Functional Data Analysis of Weather Variables Linked to Fusarium Head Blight Epidemics in the United States

In past efforts, input weather variables for Fusarium head blight (FHB) prediction models in the United States were identified after following some version of the window-pane algorithm, which discretizes a continuous weather time series into fixed-length windows before searching for summary variables associated with FHB risk. Functional data analysis, on the other hand, reconstructs the assumed continuous process (represented by a series of recorded weather data) by using smoothing functions, and is an alternative way of working with time series data with respect to FHB risk. Our objective was to functionally model weather-based time series data linked to 865 observations of FHB (covering 16 states and 31 years in total), classified as epidemics (FHB disease index ≥ 10%) and nonepidemics (FHB disease index < 10%). Altogether, 94 different time series variables were modeled by penalized cubic B-splines for the smoothing function, from 120 days pre-anthesis to 20 days post-anthesis. Functional mean curves, standard deviations, and first derivatives were plotted for FHB epidemics relative to nonepidemics. Function-on-scalar regressions assessed the temporal trends of the magnitude and significance of the mean difference between functionally represented weather time series associated with FHB epidemics and nonepidemics. The mean functional weather-variable curve for epidemics started to deviate, in general, from that for nonepidemics as early as 40 days pre-anthesis for several weather variables. The greatest deviations were often near anthesis, the period of maximum susceptibility of wheat to FHB-causing fungi. The most consistent separations between the mean functional curves were seen with the daily averages of moisture-related variables (such as average relative humidity) and with variables summarizing the daily variation in temperature (as opposed to the daily mean). Functional data analysis was useful for extending our knowledge of relationships between weather variables and FHB epidemics.