Criticality in Tropical Rainfall: A Simple Water Budget Model

Deep convective rain events in the tropics represent an essential ingredient of Earth's climate system, acting as a driver of large-scale circulation which distributes energy and moisture. Understanding how they organize remains a challenge. Observational studies indicate that tropical convection may be understood as an instance of self-organized criticality (SOC) [1]:
(i) Rain rate vs. column water vapor follows a clear "pickup curve": Essentially no rain is observed in dry areas, while at column moistures above a critical value the rain rate increases sharply.
(ii) Rain events and clusters, defined as groups of contiguous rainy points in space and/or time, have size distributions well described by power laws.
The first result indicates that the atmosphere undergoes a phase transition, separating a non-raining "inactive" phase from a rainy "active" one. The second result suggests that the system is found close to the critical transition point, where "scale-free" power law distributions are expected. Indeed, observations find typical moisture values to be close to the critical moisture value. 

SOC theory would suggest that the observational results are an emergent phenomenon, caused by simple local interactions that carry over to larger scales. However, to our knowledge, no simple SOC model linking moisture and rainfall has been suggested that explains how criticality arises from convective processes while also predicting the observed rain cluster sizes. A more complete theory, especially on spatial aspects, is lacking.
We therefore present a simple spatiotemporal model of the atmospheric water budget, exploring whether a fuller picture including spatial information can be developed. Each site of the model represents an atmospheric column, where water can enter through surface evaporation, leave as surface rain, or get redistributed among neighboring sites due to convective in- and outflows. We analyse a cloud resolving model simulation in radiative-convective equilibrium, by grouping grid points into three categories: rainy points (convectively active), neighbors of rainy points and others (convectively passive). Tendencies, evolutions and transitions are examined to identify local "rules" to inform the interactions and parameters in our model.
Hence, in this project we use a simple model approach to find whether local convection mechanisms of water rearrangements can explain why tropical rainfall seems to show critical characteristics. In addition, this might aid development of convective parameterizations for climate models: Including a few key convective scale interactions, suggested by our model, might help to better capture important effects of subgrid correlations in a simple way.
 
[1] Peters, O., and J. D. Neelin (2006), Critical phenomena in atmospheric precipitation, Nat. Phys., 2(6), 393-396, doi:10.1038/nphys314.