Fine tuning of heat fluxes

As an illustration of the technique, we apply the single constraint results of the previous section to fine tune the heat fluxes, independently of the fresh water fluxes. The consistent tuning of heat and fresh water fluxes will be discussed in section 9.4.

Non-dimensional parameters , , , , , and, are introduced in the bulk formulas

In the short wave parameterization (58), the tuning parameter is roughly associated with the transmission coefficient and water vapor absorption coefficient (section 7.5), and is related to the cloud cover coefficient. In the long wave radiation formula (59), is associated with the parameterized water vapor effect, and with the tuning parameter for the cloud cover correction. In the latent and sensible heat flux parameterizations, we have specified a single tuning parameter for each formula ( and ), representing primarily the uncertainties in the transfer coefficients. To be consistent with the maximum likelihood principle used to derive (55), one only needs to assume that the tuning parameter errors are normally distributed. We have made the additional assumption that the parameter errors are also uncorrelated, leading to a diagonal matrix . Note, however, that uncertainties in the sensible and latent heat fluxes can be associated with errors in wind speed, and need not be uncorrelated. At this time, however, we neglect this correlation.

Currently, all non-dimensional tuning parameters are set to 1 () and we seek small corrections . In order to apply the results of the previous section we need to specify error estimates . As can be seen from (55), the correction is proportional to the parameter error covariance matrix . It has been our experience that the results are extremely dependent on the particular choice of . Unfortunately, it is very difficult to obtain reliable estimates for the error variances of . (Note that correspond to the random part of the errors in and should not include bias.) Our approach, therefore, is to provide the necessary fields to allow users of UWM/COADS to perform their own fine tuning of the surface marine fluxes (see section 9.6). For the sake of illustration, we present results with the error estimates

This choice reflects the large scatter associated with the turbulence measurements used to obtain the base value for the transfer coefficients and . Table 11 presents the result of single constraint calculations. As northern boundary conditions we specify a northward transport of 0.1 PW at 65° N in the North Atlantic, and 0 PW at 65° N in the North Pacific (Aagaard and Greismann 1975). As single-constraints in the southern boundary we specify: a) no transport at the southern-most latitude not covered by climatological ice; b) 1.22 PW at 25° N according to Hall and Bryden (1982); and c) 0.6 PW at the equator in the Atlantic (Wunsch 1984). The last column in Table 11 gives the value of the constrained transport at a reference latitude. Overall, the value of the adjusted tuning parameter is fairly insensitive to the particular constraint imposed, and the constrained net surface heat flux (not shown) has a much higher degree of balance than the unconstrained product in Fig. 8. The main effect on the individual heat flux components is to decrease the solar radiation and increase the heat loss due to evaporation. These results are qualitatively similar to the adjustments Oberhuber (1988) applied to his COADS based heat flux estimates to achieve a global heat balance.