AGRICULTURAL
AND FOREST METEOROLOGY
ELSEVIER
Agricultural and Forest Meteorology 70 (1994) 289- 342
COTC02: a cotton growth simulation model for global change l Gerard W. Wall*,a, Jeffrey S. Amthorb , Bruce A. KimbaW ·US Water Conservation Laboratory, 4331 East Broadway Road, Phoenix, AZ 85040, USA bThe Woods Hole Research Center, 13 Church Street, P.O. Box 296, Woods Hole, MA 02543 , USA Received 14 September 1992; revision accepted 27 December 1993
Abstract In conjunction with the Free-Air-COrEnrichment (FACE) project, a new, physiologically based, mechanistic, modular simulation model of cotton (Gossypium hirsutum L.) physiology, growth, development, yield and water use has been constructed. It is named COTC02 for cotton response to atmospheric CO 2 concentration. The model is capable of predicting cotton crop responses to elevated atmospheric CO 2 concentrations and potential concomitant changing climate variables. The major plant processes known to be influenced by CO 2 are simulated explicitly, i.e. photosynthesis, photorespiration, and stomatal conductance, and its role in leaf energy balance. The model explicitly simulates the impact of atmospheric CO2 concentration on C 3 photosynthesis and photorespiration at the level of carboxylation and oxygenation. Growth is simulated for individual organs, i.e. leaf blade, stem segment, taproot and lateral roots, and fruit which includes squares and bolls. Potential growth is calculated and the carbohydrate and nitrogen required to meet this potential are calculated. Actual growth is based on substrate availability, the potential growth, and water stress. Our intent here is to describe the overall structure of the model, its present status, and future development plans. Further development, documentation, calibration, and validation of the model is in progress. The long range goal of the project is to provide quantitative estimates of global cotton production in a future higher-C0 2 world.
1 Contribution from the Agricultural Research Service, US Department of Agriculture. Supported in part by the US Department of Energy, Carbon Dioxide Research Division, Office of Health and Environmental Research, Atmospheric and Climate Research Division under Interagency Agreement No. DE-AI05-88ER69014. * Corresponding author
0168-1923/94/$07.00 © 1994 - Elsevier Science B.Y. All rights reserved SSDI 0168-1923(94)05041-4
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1. Introduction
The carbon dioxide concentration in the atmosphere continues to rise (Stuiver, 1978; US National Research Council, 1979, 1982; Keeling et aI., 1982; Ramanathan, 1988; Schneider, 1989; Boden et aI., 1991). A need exists, therefore, to elucidate the effects of elevated CO 2 on terrestrial vegetation. Investigators of longterm climatological data have suggested that a positive correlation exists between global trends in atmospheric CO 2 concentrations and ambient temperature fluctuations (US National Research Council, 1983). If atmospheric CO2 concentrations continue to rise, then the projected global surface temperature deviations may cause spatial shifts in the location of Earth's major biomes, thus disrupting major agricultural areas and human demographics on a global scale (Smit et aI., 1988). Because uncertainty exists with respect to how global change will ultimately influence terrestrial vegetation, it is imperative to investigate these complex interactions. Experimentation, although a useful endeavor, cannot encompass all the environmental parameters that must be considered in such a complex system. It is possible, however, to identify system behavior experimentally and construct models that will predict system response to a changing environment. An increase in atmospheric CO2 concentration and potential concomitant increase of global temperature and changing precipitation patterns are primary environmental factors predicted to be altered by global climate assessments (Ramanathan, 1988). Central to accurate environmental impact analysis, therefore, is an understanding of how these changes alter net assimilation rates and associated growth. Temperature is a prominent meteorological variable that drives plant growth and development (Long and Woodward, 1988), while photosynthetic processes acclimate and adapt to the prevailing temperature (Berry and Bjorkman, 1980). Atmospheric-COrenrichmentinduced warming of plant tissue (Idso et aI., 1987), coupled with increased surface air temperature because of an enhanced greenhouse effect, is likely to affect cotton growth and developmental (Reddy et aI., 1991a,b) and CO 2 assimilation rates (Reddy et ai., 1991a; Wall et aI., 1991), which will ultimately influence yield (Reddy et aI., 1991b, 1992c). Increased atmospheric CO 2 concentration will influence individual leaf photosynthesis, stomatal conductance, transpiration and energy balance, but acclimation of the photosynthetic machinery to temperature and CO 2 change (Mooney and Harrison, 1970; Mooney et ai., 1978; Berry and Bjorkman, 1980; Sasek et ai., 1985), feedback inhibition of photosynthesis by assimilate levels (Foyer, 1988), and effects of CO 2 concentration on apparent dark respiration (Gifford et aI., 1985; Amthor, 1991; Amthor et ai., 1992) are processes that are not well understood. In general, however, increases in atmospheric CO 2 concentrations cause an increase in photosynthesis and a decrease in stomatal conductance. The latter causes a decrease in leaf transpiration, which in turn increases foliage temperatures (Kramer, 1981; Kimball, 1983; Lemon, 1983; Strain and Cure, 1985; Cure and Acock, 1986; Enoch and Zieslin, 1988; Kimball et aI., 1993). Mechanistic models of C 3 photosynthesis that address many of these issues have been reviewed by Evans and Farquhar (1991), and Harley and Tenhunen (1991).
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Global change with respect to rising atmospheric CO 2 concentrations is presently being investigated through the use of general circulation models (GCMs) (Hanson et aI., 1983, 1984; Grotch, 1988) that predict potential shifts in atmospheric circulation patterns. Outputs from these GCMs have been used as inputs to crop growth models to predict the influence of climate change on agricultural crops. This has been accomplished by simply altering the rates of biomass conversion efficiency and water usage as a function of CO 2 concentration (Rosenzweig, 1985; Adams et aI., 1990), an empirical approach. The CERES group of crop growth models (Wilkerson et aI., 1983; Ritchie and Otter, 1985; Jones and Kiniry, 1986) do not address the fundamental effects of CO2 on the behavior of terrestrial vegetation with respect to morphology, phenology, nutrient and water usage, assimilate partitioning, energy balance, and the biochemistry of CO 2 metabolism. These models were developed for different applications at present-day CO 2 concentrations (Whisler et aI., 1986) and have not been validated with respect to their CO 2 response aspects. The overall objective of this modeling effort is to predict cotton crop responses to increasing atmospheric CO 2 concentrations and potential concomitant changing climate variables. Interpretation of model output is not the intent of this report, although preliminary validation studies have given realistic simulations. Our intent is to describe the fundamental model structure, outline the most relevant mechanisms, give key equations and associated parameters, and discuss future plans. Emphasis has been placed on describing the major plant processes known to be influenced directly by CO 2 , i.e. photosynthesis, photorespiration, stomatal conductance, and its role in leaf energy balance. Potential growth of plant organs is also discussed in detail. Soil physical and canopy microclimate processes, however, are described in less detail. Subsequent work will focus on the testing of individual model components and the entire model.
2. Conceptual development In conjunction with the Free-Air-C0 2-Enrichment (FACE) program (Hendrey, 1993; Hendrey and Kimball, 1994), a new physiologically based, mechanistic, modular simulation model of cotton (Gossypium hirsutum L.) physiology, development, growth, yield and water use has been constructed (Amthor and Kimball, 1990a,b). Model development, as a component of the overall FACE project, assisted in experimental design and protocol to ensure that appropriate model development and validation data were collected (Wall and Kimball, 1993). Because the model should extrapolate beyond the available model development database (Dahlman, 1985; Reynolds and Acock, 1985; Reynolds et aI., 1993), whenever possible explicit physiological mechanisms were used to minimize reliance on empirical relationships, which are data-set dependent. The model has been named COTC02, for cotton response to atmospheric CO 2 concentration. Several model characteristics were explicitly identified at the outset. A time step of less than a day was desired because days with similar mean temperatures, but with different amplitude, give rise to varied physiological response (Ng and Loomis, 1984).
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The model should have the potential to work on a variable time step within a day. During development, however, a 1 h time step was used for plant and aboveground environmental processes, while soil processes were evaluated every minute. The model should simulate the growth of a cotton crop with explicit phenological, morphological, physiological, and biochemical processes, as they are influenced by environmental parameters that may be affected by global change. Individual organs should be simulated. Organs should be initiated from meristems and grow at their own temperature rather than that of the ambient air. The biochemistry of photosynthesis and respiration should occur for individual leaves and reproductive organs. All organ types should have their own specific glucose equivalent requirement for biosynthesis and contain soluble and insoluble carbohydrate pools. Whole-plant nitrogen uptake and assimilation, and translocation of carbon and nitrogen among organs should be dynamic processes. Senescence and shedding of organs should occur, as should exudation of assimilates by the root system. Water and energy fluxes should be computed. A framework should be provided to simulate the acclimation and adaptation of the photosynthetic machinery to an increased concentration of atmospheric CO 2 , Lastly, the model should be modular to ensure transferability of individual modules into other modeling projects when applicable. Ultimately, the model will provide quantitative estimates of global cotton production in a COrenriched world. Existing cotton crop growth models, namely COTTON (Stapleton et aI., 1973), SIMCOT/II (McKinion et aI., 1975), GOSSYM (Baker et aI., 1983), COTCROP (Brown et aI., 1985), CALEX/Cotton (Wilson et aI., 1987), COTS 1M (Gutierrez et aI., 1984), as well as other models, were reviewed to determine their usefulness in the development of COTC02. Although components of these models aided in developing COTC02, they lacked the physiological detail required to meet the objectives of the project. In contrast, the morphogenetic template concept in the KUTUN model (Mutsaers, 1984), and the physiological detail in the alfalfa model ALFALFA (Denison and Loomis, 1989) served as prototypes for the COT C02 model.
3. Model characteristics 3.1. Modular structure
The model is modular (sensu Reynolds and Acock, 1985). A modular structure facilitates ease in updating algorithms whenever our understanding of a particular mechanism governing a physical or physiological process improves (Reynolds et aI., 1989). Furthermore, modules of various levels of sophistication can be interchanged quantitatively to assess the level of complexity required to obtain suitable predictions (Reynolds et aI., 1992). In its present configuration, there are nine modules that contain 71 subroutines, and 13 functions involving over 1000 variables and parameters in approximately 3000 lines of ANSI FORTRAN 77 code. When compiled with SUN FORTRAN on a SPARCstation-2 workstation (SUN Micro-
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system, Computer Corp., Mountain View, CA, USA)2, it can perform a season-long simulation in about 30 min, including SUNPHIGS run-time graphics software. A summary of COTC02's structure is given in Fig. I and subroutines are listed in Table 1. 3.2. Input and output
Input routines were designed following the IBSNAT (1986, 1988) standard as modified for cotton by Kimball et al. (1992, 1993), which includes daily weather, soil profile properties, soil organic residue, soil profile initial conditions, irrigation management, fertilizer management, treatment management, measured cotton crop harvest summary, and measured cotton intermediate growth data. Input categories include: (i) agronomic characteristics, i.e. field site, growing season, cultivar, planting and harvest dates, row spacing and plant population, initial seed mass and nitrogen pool size; (ii) meteorological parameters on a daily or hourly time interval, i.e. solar radiation, ambient air temperature, incident photosynthetically active radiation (PAR), wind speed at a reference height of 2.6 m, dew point temperature, and soil temperature at 0.05 m depth; (iii) soil physical characteristics, fertility status, and volumetric water content (Appendix 5); (iv) parameters associated with CO2 metabolism (Appendices 1 and 2); (v) parameters associated with potential growth and development (Appendices 3 and 4); and (vi) table look-up functions (Table 2). Whenever possible, inputs were structured similar to the format used in the ALF ALF A model (Denison and Loomis, 1989), particularly those for cultivar-specific, initial conditions, and location-specific inputs. Output can be in the form of ASCII files and run-time graphics for a set of state variables that are predetermined prior to run-time on either diurnal or seasonal temporal scales. 3.3. Initial and boundarJ' conditions
Model solutions are dependent on initial and boundary conditions. These conditions define the plant and its environment on the day of emergence. The plant canopy is divided into 25 horizontal layers, each 0.1 m thick (CLYTHY). A two-dimensional soil physics model is used to simulate belowground processes. Twenty layers and five columns have been used during model development. Soil layers can be set to any thickness, and are thinner near the surface where large gradients in soil moisture and temperature occur. Soil water potential is calculated separately for each of the cells in the two-dimensional array, and water moves both vertically and horizontally. The soil temperature model is one dimensional, so that all the cells in a particular layer in the soil have the same temperature. 3.4. Canopy architecture
The architectural configuration of the cotton plant is defined by the maximum 2 Mention of this or other proprietary products does not imply an endorsement or recommendation by the authors or their institution over other products not mentioned.
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Fig. I. Flow diagram of the COTC02 model. The main control module COTC02 calls all other modules. Initialization of variables and parameters occurs in INITAL, germination of the seed occurs in GEMRGE, while the status of the microclimate is determined in the ENVIRN module. The FIZIO L module consists of
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the canopy, CANFIZ, and individual leaf, PHYSLF, physiology plant process modules. Individual organ growth occurs in the GRO WTH module. The DROUT and DA YOUT modules control output of desired state variables on diurnal and daily temporal scales, respectively.
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Table I Summary of subroutines, functions, and modular structure of COTC02. Name
Description
Module
COT C02 DUNCAN INSECT
Main control algorithm Canopy-shortwave radiation interactions Damage to leaves and squares by insects herbivory
COTC02 COTC02 COTC02
INITIAL LlSTID PARMIN PARAMO PDVOOI PDVOUT READDA RETRVE VALFAB
Initialize variables Read PATHINC file to identify IBSNAT input files Parameter input file (table look-up response functions) Listing of parameters for COTC02 run (banner page) Quantiative biochemistry of biosynthesis Output table of biosynthetic parameters Reads input files and interfaces with COTC02 Control algorithm for IBSNAT input files Reads IBSNAT validation input file
INITAL INITAL INITAL INITAL INITAL INITAL INITAL INITAL INITAL
DISTRT DISTST GEMRGE GROWFR GROWLF GROWMR GROWRT GROWST GROWTH
Mass and distribution of root system in soil cells Stem segment mass distribution Gennination and growth to emergence Fruit growth Cotton leaf growth Growth of meristem Growth of the taproot and lateral roots Growth of stem segment Control algorithm for organ growth
GROWTH GROWTH GEMRGE GROWTH GROWTH GROWTH GROWTH GROWTH GROWTH
CANVP DARCY
ENVIRN ENVIRN
ENVIRN FIELDC LFLOCA PRO FWD SOILN SOLARI SURFAC UPTAKE
Vapor pressure of air in canopy layer Darcian flow of water among soil cells (surface energy balance evaporation, soil heat flow and soil temperature) Air and soil physical conditions of microclimate Distribution of irrigation or rain water Location of leaves and leaf area indicies within canopy layers Profile of wind speed above and within the canopy Soil nitrogen transformation Sun/Earth geometry and solar radiation at top of canopy Steady state soil surface energy balance Water and N03 uptake by roots
CANFIZ FIZIOL MRFRUT MRROOT MRSTEM PROFLW REDIST SNSCRT
Physiology within canopy layer Plant control algorithm for plant physiology Maintenance respiration by fruit tissue Maintenance respiration by root tissue Maintenance respiration by stem tissue Long wave radiation absorbed by leaves in canopy layers Redistribute phloem among organs Senescence of lateral roots
FIZIOL FIZIOL FIZIOL FIZIOL FIZIOL FIZIOL FIZIOL FIZIOL
CANOPY CANOPY CANOPY CANOPY CANOPY CANOPY CANOPY CANOPY
BLAYER FRQHRI FRQHR2 LEA FEB MRLEAF PHYSLF PLOAD STCOND
Leaf boundary layer characteristics Farquhar's photosynthesis model Internal part of Farquhar's photosynthesis model Leaf equilibrium energy budget and temperature Leaf blade maintenance respiration rate Leaf physiology control algorithm for leaf physiology Phloem loading and associated respiration Empirical equations for stomatal conductance (initial guess)
FIZIOL FIZIOL FIZIOL FIZIOL FIZIOL FIZIOL FIZIOL FIZIOL
LEAF LEAF LEAF LEAF LEAF LEAF LEAF LEAF
ENVIRN ENVIRN ENVIRN ENVIRN ENVIRN ENVIRN ENVIRN ENVIRN
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Table I Continued. Name
Description
Module
DIURNL DROUT MAPLWR MAPSQS MAPSWV MAPWND
Output of diurnal ASCII files Control algorithm for diurnal output Map of long wave radiation fluxes above, in and below canopy Map of square carbohydrate content Map of absorption of short wave radiation in canopy layers Map of wind speed profile through the canopy
DROUT DROUT DROUT DROUT DROUT DROUT
DAILY DAYOUT MAPFRM MAPFRT MAPLA MAPLMT MAPN03 MAPRT MAPSAB MAPST MAPSTL MAPSWC MAPSWP
Output of daily ASCII files Control algorithm for daily output Map of fruit structural masses Map of fruit developmental stage and distribution Map of leaf area Map of limitation to root growth in each soil cell of half slab Map of soil cell nitrate content Map of root mass distribution Map of stem mass above each stem segment Map of soil temperature in each layer Map of stem segment lengths Map of soil cell volumetric water content Map of soil cell matric potential
DAYOUT DAYOUT DAYOUT DAYOUT DAYOUT DAYOUT DAYOUT DAYOUT DAYOUT DAYOUT DAYOUT DAYOUT DAYOUT
STATPL CARBON SHOOT
Output some current values of accumulators Cumulative carbon balance Structural mass of shoot organs by type carbon and nitrogen contents of shoot structural mass Whole plant soluble sugar content Run-time graphics
DROUT/DAYOUT DROUT/DAYOUT DROUT/DAYOUT
Absolute humidity Air temperature ("C or OK) from time of day and daily maximum and minimum temperatures Convert integer day/year to character month/day Height of right circular cone from radius at base and volume Base radius of right circular cone from height and volume Volume of right circular cone from height and base radius Deep soil (below bottom layer) temperature Latent heat of vaporization Linear interpolation of x:y values Relative rate based on the Arrhenius equation Relative respiration rate temperature factor Locates soil layer within soil slab Saturation vapor pressure of water
FUNCTION FUNCTION
ALLSUG RTPLOT ABHUM AIRTMP CDATE CONEH CONER CONEY DEEPST LATENT LINTRP RELRAT RESPTF SLAYER SVP
DROUT/DA YOUT DROUT/DAYOUT
FUNCTION FUNCTION FUNCTION FUNCTION FUNCTION FUNCTION FUNCTION FUNCTION FUNCTION FUNCTION FUNCTION
number of monopodia, 1M; maximum number of nodes on a monopodium, IMXMNN; maximum number nodes on a sympodium, IMXSYN; and the lowest monopodium node with a sympodium branch attached, ILWSYM. The angle of the monopodium, SINMON; sympodium branches, SINSYM; and petioles, SINPET, are derived with respect to the horizontal plane, thereby specifying the location of aboveground plant organs within the foliage space, i.e. plant map (Appendix 4). The heliotropic leaf tracking characteristics of cotton leaves is simulated explicitly. The degree of solar tracking is a function of time of day, water
Table 2 Response function of x;y pairs
N >0
00
Parameter
Description
Units
Value x : y pair"
H20FAC
Soil matric potential effect on sink strength of root system Soil cell temperature effect on thermal conductivity of water vapor
MPa
x: y:
TCWV
WPFUNC WPLIMT POS/TN
RRDRWS
CYTOKl
MCR
MONSNK
a
Leaf water potential on potential leaf growth Soil matric potential limitation on root growth Potential stem length to characteristic dimension of the subtending leaf blade relationship as effected by position of node (node number) Soil matric potential effect on lateral root senesence coefficient Soil matric potential effect on relative cytokinin production by root tips Physiological age effect on fruit maintenance basal respiration coefficient
Effect of monopodium number on relative sink strength of meristem
* °C J m- I
-10000.0, -5.0, -4.0, -3.0, -2.0, -1.0, 0.0 0.90, 0.60, 0.55, 0.45, 0.20, 0.10, 0.05
~
-1.0,0.0, 10.0,20.0,30.0,40.0,50.0,60.0,70.0 y; 0.020,0.0247,0.0419,0.0799,0.1260, 0.2470, 0.3810,0.6500, 1.17
:::::
x:
s-I
°C- I
~
.,,.....~
MPa
x:
*
y;
-100.0, -5.0, -4.0, -3.0, -2.0, -1.5, -J.O, -0.5, -0.1,0.0 0.00,0.00,0.01,0.05,0.10,0.40,0.85,0.90, 1.0 -10000.0, -5.0, -3.0, -2.0, -1.0, -0.5, 0.0 0.00,0.00,0.1,0.40,0.95,0.99, 1.00 node number (0-40) 1.30, 1.10, 1.00,0.95,0.90,0.87,0.85,0.80,0.75,0.70, 0.60,0.55,0.55,0.55,0.55,0.55,0.55,0.55,0.55,0.55, 0.55,0.50,0.50,0.50,0.50,0.50,0.50,0.50,0.50, 0.50, 0.50 0.45, 0.45, 0.45, 0.45, 0.45, 0.45, 0.45, 0.45, 0.45, 0.45 -1000.01 -4.0, -3.0, -2.0, -1.0, -0.1, 0.0 1.0(10)- ,1.0(10)-4,1.0(10)-5,5.0(10)-6, 1.0(lOr6 , 1.0(10)-7,0.0
MPa
x:
-10000.0, -5.0, -4.0, -2.0, -1.5, -1.0, -0.5, -0.1,0.0
*
y: 0.00,0.01,0.02,0.10,0.15,0.70,0.90,1.00,1.00
""~
tp
x: physiological age as fraction of boll maturation period y: 0.0400, 0.0400, 0.0398, 0.0389, 0.0335, 0.0265, 0.0175,0.0095,0.0076,0.0072,0.0069,0.0068, 0.0068, 0.0068, 0.0068, 0.0068, 0.0068, 0.0068, 0.0068, 0.0034, 0.0000 x: monopodium number, (1M) y: 1.0,0.86,0.70,0.60,0.50
..... -----
MPa
*
x: y:
MPa
x:
*
y:
*
x;
CH 2 0g- 1 s-J
*
*
y;
Interpolation function (LlNTRP) used to derive actual parameter value based on x : y paired array.
* dimensionless.
~
~
~
~
e..
§ .".
~
~
~
'"
~
~
~
'--
~
~
"->
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potential of the leaf, and the vertical position of the leaf in the canopy (Denison and Loomis, 1989). 3.5. Individual organ arrays
The growth and development of individual plant organs for" a single representative cotton plant within a crop is simulated explicitly. Because such a plant does not exist, the solutions of the simulations attempt quantitatively to represent the performance of an average plant. The shoot is composed of both vegetative and reproductive organs which include the apical meristem; ancillary bud meristematic tissue at the end of each branch; leaf primordia; growing and mature leaves (petiole and blade separately); stem segment between nodes; squares; bolls, both growing and mature; the taproot; lateral roots. 3.6. Organ location
Plant organ variables are stored in two-dimensional arrays (x, xx). The first array element is the monopodium number (x, n), while the second element is used to index an organ's location on that monopodium (n, xx). The second element in the array contains both vertical and horizontal displacement information within the foliage space. The rightmost digit of the second element in the array, i.e. 0-9, (n, nx) refers to the number ofsympodial nodes away from the monopodium, with zero referring to the monopodial node itself. It should be noted that this array indexing technique limits the number of nodes on a sympodial branch to nine locations. The leftmost digit, of the second element in the array, i.e. 0-39, (n, xn) identifies the monopodial node, counting from the bottom where the cotyledonary node is (l, 0). Therefore, the array LFMASS (2, 52) is the leaf mass of the second leaf (x, x2) away from the fifth, node (x, 5x) on the second monopodium (2, xx), first vegetative branch. This array index strategy essentially employs a two-dimensional array indexing technique to describe a three-dimensional one. 3.7. Physiological time
Physiological age is the time-integrated value of developmental rate (Thornley and Johnson, 1990). Physiological aging rate places an upper limit on growth rate, and physiological age determines organ phenological state. The simulated plant does not develop, nor is its phenology based, on calendar days. Rather, plant development and growth rates are based on a time-temperature running sum. The units of physiological age will be days when developmental rate is in physiological days per calendar day. The response of physiological time to calendar time is based on an Arrhenius equation with both low and high temperature inhibition [Johnson and Thornley, 1985; Thornley and Johnson, 1990, (Chapter 5)]. At the reference temperature (Tr ), e.g. 25°C, a physiological day is equal to a calendar day (Fig. 2). At temperatures below the reference temperature, physiological time proceeds slower than calendar
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2.0 PARAMETERS EA = 35,000 J mol -1 T, = 25°C TOL
1.5
=
18- °C
TOH = 35°C
w
TH/2 = 40°C
~
TL/ 2 = 12°C
0:::
w
>
1.0
----------
3 w
0:::
0.5
Let: To = 25°C
o. 0 +------.--~::.......,---,--
o
10
20
30
40
50
TEMPERATURE (oC) Fig. 2. Illustration of function RELRAT (R r ), the relative growth rate to that at a reference temperature (Tr) (Appendix 3, Eqs. 1-6). Function is used to determine actual physiological time based on an organ's temperature (To). Function RESPTF uses a similar relationship, excluding low temperature inhibition, to determine temperature dependent maintenance respiration rates of plant organs.
time. At temperatures above the reference, physiological time proceeds faster than calendar time, but at very high temperatures developmental rate slows with an increase in temperature and physiological time even becomes slower than calendar time at very high temperatures, near the upper limit for biological activity. The function RELRAT (R r ), calculates physiological time as a ratio with calendar time; the two times are congruent at Tr (Appendix 3, Eqs. 1-6). 3.8. Linear interpolation
A linear interpolation table look-up routine is employed to implement arbitrary functional relationships between variables (Table 2). Response functions, derived directly from figures in the literature or current experimental results, can be included in simple x:y tables. Response functions for a particular physiological process or cultivar specific response can be generated, thereby negating the need for actual mathematical formulations. Furthermore, this technique facilitates ease in altering the shape of a response function by allowing a simple alteration in any or all of the individual x:y pairs. Some of these response functions reflect empirically derived relationships, while others are a component of mechanistic portions of the model.
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3.9. Insect herbivory
Insect damage is an input to the model. It is based on a physiological time window during which each leaf or square is susceptible to herbivory, the day of year insects appear, the number of days insects have been feeding on susceptible tissue, and the fraction of plant tissue consumed each day during the susceptible period. Leaf area is reduced, as are the carbon, nitrogen, starch, soluble carbohydrate content and mass of the leaf. If squares are damaged by an insect during their susceptible window their carbon, structural mass, nitrogen and soluble carbohydrate content are reduced to zero, i.e. the square is killed. When available, this simple algorithm could be replaced with a more sophisticated insect model which could be a separate module. 3.10. Quantitative biochemistry of biosynthesis
Plant tissue is composed of carbohydrate, fat, lignin, protein, organic acid, and mineral components. This composition determines the glucose and nitrogen required and the CO 2 produced during biosynthesis, i.e. growth respiration, of plant organs (Penning de Vries et aI., 1989; Table 3; Appendix 4). A glucose equivalent is calculated based on the mass of glucose required for the biosynthesis of a unit mass of dry structural phytomass which includes both carbon skeletons and energy from Table 3 Derivation of biosynthetic parameters, i.e" glucose (CRG) and nitrogen (NR) required for growth, CO2 produced (growth respiration) (CPG) during biosynthesis, and final fraction of structural tissue which is carbon (FC). Final biosynthetic parameters derived from the biosynthesis coefficients and the fraction of tissue, i.e., leaf, stem segment, root and boll, which are composed of carbohydrate (Fe), protein (Fp), fat (Fr), lignin (F1), organic acids (Fo), and minerals (Frn) [Eqs 7-10, Appendix 3] (Penning de Vries et al., 1989). Parameter Tissue type Fe Fp Fr FI
Fo Frn
Leaf a
Stem
Root
Boll
0.52 0.25 0.05 0.05 0.05 0.08
0.62 0.10 0.02 0.20 0.02 0.04
0.56 0.10 0.02 0.20 0.02 0.10
0.40 0.21 0.23 0.08 0.04 0.04
1.3807
1.4326
1.3600
1.7636
0.3406
0.2906
0.2832
0.6054
0.0377
0.0151
0.0151
0.0317
0.4595
0.4938
0.4667
0.5403
Final biosynthesis parameters
Glucose required (CRG) (g glucose g-I tissue) Growth respiration (CPG) (g (C0 2) g-I tissue) Nitrogen required (NR) (g N g-I tissue) Carbon content (FC) (g C g-I tissue) a
Squares have same biochemical composition as leaves.
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respiration (Appendix 3, Eqs. 7- I 0). The potential growth amount of a given plant organ and the glucose equivalent cost for that production are used to determine assimilate demand for growth. Similarly, nitrogen required for growth of a given mass of plant tissue is also determined.
4. Implementation 4.1. Run-time sequence
The sequence of computations at run-time is illustrated in the left column of Fig. I and by the pseudocode listing for the main COTC02 control module in Table 4. During runtime, the initial and boundary conditions are established, and all external input and parameter files are read. Germination of the cotton seed occurs. In the initial portion of the diurnal loop, insect damage is simulated. The diurnal loop is within the daily one. It has an arbitrary time step, normally I h. Next the status of the microclimate is determined, accounting for absorbed, reflected, and transmitted fluxes. The shortwave radiation balance for a horizontal layer within the foliage space is calculated based on Duncan et al. (1967). Canopy physiological processes are simulated next. These processes are affected by two separate components, one being the physiological response of the plant to the state of the microclimate on a whole canopy basis and the other being the individual leaf position and characteristics. When all environmental and plant physiological processes have been comTable 4 Pseudocode listing of main control program COTC02. Program CO TC02 (Main program; coordinates time) Call INITAL (initialize crop) Call GEMRGE (germinate seed and grow plant to emergence) Do daily loop from emergence to maturity Call INSECT (herbivory) Set temperature of soil under soil slab Apply irrigation if appropriate Do diurnal loop over hours (or other time steps) in the day Final time of the day Call ENVIRN (environmental conditions above crop) Call DUNCAN (canopy-radiation interactions) Call FIZIO L (plant physiology control program) Calculate net radiation Call GROWTH (plant growth control program) Call DROUT (output desired diurnal state variables) End do Call DAYOUT (output desired daily state variables) End do Output final state of crop Stop
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pleted, potential growth of organs occurs. Actual growth occurs based on potential growth and limits placed on that potential growth. 4.2. Initialization
The initial condition of the plant and its environment is defined at the beginning of each simulation (Fig. 1, Table 4). Time step variables, row width, and plant variables such as shoot and root constants are initialized. Plant organ arrays are zeroed for meristems, leaf primordia, unfolded leaves, squares, immature bolls, mature bolls, monopodium, sympodium branches, taproot, and lateral roots. Meteorological inputs generated internally can be used in lieu of usersupplied data. If the user supplies daily weather data, the algorithm can generate diurnal trends in meteorological variables, i.e. hourly air temperature from minimum and maximum air temperature and hourly solar radiation from daily totals following Kimball and Bellamy (1986). Precipitation, irrigation, windspeed, and CO 2 concentrations, as well as soil parameters, including temperature, bulk density, specific heat, porosity, thermal conductivity, volumetric water content, matric potentials and nitrate concentrations in each soil cell are initialized (Appendix 5). If real-world input data exist for a particular simulation run, then these input data can be initialized instead of those variables previously initialized. The model can therefore run on a default set of initialization parameters or those input from an external set of input files. 4.3. Germination
The germination of a cotton seed and growth of a cotton plant through emergence to the cotyledon stage is simulated explicitly (Fig. 1). The seed is initiated with an initial meristem, radical, combined hypocotyl and epicotyl, a pair of cotyledonary leaf primordia, a shoot meristem and a soluble nonstructural carbohydrate pool. The seed imbibes water and grows, using the growth routines, from planting until emergence. Thus, the state of the seedling at emergence is predicted by the model based on seed size at planting. At present, seed germination is not based on any soil or environmental conditions. It simply grows a cotton seed from planting until emergence based on the parameter, IGERMD, the number of physiological days between germination and emergence (Appendix 4). It is assumed that all this time takes place at a reference temperature of 30°C, so this process is decoupled from anything that might happen in the real soil. The value for IGERMD was selected based on observations on the appearance of an average cotton seedling at emergence, and how much physiological time was required to grow this plant to that status at a reference temperature of 30°C. This module eliminated the need arbitrarily to initialize a multitude of plant organ variables. In short, the germination process is simply a means of using the growth routines to convert the seed into a plant, thereby initializing the state of the plant at emergence.
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5. Microclimate
5.1. Canopy processes
Physiological process rates are calculated for individual organs, but organs are located within a canopy layer. Furthermore, the C 3 biochemically based leaf physiology (PHYSLF) module requires information on the canopy microclimate by layer, specifically, wind speed, air temperature, H 2 0 vapor pressure, CO 2 concentration, direct and diffuse shortwave radiation fluxes, and longwave radiation flux. Wind speed is calculated at the midpoint of each horizontal layer throughout the canopy according to Norman (1979). Air temperature within the canopy is linearly interpolated between air temperature above the canopy (at the reference height) and soil surface temperature. A single canopy H 20 and CO 2 partial pressure is calculated based on whole-canopy H 20 and CO 2 , The direct and diffuse components of global radiation are calculated according to Spitters et al. (1986) (Appendix 5). Individual leaves within a canopy layer are divided into two separate leaf classes, i.e. sunlit and shaded. Calculations of Sun/Earth geometry are also performed. The vertical longwave radiation profile within the canopy is calculated by the method of Caldwell et al. (1986). 5.2. Soil processes
The soil module is concerned primarily with the fluxes of water, solutes, and heat among soil cells. Soil models like RHIZOS (Lambert et aI., 1976) and ENWATBAL (Van Bavel and Lascano, 1987) were reviewed as candidate soil routines. We anticipate that the two-dimensional VAM2D (Huyakorn et aI., 1989) model, as implemented by Pachepsky et al. (1993), will replace the simple concentration-gradientbased Darcian flow approach presently being used (Hanks and Ashcroft, 1980). The daily input of irrigation and rainfall determines water addition to the soil. Rainfall is diminished as a function of leaf area index to calculate the amount intercepted and retained by the canopy. Water is added to the soil cells which first come into contact with rainfall or irrigation, i.e. furrow or sub-surface drip tape application. Any soil cell above field capacity becomes a source for gravimetric flow of water. This process is repeated until no cell is above field capacity. Water drained from the bottom layer is lost from the soil slab. Nitrogen transformations within the soil slab are not yet accounted for. Presently, all simulations are conducted with ample soil nitrogen concentrations for the crop. The movement of solutes among soil cells occurs through mass flow of the water (Appendix 5).
6. Whole-plant physiology
6.1. Nonstructural carbohydrate pool dynamics
The whole-plant non structural carbohydrate pool is divided between long- and
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short-term pools, with the long-term pool being in the form of reserve starch in stem segments and taproot. Every organ has a short-term pool. Leaves have separate starch and nonstructural carbohydrate pools. A balance exists throughout the entire system of carbohydrate pools (Fig. 3). Short-term reserves are immediately accessible for growth and respiration. In contrast, the long-term storage pools of starch must be hydrolyzed to glucose prior to being used in growth and respiration processes (Appendix 3, Eq. 11). The individual organ short-term reserve carbohydrate pool is translocated to the long-term pool each time step; all except that which must be left behind for respiration, MINCHO (Appendix 4). Long-term reserves are built up during early growth stages of the plant after the seed has been metabolized. During rapid vegetative growth, photosynthesis rates are high because of an abundance of leaves. However, demand for assimilate lags behind production, thereby enabling the build-up of a long-term reserve. Upon further vegetative and subsequent reproductive growth, assimilate demand increases because of development of fruit which rely on this reserve to maintain their growth. As the demand for assimilates of growing fruit exceeds that produced by leaves, long-term reserves are depleted to maintain fruit growth. 6.2. Partitioning
Maintenance respiration by shoot and root has first priority for photosynthate. After maintenance respiration has consumed carbohydrates, carbohydrates from source leaves move either into immature organs at the same mainstem node or into the mainstem phloem. Growing bolls are given a higher priority than squares, leaves, or stem segments for photosynthate, as are organs closer to the mainstem. Sympodium leaves allocate a portion of their carbohydrate pool to the subtending reproductive structure and to other organs growing on the same branch. The remainder of the nonstructural carbohydrate is available for the rest of the plant. This approach to short-distance transport keeps a greater proportion of the available carbohydrates assimilated by a given leaf near that leaf. Constant partitioning coefficients, in many cases derived from educated guesses because information on this topic is limited, are used to distribute the nonstructural carbohydrates throughout the various organs and in the long-term pool (Appendix 4). A rate constant, SEEDBD, controls the rate of metabolism in the seed to breakdown its contents into usable carbohydrates. Another rate constant, SUGKl, controls translocation of non structural carbohydrates into long-term reserves. In long-term reserves, the carbohydrates are converted into starch. They can then be hydrolyzed back to glucose when needed (Appendix 3, Eq. 11). Yet another rate constant, SUGK2, controls translocation from long-term reserve into a short-term one. These constants were derived by running the model with a range of values and determining how large reserves became and how rapidly they were depleted when photosynthesis declined, or when demand for substrate was greatly increased when boll growth occurred rapidly. The short-term carbohydrate pool can be distributed to roots within a time step. Distribution of carbohydrates between roots and shoots is based on the root to shoot
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CARBOHYDRATE POOL DYNAMICS
RESPIRATION LATERAL ROOT CARBOHYDRATE
STRUCTURE NONSTRUCTURE
Fig. 3. Carbohydrate pool dynamics for a cotton plant as implemented in the COTC02 simulation model.
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living mass ratio, a size factor which weights transport by the size of the taproot, i.e. long-distance transport of assimilates in a large cotton plant may take longer than a typical time step used during a given simulation run, so translocation can be reduced empirically by a size factor. Under water stress, a larger proportion of resources must be allocated to the root system for exploring the soil profile for any available water. A water potential effect, H20FAC (Table 2), also partitions carbohydrates between shoot and root. The x-variable is the effective soil matric potential, and the y-variable is the relative strength of roots for non structural carbohydrates. Finally, a cap of 45% of the total short-term carbohydrate pool in the plant can be located in the roots. Once carbohydrates have been translocated into the root system, the relative sink strength of the taproot compared with lateral roots, TAP LAT, partitions carbohydrate among the components of the root system (Appendix 4). 6.3. Carbon balance
A detailed carbon balance is maintained throughout a seasonal simulation. Inputs include the carbon content of the seed endosperm and photosynthate input from leaves and fruit. Total carbon losses include those associated with respiration for growth, maintenance, nitrate assimilation, and nutrient uptake. Carbon loss as a result of herbivory, root death, fruit shedding, senescing leaves, and root exudation are also accounted for in the overall balance. Senescence and abscission of individual leaves within a canopy layer occur. When maintenance respiration needs for a leaf are not satisfied by the available carbohydrate pool, starch is converted to non structural carbohydrate. If the individual leaf starch pool does not meet the maintenance respiration requirement, then a carbohydrate deficit exists. In a young unfolding leaf, this deficit is assumed to be the result of over-estimation of maintenance respiration. A reduction in respiration occurs to alleviate the deficit. In a mature leaf, however, if the leaf nonstructural carbohydrate and starch pools cannot satisfy maintenance needs, SNSC ED (Appendix 4), structural tissue is consumed, or catabolized. A mature leaf, therefore, will senesce. If the carbon economy within a leaf continues to decline, it will abscise. Lateral roots exude carbohydrate into the surrounding soil system, thereby increasing the substrate pool for microbial activity. Although this component of the model is underdeveloped, it is still considered in the overall carbon balance. Senescence of lateral roots depends on the soil matric potential within a soil cell. Lateral root senescence is determined with an exponential equation (Appendix 3, Eq. 31) based on present lateral root mass, LRM , a relative rate of root senescence coefficient, Y, which is modified by the soil mat ric potential within the soil cell with function RRDRWS (Table 2). Fruits have a window of physiological time when they are susceptible to abortion (Fig. 4). If the actual structural mass of a square is less than 60% of its potential, SQSHED, during a window of susceptibility, SWIND W, than the square is shed. Square shedding can occur within the first lO days of square grow. If a square is shed, its carbon content and mass are set to zero. The nonstructural carbohydrate content, if any, in a shed square is added back to the whole-plant nonstructural carbohydrate pool.
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EXPONENTIAL I f-
S: 0
0::
0 f-
:=> 0::
u... --.J
~
f-
Z
w
f-
3:
0
z
0
::L
~
(/)
r===1 <------
"'-
ANTHESIS
SMP - - - - - - > < - - - - - - - BMP - - - - - - - >
RELATIVt: PHYSIOLOGICAL AGt: (%) Fig. 4. Illustration of the strategy for potential fruit growth. During the square maturation period (SMP) relative fruit growth is exponential (Appendix 3. Eq. 32). Relative boll growth is logistic (Appendix 3, Eq. 33) during the boll maturation period (BMP). At anthesis, both functions are joined. In both phases of growth, a fruit has a susceptible period when it can be shed if actual growth is less than 60% of potential (SWIND Wand BWIND W, for square and boll growth, respectively).
Similar to squares, there is a period of time when bolls are susceptible to shedding, BWINDW. If the boll mass is not at least 60% of its potential, BLSHED, during the first 7 physiological days of growth, then the boll will be shed. If the boll is shed, all processes described for square shedding occur. This strategy is consistent with a commonly accepted mechanism of reproductive organ shedding in cotton (Guinn, 1982).
7. Leaf physiology
Leaf physiology is central to simulating plant response to the environment in COTC02. Whereas leaf temperature affects leaf physiology, leaf physiology processes in turn affect leaf temperature, because of stomatal regulation of transpiration and to a lesser extent metabolic energy exchange. A CO 2 responsive cotton growth model must include a biochemical model of C 3 photosynthesis and photorespiration with CO 2 concentration and tissue temperature as an intimate component. This stand-alone model of C 3 photosynthesis calculates carbon dioxide flux, stomatal conductance, transpiration, and leaf energy balance for each unfolded leaf (Appendices 1 and 2). It consist of three components; (1) a leaf energy balance (Nobel, 1983) to account for stomatal effects on leaf temperature, transpiration and
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assimilation (Farquhar and Sharkey, 1982), (2) a stomatal conductance model (Farquhar and Wong, 1984), and (3) a biochemical chloroplast CO 2 assimilation model (Farquhar et aI., 1980; Farquhar and Von Caemmerer, 1982; Farquhar, 1988). 7.1. Leaf energy balance
Components of leaf-environment energy exchange include: absorbed shortwave solar plus longwave sky radiation, emitted long wave radiation, and latent, sensible, and metabolic energy exchanges (Appendix 1, Eq. 1). The total absorbed radiant energy flux (Ra) is an input to the leaf physiology module that is calculated by the canopy model. Emitted long wave radiation is a function of leaf temperature (Appendix 1, Eq. 2). Latent heat flux is the product of the flux of water vapor from the leaf (Appendix 1, Eq. 3) (Farquhar and Sharkey, 1982) and the temperature dependent latent heat of vaporization (Appendix 1, Eq. 5). Saturation vapor pressure is calculated according to Lowe (1977). Dew forms on the leaf when ei < ea. In this case the flux of water vapor away from the leaf is given in Appendix 1, Eq. 4. Sensible heat exchange is based on leaf and ambient air temperatures (Appendix 1, Eq. 6), and the whole leaf convective heat transfer in the boundary layer (Appendix 1, Eq. 7). The convective heat transfer coefficient is derived from the temperature dependent thermal conductivity coefficients of air at ambient and leaf temperature, respectively (Appendix 1, Eq. 8). Although a small component, the metabolic leaf free energy content because of carbon metabolism (Appendix 1, Eq. 9) is considered in the overall energy balance. The mean boundary layer thickness over one side of the leaf is a function of the characteristic dimension of that leaf and wind speed outside the boundary layer (Appendix 1, Eq. 10). Boundary layer thickness is assumed to be similar over both sides of the leaf. The boundary layer conductance of water vapor diffusion for one side of the leaf is given by Nobel (1983) (Appendix 1, Eq. 11). During the daytime, when stomata are open, the effective whole-leaf boundary layer resistance to water vapor diffusion for a leaf within a canopy layer is the ratio of stomata on the adaxial and abaxial leaf surfaces (Appendix 1, Eq. 12) (Welles, 1986). At night, when stomata are closed, whole-leaf boundary resistance is given in Appendix 1, Eq. 13. The secant method (Press et aI., 1986) is used iteratively to solve for the leaf temperature at which the radiant energy absorbed is balanced with sensible, latent, metabolic energy exchange and long wave radiation emitted. 7.2. Stomatal conductance
Leaf surface resistance to water vapor diffusion is the reciprocal of the sum of stomatal and cuticular conductance (Appendix 1, Eq. 14). The total whole-leaf conductance of water vapor diffusion is the reciprocal of the sum of whole-leaf boundary layer resistance and whole-leaf surface resistance (Appendix 1, Eq. 15). Stomatal conductance is related to mesophyll metabolism with the model of Farquhar and Wong (1984), and soil water content, i.e. root signal (Appendix 1, Eq. 16). Vapor pressure at the leaf surface is given by Appendix 1, Eq. 17. Ifphotosynthesis is limited
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by rubisco activity, Appendix I, Eq. 18 is used to calculate cil10roplast ATP concentration, otherwise Appendix I, Eq. 19 is used to calculate ATP. Whole-leaf boundary layer conductance of CO 2 diffusion is related to boundary layer resistance to water vapor (Appendix I, Eq. 20). Similarly, leaf surface conductance of CO 2 , which included cuticular and stomatal conductance, is related to their respective conductances to water vapor (Appendix I, Eqs. 21 and 22, respectively). A total boundary layer plus leaf surface conductance of CO 2 is thereby defined (Appendix I, Eq. 23). An additional conductance term is derived to calculate the CO 2 partial pressure in the chloroplast, that is, the conductance of CO 2 between the intercellular spaces and chloroplast stroma (Appendix I, Eq. 24). An intercellular CO 2 partial pressure is then derived (Appendix I, Eq. 25: Von Caemmerer and Farquhar 1981), as is the partial pressure of CO 2 in the chloroplast stroma (Appendix 1, Eq. 26). 7.3. Biochemical chloroplast CO 2 assimilation
A biochemically based C3 photosynthetic model is employed to simulate the competitive Michaelis-Menten enzyme kinetics of ribulose bisphosphate (RuP 2 ) carboxylase/oxygenase in the photosynthetic carbon reduction (PCR) and photorespiratory carbon oxidation (PCO) cycles (Farquhar et al., 1980). In this approach, the effects of CO 2 concentration on photosynthesis can be modeled explicitly at the level of RuP2 carboxylase-oxygenase enzyme kinetics and chloroplast thylakoid membrane reactions. The rate at which inorganic phosphorous (Pi) is released during triose-P/hexose-P use (TPU) may limit photophosphorylation, thereby placing a limit on assimilation rates (Sharkey, 1985). This model has been tested in a number of cases and has proven to give reliable results when parameterized correctly (Von Caemmerer and Farquhar, 1981; Farquhar and Von Cammerer, 1982; Long, 1985; Long and Drake, 1991). The pseudocode for this C 3 photosynthesis model is given in Table 5. After the initial conditions are established, the C 3 biochemical calculations are made. Based on leaf temperature, the maximum RuP2 carboxylation and oxygenation velocities (Appendix I, Eqs. 27 and 28, respectively), the Arrhenius-based temperature dependent Michaelis-Menten constants for CO2 and O2 (Appendix 1, Eqs. 29 and 30, respectively), the stromal CO 2 compensation partial pressure in the absence of dark respiration (Appendix I, Eq. 31), and the maximum and actual chloroplast thylakoid membrane electron transport rates are determined (Eqs. 32 and 33, respectively). During the daylight hours, the net carbon dioxide flux at any temperature and photon flux is a function of the partial pressure of CO 2 in the chloroplast stroma, which in turn is dependent on assimilation rates. For each leaf class, i.e. sunlit and shaded, a value of the partial pressure of CO 2 in the chloroplast stroma (Appendix I, Eq. 26) is calculated via the secant method (Press et al., 1986), which is consistent with assimilation rate for a given temperature, photon flux, and stomatal conductance. In this iterative process, the following are calculated: the RuPrsaturated, electron transport-, and Pi-limited rates of carboxylation (Appendix I, Eqs. 34, 35 and 36, respectively), actual rate of carboxylation based on the
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minimum of the carboxylation-limited rates, and chloroplast chlorophyll ATP concentration (Appendix I, Eqs. 18 or 19) (Farquhar and Wong, 1984). The actual net CO 2 flux (Appendix I, Eq. 37), and a new chloroplast CO2 partial pressure, based on assimilation rate, are also computed. This procedure is repeated (Secant method, Press et aI., 1986) until the partial pressure of CO 2 in the chloroplast is unchanged. Lastly, stomatal conductance is computed based on the new estimate of A TP concentration. Leaf apparent dark respiration has two components, growth and maintenance (Appendix I, Eq. 38). Growth respiration is input into the C 3 leaf physiology module from the leaf growth module (Appendix 3, Eq. 7). Leaf maintenance respiration (Appendix I, Eq. 39) is calculated from the temperature dependent relative respiration function (Appendix 3, Eqs. 1-6), maintenance coefficients for protein turnover and intracellular metabolite gradient maintenance, structural protein content, and leaf mass (Amthor, 1989, 1994). At night, the stomata are closed and dark respiration is calculated based on the steady-state leaf temperature derived from the ambient air temperature. Respiration rate decreases with increasing physiological age because of mobilization of nitrogen out of leaf (Appendix 3, Eq. 24). 7.4. CO 2 metabolism in reproductive organs
Squares and immature bolls are treated as semi-autonomous plant organs (Constable and Rawson, 1980a,b). Reproductive organs are considered spheres, so that their photosynthetic surface area can be estimated. Fruit photosynthesis is based on size or surface area, atmospheric CO 2 concentration, intercepted light, and physiological age. The surface area of the fruit is assumed to correspond to the area of the brack which is irradiated and fixing carbon. A mass to density relationship is used to determine the surface area of the bracks which are capable of assimilation (Constable and Rawson, 1980a). An entire square, but only two-thirds of an immature boll's surface area can assimilate carbon. Mature bolls do not fix carbon. An empirical light-response function with parameters Pm, the asymptotic limit, and 0:, the initial light conversion efficiency (Ziegler-Jons and Selinger, 1987) is employed to simulate carbon assimilation in squares and immature bolls (Appendix 3, Eq. 34). The Pm coefficient is a direct function of ambient CO 2 concentration. A physiological age effect on Pm for square organs is derived from relating the present age of the square to that of the square maturation period (SMP). Immature bolls do not have a physiological age effect on Pm. 0: is derived from the maximum light conversion efficiency (Eh1eringer and Bjorkman, 1977; Ehleringer and Pearcy, 1983). Temperature effects on Pm and 0: are not accounted for in this version of COTC02. 7.5. Respiration
Apparent dark respiration of eXlstmg phytomass (maintenance respiration: Penning de Vries, 1975; Amthor, 1989) and that linked to growth (growth respiration: Penning de Vries et aI., 1974) are calculated separately. Growth respiration is calculated separately for leaf blade, stem segment, taproot, lateral root and
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Table 5 Pseudocode listing for the individual leaf physiology control subroutine (PHYSLF), leaf energy balance (LEAFEB), and the biochemically based CO2 assimilation (FRQHRI and FRQHR2) subroutines. Subroutine P HYSLF (Leaf physiology control routine) If leaf is unfolded then Interface CO TC02 leaf state variable values of LEAF PHYSIOLOGY model state variables Check input to Leaf Physiology model Call BLAYER (calculate leaf boundary layer conductance) If nighttime Calculate stomatal conductance Call LEAFEB (calculate leaf energy balance and temperature) Call M RLEAF (calculate leaf maintenance respiration rate) Call PLOAD (export carbohydrates) Calculate respiration rate (same as CO2 assimilation rate) Calculate intercellular CO2 partial pressure (CJ Else (daytime) then Check sunlit/shaded value Do separately for sunlit and shaded leaves If light level exists then Retrieve radiation data Call STCOND (calculate stomatal conductance) Do until stomatal conductance is stable Call LEAFEB (calculate leaf energy balance temperature) Call MRLEAF (calculate leaf maintenance respiration rate) Call PLOAD (export carbohydrates) Calculate respiration rate Calculate total conductance of CO2 Call FRQHR1 (biochemical photosynthesis model - empirical stomatal conductance) Calculate change in stomatal conductance from last value Calculate new value of stomatal conductance based on previous two estimates End if Store LEAF PHYSIOLOG Y model output in COTC02 variables Else Set all physiology rates to zero End if End do Calculate physiological rates for COTC02 time step End if Calculate leaf temperature Update temperature ofleaves in canopy layer containing this leaf If final call to subroutine for this leaf during this time step then Calculate leaf water potential and transpiration rate Update leaf sugar pool based on leaf CO 2 exchange rate If daytime then Move some leaf sugars into leaf starch Else Move some starch into leaf sugar pool End if Update carbon balance accumulator variables If leaf sugar level is equal to or less than zero then If leaf contains enough starch to make up for sugar deficit then
G. W. Wall et al. / Agricultural and Forest Meteorology 70 (1994) 289-342 Table 5 Continued. Convert some starch to sugar Else Convert all starch to sugar If leaf is still expanding then Decrease leaf maintenance respiration amount Else Senescence some of the leaf Breakdown part of leaf structure Update leaf state variables to account for senescence If total senescence has reached a threshold then Shed the leaf Update leaf state variables to account for loss of leaf End if End if End if End if End if End if Return
Subroutine LEAFEB (leaf energy balance and steady state temperature) Declare functions for: thermal conductivity coefficient of air convective heat transfer coefficient between leaf and air convective heat exchange rate between leaf and air leaf evaporation rate longwave emission from leaf sum of convective, latent, and longwave emission energy exchanges by leaf Pick two leaf temperatures based on air temperature Do until leaf temperature is constant (by secant method) Solve leaf energy balance (inputs minus outputs) for given leaf temperature Update leaf temperature End do Return
Subroutine FRQHRI (Farquhar-Wong photosynthesis/conductance mode, part I) Based on leaf temperature, calculate: Maximum RuP2 carboxylation and oxygenation Michaelis-Menten constants for CO 2 and O2 (rubisco) CO 2 compensation point in the absence of dark respiration Maximum electron transport rate Do until CO2 partial pressure in chloroplats (Ce ) is constant (by secant method) Call FRQHR2 Set new value of Cc End do Calculate stomatal conductance based on estimated ATP concentration Return
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Table 5 Continued Subroutine FRQHR2 (Farquhar-Wong photosynthesis/conductance model, part 2) For given Cc: Calculate RuP2-saturated rate of carboxylation (We) Calculate e1ectron-transport-limited rate of carboxylation (Wj) Calculate inorganic phosphorus-limited rate of carboxylation (Wp) Calculate rate of carboxylation (minimum of We' ffj, and W p ) Calculate ATP concentration Calculate leaf CO2 assimilation rate Calculate intercellular CO 2 partial pressure Calculate Cc based on CO 2 assimilation rate Return
reproductive organs (Penning de Vries et aI., 1989). It is based on the biochemical composition of a particular tissue type and the CO 2 evolved during its production (Appendix 3, Eq. 7). Apparent dark respiration for an individual leaf blade is the sum of growth and maintenance respiration, as previously discussed in the leaf physiology section. Maintenance respiration for all other organs, i.e. stem segment, taproot, lateral roots and fruit are modeled differently than a leaf blade (Appendix 1, Eq. 40). A basal respiration coefficient for each organ type is modified by temperature in the Rr function (Appendix 3, Eqs. 1-6). In reproductive organs the basal maintenance coefficient, M CB, is derived as a function of physiological age. Physiological age effects are explicitly derived from a table of maintenance coefficients for squares and bolls as a function of relative physiological age at 30°C (Table 2) (Mutsaers, 1976a,b). Mature fruit which have a physiological age greater than the boll maturation period (BMP) do not respire. In stem segments the basal maintenance coefficient, B s' only affects living tissue. The heartwood portion of the stem does not respire. A separate basal maintenance respiration coefficient exists for the taproot, B t , and the lateral roots, B LR . The mature woody taproot has a lower specific maintenance respiration rate than the lateral roots, so that the maintenance coefficient increases from the root:shoot interface to the taproot tip where more metabolic activity occurs. This is similar to having a non-respiring heartwood component of the taproot, as is done for stem segments. Actual maintenance respiration is the product of the organspecific temperature dependent basal maintenance coefficient and the mass of the living structural tissue (Appendix 1, Eq. 40).
8. Growth of organs
8.1. Potential growth
Analytical models simulate potential growth of individual plant organs with geometric objects, i.e. cylinders, ellipsoids, conics, spheres, etc. A similar approach was employed to simulate the potential growth of individual meristem, stem segment, leaf blade, taproot, lateral root and fruit organs (Appendices 3 and 4).
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8.2. Meristems At emergence an apical meristem exists. The mass of a meristem at the beginning of a defined period of exponential growth is given by Eq. 12, Appendix 3. The mass of a meristem that triggers a leaf blade, stem segment, or fruit plant organ is input, AIO. The initial mass of an organ will influence its final mass when the organ is physiologically mature. Therefore, to simulate progressively larger organs on a monopodium, as the overall plant increases in size, the initial size of the meristem is increased, BIGGER, after an organ has been initiated. In contrast, on sympodial branches, organs are progressively smaller as they move out along a branch. Meristems, therefore, are made progressively smaller, SMALLR, as organs are initiated. Potential growth of a meristem is an exponential function (Mutsaers, 1983a,b) based on the existing meristem mass MR M , monopodium weighing factor, WTm, meristem rate constant, RIm, and physiological age, 6.t p derived from the Rr function (Appendix 3, Eqs. 12 and 13). A hormonal signal, H 3 , determined by the ratio of actual growth to that of potential growth, alters the potential growth of meristems. This approach enables multiple environment factors to affect meristem growth, instead of just physiological time and simple temperature based degree-day equations. When the meristem attains a certain predetermined size, a new leaf, square, or branch primordia is formed. Leaf meristems are initiated at predetermined intervals; monopodium, MLI, and sympodium, SLI. If availability of substrates does not meet demand for a particular meristem within a physiological window of time, then that meristem will become inactive; it will enter a state of dormancy. Meristems for initiation of vegetative and reproductive branches are also dormant if they are below a predetermined node number on a monopodium, ILWMON, and sympodium, ILWSYM, as are those above the highest node carrying a monopodium, IHIMON (Appendix 4). 8.3. Stem segment Stem segments are modeled as cylinders, characterized by their dimensions of length and radius, and also by their density. Like a tree trunk, each segment contains both living sap wood on the exterior portion and a hard non-living heartwood in the interior. Potential stem segment length and radius are calculated to determine the new potential volume of the stem segment. The volume of the heartwood section is modeled as an inner cylinder. Maintenance respiration costs are based on the living stem tissue and not on the heartwood, which is less metabolically active. An alternative approach would be to treat the stem as one cylinder and establish a maintenance respiration coefficient that decreases as the stem radius increases. Carbon loss, therefore, would be a direct function of the amount of metabolically active stem tissue, as is done in the taproot. Potential stem elongation is determined from a relationship between the characteristic dimension of the subtending leaf and the present stem segment length. A function, POSITN (Sp), (Table 2) relates the potential stem segment length to the characteristic dimension of the sub tending leaf which decreases from the bottom to
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the top of the plant. Therefore, stem segments grow longer for the same amount of leaf growth near the bottom of the plant than they do at the top. This approach assumes that a functional relationship exists between leaf characteristic dimension, the position of that leaf on the plant, and the length of an individual stem segment. Stem segment elongation ceases at maturity, based on the physiological age of the subtending leaf. It can, however, continue radial growth. An upper limit is placed on stem segment elongation using the Rr function and canopy temperature to derive a temperature factor, Te. This absolute maximum value for stem segment elongation, T, is based on literature and an educated guess, and is cultivar specific. The whole plant can be growing taller faster than this basal rate, however, because each stem segment can be growing simultaneously. The potential stenl elongation, therefore, is the minimum of the potential and maximum elongation (Appendix 3, Eq. 14) Potential radial growth of a stem segment has a required minimum, Rmin. This minimum growth is proportional to the stem segment length, because the radius of any stem segment must not be too small compared with the length of that stem segment. Potential stem segment radial growth is also dependent on the mass distribution of the plant above that particular segment. An empirical ratio, R e, relates the radius of the stem segment to the square root of the whole mass of stem tissue above that segment. The stem mass is the actual structural mass of the stem segments, so that the cumulative nonstructural carbohydrate pool in stem segments above this segment is an additional weight. Furthermore, potential radial stem growth is also modified with a wind factor, We, to add the required support to the stem segment under windy conditions. A 10 day running average wind speed is calculated based on the average wind speed from the meteorological input datafile. A basal wind speed, BASE, determines the impact of wind speed on radial growth. A running average higher than the basal level will increase radial growth, while one lower will decrease it. Therefore, when the wind speed is high, stem segments are simulated to be shorter and thicker. In contrast, under low wind conditions, they are simulated to be longer and thinner. An upper limit is placed on stem radial growth. A maximum potential radial growth is determined with an exponential function which uses a rate constant, Rl s , for stem growth and a similar temperature factor used to determine the limits to stem elongation. Potential stem segment radial growth, therefore, is the maximum of either the required radial growth, or that growth which is dependent on the stem segment mass above that stem segment, all multiplied by the We. Finally, the minimum of the aforementioned potential radial growth and the upper limit determines the real potential growth (Appendix 3, Eq. 15). The final stem segment radius following elongation is given by Eq. 16, Appendix 3. The partitioning equations that define how much nonstructural carbohydrate is translocated into the stem segment may in some cases impose some limitation on stem growth. Under other circumstances the supply of carbohydrates will be ample, and wind run and leaf size will define the size of the stem segment. A balance is kept, therefore, in the partitioning of carbon between stems and leaves. 8.4. Leaf growth
The canopy in COTC02 is composed of individual leaves, each one being
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composed of a leaf blade and a petiole. Leaf growth can be divided into three stages; primordia, expanding which includes initiation of the petiole, and mature. 8.4.1. Leafprimordial growth Potential leaf primordial growth is exponential (Appendix 3, Eq. 17). When a leaf primordia is initiated, it is defined to have a negative physiological age. When the physiological age becomes positive the leaf blade unfolds and the leaf expands. Physiological age is determined with function, Rn based on the temperature of the canopy and a reference temperature of 25°C. Aging is modified by a hormonal factor, H 3 • This slows down the aging of primordia, so that if growth is not occurring because of a lack of substrate, physiological aging is reduced. This limits primordia from reaching the physiological age of zero and unfolding when they are too small. An age reduction parameter, An (Appendix 3, Eq. 18) is based on the value of C 1, a cytokinin root response (CYTOKl; Table 2), or in the case of an unfolded leaf, a leaf water potential, WI, response (WPFUNC; Table 2). This enables environmental stress directly to affect development. Physiological aging and growth, therefore, are both reduced by water stress, but they are not reduced equally. Growth is reduced more than aging so that leaves will be smaller when they reach a physiological age of zero if there has been low water potential in the soil, but they will not be extremely small when they reach unfolding (Mutsaers, 1984). 8.4.2. Expanding leaf When the physiological age of a leaf becomes greater than zero, then the leaf is defined as unfolded. Its physiological age is assigned, AGEUNF, the age at unfolding, and it is initialized with a chlorophyll content, CHLP RN. Chlorophyll concentration in a leaf blade places a limit on the photosynthetic capacity of the leaf. The area of the leaf at unfolding, i.e. with physiological age equal to zero, is given by the leaf mass divided by the specific leaf weight. The characteristic dimension of a leaf is assumed to be equal to the square root of the leaf blade area. Physiological time is computed based on function Rr at a reference temperature. The potential area, PGA, (Appendix 3, Eq. 22) of a leaf blade is based on a function that relates potential leaf size to physiological age of the leaf. Leaf size is normalized to unity at full expansion (Constable and Rawson, 1980b). If physiological age is less than mature, MATURE, then the leaf is still expanding. The physiological days to MATURE were determined by using the PG A equation; when <1> equals 29 days, the leaf is fully expanded. The percent of physiological time that has elapsed with respect to that of a mature leaf defines the potential area of the leaf blade. The age reducing factor (Appendix 3, Eq. 18) places a limit on potential growth by reducing the physiological age of the leaf blade. Function PG SLW calculates the potential specific leaf weight per square meter ofleaf area (Appendix 3, Eq. 23). This relationship is also a function of physiological age, so that the leaves become thicker as they mature. This function ranges from half of the specific leaf weight of a leaf at a physiological age of zero, IsLw , to the final specific leaf weight at MATURE. Therefore, Appendix 3, Eqs. 22 and 23 define the relative potential changes in area and specific leaf weight, respectively. The relative growth rate, therefore, is derived regardless of what the
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actual area of the leaf might be. The ratio of the relative growth rate for the present, over that in the previous time interval, represents the percent change in relative area and thickness of the leaf. The actual change in leaf blade area and thickness is then the product of their respective percent change and the existing area and thickness. Hormones do not effect growth of expanding leaves as they do with primordial mass growth. They are influenced, however, by the calculated leaf water potential (WPFUNC; Table 2). Finally, potential growth rate of the leaf blade is simply the sum of that required for changes in area and thickness. 8.4.3. Petiole growth During leaf unfolding, a petiole is initiated. Potential petiole growth is dependent on leaf blade area. Petiole dry mass density, PP' which is based on half the density of water, Prj], the ratio of petiole radius to petiole length, and trigonometric, 'IT, are used to calculate the petiole density to leaf area relationship, w (Appendix 3, Eq. 20). The leaf water potential function, WPFUNC, limits potential petiole growth because of its influence on leaf blade area. An upper limit is placed on potential petiole growth, which is dependent on the existing petiole mass, a rate constant, RI], and physiological time. Potential petiole growth, therefore, is the minimum of potential growth defined by the leaf blade area and the upper limit based on existing mass. Final petiole length is given by Appendix 3, Eq. 21. Petiole mass is defined by a ratio between the leaf blade and petiole mass, PTTO LF. Carbon and nitrogen pools of petioles are also dependent on this ratio. The leaf mass is decremented by the newly derived petiole mass. The carbon and nitrogen content of the leaf are then also decremented by the carbon and nitrogen amount used for petiole growth. 8.4.4. Mature leaves Photosynthetic and respiration rates of mature leaves decline with age because their nitrogen content declines (Constable and Rawson, 1980c). Nitrogen is mobilized from leaves with an exponential equation, a rate constant, R N , and physiological time (Appendix 3, Eq. 24). Leaves reach a physiologically inactive state and senesce within 60-70 physiological days, the life expectancy of a cotton leaf. Mobilization of nitrogen affects the photosynthetic capacity of leaves by reducing the chlorophyll content, concentrations of photosynthetic proteins, and by reducing maintenance respiration.
8.5. Taproot growth
The taproot is modeled as a right circular cone which grows in the first column of the soil slab. The soil is considered to be symmetrical about the row in the field. However, the taproot is contained entirely within soil column one. No taproot is simulated in the symmetrical mirror image of the two-dimensional soil slab. The taproot grows downward in column one of the soil slab and is completely contained within that column, with no horizontal growth into adjacent cells. The depth of the furthest advance of the taproot is calculated with function SLAYER (Table 1). The maximum depth to which the taproot can grow is set to the total depth to the bottom
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of the deepest soil layer. Again, as in the stem, a non-living heartwood component of the taproot is simulated, primarily to separate out living vs non-living structural mass for maintenance respiration cost. The radius at the top of the taproot conic is determined by the stem segment radius at the shoot-root interface. If stem radial growth occurs, then the radial growth of the taproot required to keep up with that of the stem is determined. It is assumed that this interface occurs at the soil surface. Based on the existing length, i.e. height, H T , and the existing radius, R T , a new taproot volume, VT , is determined (Appendix 3, Eqs. 25, 26 and 27, respectively). This growth is required. Therefore, substrate pools are used for radial growth to keep up with the stem even if a deficit in assimilates occurs. Any deficits will reduce future potential growth until deficits are eliminated. In this strategy, stem growth impacts that of the taproot both of which influence carbohydrate and nitrogen pools which will impact later organ growth. Therefore, a feedback control exists which influences stem and root growth. Potential taproot length is based on genetic limitations, i.e. maximum rate of taproot elongation, IJ, which is cultivar specific. A taproot elongates more rapidly during germination and early seedling development. Therefore, during this period the maximum elongation rate is doubled. This fosters rapid taproot growth during the seedling stage. Potential growth in taproot length is also limited by the temperature and the matric potential, limT[,W, (Appendix 3, Eq. 28) of the soil cell in which it is growing. A change in length is used to calculate a new taproot volume. Once the potential radius and length of the cone have been determined, the new potential volume and constant for taproot density, PT, will determine the potential growth. Physiological aging only influences the growth of the heartwood component of the taproot, not taproot senescence. 8.6. Lateral root growth
Lateral roots grow in any soil cell, but their growth is restricted to lateral horizontal movement within a soil layer, not vertically across adjacent soil layers. Their growth is based on a volume and structural mass density relationship, PLR' They are initiated per unit length of taproot, RPERM, a variable which is modified by the nonstructural carbohydrate content of the taproot. If this pool is high, then there will be greater meristematic activity for lateral root initiation. Lateral roots are not initiated on the taproot tip, T APTIP, or above a minimum depth in the soil profile, FIRSTR. Within a time step, a part of a lateral root can be initiated, but only a whole lateral root will start growing. Function SLA YER is used to determine in which soil layer the new lateral root is initiated. Half of the lateral roots are on one side of the row, while the other half are on the other side. This is a result of the assumption of a symmetrical mirror image of the soil slab. The potential growth of lateral roots (Appendix 3, Eq. 29) is based on an exponential equation, a maximum relative growth rate, 'T}, and a density factor, Pr, in a soil cell (Appendix 3, Eq. 30). If lateral root density is high, then relative lateral root growth, will be slowed. Physiologically, a high density of lateral roots will consume 02, thereby decreasing the concentration in the soil cell, which will inhibit
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root growth. If lateral root density within a given soil cell exceeds SPILL, i.e. the lateral root density which is required to foster growth into an adjacent cell, then the lateral roots will grow into an adjacent cell. If RGLIMT for the next soil column is greater than zero, then some root growth can occur. A parameter, OUTER, keeps track of how many of these roots are on the outer side of a soil cell which can be involved in growing roots into the next cell. The temperature factor which limits growth is based on an optimal growth rate at a reference temperature using function Rr (Appendix 3, Eqs. 1-6). Water stress also limits lateral root growth within a soil cell through use of a relationship between the soil matrix potential and relative potential growth rate using function WP LIMT (Table 2). The final limitation to potential root growth is calculated as a multiple of the temperature and water limitation. Limits to root growth based on high soil bulk density, low oxygen concentration, toxins, salinity, or other physical or chemical limitations to growth are not included at this time. Potential growth, therefore, is based on temperature, lateral root density, soil matric potential in each soil cell, and the maximum relative growth rate. 8.7. Fruit growth
A fruit is simulated first as a square, then as a flower, and finally as a boll. The potential growth of the fruit is divided into two phases, a simple exponential growth phase when the fruit is a square and a monomolecular equation when it is a boll (Mutsaers, 1976a,b; Marani, 1979). Anthesis is an instantaneous point that joins these two curves (Fig. 4). If the physiological age of the fruit is less than zero, then the fruit is a square. Physiological aging for squares is determined using the function Rn with the temperature of the canopy as a reference temperature. The potential growth of a square depends on the existing mass, SQM, a rate constant, Rl sqn and the fraction of physiological time that has elapsed compared with the SMP (Appendix 3, Eq. 32). If the physiological age of the fruit plus the incremental increase in physiological age for this time step is greater or equal to zero, then anthesis has occurred. This physiological time, ANTHES, is used to assign an age to a number very near zero at flowering, i.e. the transition from square growth to boll growth. Aging is set equal to anthesis minus the physiological age of the fruit so that enough aging takes place to drive the square into anthesis, but not beyond. The second half of the logistic curve for fruit growth, that is boll growth following anthesis, is dependent on an initial boll mass at anthesis, B j , and the maximum boll mass, BM , i.e. the weight of a boll at maturity when growth has occurred without limits (Appendix 3, Eq. 33). Boll growth is driven by physiological time expressed as the fraction of time which has elapsed from anthesis to the BMP (Mutsaers, 1976a,b; Constable and Rawson, 1980b). Once the age of the fruit reaches BMP, then the boll is considered mature and no more growth will occur. It is assumed that plant water stress does not affect fruit growth directly (Westgate and Grant, 1989). 8.9. Actual growth
Actual growth of organs occurs similarly across all organ types. Potential growth is
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determined, which increases the volume of the geometric object used to grow a particular organ type. The required mass to meet this increment in potential volume is determined from the volume to density relationship, where each organ type has a predetermined density. An assimilate demand for that mass increment is calculated based on the organ specific glucose equivalent cost (Table 3) (squares are assumed to have the same glucose equivalent cost as leaves). Similarly, nitrogen demand to meet potential growth is determined. A minimum amount of carbohydrate must be left behind in the organ following growth for maintenance respiration processes, i.e. MINCHO times the existing organ mass. If available carbohydrates exceed that which must remain behind, then some growth can occur. In fruit tissue, it is scaled so that as the fruit reaches maturity, the amount of non-structural carbohydrate that must be left behind, as a percentage of the fruit mass, decreases as the fruit grows. For fruit at maturity, there is no requirement that any carbohydrate be left behind following growth, primarily because there is no maintenance respiration in mature fruit. A carbon limit to growth is calculated, i.e. the amount of carbohydrate available for growth divided by the assimilate demand to grow that organ. Similarly, a nitrogen limitation is calculated based on the nitrogen content of the structural tissue, given by the nitrogen to carbon ratio in structural carbohydrate divided by the nitrogen demand for that organ. If either carbohydrate or nitrogen are limiting, than no growth will occur. Finally, the growth fraction, Gr, that actually takes place is then the minimum of the carbon and nitrogen limits. The supply:demand ratio, or Gr, i.e. 0-1, is multiplied by potential growth to give actual growth. Actual growth of stem segments is partitioned between length and radial growth. Elongation of a stem segment has priority over radial growth, except once the leaf reaches maturity, no more stem segment elongation can take place. Therefore, this priority for stem growth is linked to its dependency on the duration of the leaf growth phase. The Gr places a direct limit on stem segment elongation. For lateral roots, actual growth occurs as a fraction of their potential growth throughout the whole soil profile. The growth fraction is calculated for the entire lateral root system, thereby negating any preferential root growth depending on location within the soil slab. After growth of the organ, the new carbon and nitrogen content are determined, and carbohydrate and nitrogen pools and whole-plant accumulators are updated.
9. Model development status
A working version of COTC02 exists, a copy of which is available from the authors upon request. Experimental databases obtained using cotton cultivar Delta 77 grown under ambient air and air enriched to 550 j,tmol CO 2 mol- i with FACE technology (Hendrey, 1993; Hendrey and Kimball, 1994) during the 1989 through 1991 growing seasons at Maricopa, Arizona (Kimball et aI., 1993) have been compared with simulated output. Simulation of the growth, development and physiological response of cotton to atmospheric CO 2 concentrations has also been performed and compared with observed data sets derived from Open-Top-Chamber (OTC)
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(1983-1987) (Kimball et ai., 1992) and Soil-Plant-Atmosphere-Research (SPAR) studies (Wall et aI., 1991; Reddy et aI., 1992b). Although not expressed quantitatively herein, preliminary model testing indicates that the basic structure of the model is sound. Results indicate that alterations in parameters and response functions are required, particularly those which pertain to growth of organs and partitioning of assimilates. Eventually, cultivar-specific parameter files will be developed. Further development, documentation, calibration and testing of the model is in progress. A sensitivity analysis using a latin hypercube sampling algorithm, PRISM (Gardner et ai., 1983) will be performed to test the stability of the model with respect to its most influential parameters.
10. Conclusion
Uncertainty exists with respect to global change, as well as with the inevitability of concomitant changing climatic conditions. An imperative exists, therefore, accurately to assess the potential range in biotic response of teresterial vegetation to varying environmental extremes. Essential for predicting the response of vegetation to a CO 2 -enriched world are physiologically based mechanistic simulation models, which explicitly simulate the major physiological processes known to be directly influenced by CO 2 , Such models can be run under many environmental scenarios encompassing a broad range of biotic and abiotic conditions. Reported herein is such a model. The descriptions given have detailed the level of resolution obtained during the development of COTC02. This model can potentially predict cotton production over a broad environmental range, while providing the means to predict the impact of change in atmospheric CO 2 concentrations and any associated potential climate change on global cotton production. Ultimately, it will aid in the development of strategies to mitigate the adverse effects of global change, while optimizing those that are beneficial.
Acknowledgments
This work was supported, in part, by the Carbon Dioxide Research Program of the Office of Health and Environment Research, US Department of Energy and the Agricultural Research Service, US Department of Agriculture.
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Kimball, B.A., Mauney, J.R., La Morte, R.L., Guinn, G., Nakayama, F.S., Radin, J.W., Lakatos, E.A., Wall, G.W., Mitchell, S.T., Parker, L.L., Peresta, G.J., Nixon, P.E. II, Savoy, B., Harris, S.M., MacDonald, R., Pros, H., Martinez, J. and Reaves, M., 1992. Response of cotton to varying CO2 • irrigation, and nitrogen: data for growth model validation. In: Carbon Dioxide Enrichment: Data on the Response of Cotton to Varying CO 2, Irrigation, and Nitrogen, ORNL/CDIAC-44 NDP-037, Oak Ridge National Laboratory, Oak Ridge, TN. pp. A1-A562. Kimball, BA., La Morte, R.L., Peresta, G.J., Mauney, J.R., Lewin, K. and Hendrey, G.R., 1993. Appendices: weather, soils, cultural practices, and cotton growth data from the 1989 FACE experiment in IBSNAT format. In: G.R. Hendrey (Editor), Free-Air CO 2 Enrichment for Plant Research in the Field. CRC Press, Boca Raton, FL, pp. 271-272. Kramer, P.J., 1981. Carbon dioxide concentrations, photosynthesis, and dry matter production. Bioscience, 31: 29-33. Lambert, J.R., Baker, D.N. and Phene, C.J., 1976. Dynamic simulation processes in the soil under growing row crops: RHIZOS. (unpublished, available from J.R. Lambert, Clemson University, Clemson, sq. Lemon, E.R. (Editor), 1983. CO 2 and plants: the response of plants to rising levels of atmospheric carbon dioxide. American Association for the Advancement of Science Symposium, 84. Int. Conf. on Carbon Dioxide and Plant Productivity, 1982, Athens, GA, Westview Press, Boulder CO, 280 pp. Long, S.P., 1985. Leaf gas exchange. In: J. Barber and N.R. Baker (Editors), Photosynthetic Mechanisms and the Environment. Elsevier. Amsterdam, pp. 453-500. Long. S.P. and Drake, B.G., 1991. Effects of the long-term elevation of CO2 concentration in the field on the quantum yield of photosynthesis of the C3 sedge, Scirpus olneyi. Plant Physio!., 96: 221-226. Long, S.P. and Woodward, F.1. (Editors) 1988, Plants and Temperature. Symposia of the Society for Experimental Biology, Cambridge, No. 42. Lowe, P.R., 1977. An approximating polynomial for the computation of saturation vapor pressure. J. App!. Meteoro!., 16: 100-103. Marani, A .. 1979. Growth rate of cotton bolls and their components. Field Crops Res., 2: 169-175. McKinion, J.M., Baker, D.N .. Hesketh, J.D., and Jones, J.W., 1975. SIMCOT II: a simulation of cotton growth and yield. In: Computer Simulation of a Cotton Production System-Users Manual, ARS-S-52, pp.27-82. Mooney, H.A. and Harrison, A.T., 1970. The influence of conditioning temperature on subsequent temperature-related photosynthetic capacity in higher plants. In: I. Setlik (Editor), Prediction and Measurement of Photosynthetic Productivity. Pudoc, Wageningen. pp. 411-417. Mooney, H.A., Bjorkman. O. and Collatz, G.J., 1978. Photosynthetic acclimation to temperature in the desert shrub, Larrea divaricata. Plant Physio!., 61: 406-410. Mutsaers, H.J.W., 1976a. Growth and assimilate conversion of cotton bolls (Gossypium hirsutum L.). I. Growth of fruits and substrate demand. Ann. Bot., 40: 301-315. Mutsaers, H.J.W., 1976b. Growth and assimilation conversion of cotton bolls (Gossypium hirsutum L.) 2. Influence of temperature on boll maturation period and assimilate conversion. Ann. Bot., 40: 317324. Mutsaers. H.J.W., 1983a. Leaf growth in cotton (Gossypium hirsutum L.). 1. Growth in area of main stem and sympodial1eaves. Ann. Bot.. 51: 503-520. Mutsaers, H.J.W., 1983b. Leaf growth in cotton (Gossypium hirsutum L.). 2. The influence of temperature, light, water stress and root restriction on the growth and initiation of leaves. Ann. Bot., 51: 521-529. Mutsaers, H.J.W., 1984. KUTUN: a morphogenetic model for cotton (Gossypium hirsutum L.). Agric. Syst., 14: 229-257. Ng. N. and Loomis, R.S., 1984. Simulation of Growth and Yield of the Potato Crop. PUDOC, Wageningen. Nobel. P.S., 1983. Biophysical Plant Physiology and Ecology. Freeman, San Fransisco. Norman, JM., 1979. Modeling the complete crop canopy. In: B.J. Barfield and J. Gerber (Editors), Modification of the Aerial Environment of Crops. ASAE, St. Joseph, MI, pp. 249-277. Pachepsky, Y, Timlin D., Acock A., Lemmon H. and Trent A., 1993. 2DS01L-A New Modular Simu-
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Appendix 1 Model of leaf physiology (symbol definitions given in Appendix 2). Energy balance
o = Ra -
Re - >"E - S + M
Re = 2m(T1,k)4
(1) (2)
when (ej 2': ea ) E=
gtw(ej - ea )
' (P - (ej
+ ea )/2)
(3)
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when (ei < ea) E = 2gb (I),w(ei - ea )
(4)
>. = 45064 - 42.9143T1
(5)
S
= hc(~
he =
Ka,a
- Ta)
(6)
+ Ka,l
(7)
8 Ka = 0.02429 + 6.l25(1O)-5 T
(8)
AflGO' M=-6
(9)
Boundary layer thickness and conductance for H 2 0 vapor diffusion
8 = 0.004) d/v
(10) (11 )
Daylight - stomates opened
(12)
Nightime - stomates closed 1 rbw=--
,
rl w
,
2gb (I),w 1
= -;-----..,. (gs,w
+ gc,w)
(13)
(14) (15)
Stomatal conductance for H 2 0
(16)
G. W. Wall et al. / Agricultural and Forest Meteorology 70 (1994) 289-342
When photosynthesis limited by rubisco activity
(We ::;
329
~)
ATP = At - WcSp/Wj
(18)
When photosynthesis limited by RuP2 regeneration (We
>
~)
ATP = (At - Sp)(Rp - Et ) Wj
(19)
WcRp - WjEt Boundary layer, cuticular, and stomatal conductance for CO 2 diffusion gb,c
=
(20)
1. 37 rb,w
(21 )
(22)
gt,c
(23)
= 1
-+--gb,c gc,c + gs,c
_ (1 _
C
gw,c - gw,c(O)
Cl,st I,st
+ W 1)
(24)
Leaf internal CO 2 partial pressure
Ci
=
(gt,c -
Ej2)Ca - AP + E/2
(25)
gt,c
(26) Biochemical chloroplast CO 2 assimilation
vcmax --
E t chlA LKC e (-ELKC/RT'.d
(27)
(28)
330
G. W. Wall et al. / Agricultural and Forest Meteorology 70 (1994) 289-342
(29) (30)
= 0.5VornaxKeOj
f.
(31 )
VernaxKo
(32) 2
[
8J -
Jmax
(I-f)] (I-f) + Ia --2J + JrnaxIa --2- =
0
(33)
We =
VernaxCe Ce + Ke[1 + OdKol
(34)
W-
J (4.5 + 1O.5f./Ce )
(35)
J -
W - V cmax p-
A
(36)
2
= [1 -
~:] min{We, Wi' W
p} -
R.i
(37)
Apparent dark respiration Rd
= Rg+Rm
Rrn ,1 =
(38)
Rr(T" Tr,l)(mplpr + mJm)CP -"----'--'--'--'--'----'-Y ATP
Rrn,o = MeMoD..tRr(To, Tr,o)
(39) (40)
Appendix 2
Definition of symbols for equations, parameters, constants and variables used to describe leaf physiology model in Appendix I (symbols within an appendix are unique). Values in parenthesis are those used in simulation, unless stated otherwise Symbol Definition (value, units) f.
D..t {j
to
Stromal CO 2 compensation partial pressure in the absence of dark respiration (Pa) Time step (s) Mean boundary layer thickness over one side of the leaf (m) Leaf long wave emissivity (0.97, dimensionless)
G. W. Wall et al.; Agricultural and Forest Meteorology 70 (1994) 289-342
e
n A
ATP A KC A KO
A LKC At
Ca Cc chi Cj Cl,sl
CP d
es E Ej
EKC
EKO ELKC Et
f gb,c gc,c gs,c gt,c gw,c(o)
331
Empirical factor relating mesophyll chloroplast ATP content (mol m -2) to stomatal conductance (mol (H 2 0) m- 2 S-I), (2 (10)5 mol (H 2 0) s-I mol-I ATP) Convexity of potential electron transport-absorbed PAR relationship (0.69, dimensionless) Latent energy of water vaporization (J mol-I) Stefan-Boltzmann constant (S.67 (10r 8 Wm- 2 K- 4) Relative signal from root system limiting stomatal conductance (0 = full closure, I = no effect on gs,w, dimensionless) Ratio of abaxial rl w to adaxial rl w (1.0, dimensionless) Net CO 2 flux into the leaf (mol (C0 2 ) m- 2 S-I) Concentration of adenosine triphosphate in chloroplast (mol (ATP) m -2) Arrhenius coefficient for Michaelis-Menten constant for CO 2 (7.6 (10)12 Pa) Arrhenius coefficient for Michaelis-Menten constant for O 2 (3.1 10 10 Pa) Arrhenius coefficient for turnover of carboxylase sites (S.3 (10)10 S-I) Concentration of adenylates in chloroplast (12.6 (10)-3 mol (mol chl)-I) Ambient atmospheric CO 2 partial pressure (Pa) Partial pressure of CO 2 in the chloroplast stroma (Pa) Leaf chlorophyll area density (mol (chi) m- 2 ) Intercellular CO 2 partial pressure (Pa) Starch area density (initial) (S g m -2) CO 2 produced/consumed in respiration (6 mol CO 2 (mol hexose)-I) Leaf characteristic dimension, square root of leaf area (m) Diffusion coefficient of water at O°C and I atmosphere pressure (2.13 (10)-5 m2 s-l) Ambient vapor pressure in canopy layer, saturated vapor pressure at ambient dewpoint temperature (Pa) Vapor pressure inside the leaf, assumed to be saturated vapor pressure at TI (Pa) Vapor pressure at the leaf surface (Pa) Flux area density of water vapor away from the leaf (mol (H 20) m -2 s -I) Activation energy term in lmax (3.7 (10)4 Jmol- I ) Activation energy for Michaelis-Menten constant for CO 2 (6.S (10)4 Jmol- I ) Activation energy for Michaelis-Menten constant for O 2 (3.6 (10)4 J mol-I) Activation energy for turnover of carboxylase (S.8S2 (10)4 J mol-I) Concentration of carboxylase sites (0.067 mol (mol chl)-I) Fraction of absorbed photons unavailable for PCR/PCO cycles (O.lS, dimensionless) Whole-leaf boundary layer conductance of CO 2 diffusion (mol (C0 2) m- 2 S-I) Cuticular conductance of CO 2 diffusion (mol (C0 2 ) m -2 S-I) Stomatal conductance of CO 2 diffusion (mol (C0 2 )m- 2 s- l ) Total boundary plus leaf surface conductance of CO 2 (mol (C0 2) m- 2 S-I) Basal cell wall plus plasmalemma conductance of CO2 diffusion (0.9 mol (C0 2)m- 2 s-I)
332
gb('),w ge,w gs,w gl,w ,
l1Go
he
M
G. W. Wall et at.
I Agricultural and Forest Meteorology 70 (1994) 289-342
Conductance of CO 2 between intercellular spaces and chloroplast stroma (mol (C0 2)m- 2 s-') Boundary layer conductance of H 2 0 vapor diffusion for one side of the leaf (mol (H 20)m- 2 s-') Cuticular conductance of H 2 0 vapor diffusion (0.005 mol (H 2 0)m- 2 s-') Stomatal conductance of H 20 vapor diffusion (mol (H 2 0) m -2 s-') Whole-leaf total conductance of HzO vapor diffusion (mol (H 20) m- 2 s-') Standard free energy change of glucose oxidation (-2.87 (10)6 J mol-I) Whole-leaf convective heat transfer coefficient of the boundary layer (Wm- 2 K-') Term in J max on mass basis of leaf (2.2 (10)5 J mol-') Absorbed photosynthetically active radiation (mol (photons)m- 2 s-') Potential rate of electron transport (mol (electrons) m -2 s-') Maximum potential rate of electron transport (mol (electrons)m- 2 s-') Turnover number of oxygenase divided by turnover number of carboxylase (0.21, dimensionless) Thermal conductivity coefficient of air at ambient (Ka a) and leaf temperature (Ka,l) (Wm- 2 K- I ) , Michaelis-Menten constant for CO 2 (Pa) Michaelis-Menten constant for O 2 (Pa) Leaf structural mass (g) Leaf protein mass (g protein) Maintenance coefficient for ion gradients (0.03 (10)-6 mol (ATP)g-1 leafs-I) Maintenance coefficient for protein turnover (0.15 (10)-6 mol (ATP) g-I protein s-I) Areal rate of change of leaf free energy content due to carbon metabolism (Wm- 2) Organ specific basal maintenance respiration coefficient for stem segment (6.0 (10)-z), fruit (B MCB , Table 2), taproot (8.6 (10)-z) or lateral root (8.6 (10)-2) tissue (gCH 2 0g- 1 s-') Mass of plant organ for stem segment, fruit, taproot or lateral root (g) Partial pressure of Oz in the stroma (21000 Pa) Atmospheric pressure (Pa) Standard atmospheric pressure at 1 atm (101 325 Pa) Whole-leaf surface resistance of H 20 vapor diffusion (m 2 s mol- I (H 20» Effective whole-leaf (both surfaces) boundary layer resistance of water vapor diffusion (m 2 smol-' (H 20» Gas contant (8.3143Jmol-' K- 1) Absorbed total radiant energy flux (W m -2) Dark respiration rate (mol (COz)m- z S-I) Long wave radiant energy flux exitance (W m- 2 ) Organ specific growth respiration for leaf, stem segment, fruit, taproot or lateral root tissue [Eq. 7, Appendix 3], (g (CO z) g-I) Total maintenance respiration for leaf (Rm I) or for stem segment, fruit, taproot or lateral root plant organs (Rm,o), (mol (COz) s -I)
G. W. Wall et al. / Agricultural and Forest Meteorology 70 (1994) 289-342
Ta,k Tj,k
v Vemax Vomax We
nJ Wj Wp
YATP
333
Potential pool size of RuP2 (0.15mol (mol chl)-I) Relative rate of respiration function (0-1 , dimensionless) Maintenance respiration rate for leaf (mol (C0 2)m- 2 s- l ) Organ maintenance respiration rate for stem segment, fruit, taproot or lateral roots (mol (C0 2)m-2 S-I) Flux of sensible energy away from leaf (W m -2) Term in Jmax (710 Jmol- I K- I) Concentration of phosphorylation sites (2.5 (10)-3 mol (mol chI) -I) Temperature term for either ambient (Ta) or leaf (Tj) temperature Cc) Ambient air temperature Cc) Leaf blade temperature Cc) Plant organ temperature for either stem segment, fruit, taproot or lateral root Cc) Reference temperature for maintenance respiration rate of stem segment (30°C), fruit (28°C), taproot (30°C), or lateral root (30°C) Reference temperature for maintenance respiration rate of leaf (30°C) Absolute temperature of the air in the boundary layer, i.e., mean of ambient (Ta,k) and leaf (Tj,k) absolute temperature (K) Absolute ambient temperature (K) Absolute leaf temperature (K) Wind speed outside boundary layer (ms- I) Maximum rate of RuPrsaturated rate of carboxylation (mol (C0 2) m- 2 s-I) Maximum rate of RuPrsaturated rate of oxygenation (mol (02)m- 2 s-I) RuP2-saturated rate of carboxylation (mol (C0 2)m- 2 s- l ) Water (liquid) on leaf surface (mol (H 20)m- 2) Electron transport-limited rate of carboxylation (mol (C0 2) m- 2 s-I) Inorganic-Pj-limited rate of carboxylation (mol (C0 2) m- 2 S-I) ATP formed per hexose oxidized in respiration (34 mol ATP mol- I hexose)
Appendix 3 Potential growth of organs (symbol definitions given in Appendix 4) Relative temperature response
(I) K=
1.0 e(-E./RT,)
(2)
(3)
334
G. W. Wall et al. / Agricultural and Forest Meteorology 70 (1994) 289-342
(-kRToHTH/2)!(ToH - T / )
H2 = -----'-------'--
~SH
(4)
TH/2 kRT
oLh/2 = ----:----'-
(5)
- TL/2) = _'(-kRToLTL/2)!(ToL _______~-'--------!..-C...
(6)
~HL
TOL - h/2
~SL
TL/2
Biochemical composition
+ 0.679Fp + 1.606Ff + 0.576Fl - 0.045Fo + O.OFm CRG = 1.211Fc + 1.793Fp + 3.03Ff + 2.119F, + 0.906Fo + O.OFm CPG = O.l23Fc
FC
=
(7) (8)
CPRg1uCRG - CPRC02 CPG
(9) (10)
NR = 0.151Fp Starch hydrolysis
(11 ) Potential meristem growth B
m
=
Mr
( 12)
e ( Rim L...Jt~Op Tp ) ",I-I
(13) Potential stem growth PGSE
= min{(Sp0a -
PGS R
= min{[max{RminSLl Rf\/SMabv } W f -
(14)
Sd, TfT}G r SR],
JS~.e(RI,Tft:.t)
-
SR}
(15) (16)
Potential leaf blade and petiole growth
( 17)
G. W. Wall et at. / Agricultural and Forest Meteorology 70 (1994) 2R9-342
Ar
= {0.3 + 0.7C], 0.3 + 0.7W]}
PG p
= min{[w( vi;,.) 3 -
PL =
335
(18)
PM], [PM (e{RlIAlp )
-
I)]}
ifq-
(19)
(21)
Relative growth rate for leaf blade area and specific leaf weight
(22) (23) (24) Potential taproot growth
H~~ T
(25)
~ 1.05R}
(26) (27) (28) Potential lateral root growth PG LR
= lim Tr,W, (LR M e(7)PrA1 ) -
LR M )
(29) (30)
(31 ) Potential fruit growth
(32)
336
G. W. Wall et al. / Agricultural and Forest Meteorology 70 (1994) 289-342
(33) (34) Appendix 4
Definition of symbols for equations, parameters, constants and variables used to describe potential growth of organs in Appendix 3 (symbols within an appendix are unique). Values in parenthesis are those used in simulation, unless stated otherwise. *Symbols not referenced in main body of text; definitions given only for completeness. Symbol
Definition, (value, units)
Relative temperature response Ea Activation energy (35000Jmol- l ) 6.HH Enthalpy high temperature response (Jmol- I) 6.HL Enthalpy low temperature response (Jmol- I) k Constant such that e(-k) is close to zero (5.0, dimensionless) K Scaling constant of Arrhenius equation (dimensionless) R Gas constant (S.3143Jmol- 1 K- I) Rr Relate rate to that of the process of interest at Tn where rate is unity at Tr (dimensionless) Entropy high temperature response (J K- I mol-I) Entropy low temperature response (JK- I mol-I) Absolute temperature of the organ tissue of interest (K) Reference temperature, in K (25°C) Absolute temperature, in K, at which high temperature denaturation is just starting (35°C) Absolute temperature, in K, at which low temperature inhibition is just starting (1S°C) Absolute temperature, in K, at which the Arrhenius equation solution is halved due to high temperature inhibition (denaturation) (40°C) Absolute temperature, in K, at which the Arrhenius equation solution is halved due to low temperature inhibition (denaturation) (l2°C) Biochemical composition CPG Growth respiration, CO 2 produced during biosynthesis (g (C0 2) g-I tissue) Carbon content of CO 2 (0.27 g C g-I CO 2) CPRco2 Carbon content of glucose (0.40 gC g-I glucose) CPR glu Glucose required for biosynthesis (g glucose g-I tissue) CRG Fraction of tissue that is carbon (g C g-I tissue) FC Fraction of tissue that is carbohydrate (Table 3)
G. W. Wall et al. / Agricultural and Forest Meteorology 70 (1994) 289-342
Fr Fl
Fm Fo Fp NR
337
Fraction of tissue that is fat (Table 3) Fraction of tissue that is lignin (Table 3) Fraction of tissue that is mineral (Table 3) Fraction of tissue that is organic acid (Table 3) Fraction ot tissue that is protein (Table 3) Nitrogen required for biosynthesis (g N g-1 tissue)
Morphology and canopy architecture IGERMD Number of physiological days between planting and germination (5 days) IHIMON Highest mainstem node carrying a monopodium (lLWMON + IM-2) ILWMON Lowest mainstem node carrying a monopodium (3rd node) ILWSYM Lowest monopodial node with a sympodium branch attached (4th monopodium node) Number of monopodium on plant where mains tern equals the first 1M monopodium (2 monopodia) IMXLVS* Maximum number of potential leaves on plant (10 IS) IMXMNN Maximum number of nodes on a monopodium (IS - 1) IMXSYN Maximum number of nodes on a sympodium branch (9 nodes) INMSYM Lowest node for sympodium branch on a nonmainstem monopodium (2nd node) Maximum number of sympodium branches (40 sympodia) IS* Leaf angle above the horizontal (1.5 radian) LANGL SINMON Monopodial branch angle from horizontal (sin 0.87) SINPET Petiole angle from horizontal (sin 0.70) SINSYM Sympodial angle from horizontal (sin 0.40) Partitioning of carbohydrates Time step in calendar time (s) HM Amount of starch hydrolyzed into glucose (g glucose) H30 Maximum rate of starch hydrolysis at 30°C (3.5 (10)-4 gm- 2 (leaf) S-I) Ht Ratio of vegetative growth demand to total growth demand (dimensionless) Hf Ratio of vegetative growth to total growth (dimensionless) H3 Ratio of total growth to total growth demand (dimensionless) Ht Ratio of N used in growth to N demand in potential growth (dimensionless) La Leaf area, one side (m-2) MINCHO Minimum nonstructural carbohydrate remaining in tissue after growth of meristem, stem segment, leaf blade, taproot and lateral root (0.03, 0.03, 0.05, 0.03, and 0.03 g glucose (g tissue)-1 respectively) MXSUSE* Maximum fraction of root nonstructural carbohydrate that can be used for N0 3 reduction (0.5 dimensionless) OVERDM Fraction of nonstructural carbohydrate over demand that can be translocated (1.2, dimensionless) PLCON* Rate constant for phloem loading (0.9 (10)-4 s-l)
6.t
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SEEDBD SINKSQ* SNSCED SUGKI
SUGK2 TAPLAT
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Rate constant for seed breakdown (1.0 (10)-5 s-1) Maximum carbohydrate to structure maintained by phloem unloading (0.30, dimensionless) Threshold value of senescence for leaf death (0.95, dimensionless) Rate constant for partitioning of non-structural carbohydrates into long-term reserves which are not available for growth or respiration (1.0 (10)-6 S-I) Rate constant for partitioning non-structural carbohydrates from long-term (RESRVI) into short-term (PHLOEM) storage (l.5 (10)-6 S-I) Relative sink strength of the taproot compared to lateral roots (0.85, dimensionless) Leaf blade temperature Cc) Reference temperature for starch hydrolysis (25°C)
Meristem growth D.tp Physiological time calculated with Rr this time step (d) AIO Dry structural mass of meristem that triggers leaf blade, stem segment or fruit initiation, i.e., M f in function Bm (1.0 g) Factor to increase AIO for meristems, i.e., leaf blade, stem segment BIGGER or fruit, initiated on monopodium, causes successive organs to be potentially bigger as nodes move up the monopodium (1.01, dimensionless) Mass of a meristem at the beginning of a defined period of exponential growth in a given physiological time, i.e., T p , (g) Mf Final mass of meristem when organ is initiated (g) MLFRAC* Fraction of meristem which is converted into a leaf at leaf initiation (0.85, dimensionless) Interval in physiological time between initiation of monopodium MLI leaves, i.e., Tp in function Bm for monopodium leaves (3.0 day) Dry structural mass of meristem at beginning of time step (g) MRM PG M Potential increment in dry structural mass (g) Rate constant for meristem growth (0.65 day-I) RIm SLFRAC* Fraction of meristem dome that is converted to leaf and stem tissue when a leaf/stem primordia is initiated (0.53, dimensionless) Interval in physiological time between initiation of sympodialleaves, Tp SLI in function Bm for sympodialleaves (8.0 days) SMALLR Factor to decrease AIO for meristems, i.e., leaf blade, stem segment or fruit on sympodial branches compared to monopodium, causes successive organs to be potentially smaller as nodes move out along a sympodial branch (0.90, dimensionless) STTOLF* Fraction of newly initiated leaf blade/stem segment that is a stem segment (0.2, dimensionless) Total physiological time (Tp) from the beginning of growth of a meristem (t = 0) until the initiation of an organ from that meristem (t = tp), i.e., SMP for squares, MLI for monopodium leaves, and SLI 1=0 for sympodium leaves (d)
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WTm
339
Weighting function for meristem based on monopodium number (1M). Potential growth of mainstem monopodium is greater than that of monopodium 2 or 3, etc. [WTm = 1.0 - 0.1 (1M - 1)]
Stem growth Ps 7r T
BASE
Stem structural density (0.5 (10)6 gm- 3 ) Trigonometric pi (3.14159, dimensionless) Maximum stem elongation during a day at reference temperature (0.01 mday-I) Basal level wind run effecting radial growth (5.0ms- l ) Fraction of potential to actual growth (0-1, dimensionless) Potential stem segment elongation (m) Potential stem segment radial growth (m) Minimum stem radius as a proportion of stem segment length (0.005mday-l) Coefficient relating stem radius to square root of stem mass above this segment (0.0015 m) Rate constant for stem growth rate in physiological time (0.66 day-I) Stem segment length (m) Stem segment length: characteristic dimension vs. position effect within the canopy (POSITN; Table 2) Stem segment dry structural mass (g) Stem radius (m) Cumulative stem segment mass above a stem segment (g) Temperature factor based on tissue temperature using Rp (dimensi onless) Wind factor (dimensionless)
Leaf blade and petiole growth Petiole structural mass density (0.5 (10)6 gm 3 ) Pset Leaf structural mass area density at unfolding (25 gm- 2 ) Physiological time which has elapsed from leaf unfolding until maturation (days) Leaf water potential effect on leaf growth function [WPFUNC in Table 2] Petiole density to area ratio (g m -I) w AGEUNF Physiological age of leaf at unfolding (1.0 (10)-6 day) Reduction in physiological age of leaf primordia; cytokinin root function (C I), or for unfolding and expanding leaves; water potential function (WI)' (Table 2) CI Cytokinin root response effect on potential growth [CYTOKl; Table 2] CHLPRN Leaf blade chlorophyll content per nitrogen (3.5 (l0)-4 mol chl (gN)-I) DAZUNF* Physiological days to leaf unfolding (15 days) Leaf structural mass area density at unfolding (25 g m -2) ISLw Dry structural mass of leaf blade (g) LM MATURE Physiological age at maturity of leaf blade (29 days)
{Jp
340
PTTOLF R11
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Nitrogen content of leaf (g N) Nitrogen remobilized out of leaf blade (g N) Petiole length (m) Ratio of petiole radius to length (0.008 m m -I) Relative potential growth of leaf blade area, as a fraction of its maximum, for a given physiological time (q», (dimensionless) Potential growth of petiole (g) Potential growth of leaf primordia (g) Dry structural mass of petiole (g) Relative potential growth in specific leaf weight, as a fraction of its maximum, for a given physiological age (q» (gm- 2 ) Petiole to leaf blade mass ratio at leaf unfolding (0.06gg- l ) Rate constant for potential growth of leaf primordia in physiological days (0.65day-l) Nitrogen remobilization rate (1.77 (10)-7 s)
Taproot and lateral root growth Pr Density factor which places limits on lateral root growth within a
PT v T/
Y
FIRSTR
OUTER
PGLR PGTL
RPERM
RT SPILL TAP TIP
soil cell (g m -3) Lateral root density within a soil cell (g cm -3) Lateral root length density (130mg- l ) Dry structural mass density of taproot (0.5 (10)6 gm- 3) Maximum possible rate of taproot elongation (4.17 (lO)-5 m S-I) Maximum possible rate of lateral root elongation (5.0 (10)-6 S-I) Relative rate of root senescence modified by soil matric potential with function, RRDRWS (S-I) (Table 2) Minimum depth of lateral root branching (0.0035 m) Height of right circular cone from radius base and volume (m) Structural dry mass of lateral roots at initiation (5.0 (10)-6 g) Lateral root dry structural mass (g) Mass of lateral root senesced (g) Limitation to root growth due to soil temperature factor (Tr) and soil matric water potential factor (\II s) (0-1, dimensionless) Fraction of soil column, farthest away from the row crop, that can contribute roots to the next column during lateral root growth (0.1, dimensionless) Potential growth of lateral root (g) Potential growth of taproot length (m) Lateral roots initiated per number roots m -I unit length of taproot [400 (gglucose g-Itissue/(l + gglucoseg- I tissue))] Radius base of right circular cone from height and volume (m) Lateral root density required for growth to spill over into next cell in the same layer, farthest away from the row crop (0.15 (10)-6 gcm- 3 ) Length of taproot tip where no lateral roots are initiated (0.01 m) Volume of right circular cone from radius base and height (m 3)
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341
Fruit growth and photosynthesis
Initial slope of light response curve (0.07 mol (C0 2) mol photons-I) Fraction of physiological time which has elpased from anthesis to the BMP (d) PSQ Square dry structural density (0.5 (10)6 gm- 3 ) ANTHES Physiological age of fruit at anthesis (1.0 (10)-6 day) Bj Initial potential boll mass at anthesis on a sympodial branch when optimal growth has occurred (0.20 g) Maximum potential boll mass on a sympodial branch when optimal growth has occured (6.0 g) BLSHED Actual to potential boll mass that triggers boll shedding (0.6gg- l ) BMP Boll maturation period in physiological time (50 days) BWIND W Window of boll shedding susceptibility, physiological time before anthesis (7 day) Absorbed photosynthetically active radiation by square or bracks of boll (/lmol (photons) m -2 s-2) Net photosynthetic rate of fruit (mol (C0 2)m- 2 s-I) Maximum rate of photosynthesis at light-saturation, dependent on [C0 2] (mol (C0 2)m- 2 s- 1) Relative potential growth of boll at age ({3), to that of the maximum boll mass, B M , (0 - 1, dimensionless) (g) Potential growth of square in dry structural mass (g) PGSQR Rate constant for potential square growth (0.65 day-I) Rl sqr Square maturation period, physiological time (30 days) SMP Square dry structural mass (g) SQM SQSHED Actual to potential square mass that triggers shedding (0.6 g g-I) SWINDW Window of square shedding susceptibility (10 days) Q
{3
Appendix 5
Definition of symbols for equations, parameters, constants and variables used to describe soil and canopy microclimate (symbols within an appendix are unique). Values in parenthesis are those used in simulation, unless stated otherwise. * Symbols not referenced in main body of text; definitions given only for completeness. Symbol
Definition, (value, units)
Microclimate (soil)'
8* B*
Bj *
P6 we* Wi*
Field capacity (0.31 m 3 (H 20)m- 3) Volumetric water content (m 3 m- 3) Initial volumetric water content (0.12 m 3 m -3) Bulk density, (1.2 (l0/m3 m- 3 ) Initial effective water potential of soil (-0.1 MPa) Initial water potential of soil cell (-0.1 MPa)
342
G. W. Wall et al.
\1\* W~OEF
W/xp COSTNR* CPA V CPH20* DEPTH FRACRT*
K:
K~OEF K~xp
[N0 3] PORSTY RGLlMT
TCONDS TCONDW* Ts ZOSOIL*
I Agricultural and Forest Meteorology
70 (1994) 289-342
Water potential of soil cell [where Ws = WCOEF eWEXP ], (MPa) Coefficient for soil water potential (-4.24 (lOr 4 MPa) Exponent for soil water soil potential (-2.61, dimensionless) Cost ofN0 3 reduction (1.27 g glucose (gN0 3 )-I) Specific heat of soil solid constituents (0.84 J g -1o C-I) Specific heat of water, (4.18J g-I DC-I) Depth of soil for 20 layers (0.02, 0.02, 0.02, 0.025, 0.03, 0.035, 0.05,0.075,0.1,0.1,0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.2, 0.2, m) Fraction of whole-plant N0 3 reduction occurring in roots (0.1, dimensionless) Hydraulic conductivity [where Kw = KCOEFeKEXP], (m 2 S-I Pa -I) Coefficient for hydraulic conductivity (9.1 (10)-10 m 2 S-I Pa- I ) Exponent for hydraulic conductivity (4.55, dimensionless) Initial nitrate concentration of soil cell (50 g N0 3 m -3) Porosity of soil (0.45, dimensionless) Limitations to root growth due to physical attributes of soil (1.0, dimensionless) Thermal conductivity of solids in soil (4.2J m- I s-I DC-I) Thermal conductivity of liquid water (0.57 J m- I s-I °C- I) Initial temperature of soil at midpoint of layer (15 DC) Surface roughness of soil (0.01 m)
Microclimate (canopy) CLYTHY Thickness of canopy layer (0.1 m) PARFLC* Leaf reflectivity of photosynthetically active radiation (0.06, dimensionless) Leaf transmissivity of photosynthetically active radiation (0.07, PARTRN* dimensionless) Soil reflectivity of photosynthetically active radiation (0.15, SRPAR* dimensionless) Soil reflectivity of short wave greater than photosynthetically active SRSW* radiation (0.3, dimensionless) Elevation of sun at start/end of the day (0.05 radian) SUNUP* Leaf reflectivity of short wave greater than photosynthetically active SWRFLC* radiation (0.4, dimensionless) SWTRN* Leaf transmissivity of short wave greater than photosynthetically active radiation (0.18, dimensionless) 1 Default
soil parameters
