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

Abstract. While the stationary intensity loss function is fundamental to drought impact assessment, the relationship between drought loss and intensity can change as time progresses owing to socio-economic developments. This paper addresses this critical gap by modelling nonstationary drought losses. Specifically, time is explicitly formulated by linear and quadratic functions and then incorporated into the magnitude, shape and location parameters of the logistic function to derive six nonstationary intensity loss functions in total. To examine the effectiveness of this approach, a case study is designed for drought-affected populations 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 the standard precipitation index but also with time. The proposed nonstationary intensity loss functions are shown to outperform not only the classic logistic function but 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 location parameter acts by shifting the response curves along the axis by year. Among the nonstationary logistic functions, the function incorporating the linear function of time into the magnitude parameter generally outperforms the others in terms of having a high coefficient of determination, a low Bayesian information criterion and an explicit physical meaning. Taken together, the nonstationary intensity loss functions developed in this paper can serve as an effective tool for drought management.