In the present paper is shown that the ageostrophic wind may be found approximately by the
isogeostrophics, which are defined as the lines of equal geostrophic wind.
§1. Ageostrophic wind
The equa_??_ions of frictionless motion are (the notations are the same as those in Brunt's book)
Neglecting the horizontal gradient of ρ and
l, (1) is easily transformed as follows:-
Now if the time variation of the velocity is small where
ug,
vg are the components of geostrophic wind velocity and _??_=∂
p/∂
t.
Neglecting the products of small terms,
u,
v become, from (3)
When the pressurè variations are neglected, where
q is geostrophic wind velocity.
Further, when the gradient of geostrophic wind velocity is small,
From (6) it is seen that the direction of the ageostrophic wind is parallel to the isogeostrophies and keeps the large geostrophic wind to the righthandside in the northern hemisphere.
(4), (5) and (6) give a good approximation to the true wind, but as it is troublesome to map out (4), (5) within few hours, it will be convenient to use the isogeostrophics with the isallobars, though (6) will fall below (4) more or less in accuracy.
§2. Convergence.
Integrating the equation of continuity from
Z1, to
Z2, and neglecting small terms, the following equation is easily obtained: where
u',
v' are ageostrophic wind velocity components, _??_ mean vertical velocity and divergence through the layer between the heíght
Z1, and
Z2.
From (6) it is known that, at the region where there is divergence of the isogeostrophics, there is convergence of the horizontal flow. Therefore, from (2.1) _??_ may be evaluated, and then the precipitation will roughly calculated. The author used this method to the surface isobars and the estimated isobars at the height of 1km and 2km.
The author applied the isogeostrophics to every day weather forecasting and found that the divergence (convergence) agrees with the rainy or cloudy region (the fairy), and the estimated precipitation, agrees with the actul one.
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