Exploring Ultra Rapid Data Assimilation Based on Ensemble Transform Kalman Filter with the Lorenz 96 Model

TL;DR

This paper investigates the properties and enhancements of ultra-rapid data assimilation (URDA) using the Ensemble Transform Kalman Filter with the Lorenz 96 model, focusing on inflation and localization techniques.

Contribution

It analytically demonstrates URDA's approximate equivalence to traditional forecasts and explores effective inflation and localization methods for nonlinear models.

Findings

Deflating forecast ensemble perturbations improves accuracy and spread.

R-localization is essential, and advective localization is more effective.

URDA's properties are validated in the Lorenz 96 model.

Abstract

Ultra-rapid data assimilation (URDA) is a method that rapidly updates preemptive forecasts derived from observations without integrating a dynamical model each time additional observations become available. Due to its computational efficiency, we anticipate that URDA will be beneficial for application to numerical weather prediction (NWP); however, the properties of URDA in nonlinear models and its applicability to NWP have not been sufficiently elucidated. Therefore, this study investigates the analytical properties of URDA in nonlinear models and explores inflation and localization that effectively enhance its performance, both of which are generally essential for NWP. We first analytically demonstrate that preemptive forecasts obtained by URDA in nonlinear models are approximately equivalent, under the tangent linear approximation, to forecasts integrated from the analysis. Furthermore, we conduct numerical experiments using the 40-variable Lorenz 96 model. The results show that multiplicative inflation that deliberately deflates (i.e., using an inflation factor less than 1) the forecast ensemble perturbations used to compute the ensemble transform matrix of URDA improves forecast accuracy and inflates ensemble spread moderately. This is presumably attributable to the fact that deflating the forecast ensemble perturbations brings the ensemble transform matrix closer to the identity matrix and reduces the increment of the ensemble mean. With regard to localization, we show that, although R-localization is crucial, advective localization that accounts for the advection of the influence of observations is more effective.