Abstract
AbstractRealistic stochastic simulation of hydro‐environmental fluxes in space and time, such as rainfall, is challenging yet of paramount importance to inform environmental risk analysis and decision making under uncertainty. Here, we advance random fields simulation by introducing the concepts of general velocity fields and general anisotropy transformations. This expands the capabilities of the so‐called Complete Stochastic Modeling Solution (CoSMoS) framework enabling the simulation of random fields (RF's) preserving: (a) any non‐Gaussian marginal distribution, (b) any spatiotemporal correlation structure (STCS), (c) general advection expressed by velocity fields with locally varying speed and direction, and (d) locally varying anisotropy. We also introduce new copula‐based STCS's and provide conditions guaranteeing their positive definiteness. To illustrate the potential of CoSMoS, we simulate RF's with complex patterns and motion mimicking rainfall storms moving across an area, spiraling fields resembling weather cyclones, fields converging to (or diverging from) a point, and colliding air masses. The proposed methodology is implemented in the freely available CoSMoS R package.
Highlights
The Rainfall Paradigm “The little reed, bending to the force of the wind, soon stood upright again when the storm had passed over.” ~ AesopThe complexity of hydro-environmental fluxes, such as weather systems, often prevents deterministic modelling via numerical models discretizing systems of partial differential equations, especially when focusing on high spatial and temporal resolution required in water resources planning and management
This expands the capabilities of the so-called Complete Stochastic Modeling Solution (CoSMoS) framework enabling the simulation of random fields preserving: (1) any non18 Gaussian marginal distributions, (2) any spatiotemporal correlation structure, (3) general advection expressed by velocity fields with locally varying speed and direction, and (4) locally varying anisotropy
Precipitation is characterized by spatiotemporal dependence, anisotropy and advection related to the physics and the spatiotemporal evolution of the weather systems
Summary
The Rainfall Paradigm “The little reed, bending to the force of the wind, soon stood upright again when the storm had passed over.” ~ Aesop. Fourier power spectra (where the latter are the Fourier transform of former according to the Wiener-Khinchin theorem) have been extensively used to study the spatial structure of precipitation fields (e.g., Zawadzki, 1973; Krajewski, 1987; Sinclair & Pegram, 2005; Mandapaka and Qin, 2013; Niemi, Kokkonen and Seed, 2014; Gyasi-Agyei, 2016 Cassiraga et al, 2020) They are the basis of methods, such as the Generalized Scale Invariance (GSI; Lovejoy and Schertzer, 1985), that allow one to quantify the scaling of anisotropic systems, accounting for the different anisotropy of cells and rain bands The foregoing discussion highlights the importance of developing effective stochastic models for environmental/geophysical flows, such as rainfall, that account for possibly complex (non-Gaussian) marginal distributions, spatiotemporal correlation, anisotropy, and advection. CoSMoS is a general stochastic modeling framework that can be applied to any geophysical process, yet rainfall is the most natural example for this type of models
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
