Estimating the population mean for a vertical profile of energy dissipation rate

TL;DR

This paper introduces a novel method to estimate the average energy dissipation rate in ocean turbulence profiles by leveraging their scaling properties and a cascade model, improving regional energy budget assessments.

Contribution

The study proposes a new approach using the universal multifractal model and Monte Carlo simulations to accurately estimate the population mean of energy dissipation rates from limited observational data.

Findings

Profiles exhibit a scaling property consistent with the universal multifractal model.

The method can distinguish between large individual profiles and a genuinely large population mean.

Application enhances regional ocean energy budget estimates with sparse data.

Abstract

Energy dissipation rates are an important characteristic of turbulence; however, their magnitude in observational profiles can be incorrectly determined owing to their irregular appearance during vertical evolution. By analysing the data obtained from oceanic turbulence measurements, we demonstrate that the vertical sequences of energy dissipation rates exhibit a scaling property. Utilising this property, we propose a method to estimate the population mean for a profile. For scaling in the observed profiles, we demonstrate that our data exhibit a statistical property consistent with that exhibited by the universal multifractal model. Meanwhile, the population mean and its uncertainty can be estimated by inverting the probability distribution obtained by Monte Carlo simulations of a cascade model; to this end, observational constraints from several moments are imposed over each vertical sequence. This approach enables us to determine, to some extent, whether a profile shows an occasionally large mean or whether the population mean itself is large. Thus, it will contribute to the refinement of the regional estimation of the ocean energy budget, where only a small amount of turbulence observation data is available.