On a probabilistic evolutionary approach to ocean modelling: From Lorenz-63 to idealized ocean models

TL;DR

This paper introduces a probabilistic evolutionary approach for ocean modeling that captures chaotic flow dynamics without relying on explicit physical equations, demonstrating effectiveness on Lorenz-63 and idealized ocean models.

Contribution

It presents a data-driven probabilistic modeling framework that does not require prior knowledge of flow physics and can be integrated with existing ocean models.

Findings

Successfully reproduces flow features in Lorenz-63 and quasi-geostrophic models.

Does not require modification of existing ocean models.

Works with both simulated and real measurement data.

Abstract

In this study we develop an alternative way to model the ocean reflecting the chaotic nature of ocean flows and uncertainty of ocean models -- instead of making use of classical deterministic or stochastic differential equations we offer a probabilistic evolutionary approach (PEA) that capitalizes on the use of probabilistic dynamics in phase space. The main feature of the data-driven version of PEA proposed in this work is that it does not require to know the physics behind the flow dynamics to model it. Within the PEA framework we develop two probabilistic evolutionary methods, which are based on probabilistic evolutionary models using quasi time-invariant structures in phase space. The methods have been tested on complete and incomplete reference data sets generated by the Lorenz 63 system and by an idealized multi-layer quasi-geostrophic model. The results show that both methods reproduce large- and small-scale features of the reference flow by keeping the probabilistic dynamics within the reference phase space (the phase space of the reference flow). The proposed approach offers appealing benefits and a great flexibility to ocean modellers working with mathematical models and measurements. The most remarkable one is that it provides an alternative to the mainstream ocean parameterizations, requires no modification of existing ocean models, and easy to implement. Moreover, it does not depend on the nature of input data, and therefore can work with both numerically-computed flows and real measurements from different sources (drifters, weather stations, etc.).