Heat and water budgets

  At thermal equilibrium, and characterized by a constant mean annual temperature of sea water, the heat budget of the Mediterranean Sea may be summarized by:
 
where is the solar heat input, A is the mean albedo, is the heat gained by marine advection at the strait of Gibraltar, is the flux of latent heat (evaporation), the flux of sensible heat and the net longwave radiation. Advection to the Mediterranean Sea may be written as:

where represents the mean density of water, is the specific heat, V equals flow, T represents temperature, with i and o subscripts for inflow and outflow, respectively, at the Strait of Gibraltar, and the mean temperature of evaporated water (E), precipitation (P), and river runoff (R), respectively. A rough estimate of mean can be obtained from mean surface temperature, , which is not very different from either the outflow temperature, , or from the mean inflow temperature . Using values of = 1027 kg , = 0.95 cal , = 15.4 , = 13.4 and = 1.6 Sv (1 Sv = ), was calculated to be 5 [Béthoux and Gentili, 1997]. It is noteworthy that this thermal input, , is in addition to a solar radiation input of about 200 , together with a third and less influential thermal input of earth heat flow across the sea-floor, at about 0.1 , neglected in Eq. 1. An increase in water temperature over the 1959-1997 period denotes continuous changes in the different terms of heat budget. Changes in water temperatures permit estimates of changes in marine advection, d , and in heat content of the water column, d . If the solar radiation input, (1-A), is assumed to be constant, marine data permits estimates to be made of changes in atmospheric transfer, as d - d = d( + + ). Changes in thermal advection, d , and in evaporation loss, d , occur concomitantly with changes in water budget, which may therefore be written as: .

An increase in water salinity denotes a change in evaporation (with links to the term in the heat budget and changes in water temperature) and/or freshwater input by precipitation and river runoff (with concomitant changes to the resultant - and heat advection ).