Stochastic models for spatio-temporal transport face a critical trade-off between physical realism and interpretability. The advection model with a single constant velocity is interpretable but physically limited by its perfect correlation over time. This work aims to bridge the gap between this simple framework and its physically realistic extensions. Our guiding principle is to introduce a spatial correlation structure that vanishes over time. To achieve this, we present two distinct approaches. The first constructs complex velocity structures, either through superpositions of advection components or by allowing the velocity to vary locally. The second is a spectral technique that replaces the singular spectrum of rigid advection with a more flexible form, introducing temporal decorrelation controlled by parameters. We accompany these models with efficient simulation algorithms and demonstrate their success in replicating complex dynamics, such as tropical cyclones and the solutions of partial differential equations. Finally, we illustrate the practical utility of the proposed framework by comparing its simulations to real-world precipitation data from Hurricane Florence.

翻译：时空输运的随机模型面临着物理真实性与可解释性之间的关键权衡。具有单一恒定速度的平流模型虽可解释，但其在时间上的完美相关性限制了物理真实性。本研究旨在弥合这一简单框架与其物理上更现实的扩展之间的差距。我们的指导原则是引入一种随时间衰减的空间相关结构。为此，我们提出了两种不同的方法。第一种方法通过平流分量的叠加或允许速度局部变化来构建复杂的速度结构。第二种是谱技术，它用更灵活的形式取代刚性平流的奇异谱，并引入由参数控制的时序去相关。我们为这些模型配备了高效的模拟算法，并展示了它们在复制复杂动力学（如热带气旋和偏微分方程的解）方面的成功。最后，通过将所提框架的模拟结果与飓风佛罗伦萨的真实降水数据进行比较，我们阐明了该框架的实际效用。