Continuous Structural Parameterization: A Proposed Method for Representing Different Model Parameterizations Within One Structure Demonstrated for Atmospheric Convection

Continuous structural parameterization (CSP) is a proposed method for approximating different numerical model parameterizations of the same process as functions of the same grid‐scale variables. This allows systematic comparison of parameterizations with each other and observations or resolved simulations of the same process. Using the example of two convection schemes running in the Met Office Unified Model (UM), we show that a CSP is able to capture concisely the broad behavior of the two schemes, and differences between the parameterizations and resolved convection simulated by a high resolution simulation. When the original convection schemes are replaced with their CSP emulators within the UM, basic features of the original model climate and some features of climate change are reproduced, demonstrating that CSP can capture much of the important behavior of the schemes. Our results open the possibility that future work will estimate uncertainty in model projections of climate change from estimates of uncertainty in simulation of the relevant physical processes.

Plain Language Summary

Numerical models are used to provide estimates of future weather and climate change. The models contain “parameterizations,” which are algorithms that simulate the effect of processes too small or poorly understood to represent using physical equations. Although they are based as much as possible on physics, parameterizations are a large source of modeling uncertainty because there can be large disagreements on how to best represent a given process. The method and even the variables used by two different parameterizations may differ. It is therefore very difficult to know how different parameterizations cause numerical models to produce different results and whether the parameterizations we have are adequate and span the range of uncertainty concerning our knowledge of the processes they represent. Using the example of small‐scale atmospheric convection linked to rain and thunderstorms, this paper describes a mathematical method for expressing different parameterizations within the same framework. This allows easy but formal mathematical comparison of different parameterizations and gives future work the potential to understand whether our parameterizations perform as they should in conjunction with future observations.