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Sigma-Coordinate Correction

In regions of steep topography, sigma-coordinate models are prone to errors in the calculation of pressure gradient and horizontal diffusion terms (Beckman and Haidvogel, 1993). In the modeling here, initial stratification results were not encouraging in that the modeled temperature stratification during the summer was 50% weaker than observed at the future outfall site (Figure 2.9) and in Stellwagen Basin.

  
Figure 2.9: Observed and modeled temperature difference (5 m - 23 m) at Station BB (see Figure 2.2). Before the correction, the model greatly underpredicted the degree of temperature stratification in the summer months. Observed data is missing from late August to November.

Although vertical mixing was initially suspected, the problem turned out to be caused by spurious up-slope mixing caused by -coordinate errors. These errors were significantly reduced by removing the domain-averaged vertical salinity, temperature, and density profiles before calculating horizontal differences (e.g. Beckmann and Haidvogel, 1993). The effectiveness of this technique depends upon the degree to which the vertical structure varies over the domain. In domains such as Massachusetts Bay, in which the stratification is nearly uniform over the region, this technique greatly improves the model prediction in comparison to observed data (Figure 2.9). The more the vertical structure varies over the domain, however, the less useful the technique in reducing -coordinate errors. In domains where both stratified and well-mixed regions exist, errors would actually increase in the well-mixed region since subtracting the domain-averaged vertical profile would result in more vertical structure locally.