Technical note: Evaluation of conceptual predator-prey models for the quantitative modeling of precipitating open-cell stratocumulus via feature-based Bayesian inversion of a suite of Large eddy simulations

Abstract. We consider two very different types of models of precipitating open-cell stratocumulus clouds. The first model type is a computationally expensive large eddy simulation (LES), that resolves convection and clouds at high temporal and spatial resolutions. The second model type is the nonlinear cloud and rain (C&R) equation, a scalar delay differential equation (DDE) that interprets interactions of precipitation and clouds phenomenologically by predator (rain) and prey (cloud) dynamics. We evaluate the extent to which one may use the C&R equation as a quantitative tool for representing selected aspects of an LES. Specifically, we estimate parameters of the C&R equation from a suite of LES via feature-based Bayesian inversions and track the evolution of posterior distributions over C&R model parameters under changing meteorological conditions in the LES. Our inversions show that the C&R equation can be calibrated to generate limit cycles that are quantitatively compatible with cycles of cloud growth and decay across a wide spectrum of meteorological conditions. The successful inversions reiterate the robustness of the predator-prey analogy to the dynamics of precipitating open-cell stratocumulus. When we interpret the inversions jointly, however, we observe counterintuitive and partially nonphysical shifts and changes in the posterior distributions over the C&R model parameters. Our evaluation study thus highlights the challenges one faces when mapping LES dynamics to a scalar DDE, which can stem either from structural inadequacies in the DDE model, or from the specific feature-based inversion framework, or a mixture of both.