A Relaxed Direct-insertion Downscaling Method For Discrete-in-time Data Assimilation

TL;DR

This paper introduces a relaxation parameter into the direct-insertion downscaling method for data assimilation, enabling flexible observation frequencies while ensuring convergence, and analytically connects it to continuous nudging as observation frequency increases.

Contribution

It presents a novel relaxation-enhanced downscaling method that overcomes observation frequency constraints and links discrete and continuous data assimilation techniques.

Findings

Relaxation parameter improves flexibility in observation frequency.

Method maintains convergence with variable observation intervals.

Analytical proof connects discrete method to continuous nudging as frequency increases.

Abstract

This paper improves the spectrally-filtered direct-insertion downscaling method for discrete-in-time data assimilation by introducing a relaxation parameter that overcomes a constraint on the observation frequency. Numerical simulations demonstrate that taking the relaxation parameter proportional to the time between observations allows one to vary the observation frequency over a wide range while maintaining convergence of the approximating solution to the reference solution. Under the same assumptions we analytically prove that taking the observation frequency to infinity results in the continuous-in-time nudging method.