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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 December2013 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 5cmand 15cmdue 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.

Proudman resonance is a primary amplification mechanism for meteotsunamis, which are shallow-water waves generated by atmospheric forcings. The effect of tides, sloping bathymetry and the speed, amplitude and aspect ratio of the atmospheric forcing on Proudman resonant wave growth are investigated using analytical approximations and numerical models. With tides included, maximum wave growth through Proudman resonance occurred when the atmospheric-forcing speed matched the tidal-wave speed. Growth greater than Proudman resonance occurred with a positive tidal elevation together with a tidal current in the opposite direction to wave propagation, due to linear growth combined with further amplification from wave-flux conservation. Near-Proudman resonant growth occurred when the forced-wave speed or free-wave speed varied by either a small amount, or varied rapidly, around a speed appropriate for Proudman resonance. For a forcing moving at Proudman resonant speed, resultant wave growth was proportional to the total, time-integrated forcing amplitude. Finally, Proudman resonant wave growth was lower for forcings with lower aspect ratios (AP), partly because forced-wave heights are proportional to 1 + A 2P , but also because free waves could spread in two dimensions. Whilst the assumptions of strict Proudman resonance are never met, near-Proudman resonant growth may occur over hundreds of kilometres if the effective Froude number is near 1 and the resultant wave propagates predominantly in one dimension.

On the morning of 23 June 2016, a 0.70 m meteotsunami was observed in the English Channel between the UK and France. This wave was measured by several tide gages and coincided with a heavily precipitating convective system producing 10 m s−1 wind speeds at the 10-m level and 1–2.5 hPa surface pressure anomalies. A combination of precipitation rate crosscorrelations and NCEP/NCAR Reanalysis 1 data showed that the convective system moved northeastward at 19 ± 2 m s−1. To model the meteotsunami, the finite element model Telemac was forced with an ensemble of prescribed pressure forcings, covering observational uncertainty. Ensembles simulated the observed wave period and arrival times within minutes, and wave heights within tens of centimeters. A directly forced wave and a secondary coastal wave were simulated, and these amplified as they propagated. Proudman resonance was responsible for the wave amplification, and the coastal wave resulted from strong refraction of the primary wave. The main generating mechanism was the atmospheric pressure anomaly with wind stress playing a secondary role, increasing the first wave peak by 16% on average. Certain tidal conditions reduced modeled wave heights by up to 56%, by shifting the location where Proudman resonance occurred. This shift was mainly from tidal currents, rather than tidal elevation directly affecting shallow water wave speed. An improved understanding of meteotsunami return periods and generation mechanisms would be aided by tide gage measurements sampled at less than 15-minute intervals.

Tide predictions based on tide-gauge observations are not just the astronomical tides; they also contain radiational tides – periodic sea-level changes due to atmospheric conditions and solar forcing. This poses a problem of double-counting for operational forecasts of total water level during storm surges. In some surge forecasting, a regional model is run in two modes: tide only, with astronomic forcing alone; and tide and surge, forced additionally by surface winds and pressure. The surge residual is defined to be the difference between these configurations and is added to the local harmonic predictions from gauges. Here we use the Global Tide and Surge Model (GTSM) based on Delft-FM to investigate this in the UK and elsewhere, quantifying the weather-related tides that may be double-counted in operational forecasts. We show that the global S2 atmospheric tide is captured by the tide-and-surge model and observe changes in other major constituents, including M2. The Lowest and Highest Astronomical Tide levels, used in navigation datums and design heights, are derived from tide predictions based on observations. We use our findings on radiational tides to quantify the extent to which these levels may contain weather-related components.

For a simple dynamical system, such as a pendulum, it is easy to deduce where and when applied forcing might produce a particular response. However, for a complex nonlinear dynamical system such as the ocean or atmosphere, this is not as obvious. Knowing when or where the system is most sensitive, to observational uncertainty or otherwise, is key to understanding the physical processes, improving and providing reliable forecasts. We describe the application of adjoint modeling to determine the sensitivity of sea level at a UK coastal location, Sheerness, to perturbations in wind stress preceding an extreme North Sea storm surge event on 9 November 2007. Sea level at Sheerness is one of the most important factors used to decide whether to close the Thames Flood Barrier, which protects London. Adjoint modeling has been used by meteorologists since the 1990s, but is a relatively new technique for ocean modeling. It may be used to determine system sensitivity beyond the scope of ensemble modeling and in a computationally efficient way. Using estimates of wind stress error from Met Office forecasts, we find that for this event total sea level at Sheerness is most sensitive in the 3 h preceding the time of its unperturbed maximum level and over a radius of approximately 300 km. We also find that the pattern of sensitivity follows a simple sequence when considered in the reverse-time direction.

We use a novel statistical approach to analyse changes in the occurrence and severity of storm surge events in the southern and central North Sea over the period 1955-2000, using 1) output from a numerical storm surge model and 2) in situ data on surge levels at sites for which sufficiently long observational records are available. The methodology provides a robust diagnostic tool for assessing the ability of models to reproduce the observed characteristics of storm surges, in a fashion that properly accounts both for variability within a single long run of the model and for recording error in observational data on sea levels. The model re-analysis data show strong positive trends in the frequency and severity of storm surge events at locations in the north-eastern North Sea, whilst trends at locations in the southern and western North Sea appear to be dominated by decadal variability. Trends in in situ data for sites along the North Sea coast are fairly synchronous with corresponding trends in the model re-analysis data, with the most serious discrepancies attributable to known problems in the observational record.

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 M2 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 View the MathML source 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.

Two-dimensional paleotidal simulations have been undertaken to investigate tidal and tide-dependent changes (tidal amplitudes, tidal current velocities, seasonal stratificafion, peak bed stress vectors) that have occurred in the NW European shelf seas during the last 20 ka. The simulations test the effect of shelf-wide isostatic changes of sea level by incorporating results from two different crustal rebound models, and the effect of the ocean-tide variability by setting open boundary values either fixed to the present state or variable according to the results of a global paleotidal model. The use of the different crustal rebound models does not affect the overall changes in tidal patterns, but the timing of the changes is sensitive to the local isostatic effects that differ between the models. The incorporation of ocean-tide changes greatly augments the amplitude of tides and tidal currents in the Celtic and Malin seas before 10 ka BP, and has a large impact on the distribution of seasonally stratified conditions, magnitude of peak bed stress vectors and tidal dissipation in the shelf seas. The predictions on seasonal stratification are supported by well-dated evidence on tidal mixing front migration in the Celtic Sea. Additional experiments using the global model suggest that the variability of offshore tides has been caused mainly by changes of eustatic sea level and ice-sheet extent. In particular, a large decrease observed at 10-8 ka BP is attributed to the opening of Hudson Strait accompanied by the retreat of the Laurentide Ice Sheet.

A semi-implicit version of the Princeton Ocean Model, ECOMsi, was used to simulate the cyclonic gyre that is found in the western Irish Sea during the spring and the summer. Mesoscale, seasonal, density-driven circulations such as this are an important component of the long-term flow in shelf seas, and they pose a challenge to coastal ocean models. Extensive comparisons are made here with observational data to assess model performance. The model successfully reproduced the development of the temperature field, and the associated density-driven currents, throughout seasonal simulations. The results demonstrate conclusively that the gyre is density-driven and reinforce the dynamical importance of strong nearbed horizontal density gradients. Maximum baroclinic currents of 0.14 m s−1 were obtained, and results showed that the regional kinetic energy due to the residual flow was 20%–25% of that due to tidal flow during periods in which density gradients were strongest. The model revealed important interactions between both wind and tide and the density structure; these interactions can direct and modulate density-driven flow.