Abstract. Numerical weather prediction models rely on parameterizations for subgrid-scale processes, e.g., for cloud microphysics, which are a well-known source of uncertainty in weather forecasts. Via algorithmic differentiation, which computes the sensitivities of prognostic variables to changes in model parameters, these uncertainties can be quantified. In this article, we present visual analytics solutions to analyze interactively the sensitivities of a selected prognostic variable to multiple model parameters along strongly ascending trajectories, so-called warm conveyor belt (WCB) trajectories. We propose a visual interface that enables to a) compare the values of multiple sensitivities at a single time step on multiple trajectories, b) assess the spatio-temporal relationships between sensitivities and the trajectories' shapes and locations, and c) find similarities in the temporal development of sensitivities along multiple trajectories. We demonstrate how our approach enables atmospheric scientists to interactively analyze the uncertainty in the microphysical parameterizations, and along the trajectories, with respect to the selected prognostic variable. We apply our approach to the analysis of WCB trajectories within the extratropical cyclone "Vladiana", which occurred between 22–25 September 2016 over the North Atlantic.

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Cloud microphysical processes are highly relevant for cloud and precipitation characteristics, cloud radiative properties and the latent heat release during phase changes of water can interact with atmospheric dynamics. These sub-grid scale processes are typically parameterized in numerical weather prediction models, introducing parametric uncertainty in weather forecasts. The analysis of uncertainties related to these parameterizations imposes multiple challenges: On the one hand, it requires robust quantification of the impact of hundreds of uncertain model parameters. On the other hand, it requires adequate tools to filter, visualize, and understand the parameter impacts. Algorithmic Differentiation (AD) is a tool to efficiently evaluate the magnitude and timing at which a model state is sensitive to a model parameter [1]. We demonstrate the capabilities of AD, focusing on uncertain parameters in a two-moment cloud microphysics scheme along trajectories of a warm conveyor belt, which is the primary cloud- and precipitation-forming airstream in extratropical cyclones. To understand the parameter influence, we here introduce methods to systematically analyze different impacts in different warm conveyor belt ascent scenarios [2]. For example, this includes an objective clustering of trajectories w.r.t to parameter sensitivities. Met.3D, an open-source tool for interactive, three-dimensional visualization of numerical atmospheric model datasets, then provides a visual interface to compare multiple sensitivities on multiple trajectories from each cluster, assess the spatio-temporal relationships between the sensitivities and the trajectories’ shapes and locations, and find similarities in the temporal development of sensitivities along various trajectories’ location and time for ascent.    [1] Hieronymus, M., Baumgartner, M., Miltenberger, A. and Brinkmann, A.: Algorithmic Differentiation for Sensitivity Analysis in Cloud Microphysics, J. Adv. Model Earth Syst. (2022), 10.1029/2021MS002849.  [2] Neuhauser, C., Hieronymus, M., Kern, M., Rautenhaus, M., Oertel, A., and Westermann, R.: Visual analysis of model parameter sensitivities along warm conveyor belt trajectories using Met.3D (1.6.0-multivar0), Geosci. Model Dev. Discuss. [preprint], https://doi.org/10.5194/gmd-2023-27, in review, 2023. 

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.

Fig. 1. Visual analysis of the sensitivity of a state variable to selected model parameters (red names in curve-plot overlay) along warm conveyor belt trajectories in the extratropical cyclone "Vladiana", to assess uncertainties of parameterizations in numerical weather prediction models. State variable (blue) and maximum sensitivity (red) are color coded in view-aligned bands along trajectories. Embedded curve-plot shows statistical summaries of state variables and sensitivities. Selected sensitivities and state variables (in top to bottom order) are assigned to pie charts in the 3D view in clockwise order. Pie charts show values of multiple sensitivities or state variables along trajectories at selected time steps, or (as shown in Fig. 10) aligned to the time of ascent of each trajectory. View-aligned pie charts enable an effective comparison of sensitivities on multiple trajectories. The blue color on the ground shows surface precipitation.