Ocean Dynamics (2016) 66:1037–1050 DOI 10.1007/s10236-016-0962-y Adjoint free four-dimensional variational data assimilation for a storm surge model of the German North Sea Xiangyang Zheng 1 · Roberto Mayerle 1 · Qianguo Xing 2 · Jos´ e Manuel Fern´ andez Jaramillo 1 Received: 30 September 2015 / Accepted: 30 May 2016 / Published online: 15 June 2016 © Springer-Verlag Berlin Heidelberg 2016 Abstract In this paper, a data assimilation scheme based on the adjoint free Four-Dimensional Variational(4DVar) method is applied to an existing storm surge model of the German North Sea. To avoid the need of an adjoint model, an ensemble-like method to explicitly represent the linear tangent equation is adopted. Results of twin experiments have shown that the method is able to recover the contami- nated low dimension model parameters to their true values. The data assimilation scheme was applied to a severe storm surge event which occurred in the North Sea in December 5, 2013. By adjusting wind drag coefficient, the predic- tive ability of the model increased significantly. Preliminary experiments have shown that an increase in the predictive ability is attained by narrowing the data assimilation time window. Keywords Storm surge model · Wind drag coefficient · Data assimilation · Adjoint free 4Dvar This article is part of the Topical Collection on the 7th Interna- tional Workshop on Modeling the Ocean (IWMO) in Canberra, Australia 1-5 June 2015 Responsible Editor: Yign Noh  Xiangyang Zheng xyzheng@corelab.uni-kiel.de 1 Research and Technology Centre Westcoast, University of Kiel, Kiel, Germany 2 Yantai Institute of Coastal Zone Research, Chinese Academy of Sciences, Yantai, China 1 Introduction Storm surges are exceptional water level changes caused by the strong tangent wind on the sea surface. Storm surge is one of the most destructive natural disasters in coastal areas. On February of 1962, a severe storm swept the Ger- man Bight, causing severe damage along the German North Sea coast and costing more than 300 lives in Hamburg (Von Storch et al. 2008). The hurricane Katrina hit the south coast of the USA in August 2005. The total number of fatal- ities directly related to the extreme event exceeded 1200 (Fritz et al. 2007). The Bay of Bengal is another coastal area susceptible to tropical storm surges. The severe storm in October 1999 killed more than 15,000 people and caused enormous property losses (Dube et al. 2009). Although much attention has been paid to coastal protection and the number of casualties has decreased considerably, storm surge remains the main natural hazard in coastal areas. Thus, accurate forecast of such events is essential for early warning. With the enhancement in computing power and improvement in the accuracy of meteorological models, sys- tems for the nowcasting and forecasting of storm surges are at reach. Storm surge is caused by strong meteorological forcing due to wind and low air pressure. The effect of air pressure is straightforward and easy to simulate. Proper specifica- tions of wind shear stress is probably the most critical issue for a storm surge model but may have the most uncertain- ties (Bode and Hardy 1997). For most storm surge models, the wind shear stress is expressed as a quadratic function of wind speed as follows (Hydraulics 2011): τ = ρ a C d |U 10 |U 10 (1)