Vertical distributions of temperature, T, specific humidity, q, and height, z, avergaed over either globe or tropics are demonstrated in the following figures. Figure 1 shows the global mean of individual variables and moist static energy (unit:m) over the period of 1985 - 1990.  Figure 2 shows the same variables but averaged over tropics (30S, 30N) for the period of 1985 - 1990. Figure 3 is the same as Figure 1 except for the period of 1992 -1997. Figure 4 is similar to Figure 2 except for the period of 1992 - 1997.

The profiles of moist static energy over tropics are almost constant below 300mb level. This is probably due to the active convection over tropical regions. While averaged over the globe, the moist static energy increases slight with height, reflecting the fact that the convection is less active at high latitudes than in tropics.

As found out by Guido and Hideki, inbalance of air mass in the datasets may cause big error in the divergence of the sensible heat fluxes due to mean transport. In my cases, I saw the divergence of mean sensible heat fluxes are as large as 10000 W/m^2 at high mountain locations (Figure 5, mean sensible heat dvergence, i.e. div(UT, VT) where U, V, T mean monthly mean wind velocities and temperature). As suggested by Alestalo (Tellus, 1981, 33, 360-371), the unbalanced air mass must be subtracted in order to get the divergence of heat fluxes right.  Figure 6 (b) shows the mass balance diagnosis of the ECMWF data. It seems the significant inbalance of the air mass only occurs over high mountain areas. Figure 6 (a) shows the divergence of mean sensible heat fluxes with the terms due to the inbalanced air mass, T*div(U,V) according to Alestalo, being subtracted. The resultant divergence of sensible heat fluxes looks a lot better over the high mountain  regions with the values reduced from 10000 W/m^2 to 1000 W/m^2. Over the low altitude regions, the values of the divergence remain in the range of 100 - 300 W/m^2. This fact suggests, of my opinion,  that the quality of the ECMWF data in terms of air mass balance is satisfactory.
 

The basic energu budget equation (Eq (7.1) in the proposal) has been rederived for the case where the state variables are  decomposed into mean and (turbulent) perturbation components. Please see  document  for details (latex dvi format).