| 18 Jun 2026
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.
Competing interests: At least one of the (co-)authors is a member of the editorial board of Atmospheric Chemistry and Physics.
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Review of egusphere-2026-2871: “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”
In this manuscript, the authors utilize a low-complexity predator-prey model to simulate limit cycles in precipitating open-cell stratocumulus. The cloud and rain model is calibrated via feature-based Bayesian inversion to generate limit cycles similar to those of cloud growth and decay seen in the LES across varying meteorological conditions. seen in the LES across varying meteorological conditions. The authors note the skill of the C&R model in reproducing limit cycling, but also discuss that the inferred posterior distributions over the C&R model parameters shift in ways that appear physically implausible as the LES boundary conditions change, likely due to the simplified physics of the C&R equations. This is an interesting paper that presents a balanced overview of the usefulness and limitations of low-order modeling. Overall, I recommend publication after revision, as addressing the comments below would strengthen both the presentation and interpretation of the results.
Major comments:
Ln 94: Something that is not clearly stated in the text is that Ho itself implicitly depends on rain. Reevaporation of drizzle beneath the cloud base can act as a sink of turbulent kinetic energy, promoting boundary-layer decoupling and thereby influencing Ho. Could the authors discuss whether this missing feedback contributes to the nonphysical shifts in the inferred posterior parameters?
Since both formulations produce nearly identical posterior distributions and similar skill in reproducing the LES features, what additional physical insight is gained by introducing the accretion formulation? Does this suggest that the qualitative predator-prey dynamics are insensitive to the exact precipitation parameterization, or are there situations where the two models are expected to diverge?
What is the outlier in Figure 2a+b that is not labeled?
The posterior distributions exhibit substantial parameter degeneracies. Could the authors discuss whether these arise primarily because the selected feature (the average cloud growth-decay cycle) is insufficient to uniquely constrain the model, rather than only reflecting structural deficiencies in the C&R equations? Would incorporating additional observables (e.g., rain rate, cloud fraction, or LWP) help distinguish among parameter combinations?
Minor comments:
Ln 35-40: Perhaps it is worth noting the “intermediate” complexity mixed-layer model (Nicholls 1984, Bretherton & Wyant, 1997, etc) that bridges the gap between LES and the conceptual predator-prey model.
Ln 45: The introduction could more clearly define the features used in the inversion (e.g., cycle amplitude, duration, and shape), since this is not obvious until Section 5.
Eq (3), Eq (14): Citations for these?
Figure 1: It may be helpful to the reader to mark the location of the lines in Figure 1d on the phase space in Figure 1b. Additionally, in the axes labels, it would be helpful to define the nondimensional variables (i.e., D = T/tau) so that the reader does not have to flip back and forth to remind themselves.
Including representative oscillations from one or two LES in an appendix would help readers assess how well the conceptual model reproduces the original simulations.