Evaluating the benefits of bayesian hierarchical methods for analyzing heterogeneous environmental datasets: a case study of marine organic carbon fluxes

Large compilations of heterogeneous environmental observations are increasingly available as public databases, allowing researchers to test hypotheses across datasets. Statistical complexities arise when analyzing compiled data due to unbalanced spatial sampling, variable environmental context, mixed measurement techniques, and other reasons. Hierarchical Bayesian modeling is increasingly used in environmental science to describe these complexities, however few studies explicitly compare the utility of hierarchical Bayesian models to simpler and more commonly applied methods. Here we demonstrate the utility of the hierarchical Bayesian approach with application to a large compiled environmental dataset consisting of 5,741 marine vertical organic carbon flux observations from 407 sampling locations spanning eight biomes across the global ocean. We fit a global scale Bayesian hierarchical model that describes the vertical profile of organic carbon flux with depth. Profile parameters within a particular biome are assumed to share a common deviation from the global mean profile. Individual station-level parameters are then modeled as deviations from the common biome-level profile. The hierarchical approach is shown to have several benefits over simpler and more common data aggregation methods. First, the hierarchical approach avoids statistical complexities introduced due to unbalanced sampling and allows for flexible incorporation of spatial heterogeneitites in model parameters. Second, the hierarchical approach uses the whole dataset simultaneously to fit the model parameters which shares information across datasets and reduces the uncertainty up to 95% in individual profiles. Third, the Bayesian approach incorporates prior scientific information about model parameters; for example, the non-negativity of chemical concentrations or mass-balance, which we apply here. We explicitly quantify each of these properties in turn. We emphasize the generality of the hierarchical Bayesian approach for diverse environmental applications and its increasing feasibility for large datasets due to recent developments in Markov Chain Monte Carlo algorithms and easy-to-use high-level software implementations

Mass balance of the Greenland Ice Sheet from 1992 to 2018

In recent decades, the Greenland Ice Sheet has been a major contributor to global sea-level rise1,2, and it is expected to be so in the future3. Although increases in glacier flow4–6 and surface melting7–9 have been driven by oceanic10–12 and atmospheric13,14 warming, the degree and trajectory of today’s imbalance remain uncertain. Here we compare and combine 26 individual satellite measurements of changes in the ice sheet’s volume, flow and gravitational potential to produce a reconciled estimate of its mass balance. Although the ice sheet was close to a state of balance in the 1990s, annual losses have risen since then, peaking at 335 ± 62 billion tonnes per year in 2011. In all, Greenland lost 3,800 ± 339 billion tonnes of ice between 1992 and 2018, causing the mean sea level to rise by 10.6 ± 0.9 millimetres. Using three regional climate models, we show that reduced surface mass balance has driven 1,971 ± 555 billion tonnes (52%) of the ice loss owing to increased meltwater runoff. The remaining 1,827 ± 538 billion tonnes (48%) of ice loss was due to increased glacier discharge, which rose from 41 ± 37 billion tonnes per year in the 1990s to 87 ± 25 billion tonnes per year since then. Between 2013 and 2017, the total rate of ice loss slowed to 217 ± 32 billion tonnes per year, on average, as atmospheric circulation favoured cooler conditions15 and as ocean temperatures fell at the terminus of Jakobshavn Isbræ16. Cumulative ice losses from Greenland as a whole have been close to the IPCC’s predicted rates for their high-end climate warming scenario17, which forecast an additional 50 to 120 millimetres of global sea-level rise by 2100 when compared to their central estimate

Understanding Regional Ice Sheet Mass Balance: Remote Sensing, Regional Climate Models, and Deep Learning

The Antarctic and Greenland ice sheets are experiencing significant mass change with heterogeneous spatial and temporal characteristics and global consequences such as sea level rise affecting millions of people in low-lying coastal areas. Advances in large-scale satellite remote-sensing, modeling, and machine learning have ushered a new era of improved monitoring and understanding of these changes. In this dissertation, we analyze the mass balance of glaciers across the ice sheets at basin and sub-basin scales using satellite gravimetric data from the Gravity Recovery and Climate Experiment (GRACE) mission using a novel regionally-optimized mascon methodology, as well as Mass Budget Method (MBM) estimates from grounding line discharge measurements and surface mass balance from regional climate models. We find that Totten and Moscow University glaciers in the marine sector of East Antarctica, with a total 5-meter sea level rise potential, have been losing mass at a rate of 18.5±6.6 Gt/yr from April 2002 to August 2016. The MBM estimate obtained with RACMO2.3p1 (Regional Atmospheric Climate Model version 2.3 part 1) is in excellent agreement with GRACE at a sub-basin scale, while those obtained with RACMO2.3p2 and MAR (Modèle Atmosphérique Régional) version 3.6.41 show less negative trends. These results are robust with respect to Glacial Isostatic Adjustment (GIA) uncertainty. By extending this methodology to the Amery Ice Shelf drainage basin in East Antarctica, we find this basin is in balance and is also in agreement with MBM/RACMO2.3p1 at a sub-basin scale, while MBM/RACMO2.3p2 and MBM/MAR3.6.41 produce more positive trends. The discrepancies shown by RACMO2.3p2 and MAR3.6.41 in these regions of East Antarctica are attributed to larger mean monthly SMB magnitudes. By adjusting all models to have the same mean magnitude as RACMO2.3p1, all MBM time-series fall into agreement with the independent gravimetric data. Furthermore, we implement the regional optimization approach in the Getz Ice Shelf drainage basin in West Antarctica, where previous studies have shown disagreements between GRACE and MBM estimates, and find that by minimizing leakage in the GRACE estimate, all MBM estimates are in excellent agreement with the gravimetric result. The Getz Ice Shelf basin is found to have a mass loss rate of 22.9±10.9 Gt/yr with an acceleration of 1.6±0.9 Gt/yr2 from April 2002 to November 2015 (the common time-period with the MBM estimates). We use an ensemble of 128,000 GIA forward models to ensure the results are robust with respect to GIA uncertainty. Lastly, we focus on improving the monitoring and understanding of glacier dynamics by implementing a deep Convolutional Neural Network (CNN) to automatically delineate glacier calving fronts from Landsat imagery on the Greenland Ice Sheet. By training the network on Jakobshavn, Sverdrup, and Kangerlussuaq glaciers and testing it on Helheim glacier, we demonstrate that the performance of the network is comparable to that of a human investigator, with a mean CNN error of 1.97 pixels (96.3 meters) compared to a mean human error of 1.89 pixels (92.5 meters) on the same resolution images. Thus, we show that CNNs enable large-scale monitoring of glacier dynamics across the globe, which offers new possibilities for an improved understanding of the processes affecting the mass balance of glaciers. Ultimately, a better understanding of the ice sheets is crucial for a better assessment of the effects of a changing cryosphere and sea level rise around the globe

Detection of Glacier Calving Margins with Convolutional Neural Networks: A Case Study

The continuous and precise mapping of glacier calving fronts is essential for monitoring and understanding rapid glacier changes in Antarctica and Greenland, which have the potential for significant sea level rise within the current century. This effort has been mostly restricted to the slow and painstaking manual digitalization of the calving front positions in thousands of satellite imagery products. Here, we have developed a machine learning toolkit to automatically detect glacier calving front margins in satellite imagery. The toolkit is based on semantic image segmentation using Convolutional Neural Networks (CNN) with a modified U-Net architecture to isolate the calving fronts from satellite images after having been trained with a dataset of images and their corresponding manually-determined calving fronts. As a case study we train our neural network on a varied set of Landsat images with lowered resolutions from Jakobshavn, Sverdrup, and Kangerlussuaq glaciers, Greenland and test the results on images from Helheim glacier, Greenland to evaluate the performance of the approach. The neural network is able to identify the calving front in new images with a mean deviation of 96.3 m from the true fronts, equivalent to 1.97 pixels on average, while the corresponding error for manually-determined fronts on the same resolution images is 92.5 m (1.89 pixels). We find that the trained neural network significantly outperforms common edge detection techniques, and can be used to continuously map out calving-ice fronts with a variety of data products

Automatic delineation of glacier grounding lines in differential interferometric synthetic-aperture radar data using deep learning.

Delineating the grounding line of marine-terminating glaciers-where ice starts to become afloat in ocean waters-is crucial for measuring and understanding ice sheet mass balance, glacier dynamics, and their contributions to sea level rise. This task has been previously done using time-consuming, mostly-manual digitizations of differential interferometric synthetic-aperture radar interferograms by human experts. This approach is no longer viable with a fast-growing set of satellite observations and the need to establish time series over entire continents with quantified uncertainties. We present a fully-convolutional neural network with parallel atrous convolutional layers and asymmetric encoder/decoder components that automatically delineates grounding lines at a large scale, efficiently, and accompanied by uncertainty estimates. Our procedure detects grounding lines within 232 m in 100-m posting interferograms, which is comparable to the performance achieved by human experts. We also find value in the machine learning approach in situations that even challenge human experts. We use this approach to map the tidal-induced variability in grounding line position around Antarctica in 22,935 interferograms from year 2018. Along the Getz Ice Shelf, in West Antarctica, we demonstrate that grounding zones are one order magnitude (13.3 ± 3.9) wider than expected from hydrostatic equilibrium, which justifies the need to map grounding lines repeatedly and comprehensively to inform numerical models