On Computing the Surface Horizontal Pressure Gradient over Elevated Terrain

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Methods are proposed for calculating the surface horizontal pressure gradient or geostrophic wind in a local area over elevated terrain from randomly spaced surface observations. These procedures avoid many of the problems associated with sea-level pressure. One technique is to compute pressure at the mean terrain elevation using the same procedure as for sea-level pressure. Another method, which is the main contribution of this paper, is based on sigma coordinates. Temperatures and geopotentials in a reference atmosphere are subtracted from those in the actual atmosphere to reduce the magnitudes of the compensating terms in the expression for the horizontal pressure gradient, and therefore decrease roundoff error. A geostrophic streamfunction is derived whose gradient is then determined by least squares fit to observations. Temperature gradients in the atmospheric boundary layer are also calculated in the sigma coordinates method. An iterative procedure to compute the mean and standard deviation of wind angles is presented, which can also be used in air quality applications. The techniques are applied to southwestern Alberta using data at 0000 and 1200 UTC for January to March inclusive for 1985 and 1986. There are significant discrepancies between the geostrophic wind computed at the mean terrain elevation compared to that at sea level. Average differences between the two geostrophic winds depend on wind direction and are as much as 87° for direction and 10 m s−1 for speed. The geostrophic wind calculated from the sigma coordinates method also differs from that at the mean terrain elevation. The standard deviation of the direction difference is 18°.