A Case Study Competition Among Methods for Analyzing Large Spatial Data

The Gaussian process is an indispensable tool for spatial data analysts. The onset of the "big data" era, however, has lead to the traditional Gaussian process being computationally infeasible for modern spatial data. As such, various alternatives to the full Gaussian process that are more amenable to handling big spatial data have been proposed. These modern methods often exploit low-rank structures and/or multi-core and multi-threaded computing environments to facilitate computation. This study provides, first, an introductory overview of several methods for analyzing large spatial data. Second, this study describes the results of a predictive competition among the described methods as implemented by different groups with strong expertise in the methodology. Specifically, each research group was provided with two training datasets (one simulated and one observed) along with a set of prediction locations. Each group then wrote their own implementation of their method to produce predictions at the given location and each was subsequently run on a common computing environment. The methods were then compared in terms of various predictive diagnostics. Supplementary materials regarding implementation details of the methods and code are available for this article online.

ELECTRONIC SUPPLEMENTARY MATERIAL

Supplementary materials for this article are available at 10.1007/s13253-018-00348-w.

An assessment of forward and inverse GIA solutions for Antarctica

In this work we assess the most recent estimates of glacial isostatic adjustment (GIA) for Antarctica, including those from both forward and inverse methods. The assessment is based on a comparison of the estimated uplift rates with a set of elastic-corrected GPS vertical velocities. These have been observed from an extensive GPS network and computed using data over the period 2009-2014. We find systematic underestimations of the observed uplift rates in both inverse and forward methods over specific regions of Antarctica characterized by low mantle viscosities and thin lithosphere, such as the northern Antarctic Peninsula and the Amundsen Sea Embayment, where its recent ice discharge history is likely to be playing a role in current GIA. Uplift estimates for regions where many GIA models have traditionally placed their uplift maxima, such as the margins of Filchner-Ronne and Ross ice shelves, are found to be overestimated. GIA estimates show large variability over the interior of East Antarctica which results in increased uncertainties on the ice-sheet mass balance derived from gravimetry methods.

Spatial and temporal Antarctic Ice Sheet mass trends, glacio-isostatic adjustment, and surface processes from a joint inversion of satellite altimeter, gravity, and GPS data

We present spatiotemporal mass balance trends for the Antarctic Ice Sheet from a statistical inversion of satellite altimetry, gravimetry, and elastic-corrected GPS data for the period 2003-2013. Our method simultaneously determines annual trends in ice dynamics, surface mass balance anomalies, and a time-invariant solution for glacio-isostatic adjustment while remaining largely independent of forward models. We establish that over the period 2003-2013, Antarctica has been losing mass at a rate of -84 ± 22 Gt yr^-1, with a sustained negative mean trend of dynamic imbalance of -111 ± 13 Gt yr^-1. West Antarctica is the largest contributor with -112 ± 10 Gt yr^-1, mainly triggered by high thinning rates of glaciers draining into the Amundsen Sea Embayment. The Antarctic Peninsula has experienced a dramatic increase in mass loss in the last decade, with a mean rate of -28 ± 7 Gt yr^-1 and significantly higher values for the most recent years following the destabilization of the Southern Antarctic Peninsula around 2010. The total mass loss is partly compensated by a significant mass gain of 56 ± 18 Gt yr^-1 in East Antarctica due to a positive trend of surface mass balance anomalies.

Multivariate spatio-temporal modelling for assessing Antarctica's present-day contribution to sea-level rise

Antarctica is the world's largest fresh-water reservoir, with the potential to raise sea levels by about 60 m. An ice sheet contributes to sea-level rise (SLR) when its rate of ice discharge and/or surface melting exceeds accumulation through snowfall. Constraining the contribution of the ice sheets to present-day SLR is vital both for coastal development and planning, and climate projections. Information on various ice sheet processes is available from several remote sensing data sets, as well as in situ data such as global positioning system data. These data have differing coverage, spatial support, temporal sampling and sensing characteristics, and thus, it is advantageous to combine them all in a single framework for estimation of the SLR contribution and the assessment of processes controlling mass exchange with the ocean. In this paper, we predict the rate of height change due to salient geophysical processes in Antarctica and use these to provide estimates of SLR contribution with associated uncertainties. We employ a multivariate spatio-temporal model, approximated as a Gaussian Markov random field, to take advantage of differing spatio-temporal properties of the processes to separate the causes of the observed change. The process parameters are estimated from geophysical models, while the remaining parameters are estimated using a Markov chain Monte Carlo scheme, designed to operate in a high-performance computing environment across multiple nodes. We validate our methods against a separate data set and compare the results to those from studies that invariably employ numerical model outputs directly. We conclude that it is possible, and insightful, to assess Antarctica's contribution without explicit use of numerical models. Further, the results obtained here can be used to test the geophysical numerical models for which in situ data are hard to obtain. © 2015 The Authors. Environmetrics published by John Wiley & Sons Ltd.

Resolving the Antarctic contribution to sea-level rise: a hierarchical modelling framework

Determining the Antarctic contribution to sea-level rise from observational data is a complex problem. The number of physical processes involved (such as ice dynamics and surface climate) exceeds the number of observables, some of which have very poor spatial definition. This has led, in general, to solutions that utilise strong prior assumptions or physically based deterministic models to simplify the problem. Here, we present a new approach for estimating the Antarctic contribution, which only incorporates descriptive aspects of the physically based models in the analysis and in a statistical manner. By combining physical insights with modern spatial statistical modelling techniques, we are able to provide probability distributions on all processes deemed to play a role in both the observed data and the contribution to sea-level rise. Specifically, we use stochastic partial differential equations and their relation to geostatistical fields to capture our physical understanding and employ a Gaussian Markov random field approach for efficient computation. The method, an instantiation of Bayesian hierarchical modelling, naturally incorporates uncertainty in order to reveal credible intervals on all estimated quantities. The estimated sea-level rise contribution using this approach corroborates those found using a statistically independent method. © 2013 The Authors. Environmetrics Published by John Wiley & Sons, Ltd.

An anatomically unbiased approach for analysis of renal BOLD magnetic resonance images

Oxygenation defects may contribute to renal disease progression, but the chronology of events is difficult to define in vivo without recourse to invasive methodologies. Blood oxygen level-dependent magnetic resonance imaging (BOLD MRI) provides an attractive alternative, but the R2* signal is physiologically complex. Postacquisition data analysis often relies on manual selection of region(s) of interest. This approach excludes from analysis significant quantities of biological information and is subject to selection bias. We present a semiautomated, anatomically unbiased approach to compartmentalize voxels into two quantitatively related clusters. In control F344 rats, low R2* clustering was located predominantly within the cortex and higher R2* clustering within the medulla (70.96 ± 1.48 vs. 79.00 ± 1.50; 3 scans per rat; n = 6; P < 0.01) consistent anatomically with a cortico-medullary oxygen gradient. An intravenous bolus of acetylcholine caused a transient reduction of the R2* signal in both clustered segments ( P < 0.01). This was nitric oxide dependent and temporally distinct from the hemodynamic effects of acetylcholine. Rats were then chronically infused with angiotensin II (60 ng/min) and rescanned 3 days later. Clustering demonstrated a disruption of the cortico-medullary gradient, producing less distinctly segmented mean R2* clusters (71.30 ± 2.00 vs. 72.48 ± 1.27; n = 6; NS). The acetylcholine-induced attenuation of the R2* signal was abolished by chronic angiotensin II infusion, consistent with reduced nitric oxide bioavailability. This global map of oxygenation, defined by clustering individual voxels on the basis of quantitative nearness, might be more robust in defining deficits in renal oxygenation than the absolute magnitude of R2* in small, manually selected regions of interest defined exclusively by anatomical nearness.