A Simple Model for Snap Bean (Phaseolus vulgaris L.) Development, Growth and Yield in Response to Nitrogen.

Irrigated processing snap bean (Phaseolus vulgaris L.) production in Wisconsin, mostly in the central sands region, ranks first in both yield and harvested area in the U.S. However, little crop modelling effort has been made to simulate the nitrogen (N) effects on growth and yield of non-nodulating snap bean variety, which demands high N inputs and imposes risks on groundwater nitrate-nitrogen (NO₃-N) leaching in sandy soils. The objective of this study was to develop a simple model for non-nodulating snap bean development, growth and yield under N limitation, following a phenomenological and physiological framework, and applying the 4-N-pool approach to quantify the crop N demand. The two mechanisms under N deficiency were tested and incorporated into the crop modelling, 1) reducing green leaf area while maintaining specific leaf N (SLN, g m^-2), and (2) diluting the SLN which further reduces radiation use efficiency (RUE, MJ m^-2) while maintaining green leaf area. The 2015 dataset with six N treatments, five plant densities and two sowing dates was used to develop the model, and independent 2014, 2013 dataset from four commercial fields were used to validate the model. The model was first tested with 2015 dataset by comparing predicted and measured leaf area index (LAI), yield (pod dry weight, g m^-2), above ground biomass (AGB, g m^-2) and cumulative crop N uptake (CNUP, g m^-2), high coefficients of determination (R², 0.83-0.90) and low root-mean-square errors (RMSE, 7.64-8.60% of the whole range of the target crop attributes) were reported. The external validation was conducted with the 2013 and 2014 datasets by comparing the yield, AGB and CNUP, a good agreement was found, with standard deviation (SD) lower than 10% of the mean (range, 1.90-9.00%), except for yield in one field in 2013 (SD=19.47%). The results proved the robustness of the model to simulate snap bean growth and yield under various management strategies.