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

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.