HW2-Siwon

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#5-a.
- Vertical integral heating value = 8.90333 for all cases

#5-b.
m1: 466.667 km m2: 233.333 km

#5-d. Discussion: Explain the nonlinear curve of KE with S.
Kinetic Energy (KE) is calculated as KE=(V^2)/2, and it depends on heating profile (q) because V is generated by heating. Therefore, q and q^2 profiles are compared each other below at S=-0.5, -0.3, -0.1, and 0 (shallow convection cases).

mode 1 = sin(m1z) mode 2 = -S*sin(m2z) q = mode 1 + mode 2 q^2 = q*q

As we can see, e**ven though cumulated q(solid line) is same (=8.90333) all the cases, cumulated q^2(red solid line) is increased as absolute(S) increases.**

cumulated q^2 = 8.75 (S=-0.5), 7.63 (S=-0.3), 7.07 (S=-0.1), and 7.0 (S=0).

Therefore, KE has minimum value when S=0, and maximum when S=-0.5 and 0.5.
 * This increasing is related to increased amplitude of mode 2 of heating as absolute(S) increases.**

T is calculated as below.

h = h0*exp(-x/Lr) PHI(=geopotential) = gh = gz p = (rho)RT & p = (rho)gz --> RT=gz = gh

T = (g/R)*h
Therefore, T_mode1 = (g/R)* h0*exp(-x/Lr_m1) T_mode2 = -S*(g/R)* h0*exp(-x/Lr_m2) T = T_mode1*sin(m1z) + T_mode2*sin(m2z)

This is Temperature profile at **S=0.5 (stratiform case)**. As we can see, mode 1 and mode 2 has opposite sign of temperature in lower levels. In lower levels, **mode 2**(=stratiform mode) causes cold temperature and **downdraft** by evaporating cooling as it rains, while **mode 1**(=convective mode) still causes **updraft**. Therefore, anticyclone by mode 2 and cyclone by mode 1 will be cancelled out, so cyclone will be weakened. This is unfavorable condition for cyclogenesis.

The opposite case is **S=0.5 (shallow convection case)** below. In this case, mode 2(=shallow convection mode) will help to enhance cyclogenesis at lower levels.



+ about h0:
All calculations are performed without specified h0 in h=h0*exp(-x/Lr). (h0 is supposed to be 1 here.) Therefore, all values are not realistic. If h0 is given, they would get more realistic values.