An Investigation of Adaptive Radius for the Covariance Localization in Ensemble Data Assimilation

The covariance matrix estimated from the ensemble data assimilation always suffers from filter collapse because of the spurious correlations induced by the finite ensemble size. The localization technique is applied to ameliorate this issue, which has been suggested to be effective. In this paper, an adaptive scheme for Schur product covariance localization is proposed, which is easy and efficient to implement in the ensemble data assimilation frameworks. A Gaussian-shaped taper function is selected as the localization taper function for the Schur product in the adaptive localization scheme, and the localization radius is obtained adaptively through a certain criterion of correlations with the background ensembles. An idealized Lorenz96 model with an ensemble Kalman filter is firstly examined, showing that the adaptive localization scheme helps to significantly reduce the spurious correlations in the small ensemble with low computational cost and provides accurate covariances that are similar to those derived from a much larger ensemble. The investigations of adaptive localization radius reveal that the optimal radius is model-parameter-dependent, vertical-level-dependent and nearly flow-dependent with weather scenarios in a realistic model; for example, the radius of model parameter zonal wind is generally larger than that of temperature. The adaptivity of the localization scheme is also illustrated in the ensemble framework and shows that the adaptive scheme has a positive effect on the assimilated analysis as the well-tuned localization.

Deep Learning for Latent Space Data Assimilation LSDA in Subsurface Flow Systems

We present a deep learning architecture for efficient reduced-order implementation of ensemble data assimilation. Specifically, deep learning is used to improve two important aspects of data assimilation workflows: (i) low-rank representation of complex reservoir property distributions for geologically consistent feature-based model updating, and (ii) efficient prediction of the statistical information that are required for model updating. The proposed method uses deep convolutional autoencoders to nonlinearly map the original complex and high-dimensional parameters onto a low-dimensional parameter latent space that compactly represents the original parameters. In addition, a low-dimensional data latent space is constructed to predict the observable response of each model parameter realization, which can be used to compute the statistical information needed for the data assimilation step. The two mappings are developed as a joint deep learning architecture with two autoencoders that are connected and trained together. The training uses an ensemble of model parameters and their corresponding production response predictions as needed in implementing the standard ensemble-based data assimilation frameworks. Simultaneous training of the two mappings leads to a joint data-parameter manifold that captures the most salient information in the two spaces for a more effective data assimilation, where only relevant data and parameter features are included. Moreover, the parameter-to-data mapping provides a fast forecast model that can be used to increase the ensemble size for a more accurate data assimilation, without a major computational overhead. We implement the developed approach to a series of numerical experiments, including a 3D example based on the Volve field in the North Sea. For data assimilation methods that involve iterative schemes, such as ensemble smoothers with multiple data assimilation or iterative forms of ensemble Kalman filter, the proposed approach offers a computationally competitive alternative. Our results show that a fully low-dimensional implementation of ensemble data assimilation using deep learning architectures offers several advantages compared to standard algorithms, including joint data-parameter reduction that respects the salient features in each space, geologically consistent feature-based updates, increased ensemble sizes to improve the accuracy and computational efficiency of the calculated statistics for the update step.

Propagating information from snow observations with CrocO ensemble data assimilation system: a 10-years case study over a snow depth observation network

The mountainous snow cover is highly variable at all temporal and spatial scales. Snowpack models only imperfectly represent this variability, because of uncertain meteorological inputs, physical parameterisations, and unresolved terrain features. In-situ observations of the height of snow (HS), despite their limited representativeness, could help constrain intermediate and large scale modelling errors by means of data assimilation. In this work, we assimilate HS observations from an in-situ network of 295 stations covering the French Alps, Pyrenees and Andorra, over the period 2009–2019. In view of assimilating such observations into a spatialised snow cover modelling framework, we investigate whether such observations can be used to correct neighbouring snowpack simulations. We use CrocO, an ensemble data assimilation framework of snow cover modelling, based on a Particle Filter suited to the propagation of information from observed to unobserved areas. This ensemble system already benefits from meteorological observations, assimilated within SAFRAN analysis scheme. CrocO also proposes various localisation strategies to assimilate snow observations. These approaches are evaluated in a Leave-One-Out setup against the operational deterministic model and its ensemble open-loop counterpart, both running without HS assimilation. Results show that intermediate localisation radius of 35–50 km yield a slightly lower root mean square error (RMSE), and a better Spread-Skill than the strategy assimilating all the observations from a whole mountain range. Significant continuous ranked probability score (CRPS) improvements of about 13 % are obtained in the areas where the open-loop modelling errors are the largest, e.g. the Haute-Ariège, Andorra and the Extreme Southern Alps. Over these areas, weather station observations are generally sparser, resulting in more uncertain meteorological analyses, and therefore snow simulations. In-situ HS observations thus shows an interesting complementarity with meteorological observations to better constrain snow cover simulations over large areas.

Ensemble Riemannian data assimilation over the Wasserstein space

In this paper, we present an ensemble data assimilation paradigm over a Riemannian manifold equipped with the Wasserstein metric. Unlike the Euclidean distance used in classic data assimilation methodologies, the Wasserstein metric can capture the translation and difference between the shapes of square-integrable probability distributions of the background state and observations. This enables us to formally penalize geophysical biases in state space with non-Gaussian distributions. The new approach is applied to dissipative and chaotic evolutionary dynamics, and its potential advantages and limitations are highlighted compared to the classic ensemble data assimilation approaches under systematic errors.

Technical Note: Sequential ensemble data assimilation in convergent and divergent systems

Data assimilation methods are used throughout the geosciences to combine information from uncertain models and uncertain measurement data. However, the characteristics of geophysical systems differ and may be distinguished between divergent and convergent systems. In divergent systems initially nearby states will drift apart, while they will coalesce in convergent systems. This difference has implications for the application of sequential ensemble data assimilation methods. This study explores these implications on two exemplary systems, i.e., the divergent Lorenz 96 model and the convergent description of soil water movement by the Richards equation. The results show that sequential ensemble data assimilation methods require a sufficient divergent component. This makes the transfer of the methods from divergent to convergent systems challenging. We demonstrate, through a set of case studies, that it is imperative to represent model errors adequately and incorporate parameter uncertainties in ensemble data assimilation in convergent systems.

Novel iterative ensemble smoothers derived from a class of generalized cost functions

Iterative ensemble smoothers (IES) are among the state-of-the-art approaches to solving history matching problems. From an optimization-theoretic point of view, these algorithms can be derived by solving certain stochastic nonlinear-least-squares problems. In a broader picture, history matching is essentially an inverse problem, which is often ill-posed and may not possess a unique solution. To mitigate the ill-posedness, in the course of solving an inverse problem, prior knowledge and domain experience are often incorporated, as a regularization term, into a suitable cost function within a respective optimization problem. Whereas in the inverse theory there is a rich class of inversion algorithms resulting from various choices of regularized cost functions, there are few ensemble data assimilation algorithms (including IES) which in their practical uses are implemented in a form beyond nonlinear-least-squares. This work aims to narrow this noticed gap. Specifically, we consider a class of more generalized cost functions, and establish a unified formula that can be used to construct a corresponding group of novel ensemble data assimilation algorithms, called generalized IES (GIES), in a principled and systematic way. For demonstration, we choose a subset (up to 30 +) of the GIES algorithms derived from the unified formula, and apply them to two history matching problems. Experiment results indicate that many of the tested GIES algorithms exhibit superior performance to that of an original IES developed in a previous work, showcasing the potential benefit of designing new ensemble data assimilation algorithms through the proposed framework.

Parameter estimation for ocean biogeochemical component in a global model using Ensemble Kalman Filter: a twin experiment

<p>Ocean biogeochemical (BGC) models utilize a large number of poorly-constrained global parameters to mimic unresolved processes and reproduce the observed complex spatio-temporal patterns. Large model errors stem primarily from inaccuracies in these parameters whose optimal values can vary both in space and time. This study aims to demonstrate the ability of ensemble data assimilation (DA) methods to provide high-quality and improved BGC parameters within an Earth system model in idealized twin experiment framework.  We use the Norwegian Climate Prediction Model (NorCPM), which combines the Norwegian Earth System Model with the Dual-One-Step ahead smoothing-based Ensemble Kalman Filter (DOSA-EnKF). The work follows on Gharamti et al. (2017) that successfully demonstrates the approach for one-dimensional idealized ocean BGC models. We aim to estimate five spatially varying BGC parameters by assimilating Salinity and Temperature hydrographic profiles and surface BGC (Phytoplankton, Nitrate, Phosphorous, Silicate, and Oxygen) observations in a strongly coupled DA framework – i.e., jointly updating ocean and BGC state-parameters during the assimilation. The method converges quickly (less than a year), largely reducing the errors in the BGC parameters and eventually it is shown to perform nearly as well as that of the system with true parameter values. Optimal parameter values can also be recovered by assimilating climatological BGC observations and challenging sparse observational networks. The findings of this study demonstrate the applicability of the approach for tuning the system in a real framework.</p><p> </p><p><strong>References</strong>:</p><p>Gharamti, M. E., Tjiputra, J., Bethke, I., Samuelsen, A., Skjelvan, I., Bentsen, M., & Bertino, L. (2017). Ensemble data assimilation for ocean biogeochemical state and parameter estimation at different sites. Ocean Modelling, 112, 65-89.</p>

Assimilating sea ice deformation observations using a multiscale alignment ensemble data assimilation method

<p>A multiscale alignment (MSA) method was proposed by Ying (2019) for ensemble data assimilation to reduce the errors caused by displacement of coherent features. The MSA method decomposes a model state into components ranging from large to small spatial scales, then applies ensemble filters to update each scale component sequentially. After a larger scale component analysis increment is derived from the observations, displacement vectors are computed from the analysis increments through an optical flow algorithm. These displacement vectors are then used to warp the model mesh, which reduces position errors in the smaller scale components before the ensemble filter is applied again.</p><p>The MSA method is now applied to a sea ice prediction problem at NERSC to assimilate satellite-derived sea ice deformation observations into the next generation Sea Ice Model (neXtSIM) simulations. Preliminary results show that the MSA can more effectively reduce the position errors of the linear kinematic features of sea ice than the traditional ensemble Kalman filter. The alignment step is shown to be a big contributor for error reduction in our test case. We will also discuss the remaining challenges of tuning parameters in the MSA method and dealing with model deficiencies.</p>