Error covariance tuning in variational data assimilation: application to an operating hydrological model

Abstract

Because the true state of complex physical systems is out of reach for real-world data assimilation problems, error covariances are uncertain and their specification remains very challenging. These error covariances are crucial ingredients for the proper use of data assimilation methods and for an effective quantification of the a posteriori errors of the state estimation. Therefore, the estimation of these covariances often involves at first a chosen specification of the matrices, followed by an adaptive tuning to correct their initial structure. In this paper, we propose a flexible combination of existing covariance tuning algorithms, including both online and offline procedures. These algorithms are applied in a specific order such that the required assumption of current tuning algorithms are fulfilled, at least partially, by the application of the ones at the previous steps. We use our procedure to tackle the problem of a multivariate and spatially-distributed hydrological model based on a precipitation-flow simulator with real industrial data. The efficiency of different algorithmic schemes is compared using real data with both quantitative and qualitative analysis. Numerical results show that these proposed algorithmic schemes improve significantly short-range flow forecast. Among the several tuning methods tested, recently developed CUTE and PUB algorithms are in the lead both in terms of history matching and forecast.

Observation Error Covariance Specification in Dynamical Systems for Data assimilation using Recurrent Neural Networks

“…In brief, they have mathematically proved that, by using a semi positive definite matrix as an initial guess, D05 iterative method converges on the exact * time-invariant (at least over a sufficiently long time period) observation error covariance when the background matrix and the transformation operator (which maps the state variables to real-time observations) are perfectly known a priori. On the other hand, it is also mentioned by [29] that a regularization step is necessary in practice for applying D05 and the convergence of the regularized iterations remains an open question [29,3]. To deal with time-varying systems, lag-innovation statistics are used for error covariance estimation [30].…”

“…In order to improve the reconstruction and prediction of dynamical systems with uncertainties, data assimilation (DA) techniques, originally developed in numerical weather prediction (NWP) [1] and geosciences [2], are widely applied to industrial problems, such as hydrology [3], wildfire forecasting [4], drought monitoring [5] and nuclear engineering [6]. DA algorithms aim to find the optimal approximation (also known as the analyzed state) of the state variables (usually representing a physical field of interest, such as velocity, temperature etc.…”

“…The problem statement and the contribution of this paper is described in Sect. 3. Data assimilation techniques and the ensemble methods are introduced briefly in Sect.…”

Real-time Updating of Dynamic Social Networks for COVID-19 Vaccination Strategies

“…In this paper, by investigating how the accuracy of network data could impact vaccination effectiveness, we propose a real-time network updating approach based on sequential data assimilation (DA) techniques. Originally developed in the field of meteorological and environmental science, DA has been applied to a wide variety of industrial domains, including geophysical modelling [10], hydrology [14] and economics [49]. Recently, sequential DA algorithms have also been used for real-time parameter identification in the SIR model for COVID spread simulation [61,50,22].…”

Advances in uncertainty quantification for water resources applications

“…With daily precipitation-runoff prediction applications, they compare the dropout ensemble with multiple NN model-based ensemble to illustrate the computational efficiency of the propose method while offering a reasonable accuracy. Cheng et al (2021) address the topic of variational data assimilation aiming to improve the estimation of background and observation error covariance matrices. Based on the advantages and limitations of several online and offline covariance matrix tuning algorithms with an convergence analysis, they propose a multi-stage tuning approach by tuning the error magnitude using the offline methods followed by correcting the covariance structure with the online approaches.…”