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Numerical storm surge models are essential to forecasting coastal flood hazard and informing the design of coastal defences. However, such models rely on a variety of inputs, many of which carry uncertainty. An awareness and understanding of the sensitivity of model outputs with respect to those uncertain inputs is therefore essential when interpreting model results. Here, we use an unstructured-mesh numerical coastal ocean model, Thetis , and its adjoint, to perform a sensitivity analysis for a hindcast of the 5th/6th December 2013 North Sea surge event, with respect to the bottom friction coefficient, bathymetry and wind stress forcing. The results reveal spatial and temporal patterns of sensitivity, providing physical insight into the mechanisms of surge generation and propagation. For example, the sensitivity of the skew surge to the bathymetry reveals the protective effect of a sand bank off the UK east coast. The results can also be used to propagate uncertainties through the numerical model; based on estimates of model input uncertainties, we estimate that modelled skew surges carry uncertainties of around 5 cm and 15 cm due to bathymetry and bottom friction, respectively. While these uncertainties are small compared with the typical spread in an ensemble storm surge forecast due to uncertain meteorological inputs, the adjoint-derived model sensitivities can nevertheless be used to inform future model calibration and data acquisition efforts in order to reduce uncertainty. Our results demonstrate the power of adjoint methods to gain insight into a storm surge model, providing information complementary to traditional ensemble uncertainty quantification methods. • We calibrate an unstructured-mesh finite element storm surge model of the North Sea • We use an adjoint approach to perform sensitivity analysis for modelled skew surges • We compare spatial and temporal patterns of sensitivity with respect to three inputs • We demonstrate the physical insight available through numerical adjoint methods. [ABSTRACT FROM AUTHOR]

Abstract: The Seto Inland Sea is a partially enclosed shallow sea with a complex bathymetry involving several basins, separated by narrow straits, and numerous islands. The influence of tidal stirring on density stratification and on the distribution of nutrients and chlorophyll in this region has been investigated using a combination of a numerical model of the tidal flow and the results of two extensive surveys of property distributions in the summer regime. The Princeton Ocean Model (POM) has been used to determine the spatial structure of the tidal flow and the results have been verified by comparison with an extensive database of current and elevation measurements. The model indicates a large difference in total energy flux between the western entrance section, which is controlled by a progressive wave regime, and the eastern entrance section which is associated with a predominantly standing wave regime. The combined energy flux input matches the total energy dissipation for the M 2 in the Inland Sea which is found to be ∼3.4×109 W. Two ship surveys in August 2002 and 2003 along a central section show a highly differentiated pattern of vertical structure. The potential energy anomaly ϕ, an index of vertical stability based on density, exhibits a marked inverse correlation with tidal energy dissipation thus confirming the control of stratification by tidal stirring. In most straits, vertical differences of nutrients and chlorophyll are small or negligible while in the low-energy basins there are pronounced vertical differences associated with density stratification. These sluggish basins exhibit oligotrophic conditions in the surface layer but large nitrate concentrations below the pycnocline and significant chlorophyll maxima in subsurface layer. The physical pattern of varying stratification and fronts is reflected to a considerable degree in the distributions of biochemical properties. [Copyright &y& Elsevier]