Variational Data Assimilation to improve subsurface drainage model parameters

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.

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

Journal of Fluid Mechanics ◽

10.1017/jfm.2017.313 ◽

2017 ◽

Vol 823 ◽

pp. 230-277 ◽

Cited By ~ 12

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.

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

Journal of Applied Meteorology and Climatology ◽

10.1175/2008jamc1930.1 ◽

2009 ◽

Vol 48 (3) ◽

pp. 644-656 ◽

Cited By ~ 5

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.

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Learning missing part of physics-based models within a variational data assimilation scheme

10.5194/egusphere-egu2020-285 ◽

2020 ◽

Author(s):

Arthur Filoche ◽

Julien Brajard ◽

Anastase Charantonis ◽

Dominique Béréziat

Keyword(s):

Machine Learning ◽

Data Assimilation ◽

Hybrid Model ◽

Automatic Differentiation ◽

Variational Data Assimilation ◽

Model Parameters ◽

Time Data ◽

Physical Knowledge ◽

Data Assimilation Scheme ◽

Assimilation Scheme

The analogy between data assimilation and machine learning has already been shown and is still being investigated to address the problem of improving physics-based models. Even though both techniques learn from data, machine learning focuses on inferring model parameters while data assimilation concentrates on hidden system state estimation with the help of a dynamical model.&#160; &#160; Also, neural networks and more precisely ResNet-like architectures can be seen as dynamical systems and numerical schemes, respectively. They are now considered state of the art in a vast amount of tasks involving spatio-temporal forecasting. But to train such networks, one needs dense and representative data which is rarely the case in earth sciences. At the same time, data assimilation offers a proper Bayesian framework allowing to learn from partial, noisy and indirect observations. Thus, each of this field can profit from the other by providing either a learnable class of dynamical models or dense data sets.In this work, we benefit from powerful and flexible tools provided by the deep learning community based on automatic differentiation that are clearly suitable for variational data assimilation, avoiding explicit adjoint modelling. We use a hybrid model divided into 2 terms. The first term is a numerical scheme that comes from the discretisation of physics-based equations, the second is a convolutional neural network that represents the unresolved part of the dynamics. From the Data Assimilation point of view, our network can be seen as a particular parametrisation of the model error. We then jointly learn this parameterisation and estimate hidden system states within a variational data assimilation scheme. Indirectly, the issue of incorporating physical knowledge into machine learning models is also addressed.&#160;We show that the hybrid model improves forecast skill compared to traditional data assimilation techniques. The generalisation of the method on different models and data will also be discussed.

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The Impact of Length-Scale Variation When Diagnosing the Standard Deviations of Background Error in a 4D-Var System and Filtering Method Investigation

Advances in Meteorology ◽

10.1155/2020/8885607 ◽

2020 ◽

Vol 2020 ◽

pp. 1-13

Author(s):

Xiang Xing ◽

Bainian Liu ◽

Weimin Zhang ◽

Xiaoqun Cao ◽

Hongze Leng

Keyword(s):

Standard Deviation ◽

Data Assimilation ◽

Variational Data Assimilation ◽

Small Scale ◽

Model Parameters ◽

Spatial Averaging ◽

Background Error ◽

Operational System ◽

Filtering Method ◽

Standard Deviations

The four-dimensional variational data assimilation (4D-Var) method has been widely employed as an operational scheme in mainstream numerical weather prediction (NWP) centers. In addition to the ensemble data assimilation method, the randomization technique is still used to diagnose the standard deviations of background error in variational data assimilation (VAR) systems; however, such randomization techniques induce sampling noise, which may contaminate the quality of the standard deviations. First, this paper studies the properties of the sampling noise induced by the randomization technique. The results show that the sampling noise is on a small scale displaying high-frequency oscillations around the estimate compared with the estimate and this difference motivates the use of filtering techniques to eliminate the sampling noise effects. The characteristics of the standard deviation field of the control variables are also investigated, and the standard deviation fields of different model parameters have different scales and vary with the vertical model levels. To eliminate such sampling noise, the spectral filtering method used widely in the operational system and a modified spatial averaging approach are investigated. Although both methods have splendid performance in eliminating sampling noise, the spatial averaging approach is more efficient and easier to implement in operational systems. In addition, the optimal filtered results from the spatial averaging approach are dependent on model parameters and vertical levels, which is consistent with the variation in the standard deviation field. Finally, the spatial averaging approach is tested on the operational system at the global scale based on the YH4DVAR and the global NWP system, and the results indicate that the spatial averaging approach has positive effects on both analysis and forecast quality.

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