Optimal sensor placement for variational data assimilation of unsteady flows past a rotationally oscillating cylinder

2017 ◽  
Vol 823 ◽  
pp. 230-277 ◽  
Author(s):  
Vincent Mons ◽  
Jean-Camille Chassaing ◽  
Pierre Sagaut
Keyword(s):  
Data Assimilation ◽  
Sensor Placement ◽  
Computational Cost ◽  
Unsteady Flows ◽  
Variational Data Assimilation ◽  
Model Parameters ◽  
Oscillating Cylinder ◽  
Optimal Sensor Placement ◽  
Initial Flow ◽  
Placement Procedure

An optimal sensor placement procedure is proposed within the framework of variational data assimilation (DA) for unsteady flows, with the aim of maximizing the efficiency of the DA procedure. It is dedicated to the a priori design of a sensor network, and relies on a first-order adjoint approach. The proposed methodology first consists in identifying, via optimal control, the locations in the flow that have the greatest sensitivity with respect to a change in the initial condition, boundary conditions or model parameters. In a second step, sensors are placed at these locations for DA purposes. The use of this optimal sensor placement procedure does not require extra development in the case where a variational DA suite is available. The proposed methodology is applied to the reconstruction of unsteady bidimensional flows past a rotationally oscillating cylinder. More precisely, the possibilities of reconstructing the rotational speed of the cylinder and the initial flow, which here encompasses upstream conditions, from various types of observations are investigated via variational DA. Then, the observation optimization procedure is employed to identify optimal locations for placing velocity sensors downstream of the cylinder. Both reduction in the computational cost and improvement in the quality of the reconstructed flow are achieved through optimal sensor placement, encouraging the application of the proposed methodology to more complex and realistic flows.

scholarly journals Optimal solution error covariance in highly nonlinear problems of variational data assimilation

2012 ◽  
Vol 19 (2) ◽  
pp. 177-184 ◽  
Author(s):  
V. Shutyaev ◽  
I. Gejadze ◽  
G. J. M. Copeland ◽  
F.-X. Le Dimet
Keyword(s):  
Nonlinear Dynamics ◽  
Data Assimilation ◽  
Optimal Solution ◽  
Nonlinear Problems ◽  
Variational Data Assimilation ◽  
Model Parameters ◽  
Efficient Computation ◽  
Viscous Term ◽  
Highly Nonlinear ◽  
The Cost

Abstract. The problem of variational data assimilation (DA) for a nonlinear evolution model is formulated as an optimal control problem to find the initial condition, boundary conditions and/or model parameters. The input data contain observation and background errors, hence there is an error in the optimal solution. For mildly nonlinear dynamics, the covariance matrix of the optimal solution error can be approximated by the inverse Hessian of the cost function. For problems with strongly nonlinear dynamics, a new statistical method based on the computation of a sample of inverse Hessians is suggested. This method relies on the efficient computation of the inverse Hessian by means of iterative methods (Lanczos and quasi-Newton BFGS) with preconditioning. Numerical examples are presented for the model governed by the Burgers equation with a nonlinear viscous term.

scholarly journals Some Aspects of Sensitivity Analysis in Variational Data Assimilation for Coupled Dynamical Systems

2015 ◽  
Vol 2015 ◽  
pp. 1-22 ◽  
Author(s):  
Sergei Soldatenko ◽  
Peter Steinle ◽  
Chris Tingwell ◽  
Denis Chichkine
Keyword(s):  
Sensitivity Analysis ◽  
Dynamical Systems ◽  
Data Assimilation ◽  
Weather Prediction ◽  
Computational Cost ◽  
Variational Data Assimilation ◽  
Practical Implementation ◽  
Parameter Uncertainties ◽  
Sensitivity Functions ◽  
Sensitivity Analysis Method

Variational data assimilation (VDA) remains one of the key issues arising in many fields of geosciences including the numerical weather prediction. While the theory of VDA is well established, there are a number of issues with practical implementation that require additional consideration and study. However, the exploration of VDA requires considerable computational resources. For simple enough low-order models, the computational cost is minor and therefore models of this class are used as simple test instruments to emulate more complex systems. In this paper, the sensitivity with respect to variations in the parameters of one of the main components of VDA, the nonlinear forecasting model, is considered. For chaotic atmospheric dynamics, conventional methods of sensitivity analysis provide uninformative results since the envelopes of sensitivity functions grow with time and sensitivity functions themselves demonstrate the oscillating behaviour. The use of sensitivity analysis method, developed on the basis of the theory of shadowing pseudoorbits in dynamical systems, allows us to calculate sensitivity functions correctly. Sensitivity estimates for a simple coupled dynamical system are calculated and presented in the paper. To estimate the influence of model parameter uncertainties on the forecast, the relative error in the energy norm is applied.

scholarly journals A Sequential Variational Algorithm for Data Assimilation in Oceanography and Meteorology

2009 ◽  
Vol 137 (1) ◽  
pp. 269-287 ◽  
Author(s):  
Srdjan Dobricic
Keyword(s):  
Data Assimilation ◽  
Computational Cost ◽  
Model Space ◽  
Variational Data Assimilation ◽  
Computer Memory ◽  
Optimal Model ◽  
State Estimate ◽  
Optimal State ◽  
Model State

Abstract This study theoretically establishes a sequential variational (SVAR) method for the data assimilation in oceanography and meteorology defined on the model space. Requiring a significantly smaller amount of computer memory, theoretically SVAR gives the same optimal model state estimate as the four-dimensional variational data assimilation method. Its computational cost is similar to that of the four-dimensional variational data assimilation and representer methods. In addition to the optimal state estimates, SVAR computes error covariances at the end of the assimilation window. These advantageous properties of the new algorithm are obtained by combining the sequential methodology with suitable definitions of several new l2 norms, which implicitly provide required estimates.

Intercomparison and Coupling of Ensemble and Four-Dimensional Variational Data Assimilation Methods for the Analysis and Forecasting of Hurricane Karl (2010)

2014 ◽  
Vol 142 (9) ◽  
pp. 3347-3364 ◽  
Author(s):  
Jonathan Poterjoy ◽  
Fuqing Zhang
Keyword(s):  
Tropical Cyclone ◽  
Data Assimilation ◽  
Hybrid System ◽  
Ensemble Kalman Filter ◽  
Computational Cost ◽  
Wrf Model ◽  
Variational Data Assimilation ◽  
Weather Research And Forecasting ◽  
Forecast Errors ◽  
Verification Methods

This study examines the performance of ensemble and variational data assimilation systems for the Weather Research and Forecasting (WRF) Model. These methods include an ensemble Kalman filter (EnKF), an incremental four-dimensional variational data assimilation (4DVar) system, and a hybrid system that uses a two-way coupling between the two approaches (E4DVar). The three methods are applied to assimilate routinely collected data and field observations over a 10-day period that spans the life cycle of Hurricane Karl (2010), including the pregenesis disturbance that preceded its development into a tropical cyclone. In general, forecasts from the E4DVar analyses are found to produce smaller 48–72-h forecast errors than the benchmark EnKF and 4DVar methods for all variables and verification methods tested in this study. The improved representation of low- and midlevel moisture and vorticity in the E4DVar analyses leads to more accurate track and intensity predictions by this system. In particular, E4DVar analyses provide persistently more skillful genesis and rapid intensification forecasts than the EnKF and 4DVar methods during cycling. The data assimilation experiments also expose additional benefits of the hybrid system in terms of physical balance, computational cost, and the treatment of asynoptic observations near the beginning of the assimilation window. These factors make it a practical data assimilation method for mesoscale analysis and forecasting, and for tropical cyclone prediction.

scholarly journals Deriving the Surface Soil Heat Flux from Observed Soil Temperature and Soil Heat Flux Profiles Using a Variational Data Assimilation Approach

2009 ◽  
Vol 48 (3) ◽  
pp. 644-656 ◽  
Author(s):  
R. J. Ronda ◽  
F. C. Bosveld
Keyword(s):  
Heat Flux ◽  
Data Assimilation ◽  
Soil Temperature ◽  
Surface Soil ◽  
Soil Column ◽  
Soil Heat Flux ◽  
Variational Data Assimilation ◽  
Shortwave Radiation ◽  
Model Parameters ◽  
Vegetation Canopy

Abstract A novel approach to infer surface soil heat fluxes from measured profiles of soil temperature, soil heat flux, and observations of the vegetation canopy temperature and the incoming shortwave radiation is evaluated for the Cabauw measurement facility in the Netherlands. The approach is a variational data assimilation approach that uses the applied measurements to optimize, on a daily basis, parameter values of a model that describes the heat transport between the vegetation canopy and the surface and within the soil column. Insertion of error characteristics that either are inferred from the field data themselves or are derived from literature leads to valid estimates of the cost function for about 100 days in 2003. The approach gives values of the model parameters that compare well to values derived from the literature, although values for the soil conductivity and the volumetric heat capacity of the soil start to differ from the literature values at the end of 2003, possibly because of specific soil characteristics and the extreme dryness of the summer of 2003. The model gives estimates of the surface soil heat flux that compare well to estimates using the currently operational lambda approach, provided that the latter is adapted to account for the disturbance of the soil heat flux at the locations of the heat flux plates. Only when the surface soil heat flux is very small or very large does the new approach give estimates of the surface soil heat flux that differ from those obtained with the lambda approach.

Bayesian Optimal Sensor Placement for Modal Identification of Civil Infrastructures

2017 ◽  
Vol 2 (2) ◽  
Author(s):  
Costas Argyris ◽  
Costas Papadimitriou ◽  
Panagiotis Panetsos
Keyword(s):  
Posterior Distribution ◽  
Sensor Placement ◽  
Modal Identification ◽  
Model Parameters ◽  
Optimal Sensor Placement ◽  
Civil Infrastructures ◽  
Spatially Correlated ◽  
Placement Algorithm ◽  
Insightful Analysis ◽  
Stochastic Optimization Algorithm

A Bayesian optimal experimental design (OED) method is proposed in this work for estimating the best locations of sensors in structures so that the measured data are most informative for estimating reliably the structural modes. The information contained in the data is measured by the Kullback-Leibler (K-L) divergence between the prior and posterior distribution of the model parameters taken in modal identification to be the modal coordinates. The optimal sensor placement that maximizes the expected K-L divergence is shown also to minimize the information entropy of the posterior distribution. Unidentifiability issues observed in existing formulations when the number of sensors is less than the number of identified modes, are resolved using a non-uniform prior in the Bayesian OED. An insightful analysis is presented that demonstrates the effect of the variances of Bayesian priors on the optimal design. For dense mesh finite element models, sensor clustering phenomena are avoided by integrating in the methodology spatially correlated prediction error models. A heuristic forward sequential sensor placement algorithm and a stochastic optimization algorithm are used to solve the optimization problem in the continuous physical domain of variation of the sensor locations. The theoretical developments and algorithms are applied for the optimal sensor placement design along the deck of a 537 m concrete bridge.

Development of an Efficient Regional Four-Dimensional Variational Data Assimilation System for WRF

2014 ◽  
Vol 31 (12) ◽  
pp. 2777-2794 ◽  
Author(s):  
Xin Zhang ◽  
Xiang-Yu Huang ◽  
Jianyu Liu ◽  
Jonathan Poterjoy ◽  
Yonghui Weng ◽  
...  
Keyword(s):  
High Resolution ◽  
Data Assimilation ◽  
Computational Cost ◽  
Wrf Model ◽  
Forecast Accuracy ◽  
Hurricane Sandy ◽  
Variational Data Assimilation ◽  
Full Resolution ◽  
Computational Performance ◽  
Multiple Data

Abstract This paper presents the development of a single executable four-dimensional variational data assimilation (4D-Var) system based on the Weather Research and Forecasting (WRF) Model through coupling the variational data assimilation algorithm (WRF-VAR) with the newly developed WRF tangent linear and adjoint model (WRFPLUS). Compared to the predecessor Multiple Program Multiple Data version, the new WRF 4D-Var system achieves major improvements in that all processing cores are able to participate in the computation and all information exchanges between WRF-VAR and WRFPLUS are moved directly from disk to memory. The single executable 4D-Var system demonstrates desirable acceleration and scalability in terms of the computational performance, as demonstrated through a series of benchmarking data assimilation experiments carried out over a continental U.S. domain. To take into account the nonlinear processes with the linearized minimization algorithm and to further decrease the computational cost of the 4D-Var minimization, a multi-incremental minimization that uses multiple horizontal resolutions for the inner loop has been developed. The method calculates the innovations with a high-resolution grid and minimizes the cost function with a lower-resolution grid. The details regarding the transition between the high-resolution outer loop and the low-resolution inner loop are introduced. Performance of the multi-incremental configuration is found to be comparable to that with the full-resolution 4D-Var in terms of 24-h forecast accuracy in the week-long analysis and forecast experiment over the continental U.S. domain. Moreover, the capability of the newly developed multi-incremental 4D-Var system is further demonstrated in the convection-permitting analysis and forecast experiment for Hurricane Sandy (2012), which was hardly computationally feasible with the predecessor WRF 4D-Var system.

scholarly journals Variational Data Assimilation to improve subsurface drainage model parameters

2021 ◽  
Author(s):  
Samy Chelil ◽  
Hind Oubanas ◽  
Hocine Henine ◽  
Igor Gejadze ◽  
Pierre-Olivier Malaterre ◽  
...  
Keyword(s):  
Data Assimilation ◽  
Subsurface Drainage ◽  
Variational Data Assimilation ◽  
Model Parameters
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