Development and evaluation of ordinary least squares regression models for predicting irrigated and rainfed maize and soybean yields

Understanding the relationships between climatic variables and soil physical and chemical properties with crop yields on large scales is critical for evaluating crop productivity to make better assessments of local and regional food security, policy, land and water resource allocation, and management decisions. In this study, ordinary least squares (OLS) regression models were developed to predict irrigated and rainfed maize and soybean yields at the county level as a function of explanatory variables [precipitation (P), actual crop evapotranspiration (ET_a), organic matter content (OMC), cation exchange capacity (CEC), clay content (CC), and available soil water capacity (ASW)] of the dominant soil type in each of the 93 counties in Nebraska. Models were developed for the statewide average dataset (state models) as well as for the four major climatic zones (zonal models). Spline interpolation was used to spatially interpolate all independent variables across all 93 counties. The results of the OLS state models showed a very good performance for predicting rainfed maize and soybean yields. For rainfed maize, about 73% of the variation in yield (RMSD = 867 kg ha^-1) was explained by ET_a alone, and 83% of yield variability (RMSD = 690 kg ha^-1) was explained by the model Yield = f(ET_a, P, ASW, CEC, CC). For rainfed soybean, about 69% of the variability (RMSD = 238 kg ha^-1) was explained by ET_a alone, and a maximum of 85% (RMSD = 164 kg ha^-1) of the variability was explained by the model Yield = f(ET_a, P, ASW, CEC, CC). No additional variation in yield was explained by adding OMC to the rainfed maize and soybean yield models. Less correlation was found between the predicted and observed yields for irrigated maize and soybean than for the rainfed yields for both crops. For irrigated maize and soybean, a maximum of 45% (RMSD = 533 kg ha^-1) and 36% (RMSD = 218 kg ha^-1) of the variability in yield was explained by the models Yield = f(ET_a, P, ASW) and Yield = f(ET_a, P, ASW, CEC, CC, OMC), respectively. For the rainfed crops, ET_a played a major role in predicting yield, whereas P and ASW played a major role in predicting irrigated yields. ET_a and P accounted for 96%, 73%, and 67% of the total explained variation in rainfed soybean yield for zones 2 (drier), 3, and 4 (wetter), respectively, whereas soil physical and chemical properties accounted for 4%, 27%, and 33%, respectively. Unlike rainfed conditions, irrigated maize and soybean yield predictions were improved by applying the zonal models rather than the state models.