Detrending crop yield data for spatial visualization of drought impacts in the United States, 1895–2014

Historical drought events have had severe impacts on United States agriculture, but attempts to quantify and compare these impacts across space and time have been challenging because of the nonlinear and non-stationary nature of the crop yield time series. Here, we address this challenge using long-term state- and county-level corn yield data from 1895 to 2014. We apply and compare six trend simulation models – simple linear regression, second order polynomial regression, centered moving average, locally weighted regression, spline smoothing, and empirical mode decomposition – to simulate the nonlinear trend, and two decomposition models – an additive decomposition model and a multiplicative decomposition model – to remove the nonlinear trend from the yield time series. Our comparison of each method evaluates their respective advantages and disadvantages with respect to applicability across time and space, efficiency, and robustness. We find that a locally weighted regression model, coupled with a multiplicative decomposition model, is the most appropriate data self-adaptive detrending method. Detrended crop yield minus one represents the percentage lower or higher than normal yield conditions, termed “crop yield anomaly”. We then apply this detrending method and perform correlation analysis to show the quantitative relationship between state-level corn yield anomalies and multiple drought indices. We find that the 3-month Standardized Precipitation Index (SPI) in August and Palmer Z-index in July correlate most closely with corn yield anomalies. This correlation is higher east of the 100° W meridian, where irrigation is not as extensively used. Finally, we show how the detrending process allows spatial visualization of drought impact on corn yield in the US using gridded August 3-month SPI values with examples from six major droughts. Our focus on comparing detrending methods produces a methodology that can aid analysis of agricultural yield for both empirical and modeling studies connecting environmental and climate conditions to crop productivity.