Dallas Foster

Dallas Foster

Postdoctoral Research Associate, MIT

Probabilistic Machine Learning Estimation of Ocean Mixed Layer Depth from Dense Satellite and Sparse In-Situ Observations

Published in Journal of Advances in Modeling Earth Systems (Accepted), 2021

The ocean mixed layer plays an important role in the coupling between the upper ocean and atmosphere across a wide range of time scales. Estimation of the variability of the ocean mixed layer is therefore important for atmosphere-ocean prediction and analysis. The increasing coverage of in-situ Argo profile data allows for an increasingly accurate analysis of the mixed layer depth (MLD) variability associated with deviations from the seasonal climatology. However, sampling rates are not sufficient to fully resolve subseasonal ($<90$ day) MLD variability. Yet, many multivariate observations-based analyses include implicit modeled subseasonal MLD variability. One analysis method is optimal interpolation of in-situ data, but the interior analysis can be improved by leveraging surface data with regression or variational approaches. Here, we demonstrate how machine learning methods and satellite sea surface temperature, salinity, and height facilitate MLD estimation in a pilot study of two regions: the mid-latitude southern Indian and the eastern equatorial Pacific Oceans. We construct multiple machine learning architectures to produce weekly 1/2 degree gridded MLD anomaly fields (relative to a monthly climatology) with uncertainty estimates. We test multiple traditional and probabilistic machine learning techniques to compare both accuracy and probabilistic calibration. We validate our methodology by applying it to ocean model simulations. We find that incorporating sea surface data through a machine learning model improves the performance of spatio-temporal MLD variability estimation compared to optimal interpolation of Argo observations alone. These preliminary results are a promising first step for the application of machine learning to MLD prediction.

Recommended citation: D. Foster, David John Gagne II, Daniel B. Whitt, Probabilistic Machine Learning Estimation of Ocean Mixed Layer Depth from Dense Satellite and Sparse In-Situ Observations, Submitted to Journal of Advances in Modeling Earth Systems, Oct. 2021. https://doi.org/10.1029/2021MS002474

Dynamic Likelihood Filter: A Data Assimilation Scheme that Exploits Hyperbolicity in Wave Problems to Propagate Observations

Published in AMS Monthly Weather Review (Submitted), 2021

We extend the capabilities of the Dynamic Likelihood Filter (DLF). The DLF creates richer and more informative likelihoods from observations by evolving their information along characteristics via stochastic differential equations. Through this approach the DLF approach can generate approximate likelihoods in the near future, enabling Bayesian, conditional prediction. The DLF is particularly effective when observations have small inherent measurement errors and are sparse in space and time, a common situation in geophysical and optics wave problems.

Recommended citation: D. Foster, J.M. Restrepo, Dynamic Likelihood Filter: A Data Assimilation Schemethat Exploits Hyperbolicity in Wave Problems to Propagate Observations, AMS MWR (submitted), 2021

A Bayesian Approach to Regional Decadal Predictability: Sparse Parameter Estimation in High-Dimensional Linear Inverse Models of High-Latitude Sea Surface Temperature Variability

Published in Journal of Climate, 2020

Stochastic reduced models are an important tool in climate systems whose many spatial and temporal scales cannot be fully discretized or underlying physics may not be fully accounted for. One form of reduced model, the linear inverse model (LIM), has been widely used for regional climate predictability studies—typically focusing more on tropical or midlatitude studies. However, most LIM fitting techniques rely on point estimation techniques deriving from fluctuation–dissipation theory. In this methodological study we explore the use of Bayesian inference techniques for LIM parameter estimation of sea surface temperature (SST), to quantify the skillful decadal predictability of Bayesian LIM models at high latitudes. We show that Bayesian methods, when compared to traditional point estimation methods for LIM-type models, provide better calibrated probabilistic skill, while simultaneously providing better point estimates due to the regularization effect of the prior distribution in high-dimensional problems. We compare the effect of several priors, as well as maximum likelihood estimates, on 1) estimating parameter values on a perfect model experiment and 2) producing calibrated 1-yr SST anomaly forecast distributions using a preindustrial control run of the Community Earth System Model (CESM). Finally, we employ a host of probabilistic skill metrics to determine the extent to which an LIM can forecast SST anomalies at high latitudes. We find that the choice of prior distribution has an appreciable impact on estimation outcomes, and priors that emphasize physically relevant properties enhance the model’s ability to capture variability of SST anomalies.

Recommended citation: D. Foster, D. Comeau, and N. M. Urban, A Bayesian Approach to Regional Decadal Predictability: Sparse Parameter Estimation in High-Dimensional Linear Inverse Models of High-Latitude Sea Surface Temperature Variability, \textit{J. Climate}, 33, 6065-6081. https://journals.ametsoc.org/view/journals/clim/33/14/jcliD190769.xml

On the Definition of Marginal Ice Zone Width

Published in Journal of Atmospheric and Oceanic Technology, 2017

Sea ice features a dense inner pack ice zone surrounded by a marginal ice zone (MIZ) in which the sea ice properties are modified by interaction with the ice-free open ocean. The width of the MIZ is a fundamental length scale for polar physical and biological dynamics. Several different criteria for establishing MIZ boundaries have emerged in the literature—wave penetration, floe size, sea ice concentration, etc.—and a variety of definitions for the width between the MIZ boundaries have been published. Here, three desirable mathematical properties for defining MIZ width are proposed: invariance with respect to translation and rotation on the sphere; uniqueness at every point in the MIZ; and generality, including nonconvex shapes. The previously published streamline definition is shown to satisfy all three properties, where width is defined as the arc length of a streamline through the solution to Laplaces’s equation within the MIZ boundaries, while other published definitions each satisfy only one of the desired properties. When defining MIZ spatial average width from streamline results, the rationale for averaging with respect to distance along both MIZ boundaries was left implicit in prior studies. Here it is made rigorous by developing and applying the mathematics of an analytically tractable idealization of MIZ geometry—the eccentric annulus. Finally, satellite-retrieved Arctic sea ice concentrations are used to investigate how well streamline-based MIZ spatial average width is approximated by alternative definitions that lack desirable mathematical properties or local width values but offer computational efficiency.

Recommended citation: C. Strong, D. Foster, E. Cherkaev, I. Eisenman, K.M. Golden, On the definition and analysis of marginal ice zone width, \textit{Journal of Atmospheric and Oceanic Technology}, Vol. 34, 2017. https://doi.org/10.1175/JTECH-D-16-0171.1