Calibration of a Numerical Model with a Limited Number of Tidal Constituents

The response of numerical models to small variations in depth, coefficient of bottom friction and the number of tidal harmonics is considered with particular reference to a model of the Bristol Channel. The model is tuned by using an input of 23 largest gravitational and non-linear constituents from a continental shelf model at its open boundary along the longitude 5° west. In the process of tuning the drag coefficient of the bottom friction, water depth and grid scales are adjusted. The modified version of the model has considerably improved the distribution of the M2and S2tidal constituents. Subsequently, the model is tuned for the M2and S2tides alone to investigate the essential adjustments. The results suggest that some additional changes in the parameters are essential when the model is driven with an individual constituent. Small constituents such as the S2and N2can also be reproduced quite accurately in addition to the dominant constituent. However, the increase required in the drag coefficient of the bottom stress is very large when a small constituent is considered alone. In the case of the Bristol Channel model, it is found that the drag coefficient of friction should be increased by a factor of 1•20 and 4•33 for the M2and S2constituents, respectively. This factor increases almost linearly with the ratio of the total variance in the tidal spectrum to the variance of the constituent under investigation when the ratio exceeds 7. The influence of all the constituents in the tidal spectrum on the bottom stress of each constituent can be estimated by computer simulations. The adjustments required to improve results for the principal constituents and non-linear constituents are contradictory. The model results conform to analytical approximations. It is shown that non-linear constituents generated by a model driven by a single constituent are unreliable. Even those non-linear constituents that appear to be generated by the principal constituent under investigation in the model are not reliable. The results from this investigation provide some insight into the problem of choosing the value of drag coefficient of bottom friction for large-scale (ocean-wide) models. These models cover regions where the tidal regime changes from semi-diurnal to diurnal and bottom topography varies significantly in the continental shelf and coastal areas. Under those circumstances, a model may require a spatially variable drag coefficient when driven by a limited number of constituents (e.g. M2or K1).