The lapse rate is the rate at which the temperature T decreases in the atmospher

Question

The lapse rate is the rate at which the temperature T decreases in the atmosphere with respect to increasing altitude z. It is reported in units of

The lapse rate is the rate at which the temperature T decreases in the atmosphere with respect to increasing altitude z. It is reported in units of degree C/km and is defined by gamma= -dT/dz. When the lapse rate is greater the 7 degree C/km and other conditions are met, it indicates favorable conditions for tornado formation. Suppose the at z = 2.9km the temperature T = 7.6 degree C and at z = 5.6km T = -14.3 degree C. Assume that the temperature function is continuous and differentiable at all altitudes. What can a meteorologist conclude from these data?

Explanation / Answer

Since the temperature function is continous and differentiable, then by using mean value theorem for function T, we can find a point in interval (2.9, 5.6)

Such that

T'(c) = T(5.6)-T(2.9)/(5.6-2.9) =-14.3-7.6/(5.6-2.9) = -21.9/2.7 = -8.1

And so this means that we can get some point in interval (2.9,5.6) or when altitude is between 2.9 to 5.6 then at some point the lapse is greater then 7 that is 8.1 and hence there is a surity of tornado formation somewhere between these altitude points>

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