Development and evaluation of the probability density distribution for mixed layer depth over the global oceans

Development of theoretical probability density function (PDF) for MLD over the oceans is important, as such a function provides a novel avenue for diagnostics of the numerical experiments with ocean GCMs and for comparison of the model results with observational data such as Argo floats. We built a new PDF based upon the Censored Modified Fisher-Tippet distribution (CMFT PDF herein). CMFT PDF represents a 2.5 – parameter distribution with the shape and location parameters steering the PDF and a pre-defined minimum of sample. CMFT distribution provides explicit equations for the mean and variance and also allows for estimating extreme values of MLD corresponding to high percentiles. A newly developed CMFT PDF was applied to GLORYS12 reanalysis to diagnose the characteristics of MLD in terms of MLD statistics. For application we used 3-degree spatial averaging of GLORIS12 profiles to provide the results which can further analyzed and intercompared to different alternative MLD estimates. This provided quite a rich sample which was further used for computation of the PDF parameters and higher order percentiles over the global oceans. This analysis shows that characteristics of probability density distributions are quite different for different regions with e.g. Labrador Sea demonstrating much heavier tails compared to the Irminger Sea and the NAC. Extreme values of MLD for March can amount to more than 3000 meters in the Labrador Sea. This provides an effective diagnostic approach for intercomparison of different model experiments and also for validation of the model results against observational data, such as e.g. Argo buoys. We also provide the analysis of climate variability of MLD statistics derived from CMFT PDF demonstrating in particular different tendencies in the mean and extreme MLD values. Further we also discuss the links between the statistics of the ocean MLD with those of surface fluxes as well as atmospheric variability.