Untangling spatial and temporal trends in the variability of the Black Sea Cold Intermediate Layer and mixed Layer Depth using the DIVA detrending procedure

Current spatial interpolation products may be biased by uneven distribution of measurements in time.
This manuscript presents a detrending method that recognizes and eliminates this bias.
The method estimates temporal trend components in addition to the spatial structure and has been implemented within the Data Interpolating Variational Analysis (DIVA) analysis tool.
The assets of this new detrending method are illustrated by producing monthly and annual climatologies of
two vertical properties of the Black Sea while recognizing their seasonal and interannual variabilities : the mixed layer depth, and the cold content of its Cold Intermediate Layer (CIL).
The temporal trends, given as by-products of the method, are used to analyze the seasonal and interannual variability of these variables over the past decades (1955-2011).
In particular, the CIL interannual variability is related to the cumulated winter air temperature anomalies, explaining 88\% of its variation.