Continuous Structural Parameterization (CSP) is a method for approximating different numerical model parameterizations of the same process as functions of the same gridscale 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.