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The deterministic shallow water equations (SWEs) are frequently used as a toy model to verify new techniques supposed to enter the milieu of numerical weather prediction. To combine stochastic and deterministic modeling, we propose a random field whose dynamics are governed by the shallow water formalism. The dynamics are introduced by embedding deterministic velocities into a stochastic tempospatial Gaussian model. In this way, a dynamically inactive stochastic field with given spatial and temporal covariance structure gains dynamics that in general follow a deterministic pattern. The observed motion can be interpreted as movement of a stochastically distorted shallow water flow. Introduction Motivation Other than the name suggests, the carrying medium of a shallow water flow is not solely water. Although liquids might be the most prominent carriers of shallow water movement, so does a very special gas: the Earth’s atmosphere. Principally, whenever the vertical extend of a fluid continuum is relatively small to its horizontal length scale, its movement can be modelled by SWEs. This will be clear from the derivation of the set of shallow water equations which is presented in Section 1.2. Here, it suffices to note that – with different levels of complexity – SWEs are used to model a variety of phenomena: e.g. Tsunami waves, internal waves between layers separating liquids of different density, flows in rivers, atmospheric waves and the general circulation in the oceans. In a meteorological context the shallow water equations describe fundamental mechanisms which govern the large scale circulation in the atmosphere. In fact, the first numerical weather prediction [Charney et al., 1950] was based on the integration of a set of equations derived from shallow water theory. Stochastics can be introduced to a model described by differential equations through various manners: random initial conditions [Gneiting and Raftery, 2005], random excitations added to the model or randomized parameters [Wilks, 2005]. These cases have in common that stochastics is imposed on a deterministic model, while we seek the reverse approach: A deterministic shallow water flow alters the behavior of a Gaussian stochastic field. Hereby, we incorporate stochastics into the shallow water formalism in a manner that allows full con-