A Global-Scale Investigation of Stochastic Similarities in Marginal Distribution and Dependence Structure of Key Hydrological-Cycle Processes

Abstract

To seek stochastic analogies in key processes related to the hydrological cycle, an extended collection of several billions of records from hundred thousands of worldwide stations is used in this work. The examined processes are the near-surface hourly temperature, dew point, relative humidity, sea level pressure, and atmospheric wind speed, as well as the hourly/daily streamflow and precipitation. Through the use of robust stochastic metrics such as the K-moments and a second-order climacogram (i.e., variance of the averaged process vs. scale), it is found that several stochastic similarities exist in both the marginal structure, in terms of the first four moments, and in the second-order dependence structure. Stochastic similarities are also detected among the examined processes, forming a specific hierarchy among their marginal and dependence structures, similar to the one in the hydrological cycle. Finally, similarities are also traced to the isotropic and nearly Gaussian turbulence, as analyzed through extensive lab recordings of grid turbulence and of turbulent buoyant jet along the axis, which resembles the turbulent shear and buoyant regime that dominates and drives the hydrological-cycle processes in the boundary layer. The results are found to be consistent with other studies in literature such as solar radiation, ocean waves, and evaporation, and they can be also justified by the principle of maximum entropy. Therefore, they allow for the development of a universal stochastic view of the hydrological-cycle under the Hurst–Kolmogorov dynamics, with marginal structures extending from nearly Gaussian to Pareto-type tail behavior, and with dependence structures exhibiting roughness (fractal) behavior at small scales, long-term persistence at large scales, and a transient behavior at intermediate scales.

Local climate change projections and impact on the surface hydrology in the Vea catchment, West Africa

“…This is because analysis of these predictive uncertainty helps in capturing the overall range of expected uncertainty propagated through the modelling (Badou et al 2018). Furthermore, it is important to understand the long-term persistence behaviour of hydrometeorological series, otherwise known as the Hurst-Kolmogrov Dynamics (HKD) (Dimitriadis et al 2021). The importance of this behaviour in the hydrometeorological process is that it increases the statistical bias from all the estimation metrics from time series that are being affected by the autocorrelation structure such as marginal moments (mean, variance etc.)…”

Spatial Hurst–Kolmogorov Clustering

“…Based on this, Koutsoyiannis [4] coined the term Hurst-Kolmogorov (HK) dynamics (Figure 2), so as to give credit to both contributing scientists and to expand it from the narrower Gaussian LTP processes (e.g., fractional Gaussian noise [5]). The HK dynamics also incorporate short-range dependence (e.g., fractal-type behavior [6]) and intermediate-scale behavior often observed in global-scale hydrological-cycle and turbulent processes [7].…”

Towards Generic Simulation for Demanding Stochastic Processes

“…Despite their popularity, these models have several problems, such as their lack of parsimony (except for the simplest of them, e.g., the ARMA(1,1), summarized in the Appendix A), as well as the inability to model long-range dependence (LRD) and to simulate non-Gaussian processes. On the other hand, both of these features are profoundly present in most geophysical processes [9]. An extension of these models, applicable to processes with LRD, was proposed by Hosking [10] under the acronym ARFIMA (with the letter 'F' standing for fractional differencing and the letter 'I' for integrated).…”

“…Non-central moments of common distributions with upper-tail index ξ (moments and cumulants exist for p < 1/ξ). Here, the cumulants do not have simple explicit expressions but can be readily calculated from Equation(9).…”