Using Model Reduction Methods within Incremental Four-Dimensional Variational Data Assimilation

2008 ◽  
Vol 136 (4) ◽  
pp. 1511-1522 ◽  
Author(s):  
A. S. Lawless ◽  
N. K. Nichols ◽  
C. Boess ◽  
A. Bunse-Gerstner
Keyword(s):  
Data Assimilation ◽  
Model Reduction ◽  
Variational Data Assimilation ◽  
Superior Performance ◽  
Water Model ◽  
Computationally Efficient ◽  
Full System ◽  
Ocean Data Assimilation ◽  
Reduction Techniques ◽  
Reduction Methods

Abstract Incremental four-dimensional variational data assimilation is the method of choice in many operational atmosphere and ocean data assimilation systems. It allows the four-dimensional variational data assimilation (4DVAR) to be implemented in a computationally efficient way by replacing the minimization of the full nonlinear 4DVAR cost function with the minimization of a series of simplified cost functions. In practice, these simplified functions are usually derived from a spatial or spectral truncation of the full system being approximated. In this paper, a new method is proposed for deriving the simplified problems in incremental 4DVAR, based on model reduction techniques developed in the field of control theory. It is shown how these techniques can be combined with incremental 4DVAR to give an assimilation method that retains more of the dynamical information of the full system. Numerical experiments using a shallow-water model illustrate the superior performance of model reduction to standard truncation techniques.

Balanced Ocean-Data Assimilation near the Equator

2002 ◽  
Vol 32 (9) ◽  
pp. 2509-2519 ◽  
Author(s):  
Gerrit Burgers ◽  
Magdalena A. Balmaseda ◽  
Femke C. Vossepoel ◽  
Geert Jan van Oldenborgh ◽  
Peter Jan van Leeuwen
Keyword(s):  
Data Assimilation ◽  
Shallow Water ◽  
General Circulation ◽  
General Circulation Models ◽  
Density Field ◽  
Water Model ◽  
Optimal Interpolation ◽  
Shallow Water Model ◽  
Ocean Data Assimilation ◽  
Zonal Velocity

Abstract The question is addressed whether using unbalanced updates in ocean-data assimilation schemes for seasonal forecasting systems can result in a relatively poor simulation of zonal currents. An assimilation scheme, where temperature observations are used for updating only the density field, is compared to a scheme where updates of density field and zonal velocities are related by geostrophic balance. This is done for an equatorial linear shallow-water model. It is found that equatorial zonal velocities can be detoriated if velocity is not updated in the assimilation procedure. Adding balanced updates to the zonal velocity is shown to be a simple remedy for the shallow-water model. Next, optimal interpolation (OI) schemes with balanced updates of the zonal velocity are implemented in two ocean general circulation models. First tests indicate a beneficial impact on equatorial upper-ocean zonal currents.

An Ensemble-Based Four-Dimensional Variational Data Assimilation Scheme. Part I: Technical Formulation and Preliminary Test

2008 ◽  
Vol 136 (9) ◽  
pp. 3363-3373 ◽  
Author(s):  
Chengsi Liu ◽  
Qingnong Xiao ◽  
Bin Wang
Keyword(s):  
Data Assimilation ◽  
Preliminary Test ◽  
Background Field ◽  
Variational Data Assimilation ◽  
Water Model ◽  
Observation Error ◽  
Ensemble Forecasts ◽  
Background Error ◽  
Background Error Covariance ◽  
Error Covariance

Abstract Applying a flow-dependent background error covariance (𝗕 matrix) in variational data assimilation has been a topic of interest among researchers in recent years. In this paper, an ensemble-based four-dimensional variational (En4DVAR) algorithm, designed by the authors, is presented that uses a flow-dependent background error covariance matrix constructed by ensemble forecasts and performs 4DVAR optimization to produce a balanced analysis. A great advantage of this En4DVAR design over standard 4DVAR methods is that the tangent linear and adjoint models can be avoided in its formulation and implementation. In addition, it can be easily incorporated into variational data assimilation systems that are already in use at operational centers and among the research community. A one-dimensional shallow water model was used for preliminary tests of the En4DVAR scheme. Compared with standard 4DVAR, the En4DVAR converges well and can produce results that are as good as those with 4DVAR but with far less computation cost in its minimization. In addition, a comparison of the results from En4DVAR with those from other data assimilation schemes [e.g., 3DVAR and ensemble Kalman filter (EnKF)] is made. The results show that the En4DVAR yields an analysis that is comparable to the widely used variational or ensemble data assimilation schemes and can be a promising approach for real-time applications. In addition, experiments were carried out to test the sensitivities of EnKF and En4DVAR, whose background error covariance is estimated from the same ensemble forecasts. The experiments indicated that En4DVAR obtained reasonably sound analysis even with larger observation error, higher observation frequency, and more unbalanced background field.

scholarly journals Hyper-Reduction Over Nonlinear Manifolds for Large Nonlinear Mechanical Systems

2019 ◽  
Vol 14 (8) ◽  
Author(s):  
Shobhit Jain ◽  
Paolo Tiso
Keyword(s):  
Finite Element ◽  
Model Reduction ◽  
Computational Cost ◽  
Galerkin Projection ◽  
Dimensional Linear Subspace ◽  
Reduction Techniques ◽  
Energy Conserving ◽  
Reduction Methods ◽  
Wing Structure ◽  
Nonlinear Manifolds

Common trends in model reduction of large nonlinear finite element (FE)-discretized systems involve Galerkin projection of the governing equations onto a low-dimensional linear subspace. Though this reduces the number of unknowns in the system, the computational cost for obtaining the reduced solution could still be high due to the prohibitive computational costs involved in the evaluation of nonlinear terms. Hyper-reduction methods are then used for fast approximation of these nonlinear terms. In the finite element context, the energy conserving sampling and weighing (ECSW) method has emerged as an effective tool for hyper-reduction of Galerkin-projection-based reduced-order models (ROMs). More recent trends in model reduction involve the use of nonlinear manifolds, which involves projection onto the tangent space of the manifold. While there are many methods to identify such nonlinear manifolds, hyper-reduction techniques to accelerate computation in such ROMs are rare. In this work, we propose an extension to ECSW to allow for hyper-reduction using nonlinear mappings, while retaining its desirable stability and structure-preserving properties. As a proof of concept, the proposed hyper-reduction technique is demonstrated over models of a flat plate and a realistic wing structure, whose dynamics have been shown to evolve over a nonlinear (quadratic) manifold. An online speed-up of over one thousand times relative to the full system has been obtained for the wing structure using the proposed method, which is higher than its linear counterpart using the ECSW.

scholarly journals An Ensemble-Based Four-Dimensional Variational Data Assimilation Scheme. Part II: Observing System Simulation Experiments with Advanced Research WRF (ARW)

2009 ◽  
Vol 137 (5) ◽  
pp. 1687-1704 ◽  
Author(s):  
Chengsi Liu ◽  
Qingnong Xiao ◽  
Bin Wang
Keyword(s):  
Data Assimilation ◽  
System Simulation ◽  
Variational Data Assimilation ◽  
Water Model ◽  
Sequential Algorithm ◽  
Forecast Errors ◽  
Sampling Errors ◽  
Simulation Experiments ◽  
Real Dimension ◽  
The Impact

Abstract An ensemble-based four-dimensional variational data assimilation (En4DVAR) algorithm and its performance in a low-dimension space with a one-dimensional shallow-water model have been presented in Part I. This algorithm adopts the standard incremental approach and preconditioning in the variational algorithm but avoids the need for a tangent linear model and its adjoint so that it can be easily incorporated into variational assimilation systems. The current study explores techniques for En4DVAR application in real-dimension data assimilation. The EOF decomposed correlation function operator and analysis time tuning are formulated to reduce the impact of sampling errors in En4DVAR upon its analysis. With the Advanced Research Weather Research and Forecasting (ARW-WRF) model, Observing System Simulation Experiments (OSSEs) are designed and their performance in real-dimension data assimilation is examined. It is found that the designed En4DVAR localization techniques can effectively alleviate the impacts of sampling errors upon analysis. Most forecast errors and biases in ARW are reduced by En4DVAR compared to those in a control experiment. En3DVAR cycling experiments are used to compare the ensemble-based sequential algorithm with the ensemble-based retrospective algorithm. These experiments indicate that the ensemble-based retrospective assimilation, En4DVAR, produces an overall better analysis than the ensemble-based sequential algorithm, En3DVAR, cycling approach.

scholarly journals Optimal transport for variational data assimilation

2018 ◽  
Vol 25 (1) ◽  
pp. 55-66 ◽  
Author(s):  
Nelson Feyeux ◽  
Arthur Vidard ◽  
Maëlle Nodet
Keyword(s):  
Data Assimilation ◽  
Transport Theory ◽  
Optimal Transport ◽  
Wasserstein Distance ◽  
Variational Data Assimilation ◽  
Water Model ◽  
Position Errors ◽  
Optimal Transport Theory ◽  
The Cost ◽  
Model Trajectory

Abstract. Usually data assimilation methods evaluate observation-model misfits using weighted L2 distances. However, it is not well suited when observed features are present in the model with position error. In this context, the Wasserstein distance stemming from optimal transport theory is more relevant.This paper proposes the adaptation of variational data assimilation for the use of such a measure. It provides a short introduction of optimal transport theory and discusses the importance of a proper choice of scalar product to compute the cost function gradient. It also extends the discussion to the way the descent is performed within the minimization process.These algorithmic changes are tested on a nonlinear shallow-water model, leading to the conclusion that optimal transport-based data assimilation seems to be promising to capture position errors in the model trajectory.

scholarly journals Implementation of Deterministic Weather Forecasting Systems Based on Ensemble–Variational Data Assimilation at Environment Canada. Part I: The Global System

2015 ◽  
Vol 143 (7) ◽  
pp. 2532-2559 ◽  
Author(s):  
Mark Buehner ◽  
Ron McTaggart-Cowan ◽  
Alain Beaulne ◽  
Cécilien Charette ◽  
Louis Garand ◽  
...  
Keyword(s):  
Data Assimilation ◽  
Weather Forecasting ◽  
Forecast Accuracy ◽  
Horizontal Resolution ◽  
Variational Data Assimilation ◽  
Lead Times ◽  
Environment Canada ◽  
Computationally Efficient ◽  
Full Field ◽  
New System

Abstract A major set of changes was made to the Environment Canada global deterministic prediction system during the fall of 2014, including the replacement of four-dimensional variational data assimilation (4DVar) by four-dimensional ensemble–variational data assimilation (4DEnVar). The new system provides improved forecast accuracy relative to the previous system, based on results from two sets of two-month data assimilation and forecast experiments. The improvements are largest at shorter lead times, but significant improvements are maintained in the 120-h forecasts for most regions and vertical levels. The improvements result from the combined impact of numerous changes, in addition to the use of 4DEnVar. These include an improved treatment of radiosonde and aircraft observations, an improved radiance bias correction procedure, the assimilation of ground-based GPS data, a doubling of the number of assimilated channels from hyperspectral infrared sounders, and an improved approach for initializing model forecasts. Because of the replacement of 4DVar with 4DEnVar, the new system is also more computationally efficient and easier to parallelize, facilitating a doubling of the analysis increment horizontal resolution. Replacement of a full-field digital filter with the 4D incremental analysis update approach, and the recycling of several key variables that are not directly analyzed significantly reduced the model spinup during both the data assimilation cycle and in medium-range forecasts.

A comparison of numerical methods for model reduction of dense discrete-time systems

2021 ◽  
Vol 69 (8) ◽  
pp. 683-694
Author(s):  
Robert Jendersie ◽  
Steffen W. R. Werner
Keyword(s):  
Numerical Methods ◽  
Model Reduction ◽  
Discrete Time ◽  
Digital Signal ◽  
Reduction Techniques ◽  
Use Of Resources ◽  
Discrete Time Systems ◽  
Reduction Methods ◽  
And Performance ◽  
Time Systems

Abstract Discrete-time systems are a common tool in the modeling of processes in many application areas such as digital signal processing and population dynamics. Model reduction is an essential remedy to handle high-fidelity systems in practice. To benefit from the performance gained by using reduced-order models, the computation of these models itself must be done with a reasonable use of resources. In this paper, we consider the case of medium-scale dense discrete-time systems and compare the performance of different numerical methods for the implementation of two basic model reduction techniques. Therefore, we give an overview of the considered model reduction methods and of the techniques used in underlying implementations. The outlined methods are then compared with established implementations in several numerical examples in terms of accuracy and performance.

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