Dutch Continental Shelf Model Research Articles

The impact of nonlinear tide–surge interaction on satellite radar altimeter-derived tides

Both empirical and assimilative global ocean tidal models are significantly more accurate in the deep ocean than in shelf and coastal waters. In this study, we answered whether this is due to the quality of the models used to reduce tide and surge or the general approach to treat tide and surge as two separate components of the water level obtained from stand-alone models, which ignores the nonlinear tide–surge interaction. In doing so, we used tide gauge observations as partially synthetic altimeter time series, tide–surge water-level time series obtained with the 2D Dutch Continental Shelf Model – Flexible Mesh (DCSM), and tide and surge water-level time series obtained using the DCSM, FES2014 (FES) and the Dynamic Atmospheric Correction (DAC) product. Expressed in the root-sum-square (RSS) of the eight main tidal constituents, we obtained a reduction % when removing the DCSM tide–surge water levels compared to when we removed the sum of the DCSM tide and DCSM surge water levels. The RSS obtained in the latter case was only 3.3% lower than with FES and DAC. We conclude that the lower tidal estimates accuracy in shelf-coastal waters derives from the missing nonlinear tide–surge interactions.

Modelling of annual sand transports at the Dutch lower shoreface

Dutch coastal policy aims for a safe, economically strong and attractive coast. This is achieved by maintaining the part of the coast that support these functions; the coastal foundation. The coastal foundation is maintained by means of sand nourishments. Up to now, it has been assumed that net transports across the coastal foundation’s offshore boundary at the 20 m depth contour are negligibly small. In the framework of the Coastal Genesis 2.0 program we investigated sand transports across this boundary and across other depth contours at the lower shoreface.This paper presents a computationally efficient approach to compute the annual sand transport rates at the Dutch lower shoreface. It is based on the 3D Dutch Continental Shelf Model with Flexible Mesh (3D DCSM-FM), a wave transformation tool and a 1DV sand transport module. We validate the hydrodynamic input against field measurements and present flow, wave and sand transport computations for the years 2013–2017.Our computations show that the net annual sand transport rates along the Dutch coast are determined by peak tidal velocities (and asymmetry thereof), density driven residual flows, wind driven residual flows and waves.The annual mean alongshore transports vary along the continuous 20 m depth contour. The computed total cross-shore transports are onshore directed over the continuous 20 m, 18 m and 16 m depth contours and increase with decreasing water depth.The effect of density difference and wind on the 3D structure of the flow and on the sand transports cannot be neglected along the Dutch lower shoreface. Our computations show that excluding the effect of density results in a significant decrease of the onshore directed transports. Also switching off wind largely counteracts this effect.The net cross-shore transport is determined by a delicate balance between gross onshore and offshore transports, where wave conditions are important. We show an example for Scheveningen where the net cross-shore transport is onshore directed when including all wave conditions but would be offshore directed when excluding waves higher than 3.5 m. In contrast, at Callantsoog the highest waves contribute more to the offshore directed transports. These results suggest that storm conditions play an important role in the magnitude and direction of the net annual transport rates at the lower shoreface.

Observation impact analysis methods for storm surge forecasting systems

This paper presents a simple method for estimating the impact of assimilating individual or group of observations on forecast accuracy improvement. This method is derived from the nsemble-based observation impact analysis method of Liu and Kalnay (Q J R Meteorol Soc 134:1327–1335, 2008). The method described here is different in two ways from their method. Firstly, it uses a quadratic function of model-minus-observation residuals as a measure of forecast accuracy, instead of model-minus-analysis. Secondly, it simply makes use of time series of observations and the corresponding model output generated without data assimilation. These time series are usually available in an operational database. Hence, it is simple to implement. It can be used before any data assimilation is implemented. Therefore, it is useful as a design tool of a data assimilation system, namely for selecting which observations to assimilate. The method can also be used as a diagnostic tool, for example, to assess if all observation contributes positively to the accuracy improvement. The method is applicable for systems with stationary error process and fixed observing network. Using twin experiments with a simple one-dimensional advection model, the method is shown to work perfectly in an idealized situation. The method is used to evaluate the observation impact in the operational storm surge forecasting system based on the Dutch Continental Shelf Model version 5 (DCSMv5).

Application of data assimilation for improved operational water level forecasting on the northwest European shelf and North Sea

For the Netherlands, accurate water level forecasting in the coastal region is crucial, since large areas of the land lie below sea level. During storm surges, detailed and timely water level forecasts provided by an operational storm surge forecasting system are necessary to support, for example, the decision to close the movable storm surge barriers in the Eastern Scheldt and the Rotterdam Waterway. In the past years, a new generation operational tide-surge model (Dutch Continental Shelf Model version 6) has been developed covering the northwest European continental shelf. In a previous study, a large effort has been put in representing relevant physical phenomena in this process model as well as reducing parameter uncertainty over a wide area. While this has resulted in very accurate water level representation (root-mean-square error (RMSE) ∼7–8 cm), during severe storm surges, the errors in the meteorological model forcing are generally non-negligible and can cause forecast errors of several decimetres. By integrating operationally available observational data in the forecast model by means of real-time data assimilation, the errors in the meteorological forcing are prevented from propagating to the hydrodynamic tide-surge model forecasts. This paper discusses the development of a computationally efficient steady-state Kalman filter to enhance the predictive quality for the shorter lead times by improving the system state at the start of the forecast. Besides evaluating the model quality against shelf-wide tide gauge observations for a year-long hindcast simulation, the predictive value of the Kalman filter is determined by comparing the forecast quality for various lead time intervals against the model without a steady-state Kalman filter. This shows that, even though the process model has a water level representation that is substantially better than that of other comparable operational models of this scale, substantial improvements in predictive quality in the first few hours are possible in an actual operational setting.

A validation of an operational wave and surge prediction system for the Dutch coast

Abstract. Knowledge of the actual condition of hydrodynamics in the nearshore and coastal area is essential for coastal monitoring activities. To this end, a coastal operational model system can serve as a tool in providing recent and up-to-date, state-of-the-art hydrodynamics along the coast. In this paper, we apply CoSMoS (Coastal Storm Modeling System), a generic operational wave and tide-surge modelling system applied here to predict waves and water levels along the Dutch coast. The CoSMoS application is not limited to storm impact prediction on the Dutch coast, but can also be applied to other coastal hazards such as rip currents and coastal flooding, in other environments. In this paper, we present the set-up of the CoSMoS system and a validation of the wave and surge model, with deep-water wave buoy data and tidal gauge measurements as ground truth validation material. The evaluation is presented as monthly error measures between computed parameters and observed ones. Hindcast results over the whole year of 2009 show that the simulated wave parameters and surge elevation from the CoSMoS are in good agreement with data, with average root mean square (rms) error over the year of 0.14 m for the surge elevation and 0.24 m for the significant wave height. It is noted that there is a tendency of the wave model to underestimate the height of northerly waves with lower frequencies (swell). Additionally, when a wave separation algorithm is applied on the overall spectrum, results show consistent underestimation of the swell component by the model, which for the Dutch coast will mainly come from the north, where the North Sea is open to the Atlantic Ocean. In the proposed model system, the swell boundary can have a significant effect on the simulated wave results, suggesting room for improvement for the swell boundary conditions to the north and the swell propagation within the Dutch Continental Shelf Model. Finally, we show that in forecast mode, CoSMoS can provide reasonably good wave and surge prediction.

Obtaining instantaneous water levels relative to a geoid with a 2D storm surge model

Current and new applications of 2D storm surge models such as the Dutch Continental Shelf Model (DCSM) require that the models provide proper estimates of the instantaneous water levels expressed relative to a particular geoid, rather than only the tide and surge components expressed relative to the ill-defined model's zero height surface. For DCSM, this is realized by adding the depth-averaged horizontal baroclinic pressure gradients to the model equations, which are derived from 4D salinity and temperature fields provided by the Proudman Oceanographic Laboratory hydrodynamic model (POL's hindcast). The vertical datum of the extended model is fixed to that of the European Gravimetric Geoid model 2008 (EGG08). This is done by an adjustment of the model parameters that depend on the choice of the reference surface (e.g., bathymetry) and by referring the water levels along the open boundaries to this reference surface. Using different numerical experiments we investigate the effects on the water levels of several approximations we have made during the implementation. The ability of the model to reproduce both the mean sea level (MSL) and instantaneous water levels is assessed by a comparison with the MSL derived from POL's hindcast as well as with instantaneous water levels acquired by various radar altimeter satellites. From this comparison we conclude that our modeled MSL is in good agreement with the MSL derived from POL's hindcast; the standard deviation of the differences is below 2cm. However, larger differences in MSL are observed when comparing the model output with the MSL derived from radar altimeter data. They are attributed to either geoid errors or errors in the used salinity and temperature fields. The root mean squared (rms) differences between observed and modeled instantaneous water levels over the entire model domain varies from 9cm for data acquired by the TOPEX satellite to 11cm for data acquired by the GFO-1 satellite. These numbers improve to 8–10cm on the North Sea, for data acquired by the TOPEX and ERS-2 satellites, respectively. These numbers are a factor two to three larger than the expected accuracy of water levels derived from radar altimeter data (which is ∼4cm). About 25% of these differences can be explained by a bias between the modeled and observed water levels of a single satellite pass. These biases are attributed to errors in the applied correction for the net steric expansion/contraction of the global oceans as this is not captured by DCSM that makes use of the Boussinesq approximation, as well as other errors in model and data.

The impact of future sea-level rise on the European Shelf tides

This paper investigates the effect of future sea-level rise (SLR) on the tides of the northwest European Continental Shelf. The European shelf tide is dominated by semidiurnal constituents. This study therefore focuses primarily on the changes in the M2 tidal constituent and the spring and neap tidal conditions. The validated operational Dutch Continental Shelf Model is run for the present day sea-level as well as 2 and 10m SLR scenarios.The M2 tidal amplitude responds to SLR in a spatially non-uniform manner, with substantial amplitude increases and decreases in both scenarios. The M2 tidal response is non-linear between 2 and 10m with respect to SLR, particularly in the North Sea. Under the 2m SLR scenario the M2 constituent is particularly responsive in the resonant areas of the Bristol Channel and Gulf of St. Malo (with large amplitude decreases) and in the southeastern German Bight and Dutch Wadden Sea (with large amplitude increases). Changes in the spring tide are generally greater still than those in the M2 or neap tides. With 2m SLR the spring tidal range increases up to 35cm at Cuxhaven and decreases up to −49cm at St. Malo. Additionally the changes in the shallow water tides are larger than expected. With SLR the depth, wave speed and wave length (tidal resonance characteristics) are increased causing changes in near resonant areas. In expansive shallow areas SLR causes reduced energy dissipation by bottom friction. Combined these mechanisms result in the migration of the amphidromes and complex patterns of non-linear change in the tide with SLR.Despite the significant uncertainty associated with the rate of SLR over the next century, substantial alterations to tidal characteristics can be expected under a high end SLR scenario. Contrary to existing studies this paper highlights the importance of considering the modification of the tides by future SLR. These substantial future changes in the tides could have wide reaching implications; including for example, correctly calculating design level requirements for flood defences, the availability of tidal renewable energy and dredging requirements.

Simultaneous perturbation stochastic approximation for tidal models

The Dutch continental shelf model (DCSM) is a shallow sea model of entire continental shelf which is used operationally in the Netherlands to forecast the storm surges in the North Sea. The forecasts are necessary to support the decision of the timely closure of the moveable storm surge barriers to protect the land. In this study, an automated model calibration method, simultaneous perturbation stochastic approximation (SPSA) is implemented for tidal calibration of the DCSM. The method uses objective function evaluations to obtain the gradient approximations. The gradient approximation for the central difference method uses only two objective function evaluation independent of the number of parameters being optimized. The calibration parameter in this study is the model bathymetry. A number of calibration experiments is performed. The effectiveness of the algorithm is evaluated in terms of the accuracy of the final results as well as the computational costs required to produce these results. In doing so, comparison is made with a traditional steepest descent method and also with a newly developed proper orthogonal decomposition-based calibration method. The main findings are: (1) The SPSA method gives comparable results to steepest descent method with little computational cost. (2) The SPSA method with little computational cost can be used to estimate large number of parameters.

Inverse Shallow-Water Flow Modeling Using Model Reduction

The idea presented in this paper is variational data assimilation based on model reduction using proper orthogonal decomposition. An ensemble of forward model simulations is used to determine the approximation of the covariance matrix of the model variability, and only the dominant eigenvectors of this matrix are used to define a model subspace. An approximate linear reduced model is obtained by projecting the original model onto this reduced subspace. Compared to the classical variational method, the adjoint of the tangent linear model is replaced by the adjoint of a linear reduced forward model. Thus, it does not require the implementation of the adjoint of the tangent linear model. The minimization process is carried out in reduced subspace and hence reduces the computational cost. Twin experiments using an operational storm surge prediction model in the Netherlands, the Dutch Continental Shelf Model are performed to estimate the water depth, with the findings that the approach with relatively little computational cost and without the burden of implementation of the adjoint model can be used in variational data assimilation.

Operational storm surge forecasting in the Netherlands: developments in the last decade

The accurate forecasting of storm surges is an important issue in the Netherlands. With the emergence of the first numerical hydrodynamic models for surge forecasting at the beginning of the 1980s, new demands and possibilities were raised. This article describes the main phases of the development and the present operational set-up of the Dutch continental shelf model, which is the main hydrodynamic model for storm surges in the Netherlands. It includes a brief discussion of applied data-assimilation techniques, such as Kalman filtering, the model calibration process and some thoughts on quality assurance in an operational environment. After further describing some select recent investigations, the paper concludes with some remarks on future developments in a European context.

A modelling study of tidally induced equilibrium sand balances in the North Sea during the Holocene

The present paper describes a depth-integrated modelling approach for tide-induced sediment transport, and its application to the North Sea for various cases during the Holocene sea level rise. The flow model is based on the shallow water equations, while the transport model is based on Galappatti’s asymptotic approach for rivers, now applied to tidal flow situations in two horizontal dimensions ( Galappatti, 1983, Galappatti and Vreugdenhil, 1986). The empirical Engelund–Hansen formula for sedimentation / erosion is used as a closure for the sediment exchange term in the transport equation, while variation of the bed height is neglected. The various assumptions in the derivation of the sediment model, and their consequences are addressed step by step. The North Sea area considered in the application is the whole North west European continental shelf, as mapped onto the Dutch Continental Shelf Model. In a series of cyclic period simulations of the present day situation, the sensitivity to parameter variations such as diffusion, equilibrium concentration and adaptation time is analysed, as well as the effect of bathymetry smoothing. Using a suitable and fixed parameter setting, the North Sea tidally induced equilibrium sand balances are simulated for several epochs during the Holocene sea level rise. Both uniform sea level reductions (0, −5, −15, and −35 m. and non-uniform sea level reductions (8500 BP, 8100 BP are considered, based on Jelgersma’s geological uniform sea level curve, and glacio-hydro-isostatic rebound modelling results, respectively. It is concluded that the derived Galappatti model for 2D tidal flow is a feasible approach to get a first assessment of equilibrium sedimentation balance on North Sea scale, and of its possible changes due to the Holocene sea level rise under various simplified assumptions regarding the evolution of coastline and bathymetry, both uniform and non-uniform.

Impact of a wind climate change on the surge in the southern North Sea

The aim of this paper is to gain quantitative insights into the surge-impact of a possible change of the wind climate in the southern part of the North Sea. The approach taken is based upon an initial review of the results of General Circulation Model scenarios for climate change under greenhouse forcing and of their likely effects upon wind climate. Two scenarios of possible wind climate change are formulated. Scenario 1 assumes a northward shift of the entire wlnd climate system in the southern part of the North Sea; scenario 2 describes an increase of the intensity of storms in this area. To model these scenarios, the concept of 'parametric storms' is presented, which considers the character~stlcs of a storm to be conditional upon a limited number of parameters. Applying this concept to the well-known 1953 storm yields promising results. On the b a s ~ s of this parametric 1953 storm, a large set of storms which are assumed to be consistent with the present (surge generating) wind climate in the southern part of the North Sea is generated. Because these storms do not all have equal chances of occurrence, this set is supplemented by a probability distribution. The future wind climate, which might develop as a result of the 2 wind climate change scenarios, is then modelled by changing this probability distribution and/or some parameters of the storm set. The surge-impact of the 2 modelled scenarios of wind climate change is determined using the Dutch Continental Shelf Model, which describes the depth-averaged tidal flow and storm surges in the North Sea and surrounding areas. For several locations in the southern part of the North Sea, the model output is analyzed and presented in terms of a frequency distribution of storm surge levels. With respect to scenario 1, these simulation results show that a relatively large northward shift of the entire wind climate system in the southern part of the North Sea will only have a small impact on the storm surges in this area In the case of scenano 2, however, the results show that a relatively small increase of the intensity of depressions in the southern North Sea will result in a relatively large impact on the storm surges in this area.