OZCOT: A simulation model for cotton crop management

Agricultural Systems 44 (1994) 257-299

OZCOT: A Simulation Model for Cotton Crop Management

A. B. Hearn CSIRO Division of Plant Industry, Narrabri, NSW 2390, Australia (Received 18 September 1992; accepted 4 March 1993)

ABSTRACT A cotton crop simulation model was constructed by linking a simple temperature-driven model of the fruiting dynamics to the widely used Ritchie (1972) soil water balance model. The function describing the processes in the fruiting model were made sensitive to solar radiation, water and nitrogen stress and water logging. A leaf area generator, a boll growth model and an elementary nitrogen model were added. The model was validated against six data sets from agronomic experiments over a period of 30 years covering the range of Australian cotton growing regions from 15” to 34”s. The model responded to climatic and agronomic (irrigation regime, nitrogen fertiliser rate and sowing date) variables at all sites, and without bias at 5 out of 6; a dtrerence in soil type probably caused the bias at one site. Decision support needs dictated development of the model, which is no more complex than needed to supply information for management decisions. The project demonstrates that such a ‘top down ’ approach can produce a simple yet powerful simulator.

INTRODUCTION Many cotton crop simulation models have been built over the last 20 years with a decision support role in view, for example COMAX : GOSSYM (Baker et al., 1983; Lemon, 1986), COTCROP (Brown et al., 1985), KUTUN (Mutsaers, 1982), Wallach’s (1978) model, 257 Agricultural Systems 0308-521X/94/$07.00 0 Printed in Great Britain

1994 Elsevier Science Limited,

England.

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A. B. Hearn

and those incorporated in the decision support systems TEXCIM (Dr W. Sterling, pers. comm.) and CALEX (Dr L. T. Wilson, pers. comm.). Some have followed the ‘bottom up’ approach of attempting to integrate all known physiological relationships to provide as complete a physiological description of the plant as is possible. As Wang et al. (1977) and Wallach (1978) note, such detailed complex models are frequently as difficult to understand as the biological systems they mimic; moreover, they are also slow to run for decision support on micro-computers. This paper describes the use of the alternative ‘top down’ approach to develop the OZCOT model for decision support in cotton production. This approach starts with the production system and breaks it down no further than needed to provide information for management. Hearn and da Rosa (1985) described a simple model for pest management applications which captured the dynamics of fruiting of cotton, and which has been widely used in the SIRATAC pest management system (Ives & Hearn, 1987). The model assumed growth is not limited by water and nitrogen. While this is frequently true of the well irrigated heavily fertilised crops that characterise much of Australian cotton production, supplies of irrigation water are sometimes inadequate and denitrification or inadequate fertilisation may render a crop deficient in nitrogen. Such shortages of water or nitrogen influence a crop’s capacity to compensate for pest damage and should be taken into account in pest management decisions. Furthermore, with a reduced irrigation water supply, decisions have to be made about the area of crop to grow. Interest in raingrown cotton is increasing in Australia; demarcation of suitable areas and sowing dates is needed and risks assessed. With these decision support needs in mind, the original model has been linked to the widely used Ritchie (1972) row crop soil water balance model, adding an elementary soil and crop nitrogen model, to create OZCOT, a whole crop model. A further development is to model photosynthesis and respiration explicitly instead implicitly in order to simulate the response of some crops to very heavy damage (e.g. Brook et al., 1992). This response featured a large increase in production of squares (flower buds) but a reduction in the number of bolls set. It was postulated that the increase in fruiting sites resulted in larger heavier plants with increased respiratory requirements which, without a commensurate increase in photosynthesis, would reduce the supply of assimilates available for boll growth, resulting in fewer being set and matured. The original model was unable to simulate this response because the model was built on the concept of crop-carrying capacity which assumed the proportion of assimilates being used in respiration was constant.

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THE MODEL The procedural structure of the model is illustrated by the flow chart in Fig. 1, which shows the subroutines that simulate the processes modelled. Subroutines that simulate management decisions are also included but those dealing with input and output are not. The two original models, Ritchie’s water balance and the SIRATAC fruit model, are identified. In the following description of the model, bold capital letters are used for subroutine names. There are three sets of stresses associated with shortage of nitrogen, water and carbon respectively. The information flow linking the three sources of stress to the processes affected by them are shown in Fig. 1. The model distinguishes between a stress and its effect. A stress is described by an index based on the ratio either between supply and demand for a resource or between the current and maximum value of a state variable. In most cases an effect is expressed as a factor modulating the rate of a process. Both index and factor are on a scale of 0 to 1 and the relationship between them is generalised in Fig. 2, which shows a threshold stress above which the stress does not affect a process (effect = 1). Below the threshold stress the effect decreases, usually linearly from 1 to zero. Simulation of these stresses and their effects is described in detail later. Water Balance (subroutines SOLWAT, SEVAP and SWBAL) The water balance is the Ritchie (1972) model for row crops as used in the model CORNF @tapper & Arkin, 1980). The distinctive features are the partition of soil and plant evaporation and the separation of each into energy and supply limited phases. The model maintains a daily balance of the plant available water content of the soil (PAW). The soil moisture index (SMI), an index of water stress that affects a number of the process functions in the plant model, is PAW expressed as a fraction of plant available water-holding capacity (PAWC), calculated for the current rooting depth and for the top 300 mm, with the larger value selected. The model has been calibrated and applied locally (Cull et al., 1981; Hearn & Constable, 1981, 1984). Two further modifications have been made. Firstly, testing over a wider range of seasons showed that because of the great variation from season to season in atmospheric aridity neither the Priestly and Taylor (1972) coefficient originally used, nor the Doorenbos and Pruit (1977) and Wright and Jensen (1978) equations subsequently tried, satisfactorily accounted for the aerodynamic component of evaporation. Consequently

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OZCOT: a simuhion

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I

INDEX Fig. 2.

Generaked

relationship between a sIrcss index and the factor expressmg IIS efkt.

da Rosa (pers. comm.) calibrated the following aerodynamic 37 data points from three seasons in the Namoi Valley

terms with

AT = (I -- DELTA/(DELTA

+ GAMMA))*( 1 + 0~028*WIND)*VPD*lOO (R’ - 0.51) AT = -119.813 + I2.O*VPD + 0.404+TK (R’ = 0.71) AT = -204.355 + 0697*TK (R’ = 0.75) where AT is the aerodynamic component of evaporation in mm d ‘. WIND is wind run in km d ‘, VPD is vapour pressure deficit in Pa. TK is absolute temperature, DELTA the psychrometric constant and GAMMA the slope of the saturation vapour pressure curve. The particular form used depends on the meteorological data available. Secondly. the empirical equations relating the plant component of cvapotranspiration to leaf area index (LAI) were revised (Mateos, pet-s. comm.) LA1 = < 1.6 1-6 < LA1 < 3 LAI>=Z

EP = (0.08 + 0.3066*LAI)*EO EP = (I - EXP(-0,5186*LAI) EP = EO - ES

where EP is plant evaporation, EO is potential evaporation soil evaporation, all in mm d ’ and LA1 as defined. Nitrogen

and ES is

(subroutines SNBAL and CROPN)

Soil and fertiliser nitrogen are entered as inputs. OZCOT does not maintain a dynamic daily soil nitrogen balance analogous to the soil water bdhCe. Instead, at the start of the season subroutine SNBAL predicts the potential nitrogen uptake for the season on the basis of soil nitrogen and any fertiliser already applied. This estimate is reviewed every day, reducing it when waterlogged or dry conditions occur and increasing it when fertiliser nitrogen is applied.

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Soil nitrogen input is either based on previous crop (Hearn, 1986) or soil nitrate measurements (Constable & Rochester, 1988). All soil nitrogen is added to the potential uptake pool, UPTAKN, on the first day of the simulation. A fraction of fertiliser N is added to the pool on the day of application. In order to compute this fraction it is assumed uptake of nitrogen is sink limited and the maximum size of the pool is set at UPTAKN_MAX. The fraction of fertiliser N applied that is added to the pool is a function of the ratio between the current and maximum sizes of the pool. On the day N fertiliser is applied, SNBAL iteratively computes the fraction of each successive kg of fertiliser N applied to be added and adds it to the pool UPTAKN, before proceeding to the next kg, thus: FRACTION

= 1 - UPTAKN/UPTAKN_MAX

A value of 240 kg ha ’ for UPTAKN_MAX is based on Basinski et al. (1975); amounts approaching this have occasionally been obtained in unpublished data at the Narrabri Research Station. With 40 kg hail’ of soil N, this procedure gives a potential recovery of 68% for an application of 100 kg ha-’ which is in accord with experience, with due allowance for reduction by waterlogging or dry conditions. Each day the soil is waterlogged (defined below) the potential uptake pool is reduced by 0.983 kg ha-’ and each day the soil is too dry for N uptake (SMI < 0.3) the pool is reduced by factor of 0.0316 of the total fertiliser N applied (Hearn & Constable, 1984). In subroutine CROPN a vegetative nitrogen stress factor, VNSTRS, is calculated: VNSTRS = (UPTAKN

- lO)/UPTAKN

VNSTRS reduces fruiting site production in subroutine FRUGEN and leaf growth in subroutine LAIGEN with a threshold of 0.9 (eqns (11) & (12) respectively). The quantity 10 is the expected cumulative uptake in kg N ha-’ at the time of the first flower in a crop in which nitrogen is not limiting. Consequently, for crops with UPTAKN less than or close to 10, VNSTRS is zero or very small and growth is negligible. For crops well supplied with N, UPTAKN > 100 giving VNSTRS > 0.9 and with the threshold of 0.9, N has no effect on growth. A limit to the amount of nitrogen that can accumulate in the fruit and thus be removed in harvest, HARVEST-N, is calculated: HARVEST-N

= UPTAKN*O.85

The factor 0.85 is the largest value for nitrogen harvest index found by

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263

Constable and Rochester (1988). From this the carrying capacity of the crop based on available nitrogen is calculated: CARCAP_N

= HARVEST_N/(BGR_VAR*(

l-PC_LINT)*0.03)

CARCAP_N is bolls m-2, BGR_VAR is daily boll growth rate defined in subroutine BOLLWT (eqn (13)) and PC-LINT is lint percentage from Table 1. If the number of bolls exceeds CARCAP_N, action is initiated in two places. Subroutine OVERLOAD is called to abort the excess, as described later. A fruiting nitrogen stress factor, FNSTRS, is constructed to reduce boll growth in subroutine BOLLWT, thus: FNSTRS = 1 - FRU_N/HARVEST_N FRU_N is the simulated amount of N in green and open bolls, computed each day during the simulation thus: FRU_ N = (FRU_DW + OPEN_DW)*((l + (1 - F_BURR*0.005)

- PC_LINT)*SEED_NC

where FRU_DW and OPEN_DW are the weight of seed cotton in green and open bolls respectively in g m-2, PC-LINT is lint percentage (Table 1) and F-BURR is a factor to convert seed cotton to total boll weight including the burr or capsule wall, with a value of 1.23 from Baker et al., (1983). SEED-NC is the nitrogen content of the seed obtained from the following equation fitted to Constable and Rochester’s (1988) data: SEED-NC

= 0.02407 + O.O00147*UPTAKN - O.O000003*UPTAKN**2

The value of FNSTRS decreases from 1, when boll growth starts, to zero when the simulated nitrogen content of the fruit (FRU_N) equals the potential amount of harvestable nitrogen (HARVEST-N). When FNSTRS becomes small (i.e. the simulated nitrogen content of the fruit approaches the potential amount of harvestable nitrogen), it is the dominant factor controlling and eventually stopping boll growth in subroutine BOLLWT. Empirical Equation DP61 or page A-PLANT C F SC-BOLL PC-LINT F-LA1

eqn (6) eqn (5) eqn (3) p. 17 P. 7 p. 16

0.021 0 0.478 4 0.025 0 5.0 0.38 1.0

TABLE 1. Varietal Constants

DP90

Siokra

in OZCOT Source

0.020 6 0.022 8 Fitted by least-squares to SIRATAC farm data 0.478 4 0.541 1 Fitted by least-squares to SIRATAC farm data 0.023 1 0.015 9 Fitted by least-squares to SIRATAC farm data N. J. Thomson (pers. comm.) 4.1 4.5 N. J. Thomson (pers. comm.) 0.39 0.42 unpublished experiment data 1985/86 0.87 0.52

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Fruiting dynamics (subroutines FRUIT, FRUGEN, SURVIVE and OVERLOAD)

CARRYING-CAPACITY,

While retaining the simplicity of the original, the fruiting model (Hearn & Da Rosa, 1985) has been modified in two ways: (i) carrying capacity is estimated directly from photosynthesis and respiration, instead of indirectly from empirical constants derived from fruit counts; and (ii) production of fruiting sites has been changed from per square metre to per plant. Subroutine FRUIT (Fig. 1) simulates fruit development and keeps account of the state variables, and calls CARRYING-CAPACITY to simulate the boll- (or fruit)-carrying capacity of the crop, FRUGEN to simulate generation of fruiting sites, SURVIVE to simulate fruit shedding and survival, and OVERLOAD to abort excess fruit. A description of crop development explains how the model captures the dynamics of fruiting. Nodes on the lateral fruiting branches of the cotton plant are termed fruiting sites. Each is initially occupied by a square which develops into a green boll and then into an open (mature) boll. Young squares and bolls may be shed from the plant leaving the site vacant. As the crop develops and the number of bolls increases, production of new fruiting sites competes with growth of older fruit for assimilates. The competition results in metabolic stress which causes young fruit to shed and production of fruiting sites (morphological development or ‘squaring’) to slow down. As the fruit load increases, the competition eventually becomes so severe that fruiting site production stops, an event popularly referred to as ‘cutout’. A related event occurs later when competition among the growing fruit (as opposed to that between the growing fruit and production of fruiting sites) becomes so severe that all new fruit are shed physiologically. The model has four state variables: fruiting sites; squares; bolls; and open bolls, and simulates three processes: production of fruiting sites; development of fruit; and shedding of fruit. The relationships between them are shown in Fig. 3. Two of the processes, production of fruiting nodes and shedding of fruit, are related because they are both functions of the crop-carrying capacity which depends on the photosynthetic capacity of the crop. The crop-carrying capacity, CARCAP, is the fruit load that causes all young fruit to shed and is estimated in subroutine CARRYINGCAPACITY by simulating both photosynthesis and respiration. Other management models at this level of complexity (Ritchie, 1991) assume, as did the original fruiting model, that a constant proportion of assimilates is used in respiration, by simulating dry weight increase as an empirical function of intercepted radiation and ignoring effects of age and temper-

OZCOT: a simulation model for cotton crop management

Fruiting Site Product Ion

265

. .. . .. . .. .. . .. . . .. . .. . .. . .. . ... .. .. . ... .. .. .. ;

-ve

feedback

i i : : ; ;

Fig. 3.

The relationship

between state variables and processes in the model of fruiting dynamics.

ature on both processes. OZCOT separates photosynthesis and respiration in order to simulate the effect of an increased respiratory load in rank crops. Photosynthesis is driven by radiation and both processes are affected by temperature and age of organs. The effects of age tend to balance each other out, and their effects and those of temperature are taken into account in the calibration of the empirical constant F in eqn (3) below. Photosynthesis is estimated using a function from the GOSSYM model with empirically determined parameters (Baker et al., 1983): P-POTENTIAL

= 2.391 + RADN*(1.374

- RADN*0.0005414)

(1)

where P-POTENTIAL is potential rate of gross photosynthesis in mg CO2 dmm2ground area d-’ and RADN is solar radiation in watts mm2d-‘. These are the original units and rate is converted to g carbohydrate mm2 d-‘. Interception of solar radiation by the crop is estimated: INT = (1.0 - EXP(-E*LAI))

(2)

where INT is the fraction of radiation intercepted, LA1 is leaf area index and E is the extinction coefficient with a value of 1.O (Stern, 1965; Hearn, 1972; Constable, 1986). Respiration is simulated as a function of the size of the plant thus: R = F*SITES*R_FAC where R is respiration

in the same units as P-POTENTIAL,

(3) SITES is

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A. B. Hearn

the cumulative number as a surrogate for the parameter. R_FAC is (Horie, 1977) calculated

of fruiting sites defined previously and is used weight of respiring tissue and F is an empirical a factor to adjust respiration for temperature as follows:

R_FAC = 2.2**((TEMP - 35)/10) with TEMP the mean temperature. Carrying capacity is computed from the amount of assimilates available for dry weight increase, the product of P-POTENTIAL and INT, less respiration, divided by the boll growth rate: CARCAP = (P_POTENTIAL*INT

- R)/(BGR_VAR*F_BURR)

(4)

where CARCAP is carrying capacity in number of bolls mm2P_POTENTIAL, INT and R are defined by eqns (l), (2) and (3) respectively, BGR_VAR is the potential boll growth rate for the day in g seed cotton bolll’ de’ (computed in eqn (13) subroutine BOLLWT below) and F-BURR as previously defined. CUTOUT is the size of fruit load that causes fruiting site production to stop and is related to CARCAP thus: CUTOUT = C*CARCAP in which C is an empirical parameter. The production of fruiting sites is simulated in subroutine by the following equation: D-SITES-PLANT = A_PLANT*SQRT(SITES_PLANT)*(

(5) FRUGEN

1 - LOAD/CUTOUT)

(6)

where D-SITES-PLANT is the increase in the number of fruiting sites plants ’ DD-’ (day degree base 12°C) SITES-PLANT is the cumulative number of fruiting sites plant ‘, A-PLANT is an empirical constant and LOAD is the fruit load. The first term in equation (6), A_PLANT*SQRT(SITES_PLANT), provides positive feedback; as the crop develops and plants get bigger, SITES-PLANT increases and new sites are produced faster. The square root form was derived by Hearn and da Rosa (1985) from the geometry of the branching structure. The second term 1 - LOAD/CUTOUT provides negative feedback from metabolic stress which slows fruiting site production and eventually halts it when LOAD > = CUTOUT. The shedding of young fruit is computed in function SURVIVE from SURVIVE = D*( 1.O - LOADKARCAP)

(7)

OZCOT:

a simulation

model for

cotton

crop management

261

where SURVIVE is the probability of a fruit surviving to harvest (i.e. not shedding). The proportion of each day’s production of fruit that are shed is l-SURVIVE. LOAD is as previously defined and CARCAP is carrying capacity from eqn (4), the value of LOAD that causes all new fruit to shed. The parameter D is the maximum value of SURVIVE and reflects shedding caused by pest populations below the economic action thresholds. Therefore when LOAD is zero, SURVIVE is D and is nil when LOAD is equal or greater than CARCAP. Both the original and the new models are population models that account for the dynamics of a population of fruit on a square metre of land. In order to take variation in plant population into account, the units of D-SITES in eqn (6) were changed to plant-’ from mm2in the original model. The rate of site production rnd2 is the product of D-SITES and PPM, plant population rnm2.LOAD and CUTOUT remain on a me2 basis but LOAD/CUTOUT does not provide sufficient negative feedback at high population densities to slow down the rate of production of fruiting sites plant- ‘, D-SITES. For this purpose a population factor was introduced: POP_FAC = I/( 1 + POP_CON*PPM)

(8)

where POP_CON is an empirical constant with a value of 0.03633 fitted by least squares to unpublished data from an experiment in 1982/83 in the Namoi Valley. The rate of site production m-2 d-’ is: D-SITES = D_SITES_PLANT*DD*PPM*POP_FAC Each day’s production of fruiting sites is accounted for separately in order to abscise the fruit according to eqn (7) or to develop them through to maturity. In the original model, development was simulated by accumulating day degrees (DD) for each day’s fruiting sites. DD are computed with a base temperature of 12°C and the requirements for developmental stages are given in Table 2. This procedure has been retained for development of squares from appearance to anthesis but has been replaced for development of bolls from anthesis to dehiscence by an exponential function: B-PER = l/EXP (5.385 - O.O512*T)

(9)

where B-PER is the reciprocal of the boll period in days and T is daily mean temperature with the empirical constants obtained by Constable (1991). B-PER is thus the fraction of boll development completed on any day. The exponential function is used because it is more robust at lower temperatures at the end of the season when use of day degrees is extrapolating beyond the range in which they are valid. This functional form

A. B. Heurn

268

TABLE 2 Fruit Age Classes Used in the OZCOT Model Fruit age class

Size (mm)

Accumulated DD,,

Small squares Medium squares Large squares

3G5.0 50-10~0 > 10.0

o-5 SO-180 180-350

Flowers Small bolls Medium bolls Large bolls Inedible bolls

< 250 250-37.5 37.542.5 37.5-42.5

O-30 30-170 17&310 310-520 520-750

Fractional development

0~0-0~07 0.07-0.2 1 0.21-0.33 0~33~0~55 0.55-1.0

is also preferred by Mutsaers (1976) amongst others, although Constable (1991) found little to choose between them. B-PER is calculated every day of the simulation from the day’s temperature. For each day’s production of bolls the fraction of development completed each day (B-PER) is accumulated until a sum of 1.0 is reached. Squares and bolls are broken down in age categories given in Table 2 for various purposes, including interfacing with the Heliuthis feeding model (Wilson & Gutierrez, 1980). If in spite of shedding of new squares and bolls the number of fruit exceeds either the carrying capacity based on carbon (CARCAP from subroutine CARRYING-CAPACITY) or that based on nitrogen (CARCAP-N from subroutine CROPN), subroutine FRUIT calls OVERLOAD which aborts the. excess bolls, taking progressively older bolls if necessary up to large bolls (Table 2). This procedure simulates the abortion of older fruit that sometimes occurs under stress. Such loss often results in the bolls drying in situ on the plant instead of falling off and is popularly described as ‘freezing’ or ‘mummifying’. In OVERLOAD the effect is buffered by requiring the number of fruit to exceed the carrying capacity for 2 successive days before aborting the excess on the third day in order to simulate the storage of assimilates in the plant and prevent a single day of water stress, low radiation or waterlogging precipitating abortion. Shading experiments have shown that reserves are depleted after 2 days. The effect is further dampened by aborting only one-tenth of the excess in one day. The values of the empirical parameters are given in Table 1. The empirical parameters C, A-PLANT and F in eqns (5), (6) and (3) were fitted by the least-squares method described by Talpaz et al., (1987) using

OZCOT: a simulation model for cotton crop management

269

the non-linear optimisation package MINOS (Murtagh & Saunders, 1980). The data for fitting were weekly fruit counts taken on farms in the SIRATAC pest management system (Ives & Hearn, 1987). There were 32 farms selected for the variety DP61 between the 1981/82 and 1983184 seasons, 35 for DP90 and 17 for Siokra in the 1984/85 and 1985/86 seasons. Farms were selected where counts were reliable, done regularly and sustained to the end of the season, and where yields were neither excessively high nor low. The parameter POP-CON was fitted in a similar way with MINOS using fruit count data from a population density experiment done in 1982/83. Parameter D in eqn (7) was set at 0.8, based on the observation that the probability of survival of fruit in the field rarely exceeds 0.8 (e.g. Hearn & Room, 1979; Turner et al., 1986). Water stress

A major enhancement incorporated in OZCOT is making the fruiting model sensitive to water stress. The soil moisture index SMJ, from the soil water balance SOLWAT, is used to simulate the effect of water stress on a number of processes in the fruiting model. Equations (6) and (7) were calibrated with relatively unstressed irrigated cotton in which SMI was > 0.5. Any effects of water stress with SMI > 0.5 are accounted for in the values of the empirical constants. Therefore in OZCOT water stress only affects the fruiting processes when SMI < 0.5. Turner et al. (1986) found in the Namoi valley that the reduction of the rate of net photosynthesis of cotton by water stress, relative to an unstressed control, was expressed , by the relationship: REL_P = 0.25 + 0.864*SMI

(10)

where REL_P is the relative rate of photosynthesis. Water stress increases tissue temperature which will affect respiration. However, effects of SMI on respiration are accounted for in the empirical constant F in eqn (3) when SMI > 0.5. To account for the effect of water stress when SMI < 0.5, the calculation of R_FAC, the factor to adjust respiration for temperature in eqn (3), is revised by using T-PLANT instead of TEMP. T-PLANT

= TEMP + 5 - lO*SMI

where T-PLANT is leaf temperature, allowing plant temperature to be 5°C above TEMP (mean ambient temperature) when at maximum stress. Water stress reduces the assimilates available for boll growth, not only by reducing photosynthesis and increasing respiration but also by changing the partitioning between root and shoot. This effect is simulated by

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A. B. Hearn

increasing the effect of water stress by revising the value of REL_P (eqn (10)) thus: REL_P = (REL_P - 0.25)**2 + 0.25 The value 0.25 is the intercept in eqn (10). In order to simulate the effect of water stress on fruiting site production and fruit shedding, eqn (4) is modified to include REL_P and the revised value of R (respiration) thus: CARCAP = (P_POTENTIAL*REL_P*INT

- R)/(BGR_VAR*F_BURR)

Because CARCAP is now adjusted for water stress, the effect of water stress on shedding of bolls and squares is simulated in eqn (7). Similarly, when CARCAP is used in eqn (5) to obtain CUTOUT which in turn is used in eqn (6) the effect of water stress on fruiting site production is simulated. Waterlogging

Some waterlogging is unavoidable on the heavy vertisols on which cotton is grown in Australia (Hearn & Constable, 1984; Hodgson, 1982). It reduces yield by reducing nitrogen uptake and by reducing the lint produced from each kg of N uptake. Hodgson also found that waterlogging reduced photosynthesis. Hodgson (1982) defined waterlogging as soil with air filled porosity less than 10%. Analysis of his results showed this corresponded with a soil water deficit (PAWC - PAW) < 25 mm or SMI < 0.87 was taken as a threshold for waterlogging. When waterlogging occurs, N uptake is reduced in subroutine SNBAL. The additional yield reduction, over and above that caused by reduced N uptake, is assumed to be associated with reduced photosynthesis. Accordingly, when the soil is waterlogged, CARCAP is reduced in subroutine CARRYING-CAPACITY. There is a perception that waterlogging effects are more severe after water stress following loss of roots near the surface. Therefore, if the crop is waterlogged after the crop has cut out as a result of water stress (LOAD > CUTOUT and SMI < 0.75) CARCAP is reduced to zero. If there is no prior stress CARCAP is reduced to 20%. Nitrogen stress

Nitrogen stress is applied to fruiting sites production D-SITES = D_SITES*VSNSTR

(11)

VSNSTR is the vegetative nitrogen stress factor derived with a threshold of 0.9 from the index VNSTRS computed in subroutine CROPN.

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211

Plant population and row spacing

The model was developed for the standard spacing of 1 m between rows. Provision has been made for other row spacings, particularly for skip row and other configurations used for rain grown crops. When a row spacing wider than 1 m is used, plant population m-* is reduced, calculated from plants m-’ of row, PPM, and used for computing LA1 and fruit m-*. However, plants m-i of row is still used in eqn (8) in computing the factor POP_FAC that enables plant population density to reduce the rate of production of fruiting sites plant-‘, as this depends on within row rather than between row competition. First square (subroutine ISTSQ) Constable (pers. comm.) re-examined his data (Constable, 1976) and found that 420 day degrees elapsed between sowing and the appearance of the first square, with an addition of 5.2 DD for cold shock on each day with a minimum temperature below 11°C. This requirement is common to all ‘delta’ type cotton varieties examined so far. The appearance of the first square on a plant is simulated when the requisite number of day degrees has elapsed. The production of SITES-PLANT for that day is 1, and SITES = SITES_PLANT*PPM. Leaf area (subroutines LAIGEN SENLF) On the day of emergence, LA1 is initialised with the product of plant population and the area of the cotyledons per plant. LA1 then expands exponentially until the first square event: D-LA1 = LAI*R_LAI*FLFSMI D-LAX is the day’s increase in leaf area, R-LA1 is the relative growth rate and FLFSMI is the water stress effect, derived from SMI with a threshold of 0.5 (Rosenthal et al., 1987). The initial area per plant, 0.00035 m2 and R-LA1 were determined from leaf area measurements in unpublished experiments in 1982/83 and 1983/84. After the first square event, leaf area index increases as a function of the number of fruiting sites (SITES). The rationale for this is that branching and fruiting site production are regular and systematic, with site production related to mainstem node production (Hearn & da Rosa, 1985). Each fruiting site and each main stem node subtends a leaf. The effect of water stress is taken into account in the following equation: DL_DS = 0.1847 - O.l165*SMI - 1.514*VPD + 1*984*SMI*VPD

272

A. B. Hearn

where DL_DS is the square root of leaf area increase per site, SMI is as defined previously and VPD is vapour pressure deficit in Pa. The empirical parameters were obtained by regression analysis of leaf area and fruit count data for the variety DP61 from experiments at the Research Station in 1982/83 and 1983/84. The former was a dry year and the latter an exceptionally wet year which emphasised the effect of VPD. The effect of variety on leaf area is simulated thus: D-LA1 = DL_DS**2*F_LAI where D-LA1 is again the day’s increase in LAI, F-LA1 is a factor to adjust leaf areas for other varieties introduced since 1984, obtained in an experiment in 1985/86. There was no difference among varieties in leaf area before the first square appeared. The day’s increase in LAI, D_LAI, both before and after first square is adjusted for nitrogen stress: D-LA1 = D_LAI*VLNSTR

(12)

The nitrogen stress factor, VLNSTR, is derived from nitrogen stress index, VNSTRS, with a threshold of 0.9 (Fig. 2). Each day’s increment of leaf area is accounted for separately in order to facilitate senescence of leaves. Data on leaf longevity are sparse and variable; values range from 55 to 99 days and 500 to 1300 DD. Water stress early can delay development and lengthen life, while late in life it can accelerate senescence. Senescence appears to be accelerated when the crop has a full boll load, probably reflecting faster remobilisation of nitrogen. On the basis of Hesketh et al. (1977) and McMichael and Hesketh (1982) the day degree requirement for leaf senescence, SENLF, has been set to vary between 833 and 1100 as a function of SMI and fruit load thus: SENLF = 833 + 277*FB*FW where FW decreases linearly from SMI = 0.0, and FB in defined by CARCAP being defined previously. appropriate day degree requirement

1.O when SMI = 0.25 to 0.0 when 1 - LOADKARCAP, LOAD and A day’s leaves are senesced when the has been met.

Fruit Growth (subroutine BOLLWT)

The weight of seed cotton per boll is a conservative varietal character. Consequently, in the application of the original model in SIRATAC boll growth was not simulated but yield estimated as a function of the

OZCOT:

a simulation model for cotton crop management

273

number of open bolls at the end of the season using a conversion factor of 1 bale of lint ha-’ for every 16 open bolls mm2for the varieties DP16 and DP61. This factor allows for picking losses and the moderate levels of metabolic stress that result from competition among bolls for diminishing assimilate supplies after the crop has cut out but does not take into account effects of more severe stress from inadequate supplies of water and nitrogen. In order to account for these severe stresses, the current model simulates daily boll growth. The accepted value for weight of seed cotton per boll for a variety, determined in variety trials, is included in OZCOT as an empirical constant, SC-BOLL. The weight of seed cotton per boll is reduced by extremes of temperature (Hesketh & Low, 1968; Hesketh et al., 1972). Accordingly, a temperature factor, F_TEMP, is calculated which decreases from a value of 1 to 0 as mean daily temperature rises from 30 to 35°C or falls from 20 to 15°C. During simulation each day’s increment in weight of seed cotton for a boll is computed thus: BGR_VAR = SC_BOLL*B_PER*F_TEMP*

1.3

(13)

where BGR_VAR is g seed cotton boll-’ d-‘, SC-BOLL and F_TEMP are as defined above, and B-PER is the reciprocal of the boll period defined by eqn (9). The factor 1.3 is to obtain the potential boll growth rate unconstrained by the moderate levels of stress, to which reference has just been made and which have influenced the value of SC-BOLL. The value 1.3 was derived from data of Constable (1991). The effect of stress on boll growth is then simulated thus: BOLL_GR = BGR_VAR*STRSBL where STRSBL is the minimum of FBCSTR and FBNSTR, the effects of carbon and nitrogen stress respectively. FBCSTR is derived from CARCAP/LOAD (the carbon supply demand ratio) with a threshold of 1 (Fig. 2) when LOAD > CARCAP. It is assumed that nitrogen supply does not affect boll growth until the number of green and open bolls exceeds CARCAP_N, the nitrogen-based carrying capacity computed in subroutine CROPN. FBNSTR is then calculated with a threshold of 0.5 from FNSTRS, the fruit nitrogen stress index from subroutine CROPN. The effect of water stress on boll growth is mediated through CARCAP and FBCSTR. Bolls developed from each day’s production of SITES are accounted for separately. The product of BOLL_GR and the number of bolls for each day’s production is accumulated daily until that day’s bolls have opened, whereupon the accumulated amount is added to the variable OPEN_WT, the total weight of seed cotton in the open bolls.

NOTE:

the format

Boll growth

Leaf area

Fruiting

TABLE

3 Model

in SENLF

‘factor

that the factor

is derived

1st square

0.5) rate = f(SMI, VPD)

of n in Fig. 2

Indirect effect of SMI via CARCAP via CARCAP/LOAD ratio when LOAD > CARCAP

SMI affect leaf longevity

After

Before 1st square factor FLFSMI = F(SMI, reduces rate

from the index with a threshold

Factor FBCSTR = f(CARCAP/LOAD, 1 .O) reduces rate when LOAD > CARCAP

= f(index, n)’ indicates

BOLLWT selects minimum

Senescence

Growth in LAIGEN

indirect effect of SMI via CARCAP via photosynthesis

When LOAD

Abort excess fruit in OVERLOAD > CARCAP

Indirect effect of SMI via CARCAP via photosynthesis

Indirect effect of SMI via CUTOUT via photosynthesis

Soil water content to capacity ratio SMI = PAWIPAWC

Water stress

in the OZCOT

Rate is function of index 1 - LOADCARCAP

Effects

Survival of fruit in SURVIVE

Function of fruit supply demand ratio: CARCAPILOAD

Function of fruit demand supply ratio: LOAD/CUTOUT

Carbon stres.r

Their

Rate is function of index 1 - LOAD/CUTOUT

and subroutines

-

and

Fruit production in FRUGEN

Effects: Crop attributes affected

Indices

Stresses

of bolls

Factor FBNSTR = f(FNSTRS, 0.50) reduces when bolls z CARCAP_N

Factor VLNSTR = f(VNSTRS, 0.9) reduces

When number > CARCAP_N

Factor VSNSTR = f(VNSTRS, 0.9) reduces

Function of current and maximum fruit content: FNSTRS = I- FRU_N/0,85*UPTAKN

Function of uptake: VNSTRS = (UPTAKN-lO)/UPTAKN

Nitrogen stress

rate

rate

rate

&

3

,s: B

!JJ

OZCOT: a simulation,mo&l for cotton crop management

275

Stresses Table 3 and Fig. 1 summarise the stresses that are simulated in OZCOT and the processes they affect directly and also shows whether the concept in Fig. 2 is used. Important indirect effects of water stress, operating through photosynthesis, on fruit production, survival and growths are shown in Table 3. There are other indirect effects not shown, such as the effect of water stress on leaf area via photosynthesis and fruiting site production, and the effect of nitrogen stress on fruiting site production indirectly affecting leaf area and then in turn photosynthesis, carrying capacity, fruit survival and growth and further fruit production. Management

(subroutines SOWDAY,

DECIDE_IRG

and HARVEST)

OZCOT can simulate some management decisions: sowing, irrigation, defoliation, harvest, cultivation. For tactical applications and validation, decisions such as dates of sowing or irrigation are part of the agronomic input data and their simulation is not required. On the other hand for strategic applications, risk analysis for example, it is necessary to simulate them. In subroutine SOWDAY the decision to sow is simulated for strategic use of OZCOT, particularly for rain grown cotton. There are three rules to be satisfied: (i) the soil is warm enough; (ii) there has been a rainfall event which wetted the surface soil sufficiently; and (iii) the soil surface has dried sufficiently to become trafficable. SOWDAY requires as input a sowing window within which to look for a suitable sowing date. Soil temperature greater than 15°C at 9 am on 3 successive days is the industry standard defining suitable conditions for sowing. When soil temperature data are not available, a running 3-day mean screen temperature of 18°C is used instead because it correlates well with a soil minimum greater than 15°C on 3 successive days in spring on the soils on which cotton is grown in the Namoi valley. For the soil to be wet enough and trafficable, the value of SMI for the upper 100 mm of soil must exceed 0.75 and then dry down to between 0.67 and 0.5. The threshold of 0.67 on a vertisol is from Bridge and Muchow (1982). When these three conditions are met within the nominated window, sowing is simulated. Subroutine DECIDE_IRG simulates an irrigation decision. The time window for irrigation of the crop, the threshold soil water deficit (PAWC - PAW) in mm at which to irrigate and the amount of irrigation water available are required as input. The start of the window is defined in days after first square and the end of the window in terms of percent-

276

A. B. Heat-n

age of the bolls open. Within the window an irrigation decision is simulated when the soil water deficit is greater than the threshold, provided more than half the water needed is available. The amount of water needed and applied to vertisols under furrow irrigation (used almost exclusively for cotton in Australia) is equal to the soil water deficit. This amount is calculated in DECIDE_IRG and adjusted for the engineering efficiency (ratio evapotranspiration/water pumped) which is entered as an input. When the crop is irrigated, the irrigation water supply is reduced by the amount applied. The calender date of pre-irrigation is an input. At the end of a season simulation of crop growth is terminated by one of three events, whichever occurs first: by a frost; by all bolls being open; or by defoliation. When growth is terminated by a frost, all bolls that have completed 90% or more of their development are opened. After growth has stopped, yield is calculated in subroutine YIELD as the product of the variable OPEN_WT, the total weight of seed cotton in the open bolls, and PC-LINT, the lint percentage (Table 2). Subroutine HARVEST simulates the defoliation decision, and the decision to pick when this is not pre-empted by all bolls being open or by frost. A defoliation decision is made when 60% of the bolls are open, which is the industry standard, although other developmental criteria could be used. Ten days after the first defoliation a second defoliation is flagged if the LA1 exceeds 0.2; if not, the crop is flagged for picking. Ten days after the second defoliation the crop is flagged for picking. The defoliation flag from HARVEST is picked up by subroutine SENLF called from LAIGEN. The first defoliation reduces the day degree requirement to one-third of its current value, thus simulating rapid shedding of leaves. The second defoliation reduces the day degree requirement to zero, thus simulating immediate shedding of all remaining leaves. The defoliation flag from HARVEST accelerates the opening of bolls in subroutine FRUIT so that when picking is signalled, bolls that have completed 80% or more of their development are opened (Walhood & Addicott, 1968). Cultivation of the soil for land preparation between seasons will cause the upper layers of soil to dry out (Freebairn et al., 1986). This loss needs to be taken into account to estimate the amount of water used in pre-irrigation and to determine if the soil water conditions are satisfied for rain grown crops. Accordingly, in SOLWAT on any days of the year nominated for cultivation, the soil of the uppermost two layers can be dried to a specified fraction of PAWC, unless PAW in that layer is already depleted to that level.

OZCOT: a simulation model for cotton crop management

271

Input required Essential daily weather data required are rainfall and maximum and minimum temperature. Solar radiation and dry and wet bulb temperatures are desirable; the former can be synthesised from extra-terrestrial radiation and days since last rainfall (Hearn & Constable, 1981). Agronomic input is variety, row spacing and plants m-l of row, soil nitrogen and rates and dates of N fertilisation. Sowing and irrigation dates are optional, and can be simulated, but require the relevant window to be defined. If irrigation dates are not given, irrigation water supply and engineering efficiency are also required. PAWC and initial PAW are required. VALIDATION

OF THE MODEL

In this paper validation is limited primarily to the response of the model to weather and agronomic variables. The response to variety and pest damage will be the subject of another paper. The six sets of experimental data listed in Table 4 were available for validation of the model. In every case yield data were available and in some cases yield components, growth and phenological data as well. The relationships between simulated and actual values for yield, and for yield components, nitrogen uptake and maximum LA1 when available, were evaluated by determining the line of best fit obtained by the method of Kendall and Stuart (1979) using the maximum likelihood estimate of parameters. Such a functional relationship is more appropriate than the regression of actual on simulated values, since both actual and simulated values are subject to error. The slopes and intercepts of the resultant equations are presented in Tables 5-7, with the correlation coefficients. Success of simulation is judged not only by the correlation coefficient but by determining whether the estimates are biased, that is whether the line of best fit differs significantly from the 1 : 1 line. The slopes and intercepts are tested for departure from unity and zero respectively. Kendall & Stuart’s (1979) maximum likelihood estimate does not provide standard errors for the parameters. Confidence limits can be calculated for the slope but the deviation of the intercept from zero can be judged from the standard error of the experimental data. Validation in respect to the expansion of LAI, changes in soil water content and fruiting dynamics were done by comparing the actual and simulated patterns through time. Representative examples are given for some data sets.

nitrogen,

nitrogen

Raingrown

Irrigation, soil types Irrigation,

1981-1991

1984-1985

1971-1973

1961-1963

Namoi Valley Central Queensland

Emerald

Ord River Valley

MIA

Date of sowing, irrigation

varieties

Date of sowing

196991973

Valley

Namoi

nitrogen,

Irrigation, variety

Type of experiment

19741990

Years

Data-sets

Namoi Valley

Region

Experimental Data

Model

et al., 1976

& Hearn

Ockerby

Hearn

Saunt,

Yield, number of bolls, boll weight, LAI, N uptake, fruit counts, soil water Yield, number of bolls, boll weight, LAI, boll curves

44

14

1967

1975a,b

et al., 1992

Reid (pers. comm.)

Constable

Constable 1981

Reference

Yield, LAI, N uptake

Yield

Yield

Yield, number of bolls, boll weight, LAI, N uptake, fruit counts, soil water

the OZCOT

72

39

21

218

Number of crops simulated

TABLE 4 Used to Validate

% a 3

per

A

219

OZCOT: a simulation model for cotton crop management

Namoi valley irrigation and nitrogen experiments 1974-90 Between 1974 and 1990, 11 experiments were done at the Narrabri Research Station (lat. 30” 13’ S), some of which have been published (Constable & Hearn, 1981). The treatments were nitrogen fertiliser rates, varieties and irrigation regimes in which irrigation started or stopped at different stages of the season, or was done at different soil water deficits, or was omitted entirely (i.e. a raingrown crop). Altogether there were 218 treatment by year combinations. Each treatment was simulated using the actual management practised as input. The assumptions for soil nitrogen were based on the previous crop (Hearn, 1986). Fig. 4a compares actual and simulated lint yields. The functional relationship is given in Table 5. Agreement between actual and simulated values is reasonably good, with 70% of the variance in actual yields accounted for by the simulation. The intercept is not significantly different from zero, as judged by the standard errors of the actual yields, but the slope is significantly less than unity, implying the model is overestimating yields. However, over the period of these experiments commercial yields increased by 1.75% per year as a result of better management (including avoidance of soil compaction), better varieties (Siokra) and more effective insecticides (synthetic pyrethroids). These factors limited the yields of the experimental treatments with full irriga-

Functional Data-set

Relationships

TABLE 5 Between Actual and Simulated Yields (kg lint ha-‘)

Experimental treatments

n

R

Namoi Valley 19761990

Irrigation, nitrogen, variety

218

0.8335***

Namoi Valley 1969-1973

Date of sowing

21

0,9725***

Namoi Valley & Central Queensland 1981-1991

Rain grown varieties

39

Emerald 1984-1985

Irrigation, nitrogen, soil types

Ord River Valley 1971-1973 MIA 1961-1963

Intercept

Slope

95% Confidence intervals

0.86##

0.79-0.94

-86.1

1.08

0.961.21

0.6301***

-53.74

1.11

0.72-1.73

72

0.7009***

78.6

1.09

0.85-1.40

Irrigation, nitrogen

45

0.7680***

184.7

0.88

0.67-1.13

Date of sowing, irrigation

14

0.8281***

424.4

0.43##

0.25-0~63

*** Correlation coefficient significant at p < OGOl.

##Slope is significantly different from unity at p < 0.01.

18.8

280

A. B. Hearn

(a) Namof

Valley

3000 4

Water

-

and Nitrogen

Experiments

1974-90 /

.

8

0

2500.

1000

1500

2000

2500

3000

Simulated

(b) Namol

Valley

Date

of Sowing

Experiments

1969-73

2000,

1600.

.

0

400

I,.

.

I..

.

600

1200

.

.

.

.

1600

2000

1600

2000

simulated

(c)

Ralngrown

Experiments

1975-91

1600.

0

400

800

1200

Simulated

Fig. 4.

Comparison

of actual and simulated yields in kg lint per ha; solid line is line of best fit, parameters in Table 5; broken line is 1 : 1 line.

281

OZCOT: a simulation model for cotton crop management Cd) Emerald

2000

Water

and Nitrogen

Experiments

1984-85

.

1600. 5 t; Q

1200.

800

.

I600

1200

2000

2400

Simulated (e) Ord Valley

Water

and Nitrogen

Experiments

197 l-73

Simulated (r) Murrumbldgee

Valley

Date of Sowing

1961-63

1400 I200 1000 5 5

800 600 400 0

200

/ /

0 0

r 2uo

400

600

800

Simulated Fig. 4.-contd.

1000

I200

140 0

A. B. Hearn

282

(a)

Namoi

0

pooled

50 nitrogen

(b) Ord pooled

i

data for 1975-78.

100

A

limited actual

--*--

full simulated

--@--limited

150

simulated

kg per ha

data for

1971-73

!L+E=s5

E

34 nitrogen

Fig. 5.

Interaction

kg per

ha

between nitrogen and irrigation:

actual

and simulatedyields in two

sets of experiments. tion and heavy application of nitrogen in the 1970s. When experimental yields are adjusted for the effect of years, the bias is removed. When a subset of the data was taken, consisting of all the fully fertilised treatments so the main differences were irrigation treatments, including raingrown treatments, the correlation coefficient fell from 0.834 to 0.798. In another subset of the data, consisting of all the fully irrigated treatments, so that the main differences were nitrogen rates, the correlation coefficient rose to 0.904. In the subset consisting of the fully irrigated and fertilised treatments, so that the differences were varieties and seasons, the correlation coefficient was 0.796. Fig. 5a shows that the model simulated, but dampened, the interaction between rate of nitrogen and irrigation regime reported by Constable and Hearn (198 1). Table 6 gives the relationships between actual and simulated values for the components of yield: boll numbers and seed cotton per boll. Both have intercepts close to zero and slopes not differing significantly from unity, though the agreement is much better for number of bolls (with a correlation coefficient similar to that for yield) than for boll weight. Nitrogen uptake and LA1 data are limited because they were not measured on every treatment. Table 7 gives the relationships between

283

OZCOT: a simulation model for cotton crop management

Functional

Relationships

TABLE 6 Between Actual and Simulated Values for Components

Experimental treatments

Data-set

Numbers of bolls rn-’ Namoi Valley Irrigation, nitrogen, 19741990 Ord River Valley 1971-1973 MIA 1961-1963

variety Irrigation, nitrogen Date of sowing, irrigation

Boll weight, g seed cotton boll-’ Namoi Valley Irrigation, nitrogen, 19741990 variety Ord River Valley Irrigation, nitrogen 1971-1973 MIA 1961-1963 Date of sowing, irrigation

n

R

Intercept

218

0.7753***

-470

45

0,5340***

14

Slope

of Yield

95% Confidence intervals

0.95

0.85-1Il6

19.72

0.81

0.461.33

0.7789***

19.71

0.32”

0~160.49

218

0.5324***

-0.147

1.01

0.82-1.26

45

0.4524***

14

0.1575

2.299 0.43”

0.184.74

No Functional Relationship

**, *** Correlation coefficient significant at p < 0.01 or p < 0.001 respectively. ## Slope is significantly different from unity at p < 0.01.

actual and simulated values. Closeness of fit is good for N uptake and poor, though still significant at the p = 0.001 level, for maximum LAI. Both have intercepts significantly less than zero and slopes greater than unity. N uptake is under-estimated at low levels but of the right order at high levels, while maximum LA1 is under-estimated over the whole range, but more so a low levels. Functional

Relationships

Data-set

TABLE 7 Between Actual and Simulated Values for Seasonal N Uptake and Maximum LA1

Experimental treatments

Seasonal N uptake, kg me2 Namoi Valley Irrigation, nitrogen, 1974-1990 variety Emerald Irrigation, nitrogen, 1984-1985 soil types Ord River Valley Irrigation, nitrogen 1971-1973 Maximum LA1 Namoi Valley 1974-1990 Emerald 1984-1985 MIA 1961-1963

Irrigation, nitrogen, variety Irrigation, nitrogen, soil types Date of sowing, irrigation

n

R

Intercept

Slope

95% Confidence intervals

92

0.8563***

-38.4

1.38#*

1.21-1.57

72

0.7147

-81.2

1,72##

1.37-2.21

27

0.9*++

28.1

1.23’

1.01-1.52

0.5388***

-2.49

1.86##

1.45-2.49

0.3084*

-2.07

2.62#

1.2tX27.29

218 48

*3*** Correlation coefficient significant at p < 0.05 or p < 0.001 respectively. W# Slope is significantly different from unity at p < 0.05 or p < 0.01 respectively.

284

A. B. Heurn

Fig. 6. compares the actual and simulated course of LA1 development in a raingrown (Figs 6a, 6c) and a fully irrigated (Figs 6b, 6d) treatment in each of two experiments. The model accurately simulated the slower expansion of leaf area in the first 100 days caused by water stress in raingrown cotton. In 1975-76 the model failed to simulate the rapid increase in leaf area caused by regrowth following rain on day 105 after a long period of stress. Figs 7a, 7b give actual and simulated soil water content for raingrown and fully irrigated treatments in one experiment in the Namoi valley. The model tracks the decline in PAW in the raingrown crop and at the end of the season in the irrigated crop. In this particular example the model slightly over-estimated water content during the irrigated period. Fig. 8 shows some of the actual and simulated fruit curves from two experiments. The modification to the original fruit model enabled OZCOT to simulate the fruiting dynamics of crops with limited water and nitrogen with varying success. In 1982-83 the differences in water stress caused by three irrigation treatments (nil, limited, and full; Figs 8a, 8b, 8c) had little effect on square production up to peak squares but a major effect on the number of bolls set and harvested; the model faithfully reflected these effects. Also for 1982-83 the effect of N is shown by Figs 8c and 8d, which compare the fully irrigated treatments with and without fertiliser. In contrast to water stress, N stress reduced square number as well as boll numbers and the model faithfully simulated both. In 1985-86 square production was reduced in the raingrown crop but the model did not fully simulate this effect (Figs 8e, 8f), although reduced number of bolls set and harvested was simulated well. In 1985-86 the model failed to simulate the earlier opening of bolls on the raingrown crop. Namoi valley date of sowing experiments 1969-73 Constable et al., (1976) reported three experiments, also done at the Narrabri Research Station (lat. 30” 13’S), in each of which there were seven dates of sowing at lo-day intervals beginning on September 30. The actual management practised was used as input for the simulation, except for dates of irrigation which were simulated by subroutine DECIDE_IRG. In the 1972-73 season a plague of Heliothis armigera resistant to DDT reduced the Namoi valley average yield by 50%; this effect was simulated by multiplying the probability of fruit surviving by 0.33 (variable SURVIVE from equation (7)). The yields were simulated for the variety Deltapine Smooth leaf using model varietal parameters for Deltapine 16, its immediate successor, which only marginally out-

OZCOT: a simulation model for cotton crop management

?I

2x5

SPl

*El 1 .p 091 S8 002

0

e

szt

ii

OE 1

0

g

Sll

JLI 0

211

E

e

001

-

0

001

se

98

P

p”

PL

SL

.

??

ss

s9

09

OS

T

m

cu

-

0

02

IV1

S61 Of 1

1 SPl

OPL O&l

p

021

‘s ::

011 001

E

06

;

nn

F P

OL

& tf ,g

09 1

ZSl

.-P b

‘5

Sll

p E g

!3 z

001

09 OS

IV1

C

OEl

Fig. 7.

Ord

Valley

irrigation

Raingrown

Infrequent

19X5-86

1971-72

Valley

Ord

,

00 7

, P r

, :

Days from sowing

7

, E? 0

I

:

,

irrigation

irrigation

,

Solid circles are actual data, continuous

_YT_7-.-.-

z

Full

Frequent

1985-86

1971-72

Valley

Valley

0-l , 2 :

IOO-

(d)

150-

: 3 a

200-

(b) Namoi

Actual and simulated plant available water (PAW) in two irrigation experiments. simulated values.

(c)

(a) Namoi

lines are

OZCOT: a simulation model for cotton crop management

actual

Legend: green open

simulated

__ ___

A

squares

0 0

bolls bolls

(a) 1982-83 rain grown,

high N.

(b) 1982-83 limited

160

z’ “E

water,

high N.

160 E

E ; P t

281

120 80

ti 0 ii

40

I2

0

120 80 40 0

oo)u)*(Yo(Du) 0 0 (D m Days

0 F

from

Olc-3rcolnNO) Ob(Dcoul-O*

cy 0 In r v- r

Days

sowing

(c) 1982-83 full irrigation,

nil N.

from

irrr sowing

(d) 1982-83 full irrigation,

high N.

160,

m~(Dcom-mP r-r

Days

from

(e) 198586

sowing

raingrown.

140 E 120

Days

(f) 198586

from

sowing

full irrigation.

140 E 120

-4

;

100

a 80 u’ 60 “E z

40 20 0

Days

Fig. 8.

from

OV)Qu#00(010 (v(Dcoo)N~u)rc S-,-F%-

sowing

Numbers

of fruit in two Namoi

Days

from

sowing

Valley experiments.

yielded it. Actual and simulated yields are compared in Fig. 9, which shows that the model simulated the effect of date of sowing on yield exceptionally well. The functional relationship between actual and simulated yields is shown in Fig. 4b. The correlation coefficient was 0.973 with the parameters given in Table 5. The intercept and the slope do not show any significant bias. No data were available on components of yield, N uptake or LAI.

288

A. B. Hearn

5

AON-Or AONAON-

I

uo-or

VI

9

vo-oz 330-o

das-or

.2 x I

OZCOT: a simulation mqdel for cotton crop managementt

289

Raingrown cotton in Namoi Valley and Central Queensland The capability of OZCOT to reflect the year-to-year variation of raingrown cotton was tested with two sets of data. The first was a sub-set of the Namoi Valley nitrogen and irrigation experiments consisting of the raingrown treatments that were done in 9 of the 11 years. The experiments and simulation have already been described. A second data set was the yield of Deltapine 61 or 90 in 16 raingrown variety trials (P. Reid pers. comm.) done between 198 1 and 1991 in Central Queensland (lat. 2425%) and the Namoi Valley (lat. 30” 13’S). For simulation of the variety trial it was assumed that nitrogen was adequate and plant population was 12 per metre of row. The soil water holding capacity of the Narrabri Research Station was used. For the Namoi Valley soil water was initialised with a preirrigation. In Queensland the water balance was arbitrarily initialised 2 years before the trials and maintained through the winter in a sequence of alternating fallow/crop. Subroutine SOWDAY was used to simulate sowing at the first available opportunity. Simulated and actual yields are compared in Fig. 4c. The correlation between actual and simulated was not as close as with other data sets (R = 0.632), although still significant at the p = 0.001 level, and without bias (Table 5). When the data sets were examined separately, the correlation between actual and simulated yields was much closer in the raingrown subset of the Namoi nitrogen and irrigation experiments than in the raingrown variety trials (R = 0.843 vs. R = 0.672). The difference reflects using actual agronomic inputs in the nitrogen and irrigation experiments compared with assuming agronomic inputs for the variety trials, and variation in soil type associated with the wide geographical spread. Emerald irrigation and nitrogen experiment 1984-85 This data set is from three experiments done at Emerald (lat. 23” 5’ S) and reported by Ockerby et al., (1992) with four frequencies of irrigation and six rates of nitrogen fertiliser (O-300 kg ha-‘). The experiment was done at three sites, each with a different soil type differing in PAWC: AUg, TbUg and BUg with 100, 115 and 103 mm respectively between 0.15 and 0.85 m. The PAWC between 0 and 0.15 m was assumed to be the same per unit depth as for 0.15-0.25m layer. Below 0.85 m PAWC was assumed to decrease linearly to zero at 1.25 m for the AUg and TbUg soils. For the shallow BUg soil is it was assumed PAWC was nil below 0.85 m. The paper provided agronomic and climatic input data and rainfall for each site.

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The actual and simulated yields and the functional relationships between them are given in Fig. 4d for all sites pooled. Parameters for the relationship is given in Table 5. The prediction of yield is reasonable and without bias. When the sites are considered individually, there is much closer agreement for AUg and BUg than shown in Fig. 4d with correlation coefficients 0.908 and 0.795 respectively, but not for TbUg for which the correlation of 0.263 was not significant; clearly something was happening on the TbUg soil for which the model could not account. However, the model did predict an unexpectedly lower yield on the treatment irrigated at 50% PAW compared with irrigation at either 70°h or 30% PAW at the TbUg site as well as at the BUg site. There were no data on yield components. Functional relationships for nitrogen uptake for the season and maximum LA1 pooled across sites are given in Table 7. The correlation for N uptake is significant at p = 0.001 and at p = 0.05 for LAI. Both show a bias with slopes significantly more that unity and intercepts less than zero. LA1 was underestimated over the whole range but N uptake only at low levels. When the sites are examined separately there was little difference in agreement among them for N uptake but for LA1 the result was similar to that for yield, with no relationship for TbUg, suggesting that morphological development, which drives LA1 development, was poorly predicted. Ord River Valley irrigation and nitrogen 1971-1973

Hearn (1975a, b) reported two experiments done in each of two seasons in the Ord River Valley (lat. 15” 29’S). In one experiment the treatments were irrigation at three frequencies combined with two rates of nitrogen fertiliser in one year and three the next. In the other experiment the treatments were irrigation terminated at three stages of development and combined with four rates of nitrogen fertiliser. Each treatment was simulated using the actual agronomic management as input. In keeping with commercial practice then current (Hearn, 1975c), protection of the crop from insect pests was delayed until the end of the wet season. Loss of fruit resulting from pest damage allowed by this practice was simulated by multiplying the probability of fruit surviving by 0.1 (variable SURVIVE from equation (7)) until protection started. The PAWC for the soil profile given by Bridge & Muchow (1982) was used as input. Fig. 4e compares actual and simulated yields. The correlation coefficient between them for pooled data was 0.768 without bias (Table 5). Correlation was slightly closer for the fully irrigated subset in which the only agronomic variable was nitrogen and poorer for the maximum

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nitrogen subset in which the only agronomic variable was irrigation, reflecting the result reported with the Namoi Valley. Fig. 5b shows the interaction between rate of nitrogen and irrigation regime reported by Hearn (1975b) together with simulated values. As in the case of the Namoi experiments, the model clearly simulated the interaction but dampened it. Agreement between actual and simulated values was poorer for both boll numbers and boll weight (Table 6), although the correlation was still very highly significant. There was no bias for boll numbers but simulation of boll weight was biased as a result of over-estimating boll weight at low levels. Simulation of N uptake was good with the slope significantly but only marginally greater than unity (Table 7). Figs 7c and 7d show actual and simulated plant available soil water for two treatments. Agreement in the pattern of soil water depletion was good. The main aim of one experiment (irrigation terminated at three stages of development) was to investigate the effect on termination of crop growth with a view to reducing the duration of insecticidal protection and advancing the date of picking to minimise loss of quality from exposure of lint to weather. It is therefore of particular interest to observe how successfully OZCOT simulated the dates of defoliation and harvest. The actual and simulated patterns of boll opening with and without N fertiliser in fully irrigated treatments in 1971-72 and in 1972-73 are shown in Figs 1Oc and 10d respectively. Boll opening started later in the actual crops than in the simulated crops. The difference reflects inadequacy in the assumptions made about the amount of pest damage prior to the start of insecticidal protection. Boll opening was completed at similar times in actual and simulated crops, and differences between N treatments in final numbers of simulated bolls reflect actual differences, although much better in 1972-73 than in 1971-72. Crops were picked as soon as each plot was ready with the actual dates ranging from 23 June to 24 August. The simulated dates ranged from 18 June to 28 August with a correlation coefficient of 0.758 without bias (slope 0.76 with 95% confidence intervals 0.5-l ‘11; intercept 43; units day of the year). Murrumbigee Irrigation Area date of sowing 1961-1963 Saunt (1967) reported date of sowing experiments done in successive seasons at Griffith (lat. 34” 15’S) in the Murrumbidgee Irrigation Area (MIA). There were three dates of sowing in the first year and two the next, combined with two irrigation treatments. The soil is described as a loam, in contrast to the heavy clay vertisols on which all the other

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validation data sets were obtained, with PAWC of 150 mm in 1.2 m of soil. The variety was Empire which is an early ‘delta’ type variety with a large boll. It was assumed all varietal parameters except boll weight were similar to Deltapine 16. A boll weight (SC-BOLL) of 7.0 g was derived from the data set. Each treatment was simulated using the management data given in the paper. At first attempt the simulated crops were about 3 weeks later than the actual crops, and greatly underestimated actual yields. Agreement between actual and simulated phenology was obtained by modifying subroutine ISTSQ to disable cold shock and reduce the day degree requirement for squaring to 320. These seemingly arbitrary changes are justified on the grounds that Empire is earlier than the average ‘delta’ variety, and the loam soil has a lower total water holding capacity and warms up faster than a vertisol as air temperatures rise in spring; cold shock may relate as much to temperature of the soil as to that of the air. Correlation between actual and simulated yields and boll numbers was good (Fig. 4f; Tables 5 and 6) showing that OZCOT is sensitive to the effects of weather and water supply in this environment and can detect the decline caused by late sowing and the effect of irrigation. However, there was considerable bias, with slopes significantly less than unity and intercepts significantly more than unity. The bias is the result of overestimating the yield of the heavier yielding early sowings and suggests there is an additional factor limiting yields at this site not accounted for in the model. Figs 10a and lob shows actual and simulated boll numbers for the first and last sowing dates in each season. Adjustments in subroutine ISTQ clearly flowed through to simulate the start of boll setting accurately. The difference between sowing dates in final numbers set is also accurate, though in 1961-62 the level of actual is lower than the simulated.

GENERAL

DISCUSSION

Overall agreement between actual and simulated yields was good. Apart from the MIA, there was no bias in the estimates. It is concluded that OZCOT can predict the effects on cotton yield of climate, irrigation and nitrogen on the vertisols on which most of Australia’s cotton is produced. This result is encouraging considering that the model was developed in the Namoi Valley at lat 30” S and tested at locations ranging from the tropical north (Ord River, 15” S and Emerald, 23” S) to the more temperate south (MIA, 34” S), as well as the Namoi Valley itself. The model clearly identified the lower yield potential of the MIA

294

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compared with more northerly regions. An attempt was made to simulate historical commercial yields and variety trial yields in each region. The model clearly identified seasons (e.g. 1975-76, 197677, 1982-83) and regions (e.g. the Breeza Plains) with exceptionally low yields, but was unable to simulate normal year-to-year variation as clearly because of uncertainty about agronomic inputs. Correlations between actual and simulated yields within sub-sets of the irrigation and nitrogen experiments in the Namoi and Ord Valleys suggested that OZCOT can simulate N effects better than water effects. This may be an artifact of the way water and nitrogen effects are simulated. Water effects are more open ended than nitrogen effects which are constrained by OZCOT’s empirical estimate of seasonal uptake. Agreement for components of yield was also without bias, except for boll weight in the Ord valley, and was almost as close for boll numbers as for yield but not so close for boll weight. Poorer agreement for boll weight is expected for two related reasons. Firstly, number of bolls is more sensitive to environmental factors than boll weight. Consequently, most of the effect of agronomic treatments is produced by variation in boll number rather than boll weight by a factor of 2 or 3 to 1. Secondly, the closeness of fit expressed by the correlation coefficient is influenced by the range in the experimental data. Yield in the data-sets varied by a factor of 10, boll numbers by a factor of 8 and boll weight by a factor of 2. Where the range is small as in the case of boll weight it is difficult to get a close correlation. Where seasonal N uptake had been measured, correlation between actual and simulated values was very good, closer than for yield. However, there was a marked bias with a slope significantly greater than unity in all cases and an intercept less than zero in two cases out of three, resulting from under-estimation of uptake at low levels. It is postulated that this results from under-estimating the contribution of soil nitrogen and over-estimating that of fertiliser nitrogen. The need for a process-based nitrogen model is emphasised. Because research to this end is in hand, further tuning of the existing elementary model is not justified. Correlation between actual and simulated values of maximum LA1 was poor with a marked bias: slopes significantly greater than unity and intercepts less than zero, indicating an under-estimation of LAI, particularly at low levels. Crop simulation models frequently fail to estimate LA1 well. This shortcoming does not inhibit the model as a yield predictor, since LA1 is not a strong determinant of yield. LA1 has little influence above values of 2.5 because interception of radiation, and therefore rates of photosynthesis and transpiration, are approaching asymptotic values. In

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any case yield is nitrogen- rather than carbon-limited. The situation might be different with the more mechanistic nitrogen model under development and referred to below, in which the role of the leaf canopy as a reservoir of stored nitrogen might be more significant. It is instructive to consider the decreasing order of success in simulation of nitrogen uptake, yield, boll numbers and boll weight. The model is driven by weather and water supply but constrained by nitrogen supply. It is asserted that this truly reflects the real world priorities, but because of the limitations of the soil nitrogen uptake model this constraint is probably too rigid. The constraint enables the model to compensate for under- or over-estimates of numbers of bolls by increasing or decreasing boll weight. As a result yield is more closely simulated than numbers of bolls. This compensation confers a useful degree of homo-stasis to estimates of yield. Such compensation is in addition to that deliberately built into it to reflect fruiting dynamics resulting from the crop’s indeterminate habit to provide the capability of compensating for pest damage seen in the original model (Hearn & da Rosa, 1985). The experience with the MIA data suggests that OZCOT may be specifically calibrated for vertisols, as expected. Although most cotton in Australia is produced on vertisols, current research is aimed at making the model more general and applicable to other soil types by including a process-based nitrogen model. This development will remove the artificial constraint imposed by the empirical estimate of seasonal N uptake in the present model. It will also meet the needs for information on the risk of denitrification in the short term and depletion of soil nitrogen and organic matter in the long term in order to manage nitrogen in cotton production. Several applications of OZCOT are current. The hydroLOGIC irrigation decision support system for cotton is based on the model (Wells & Marsden, 1989) providing tactical support for a single field for a single year. As well as recommending the date of the next irrigation and the yield expected, the system allows the users to explore a large number of ‘what if scenarios, such as varying the irrigation water supply, nominating a date of next irrigation different from that recommended and selecting the future weather anticipated. OZCOT has been used for analysis of risk associated with decisions about the area of crop to grow with a limited water supply taking into account variable rainfall and for risks associated with raingrown cotton (Hearn, 1990a, b, 1992). Such studies have been extended to policy for reservoir management using OZCOT in a dynamic programming framework (Dudley & Hearn, 19934 b). A strategic water supply decision support system with such capability is being planned.

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The continued development of the model described by Hearn and da Rosa (1985) has been dictated by management needs and has consequently been ‘top down’ rather than ‘bottom up’. As more issues were addressed the model has become more complex, but no more than needed to provide information for management decisions. OZCOT does not purport to be a complete description of the soil, plant and atmospheric processes that constitute the cotton crop system. The results show that such ‘top down’ development can result in a simple yet powerful simulator. ACKNOWLEDGEMENTS I gladly acknowledge countless valuable discussions with many colleagues and I am particularly indebted to Greg Constable, Ken Brook, Geoff da Rosa, Luciano Mateos and Steve Marsden, who also assisted in the current calibration of the fruiting model.

REFERENCES Baker, D. N., Lambert, J. R. & McKinion, J. M. (1983). GOSSYM: a simulator of cotton crop growth and yield. Tech Bull., 1086, S. C. Agricultural Experiment Station, Clemson, South Carolina, USA. Basinski, J. J., Wetselaar, R., Beech, D. F. & Evenson, J. P. (1975). Nitrogen supply, nitrogen uptake and cotton yields. Cotton Grow. Rev., 52, l-10. Bridge, B. J. & Muchow, R. C. (1982). Soil water relationships for Cununurra clay and Ord sandy loam in the Ord River Irrigation Area. Tropical Agronomy Technical Memorandum, Number 30, CSIRO Division of Tropical Crops and Pastures, Brisbane. Brook, K. D., Hearn, A. B. & Kelly, C. F. (1992). Response of Cotton (Gossypium hirsutum L.) to damage by insect pests in Australia: manual simulation of damage. J. Econ. Entomol., 85, 1368-77. Brown, L. G., Jones, J. W., Hesketh, J. D., Hartsog, J. D., Whisler, F. D. & Harris, F. S. (1985). COTCROP: computer simulation of growth and yield. Mississippi Agricultural and Forestry Bulletin No. 69. Mississippi State, USA.

Experiment

Station,

Information

Constable, G. A. (1976). Temperature effects on the early field development of cotton. Aust. J. Exp. Agric. & Anim. Hush., 16, 905-10. Constable, G. A. (1986). Growth and light receipt by mainstem cotton leaves in relation to plant density in the field. Agric. & For. Meteorol., 37, 279-92. Constable, G. A. (1991). Mapping the production and survival of fruit on fieldgrown cotton. Agron. J., 83, 37478. Constable, G. A. & Hearn, A. B. (1981). Irrigation for crops in a sub-humid environment. VI. Effect of irrigation and nitrogen fertilizer on growth, yield and quality of cotton. Irrig. Sci., 3, 17-28.

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Constable, G. A. & Rochester I. J. (1988). Nitrogen application to cotton on clay soil: timing and soil testing. Agron. J., 80, 498-502. Constable, G. A., Harris, N. V. & Paull, R. E. (1976). The effect of planting date on yield and some fibre properties of cotton in the Namoi Valley. Aust. J. Exp. Agric. Anim Husb., 16, 265-71. Cull, P. O., Smith, R. C. G. & McKaffery, K. (1981). Irrigation scheduling of cotton in a climate of uncertain rainfall. II. Development and application of a model for irrigation scheduling. Zrrig. Sci., 52, 141-54. Doorenbos, J. and Pruitt, W. 0. (1977). Guidelines for predicting crop water requirements. F. A. 0. Irrigation and Drainage Paper. F. A. O., Rome. Dudley, N. J. & Hearn, A. B. (1993~). Systems modelling to integrate river valley and water supply and irrigation decision making under uncertainty. Agricultural Systems, 42, 3-23. Dudley, N. J. & Hearn, A. B. (19936). El Nino effects hurt Namoi cotton growers, but they can do little to ease the pain. Agricultural Systems, 42, 103-26. Freebairn, D. M., Hancock, N. H. & Lott, S. C. (1986). Soil evaporation studies using shallow weighing lysimeters: techniques and preliminary results. Conference on Agricultural Engineering, Adelaide, S. Australia, 24-28 August, 1986. The Institution of Engineers, Sydney, Australia. Hearn, A. B. (1972). The growth and performance of raingrown cotton in a tropical upland environment. I. Yields, water relations and crop growth. J. Agric. Sci., Camb., 79, 121-35. Hearn, A. B. (1975a). Response of cotton to water and nitrogen in a tropical environment. I. Frequency of watering and method of application of nitrogen. J. Agric. Sci., Camb., 84, 407-17. Hearn, A. B. (1975b). Response of cotton to water and nitrogen in a tropical environment. II. Date of last watering and rate of application of nitrogen fertilizer. J. Agric. Sci., Camb., 84, 419-30. Hearn, A. B. (1975~). Ord Valley cotton crop: development of a technology. Cotton Grow. Rev., 52, 77-102. Hearn, A. B. (1986). Effect of preceding crop on the nitrogen requirements of irrigated cotton (Gossypium hirsutum L.) on a vertisol. Field Crops Res., 13, 159-75. Hearn, A. B. (1990a). Climatic Risk in Australian Cotton Production. Models and Management in the Semi-Arid Tropics and Subtropics, eds R. C. Muchow & J. A. Bellamy. Poster papers from the International Symposium, Brisbane, 2-6 July, 1990, pp. 48849. CSIRO Division of Tropical Crops and Pastures, Brisbane. Hearn, A. B. (19906). Prospects for rainfed cotton. Fifth Australian Cotton Conference, Broadbeach, 8-9 August, 1990, pp. 135-144. ACGRA, Wee Waa. Hearn, A. B. (1992). Risk and reduced water allocations. The Australian Cotton Grower, 13(4), 50-5. Hearn, A. B. & Room, P. M. (1979). Analysis of crop development for cotton pest management. Prot. Ecol., 1, 265-77. Hearn, A. B. & Constable, G. A. (1981). Irrigation for crops in a sub-humid environment. V. Stress day analysis for soybeans and an economic evaluation of strategies. Zrrig. Sci., 3, 1-15. Hearn, A. B. & Constable, G. A. (1984). Irrigation for crops in a sub-humid

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environment. VII. Evaluation of irrigation strategies for cotton. Zrrig. Sci., 5, 75-194. Hearn, A. B. & da Rosa, G. D. (1985). A simple model for crop management applications for cotton (Gossypium hirsutum L.). Field Crop Rex, 12, 49969. Hesketh, J. D. & Low, A. (1968). Effect of temperature on components of yield and fibre quality of cotton varieties of diverse origins. Cott. Grow. Rev., 45, 243-57.

Hesketh, J. D., Fry, K. C., Guinn, G. & Mauney, J. R. (1972). Experimental aspects of growth modelling: potential carbohydrate of cotton bolls. In Proceedings of a Workshop on Tree Growth Dynamics and Modelling, ed. C. Murphy, Duke University, Ott 12, 1972, pp. 123-127. Hesketh, J. D., McMichael, B. L. & Teramura, A. (1977). Temperature studies of axillary branch growth and leaf duration. Proc. Beltwide Cotton Prodn. Res. Conf, Atlanta Ga. National Cotton Council of America, Memphis, TN 38112. Hodgson, A. S. (1982). The effects of duration, timing and chemical amelioration of short-term waterlogging during furrow irrigation of cotton in a cracking grey clay. Aust. J. Agric. Res., 33, 1019-28. Horie, T. (1977). Simulation of sunflower growth. I. Formulation and parameterisation of dry matter production, leaf photosynthesis, respiration and partitioning of photosynthates. Bull. Nat. Inst. Agric. Sci. (Japan) Series A, 1, l-54. Ives, P. M. & Hearn. A. B. (1987). The SIRATAC system for cotton pest management in Australia. In Crop Loss Assessment and Pest Management, ed. P. S. Teng, APS Press, St Paul, Minnesota. Kendall, Sir M. & Stuart, A. (1979). The Advanced Theory of Statistics, Vol. 2, 4th Edn. Griffin, London. Lemon, H. (1986). Comax: an expert system for cotton crop management. Science, 233, 29-33.

McMichael, B. L. & Hesketh J. D. (1982). Field investigation of the response of cotton to water deficits. Field Crops Rex, 5, 319-33. Mutsaers, H. J. W. (1976). Growth and assimilate conversion of cotton bolls II. Influence of temperature on boll maturation period and assimilate conversion. Ann. Bot., 40, 301-I 5. Mutsaers, H. J. W. (1982). KUTUN, a morphogenetic model for cotton Gossypium hirsutum L. Doctoral thesis, Agricultural University, Wageningen. Murtagh, B. A. & Saunders, M. A. (1980). MINOYAugmented User’s Manual. Technical Report SOL 80-14, Stanford University, Stanford, California. Ockerby, S. E., Lyons, D. J., Keefer, G. D. & Blarney, F. P. C. (1992). Responses to irrigation frequency and nitrogen fertiliser in field grown cotton. Aust. J. Agric. Rex, 44, 1389-1402. Priestley, C. H. B. & Taylor, R. J. (1972). On the assessment of surface heat flux and evaporation using large-scale parameters. Monthly Weather Review, 100, 81-92. Ritchie, J. T. (1972). Model for predicting evaporation from a row crop with incomplete cover. Water Resources Research, 8, 1204-13. Ritchie, J. T. (1991). Specifications for the ideal model for predicting crop yields. In Climatic Risk in Crop Production, eds R. C. Muchow, 8c J. A. Bellamy, C.A.B. International, Wallingford, UK, pp. 97-122.

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Rosenthal, W. D., Arkin, G. F., Shouse, P. J. and Jordan, W. R. (1987). Water deficit effects on transpiration and leaf growth. Agron. J., 79, 1019-26. Saunt, J. E. (1967). Sowing date, development and yield of cotton in the Murrumbidgee Irrigation Areas, New South Wales. Cotton Grow. Rev., 44, 2-22. Stapper, M. & Arkin, G. F. (1980). CORNF: a dynamic growth and development model for maize (Zea mays L.), Program and Model Documentation No. 80-2. Texas Agricultural Experiment Station, College Station, Texas. Stern, W. R. (1965). The seasonal growth characteristics of irrigated cotton in a dry monsoonal environment. Amt. J. Agric. Rex, 16, 347-86. Talpaz, H., da Rosa, G. D. & Hearn, A. B. (1987). Parameter estimation and calibration of simulation models as a non-linear optimisation problem. Agric. Sys., 23, 107-16. Turner, N. C., Hearn, A. B., Begg, J. E. & Constable, G. A. (1986). Cotton (Gossypium hirsutum L.): physiological and morphological responses to water deficits and their relationship to yield. Field Crops Rex, 14, 153-70. Walhood, V. T. & Addicott, F. T. (1968). Harvest-aid programs: principles and practices. In Advances in Production and Utilization of Quality Cotton: Principles and Practices. eds. F. C. Elliot, M. Hoover, & W. K. Porter, Iowa University Press, Ames, pp. 40743 1. Wallach, D. (1978). A simple model of cotton yield development. Field Crops Res., 1, 269-8 1. Wang, Y., Gutierrez, A. P., Oster, G. & Daxl, R. (1977). A general model for plant growth and development: coupling plant herbivore interaction. Can. Ent., 109, 1359-74. Wells, A. T. & Marsden, S. G. (1989). hydroLOGIC. Australian Cotton Grower, 10(3), 7-9. Wilson, L. T. Gutierrez, A. P. (1980). Fruit predation submodel: Heliothis larvae feeding upon cotton fruiting structures. Hilgardia, 48, 2436. Wright, J. L. & Jensen, M. E. (1978). Development and evaluation of evapotranspiration models for irrigation scheduling. Trans. ASAE, 88, 91.