Efficient data assimilation for spatiotemporal chaos: A local ensemble transform Kalman filter

Abstract

Data assimilation is an iterative approach to the problem of estimating the state of a dynamical system using both current and past observations of the system together with a model for the system's time evolution. Rather than solving the problem from scratch each time new observations become available, one uses the model to "forecast" the current state, using a prior state estimate (which incorporates information from past data) as the initial condition, then uses current data to correct the prior forecast to a current state estimate. This Bayesian approach is most effective when the uncertainty in both the observations and in the state estimate, as it evolves over time, are accurately quantified. In this article, we describe a practical method for data assimilation in large, spatiotemporally chaotic systems. The method is a type of "ensemble Kalman filter", in which the state estimate and its approximate uncertainty are represented at any given time by an ensemble of system states. We discuss both the mathematical basis of this approach and its implementation; our primary emphasis is on ease of use and computational speed rather than improving accuracy over previously published approaches to ensemble 1 Kalman filtering. We include some numerical results demonstrating the efficiency and accuracy of our implementation for assimilating real atmospheric data with the global forecast model used by the U.S. National Weather Service.

Assessment of a Nonlinear Ensemble Transform Filter for High-Dimensional Data Assimilation

“…Observation localization (OL; Hunt et al 2007) suppresses spurious correlations associated with distant locations and increases the rank of the analysis covariance by partitioning the state vector into subsets, the so-called local domains. Typically, a local domain contains all state variables at each grid point or in each vertical column (e.g., Houtekamer and Mitchell 1998;Losa et al 2012).…”

“…Over the past two decades, the EnKF has evolved to a robust scheme that is applicable to largescale systems with small ensemble sizes, such as in numerical weather prediction (e.g., Reich et al 2011;Miyoshi and Kunii 2012) or oceanography (e.g., Nerger et al 2007;Losa et al 2012). Deterministic variants such as the (local) ensemble transform Kalman filter [(L)ETKF, Bishop et al 2001;Hunt et al 2007] avoid sampling noise in the analysis step by applying a matrix square root transform. However, the implicit Gaussian assumption leads to a linear update mechanism and renders the analysis suboptimal in nonlinear systems (Lei and Bickel 2011).…”

30-second-Update 100-m-Mesh Data Assimilation Experiments: A Sudden Local Rain Case in Kobe on 11 September 2014

“…Recently, Miyoshi et al (2016aMiyoshi et al ( , 2016b reported an innovation of the "Big Data Assimilation" (BDA) technology, implementing a 30-second-update, 100-m-mesh local ensemble transform Kalman filter (LETKF; Hunt et al 2007) to assimilate data from a Phased Array Weather Radar (PAWR) at Osaka University (Ushio et al 2014) into regional NWP models known as the Japan Meteorological Agency non-hydrostatic model (JMA-NHM, Saito et al 2006Saito et al , 2007 and the Scalable Computing for Advanced Library and Environment-Regional Model (SCALE-RM, Nishizawa et al 2015). The PAWR captures the rapid development of convective activities every 30 seconds at approximately 100-m resolution.…”

“…Among others, much attention has been paid to skillful NWP for severe weather (e.g., Kain et al 2006, Hohenegger and Schär 2007a, b;Kawabata et al 2007;Roberts and Lean 2008). Recently, the ensemble Kalman filter (EnKF;Evensen 1994Evensen , 2003 has become a major method in data assimilation (DA), and has contributed to investigate convection-permitting regional NWP (e.g., Zhang et al 2007;Stensrud et al 2009Stensrud et al , 2013Clark et al 2010;Schwartz et al 2010; Baldauf et al 2011;Melhauser and Zhang 2012; Yussolf et al 2013, Kunii 2014a, Weng and Zhang 2016.Recently, Miyoshi et al (2016aMiyoshi et al ( , 2016b reported an innovation of the "Big Data Assimilation" (BDA) technology, implementing a 30-second-update, 100-m-mesh local ensemble transform Kalman filter (LETKF;Hunt et al 2007) to assimilate data from a Phased Array Weather Radar (PAWR) at Osaka University (Ushio et al 2014) into regional NWP models known as the Japan Meteorological Agency non-hydrostatic model (JMA-NHM, Saito et al 2006Saito et al , 2007 and the Scalable Computing for Advanced Library and Environment-Regional Model (SCALE-RM, Nishizawa et al 2015). The PAWR captures the rapid development of convective activities every 30 seconds at approximately 100-m resolution.…”

Data assimilation of radar reflectivity volumes in a LETKF scheme

“…The KENDA system implements for the COSMO model the LETKF scheme described by Hunt et al (2007). In this implementation, the method is fully four dimensional, that is all observations collected during the assimilation 5 window contribute to determine the analysis and the related model equivalents are computed using the prognostic variables at the proper observation time.…”