Study Note Estimation of Geostrophic Wind Speeds from Wind Speed Maps

Study Note – Estimation of geostrophic wind speeds from wind speed maps

We have seen that the Geostrophic Wind Speed (G) is related to the pressure (P) gradient by

dP G  dn  f where dP/dn is the horizontal pressure gradient, n is a distance measured normal to an isobar at a constant height,  is the air density and f is called the Coriolis parameter, where f = 2  sin  (with  = 0.7292 x 10-4 rad/sec being the rotational speed of the earth and  being the latitude of the point being considered).

On weather maps the pressure is given in terms of an equivalent hydrostatic height, called the Geopotential Height Z (in metres), such that P =  g Z. Substituting this expression into the equation above gives us:

g dZ G  f dn which eliminates density from the equation. Gravitational acceleration is taken as g =9.81m/s2.

If we know the latitude of our location then we can readily compute f. Upper level weather maps have contours of Geopotential Height values. If the contour label begins with a 9 or 10 then add a 0 to the end to get the value of Z in metres. On some maps, with labels that begin with a 0, add a 10 to the front of the number to get Z in metres.

From the contours we can readily determine the pressure drop, expressed as Geopotential Height (dZ) measured in a normal direction between two contour intervals.

Now we have to find the physical distance between those two contours (dn in metres). Fortunately, such maps are plotted so that the x and y scales (representing latitude and longitude) at any given location are the same. Note that these scales vary across the map and so any measured scale can only be used locally. Based on the diameter of the earth we know that 1o of latitude = 111 km. Hence, we can use a ruler to measure the distance in mm on our map between two marked latitude lines (say one at 50o and the other at 55o). If this distance is, say, 34 mm then we know that 1 mm on our map is equal to: (34 / 5) x 111 = 16.32 km. If we go back to our two Geopotential Height contours and find they are, say, 23 mm apart on the map then we know this means they are physically 23 x 16.32 = 375.4 km apart.

From these data we can compute the Geostrophic Wind Speed in m/s. Conventionally, this is expressed in knots, where 1 knot = 0.515 m/s. For cases where the isobars are curved and we wish to calculate the Gradient Wind Speed (Vgr) we need to estimate the radius of curvature, r, of the nearby isobars by taking two lines normal to the isobar passing through the point of interest and noting where they intersect.

Using the Geopotential Height gradient (dZ/dn) we use:

1 2 2 r f  dZ  r f   Vgr    r g     2  dn  2   for cyclonic winds (curvature around a low pressure region) and

1 2 2 r f   r f  dZ  V gr       r g  2   2  dn  for anticyclonic winds (curvature around a high pressure region)

A note about wind speed symbols (wind direction shown is right to left):

1 – 2 knots

5 knots

10 knots

15 knots

25 knots (etc)

50 knots

So each half tick represents 5 knots, each full tick is 10 knots and each full triangle is 50 knots. These are additive and any value is given as accurate to +/- 2 knots.

Exercise

The following page shows a recent upper level weather map from the Northern Hemisphere. The subsequent three pages show details from this map. Use the concepts outlined in this note, together with measurements from the detailed maps to compute the wind speeds at points A, B and C, as indicated on the maps. Compare your results with the measured values shown on the map. Note that the Geopotential Height values for each contour are given as white numbers in a small, black rectangular box.

Wind motion around a low pressure region (cyclonic circulation) Wind motion in approximately a straight line Wind motion around a high pressure region (anticyclonic circulation)