calculate the estimated geostrophic wind speed and direction for the following l
ID: 108594 • Letter: C
Question
calculate the estimated geostrophic wind speed and direction for the following layer at 550 hPa. The layer is between 925 and 550 hPa at 28N. The mean temperature in the layer is increasing eastward by 3.7C per 100 km. the 925 hPa geostrophic wind is from the southwest at 17 m s-1. calculate the estimated geostrophic wind speed and direction for the following layer at 550 hPa. The layer is between 925 and 550 hPa at 28N. The mean temperature in the layer is increasing eastward by 3.7C per 100 km. the 925 hPa geostrophic wind is from the southwest at 17 m s-1.Explanation / Answer
The pressure gradient force P is directed northward across the isobars and its magnitude is given by g (sigma Z/sigma n) where g is the gravitational acceleration, Z is geopotential height, and n is the direction (locally) normal to the isobars. The derivative sigma Z/sigma n can be interpreted as the geometric slope of the isobars. Here geo-potential height decreases at a rate of 3.70 C per 100 km or 2×10-4. For geostrophic balance,
fVg = |P| or Vg = |P| /f. Substituting values yields
Vg = 2 × 10-4 / 2 sin 40 = 2 × 10-4 / 0.95 × 10-4 = 21 m s-1.
Since the isobars are oriented south-west, with lower pressure toward the pole, the geostrophic wind is from the west. Applying equation to south west direction:
Sigma p0 / sigma t = +3 hPa / 10.8 × 103 s.
+3 hPa / 10.8 × 103 s = (+3 hPa / 10.8 × 103 s ) 5 m s-1 × sigma p0 / sigma x
= 300 Pa / (10.8 × 103 s × 10 m s-1) = 2.78 × 10-3 Pa m-1
From the geostrophic wind equation:
ug = 2.78 × 10-3 / (1.25 × 2 × 7.29 × 10-5 sin 50) = 19.9 m s-1.
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