An adapted Weibull function for agricultural applications

Abstract

The Weibull function is applied extensively in the life sciences and engineering but underused in agriculture. The function was consequently adapted to include parameters and metrics that increase its utility for characterizing agricultural processes. The parameters included initial and final dependent variables (Y0 and YF, respectively), initial independent variable (x0), a scale constant (k), and a shape constant (c). The primary metrics included mode, integral average, domain, skewness, and kurtosis. Nested within the Weibull function are the Mitscherlich and Rayleigh functions where c is fixed at 1 and 2, respectively. At least one of the three models provided an excellent fit to six example agricultural datasets, as evidenced by large adjusted coefficient of determination (RA2 ≥ 0.9266), small normalized mean bias error (MBEN ≤ 1.49%), and small normalized standard error of regression (SERN ≤ 8.08%). The Mitscherlich function provided the most probable (PX) representation of corn (Zea mays L.) yield (PM = 87.2%); Rayleigh was most probable for soil organic carbon depth profile (PR = 96.4%); and Weibull was most probable for corn seedling emergence (PW = 100%), nitrous oxide emissions (PW = 100%), nitrogen mineralization (PW = 58.4%), and soil water desorption (PW = 100%). The Weibull fit to the desorption data was also equivalent to those of the well-established van Genuchten and Groenevelt–Grant desorption models. It was concluded that the adapted Weibull function has good potential for widespread and informative application to agricultural data and processes.