Published online 19 October 2005
Published in Agron J 97:1478-1484 (2005)
DOI: 10.2134/agronj2004.0227
© 2005 American Society of Agronomy
677 S. Segoe Rd., Madison, WI 53711 USA
Agroclimatology
Modification of a Crop-Specific Drought Index for Simulating Corn Yield in Wet Years
Kenneth G. Hubbarda,* and
Hong Wua,b
a High Plains Regional Climate Center, Univ. of Nebraska, Lincoln, NE 68583-0728
b Current address: Texas Inst. for Appl. Environ. Res., Tarleton State Univ., Stephenville, TX 76402
* Corresponding author (khubbard1{at}unl.edu)
Received for publication August 27, 2004.
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ABSTRACT
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Drought occurs when there is a deficit in soil water supply to the plant. Severe drought limits crop yield by causing the plant's water use to be limited compared with a well-watered crop. Too much water (flooded soils) also causes stress to the plant whose roots are in saturated soil for long periods. Both situations lead to crop water stress, ultimately resulting in reduced crop yield. Since flood and drought can occur intermittently in cropping, an effective yield predictor should contain both flood and drought stress components for better representation of the range of natural conditions the plant might encounter during its growth period. This paper details the modification of the Crop-Specific Drought Index (CSDI) model by introducing a soil saturation factor, resulting in a Crop-Specific Stress Index (CSSI) model. The study was conducted in eastern Nebraska and southeastern Minnesota. The coefficients used in the CSSI model were estimated by a jackknifing procedure based on 1971–2002 climate data, nonirrigated yield data of corn (Zea mays L.), and soil information retrieved from the STATSGO database in the crop districts. Results show that all indicators of agreement between the estimated and actual yields show improvement of the new CSSI model over the old CSDI model in all districts. Results also show that the CSSI model outperforms the CSDI model in years characterized by soil saturation. For instance, the CSDI for 1993 overestimates the relative yield in northeastern Nebraska by about 28% while the CSSI underestimates the 1993 yield by 3%.
Abbreviations: COOP, Cooperative Weather Station Network • CSDI, Crop-Specific Drought Index • CSSI, Crop-Specific Stress Index • ET, evapotranspiration • RMSE, root mean square errors • STATSGO, State Soil Geographic database
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INTRODUCTION
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A SUFFICIENT SUPPLY of soil water is essential for crop growth, replacement of transpiration loss, and transportation of crop nutrients to roots. Drought occurs when there is a deficit in soil water supply to the crop. Severe drought limits crop water use and reduces yield. Earl and Davis (2003) summarized three main mechanisms through which corn yield is reduced by soil water deficit: (i) reduced canopy absorption of incident photosynthetically active radiation, (ii) decreased radiation use efficiency, and (iii) reduced harvest index.
In rainfed cropping regions, heavy rainfalls may cause excessive soil water, leading to waterlogging. Waterlogging reduces crop yield by adversely affecting a number of biological processes in crops and soil: (i) oxygen deficiency is prolonged in the root zone, (ii) water uptake is affected by decreased root growth and distribution, (iii) N uptake is reduced because large amounts of N are lost during flooding, (iv) toxic compounds are increased in the soil and the plant, and (v) crops are more susceptible to disease and drought (Ritter and Beer, 1969; Wenkert et al., 1981; Kanwar et al., 1988; Mukhtar et al., 1990).
Meyer et al. (1993a) developed the CSDI to function as a drought monitoring and assessment tool. The CSDI integrates three critical factors: crop specificity, soil specificity, and weather specificity. The main factors addressed were the ratio of water consumed by the crop to the potential consumption and crop sensitivity during the growth stages in which water stress occurs. Currently, the CSDI was parameterized for corn (Meyer et al., 1993a), soybean [Glycine max (L.) Merr.] (Meyer and Hubbard, 1995), wheat (Triticum aestivum L.) (Xu, 1996), and sorghum [Sorghum bicolor (L.) Moench] (Camargo and Hubbard, 1999). Meyer et al. (1993b) demonstrated that the CSDI model was an effective drought monitoring and assessment tool in the east central crop-reporting district of Nebraska that will objectively and reliably monitor and assess probable weather impact on corn yields at any point during the growing season.
In cropping, flood and drought can occur intermittently leading to yield losses. Therefore, an effective yield predictor should represent the influence of both flood and drought stress. However, the CSDI model does not distinguish between optimum moisture supply and moisture surplus.
In addition, the original CSDI model was developed and validated with data from the 1970s and 1980s from Nebraska's East Central Crop Reporting District. Although both the coefficients of determination and D-index of agreement values indicated good agreement between the predicted and observed values, there is no guarantee that a model will perform at an equal level when used to predict the future even if the model result is consistent with historical data (Oreskes et al., 1994). Therefore, the model should be periodically calibrated using recent data (Konikow and Bredehoeft, 1992). In the interim, hybrids and farm management practices have likely changed. Plus, the soil information used by the CSDI model should be updated to the latest available digital soil information.
The objectives of this paper were to (i) modify the CSDI by introducing a soil saturation factor to better represent corn yields influenced by both drought and flooded soils, resulting in a new index, CSSI; (ii) estimate the parameters used in the CSSI model using recent weather information, updated soil information, and National Agricultural Statistics Service data; and (iii) evaluate the new model in regions with contrasting moisture supplies: the northeastern, east central, and southeastern crop districts in Nebraska and the southeastern crop district in Minnesota. In this study, the estimated parameters will be district specific.
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CSDI BACKGROUND
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The CSDI is a combination of physical and empirical relationship between evapotranspiration (ET) in each growth stage and the yield:
 | [1] |
where Y is detrended actual crop yield, YP is potential crop yield, and ETi and ETpc are the actual and potential ET of the crop at the ith growth stage. The ratio of ET and ETpc reflects the degree to which the crop could meet the atmospheric demand for ET; n is the number of growth stages considered here, and the exponent 
i indicates sensitivity of the crop to soil water stress in the ith stage. The crop's growth stages, determined by the accumulated growing degree days (GDD), and their respective i values derived by Meyer et al. (1993a) are presented in Table 1.
The foundation of the CSDI model is the soil water balance that takes the form:
 | [2] |
where S (mm) is the total soil water in the root zone, t is time, P (mm) is precipitation, ET (mm) is actual ET, RO (mm) is runoff, Dr (mm) is drainage below the root zone, and I (mm) is irrigation. This study only considers rainfed corn so that irrigation is zero in the model. A 24-h time step is used with daily precipitation as input to the model. Runoff is estimated from the total precipitation, relative fraction of soil water present, and soil water retention factor (McCuen, 1982). The drainage is computed by Campbell's equation (Campbell, 1985). This soil water model performed satisfactorily in estimating total soil water over a range of soil types, weather, and vegetation landscapes (Robinson and Hubbard, 1990; Mahmood and Hubbard, 2003).
Potential ET (ETp) is calculated using the Penman (1948) approach with the wind function derived by Kincaid and Heermann (1974). The ET is the summation of actual evaporation (E) and transpiration (T). The relation between E and ETp is presented as follows:
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where d is the number of days since the last precipitation. A function of crop and phenology specific crop coefficient (Kc), ETp, and a soil water reduction factor (f) provides actual transpiration:
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The f is a function of available soil water and water-holding capacity of the soil and changes in response to the ratio of available water to potential available water:
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where WHC is water-holding capacity and F a critical ratio of available water to potential available water. For this study, F = 0.5.
Potential ET of a specific crop is
 | [6] |
From Eq. [1], it can be shown that the impact of drought on crop yield is estimated by two very important criteria: one is the moisture actually used by the crop compared with the moisture that crop could potentially use; the other is the sensitivity of the crop to moisture stress during different growth stages.
The CSDI calculation requires three types of data: weather, soil, and crop phenology. Weather data include precipitation, maximum and minimum temperatures, dew point temperature, wind speed, and solar radiation, used in determining soil moisture and ET. Wind speed is estimated by the approach derived by Kincaid and Heermann (1974). Dew point temperature and solar radiation are estimated from the observed maximum and minimum temperature (Hubbard et al., 2003; Mahmood and Hubbard, 2002).
The CSDI model estimates water status for specified soil layers on a daily basis. Three soil water-holding characteristics are specified for the model: the wilting point, field capacity, and saturation. In addition, coefficients for the runoff curve and for the drainage parameterization are specified. Phenology data, used to determine crop maturation rates and growth cycles, consist of emergence and maturity dates.
The model is valid where soil moisture is limiting, provided other factors such as fertilizer, insects, disease, hail, wind damage, etc., are not limiting and yield is not reduced by these factors (Camargo and Hubbard, 1999).
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DATA AND METHODS
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Study Region
This study was conducted in two regions within the Corn Belt: eastern Nebraska and southwestern Minnesota. Nebraska has experienced many droughts of varying magnitude, duration, and extent since precipitation was first recorded in the state. For instance, the recent 2002 drought caused a loss of $1.2 billion in agriculture in Nebraska (IANR, 2003). According to a report created by the National Climatic Data Center (NCDC) of NOAA, the 1971–2000 annual temperature and precipitation normals are 9.1°C/68.2 cm, 10°C/75.1 cm, and 10.08°C/78.8 cm for northeastern, east central, and southeastern Nebraska, respectively. The 1971–2000 temperature/precipitation normals are 6.9°C/84.7 cm for southeastern Minnesota. Thus, southwestern Minnesota has more moisture supply and likely has lower ET than does eastern Nebraska.
Data and Sources
The period of the study was 1971–2002. The Cooperative Weather Station Network (known as COOP stations in the United States) records, including temperature and precipitation, during 1971–2002 in three crop districts in Nebraska and one district in Minnesota were obtained from the High Plains Regional Climate Center (HPRCC). Figure 1
shows locations of the weather stations used in the study.
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Fig. 1. Distribution of COOP stations used in the study in eastern Nebraska and southeastern Minnesota.
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Soil information was retrieved from the USDA–NRCS soil geographic databases—the State Soil Geographic database (STATSGO) (Earth Syst. Sci. Cent., 1998)—for the selected COOP weather stations in the two states. Hydrologic group (a soil classification system developed by SCS), soil texture, and bulk density were obtained for each station on the basis of its location. The percentages of sand and clay were obtained for the soil texture according to Table 2. Finally, the field capacity, wilting point, and saturation were estimated based on the percentages of sand and clay using the Soil Texture Triangle Hydraulic Properties Calculator (Oram, 2005).
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Table 2. The relative amounts of sand, soil, and clay in the <2-mm fraction of the component layer (Source: Earth System Science Center, 1999).
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Yields of nonirrigated corn for grain by district in Nebraska and Minnesota during 1971 to 2002 were obtained from the online database of the National Agricultural Statistics Service of the USDA (USDA-NASS, 2004). It was noticed that a marked upward trend in yields with time exists for corn. This trend is the result of advances in agricultural technology (e.g., increases in rates of fertilizer application and use of new varieties) (Starr and Kostrow, 1978; Dennett et al., 1980). The technological trend was defined to be a linear function of the year (Hill et al., 1980). To eliminate bias due to technological trend, yield was detrended by regressing it against the linear time trend variable. Furthermore, the residuals of the detrended yield were determined because the residual variation reflects the effects of weather on yield (Dennett et al., 1980; da Mota, 1983). The detrended yield and its residual were computed by the following expressions (Starr and Kostrow, 1978):
 | [7] |
where yj is the corn yield residual (unitless), j is the year, zj is the detrended yield, and sz is the standard deviation of the detrended yield; and
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where Yj is the yield for the year j, a is the intercept of the trend line, b is the slope, and 1971 is the origin of the x-axis.
To estimate the potential yield for the period 1971–2002, a cumulative probability distribution of the historical yields during the 32 yr was drawn for each respective crop district. Cumulative probability is the probability that yield takes a value less than or equal to a given amount. Potential yield was taken from a best-fit line of the yield versus cumulative probability at the 99% level.
Development of the CSSI Model
The number of days during which the soil water exceeds field capacity is a measure of the degree to which the fields are saturated. The CSDI model was modified to identify soil saturation days by examining the estimated soil water (S) compared with the field capacity value (Sfc). A waterlogged or flood day (fday) was noted when S exceeds Sfc:
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For each crop growth stage, the flood days (
fi) were accumulated, and the number of total growing days at the ith stage (Ni) were recorded.
To represent both drought and saturation conditions, the new formulation of the CSSI was derived with the inclusion of the soil saturation factor:
 | [10] |
where 
i represents the crop's sensitivity to saturated soils in the ith growth stage, fi is the accumulated days of saturated soil at the ith growth stage, and Ni is the number of total growing days at the ith growth stage. 
is called the soil saturation factor. Other parameter definitions are the same as in Eq. [1]. The number 0.9 in the denominator is added to avoid dividing by zero when fi = Ni in extreme wet years. The coefficients i and i were determined by a jackknife methodology (Jones and Carberry, 1994). One should note that the CSSI model reduces to the original CSDI when the soil saturation factor is excluded.
Computations of ET, ETpc (used the same methods described in the CSDI background section), accumulated days of saturated soil, and total growing days for each stage were made for 1971–2002 for each selected COOP station. Station values were averaged over the individual crop districts in Nebraska and for one district in Minnesota.
To estimate the coefficients i and i for the CSSI model (see Eq. [10]), the typical practice is to split data into two groups, one group for model development and the other for model testing. However, because the amount of the data for this study was limited (32 observations for each district), the typical practice of splitting the data was passed over in favor of the jackknifing procedure (Jones and Carberry, 1994). The jackknifing procedure is conducted by dividing the data of n observations into r subgroups of size h. In this study, there were 32 observations in each district, and thus, n = 32. We chose the size of each subgroup h = 1. As a result, there were r = 32 subgroups. In brief, the jackknifing procedures are (i) to estimate the coefficient P (i.e., i and i in this study) using all the observations with the techniques of regression. The resulting estimate is referred to as 
; (ii) to remove one observation from the observations and estimate the coefficients using the remaining data, referred to as (1); (iii) to repeat the process by removing each observation in turn and obtain estimates (2), (3)...(r), referred to as "partial estimates"; and (iv) to combine these two kinds of estimated coefficients as follows:
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where * is the "jackknifed" estimate and 
is the mean of the partial estimates,
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It is well known from historical records that the number of years with saturated soil is rare compared with the number of drought years in Nebraska and Minnesota. If the regular jackknifing procedure is used, which removes each observation in turn, the wet years will not play an overly dominate role in the estimation of the coefficients. A small sample size can lead to inaccurate results (Rawlings et al., 1998; Algina and Olejnik, 2000). Good estimates of the regression coefficients, therefore, require many past occurrences (many samples). As a result, the years were ranked according to the ratio of saturation days over the total number of growing days in each stage for each division. It was indicated that the following years were the wettest 6 yr among those divisions: 1984, 1990, 1993, 1996, 1998, and 1999. These 6 yr were kept in the data set to estimate the coefficients i and i as a way for increasing sample sizes while other years were included but in the jackknife manner (i.e., each of the years is removed in turn).
Three indicators of the agreement between the estimated and actual yields were compared: correlation coefficient, the root mean square errors (RMSE) when using jackknife procedure, and RMSE when using regular regression procedure. In addition, to determine whether it is important to calibrate the model periodically using recent data, the coefficients of the CSDI model were computed from 1971–1980 and 1971–2002, respectively. Then the two sets of coefficients were compared for the east central district of Nebraska, the original region in which the CSDI model was developed.
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RESULTS AND DISCUSSION
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Table 3 shows the estimated coefficient values i obtained through the jackknifing procedure when the soil saturation factor was excluded (i.e., the original CSDI model Eq. [1]), along with the correlation coefficients, and RMSEs when using jackknife procedure and when using regular regression procedure between the actual and estimated yields. The RMSE is unitless because yield residuals were used. Overall, the RMSEs are slightly higher when the jackknifing procedure is used compared with the regular regression approach.
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Table 3. The coefficient values i without flooding factor using CSDI (Crop-Specific Drought Index), no irrigation.
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The i values are exponential coefficients. Thus, a large positive i value implies that yield is adversely impacted by water stress during the specific growth stage while a large negative i value suggests that yield is enhanced by water stress during the stage. A i value with small magnitude, regardless of sign, indicates that yield is insensitive to water stress. Compared with the original values, derived with 8 yr of data during the 1970s and 1980s from Nebraska's East District by Meyer et al. (1993a) in Table 1, the i values change in magnitude and sign. This is because the data used to derive the coefficients were region specific and were from 1971–2002. As can be seen in Table 3, the yield sensitivity coefficients to water stress in the four stages have relatively small magnitudes in northeast Nebraska and southeast Minnesota. Yield is very sensitive to water stress during Stage 2 in east central Nebraska and during Stage 3 in southeast Nebraska while yield is enhanced by water stress during Stage 4 in southeast Nebraska. These discrepancies in sensitivity to drought may be because the soil productivities, field management, corn hybrids, plant densities, and planting dates among the districts are different, leading to spatial variation in corn yield (Lamb et al., 1997; Dobermann et al., 2003; Shanahan et al., 2004).
The yield sensitivity coefficients for east central Nebraska computed from 1971–1980 data are 0.58, –0.63, 1.85, and –0.57 for the corresponding four growth stages. These values are quite different from those derived from the 1971–2002 data. It suggests that local calibrations are needed on a periodic basis. It was also found that the RMSE is 0.57 if using the regular regression while the RMSE is 0.37 if using the jackknifing procedure to estimate the coefficients from the 1971–1980 data.
Table 4 summarizes the estimated coefficient values i and i obtained through the jackknifing procedure with the soil saturation factor included, along with the correlation coefficients, and the jackknifing and regular regression RMSEs. In contrast to the i value, a i with a relatively large positive magnitude suggests that yield may be enhanced by saturated soil during the specific growth stage while a i with a relatively large negative magnitude suggests that yield may be adversely impacted by saturated soil during the stage. Similarly, a i with small magnitude, regardless of sign, indicates that yield is not sensitive to saturated soil.
All three indicators of agreement between the estimated and actual yields show improvement of the new CSSI model over the old CSDI model in all districts. The correlation coefficients are statistically significant (for R2, all p values < 0.0001 in Table 4). It was also noticed that the RMSEs from the jackknife procedure are close to those from regular regression procedure. Adding the soil saturation factor resulted in very little change in i values at northeastern Nebraska. The change in i values is significant for Stage 1 for east central Nebraska and for Stage 1 and 2 for southeastern Nebraska. For the i values found in this study, the yield is generally negatively affected by saturated soil during Stage 3 and is enhanced by saturated soil during Stage 4.
From May through September of 1993, there were heavy rainfalls across the Corn Belt and much flooding (Kunkel et al., 1994). The 1993 excessive rains led to one-half of the stations in the Northeastern Division of Nebraska receiving more than 73 cm of precipitation between 1 April and 30 September, greater than 150% of normal. As a result, 1993 corn yields were very poor. Damage approached $15 billion (Larson, 1996). Figure 2
shows schematically the time trace of soil water estimated by Eq. [2] in the 1993 growing season for Mead, located in the east central Nebraska. As indicated, soil moisture continuously exceeds field capacity for 15 d (DOY 201–215). Figure 3 illustrates the comparison between the CSDI and CSSI in northeastern Nebraska. The CSDI for 1993 overestimates the relative yield in northeastern Nebraska by about 28% while the CSSI underestimates the 1993 yield by 3%.
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Fig. 2. The time trace of soil water in the root zone in 1993 for Mead, NE. Wilting point (thin line) is the value of soil water below which the plants cannot extract moisture through the root system. Field capacity (thick line) is the level of soil water that is reached when the saturated soil is allowed to drain for a few days with no new rainfall, irrigation, or significant evapotranspiration. The real-time soil moisture (broken line) is estimated by Eq. [2].
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Fig. 3. Comparison between CSDI (Crop-Specific Drought Index) and CSSI (Crop-Specific Stress Index) during 1971–2002 in northeastern Nebraska.
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Before this study, we expected a significant sensitivity to saturated soil and a large improvement of the CSSI model over the CSDI model in Minnesota. Results were consistent with this expectation, and the overall RMSE improved significantly for southeastern Minnesota. The empirical indices found in this study reflect the prevailing farming practices in the crop-reporting districts. For example, the indices will reflect the fact that farming practices have included tile drains since the 1930s to drain agricultural fields in southeastern Minnesota to maintain optimal soil moisture, improve field operations, and stabilize yield variability (James Nesseth, personal communication, 2004).
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SUMMARY
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This paper demonstrates the modification and calibration of the CSDI model for the northeastern, east central, and southeastern crop districts in Nebraska and the southeastern crop district in Minnesota during 1971–2002. Based on the findings of this study, it is suggested that the introduction of a soil saturation factor will make the modified CSDI model perform better than the original model in years characterized by soil saturation. The jackknife procedure is a useful method to derive the coefficients used in the CSSI model when observation numbers are limited. Finally, because of variations in farming practices from district to district, it appears that each district will have different coefficients and recalibration may be needed on a periodic basis.
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ACKNOWLEDGMENTS
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We thank Dr. Donald Wilhite and Dr. George Meyer for their review of the manuscript. We also express our appreciation to the anonymous reviewers assigned by the Agronomy Journal.
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TOP
ABSTRACT
INTRODUCTION
