An extension of the logistic function to account for nonstationary drought losses

Abstract. While the intensity loss function is fundamental to drought impact assessment, the relationship between drought loss and intensity can be nonstationary, i.e., changing as time progresses, owing to socio-economic developments. This paper builds three novel intensity loss functions upon the classic logistic function to account for nonstationary drought losses. Specifically, the time is explicitly formulated as an explanatory variable and respectively incorporated into the magnitude, shape and location parameters of the logistic function to derive three nonstationary intensity loss functions. To examine the effectiveness, a case study is devised for the drought-affected population by province in mainland China during the period from 2006 to 2023. The results highlight the existence of nonstationarity in that the drought-affected population exhibits significant correlation not only with standard precipitation index but also with year. The three nonstationary intensity loss functions are shown to outperform the classic logistic function and also the linear regression. They present effective characterizations of observed drought loss in different ways: 1) the nonstationary function with the flexible magnitude parameter fits the data by adjusting the maximum drought loss by year; 2) the nonstationary function with the flexible shape parameter works by modifying the growth rate of drought loss with intensity; and 3) the nonstationary function with the flexible shape parameter acts by shifting the response curves along the axis by year. In general, the nonstationary function with the flexible magnitude parameter is shown to be the most promising in terms of high coefficient of determination, low Bayesian information criterion and explicit physical meaning. Taken together, the nonstationary intensity loss functions developed in this paper can serve as an effective tool for drought management.