To resolve the bed elevation of Antarctica, we present DeepBedMap – a novel machine learning method that can produce Antarctic bed topography with
adequate surface roughness from multiple remote sensing data inputs. The super-resolution deep convolutional neural network model is trained on
scattered regions in Antarctica where high-resolution (250
The bed of the Antarctic ice sheet is one of the most challenging surfaces on Earth to map due to the thick layer of ice cover. Knowledge of bed
elevation is however essential for estimating the volume of ice currently stored in the ice sheets and for input to the numerical models that are
used to estimate the contribution ice sheets are likely to make to sea level in the coming century. The Antarctic ice sheet is estimated to hold a
sea level equivalent (SLE) of 57.9
Estimating bed elevation directly from geophysical observations primarily uses ice-penetrating-radar methods
To overcome these limitations, indirect methods of estimating bed elevation have been developed, and these include inverse methods and spatial
statistical methods. Inverse methods use surface observations combined with glaciological-process knowledge to determine ice thickness
We present a deep-neural-network method that is trained on direct ice-penetrating-radar observations over Antarctica and one which has features from
both the indirect inverse modelling and spatial statistical methodologies. An artificial neural network, loosely based on biological neural networks,
is a system made up of neurons. Each neuron comprises a simple mathematical function that takes an input to produce an output value, and neural
networks work by combining many of these neurons together. The term deep neural network is used when there is not a direct function mapping between
the input data and final output but two or more layers that are connected to one another
Super resolution involves the processing of a low-resolution raster image into a higher-resolution one
Network conditioning means having a neural network process one source of information in the context of other sources
An example similar to this DEM super-resolution problem is the classic problem of pan-sharpening, whereby a blurry low-resolution multispectral image
conditioned with a high-resolution panchromatic image can be turned into a high-resolution multispectral image. There is ongoing research into the use
of deep convolutional neural networks for pan-sharpening
Our convolutional neural network model works on 2-D images, so we ensure all the datasets are in a suitable raster grid format. Ground-truth bed
elevation points picked from radar surveys (see Table
High-resolution ground-truth datasets from ice-penetrating-radar surveys (collectively labelled as
Remote sensing dataset inputs into the DeepBedMap neural network model.
DeepBedMap generator model architecture composed of three modules. The input module processes each of the four inputs (BEDMAP2,
To create the training dataset, we use a sliding window to obtain square tiles cropped from the high-resolution (250
Our DeepBedMap model is a generative adversarial network
The objective of the main super-resolution generator model
Noting that the objective of the generator
DeepBedMap_DEM over the entire Antarctic continent. Plotted on an Antarctic stereographic projection (EPSG:3031) with elevation referenced to the WGS84 datum. Grounding line is plotted as thin black line. Purple box shows Pine Island Glacier extent used in Fig.
DeepBedMap's model architecture is adapted from the Enhanced Super-Resolution Generative Adversarial Network
The main differences between the DeepBedMap generator model and ESRGAN are the custom input block at the beginning and the deformable convolutional
layers at the end. The custom input block is designed to handle the prior low-resolution BEDMAP2 image and conditional inputs (see
Table
Besides the generator model, there is a separate adversarial discriminator model
Here we present the output digital elevation model (DEM) of the super-resolution DeepBedMap neural network model and compare it with bed topography
produced by other methods. The resulting DEM has a 250
Comparison of interpolated bed elevation grid products over Pine Island Glacier (see extent in Fig.
Close-up views of DeepBedMap_DEM around Antarctica. Panels
We now highlight some qualitative observations of DeepBedMap_DEM's bed topography beneath Pine Island Glacier (Fig.
Spatial 2-D view of grids over Thwaites Glacier, West Antarctica. Plotted on an Antarctic stereographic projection (EPSG:3031) with elevation and SD values in metres referenced to the WGS84 datum.
We compare the roughness of DeepBedMap_DEM vs. BedMachine Antarctica with ground-truth grids from processed Operation IceBridge data
Taking a 1-D transect over the 250
Comparing bed elevation
In Sect.
Another issue is that DeepBedMap will often pick up details from the high-resolution ice surface elevation model
The hummocky wave-like (W) patterns we observe over the relatively flat and slower-flowing areas are likely to result from surface megadune
structures
In Sect.
DeepBedMap_DEM manages to capture much of the rough topography found in the Operation IceBridge ground-truth data, especially near the coast (see
Fig.
In general, DeepBedMap_DEM produces a topography that is rougher, with SD values more in line with those observed in the ground truth (see
Fig.
In terms of bed roughness anisotropy, DeepBedMap is able to capture aspects of it from the ground-truth grids by combining (1) ice flow direction via
the ice velocity grid's
The DeepBedMap model is trained only on a small fraction of the area of Antarctica, at less than 0.1 % of the grounded-ice regions (excluding ice
shelves and islands). This is because the pixel-based convolutional neural network cannot be trained on sparse survey point measurements, nor is it
able to constrain itself with track-based radar data. As the along-track resolution of radar bed picks are much smaller than 250
An inherent assumption in this methodology is that the training datasets have sampled the variable bed lithology of Antarctica
The way forward for DeepBedMap is to combine quality datasets gathered by radioglaciology and remote sensing specialists, with new advancements made
by the ice sheet modelling and machine learning community. While care has been taken to source the best possible datasets (see
Tables
A way to increase the number of high-resolution ground-truth training data further is to look at formerly glaciated beds. There are a wealth of data
around the margins of Antarctica in the form of swath bathymetry data and also on land in areas like the former Laurentide ice sheet. The current
model architecture does not support using solely “elevation” as an input, because it also requires ice elevation, ice surface velocity and snow
accumulation data. In order to support using these paleobeds as training data, one could do one of the following:
Have a paleo-ice-sheet model that provides these ice surface observation parameters. However, continent-scale ice sheet models quite often
produce only kilometre-scale outputs, and there are inherent uncertainties with past ice sheet reconstructions that may bias the resulting trained
neural network model. Modularize the neural network model to support different sets of training data. One main branch would be trained like a single-image super-resolution problem
From a satellite remote sensing perspective, it is important to continue the work on increasing spatial coverage and measurement precision. Some of
the conditional datasets used such as REMA
The DeepBedMap model's modular design (see Sect.
The DeepBedMap convolutional neural network method presents a data-driven approach to resolve the bed topography of Antarctica using existing data. It
is an improvement beyond simple interpolation techniques, generating high-spatial-resolution (250
The work here is intended not to discourage the usage of other inverse modelling or spatial statistical techniques but to introduce an alternative
methodology, with an outlook towards combining each methodology's strengths. Once properly trained, the DeepBedMap model runs quickly (about 3 min for the
whole Antarctic continent) and produces realistic rough topography. Combining the DeepBedMap model with more physically based mass conservation
inverse approaches
The loss function, or cost function, is a mathematical function that maps a set of input variables to an output loss value. The loss value can be thought of as a weighted sum of several error metrics between the neural network's prediction and the expected output or ground truth. It is this loss value which we want to minimize so as to train the neural network model to perform better, and we do this by iteratively optimizing the parameters in the loss function. Following this are the details of the various loss functions that make up the total loss function of the DeepBedMap generative adversarial network model.
To bring the pixel values of the generated images closer to those of the ground truth, we first define the content-loss function
Next, we define an adversarial loss to encourage the production of high-resolution images
The generator network's adversarial loss is in a symmetrical form:
We further define a topographic loss so that the elevation values in the super-resolved image make topographic sense with respect to the original low-resolution image. Specifically, we want the mean value of each 4
First, we apply a 4
Lastly, we define a structural loss that takes into account luminance, contrast and structural information between the predicted and ground-truth
images. This is based on the structural similarity index
Finally, we compile the loss functions for the discriminator and generator networks as follows:
The neural networks were developed using Chainer v7.0.0
To check for overfitting, we evaluate the generative adversarial network model using the validation dataset after each epoch using two performance metrics – a peak signal-to-noise ratio (PSNR) metric for the generator and an accuracy metric for the discriminator. Training stops when these validation performance metrics show little improvement, roughly at 140 epochs.
Optimized hyperparameter settings.
Next, we conduct a full evaluation on an independent test dataset, comparing the model's predicted grid output with actual ground-truth
Neural networks contain a lot of hyperparameter settings that need to be decided upon, and generative adversarial networks are particularly sensitive
to different hyperparameter settings. To stabilize model training and obtain better performance, we tune the hyperparameters (see
Table
Python code for data preparation, neural network model training and visualization of model outputs is freely available at
The DeepBedMap_DEM is available from Zenodo at
WJL was responsible for data curation, formal analysis, methodology, software, visualization and writing the original draft. HJH was responsible for funding acquisition and supervision. Both authors conceptualized the work and contributed to the reviewing and editing stages of the writing.
The authors declare that they have no conflict of interest.
We are grateful to Robert Bingham and Edward King for the Pine Island Glacier and Carlson Inlet data and to all the other researchers in the British Antarctic Survey and Operation IceBridge team for providing free access to the high-resolution bed elevation datasets around Antarctica. A special thanks to Ruzica Dadic for her help in reviewing draft versions of this paper. This research was funded by the Royal Society of New Zealand's Rutherford Discovery Fellowship (contract RDF-VUW1602), with additional support from the Erasmus+ programme and International Glaciological Society early-career travel award for presenting earlier versions of this work at the 2019 EGU General Assembly and IGS Symposium on Five Decades of Radioglaciology.
This research has been supported by the Royal Society of New Zealand (Rutherford Discovery Fellowship – contract no. RDF-VUW1602).
This paper was edited by Olivier Gagliardini and reviewed by Martin Siegert and one anonymous referee.