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dissertation entitled
Modeling the Concentration of Nitrogen in the Root Zone

of Container-grown Chrysanthemum

presented by

Mark V Yelanich

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Modeling the Concentration of Nitrogen in the Root Zone
of Container-grown Chrysanthemum

By

Mark V. Yelanich

A DISSERTATION

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

DOCTOR OF PH]LOSOPHY
Department of Horticulture

1995

ABSTRACT

Modeling the Concentration of Nitrogen

in the Root Zone of Container-grown Chrysanthemum

By

Mark V. Yelanich

The production of greenhouse container- grown crops requires the frequent application of
N applied to the medium in a water-sohrble form in the irrigation water. The management
of these crops requires that growers periodically monitor the medium to determine if the
correct concentrations of nutrients are being applied. The goal of this project was to
develop a better rmderstanding of the mechanisms influencing the root zone medium N
concentration. A model was developed to predict the root zone N content by integrating
the rates of N application, movement into the top layer and plant uptake. The rate of N
application was modeled as function a of the rate of water loss and the water holding
capacity of the medium The water vohime of the medium was modeled as a fimction of
the rates of evaporation and transpiration and were predicted using an empirical Penman
equation. The rate of N movement to the top layer was modeled as a fimction of the rate
of water evaporation and of irrigation rate and voMe. Plant N uptake was based on the
dry mass accumulation rate of the plant. The plant response to low concentrations of N in
the medium is modeled through a decrease in shoot N concentration, followed by a

decrease in the rate of leaf area expansion. The individual models were validated in

separate greenhouse and growth chamber experiments. The fill] model was validated by
producing Chrysanthemum ‘Bright Golden Anne’ at two times of the year (winter and
spring), three fluencc levels (70% shade, ambient and HPS) and with three N fertilizer
concentrations (3.5, 7, 10.5 mol-m’3 N). Plants were evaluated biweekly for leaf area,
total plant dry mass, plant chldahl N, root zone NO3-N and NH4-N content. Water loss
was evaluated daily gravimetrically. The model predicted the general trends of leaf area,
dry mass and plant N as well as N03-N and NH4-N contents. The model was used to

develop fertilization strategies to apply N more eficiently to the medium

Acknowledgments

I would like to thank all of the people who have helped me in different ways during
my time at MSU.

I would like to especially thank my advisor John Biembaum for his support and
encouragement of my pursuit of a career in science.

Appreciation also goes to the members of my guidance committee Drs.

R.D. Heins, I.E. Widders, D.D. Warncke and J .T. Ritchie. Of all the many people I have
come in contact at MSU, they have had greatest influence on my thinking about plants,
modeling and nutrition.

Many thanks to my friends and colleagues Jim Faust and Bill Argo, for their many
opinions and suggestions.

I would also like to thank my parents Loretta and Robert Yelanich, for their faith

and encouragement after all of these years of school.

I am also very gratefiil for the love and support of my wife Lisa.

iv

Guidance Committee:
The paper format was adopted for this dissertation in accordance with
departmental and university regulations. The papers are to be submitted to the Journal of

the American Society for Horticulture Science.

TABLE OF CONTENTS

Page
List Of Tables ............................................................................................................... viii
List Of Figures ................................................................................................................ ix
INTRODUCTION ......................................................................................................... 12
SECTION I A model to predict root medium evaporation and transpiration from
container-grown Chrysanthemum ..................................................................................... 7
Abstract ....................................................................................................................... 8
Materials and Methods ............................................................................................... 11
Results and Discussion ............................................................................................... 13
Literature Cited ......................................................................................................... 16
SECTION H A model to predict changes in the rate of leaf area expansion of
Chrysanthemum ‘Bright Golden Anne’ in response to shoot nitrogen .......................... 25
Abstract ..................................................................................................................... 26
Materials and Methods ............................................................................................... 28
Results and Discussion ............................................................................................... 31
Literature Cited ......................................................................................................... 34

SECTION III A model to predict the movement of nitrate and ammonium in a peat-based

root-medium. ............................................................................................................ 42
Abstract ..................................................................................................................... 43
Materials and Methods ............................................................................................... 46
Results and Discussion ............................................................................................... 49
Literature Cited ......................................................................................................... 50

SECTION IV A model to predict the rate of whole plant nitrogen accumulation in

subirrigated container-grown Chrysanthemum ‘Bright Golden Anne’ .......................... 56
Abstract ..................................................................................................................... 57
Materials and Methods ................................................................................................ 59
Results and Discussion ............................................................................................... 62
Literature Cited ........................................................................................................... 64

vi

SECTION V Validation of a model to predict the nitrogen content in the root zone of

container-grown Chrysanthemum ‘Bright Golden Anne’. ............................................ 73
Abstract ..................................................................................................................... 74
Materials and Methods ............................................................................................... 76
Results and Discussion ............................................................................................... 84
Abbreviations ............................................................................................................. 90
Literature Cited ......................................................................................................... 92
APPENDIX ................................................................................................................. 113

vii

LIST OF TABLES

Table Page

SECTION I

The 24 hour average of environmental parameters for the three days of the
experiment. Averages are calculated from .15 minute readings. . Numbers in
parenthesis are the minimum and maximum values for the 24 hour period. .............. 18

Mean (n=5) water loss per day (ml-day'l) for the 3 days of the experiment for 7
consecutive planting weeks of Chrysanthemum ....................................................... 18

SECTION II

Least squares estimates of the nonlinear regression parameters used to determine
shoot nitrogen concentration (Nam), rate of leaf expansion (LAM), and the response
of rate area leaf area expansion to shoot N concentration (fLA). Equation (eq.)

numbers refer to equations found in text. ............................................................... 37
SECTION IV

Parameter estimates for the nonlinear models describing plant dry mass (Eq [4] and

[5]) and plant N content (Eq [2]) ............................................................................ 66
SECTION V

Physical properties and saturated medium extraction (SME) parameters of the
medium used in the validation experiments. ............................................................ 95

Photosynthetic active radiation (PAR), dry and wet bulb temperatures and statistics
from winter and spring weather data ....................................................................... 95

Photosynthetic active radiation (PAR), dry and wet bulb temperatures and solar
irradiation statistics from generated weather data. .................................................. 96

Analysis of variance of leaf area, dry mass, plant N, total N applied and nitrate-N
concentration and ammonium N concentration 70 days since the start of short days.97

Optimization parameters for the 5 fertilizer strategies (F S) evaluated. ..................... 98

viii

Optimized leaf area, plant N, dry mass, total N applied, medium top layer (TLN),
medium root zone (RZN), and mean and standard deviation of root zone N at 70
days since start of short days of the 5 fertilization strategies (F S). Mean and standard
deviations were calculated over the entire 70 day period ......................................... 98

ix

List Of Figures
Figure Page

SECTION I

1. Total leaf area (cross hatched) and flower area (shaded) of Chrysanthemum from 7
consecutive planting weeks on Julian day 190. The lines at the top of each bar are
standard deviations of the mean (n=10). Leaf area did not decrease, plants were
smaller due to environmental conditions during rooting and growth. ....................... 19

2. Actual water loss compared with the model predictions for pots with (upper graph)
or without (lower) an evaporative barrier. The line in the upper graph corresponds to
the regression equation Actual Water loss = 1.14 * Predicted Water Loss -9. 05 (R2
= 0.87 n=120). The line in the lower graph corresponds to the regression equation
Actual Water loss = 1.07 * Predicted Water Loss -3.87 (R2 = 0.90 n=120) ............. 21

3. Simulated total (dashed line), transpirational (solid line) and evaporative (dotted line)
water loss for leaf area indexes from 0 to 12. Weather data from Julian day 190 was
used as model inputs. The leaf area was set to be 1000 cm2 at a leaf area index of 12.23

SECTION H
1. Predicted (lines) and actual (triangles) shoot N concentration at different times since
planting. The actual shoot N concentration is the mean of 5 replicates with the bars
above and below the points indicating the standard deviation of the mean. The arrows
pointing upwards indicate the time when the N starvation period was initiated. The
downward pointing arrows indicate the time when the N supply was replenished after
a starvation period .................................................................................................. 38

2. Predicted (lines) and actual (triangles) leaf area at difi‘erent times since planting. The
actual leaf area is the mean of 5 replicates with the bars above and below the points
indicating the standard deviation of the mean. The arrows pointing upwards indicate
the time when the N starvation period was initiated. The downward pointing arrows
indicate the time when the N supply was replenished after a starvation period ......... 40

SECTION HI
1. Before subirrigation (no fill), afier subirrigation (horizontal hatched) and model
(cross hatch filled) nitrate N contents (top graph) or ammonium N (lower graph) in
the root zone of a fallow pots filled with 100% peat. Bars over data are the standard
deviation of the mean (n = 5). Nitrogen was incorporated into to the medium prior
to filling at rates of 0.03, 0.06 and 0.12 kg ~m'3. The N concentration in the nutrient
solution was 133 mg-liter'l N03-N and 63 mg-liter'1 NIL-N. ................................ 52

2. Model (lines) and actual (0) water volumes (top graph), nitrate N content (middle
graph) or ammonium N content (lower graph) for the root zone of a fallow pot filled
x

with 100% peat . Bars over data points are the standard deviation of the mean (11 =
5). The volume of water applied to the medium was 0.2 liters on days 0, 9, 18 and
27. The concentration of nitrate-N applied to the medium was 102 mg - liter'l on days
0 and 18 and 33 mg-liter'lon days 9 and 27 . The concentration of ammonium-N
applied to the medium was 48 mg-liter'l on days 0 and 18 and 17 mg-liter'lon days 9
and 27. ................................................................................................................... 54

SECTION IV
Mean nitrate (right figures) and ammonium (left figures) N concentrations from the
medium of Chrysanthemums grown at 4 mol - day'l (top figures), 7 mol° day'l (middle
figures) or 11 mol-day'l (bottom figures) PAR. Concentrations were determined

from saturated medium extracts. Bars around triangles are the standard deviation of
the means (n=4). .................................................................................................... 67

Actual (triangles) and model predicted (lines) dry mass over time since start of short
days for Chrysanthemums grown at 4 mol-day'l (top figure), 7 mol-day" (middle
figure) or 11 mol- clay'l (bottom figure) PAR Bars around triangles are the standard
deviation of the mean dry mass (n=4). .................................................................... 69

Actual (triangles) and model predicted (lines) plant N content (mg) over time since
start of short days for Chrysanthemums grown at 4 mol-day'l (top figure), 7
mol-day'l (middle figure) or 11 mohday’l (bottom figure) PAR Bars around
triangles are the standard deviation of the mean plant N content (n=4) .................... 71

SECTION V
Diagram representing the various components of a model to predict N content in the
root zone of container-grown Chrysanthemum. I represents integration of a rate. 99

Leaf area over time since the start of short days under various light and fertilizer
treatments. Graphs in left column are the leaf area of plants receiving 3.6 mol -m‘3
(50 mg-liter'1) N, graphs in the middle column are plants receiving 7.1 mol-m”3 (100
mg-liter'l) N, and graphs in the right column are plants receiving 10.7 mol-m'3 (150
mg ~1iter") N. The top three rows are plants from the winter experiment and the
bottom three rows are from the spring experiment. Graphs in rows 1 and 4 are plants
grown under 30% shade, 2 and 5 are plants grown under ambient light conditions and
3 and 6 were grown under supplemental HID lighting. ......................................... 101

Dry mass over time since the start of short days under various light and fertilizer
treatments. Graphs in left column are the dry mass of plants receiving 3.6 mol - m'3
(50 mgsliter") N, graphs in the middle column are plants receiving 7.1 mol °m'3 (100
mg-liter'l) N, and graphs in the right column are plants receiving 10.7 mol-m'3 (150
mg'liter") N. The top three rows of graphs are plants fiom the winter experiment
and the bottom three rows are from the spring experiment. Graphs in rows 1 and 4

xi

are plants grown under 30% shade, 2 and 5 are plants grown under ambient light
conditions and 3 and 6 were grown under supplemental HID lighting. .................. 103

Plant N over time since the start of short days under various light and fertilizer
treatments. Graphs in left column are the plant N of plants receiving 3.6 mol-m'3 (50
mg-liter'l) N, graphs in the middle column are plants receiving 7 .1 mol-m'3 (100
mg-liter'l) N, and graphs in the right column are plants receiving 10.7 mol-m'3 (150
mg 01iter") N. The top three rows of graphs are plants from the winter experiment
and the bottom three rows are from the spring experiment. Graphs in rows 1 and 4
are plants grown under 30% shade, 2 and 5 are plants grown under ambient light
conditions and 3 and 6 were grown under supplemental HID lighting. .................. 105

Water loss over time since the start of short days under various light and fertilizer
treatments. Graphs in left column are the water loss of plants receiving 3.6 mol-m'3
(50 mg-liter'l) N, graphs in the middle column are plants receiving 7.1 mol- In3 (100
mg-liter'1) N, and graphs in the right column are plants receiving 10.7 mol'm'3 (150
mg ~1iter") N. The top three rows of graphs are plants from the winter experiment
and the bottom three rows are fi'om the spring experiment. Graphs in rows 1 and 4
are plants grown under 30% shade, 2 and 5 are plants grown under ambient light
conditions and 3 and 6 were grown under supplemental HID lighting. .................. 107

Root zone N content over time since the start of short days under various light and
fertilizer treatments. Graphs in left column are the root zone N content of plants
receiving 3.6 molom"3 (50 mg-liter") N, graphs in the middle column are plants
receiving 7 .1 mol-m'3 (100 mg-liter'l) N, and graphs in the right column are plants
receiving 10.7 mol-m'3 (150 mg-liter'l) N. The top three rows of graphs are plants
from the winter experiment and the bottom three rows are from the spring
experiment. Graphs in rows 1 and 4 are plants grown under 30% shade, 2 and 5 are
plants grown under ambient light conditions and 3 and 6 were grown under
supplemental HID lighting. ................................................................................... 109

Predicted root zone N concentration of saturated medium extracts over time since the
start of short days at two times of the year. Graphs in left column are the root zone N
concentration of plants grown during the winter experiment and graphs in the right
column are from the spring experiment. The graphs in row 1 (top) are predicted
results for plants grown with a constant fertilizer concentration, row 2 through 4 are
plants grown using a PD controller and with weekly medium sampling (row 2 and 4)
or daily medium sampling (row 3 and 5). The graphs in rows 2 and 3 were from
plants grown using a constant setpoint of 48 mg N where graphs 4 and 5 were based
on plants grown with optimized setpoints. ............................................................ 11]

xii

INTRODUCTION

Introduction

The production of floriculture crops is an intensive process, requiring frequent
applications of nitrate and phosphate fertilizer, micronutrient heavy metals, pesticides, and
fungicides. The public’s negative perception of fertilizer and chemical usage has resulted in
legislation to limit the amount of chemical residue on the surface of fruits and vegetable.
Laws have also been passed restricting and regulating the application of pesticides to
plants in many states.

The increased regulation of chemical use and the poor public perception of these
chemicals will force changes in the production of ornamental crops. One change is a
reduction in the availability of chemicals used in crop production. For example, after the
elimination of food crops from the label of Aldicarb (Temik) the manufacturer stopped
Aldicarb production, preventing its use in ornamental production, even though it was still
legal. This has resulted in dramatic changes in the way ornamental producers control pests
in their crops and a long period of learning new methods of pest control. Another example
was the use of Alar (B-Nine) on apples resulting in a negative perception of the whole
apple industry. The “Alar-scare” briefly affected the ornamental industry for a period of
time because of the uncertainty about B-Nine availability for non-food crops. The negative
public perception of the apple industry did not pass on to the production of ornamental
crops but the potential was there.

The other aspect of possible environmental contamination from ornamental crop
production is through the use of fertilizers. Greenhouses [are a point source of water and
fertilizer runofi‘ since the source of pollution is confined. Fertilizers are applied by a pre-

1

2
plant incorporation into the medium and in the irrigation water in the form of water-
soluble nutrients. The most common way of applying the fertilizer in the irrigation water is
by top watering with drainage of excess fertilizer out the bottom of the growing
container.

In the 1960’s, three major developments occurred changing the way growers
produced flowering pot grown crops. One was the widespread availability of peat-based
media, another was the use of drip irrigation, and the third was the increased use of water
soluble fertilizers and proportioners. Peat-based media were designed to be very porous
and very hard to over water. Water soluble fertilizers and drip irrigation allowed growers
to easily apply fertilizer with every irrigation. These three developments, while
revolutionizing the way a plant could be grown in a pot, triggered a trend for increasing
water soluble fertilizer application.

One draw back with the use of drip irrigation is that high volumes of water are
applied to provide uniform irrigation of a crop. With high volumes of water was applied in
excess of the water holding capacity of the medium and fertilizer or excess salts are
removed from the pot, so higher fertilizer concentrations are required. Growers not using
drip irrigation or high volume applications, but trying the higher concentrations of
fertilizer that were being recommended, found that higher volumes of solution were
required to keep salts from building up in the media. Over the years a wide variety of
irrigation methods and a range of fertilizer concentration have evolved and has led to
confusion among growers.

To better understand how the fertilizer concentration applied and the leaching

3

volume influence medium nutrient concentration, experiments were carried out at
Michigan State University from 1988 to 1991 (Y elanich, 1991;Yelanich and Biembaum,
1993; Yelanich and Biembaum, 1994). Poinsettias were grown using 3 fertilizer
concentrations (100, 200, and 400 ppm N and K), and 4 leaching fi'actions (0.00, 0.10,
0.20 and 0.40). Plants were also grown using subirrigation at the 3 fertilizer
concentrations. Leaching fraction is the volume solution leached divided by the volume of
solution applied. Multiplying the leaching fraction by 100 equals the leaching percentage,
therefore a 0.10 leaching fraction equals a 10% leaching percentage. Poinsettia was used
in these experiments since it has a reported to have a “high” requirement for fertilizer and
is produced by many growers.

There were several conclusions drawn from this work. The first conclusion was
that leaching fraction and the fertilizer concentration applied interact in determining the
concentration of nutrients in the medium. Historically fertilizer recommendations were
made based on a fertilizer concentration to apply without regards to the leaching volume
used. One finding from this work was that a range of leaching fractions and fertilizer
concentrations could be used to achieve the same concentration of nutrients in the
medium. However, combinations of “high” fertilizer concentrations and “high” leaching
fraction resulted in higher quantities of fertilizer leaving the pot and potentially entering
into the environment. It is therefore possible to reduce fertilizer concentration and
leaching fraction to achieve a desired medium nutrient concentration while reducing
nutrients being leached from the pot. The most interesting finding was that it was possible

to eliminate leaching by reducing the fertilizer concentration and maintain the nutrients at

4
acceptable ranges in the medium. From this work a series of best management practices
for fertilizing container-grown crops were developed:

1. Reduce the volume of leachate that occurs with every irrigation or use zero

leaching systems when possible. Irrigation water quality will ultimately determine

the amount of leaching required.

2. Reduce the concentration of fertilizer applied when using lower leaching

volumes. The correct concentration of fertilizer applied will ultimately be

determined by the weekly media tests.

3. Monitor the nutrient levels in the medium by media testing. Using more efficient

methods of fertilizing crops requires closer monitoring of the medium to prevent

troubles from occurring.

A greater reliance on medium testing requires a better understanding of the processes
that influence nutrient intensity, balance and availability in the root zone of a pot grown plant.
Since medium nutrient testing occurs at discrete intervals during the crop, how rapidly the
medium nutrient concentration changes will influence what types of decisions can be made
based on these tests. One way of understanding the way a system works is through
construction of a model. Simulation models allow researchers to evaluate, in real time, how
different strategies influence the outcome of some process (Ritchie, 1986). By constructing a
model we hope to better understand what happens to the nutrients that are applied and through
this understanding develop better fertilization recommendations for container-grown plants.
These recommendations would be unlike fertilization recommendations made in the past in that

they would:

5
1. Be based on the current medium nutrient concentrations instead of a concentration
of fertilizer to apply,
2. Limit the use of fertilizer or at least apply the fertilizer in a way for the most
eflicient use by the plant,
3. Be based on best management practices and use a zero leaching system.
The use of a model will also allow researchers and growers to see in real time how the N
concentration in the medium changes in response to some strategy and test various strategies
quickly.

Plants provide color and beauty to the world. The very existence of public and
private gardens, gardening clubs, books and magazines provide tangible proof of the value
people attribute to plants. People have strong associations between plants and difl‘erent
events and holidays, such as roses at Valentines day, poinsettias at Christmas and lilies at
Easter. People use plants to comfort people at a firneral or to cheer up some one who is
sick. The main theme of all of these examples is there is generally a good perception of
plants and the floriculture industry. A better understanding of fertilization of container-
grown plants and a reduction of fertilizer runoff will promote this perception.

Literature Cited

George RK. 1989. Flood subirrigation systems for greenhouse production and potential for
disease spread. MS Thesis, Michigan State Univ, East Lansing.

Ritchie J .T. 1986. Using simulation models for, predicting crop performance. ISSS Congress
Hamburg FRG. 1-8.

Yelanich, M.V. 1991. Methods to improve fertilization to minimize nitrogen runofl‘. MS thesis.
Michigan State Univ, East Lansing.

6

Yelanich, M.V. and J .A Biembaum. 1993. Root-medium nutrient concentration and growth of
poinsettia at three fertilizer concentration and four leaching fractions. J. Amer. Soc.
Hort. Sci. 118177 1-776.

Yelanich, M.V. and J .A. Biembaum. 1994. Fertilizer concentration and leaching affect nitrate-
nitrogen leaching from potted poinsettia. HortScience 29:874-875.

SECTION I

A MODEL TO PREDICT ROOT MEDIUM EVAPORATION
AND TRAN SPIRATION FROM CONTAIN ER-GROWN
CHRYSANTHEMUM

A Model To Predict Root Medium Evaporation And Transpiration From

Container-grown Chrysanthemum

Mark V. Yelanich and John A. Biembaum

Department of Horticulture, Michigan State University, East Lansing, 114] 48824-1325

Received for publication_. Acknowledgment is made to the Michigan State Agriculture
Experiment Station. The use of trade names in this publication does not imply
endorsement by the MSAES of the products named, nor criticism of similar ones not

mentioned.

Soils, Nutrition and Fertilizers

A model to predict root medium evaporation and transpiration for container-grown
chrysanthemum

Additional index words: Dendranthemum morifolium, peat-based medium, Penman

equation, mathematical model.

Abstract

The empirical form of the Penman equation was validated for use in predicting
water loss from container-grown chrysanthemum. Thirty pots of chrysanthemum were
planted at one week intervals for 7 weeks. On the eighth week, all of the plants and
medium were subirrigated, and then weighed 0.5 and 24 hours later to determine the
amount of transpiration and evaporation occurring during that time period. This was
repeated for 3 sequential days. To separate plant transpiration fiom medium evaporation,
fifleen pots per planting week had an evaporative banier placed on the surface of the root
medium. Total leaf area, wet and dry bulb temperature and photosynthetic radiation were
also measured. An empirical equation was used to estimate the net radiation. There were
significant decreases in water loss by covering the medium surface only for fallow pots and
for plants 1 and 3 weeks from planting. Regression equation slopes for covered and
uncovered pots comparing the model predictions with the actual water loss were 0.99 and
1.03 indicating a near 1:1 relationship. The model predicts that as leaf area increases the
water loss due to evaporation from the medium surface decreases and the water loss due

to transpiration by the plant increases.

9

Many processes occurring in the production of container-grown crops are
influenced by water loss from the medium surface and by the plant. Evaporation and
transpiration, while obviously influencing the water balance of a container-grown plant,
also influence the volume of water soluble fertilizer applied and the movement of fertilizer
salts to the top layer of root-medium in a pot. When an evaporative barrier was placed on
the surface of the medium of an Easter lily the average water applied was reduced by 37%
and the average N fertilizer applied was reduced by 35% (Argo and Biembaum, 1994).
Hunt (1988) reported the electrical conductivity top-watered chrysanthemum built up
more rapidly in the summer than in winter when the irrigation frequency was reduced.

Chen and Lieth (1992) constructed a model accurately predicting water loss from
container-grown chrysanthemum using the Penman-Monteith combination equation.
While this was a successful approach, often a more simplified form of this equation can be
used where an empirical wind fimction replaces the more complicated resistance terms
(Allen et al. 1989). 'The goal of this research was to test a simplified version of the
combination equation to predict evaporation and transpiration of water from container-
grown chrysanthemum.

The Penman equation provides the basis for the loss of water from the plant and
medium surface. Potential transpiration from the plant is described by

A- Rplant+Y°6.43'f(U)‘(Ca-ed)

AET r:
M A+y

 

[1]

where XETPM is the vapor flux density from the plant (MJ - rrr'3 - d'l), A is the slope of the

saturation vapor pressure function, y is the psychometric constant, Rnpm is the net

10
radiation (MJ - rn’2 - d'l), e. is the saturated vapor pressure (KPa), ed is the saturation vapor
pressure at the dew point temperature (KPa), and flu) is the empirical wind function
(Allen et al. 1989). The evaporation of water from the surface of the medium can be
described by a similar equation,

Atrium...- G)-1~'yo6.43-f(u)-(e.-ed)
A+y

71. ' ETmedium =

 

[2]

in where ancdm is the medium net radiation, G is the medium storage of heat. The net

radiation budget of the plant (Rnpm) and medium (andim) are described by,

Rnpm = a*(l+r)*S+a1r*o *[(r...)‘ +(r...)‘]— 2 *e.*o*(r1..r)‘ [3]

Ram... = (1 —a) *s +a. *0 *[(r...)‘ + (r...)‘]— e. *0 *(T.......)‘ [4]
in where S is solar radiation, a is the absorbance coemcient, at, is the infrared radiation
(IR) absorbance coefficient, r is the reflectance coefficient, er, is emmisivity of IR, 0 is the
Stephan-Boltzman constant (4.903 x 10'9 MJ -m’2- d'1 ~K") and Tm, TM, TN, and
Twin... are the surrounding, sky (glass), leaf and medium temperatures. One limitation to
using equations [3] or [4] is that only air temperature is commonly available in commercial
greenhouses. An alternative to using equations [3] and [4] is to estimate net radiation
based upon the solar radiation, average daily air temperature (ADT) and saturated vapor
pressure (ed) using the form described by

Rnplant = (1" a) * RSplant - O’ * (ADT + 273)‘ * (0.39 — 0.1585) * (7:57) [5]

0

anmm = (1 —a) *Rsmr..- o * (ADT+ 273)‘ *(039 — 0.1585) {£1} [6]

0

11
were at is the crop or medium albedo, and R,o is the clear sky solar radiation
(MJ-m'z-d"), Rs is the actual solar radiation (MJ-m'Z-d"), Rsplmt is the short wave
radiation reaching the plant canopy (MJ 'm'z - d"), and Rsmcdium is the short wave radiation
reaching the medium surface (MJ -m'2-d") (Jensen et al. 1989). Rsmfium can be modeled
as a fimction of the incoming Rs, the plant leaf area index (LAI) and the albedo of the
medium (amalgam) (Chen and Leith, 1992) and is described by,
Rsmedium = amedium * RS * 6032.”? [7]
Chen and Leith found values of 0.25 for chrysanthemum am and 0.2 for peat medium
(Imam. Rs can be estimated from PAR measurement based on values found in Thimijan
and Heins (1983).
The empirical wind function f(u) generally has the form of
flu} = aw+ bw * u [8]

in where u is the wind speed at 2 m above the ground. Air velocity has been treated as a
constant value of 1.2 m-sec'l by Chen and Lieth (1992) simplifying f(u) to 1.4. Using a
typical air exchange values of 1 to 2 exchanges per minute, greenhouse air velocities could
range from 0.5 to 1 m-sec'l and from 0.2 to l m'sec'l due to horizontal air flow fans
(Nelson, 1994). Values for aw and bw of 1 and 0.53 respectively were used by Penman

(1943)

Materials and Methods

Ten pots of chrysanthemum "Kory" were planted each week for 7 consecutive weeks.

Three unrooted cuttings were planted in a 100% Sphagnum peat media in 110 mm tall by 130-

12
mm wide plastic-pots (690 cm3) and placed under intermittent mist. After 1 week the plants
were removed from the mist bench and placed in a 20 C greenhouse and then pinched to 6
nodes 1 week later. Plants were subirrigated every 3-4 days using a nutrient solution consisting
of 5.7 mol-m'3 (80 mg-liter'l) NO3-N, 1.4 mol-m'3 (20 mg-liter'l) NH4-N, 0.7 mol-m'1 (21.7
mg-liter'l) P, 2.1 mol-m'3 (82 mg-liter'l) K (Peters 20-10-20, Scotts, Marysville, Ohio), plus
a micronutrient mix at a rate 2.5 mg - liter'l (STEM, Scotts, Marysville, Ohio).

Eight weeks after the start of the experiment a polyethylene film evaporative banier
was placed on the surface of the medium on 5 pots fiom each planting date plus the surface of
5 fallow pots. The plants were then subirrigated with water at 23 :00 hr, allowed to drain,
weighed, and weighed again 24 hours later. For plants without the evaporative barrier the
difi‘erence between these two measurements was the amount of water lost by evaporation and
transpiration for that time period. For plants with an evaporative barrier, the difl‘erence
between these two measurements was the water lost only by transpiration Irrigation and water
loss measurements were repeated on three consecutive days. After the final water
measurement on the third day, plant fiesh mass, leaf area, shoot and root dry mass were
measured. Wet and dry bulb air temperature and PAR radiation were measured throughout the
experiment. Relative humidity and vapor pressure were determined from the wet and dry bulb
measurements.

The model was run using the leaf area for each planting date and the average daily
dry bulb temperature, average daily wet bulb temperatures and solar radiation for each

house. Total water loss (dWL/dt) (liters- day'l) was calculated from,

dWL/dt = dWLphm/dt + dWLm/dt, [9]

13
in where WLmdium is the medium water loss and WLle is the plant water loss. WLplam
was determined from,
dWLplant/dt =7tETplant * fplmfiLA/ (2.45 liters 0 MT 1), [10]
in where LA is the leaf area (m2) and film, is the correction factor for chrysanthemum.
Wlmdimn was determined from
dWmedint =kETmedium *fmdi.*MA/ (2.45 liters °MJ"1) [11]
in where MA is the exposed medium area (m2) and fmfi. is the correction factor for
chrysanthemum. To simulate pot covering, WLmdi. was multiplied by the effectiveness of
the pot cover, a constant based on the covered and uncovered fallow pots.
The least squares estimates of fphm and fmcdi. were determined by using the NLIN

procedure (SAS institute, 1990).

Results and Discussion

The three days water loss was measured provided a range of solar environments
however the vapor pressure deficit (VPD) was fairly low for all three days due to humid
conditions and rain on day 2 (Julian day 191) of the experiment (Table 1). Other studies
(Stanghellini,1987) had VPD range from 0 to 1.2 kPa, where our values range 0 to 0.3
kPa. The variability in leaf area from week to week was probably due to variation in
temperature during the period from propagation to the start of the experiment and does
not represent a typical growth curve for chrysanthemum (Figure 1).

The reduction in evaporation due to covering the medium was greatest for the

younger plants and was nonsignificant when leaf area was greatest (Table 2). This appears

14

to contradict results for Easter Lily and poinsettia (Argo and Biembaum, 1994, 1995)
where covering the surface of the medium with an evaporative barrier reduced the quantity
of water applied to the pot by up to 37%. In both studies with Easter Lily and poinsettia
the cover was on for the entire duration of the crop and had an influence on the plant
architecture and medium nutrient concentration and may have affected the results. In the
current study, the cover was only placed on the medium surface for three days and had no
impact on plant morphology. Also, since the pots were irrigated at the start of each day
the medium nutrient concentration did not vary greatly between covered and uncovered
treatments. Another possible explanation for these differences are the difi‘erences in
architecture between chrysanthemum, poinsettia and Easter lily. It is possible that more
solar radiation reaches the medium surface per unit LA] of poinsettia or Easter lily than in
chrysanthemum, resulting in more evaporation.

The least squares estimates of film and fmdi. were 0.46 and 1.43 and resulting in an
R2 of 0.97 (n=240). The cover was 74% effective in reducing the evaporation of fallow
pots. Regression equations comparing the predicted evapotranspiration and the measured
water loss (Figure 2) were determined for covered and uncovered pots. Regression
equation slopes for uncovered and covered media were 1.14 and 1.07 indicating a near 1:1
correspondence between the predicted water loss and measured water loss. One
consideration when covering the surface of the medium is the reduction of the vapor
pressure of the air around the plant influencing the water loss due to transpiration (Ritchie,
1983). The assumption for this experiment was that covering only influenced medium

evaporation of water and had no influence on plant transpiration. No measurements of

15
canopy humidity levels were made to determine if there was an influence of covering on
humidity inside the canopy. If there was an influence of covering on transpiration the
regression equation slopes for the plants with an evaporative barrier plants would have
been less than the plants without an evaporative barrier since the VPD would have been
greater resulting in more water loss via transpiration. A t-test comparing the two slopes
(Steel and Torrie, 1980) was found non-significant (t = 0.24118, 11 = 23 6).

The evaporation of water from the surface of the medium is one driving force for
the movement of salts to the surface of the medium (Guttormsen, 1969; Yelanich, 1994).
To demonstrate the influence of leaf area on WL a simulation was run using the weather
data fiom Julian day 190 and leaf area indexes from 0 to 12 (Figure 4). Increases in LAI
resulted in decreased WLmdium and increased WLPM. The potential for salt movement
toward the medium surface is therefore greatest earlier in the crop and decreases as the
leaf area increases. The magnitude of this salt movement with subirrigation was
demonstrated by Argo and Biembaum (1994) who found that a majority of the nutrients
initially incorporated into the medium moved toward the surface within days of planting
the crop.

Currently the model does not respond to the moisture status of the medium. The
plants in this experiment were subirrigated at the start of each day so the medium moisture
tensions were low throughout the day. Chen and Leith (1992) incorporated hydraulic
conductivity terms into their model, and accurately simulated medium water loss as a
firnction of the moisture content of the medium. A more simplified relationship is

described by Priestley and Taylor (1972) where the drying cycle is broken down into a

16
maximum rate phase and a falling rate phase. After an irrigation the water loss from the
medium is at the maximum rate and is only limited by environmental conditions. At some
media specific water content the rate begins to fall as a firnction of the medium water
content until the rate becomes zero.

The current model also does not take into account the possibility for high
concentrations of fertilizer salt decreasing the osmotic potential of the water, thereby
decreasing transpiration. Increases in medium EC would not be expected with
subirrigation unless the concentration applied was dramatically increased. A simple
empirical model could be constructed to reduce the potential transpiration rate as a
function of the medium nutrient concentration.

This feasibility of using a simplified version of the Penman combination equation to
predict evaporation and transpiration of water form container-grown chrysanthemum was
demonstrated. The main benefit of using the simplified form of the Penman equation is that

fewer environmental measurements are needed.

Literature Cited

Allen RG., M.E. Jensen, J.L. Wright and RD. Burman. 1989. Operational estimates of
reference evapotranspiration. Agron J. 81:650-662.

Argo, W.R and J .A Biembaum. 1994. Irrigation requirements, root-medium pH, and
nutrient concentrations of Easter lilies grown in 5 peat-based media with and without
anevaporative barrier. J. Amer. Soc. Hort. Sci. 119:1151-1156.

Argo, W.R and J A Biembaum. 1994. Availability and persistence of macronutrients from
preplant nutrient charge materials and lime in peat-based root media. HortScience
292253 (Abstract).

17

Argo, W.R and J .A Biembaum. 1995. The effect of irrigation method, water-soluble
fertilization, preplant nutrient charge, and surface evaporation on early vegetative and
root growth of poinsettia. J. Amer. Soc. Hort. Sci. 120:163-169.

Bunt, AC. 1988. Media and mixes for container-grown plants. 2nd ed. Unwin Hyman,
London.

Chen, D. and J .H. Lieth. 1992. Two-dimensional model of water transport in the root zone
and plant for container-grown chrysanthemum. Agricultural and Forest Meteorology
59:129-148.

Guttormsen, G. 1969. Accumulation of salts in the subirrigation of pot plants. Plant and Soil
31 :425z438.

Jensen, ME. 1973. Consumptive use of water and irrigation requirements. Technical
committee on irrigation water requirements, AS.C.E, New York pp. 24-28.

Nelson P.V. 1994. Greenhouse operation and management. 4th edition Prentice Hall, New
Jersey.

Penman, H.L. 1948. Natural evaporation fi'om open water, bare soil and grass. Proc. R Soc.
London, A193: 120-146.

Priestley, C.H.B. and RJ. Taylor. 1972. On the assessment of surface heat flux and
evaporation using large-scale parameters. Monthly Weather Review 100:81-92.

Ritchie, J .T. 1983. Eficient water use in crop production: Discussion on the generality of
relations between biomass production and evapotranspiration, p. 29-44. In HM.
Taylor, W.R Jordon and TR Sinclair (eds). Limitation to eflicient water use in crop
production. ASA-CSSA-SSSA Madison, WI.

Stanghellini, C. 1987. Transpiration of greenhouse crops an aid to climate management.
Instituut voor Mechanistatie, Arbeid en Gebousen. Wageningen, 1987.

Steel RG and J .H. Torrie. 1980. Principles and procedures of statistics: A biometric approach.
McGraw-Hill New York.

Thimijan RW. and RD. Heins. 1983. Photometric, radiometric and quantum light units of
measure: A review of procedures for interconversion. HortScience 18:818-822.

Yelanich, M.V. 1995. Modeling the concentration of nitrogen in the root zone
of container-grown chrysanthemum. Ph.D. dissertation Michigan State Univ.

11$

18

Table l. The 24 hour average of environmental parameters for the three days of the
experiment. Averages are calculated from 15 minute readings. Numbers in
parenthesis are the minimum and maximum values for the 24 hour period.

 

 

 

Julian Date PAR Solar Dry Bulb Wet Bulb Average VPD
mol ‘day'l MJ ' m'2 - d'1 C C KPa
Mean

190 18.3 9.4 21.4 19.8 0.35
(17.6-27.9) (15.9-26.2) (0.22-0.49)

191 5.4 2.8 22.1 21.0 0.25
(18.9-26.8) (16.8-25.4) (0.07-0.54)

192 12.4 6.3 22.7 21.4 0.31

(20.0-26.4) (19.4-23.5) (0.07-0.80)

Table 2. Mean (n=5) water loss per day (ml- day") for the 3 days of the experiment for 7
consecutive planting weeks of chrysanthemum.

 

 

 

 

 

 

 

 

 

 

Weeks Since Planting
fa_llow 1 2 3 4 5 6 7
wmmmmmnmmy 190
-Cover 41 66 87 77 102 84 86 84
+Cover 10 48 76 64 92 90 80 74
t-test * * ns * ns 11s ns ns
WW3! 19L
-Cover 12 24 28 25 27 26 26 28
+Cover 7 16 24 11 28 29 25 28
t-test * * gas * ns ns ns ns
wammmmmnmmy L93
-Cover 25 48 61 52 63 54 51 49
+Cover 5 39 55 34 58 58 49 47
t-test * * ns * ns ns ns ns

 

 

ns and * refer to significance at 0.05 or nonsignificant, respectively

19

Figure 1. Total leaf area (cross hatched) and flower area (shaded) of chrysanthemum from
7 consecutive planting weeks on Julian day 190. The lines at the top of each
bar are standard deviations of the mean (n=10). Leaf area did not decrease,
plants were smaller due to environmental conditions during rooting and

growth.

20

 

 

 

1200

 

Weeks Since Pinch

21

Figure 2. Actual water loss compared with the model predictions for pots with (upper
graph) or without (lower) an evaporative barrier. The line in the upper graph
corresponds to the regression equation Actual Water loss = 1.14 * Predicted
Water Loss -9. 05 (R2 = 0.87 n=120). The line in the lower graph corresponds
to the regression equation Actual Water loss = 1. 07 * Predicted Water Loss -

3.87 (R2= 0.90 n=120).

22

 

120

100

l

80

l

60

l

A
O
l

N
O
l

 

100 a

Actual Water Loss (ml day'l)

60

l

40-

20

l

 

 

 

 

O l l I l
0 20 40 60 so

Predicted Water Loss (ml day'l)

1

100

120

23

Figure 3. Simulated total (dashed line), transpirational (solid line) and evaporative
(dotted line) water loss for leaf area indexes from 0 to 12. Weather data from

Julian day 190 was used as model inputs. The leaf area was set to be 1000

cm2 at a leaf area index of 12.

24

 

 

 

 

100

_

O
00

_

O
6

A196 :5 mac.“ 683

12

10

Leaf Area Index (LAI)

SECTION II

A MODEL TO PREDICT CHANGES IN THE RATE OF LEAF
AREA EXPANSION OF CHRYSANTHEMUM ‘BRIGHT
GOLDEN ANNE’ IN RESPONSE TO SHOOT NITROGEN

A Model To Predict Changes In The Rate Of Leaf Area Expansion Of

Chrysanthemum ‘Bright Golden Anne’ In Response To Shoot Nitrogen

Mark V. Yelanich, John A. Biembaum and Royal D. Heins

Department of Horticulture, Michigan State University, East Lansing, 114] 48824-1325

Received for publication . Acknowledgment is made to the Michigan State
Agriculture Experiment Station (MSAES). The use of trade names in this publication
does not imply endorsement by the MSAES of the products named, nor criticism of

similar ones not mentioned.

25

26

Soils, Nutrition and Fertilizers
A model to predict changes in the rate of leaf area expansion of chrysanthemum

‘Bright Golden Anne’ in response to shoot nitrogen

Additional index words: Dendranthemum morifolium, peat-based medium, mathematical

model, subirrigation.

Abstract

A model was constructed to predict how changes in shoot N concentration
influence the rate of leaf expansion of chrysanthemum. The model is based on a linear
relationship between a minimum shoot N (NM) where no leaf expansion occurs and a
maximum shoot N (NM) where there is no improvement in leaf expansion. To calibrate
the model, the N in the root zone of chrysanthemum ‘Bright Golden Anne’ was removed
at 5-day increments from 10 days after planting until 30 days after planting and also was
added back at 5 day intervals, producing plants experiencing N deprivation from 0 to 20
days. From this experiment, values of Nm and N,m were determined to be 2.7 and 6.8 %
(dry weight basis), respectively. The model successfully simulated the changes in the rate

of leaf area expansion occurring due to changes in shoot N.

27

One response of plants to N deficiency is a limitation of expansive leaf growth
(Charles—Edwards, 1979) thus limiting ultimate biomass production and potentially
reducing yield (Greenwood, 1976). In container-grown chrysanthemum (Dendranthemum
morifolium), leaf area is also a plant parameter determining plant quality. Leaf area also
influences processes such as transpiration and evaporation from the root medium surface
(Cheng and Lieth, 1991). The chrysanthemum has been selected for dark green foliage
with high N concentrations in the leaves, and is sensitive to low N availability (Elliot and
Nelson, 1983). While models exist to predict various aspects of chrysanthemum growth
and development, there are none available to dynamically predict the changes in the rate of
chrysanthemum leaf area expansion in response to differences in N availability.

In crops such as corn and wheat, the equation

0 ---for Nm<Nm
fLA= (Nam-Nm)/(Nm-Nm) ---for Nnin<Nshoot<Nmax [I]
l ...for Nshoot>Nmnx

has been used to simulate the relationship between the rate of expansive leaf grth and
the N concentration in plant tissue (Goodwin and Jones, 1991). In equation [1], New is
the N as a percentage of dry mass in the shoot tissue, Nmin is the percent N in the shoot
tissue where no expansion occurs and NM is the percent N in the shoot tissue where
there is no improvement in leaf expansion. When NM» is greater than or equal to N...“ the
rate of leaf expansion is at the maximum potential rate, and when Nam. is less than NM

the rate of leaf expansion is reduced as a function of Nam. When Nam is less than or

28
equal Nmin, the rate of leaf expansion is zero. The rate of leaf area expansion as a function

of the shoot N concentration can be described by,

dLA_dLAm*
dt dt

 

fu [2]

where dLAmx/dt is the maximum potential rate of leaf area expansion. When fiA is equal
to 1, dLA/dt is equal to dLAmx/dt. The objective of this research was to determine Nmin
and N"...x and to test the hypothesis that fLA describes the response of chrysanthemum leaf
area expansion to shoot N concentration. If successful, fLA will be incorporated into a

larger model of the N flow in container-grown chrysanthemum

Materials and Methods

One rooted cutting of chrysanthemum ‘Bright Golden Anne’ was placed in a 9-cm
tall by 12.5-cm wide pot (754 cm3 volume) filled with a 100% sphagnum peat medium.
Prior to planting, KN03 (0.06 kg-m'3), Ca(N03)2 (0.06 kg-m'3), MgSO4 (0.03 kg-m'a),
02130. (0.06 kgsm’3), CaHPO4 (0.06 kg-m'3), hydrated lime (0.21 kg'm'3) and a
micronutrient mix (F TB 555, 0.01 kg-m'3 Scotts, Marysville, Ohio) were incorporated
into the medium.

Plants were placed in a 1.3 by 2.5 m growth chamber with day and night
temperatures of 20 C and exposed to 16-l-IR photoperiods for the first 7 days, after when
the shoots were pinched to 6 nodes and placed under 10-HR per day photoperiods. Plants
were pruned to 3 shoots per plant when the shoots were 1 cm in length. Irradiance in the

chambers was supplied by cool-white fluorescent tubes (Philips VHO F96712/CW/VHO)

29
and incandescent bulbs (Sylvania 60-W) with an input wattage of 77% and 22%,
respectively. The light source supplied an average fluence rate of 317 umol-m'z-sec'l
(11.4 mol -m'2- (1").

Plants receiving N were fertilized at every irrigation with 9.5 mol-m'3 (133
mg-liter") N03-N, 4.5 mol0m’3 (63 mg°liter") NIL-N mol-m'3 and 5 mol-m‘3 (195
mg-liter") K made from KNO3 and NH4N03. Plants not receiving N were fertilized 5
mol'm'3 (195 mg-liter'l) K made from KSO4. Both solutions contained 0.48 mol-m‘3 (15
mg liter”) P from 85% phosphoric acid and micronutrients supplied fi'om 50 mg-liter'l of
Compound 111 (Scotts, Marysville, Ohio). Water used to make the nutrient solution had
an initial alkalinity of 1.7 mol°m'3 (170 mg-liter'l) CaC03 , pH of 6.4 and an EC of 0.3
dS 0m". Plants were weighed daily and irrigated when the mass of the plant, pot and
medium was less than 350 grams. This weight corresponded to approximately 55% of the
total water lost and resulted in no visible wilting. Plants were kept in individual water
tight trays and were subirrigated by pouring 0.2 liters of solution into the tray, a volume of
solution that could be absorbed by the medium within 0.5 hr of the application.

Groups of 25 plants were fertilized with the N solution until either day 10, 15, 20,
25 or 30 after planting when the N supply to the plant was withheld exposing plants to 20,
10, 15, 5 or 0 days, respectively, without N being applied. On the first day when the N
supply was withheld individual plants were irrigated from the top one time with 3 liters of
the minus N solution. All subsequent irrigations to these plants were made with the minus

N solution and applied by subirrigation. An initial experiment determined that 3 liters of

30
the minus N solution removed more than 90% of the SME N. In addition to the above
treatments, on day 10, 25 plants were leached with 3 liter of minus N solution and had the
N supply withheld until either day 10, 15, 20, 25 or 30 respectively. This resulted in plants
not being supplied with N for 0, 5, 10, 15 or 20 days. Five plants per treatment were
collected at 5 day increments from day 10 to 30 for a total of 5 sampling dates. Total leaf
area (Delta-T Devices, Cambridge, England), shoot Kjeldahl N concentration (Diamond,
1992), root medium N03-N, and NH4-N concentration (W arncke, 1986 ) were determined
at each sampling date.
A model was constructed to predict Nd“... the shoot percent N as a firnction of the
days since planting, days since termination of N supply and days of re-application of N
after its removal, and is described by,
Nshoot = be + b1 *t + fstarv+ free, [3]
where b0 and b1 are parameters to be estimated, t is the days since planting, fm is a
function of days since the N supply was terminated, frec is function of the number of days
since N supply was resumed after a period of no N application. The firnction fm reduces
Nam. as a function of the days of no N application and is described by,
fstarv = b2 * tstarv, [4]
where b; the parameter to be estimated and tum, is the number of days since the N was
leached from the medium and no other N being applied. The function f...c increases Nam. as

a firnction of the days since the resumption of N application and is described by,

free = b3 * tree, [5]

31

where b; is the parameter to be estimated and t,cc is the number of days of N re-
application. The maximum value of Nam. is described by,

Nshootmax = be + b1 * t. 16]
The least squares estimates of b0, b1, b2 and b3 were determined by using the NLIN
procedure (SAS institute, 1990). The values of b0, b1, b2 and b3 were used to predict Nam
and allowed for the least squares estimates of LAM, Nm and Nmin to be determined using
the NLIN procedure. The first derivative of a quadratic equation describing LA was used
to estimate LAmax and was described by,

id}?=u+2*u*t, [7]

where Lo and L1 are the parameters to be estimated. LA was calculated by numerically

integrating dLA/dt using the equation,
LA(t + A) = LA(t) + A * (icgglfm) , [8]

where the time step of integration (A) was 1 day and the period of integration was from
day 10 to the time of the harvests (i.e. day 10, 15, 20, 25 or 30). The initial values of LA

were based on the average leaf area for plants harvested on day 10.

Results and Discussion

Total leaf expansion was reduced by 58% and shoot N was reduced by 60% for
plants with N application withheld the full 20 days. During the time period between days

25 and 30, dLA/dt for these plants was reduced by 87% when compared with plants

32
where the N supply was never removed. The average shoot N for plants with no N
removal was 5.66% of dry mass.

Parameter estimates of 2.7% and 6.8% were found for Nmin and NM, respectively
(Table 1). The biological significance of ngn and N"...x relates in many ways to critical
concentration values reported in the literature. Lunt and Kofranek (1957) established leaf
N values of 2.25 to 2.74% to be slightly deficient, and plants with values less than 2% to
be seriously deficient, based on flesh and dry mass accumulation of the plant. Lunt and
Kofranek found plants with leaf N concentration greater than 4 to 4.5% had the greatest
fresh and dry mass. A higher desirable range of 4.5 to 5% was established by Woltz
(1956). Willits et al. (1992) reported values of N for leaves near 6% from chrysanthemum
produced in solution culture. While our values appear to be higher than those reported,
most other reports have dealt with whole plant responses, such as fresh mass or dry mass,
that may be less sensitive to shoot N than leaf area expansion.

None of the plants in this experiment displayed “classical” N deficiency symptoms,
such as chlorosis of the lower leaf blades or the necrosis and abscission of lower leaves
(Nelson, 1994). There is a possibility that in this experiment the decrease in leaf expansion
may be due to some osmotic effects occurring in the leaf cells and not due to some
physiological disruption in cell wall expansion caused by a deficiency of N. Since NOg' is
the major anion accumulated by the plant and would balance cation uptake, a reduction in
nitrate uptake would possibly influence anion uptake (Kirkby, 1968; Mengel and Kirby,
197 9). Reducing the concentration of N applied has been shown to reduce the leaf K

concentration in chrysanthemum variety ‘Bluechip’ as well as reducing stem length

33
(Joiner, and Smith 1961). This reduction in cation uptake, especially of osmotically
important cations such as K, could have an impact on the osmotic potential of the cell and
the rate of cell expansion. It should also be noted that in this study K supply was
maintained while in production conditions N and K supply are usually related. Under
commercial production conditions water may also be limiting.

The relationship used in equations [3] and [4] of a linear decrease in shoot N in
response to N removal and a linear increase in recovery from N removal worked very well
(Figure 1). The equation relating predicted shoot N to actual shoot N was Nam .ch =
N1... * 1.00 + 0.00, with an R2 = 0.89 (n = 250). The linear functions used in this
experiment worked well since the plants were kept under uniform environmental
conditions in grth chambers. Under the variable environments found in greenhouses
more elaborate functions may be needed.

The Nam. parameters b2 and b3 give some indication of how quickly the plants
respond to a N removal episodes. With a b; value of -0.132 %/day after N removal, a
plant initially starting at the NW of 6.8% would take 31 days to reach the Nut“ value of
2.7%. Once N was re-supplied, a plant starting at 2.7% would take 44 days to reach a
shoot N of 6.8%, based on a b3 value of 0.093%/day of recovery. Therefore a plant under
going a N removal would take a slightly longer period of time to recover from the
starvation episode once the N supply was replenished. The values of 31 and 44 days are
specific to the growth conditions in this experiment, but the general relationship between

starvation and recovery should be similar for other environmental conditions.

34

The firnctionfLA accurately simulated the reduction in leaf area occurring during N
starvation and recovery from starvation (Figures 2). The equation relating predicted leaf
expansion to actual total leaf expansion was LA.¢m.1= LA * 1.00 + 0.09, with an R2 = 0.95
(n = 250). Under the conditions of this experiment it would take 16 days for a 50%
reduction indLA/dt to occur after the start of a N starvation episode. The relatively long
time frames for the influence of a starvation episode to be markedly seen in plant
development (i.e. >50% reduction in dLA/dt) would indicate that weekly medium testing
would be adequate to determine if N starvation conditions existed and allow for
corrections to be made in the fertilization program. Chrysanthemums reportedly require
high concentrations of N after pinch (Crater, 1980). In this study there was not a
difi’erence in the efi’ect of N removal between day 10 and day 30.

One improvement to the model would be to include nitrate-N storage pools in the
leaves since this storage supply would influence how quickly the plant would respond to a
N deficiency in the medium (Elliot and Nelson, 1983). Previous studies using
chrysanthemum have found nitrate-N to account for 13% of the total N in the leaves
indicating that it could be a potential source of N for growth under deficiency conditions
(Woodson and Boodley, 1983). Shoot tissue with nitrate reserves could take a longer
period of time before a reduction in grth would occur. The actual dynamics of nitrate-N

in chrysanthemums would be an interesting area for firrther research.

Literature Cited

Charles-Edwards, DA. 1979. Amodel for leaf-growth. Ann. Bot. 44:523-535.

35

Chen, D. and J.H. Lieth. 1992. Two-dimensional model of water transport in the root zone
and plant for container-grown chrysanthemum. Agricultural and Forest Meteorology
59:129-148.

Crater, D. 1980. Pot mums. In: R. Larson (ed). Introduction to floriculture. Academic Press.
New York, New York.

Diamond, D. 1992. Total Kjeldahl nitrogen in Soil/Plants. Lachat Instruments QuikChem
Method 13-107-06-2-D.

Draper, D. and H. Smith. 1981. Applied regression analysis 2nd edition. John Wiley and
Sons , New York.

Elliot GO and RV. Nelson. 1983. Relationships among nitrogen accumulation nitrogen
assimilation and plant grth in chrysanthemums. Physiol. Plant. 57:250-259.

Goodwin , DC. and CA Jones. 1991. Nitrogen dynamics in soil-plant systems, p. 287-340.
In: J. Hanks and J .T. Ritchie (eds). Modeling plant and soil systems. Agronomy 31.
Amer. Soc. of Agronomy Inc, Madison, WI.

Greenwood, E.A.N. 1976. Nitrogen stressinplants. Adv. Agron. 28:1-35.

Joiner, IN. and TC. Smith. 1961. Effects of nitrogen and potassium levels on the
growth flowering response and foliar composition of Chrysanthemum morifolium
'Bluechip'. J. Amer. Soc. Hort. Sci. 80:571-580.

Kirkby, EA. 1968. Influence of ammonium and nitrate nutrition on the cation-anion
balance and nitrogen and carbohydrate metabolism of white mustard plants grown
in dilute nutrient solutions. Soil Science 105:1232141.

Lunt, OR and AM. Kofranek. 1957. Nitrogen and potassium nutrition of chrysanthemum.
J. Amer. Soc. Hort. Sci. 72:487-497.

Mengel, K. and Kirkby, EA. 1979. Principles of plant nutrition 2nd ed. International Potash
institute. Bern.

Nelson P.V. 1994. Greenhouse operation and management. 4th edition. Prentice Hall, New
Jersey.

SAS Institute Inc. 1990. SAS/STAT user’s guide, volume 2, GLM-VARCOMP, version 6
(ed). SAS Institute, Inc, Cary, NC.

Wamcke, DD. 1986. Analyzing greenhouse grth media by the saturation extraction
method. HortScience 21 :223 -225.

36

Willits, D.H., P.V. Nelson, M.M. Peet, M.A Depa and 18. Kuehny. 1992. Modeling
nutrient uptake in chrysanthemum as a firnction of grth rate. J. Amer. Soc. Hort.
Sci. 117:769-774.

Woltz, SS. 1956. Studies on the nutritional requirements of chrysanthemums. Proc. Fla.
State Hort. Soc. 70:352-356.

Woodson W.R and J .W. Boodley. 1983. Accumulation and partitioning of nitrogen and dry
matter during the grth of chrysanthemum. HortScience 18(2): 196-197.

37

Table 1. Least squares estimates of the nonlinear regression parameters used to
determine shoot N concentration (Nnm), rate of leaf expansion (LAmx), and the
response of leaf area expansion to shoot N concentration (fLA). Equation (eq.)
numbers refer to equations found in text.

 

 

 

Nshoot fstarv free LArmx ILA
eq. 6 eq. 7 eq. 8 eq. 10 eq. 2
b0 b1 b2 b3 lo I] NIL“ Niam—
Parameter 5.10 0.027 -0.132 0.093 -6.8 1.13 6.8 2.7

Estimate

38

Figure 1. Predicted (lines) and actual (triangles) shoot N concentration at different times
since planting. The actual shoot N is the mean of 5 replicates with the bars
above and below the points indicating the standard deviation of the mean. The
arrows pointing upwards indicate when the N was removed and withheld. The
downward pointing arrows indicate the time when the N supply was

replenished.

39

 

 

 

L

I

no

I

my

I

D

l

E

 

 

 

 

 

Amman. be we e\ev moweEZ Seam

 

_ ____ ____ ____ ___
32654326543265432654

 

10 15 20 25 30
Days Since Planting

15 20 25 3O

10

40

Figure 2. Predicted (lines) and actual (triangles) leaf area at different times since planting.
The actual leaf area is the mean of 5 replicates with the bars above and below
the points indicating the standard deviation of the mean. The arrows pointing
upwards indicate when the N was removed and withheld. The downward

pointing arrows indicate the time when the N supply was replenished.

Leaf Area (cmz)

 

800
600 -
400 e
200 -

—r
q
I I

 

600 4
400 -
200 -

 

600 -
400 —
200 —

/ :

 

600 -
400 -
200 -

 

D

/l\

 

600 -
400 -
200 -

 

—J
ft

[I
/ :
J
1
1

1A
\ 1 1 1 1
B
1 1 1 1
C
!
1 I 1
1 1 1 1
E
1 1 1 l l

 

At.

 

 

10

15

20 25 30 10 15 20
Days Since Planting

25 30

 

SECTION III

A MODEL TO PREDICT THE MOVEMENT OF NITRATE
AND AMMONIUM IN A PEAT-BASED ROOT-MEDIUM.

A Model To Predict The Movement Of Nitrate And Ammonium In A Peat-based

Root-medium.

Mark V. Yelanich and John A. Biembaum

Department of Horticulture, Michigan State University, East Lansing, MI 48824-1325

Received for publication_. Acknowledgment is made to the Michigan State Agriculture
Experiment Station. The use of trade names in this publication does not imply
endorsement by the MSAES of the products named, nor criticism of similar ones not

mentioned.
42

43
Soils, Nutrition and Fertilizers
A model to predict the movement of nitrate and ammonium in a peat-based root-
medium.
Additional index words: Dendranthemum morifolium, mathematical model, peat-based

medium, salt stratification.

Abstract

A model was constructed to predict the movement of nitrate and ammonium out of
the root zone and into the top layer from the root-medium of subirrigated pots. The
movement of nitrate and ammonium was modeled to occur due to the rapid movement of
salts during a fertilization and due to the slower movement of salts in the mass flow of
water. To quantify the rates of movements of N the concentration of nitrate and
ammonium was determined in fallow pots before and after sub-irrigation with fertilizer
over 4 wetting and drying cycles. The NO3-N content in the root zone was reduced on
average by 46% between irrigations. The amount of N removed fiom the root zone during
an irrigation was 3.4 mg for NO3-N and 1.8 mg for NH4-N average over the four
fertilizations, accounting for a loss of fi'om 26 to 40% of the N03-N and 27% to 94% of
the NH4-N was initially present before the irrigation. The predicted rate of movement out
of the root zone averaged over the 27 day period was 1.2 mg- day'1 for N03-N (range 0.5

to 2.0 mg-day'l) and 0.5 mg- day'1 NIL-N (range 0.2 to 0.8 mg-day").

44

High concentrations of nutrients occur in the upper layer of peat-based root-media
of both top watered and subirrigated container-grown plants (Guttormsen 1969; Argo,
1993; Argo and Biembaum, 1994). Nutrients in the upper layer of the media are less
available to the plant than nutrients in the root zone due to low water contents, low root
infiltration or excessive salt concentration and therefore constitute a significant loss of
nutrients fi'om the root zone (Biembaum et al. 1993). The root-medium of container-
grown plants can be partitioned into two layers (Argo, 1993) . The root zone is the layer
where the majority of a plants roots would be found. The top layer is the upper most
volume of medium and where few roots grow. In experiments reported by Argo (1993)
and Argo and Biembaum (1994), when the surface of a medium was covered with an
evaporative barrier, the concentration of salt in the top layer of the medium was reduced.

The chemical potential of the system, having activity, pressure, electrical and
gravity components is the driving force for ion movement (Nobel, 1991). While
considerable concentration gradients have been reported to exist between the top layer and
root zone, (i.e. a driving force for the activity and electrical components), the diffusion
coefficients for ions are too low (e. g. 1.9E10'9 m2- sec'1 for K) to explain the formation
of the top layer over the distance from the bottom to the top of growing container. Also
when the pot is first filled with a homogenous medium, the gradients between the top layer
and root zone would be very small or non existent. The gravitational potential would also
be fairly small due to the relatively small distances involved and would be a driving force

moving the ions from the top layer into the root zone. This leaves the pressure potential,

45
driven by the mass flow of water, dWathp/dt, as the dominant driving force for salt

movement. An equation describing this phenomena is,

WOW: = dwatl-Zvap * NRZ [1]
dt dt WatRz’

 

where dNRZodet is the rate of N movement out of the root zone and into the top layer
(mg-day”), dWatEv.p/dt is rate of evaporation from the medium surface (liter-day") and
NRZ/WatRZ is the root zone nutrient concentration (mg - liter").

Equation [1] would predict that if evaporation was reduced, the formation of a top
layer of salts would be reduced. However, in an experiment by Yelanich and Biembaum
(1994) poinsettias were grown with and without an evaporative barrier on the medium and
were given the same quantity of fertilizer, the top layer of salt was reduced but not
eliminated for covered medium. Plants grown in covered medium received 38% less
water than uncovered controls. One hypothesis to explain why evaporation was reduced
and top layer formation still occurred is that nutrient salts must also be moving into the
top layer with the mass movement of water during an irrigation. The salts probably
accumulate in the top layer since few roots form near the surface of the medium (Chen and
Lieth, 1993; Guttormsen, 1969).

During fertilization by subirrigation, it is hypothesized that the applied N moving
through the root zone to the top layer of the medium will mix with the N currently in the
root zone. This would be analogous to mixing which occurs during leaching that occurs

during top watering (W agenet, 1983). A proposed equation to describe this is,

46

dNRZorm _ dWatrL * NRZ

dt dt WatRZ

 

* meA [2]

where dNRZomt/dt (mg day") is the rate of N entering the top layer from the root zone
with the irrigation water and dWatn/dt (liter-day“) is the volume of water passing
through the root zone and entering the top layer after an irrigation. The firnction fMixA
predicts the amount of root zone N available for removal during an irrigation and would
probably be influenced by the initial water content and medium physical and chemical
properties (Kerr and Hanan, 1985). Under the conditions of this experiment it is simplified
to a constant since one media was used and irrigations occurred at a uniform water
content. A model predicting removal of N out of the root zone and into the top layer

would incorporate both of these concepts presented,

dNRZout _ dNRZorrre + dNRZorm

dt dt dt

 

 

[3]

The objective of this paper was to test the ability of equations [1], [2] and [3] to predict
the rate of movement of nitrate and ammonium N out of the root zone of a subirrigated

container medium.

Materials and Methods

To determine the values of firm, fallow pots of medium with three initial root zone
N concentrations were subirrigated with a fertilizer solution and the root zone medium
concentration was determined before and after the irrigation. Nine cm tall by 12.5 cm
wide pots (total pot volume 754 cm’) were filled with a 100% sphagnum peat medium

with a common starting base charge of MgSO4 (0.03 kg-m"), CaSOt (0.06 kg-m's),

47

Cal-IP04 (0.06 kg-m’3), hydrated lime (0.21 kg-m'3), and a micronutrient mix (FTE 111
0.01 kg0m'3). The three initial medium N concentrations were obtained by incorporating
both KNO; and Ca(NO3)2 at the same rate of 0.03, 0.06 or 0.12 kg-m's. Alter filling the
pots, the conducting pores in the medium were allowed to stabilize by allowing the
medium to go through one wetting and drying cycle. The pots of medium were kept in
individual shallow water tight trays and all irrigations were made by pouring 0.2 liters of
solution into the tray, a volume of solution taken up by capillarity within 0.5 hr of the
application. The pots of medium were subirrigated with water and allowed to dry until the
pots achieved a mass of 250 grams when the experiment was started. This weight
corresponded to approximately 45% of the total water holding capacity. The pots of
medium were then irrigated with a nutrient solution consisting of 9.5 mol ~rn'3 (133
mg-liter") NO3-N, 4.5 mol°m'3 (63 mg-liter") NIL-N, 0.5 mol-m'3 (15.5 mg'liter'l) P,
5 mol-m"3 (195 mg-liter")K, and 50 mg-liter'l Compound 111 (Scotts, Marysville, Ohio).
Macronutrient sources were KNOg, NH4N03, and H3P04.

Before and afier irrigation, five pots per treatment were cut into a top layer and
root zone by slicing the medium into two sections at a height 5 cm from the bottom and
allowed for a adequate sample size for extraction and analysis using the saturated medium
extraction method (W amcke, 1986). The extract was analyzed for nitrate N, nitrite N and
ammonium N using colormetric methods (Diamond, 1986a and Diamond,1986b). The
concentration of nitrite N was considered negligible (< 0.07 mol - m3) and will not be

reported. A sub-sample of the saturated medium paste was weighed before and after

49

Results and Discussion

Values of 0.68 for NO3-N and 1.08 for NIL-N were determined for fMixA and
provided good predictions of the root zone N content after an irrigation (Figures 1). A
higher value of fMixA would indicate that more of the initial solution is available for
transport to the upper layer during an irrigation. It was surprising that the value of fMtxA
was lower for NO3-N than for NIL-N since there is little anion exchange in peat-based
medium as compared with cation exchange. The term fun». probably has similar attributes
to equations used in predicting leaching of salts from medium (Wagenet, 1983). The
medium physical could influence capillarity and water movement in the medium as well as
the mixing occurring between the applied and medium solutions. The medium chemical
properties could influence retention of salts by the exchange sites and could influence the
quantity of salts moving towards the medium surface. However at this stage of
development attributing chemical and physical basis to fngAis probably not advisable.

The model worked well in predicting the rates of water loss from the root zone
and the amount of NOs-N and NIL-N removed after an irrigation (Figure 2). The model
predicted that the rate of movement out of the root zone averaged over the 27 day period
was 1.2 mg-day'l for N03-N (range 0.5 to 2.0 mg°day'l) and 0.5 mgsday‘l NI-L-N (range
0.2 to 0.8 mg0 clay'1 ). The NO3-N content in the root zone was reduced on average by
46% between irrigations, demonstrating the large influence the outflow rate of N would
have on the N status of the root zone. The rate of N applied to the root zone, averaged

over the 27 day period, was 1.3 mg-day" for N03-N and 0.64 mg-day'l NIL-N. The

50

values presented in this paper are higher than would be observed if there was a plant
growing in the pot, since the plant canopy would reduce the amount of water evaporation
and upward movement of water, therefore reducing the upward movement of N
(Y elanich, 1995). The amount of N lost during an irrigation was 3.4 mg for NOg-N and
1.8 mg for NH4-N average over the four fertilizations, accounting for a loss of from 26 to
40% of the NOg-N and 27% to 94% of the NH4-N initially present before the irrigation.

The movement of salts out of the root zone can be reduced by placing an
evaporative barrier over the surface of the medium (Argo and Biembaum, 1995). Over the
30 day period of this experiment, an average of 39 mg of NO3-N was applied with 36 mg
of this moving into the top layer. If the evaporation water lost was eliminated the
movement out of the root zone would have been reduced 89% (32 mg) for the 30 day
time period (assuming 1 irrigation). If a plant was added to this system the movement of
N into the top layer would probably be greater since more irrigations would be necessary

due to transpirational water loss.

Literature Cited

Argo, W.R 1993. The role of peat-based root-media in water and nutrient eficiency of
greenhouse crops. MS thesis. Michigan State Univ, East Lansing.

Argo, W.R and J .A Biembaum. 1994. Irrigation requirements, root-medium pH, and
nutrient concentrations of Easter lilies grown in 5 peat-based media with and without
anevaporative banier. J. Amer. Soc. Hort. Sci. 119:1151-1156.

Argo, W.R. and J .A Biembaum. 1995. The efi‘ect of irrigation method, water-soluble
fertilization, preplant nutrient charge, and surface evaporation on early vegetative and
root growth of poinsettia. J. Amer. Soc. Hort. Sci 120:163-169.

51

Biembaum, J .A, WA. Argo and M. Yelanich. 1992. Effect of a pot cover on irrigation and
fertilization requirements and media nutrient stratification. HortScience 26:7 64
(Abstract).

Chen, D. and J .H. Lieth. 1993. A two-dimensional, dynamic model for root growth
distribution of potted plants. J. Amer. Soc. Hort. Sci. 118:181-187.

Diamond D., 1986. Ammonia. QuickChem method 12-107-06-02-A. Iachat Instruments,
Mequan, WI.

Diamond D., 1986. Nitrate + nitrite. QuickChem method 12-107-06-02-A Lachat
Instruments, Mequan, WI.

Guttorrnsen, G. 1969. Accumulation of salts in the subirrigation of pot plants. Plant and Soil
3 l 2425 :43 8.

Hillel, D. 1982. Introduction to soil physics. Academic Press, San Diego, Ca..

Kerr, GP. and U. Hanan. 1985. Leaching of container media. J. Amer. Soc. Hort. Sci.
110:474-480.

Nobel, P. 1991. Physicochemical and environmental plant physiology. Academic Press. New
York. New York.

SAS Institute Inc. 1990. SAS/STAT user’s guide, volume 2, GLM-VARCOMP, version 6
(ed). SAS Institute, Inc, Cary, NC.

Wagenet, RJ. 1983. Principle of salt movement in soils, p. 123-140. In: D.W. Nelson et al.
(eds). Chemical mobility and reactivity in soil system. Proc. Amer. Soc. Agron and
Soil Sci. Symp, 28 Nov-3 Dec. 1981.

Wamcke, DD. 1986. Analyzing greenhouse growth media by the saturation extraction
method. HortScience 21 :223-225.

Yelanich, M.V. and J .A Biembaum. 1994. Growth and media nutrient concentration of
poinsettia as influenced by a pot cover. HortScience 29:502 (Abstract)

Yelanich, M.V. 1995. Modeling the concentration of nitrogen in the root zone of container-
grown chrysanthemum. Ph.D. Dissertation. Michigan State Univ, East Lansing.

52

Figure 1. Before subirrigation (no fill), after subirrigation (bottom to top lines) and model
(top to bottom lines) nitrate N contents (top graph) or ammonium N (lower
graph) in the root zone'of fallow pots filled with 100% peat. Bars over data are
the standard deviation of the mean (u = 5). Nitrogen was incorporated into the
medium prior to filling at rates of 0.03, 0.06 and 0.12 kgom'3. The N
concentration in the nutrient solution was 133 mg oliter'l NO3-N and 63

mg 0 liter'1 NH4-N.

53

 

 

   

        

   

0.12

\

 

/

    

    

 

 

  

N

\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\

0.06

kgm'3N

      

     

A.
0.03

  
 

 

_ _ _ _ _ _
0 O 0 0 0 0 00 6 4 2 0
4 3 2 .I. 1

3:5 2.88: Z 3.5 2.8388:

54

Figure 2. Model (lines) and actual (0) water volumes (top graph), nitrate N content
(middle graph) or ammonium N content (lower graph) for the root zone of a
fallow pot filled with 100% peat . Bars over data points are the standard
deviation of the mean (u = 5). The volume of water applied to the medium
was 0.2 liters on days 0, 9, 18 and 27. The concentration of nitrate-N applied
to the medium was 102 mg-liter'l on days 0 and 18 and 33 mg -liter"on days 9
and 27 . The concentration of ammonium-N applied to the medium was 48

mg-liter'l on days 0 and 18 and 17 mg-liter'lon days 9 and 27.

55

 

 

 

 

 

 

 

 

 

 

 

 

 

0.300

C85 “855

o 1 t
_ _ _ _ _ d _ _ _ _ _ _ _ fl _
0 0 0 0 0 0 0 5 0 0 8 7 6 5 4 3 2
. . . . . . E .. E EE<
0 0 0 0 0 0 AwEV 2-88: Z Z .

1

15 20 25 30

1 0
Day of Experiment

SECTION IV

A MODEL TO PREDICT THE RATE OF WHOLE PLANT
NITROGEN ACCUMULATION IN SUBIRRIGATED
CONTAIN ER-GROWN CHRYSANTHEMUM
‘BRIGHT GOLDEN ANNE’

A Model To Predict The Rate Of Whole Plant Nitrogen Accumulation In

Subirrigated Container-grown Chrysanthemum ‘Bright Golden Anne’

Mark V. Yelanich and John A. Biembaum

Department of Horticulture, Michigan State University, East Lansing, MI 48824-1325

Received for publication . Acknowledgment is made to the Michigan State
Agriculture Experiment Station. The use of trade names in this publication does not imply
endorsement by the MSAES of the products named, nor criticism of similar ones not

mentioned.

56

57
Soils, Nutrition and Fertilizers
A model to predict the rate of whole plant nitrogen accumulation in subirrigated

container-grown chrysanthemum ‘Bright Golden Anne’

Additional index words: Dendranthemum morifolium, mathematical model, peat-based

medium, nutrition.

Abstract

The rate of whole plant N accumulation by chrysanthemum ‘Bright Golden Anne’ was
modeled based on the dry mass accumulation rate of the plant. The model was based on
demands of N needed for new growth and for maintenance of the standing dry mass. The new
growth demand was modeled as a firnction of a critical plant N concentration (Named) and the
rate of dry mass. The maintenance demand was modeled as a function of the total dry mass, the
current plant N concentration and Named. To calibrate the model and estimate a value for Name“
three growth rates were created by growing plants in a growth chamber using fluence rates of
4, 7 and 11 mol - clay'l PPF and weekly harvesting 4 plants per treatment. The least squares
estimate of Ngifiul was determined to be 3.4%. Using this value of New“, the R2 for the
predicted plant N content was 97%, indicating the N demand model was a good approach for

predicting chrysanthemum N accumulation.

58

Nitrogen fertilization of container-grown plants needs to be reduced to minimum levels
required for adequate growth to prevent N runofl‘ from greenhouses and nurseries (Biembaum,
1992). The rate of N accumulation by a plant is influenced by factors such as medium N
concentration (Siddiqi et a1, 1990.), N form (Cox and Reisenauer, 1973; Elliot and Nelson,
1983), and root activity (Raper et al, 1978). It has been possible to predict the rate of N
accumulation based on the dry mass accumulation rate of the plant (Raper et al., 1977)
implying that there is a constant relationship between dry mass accumulation and N
accumulation.

Willits et al. (1992) found a 1:1 relationship between relative grth rate (RGR)
and the relative accumulation rate (RAR) of N for hydroponically grown chrysanthemums
but had to make corrections for the age of the plants. RAR was found to decrease with
respect to RGR as the plant progressed toward flowering, with a more rapid decrease as
flower formation began to occur. There was also a decrease in the total concentration of
N in the plant with most of this decrease occurring in the stems. Woodson and Boodley
(1983) also found that as container-grown chrysanthemum aged there was a decrease in
the rate of N accumulation and that at flower formation there was a loss of N from the
leaves and stems and an increase of N in the flower. While there has been much work on
the N nutrition of chrysanthemum, a usable model has not been developed for the
prediction of N uptake.

The rate of N uptake has been modeled for other field grown crop plants using the

concept of maintenance and new grth demands with the form of,

59

de=dem+den
dt dt dt’

 

[1]

where Npm is equal the maintenance demand for N and Npn is equal to the new growth
demand for N (Goodwin and Jones, 1991). The rate of Npm has been modeled as a
fimction of the standing dry mass (DM) of the plant and the concentration of N in the
shoot and is described by

d NPm _ (Named - Nnct'ml)

* DM [2]
dt 100

 

where Nam“; is the critical percent N in the dry matter necessary for normal firnctioning,
and Nun.“ is the current percent N of the plant. Npn is the N uptake needed to support the
new dry mass of the plant and is described by,

dNPn _ Notified * dDM

3
dt 100 dt [ ]

 

 

Our objective was to test the validity of using equations [1], [2] and [3] to predict
N accumulation by container-grown chrysanthemum. Our intent is to incorporate this
model into a larger model to predict the N content in the root zone of container-grown

chrysanthemum.

Materials and Methods

One rooted cutting of chrysanthemum ‘Bright Golden Anne’ was placed in a 10
cm pot filled with a 100% peat medium. Prior to planting KN 03 (0.06 kg-m'3), Ca(N03)2
(0.06 kg'm'3), Mgso. (0.03 kg0m'3), Caso. (0.06 kg-m°3), CaHPo. (0.06 kgom's),

hydrated lime (0.21 kg-m'3) and a micronutrient mix (FTE 555 0.01 kg-m’3) were

 

60
incorporated into the medium. Plants were placed in a 1.3 m by 2.5 m growth chamber
with day and night temperature set points of 20 C. Plants were exposed to a day-length of
16 hours for the first 7 days, after when they were pinched to 6 nodes and placed under a
day-length of 10 hours. Plants were pruned to 3 shoots per plant when the shoots were
large enough to handle. Irradiance in the chambers was supplied by cool-white fluorescent
tubes (Philips VHO F96712/CW/VHO) and incandescent bulbs (Sylvania 60-W) with an
input wattage of 7 7% and 22%, respectively. Plants in the highest light treatment were
exposed to a PPF of 11 mol -m '2- day]. Two other fluence treatments were obtained by
placing 1 or 2 layers of shade cloth beneath the lamps resulting in fluence rates of 7 or 4
mol-m'z-day'l . Plants were fertilized at every irrigation with 9.5 mol-m'3 (133
mg-liter'l) NO3-N, 4.5 mol-m'3 (63 mg°liter") NIL-N, 0.5 mol-m'3 (16 mg°liter'l) P, 5
mol-m'3 (195 mg-liter") K and with micronutrients supplied from 50 mg-liter'l of
Compound 111 (Scotts, Marysville, Ohio). Water used to make the nutrient solution had
an initial alkalinity of 1.7 mol-m3 (170 mg-liter'l) CaCO; , pH of 6.4 and an electrical
conductivity (EC) of 0.3 dS -m'. Plants were weighed daily and irrigated when the mass
of the plant, pot and medium was less than 350 grams. Plants were kept in individual
water tight trays and were subirrigated by pouring 0.2 liters of solution into the tray, a
volume of solution absorbed by the medium within 0.5 hr of application. Five plants per
treatment were randomly selected for evaluation weekly. The root-medium in the pots selected
for sampling was first sliced into two vertical halves, one half was used to collect the roots for
dry mass and the other half was used for medium N determination The halfused for the root

dry mass determination was rinsed with water over a mesh screen to remove the media

61
particles from the roots. Primary and secondary leaf area, shoot and root dry mass, shoot
and root Kjeldahl N (Diamond, 1992) and medium NO3-N, NOz-N (Diamond, 1986a) and
NH4-N (Diamond, 1986b) concentrations as well as pH and electrical conductivity of a
saturated media extract (W amcke, 1986) were determined at each sampling date.

The two main inputs into equations [2] and [3], DM and dDM/dt, were modeled
as functions of time and the average photosynthetic flux intercepted by the plant. Dry mass
was modeled using an exponential equation and is described by,

DM = be + (1 - cw") * (far) [4]
where b0 is the initial DM, b; is a parameter to be estimated, and t is the day of the
experiment (days) (Causton, 1983). The function fppf is described by,

fnt=ct* PPF , [5]
where PPF is photosynthetic photon flux (mol - day") and ct is a constant. Least squares
estimates were determined for b1 and C; using the weekly total dry mass data (NLIN
procedure, SAS, 1990). The first derivative of equation [4] is the rate of dry mass
accumulation, dDM/dt and is described by,

fiat! = b‘ * ('ew'”) * (fwr). [6]

Equation [6] was used as an input into equation [3] to determine the nonlinear least
squares estimate of Nan-aw using the weekly total plant N contents (mg N) (NLIN

procedure, SAS institute, 1990). Np and DM were determined by numerical integration

using the form,

62

 

N”) 171

Np(t+A)= Np(t)+A*( dt

 

dDM) [8]

DM(t + A) = DM(t) + A *( at
where A is the time step of integration.

Results and Discussion

Values of Np(t=0) of 19 mg and DM(t=0) of 0.75 g were used to initialize the model
and are based on the mean actual data from the initial harvest. The root medium
concentration of nitrate and ammonium N was 68 and 15 mg- liter", respectively,
averaged over PPF and samples (Figure l). The medium NO3-N concentrations fell near
the lower end of the 40-200 mg - liter'l NO3-N acceptable range for the SME (W amcke
and Krauskopf, 1983). Total plant dry mass and plant N increased as a fimction of time
since the start of short days (Figures 2 and 3). There were significant, linear increases in
dry mass and plant N in response to the PPF treatments for the plants from the day 70
sample.

The parameters determined for equations [4] and [5] are found in Table 1. The
equation relating predicted dry mass to actual dry mass was DM,,M = DM * 1.0 with an
R2 = 0.95 (n = 132). Equation [5], relating PPF to the rate of dry mass accumulation
simulating net photosynthesis, is limited to plants grown at the constant 20 C. Equation
[5] predicts a linear relationship between PPF and the rate of dry mass accumulation.
Holcomb et al.(1988) found that chrysanthemum single leaf photosynthesis rates were

asymptotically related to irradiance rates in the range of 0 to 1200 umol - s'l - m'z, with the

63
plateau, for plants grown at greater than 325 umol - s'l - m'z, in the range of 900-1200
umol - 8'10 m'z. The maximum irradiance rate in this experiment was 305 umol - s'l -rn'2 is
well below the 900 umol - s'l - rrr'2 plateau value. A more complicated firnction would have
been necessary for fppf if fluence levels greater than 900 umol - 8'10 m'2 would have been
used in this experiment.

The R2 (sum of square residual divided by sum of square total) for the predicted
plant N was 97% (N= 132) indicating that the model was working very well. A value of
0.034 was predicted for New“; (Table 1). Nan-m. is not related to the plant N
concentration where deficiency symptoms would begin to occur, but is the concentration
the plant N concentration maintains under non-limiting N conditions. There are only
limited reports of whole plant chrysanthemum N concentrations since leaf N
concentrations are typically reported. In the most recent report by Willits et al. (1992),
whole plant N ranged from 5% early in the crop to 3.5% later in the crop for solution
grown chrysanthemum. In this experiment values of whole plant N concentrations for
plants were in the range of 2 to 5% indicating that medium grown plants may have a lower
value of Name,“ than solution grown plants.

There are many possible improvements to the model excluded in favor of
simplicity. One improvement is to incorporate root parameters such as length to
determine a maximum rate of N accumulation (Goodwin and Jones; 1991). This is

especially important earlier in the crop when both the root density and medium

64
concentrations are low. This would also allow for prediction of conditions when roots
become damaged and N accumulation is reduced.

Another possible improvement would be to simulate the movement of N within the
plant. Currently the model simulates the N in the plant as one pool, when realistically
there is movement between the roots, stems, leaves and flowers (W oodson and Boodley,
1983). While under the conditions of this experiment treating the N as one pool worked,
this method may not work under conditions of plant stress where remobilization of N from

one plant part to another would become important.

Literature Cited

Biembaum J .A 1992. Root-zone management of greenhouse container-grown crops to control
water and fertilizer use. HortTechnology 2: 127-132.

Causton, DR 1983. A biologist basic mathematics. Arnold. Baltimore, Maryland.

Cox, W.J. and HM. Reisenauer. 1973. Growth and ion uptake by wheat supplied nitrogen
as nitrate, or ammonium , or both. Plant and Soil 38:363-380.

Diamond D., 1986a. Ammonia. QuickChem method 12-107-06-02-A Lachat Instruments,
Mequan, WI.

Diamond D., 1986b. Nitrate + nitrite. QuickChem method 12-107-06-02-A Lachat
Instruments, Mequan, WI.

Diamond, D. 1992. Total Kjeldahl nitrogen in Soil/Plants. QuikChem Method 13-107-06-2-D
Lachat Instruments, Mequan, WI.

Elliot GO and RV. Nelson 1983. Relationships among nitrogen accumulation nitrogen
assimilation and plant growth in chrysanthemums. Physiol. Plant. 57:250-259.

Goodwin , DC. and CA Jones. 1991. Nitrogen dynamics in soil-plant systems, p. 287-340.
In: J. Hanks and J .T. Ritchie (eds). Modeling plant and soil systems. Agronomy 31.
Amer. Soc. of Agronomy Inc, Madison, WI.

65

Karlsson, M. G. 1987. Characterization of development and grth response to irrandiance

and temperature for model development in chrysanthemum. Ph.D. Dissertation
Michigan State University.

Raper, C.D., LR Parsons, D.T. Patterson and R]. Kramer. 1977. Relationship between

growth and nitrogen accumulation for vegetative cotton and soybean plants. Bot.
Gaz. 138:129-137.

Raper, C.D., D.L. Osmond, M. Warm, and W.W. Weeks. 1978. Interdependence of root

and shoot activities in determining nitrogen uptake rate of roots. Bot. Gaz.
139:289-294.

SAS Institute Inc. 1990. SAS/STAT user’s guide, volume 2, GLM-VARCOMP, version 6
(ed). SAS Institute, Inc, Cary, NC.

Siddiqi, M.Y., ADM. Glass, T.J. Ruth, T.W. Rufly, 1990. Studies of the uptake of nitrate
in barley. 1. Kinetics of ”NO; influx. Plant Physiol. 93:1426-1432.

Wamcke, DD. and D.M. Krauskopf. 1983. Greenhouse growth media: Testing and nutrition
guidelines. Mich. State Univ. Ext. Bull. E-1736.

Wamcke, DD.

1986. Analyzing greenhouse growth media by the saturation extraction
method. HortScience 21:223-225.

Willits, D.H., .P.V. Nelson, M.M. Peet, MA Depa and IS. Kuehny. 1992. Modeling

nutrient uptake in chrysanthemum as a firnction of growth rate. J. Amer. Soc. Hort.
Sci. 117:769-774.

Woodson W.R. and J.W. Boodley. 1983. Accumulation and partitioning of nitrogen
and dry matter during the grth of chrysanthemum. HortScience. 18:196-197.

66

Table 1. Parameter estimates for the nonlinear models describing plant dry mass (Eq [4]
and [5]) and plant N content (Eq [2]).

 

 

D] C] Ncritical
(%)
qu4] EC115] E4121

0.02 -0.507 3.4

 

67

Figure 1. Mean nitrate (left figures) and ammonium (right figures) N concentrations from
the medium of chrysanthemums grown at 4 mol- day’l (top figures), 7
mol-day'l (middle figures) or 11 mol-day'l (bottom figures) PAR.

Concentrations were determined from saturated medium extracts. Bars around

triangles are the standard deviation of the means (n=4).

Medium Nitrate-N (mg/liter)

250

 

200 ~—

150 ~

100—

‘Jl
O
l

O

 

 

N
8
l

y—e

M

O
l

'8'
l

M
O
l

O

_

 

 

200 ~—

 

 

 

Days Since Start of Short Days

 

I II 11111
01020304050607080

68

Medium Ammonium-N (mg/liter)

'35-

50

 

45-
40—

30‘
25‘
20c
15“
lop

5A

 

45-
40-
35—
30H
25~
20-1
15-1
10-4

5—1

 

45-1
40—
35-
30-
25-
20-
15—
10—

5-

 

 

 

I I T 1 I I I I
01020304050607080

Days Since Start of Short Days

69

Figure 2. Actual (triangles) and model predicted (lines) dry mass over time since the
start of short days for chrysanthemums grown at 4 mol- day'l (top figure), 7
mol'day‘1 (middle figure) or 11 mol-day'l (bottom figure) PPF. Bars around

triangles are the standard deviation of the mean dry mass (n=4).

Dry mass (g)

Clo-50‘

70

 

 

 

l

 

—(

 

O

Days Since Start of Short Days

70

 

80

Figure 3. Actual (triangles) and model predicted (lines) plant N content (mg) over time
since start of short days for chrysanthemums grown at 4 mol- day’l (top figure),
7 mol-day" (middle figure) or 11 mol°day'l (bottom figure) PPF. Bars around

triangles are the standard deviation of the mean plant N content (n=4).

Plant Nitrogen (mg)

700

72

 

600 r
500 4
400 -
300 —
200 4
100 d

 

600 n
500 -
400 -
300 —
200 -
100 -

_{

 

600—
5004
400—
300—
200—
100—

 

..I

 

 

0—1

1 I l I I 1
10 20 30 40 50 60

Days Since Start of Short Days

1
70

80

SECTION V

VALIDATION OF A MODEL TO PREDICT THE NITROGEN
CONTENT IN THE ROOT ZONE OF CONTAIN ER-GROWN
CHRYSANTHEMUM ‘BRIGHT GOLDEN ANNE’.

Validation Of A Model To Predict The Nitrogen Content In The Root Zone Of

Container-Grown Chrysanthemum ‘Bright Golden Anne’.

Mark V. Yelanich, John A. Biembaum and Royal D. Heins

Department of Horticulture, Michigan State University, East Lansing, MI 48824-1325

Received for publication . Acknowledgment is made to the Michigan State
Agriculture Experiment Station. The use of trade names in this publication does not imply
endorsement by the MSAES of the products named, nor criticism of similar ones not

mentioned.

73

74
Soils, Nutrition and Fertilizers
Validation of a model to predict the nitrogen content in the root zone of container-
grown chrysanthemum ‘Bright Golden Anne’.
Additional index words: Dendranthemum morifolium, mathematical model, peat-based

medium, nutrition.

Abstract

A model was constructed to describe the dynamics of N in the root zone of
subirrigated container-grown chrysanthemum. The daily root zone content N content was
determined by numerical integration of the rates of N applied, plant uptake and top layer
formation. The root zone N concentration at any time period was based on the root zone
water volume, determined by numerical integration of the rates of evaporation,
transpiration and application. To validate the model, chrysanthemum ‘Bright Golden
Anne’ was produced at two times of the year (winter and spring), with three fluence levels
(70% shade, ambient and HPS) and with three N fertilizer concentration (3.5, 7, 10.5
mol-m'3 N). Leaf area, total plant dry mass, plant Kjeldahl N, root zone NO3-N content
and NH4-N content were determined biweekly. Water loss was evaluated daily by
weighing the pot, medium and plant. The model was able to predict the general trends of
leaf area, dry mass and plant N as well as root zone NO3-N and NH4-N contents. The

model was used to develop fertilization strategies to more efficiently apply N.

75

\Vrth a move towards management strategies limiting leaching and reducing the applied
fertilizer concentration, a better understanding of the processes influencing the medium nutrient
concentration becomes more critical (Biembaum, 1992). Nutrients in the medium of container-
grown plants are maintained by the frequent application of water soluble nutrients with the
irrigation water. To ensure that the correct concentration of fertilizer is being applied, the
nutrient concentration of the medium is evaluated on a periodic basis (Nelson, 1994). The
results fiom the medium evaluation are interpreted using recommended guidelines giving upper
and lower values selected to supply plants with the nutrient concentrations required for optimal
growth (W arncke and Krauskopf, 1983). If the medium nutrient concentration is outside of
the acceptable range, the typical course of action is to make a change in the concentration of .
the applied water soluble fertilizer concentration. The magnitude of the change in fertilizer
concentration is based on grower experience interpreting the medium tests and growing the
crop. If insuficient fertilizer is applied then crop failure could result. If excess fertilizer applied
leaching may be necessary resulting in fertilizer being wasted and entering the environment
(Y elanich and Biembaum, 1993,1994). A better understanding of the processes influencing the
medium nutrient concentration would allow growers to apply the correct quantity of fertilizer
to the pot so that less fertilizer is wasted or lost to the environment. One way of achieving this
understanding is through the use of models. Models development has the advantage over
conventional research methods in that models allow the real time evaluation of various
strategies on long time fiame processes (Ritchie, 1986). Our objective was to develop and

validate a simulation model of the root zone N concentration of container-grown

76
chrysanthemum using a limited set of environmental inputs. Once validated the model was
then used to develop strategies limiting the quantity of N applied while maintaining the

nutrients at desired levels.

Materials and Methods

Model Development. Chrysanthemum was chosen as the model crop plant because of the
large amount of information available on its growth and development. The system used in
this project is based on the root-medium being divided into two layers. The root zone is
were the majority of a plants roots would be found. The top layer is the upper most
volume of the container where few roots grow. The majority of the N is supplied to the
pot in the irrigation water, applied by subirrigation. The model predicts the rate of N
inflow and outflow for the root zone, and through integration of these rates predicts the N
content in the root zone at any time period and is illustrated in Figure l.
The rate of N flow in the root zone of a chrysanthemum pot is described by,
dNRZ/dt=dNRZAp/dt + dPN/dt +dNRZ/u/dt [1]

where dNRZ/dt is the rate of N content change in the root zone (mg 0 day"), dNRZAp/dt is the
rate of N applied (mg - day'l), aPN/dt is the rate of plant accumulation of N (mg - day") and
aNRZ/u/dt is the rate of N moving to the top layer (mg - day"). The term dNRZAp/dt is a

fimction of the rate of water loss and can be described by,

 

dNRZAp _ {dWRZAP * Nconc if WRZ < mm

2
dt 0 ifWRZ>WRZntn []

77

where is the volume of solution applied (liter. day") remaining in the root zone, WRZ is the
current volume of water in the root zone (liter), WRZ“, is the volume of water in pot
triggering an irrigation (liter) and Nconc is the concentration of N applied (mg-liter“). The
integral of dNRZAp/dt is the content of N applied to the root zone over the time period of
integration.

The rate of PN is modeled as a function of the dry mass accumulation of the plant and
separates N accumulation as N needed by the plant for maintenance of the standing dry mass
and N needed for new growth (Y elarrich and Biembaum, 1995a). The equation describing

plant uptake is,

 

 

dPN = [dDM * N......]+[(Nmt - New)
at at 100 100

* DM] , [3]

where dDM/dt is the rate of dry mass accumulation (mg-day”), DM is the total dry mass of the
plant (mg), Nam; is the critical percent plant N, and NM is the current plant percent N. A
value of 3.4% was used for Nan-mt based on Yelanich and Biembaum (1995).

The rate of NRZrL is modeled based on the medium evaporation of water as well as
mixing of the irrigation and medium solution (Y elanich and Biembaum, 1994c). The equation
describing dNRZu/dt is,

dNRZ/rr/dt = (NRZ NVRZ) *fmn * dWTLAP/dt + dWRvanp/dt * (NRZ W). [4]
The term dWRZEVAp/dt is the rate of evaporation of water from the medium surface
(liters/day), dWTLAp/di ‘is the volume of the water entering the top layer during an irrigation

(liter/day), and fm is an empirically determined mixing function The model of dWRZAp/dt is

based upon the maximum water holding capacity of the root zone WRZ...“ and is described by,

78

WRZm-WRZ 'f(WRZm-WRZ < Wt t

dWRZAy / dt = i ) ° [5]
Wtot rf (WRZmax -WRZ) > Wtot

dWTLAp/dt =Wtot -dWRZAp/dt [6]

where Wtot is the total volume of water applied. The rate of water change in the root zone,
dWRZ/dt is described by,

dWRZ/dt = ClWRZAp/dt + WEVAp/dt + dWRZW/dt [7]
where dWRZme/dt is the rate of transpiration from the canopy. The terms dWRZEVAp/dt and
dWRZpLANr/dt are modeled using the combination equation (Penman, 1942) and incorporates
equations found in Yelanich and Biembaum (1994d) and Chen and Lieth (1994) and are
described by,

dWRanm= A'Rnphnt+7'6.43'f(U)°(eu-ed)*LA*O'69 [8]

dt A+y

 

dt A+y '

 

where A is the slope of the saturation vapor pressure firnction, 'y is the psychometric
constant, Rnphn. is the plant net radiation (MJ -m'2-d'1), Rnan is the medium net
radiation (MJ - rn'2 - d"), e. is the saturated vapor pressure (KPa), ed is the saturation vapor
pressure at the dew point temperature (KPa), LA is the plant leaf area (m'z), MA is the
media surface area (m’z) and flu) is the empirical wind fimction (Allen et al. 1989). The
terms Rn,“ and andim are modeled using empirical equations (Jensen et al. 1989) and

are described by,

79

(1‘ 0‘9“”) * 115...... ‘ 9 * (ADT+273)‘ * (0.39 — 01585) *(&)i
and... = [10]

 

2.45 liter. MJ'1

(1 "m“m“) * RM“: 9 *(ADT+273)‘ * (0.39 — 0.158722) *ifiji

anedrum = [ 0

 

11
2.45 liter. M;-l [ ]

were ocptm. is the crop albedo, ocmedtnm is the medium albedo, o is the Stephan-Boltzman
constant (4.903 x 10'9 MJ°m'2°d'l 0K4) ed is the saturation vapor pressure at the dew
point temperature (KPa), R.o is the clear sky solar radiation (MJ -m'2 - (1"), Rs is the actual
solar radiation (MJ - rn'2 - d"), Rsptm is the short wave radiation reaching the plant canopy
(MJ 0m“. d"), Rsmdium is the short wave radiation reaching the medium surface
(MJ -m’2- d"). Rsmd;um was modeled as a function of the incoming Rs, the plant leaf area
index (LAI), and the albedo of the medium (amcdtum) (Chen and Leith, 1992) and is
described by,
RSmeditnn = (Imam * RS * Chain)- [12]

Chen and Leith found values of 0.25 for chrysanthemum 051..., and 0.2 for peat medium
(Imam. Rs was not directly measured but was converted from PAR measurement based on
values found in Thimijan and Heins (1983). The empirical wind function flu) was set to a
constant value of 1.4 based upon Chen and Lieth (1992) and Yelanich and Biembaum
(1995)

The plant portion of the model consists of the leaf area (LA) and dry mass (DM). The
plant response to N deficiency in the medium is modeled by a reduction in concentration of N

in the shoot, leading to a reduction in the rate of leaf area expansion. The response of the rate

80
of leaf area expansion to the N concentration of the plant is modeled by defining a plant critical
N concentration, NW, where there is no improvement in the rate of leaf expansion and a
minimum N concentration, NW, where there is no leaf area expansion (Goodwin and Jones,

1991). The equations describing this are,

0 for Nshoot<NminLA
fLA= (N5hoot'NminLA)/(Nnnxl.A'NnmrLA) for NrrinLA<Nshoot<NmaxLA [13]
I for Nshoot>NrmeA

where fur is a 0 to 1 firnction limiting the rate of leaf expansion in response to the current shoot
N. Values of 0.0135 and 0.034 were used for NW and Nmmbased upon Yelanich and
Biembaum (1995). The rate of leaf expansion, is described by the equation,
dLA/dt = (c1+2*c2*t)*fLA [14]
where dLA/dt is the rate of leaf expansion in mz/day, and c1 and c2 are constants. The rate of
dry mass accumulation was modeled as a firnction of the photosynthetic active radiation (PAR)
and the total leaf area and is described by,
dDM/dt = (PAR*d1+PAR2*d2+d3)*LA [15]
where dDM/dt is the rate of dry mass accumulation in gm/day, dt,d2 and d; are constants.
The model was run using a one day time step. The various parameters were determined
from the rates using numerical integration using the form,
Z(t+ dt) = Z(t) + dt*( CZ/ dt). [16]
Validation. To validate the model chrysanthemums were grown at two times of the year
(winter, 7 January to 25 March; spring, 14 April to 30 June), with three fertilizer

concentrations (3.6, 7.1, 10.7 mol'm'3 N), and at three fluence levels (30% shade,

81

ambient or supplemented with high pressure sodium, HPS 6 (mol-day"). One rooted
cutting of chrysanthemum ‘Bright Golden Anne’ was placed in a 10 cm pot filled with a
75% peat, 25% perlite (winter experiment) or 100% peat (spring) medium (Table 1) . The
amendments KN03 (0.06 kg-m'3), Ca(No3 )2 (0.06 kgom”), Mgso. (0.03 kg-m'3)
CaSOa (0.06 kg-m'3), Cal-IP04 (0.06 kg0m'3), hydrated lime (0.21 kg-m'3) and a
nricronutrient mix (FTE 555, 0.01 kg-m'3) were incorporated into the medium prior to
planting.

Plants were placed in a 3 m by 4 m glass greenhouse with day and night
temperature set points of 20 C and were exposed to day-lengths of 16 HR for the first 7
days, after when the shoots were pinched to 6 nodes and placed under day-lengths of 10
hours per day. Plants were pruned to 3 shoots per plant when the laterals were large
enough to handle. Water used to make the nutrient solution had an initial alkalinity of 170
mg-liter'l CaC03, pH of 6.4 and an EC of 0.30 dS-m". The three fertilizer treatments
were made from KN03 and N1-14N03 in a ratio to provide 64% NO3-N and 36% NH4 -N.
All fertilizer treatments also had 0.5 mol-m'3 P fiom H3PO4 and 50 mg-liter’1 of a
chelated micronutrient mix (Compound 111, Scotts, Marysville, Ohio). Plants were
weighed daily and irrigated when the mass of the plant, pot and medium was less than 250
grams. Pots were kept in individual water tight trays and were subirrigated by pouring 0.2
liters of solution into the tray, a volume of solution absorbed by the medium 0.5 hr after an
irrigation. Three plants per treatment were randomly selected for evaluation biweekly. Leaf
area, plant dry mass, and shoot and root Kjeldahl N (Diamond, 1992) were determined at

each sampling date. The root-medium selected for sampling was first sliced into vertical

82

halves, one half was used to collect the roots for dry mass and the other half was used for
medium N determination. The half used for medium N analysis was cut into top and root
zone layers, at a height 5 cm from the bottom. The top layer and root zone, were
extracted using the saturated medium extraction method (W arncke, 1986). Only the root
zone data are reported. The extract was analyzed for nitrate N, nitrite N and ammonium
N using colormetric methods (Diamond, 1986a and Diamond, 1986b). The concentration
of nitrite N was less than 1 mg-liter'l and will not be reported. A sub-sample of the
saturated medium paste was weighed before and after saturation, oven dried for 4 days at
60 C and weighed again, to determine the water content of the paste. Nitrogen contents
were determined using the following formula,

Sample Water Mass * Bulk Density
Sample Mass Density of Water

 

N(mg) = N (mg / liter) * * Layer Volume [ l7]

(Hillel, 1982). Bulk density was determined in a separate experiment and was found to be
0.0786 and 0.0580 g-literl for the 75% and 100% peat media, respectively and the
volume of the root zone was 440 cm3 for the winter experiment and 366 cm3 for the
spring experiment (Table 1). The LA parameters in equation [14] (c1 and c2) were determined
using the supplemented light and high fertilizer treatments. The DM parameters in equation
[15] (d1,d2 and d3) were determined using the entire data set and the measured daily PAR
values.

Optimization. Five fertilization strategies (F S) were developed and calibrated using the SAS
PROC NLIN algorithm (SAS institute, 1995) and the ambient weather data from the winter

and spring experiments. The first strategy was developed to determine what concentration of N

83
to apply to minimize the quantity of N applied while maintaining the saturated medium extract
(SME) N concentration in the root zone in the reported optimal range of 7 to 14 mol°m'3 N.
A penalty function of the form

(NRZ - 48)2 NRZ < 32
fpemlty = 0 32 <= NRZ <= 64 [18]
(NRZ — 64)2 NRZ > 64

was used to constrain the model to maintain NRZ within the optimal range.

Four additional strategies were developed and calibrated using the concept of
proportional integral derivative control (PID). PID control uses the output fi'om a process as a
means of determining a new input into that process. In this case the output fiom this system,
NRZ, is used to determine the Nconc to apply to the system. Alter experimenting with the
PID controller a PD controller was found to give the most stable over all response. The

general equations used in the controller were,

NRZerra(t) = (NRZtetpomt-NRZ) [19]
———dNR:"(’) = NRZam(t) - Nazmn - dt) [20]
Nconc(t +dt) = Nconc(t) +[Nerror(t) * P. + gN—Rjt—mfl * P2] [21]

were W is the desired root zone N content and NRZ...“ is the deviation from that
setpoint. The parameters P1 and P2 determined how quickly the controller responds to
deviations from the NRZM. Strategies were developed based on daily (F S 2 and 4) or
weekly (F S 3 and 5) determinations of NRZ and NRZ.“ A NRZM of 3.4 mmol (48 mg) N

was used fertilization strategies 2 and 3 in the determinations of P1, P2 and the initial applied

84
Nconc (t=0). The constraints placed upon this determination were to minimize the N applied
while maintaining the N concentration within the optimal range using the penalty fimction in
equation [16]. Fertilization strategies 4 and 5 involved determination of the NRZWm in
addition to determining P1,P2 and the initial Nconc. These determinations had the constraint of
minimizing the N applied while maintaining the N concentration in the plant at Named. A

penalty fimction of the form

(Nactual - Nuilml)2 Nat-mar < Neritcel

f‘m" = i 0 NRZ > Na... [22]

was used to constrain the model to maintain NW above the critical concentration.

Results and Discussion

There was a significant response of LA to increased fertilizer concentration. The mean
LA across light and experiments was 707, 960 or 1067 cm2 when 3.6, 7.1 or 10.7 mol-m'3 N
was applied respectively. There was less of a response to the light treatments in the spring
experiment than in the winter experiment. The LA model, made up of equations [13] and [14],
worked very well across the environments tested in this experiments with an R2 of 0.95
(n=270) (Figure 2). The LA model could be further improved by basing the equation [14] on
temperature rather than time since planting, however there was insufficient data to construct
such a model from this experiment.

Plant dry mass followed a similar trend to LA, with increasing dry mass as the fertilizer
concentration increased as well as the significant interaction between experiment and light

treatments. The average across fertilizer treatment dry mass was 12, 19 and 19 g for the

85

shaded, ambient and HID treatment, respectively, indicating that there was little improvement
of the supplemental lighting in the winter. In the spring experiment there was a benefit of the
supplemental fighting, with the average across fertilizer treatment dry mass was 13, 16 and 24
g for the shaded, ambient and HID treatments, respectively. The R2 for the predicted DM
(Figure 3) was high at 0.91 (n=270), though the model could be improved with the
incorporation of temperatures in equation [15] to better simulate plant respiration.

Plant N increased with increasing fertilizer concentration (321, 457, 545 mg for 3.6,
7.1 and 10.7 mol-m'3 N, respectively), with increasing light (321, 457 560 mg for shaded,
ambient and HID, respectively) but decreased between winter and spring (463 and 420 mg
respectively). The R2 for the PN predictions were lower than DM or LA at 0.88 (n=270) and
tended to over predict N accumulation at the end of the crop. The PN model could be
improved by making Nam“; a function of the since NW as been shown to vary with the age of
the plant (Willits et al., 1992). The PN model could further be improved with the addition of
sub-models separating nitrate and ammonium uptake and base N uptake as a fimction of
concentration, pH and root activity. The over prediction of N accumulation at the end of the
crop could be due to remobilization of the N from the leaves, stems and roots and into the
flower. The current model predicts N for flower formation would come from the medium

The water loss model worked well considering the simplicity of the equations used
(Figure 5). The prediction of water loss could be improved with the addition of the relationship
between water potential of the medium and water loss. The assumption that plant temperature
was equal to air temperature, while necessary for simplification purposes, has been shown to be

false (Faust, 1994), especially for plants grown using supplemental lighting.

86

The root zone N content increased as the concentration of fertilizer applied
increased. At the final sampling, the medium N concentration was dependent on the
fertilizer concentration applied but independent of light intensity (Table 5). The model
simulated these general trends very well with the NRZ increasing as the fertilizer
concentration applied but not changing as the light intensity increased fi'om the shade to
supplemented light treatments (Figure 6). The model predicted very rapid day to day
changes in the medium N content. These rapid changes would indicate that the pool of N
in the root zone is very labile, requiring frequent replenishment to maintain a set quantity
of N. The large increase in the N concentration in the medium at the final sample was not
predicted by the model and is probably due to the over prediction of plant N uptake
discussed earlier.

The predicted optimal solution of FS 1 to maintain a root zone concentration of 7
to 14 mol°m'3 N was for an applied N concentration of 16.3 mol-m'3 (229 mg-liter")
(Table 5) is near the typically recommended concentration of N to apply for top watered
plants. All five strategies tested were able to maintain the concentration of nutrients near
the set point values (Figure 7). The medium N concentration data presented in Figure 7 are
actually the concentration of saturated medium extracts (SME), the preferred test method for
peat-based media (W amcke, 1988). To obtain concentration data, the model output and actual
N content data were divided by the average volume of water (0.317 liters, corrected for
volume) in a SME from the two experiments (Table 1). The setpoint values of 6.3 mol- m"
(88 mg-liter") determined for PS 4 is lower than the midpoint value of 10.7 mol-m'3

(150 mg-liter") typically used, indicating that a lower optimal range could be used for

87

subirrigated chrysanthemum. The model predicted that using a lower setpoint value would
result in less N being applied than if the standard setpoint values was used (F S 2 vs. F S4).
The lower setpoint also resulted in less change in Nconc to compensate for changes in
medium N content. There was no clear cut improvement in using daily medium testing as
compared to weekly medium testing indicating that the weekly testing frequency is
adequate. All FS tested predicted plants with comparable leaf area, dry mass and plant N.

Subirrigated plants have been reported to have a lower root zone concentration of
N than top watered plants when fertilized with the same fertilizer N concentration
(George, 1989). Paradoxically subirrigated plants are commercially fertilized with lower
concentrations of N than top watered plants (Biembaum, 1993). These two finding fit well
with the optimization results since a higher than typically commercially applied N
concentration was necessary (F S 1, 16.3 mol-m'3 N) to maintain the root zone N
concentration within the 7 to 14 mol 0 m’3 N accepted range, but a lower root zone N
concentration could be maintained with little detrimental efi‘ect on plant grth (F S 3). It
may be possible, at least for subirrigated chrysanthemums, to establish a lower range of

acceptable medium test values and allow growers to apply less fertilizer to their crop.

The apparent simplicity of this container-grown plant system is deceiving, since
there are many possible interactions influencing the medium N concentration. The model
is based on the hypothesis that the N concentration in the medium is dependent on the
rates of N application, uptake by the plant and movement into the top layer. The

prediction of the rate of plant N uptake is in turn dependent on the prediction of dry mass.

88
Dry mass is dependent on the leaf area expansion and the PAR available. The rate of leaf
area expansion is modulated by the N concentration of the shoot, and is ultimately
dependent on the N concentration of the medium. Leaf area influences the rate of water
loss and ultimately determines the frequency of N fertilizer application. With all these
interactions, container-grown plants are typically produced using the simplest of all
control strategies, that of a constant input of N, applied with every irrigation. One
hypothesis has been that a single concentration of nutrients would be unable to
compensate for variations in plant grth and that more elaborate control strategies are
needed to handle these variations in growth (Fynn and Bauerle, 1988). This did not appear
to be the case since a single concentration of applied N supplied sufficient N under both
winter and spring conditions as well as under high (HID) and low (shade) irradiance

conditions.

Using a control strategy where RZN was determined daily and used to determine
the N concentration to apply did reduce the quantity of N applied by an average of 32%
when compared with using a single concentration. The benefit of this reduction in N
applied, at least in a subirrigated system, is limited since the fertilizer cost is a small cost
of total production, and any extra N applied is lost to the top layer instead of entering the
environment. In the future when reliable insitu N detectors are developed it will be

possible to use this control strategy to better maintain the root zone N content.

There may be an implication based on the results from this model that medium

testing is not a necessary requirement for maintaining the nutrient status in the root zone

89
of chrysanthemum. It appears, at least under the conditions of this experiment, that
applying a constant concentration N of greater than 16.4 mol-m'3 (229 mg-liter") will
maintain the nutrients in a range needed for adequate growth. However, medium testing
is necessary since it is used to determine when problems such as injector failure or
misapplication of fertilizer have occurred. The rapid rate the medium N concentration
changes would indicate that daily monitoring of the medium N levels are necessary to
determine when problems occurs. Chrysanthemum has been shown to tolerate periods of
N deprivation of a week or less (Y elanich and Biembaum, 1995b) so that weekly

monitoring is probably suficient.

There are many possible improvements to the model with the most pressing need a
model to predict the flower response to N deficit. While the model appears to adequately
deal with the total dry mass and leaf area of the plant it does not deal with flower size and
mass reductions expected when N deficiencies occur. The flower is the main selling
feature of a chrysanthemum and little work has been done to quantify the flower size
response to N deficiency. The general form of the flowering model would be probably

similar to the leaf area N function, fLA used in this paper.

Further work is needed to characterize the response of chrysanthemum to excess
concentrations of N and other salts. Since the model is unable to handle excess N, efforts
were made in the modeling process to exclude conditions where reductions in plant size
could occur due to excess salts in the medium. The form of N also can cause differences

in plant morphology and has not been addressed in this model.

90
The model presented in this paper demonstrates the dynamics of the N flow in the
root zone of a chrysanthemum. A potential use of the model will be to link the model with
a medium testing diagnosis and interpretation program, and will allow growers to better
interpret and make logical choices in their fertilization program. The concepts presented
here could be expanded to study the dynamics of N supply in top water situations as
described by Argo and Biembaum (1995) or be used to interpret simple N petiole sap

testing results.

Abbreviations
1. ADT = average daily temperature (C).
2. cumin... = Medium albedo.
3. up]... = Plant albedo.
4. DM = Total dry mass (mg).
5. A = Slope of the saturation vapor pressure fimction.
6. y = Psychometric constant.
7. 0' = Stephan-Boltzman constant (4.903 x 10°9MJ- m'2 - d'1 0 K").
8. Rnptmt = Plant net radiation (MJ - rn'2 ° d'l).
9. ancdm = Medium net radiation (MJ - rn'2 - d").
10. e. = Saturated vapor pressure (kPa).
11. ed = Saturation vapor pressure at the dew point temperature (KPa).
12. fut, = Function influences leaf area based on plant % N.

13. fm = Function influencing N movement into top layer.

14.

15.

l6.

l7.

l8.

19.

20.

21.

22.

23.

24.

25.

26.

27.

28.

29.

30.

31.

32.

33

34

35.

91

LAI = leaf area index.

LA = leaf area (m2).
MA = medium area (m2).
N.“ = current plant percent N (%).
Nconc = N concentration applied (mg - liter") .

Nan-mt = critical plant percent N (%).

NW = Maximum plant N concentration for leaf expansion (%).
NW = Minimum critical plant N concentration for leaf expansion (%).
NRZ = N in the root zone (mg).

NRZAp = N applied to root zone (mg).

NRZ/n, = N moved from the root zone to the top layer formation (mg).
PAR = photosynthetic active radiation (mol - day").

PN = Plant N uptake (mg).

Rs = Actual solar radiation (MJ - m'zd").

RM“... = Short wave radiation reaching medium (MJ - m'zd'l).
Rso = Clear sky solar radiation (MJ ~m'2d").

Rspm = Short wave radiation reaching plant (MJ - m'zd'l).

WRZ = Root zone water vohrme (liter).

WRZAp = Water applied to the root zone (liter).

WRZEVAP = Water evaporated from medium surface (liter).
WRZm = Maximum water volume of root zone (liter).

WRZmin = Water volume when an irrigation occurs (liter).

92
36. WRZptm = Water transpired by plant (liter).
37. WTLAp= Water applied to the top layer (liter).

3 8. Wtot = Total water volume applied (liter).

Literature Cited

Argo, W.R and J .A. Biembaum. 1995. The effect of irrigation method, water-soluble
fertilization, preplant nutrient charge, and surface evaporation on early vegetative and
root growth of poinsettia. J. Amer. Soc. Hort. Sci. 120:163-169.

Biembaum J .A 1992. Root-zone management of greenhouse container-grown crops to control
water and fertilizer use. HortTechnology 2: 127-132.

Biembaum J .A 1993. Subirrigation could make environmental and economical sense for your
greenhouse. PPGA News 24(4):2-14.

Cox W.J. and HM. Reisenauer. 1973. Growth and ion uptake by wheat supplied nitrogen as
nitrate, or ammonium or both. Plant and Soil 38:363-380.

Diamond D., 1986a. Nitrate + nitrite. QuickChem method 12-107-06-02-A Lachat
Instruments, Mequan, WI.

Diamond D., 1986b. Ammonia. QuickChem method 12-107-06-02-A Lachat Instruments,
Mequan, WI.

Diamond, D. 1992. Total Kjeldahl nitrogen in Soil/Plants. Lachat Instruments QuikChem
Method 13-107-06-2-D.

Elliot GO and RV. Nelson 1983. Relationships among nitrogen accumulation nitrogen
assimilation and plant growth in chrysanthemums. Physiol. Plant. 57 :250-259.

Faust, J .E. 1994. Modeling shoot tip temperature. Ph.D. Dissertation. Mch. State Univ, East
Lansing.

Fynn, RP., W.L. Roller, and W.L. Bauerle. 1988. Nutrient selection by decision analysis and
expert systems. Amer. Soc. of Ag. Engin. 88-7529:l-10.

George R. K. 1989. Flood subirrigation systems for greenhouse production and potential for
disease spread. MS Thesis, Michigan State Univ, East Lansing.

93

Goodwin , DC. and CA Jones. 1991. Nitrogen dynamics in soil-plant systems, p. 287-340.
In: J. Hanks and J .T. Ritchie (eds). Modeling plant and soil systems. Agronomy 31.
Amer. Soc. of Agronomy Inc, Madison, WI.

Karlsson, MG. 1987. Characterization of development and growth response to irrandiance
and temperature for model development in chrysanthemum. Ph. D. Dissertation
Michigan State University.

Manetsch, T.J. 1987. Improving the global convergence of Box’s complex heuristic, System
Science Program, Michigan State University.

Nelson P.V. 1994. Greenhouse operation and management. 4th edition. Prentice Hall, New
Jersey.

Ritchie, J .T. 1986. Using simulation models for predicting crop performance. Symposium on
the role of soils in systems analysis for agrotechnology transfer. ISS Congress.
Hamburg, FRG.

Wamcke, DD. and BM. Krauskopf. 1983. Greenhouse growth media: Testing and nutrition
guidelines. Mich. State Univ. Ext. Bull. E-1736.

Wamcke, DD. 1986. Analyzing greenhouse growth media by the saturation extraction
method. HortScience 21 :223-225.

Wamcke D. 1988. Recommended test procedure for greenhouse growth media, p. 34-37. In:
W.C. Danhke (ed). Recommended chemical soil test procedures for the north central
region. N. Dakota Ag. Expt. Sta. Bul. 499.

Willits, D.H., P.V. Nelson, M.M. Peete, MA Depa and IS. Kuehny. 1992. Modeling
nutrient uptake in chrysanthemum as a fimction of growth rate. J. Amer. Soc. Hort.
Sci. 117:769-774.

Yelanich, M.V. and J .A. Biembaum 1993. Root-medium nutrient concentrations and
growth of poinsettia at three fertilizer concentrations and four leaching fractions. J.
Amer. Soc. Hort. Sci. 118:771-776.

Yelanich, M.V. and J .A Biembaum. 1994. Fertilizer concentration and leaching afl‘ect nitrate-
nitrogen leaching fi'om potted poinsettia. HortScience 292874-875.

Yelanich, M.V. and J.A. Biembaum. 1995a. A model to predict the rate of whole plant
nitrogen accumulation in container-grown chrysanthemum ‘Bright Golden Anne’. (in
review for submission to J. Amer. Soc. Hort. Sci).

94

Yelanich, M.V. J .A Biembaum and RD. Heins. 1995b. A model to predict changes in the
rate of leaf area expansion of chrysanthemum ‘Bright Golden Anne’ in response to
shoot nitrogen. (in review for submission to J. Amer. Soc. Hort. Sci).

Yelanich, M.V. and J .A. Biembaum. 19950. A model to predict the movement of nitrate and
ammonium in a container. (in review for submission to J. Amer. Soc. Hort. Sci).

Yelanich, M.V. and J .A Biembaum 1995d. A model to predict evaporation and transpiration
from container-grown chrysanthemum. (in review for submission to J. Amer. Soc.
Hort. Sci).

95

Table 1. Physical properties and saturated medium extraction (SME) parameters of the
medium used in the validation experiments.

 

 

Winter Spring
Experiment Experiment

Peat (%) 7 5% 100%
Perlite (%) 25% 0%
Pot Volume (cm’) 725 754
Root Zone Vol. (cm3) 440 366
Bulk Density (g/cm’) 0.074 0.058
Water Volume (cm’) 306 291
Air Space (cm’) 73 56
Solid (cm’) 62 21
Avg. .SME Volume (liters) 0.366 0.268
Max. .SME Volume (liters) 0.520 0.344
Min. .SME Volume (liters) 0.295 0.149
Std. .SME Volume (liters) 0.052 0.032

 

96

Table 2. Photosynthetic active radiation (PAR), dry and wet bulb temperatures and
statistics from winter and spring weather data.

 

PAR Dry Bulb Wet Bulb PAR Dry Bulb Wet Bulb

 

 

(mol'm'z'day") (C) (C) (mol-m"-day") (C) (C)
Winter Spring
Average 7.29 20.1 13.9 11.3 20.8 17.8
Std Dev 5.00 0.5 1.3 4.7 2.4 3.4
Maximum 20.50 21.8 17.1 22.8 27.7 25.9
Minimum 0.40 18.9 11.1 1.3 17.3 11.5

 

Table 3. Photosynthetic active radiation (PAR), dry and wet bulb temperatures and solar
irradiation statistics from generated weather data.

 

 

PAR Dry Bulb Wet Bulb Solar
(molm'ztday'l) (C) (C) (MJ-m'z-day")
Average 16.3 20.9 15.1 8.3
Std Dev. 7.5 0.8 4.3 3.8
Maximum 28.2 23.5 21.0 14.4
Minimum 5.0 20.3 7.2 2.6

Number 208 208 208 208

97

Table 4. Analysis of variance of leaf area, dry mass, plant N, total N applied and nitrate-

N concentration and ammonium N concentration 70 days since the start of short

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

N Applied Dry Mass Leaf Area Plant N Root Zone N
mol 0 m’ mg m2 mg mg
Winter Experiment
Shade
3 .6 1 1 824 278 15
7.1 12 934 330 50
10.7 14 1068 402 102
Ambient
3 .6 17 846 309 16
7.1 20 1050 513 46
10.7 21 1165 611 74
Supplemented
3 .6 15 528 408 6
7 .1 18 932 629 50
10.7 25 992 684 91
Spring Experiment
Shade
3 .6 13 613 277 5
7.1 13 952 269 29
10.7 14 1049 363 57
Ambient
3 .6 13 682 256 6
7 .1 17 786 422 32
10.7 19 1005 548 40
Supplemented

3 .6 21 749 398 0
7 .1 26 1103 580 17
10.7 26 1120 663 45
EXP ns ns 91“ H916
PPF W ns Halt ns
EXP*PPF 9* 916* ns ns
FERT 91616 9161916 $191916 Hale
EXP*FERT ns ns ns H
PPF*FERT ns ns 9* ns
EXP*PPF*FERT ns ns ns ns

ns, *,**,*** Nonsignificant or significant at P=0.05, 0.01, or 0.001, respectively.

98

Table 5. Optimization parameters for the 5 fertilizer strategies (F S) evaluated.

 

 

FS 1 FS 2 FS 3 FS 4 FS 5
Starting N (mg - liter") 228 253 139 192 200
PD. 1.98 -1.13 -049 -1.63
PD2 4.06 3.74 0.50 1.98
set point (mg-liter:l SME) 150 150 87 44

 

Table 6. Optimized leaf area, plant N, dry mass, total N applied, medium top layer (TLN),
medium root zone (RZN), and mean and standard deviation of root zone N at 70
days since start of short days of the 5 fertilization strategies (F S). Mean and
standard deviations were calculated over the entire 70 day period.

 

 

 

 

 

Leaf Plant Dry N TLN RZN Initial Mean Std
Area N mass Applied N RZN RZN
cm2 mg g mg mg mg mg mg mg
Winter Experiment
FS 1 1072 768 22.2 968 237 43 80 149 45
PS 2 1072 768 22.2 1071 321 62 80 194 59
FS 3 1072 768 22.2 1058 324 47 80 193 55
PS 4 1072 754 22.2 844 138 32 80 104 37
PS 5 1072 754 22.2 760 74 13 80 80 36
Spring Experiment
FS 1 1072 694 20.0 1263 607 42 80 224 76
FS 2 1072 694 20.0 1140 485 41 80 187 56
PS 3 1072 694 20.0 1180 536 30 80 200 58
F8 4 1072 694 20.0 962 335 12 80 144 41
PS 5 1072 689 20.0 759 145 6 80 81 30

 

99

Figure 1. Diagram representing the various components of a model to predict N content
in the root zone of container-grown chrysanthemum. I represents integration of a

rate.

 

100

 

 

 

dLA/dt <_, ,
eq. [14] Envrronment

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

LA
‘1/
Environment
WNW/d: dWRme/dt
eq. [80 eq. [9]

 

 

 

 

 

 

 

 

 

 

 

 

 

\ 1
dWRZAP/dt

 

 

 

 

 

 

 

 

 

 

 

 

99.15]
l
v JINVIIC)
dNRZTL/dt + dNRZAP/dt +
eq. [4] 6C1. [2]

 

 

 

 

 

dDM/dt
eq. [15]

 

 

 

 

 

 

 

 

 

fLA
eq. [13]

 

 

 

 

 

 

 

PN DM

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

--—>l§

 

 

 

101

Figure 2. Leaf area over time since the start of short days under various light and
fertilizer treatments. Graphs in left column are the leaf area of plants receiving
3.6 mol-m'3 (50 mg-liter'l) N, graphs in the middle column are plants
receiving 7 .1 mol-m‘3 (100 mg-liter") N, and graphs in the right column are
plants receiving 10.7 mol-m'3 (150 mg-liter") N. The top three rows are
plants from the winter experiment and the bottom three rows are fi'om the
spring experiment. Graphs in rows 1 and 4 are plants grown under 30% shade,
2 and 5 are plants grown under ambient light conditions and 3 and 6 were

grown under supplemental HID lighting.

102

 

2”.
1‘” -
11" --

800 -

 

I“. '-
12” '-
8“ —

400-

*0

 

I“. -
12” '-
8“ -

4“"

 

1‘00 -
12“ J

I” -

Leaf Area (cmz)

4.0-4

I

III

I

I

 

I“. -
12.. -
8” -

I

I

ITTII

I I

 

I“. '—
12” '—
8” '-

“0—

 

ITII

 

 

I

I

I

I

I

I I

 

I7

I I

I

I

I

I

 

I

7 1421283542495‘fl70 0 7 “21183542495667. I

 

I I I I I I I I I I
71421283504956‘37077

Days Since Start of Short Days

103

Figure 3. Dry mass over time since the start of short days under various light and
fertilizer treatments. Graphs in left column are the dry mass of plants receiving
3.6 mol-m3 (50 mg-liter") N, graphs in the middle column are plants
receiving 7.1 mol-m'3 (100 mg-liter'l) N, and graphs in the right column are
plants receiving 10.7 mol°m'3 (150 mg-liter") N. The top three rows of
graphs are plants from the winter experiment and the bottom three rows are
from the spring experiment. Graphs in rows 1 and 4 are plants grown under
30% shade, 2 and 5 are plants grown under ambient light conditions and 3 and

6 were grown under supplemental HID lighting.

Dry Mass (gram)

104

 

 

 

 

 

 

10 — -1 d —
5 _ _ ....

 

20" ‘ —‘
15—1 i -' i — i -—
10" — “ . -
5- ._ .. _

IIIII ITIIIITIW

 

 

'IIIII

 

 

 

IIIIIIIIIIIIIIIIVIIIIIIII

7 “21283542056637. 0 7 “21283542495607. I 7 “212835424956637077

Days Since Start of Short Days

105

Figure 4. Plant N over time since the start of short days under various light and fertilizer
treatments. Graphs in left column are the plant N of plants receiving 3.6
mol - m'3 (50 mg - liter") N, graphs in the middle column are plants receiving 7.1
mol o m3 (100 mg ~1iter") N, and graphs in the right column are plants receiving
10.7 mol-m'3 (150 mg-liter'l) N. The top three rows of graphs are plants from
the winter experiment and the bottom three rows are from the spring
experiment. Graphs in rows 1 and 4 are plants grown under 30% shade, 2 and
5 are plants grown under ambient light conditions and 3 and 6 were grown

under supplemental HID lighting.

Plant Nitrogen (mg)

106

 

 

1000
m— - — J
cu- — - .1
m— o “/o‘/'_
200—/— — g _
'TTIIIIIIIIITITIIIIIIITIIIITIII

8” - ~— - ..I

:3: I -Z '2
2.. ‘M‘/ p -

 

 

 

 

 

 

 

 

 

su— -+ — --
‘OO- - — -
m“ ‘ ‘ 2 or
2” -M‘ ._ _.
. I I I I I I I I I I I I I I I I I I I I I I I I I I I I I
m- — J _
cu— — - -
- e i— -
2»— § §— - -—
' I I I I I r FFI I I I I I I I I I I I I I I I I I I I I I
no— -I - A
coo-I - i— I i—
m— o— i — -
O
2»- - — —
. I I I I III I I I I I I II—II I I I I I I I I I I II
0 714212835424956‘3700 714212835424956‘3700 714212835424956637077

Days Since Start of Short Days

107

Figure 5. Water loss over time since the start of short days under various light and
fertilizer treatments. Graphs in left column are the water loss of plants
receiving 3.6 mol-m'3 (50 mg-liter'l) N, graphs in the middle column are
plants receiving 7.] mol-m'3 (100 mg-liter") N, and graphs in the right
column are plants receiving 10.7 mol-m'3 (150 mg-liter") N. The top three
rows of graphs are plants from the winter experiment and the bottom three
rows are from the spring experiment. Graphs in rows 1 and 4 are plants grown
under 30% shade, 2 and 5 are plants grown under ambient light conditions and

3 and 6 were grown under supplemental HID lighting.

Water Loss (ml/ day)

108

 

250
2“ -
15. -
1|. '—

50—

 

2“ '-
15. '-
1" -

50 —

 

2.0 J

150 —
ru -J

50-

 

2” '-
15. -
1” '-

50 '-

 

2“ -
150 —
I“ -

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2“ -
150 -
l“ -
5O .4

 

 

 

 

 

 

I

I I

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IIIIIIIIIIII IIIII

I

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I I

O 714212835424956‘370 O 7 “21283542495663” 0 7 14212835424956‘37077

Days Since Start of Short Days

109

Figure 6. Root zone N content over time since the start of short days under various light
and fertilizer treatments. Graphs in left column are the root zone N content of
plants receiving 3.6 mol -m'3 (50 mg- liter") N, graphs in the middle column are
plants receiving 7.1 mol -m'3 (100 mg-liter'l) N, and graphs in the right column
are plants receiving 10.7 mol-m’3 (150 mg-liter") N. The top three rows of
graphs are plants from the winter experiment and the bottom three rows are
from the spring experiment. Graphs in rows 1 and 4 are plants grown under
30% shade, 2 and 5 are plants grown under ambient light conditions and 3 and 6

were grown under supplemental HID lighting.

Root Zone Nitrogen (mg)

150
125 - A — —
m — ~ — i—
75 — - d -
50 q - Q— —
25 —< — — C -
. W MW—
125 — - — -
m - - - -
75 — _ _ E.
5. .4 J i.— i _
' I
125 — A — —
m - —~ — a
75 - - — —
5' ‘ ‘ 84 o -
25 — — a q
125 — - - -
m — _ _ __
75 - - -
50 - - A —
25 -1 — —\I\WWM -
' WWTT4FT—WTW
125 — -1 - d
1» - — — —
75 - - — -
50 - - — —
25 —\, -: g, : g - . . m
' I I I I I I I I I I I I
125 - - — —
m — - ~ — -
75 - — - —
50 — -« — -
25 - — ~W-
' ‘me

110

 

 

 

 

 

 

 

 

 

 

 

8 7 142128354249566378 8 7142128354249566378 8 714212835424956637877

Days Since Start of Short Days

111

Figure 7. Predicted root zone N concentration of saturated medium extracts over time
since the start of short days at two times of the year. Graphs in left column are
the root zone N concentration of plants grown during the winter experiment
and graphs in the right column are from the spring experiment. The graphs in
row 1 (top) are predicted results for plants grown with a constant fertilizer
concentration, row 2 through 4 are plants grown using a PD controller and
with weekly medium sampling (row 2 and 4) or daily medium sampling (row 3
and 5). The graphs in rows 2 and 3 were from plants grown using a constant
setpoint of 48 mg N where graphs 4 and 5 were based on plants grown with

optimized setpoints.

Nitrogen Concentration (mgoliter'l)

112

 

 

 

 

 

 

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r/ ’4
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200- I A» VV\WN~ H 10 A A» I .—
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14212835424956637014212835424956637077
Days Srnce Planting

l

     

 

 

 

 

APPENDIX ’

113

Appendix

/* SAS (version 6. 04) for Windows 3.1 Code to run nitrogen model */
LIBNAME ‘H:\MVY\MODEL’;

/* MODELO U IDES contains output data */
/* DDE link to range in Microsoft EXCEL 6. 0 spreadsheet */

filename modout dde
'Excel|H:\MVY\MODEL\[MODELOUT.XLS]output!R3C1 :R1244C 14';

DATA MOD.RUNMOD;

/* Input weather file =mod nlindata */
set mod.nlindata;

file modout;

ARRAY DBTa{2,69} T1-T138;
ARRAY Rsa{2,69} TAl-TA138;
ARRAY RsMaxa{2,69} TBl-TBl38;
ARRAY ESAIRa{2,69} TCl-TC138;
ARRAY GAMMAa{2,69} TDl-TD138;
ARRAY DELTAa{2,69} TEl-TE138;
ARRAY VPDa{2,69} TF1-TF138;
ARRAY PARa{2,69} TGl-TG138;

if F ert=l then Ncnc=50;
if Fert=2 then Ncnc=100;
if F ert=3 then Ncnc=150;
/* Initialize rate and state variables */

dLA=O;

dLAb=0;

dDM=0;

dPN=0;

dWL=0;

dWA=0;

dWA=0;

dNRZap=0;

dNRZtl=O;

PLA=12;
PLAb=12;
PDM=.903;

114

PPN=45;
PWRZ=3 00;
PNRZ=30;

LAI=(PLA/ l OOOO)/0. 01 13;

/ *C ontants for leaf area and dry mass models */
E0=2.495516413;
E1=0. 177082945;
E2=—0.000576443;

Bl=31.81604872;
B2=-0.23523788;

WRZmin=1 80;
WRZmax=3 00;

/**************** Simulation LOOP *4!******************************/

DO Cnt=1 to DOE BY 1;

DBT=DBTa{EXP,CNT};
Rs=Rsa{EXP,CNT};
RSMAX=RsMaxa{EXP,CNT};
ESAIR=ESAIRa{EXP,CNT};
Gamma=GAMMAa{EXP,CNT};
Delta=DELTAa {EXP, CNT} ;
VPD=VPDa{EXP,CNT};
PAR=PARA{EXP,CNT};

PLA=PLA+dLA;
PDM=PDM+dDM;
PPN=PPN+dPN;

PNRZ=PNRZ+(dNRZap-dPN-dNRZtl);
PNRZtest=PNRZ+dPN+dNRZtl;
PWRZ=PWRZ+(dWA-dWL);

PNcRZ=PNRZ/(PWRZ/ 1000);
PNsRZ=PNRZ/.25;
PNCact=PPN/(PDM* 1000);

/* ***#**** Water Rates *************************/

RsMedia=Rs* EXP(-.22*LAI)*(1-0.2);
RsShoot=Rs*(l-0.25);

115
FWIND=1.6636;

RB=(0.39-0. l58*sqrt(esair))*(Rs/RsMax)*((DBT+273)* *4)*(4. 93 E-9);
RNIVIED=RsMedia-(RB);

RNCAN=RsShoot-(RB);

RNMED=RsMedia-RB;

RN CAN=RsShoot-RB; ,

EMED=(DELTA*RNMED+6.43 *GAWA*FWIND*VPD)/(DELTA+GAMMA)* .62;
ECAN =(DELTA*RN CAN +6.43 *GAWA*FWII\ID*VPD)/(DELTA+GAMMA)* .69;

dWLmed=EMED*0.0133/2.45 *1000;
dWLplt=(ECAN*PLA/10000/2.45 * l 000)* .7;
dWL=dWLmed+dWLplt;
dWLb=dWLmed+dWLplt/ .7;

if PWRZ<WRZmin then do;
dWA=WRZmax-PWRZ;
if dWA>200 then dWA=200;
dNRZap=dWA/ l 000*Ncnc;
dWAtl=200-dWA;
end;
else do;
dWA=0;
dNRZap=0;
dWAtl=0;
end;

/* ********Plant Rates *************************/

if PNCact<.0135 then fl.A=0;
else if PNCact>.034 then fl..A=1;
else fl..A=(PNCact-.Ol35)/(.034-.0135);

dLA=(b1+2*b2*cnt)*tLA;
dDM=(PAR*e1+PAR* *2*e2+e0)*PLA/ 10000;
LAI=(PLA/10000)/0.0l 13;

dPN=dDM* 1 000*(.03 4);

if PNCact<.034 then

do;

dPN=dPN+PDM* 1000*(.034-PNCact);
end;

if (PNRZ+dNRZap)<=0 then dPN=0;
else if (PNRZ+dNRZap-dPN)<0 then dPN=(PNRZ+dNRZap);

116

if (PNRZ+dNRZap-dPN)<=0 then dNRZtl=(dWAtl/l000)*.68*PNcRZ; else
dNRZtl=dWLmed/1000*PNCRZ+(dWAtl/l 000)* .68 *PNcRZ;

if (PNRZ+dNRZap-dPN-dNRZtl)<0 then dNRZtl=(PNRZ+dNRZap-dPN);

/* Outputs data to excel file */
IF REP=3 AND DOE=69 THEN DO;
PUT PPF FERT EXP CNT PLA PPN PDM PNRZtest dWLb dNRZap dPN dNRZtl
PNRZ PNsRZ; ‘
END;
end; /*D0 LOOP */
output;
RUN;

"I111111171111III/71117111”