Exponential leap-forward gradient scheme for determining the isothermal layer depth from profile data

Abstract

Two distinct layers usually exist in the upper ocean. The rst has a near-zero vertical gradient in temperature (or density) from the surface and is called the iso-thermal layer (or mixed layer). Beneath that is a layer with a strong vertical gradient in temperature (or density), called the thermocline (or pycnocline). The isothermal layer depth (ILD) or mixed layer depth (MLD) for the same pro le var- ies depending on the method used to determine it. Also, whether they are subjective or objective, existing methods of determining the ILD do not estimate the thermocline (pycnocline) gradient. Here, we propose a new exponen- tial leap-forward gradient (ELG) method of determining the ILD that retains the strengths of subjective (simplicity) and objective (gradient change) methods and avoids their weaknesses (subjective methods are threshold-sensitive and objective methods are computationally intensive). This new method involves two steps: (1) the estimation of the ther- mocline gradient Gth for an individual temperature pro le, and (2) the computation of the vertical gradient by averag- ing over gradients using exponential leap-forward steps. Such averaging can lter out noise in the pro le data. Five existing methods of determining the ILD (difference, gra- dient, maximum curvature, maximum angle, and optimal linear tting methods) as well as the proposed ELG method were veri ed using global expendable bathythermograph (XBT) temperature and conductivity–temperature–depth (CTD) datasets. Among all the methods considered, the ELG method yielded the highest skill score and the lowest Shannon information entropy (i.e., the lowest uncertainty).