A Dual-Weighted Approach to Order Reduction in 4DVAR Data Assimilation

By Dacian N. Daescu, Ionel M. Navon. Monthly Weather Review, 2008

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Strategies to achieve order reduction in four-dimensional variational data assimilation (4DVAR) search for an optimal low-rank state subspace for the analysis update. A common feature of the reduction methods proposed in atmospheric and oceanographic studies is that the identification of the basis functions relies on the model dynamics only, without properly accounting for the specific details of the data assimilation system (DAS). In this study a general framework of the proper orthogonal decomposition (POD) method is considered and a cost-effective approach is proposed to incorporate DAS information into the order-reduction procedure. The sensitivities of the cost functional in 4DVAR data assimilation with respect to the time-varying model state are obtained from a backward integration of the adjoint model. This information is further used to define appropriate weights and to implement a dual-weighted proper orthogonal decomposition (DWPOD) method for order reduction. The use of a weighted ensemble data mean and weighted snapshots using the adjoint DAS is a novel element in reduced-order 4DVAR data assimilation. Numerical results are presented with a global shallow-water model based on the Lin–Rood flux-form semi-Lagrangian scheme. A simplified 4DVAR DAS is considered in the twin-experiment framework with initial conditions specified from the 40-yr ECMWF Re-Analysis (ERA-40) datasets. A comparative analysis with the standard POD method shows that the reduced DWPOD basis may provide an increased efficiency in representing an a priori specified forecast aspect and as a tool to perform reduced-order optimal control. This approach represents a first step toward the development of an order-reduction methodology that combines in an optimal fashion the model dynamics and the characteristics of the 4DVAR DAS.

Subfields: Atmospheric Science, Computational Mechanics, Global and Planetary Change

View Paper: https://www.semanticscholar.org/paper/264ba4a04a3cdba041ef6b0f481fbb70e337eb5d

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Citations in the corpus

Proper orthogonal decomposition closure models for turbulent flows: A numerical comparison (2011, background): “…et al. 1999; Cohen et al. 2003; Bergmann et al. 2005; Lehmann et al. 2005; Hoepffner et al. 2006; Bagheri et al. 2009; Barbagallo et al. 2009; Ahuja & Rowley 2010; Akhtar & Nayfeh 2010) and data assimilation of atmospheric and oceanic flows (Luo et al. 2007; Daescu & Navon 2008; Fang et al. 2009).”
Non-intrusive reduced order modelling of the Navier-Stokes equations (2015, methodology): “Its application includes the work of Daescu and Navon [7], Stefanescu et al.”
Model Order Reduction in Fluid Dynamics: Challenges and Perspectives (2014, methodology): “[31, 36, 37]) Navon et al proposed a dual-weighted POD method, where the weights assigned to each snapshot were derived from an adjoint related to the optimality system of a variational data assimilation problem in meteorology.”
Reduced basis approximation and a posteriori error bounds for 4D-Var data assimilation (2018, methodology): “ata assimilation 3 Another possibility to speed-up the solution process are reduced-order approaches which have been proposed successfully for the strong-constraint 4DVar formulation in, for example, [5,9,11,22,46,52]. There are two kinds of 4D-Var reduced-order approaches in the literature: In the ”