Modelling Over- and Compound Tides of the Irish and Celtic Seas Using Variational Data Assimilation Methods

Abstract

A data assimilation procedure is developed and applied to a 5 minutes resolution non-linear tidal model of the Irish and Celtic Seas making use of an efficient iterative method for the solution of the minimization problem. M2 and S2 tidal constituents are used for defining the external forcing at the open boundary nodes. As a rule periodicity does not apply to tidal signals due to two or more astronomical partial tides because of the incommensurability of tidal frequencies. So M2 and S2 have a beat period of 14.7 days, but according to incommensurability their superposition is not periodic. Therefore a certain time interval must be used for data assimilation purposes, where initial conditions (continuation conditions) must be introduced.

Firstly, the method is applied to a canal model scenario with a dynamic model yielding results defined as real and a dynamical model made deficient and producing results that are to be corrected making use of values taken from the field regarded as real. The canal with constant depth has a closed end and an open end, at which the tidal wave being determined by two astronomical constituents enters the canal. The experiments show that by applying the assimilation procedure, the deviation of the “to be corrected” solution from the “reference” solution can be reduced significantly, from 35.68% to less than 5%. The first and second order differences of the dynamical residuals are also introduced in the minimization functional. From the investigation of the dynamical residuals it follows that using this method of data assimilation, information on the deficiencies of the classical model can be taken from the resulting dynamic residuals.

After successfully applying this method to a fictive data assimilation scenario, a non-linear depth averaged assimilation model is developed and applied to the Irish and Celtic Seas. Observations from 24 positions are assimilated, and the solution is then compared with that one of the classical model, with those of other available models as well as with data from independent stations. The evaluations suggest that the data assimilation procedure is working well and yields a very significant improvement of the solution. Results for M2, S2, 2SM2, M2, MS4, M6, 2MS6, and 2SM6 are obtained which agree well with observations as well as with reliable results of high resolution models and other data assimilation models. First order differences of the dynamical residuals are introduced into the minimization functional and by it evidently an adequate spatial smoothing of the residuals is reached. The length scale of the residuals then corresponds to the decorrelation lengths assumed for the dynamical errors and hopefully to the scale of the compensated deficiencies, as applying to the fictive data assimilation scenario.

The data assimilation procedure, thus having successfully been tried out for a specific adjacent sea area comprising marked shallow water areas, is ready for directly being applied to arbitrary adjacent sea and shelf regions, taking into account as many astronomical tidal constituents as regarded necessary. The incorporation of this type of model into global ocean models guarantees proper consideration of shallow water effects, at the same time effectively assimilating data also from near coastal areas.