Heat budget and surface temperature increase

  From calculated or measured temperature changes in different layers and locations, the change in the heat content of the Mediterranean Sea, d , amounts to a mean value of 0.65 between 1940 and 1995 (derived from 0.70 and 0.53 in the eastern and western basin, respectively). Changes in marine advection must be considered given the temporal changes in deep water temperature and salinity as well as changes in water deficit and flows. An almost constant density of western deep-water means a constant deep outflow, , while the temperature of Atlantic inflow, , is assumed constant. Using to approximate , temporal changes in marine advection may be written as:

For an initial E - P - R = 2.38 kg and a d(E - P - R) of 4.6 kg , the 20-box model calculations give mean for , d and d of 13.25 , 7.34 and 2.9 , respectively. The calculated temperature change in deep outflow, d , is slightly lower than that measured in the western deep waters, being 3.47 , due to vertical mixing in the Alboran Sea between the Mediterranean outflow and the Atlantic inflow. The resulting advection change, d , over the 1940-1995 period amounts to: -0.44 in 1995. The shift is linked mainly to the temperature change in deep outflow (second term on the right-hand side of Eq.3). In considering the initial driving force, 1.5 in 1995, part of this energy compensates for the advection decrease, d (-0.44 ), some of it contributes to an increase in the heat content of the water column, d = 0.65 , while the remainder 0.41 corresponds to an increase in heat transferred towards the atmosphere by either evaporation, sensible heat flux or longwave radiation. Inasmuch as there is no evidence of continuous changes in wind speed and/or air humidity, the changes in heat transfers result from d and d . From previous studies of air-sea heat exchanges in the Mediterranean Sea, preliminary estimates of changes in air-sea transfers driven by small changes in air and sea temperature were presented [Béthoux et al., 1990], where: (with d and d in , and d , d and d being in ). The sum gives:

This sum was previously assumed equal to -0.41 . With mean d being previously calculated equal to 7.34 , Eq.4 can be used to calculate the mean change in air temperature, giving d = 8.37 . This value is situated between the two estimates of global trend calculated from available climatic data over the northern hemisphere since the 1960s: 6 and 10 [Jones et al., 1988, Jones, 1994]. With known d and d values, different changes in air-sea transfers may be calculated. For instance, the resulting changes in 1995 ( when compared with transfers in 1940) for d , d and d are equal to -1.60, +0.95 and +0.24 , respectively.

With the previous hypotheses of no change in the solar radiation, nor in the Atlantic advection, the initial driving force of 1.5 may correspond to a decrease of net longwave radiation due to the change in atmospheric composition of radiative components. The calculated d corresponds to a decrease of net longwave radiation due to the evolution of water temperature, probably a feedback from the atmospheric effect. Consequently the total change in net longwave radiation, i.e. the greenhouse effect increase, amounts to 1.5 + 0.24 = 1.74 in the Mediterranean area over the 1940-1995 period.

In the previous relationships for d and d , numerical factors depend on the drag coefficient (taken equal to 1.7 ), the mean wind speed (7.1 m ) and air humidity (77% or 0.77, the d coefficient in d formula), which somewhat constrains the quantitative results. Nevertheless, drag coefficient and wind speed act both on d and d calculations and consequently they have practically no effect on the calculation of d from d (Eq.4). Similarly, a change of +/- 100% of the estimated sum ( d + d + d ), from a 30% increase of either the external driving force (1.5 ) or the estimated d (0.65 ), gives new estimates of d of 8.19 and 8.46 , respectively, i.e. rather low changes of -2% and +1%. In order to have both an increase in evaporation (d < 0, salinity increase) and a decrease in sensible heat flux (d > 0, increase), sea surface temperature change d has to be between two limits depending on air temperature change, d , and humidity, : d < d < d . This relationship illustrates that surface temperature change d in the Mediterranean is mainly driven by air temperature change d over the northern hemisphere.