To answer this question, we perform a mutual information analysis of the CRE, liquid water path, aerosol loading, and several other meteorological variables at SGP. We use the same 14-year dataset previously mentioned as well as observations and Large Eddy Simulations (LES) from the current LES Atmospheric Radiation Measurement (ARM) Symbiotic Simulation and Observation (LASSO) campaign. We use the "data bundles" produced by the LASSO project for 18 different days with non-precipitating shallow cumulus. These bundles include a multitude of observations from SGP, as well as output from many different LES run for varying choice of model initialization and forcing from observations and/or reanalysis. These standard LASSO runs use a constant aerosol concentration, so we have performed our own simulations of the same cases but with varying aerosol based on the concurrent observations at SGP. Using multiple LES as well as a long-term observational dataset allows us to tease apart the interplay of convective dynamics, micro-physics, and meteorological state that produce counter-intuitive results in this study of cloud-aerosol interactions.
We calculate the information content, or Shannon entropy, of relevant variables, and then compare their mutual information. This is similar to an analysis of covariance, but has the advantage of not needing to assume a functional form for any relationship. We then calculate the conditional mutual information to show which variables (and meteorological state) lead to a loss in mutual information between aerosol loading and cloud radiative effect. The conditional mutual information analysis allows us to quantify how much each variable leads to a loss of detectability of the aerosol indirect effect.