Algorithmic Differentiation for Sensitivity Analysis in Cloud Microphysics

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.
Plain Language Summary: The formation of clouds is determined by processes that act on smaller scales than weather prediction models can resolve. Consequently, a parameterization with typically hundreds of parameters is constructed to determine the effects of these processes on the resolved larger scales. These parameters are a well‐known source of uncertainty in weather and climate models. Classical attempts to quantify this uncertainty are typically limited to a few parameters. We propose algorithmic differentiation (AD) as a tool to detect parameters with the largest impact for any of the hundreds of parameters on multiple model state variables at every time step in our simulation. This increases the computational cost by roughly a third. The relevance of the AD‐estimated impact is demonstrated by comparing the AD results with ensemble simulations, 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 to identify parameters objectively that contribute most to uncertainty in cloud parameterizations.
Key Points: Quantification of multi‐parameter uncertainty of cloud microphysical evolution of WCB trajectories using algorithmic differentiation. Uncertainty at every time step derived with algorithmic differentiation representative for key uncertainty over at least 30 min intervals. Parameterization of CCN activation, diameter size, and fall velocity of hydrometeors have the largest mean impact on water vapor contents.
Deutsch Forschungsgemeinschaft DFG