## 1. Introduction

[2] A storm-damage function describes losses as a function of observable meteorological parameters, typically maximum wind speed. For winter storms occurring in central Europe several storm-damage functions for residential buildings are described in literature. The reinsurance company*Münchener Rückversicherungs-Gesellschaft* [1993, 2001]found a power-law damage function of maximum wind speed with varying exponents of roughly 3 as well as 4–5, depending on the storm event and country being analyzed.*Klawa and Ulbrich* [2003]proposed a power-law damage function with exponent 3, refined by*Donat et al.* [2011], using excess wind speed over threshold instead of absolute maximum wind speed. Similarly, *Heneka and Ruck* [2008]used a power-law damage-propagation function of excess wind speed with exponent of either 2 or 3, assuming proportionality to the force or the kinetic energy of the wind, respectively. Both groups define threshold wind speed as the empirical 98 percentile of the wind distribution. For the Netherlands*Dorland et al.* [1999] derived a damage function for residential property that can be reformulated as a power law of maximum wind speed with exponent 0.5. When comparing these studies with literature on hurricane losses in the United States (see *Watson and Johnson* [2004] for an overview), one must be aware of the many differences in building structure and the nature of the hazard. However, following a similar approach to this article *Huang et al.* [2001]describe an exponential damage model for residential property in the Southeastern United States based on 10min-averaged wind speed.

[3] Our work is based on daily insurance-loss data (years 1997–2007) with a regional resolution of administrative districts. From theoretical considerations we propose a stochastic power-law damage function depending on maximum daily wind speed to describe empirical losses. We find exponents typically ranging from 8 to 12. Statistical deviations are modeled by a spatially correlated stochastic variable drawn from a log-normal distribution. Correlations among parameters and with socio-demographic data are exploited to reduce the number of independent parameters to three per district. The model quality is assessed by out-of-sample calculations based on Monte Carlo simulations of losses in daily and annual resolution. We demonstrate good agreement between annual model results and empirical values, albeit observing a small, potential underestimation of high losses. For the majority of districts we find high correlations between annual loss estimates and data. Absolute daily losses in Germany for the three most severe storms show good predictions of losses across 4 orders of magnitude.

[4] This article is structured as follows: After a brief discussion of data, we describe motivation and details of the damage function in section 3. A simplified parametrization of the damage function is demonstrated in section 4. Finally, we present modeled loss estimates and close with the discussion of our results in sections 5 and 6, respectively.