Realistic 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.

中文翻译：

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推进随机场的时空模拟：从风暴到旋风及以后

在空间和时间上对水环境通量（例如降雨）进行真实的随机模拟具有挑战性，但对于在不确定性下为环境风险分析和决策提供信息至关重要。在这里，我们通过引入一般速度场和一般各向异性变换的概念来推进随机场模拟。这扩展了所谓的完整随机建模解决方案 (CoSMoS) 框架的功能，能够模拟随机场 (RF) 保留：(a) 任何非高斯边缘分布，(b) 任何时空相关结构 (STCS)，( c) 由速度和方向局部变化的速度场表示的一般平流，以及 (d) 局部变化的各向异性。我们还引入了新的基于 copula 的 STCS，并提供了保证它们正定性的条件。为了说明 CoSMoS 的潜力，我们模拟了具有复杂模式和运动的 RF，以模拟穿过一个区域的暴雨、类似天气旋风的螺旋场、会聚（或发散）一个点的场，以及碰撞的气团。建议的方法在免费提供的 CoSMoS R 包中实现。