158 MALKUS [chap. 4 



b. The heat and water- vapor budgets of the Caribbean troposphere 



The major purpose for which C/oloii undertook evakiation of sea-air fluxes 

 was to construct an atmospheric energy budget, thereby to investigate the 

 workings of the Caribbean portion of the tropical cell and the mechanisms of 

 its energy transformations. We begin by assuming steady conditions in the air 

 contained within the Caribbean ellipse from the sea surface to the tropopause. 

 When we integrate equation (27) over this volume, we have, after using Green's 

 theorem to change the flux divergence term to a surface integral, ^ 



LP + Qs + Ba = ( ( p{cpT + Agz)u-nda, (27a) 



where a is the bounding surface of the volume, 7i is the unit vector pointing 

 outward and u is the air velocity vector. In this formulation, the source and 

 sink terms LP and Ra now denote volume integrated values and Qs is summed 

 over the lower surface area, so that units of each term will be in calories per 

 second. The transport term may be further subdivided into lateral and vertical 

 fluxes, namely, 



LP + Qs + Pa = {cpT + Agz)cndl{dplg)+ pt{CpT + Agz)tWtdAt 



JpJl JJA, 



pb{CpT + Agz)bWb dAb, (27b) 



ft 



where the first integral term, the lateral flux, has been transformed into an 

 integral with respect to pressure, p, using the hydrostatic equation; c„ is the 

 normal component of the horizontal wind, positive outward, and Z is a line 

 element of the bounding surface. The last two integrals, the vertical upward 

 flux through the top, t, and the bottom, b, surface of the volume, vanish when 

 the integration is performed from the sea surface to the tropopause, where 

 the vertical air velocity, w, may be assumed to vanish, but must be included 

 when intermediate layers are considered separately. 



The water-vapor conservation equation (28) may be similarly integrated and 

 expressed in a form suitable for use with meteorological data, namely, 



Qe-LP= pLqu-nda (28a) 



or 



Qe-LP = Lqcndl{dplg)+ \\ ptLqtWt dAt- \\ pbLqbWbdAb, (28b) 



where q is the specific humidity in grams of vapor per gram of air. First LP, 

 the precipitation warming, is to be evaluated residually from integration of 

 (27b) and (28b) from the surface to the tropopause and the results compared. 



1 An excellent derivation of this equation directly from the law of total energy con- 

 servation is given by Kraus (1959). 



