (cm3 cm“)

 

 

 

9v (cm3 cm")

 

 

 

 

 

 

Figure 2.10.a. Soil water content proﬁles for proﬁle 1 of sandy loam soil during drainage
cycle at 3, 6, 9, 12, 15, and 25 cm depths.

63

 

6., (cm3 om")

 

 

 

0.31
015-,
0341
0.121

0131

9,, (cm3 cm")

 

 

 

 

 

'7 .m--Smiaedusinng0.55
(1311 1 —Smiaedusirgcaio.iaedc

9,, (cm3 cm")
§

 

 

 

 

Figure 2.10.b. Soil water content proﬁles of proﬁle 1 of sandy loam soil during drainage
cycle at 35, 45, 55, 65, and 75 cm depths.

64

 

0v ( cm“ cm'3)

 

 

9,, (01113 cm“)

 

 

0v (cm3 cm")

 

 

 

 

 

 

Figure 2.1 La. Soil water content proﬁles for proﬁle 2 of sandy loam soil during drainage
cycle at 3, 6, 9, 12, 15, and 25 cm depths.

65

 

9. (0111"1 cm“)

 

 

 

 

 

 

 

.r
"S
5.
02 L I ,
75a“ 0 1 2 3 4 5 6 7 8 9
am!
as, 0 Med
--------- SnuaedtsirngQSS
034, ——Smiaedusirgcalalaedc
48
5.

 

 

 

 

Figure 2.11.b. Soil water content proﬁles for proﬁle 2 of sandy loam soil during drainage
cycle at 35, 45, 55, 65, and 75 cm depths.

66

 

 

 

 

 

 

00
Profile 1
50 -
7'0
E 40
5
D
a 30 -
a:
0
3°
3 20 -
Q
10 -
o o
Profile 2
50 1
_A . .i‘.
it 40 _ 0 Measured
E '- ------- Simulated using C 010.55
v —— Simulated using calculated C
0
£6 30 1
0
DD
2
E 20 _.
Q
10 1
0 .
0 1

 

t(d)

Figure 2.12. Daily drainage rate of proﬁle 1 and proﬁle 2 of sandy loam soil.

67

Conclusions

A theoretical basis to explain the drainage coefﬁcient that is used in the water
balance of CERES family models was introduced. It was found that the drainage
coefficient is soil dependent. It was clear that the drainage coefﬁcient depends on the
initial soil water content. However, using a sole value of the drainage coefficient for each
soil is reasonable and simpliﬁes soil water drainage modeling. Two models were
developed to estimate the drainage coefficient from drained upper limit water content and
saturated water content. The new models gave good estimates of the drainage coefﬁcient.
Therefore, Eq. [21] is recommend to be used in the water balance of CERES instead of a
constant value of 0.55. A generic relationship between C and Q, was developed to
account for the effect of incoming ﬂow on the change of soil water content of a certain
soil layer.

A new deﬁnition to the drainable soil water was introduced. The new deﬁnition
made the drainage model in the water balance of CERES applicable under shallow soil
water table conditions. More studies are needed on the estimation of the ﬁnal soil water
content of a soil layer when that layer is affected by shallow water table. Estimating the
ﬁnal soil water content accurately would result in accurate predictions of soil water

contents during drainage cycle, drainage rate, and cumulative soil water drainage.

68

 

110

 

Proﬁle 1 .........................................

Q \I W \O O
O O O O O
m 1 1 1 1

CumulativeDrainge (mm)

{It
O
1

 

40

Proﬁle 2
100 1

80

l

70

l

 

60 1 0 Measured
' ........ Simulated using C of 0.55
—— Simulated using calculated C

Cumulative Drainage (mm)

 

 

 

40 1 l 1 r I r ‘1 1

t ((1)

Figure 2.13. Cumulative drainage of proﬁle 1 and proﬁle 2 of sandy loam soil versus time.

69

References

Ahuja, L.R., J .W. Nancy, R.E. Green, and DR. Nielsen. 1984. Macroporosity to
characterize spatial variability of hydraulic conductivity and effects of land
management. Soil Sci Soc Am. J. 48:699-702.

Ahuja, L.R., O. Wendroth, and DR. Nielsen. 1993. Relationship between initial drainage
of surface soil and average proﬁle saturated conductivity. Soil Sci. Soc. Am.
J. 57:19-25.

Black, T.A., W.R. Gardner, and G.W. Thurtell. 1969. The prediction of evaporation,
drainage, and soil water storage for a bare soil. Soil Sci. Soc. Am. J. 33:655-660.

Brooks, RH. and A.T. Corey. 1964. Hydraulic properties of porous media. Hydrology
Paper 3. Colorado State Univ., Fort Collins.

Brutsaert, W. 1967. Some methods of calculating unsaturated permeability. Trans. of
ASAE. 400-404.

Corey, AT. 1977. Mechanics of heterogeneous ﬂuids in porous media. Water Resour.
Pub., Fort Collins, CO.

Corey, G.L., A.T. Corey, and RH Brooks. 1965. Similitude for non-steady drainage of
partially saturated soils. Hydrology Paper 9. Colorado State Univ., Fort Collins.

Corwin, D.L., B.L. Waggoner, and J .D. Rhoades. 1991. A functional Model of solute
transport that accounts for bypass. J. Environ. Qual. 20:647-658.

Gabrielle, B., S. Menasseri, and S. Houot. 1995. Analysis and ﬁeld evaluation of the
CERES models water balance component. Soil Sci. Soc. Am. J. 59: 1403-1412.

Gerakis, A., and J .T. Ritchie. 1998. Simulation of atrazine leaching in relation to water
table management using CERES model. J. Env. Management 52:241-258.

Mualem, Y. 1976. A new model for predicting the hydraulic conductivity of unsaturated
porous media. Water Resour. Res. 12(3):513-522.

Mualem, Y. 1978. Hydraulic conductivity of unsaturated porous media: generalized
. 'macroscopic approach. Water Resour. Res. 14(2):325-334.

Montas, H.J., J .D. Eigel, B.A. Engel, and K. Haghighi. 1997. Deterministic modeling of
solute transport in soils with preferential ﬂow pathways-Part 1. Model
development. Trans. ASAE. 40: 1245-1256.

Philip, J .R. 1957. Numerical solution of equations of the diffusion type with diffusivity
concentration-dependent. 11. Aust. J. Phys. 10:29-42.

70

Ratliff, L. F ., J. T. Ritchie, and D. K. Cassel. 1983. Field-measured limits of soil water as
related to laboratory-measured properties. Soil Sci. Soc. Am. J. 47:770-775.

Reichardt, K., and DR. Nielsen. 1984. Field soil-water properties measured through
radiation techniques. IAEA-TECDOC-312. Joint F AO/IAEA Div. Isotope
Radiat. Appl. Atomic Energy Food Agric. Dev. Vienna.

Ritchie, J .T. 1998. Soil Water Balance and Plant Water Stress. p. 45-58. In Tsuji Y.,
Gordon Y.Tsuji, Gerrit Hoogenboom, Philip K. Thornton (Ed.) Understanding

Options for Agricultural Production. Kluwer Academic Publishers, Dordrecht.
ISBN 0-7923-4833-8.

Ritchie, J .T., A. Gerakis, and AA. Suleiman. 1999. Simple Model to Estimate
Field-Measured Soil Water Limits. Trans. ASAE. (Accepted).

Ritchie, J .T., J .R. Kiniry, C.A. Jones, and PT. Dyke. 1986. Model inputs. pp. 37-48. In
C.A. Jones and J .R. Kiniry (Ed.) CERES-Maize: A simulation model of maize
growth and development. Texas A&M Press, College Station, TX.

Schuh, W.M., and R.L. Cline. 1990. Effect of soil properties on unsaturated hydraulic
conductivity pore-interaction factors. Soil Sci. AM. J. 54: 1 509-1519.

Suleiman, A.A., and J .T. Ritchie. 1999. Estimating saturated hydraulic conductivity from
drained upper limit water content and bulk density. Trans. ASAE. (In review).

Vanderborght, J ., C. Gonzalez, M. Vanclooster, D. Mallants, and J. Feyen. 1997. Effect
of soil type and water ﬂux on solute transport. Soil. Sci. Soc. Am. J. 61:372-389.

Youngs, E.G. 1957a. Redistribution of moisture in porous materials aﬁer inﬁltration: 1.
Agricultural Res. Council of Soil Physics. 117-125.

Youngs, E.G. 1957b. Redistribution of moisture in porous materials after inﬁltration:2.
Agricultural Res. Council of Soil Physics. 202-207.

Zacharias, S., and K. Bohne. 1997. Replacing the ﬁeld capacity concept by an internal

drainage approach -- A method for homogeneous soil proﬁles. SCIENCES of
SOILS, Rel. 2, 1997 - http://www.hintze-online.com/sos/1997/Articles/Art2.

71

CHAPTER THREE
ASSESSING AND MODELING DOWNSLOPE LATERAL SOIL WATER FLOW
ALONG A SLOPING LANDSCAPE
Introduction

Water is the medium in which biological and chemical transformations of
nutrients occur and in which different nutrient forms move and are transported in the soil
proﬁle, either to plant roots or out of the proﬁle and eventually into the ground water
(Nielsen et al., 1973). Within a sloping landscape, soil water may move laterally from one
soil proﬁle to another carrying nutrients with it. Such movement of soil solution could be
a main reason behind the spatial variability of crop yield within sloping landscapes.
Effective management of soil water within agricultural landscape requires a solid
understanding of the mechanisms that regulate soil-water-landscape interaction. Soil
physical properties and the amount of soil water within a sloping landscape are largely
determined by landscape position (Rosek, 1995).

Lateral downslope saturated and unsaturated soil water ﬂow in the root zone of a
hillslope with homogeneous and heterogeneous soils has been observed (Beven, 1982;
Jackson, 1992; McCord et al., 1991; and Tsuboyama et al., 1994). McCord and Stephens
(1987) conducted a tracer study that showed a strong lateral downslope component in
vadose ﬂow in sand dunes with surface s10pe of 23° (Jackson, 1992). That led them to
conclude that even in permeable sandy locations, where the soil proﬁle is uniform and
deep, water will ﬂow laterally downslope on the hillside. McCord et a1. (1991) showed
that for all conditions except high constant anisotropy, signiﬁcant lateral downslope ﬂow

occurred only during drainage. The lateral downslope ﬂow can become more signiﬁcant

72

when the soil has highly permeable layers, cracks, or cavities (Wallach and Zaslavsky,
1991)

Many scientists have attempted to model the lateral downslope soil water ﬂow
using a mechanistic approach. Most of these models are numerical such as Beven (1982),
Bouraoui et al. (1997), Hillel (1977), Nieber and Walter (1981), and Smith and Hebbert
(1983). Few have tried to ﬁnd analytical models for simpliﬁed cases such as Philip
(1991), Stagnitti et al. (1986), and Warrick et al. (1997). On the other hand, no attempt
has been made to produce functional models to simulate lateral downslope soil water
ﬂow.

The water balance of the CERES family soil-water-crop-atmosphere simulation
models lack a lateral downslope ﬂow component since it was built to simulate soil water
redistribution in the vertical dimension. Although lateral downslope ﬂow is not
considered in CERES model, runoff is considered and simulated using time-to-ponding
concept (Gerakis and Ritchie, 1998). Modeling the lateral downslope ﬂow and
incorporating it into the water balance of the CERES model will enable the model to
account for both surface and subsurface downslope ﬂow and to simulate the spatial
variability of crop yield more accurately.

The objective of this study was to develop a simple functional model to simulate
lateral downslope soil water ﬂow and incorporate such a model within the water balance
of CERES model. To do so, the new functional lateral downslope model has to be simple,
accurate, and not required additional inputs more than those required by the CERES

models as a minimum data set.

73

Theory

To study the lateral downslope drainage ﬂow along a sloping landscape, a layer of
isotropic homogeneous soil is considered along a planar hillslope. The slope angle is y.
Cartesian rectangular space coordinates x and z, with x taken positive in the horizontal
downslope direction and 2 positive in the downward vertical direction are introduced.

Rotated co-ordinates (x., z.) are introduced and deﬁned by (Figure 3.1).

x. = xcosy + zsiny

. (1)

z. = —xsmy + zcosy
The lateral downslope flow (q, cm (1") ( ﬂux in x. direction) subject to the
following initial and boundary conditions
9: 93 t = 0 z. 2 O
2

6<65 t>O z.20x.=0 ()
can be described by:
q = K(6)sinr (3)

where K(B) is soil water hydraulic conductivity (cm d"), 6 is soil water content cm3 cm‘3,

t is time (d), z is distance (cm), and sin y is the slope and it is equal to the hydraulic

74

 

 

 

 

Figure 3.1. Cartesian rectangular space coordinate x and z
and rotated coordinates x. and 2..

75

gradient (ah/ax). If for some reason (e. g., irregular slope) ah/ax is not equal to sin y,
ah/ax has to be used in Eq. [3] instead of sin 7. At t = O, the equipotential lines are
horizontal which results in ﬂow in the z direction only. At t > O, equipotential lines
perpendicular to the downslope surface will be formed resulting in a downslope ﬂow
component. Many scientists have found that Eq. [3] can be used to describe lateral
downslope ﬂow under different initial and boundary conditions (Jackson, 1992; Philip,
1991; Stagnitti et al., 1992).

The change of soil water content in 1 day (A0) subject to (2) can be described as:

A a: C(Q. - 6d,,)sinym Az (4)

where C sin y is the fraction of soil water content that can be drained from the soil layer
in a day.

Using the theory of vertical drainage as introduced in the previous chapter, C can
be calculated as follows:

(1— Csin7)n
1+‘(1 - Csiny)"

 

C=a (5)

where a can be written as:

6 — 6?
a=150(-‘-——4-"-'-) (6)

2
gdul

and n can be described as:

76

n = 0.8 + 29.39,", (7)

In case of inﬁltration, the inﬁltrated water can be assumed to ﬂow vertically (z
direction) only (Jackson, 1992; 1993). In case of an isotropic homogeneous soil
overlaying an impervious layer, the vertical ﬂow component will stop on the interface
between the soil and the impervious layer and a lateral downslope ﬂow component will
start parallel to the impervious layer. A maximum lateral downslope ﬂux (q,, cm d"), in
this case, occurs when the soil is saturated and the inﬁltration rate is equal to q,. Saturated
hydraulic conductivity (K) has to be used in Eq. [3] instead of K(O) to describe the
saturated lateral downslope ﬂow. According to Suleiman and Ritchie (1999), Ks (cm (1")

can be estimated as follows:

2
6:— a...) (8)

K, = 75[ ——
gdul

where 95 and 0d“, are saturated and drained upper limit soil water contents, respectively.

In general, soils on a real hillslope are never isotropic. Both saturated hydraulic
conductivities and porosities tend to decrease with depth into the soil proﬁle, sometimes
with signiﬁcant layering or other irregularities (Beven, 1982). Quite so often, impervious
layer may exist within the root zone or close to it causing signiﬁcant lateral ﬂow.
Anisotropy and layering could result in signiﬁcant lateral downslope ﬂow during
drainage (McCord et al., 1991) since they would give more time for the drainable soil
water to move laterally downslope than if the soil was isotropic and homogeneous.

Dividing a soil proﬁle into many layers as in CERES-WHEAT water balance and

77

assuming that each of them has homogenous and isotropic soil facilitates using the above
theory in ﬁeld situation.

The water table depth (WT, cm) due to lateral downslope soil water ﬂow
assuming that (1) there is no water loss during vertical drainage out of the proﬁle because
of an impervious layer, (2) water loss due to evapotranspiration does not affect the WT,

and (3) inﬁltration is zero, can be described as follows:

WT. = WT,-(1— Csmy)“ (9)

where WT, is initial water table depth (cm), L is an integer equal to 1 at day 1, then 2 at

day 2 and so on.

Material and Methods
Data Collection

A ﬁeld experiment was conducted to study the lateral downslope water ﬂow along
a sloping landscape in East Lansing, MI. A 100 m x 600 m ﬁeld was planted to AC Ron
(described in Teich et al., 1992) winter wheat variety on October 19, 1997 and harvested
on July 11, 1998. In order to monitor the soil water content at different landscape
positions along the slope, ﬁfteen ISO-cm access tubes were installed 20-m apart after
planting along a transect perpendicular to the contour lines (Figure 3.2). To label the
locations in which access tubes installed, the Ma north location was labeled as L1, the
second further north was labeled as L2, and so on until L15. A neutron probe reading
was taken in November 15' 1997. Other neutron probe readings were taken from April 15,

to harvest in 1998, once a

78

 

    

height (cm)

   

—— Soilsurfaco
0 WT on DOY124
A

 

 

 

 

50 ° WTonDOY 14s
0 A 150 cm below soil surface
1 2 34 5 6 7 8 9101112131415

Access Tube Locations

Figure 3.2. (a) Elevation , slope, and access tube locations within the ﬁeld. (b) relative
soil surface height, water table (WT) height, and the restricted layer (at 150 cm depth).

79

week and aﬁer rain events at 15, 30, 45, 60, 90, 120, and 150 cm depths. Three sets of
time-domain reﬂectometry (TDR), SO-m apart, were installed on May 1, 1998 at the top
of the hill (L10), in the middle of the southern hillside (between L12 and L13), and on the
bottom of the southern slope (L15) along a transect parallel to the access tube transect to
capture the detailed change of soil water content at different landscape positions.
Automated readings of the TDR probes were taken bi-hourly until the harvest. Fifteen
ISO-cm observation wells were installed along a transect parallel to the access tube
transect to monitor the water table level. Manual readings for the water table levels were
taken at the same dates neutron probe readings were taken from the date of installation
(April 28 ) to June 3, 1998 (on which water table was below 150 cm depth). A weather
station was installed on the top of the hill (L10) to record hourly temperature, solar
radiation, and rainfall. Daily maximum and minimum temperature, solar radiation, and
rainfall are shown in Figure 3.3. Three other rain gages ISO-m apart were installed along
a transect parallel to the access tubes transect to assess the spatial variability of rainfall.
Manual measurement of these rain gages were done after rain events. Along the transect
of access tubes, leaf area index (LAI) was measured near each of the access tubes about
weekly from April 15 until anthesis date (June 4) using LAI-2000. Leaf area index (LAI)
is needed to estimate crop transpiration (Ritchie, 1972). CERES-WHEAT was run to
estimate LAI during the entire season assuming there were neither water nor nitrogen
stresses. Then, the measured LAI using LAI-2000 was used to produce more accurate

LAI at each location during the growing season.

80

 

 

 

 

 

lll‘lumola ‘1511
o o o Jo o o .ﬂ‘wonb mw
Q o o
do o u o o0
if o o 0 go
o o ooo o oo o a“, o %
O 0" ‘0 O O ‘0 .‘w 000
0‘0 ‘ 0 “v ‘mmunmwy
O O ‘ Q 0 O ’0 0
oo w o o‘o o o & we
Jo o o..o o 0..
"Mtg. n".o C. Amumwummwmo
oo ooOo. oo o oOoopc Woo. 0 ©
.0 . “O O '0 ‘4“ quO
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Jo“ o ‘ood.
~ 0. 3m 00
. . . . 8.. a . . 55% are
f: 26 53.2va aﬂow 90V 9223th .

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0 5 0 5 0
2 1 1
955 __ac_mm .

50 75 100 125 150 175 200

25

DOY

Figure 3.3. Daily solar radiation (MJ m’z), temperature (C°), and rainfall (mm) from

DOY 1 through DOY 200 in 1998.

81

Site Description

The soil of the 6 ha ﬁeld is classiﬁed as Capac series. According to soil survey, a
Capac series consists of somewhat less poorly drained, moderately and moderately slow
permeable soils on till plains and moraines. These soils formed in medium and
moderately ﬁne textured deposits. While installing the access tubes, disturbed soil
samples were taken from 0-15, 15-30, 30-60, 60-90, 90-120, and 120—150 cm from each
proﬁle. Clay, sand, total nitrogen, and organic matter contents were determined for each
soil sample and are shown in appendix A. The soil water limits were estimated using a
procedure described in Ritchie et al. (1999). The elevation was measured at about 300
representative locations in the ﬁeld using a theodolite. The elevation ranged from about
91 to 97 m and the slope ranged approximately from 0 %t012 % (Figure 3.2).
TDR Description

Regular continuous and discontinuous 3-rod TDR probes were used to monitor
the soil moisture during the growing season (Top and Davis, 1985; Baker and Allrnaras,
1990) (Figure 3.4). A 20-cm regular continuous TDR (TDR20) and lS-cm regular
continuous TDR(TDR15) were used to measure soil moisture at soil surface.
Discontinuous TDR probes of ISO-cm (DTDR150) were used to measure soil water
proﬁle. As it is shown in Figure 3.4, each rod of DTDR150 consists of 5 parts (15, 20, 25,
25, and 25 cm, respectively) of 12.5 mm in diameter and 4 parts (10 cm each) of 6.3 mm
in diameter. All the parts of 6.3 mm in diameter were coated with resin to make their
diameter equal to 12.5 mm. Resin was chosen since it is a dielectric material. Each one of
these discontinuities was used to separate two 12.5 mm parts. A typical wave for

DTDR150 is shown in Fig.3.4.

82

 

 

 

 

“13 OSl

 

 

 

 

 

 

 

 

4000
3000 4

2000 -<

1000 j

Reﬂectance
o

-1000 -+

-2000 4

-3000 <

 

 

 

-4000 r r Y r T l f r I r 1 v
0 10 20 30 40 50 60 70 80 90 100110120130

Reading Number

Figure 3.4. A discontinuous TDR probe (DTDR150) and a typical wave.

83

Each set of TDRs consisted of 5 TDR20, 1 TDRlS, and 1 DTDR150 except the
one that was located between L12 and L13 where only 4 of TDR20 were used. The 5
TDR20 were installed horizontally at 3, 6, 9, 12, and 15 cm depths to capture the
dynamic and fast change of soil surface layer water content, while TDR15 and DTDR150
were installed vertically. The TDR15 was used to integrate the soil water content of the
surface layer. The DTDR150 was used to measure the average soil water content from 0-
15, 25-45, 55-80, 90-115, and 125-150 cm.
Data Analysis

The lateral downslope soil water ﬂow (L, m) was calculated as follows:

Lzl-E—AS—D

(10)

where I is inﬁltration (mm), B, is total evaporation and it is equal to soil and plant
evaporation (mm), AS is the change of soil water storage (mm), and D is vertical drainage
(mm). Inﬁltration and E' were estimated using CERES-WHEAT. The change of soil
water storage was calculated from the difference between soil water content
measurements. Vertical drainage was assumed zero because an impervious layer was

preventing soil water to ﬂow vertically out of the proﬁle.

Results and Discussion
Trial and error procedure was used to solve Eq. [6] to ﬁnd C at representative
combinations of 0,, OM, and sin y. A power function relationship between C, sin y and 0d,.

was shown in Figure 3.5. This relation can be described as:

84

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Sin y

Figure 3.5. Relationship between C and C sin y with sin y and 9am at

representative combinations of 0d,. and sin 'y.

85

C: a,(sin7)b' (11)

where al and b1 are functions of 0d,. and can be calculated as follows:

a, = 4.4169,, +1.02
and (12)
b, = — 127%,2 + 0.9919,“, — 0.88

The developed relationship can be used to estimate C directly from 911111 and sin 7
instead of using trial and error to solve for it. As it is shown in Figure 3.5 and Eq. [11]
and Eq. [12], C is dependent on both sin y (slope) and 0d,“. The higher sin y and greater
9.11.1 the lower C and vise versa. Although C can be greater than 1, C sin 7 must be less
than 1 because C sin y is ratio between the soil water that may drain in a day and total
drainable water.

Numerical solution was used to investigate the impact of x. on the daily change of
soil water content (0) of 1 cm thick by 200 cm long isotropic homogeneous layer of soil
of uniform slope overlaying an impervious soil layer during lateral downslope soil water
ﬂow subject to (2) for 1 day. A time increment of 1 min and distance increment of 1 cm
were used assuming that the hydraulic conductivity is constant during a time step of 1
min at any x., 9 is uniform within a distance step of 1 cm at any time, and sin y is the
hydraulic gradient during the 1 day drainage. Representative combination of 0,, 0d,], and
sin 7 were used in the numerical solutions to ﬁnd a relationship between C. (the fraction
of soil water content that can be drained from the soil layer in a day at x. ) with C and x.

(cm). A logarithmic relationship between C. and x. and a linear relationship between C.

86

 

0.5

 

 

 

o

0.4-
t
O

0.3-'

0x

021

0.1-

0.0 I I I I I I T
o 25 50 75 100 125 150 175

X (cm)

Figure 3.6. Example of a typical relationship between Cx and x. for a soil.

87

and C were found and they are shown in Figure 3.6. Using these relationships, C. can be

obtained as follows:

C. sin y = 1.13C sin y - 0.0771n(x.)- 0.03 (13)

if the calculated C. sin y is less than 0 then it is assumed 0.

Using Eq. [11] and Eq. [13] sufﬁces to describe lateral downslope drainage
subject to (2). In many cases, non uniform slope and two dimensional lateral downslope
soil water ﬂow may complicate the use of Eq. [13]. An assumption can be made that x.
has no impact on q. Parlange et a1. (1986), Stagnitti et al. (1992), and Wallach and
Zaslavsky (1991) have implemented similar assumption. Such an assumption maybe
reasonable for watershed hydrology to estimate total drainage but to determine soil water
content at any position within a ﬁeld, such an assumption may decrease the accuracy of
estimation. Another way of dealing with this problem is to study the relationship
between incoming ﬂux (Q1, cm d")) and C to a proﬁle. Such relationship will remove the
confusion of determining x. and its impact on C. More importantly, it will make it
possible to combine the lateral downslope soil water ﬂow model with a geographical
information system (GIS) ﬁamework.

A generic relationship between Cp sin y (C sin y at any landscape position) and Q,

can be introduced as follow:

Cpsinyz a+b1n(Q,.+¢,) (14)

where (I)c (cm3 cm'3) is soil effective porosity and equal to 0S - Gdul. Having in mind that

(1) when Qi = 0, Cp has to be equal to C and (2) when Qi = KS sin y, Cp is 0, a and b can

88

be deﬁned as follows:

a = —b 1n(K, sin y)

and (15)
C sin y

1n(¢,)— 1n(K, sin 7)

 

b:

To explain Eq. [14] and Eq. [15], let us assume that a soil layer overlaying an
impervious soil layer was located within a sloping landscape. The following were known:
0, = 0.4 cm3 cm‘3, 0dul = 0.2 cm3 cm”, and sin y = 0.5. The initial and boundary conditions
are similar to (2). Using Eq. [11] and Eq. [12], C sin 7 was found to be 0.32. Using Eq.
[15], a was found to be 0.221 and b was found to be -0.061. Now, assuming that Q,
ranged from 0 cm cl’l to 50 cm d“, applying Eq. [14] Cp sin 7 against Q, was plotted and
shown in Fig.3.7. It was clear that C,, sin 7 was equal to C sin y when Qi was 0 and Cp sin
7 was equal to 0 when Qi was equal to K, sin 7 (37.5 cm d"). When Qi was greater than
K, sin 7 (37.5 cm d") C,, sin y is assumed to be 0 and only K, sin 7 (37.5 cm (1") ofwater
can pass through the soil layer.

In case of a proﬁle that has both unsaturated layer on the top of a saturated soil
layer that is overlaying an impervious layer, only vertical drainage is assumed to occur in
the unsaturated layer.

Water table

A shallow water table was evident at all the observation well locations from April

89

0.35 *

 

 

 

 

 

050.2001an"
030
Kc.sin=37.5cmd‘
oas~
a=0.221
0.204 11:00:51
0
0.15«
0.10-
0.05-
0.m I *I T 7* l I
0 5 10 15 20 as 30 35 40

q (and‘)

Figure 3.7. Example of a typical relationship between Cp and Qi for a soil.

9O

28 through May 22 . On May 26, the water table level was below ISO-cm for most of the
observation wells (Figure 3.2). Existence of a water table in a sloping landscape is a
sufficient proof of a lateral downslope soil water ﬂow and depending on the slope such
lateral downslope soil water ﬂow can be signiﬁcant since part of the soil proﬁle is
saturated. The shallower a water table level is, the greater lateral downslope soil water
ﬂow is, since more of the soil proﬁle would be saturated and hence would contribute
more signiﬁcantly to the lateral downslope soil water ﬂow.

The change of a water table level at a certain location depends on E” I, incoming
and outgoing lateral downslope soil water ﬂow, vertical drainage from upper soil layers,
depth of the impervious layer and its effectiveness (depending on its K,). The simulated
(using Eq. [9]) and measured change of water table from DOY 124 to 146 was in good
agreement at most access tube locations (Figure 3.8). The root mean square error (RMSE)
was 2.84 cm during 22 days (from DOY 124 to 146). The maximum water table depth
change was about 120 cm at L5 and the lowest was about 50 cm at L2.

Leaf Area Index

A signiﬁcant grth of wheat and increase of LAI occurred on about DOY 105
and continued through DOY 130 (Figure 3.9.a and 3.9.b). A slow decrease of LAI started
on about DOY 130 until about DOY 160, after which a rapid reduction of LAI took place
until DOY 185 at all locations. Some variation of LAI at different location was noticed as
early as DOY 115. Maximum LAI varied within these locations and ranged from 1.7 at
L5 to 3.3 at L15. The standard deviation of LAI was greatest when the mean LAI was

highest on about DOY 133.

91

 

Change of WT (cm)

 

o Neasued
' -—Simlated

 

 

 

I I I I I I I

123456789101112131415
AmubeLocations

Figure 3.8. Measured and simulated change of soil water table depth (cm) from DOY
124 to 146.

92

 

3.5
3.0 < L1 1 L2
2.5 " 4

1.0 1

" O
o
5 'o
0. 1 .
‘ .' J .9
L j.

00

 

3-0 1 L3 1 L4

2.5 1 1
21). 4 ";ir-.-I.......“‘£
1.5 1 . o
'
o
1.0< I < .’ '-
o ’ .o
C .
0.5 1 o .
L ’—

01)

LAI

 

3.0 J L5 J L6

2.5 1 1 4'
2.0« < /
o
1.5 1 < ' '
:' '1.
10 1 1 ¢ 0
o
' 0
(L5 1 1 o
"’ o
(L0 J—. g_

3131
2.5 1 ,

I
1.5 1 1

(L5 1 f'

O_O . . v —r . i Y Y .
100 120 140 160 180 100 120 140 160 180 200

UN

 

LAI

 

 

 

 

Figure 3.9.a. Corrected simulated LAI at Ll through L8 from DOY 90 through 200.

93

(o)
0’!

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3.0 L9 L10
2 5 4 4
I
_ 20
s i
1.5 ; o
.- z -
1.0 1 ’0 ‘. 1 f .
’ o ; o
0.5 1 '. . 0.
J o J ..
0.0 '- 9—
3.0 « L11 4 “2
2.5 1
_ 2.04 I {I
5 1s 4 (I ‘
- o O 0
O O o O
O . . C
10 ‘ 0 '. - °
' i o I ..
’. I o
0.5 ‘J O 4 f ..
0.0 1; ’-
L13
3.01 j L“
2.5 1 .
’ ”\
_ 2.0 1 Z 1 /
o 'o
5 . O ' o
1.5 1 ' .. ‘ . 0
.° 0. 0 ‘.
1.0 « ; 0. I. '.
I o I o
0.5 1 / o </ o
O .
0.0 ‘- '-
3.0 1 L15
I ("p 11
2-5 ‘ ’9 jIIIII.
' .
5 1.5 < : °.
‘ '.
1.0 1 {I o
C
0.5 1 ° 0 loan
1 o
0.0 . . . v . 1: 1 - . . , .
100 120 140 160 180 100 120 140 160 180
DOY DOY

Figure 3.9.b. Corrected simulated LAI at L9 through L15 from DOY 90 through 200 and
mean and standard deviation of LAI for the 15 locations.

94

Total Evaporation and Inﬁltration

Mean and standard deviation of simulated actual (Em) and potential (Em) daily
evapotranspiration at all locations during the entire growing season are shown in Figure
3.10. There were no signiﬁcant differences at different locations in respect to Em and E,,,.
Daily En ranged from 0.5 mm to 4.5 mm, whereas daily Etp ranged from 1.5 mm to 7.5
mm. The highest Em occurred when soil surface was wet as on DOY 100 and 180. It was
noticed that daily simulated Em decreased continuously from about 3.5 mm on DOY 125
to about 0.8 mm at DOY 151 because of dry conditions from DOY 125 through 151.The
CERES-WHEAT underestimated Eta because it is sensitivity to water stress. Because the
water table could have supplied enough water to wheat root to prevent any water stress, it
was assumed that Em was equal to Etp during the period from DOY 124 to 146.

There was clear evident in the ﬁeld that signiﬁcant runoff took place between
DOY 95 and DOY 124. The runoff mainly resulted because of the heavy rainfall events
that occurred during that period (Figure 3.3)and because the soil was saturated. On the
other hand, only six rainfall events occurred from DOY 125 through DOY 151 on DOY
125, 126, 129, 132, 134, and 145. The inﬁltration at all these dates was assumed to be
equal to rainfall because each one of these rainfall events was less than 3.1 mm (Figure
3.3).
Lateral downslope soil water flow

The duration from DOY 124 through 146 was selected in order to study the lateral
downslope soil water ﬂow during it because during this period inﬁltration could be
estimated accurately and a shallow water table was present at all locations. Estimated C

ranged from about 5 to about 35, whereas estimated C sin y ranged from about 0.12 to

95

 

 

 

 

 

 

 

 

 

 

 

 

 

7, o 5,3("11'1
—o—Et,("m)
61
,5" 51
‘0
E 4. 1- ‘ T l' ..
£5, 0 .
.. y o l ..
LU 3- v .. o] ..
H ._ .. ., ,
2-- i 1 .. ' l
0 I I I I I I I I I I
124 1% 128 13) 13 134 13 13 140 1Q 144 16
[IN

Figure 3.10. Mean and standard deviation of simulated daily actual (Em) and potential
(Em) evapotranspiration from DOY 124 to 146.

96

4O

35

30

25

15

10

025

020

Csiny

015

 

 

 

 

 

Access Tube Location

Figure 3.11. Estimated C and C sin y at all access tube locations.

97

o
o
o
o
o
o . . 0
.o' Co
o
o
o
o o o
o
o o
o
o
o
2 3 4 5 6 7 8 9 1O 11 12 13 14 15

28 through May 22 . On May 26, the water table level was below 150—cm for most of the
meanwhile C sin 7 was highest at these locations. On the contrast, C was greatest at L2,
and L15 and C sin 7 was minimum at these locations. The driving force for lateral
downslope soil water ﬂow is sin y (slope), yet C sin 7 determines the amount of lateral
downslope drainage.

Estimated and measured cumulative lateral downslope drainage (L, m) during
that duration (22 days) for 3 different periods (124-132, 132-140, 140-146) at different
access tubes locations are shown in Figure 3.12. During 124-132, estimated and measured
cumulative L was in good agreement with RMSE of 4.41 mm. The L ranged from about
30 mm to 55 mm during DOY 124-132. During 132-140 and 140-146, estimated and
measured cumulative L was relatively in good agreement with RMSE of 16.3 mm and
8.7 mm, respectively. The higher RMSE in these two periods, 132-140 and 140-146,
could have resulted from uncertainties of estimating Em. However, in general the new
lateral downslope soil water ﬂow model performed good in estimating the downslope
lateral soil water ﬂow at most access tube locations during the 3 periods.

Time domain reﬂectometry (TDR) measurements at the middle between L12 and
L13 showed more details about lateral downslope results than was obtained from neutron
probe measurements (Figure 3.13). The estimated daily L was in good agreement with the
measured ones with RMSE of 1.81 mm d". The simulated L was close to measured L on
DOY 125, 126, 127, and 128 and 136 through 146. From DOY 129 though 135, deviation
between measured and simulated daily L was evident. This deviation can be contributed
to uncertainties of estimating Em. The maximum absolute difference between daily

measured and simulated L was about 4 mm on DOY 131. From DOY 137 through 146,

98

L (mm)

L (mm)

L (mm)

60

20

50

4O

3O

20

-20

50‘

40

30

20

10

-10

-20

 

124-132

RMSE = 4.41 mm

 

 

.1

A1
v

132-140

RMSE =16.3 mm

 

 

140-146

RMSE = 8.7 mm

0 Measured
— Simulated

 

 

I I

5

6

V

7

1

I

I I V T

10 11 12 13

Access Tube Locations

Figure 3.12. Measured and simulated cumulative lateral down slope (L) ﬂow at all
access tube locations from DOY 124-132, 132-140, and 140-146.

99

 

1‘ ‘ RMSE=1.81mnd1

o Measued
- ——Estirrated

L(mmd'1)
O.) A 01 O) \l on (D

2.1
1..

O
124 126 128 130 132 134 13 138 140 142 144 146

DOY

 

 

 

 

Figure 3.13. Measured and simulated daily lateral downslope soil water ﬂow (L) at the
middle ofL12 and L13.

100

measured daily L was assumed 0 whenever negative values was calculated.

Conclusions

A generic simple functional model was developed to simulate daily lateral
downslope drainage along a hillside. Saturated and drained upper limit soil water contents
and slope angle (or the hydraulic gradient) are needed to run the new lateral downslope
soil water ﬂow model. The developed model was built based on physical basis and tested
with real ﬁeld data. Although the new model is simple, it performed well under ﬁeld
conditions.

The developed lateral downslope soil water flow model was built in a way that
makes it possible to link it to a GIS package. A GIS can determine the directions of
stream ﬂow lines, while the lateral downslope model can account for the amount of soil
water that may drain in a day at any position of a landscape. Such combination will
produce a two-dimensional lateral downslope soil water ﬂow.

Future studies are necessary to evaluate the developed lateral downslope model
under different environmental conditions and for diverse soils within different
landscapes. Minimizing the soil water balance variables (as studying lateral downslope
soil water ﬂow from a saturated soil with its surface covered) will help verify the model
more accurately. Other useful studies will be that link the new lateral downslope model to
a GIS framework because that will produce simple yet powerful functional two

dimensional lateral downslope soil water ﬂow models.

101

References

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103

CHAPTER FOUR

ASSESSING AND MODELING THE SPATIAL VARIABILITY OF WHEAT YIELD
WITHIN A SLOPING LANDSCAPE

Introduction

Differences in crop production within agricultural ﬁelds vary by a factor of two to
four (Bouma et al., 1995). Field variability of crop yield is a consequence of variations in
the genetic properties of plants and in the microenvironment (Bresler et al., 1981). Within
a ﬁeld, variability of crop yield is a primarily consequence of environmental factors since
the genetic properties of the plants are similar. Among environmental factors, soil
variability is the major cause of variation of crop yield in a given ﬁeld. Although,
climatic variables (solar radiation, air temperature, and precipitation) do vary within a
ﬁeld, they can be assumed to be constant. Soil variability can be attributed to variations in
soil properties, such as hydraulic conductivity, drained upper limit soil water content,
and cation exchange capacity, and variations in other soil variables, such as soil water,
soil nutrients, and organic matter. (Bemdtsson and Bahri, 1995).

Among the various environmental stress factors that limit global crop
productivity, water deﬁcit is probably the most limiting factor (Boyer, 1982). The nature
and extent of damage, the ability of a plant to recover, and the degree to which the
economic yield of a crop is affected depend on the developmental stage at which a plant
encounters water deﬁcit (Saini and Lalonde, 1998). Movement of water from one soil
proﬁle to another may be enough to prevent such water deﬁcit or reduce its impact in
some areas within a ﬁeld.

Sloping landscapes enhance the spatial variability of crop yield within a ﬁeld

104

because they heighten the variability of soil properties as well as soil variables. The soil
water downslope ﬂow, surface and subsurface, causes differences in amount of soil water
available to plants Werity and Anderson, 1990; Halvorson and Doll, 1991), depth of
topsoil (Pennock and de Jong, 1990), and nutrient availability. A signiﬁcant relationship
between crop yield and landscape position has beenrdemonstrated by several researchers
(Fiez and Miller, 1995; Halvorson and Doll, 1991; and Moulin et al., 1994).
Measurements and analysis of the spatial variability of ﬁelds are two important aspects of
site-speciﬁc crop management (Yang et al., 1998). However, assessing the spatial
variability of soil properties and crop yield by classical techniques is time consuming and
expensive. Remote sensing, on the other hand, could provide inexpensive large-area
estimates of crop variability within a ﬁeld. In a study on a wheat ﬁeld, Mass (1993)
demonstrated that the use of remotely sensed infrared images enabled a crop simulation
model to predict the crop yield quite accurately. The CERES-Wheat model, as described
by Ritchie and Otter (1985), has been used to simulate cr0p yield accurately when all the
input data are available. Integrating CERES-WHEAT model with remote sensing is a
good approach to simulate crop yield variability within a ﬁeld because in most cases data
that characterize soil variability within a ﬁeld are not available.

The objectives of this research were to (1) assess the spatial variability of soil
properties and variables, leaf area index (LAI), and wheat yield within a sloping
landscape, (2) evaluate the performance of CERES-WHEAT model within a sloping
landscape, and (3) integrate remote sensing and CERES-WHEAT to simulate the spatial

variability of wheat yield within a sloping landscape.

105

Materials and Methods

A ﬁeld experiment was conducted to (1) assess the spatial variability of soil
properties and variables, leaf area index (LAI), and wheat yield within a sloping
landscape, (2) evaluate the performance of the CERES-WHEAT model within a sloping
landscape, and (3) integrate remote sensing and CERES-WHEAT to simulate the spatial
variability of wheat yield within a sloping landscape. A 100 m x 600 m ﬁeld was planted
to AC Ron (described by Teich et al., 1992) winter wheat variety on October 19, 1997
and harvested on July 15, 1998 in East Lansing, MI. In order to monitor the soil water
content at different landscape positions along the slope, ﬁfteen 150-cm access tubes were
installed 20-m apart after planting along a transect perpendicular to the contour lines
(Figure 4.1). To label the locations in which access tubes installed, the further north
location was labeled as L1, the second further north was labeled as L2, and so on until
L15. A neutron probe reading was taken on November 15, 1997, right after the
installation of the access tubes. Other neutron probe readings were taken from April 15,
until harvest in 1998 at one week intervals and after rain events. Measurements were
made at depths of 15, 30, 45, 60, 90, 120, and 150 cm. Another access tube (L16) was
installed in an area that showed less plant growth within the southern part of the ﬁeld in
mid May 1998. This area was selected based on a remotely sensed image that was
captured on April 28. The location access tubes is shown in Figure 4.1. Daily maximum
and minimum temperatures, solar radiation, and rainfall were recorded and shown in
Figure 4.2 and Appendix B. Three other rain gauges were installed 150-m apart parallel
to the access tubes transect to assess the spatial variability of rainfall. Manual

measurements of these rain gauges were done after rain events. Along the transect of

106

_

w unuuuu

“121‘“

n.3- ..._ 5....

 

 

Figure 4.1. Elevation, contours, slope, and access tube locations within the experimental ﬁeld.

107

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Figure 4.2. Daily solar radiation, maximum (T max) and minimum (Tmin) temperature,

and rainfall from DOY 1 through 200 in 1998.

108

access tubes, leaf area index (LAI) was measured near each of the access tubes weekly
from April 15 until anthesis date (June 4) using LAI-2000 (LI-COR, model LAI-2000)
(Welles and Norman, 1991). Four infrared images were captured by an airplane on April
4, April 28, June 4, and July 10, 1998 to assess the spatial variability of wheat growth
within the ﬁeld (Figure 4.3).

Using a square of 1 m2, plant density was counted near each access tube location
on April 15, 1998. Two 1 m2 wheat samples were harvested manually near each of the
access tube locations to measure heads number, grain per head, head weight, unit grain
weight, grain number, and grain yield on July 10, 1998. The ﬁeld was harvested on July
15, 1998 using a combine equipped with Global Positioning System (GPS) and yield
monitor.

Site Description

The soil of the 6 ha ﬁeld is classiﬁed as Capac series. According to soil survey, a
Capac series consists of somewhat poorly drained, moderately and moderately slowly
permeable soils on till plains and moraines. These soils formed in medium- and
moderately fme-textured deposits. While installing the access tubes, disturbed soil
samples were taken at depths of 0-15, 15-30, 30-60, 60-90, 90-120 and 120-150 cm at
each access tube location. Clay and sand, total nitrogen, and organic matter content were
determined for each soil sample and are shown in appendix A. The soil water limits were
estimated using the procedure described by Ritchie et al. (1999). Three trenches were
opened at L10, L15, and L16 to study the soil proﬁle at these locations. The elevation
was measured at about 300 representative locations in the ﬁeld using a theodolite. The

range of elevation was approximately 227 to 231 m, and the slope ranged from

109

 

Figure 4.3. Inﬁared images were captured (from left to right) on April 4, April 28, June
4, and July 14, 1998.

110

approximately'O to 12 % (Figure 4.1).

Field Management
The eastern part of the ﬁeld was planted to corn in 1995, 1996 and 1997, while the
western part of the ﬁeld was planted to corn in 1995, 1996, and to wheat in 1996-1997.
Manure was spread on September 4, 1997 and then the ﬁeld was plowed then disced on
October 14. AC Ron winter wheat (325 seeds m‘z) was sown on October 19, 1998.
Harmong Extra (0.3 oz/ac) was spread in the ﬁeld on April 22, 1998 for weed control.
Urea (1501bs/ac) was spread on April 23, 1998. Drainage pipes were installed in the

northen part of the ﬁeld.

Normalized Difference Vegetation Index and LAI
The Normalized Difference Vegetation Index (NDVI), also referred to as
vegetation index, was developed by Kriegler et al. (1969). This index can vary between -1

and 1 and is calculated as follows:

NDVIHME-JS 1
' NIR+R 0

where NIR and R are near infrared and red bands, respectively.

A linear relationship was assumed between LAI and NDVI as follows:
LAI = a + bNDVI (2)

where a and b are constants. Both a and b can vary signiﬁcantly from one infrared image

to another. On April 28 and June 4, measured LAIs near the access tube locations were

111

used as reference points to estimate a and b for the corresponding images. On the other
dates, LAI was not estimated from infrared images since April 4 and July 14 images
showed no spatial variability within the ﬁeld.
Integrating CERES-WHEAT Model and Remote Sensing

The CERES-WHEAT model estimates the grain number per square meter based
on stem weight per square meter at anthesis, adjusted using a genetic coefﬁcient (G1).
Because LAI can be obtained from infrared images, a relationship between stem weight
and LAI is needed to allow the use of the CERES-WHEAT model for estimating yield by
using infrared imagery. A linear relationship between LAI and stem weight (S, kg ha") at
anthesis was proposed as follows:
S = c + dLAI ' (3)
where c and d are constants. To ﬁnd c and d, CERES-WHEAT was run for different
environmental conditions. A relationship between simulated S and LAI was built.

To simulate grain yield for each pixel (1 m2) within the ﬁeld, the following steps
were followed:
(1) Estimating LAI from NDVI using Eq. [2] for each pixel of June 4th image. In our
experiment the anthesis was on June 4‘".
(2) Eq. [3] was then used to estimate 8 at each pixel of June 4th image. Then, CERES-
WHEAT was run to simulate grain number at each pixel. Assuming no nitrogen and
water stress, a unit weight of a grain was simulated and assumed to be constant within the
ﬁeld. By deﬁnition grain yield can be calculated by multiplying grain number by unit

grain weight.

112

 

 

 

 

Results and Discussion
Spatial Variability Along Access Tube Transect

Total nitrogen content of the soil surface layer varied spatially and ranged from
about 0.1 % at L1 1 to 0.7 % at L2 (Figure 4.4). The organic matter content of the soil
surface layer also varied spatially and ranged from about 1.9 % at L15 to 12 % at L2. The
clay and sand contents of the soil surface layer were correlated with elevation and
landscape position. The sand content of the soil surface layer increased with increasing
elevation, whereas the clay content of this layer tended to decrease with increasing
elevation. The clay content of the soil surface layer ranged from about 10 % at L16 to
34% at L2, while the sand content of this layer ranged from about 20 % at L2 to about 55
% at L16. The bulk density of the soil surface layer varied from 1.31 g cm'3 to 1.47 g cm'3
at L14.

There was signiﬁcant variability of plant density (PD) within the ﬁeld (Figure

4.5). It varied from about 190 plants m’2 at L6 to about 325 m'2 at Ll. A continuous
signiﬁcant decrease of PD occurred from L1 though L6. Maximum PD was found at the
bottom of the hill, intermediate at top of the hill, and minimum at hillside. Heads number
(HN) ranged from 270 heads m'2 at L4 to about 445 heads m’2 at L16. Highest HN was
found at L16 and then at southern bottom of the hill, intermediate at top of the hill and
northern bottom of the hill, and lowest at hillside. Number of grains per head (GNPH)
varied from about 20 grain per head at L2 to 16 grain per head at L6. Greatest GNPH was
found at the northern bottom of the hill, intermediate at top of the hill and southern
bottom of the hill, and lowest at hillside. Head weight (HW) ranged from 1.4 g at L15 to

0.85 g at L5. Maximum HW was found at the bottom of the hill, intermediate at top

113

 

 

 

 

 

 

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0246810121416024681012141618
Access'nbeslocaims AmTweLam’ms

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texture, and bulk density) of the surface layer.

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024681012141618

Figure 4.5. Crop characteristics at harvest time (plant density, heads number, number of grains per
head, head weight, unit grain weight, grain number, and grain yield.

115

of the hill, and minimum at hillside. No signiﬁcant variation was found among access
tube locations in respect to unit grain weight. An average unit grain weight was 24.5 mg.
Grain number (GN) varied signiﬁcantly and ranged from about 8000 grains m'2 to 16000
grains in2 at L13. Highest GN was found at L16 and southern bottom of the hill,
intermediate at top of the hill and northern bottom of the hill, and lowest at hillside. Grain
Yield (GY) varied signiﬁcantly and ranged ﬁ'om 4400 kg ha" at L15 to 1900 kg ha'1 at
L12. Greatest GY was found at southern bottom of the hill and L16, intermediate at top
of the hill and northern bottom of the hill, and lowest at hillside.
Model Performance Along Access Tube Transect

Measured PD near each access tube location was used to run CERES-WHEAT in
order to simulate GY accurately. Measured wheat grain yield ranged from 1827 kg ha" at
L5 to 4268 kg ha'l at L15 with an average of 2943 kg ha" (T able 4.1). Simulated grain
yield ranged from 1814 kg ha’l at L4 to 3791 kg ha'1 at L15 with an average of 3251 kg
ha‘1 (Table 4.1). It was clear that CERES-WHEAT gave good estimate of mean,
minimum, and maximum GY. The difference between simulated and measured grain
yield ranged from -615 kg ha’I at L4 to 1454 kg ha'l at L5 with an average of 308 kg ha".
However, the ratio of absolute error to measured grain yield ranged from 3% at L2 to
79% at L5. Simulated GY was within 15% error margin at 10 access tube locations; L1,
L2, L6, L7,L9, L10, L13, L14, L15, and L16. The ratio of error to measured grain yield
was 21, -25, 79, 19, 43, and 71 % at L3, L4, L5, L8, L11, and L12, respectively. The
CERES-WHEAT performed best at bottom of the hill and least at hillside landscape

position.

116

Table 4.1. Measured and simulated grain yield near all access tube locations.

 

 

 

 

Access tube Measured Grain Simulated’Grain Error
location Yield Yield
kg ha‘
L1 3325 3574 204(7%)*
L2 3301 3408 107(3%)*
L3 2936 3549 613(21%)
L4 2429 1814 -615(-25%)
L5 1827 3281 1454(79%) ﬂ.
L6 2087 2411 324(15%)* '
L7 3089 3287 198(6%)*
L8 2753 3290 537(19%)
L9 3608 3255 -353(-10%)*
L10 2759 3194 435(15%)*
L1 1 2252 3224 972(43%)
L12 1910 3274 1364(71%)
L13 3974 3395 -579(-14%)*
L14 3231 3572 341(10%)*
L15 4268 3791 -477(-l 1%)*
L16 3333 3693 360(10%)*
Mean 2942 3251 308
Standard deviation 714 490 620
Minimum 1827 1814 -615
Maximum 4268 3791 1454

 

* Absolute error is less than 15%.

117

 

Infrared Images Interpretation

The infrared image of April 4 did not show any clear variability within the ﬁeld
(Figure 4.3). That could be because (1) there was no signiﬁcant variability of wheat
growth and/or crop stands, or (2) there was signiﬁcant variability of wheat density and/or
wheat growth and infrared images did not show it. The second possibility was considered
to be right because counting plant stands near the access tube locations on April 15, 1998
showed signiﬁcant variability of plant density along access tube transect. The inability of
early-season infrared images to identify and show crop growth is due to the fact that soil
reflectance mask plant reﬂectance when plant cover is too small.

Spatial variability of wheat growth was evident in April 28, 1998 infrared image
(Figure 4.3). Four distinguishable wheat grth zones were observed within the ﬁeld
from April 28 infrared image: (1) best wheat grth at the northern bottom of the hill, (2)
less wheat growth at hillside and top of the hill, (3) good wheat growth at the southern
bottom of the hill and the south-eastem comer of the ﬁeld, and (4) less growth at the
corner of the south-westem part of the ﬁeld. As shown in Figure 4.5, PD was greater in
zone (1) and zone (3) than zone (2). In zone 4, wheat plants had less PD and were behind
about 8 days in respect to their development stage. Variability of PD may have happened
as a result of interaction between soil surface conditions, management, and weather
conditions at the time of planting through emergence. For instance, at L16 (in zone 4), the
sand content of soil surface layer was the highest within the ﬁeld. That could have
resulted of deep planting depth if the soil surface was too wet. A deeper planting depth
could have resulted in less plant stands directly by preventing some seeds from emerging

or indirectly by delaying plant emergence. A sensitivity analysis of CERES-WHEAT on

118

planting depth showed that seeds which were planted at 6 cm depth or below, could have
their emerged wheat plants killed on January 15, 1998 as a result of cold damage.

Another reason of wheat variability could have been the presence of an E horizon
within the root zone. An E Horizon (white, infertile, and high bulk density) was found in
the ﬁeld at a depth of 90 cm in zone 4, at depth of 90-120 cm in zone 2, and at depth of
150 cm in zone 1 and zone 3. Before April 28, 1998, wheat could not have had any water
deﬁcit stress because soil water was available. However, wheat plants could have had
excess water stress (oxygen shortage) because of long term saturation conditions. A
shallow B horizon could have forced such saturation conditions for longer period
resulting in a severe water stress. Such severe water stress could have resulted in delaying
the wheat development in zone 4.

Accumulation of crop residue was captured by infrared image of April 28 (Figure
4.3) as curved light color lines. Two of them were seen; one near location L3 and the
other one near L15. Such residue accumulation resulted from signiﬁcant runoff and
erosion occurred in the period between April 4 and April 28. Two heavy rain storms
occurred within that period; one on April 9 (12 mm d") and the other one on April 27 ( 28
mm d“) (Figure 4.2). Both of them could have resulted in signiﬁcant runoff and/or
erosion or most probably only the later generated that signiﬁcant runoff and erosion. If
another infrared image was taken between these two rainfall storms more certain
interpretation could have been made.

Although some of zone 4 can be noticed, not much variability of wheat growth
was evident in June 4 (anthesis date) 1998 infrared image (Figure 3.4). That is mainly

because wheat growth masked the variability of wheat within the ﬁeld and partially

119

because the relative difference between wheat growth within the ﬁeld became less. The
residue lines were not seen either because the accumulated crop residue was covered by
wheat.

The infrared image of July 14 did not show any variability of wheat growth within
the ﬁeld (Figure 4.3) because it was captured one day before wheat harvesting. That
indicated that it was impossible to assess grain yield using remotely sensed infrared
images at time of maturity. Some weed populations were evident within the ﬁeld such as
near L1 and L2.

Similar spatial variability of wheat growth within the ﬁeld from each image was
obtained by transforming raw reﬂectance data into NDVI maps (Figure 4.6). Although,
features like crop residue accumulation lines or soil color cannot be seen on NDVI maps,
they can give a more quantitative way of studying the spatial variability of wheat growth
within the ﬁeld. The NDVI ranged from -0.3 to 0.6. It ranged from -0.3 to 0 on April 4,
from -0.2 to 0.2 on April 28, 0 to 0.6 on June 4, and from -0.3 to 0.1 on July 14.

Leaf area index maps did not show any improvement in identifying wheat growth
spatial variability over NDVI (Figures 4.6 and 4.7) because LAI was a linear transform
from NDVI. However, LAI can be linked with a crop simulation model in order to better

estimate the spatial variability of wheat growth, grain yield, and evapotranspiration.

Modeling Spatial Variability of Grain Yield
Testing the relationship between stern weight and LAI at anthesis in different
environmental conditions showed that simulated stem weight was highly correlated to

simulated LAI at anthesis with r2=0.99 (Figure 4.8). Such a relationship demonstrated

120

- Access Tubes Location
Contours
Normalized Difference Vegetation Index

-0.3 - .0.2
-0.2 - -0.1

E] -0.1 - 0

o. 0.1
0.1 - 0.2

- 0.2 . 0.3

0.3 - 0.4

- 0.4. 0.5

0.5 - 0.6

-
l- No Data

 

Figure 4.6. Normalized difference vegetation index

April 28, June 4, and July 14, 1998.

121

 

 

mar-.394. f .3
51111 .li

 

111'
:1, W...
" 0:21:

\
U

H/
- its

f

 

. r

H.

._ , 14;»:
(NDVI) (ﬁ'om left to right) on April 4,

.1
.

 

 

 

. Access tubes Location
mmwn
teat Arealnder (LN)
0 - 0.35

""'"" 013507
E: 0.7.1.05
1.05 -1.4
1.4-1.75
1.75-2.1
7.1 -2.45
2.45 . 2.8
2.8 . 3.15
- 3.15-3.15

- 3.5-3.85 -
-N°°m { 1‘11
814‘;

Figure 4.7. Leaf area index (LAI) (ﬁ'om left to
April 4, April 28, June 4, and July 14, 1998.

 

 

 

      
           

‘K
. '1‘,

.N.

on

122

 

Y=507+1097*X 3:099
45001

Stem weight (kg/ha)
g i i

g

 

 

 

3

4.0

 

Figure 4.8. Relationship between simulated stem weight and simulated leaf area index at
anthesis.

123

that LAI map at anthesis can be converted accurately into stem weight map at anthesis
which was needed to use June 4 infrared image in estimating wheat grain yield. This
relationship was used to convert LAI on June 4 into stem weight as ﬁrst step of
integrating CERES-WHEAT and remotely sensed infrared image to simulate spatial
variability of grain yield. Then, the calculated stem weight was used to estimate seed
number at each pixel using the CERES-WHEAT procedure. In future, CERES-WHEAT
can be modiﬁed to estimate grain number directly ﬁ'om LAI.

Assuming a constant unit grain weight was valid within the ﬁeld (Figure 4.5 and
4.9), using an average value of 0.245 mg of a unit grain weight estimated measured grain
yield at 33 locations accurately with r2 = 0.92. That allowed us to estimate a unit grain
weight by running CERES-WHEAT just once using a representative soil proﬁle data. The
estimated (0.25 mg) and measured unit grain weight were in good agreement.

The simulated spatial variability of grain yield was in good agreement with the
measured one (Figure 4.10). Most of the high yield, intermediate yield and low yield
areas within the ﬁeld were simulated quite accurately. At the southern-east bottom of the
hill, an overestimation of grain yield was evident. Error of simulating total grain yield

(16500 kg) was about 7 % of measured total grain yield (15655 kg ).

Conclusions

Signiﬁcant spatial variability of soil properties and wheat growth and yield was
evident within the ﬁeld. Total nitrogen, organic matter, and texture of soil surface layer
were correlated with landscape position. Plant density, heads number, grain number, and

grain yield were correlated with both soil and landscape position. Unit grain weight was

124

 

§

    

Y=0245X 3:052

§§§§

Grain Yield (kg ha")

a

15CD« .

 

 

1% T l l I T
6000 8000 10000 12000 1401) 13!!) 1mm

SeedNn'ber(m‘2)

 

Figure 4.9. Relationship between measured grain yield and measured seed number near
access tube locations.

125

/\/ Contours

. Access Tubes Location
Grain Yield (kg/ha)
575 - 1175
[:1 1175 - 1775
1775 - 2375
2375 - 2975
2975 - 3575
- 3575 - 4175
- 4175 - 4775
4775 - 5375
- 5375 - 5975

- No Data

 

Figure 4.10. Measured and simulated grain yield maps.

126

not correlated to either soil nor landscape position.

The CERES-WHEAT model estimated grain yield within error margin of 15 % at
10 locations out of 16. Minimum, mean, and maximum grain yield along access tube
transect were estimated reasonably well by CERES-WHEAT. Measured plant density at
each access tube location was needed to simulate grain yield reasonably near most of
access tubes locations.

Spatial variability of grain yield within the ﬁeld could be estimated reasonably
well by integrating CERES-WHEAT and remote sensing. The new developed procedure
did not require intensive spatial sampling of soil properties nor many infrared images. An
infrared image near anthesis date is needed for best outcomes of the CERES-WHEAT
and remote sensing integration.

Although the integration procedure has answered a question, many other
questions are yet to be answered such as (1) can such an approach be used for other crops
like maize?, (2) can infrared images of one year be linked with a crop model in order to
estimate another year grain yield variability, (3) can infrared images be used to estimate
spatial variability of plant density, and (4) can infrared images help in building minimum

sampling set?. Future studies are needed to address these questions.

127

References

Bemdtsson, R., and A. Bahri. 1995. Field variability of element concentrations in wheat
and soil. Soil Sci. 159(5):311-320.

Bouma, J., J. Brouwer, A. Verhagen, and H.W.G. Booltink. 1995. Site speciﬁc
management on ﬁeld level: high and low tech approaches. Kluwer Academic
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Boyer, J.S.1982. Plant productivity and environment Potential for increasing crop plant
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Bresler, E, S. Dasbreg, D. Russo, and G. Dagan. 1981. Spatial variability of crop yield as
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Fiez, TE, and BC. Miller. 1995. Varying winter wheat seeding rates among landscape
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Halvorson, G.A., and EC. Doll. 1991. Topographic effects on spring wheat yields and
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the Sixth International Symposium on Remote Sensing of Environment;
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Maas, S. 1993. Within-season calibration of modeled wheat growth using remote sensing
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Moulin, A.P., D.W. Anderson, and M. Mellinger. 1994.Spatial variability of wheat yield,
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Ritchie, T.J., A. Gerakis, and AA Suleiman. 1999. Simple Model to Estimate Field-
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129

SUMMARY AND CONCLUSIONS

ASSESSING AND MODELING THE SPATIAL VARIABILITY OF SOIL WATER

REDISTRIBUTION AND WHEAT YIELD ALONG A SLOPING LANDSCAPE

AYMAN ABDALLAH AHMED SULEIMAN

Assessing and modeling the spatial variability of soil water redistribution and
wheat yield along a sloping landscape is a prerequisite for best site-speciﬁc-management
within sloping landscapes. The objective of this research was to (1) test upward soil water
ﬂow during second stage evaporation and downward soil water-ﬂow during vertical
drainage in the water balance of CERES, (2) develop a simple functional model to
simulate lateral downslope soil water ﬂow, and (3) integrate remote sensing and CERES-
WHEAT to simulate the spatial variability of wheat yield within a sloping landscape.

Upward soil water ﬂow dynamics during second stage soil water evaporation
model in the water balance of CERES was evaluated in laboratory and ﬁeld conditions. In
laboratory, columns were ﬁlled with soils of contrasting texture. The soils were saturated
and then allowed to drain for 14 days while their surfaces were covered. After the
drainage cycle their surfaces were uncovered for 60 days under high potential evaporative
losses. Soil water content was monitored at 11 different depths using TDRs during the

evaporation cycle. In the ﬁeld, soil water content was monitored at 11 different depths of

130

a bare soil using TDRs for about 60 days.

Results showed that, the two constants (n and a) that used in the model were soil
speciﬁc since a was soil speciﬁc. However, they did not vary much and were highly
correlated to 0d,... New linear relationships between a, n, and a with 0d,, were developed.
These relationships enabled the second stage evaporation model in the water balance of
CERES to simulate better soil water distribution and soil water evaporation for diverse
soils. It was found that the impact of water table on second stage evaporation could not be
captured by second stage evaporation theory because soil water contents at different
depths had different relationships with Boltzmann transform.

Downward soil water ﬂow dynamics during vertical drainage in the water
balance of the CERES model was evaluated theoretically and in laboratory and ﬁeld
conditions. A theory was introduced on the basis of Darcy’s Law, using the assumption
of a unit gradient for a vertical drainage cycle, and the validity of Brooks and Corey
(1964) equation for unsaturated hydraulic conductivity estimation. In laboratory, columns
were ﬁlled with soils of contrasting texture, then soils were saturated and allowed to drain
for 14 days while their surfaces were covered. Soil water content was monitored at 11
different depths using TDRs during the drainage cycle. In the ﬁeld, soil water content was
monitored at 11 different depths of a bare soil using TDRs for about 14 days during a
drainage cycle.

It was found that the drainage coefﬁcient is soil dependent. It was clear also that
the drainage coefﬁcient depends on the initial soil water content. However, using a sole
value of the drainage coefﬁcient for each soil is reasonable and simpliﬁes soil water

drainage modeling. Two methods were introduced to estimate the drainage coefﬁcient

131

from drained upper limit water content and saturated water content. The new models gave
good estimate of the drainage coefﬁcient. Therefore, these new models are recommend
to be used in the water balance of CERES instead of a constant value of 0.55. Also Eq.
[21], which calculates the drainage coefficient, could be incorporated in the drainage
model in the water balance of CERES because it is easier and gave as good results as Eq.
[20]. A new deﬁnition of the drainable soil water was introduced. The new deﬁnition
made the drainage model in the water balance of CERES applicable under shallow soil
water table conditions.

A generic simple functional model to simulate daily lateral downslope soil water
ﬂow was developed based on Darcy’s Law and the Brooks and Corey (1964) equation
for the estimation of unsaturated hydraulic conductivity. Saturated and drained upper
limit soil water contents and slope angle (or the hydraulic gradient) were needed to run
the new lateral downslope soil water ﬂow model. In order to evaluate the model, a ﬁeld
study was conducted along a sloping landscape in Lansing, Michigan in 1997-1998.
Although the new model is simple, it performed well under ﬁeld conditions. The
developed lateral downslope soil water ﬂow model was built in a way that makes
possible to link it to a GIS package. A GIS can determine the directions of stream ﬂow
lines, while the lateral downslope model can account for the amount of soil water that
may drain in a day at any position of a landscape. Such combination will produce a two-
dimensional lateral downslope ﬂow.

To integrate CERES-WHEAT with remote sensing, a 6 ha ﬁeld was planted to
wheat on October 19, 1997 and harvested using a combine equipped with GPS and yield

monitor on July 15, 1998. Four infrared images were captured during the growing season

132

 

in order to estimate the wheat growth spatial variability. Soil and plant samples were
taken along a transect.

Signiﬁcant spatial variability of soil properties and wheat growth and yield was
evident within the ﬁeld. Total nitrogen, organic matter, and texture of soil surface layer
were correlated with landscape position. Plant density, heads number, grain number, and
grain yield were correlated with both soil and landscape position. Unit grain weight was
not correlated to either soil properties nor landscape position. The CERES-WHEAT
model estimated grain yield within error margin of 15 % at 10 locations out of 16.
Minimum, mean, and maximum grain yield along access tube transect were estimated
reasonably well by CERES-WHEAT. Measured plant density at each access tube location
was needed to simulate grain yield reasonably near most of access tubes locations. Spatial
variability of grain yield within the ﬁeld could be estimated reasonably well by
integrating CERES-WHEAT and remote sensing. The new developed procedure did not
require intensive spatial sampling of soil properties nor many infrared images. An
infrared image near anthesis date is needed for best outcomes of the CERES—WHEAT

and remote sensing integration.

133

APPENDICES

Appendix A

Soil properties at access tube locations.

 

 

 

Access Tube Depth Clay Sand Carbon Total Nitrogen EC pH
Location
cm °/o dS m’l
L1 0-15 18.1 45.0 3.68 0.31 0.85 7.27
L1 15-30 19.5 47.5 3.53 0.31
L1 30-60 20.3 56.0 2.66 0.23 0.49 7.58
L1 60-90 21.3 54.8 2.20 0.19
L2 0-15 32.7 20.8 8.09 0.70 0.42 6.81
L2 15-30 32.7 24.1 7.58 0.65
L2 30-60 29.1 23.9 12.37 1.02
L2 60-90 31.0 9.6 4.96 0.36 0.47 7.10
L2 90-120 29.5 15.5 6.84 0.49 2.82 7.13
L2 120-150 23.6 14.5 3.08 0.08 2.91 7.20
L3 0-15 30.2 24.2 4.39 0.41 0.66 7.69
L3 15-30 32.8 16.0 2.15 0.17 0.46 7.88
L3 30-60 12.6 63.8 0.74 0.03 0.52 7.58
L3 60-90 10.5 76.2 0.86 0.04 0.52 8.03
L3 90-120 8.5 66.3 1.36 0.23 0.62 7.97
L4 0-15 23.6 33.2 1.61 0.18 0.78 7.84
L4 15-30 23.6 32.6 0.37 0.03 0.30 7.77
L4 30-60 21.9 34.9 0.92 0.04 0.36 7.69
L4 60-90 23.6 33.2 0.63 0.01 0.63 7.73
L5 0-15 21.8 42.2 2.31 0.22 0.53 7.78
L5 15-30 21.8 42.7 1.27 0.11
L5 30-60 19.6 44.2 0.48 0.05 0.28 7.67
L5 60-90 23.6 35.0 1.44 0.05 0.33 8.03
- L5 90-120 22.4 43.0 2.70 0.01 0.33 7.94
L6 0-15 21.8 39.4 2.36 0.22 0.39 7.60
L6 15-30 21.8 36.1 1.12 0.11
L6 30-60 27.2 36.5 0.39 0.04 0.28 7.86
L6 60-90 23.7 25.3 2.20 0.03 0.34 7.98
L6 90-120 25.0 30.7 2.42 0.04 0.42 8.04
L6 120-150 25.6 24.2 3.06 0.02 0.32 7.73

 

134

 

 

 

Depth Clay Sand Carbon Total Nitrogen EC
Access Tube pH
Location cm % dS m"

L7 30-60 21.2 48.0 0.62 0.06 0.32 7.62
L7 60-90 16.3 12.0 2.29 0.02 0.38 7.57
L7 90-120 14.6 10.9 2.43 0.01 0.34 7.61
L7 120-150 19.6 1.8 1.61 0.00 0.34 7.54
L8 0-15 15.1 48.1 1.82 0.16 0.60 7.15
L8 15-30 21.8 46.3 1.43 0.14
L8 30-60 21.8 49.3 0.52 0.05 0.27 7.48
L8 60-90 13.9 83 .6 0.48 0.02 0.38 7.52
L8 90-120 8.5 62.3 0.52 0.01 0.47 7.42
L8 120-150 18.9 44.1 1.71 0.00 0.42 7.89
L9 0-15 20.6 44.5 1.82 0.16 0.60 7.68
L9 15-30 20.6 44.0 1.44 0.13
L9 30-60 28.5 45.9 0.48 0.05 0.34 7.71
L9 60-90 13.9 48.1 0.96 0.04 0.43 7.74
L10 0-15 15.1 49.1 1.81 0.15 0.56 8.02
L10 15-30 15.1 48.2 1.37 0.13
L10 30-60 21.8 52.4 0.34 0.03 0.31 7.01
L10 60-90 19.2 54.7 0.34 0.04 0.33 7.62
L10 90-120 16.3 49.5 0.39 0.02 0.38 7.84
L11 0-15 17.6 47.9 1.30 0.13 0.49 7.68
L11 15-30 18.5 47.7 1.54 0.14
L11 30-60 16.3 49.3 0.62 0.05 0.34 7.56
L11 60-90 31.8 36.3 0.47 0.04 0.51 7.95
L1 1 90-120 10.5 46.7 0.28 0.01 0.40 7.64
L11 120-150 18.3 43.1 0.44 0.01 0.36 7.88
L12 0-15 18.5 48.6 1.40 0.16 0.77 7.62
L12 15-30 15.1 42.8 0.72 0.13
L12 30-60 24.4 43.5 0.48 0.06 0.32 7.64
L12 60-90 17.0 64.2 0.26 0.02 0.32 7.62
L12 90-120 19.3 56.7 0.25 0.02 0.46 7.74
L12 120-150 10.6 49.6 0.18 0.00 0.35 7.70
L12 150-180 20.4 42.4 0.30 0.01 0.38 7.60
L12 180-210 19.1 43.0 0.26 0.00 0.34 7 .62
L12 210-240 20.2 42.0 0.29 0.01 0.35 7.63
L13 0-15 22.1 45.2 1.60 0.23
L13 15-30 19.7 43.6 1.26 0.17
L13 30-60 20.5 40.3 0.58 0.07 0.38 7.60

 

135

 

 

 

Depth Clay Sand Carbon Total Nitrogen EC
Access Tube dS m" pH
Location cm %

L14 15-30 18.0 48.6 0.64 0.10
L14 30-60 18.0 51.2 0.35 0.04 0.24 7.55
L14 60-90 14.7 55.5 0.20 0.01 0.32 7.87
L14 90-120 13.8 58.5 0.19 0.01 0.32 7.80
L14 120-150 12.3 60.3 0.17 0.01 0.35 7.70
L15 0-15 21.8 43.9 1.09 0.21 0.39 7.08
L15 15-30 23.5 43.0 0.79 0.15
L15 30-60 20.9 43.4 0.61 0.08 0.30 7.43
L15 60-90 22.7 39.5 0.39 0.05 0.28 7.40
L15 90-120 20.8 44.0 0.22 0.02 0.26 7.38
L15 120-150 15.5 52.2 0.21 0.01 0.41 7.49
L16 0-15 9.6 56.0 1.63 0.16
L16 15-30 10.5 54.7 1.72 0.16
L16 30-60 9.4 48.8 1.33 0.12
L16 60-90 12.1 49.7 1.48 0.15
L16 90-120 16.0 44.8 0.33 0.02
L16 120-150 14.0 47.9 0.29 0.01

 

136

Appendix B

Daily solar radiation (SR), maximum (Tmax) and minimum temperature (Tmin), and
Rainfall (R) for the sloping landscape.

 

 

 

Year DOY SR Tm; Tm. R
MJ m‘2 C0 mm

97 152 8.7 16.9 9.1 0.0
97 153 7.5 15.9 9.9 1.8
97 154 4.6 15.8 12.4 2.3
97 155 17.5 21.5 9.6 0.3
97 156 27.9 23.3 4.9 0.0
97 157 25.9 24.3 6.5 0.0
97 158 26.3 23.7 11.1 0.0
97 159 29.6 21.4 12.9 0.0
97 160 28.6 23.0 10.0 0.0
97 161 28.8 26.2 8.3 0.0
97 162 29.0 28.2 9.6 0.0
97 163 21.1 27.5 11.8 0.0
97 164 15.1 23.4 15.1 5.1
97 165 21.6 26.0 13.5 4.3
97 166 29.9 21.8 9.7 0.0
97 167 29.3 25.3 8.4 0.0
97 168 10.7 22.3 15.6 7.4
97 169 23.6 21.8 9.8 0.0
97 170 25.9 25.3 12.7 0.0
97 171 21.1 26.8 13.2 0.0
97 172 8.1 26.0 17.8 8.1
97 173 13.6 28.4 17.3 10.9
97 174 28.8 27.7 16.0 0.0
97 175 18.9 29.4 14.2 4.3
97 176 25.8 30.8 21.6 0.0
97 177 23.8 27.2 21.3 0.0
97 178 29.1 26.1 15.6 0.0
97 179 30.0 28.4 11.0 0.0
97 180 27.6 29.6 13.4 0.0
97 181 27.2 30.4 15.6 0.0
97 182 17.6 27.3 18.2 2.0
97 183 16.0 26.4 19.0 1.3
97 184 22.0 29.7 16.8 0.3
97 185 6.1 20.4 16.2 0.0
97 186 14.4 19.4 12.1 0.0
97 187 25.8 23.9 7.3 0.0
97 188 23.0 24.5 10.6 1.3
97 189 28.1 22.6 12.5 0.0
97 190 10.6 24.1 14.6 4.8
97 191 26.5 21.6 11.3 0.0

137

 

Year DOY SR Tm. Tm R

 

MJ m“2 C° mm
97 192 29.7 24.4 8.7 0.0
97 193 29.3 26.3 9.0 0.0
97 194 29.2 27.9 11.2 0.0
97 195 25.0 30.2 13.3 0.0
97 196 24.4 33.0 20.0 5.1
97 197 27.7 27.1 17.3 0.0
97 198 26.5 30.8 17.4 0.0
97 199 13.2 27.4 17.8 20.3
97 200 27.3 29.5 16.7 0.3
97 201 29.2 24.1 14.5 0.0
97 202 25.1 27.3 9.4 0.0
97 203 6.6 22.2 16.2 14.4
97 204 16.4 25.0 13.1 0.0
97 205 13.9 23.8 14.4 0.0
97 206 16.0 26.4 17.2 0.0
97 207 21.2 27.7 14.6 0.0
97 208 20.3 30.5 20.2 4.3
97 209 21.3 29.0 17.7 0.0
97 210 23.9 27.2 14.9 0.0
97 211 27.7 23.6 11.6 0.0
97 212 26.5 25.5 9.1 0.0
97 213 28.1 27.7 10.1 0.0
97 214 11.3 24.9 12.2 0.0
97 215 23.5 28.7 17.8 0.0
97 216 6.6 23.0 15.7 19.0
97 217 18.1 23.5 14.7 0.3
97 218 24.9 20.7 10.5 0.0
97 219 22.1 24.0 7.8 4.3
97 220 24.7 25.1 9.6 0.3
97 221 21.5 26.9 10.4 0.0
97 222 21.5 28.1 13.1 0.0
97 223 12.4 24.1 17.2 0.8
97 224 3.8 17.6 13.0 7.6
97 225 4.7 19.7 13.1 9.1
97 226 17.9 22.6 14.0 0.3
97 227 21.3 22.7 6.7 0.0
97 228 13.0 27.1 15.4 8.9
97 229 10.4 27.6 18.1 3.0
97 230 3.4 18.7 12.2 7.1
97 231 17.8 21.5 11.0 0.0
97 232 22.1 22.7 10.5 0.0
97 233 3.5 15.6 13.8 2.5
97 234 10.1 18.3 12.4 4.6
97 235 9.5 19.6 11.6 0.0
97 236 23.6 21.7 7.4 0.0
97 237 4.7 17.6 13.5 0.0
97 238 8.8 20.6 12.6 0.0
97 239 13.8 23.6 10.8 0.0

138

 

 

 

 

Year 55Y JS_R Ln Tm R
MJ "1'2 C" mm
97 240 21.4 27.7 14.4 0.0
97 241 12.7 19.6 12.7 0.0
97 242 11.0 20.7 11.2 0.0
97 243 17.8 23.6 10.0 0.0
97 244 8.7 21.2 15.7 1.0
97 245 13.7 24.8 14.7 0.0
97 246 8.4 22.8 13.0 0.0
97 247 23.0 17.9 7.5 0.0
97 248 22.9 20.6 2.7 0.0
97 249 16.0 21.4 2.2 0.8
97 250 19.8 26.8 14.3 0.0
97 251 14.5 21.5 11.3 0.0
97 252 10.6 23.0 13.6 0.0
97 253 1.9 16.2 13.6 46.2
97 254 4.2 17.1 14.3 22.6
97 255 5.1 16.6 12.8 0.0
97 256 5.2 17.4 12.7 0.5
97 257 14.4 22.4 12.9 0.0
97 258 8.9 21.5 12.1 0.8
97 259 17.9 26.5 10.9 0.0
97 260 13.0 26.0 13.8 0.0
97 261 15.7 23.3 12.4 30.4
97 262 19.6 25.7 8.9 0.0
97 263 10.5 26.2 17.4 2.0
97 264 8.6 19.3 7.4 1.0
97 265 19.8 15.4 2.6 0.0
97 266 10.7 16.5 4.1 0.0
97 267 13.0 17.6 6.7 1.0
97 268 19.3 17.9 0.8 0.0
97 269 17.4 22.6 8.9 0.0
97 270 18.1 17.4 6.0 0.0
97 271 17.6 20.3 3.9 0.0
97 272 12.7 23.7 9.7 4.1
97 273 13.7 20.9 10.2 0.3
97 274 4.8 14.5 8.9 0.3
97 275 17.8 12.7 1.9 0.0
97 276 16.3 19.6 0.6 0.0
97 277 15.8 25.6 11.2 0.0
97 278 5.5 22.9 12.0 1.8
97 279 15.6 26.6 7.1 0.3
97 280 14.6 27.2 12.3 0.0
97 281 14.0 27.3 11.8 0.0
97 282 13.1 26.7 12.2 0.0
97 283 3.4 20.4 11.2 4.3
97 284 15.9 16.5 5.3 0.0
97 285 15.1 19.1 3.3 0.0
97 286 13.4 24.6 6.0 0.0
97 287 2.6 21.2 7.9 7.9

139

 

Year DOY SR Tm TIIIIIII R

 

MJ m'2 C° mm
97 288 10.4 9.6 1.0 0.0
97 289 11.6 10.4 0.6 0.0
97 290 6.3 9.7 -1.5 0.0
97 291 8.7 9.6 -0.6 0.0
97 292 14.2 13.5 -3.3 0.0
97 293 12.9 14.5 -1.4 0.0
97 294 10.5 11.5 -1.6 0.0
97 295 10.3 7.8 -2.4 0.0
97 296 5.4 3.2 -3.5 0.0
97 297 6.1 5.5 -4.8 0.0
97 298 2.0 6.3 2.6 1.3
97 299 5.1 7.1 -0.1 0.0
97 300 1.2 3.8 -0.5 7.6
97 301 3.4 -0.2 -3.2 0.0
97 302 11.8 7.6 -4.8 11.9
97 303 10.6 12.7 0.9 0.0
97 304 9.2 15.2 -2.4 0.0
97 305 4.5 14.4 8.9 0.3
97 306 1.8 12.1 8.3 12.9
97 307 1.6 8.7 0.9 1.3
97 308 6.0 4.0 -1.2 0.0
97 309 2.1 5.4 -0.5 1.8
97 310 4.3 5.6 1.4 0.0
97 311 6.6 16.5 2.5 11.1
97 312 3.6 7.2 1.3 0.0
97 313 9.5 9.9 -0.4 0.0
97 314 3.4 5.4 -0.2 0.0
97 315 7.9 6.1 -2.5 0.8
97 316 5.3 2.7 -5.5 0.0
97 317 5.8 -1.3 -8.9 0.0
97 318 5.1 0.0 -8.9 0.8
97 319 3.6 -0.2 -2.0 2.5
97 320 3.4 -0.9 -5.1 2.3
97 321 6.8 -1.9 -10.6 0.0
97 322 9.7 0.5 -6.1 0.8
97 323 7.7 3.4 -8.1 0.0
97 324 3.9 0.8 -1.6 0.0
97 325 4.2 5.5 -3.6 0.5
97 326 2.4 3.8 -1.5 1.0
97 327 6.9 6.1 -3.1 0.0
97 328 2.6 1.6 -6.4 0.0
97 329 5.6 -1.0 -8.7 0.0
97 330 7.4 10.9 -4.2 0.5
97 331 1.8 8.6 1.1 0.5
97 332 5.1 7.6 -3.3 1.8
97 333 1.8 10.4 3.9 0.0
97 334 1.0 6.8 4.4 3.8
97 335 1.0 4.8 1.9 0.5

140

 

 

 

 

Year DOY SR Tm 4r“, 1?
MJ m'2 C° mm

97 335 1.0 4.8 1.9 0.5
97 336 4.2 2.3 -0.8 0.0
97 337 4.5 2.7 -3.2 0.0
97 338 1.2 2.3 -23 0.3
97 339 2.3 2.1 -21 1.8
97 340 4.5 08 -3.6 0.0
97 341 3.2 1.2 -3.2 0.5
97 342 2.9 2.2 .05 0.0
97 343 2.4 0.5 -2.0 0.0
97 344 1.6 0.3 -2.1 0.0
97 345 1.5 -o.7 -2.4 0.3
97 346 4.6 -1.5 -5.7 0.0
97 347 2.5 -14 -6.0 0.0
97 348 2.2 -o.2 -4.5 0.0
97 349 7.1 4.7 -8.2 2.8
97 350 7.9 6.5 4.9 0.0
97 351 7.4 5.8 8.7 0.0
97 352 7.9 6.3 -7.o 0.0
97 353 5.8 5.4 -4.4 0.0
97 354 5.1 7.2 0.3 0.0
97 355 1.8 1.1 -2.6 0.3
97 356 2.8 -1.8 -4.1 0.0
97 357 1.0 -o.5 -3.4 2.0
97 358 2.3 0.0 -2.0 2.8
97 359 2.1 0.2 -2.8 0.5
97 360 1.3 0.2 .09 7.4
97 361 1.5 -o.2 -2.9 0.0
97 362 4.6 -1.5 -9.7 0.5
97 363 6.2 0.0 -10.6 0.0
97 364 5.1 2.1 -2.8 0.0
97 365 5.5 -1.9 -10.6 0.3
98 1 6.7 -77 -13.6 0.0
98 2 7.7 3.7 -91 0.0
98 3 4.4 7.4 1.5 0.0
98 4 0.9 10.5 5.1 4.8
98 5 0.8 7.2 -1.4 8.4
98 6 0.9 11.3 6.9 23.1
98 7 2.0 11.4 8.2 1.0
98 8 0.7 8.8 .09 9.9
98 9 1.0 -0.6 -2.3 0.0
98 10 1.6 1.4 -1.6 10.6
98 11 8.1 -1.2 -9.3 0.0
98 12 4.4 .70 .10.1 0.0
98 13 1.6 -o.2 -1o.2 0.0
98 14 7.7 -5.0 -14.6 0.0
98 15 5.1 -5.7 -16.3 0.0
98 16 3.3 -3.8 -6.9 0.0
98 17 3.2 -3.9 -6.5 0.0

141

 

Year DOY SR Tm TIIIIII R

 

MJ m" C° mm
98 18 3.5 -2.1 -4.9 0.3
98 19 4.7 -1.8 -6.0 0.0
98 20 4.7 -1.6 -5.9 0.0
98 21 6.4 -2.6 -10.4 0.5
98 22 5.4 -2.3 -7.4 0.0
98 23 4.1 -2.1 -6.2 0.0
98 24 4.6 -0.5 -5.1 0.0
98 25 7.5 -0.8 -3.6 0.0
98 26 4.8 -1.8 -4.6 0.0
98 27 5.8 1.7 -3.4 6.1
98 28 5.0 4.6 -1.2 0.0
98 29 4.1 1.6 -0.7 0.0
98 30 2.4 0.3 -1.1 3.0
98 31 3.0 0.3 -1.8 0.0
98 32 9.4 3.1 -2.0 0.0
98 33 9.5 6.4 -3.7 0.0
98 34 1.2 5.2 -5.0 0.0
98 35 9.1 0.6 -6.5 0.0
98 36 8.8 -1.7 -7.0 0.0
98 37 7.0 -2.1 -5.9 0.0
98 38 9.8 0.5 -5.8 0.0
98 39 10.4 1.2 -5.5 0.0
98 40 11.6 5.8 -8.0 0.0
98 41 11.1 8.4 -7.0 0.0
98 42 8.8 9.7 -4.8 0.0
98 43 0.9 3.5 0.7 14.4
98 44 2.6 0.7 -1.4 0.8
98 45 1.8 -0.3 -2.0 0.0
98 46 4.6 1.2 -3.4 0.0
98 47 9.4 7.7 -3.7 0.0
98 48 6.5 6.5 —0.8 7.6
98 49 1.3 4.9 2.0 18.5
98 50 1.6 3.2 0.5 2.0
98 51 2.7 3.3 0.4 0.0
98 52 2.7 2.9 0.1 3.0
98 53 2.6 2.0 0.0 0.0
98 54 7.9 7.6 -2.5 0.0
98 55 10.2 5.0 -2.2 0.0
98 56 3.9 6.1 -3.9 2.0
98 57 13.5 9.9 -2.5 0.0
98 58 11.5 10.8 0.2 0.0
98 59 6.7 12.2 3.2 3.0
98 60 13.6 12.8 -2.3 1.0
98 61 2.5 5.0 -1.0 7.4
98 62 3.3 2.0 -1.1 3.0
98 63 7.1 0.9 -3.0 0.3
98 64 5.9 1.5 -3.0 0.5
98 65 7.5 2.2 -1.9 0.0

142

 

Year DOY SR Tm TIllln R

 

MJm" 0" mm
98 66 2.8 1.7 -1.1 1.0
98 67 14.4 5.8 -33 0.0
98 68 1.4 3.1 -0.6 11.9
98 69 3.0 1.6 -8.1 24.6
98 70 13.1 -5.8 -112 0.3
98 71 16.8 -6.6 -15.0 0.0
98 72 16.4 -2.8 -11.5 0.0
98 73 9.1 92 .104 0.0
98 74 12.9 -o.2 -6.0 0.3
98 75 18.6 .29 -10.6 0.5
98 76 19.9 0.4 -123 0.0
98 77 11.7 5.2 -6.0 7.4
98 78 1.8 4.1 0.5 9.9
98 79 2.9 1.4 -21 1.3
98 80 3.6 -o.3 -23 0.0
98 81 5.1 0.1 -2.3 0.0
98 82 20.7 4.1 -4.6 0.0
98 83 16.9 4.3 -5.2 0.0
98 84 14.3 7.4 47 0.0
98 85 14.0 11.4 -1.o 0.0
98 86 12.5 21.5 9.6 0.0
98 87 15.4 23.2 16.0 0.0
98 88 6.2 17.0 11.0 7.9
98 89 18.9 22.9 5.8 0.0
98 90 11.3 24.6 17.5 0.0
98 91 2.7 19.2 11.8 16.0
98 92 11.2 13.8 3.1 6.6
98 93 5.7 7.5 2.9 1.3
98 94 5.0 5.6 2.7 0.0
98 95 22.0 , 9.5 0.0 0.0
98 96 23.4 10.9 -3.3 0.0
98 97 22.5 14.0 -3.7 0.0
98 98 19.8 14.8 0.9 0.0
98 99 4.5 8.7 3.9 11.9
98 100 2.5 5.8 3.2 4.3
98 101 23.7 10.3 0.6 0.0
98 102 23.5 14.9 -1.9 0.0
98 103 22.5 20.2 3.9 0.0
98 104 16.1 20.5 9.8 0.0
9.8 ' 105 4.9 14.2 8.1 2.0
98 106 8.9 13.2 4.2 0.0
98 107 12.0 18.0 3.2 5.6
98 108 22.4 9.0 1.0 0.0
98 109 20.9 15.3 2.8 0.0
98 110 13.3 14.7 3.6 0.0
98 111 23.3 18.4 2.5 0.0
98 112 12.6 16.7 4.8 0.0
98 113 20.9 18.5 3.7 0.0

143

 

Year DOY SR Tn, Tllllll R

 

MJ m'2 C° mm
98 114 25.9 18.9 2.5 0.0
98 115 21.4 20.7 5.2 0.0
98 116 18.9 17.5 2.4 2.8
98 117 8.9 9.6 1.4 27.6
98 118 27.0 11.2 -1.2 0.0
98 119 26.6 16.3 -2.0 0.0
98 120 13.4 17.0 0.3 0.0
98 121 6.8 16.6 10.1 7.9
98 122 11.7 20.7 12.2 22.1
98 123 5.2 15.2 10.9 4.6
98 124 8.9 18.2 9.9 1.0
98 125 17.3 21.8 9.7 2.3
98 126 24.2 23.4 7.3 0.3
98 127 16.7 24.0 12.6 0.0
98 128 16.4 22.6 13.0 0.0
98 129 14.1 18.5 11.2 1.0
98 130 26.6 19.5 9.7 0.0
98 131 22.1 20.9 6.9 0.0
98 132 14.1 18.0 9.7 1.0
98 133 21.5 22.1 8.0 0.0
98 134 19.7 ' 26.3 12.4 1.5
98 135 27.9 28.8 9.8 0.0
98 136 25.9 30.6 13.6 0.0
98 137 27.8 25.1 16.7 0.0
98 138 28.8 26.9 12.2 0.0
98 139 27.5 29.4 11.6 0.0
98 140 24.4 28.9 16.6 0.0
98 141 26.6 26.8 15.5 0.0
98 142 26.4 21.3 9.1 0.0
98 143 25.0 18.8 4.4 0.0
98 144 29.1 21.3 2.7 0.0
98 145 8.8 17.8 8.3 3.0
98 146 6.3 15.8 8.6 0.0
98 147 26.7 24.8 5.6 0.0
98 148 26.3 26.8 8.6 0.0
98 149 18.9 27.9 10.9 0.0
98 150 20.3 27.0 15.8 0.0
98 151 27.2 28.6 10.8 0.0
98 152 19.7 23.4 11.8 12.4
98 153 29.0 20.4 4.7 0.0
98 154 23.1 23.3 9.8 0.0
98 155 17.7 15.4 5.3 0.0
98 156 25.2 17.7 1.9 0.0
98 157 14.9 13.5 3.8 0.0
98 158 14.0 14.6 2.2 0.0
98 159 21.2 17.0 4.1 0.0
98 160 22.4 20.0 2.9 0.0
98 161 8.7 18.3 9.8 6.1

144

 

 

 

 

Year DOY SR Tm, Tm R
MJ rn‘2 C° mm
98 162 6.8 18.1 12.1 2.3
98 163 7.0 19.9 12.6 3.8
98 164 22.3 27.2 16.8 2.0
98 165 16.1 22.0 14.3 7.4
98 166 23.0 24.4 12.8 0.0
98 167 24.7 25.8 14.5 1.3
98 168 20.1 26.0 14.3 2.8
98 169 27.0 26.4 14.9 0.0
98 170 25.3 28.6 13.8 0.0
98 171 27.6 27.1 17.6 0.0
98 172 27.3 30.5 15.9 0.0
98 173 22.3 29.7 18.5 0.0
98 174 27.7 29.4 17.1 0.0
98 175 27.3 30.2 19.6 0.0
98 176 19.6 30.9 15.6 7.1
98 177 25.8 32.9 19.7 15.4
98 178 27.9 28.8 18.3 2.3
98 179 16.0 28.2 18.1 1.0
98 180 19.6 28.8 19.6 0.0
98 181 28.9 29.5 16.9 0.0
98 182 17.2 22.9 17.6 3.6
98 183 28.8 25.9 13.7 0.0
98 184 28.7 26.4 10.8 0.0
98 185 22.1 27.8 15.2 0.8
98 186 9.6 21.3 13.8 6.6
98 187 29.5 25.3 10.4 0.0
98 188 15.5 26.9 15.0 13.4
98 189 6.3 24.1 18.4 21.5
98 190 16.4 26.1 17.4 0.0
98 191 25.3 26.8 14.9 0.0
98 192 28.4 23.7 13.4 0.0
98 193 29.4 25.4 9.1 0.0
98 194 28.5 26.8 11.0 0.0
98 195 26.6 27.2 12.6 0.0
98 196 25.4 29.6 15.7 0.0
98 197 22.5 29.6 17.8 0.0
98 198 22.7 28.6 19.1 2.3
98 199 24.7 26.1 15.3 0.0
98 200 26.4 28.1 10.4 0.0
98 201 16.2 29.1 17.4 1.8
98 202 26.8 30.5 18.4 0.0
98 203 16.0 31.7 18.0 10.4
98 204 16.4 26.8 19.1 0.0
98 205 25.7 24.6 14.1 0.0
98 206 20.5 23.0 10.7 0.0
98 207 17.0 23.8 11.1 0.0
98 208 26.7 26.3 9.5 0.0
98 209 19.0 25.6 13.9 0.0

145

 

 

 

Year DOY SR T}... T... R

W m'2 C° mm
98 210 26.5 28.2 16.3 0.0
98 211 25.3 26.5 14.9 0.0
98 212 14.2 25.5 16.1 0.0
98 213 22.2 25.9 11.9 0.0
98 214 27.4 26.7 9.9 0.0
98 215 26.0 27.9 9.6 0.0
98 216 14.9 26.8 12.0 0.0

146

Appendix C
LIST OF ABBREVIATIONS
Chapter 1

a Constant

B Bulk density

a The slope of the relationship between cumulative soil evaporation and the square
root of time during second stage evaporation

0 Volumetric soil water content

91 Initial soil water content

05 Saturated soil water content

055 Soil water content at the soil surface

931.1 Drained upper limit soil water content

9a.: Air dry soil water content

A0 The daily change of soil water content

C The percent of evaporable soil water that can be evaporated in a day at a certain

depth

d Soil depth

E Evaporation rate

E Potential evaporation

Es Soil water evaporation

13,, Actual soil water evaporation

Ec Cumulative soil evaporation

D(0) Soil water diffusivity

K(0) Soil water hydraulic conductivity
Saturated soil water hydraulic conductivity

n Constant

t Time

2 Distance

7» Boltzmann transform

147

 

Chapter 2

pgmochpygpop crm
CD5.

Constant

Constant

Function of both saturated and drained upper limit soil water contents
Volumetric soil water content

Soil water content at the end of ﬁrst day during a drainage cycle

Soil water content at the end of second day during a drainage cycle

Initial soil water content

Residual soil water content

Saturated soil water content

Drained upper limit soil water content

The daily change of soil water content

Hydraulic gradient

The percent of drainable soil water that can be drained in a day at a certain depth
The ﬁaction of drainable soil water that can be drained from a soil layer in the
ﬁrst day during a drainage cycle.

The fraction of drainable soil water that can be drained from a soil layer in the
second day during a drainage cycle.

Soil water evaporation

Soil water hydraulic conductivity

The ﬁrst day hydraulic conductivity

Hydraulic conductivity at 01

The second day hydraulic conductivity

Hydraulic conductivity at 02

Saturated soil water hydraulic conductivity

Function of drained upper limit soil water content

Soil water ﬂux

Time

Distance

148

Chapter 3

Constant

Constant

Constant

Constant

Function of both saturated and drained upper limit soil water contents
Volumetric soil water content

Soil water content at the end of ﬁrst day during a drainage cycle
Soil water content at the end of second day during a drainage cycle
Initial soil water content

Saturated soil water content

Drained upper limit soil water content

The daily change of soil water content

Hydraulic gradient

The slope angle

C siny The percent of drainable soil water that can be drained laterally in a day at a

Es
K(O)
K1(9)
K(91)

>< "meant-1
NS "' F

9

x., z.

certain depth

Soil water evaporation

Soil water hydraulic conductivity

First day hydraulic conductivity

Hydraulic conductivity at 91

Saturated soil water hydraulic conductivity
Integer

Function of drained upper limit soil water content
Soil water ﬂux

Saturated soil water ﬂux

Time

Water table depth

Cartesian rectangular space coordinates
Rotated Cartesian rectangular space coordinates
Distance

149

"lllllllllllll111111“