The lapse rate, r, is the negative the lapse rate is given by: of the rate of te

Question

The lapse rate, r, is the negative the lapse rate is given by: of the rate of temperature change with altitude, thus r = dT/dz where T = temperature, and z = altitude. If the lapse rate exceeds 7 degree C/km in a layer of the atmosphere, it is favorable for tornado formation. Assume the temperature function is continuous and differentiable in terms of z. Concurrent measurements indicate that at an elevation of 6 km, the temp is -10 degree C and at 4 km the temp is 8 degree C. You can conclude that the lapse rate is degree C/km at some intermediate elevation. Which theorem allows you to answer Intermediate Value Theorem (IVT) or the Mean Value Theorem (MVT) Are conditions favorable for a tornado? Yes or No

Explanation / Answer

The lapse rate is negative, given by -dT/dz=r, shows that as elevation gets lower, the temperature increases and vice-versa.

Since T is a continuous function of z in the closed interval [z1=6 , z2=4], it would be f(z1)=-10 and f(z2)=8.

At 6kms, the temperature is -10oC . At 4kms it is 8oC. Hence f(z2)-f(z1)= 8- (-10)= 18 oC, over a drop in elevation z2-z1 = -2kms. Then the lapse rate is 18/2= 9oC/km.

(a) The lapse rate would be 9oC/Km at some elevation between 6km and 4 km

(b) Internediate value theorem

(c) Yes conditions are highly favorable, because the lapse rate is sufficiently more than 7oC/km

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