Return to the main PPE albedo symmetry page List of parameters The associated modules are Cloud Layers Unified by Binomials (CLUBB), Morrison-Gettelman (M-G) microphysics, aerosols and activation (A/A), Zhang-McFarlane (Z-M) deep convection, and Parameterizations for Unified Microphysics Across Scales (PUMAS). Parameter Module Reference 1.

13 February 2023 Return to the main PPE albedo symmetry page Mutual information To summarize mutual information (MI) very quickly, this quantity – coming from information theory – is a measure of how much uncertainty in the knowledge of $Y$ is reduced by having knowledge of $X$ (Shannon, 1948; Cover and Thomas, 1991). It is given as: $$ MI(X;Y) = \sum_x \sum_y P_{XY}(x,y)\mathrm{log}\frac{P_{XY}(x,y)}{P_X(x)P_Y(y)}, $$ where $P_{XY}$ is the joint probability density function of $X$ and $Y$, and $P_X$, $P_Y$ are the marginal probability density functions of $X$ and $Y$, respectively. It is essentially a ratio of the inherent joint probabilities of the data to the probabilities when assuming complete independence between the distributions. When MI is 0, having knowledge of a given variable $X$ gives us no more information for predicting $Y$.

Aiden Jönsson, Maria Rugenstein, Frida Bender Introduction This is the landing page for notes taken on the PPE albedo symmetry project. Reference contents Parameter list and notes Gaussian process emulation

Project goals / preliminary abstract $f$ is used by many people as a proxy for cloudiness. This is bad, because $f$ is arbitrary and without physical units. Furthermore, clouds are "densities", and besides spatial span they have "thickness" which $f$ completely misses. What are the different ways to quantify cloud abledo? Can we collect them and compare them? Discuss the difficulties in defining, and retrieving, $f$. This arises from the fact that the demarcation between cloud and non-cloud is nearly purely subjective. Since $f$ is necessarily parameterized in model physics, taking into account things such as convective organization, it is also necessary to provide observations of $f$ in order to calibrate our parameterizations. However, observing $f$ is nearly arbitrary since it is up to the scientist to decide where a cloud does and does not exist, and implicate that in an algorithm for producing such data. This puts us in a circular journey of defining and utilizing cloud fraction as a measure despite its difficulties. Come up with a consistent way to define and normalize cloud albedo so that it is energetically meaningful and would allow comparisons between different datasets and/or models. Each formulation of cloud albedo has been developed for a different specific purpose — it is fine to apply it to a purpose that it was meant for even if it has disadvantages, but explicitly stating why you apply that formulation should be the standard so as to avoid adding ambiguity and inconsistency across the literature to a term with specific physical meaning.