CONCEPT OF THERMAL STABILITY 261 



6.3.3. The Adiabatic Lapses of N 



Introducing the dry adiabatic variations of P, T, and e into (1.20), 

 chapter 1, one obtains the dry adiabatic decrease of A'^, N d- 



N, =N.[1- y-j |1 - -^^i^l (6.16) 



which is vaHd for 2 < (. The distribution of A" d with z may be evaluated 

 by taking the logarithms of both sides of (6.16) 



(6.17) 



and expanding the logarithms on the righthand side of (6.17) with the 

 omission of second-order terms where appropriate for our applications 

 of 2 < 3 km: 



In Ad~ln Ao - r^^ (6.18) 



or 



Arf~A^oexp i-Tdz) (6.19) 



where 



When evaluated for the standard conditions of To = 288 °K (15 °C) and 

 Po = 1013.2 mbar, r^ becomes 



Yd = 0.08 (km)-i. (6.21) 



It is sometimes more convenient to use the dry adiabatic scale height, 

 Hd-. 



Hd = — = 12.5 km. (6.22) 



1 d 



Above the local condensation level, the expression for A becomes that of 

 the wet adiabatic, A^^,: 



»..(..#•(»,(..«)-- 



+ I^, exp (I3a*z)j (6.23) 



