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Research and application of the spatiotemporal distribution function of drought intensity

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ZHOU Kai ，CHANG Jianxia ，WANG Yimin ，JIANG Yunzhong ，ZHAO Ruxin ，SUN Hongquan 3

（1. State Key Laboratory of Water Engineering Ecology and Environment in Arid Area，Xi’an University of Technology，

Xi’an 710048，China；2. State Key Laboratory of Water Cycle and Water Security，China Institute of Water Resources and

Hydropower Research，Beijing 100038，China；3. National Institute of Natural Hazards，

Ministry of Emergency Management of China，Beijing 100085，China）

Abstract：Current research on drought intensity focuses on the distribution function analysis in the time domain but
lacks consideration of the non-linear functional relationship of the characteristic variables. This limitation makes it
difficult to construct a universal distribution function equation for drought intensity in both the spatial and temporal
domains. In this paper，based on the nonlinear functional relationship of the spatiotemporal dimension，a group of dif⁃

ferential equations are formulated. The functional relationship between the average spatiotemporal intensity，time

duration，and covered area is derived theoretically，and the distribution function equations for intensity in the spatio⁃

temporal domain are proposed. The results indicate that the average intensity follows a negative exponential distribu⁃

tion in both the spatial and temporal domains. For a drought event，its drought intensity follows a functional relation⁃
ship：the product of the average spatiotemporal intensity，the negative exponential of time duration，and the negative

exponential of the covered area is proportional to the average spatiotemporal intensity and time duration. The theoreti⁃

cal validation is carried out in North China as an example，and the results confirm the reliability of the distribution
function equation in the spatiotemporal domain. Additionally，based on the aforementioned functional relationship，

the concept of composite intensity is proposed，integrating the spatiotemporal dimension of drought events and provid⁃
ing a scientific method for their comprehensive assessment.

Keywords：drought events；composite intensity；distribution function；North China

（责任编辑：韩 昆）

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