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    County-scale simulation sites.

  • View in gallery

    Yield sensitivity index of parameters (Table 1) in the Hybrid-Maize model based on OAT approach.

  • View in gallery

    Average relative change in model-simulated yield corresponding to the relative change in parameter values of the Hybrid-Maize model across 18 Corn Belt counties over 30 years (1981–2010). (The lines of G2 and G5 in the first graph overlap each other.)

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    The eight largest sensitivity indices based on the factorial design.

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    Main effect and total sensitivity indices based on the factorial design.

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    NASS-reported county corn yield and simulated yield before and after regression with survey data. [The selected three counties are 1) Johnson, Iowa; 2) Douglass, Illinois; and 3) Huntington, Indiana.] Open circles indicate observations, dashed lines indicate default value (before adjustment), and solid lines indicate model simulation yield with the adjustment factor of 0.6.

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    MAE (bu acre−1) of 18 counties before and after applying the adjustment factor of 0.6 to convert potential to actual yield. Numbers on the x axis indicate locations corresponding to Figure 1.

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Calibration and Validation of the Hybrid-Maize Crop Model for Regional Analysis and Application over the U.S. Corn Belt

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  • 1 Purdue University, West Lafayette, Indiana
  • | 2 Michigan State University, East Lansing, Michigan
  • | 3 University of Nebraska–Lincoln, Lincoln, Nebraska
  • | 4 Purdue University, West Lafayette, Indiana
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Abstract

Detailed parameter sensitivity, model validation, and regional calibration of the Hybrid-Maize crop model were undertaken for the purpose of regional agroclimatic assessments. The model was run at both field scale and county scale. The county-scale study was based on 30-yr daily weather data and corn yield data from the National Agricultural Statistics Service survey for 24 locations across the Corn Belt of the United States. The field-scale study was based on AmeriFlux sites at Bondville, Illinois, and Mead, Nebraska. By using the one-at-a-time and interaction-explicit factorial design approaches for sensitivity analysis, the study found that the five most sensitive parameters of the model were potential number of kernels per ear, potential kernel filling rate, initial light use efficiency, upper temperature cutoff for growing degree-days’ accumulation, and the grain growth respiration coefficient. Model validation results show that the Hybrid-Maize model performed satisfactorily for field-scale simulations with a mean absolute error (MAE) of 10 bu acre−1 despite the difficulties of obtaining hybrid-specific information. At the county scale, the simulated results, assuming optimal crop management, overpredicted the yields but captured the variability well. A simple regional adjustment factor of 0.6 rescaled the potential yield to actual yield well. These results highlight the uncertainties that exist in applying crop models at regional scales because of the limitations in accessing crop-specific information. This study also provides confidence that uncertainties can potentially be eliminated via simple adjustment factor and that a simple crop model can be adequately useful for regional-scale agroclimatic studies.

Corresponding author address: Dev Niyogi, Department of Agronomy and Department of Earth, Atmospheric, and Planetary Sciences, Purdue University, 915 W. State St., Lilly Hall 2420, West Lafayette, IN 47906. E-mail address: climate@purdue.edu

Abstract

Detailed parameter sensitivity, model validation, and regional calibration of the Hybrid-Maize crop model were undertaken for the purpose of regional agroclimatic assessments. The model was run at both field scale and county scale. The county-scale study was based on 30-yr daily weather data and corn yield data from the National Agricultural Statistics Service survey for 24 locations across the Corn Belt of the United States. The field-scale study was based on AmeriFlux sites at Bondville, Illinois, and Mead, Nebraska. By using the one-at-a-time and interaction-explicit factorial design approaches for sensitivity analysis, the study found that the five most sensitive parameters of the model were potential number of kernels per ear, potential kernel filling rate, initial light use efficiency, upper temperature cutoff for growing degree-days’ accumulation, and the grain growth respiration coefficient. Model validation results show that the Hybrid-Maize model performed satisfactorily for field-scale simulations with a mean absolute error (MAE) of 10 bu acre−1 despite the difficulties of obtaining hybrid-specific information. At the county scale, the simulated results, assuming optimal crop management, overpredicted the yields but captured the variability well. A simple regional adjustment factor of 0.6 rescaled the potential yield to actual yield well. These results highlight the uncertainties that exist in applying crop models at regional scales because of the limitations in accessing crop-specific information. This study also provides confidence that uncertainties can potentially be eliminated via simple adjustment factor and that a simple crop model can be adequately useful for regional-scale agroclimatic studies.

Corresponding author address: Dev Niyogi, Department of Agronomy and Department of Earth, Atmospheric, and Planetary Sciences, Purdue University, 915 W. State St., Lilly Hall 2420, West Lafayette, IN 47906. E-mail address: climate@purdue.edu

1. Introduction

This study stems from a regional, multi-institutional project titled “Useful to Usable (U2U): Transforming Climate Variability and Change Information for Cereal Crop.” The U2U project seeks to develop decision support tools and climate resiliency–related resources for sustainable agriculture and improved profitability in the U.S. Corn Belt. One of the tasks underway is to develop historical and future agroclimatic assessments for U.S. Corn Belt (www.Agclimate4U.org) by understanding the impact of current and projected climate change on corn yields (Niyogi and Andresen 2011). To that end, the approach undertaken is to apply crop models for estimating regional crop yields.

A major limitation in applying crop models at large spatial scales is the difficulty in compiling required model input data, particularly for agronomic processes and management descriptors at regional scale. Therefore, a simple but reliable regional crop simulating system is desired to meet the increasing demand for regional agroclimatic assessments.

The Hybrid-Maize model (Yang et al. 2004) is selected for this study because it is simple, fast, and has relatively fewer input requirements compared to other crop models such as Decision Support System for Agrotechnology Transfer (DSSAT) (Jones et al. 2003), Agricultural Land Management Alternatives with Numerical Assessment Criteria (ALMANAC) (Kiniry and Bockholt 1998), and the Erosion-Productivity Impact Calculator (EPIC) (Jones et al. 1991). This simplicity of crop model input is considered an advantage for developing large spatial-scale assessments. The Hybrid-Maize model has been tested and found to have reliable performance in simulating corn yield at a field scale (Yang et al. 2004, 2006a; Grassini et al. 2009). However, to date a regional-scale, multidecadal assessment of the Hybrid-Maize model is lacking.

Since the regions where the crop model will be applied have diverse environmental conditions, it is important to test, adjust, and validate model parameters. Sensitivity analysis is an effective tool for such a task (see Table 1 for a list of parameters used in the analysis). Sensitivity analysis can reveal which parameters are most highly influential to output variability (Hamby 1994). In addition, before applying the Hybrid-Maize model at a regional scale, validations and regional calibration are necessary to assess Hybrid-Maize’s performance and understand what can be done to improve the large-scale simulation performance across the Corn Belt.

Table 1.

Description of parameters used in the model sensitivity analysis [adapted from Yang et al. (2006b)].

Table 1.

The first sensitivity analysis for the Hybrid-Maize model was conducted using a single representative scenario (Yang et al. 2004). This initial study was restricted to understand the impact of a few select parameters for a single site in Lincoln, Nebraska. Since the Hybrid-Maize model is a relatively new model that has not been widely used in the Corn Belt, there is a need to understand the sensitivity of simulated corn yields to different model variables and to validate the model performance at a regional scale. Therefore, the objective of this paper is to test the Hybrid-Maize model for its sensitivity over a range of parameters, validate, and calibrate it across the Corn Belt. This study is the first step for undertaking future research on developing a Hybrid-Maize–based crop–climate modeling system at larger regional spatial scales as part of the U2U project.

2. Materials and methods

2.1. Locations and data

We evaluated the Hybrid-Maize model at two spatial scales: county scale and field scale. The county-scale study included 24 counties (Figure 1) that considered a wide range of climatic conditions and crop yields across the Corn Belt. Data availability and accessibility are also taken into consideration when selecting these counties. Yield data for 18 counties (Figure 1, labeled 1–18) were used for model calibration, and data from an additional 6 counties (Figure 1, sites 19–24) were selected for testing the model yield adjustment factor, as described in section 3.

Figure 1.
Figure 1.

County-scale simulation sites.

Citation: Earth Interactions 19, 9; 10.1175/EI-D-15-0005.1

The 30 years (1981–2010) of daily weather data (minimum temperature, maximum temperature, and precipitation) were collected from the NOAA Daily Summaries Dataset (NOAA 2015) for a select location within each county of interest. Because of the lack solar radiation data at most weather stations, solar radiation was generated synthetically using the WeatherAid utility from the Hybrid-Maize crop simulation model package (Yang et al. 2005). County-level corn yield data were collected from USDA annual surveys (1981–2010) (USDA 2015). Yield data were detrended to a 30-yr average of each county to decrease the influence of technological advancements (e.g., Andresen et al. 2001; Hansen et al. 1998). The detrending approach assumed a linear trend and was applied here as is typically used in a variety of crop–climate studies (Hansen et al. 1998; Phillips et al. 1999). No assessments were done to assess spatial changes and only temporal trends were eliminated from the datasets.

The field-scale study included data from two sites at Bondville, Illinois (40.00°N, 88.29°W), and Mead, Nebraska (41.18°N, 96.44°W). Both sites are part of the AmeriFlux network (Baldocchi et al. 2001) that is operated for capturing the water, energy, and carbon fluxes over different natural ecosystems. Half-hourly meteorological data (2001–06) and seasonal yield data were obtained from the AmeriFlux data access portal (AmeriFlux 2015). The main reason to select the AmeriFlux sites is that the meteorological data and agronomic data were collected with a high level of accuracy. Additionally, solar radiation measurements are also available at these two sites, which provided an additional opportunity to test the model’s overall performance at a field scale. The half-hourly weather dataset includes air temperature, precipitation, solar radiation, and relative humidity. Data were analyzed, paired, checked for consistency, extracted, and processed to daily weather input data for the crop model.

2.2. Model configuration

Our intent was to run and test the crop model with minimum requirements for crop and field management input and weather data. Required crop and field management input data include hybrid maturity [i.e., total growing degree-days (GDD) to maturity], planting date, and plant population. The model assumes optimal water management (i.e., nonwater limiting) for potential yield, and the corresponding meteorological input data required include daily minimum and maximum air temperature (°C) and daily solar radiation (MJ ).

As stated, this study is motivated by the objective to assess the potential for applying the Hybrid-Maize crop model at regional scales. One of the limitations is the lack of ready access to regional cultivar information, soil data, and field management information. This lack of data is a critical consideration for our study, and we intend to use the model for contemporary and future climatic impacts on crop yield in a following study (Niyogi et al. 2015). We recognize that water stress and droughts can impact crop yields. The intent here is to explore if the model is run in its simplest configuration what biases emerge and if these biases can be reduced by a simple correction. Accordingly, the model was run with minimum input requirements under optimal water conditions and default agronomic characteristics. At the county scale, the planting date was set at 1 May, plant population at 31 600 per acre (78 000 per ha), 1389 GDD (10°C base) (i.e., 2500 GDD for 50°F base). For the field-scale studies at Bondville, Illinois, and Mead, Nebraska, 3 years of corn planting data and plant population are presented in Table 2. The model input data were prescribed by regional agronomists and climatologists, and with their advice, model runs were undertaken.

Table 2.

Corn cropping information for two AmeriFlux field sites.

Table 2.

2.3. Sensitivity analysis scheme

The first set of analyses was conducted based on 30-yr (1981–2010) climate data for 18 county-scale sites (Figure 1, sites 1–18) and used a one-at-a-time (OAT) sensitivity approach (Niyogi et al. 1997). Three groups with a total of 29 model parameters were tested (Table 3), with changes prescribed at ±10%, ±20%, and ±30% of the default values. The results were presented as the relative percentage change of simulated yield to assess model sensitivity. The sensitivity index (SI) (Wallach et al. 2006) was used to study parameter sensitivity and was derived as
e1
where O is the output value, is the output value (yield) for the baseline scenario that uses the default parameter values, I is the input value, and is the original input value of the baseline scenario. The larger the SI, the more sensitive the yield output is to that parameter.
Table 3.

Changes to the model input conditions in the crop model used for the OAT analysis. The parameter description is in Table 1.

Table 3.
Because of the limitation of traditional sensitivity approaches in assessing the interaction between parameters, a global sensitivity analysis (Niyogi et al. 1997, 1999) was also undertaken. The 30-yr weather data for Johnson County, Iowa, were used in the model. Since the focus was on parameters that can possibly be calibrated at the regional scale, five parameters were selected based on the results of initial sensitivity analysis: the light extinction coefficient K, upper temperature cutoff for growing degree-days accumulation UT, threshold LAI above which leaf senescence due light competition occurs TL, initial light use efficiency (LUE), and a GDD10C requirement for germination GRG. The 10 corresponding interaction groups can be identified linking the two variable combinations as K + UT, K + TL, K + LUE, K + GRG, UT + TL, UT + LUE, UT + GRG, TL + LUE, TL + GRG, and LUE + GRG. For every interaction analysis, two parameters are changed each time, which results in a total of factorial design simulations conducted for the five parameters. For each of these factorial combinations, sensitivity indices were calculated as
e2
The term is the result using default parameter values, and are the main effects of each parameter, and is the interaction effect between two parameters. As an example, for modified input, is the simulated yield, and . Similarly, is the simulated yield when only K is changed resulting in ; correspondingly, is the simulated yield when only LUE was changed, . For the different model-estimated yields, is the main effect from parameter K. The equation yields the main effect from parameter LUE; is the interaction effect for K and LUE. The total variability is calculated as
e3
corresponding to the global result from the 960 simulations; is the sum of squares of the main effect term for parameter i, and is the sum of squares on the interaction effect between parameters.
The main effect sensitivity index is defined as
e4
The interaction effect sensitivity index is defined as
e5
The resulting total effect for the sensitivity index is
e6
For parameter LUE, , the interaction effect sensitivity index between LUE and K is , while the total effect for the sensitivity index of LUE is .

2.4. Model validation and regional calibration

This study also assessed the simulated yields against National Agricultural Statistics Service (NASS)-reported county-scale yield data. The difference Di between simulated yields and reported data were quantified using the mean absolute error (MAE):
e7
where is simulated yield data, and is the reported data. MAE was calculated as
e8
The advantage of using MAE is that it is easy to interpret and has the same unit as yield (Wallach et al. 2006).
The Hybrid-Maize model was developed to simulate the potential yield at field scale without accounting for yield losses from nutrient deficiencies, diseases, pests, and insects. To quantify the gap between the simulated potential yield and the actual yield, a regional calibration was applied for the county-scale study. After reviewing different model fits and bias correction approaches, a simple linear regression–based adjustment appeared to be sufficient. The adjustment factor is calculated as
e9
where is the simulated potential yield, is the adjustment factor, and is the simulated yield after the adjustment. After further tests, the constant in the linear regression analysis was set to zero. Although we realize that setting the constant to zero in the regression equation could limit the model calibration, it helped the process of obtaining an averaged adjustment factor for the entire Corn Belt. This simple approach was tested and allowed calibration of the model results to account for other environmental and agronomic as well as management decisions that are not available (or are difficult to obtain) as an input to the model.

3. Results and discussion

3.1. Sensitivity analysis

The sensitivity index results (Figure 2) suggest that the five most sensitive parameters are potential number of kernels per ear G2, potential kernel filling rate G5, initial LUE, upper temperature cutoff for growing degree-days accumulation UT, and growth respiration coefficient of grain RG. Both G2 and G5 are cultivar-specific genetic/management coefficients (see Table 1). The default values of G2 and G5 in this model are the mean values of common cultivars across the Corn Belt following Jones and Kiniry (1986). The relative changes for yield simulations (Figure 3) highlight the uncertainties of G2 and G5 specifications that can have the largest and almost equal impact on yield simulation.

Figure 2.
Figure 2.

Yield sensitivity index of parameters (Table 1) in the Hybrid-Maize model based on OAT approach.

Citation: Earth Interactions 19, 9; 10.1175/EI-D-15-0005.1

Figure 3.
Figure 3.

Average relative change in model-simulated yield corresponding to the relative change in parameter values of the Hybrid-Maize model across 18 Corn Belt counties over 30 years (1981–2010). (The lines of G2 and G5 in the first graph overlap each other.)

Citation: Earth Interactions 19, 9; 10.1175/EI-D-15-0005.1

For noncultivar-specific generic parameters group, the model is most sensitive to UT. It is noticeable that the model is more sensitive to lower UT values (<36°C) than for a higher UT (>36°C). This is because when using a lower UT (e.g., 27°C), compared to using the default value, the GDD accumulation in days that have maximum air temperatures higher than UT will be decreased. Similarly, when using higher UT (e.g., 40°C), GDD accumulation increases when the maximum air temperature is higher than default UT (e.g., 36°C). For the study region, during the growing season, the possibility of daily maximum temperature higher than a low UT is a realistic occurrence. Therefore, the accumulation of GDD will be impacted more when using low UT value.

Among the respiration and photosynthesis parameters, LUE, which relates to assimilation, dominates model results. The SI for the simulated yield was significantly stable across the 30 years of climatic data. Climate variation appears to have a moderate impact on the sensitivity analysis results for the optimum parameter condition set in the model.

Among the 29 parameters we tested, simulation results were not sensitive to nine of the parameters (SI = 0) because of our experimental design of optimal water conditions. These nine parameters are fraction of leaf biomass that can be translocated as carbohydrate to grain each day FT, maximum fraction of leaf biomass at silking that can be translocated as carbohydrate to grain MF, efficiency of carbohydrate translocation from stem of leaf to grain EF, senescent leaf area at maturity as a fraction of maximum LAI achieved at silking LF, empirical parameters that determine the relative contribution of a soil layer to water uptake EP, leaf water suction at permanent wilting point LWS, resistance of plant to transpiration RTT, maximum days allowed form planting to emergence MDE, and maintenance respiration coefficient for grain MRG.

Results of the OAT sensitivity analysis discussed above indicate that it is important to validate and calibrate the G2, G5, LUE, UT, and RG parameters. The goal of the broader project is to apply the model at the regional scale involving the entire U.S. Corn Belt with an aim to simulate corn yield under future climate scenarios. However, it has been a challenge to obtain the public database of the genetic and management parameters for the different cultivars for the whole region. Hence, building off the OAT sensitivity analysis results, an additional global sensitivity analysis based on a factorial design was conducted. Five parameters were selected: K, UT, TL, LUE, and GRG. In Figure 4, ignoring SI smaller than 1%, LUE has the largest SI value. Figure 5 shows LUE contributes the most to the total SI. Therefore, calibrating the LUE for different cultivar and subregion, which can possibly be aided by remote sensing data (Barton and North 2001; Nichol et al. 2000), provides an encouraging avenue for regional-scale crop modeling.

Figure 4.
Figure 4.

The eight largest sensitivity indices based on the factorial design.

Citation: Earth Interactions 19, 9; 10.1175/EI-D-15-0005.1

Figure 5.
Figure 5.

Main effect and total sensitivity indices based on the factorial design.

Citation: Earth Interactions 19, 9; 10.1175/EI-D-15-0005.1

3.2. Model validation at county and field scales

The model was validated at 18 counties for 30 years (1981–2010). The results (Figure 6) show a distinct offset with a similar, and consistent, trend between the model-simulated yield and the NASS survey–reported yield. While the results are qualitatively good, the average MAE for the 18 sites is large: 85 bu acre−1 (5.35 Mg ha−1). There are two factors that help explain the gap between the model-simulated yield and the NASS survey–reported yield: (i) the Hybrid-Maize model simulates potential yield under optimal conditions including lack of water stress, and (ii) the NASS survey data are the average yield data that includes different corn cultivars with different levels of agronomic management planted over a wide range of soils. However, the generally similar trends between simulated yield and surveyed (observed) yield indicate that the application of a regional calibration can help correct and narrow the gap between simulations and observations. This regional calibration we adopted is as discussed above [see Equation (9)]. At the field level, Table 4 shows that the 3-yr average simulated yield for Mead, Nebraska, is 136 bu acre−1 (8.54 Mg ha−1), while the 3-yr average measured yield is 138 bu acre−1 (8.67 Mg ha−1). The 3-yr average simulated yield in Bondville, Illinois, is 164 bu acre−1 (10.30 Mg ha−1), which is slightly lower than the 3-yr average measured yield data of 175 bu acre−1 (10.99 Mg ha−1). Average MAE of these two field sites is 10 bu acre−1 (0.63 Mg ha−1). The lower MAE at the field scale compared to the county scale could be because the two field sites were under optimal agronomic management, which helps the actual yield approach or even exceed the simulated potential yield.

Figure 6.
Figure 6.

NASS-reported county corn yield and simulated yield before and after regression with survey data. [The selected three counties are 1) Johnson, Iowa; 2) Douglass, Illinois; and 3) Huntington, Indiana.] Open circles indicate observations, dashed lines indicate default value (before adjustment), and solid lines indicate model simulation yield with the adjustment factor of 0.6.

Citation: Earth Interactions 19, 9; 10.1175/EI-D-15-0005.1

Table 4.

Summary of measured (reported) and simulated corn yield at the two AmeriFlux field sites.

Table 4.

3.3. Regional calibration

The difference between simulated and surveyed yield is reduced after conducting the regional calibration (Figure 6). The 18-county averaged MAE of the yield data after regression analysis lowers to 21 bu acre−1 (1.31 Mg ha−1). The MAE of each county before and after regional calibration is shown in Figure 7. The average adjustment factor of the 18 site county-scale study is 0.6 with a variance of 0.007. Therefore, if the Hybrid-Maize model is applied in simulating the county average corn yield, the model output could be calibrated by multiplying 0.6 to account for the simulated potential yield and surveyed (observed) yield.

Figure 7.
Figure 7.

MAE (bu acre−1) of 18 counties before and after applying the adjustment factor of 0.6 to convert potential to actual yield. Numbers on the x axis indicate locations corresponding to Figure 1.

Citation: Earth Interactions 19, 9; 10.1175/EI-D-15-0005.1

To verify the robustness of this adjustment factor, we used six additional counties not considered in the regional calibration process. These counties include Champaign, Illinois; Clinton, Indiana; Boone, Iowa; Buffalo, Nebraska; Wyandot, Ohio; and Reno, Kansas (Figure 1, sites 19–24). The results (Table 5) indeed indicate that this 0.6 adjustment factor is not only convenient but also yields regionally representative yields at county scale. The averaged MAE of these six counties is 22 bu acre−1 (1.37 Mg ha−1).

Table 5.

Average observed (reported) and simulated yield (bu acre−1) for 1981–2010 for six additional counties not used in developing the regression estimate for the adjustment factor 0.6.

Table 5.

4. Summary

This study is a building block for applying a relatively simple crop model, Hybrid-Maize, at regional scales. According to the results of two-level sensitivity analyses, yield simulations are sensitive to genetic and field management parameters such as potential number of kernels per ear G2 and potential kernel filling rate G5. The model results are also sensitive to initial light use efficiency (LUE). While obtaining regional crop genetic and field management parameters will be challenging, the LUE data are a promising option, particularly as more satellite products become accessible. The validation results indicate the Hybrid-Maize model has moderately good accuracy in simulating yield at the field scale. When validating the model at the county scale, there is a notable and generally consistent gap between the simulated and actual survey yield. After conducting a simple regional calibration with an adjustment factor of 0.6, the model bias was considerably lowered. Thus, the Hybrid-Maize simulation model shows good potential for regional applications using a limited set of input data to provide large-scale corn yield simulations. In future studies, the calibrated Hybrid-Maize model will be applied in a regional crop modeling using projected climatic data to assess how climate change and climate variability can impact corn yield in the U.S. Corn Belt.

Acknowledgments

Study benefitted from USDA/NIFA Grant U2U (2011-68002-30220) and Drought Trigger project through Texas A&M University (2011-67019-20042). We thank Prof. Roger Elmore at University of Nebraska–Lincoln for his comments and helpful suggestion on an earlier version of this paper. The study also benefitted from AmeriFlux data from Bondville, Illinois (PI: T. Meyers), and Mead, Nebraska (PI: A. Suyker).

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