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Traveling phenomena, frequently observed in a variety of scientificdisciplines including atmospheric science, seismography, and oceanography, havelong suffered from limitations due to lack of realistic statistical modelingtools and simulation methods. Our work primarily addresses this, introducingmore realistic and flexible models for spatio-temporal random fields. We breakaway from the traditional confines of the classic frozen field by eitherrelaxing the assumption of a single deterministic velocity or rethinking thehypothesis regarding the spectrum shape, thus enhancing the realism of ourmodels. While the proposed models stand out for their realism and flexibility,they are also paired with simulation algorithms that are equally or lesscomputationally complex than the commonly used circulant embedding for Gaussianrandom fields in $\mathbb{R}^{2+1}$. This combination of realistic modelingwith efficient simulation methods creates an effective solution for betterunderstanding traveling phenomena.

A New Class of Realistic Spatio-Temporal Processes with Advection and Their Simulation