An inter-comparison of tidal solutions computed with a range of unstructured grid models of the Irish and Celtic Sea regions

Three finite element codes, namely TELEMAC, ADCIRC and QUODDY, are used to compute the spatial distributions of the M-2, M-4 and M-6 components of the tide in the sea region off the west coast of Britain. This region is chosen because there is an accurate topographic dataset in the area and detailed open boundary M-2 tidal forcing for driving the model. In addition, accurate solutions (based upon comparisons with extensive observations) using uniform grid finite difference models forced with these open boundary data exist for comparison purposes. By using boundary forcing, bottom topography and bottom drag coefficients identical to those used in an earlier finite difference model, there is no danger of comparing finite element solutions for "untuned unoptimised solutions" with those from a "tuned optimised solution". In addition, by placing the open boundary in all finite element calculations at the same location as that used in a previous finite difference model and using the same M-2 tidal boundary forcing and water depths, a like with like comparison of solutions derived with the various finite element models was possible. In addition, this open boundary was well removed from the shallow water region, namely the eastern Irish Sea where the higher harmonics were generated. Since these are not included in the open boundary, forcing their generation was determined by physical processes within the models. Consequently, an inter-comparison of these higher harmonics generated by the various finite element codes gives some indication of the degree of variability in the solution particularly in coastal regions from one finite element model to another. Initial calculations using high-resolution near-shore topography in the eastern Irish Sea and including "wetting and drying" showed that M-2 tidal amplitudes and phases in the region computed with TELEMAC were in good agreement with observations. The ADCIRC code gave amplitudes about 30 cm lower and phases about 8A degrees higher. For the M-4 tide, in the eastern Irish Sea amplitudes computed with TELEMAC were about 4 cm higher than ADCIRC on average, with phase differences of order 5A degrees. For the M-6 component, amplitudes and phases showed significant small-scale variability in the eastern Irish Sea, and no clear bias between the models could be found. Although setting a minimum water depth of 5 m in the near-shore region, hence removing wetting and drying, reduced the small-scale variability in the models, the differences in M-2 and M-4 tide between models remained. For M-6, a significant reduction in variability occurred in the eastern Irish Sea when a minimum 5-m water depth was specified. In this case, TELEMAC gave amplitudes that were 1 cm higher and phases 30A degrees lower than ADCIRC on average. For QUODDY in the eastern Irish Sea, average M-2 tidal amplitudes were about 10 cm higher and phase 8A degrees higher than those computed with TELEMAC. For M-4, amplitudes were approximately 2 cm higher with phases of order 15A degrees higher in the northern part of the region and 15A degrees lower in the southern part. For M-6 in the north of the region, amplitudes were 2 cm higher and about 2 cm lower in the south. Very rapid M-6 tidal-phase changes occurred in the near-shore regions. The lessons learned from this model inter-comparison study are summarised in the final section of the paper. In addition, the problems of performing a detailed model-model iner-comparison are discussed, as are the enormous difficulties of conducting a true model skill assessment that would require detailed measurements of tidal boundary forcing, near-shore topography and precise knowledge of bed types and bed forms. Such data are at present not available

A model study of tidal distributions in the Celtic and Irish Sea regions determined with finite volume and finite element models

An unstructured mesh model of the west coast of Britain, covering the same domain and using topography and open boundary forcing that are identical to a previous validated uniform grid finite difference model of the region, is used to compare the performance of a finite volume (FV) and a finite element (FE) model of the area in determining tide–surge interaction in the region. Initial calculations show that although qualitatively both models give comparable tidal solutions in the region, comparison with observations shows that the FV model tends to under-estimate tidal amplitudes and hence background tidal friction in the eastern Irish Sea. Storm surge elevations in the eastern Irish Sea due to westerly, northerly and southerly uniform wind stresses computed with the FV model tend to be slightly higher than those computed with the FE model, due to differences in background tidal friction. However, both models showed comparable non-linear tide–surge interaction effects for all wind directions, suggesting that they can reproduce the extensive tide–surge interaction processes that occur in the eastern Irish Sea. Following on from this model comparison study, the physical processes contributing to surge generation and tide–surge interaction in the region are examined. Calculations are performed with uniform wind stresses from a range of directions, and the balance of various terms in the hydrodynamic equations is examined. A detailed comparison of the spatial variability of time series of non-linear bottom friction and non-linear momentum advection terms at six adjacent nodes at two locations in water depths of 20 and 6 m showed some spatial variability from one node to another. This suggests that even in the near coastal region, where water depths are of the order of 6 m and the mesh is fine (of order 0.5 km), there is significant spatial variability in the non-linear terms. In addition, distributions of maximum bed stress due to tides and wind forcing in nearshore regions show appreciable spatial variability. This suggests that intensive measurement campaigns and very high-resolution mesh models are required to validate and reproduce the non-linear processes that occur in these regions and to predict extreme bed stresses that can give rise to sediment movement. High-resolution meshes will also be required in pollution transport problem

Influence of non-linear effects upon surge elevations along the west coast of Britain

Abstract: A two-dimensional vertically integrated hydrodynamic finite-element model of the west coast of Britain is used to examine the response of the region to extreme meteorological forcing. The extent to which tide-surge interaction modifies the computed surge elevation and current distributions is examined in detail. The nature of the finite-element model with its ability to refine the mesh in nearshore regions is ideal for examining the influence of non-linear effects upon surges in these regions. Calculations using spatially uniform orthogonal wind stresses show that the surge elevation and current in shallow water are particularly sensitive to the method used to remove the tide as a result of the highly non-linear nature of the tide-surge interaction in these regions. The most accurate means of de-tiding the solution is by subtracting a tide derived by harmonic analysis of the tide and surge time series at the time of the surge. Subtracting a tide-only solution (the usual approach) leads to tidal energy leaking into the surge solution. Calculations show that this arises because the surge modifies the tidal amplitude and phase in shallow-water regions to such an extent that they are appreciably different to those found in the tide-only calculation. Results suggest that this problem becomes more important, as nearshore meshes are refined in an attempt to improve surge prediction. This suggests that in the future, highly accurate fine-mesh models will be required to compute total water levels without the present linear separation into tidal and surge signal used in operational surge prediction

Physical and dynamical oceanography of Liverpool Bay

The UK National Oceanography Centre has maintained an observatory in Liverpool Bay since August 2002. Over 8 years of observational measurements are used in conjunction with regional ocean modelling data to describe the physical and dynamical oceanography of Liverpool Bay and to validate the regional model, POLCOMS. Tidal dynamics and plume buoyancy govern the fate of the fresh water as it enters the sea, as well as the fate of its sediment, contaminants and nutrient loads. In this context, an overview and summary of Liverpool Bay tidal dynamics are presented. Freshwater forcing statistics are presented showing that on average the bay receives 233 m3 s - 1. Though the region is salinity controlled, river input temperature is shown to significantly modulate the plume buoyancy with a seasonal cycle. Stratification strongly influences the region's dynamics. Data from long-term moored instrumentation are used to analyse the stratification statistics that are representative of the region. It is shown that for 65% of tidal cycles, the region alternates between being vertically mixed and stratified. Plume dynamics are diagnosed from the model and are presented for the region. The spring-neap modulation of the plume's westward extent, between 3.5 ° W and 4° W, is highlighted. The rapid eastward erosion of the plume during spring tides is identified as a potentially important freshwater mixing mechanism. Novel climatological maps of temperature, salinity and density from the CTD surveys are presented and used to validate numerical simulations. The model is found to be sensitive to the freshwater forcing rates, temperature and salinities. The existing CTD survey grid is shown to not extend sufficiently near the coast to capture the near coastal and vertically mixed component the plume. Instead the survey grid captures the westward spreading, shallow and transient, portion of the plume. This transient plume feature is shown in both the long-term averaged model and observational data as a band of stratified fluid stretching between the mouth of the Mersey towards the Isle of Man. Finally the residual circulation is discussed. Long-term moored ADCP data are favourably compared with model data, showing the general northward flow of surface water and southward trajectory of bottom wate