Comparison of water extraction models for grain sorghum under continuous soil drying

ELSEVIER

Field Crops Research 36 (1994) 145-160

Field Crops _ Research

Comparison of water extraction models for grain sorghum under continuous soil drying M.J. Robertson a'*, S. Fukai b ~CSIRO, Division of Tropical Crops and Pastures, Private Bag, P.O. Aitkenvale, QId. 4814, Australia bDepartment of Agriculture, Universi~_ of Queensland, Brisbane, Qld,, Australia

(Received 2 June 1993; accepted 11 January 1994)

Abstract The aim of this study was to compare three contrasting models of water extraction, by comparing predictions of the models with water extraction observed under continuous soil drying from seven crops of grain sorghum in the field. Sensitivity of the model predictions to variation in evaporative demand, and soil and root characteristics were also assessed. The datasets covered soil types ranging from 68 to 252 mm of total extractable soil water (TESW), and levels of mean evaporative demand ranging from 1.8 to 4.9 mm d ~. The first model was based on the simple function relating daily relative transpiration rate (RTR), the ratio of transpiration to demand, to the fraction of extractable water (FESW) in the maximum root zone of 200 cm, where RTR declined from 1.0 to zero as FESW fell from 0.3 to zero. The second model was the same as the first, except that RTR depended on FESW in the current root zone, where the current root zone was assumed to increase by 3 cm d ~ from emergence to reach 200 cm at anthesis. The third, more complicated model calculated daily transpiration as the lesser of potential extraction and transpirational demand, with potential uptake calculated in each soil layer from root-soil diffusivity and simulated root length density. Inputs of transpirational demand and extractable soil water contents were the same for all models. All models gave good predictions of the observed pattern of RTR and cumulative extraction in the seven crops studied, despite the differences in the level of detail specified within the models. The results indicated that in most situations, RTR will decline once FESW in the maximum rooting depth reaches around 0.3. Sensivity analysis revealed that this threshold will change substantially where crops are growing on a low TESW soil under high demand, or on a high TESW soil under low demand. Of the soil and root characteristics assessed, the threshold FESW at which RTR declined was most sensitive to the downward rate of root front penetration, rather than the density of rooting or the root-soil diffusivity. This study confirms the robustness and validity of the simple relationship between RTR and extractable soil water currently used in many crop growth models. Use of the more detailed model showed under which situations the form of this relationship is likely to change. Key words: Root; Simulation; Soil water; Sorghum: Transpiration

I. Introduction W a t e r extraction by roots is an important c o m p o n e n t o f crop growth simulation in water-limiting e n v i r o n ments. Various approaches have been used to simulate *Corresponding author. 0378-4290/94/$07.00 © 1994 Elsevier Science B.V. All rights reserved S S D 1 0 3 7 8 - 4 2 9 0 ( 9 4 ) 00003-U

the extraction o f water in plant growth models, ranging f r o m m o d e l l i n g extraction at the whole-profile level (e.g. Sinclair, 1986) to the level o f individual roots (e.g. H u c k and Hillel, 1983), but there have been few attempts to c o m p a r e and contrast water extraction m o d els that differ in c o m p l e x i t y , and determine under w h i c h conditions they are likely to differ in predictions.

146

M.J. Robertson, S. Fukai / Field Crops Research 36 (1994) 145-160

This paper focusses on an important feature of water extraction models, i.e. the determination of the onset of the decline in transpiration rate when water supply becomes limiting. A relationship between the relative transpiration rate (RTR) and the degree of soil drying is a commonly used simple approach to simulating the rate of water extraction (i.e. the crop transpiration rate). The relative transpiration rate is the ratio of actual transpiration to transpirational demand, and is unity when demand is matched by extraction. Transpirational demand is defined as the potential transpiration (Ep) corrected for the fraction of crop cover. Thedegree of soil drying is expressed by the fraction of extractable water out of either the potential store of extractable water in the current root zone (FESWR) or the potential store in the totalprofile ( F E S W T ) , i.e. the maximum root depth (Tanner and Ritchie, 1974). Both approaches assume that RTR does not fall below unity until FESW declines below some threshold value. A number of studies, spanning a wide range of crop species and soil types, have shown that RTR remains at around unity under soil drying until FESWT reaches a threshold of about 0.3-0.4 (e.g. for sorghum: Kanemasu et al., 1976; Wright and Smith, 1983). The study of Rosenthal et al. (1987) provided support for the use of the second function that assumes that RTR is unity until FESWR is below 0.3-0.4. The FESWR approach has greater biological validity than the FESWT approach because transpiration is responsive to the soil water status of the current root zone rather than to that of the maximum root zone depth. Crop growth models differ in whether they use the FESWT (e.g. Muchow and Sinclair, 1991 ) or the FESWR approach (e.g. Hammer and Muchow, 1991 ), and there has been no comparison of the two approaches in their accuracy of predicting extraction. Predictions from the two models would be expected to differ most in early stages of crop growth when the depth of the root zone differs considerably from its maximum depth. A more complicated approach to predicting extraction has been proposed by Monteith (1986) and Monteith et al. (1989), and has been tested for sunflower (Meinke et al., 1993) and sorghum (Robertson et al., 1993a,b). In this approach, the crop transpiration rate is computed as the lesser of the potential extraction rate and transpirational demand, as employed in crop growth models such as CERES (Ritchie, 1985). The

potential extraction rate from the profile is calculated from the sum of the potential root water uptake from each occupied layer of the profile, and is influenced by the distribution of root length and water in the root zone. This type of model (hereafter called the ROOT model), in contrast to the FESW models, takes account of the level of transpirational demand and the role of soil and root characteristics in determining whether extraction can match demand. When potential supply exceeds demand, transpiration equals the demand, as is also the case in the FESW models. When supply becomes less than demand, the ROOT model calculates extraction as the potential extraction rate from the root zone without reference to demand, whereas in the FESW models during this phase, extraction is a function of soil water status and the level of demand. Comparision of this model with the simpler FESW model may show whether the relationship between RTR and FESW would differ due to variation in demand, and soil and root characteristics. The aim of this study is to compare and contrast these three models of water extraction in terms of the prediction of the decline in RTR under continuous soil drying. The two specific objectives are to ( 1 ) compare model predictions with water extraction observed from seven crops of grain sorghum (Sorghum bicolor (L.) Moench), and (2) describe the sensitivity of the model predictions to variation in evaporative demand, and soil and root characteristics.

2. Description of the models 2.1. The F E S W r and F E S W R models

These models assume that the rate of transpiration is equal to demand until FESW reaches a threshold of 0.3. Subsequently, the RTR declines linearly to zero at zero FESW. In the FESWT model, FESW is defined as the total extractable water (mm) in the maximum root zone depth (taken as 200 cm for sorghum) divided by the potential extractable water (i.e. when the soil is at the upper limit) in that depth. In the FESWR model, FESW is defined as the total extractable water in the current root zone depth divided by the potential extractable water in that zone. For both models, potential extractable water contents are input for each layer in the 200cm-deep profile. Extractable soil water is defined as the

M.J. Robertson, S. Fukai / Field Crops Research 36 (1994) 145-160

difference between the water content of the profile when drained after a thorough wetting (the "upper limit") and the water content of the profile after a healthy, fully-grown crop has extracted all the water possible (the "lower limit" ) (Ritchie, 1981 ). The profile is divided into two 10-cm-deep layers at the surface and nine 20-cm-deep layers. In the FESWR model, the depth of the root zone is calculated by assuming that the root zone depth increases with a velocity of 3 cm d - l from a depth of 5 cm at emergence until it reaches a maximum depth of 200 cm (Monteith, 1986; Squire et al., 1987; Robertson et al., 1989, 1993a). In both FESW models, the daily rate of extraction is calculated as the product of RTR, which depends on FESW, and the transpirational demand. Transpirational demand is estimated as the dally rate of Ep calculated from observed weather inputs, adjusted for the extent of crop cover by multiplying by the observed daily values of fractional radiation interception. Potential transpiration is estimated by the Penman (1948) equation using the algorithms of Meyer et al. (1987), and a wind function for grain sorghum from Rosenthal et al. (1989). Soil evaporation is calculated using a variant of the two-stage model of Ritchie (1972). Stage I evaporation is assumed to occur for one day after the soil surface is wetted. Soil evaporation rate is calculated from the Penman equation and is based on the amount of solar radiation which penetrates the crop canopy. During Stage II the evaporation rate declines with the square root of time with a drying coefficient of 3 mm d -°5. Soil evaporation losses are subtracted from the soil water content of the two uppermost 10-cm layers each day, after accounting for extraction losses. The soil water content in the two top layers is allowed to go below the lower limit of extractable water content, so that under lengthy drying cycles the quantity of water removed from the profile can be slightly greater than the potentially extractable water.

2.2. The ROOTmodel In this model, the daily rate of water extraction from the profile is calculated as the lesser of the potential

147

extraction rate and the transpirational demand. If the computed potential extraction from the profile exceeds demand, then the extracted water is removed from the occupied layers in proportion to the values of potential root water uptake in each layer. If the computed potential extraction from the profile is less than the demand, actual root water uptake from a layer is equal to the computed potential uptake. Potential extraction is computed as the sum of root water uptake from each profile layer occupied by roots. The potential root water uptake from each layer is calculated by assuming that the extractable water content in a layer declines exponentially with time after the arrival of the root front. The rate of exponential decline is defined by a rate constant, which is calculated as the product of root length density (1, cm c m - 3) in the layer and the root-soil diffusivity (k, cm 2 d - l) (Passioura, 1983; Monteith, 1986; Robertson et al., 1993a). The simulation of I in this model for each occupied layer follows the steps in the root growth sub-model described by Robertson et al. (1993c). The depth of the root front descends with a velocity of 3 cm d from sowing until it reaches 200 cm depth, in the same manner as used in the FESWR model. The daily growth in total root length is calculated from the inputted mean daily above-ground growth rate of the crop, using a root growth partitioning factor (R) of 0.013 km (root) g-~ (biomass). The new root length is allocated to each soil layer using a distribution function that declines exponentially with depth, and is limited by low soil water content in dry layers. Root length is lost each day at a fixed death rate of 1%. Transpirational demand and soil evaporation are calculated as in the FESW models. The inputs of potential extractable water in each soil layer, dally weather variables, and daily fractional radiation interception were the same as in the FESW models. In addition, the daily above-ground crop growth rate was input in order to calculate the growth of the root system, and a value of k was inputted for each soil layer. In the model, it is assumed that k declines with depth in the profile, in order to take account of the lower efficiency of roots at taking up water deep in the profile (Passioura, 1983; Meinke et al., 1993; Robertson et al., 1993a).

148

M.J. Robertson, S. Fukai / FieM Crops Research 36 (1994) 145-160

3. Materials and methods

3.1. Data sets of response of water extraction to soil drying The three models outlined above were tested on seven crops where the response of water extraction by grain sorghum to continuous soil drying was measured. Relevant summary information on the data sets is given in Table 1, and the soil information is given in Table 2. All crops were grown under optimal agronomy.

Redland Bay 1987 and 1989 Three of the datasets were obtained from two sowings that were conducted in 1987 and 1989 at Redland Bay, S.E. Queensland, Australia (27°37'S) (Robertson et al., 1993a). The soil was a deep oxisol with low extractable water content (Table 2). Crops were well-watered until they established and then subjected to continuous soil drying by means of an automatic rain shelter. In the 1987 sowing, the drying cycle was from 28 to 66 days after sowing (das). In the 1989 sowing, the drying cycle was from 22 to 102 das. In the 1989 sowing, the effect of a reduction in demand on water extraction was investigated by shading half of the plots to 30% of full sunlight with sarlon shade cloth from 42 to 65 das. In 1987 Ep was moderate at 4.2 mm d - i, and low at 2.9 and 1.8 mm d - ~in the unshaded and shaded treatments in 1989. Soil water content was measured gravimetrically for the 0-20-cm soil layer, and below this depth by neutron moderation at 10-20-cm depth intervals to 200 cm, every 3-4 days during the drying cycle. Evapotranspiration rate was calculated from the change in profile water content between neutron moisture meter measurements. Deduction of values for soil evaporation and deep drainage over the same periods yielded an estimate of the transpiration rate. Soil evaporation was estimated using the Ritchie (1972) model as described earlier. Ritchie's ( 1981 ) method of accounting for profile drainage was used. This method uses the theory of Black et al. (1969), which describes drainage rate as a function of the total profile water content (~9) following the equation: D = 0 . 0 5 e x p [ B ( ~ 9 - ~gd) ], where D is the drainage rate in cm d J, B is a constant,

Od is the average profile soil water content when D = 0.05 cm d - i. Data were collected to derive B and ~gdby measuring over a 13-day period the rate of water loss from a saturated profile, which was covered in plastic. The values of B and ~gd for a drained upper limit at 0.05 cm d - ~ were 390 cm d - 1 and 0.322 cm 3 c m - 3, respectively. Runoff was assumed negligible, as the site was fiat and the soil has a high infiltration rate. RTR for each 3-4-day period was calculated by dividing the transpiration rate by demand, where transpirational demand was equal to Ep multiplied by the fractional radiation interception.

Hyderabad 1988 This crop was the high-nitrogen dryland treatment of the WINE experiment, which was conducted during the 1988-89 dry season at ICRISAT Center, Hyderabad, India (17°27'N) (P. Singh, Resource Management Program, ICRISAT Center, Hyderabad, pers. commun.). The soil was a deep vertisol with a moderately high extractable water content (Table 2). The crop was well-watered until 28 das, and thereafter subjected to continuous soil drying. Potential transpiration was moderate at 4.0 mm d - ~. Profile water content was measured every 7-10 days using gravimetric and neutron moderation techniques. Evapotranspiration rate and RTR was calculated in the same manner as for the Redland Bay sowings, but deep drainage was assumed to be negligible as there was no apparent change in water content of the deepest measured layer in the profile. Temple 1969 This refers to the sorghum crop grown at Temple, TX, USA (31°03'N) in 1969 reported by Ritchie ( 1971 ) and Ritchie and Bumett ( 1971 ). The soil was a deep vertisol with high extractable soil water content (Table 2 ). The crop received rain until 62 das; thereafter it was subjected to continuous drying. The rate of water use was measured by lysimeter and transpiration rates were computed by Ritchie and Burnett ( 1971 ) by deducting an estimate of the rate of soil evaporation. Weather data are given by Ritchie (1971). Potential transpiration was moderately high at 4.9 mm d-~ due to a high saturation deficit of 2.6 kPa.

M.J. Robertson, S. Fukai / Field Crops Research 36 (1994) 145-160

149

Table I Location, sowing date, duration of the drying cycle, crop characteristics, and mean weather variables for the drying cycle, for the seven crops used to compare the models Location

Redland Bay

Redland Bay

Redland Bay

Hyderabad

Temple

Kalamazoo

Kalamazoo

Sowing date Treatment Drying cycle (days after sowing)

17 Nov. 87

16 Jan. 89 Shade 22-102

29 Oct. 88

10 April 69

28-66

16 Jan. 89 No shade 22-102

12 May 92 Clay loam 46-109

12 May 92 Sand 74-109

Crop characteristics Crop duration (days) Plant population (m 2) LAI at anthesis

90 20 4.2

103 20 2.0

103 20 2.0

95 16 2.9

105 20 2.8

125 20 3.0

125 20 3.0

Weather Minimum temp (°C) Maximum tem (°C) Radiation (MJ m 2) Saturation deficit (kPa) Ep (mm d- i)

21.2 28.3 24.1 1.1 4.2

19.1 27.3 17.1 0.8 2.9

19.1 27.3 10.1 0.8 1.8

13.6 28.5 16.6 2.1 4.0

18.8 30.7 20.0 2.6 4.9

12.6 25.1 19.8 1.8 3.5

13.2 24.6 17.6 1.6 3.1

30-95

62-105

Table 2 Extractable soil water content (cm3 cm -3) for profile layers and total for the 0-200 profile (mm) for the three locations Location

Redland Bay

Hyderabad

Temple

Kalamazoo

Soil type

Eutrosox~

Pellustertb

Pellusterta

Soil texture

Clay

Clay

Clay

Psammentic Hapludall~ Sand

Layer depth (cm) 0-10 10-20 20--40 40~0 60-80 80-100 100-120 120-140 140-160 160-180 180-200 Total extractable soil water (0-200 cm) (mm)

0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.04 0.03 0.01 86

0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.09 0.06 0.03 0.01 182

0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.11 0.08 0.02 252

0.07 0.07 0.06 0.05 0.04 0.03 0.03 0.02 0.02 0.01 0.01 68

Typic Hapludalff Silty clay

0.15 0.15 0.13 0.08 0.06 0.05 0.05 0.03 0.03 0.02 0.02 124

Sources: aRitchie et al. (1972), bp. Singh, ICRISAT Center, Hyderabad, pers. commun. (1992), CRobertsonet al. (1993a), dNeSmith and Ritchie (1992), ~J.T. Ritchie, Michigan State University, East Lansing, pers. commun. (1992). K a l a m a z o o 1992 G r a i n s o r g h u m cv. T x - 6 1 0 w a s g r o w n on t w o adjac e n t soil t y p e s u n d e r an a u t o m a t i c rain shelter n e a r K a l a m a z o o , MI, U S A . T h e t w o soils w e r e a d e e p clay loam ( T y p i c H a p l u d a l f ) and a d e e p s a n d y l o a m

( s a n d y , m i x e d , m e s i c P s a m m e n t i c H a p l u d a l f ) that diff e r e d b y 56 m m in the a m o u n t o f e x t r a c t a b l e soil w a t e r in the 2 0 0 - c m profile. T h e c r o p s w e r e s o w n o n 12 M a y 1992 and k e p t w e l l - w a t e r e d until 46 das on the clay l o a m and 74 das o n the s a n d y l o a m , after w h i c h rainfall

150

M.J. Robertson, S. Fukai / Field Crops Research 36 (1994) 145-160

was excluded by the rain shelter until 109 das. Potential transpiration was low-moderate at 3.1 and 3.5 mm d - l for the clay loam and sand, respectively. Potential transpiration differed between soil types because of differing durations of the drying cycle. Profile water content was measured every 3-4 days using neutron moderation in three access tubes in each soil type. Soil water content in the 0-20-cm layer was determined by time domain reflectometry (Techtronix model 1502). Evapotranspiration rate and RTR were calculated in the same manner as for the Redland Bay sowings, but deep drainage was assumed to be negligible as there was no apparent change in the water content of the deepest measured layer in the profile. For each crop, Ep was calculated from daily minimum and maximum temperature, solar radiation, wind run, and saturation deficit. The measured daily saturation deficit was only available for the Redland Bay and Temple sowings, and so for the other sowings it was estimated as 0.75 of the difference between saturated and actual vapour pressures calculated from daily maximum and minimum temperatures (Tanner and Sinclair, 1983). Transpirational demand was calculated by multiplying Ep by daily values of fractional radiation interception, which was obtained by interpolating between midday fractional radiation interception measured at 1-10-day intervals. At Hyderabad, fractional radiation interception was not available and so was calculated from measurements of leaf area index obtained at the biomass harvests and assuming a radiation extinction coefficient of 0.4 (Muchow, 1988). Crop growth rates derived from samples of aboveground biomass taken every 7-14 days in all crops were used to drive the ROOT model.

value was also assumed for the sandy alfisol at Kalamazoo as it has a similar extractable water content. For the vertisols at Hyderabad and Temple, k was calculated as 0.03 cm 2 d - 1 based on measured values of kl in the upper profile for the vertisol at Hyderabad of 0.015 d - i (Monteith, 1986) and estimated average l of 0.5 cm c m - 3 (Robertson et al., 1993c). In estimating k for the clay loam at Kalamazoo we used as a guide the finding of Meinke et al. (1993) that across soil types, kl is positively related to the percentage clay content of the soil. Hence the k value for the clay loam alfisol at Kalamazoo was assumed to be 0.08 d-1, which is intermediate to the values for the sandy alfisol and the vertisols. On all soils, it was assumed that below 100 cm depth, k declines with depth in the profile to reach a negligibly small value at 200 cm depth. Each model was run from the date of sowing without the water balance until the date when continuous soil drying began. On that date it was assumed that the soil was at the upper limit, except for the Temple sowing where the soil was initialised at the observed extractable water contents. Outputs from the models on each day during the drying cycle were the cumulative amount of water extracted (transpiration plus soil evaporation), the fraction of extractable water in the root zone, and RTR. The output from the models was compared with observations of the relationships between: (1) RTR and cumulative water extracted, and (2) cumulative water extraction and time after sowing. The accuracy of prediction was assessed using the root mean squared deviation (RMSD) between a number ( n ) of predicted (P) and observed (O) paired results where

3.2. Simulation of experiments

The RMSD is a measure of the accuracy of prediction and represents a mean weighted difference between predicted and observed data. As transpirational demand is calculated similarly in all three models, RSMD was calculated during the supply-limiting phase (observed RTR less than 1.0) when the three models differ in their calculation of extraction.

The three models described above were run for each of the seven crops listed in Table 1, using a daily timestep. Inputs to the three models were daily demand, and for the ROOT model daily above-ground crop growth rate. The soil inputs required by the three models were the extractable soil water content (Table 2) and, for the ROOT model only, the root-soil diffusivity (k) for each layer in the 200-cm profile. The value of k in the upper profile for the oxisol at Redland Bay was taken to be 0.20 cm 2 d - l (Robertson et al., 1993a). This

R M S D = [ (~,( O - p)2) /n) ] °'5.

3.3. Sensitivity analysis In addition to simulating the seven data sets, simulations were run to test the sensitivity of the ROOT model to variation in the parameter values. The para-

M.J. Robertson, S. Fukai / Field Crops Research 36 (1994) 145-160

meters varied were the root front velocity (RFV), the root growth partitioning factor (R) and the root-soil diffusivity (k). The model was run with the value of each parameter increased or decreased by 20%, holding all other parameters at their standard values. Simulations were conducted for a range of levels of potential evaporation, which was varied by changing the saturation deficit; and for two soil types, varying in the amount of total extractable soil water (TESW) in the 200-cm profile. To calculate demand from Ep in the sensitivity analysis, a generalised fractional interception pattern was used with a peak value of 0.8 attained

Redland Bay 1987 1.5

(a) 0

/

0

•

/

•

4. Results

•

4.1. Simulation of data sets

s

0.5

0.0

I

I

I

I

20

40

60

80

100

C u m u l a t i v e w a t e r e x t r a c t e d (ram) 100

(b) "O

o

-O

80

o

60 ¢$

at 50 das, declining to 0.5 at maturity ( 100 das). The daily above-ground crop growth rate, needed to simulate the growth of the root system, was derived as the product of the rate of transpiration and the transpiration efficiency defined as the transpiration efficiency coefficient divided by the saturation deficit (Tanner and Sinclair, 1983). The transpiration efficiency coefficient was set at 9 Pa (Hammer and Muchow, 1991 ). Simulations were also run with the FESWT and FESWR models to test the sensitivity of the amount of water transpired to variation in the chief parameters. For the FESWT model the standard 0.3 FESW threshold was varied and for the FESWR model the 0.3 FESW threshold and the standard RFV of 3 cm d-~ were varied. Simulations were conducted for a range of levels of Ep and for two soil types, as described above.

1.0 i

o

151

40

20

0

v

20

30

40 Days after

50

60

70

sowing

Fig. I. Observed data and model predictions for (a) relative transpiration rate versus cumulative water extracted, and (b) cumulative water extracted versus days after sowing lbr the 1987 crop at Redland Bay. Error bars are twice the standard error of the mean, and are shown for every second observation of the cumulative water extracted. FESW-r model ( - - ) FESW R model ( - - - - ) ROOT model ( . . . . ), observed data (@).

The sowings covered a 4-fold range in the amount of extractable soil water in the 200-cm profile and a more than 2-fold range in transpirational demand (Tables 1 and 2). The TESW in the 200-cm profile was highest for Temple ( 252 mm), followed by Hyderabad (182 ram), clay loam at Kalamazoo (124 mm) and Redland Bay sowings (86 mm) with the lowest value for the sandy loam at Kalamazoo (68 mm) (Table 2). The highest transpirational demand was experienced by the Temple crop, followed by Hyderabad, the 1987 sowing at Redland Bay, and the two crops at Kalamazoo. The 1989 sowing at Redland Bay experienced the lowest Ep of 2.9 mm d - i , and the shaded treatment of this sowing had a very low demand. In the 1987 crop at Redland Bay, observed RTR began to decline after 50-60 mm had been extracted from the profile (Fig. la). The three models predicted the pattern of RTR similarly (Table 3). All models over-predicted RTR and hence cumulative extraction in the middle stages of the drying cycle, but correctly predicted the final amount of water extracted (Fig. I b). The large scatter in the observed RTR values around the RTR = 1 line early in the drying cycle is probably due to random errors in readings from the neutron moisture meter. In the unshaded treatment of the 1989 crop at Red-

152

M.J. Robertson, S. Fukai / Field Crops Research 36 (1994) 145-160

Table 3 Root mean squared deviations for the model fits to observed (a) relative transpiration rate, and (b) cumulative water extracted during the supply-limiting phase Model Data set

(a) Relative transpiration rate Redland Bay 1987 Redland Bay 1989 Unshaded Redland Bay 1989 Shaded Hyderabad Temple Kalamazoo clay loam Kalamazoo sand (b) Cumulative water extracted (mm) Redland Bay 1987 Redland Bay 1989 Unshaded Redland Bay 1989 Shaded Hyderabad Temple Kalamazoo clay loam Kalamazoo sand

FESWr

FESWR

ROOT

0.19 0.27 0.39 0.23 0.11 0.30 0.38

0.21 0.29 0.39 0.23 0.11 0.30 0.38

0.23 0.25 0.42 0.26 0.10 0.25 0.30

13.0 7.5 5.1 4.0 16.8 3.1 5.4

land Bay, RTR declined once about 70 mm had been extracted from the profile (Fig. 2a). The decline occurred at a later stage than in the 1987 sowing at Redland Bay presumably because the demand was lower. The prediction of the decline in RTR was simulated less accurately by the ROOT model than by the two FESW models (Fig. 2a). The two FESW models did not differ in the simulation of RTR decline, because observed RTR did not decline until after the root front was at its maximum depth. The RSMD values for cumulative extraction, however, did not differ greatly (7.5-10.7 mm) (Table 3), presumably because the differences in RTR did not translate into substantial differences in total extraction because demand was low at around 2 mm d - ~. Shading during 42-65 das in the 1989 crop at Redland Bay had little effect on the decline in RTR, which fell after 60 mm had been extracted compared to 70 mm in the unshaded (Fig. 2c). All models over-predicted timing of the decline of RTR. However, there was little difference between all models in RSMD values for the prediction of cumulative extraction because of the low level of demand (Table 3). The RTR in the Hyderabad crop remained at around 1.0 until 140-150 mm had been extracted from the profile (Fig. 3a). The three models differed little in

11.3 7.4 5.1 4.0 16.8 3.1 5.4

9.2 10.7 6.4 5.4 10.8 4.0 6.1

their prediction of the decline in RTR at 140-155 mm and the RSMD for the prediction of RTR. Consequently, there was little difference between models in prediction of cumulative extraction and predictions were within the error of the observations (Fig. 3b). In the Temple crop, measurements started when 130 mm had already been extracted. The RTR declined once about 180 mm had been extracted from the profile and all models correctly predicted this decline (Fig. 4a). All models adequately predicted the time course of extraction. The RMSD values of 10.8-16.8 mm, although higher than for the other crops, were less than 10% of the final amount of water extracted (Fig. 4b and Table 3). In the crop on the clay loam at Kalamazoo, RTR declined once about 105 mm had been extracted. The models predicted the decline at 90-105 mm, with the ROOT model providing a slightly smaller RMSD for prediction of RTR (Table 3). However, the difference in simulation of RTR did not translate into large differences in cumulative extraction because of low demand of 1-2 mm d-~ late in the drying cycle. For the sandy soil at Kalamazoo, RTR declined at 50-60 mm extraction and this was predicted by all three models (Fig. 5c). For both soils, predictions of cumulative extraction were similar, mostly within the error of the

M.J. Robertson, S. Fukai / Field Crops Research 36 (1994) 145-160

R e d l a n d B a y 1989 u n s h a d e d 1.5

I

I

i

153

R e d l a n d B a y 1989 s h a d e d 1.5

I

i

(a/

I

•

i

u

(c/ I= o 1.0 "F-,

1.0

•

•

.4O, g 0.5

e

i

• "~

O

0.5

• e

el

O

0.0

I 20

0.0 20

40

Cumulative w a t e r

120

,

,

60

IO0

(ram)

extracted

,

I 40

Cumulative w a t e r

,

100

u

I

i 60 extracted

I

I 80

100

(ram)

I

(d)

(b)

,oo

80

.- . . . . .

~

80

60 60 ,o o

40

o

'~

0

20

'

'

'

40

60

80

'

100

Days a f t e r sowing

~

o

I1 20

I

I

I

40

60

80

tO0

Days a f t e r sowing

Fig. 2. Observed data and model predictions for (a) relative transpiration rate versus cumulative water extracted, and (b) cumulative water extracted versus days after sowing for the unshaded treatment of the 1989 crop at Redland Bay. Observed data and model predictions for (c) relative transpiration rate versus cumulative water extracted, and (d) cumulative water extracted versus days after sowing for the shaded treatment of the 1989 crop at Redland Bay. Symbols and lines as for Fig. 1.

observations and with low RMSD values of around 5 mm. For all crops except Redland Bay 1987 and 1989 unshaded, the two FESW models gave identical predictions because RTR did not decline until after the root front reached its maximum depth. In some of the sowings, the ROOT model predicted RTR to be less than 1.0 in the early stages of the drying cycle, even though the observed RTR was around 1.0.

The extent of root growth during early stages may be greater than assumed in the ROOT model.

4.2. Sensitivity analysis The simulations of the seven sowings showed that the FESWR and ROOT models predicted the decline in RTR similarly, thereby suggesting that the ROOT model implicitly predicts that RTR will decline when FESW reaches about 0.3. Accordingly, the ROOT

154

M.J. Robertson, S. Fukai / Field Crops Research 36 (1994) 145-160

Temple

Hyderabad 1.5

(a) 0 •~

1.0

o

0.5

1.5

|

•

!

(a)

2

•

1.0

--\

..a o

0.0

I

I

I

50

100

150

0.5

0.0

ZOO

I

0

52

I

I

I

156

208

260

Cumulative water extracted (mm)

Cumulative water extracted (ram) 22O

104

26O

I

(b)

(b)

"•176

208 o

156

~ 132

88

•

•

S

104 o

i"

0

52 ,

20

40

60

80

tOO

Days after sowing

0

6O

I

I

I

I

70

80

90

100

110

Days after sowing

Fig. 3. Observed data and model predictionsfor (a) relative transpirationrate versuscumulativewaterextracted, and (b) cumulative water extracted versus days after sowingfor the crop at Hyderabad. The FESW-rand FESWRmodel gave identicalpredictions.Symbols and linesas for Fig. 1.

Fig. 4. Observed data and model predictionsfor (a) relative transpirationrate versuscumulativewater extracted, and (b) cumulative water extracted versusdays after sowingfor the crop at Temple.The FESWTand FESWemodel gave identicalpredictions.Symbolsand lines as for Fig. 1.

model was run with various hypothetical combinations of Ep and TESW to test if the model does predict RTR to decline at FESWR = 0.3. Results of the simulations show that RTR would decline at values of FESW R ranging from 0.17 to 0.53, depending on the level of Ep and TESW (Table 4). The RTR declined earlier (i.e. FESWR was higher) as the level of Ep increased with the trend being more pronounced on the soil with the low TESW. Increasing the root front velocity (RFV), the root growth partitioning factor (R) or the root-soil diffusivity (k) delayed the decline in RTR, whereas decreas-

ing any of these three parameters brought forward the threshold F E S W R ( T a b l e 4). Of the parameters varied, the threshold value of FESWR was most sensitive to a 20% reduction in the value of RFV. The greatest impact was under low-medium Ep on the low TESW soil and under medium-high Ep on the high TESW soil. The response was small under high demand on the low TESW soil because the development of stress is rapid, and the response was small under low demand on the high TESW soil because the crop does not become water-limited until after the root front has reached its maximum depth.

155

M.J. Robertson, S. Fukai / Field Crops Research 36 (1994) 145-160

Kalamazoo 1.5

I

clay loam

l

l

Kalamazoo 1.5

I

I

•

I

o

•~ "'#

1.0 0

•

o

o

I

I

I

t

,

0.5

sand I

".

(c)

1.0

0

I

•

•

0.5

0

0.0

0

I

I

I

I

26

52

78

104

i

13.0

130

O

Cumulative water extracted (mm)

130

,

,

,

,

,

I

I

I

I

I

I

20

30

40

50

60

70

80

C u m u l a t i v e water extracted (ram)

,

(b)

I

lO

~

•

80

-

,

,

,

,

80

90

100

110

(

104

78

50 ~ 40

52

~

30

26

~

20

]

lO

~

0

i 0

40

50

60

70

80

90

100

110

120

D a y s after sowing

70

120

D a y s after sowing

Fig. 5~ Observed data and model predictions for (a) relative transpiration rate versus cumulative water extracted, and (b) cumulative water extracted versus days after sowing for the crop on the clay loam at Kalamazoo.Observed data and model pedictions for (c) relative transpiration rate versus cumulative water extracted, and (d) cumulative water extracted versus days after sowing for the crop on the sand at Kalamazoo. The FESWTand FESWRmodel gave identical predictions on both soil types. Symbols and lines as for Fig. 1. Increasing or decreasing the value of R or k had similar impact on the threshold value of FESWR, because they are multiplied in the calculation of potential extraction in each soil layer. The effect on the simulated amount of transpiration by varying the value of the threshold F E S W in the F E S W T model was investigated by running the model with values of the threshold at 0.2, 0.3 (standard), and 0.4. Simulations were run for the same three levels of potential evaporation, and two soils as in the previous

sensitivity analysis. Reducing the threshold to 0.2 increased transpiration with the greatest change in percentage and absolute terms on the high T E S W soil (Table 5). Increasing the threshold to 0.4 decreased transpiration with the greatest change occurring in situations where the crop became water-limited but did not extract all extractable water. Overall, the prediction of the amount of water transpired at anthesis (60 das) and maturity ( 100 das) was affected by less than 6% through varying the threshold between 0.4 and 0.2.

156

M.J. Robertson, S. Fukai / Field Crops Research 36 (1994) 145-160

Table 4 The fraction of extractable soil water in the root zone at which the relative transpiration rate first declines below one, for two hypothetical soil types with total extractable soil water contents (TESW) of 105 mm and 210 mm, and three levels of potential evaporation (Ep, 3, 6 or 9 mm d - ~) as predicted by the ROOT model Soil

TESW (mm)

Er ( m m d -j )

Standard values

RFV

R

k

- 20%

+ 20%

- 20%

+ 20%

- 20%

+ 20%

A

105

3 6 9

0.17 0.34 0.53

0.26 +53 0.38 +12 0.55 + 4

0.1! - 1 1 0.30 - 1 2 0.43 - 1 8

0.20 +18 0.39 +15 0.59 +11

0.14 - 1 7 0.33 - 3 0.43 - 1 9

0.20 +18 0.39 +15 0.59 +11

0.14 - 1 7 0.33 - 3 0.43 - 1 9

B

210

3 6 9

0.17 0.25 0.44

0.17 0 0.37 +48 0.53 + 20

0.13 - 2 4 0.17-32 0.34 - 23

0.19 +12 0.31 +24 0.51 + 16

0.16 - 6 0.16-36 0.38 - 14

0.19 +12 0.31 +24 0.51 + 16

0.16 - 6 0.16-36 0.38 - 14

Simulations are for standard values of the parameters: root front velocity (RFV, 3 cm d - ~), root growth partitioning factor (R, 0.013 km g J) and root-soil diffusivity (k, 0.2 cm 2 d J for soil A, 0.05 cm 2 d - J for soil B) and parameter values perturbed + / - 20% from the standard. Numbers in italics after values in each column are % change from standard. Table 5 The amount of water transpired at 60 and 100 days after sowing (das) (mm) for two hypothetical soil types (TESW = 105 and 210 mm) and three levels of potential evaporation ( Ep = 3, 6, 9 mm d - ~) as predicted by the FESWT model. Results are expressed as the percent change from the standard values of FESW threshold = 0.3 Soil

TESW (ram)

Ep ( m i n d ~)

Transpired water at 60 das A 105

B

210

Transpired water at 100 das A 105

B

210

Standard value(mm)

on water transpired

+ 1 +2 0 0 +4 +3

-3 -2 - 1 0 -5 -4

3 6 9 3 6 9

95 96 97 138 160 168

0 0 0 +5 +1 0

- 2 0 0 -5 -I 0

5. Discussion

similar

e f f e c t s to t h a t in t h e F E S W - r m o d e l ( T a b l e 6 ) . I n c r e a s J had a smaller effect

o n t r a n s p i r a t i o n t h a n d i d d e c r e a s i n g it f r o m 3 to 2 . 4 c m d-~.

0.4

72 94 97 73 134 160

had remarkably

i n g t h e R F V f r o m 3 to 3 . 6 c m d

0.2

3 6 9 3 6 9

T h e e f f e c t o f v a r y i n g t h e t h r e s h o l d in t h e F E S W R model

FESW Threshold

The greatest sensivity of the amount of water

The key finding from this study was that the three models

predicted similarly for the seven crops the

d e c l i n e in R T R u n d e r c o n t i n u o u s soil d r y i n g s t a r t i n g with a full profile, across a wide range of values of

t r a n s p i r e d in t h e F E S W R m o d e l w a s to v a r y i n g t h e

e x t r a c t a b l e soil w a t e r c o n t e n t s ( 6 8 to 2 5 2 m m )

F E S W t h r e s h o l d at a l o w v a l u e o f R F V .

l e v e l s o f t r a n s p i r a t i o n a l d e m a n d ( 1.8 to 4 . 9 m m d - ~).

and

This implies that the more detailed models, which sim-

M.J. Robertson, S. Fukai / Field Crops Research 36 (1994) 145-160

157

Table 6 The amount of water transpired at 60 and 100 days after sowing (das) ( m m ) for two hypothetical soil types ( T E S W = 105 and 210 m m ) and three levels of potential evaporation ( El, = 3, 6, 9 m m d - ~) as predicted by the FESWR model. Results are expressed as the percent change from the standard values of RFV = 3 cm d - ~ and FESW threshold = 0.3 Soil

TEWS

Ep

Standard

(mm)

(mmd -~ )

value (mm)

FESW Threshold 0.2

0.3

RFV=2.4cmd

0.4 ~

0.2

0.3

RFV=3cmd

0.4 ~

72 92 95 73 132 155

0 -10 -I1 0 -5 - 10

-4 -12 -12 0 -11 - 14

-10 -14 -14 - 1 -17 - 18

+1 +2 +1 0 +6 +4

0 0 0 0 0 0

-3 -2 -1

Transpired water at 100 das A 105 3 6 9 B 210 3 6 9

95 96 97 138 160 168

0 0 0 +5 +1 0

-1

-2

0 0 0 +6 +1 0

0 0 0 0 0 0

-2

-1

ulate extraction at the level of the root, are consistent with the profile-level models in that they predict that RTR will decline below 1.0 once about 70% of the extractable water has been extracted from the root zone. In five of the crops, observed RTR declined after the root front stopped descending (i.e. after anthesis), and so the two FESW models gave identical predictions of the decline in RTR. For the Temple crop (Fig. 4a) and the Kalamazoo crop on the sandy soil (Fig. 5c) this was undoubtedly because the drying cycle did not start until just prior to anthesis and the root front was therefore nearly at its maximum depth. In crops where drying started much earlier, such as at Hyderabad, the models also did not differ because RTR did not decline until after anthesis due to the soil having a moderatelyhigh extractable water content (Fig. 3a). In the Redland Bay 1989 shaded crop, RTR did not decline until after anthesis because of the low demand (Fig. 2c ). At Kalamazoo on the clay soil, a combination of a moderate level of extractable soil water, moderate demand and drying not starting until 46 das, meant that RTR also did not decline until after anthesis (Fig. 5a). Only in the 1987 sowing at Redland Bay did the FESW models differ noticeably in their predictions (Table 3), with

0

0 0 -8 -3 -1

0.3

0.4

RFV=3.6cmd

Transpired water at 60 das A 105 3 6 9 B 210 3 6 9

0 0 0

0.2

0 -6 -5

0 0 -5 -I -1

+1 +4 +2 0 +6 +6

0 +2 +2 0 +2 +3

0 0 0 +5 +1 0

0 0 0 0 0 0

-3 0 -1 0 -4 - I

-2 0 0 -5 -1 0

the FESWR model predicting an earlier decline in RTR than the FESWT model. This crop had an early start to its drying cycle, was on a soil with a low extractable soil water content and had a moderate level of demand - a combination which would cause an early decline in RTR. It appears that the FESWT model over-predicts the timing of the decline in RTR under conditions where stress develops early e.g. under high demand on soils with low TESW, or if the crop is sown into an already partially dry profile. Francis and Pidgeon (1982), in their water balance model for wheat, showed that the soil water status in the current root zone rather than the maximum root zone gave better prediction of transpiration during dry periods when the crop was young. One of the important differences between the FESW models on the one hand and the ROOT model on the other is that in the latter RTR is sensitive to the level of demand, whereas in the former RTR is strictly a function of FESW. Hence one would expect that under low demand conditions, the ROOT model would predict RTR to decline at values of FESW less than 0.3, due to demand being low in relation to potential extraction. This tendency is shown in the low-demand sow-

158

M.J. Robertson, S. Fukai / Field Crops Research 36 (1994) 145-160

ings at Redland Bay in 1989 (Fig. 2) and Kalamazoo (Fig. 5), although it did not result in better predictions by the ROOT model. In practice, the differences between the two types of models in the simulation of RTR under low demand is unlikely to translate into large differences in cumulative transpiration because of the low demand (Fig. 2). The crops covered a range of average demand of 1.8 to 4.9 mm d - t and a range of TESW of 68 to 252 mm. Over this range the relationship between RTR and FESW appeared conservative. However, there were no data sets where high demand was coupled with a low TESW soil, or a high TESW soil with a low demand. Sensitivity analysis was used to extend the possible combination of conditions to include these situations. The results of the sensitivity analysis showed that as Ep increased beyond the moderate range of demand experienced by the field sowings, i.e. up to 9 mm d - ~, the value of the FESW threshold simulated by the ROOT model increased from 0.17 to 0.40 on a high TESW soil and from 0.17 to 0.53 on a low TESW soil. This result agrees with the early finding of Denmead and Shaw (1962) that the threshold value of FESW does depend upon the level of demand. Denmead and Shaw's results show much higher sensitivity of RTR to demand than the simulation results reported here, which has been explained by Ritchie (1973) as being due to the plants being grown in small containers, which prevented root expansion into deeper wetter zones and upward movement of water into the root zone. However, this would only hold for soils of high extractable water content where root expansion into deeper zones would be likely to give access to enough water to maintain RTR at around 1.0 under high demand. The simulation results here also show that if the root zone is expanding, the threshold FESW at which RTR declines is still sensitive to the level of demand. The results presented here suggest that, in addition to the level of demand, the threshold will also vary with extractable water content of the soil, as shown theoretically by Gardner and Ehlig (1963). Previous studies on sorghum, which showed the consistency of the 0.30.4 threshold (e.g. Wright and Smith, 1983; Rosenthal et al., 1987) were mainly conducted on soils of medium to high extractable water content and under moderate demand. The field sowings in the current study also showed the consistency of the 0.3-0.4 threshold. The

results of the sensitivity analysis suggest, however, that on soils with an extractable water content that is lower than those used in these field studies, the threshold may change according to level of demand. The sensitivity analysis also suggests that the value of the FESW threshold simulated by the ROOT model is not very sensitive to variation in the degree of root growth or root-soil diffusivity. However, the threshold changed substantially when the root front velocity was decreased and this was reflected in a susbstantial effect on transpiration (Table 6). This suggests that the most significant determinant of the threshold is the rate at which the crop gains access to water in the profile, which is a function of the root front velocity, rather than the potential rate at which it can extract water at each depth (Monteith, 1988). This suggests that the attributes of the root system that plant breeders should focus on in the improvement of cultivars for dry environments, is the downward rate of root extension rather than the level of root production. Also, agronomic practices that encourage rapid and deep root growth will have more effect on water extraction than those that solely increase rooting density. The objective of increasing the rate of water extraction must however be balanced against the possibility in some environments of the early profligate water use leading to exhaustion of water reserves before maturity. Although the threshold value of FESW is shown to vary with the level of demand, extractable soil water content and root parameters, the sensitivity analysis showed little effect on the simulated cumulative amount of water transpired for both the FESWT (Table 5) and FESWR (Table 6) models. Varying the threshold between 0.2 and 0.4 resulted in differences in cumulative transpiration of less than 7%. The comparison of models reported here represents a limited test of their likely differences in predicting water extraction in crop growth models. Firstly, canopy cover was inputted for the calculation of demand. The small differences in water extraction shown here may result in larger errors in situations where there is feedback between water extraction, canopy expansion and senescence, and hence demand. Secondly, this study only examined the performance of the models under continuous soil drying. In situations where rewetting occurs, the models may differ substantially in predictions. Simulations with the FESWR and ROOT models

M.J. Robertson, S. Fukai / Field Crops Research 36 (1994) 145-160

(not presented here) showed that the F E S W R model, would predict less extraction than the ROOT model after partial rewetting of a dry profile, because in the FESWR model the threshold remained below 0.3 thus restricting extraction, while in the ROOT simulations, extraction occurred from the wetted surface soil layers quickly enough to match demand.

6. Conclusions The three models provided similar predictions of water extraction. On average, they all predicted that the relative transpiration rate of a crop under continuous soil drying will decline below 1.0 once 70% of the extractable water has been extracted from the root zone. This confirms the robustness and validity of the use of the FESW threshold of 0.3 in crop growth models. Small variations in the threshold do not seem to significantly affect the simulation of crop water use. Despite the lack of advantage of the ROOT model over the FESW model in predicting crop water uptake, the use of the detailed approach allowed identification of the principal soil and crop factors that control extraction namely, the level of demand, the extractable water content of the soil, and the rate of downward penetration of the root front.

7. Acknowledgement The authors wish to thank P. Singh, T. Rego and J.L. Monteith for permission to use the data from their experiment at ICRISAT Center, Hyderabad. The data from Kalamazoo was collected with the support of the Homer Nowlin Chair at Michigan State University.

8. References Black, T.A., Gardner, W.R. and Thurtell, G.W., 1969. The prediction of evaporation, drainage and soil water storage for a bare soil. Soil Sci. Am. Proc., 33: 655-660. Denmead, O.T. and Shaw, R.H., 1962. Availability of soil water to plants as affected by soil moisture content and meteorological conditions. Agron. J., 54: 385-390. Francis, P.E. and Pidgeon, J.D., 1982. A model for estimating soil moisture deficits under cereal crops in Britain. II. Performance. J. Agric. Sci. Camb., 98: 663-678.

159

Gardner, W.R. and Ehlig, C.F., 1963. The influence of soil water on transpiration by plants. J. Geophys. Res., 68:5719-5724. Hammer, G.L. and Muchow, R.C., 1991. Quantifying climatic risk to sorghum in Australia's semiarid tropics and subtropics: Model development and simulation. In: R.C. Muchow and J.A. Bellamy (Editors), Climatic Risk in Crop Production: Models and Management for the Semiarid Tropics and Subtropics. Proceedings of the International Symposium, Brisbane, Australia, 2-6 July, 1990. CAB International, Wallingford, pp. 205-232. Huck, M.G. and Hillel, D., 1983. A model of root growth and water uptake accounting for photosynthesis, transpiration and soil hydraulics. Adv. Irrig. Res., 2: 273-333. Kanemasu, E.T., Stone, L.R. and Powers, W.L., 1976. Evapotranspiration model tested for soybean and sorghum. Agron. J., 68: 569-572. Meinke, H., Hammer, G.L. and Want, P.J., 1993. Potential soil water extraction by sunflower on a range of soils. Field Crops Res., 32: 59-81. Meyer, W.S., Dunin, F.X., Smith, R.C.G., Shell, G.S.G. and White, N.S., 1987. Characterising water use by irrigated wheat at Griffith, New South Wales. Aust. J. Soil Res., 25: 499-515. Monteith, J.L., 1986. How do crops manipulate water supply and demand? Phil. Trans. R. Soc. London A., 316: 245-289. Monteith, J.L., 1988. Does transpiration limit the growth of vegetation or vice-versa? J. Hydrol., 100: 57-68. Monteith, J.L., Huda, A.K.S. and Midya, D., 1989. RESCAP: A resource capture model for sorghum and pearl millet. In: S.M. Virmani, H.L.S. Tandon and G. Alagarswarmy (Editors), Modeling the Growth and Development of Sorghum and Pearl Millet. Research Bulletin No. 12, ICRISAT, Patanchern, India, pp. 3034. Muchow, R.C., 1988. Effect of nitrogen supply on the comparative productivity of maize and sorghum in a semi-arid tropical environment. I. Leaf growth and leaf nitrogen. Field Crops Res., 18: 207-219. Muchow, R.C. and Sinclair, T.R., 1991. Water deficit effects on maize yields modeled under current and "greenhouse" climates. Agron. J., 83: 1052-1059. NeSmith, D.S. and Ritchie, J.T., 1992. Short- and long-term responses of corn to a pre-anthesis soil water deficit. Agron. J., 84: 107-113. Passioura, J.B., 1983. Roots and drought resistance. Agric. Water Manag., 7: 265-280. Penman, H.L., 1948. Natural evaporation from open water, bare soil and grass. Proc. R. Soc. London A, 193: 120--146. Ritchie, J.T., 1971. Dryland evaporative flux in a subhumid climate: I. Micrometeorological influences. Agron. J., 63:51-55. Ritchie, J.T., 1972. Model for predicting evaporation from a row crop with incomplete cover. Water Resour. Res., 8: 1204-1213. Ritchie, J.T., 1973. Influence of soil water status and meteorological conditions on evaporation from a corn canopy. Agron. J., 65: 893-897. Ritchie, J.T., 1981. Soil water availability. Plant Soil, 58: 327-338. Ritchie, J.T., 1985. A user-orientated model for the soil water balance in wheat. In: W. Day and R.K. Atkin (Editors), Wheat Growth and Modelling. Plenum, New York, NY, pp. 293-305. Ritchie, J.T. and Burnett, E., 1971. Dryland evaporative flux in a

160

M.J. Robertson, S. Fukai / Field Crops Research 36 (1994) 145-160

subhumid climate: I1. Plant influences. Agron. J., 63: 56-62. Ritchie, J.T., Burnett, E. and Henderson, R.C.. 1972. Dryland evaporative flux in a subhumid climate: III. Soil water influence. Agron. J., 64: 168-173. Robertson, M.J., Fukai, S., Ludlow, M.M. and Hammer, G.L., 1989. Water extraction by dryland grain sorghum. In: Proceedings Australian Sorghum Workshop, Toowoomba, Qld., Australia, pp. 202-210. Robertson, M.J., Fukai, S., Ludlow, M.M. and Hammer, G.L., 1993a. Water extraction by grain sorghum in a sub-humid environment. I. Analysis of the water extraction pattern. Field Crops Res., 33: 81-97. Robertson, M.J., Fukai, S., Ludlow, M.M. and Hammer, G.L., 1993b. Water extraction by grain sorghum in a sub-humid environment. II. Extraction in relation to root growth. Field Crops Res., 33: 99-112. Robertson, M.J., Fukai, S., Hammer, G.L. and Ludlow, M.M., 1993c. Modelling root growth of grain sorghum using the CERES approach. Field Crops Res., 33:113-130. 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: 1019-1026. Rosenthal, W.D., Vanderlip, R.L., Jackson, B.S. and Arkin, G.F., 1989. SORKAM: A grain sorghum crop growth model. Research

Center Program and Model Documentation, MP-1669. Texas Agricultural Experimental Station, College Station, TX. Sinclair, T.R., 1986. Water and nitrogen limitations in soybean grain production. I. Model development. Field Crops Res., 15: 125141. Squire, G.R., Ong, C.K. and Monteith, J.L., 1987. Crop growth in semi-arid environments. In: Proceedings of the International Pearl Millet Workshop, ICRISAT Center, India, April 1986. ICRISAT, Patancheru, India, pp. 219-231. Sumayao, C., Kanemasu, E.T. and Hodges, T., 1977. Soil moisture effects on transpiration and net carbon dioxide exchange of sorghum. Agric. Meteorol., 18:401-408. Tanner, C.B. and Ritchie, J.T., 1974. Evapotranspiration empiricisms and modeling. American Society of Agronomy Abstracts. ASA, Madison, WI, p. 14. Tanner, C.B. and Sinclair, T.R., 1983. Efficient water use in crop production: Research or re-search? In: H.M. Taylor, W.R. Jordan and T.R. Sinclair (Editors), Limitations to Efficient Water Use in Crop Production. American Society of Agronomy, Madison, WI, pp. 1-27. Wright, G.C. and Smith, R.C.G., 1983. Differences between two grain sorghum genotypes in adaptation to drought stress. II. Root water uptake and water use. Aust. J. Agric. Res., 34: 627-636.