There is typically a mismatch between observations of a process, and its representation in a mathematical or numerical model. Such error arises because the model is incomplete or approximate, and errors are amplified by noise in the observations, as well as uncertain, or completely unknown, model states and parameters. In Earth science, errors of these types must be quantified, and a natural tool to do so is Bayesian inference, where errors are described via conditional probabilities defined for the model, its parameters, and the observations.
This mini-symposium will focus on the numerical solution of Bayesian inference problems in Earth sciences which are usually characterized by a large dimension (many parameters and states) and few observations (relative to the number of states and parameters). Moreover, Earth science applications require solutions to three types of Bayesian inference problems: state estimation (data assimilation), parameter estimation, and joint state and parameter estimation.
Our mini-symposium will showcase Bayesian inference "in action" in Earth science. It will provide an opportunity for interaction among applied mathematicians, interested in the numerics of Bayesian inference, and Earth scientists, who use Bayesian inference to break new ground in their respective fields.
14:00
- CANCELED - Simultaneous parameter and state estimation by derivative-free optimization of ensemble Kalman filter residuals
Spencer Lunderman | University of Arizona | United States
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Spencer Lunderman | University of Arizona | United States
Data assimilation (DA) is often formulated as a Bayesian state estimation problem, in which the state of the model is updated, but the model itself remains unchanged. In many geophysical problems, e.g., in high spatial resolution modeling of cloud systems, model parameters are uncertain or completely unknown, which implies that "pure" state estimation is of limited use. In such problems, one needs to formulate and solve simultaneously a state and parameter estimation problem, i.e., the model parameters and the state are jointly updated by observations.
We present a new framework for simultaneous state and parameter estimation by combining global Bayesian optimization (GBO) with an ensemble Kalman filter (EnKF). The GBO is a derivative-free optimization technique that minimizes a specified cost function by balancing the need to explore the cost in thus far unknown territory, with the need to zoom in on regions where low costs have been encountered. The cost function we minimize are the residuals of an EnKF (observations minus filter estimates). Our construction is designed to make use of linear/Gaussian approximations and nonlinear/non-Gaussian techniques where appropriate: during the state estimation, the EnKF exploits near linearity of the state estimation problem, and the GBO allows for severe nonlinearities in parameter estimation.
14:30
- CANCELED - Fitness of the ensemble approach in data assimilation system
Kayo Ide | University of Maryland, College Park | United States
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Kayo Ide | University of Maryland, College Park | United States
In ensemble-var data assimilation (DA), ensemble is used in several ways. One is to provide the dynamically-estimated prior (background) error covariance information for the analysis process. Another is to propagate the posterior (analysis) uncertainty information during the model forecast. Ensembles can be used in the evaluation of DA performance as the approximation to the tangent linear or adjoint models. In this talk, we propose a practical procedure to evaluate the fitness of the ensemble approach in place for the approximation to the tangent linear and adjoint model. We also present a simple diagnostics tool to evaluate its spread in the relative sense with respect to the observation error covariance and the necessity of the inflation. Finally we shed light on the application of machine learning techniques to better represent the uncertainty propagation via ensemble.
15:00
- CANCELED - Bayesian hierarchical modeling of spatial rainfall extremes using rate mixtures
Rishikesh Yadav | King Abdullah University of Science and Technology (KAUST) | Saudi Arabia
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Rishikesh Yadav | King Abdullah University of Science and Technology (KAUST) | Saudi Arabia
We develop new flexible univariate models for light-tailed and heavy-tailed data, which extend a hierarchical representation of the generalized Pareto (GP) limit for high threshold exceedances. These models can accommodate departure from asymptotic threshold stability in finite samples while keeping the asymptotic GP distribution as a special (or boundary) case and can capture the tails and the bulk jointly without losing much flexibility. Adapting a Bayesian hierarchical framework, our proposed model captures spatial dependence through a latent process, while the data are assumed to be conditionally independent. We design penalized complexity priors for crucial model parameters, shrinking our proposed spatial Bayesian hierarchical model toward a simpler reference whose marginal distributions are GP with moderately heavy tails. Our model can be fitted in fairly high dimensions using Markov chain Monte Carlo by exploiting the Metropolis-adjusted Langevin algorithm (MALA), which guarantees fast convergence of Markov chains with efficient block proposals for the latent variables. We also develop an adaptive scheme to calibrate the MALA tuning parameters. Moreover, our Bayesian approach avoids the expensive numerical evaluation of multifold integrals in censored likelihood expressions. We demonstrate our new methodology by simulation and application to a dataset of extreme rainfall episodes that occurred in Germany. Our fitted model provides a satisfactory performance and can be successfully used to predict rainfall extremes at unobserved locations.
15:30
Challenges in Simulating Cloud and Precipitation Processes: Frontiers for Bayesian Inference, Model Selection, and Machine Learning
Marcus van Leir Walqui | NASA Goddard Institute for Space Studies | United States
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Marcus van Leir Walqui | NASA Goddard Institute for Space Studies | United States
Errors and uncertainties in numerical weather and climate simulations are often associated with so-called parameterization schemes, which represent the resolved-scale effect of physical processes (such as clouds) that occur at the sub-grid scale. Some errors arise unavoidably out of the coarse representation of microscale physical processes; these errors are poorly understood, and little systematic work has been taken to reduce or quantify them with available observations. Bayesian inference, together with the wealth of available meteorological observations, has the potential to quantify and reduce parameterization uncertainty — a result that would improve physical process understanding as well as forecasts. However, many errors are caused not just by poorly chosen parameter values, but also by inappropriate or sub-optimal structural choices "hard-coded" into the parameterization schemes. We present a new cloud microphysics parameterization framework for addressing both parametric and structural uncertainties such that tools for Bayesian parameter estimation and model selection can be meaningfully applied. We present preliminary results, identify current and outstanding challenges, and suggest some promising potential applications for Bayesian parameter estimation, model selection, and machine learning methodologies in improving physical understanding and numerical representation of cloud and precipitation microphysical processes within numerical models of the atmosphere.