Calibration of the K-Profile Parameterization of ocean boundary layer mixing. Part I: Development

In model comparisons with observational data, not all data contain information that is useful for answering a specific science question. If non-relevant or highly uncertain data are included in a comparison metric, they can reduce the significance of other observations that matter for the scientific process of interest. Sources of noise and correlations among summed quantities within a comparison metric affect the significance of a signal that is useful for testing model skill. In the setting of the tropical Pacific, we introduce an "inquiry dependent" (ID) metric of model-data comparison that determines the relative importance of the TOGA-TAO buoy observations of the ocean temperature, salinity, and horizontal currents for influencing upper-ocean vertical turbulent mixing as represented by the K-Profile Parameterization (KPP) embedded in the MIT general circulation model (MITgcm) for the 2004-2007 time period. The ID metric addresses a challenge that the wind forcing is likely a more significant source of uncertainty for the ocean state than the turbulence itself, and that the observations are correlated in time, space, and across ocean state variables. In this approach the MITgcm is used to infer variability and relationships in and among the data, and to determine the response structures that are most relevant for constraining uncertain parameters. We demonstrate that the ID metric is able to distinguish the effects due to parameter perturbations from those due to uncertain winds and that it is important to include multiple kinds of data in the comparison, suggesting that the ID metric is appropriate for use in a calibration of the KPP model parameters using mooring observations of the ocean state.