Modeling vertical gradients in water columns: A parametric autoregressive approach

Abstract

Vertical gradients (e.g., water temperature and density) are a measurable expression of the potential energy of a water body, which is a fundamental driver for biogeochemical processes in aquatic ecosystems. Seasonal vertical stratification is typically described by the mixed layer and thermocline depths, and these metrics are often estimated through visual assessment of graphical plots or using numerical methods. The most widely used numerical method estimates the derivative of temperature (or density) along the depth, but it is sensitive both to profile data resolution and presence of nonconforming observations. In this study, we propose a new method of modeling vertical gradients using a four-parameter sigmoidal function, including temporal autocorrelation. The parameters were estimated through Bayesian nonlinear regression with conditional autoregressive errors. The proposed method provides a quantitative and automated way to estimate the mixed layer and thermocline depths even for data profiles with a poor resolution. It also showed good performance against high-frequency measurement data.