Data Assimilation for Systems with Multiple Timescales

Abstract: This text provides an overview of problems in the field of data assimilation. We explore the possibility of recreating unknown data by continuously inserting known data into certain dynamical systems, under certain regularity assumptions. Additionally, we discuss an alternative statistical approach to data assimilation and investigate the utilization of the Ensemble Kalman Filter for assimilating data into dynamical models. A key challenge in numerical weather prediction is incorporating convective precipitation into an idealized setting for numerical computations. To answer this question we examine the modified rotating shallow water equations, a nonlinear coupled system of partial differential equations and further assess if this primitive model accurately mimics phenomena observed in operational numerical weather prediction models. Numerical experiments conducted using a Deterministic Ensemble Kalman Filter algorithm support its applicability for convective-scale data assimilation. Furthermore, we analyze the frequency spectrum of numerical forecasts using the Wavelet transform. Our frequency analysis suggests that, under certain experimental settings, there are similarities in the initialization of operational models, which can aid in understanding the problem of intialization of numerical weather prediction models.