Feature-based data assimilation in geophysics

Morzfeld, Matthias; Adams, Jennifer; Lunderman, Spencer; Orozco, Rafael

doi:10.5194/npg-2017-52

Cited by 11 publications

(14 citation statements)

References 38 publications

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“…In parameter estimation problems for chaotic dynamical systems, such as those arising in climate modeling [12,34,65], data may only be available in time-averaged form; or it may be desirable to study time-averaged quantities in order to ameliorate difficulties arising from the complex objective functions, with multiple local minima, which arise from trying to match trajectories [1]. Indeed the idea fits the more general framework of feature-based data assim-ilation introduced in [51] which, in turn, is closely related to the idea of extracting sufficient statistics from the raw data [21]. The methodology developed in this section underpins similar work conducted for a complex climate model described in the paper [12].…”

Section: Time-averaged Datamentioning

confidence: 99%

Calibrate, emulate, sample

Cleary

Garbuno-Iñigo

Lan

et al. 2021

Journal of Computational Physics

173

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Many parameter estimation problems arising in applications are best cast in the framework of Bayesian inversion. This allows not only for an estimate of the parameters, but also for the quantification of uncertainties in the estimates. Often in such problems the parameterto-data map is very expensive to evaluate, and computing derivatives of the map, or derivative-adjoints, may not be feasible. Additionally, in many applications only noisy evaluations of the map may be available. We propose an approach to Bayesian inversion in such settings that builds on the derivative-free optimization capabilities of ensemble Kalman inversion methods. The overarching approach is to first use ensemble Kalman sampling (EKS) to calibrate the unknown parameters to fit the data; second, to use the output of the EKS to emulate the parameter-to-data map; third, to sample from an approximate Bayesian posterior distribution in which the parameter-to-data map is replaced by its emulator. This results in a principled approach to approximate Bayesian inference that requires only a small number of evaluations of the (possibly noisy approximation of the) parameter-to-data map. It does not require derivatives of this map, but instead leverages the documented power of ensemble Kalman methods. Furthermore, the EKS has the desirable property that it evolves the parameter ensembles towards the regions in which the bulk of the parameter posterior mass is located, thereby locating them well for the emulation phase of the methodology. In essence, the EKS methodology provides a cheap solution to the design problem of where to place points in parameter space to efficiently train an emulator of the parameter-to-data map for the purposes of Bayesian inversion.

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Section: Time-averaged Datamentioning

confidence: 99%

Calibrate, emulate, sample

Cleary

Garbuno-Iñigo

Lan

et al. 2021

Journal of Computational Physics

173

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“…Rather, we extract "features" from the data and find model parameters such that the model produces comparable features. The features are based on PSDs of the Sint-2000, PADM2M and CALS10k.2 data sets as well as the reversal rate, time average VADM and VADM standard deviation (see Morzfeld et al (2018) for a more in depth explanation of feature-based approaches to data assimilation).…”

Section: Feature-based Likelihoodsmentioning

confidence: 99%

“…Buffett and Matsui (2015) derived an extension of the B13 model to extend it to time scales of thousands of years, by adding a time-correlated noise process. An extension of B13 to represent changes in reversal rates over the past 150 Myrs is considered by Morzfeld et al (2018). Its use for predicting the probability of an imminent reversal of Earth's dipole is described by Morzfeld et al (2017); Buffett and Davis (2018).…”

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confidence: 99%

“…For example, a point-wise mismatch of model and data is not useful when two different data sets report two different values for the same quantity (see, e.g., Figure 1). We thus substitute likelihoods based on point-wise mismatch of model and data by a "featurebased" likelihood, as discussed by Maclean et al (2017); Morzfeld et al (2018). A feature-based likelihood is based on error in "features" extracted from model outputs and data rather than the usual point-wise error.…”

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confidence: 99%

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A comprehensive model for the kyr and Myr time scales of Earth's axial magnetic dipole field

Morzfeld¹,

Buffett²

2018

Preprint

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Abstract. We consider a stochastic differential equation model for Earth's axial magnetic dipole field. The model's parameters are estimated using diverse and independent data sources that had previously been treated separately. The result is a numerical model that is informed by the full paleomagnetic record on kyr to Myr time scales and whose outputs match data of Earth's dipole in a precisely defined feature-based sense. Specifically, we compute model parameters and associated uncertainties that lead to model outputs that match spectral data of Earth's axial magnetic dipole field but our approach also reveals difficulties with simultaneously matching spectral data and reversal rates. This could be due to model deficiencies or inaccuracies in the limited amount of data. More generally, the approach we describe can be seen as an example of an effective strategy for combining diverse data sets that is particularly useful when the amount of data is limited.

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“…Thus, it is not straightforward to compare KTF17 to LES output. We address this issue by using "feature-based" likelihoods (Maclean et al, 2017;Morzfeld et al, 2018). The basic idea is that compressing the data into suitable features can bridge gaps between drastically simplified models and complex processes.…”

mentioning

confidence: 99%

Estimating parameters of the nonlinear cloud and rain equation from a large-eddy simulation

Lunderman

Morzfeld

Glassmeier

et al. 2020

Physica D: Nonlinear Phenomena

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Predator-prey dynamics have been suggested as simplified models of stratocumulus clouds, with rain acting as a predator of the clouds. We describe a mathematical and computational framework for estimating the parameters of a simplified model from a large eddy simulation (LES). In our method, we extract cycles of cloud growth and decay from the LES and then search for parameters of the simplified model that lead to similar cycles. We implement our method via Markov chain Monte Carlo. Required error models are constructed based on variations of the LES cloud cycles. This computational framework allows us to test the robustness of our overall approach and various assumptions, which is essential for the simplified model to be useful. Our main conclusion is that it is indeed possible to calibrate a predator-prey model so that it becomes a reliable, robust, but simplified representation of selected aspects of a LES. In the future, such models may then be used as a quantitative tool for investigating important questions in cloud microphysics.

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Feature-based data assimilation in geophysics

Cited by 11 publications

References 38 publications

Calibrate, emulate, sample

Calibrate, emulate, sample

A comprehensive model for the kyr and Myr time scales of Earth's axial magnetic dipole field

Estimating parameters of the nonlinear cloud and rain equation from a large-eddy simulation

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