A Predator-Prey Model for Nonlinear Precipitation Oscillations in Hothouse Climates

Cloud-resolving simulations of hothouse climates show nonlinear oscillations in precipitation: Precipitation occurs in brief, yet intense, outbursts, separated by extended dry periods spanning multiple days. These simulations provide incredible detail, but, in and of themselves, cannot provide the theoretical understanding to predict the amplitude and period of the precipitation oscillation. Here, we approach this problem by modeling the oscillations with a set of nonlinear ordinary differential equations. In our model, the key ingredients include convective inhibition, precipitation, and their interplay with downdrafts. Precipitation generates downdrafts and surface-level density currents, triggering subsequent precipitation. On the other hand, precipitating downdrafts also bring cold and dry air to the boundary layer and increase convective inhibition, which then suppresses deep convection and precipitation. An emerging insight is that a predator-prey relationship exists between convective inhibition and precipitation. Thus, canonical predator-prey equations reproduce well the cloud-resolving simulations (Figure 1).

We then exploit analytical solutions of the model to gain physical insight. We find that the amplitude of precipitation oscillation is determined by both the mean precipitation and inhibition, while the inhibition's amplitude predominantly depends on its mean value. Additionally, the oscillation period is set by the decay timescale of convective inhibition and its mean value. This study not only provides a simple framework for further study of convection and precipitation in warm climates but also has implications for improving convection parameterizations in climate models.