Controlling model error of underdamped forecast models in sparse observational networks using a variance‐limiting Kalman filter

Abstract

The problem of controlling covariance overestimation due to underdamped forecast models and sparsity of the observational network in an ensemble Kalman filter setting is considered. It is shown in a variational setting that limiting the analysis-error covariance to stay below the climatological value and driving the mean towards the climatological mean for the unobserved variables can significantly improve analysis skill over standard ensemble Kalman filters. These issues are explored for a Lorenz-96 system. It is shown that, for large observation intervals, the climatological information assures that the statistical properties of the unobserved variables are recovered, providing superior analysis skill. This skill improvement is increased for larger observational noise. Copyright c 2012 Royal Meteorological SocietyKey Words: data assimilation; ensemble Kalman filter; Lorenz-96; model error

A mechanism for catastrophic filter divergence in data assimilation for sparse observation networks

“…We used the compactly supported localisation function introduced by Gaspari and Cohn (1999), in conjunction with a DEnKF proposed by Sakov and Oke (2008), and found that catastrophic filter diver- gence is completely suppressed for a localisation radius of ρ loc < 1.5 grid spacings. Other covariance limiting strategies such as the ensemble filters suggested in Gottwald et al (2011) and Mitchell and Gottwald (2012) were also able to suppress catastrophic filter divergence. We remark that the actual truth, however, does indeed exhibit nontrivial correlations between all variables for our parameters in this low dimension with D = 5.…”

Controlling balance in an ensemble Kalman filter

“…In previous work Gottwald et al (2011) and Mitchell and Gottwald (2012) used the ensemble transform Kalman filter (ETKF) (Bishop et al, 2001;Tippett et al, 2003;Wang et al, 2004), which seeks a transformation T ∈ R k×k such that the analysis deviation ensemble Z a is given as a deterministic perturbation of the forecast ensemble Z f via Z a = Z f T. In order to incorporate localisation needed for small ensemble sizes easily, we will implement for our VLKF here an approximate square root filter (DEnKF) proposed by Sakov and Oke (2008) where the analysis deviations are determined according to…”

“…The filter described in Gottwald et al (2011) and Mitchell and Gottwald (2012) was formulated for large ensemble sizes, ensuring invertibility of the forecast error covariance (a situation not satisfied for data assimilation in operational numerical weather forecast centres). We recast the VLKF here in a form which allows for small ensemble sizes, and redo the derivation in a slightly different manner.…”

“…This yielded a remarkable increase in the skill, even in the observed variables. The filter has since been used in Mitchell and Gottwald (2012) to control noise at the grid resolution scale caused by model error.…”

Nonglobal Parameter Estimation Using Local Ensemble Kalman Filtering

“…We choose the above form for the forcing in Equation ( 16) for both simplicity and similarity to a Fourier sine series; we do not claim that it is representative of any specific atmospheric forcing. However, there are numerous examples in the literature of similar modifications to conceptual atmospheric models; [37] modifies the Lorenz-63 by adding a sinusoidal forcing term, and both [34] and [32] use modified versions of the Lorenz-96 model as testbeds for experiments in predictability and data assimilation. To test our techniques on unobserved physics and implicit parameters in atmospheric climatology, we simulate such processes in two ways.…”