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.
16:30
- CANCELED - Bayesian Inference for Cloud and Precipitation Model Parameter Estimation
Derek Posselt | Jet Propulsion Laboratory, California Institute of Technology | United States
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Derek Posselt | Jet Propulsion Laboratory, California Institute of Technology | United States
In Earth science research, models of complex processes are required to make simplifying assumptions that often take the form of a set of rate parameters. Parameters may not be measurable or have physical units, and their values reflect assumptions about the geophysical system of interest. Poorly specified parameter values impart a measure of uncertainty (and potentially bias) to the results of any experiment. Bayesian inference can be used to estimate optimal parameter values and to quantify their uncertainty.
We focus on Bayesian inference of model parameters in simulations of clouds and precipitation. Models are used as laboratories in experiments designed to discover how cloud processes function, and are central to predictions of future climate-change induced changes in precipitation. The challenges of modeling cloud processes include: nonlinear relationships between parameters and geophysical variables (e.g., precipitation rate); parameters that are bounded (e.g., positive definite); and parameters that may not be directly observable. In addition, Bayesian solutions to parameter estimation problems for clouds and precipitation often require a reduction in dimensionality via parameter sensitivity analysis. We show results from several studies that illustrate the characteristics of the cloud and precipitation estimation problem, and also discuss the pros and cons of linear (e.g., Kalman filter) approximations to nonlinear Bayesian solutions.
17:00
Data assimilation on convective scale with positivity preservation
Tijana Janjic Pfander | University of Munich | Germany
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Tijana Janjic Pfander | University of Munich | Germany
The initial state for a geophysical numerical model is produced by combining observational data with a short-range model simulation using a data assimilation algorithm. Particularly challenging is the application of these algorithms in weather forecasting at the convective scale. For convective scale applications, high resolution nonlinear numerical models are used. In addition, intermittent convection is present in the simulations and observations, the state vector has a large size, one third of which contains variables whose non-negativity needs to be preserved and the estimation of the state vector has to be done frequently in order to catch fast changing convection.
In current practice, many data assimilation methods do not preserve the non-negativity of variables. We present an algorithm for forecasting at the convective scale, that is based on the ensemble Kalman filter (EnKF) and quadratic programming. This algorithm outperforms the EnKF as well as the EnKF with the lognormal change of variables for all ensemble sizes. For a model that was designed to mimic the important characteristics of convective motion, preserving non-negativity of rain and conserving mass reduce the error in all fields; they prevent the data assimilation algorithm from producing artificial mass or artificial rain. Finally, important reduction in the computational costs has been recently achieved, making it possible to apply this algorithm in high dimensional weather forecasting problems.
17:30
Geomagnetic data assimilation, a window to the Earth’s core dynamics
Sabrina Sanchez | Max Planck Institute for Solar System Research | Germany
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Sabrina Sanchez | Max Planck Institute for Solar System Research | Germany
The Earth’s core magnetic field is generated by a natural dynamo mechanism bearing a wide range of temporal variations. Such variability has been globally recorded through high precision satellite data through the past three decades and magnetic observatory records for the past century. Using large-scale surface data to constrain the global state of the geodynamo, remains, however, a challenging ill-posed inverse problem. One way to address this problem is by using data assimilation to merge geomagnetic data with numerical dynamo simulations. We tackle different aspects of geomagnetic data assimilation through an EnKF approach. One of these aspects is the exploration of the background model covariance from geodynamo simulations. Given the large thickness of the liquid core and the high degree of geostrophy of the system, selection rules and equatorial symmetries can be interpreted in spectral space. We present the impact of spectral covariance localization in the assimilation. Another important aspect of geomagnetic data assimilation is the rescaling of the simulations for comparison with observations. Since the simulations are performed in a parameter regime far from the Earth’s, rescaling errors can strongly impact and bias the assimilation. We explore the impact of these bias in the assimilation. Preliminary applications of the assimilation of geophysical data, such as geomagnetic field models based on satellite and observatory data are shown.
18:00
- NEW - Parameter and state estimation with ensemble Kalman filter based algorithms for convective-scale applications
Yvonne Ruckstuhl | University of Munich | Germany
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Yvonne Ruckstuhl | University of Munich | Germany
Tijana Janjic Pfander | University of Munich | Germany
Representation of clouds in convection‐permitting models is sensitive to numerical weather prediction (NWP) model parameters that are often very crudely known (for example roughness length). Our goal is to allow for uncertainty in these parameters and estimate them from data using the ensemble Kalman filter (EnKF) approach. However, to deal with difficulties associated with convective‐scale applications, such as non‐Gaussianity and constraints on state and parameter values, modifications to classical EnKF are necessary. Here we evaluate and extend several recently developed EnKF‐based algorithms that either incorporate constraints such as mass conservation and positivity of precipitation explicitly or introduce higher order moments on the joint state and parameter estimation problem. We compare their results with the localized EnKF for a common idealized test case. The test case uses perfect model experiments with the one‐dimensional modified shallow‐water model, which was designed to mimic important properties of convection. The sensitivity of the results to the number of ensemble members and localization, as well as observation coverage and frequency, is shown. Although all algorithms are capable of reducing the initial state and parameter errors, it is concluded that mass conservation is important when the localization radius is small and/or the observations are sparse. In addition, accounting for higher order moments in the joint space and parameter estimation problem is beneficial when the ensemble size is large enough or when applied to parameter estimation only.