j=i i=i k=i where p is the average pressure, s the salinity, 0 the potential temperature, p the density, V the volume, cp the specific heat content of the water cell in location
(j,l,k), and 90 is a reference potential temperature. Quantities p, 9, p, and cp can be calculated using the MATLAB Seawater Library of the Commonwealth Scientific & Industrial Research Organisation (CSIRO) Marine Research Division given the salinity, temperature and depth for a specific water cell. Knowing the seasonal distribution of H we can easily derive the amount AH of thermal energy that the Mediterranean absorbs from or provides to the environment each month. These amounts are used later in the indirect derivation of the evaporation E.
We divide the Mediterranean Sea into two-dimensional latitude-longitude water surface cells. In each cell the sensible heat flux Qh and aerodynamic latent heat flux Qea are estimated from
where pa is the air density, cpa the moist air specific heat capacity, U the scalar wind, 9a the potential air temperature. The potential temperature is defined by d = T(j)R/CP> (8-14)
where R is the gas constant and po is a reference pressure, taken as 1 bar. Thus the potential temperature of a gas is the temperature that it would have if the gas is compressed or expanded adiabatically to the pressure po. Tw is the water surface temperature, L the latent heat of evaporation, qs the saturation humidity at the water surface temperature, and q the observed specific humidity. The saturation humidity qs over salt water (assuming a salinity of 34 psu) is 98% of qs over pure water. L can be estimated from
with the air temperature Ta in C. CH and CE are turbulent exchange coefficients, estimated by a variety of methods. The derivation of CH and CE is relatively simple for neutral atmospheric stability conditions and take values of the order of 10~3 (see Brutsaert 1984), but once atmospheric instability is included in the analysis, it becomes considerably more complex. However, over periods of a day or longer the neutral forms of CH and CE can be used. We verify the validity of the above assumption in §8.9.8.
The aerodynamically derived latent heat flux Qea is one way to estimate the evaporation, quantifying the drying power of the air. Another method to derive evaporation is the heat-balance method, which assumes that the evaporation process uses all energy that is available to it. Thus, the second estimate for the evaporation is:
The heat-balance method closes the heat budget by definition.
The evaporation rate E can be derived from the latent heat flux Qe from
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