Past, present, and future of the Hurst-Kolmogorov dynamics in Stochastics: A bibliometric analysis of the last 50 years in water resources

Abstract

Hurst’s paper on the Nile’s flow variability marked a pivotal moment in hydrology and beyond by introducing what was called the Hurst phenomenon. Independently, Kolmogorov developed a mathematical model describing this behaviour a decade earlier. The Hurst-Kolmogorov dynamics (HKd) is used to express this phenomenon physically and mathematically, which is characterised by high uncertainty and persistence (across spatial and temporal scales) and challenges traditional analytical frameworks, particularly in water resources-related topics and implications in engineering designs. Given the importance of HKd, a bibliometric analysis of it in water resources is helpful to trace its historical development, current state, and (possible) future trajectories. The latter intends to offer a comprehensive perspective on HKd, serving as a guide for new readers seeking an entry point into this field. Using the Web of Science database, 617 publications from 1974 to 2023 are analysed, revealing a consistent growth trend in research outputs up to 2018. Collaborative efforts among researchers worldwide have been prominent, with the USA and China leading in international collaborations. High-impact journals on topics related to water resources and geosciences are primary outlets for research related to the HKd. Interestingly, only two journals published the 20 most cited papers on this topic. A clear pattern from “groundwater” to “streamflow” to “soil moisture” to “precipitation” was observed from the past to the present. Overall, this analysis provides a comprehensive overview of the past, present, and future trends in HKd research, and highlights its contribution to the scientific literature of water resources