Sensitivity of a Barotropic Ocean Model to Perturbations of the Bottom Topography

TL;DR

This paper investigates how small errors in bottom topography affect a barotropic ocean model's solutions, revealing high sensitivity in turbulent regions and low sensitivity in laminar areas, with sensitivity growth depending on time scale.

Contribution

It introduces an operator linking topography errors to model solutions and characterizes the sensitivity's dependence on flow regimes and time scales.

Findings

High sensitivity in turbulent flow regions

Low sensitivity in laminar flow regions

Sensitivity growth transitions from polynomial to exponential over time

Abstract

In this paper, we look for an operator that describes the relationship between small errors in representation of the bottom topography in a barotropic ocean model and the model's solution. The study shows that the model's solution is very sensitive to topography perturbations in regions where the flow is turbulent. On the other hand, the flow exhibits low sensitivity in laminar regions. The quantitative measure of sensitivity is influenced essentially by the error growing time. At short time scales, the sensitivity exhibits the polynomial dependence on the error growing time. And in the long time limit, the dependence becomes exponential.