STRESS DAY INDEX MODELS TO PREDICT CORN AND SOYBEAN YIELD RESPONSE TO WATER TABLE MANAGEMENT

R. O. EVANS1, R. W. SKAGGS2

 

1   Assistant Professor and Extension Specialist, Biological and Agricultural Engineering,  North Carolina State University, Raleigh, N.C.

2   William Neal Reynolds and Distinguished University Professor, Biological and Agricultural  Engineering, North Carolina State University, Raleigh, N.C.

 

 

15th International Congress of ICID, The Hague - ISime Congris International de Id CUD, La Haye.

Workshop on Subsurface Drainage Simulations Models - Atelier sur les modiles de simulation du drainage. ICID - CIID, CEMAGREF, 1993,219 - 234.

Printed in France.

 

 

ABSTRACT

Drainage and related agricultural water table management systems are being

designed in humid regions of the United States using the water management simulation model,

DRAINMOD. Since excessive and deficient soil-water conditions are stressful to most crops,

crop yield is a useful measure of the effectiveness of the water management system design. Stress

day index (SDI) models are presented which can be used to predict corn and soybean yield

response to excessive and deficient soil-water conditions. The relative yield - SDI models

developed herein and SDI models reported in the literature were tested using a comprehensive

data base developed from corn and soybean yield studies conducted in eastern North Carolina

over the past 35 years.

 

 

INTRODUCTION

Rainfall is extremely variable during the growing season in the southeastern U.S. It seldom occurs

in an amount and distribution necessary to achieve high yields more often than about one year in

ten. In other years, soil-water, either too much and/or too little, is usually the single most limiting

factor for high yields (Sopher, 1969).

 

Yield reductions often develop from stresses caused by excessive soil-water conditions on poorly

drained soils. The yield reductions may result either (1) from the inability to plant and tend the

crop at the right time due to poor trafficability or (2) from direct damage to the crop due to a lack

of oxygen (anaerobiosis); biochemical toxicity; and/or nutrient deficiencies; resulting from an

elevated water table or excessive soil-water condition. Although annual rainfall exceeds

evapotranspiration on the average, droughts ranging from a few days up to several weeks occur in

many years between June and September. While excessive soil-water is a major concern,

substantial yield reductions resulting from deficient soil-water conditions occur frequently, even

on poorly drained soils.

 

The primary purposes of agricultural water management systems are to increase production

efficiency and yield reliability by improving the soil-water environment. Crop yield is a practical

measure of crop response to water stresses for the purpose of optimizing the water management

system design. The stress-day-index (SDI) approach (Hiler, 1969) was developed to quantify the

cumulative effect of stresses imposed on a crop throughout the growing season.

Evans et al. (1990) reported crop susceptibility factors for corn and soybean stressed by excessive

soil-water conditions. Using these crop susceptibility factors and field data from Ohio, Evans et

al. (1991) developed yield - SDI relationships to estimate corn and soybean yield response to

excessive soil water conditions. Evans and Skaggs (1992) tested these yield - SDI relationships

along with other SDI models reported in the literature against corn and soybean yields observed in

field experiments conducted in eastern North Carolina. The purpose of this paper is to summarize

the Stress Day Index relationships developed and tested in North Carolina.

 

 

STRESS DAY INDEX APPROACH

The general form of the SDI concept described by Hiler (1969) may be expressed

 

 

 

 

where n is the number of growth periods (distinct stages of physiological development) and SD

and CS are stress day and crop susceptibility factors for period i, respectively. The subscript x has

been added herein and when replaced by w, d, or p is used to denote the specific yield reducing

condition, either wet, dry or planting delay, respectively.

 

 

Stress Day Factor

The stress day factor (SD) is a measure of the intensity and duration of stress. Sieben (1964)

related crop response to fluctuating water tables using so-called SEW30 values computed from

 

 

where xj is the water table depth below the soil surface on day i, and n is the number of days in

the period being considered. Negative terms inside the summation are neglected such that the

summation is a measure of the exceedence of some critical water table depth. Sieben (1964)

assumed the critical depth to be 30 cm, so the SEW30 value has units of cm-days.

 

Shaw (1974) related corn yield to deficient soil-water conditions. He defined a stress day factor

based on 5-day evapotranspiration (ET) deficient computed as

 

 

where SDj was the stress factor for period i, ETjj was the actual evapotranspiration that occurred

in period i, on day j, and PETjj was the potential evapotranspiration in period i, on day j. The SDj

was computed for 5-day intervals beginning 40 days prior to silking and ending 44 days after

silking for a total of 17 5-day periods. Whenever the stress day factor for two or more

consecutive 5-day periods was greater than 4.5, (maximum possible value is 5.0) a severe stress

weighting factor (WF in equation 3) of 1.5 was used; otherwise, the WF was 1.0.

 

Skaggs et al. (1982) developed a relationship to estimate the effect of planting date delay on corn

yield. Their relationship was developed from non-irrigated planting date studies presented by

Krenzer and Fike (1977). Seymour et al. (1992) conducted similar planting date studies on a field

with subirrigation. After combining results of the two studies, Seymour et al. (1992) defined the

plant delay stress day factor as the number of days planting was delayed past an "optimum" date

for a given location.

 

 

Crop Susceptibility Factor

The crop susceptibility factor is a measure of the crop susceptibility to a unit of stress and is a

function of crop species and its stage of development. The crop susceptibility factor is determined

experimentally by subjecting the crop to a critical level of stress during each discrete physiological

growth stage and measuring the yield response. The crop susceptibility factor for each growth

stage as defined by Hiier (1969) is computed by

 

 

where Xi is the harvested crop yield when subjected to the critical stress at growth stage i and X

is the crop yield when no stress is applied. Crop susceptibility factors have been reported for a

few crops (Desmond et al., 1985; Evans et al., 1990; Evans, 1991; Hiler and Clark, 1971;

Mukhtar et al., 1990; Ravelo et al., 1982; Seymour et al., 1992; Shaw, 1974; Sudar et al., 1979).

 

Evans et al. (1990) reported crop susceptibility factors determined for corn and soybean plants

stressed by excessive soil-water conditions during six physiological growth stages. Experiments

were conducted using lysimeters with stress periods induced by raising the water table to the soil

surface once for ten consecutive days for corn and for seven consecutive days for soybean. Their

results are summarized in Table 1.

 

Shaw (1974) developed crop susceptibility factors to relate corn yield to deficient soil-water

conditions, Table 2. Shaw's values were developed from controlled experiments conducted by

Denmead and Shaw (1960); Wilson (1968); Classen and Shaw (1970); and Mallett (1972.). For

periods other than shown in Table 2, a susceptibility factor of zero (0) is used.

Soybean yield response to dry stress has been reported in several studies (Brown et al., 1985;

Hiler et al., 1974; Sepaskhah, 1977; Sionit and Kramer, 1977; Smajstrla and Clark, 1982; Snyder

et al., 1982). Evans et al. (1986) compared susceptibility factors determined from these studies

and found them to be quite variable. Sudar et al. (1979) estimated soybean CS values for Iowa

from the literature. While not specifically stated, the values reported by Sudar were likely

developed for indeterminate varieties typically grown in the Midwestern U.S. Evans (1991)

combined the results reported by Sudar with other data in the literature to develop CS values to

estimate the sensitivity of determinate variety soybean to dry stress. The estimates reported by

Evans (1991) and used herein are summarized in Table 3.

 

 

 

Table 1. Growth stage and CS values used to develop SDI relationships for excessive

soil-water stresses (eq. 9 for corn, eq. 12 for soybean). (After Evans et al., 1990)

 

 

 

 

Table 2. Crop susceptibility factors used in eq. 10 to evaluate deficient soil-water

conditions on corn yield. (After Shaw, 1974).

 

 

DEVELOPMENT OF STRESS DAY INDEX MODELS

Once the crop susceptibility factors are known, the relationship between crop yield and SDI can

be determined for a given type of stress (excess, deficient, plant delay) from experimental data

using regression analysis to relate yield to the actual soil-water conditions (Stress Day Factor).

These experimental data should be different from those used to determine the CS factors. The

generalized yield SDI relationship determined from simple linear regression is given by:

 

 

 

 

 

Table 3. Crop susceptibility values used in eq. 13 to relate soybean yield (determinate

varieties) to deficient soil water stresses. (After Sudar et al., 1979; Evans, 1991).

 

where Yi is the actual yield (kg/ha) observed in year i, Yp is the potential or base maximum yield

that would occur in the absence of any soil-water related stress, a is the yield reduction per unit of

SDI (slope of regression line). The SDIi is computed from equation 1 using the appropriate CS

values from Tables 1, 2 or 3 and equation 2 or 3 to compute the SD factor. When expressed in

terms of actual yield, Yi, Yp, and a are site dependent, influenced by a variety of factors including

soil, climate, fertility, crop variety, etc. The influence of these factors can be minimized by

normalizing equation 5 to

where RYj is the relative yield, which when multiplied by 100, is expressed as a percent of

potential yield, Yp; and b is the RY reduction per unit of SDI. Equation 6 is more universal than

equation 5 because the Yp accounts for the influence of soil, climate, fertility, and crop variety.

 

Evans et al (1991) developed yield - SDI models to relate corn and soybean yields to excessive

soil-water conditions. The relative yield models were based on SDI relationships using SEW30

(0.3-m water table depth) to describe the high water table stress criteria and the CS factors

determined in studies conducted in North Carolina (Table 1). The models were developed using

existing field data for SDI and corn and soybean yield data from Ohio. The corn model was tested

against data from India and North Carolina and explained 69 % of the relative yield variance for

the pooled data, Figure 1. The soybean model explained 66 % of the variance in relative yield for

six years of soybean data from Ohio, Figure 2.

 

 

Figure 1. Corn yield SDI model developed from linear regression of corn data from Ohio

(Schwab et al., 1975,1985) and CS values from North Carolina. (After Evans et

al., 1991).

 

 

Using similar procedures, yield - SDI models have been developed to relate corn yield to deficient

soil-water conditions (Shaw, 1974) and to planting date delays (Seymour et al, 1992). Combining

data from the literature with SDI results presented by Sudar et al. (1979), Evans (1991)

developed a yield - SDI model to relate soybean yield to deficient soil-water conditions. Using

data from a 3-year study reported by Fike (1974), Evans (1991) developed a yield - SDI model to

relate soybean yield to planting delays. The above relationships and submodels are summarized in

Table 4.

 

TESTING AND VALIDATION OF STRESS DAY INDEX MODELS

The water management simulation model, DRAINMOD, (Skaggs, 1978) simulates soil-water

conditions in high water table soils. The model considers rainfall, infiltration, surface runoff,

drainage, storage and deep seepage to perform a water balance for the soil profile.

Hardjoamidjojo and Skaggs (1982) incorporated approximate methods based on the stress-dayindex

concept to predict corn yield response to stresses caused by excessive and deficient soilwater

conditions. The general crop response model represented by these modifications was

described by Skaggs et al. (1982) as

 

 

 

 

where RY is the overall relative yield for a given year, RYW is the relative yield that would be

obtained if only wet stresses occurred, RYd is the relative yield that would be obtained if only dry

stresses occurred, and RYp is the relative yield resulting from planting delays only.

 

 

Table 4. Relative yield - stress day index relationships used to predict corn and soybean yield response to excessive

and deficient soil water conditions and to planting delays.

 

 

Figure 2. Soybean yield - SDI model developed from linear regression of soybean data from

Ohio (Schwab, 1985) and CS values determined in North Carolina. (After Evans

et al., 1991).

 

 

To compare predicted yields to field measured yields, relative yield may also be expressed as:

 

 

where Y is the measured or observed yield for a given year and Y0 is the yield that would have

occurred in the absence of any soil-water related stresses. Y0 refers to the base maximum yield

that would occur for a consistent combination of agronomic inputs that were not limited by soil -

water.

The relative yield components, RYw, RYd and RYp, are assumed to be independent with

individual submodels used to calculate each component. Each yield - SDI submodel should be

developed and tested independently as discussed in the previous section. The validity of the

generalized model (equation 7) should then be tested with field data comprising different types

and amounts of soil-water stress.

 

 

Observed Yields (Field Validation Data)

Field experiments have been conducted on the Tidewater Research Station near Plymouth, N. C.

for over 50 years. The soils at the Tidewater Station are poorly drained. Drainage of most fields

has been improved by the installation of parallel ditches or drain tile/tubing so that the site is

conducive for evaluation by DRAINMOD. The drainage intensity varies from field to field as

discussed by Evans (1991). Even with improved drainage, soil wetness is a problem in some years

resulting in planting delays and high water table conditions during the growing season. Droughty

conditions develop during periods with below normal rainfall. Corn and soybean are the

predominant crops grown on the station.

 

Five independent studies were identified that provided data suitable to evaluate the SDI relations

presented in Table 4. The source and description of these yield data and soil, site, and drainage

system parameters for each study were reported by Evans (1991).

 

 

Validation Procedure

Overall relative yield (equation 7) was predicted using DRAINMOD with equations 9, 10, and 11

to predict the individual corn yield components and equations 12, 13, and 14 to predict the

individual soybean yield components. The corn yield relationship given by equation 10 was

evaluated both with (Method 2) and without (Method 1) the severe-stress dry weight factor (WF)

(equation 3) described by Shaw (1974, 1978, 1983)(See footnote at bottom of Table 4).

Measured or observed inputs were used for the DRAINMOD simulations wherever possible.

These included most of the drainage system parameters, including periods of controlled drainage

and subirrigation, hydraulic conductivity, maximum root depth, and Portsmouth soil properties

reported by Gilliam et al., 1978). Daily maximum and minimum temperatures and daily rainfall

were available from station records. Daily rainfall values were converted to hourly values by the

disaggregation methods described by Robbins (1988). Prior to predicting yield, the inputs were

calibrated by comparing 12 site-years of measured water table data to predicted values. The

calibration procedure involved starting with all known or estimated inputs, running simulations for

those fields and periods with water table data, then comparing predicted to observed water tables.

This procedure was continued while varying other "estimated" inputs, primarily surface storage,

upflux and root depth vs time relationship, until the combination of inputs providing the best

water table fit were identified. The RMSE between the observed and simulated water table depths

ranged from 12.1 to 21.2 cm/day. The RMSE and AABE of prediction for the pooled data was

15.8 and 11.3 cm/day, respectively. These results indicate that predicted values were in relatively

good agreement with observed values. Detailed input values used in the simulations were reported

by Evans (1991).

 

 

Statistical Procedures

The adequacy of the SDI models was tested by computing average error, average absolute error,

root mean square error, and correlation between predicted and observed RY using standard

statistical procedures (Evans, 1991). The fit of the predicted yields to the 1:1 line (perfect model)

was compared by first determining the best fit linear regression line between predicted and

observed yield using the method of least squares (SAS, 1985; Sendecor and Cochran, 1967). The

intercept and slope of the best fit regression line was compared to those of the 1:1 line (intercept

= 0, slope = 1) using the methods described by Ostle (1963). Finally, the fit of the data (predicted

vs observed relative yield) was compared to the 1:1 line. The coefficient of determination, r2, of

this comparison was determined by dividing the best fit regression model sum of squares by the

corrected total sum of squares. The corrected total sum of squares for this comparison was the

best fit regression model sum of squares plus the error sum of squares (RYi - RY'i)2 where RYi is

the relative yield predicted by the simulation model (not regression model) and RY'i is the

observed relative yield.

 

 

Predicted Corn Yield

Predicted relative yield components (wet, dry, plant delay), overall predicted relative yield and

observed yields were reported in detail by Evans (1991). Space constraints prohibit their

presentation here. Observed and predicted relative yield covered the full range of values from 0 to

100 percent, although a majority of values (about 80 percent) occurred in the upper half of the

range (RY values between 50 and 100 percent). Over the total period, wet and dry stresses

reduced average predicted RY about equally (about 15 percent each). In some years, predicted

RY reduction was due entirely to wet or dry stress, but in most years, both wet and dry stresses

contributed to the predicted RY reduction.

 

The AE, AABE, and RMSE for the pooled data are summarized in Table 5. The average error

helps identify systematic errors in the prediction method. When the AE is greater than zero

indicates that the model may be systematically overestimating observed values or underpredicting

if the AE is less than zero. As seen in Table 5, the negative AE indicates yields were slightly

underpredicted on average.

 

The AABE and RMSE provide an indication of the overall performance of the model in terms of '

the variation between predicted and observed values. The AABE indicates the average magnitude

(sign ignored) of the error of each predicted value, with all errors weighted the same. If all errors

are about the same magnitude, the AABE and RMSE will be about the same. The RMSE '

increases above the AABE as the number and magnitude of the poorer predictions increase. Thus, '

the RMSE provides a better indication of the range of errors.

Combining the results of the AABE and RMSE indicates that both methods had prediction errors j

of similar magnitude on average (AABE of 7.95 vs 8.89), but, prediction errors involving the

severe-stress WFd (Method 2) had a larger variation within individual observations (RMSE 9.89 j

vs 13.05).

 

 

 

Table 5. Goodness of fit evaluation of predicted to observed overall RY.

 

 

The sensitivity of the prediction methods to year to year variation in soil-water stresses is best

evaluated by comparing correlation between observed and predicted RY. These results are also

summarized in Table 5. The intercept of the best fit regression lines for Methods 1 and 2 did not

test significantly different from zero (0) at the 5 percent level of significance. The regression lines

shown were then forced through the 0 intercept and the slope re-computed and tested against the

slope of the 1:1 line (perfect model). The slope of Method 1 was not significantly different from 1

while the slope involving a severe-stress dry weight factor was significantly less than 1 indicating

that RY was underpredicted when the severe-stress weight factor was used. Relative yield

predicted by Method 1 is plotted against observed RY in Figure 3. Method 1 accounted for nearly

80 percent of the year to year variation in observed corn yield.

 

 

Figure 3. Observed and predicted corn relative yield, best fit regression line for pooled data

from all North Carolina data (94 observations) and 1:1 line. (After Evans and

Skaggs, 1992).

 

 

Predicted Soybean Yield

Soybean RY was predicted by equation 7 using equations 12, 13, and 14 to compute the

individual yield components (wet, dry, and plant delay). The individual relative yield components,

overall relative yield, and observed relative yield were summarized by Evans (1991).

Predicted and observed RY are plotted in Figure 4. Over 90 percent of the RY values (both

predicted and observed) lie between 60 and 100 percent. Relative yields less than 50 percent were

observed for only 6 cases. Average error, AABE and RMSE are summarized in Table 5. The AE

was -0.44 percent, a slight underprediction.

 

 

The intercept of the best fit regression line between predicted and observed RY yield tested

significantly greater than zero, Table 5. This could be due to the lack of data points at the lower

end of the range. It could also be due to inadequacy of the prediction method. Predictions and

trends were good for some years and completely reversed for others. Regardless, the adequacy of

the model is best described in terms of correlation to the 1:1 line. The slope of the regression line

forced through the intercept did not test significantly differently from 1, but the model explained

only 47.9 percent of observed RY variation when compared to the 1:1 line.

The poor correlation between predicted and observed soybean RY may be due to several factors.

Soybean can tolerate short term stress with little effect on yield. For example, if dry conditions

exist during the pod set period, fewer pods are set. If conditions become more favorable during

the subsequent pod fill stage, larger beans can be produced in each pod resulting in about the

same yield as would have occurred if more pods had been set but filled with smaller beans. During

stressful periods, some physiological processes can even be temporarily halted until more

favorable conditions develop (Dunphy, not dated). The simple prediction methods evaluated

herein are not capable of predicting these complex physiological recovery processes.

 

 

 

Figure 4. Observed and predicted soybean relative yield, best fit regression line for pooled

data from North Carolina (128 observations) and 1:1 line. (After Evans and

Skaggs, 1992.)

 

 

 

SUMMARY AND CONCLUSIONS

Crop susceptibility factors were presented for corn and soybean subjected to wet soil-water

conditions (wet stresses). Using regression analysis, the crop susceptibility factors were used to

develop Stress Day Index Models to predict corn and soybean yield response to high water table

conditions.

 

Corn and soybean relative yield-stress day index models were tested with yields observed in field

experiments conducted in eastern North Carolina. The yields were observed over a wide range of

weather and soil-water conditions. Daily soil-water stresses resulting from the variable weather

conditions were predicted using DRAINMOD. Yield reduction resulting from excessive and

deficient soil-water stresses and planting delays were then predicted. All predicted yields were

compared to observed yields with the goodness of fit evaluated using several statistical indicators.

The results presented showed that long-term average corn and soybean yields can be predicted

with DRAINMOD using SDI models to predict the individual yield components (wet, dry and

plant delay). The data tested suggest that severe-stress dry weight factors are not necessary to

predict corn yield response to deficient soil-water stresses under traditionally high water table

conditions such as exist in eastern North Carolina. Minor modifications to DRAINMOD would

facilitate omission of the severe-stress criteria. This would reduce the required yield inputs

because several 5-day CS values with the same value could be combined as one input. The

methodology used to describe the deficient yield-SDI would then parallel the methods currently

used to describe the wet yield-SDI relationship.

 

 

 

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