Statistical characterization of environmental hot spots and hot moments and applications in groundwater hydrology

Abstract

Abstract. Environmental hot spots and hot moments (HSHMs) represent rare locations and events that exert disproportionate influence over the environment. While several mechanistic models have been used to characterize HSHM behavior at specific sites, a critical missing component of research on HSHMs has been the development of clear, conventional statistical models. In this paper, we introduced a novel stochastic framework for analyzing HSHMs and the uncertainties. This framework can easily incorporate heterogeneous features into the spatiotemporal domain and can offer inexpensive solutions for testing future scenarios. The proposed approach utilizes indicator random variables (RVs) to construct a statistical model for HSHMs. The HSHM indicator RVs are comprised of spatial and temporal components, which can be used to represent the unique characteristics of HSHMs. We identified three categories of HSHMs and demonstrated how our statistical framework is adjusted for each category. The three categories are (1) HSHMs defined only by spatial (static) components, (2) HSHMs defined by both spatial and temporal (dynamic) components, and (3) HSHMs defined by multiple dynamic components. The representation of an HSHM through its spatial and temporal components allows researchers to relate the HSHM's uncertainty to the uncertainty of its components. We illustrated the proposed statistical framework through several HSHM case studies covering a variety of surface, subsurface, and coupled systems.

Modeling Hydrologically Mediated Hot Moments of Transient Anomalous Diffusion in Aquifers Using an Impulsive Fractional‐Derivative Equation

“…Arora, Dwivedi, et al (2016) introduced wavelet and entropy methods to detect geochemical hot moments, while J. Chen et al (2021) developed the indicator random variable approach to characterize environmental hot phenomena. Additionally, Kuzyakov & Blagodatskaya (2015) briefly surveyed an array of spatial statistical analysis techniques to identify microbial hot spot distributions within soil.…”

“…HM‐HMs of transient pollutant dynamics in aquifers can arise from a variety of natural or human‐induced triggers (J. Chen et al., 2021). For example, abrupt shifts in groundwater flow or transport dynamics can be instigated by global seismicity activity (Barberio et al., 2020), along with other hydraulic alternations such as sudden changes of recharge/discharge patterns (Dudley‐Southern & Binley, 2015), transient boundary conditions attributed to shifts in land/water usage, interactions between surface water and groundwater, changes in recharge/discharge rates or sources such as pumping rates and well distributions, or other external/internal driving factors (Guo et al., 2020).…”