The uncertainties in the parameter error covariance matrix and the need to adjust the flux based on measurements for a particular area will undoubtedly require users to produce their own fine tuning of the heat and fresh water fluxes. To this end, we provide users of UWM/COADS with sensitivity fields associated with each of the tuning parameters discussed in this section. For example, the net heat flux can be written as
The corresponding sensitivity fields are
The sensitivity fields , and are equal to , and which are the full unconstrained fields already included in UWM/COADS. The other sensitivity fields are computed either from individual observations with climatology and anomalies analyzed the same way as the other UWM/COADS fields ( and ), or derived from analyzed fields ().
In order to produce constrained estimates of the individual heat flux components, one can calculate
where denotes the unconstrained estimate of the heat flux component as included in UWM/COADS. Likewise, constrained evaporation and precipitation fields can be computed from
The parameters in Tables 11-13 can be used to produce several versions of the constrained heat and fresh water fluxes. In addition, new values for the tuning parameters can be obtained as follows. The sensitivity matrix can be computed by integrating the sensitivity fields at a given latitude, e.g.,
(assuming is the th parameter). The new tuning parameters can be obtained by solving (55), given estimates for the parameter error covariance matrix and oceanographic measurements with error covariance matrix .