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