Kalman filter data assimilation: Targeting observations and parameter estimation

Abstract

This paper studies the effect of targeted observations on state and parameter estimates determined with Kalman filter data assimilation (DA) techniques. We first provide an analytical result demonstrating that targeting observations within the Kalman filter for a linear model can significantly reduce state estimation error as opposed to fixed or randomly located observations. We next conduct observing system simulation experiments for a chaotic model of meteorological interest, where we demonstrate that the local ensemble transform Kalman filter (LETKF) with targeted observations based on largest ensemble variance is skillful in providing more accurate state estimates than the LETKF with randomly located observations. Additionally, we find that a hybrid ensemble Kalman filter parameter estimation method accurately updates model parameters within the targeted observation context to further improve state estimation. V C 2014 AIP Publishing LLC.[http://dx.doi.org/10.1063/1.4871916]For chaotic systems like the weather, an accurate forecast requires an accurate representation of the current state. Data assimilation (DA) is a methodology that reinitializes the current state of a system by combining observational data along with an estimated state determined by a forecast model. Within data assimilation schemes, the spatial locations of the observational data can have a significant effect on the accuracy of the analysis (re-initialized) state. In this work, we use a particular strategy for locating observations and show that this targeting strategy is successful in reducing state estimation error for a conceptual chaotic model, as compared to fixed or randomly located observations. An additional facet of weather modeling that we investigate is the estimation of model parameters. Parameter estimation is a technique used within modeling that often seeks to fit parameters with historical data or to characterize subgridscale effects. We show that our utilized observation targeting strategy within a particular parameter estimation scheme is successful in accurately estimating a model parameter for this chaotic model. To motivate our study of this chaotic model, we first establish a theorem which is used to justify the use of targeted observations for a linear data assimilation scheme.

The assessment of potential observability for joint chemical states and emissions in atmospheric modelings

“…Langland et al (1999), Szunyogh et al (1999)]. Theoretical studies are presented, for example by Berliner et al (1999), or recently by Bellsky et al (2014) for a case of study of highly nonlinear dynamics and Wu et al (2016) for the optimal deployment of observations for time-varying system in a infinite dimensional domain within a finitetime interval. Secondly, the problem addressing the benefit assessment of individual observations or types of measurements has been investigated by Cardinali et al (2004) and a sequence of related papers.…”

“…Several methodologies have been proposed to account for model and estimation errors in both variational and ensemble data assimilation [e.g. Bellsky et al (2014), Daescu and Navon (2004), , , Li et al (2009), Sharma et al (2014), Smith et al (2013), Zupanski et al (2007)]. Navon (1997) outlined the perceptibility and stability in optimal parameter estimation in meteorology and oceanography.…”

The Assessment of Potential Observability for Joint Chemical States and Emissions in Atmospheric Modelings

“…Several methodologies have been proposed to account for model errors in both variational and ensemble data assimilation (e.g. [2], [13], [29], [41], [49]). In [35], the authors outlined the perceptibility and stability in optimal param-eter estimation in meteorology and oceanography.…”

“…The advanced concept of targeted observations has been popularized during the FASTEX campaign (e.g [28], [43]). Theoretical studies are presented, for example by [3], or recently by [2] for a case of study of highly nonlinear dynamics, and [46] for the optimal deployment of observations for time-varying system in a infinite dimensional domain within a finite-time interval. The problem (ii) addressing the benefit assessment of individual observations or types of measurements has been investigated by [10] and a sequence of related papers.…”

The degree of freedom for signal assessment of measurement networks for joint chemical state and emission analysis

“…Several methodologies have been formulated to account for model errors in both variational and ensemble data assimilation (e.g. Bellsky et al 2014;Gillijns and De Moor 2007;Li et al 2009;Smith et al 2013;Tremolet 2007). With focus on the observability, Daescu (2004) presented a method, resting on only one additional adjoint model integration for measurement network optimization.…”