Nonlinear Quantitative Relationship Between the Duration and Occurrence Frequency of Droughts

Abstract. This study aims to quantify the relationship between the duration and occurrence frequency of droughts in China, particularly focusing on different drought intensities. By analyzing daily meteorological drought composite index (MCI) data from 1897 meteorological stations across China spanning from 1961 to 2020, the study reveals a significant double-logarithmic relationship between drought duration and occurrence frequency. The results show that shorter drought durations are associated with higher occurrence frequencies, while longer durations correspond to lower frequencies. This relationship is characterized by one parameter (k or b), which can independently describe the nonlinear association between drought duration and frequency. Spatially, the values of the parameter exhibit a gradient from northwest to southeast, with higher values in arid and semi-arid regions and lower values in humid and semi-humid regions. Notably, the parameter k aligns well with precipitation isolines, effectively distinguishing arid, semi-arid, and humid regions. Additionally, droughts in arid and semi-arid regions tend to last longer (often exceeding 60 days), while those in humid and semi-humid regions are shorter but more frequent. These findings provide critical insights for optimizing water resource management, agricultural planning, and disaster mitigation strategies, enhancing societal resilience to drought impacts.