Algorithmic differentiation for sensitivity analysis in cloud microphysics

Abstract

The role of clouds for radiative transfer, precipitation formation, and their interaction with atmospheric dynamics depends strongly on cloud microphysics. The parameterization of cloud microphysical processes in weather and climate models is a well-known source of uncertainties. Hence, robust quantification of this uncertainty is mandatory. Sensitivity analysis to date has typically investigated only a few model parameters. We propose algorithmic differentiation (AD) as a tool to detect the magnitude and timing at which a model state variable is sensitive to any of the hundreds of uncertain model parameters in the cloud microphysics parameterization. AD increases the computational cost by roughly a third in our simulations. We explore this methodology as the example of warm conveyor belt trajectories, that is, air parcels rising rapidly from the planetary boundary layer to the upper troposphere in the vicinity of an extratropical cyclone. Based on the information of derivatives with respect to the uncertain parameters, the ten parameters contributing most to uncertainty are selected. These uncertain parameters are mostly related to the representation of hydrometeor diameter and fall velocity, the activation of cloud condensation nuclei, and heterogeneous freezing. We demonstrate the meaningfulness of the AD-estimated sensitivities by comparing the AD results with ensemble simulations spawned at different points along the trajectories, where different parameter settings are used in the various ensemble members. The ranking of the most important parameters from these ensemble simulations is consistent with the results from AD. Thus, AD is a helpful tool for selecting parameters contributing most to cloud microphysics uncertainty.