Modelling root growth of grain sorghum using the CERES approach

Field Crops Research, 33 (1993) 113-130

113

Elsevier Science Publishers B.V., Amsterdam

Modelling root growth of grain sorghum using the CERES approach M.J. Robertson a, S. Fukaia, G.L.

Hammer b and M.M. Ludlow c

a Department of Agriculture, University of Queensland, St. Lucia, Qld., Australia b Queensland Department of Primary Industries, Toowoomba, Qld., Australia c CSIRO Division of Tropical Crops and Pastures, St. Lucia, Qld., Australia (Accepted 1 July 1992)

ABSTRACT Robertson, M.J., Fukai, S., Hammer, G.L. and Ludlow, M.M., 1993. Modelling root growth of grain sorghum using the CERES approach. Field Crops Res., 33:113-130. A simple model is described, based on the approach used in the CERES crop growth models, which simulates the depth of rooting and root length density in each soil layer for grain sorghum growing under soil drying. The model has five main components: ( i ) daily accumulation of root length is proportional to above-ground biomass growth, (2) the root front descends at a constant rate from sowing until early grain-filling, ( 3 ) daily accumulation of root length in water non-limitingconditions is partitioned among the occupied soil layers in an exponential pattern with depth, (4) proliferation of root length is restricted in any layer if the extractable soil water in that layer declines below a threshold, and ( 5 ) a fixed proportion of existing root length is lost due to senescence each day. The parameter values for the relationships were derived from analysis of measured depth distributions of root length from crops of grain sorghum grown in the sub-humid subtropics of Australia, on oxisol and vertisol soil types. The soils had no physical or chemical restrictions to root growth. The model was validated using four independent data sets. Overall, the model simulated the root distribution with depth well, but predictions of accumulated root length were less reliable. One of the most sensitive parameters affecting the modelled distribution of root length with depth was the factor used to partition daily accumulation of root length among the occupied layers, and the value of this parameter varied between well-watered and water-limited crops.The study shows that it is possible to model root growth of field crops using only five simple relationships, with inputs that are already used in most crop growth models.

INTRODUCTION

The process of root growth is central to determining the growth and yield of crops in water-limited environments. Despite being severely stressed, many droughted crops leave a substantial amount of apparently available water in the subsoil at maturity (Hamblin, 19 8 5 ), suggesting that root characteristics may be limiting extraction. In some instances, the amount of unused and apCorrespondence to: M.J. Robertson, CSIRO Division of Tropical Crops and Pastures, Private Bag P.O., Aitkenvale, Qld. 4814, Australia.

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M.J. ROBERTSON El" AL.

parently available water is negatively related to root length density (Barraclough and Weir, 1988). Crop models can allow us to evaluate the consequences of variation in root growth for water extraction and address such questions as "Is there an adavantage in yield for a crop genotype that has altered root characteristics?". However, most crop models do not attempt to simulate the dynamics of root growth for the determination of the pattern of water extraction, and are therefore not appropriate for examining such issues. The lack of attention given to root growth in crop models is partly because little is known about the functioning, growth and architecture of root systems. The few models that do simulate the dynamic processes of root growth and water extraction are exceedingly complicated and have little application to the simulation of field crops on a daily basis from the seedling stage to maturity (e.g. Huck and Hillel, 1983). There is a need to identify conservative quantities that characterise root growth in a simple manner, and which can be used in crop simulation models. Models of root growth range in complexity from detailed morphological models (e.g. Rose, 1983 ) to models that simply predict the daily increase in the depth of the root zone (e.g. Rosenthal et al., 1989). Few of the detailed models attempt to deal with the extension of the root zone into unoccupied soil nor the partitioning of root growth amongst the various layers in the root zone, and so have limited applicability for realistic simulation of crop growth. There are a number of sub-models of root growth currently used in sorghum crop growth models and each uses a different approach to simulate root growth. In the model SORKAM (Rosenthal et al., 1989), rooting depth is simulated as a sine function of phenological time. Root length density (length of root per unit of soil volume) is not predicted. In the model of Monteith et al. (1989), the rooting depth increases at a rate of 3.5 cm d a y - i after an establishment phase. A "typical" root length density pattern is simulated on a daily basis, and this model assumes that the size of the root system does not vary from crop to crop. Both of these models are unsatisfactory as a basis for developing a root growth model, because they do not dynamically simulate root length density in each occupied layer of the soil profile. The aim of this paper is to present the development and testing of a simple model that simulates root length density in each layer of the profile on a daily basis, and has no more inputs than are currently required by most crop models. The root growth subroutine from the CERES-Wheat (Ritchie et al., 1984) and CERES-Maize models (Jones and Kiniry, 1986) meets these requirements and therefore provides a simple quantitative framework upon which to base a model for root growth of sorghum. This paper presents the development and validation of a root growth model for grain sorghum, based on the approach used in CERES. Emphasis in the model is placed upon the simulation of root growth under conditions of soil drying, because it is in these situations that the accurate simulation of the root growth pattern will be cru-

MODELLING ROOT GROWTH OF GRAIN SORGHUM

1 15

cial to prediction of crop productivity. No tests have been published of the accuracy of the CERES framework for modelling root growth, and so this paper is also a general test of the usefulness of the modelling framework for predicting root growth. MATERIALS AND METHODS

Database There were 9 data sets used to derive the parameter values used in the model (data sets 1-9, Table 1 ). These data sets were from field experiments on an oxisol soil type, in which crops of grain sorghum were subjected to various conditions of water supply over two growing seasons. Another 4 data sets ( 1013 ) were reserved for validation purposes. Two of the validation data sets were from experiments on the oxisol, in which cultivars were subjected to continuous drying from 22 days after sowing (das) to anthesis, and the other two data sets were from experiments on a deep alluvial vertisol, in which crops were grown under rain-fed conditions. Standard errors of the observed values were not available for any of the 4 validation data sets. Both soil types were located in subtropical, sub-humid environments of south-east Queensland, Australia. Basic information on the two soil types is given in Table 2. Both soils were more than 3 m deep, with no obvious physical or chemical impediments to root growth. The sorghum cultivars were of similar phenology, taking 55-60 days from sowing to 50% anthesis. All crops were grown with 0.5 m row spacing (except data set 12 ) under standard cultural conditions, with adequate nutrients, and with levels of weeds, pests and diseases kept to a minimum. For all data sets, roots were sampled in 20-cmdeep increments with a 4.2 cm i.d. core, except in data set 3 at 24 and 32 das, when the core was 9.4 cm i.d. Two cores per plot were taken, one at the midinterrow position and the other on the row, except in data set 3, when 4 cores per plot were taken. Root length in data sets 1-9 was determined by the line intersect method using a digital scanner (see Robertson et al. ( 1993a) for full description). The scanner detected only live, white roots. Length in data sets 10-13 was determined by the line intersect method of Newman (1966) as modified by Torsell et al. ( 1968 ) and Hignett (1976).

Data analyses The CERES root growth model is based on five simple relationships. Firstly, new root length is produced in proportion to the amount of above-ground biomass produced by the crop each day. Secondly, the root front descends at a rate determined by temperature - e.g. 0.22 cm per degree day in the CERESMaize model. Thirdly, in the absence of soil water limitations, the daily growth in root length is partitioned amongst the layers in the root zone according to a dimensionless weighting factor. Fourthly, a multiplicative stress factor for

116

M.J. ROBERTSON ET AL.

TABLEI Details of the data sets used in the model development and validation. For each sampling is given: the crop watering regime ( W W = well-watered, CD = continuous soil drying, RF = rainfed ), cultivar, day after sowing when the sample was taken, the depth of rooting, total root length (L~), aboveground biomass ( T D M ) , and the ratio ( R ) of La to TDM. Data sets are grouped according to the type of watering regime that the crops experienced Data Watering set regime

Oxisol 1 CD to anthesis

Cultivar Sample Depth time (cm) (das)

0.015 1 0.012 1 0.013 6 0.015 6 0.015 2 0.015 2 0.014 2 0.013 2 0.010 2 0.010 2 0.021 2 0.013(+0.0009) 0.013 1. 0.011 I 0.005 6 0.010( +0.0021 ) 0.006 6 0.009 6 0.010 6 0.017 6 0.007 6 0.006 6 0.009(+0.0017) 0.003 6 0.003 6 0.014 3 0.014 3

35 66 67

150

3.3 11.3 3.1

Pride E57 Pride Pride b Pride Pride a

104 104 102 102 79 102

190 190 170 190 175 180

8.0 9.1 4.0 6.5 4.5 4.1

WW to maturity Pride E57 10 CD to anthesis Tx 610 11 E57 Vertisol 12 RF Pride c 13 RF Tx610

104 104 57 60

190 190 165 185

4.4 5.7 7.0 8.4

156 800 424 429 40 60 110 180 280 500 260 mean d 181 1000 670 mean 1247 969 400 380 610 670 mean 1453 1649 515 580

65 49

165 145

9.3 6.4

830 500

4

WW to anthesis

5 6 7 8

9

CD to maturity

Pride Pride Pride

R (km g-~)

2.3 9.8 5.7 6.3 0.6 0.9 1.5 2.4 3.9 5.0 5.5

3

35 66 67 67 24 32 39 46 56 67 67

TDM (g m -2)

130 150 150 70 90 I l0 120 145 170 175

2

Pride Pride Pride E57 Pride Pride Pride Pride Pride Pride Pride a

La (km m -2)

0.011 0.013

Reference

4 5

ashaded for 45-65 das, Uuniculm crop, ¢0.33 row spacing, aexcluding shaded crop, eindicates that core sample was not taken to full rooting depth. References: 1 =Robertson et al. (1993a), 2 = R o b e r t s o n et at. (1993b), 3 = S a n t a m a r i a (1987), 4 = Peries (1990), 5 = Herbert ( 1984 ), 6 = Robertson ( 1991 ).

the limitation o f soil strength on root proliferation in a soil layer, decreases from 1.0 at 25% o f extractable water to 0 at 0% extractable water. Fifthly, the model assumes that root loss is 0.5% o f existing root length per day. In order

117

MODELLING ROOT GROWTH OF GRAIN SORGHUM

TABLE 2 Characteristics of the two soil types used in model development and calibration Soil type

Oxisol

Vertisol

Location Latitude Texture Extractable water (0-200 cm) (mm) Bulk density (gcm -3)

Redland Bay 27 ° 37'S clay loam

Lawes 27 ° 34'S clay loam/silt loam

80' 1.0-1.43

2502 1.2-1.42

'from Robertson et al. (1993a). 2from Peries (1990). 3from Kirkegaard ( 1990 ).

Above-ground biomass growth

Days after sowing i

roo~ length ~ (total)

Root front depth i

ew

lOccupied

Soil water Ibalance

layers

Layer weighting factors (for non-

limiting conditions)

New root length (each layer)

~,

Layer weighting factors (limiting

ISoil water ]content 4--~rofile

conditions)

] Rootlengthdenslty = profile __ I

1

Fig. 1. Daily calculation steps in the model.

to develop the model, the five functions had to be established, using data sets 1-9. The model framework and daily simulation steps are outlined in Fig. 1. The model was designed to run with 10-cm-deep layers and a daily time step.

Total root length production In the present model, as in CERES-Wheat (Ritchie et al., 1984), daily growth in root length is produced in proportion to the amount of above-ground biomass produced by the crop. The relationship was devised, using data sets 1-9, where total root length and above-ground biomass were sampled at the same time. Total root length and above-ground biomass ranged widely among the crops and treatments, but when these were arranged into four groups, based on phenological stage and water regime, there was a consistent ratio (R) of total root length to above-ground biomass at the time of root sampling (Table

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M.J. ROBERTSONET AL.

1 ). For example, in data set 1 at 66 das, the crop had a total root length of 9.8 km m -2 after a 40-day drying cycle, whereas in data set 2, a crop sampled at a similar stage of growth produced only 5.7 km m -2. The difference between the two crops was that in data set l, 800 g m -2 of above-ground biomass was present at the time of root sampling whereas this figure was only 424 g m -2 in data set 2. The four discernable watering-regime groups were as follows. Crops grown under continuous soil drying up to anthesis produced 0.010-0.015 km (root) g-~ ( D M ) (mean=0.013 km g-~ ). The measurements from data set 3 show that the ratio of total root length to above-ground biomass declined slightly with time from 24 to 67 das. The major exception in this group is the shaded treatment in data set 3. This treatment at 67 das had the same total root length as the unshaded, but it had only 260 g m -2 of above-ground biomass compared to the 500 g m -2 in the unshaded. Assimilate reduction in this treatment, therefore, had no apparent effect on root production (see Robertson et al., 1993b). The measurements from the three crops that were well-watered up to anthesis gave slightly less root length per unit of biomass than those grown under continuous drying, at 0.005, 0.013 and 0.011 km g - I (mean = 0.010 km g-l ). The ratios for both droughted and well-watered crops were lower at maturity, presumably because there was little root growth during grain-filling, whereas above-ground biomass increased (0.009 and 0.003 km g-~ for droughted and well-watered crops, respectively). Also, the ratio was more variable at maturity, because environmental conditions during grainfilling that affect root growth (e.g. rewetting of the profile ) and above-ground biomass accumulation, varied among crops. For the purposes of the present model for simulating root growth up to anthesis under soil drying, the value of R for the model was set to 0.014 km g - ~, slightly higher than the mean value across crops of 0.013 km g- ~ (Table 2 ), in order to allow for losses of root length due to death (see below). Taking R = 0 . 0 1 4 km g-I and assuming a length:weight ratio for sorghum roots of 100 m g - l (Retta et al., 1984), the proportion of total crop biomass present in the roots can be estimated as about 12%. This is a typical value for sorghum during the period from late vegetative growth to early grain-filling (Kaigama et al., 1977; Myers, 1980).

Depth of rooting Information on the rate of root penetration can be gained from observations of root activity as a function of depth. Measurements of water extraction with depth have shown that the front of root activity in field-grown grain sorghum and other tropical cereals descends at about 3 to 4 cm day- ~after a lag period of 10-20 days after sowing (Monteith, 1986; Squire et al., 1987; Robertson et al., 1989, 1993a). The downward penetration of the root front probably starts from germination and proceeds at a slower rate than the front

MODELLING ROOT GROWTH OF GRAIN SORGHUM

1 19

of activity, giving rise to the root front proceeding ahead of the front of root activity (Robertson et al., 1993b). It was decided to simulate the descent of the root front using the value of downward penetration rate of 2.7 cm daydetermined by Robertson et al. (1993a) for grain sorghum in a subtropical environment. In a more sophistocated model, this rate could be made a function of temperature, as is used in CERES. Under well-watered conditions (data sets 4,5,9), roots in crops measured after anthesis were as deep as 190 cm, which was the same as the maximum depths recorded for the droughted crops (data sets 2,3,7,8 ) (Table 1 ). Other studies have shown that the maximum depth of rooting for sorghum is in the range 160-200 cm (Mayaki et al., 1976; Kaigama et al., 1977), and that maximum depth is independent of water supply (Mayaki et al., 1976). This implies that the amount of water received by a crop does not influence the rate of the descent of the root front. Under conditions where the root front encounters dry soil then the rate of downward penetration may be slowed considerably (Tennant, 1976), but this effect is not considered here, as all crops grew on profiles that were initially wet. Root distribution under well-watered conditions In CERES-Maize, weighting factors for root growth in each layer are used to express the "preference" for roots to grow at a particular depth relative to other depths, and can be envisioned as the relative amount of new root growth at each soil depth, in the absence of any water, chemical or physical constraints. These weighting factors are supplied by the model user, and take account of the perceived "hospitality" of each layer to new root growth. For the present model, an attempt was made to derive such weighting factors, and use them as an integral part of the model, rather than require the user to estimate them. When soil physical and chemical factors are not limiting root growth, root length density in many crop species declines exponentially with depth in the profile (Gerwitz and Page, 1974). This is also the pattern recorded in sorghum (e.g. Bloodworth et al., 1958 ). This predictable pattern of root growth can be used to derive weighting factors for growth in each layer, which are characteristic for a given species. Sorghum exhibits a particularly steep decline of root length density with depth, with commonly 80-90% of the total root system length found in the top 30 cm (Bloodworth et al., 1958; Mayaki et al., 1976; Myers, 1980). The vertical distribution of root length density at maturity under wellwatered conditions (data sets 4, 5 and 9) represents the inherent preference for rooting in each soil layer of the profile. The distribution pattern of data sets 4, 5 and 9 was analysed to derive weighting factors as a function of depth that were to be used in the model to partition root growth among the soil layers on each day of the simulation. The distribution followed an exponential decay pattern with depth (Fig. 2 ). The root length density profiles were

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M.J. R O B E R T S O N ET AL.

Root 0.0 0

length

density

(cm

cm -3)

0.3

0.6

0.9

1.2

i

i

i

i

20

1.5

D

40

60

v

80

1 O0

120 O C,Q

CV 140

160

180

Data Data Data Data

set set set set

4 5 9 9

Pride 0 Pride • Pride v E57 • H

2O0

Fig. 2. Distribution of root length density with depth for four well-watered crops at or after anthesis. Fitted line: Y=0.81 (_+0.07) exp( - 0 . 0 1 8 ( + 0.002)X), omitting outlier "D". Horizontal bars are twice the average standard error of means. Data set 4 was sampled at 66 das.

similar for crops measured just after anthesis (data sets 4 and 5 ) and maturity (data set 9), indicating that there was little or no root growth during grain-filling under well-watered conditions. The exponential pattern of root length density with depth can be fitted to the function Lv=LO e x p ( - q z )

( 1)

where I~ (cm cm -3) is the root length density at a given depth, z (cm), in the soil, L o is the root length density at depth z = 0 cm, and q ( c m - ~ ) is a decay constant (Gerwitz and Page, 1974). An equation of the form of (1) was fitted to the data in Fig. 2, yielding values of L o = 0 . 8 1 cm cm -3 and q= 0.018 c m - ~ . The decay constant q can be normalised for the maximum rooting depth (rtdePmax) to give the parameter wcg - a dimensionless "weighting coefficient" for root system growth habit, where wcg = rtdepma~ X q. Values ofwcg range from 1 for crops with relatively uniform root distribution to 3 for crops with roots concentrated near the surface (Jones et al., 1991 ). If the maximum rooting depth is taken to be 190 cm, then wcg is 3.42 (0.018 cm - ~ × 190 cm), which is close to the value of 3 used for sorghum in the

MODELLING ROOT GROWTH OF GRAIN SORGHUM

121

root growth model of Jones et al. ( 1991 ). This value of wcg is indicative of the steep decline of Lv with depth observed for irrigated sorghum root systems. Following the procedure of Jones et al. ( 1991 ), wcg is used in the model to calculate the weighting factor for root growth, wr(l), in each 10 cm layer on each day of the simulation, from: wr (1) = ( 1 - cumdep (l) / rtdep ) wcg

(2 )

where cumdep (l) (cm) is the cumulative depth from the soil surface to the layer, 1, and rtdep (cm) is the depth of rooting at the time. If the bottom of the root system does not fully occupy the depth of the layer that it is in, then wr(l) for that bottom layer can be reduced in proportion to the extent of occupation. In the model, values of wr(l) are firstly calculated for each occupied layer of the profile, then normalised, to give a proportional factor, rf(l), for root growth in each layer,

(3)

rf(l) = wr ( l ) / S w r ( l )

where Zwr(l) is the sum of the weighting factors for layers in the rooting zone. The factor if(l), is then multiplied by the total root length growth for that day (trl) to give the increase in root length in each layer, rlv (l) rlv (I) = t r l × r f ( l )

(4)

The increase in root length in each layer on each day is accumulated with time to give root length density.

Root distribution under water-limiting conditions Pre-anthesis drought generally has the effect of modifying the exponential pattern of Lv with depth found under well-watered conditions (Mayaki et al., 1976; Kaigama et al., 1977 ). A dry soil surface limits root growth (Blum and Arkin, 1984), presumably through an effect of soil strength (Merrill and Rawlins, 1979). This commonly leads to a compensatory increase in root growth at depth. In the present model, a function of the type used in CERES-Maize to limit proliferation, is used: swdf(l) = 1.0

few (l) > thfew

(5a)

swdf(/)=few(/)/thfew

few(l)
(5b)

where swdf(l) is the soil water stress factor for root proliferation in the layer l, few(l) is the fraction of extractable water content in the layer l, and thfew is the threshold fraction of extractable water content at which swdf(l) is affected by water content. The time course of root length in each layer in data set 3 (Robertson et al., 1993b) showed that root proliferation continued until

122

M.J. ROBERTSON ET AL.

about 40-20% of the extractable water was remaining in each layer. Conceivably, soil drying would begin to limit root proliferation before any noticeable effect on net increase in root length occurred. The value of thfew was therefore set to 0.5, instead of the original value ( 0.25 ) (Ritchie, 1986 ). The stress factor, swdf, limits root proliferation by multiplicatively reducing wr(l), the weighting factor for root growth in each layer, 1. wr ( l ) * = w r ( l ) X swdf(l)

(6)

where wr(l) ° is the weighting factor for root growth in each layer,/, after accounting for effects of low soil water content. These new values of wr(l)* are then used to partition root length in the root zone, in the same way as under non-stress conditions, according to equations 3 and 4. Root death In the CERES model, root length in each layer is decremented by 0.5% each day to account for loss in root length. Without any reliable data set the value of 0.5% per day was retained. Soil water balance The simulation of soil water content is necessary in order that the effect of a drying soil on root proliferation can be estimated. The time course of soil water content in each layer was simulated by using a simple model (Monteith, 1986; Robertson et al., 1993a). The transpiration rate is computed as the lesser of the potential extraction rate and demand, which is calculated from the Penman equation and crop cover. The potential extraction rate from each occupied layer of the root zone is characterised by the time required to extract 90% of the extractable water at each depth once the root front arrives. The time constant for extraction of 90% of the extractable water at each depth was assumed similar for both soils: 20 days for the depths from 0 to 90 cm and then increasing (i.e. slower extraction) to 100 days at 200 cm. These are typical values for the experiments in this study (see Robertson et al., 1993a ). For the soil water balance on the oxisol, the extractable water content was set to 0.05 cm 3 cm -3 from 0 to 120 cm and then declining with depth to 0 cm 3 cm -3 at 200 m, giving 80 m m total extractable water for the profile; for the vertisol the extractable water content was set to 0.15 cm 3 cm -3 down to 120 cm (Peries, 1990), and thereafter declining with depth to be 0 at 200 cm, and giving 250 m m total extractable water in the profile. In two of the data sets, rainfall was received by the crop between sowing and the date of root sampling, therefore the model was modified to accomodate rewetting of the soil. Rainfall data for both data sets were reported as weekly totals. In data set 12, the crop received rainfall totals of 5-20 m m in 5 of the 9 weeks of the drying cycle. In data set 13, the crop received 60 m m at 20 das, 130 m m at 25 das, and two falls of 30-40 m m from 25 das until the

MODELLING ROOT GROWTH OF GRAIN SORGHUM

123

time of root sampling at 49 das. In the model, a simple infiltration process was assumed, where the weekly total of rain was received on the middle day of the week. Runoff was assumed negligible, as the site was flat and the soil has high infiltration rates. Rainfall "cascaded" from the surface down the profile, filling, in turn, each layer up to the upper limit, until all the applied water had infiltrated. Infiltration was assumed to be instantaneous. The descent of extraction front was assumed, for simplicity, to be not affected by the rewetting, whereas in reality it is actually halted when rewetting occurs. After rewetting, energy-limited evaporation of 3 m m was assumed to last one day, and thereafter soil-limited evaporation declined with the square-root of time. RESULTS

Sensitivity analysis and calibration Figures 3a and b show the sensitivity of predictions to variation in the model parameters wcg and thfew for root length at 66 das in data set 1. Observed and predicted total root length was 9.82 and 9.63 km m -2, respectively. Figure 3a shows that the predictions of root length density are fairly insensitive to the choice of the value of thfew in eqn. 5, with threshold values ranging from 0.1 to 0.5. Deviation of the predictions from the observed values changed from 5 to 0% at 45 cm and from 0 to 10% at 145 cm as thfew was increased from 0.10 to 0.50. The model predictions in Fig. 3a used the growth habit weighting factor (wcg) of 3. The model over-predicts root length density at the surface and under-predicts at depth, regardless of the choice of the threshold. Figure 3b shows the sensitivity of predictions to variation in the value of wcg. Deviation decreased from +45 to - 3 % at 25 cm and increased from - 32 to + 59% at 125 cm as wcg was reduced from 3 to 0. The over-prediction at the surface is gradually improved as wcg is lowered from 3 to a value of l, thereby making the root distribution more even with depth. With wcg = 0, the partitioning pattern is too even with depth, and the model under-predicts root length density at the surface and over-predicts at depth. Minimal overall deviation from the observed was obtained with wcg = 1. On the basis of the sensitivity analyses shown in Figs. 3a and b, the model was modified so that wcg= 1. The threshold for stress effects on proliferation (thfew) remained at a value of 0.5. Figure 3c shows the predictions from the modified version of the model for data sets 1 and 2, which differed in total root length by a factor of two. Observed and predicted total root length were 9.82 and 9.63 km m -2 for data set l, and 5.31 and 5.72 km m -2 for data set 2. The model was sensitive to the greater observed root production in the data set 1 crop, as well as simulating the correct general distribution with depth. The ability of the model to predict early root growth was tested by running the model for the data set 1 crop at 35 das (Fig. 4 ). Simulated and observed total root length was 3.01 and 2.30 km m -2, respectively. The reasonable

124

MJ. ROBERTSON

ETAL.

Root length density ( c m c m 3) O0 0

0.4

08

1.2

1.6

2.0

0.0

0.4

0.8

1.2

1.6

20

0.4

0.0

i

(o)

0.8

1.2

,'~/

'0

1.6

2.0

20 40

H

I

60

H

0

• /

80

H

100

H

O~

"d 120 0

,'

140

0 .....

,' (

,c

H

9

1-/'

i

/

data set

.......

H

9 ..... H

H

160

H

,'

180 200

H

l

J

i

i

l

,

I

I

I

Fig. 3. Observed and simulated root length density for data set 1 (66 das) with various values of (a) thfew and (b) wcg, used in the model. (c) Observed and simulated root length density for data sets l (66 das) and 2 (cv. Pride) with thfew=0.5 and wcg= 1 used in the model. Horizontal bars are twice the standard error of the observed mean.

Root length density (cm e m -3) 0.0

0.2

0.4

i

i

0

0.6

0.8

1.0

i

i

I

0

1.2

1.4

I I

//" J /

20 C)/,/

I

//

I

// 40

/:/ ///

0 v ~-

@

i

i

//' 60 //

(3

// 8O ©

Simulated-Observed

0

100

120

Fig. 4. Observed and simulated root length density for data set 1 (35 das). Horizontal bars are twice the standard error of the observed mean.

MODELLING ROOT GROWTH OF GRAIN SORGHUM

125

agreement between the observed and predicted root distribution and rooting depth shows that the model performs well for early stages of crop growth. Validation The model was tested with the independent data sets 10-13. The results of the simulations are presented for total root length in Table 3 together with goodness-of-fit statistics for root length density from each 10-cm layer. The simulated and observed root length density profiles are presented in Fig. 5. The model predicted total root length to within 20% for data sets 12 and 13, but under-predicted to an unacceptable extent for the other crops. TABLE3 Observed and simulated total root length, and goodness-of-fit statistics for simulated versus observed root length density for the four validation data sets. R 2 (%) and slope is for the relationship between predicted and observed root length density. Values in brackets for data set 13 refer to simulations for wcg= 3, rather than wcg= l, where wcg is the weighting coefficient for root growth habit Data set

Cultivar

10 11 12 13

Total root length (km m -2 )

Tx 610 E57 Pride Tx 610

Simulated vs. observed root length density

Observed

Simulated

R2

Slope

7.0 8.4 9.3 6.4

5.3 5.6 9.0 5.3

82 85 78 71 (75)

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Model predictions for data set 13 (Fig. 5b) tended to under-predict root length density at the surface and over-predict it at depth, indicating that the model was biasing root growth at depth at the expense of root growth at the surface. This crop received considerable amounts of rain during its growth, and so it was thought that the assumption in the model of a dry soil preventing penetration of adventitious roots at the surface was not valid. When the model was re-run with wcg= 3, rather than wcg= l, thus mimicking normal root development under well-watered conditions, the fit for root length density was improved (Table 3 ) and the under-prediction at the surface and overprediction at depth was lessened (Fig. 5b). Under rainfed conditions where rewetting is likely to occur, it appears that the parameter wcg cannot be assumed to be characteristic of that of a crop growing under continuous drying. In general, the model tended to under-predict root length density for depths between 40 and 100 cm for the other crops, but the fit at the surface and at depth was within 15% of the observed values. The small falls of rain received by the data set 12 and 13 crops led to the model predicting high root length densities in the surface layer compared to the 10-20 cm layer, because the soil water stress factor for root growth was kept high at the surface (i.e. no stress) compared to lower layers, due to the rewetting. DISCUSSION

This paper presents the first published test of a crop root growth model using the CERES framework. The results show that root growth of sorghum under soil drying can be modelled using five simple relationships: the production of new root length as a function of above-ground crop growth; the rate of descent of the root system; the distribution of the new root length with depth, the limitation to root proliferation as a function of soil water content, and a fixed rate of root death.

Root distribution This model improves upon the CERES approach, incorporating the procedure of Jones et al. ( 1991 ), by defining within the model the depth distribution of wr(l), the growth weighting factor, rather than requiring the user to provide a subjective estimate of wr(l) as an input for each soil layer. The distribution of wr(l) that is used in the model assumes an exponential depthdistribution of root length density, and that there are no significant chemical or physical constraints that limit the proliferation of roots under well-watered conditions. The effects of these constraints on proliferation could be added to the model in the form of stress factors that range from 0 to I. Jones et al. ( 1991 ) have described a number of functions that can be used to account for physical and chemical factors that may limit root proliferation e.g. aluminium toxicity and aeration.

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The most significant alteration to the CERES framework, was allowance for the more even partitioning pattern of root length with depth under soil drying, which was achieved by decreasing the parameter wcg from 3 to 1. The improved fit of the model predictions to observed data, after this alteration was made, suggests that soil drying alters the partitioning of root length with depth apart from the effect of low soil water contents on root proliferation. This can possibly be explained as the effect of a dry soil surface inhibiting adventitious root establishment, thus giving rise to a root distribution that is less skewed towards the surface. Blum and Ritchie (1984) showed that penetration of adventitous sorghum roots at the soil surface was inhibited if the soil water content fell below 70% of the extractable water content. The inhibition of penetration had the result of reducing root proliferation near the soil surface, but root growth at depth increased in compensation. A similar result was found by Jordan et al. (1979a): when adventitious roots were pruned at the surface, root growth increased at depth. Lowering the value of wcg may therefore, mimick the effect that soil drying has on inhibiting adventitious root penetration, thereby making the rooting distribution more even with depth. In a more dynamic root growth model, the parameter wcg could be made a function of the surface soil water content, though more information needs to be collected to construct such a function. For instance, the finding of Blum and Ritchie (1984) could be used, viz that adventitous root establishment is inhibited when the fractional extractable water in the surface soil becomes less than 0.7.

Root production This model uses the simple approach of assuming a constant conversion factor for root length growth from production of above-ground biomass. This simplification avoids the need to explicitly account for the dynamic partitioning of biomass to the root system, the losses of root biomass due to exudation and sloughing, and the conversion of root biomass to length via a specific root length. In the data sets used to develop the relationship between root length and above-ground biomass production, the ratio of root length to aboveground biomass appeared to decrease slightly at later stages of crop development. The assumption of a fixed ratio in the model, however, did not introduce large errors in the prediction of total root length, for crops at varying stages of development, except for data set 11. The ratio of root length to above-ground biomass was relatively stable across the experiments reported here, except for the shaded crop, but it may vary more under a wider range of stress levels. A more comprehensive model would take into account the dynamic nature of root growth in relation to shoot growth under varying levels of stress. Some models attempt this. For instance, ROOTSIMU (Huck and Hillel, 1983) partitions total growth between the root and shoot depending on the shoot water status. Under high shoot water

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status, little biomass is partitioned to roots, but under greater levels of stress a greater proportion is partitioned to the root system. For the validation data sets, the model tended to under-predict total root production. This may have been because the relation between above-ground growth and root length production, determined for the oxisol at Redland Bay, was not applicable to the vertisol at Lawes. Alternatively, the under-prediction may have been caused by the different techniques used to sample root length. The size and intensity of core sampling was similar for the two groups of data sets, so the difference may have been due to the technique used to measure root length. It is possible that the digital scanner technique, used to measure length in data sets 1-9, is better able to distinguish dead from live roots compared to the traditional line-intersect technique, used in the validation data sets 10-13. Studies with other crop species in the Department of Agriculture, University of Queensland, have shown that the scanner technique gives lower root length densities that the traditional technique (J.A. Kirkegaard, pers. commun., 1989). The model developed from the image analysis technique would then be expected to under-estimate root production measured by the line-intersect method. This model is limited to simulating root growth only until early grain-filling. This is because the ratio of root length production to above-ground biomass growth was more consistent for samplings taken before, compared to after, early grain-filling. There is little quantitative understanding of the effect of above-ground growth and soil conditions on root growth during grainfilling. Some studies suggest that there is no root growth in grain sorghum after anthesis (e.g. Kaigama et al., 1977), but others have found that roots continue to grow during grain-filling (e.g. Wright and Smith, 1983). The disparity between these results may be due to the differing balances between new root growth and root loss, which depends upon the particular conditions being experienced by the crop and other factors such as the source/sink balance of the crop (Zartman and Woyeroodzic, 1979) and its degree of perenniality. Also, during grain-filling, root senescence can be substantial (Blum and Arkin, 1984; Robertson et al., 1993b) and little quantitative information exists concerning its control. In CERES-Maize, it is assumed that roots are grown during grain-filling only when there is assimilate available in excess of that required for grain-filling. However, at present there is little quantitative information available to support this assumption. A clearer understanding of the factors controlling root growth during grain-filling is needed, and is particularly important for simulation of crop growth in environments where terminal drought occurs and crop productivity is closely linked to water extraction after flowering (Ludlow and Muchow, 1990). In conclusion, this paper has shown that root growth of an annual cereal crop can be simulated using five simple relationships. However, the model needs futher testing under a wider range of conditions. The components of

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the model that need particular attention are: the lowering the root growth habit factor (wcg) under soil drying to make root growth more even with depth, and the consistency of the ratio between root length production and above-ground biomass growth. ACKNOWLEDGMENTS

P.S. Carberry, of CSIRO Division of Tropical Crops and Pastures, made valuable comments on an early draft of the manuscript. Thanks to R. Peries for permission to use his root length data.

REFERENCES Barraclough, P.B. and Weir, A.H., 1988. Effects of a compacted subsoil layer on root and shoot growth, water use and nutrient uptake of winter wheat. J. Agric. Sci., Camb., 110:207-216. Bloodworth, M.E., Burleson, C.A. and Cawley, W.R., 1958. Root distribution of some irrigated crops using undisrupted soil cores. Agron. J., 50:317-320. Blum, A. and Arkin, G.F., 1984. Sorghum root growth and water use as affected by water supply and growth duration. Field Crops Res., 9:13 l-142. Blum, A. and Ritchie, J.T., 1984. Effect of soil surface water content on sorghum root distribution in the soil. Field Crops Res., 8:169-176. Gerwitz, A. and Page, E.R., 1974. An empirical mathematical model to describe plant root systems. J. Appl. Ecol., I l: 773-782. Hamblin, A., 1985. The influence of soil structure on water movement, crop root growth and water uptake. Adv. Agron., 38:95-158. Herbert, S.W., 1984. Development of yield in dryland grain sorghum hybrids. M. Agr. Sci. Thesis, University of Queensland, 243 pp. Hignett, C.T., 1976. A method of sampling and measuring cereal roots. J. Aust. Inst. Agric. Sci., 42: 127-129. 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. Jones, C.A. and Kiniry, J.R., 1986. CERES-Maize: A simulation model of maize growth and development. Texas A&M University Press, College Station, TX, 194 pp. Jones, C.A., Bland, W.L., Ritchie, J.T. and Williams, J.R., 199 I. Simulation of root growth, ln: R.J. Hanks and J.T. Ritchie (Editors), Modeling Plant and Soil Systems. ASA, Madison, WI, pp. 74-101. Jordan, W.R., McCrary, M. and Miller, F.R., 1979. Compensatory growth in the crown root system of sorghum. Agron. J., 71: 803-806. Kaigama, B.K., Teare, I.D., Stone, L.R. and Power, W.L., 1977. Root and top growth of irrigated and non-irrigated grain sorghum. Crop Sci., 17: 555-559. Kirkegaard, J.A., 1990. The effects of compaction on the growth of pigeonpea on clay soils. Ph.D. Thesis, University of Queensland, Australia, 324 pp. Ludlow, M.M. and Muchow, R.C., 1990. A critical evaluation of the traits for improving crop yields in water limited environments. Adv. Agron., 43:107-153. Mayaki, W.C., Stone, L.R. and Teare, 1.D., 1976. Irrigated and non-irrigated soybean, corn and grain sorghum root systems. Agron. J., 68: 532-534. Merrill, S.D. and Rawlins, S.L., 1979. Distribution and growth of sorghum roots in response to irrigation frequency. Agron. J., 71: 735-745.

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Monteith, J.L., 1986. How do crops manipulate water supply and demand? Phil. Trans. R. Soc. London A, 316: 245-289. 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, Patancheru, India, pp. 30-34. Myers, R.J.K., 1980. The root system of a grain sorghum crop. Field Crops Res., 3: 53-64. Newman, E.I., 1966. A method of estimating the total length of root in a sample. J. Appl. Ecol., 3: 139-145. Peries, R.R.A., 1990. Water use, water use efficiency and yield in dryland grain sorghum (Sorghum bicolorL. Moench). Ph.D. Thesis, University of Queensland, Australia, 213 pp. Retta, A., Sullivan, C.Y. and Watts, D.G., 1984. Relationships of root length to root dry weight in grain sorghum. Sorghum Newsletter, 27" 146-147. Ritchie, J.T., 1986. The CERES-Maize model. In: C.A. Jones and J.R. Kiniry (Editors), CERESMaize: A Simulation Model of Maize Growth and Development. Texas A&M University Press, College Station, TX, pp. 3-6. Ritchie, J.T., Godwin, D.C. and Otter, S., 1984. CERES-Wheat: A user orientated wheat yield model. Preliminary documentation, Agristars Publication No. YM-U3-04442-JSC-18892. Michigan State University, MI, 252 pp. Robertson, M.J., 1991. Water extraction by field-grown grain sorghum. Ph.D. Thesis, University of Queensland, Australia. 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, Queensland, Australia. QDPI, Warwick, 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. Rose, D.A., 1983. The description of the growth of the root system. Plant Soil, 75: 405-416. Rosenthal, W.R., Vanderlip, R.L., Jackson, B.S. and Arkin, G.F., 1989. SORKAM: A grain sorghum crop growth model. Research Center Program and Model Documentation. MP1669. Texas Agricultural Experimental Station, College Station, TX. Santamaria, J.M., 1987. Study of traits for drought resistance in Sorghum bicolor L. Moench, with emphasis on osmotic adjustment. M. Agr. Sci. Thesis, University of Queensland, Australia, 192 pp. 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. Tennant, D., 1976. Wheat root penetration and total available water on a range of soil types. Aust. J. Exp. Agric., 16: 570-577. Torsell, B.W.R., Begg, J.E., Rose, C.W. and Byrne, G.F., 1968. Stand morphology of Townsville lucerne (Stylosanthes humulis). Seasonal growth and root development. Aust. J. Exp. Agric. Anim. Husb., 8: 533-543. 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. Zartman, R.E. and Woyeroodzic, R.T., 1979. Root distribution patterns of 2 hybrid grain sorghums under field conditions. Apron. J., 71: 325-328.