Earth System Modeling 2.0: A Blueprint for Models That Learn From Observations and Targeted High-Resolution Simulations

Climate projections continue to be marred by large uncertainties, which originate in processes that need to be parameterized, such as clouds, convection, and ecosystems. But rapid progress is now within reach. New computational tools and methods from data assimilation and machine learning make it possible to integrate global observations and local high-resolution simulations in an Earth system model (ESM) that systematically learns from both. Here we propose a blueprint for such an ESM. We outline how parameterization schemes can learn from global observations and targeted high-resolution simulations, for example, of clouds and convection, through matching low-order statistics between ESMs, observations, and high-resolution simulations. We illustrate learning algorithms for ESMs with a simple dynamical system that shares characteristics of the climate system; and we discuss the opportunities the proposed framework presents and the challenges that remain to realize it.Comment: 32 pages, 3 figure

Realtime reservoir characterization and beyond: cyber-infrastructure tools and technologies

The advent of the digital oil _x000C_eld and rapidly decreasing cost of computing creates opportunities as well as challenges in simulation based reservoir studies, in particular, real-time reservoir characterization and optimization. One challenge our e_x000B_orts are directed toward is the use of real-time production data to perform live reservoir characterization using high throughput, high performance computing environments. To that end we developed the required tools of parallel reservoir simulator, parallel ensemble Kalman _x000C_lter and a scalable work ow manager. When using this collection of tools, a reservoir modeler is able to perform large scale reservoir management studies in short periods of time. This includes studies with thousands of models that are individually complex and large, involving millions of degrees of freedom. Using parallel processing, we are able to solve these models much faster than we otherwise would on a single, serial machine. This motivated the development of a fast parallel reservoir simulator. Furthermore, distributing those simulations across resources leads to a smaller total time to completion by making use of distributed processing. This allows the development of a scalable high throughput work ow manager. Finally, with thousands of models, each with millions of degrees of freedom, we end up with a super uity of model parameters. This translates directly to billions of degrees of freedom in the reservoir study. To be able to use the ensemble Kalman _x000C_lter on these models, we needed to develop a parallel implementation of the ensemble Kalman _x000C_lter. This thesis discusses the enabling tools and technologies developed to address a speci _x000C_c problem: how to accurately characterize reservoirs, using large numbers of complex detailed models. For these characterization studies to be helpful in making production decisions, the time to solution must be feasible. To that end, our work is focused on developing and extending these tools, and optimizing their performance

Continuous reservoir model updating by ensemble Kalman filter on Grid computing architectures

A reservoir engineering Grid computing toolkit, ResGrid and its extensions, were developed and applied to designed reservoir simulation studies and continuous reservoir model updating. The toolkit provides reservoir engineers with high performance computing capacity to complete their projects without requiring them to delve into Grid resource heterogeneity, security certification, or network protocols. Continuous and real-time reservoir model updating is an important component of closed-loop model-based reservoir management. The method must rapidly and continuously update reservoir models by assimilating production data, so that the performance predictions and the associated uncertainty are up-to-date for optimization. The ensemble Kalman filter (EnKF), a Bayesian approach for model updating, uses Monte Carlo statistics for fusing observation data with forecasts from simulations to estimate a range of plausible models. The ensemble of updated models can be used for uncertainty forecasting or optimization. Grid environments aggregate geographically distributed, heterogeneous resources. Their virtual architecture can handle many large parallel simulation runs, and is thus well suited to solving model-based reservoir management problems. In the study, the ResGrid workflow for Grid-based designed reservoir simulation and an adapted workflow provide tools for building prior model ensembles, task farming and execution, extracting simulator output results, implementing the EnKF, and using a web portal for invoking those scripts. The ResGrid workflow is demonstrated for a geostatistical study of 3-D displacements in heterogeneous reservoirs. A suite of 1920 simulations assesses the effects of geostatistical methods and model parameters. Multiple runs are simultaneously executed using parallel Grid computing. Flow response analyses indicate that efficient, widely-used sequential geostatistical simulation methods may overestimate flow response variability when compared to more rigorous but computationally costly direct methods. Although the EnKF has attracted great interest in reservoir engineering, some aspects of the EnKF remain poorly understood, and are explored in the dissertation. First, guidelines are offered to select data assimilation intervals. Second, an adaptive covariance inflation method is shown to be effective to stabilize the EnKF. Third, we show that simple truncation can correct negative effects of nonlinearity and non-Gaussianity as effectively as more complex and expensive reparameterization methods

Reconstructing Cardiac Electrical Excitations from Optical Mapping Recordings

The reconstruction of electrical excitation patterns through the unobserved depth of the tissue is essential to realizing the potential of computational models in cardiac medicine. We have utilized experimental optical-mapping recordings of cardiac electrical excitation on the epicardial and endocardial surfaces of a canine ventricle as observations directing a local ensemble transform Kalman Filter (LETKF) data assimilation scheme. We demonstrate that the inclusion of explicit information about the stimulation protocol can marginally improve the confidence of the ensemble reconstruction and the reliability of the assimilation over time. Likewise, we consider the efficacy of stochastic modeling additions to the assimilation scheme in the context of experimentally derived observation sets. Approximation error is addressed at both the observation and modeling stages, through the uncertainty of observations and the specification of the model used in the assimilation ensemble. We find that perturbative modifications to the observations have marginal to deleterious effects on the accuracy and robustness of the state reconstruction. Further, we find that incorporating additional information from the observations into the model itself (in the case of stimulus and stochastic currents) has a marginal improvement on the reconstruction accuracy over a fully autonomous model, while complicating the model itself and thus introducing potential for new types of model error. That the inclusion of explicit modeling information has negligible to negative effects on the reconstruction implies the need for new avenues for optimization of data assimilation schemes applied to cardiac electrical excitation.Comment: main text: 18 pages, 10 figures; supplement: 5 pages, 9 figures, 2 movie

Data Assimilation Fundamentals

This open-access textbook's significant contribution is the unified derivation of data-assimilation techniques from a common fundamental and optimal starting point, namely Bayes' theorem. Unique for this book is the "top-down" derivation of the assimilation methods. It starts from Bayes theorem and gradually introduces the assumptions and approximations needed to arrive at today's popular data-assimilation methods. This strategy is the opposite of most textbooks and reviews on data assimilation that typically take a bottom-up approach to derive a particular assimilation method. E.g., the derivation of the Kalman Filter from control theory and the derivation of the ensemble Kalman Filter as a low-rank approximation of the standard Kalman Filter. The bottom-up approach derives the assimilation methods from different mathematical principles, making it difficult to compare them. Thus, it is unclear which assumptions are made to derive an assimilation method and sometimes even which problem it aspires to solve. The book's top-down approach allows categorizing data-assimilation methods based on the approximations used. This approach enables the user to choose the most suitable method for a particular problem or application. Have you ever wondered about the difference between the ensemble 4DVar and the "ensemble randomized likelihood" (EnRML) methods? Do you know the differences between the ensemble smoother and the ensemble-Kalman smoother? Would you like to understand how a particle flow is related to a particle filter? In this book, we will provide clear answers to several such questions. The book provides the basis for an advanced course in data assimilation. It focuses on the unified derivation of the methods and illustrates their properties on multiple examples. It is suitable for graduate students, post-docs, scientists, and practitioners working in data assimilation

Ensemble Kalman Methods: A Mean Field Perspective

This paper provides a unifying mean field based framework for the derivation and analysis of ensemble Kalman methods. Both state estimation and parameter estimation problems are considered, and formulations in both discrete and continuous time are employed. For state estimation problems both the control and filtering approaches are studied; analogously, for parameter estimation (inverse) problems the optimization and Bayesian perspectives are both studied. The approach taken unifies a wide-ranging literature in the field, provides a framework for analysis of ensemble Kalman methods, and suggests open problems