Tropical cyclones (TCs) cause devastating damage to life and property. Historical TC data is scarce, complicating adequate TC risk assessments. Synthetic TC models are specifically designed to overcome this scarcity. While these models have been evaluated on their ability to simulate TC activity, no study to date has focused on model performance and applicability in TC risk assessments. This study performs the intercomparison of four different global-scale synthetic TC datasets in the impact space, comparing impact return period curves, probability of rare events, and hazard intensity distribution over land. We find that the model choice influences the costliest events, particularly in basins with limited TC activity. Modelled direct economic damages in the North Indian Ocean, for instance, range from 40 to 246 billion USD for the 100-yr event over the four hazard sets. We furthermore provide guidelines for the suitability of the different synthetic models for various research purposes.

We develop a general mathematical framework for variational problems where the unknown function takes values in the space of probability measures on some metric space. We study weak and strong topologies and define a total variation seminorm for functions taking values in a Banach space. The seminorm penalizes jumps and is rotationally invariant under certain conditions. We prove existence of a minimizer for a class of variational problems based on this formulation of total variation, and provide an example where uniqueness fails to hold. Employing the Kantorovich-Rubinstein transport norm from the theory of optimal transport, we propose a variational approach for the restoration of orientation distribution function (ODF)-valued images, as commonly used in Diffusion MRI. We demonstrate that the approach is numerically feasible on several data sets.

Tropical cyclones (TCs) cause devastating damage to life and property. Historical TC data is scarce, complicating adequate TC risk assessments. Synthetic TC models are specifically designed to overcome this scarcity. While these models have been evaluated on their ability to simulate TC activity, no study to date has focused on the model performance and applicability in TC risk assessments. This study performs the first model intercomparison of four different global-scale synthetic TC datasets in the impact space, comparing impact return period curves, probability of rare events, and hazard intensity distribution over land. We find that the model choice influences the costliest events, particularly in basins with limited TC activity. Modelled direct economic damages in the North Indian Ocean, for instance, range from 40 to 246 billion USD for the 100-yr event over the four synthetic hazard sets. We furthermore provide guidelines for the suitability of the different synthetic models for various research purposes.

We propose a functional lifting-based convex relaxation of variational problems with Laplacian-based second-order regularization. The approach rests on ideas from the calibration method as well as from sublabel-accurate continuous multilabeling approaches, and makes these approaches amenable for variational problems with vectorial data and higher-order regularization, as is common in image processing applications. We motivate the approach in the function space setting and prove that, in the special case of absolute Laplacian regularization, it encompasses the discretization-first sublabel-accurate continuous multilabeling approach as a special case. We present a mathematical connection between the lifted and original functional and discuss possible interpretations of minimizers in the lifted function space. Finally, we exemplarily apply the proposed approach to 2D image registration problems.

Abstract. This paper describes the rationale and the protocol of the first component of the third simulation round of the Inter-Sectoral Impact Model Intercomparison Project (ISIMIP3a, www.isimip.org) and the associated set of climate-related and direct human forcing data (CRF and DHF, respectively). The observation-based climate-related forcings for the first time include high-resolution observational climate forcings derived by orographic downscaling, monthly to hourly coastal water levels, and wind fields associated with historical tropical cyclones. The DHFs include land use patterns, population densities, information about water and agricultural management, and fishing intensities. The ISIMIP3a impact model simulations driven by these observation-based climate-related and direct human forcings are designed to test to what degree the impact models can explain observed changes in natural and human systems. In a second set of ISIMIP3a experiments the participating impact models are forced by the same DHFs but a counterfactual set of atmospheric forcings and coastal water levels where observed trends have been removed. These experiments are designed to allow for the attribution of observed changes in natural, human and managed systems to climate change, rising CH4 and CO2 concentrations, and sea level rise according to the definition of the Working Group II contribution to the IPCC AR6.