Estimating the internal pressure gradient errors in a σ-coordinate ocean model for the Nordic Seas

Internal pressure gradient estimation is problematic in sigma-coordinate ocean models and models based on more generalised topography following coordinate systems. Artificial pressure gradients in these models may create artificial flow. In recent literature, several methods for reducing the errors in the estimated internal pressure gradients are suggested. A basin with a bell-shaped seamount in the middle has often been applied as a test case. To supplement the findings from these more idealised experiments, the internal pressure gradient errors in a sigma-coordinate ocean model for the Nordic Seas are discussed in the present paper. Three methods for estimating internal pressure gradients are applied in these experiments. The sensitivity of the results to the subtraction of background stratification and to the horizontal viscosity are also investigated. For the extended Nordic Seas case, basin scale modes dominate after a few days of simulation. The errors in the transports across some sections may be larger than 1 Sv (1 Sv = 10(6) m3(s) s(-1) in these studies with 16-km grid resolution. The order of magnitude of the errors in the transports of Atlantic water into the Nordic Seas is approximately 0.5 Sv or between 5 and 10 % of recent transport estimates based on measurements. The results do not indicate that the errors are generally reduced if the background stratification is subtracted when estimating internal pressure gradients in terrain following models. However, the results from the experiments initialised with the background stratification show that the erroneous flows may be reduced considerably by using more recent techniques for estimating internal pressure gradients, especially for higher values of horizontal viscosity.