# Calculating glacier volume change from Space

This article on glacier volume change was written by Ethan Lee, from Newcastle University.

## Introduction

Around the world, glaciers provide water for 2 billion people, however almost all glaciers are melting and shrinking reducing the amount of water available to them. We need to know how much glaciers are melting by and at what rate, because glacier melt contributes to sea level rise1, 2 and reduce water storage for the future. Glaciers will continue to melt and will increase in their rate of melt globally due to future climate change3, 4. But how do we know how much glacier volume has been lost?

However, many glaciers are difficult to access, and only a few have long-term measurements. We can use satellite imagery, from the 1970s onwards, to map glacier extent change, and to work out how much snow and ice has been lost from glaciers each year. This includes both how much the glacier has shrunken, with the terminus of the glacier receding, but also how much the glacier has thinned, with surface of the glacier melting away (shown in the image below).

## Using satellites to determine glacier mass and volume change

Satellites are used extensively to map and understand glacier changes in glaciological research. They have primarily been used to create inventories of glaciers globally6, 7, map glacier recession by mapping glacial depositional landforms to reconstruct past glacial extents8, 9, 10, and map glacier extents over time from old satellite images or aerial photography11, 12.

Mapping extents are great, and understanding how much glaciers have, and are, retreating by provides us with information on the state of glaciers. However, frontal retreat is not the entire story and understanding glacial change in three-dimensions allows us to understand more of the change being seen.

## How do we determine three-dimensional glacier change?

Satellites are the answer. Satellites can give us the elevation of the ground they take an image of, which will include the surface elevation of the ice at that period of time. These are called Digital Elevation Models (DEMs). There are a number of global DEMs generated from these satellites.

Some of these DEMs are generated from overlapping satellite images (such as ASTER imagery). Other sensors use different techniques. The ICESat satellite, for example, measures ice surface elevation along a track, and repeated tracks show elevation change through time.

DEMs can also be generated from aerial photographs if they have stereo-pairs, this is if they have two (or more) overlapping images taken at the same time. There are a number of satellite platforms and arial systems that provide us with such information:

### DEMs of Difference

Using DEM data, if we have two DEMs that cover the same area that were taken at different dates, we can ‘difference’ these images to create a ‘image of difference.’  Differencing two DEMs is as simple as taking away the values from one image from the other. This is shown simply by the equation:

Where dh is the change in surface elevation, and ht2 and ht1 are the two DEMs taken at time1 and time2 . This will give the total elevation change between the two dates.

We want to then know the rate of this change, and how this rate has increased or decreased over time. Calculating the rate is dividing the total elevation change by the difference in time between the two DEMs. This is shown by the equation:

Where dh/dt is the elevation change over time, this is generally shown per year or per annum (yr-1 / a-1), and t is the length of time (in years) between the two DEM images. The outcome of this is an image showing where glacial ice is thinning (negative change) and places where ice is increasing in height (positive change). Examples of where you can find such data to view or to download and use are from Theia cartographica and from Hugonnet et al.2.

### Calculating glacier volume change

Due to elevation change of the glaciers surface not providing much useful information, we convert elevation change into information that can be used to aid in comparisons. We can convert elevation change into volume change (km3), that can be used to understand any potential sea level rise from glacial melt. Volume change is shown in the equation below:

Where V is the volume loss you want to figure out for each cell, cell size is the ‘resolution’ of the DEM. Total volume loss can then be summed for each glacier.

Many scientists also show ice loss as ‘meters water equivalent (m w. e.)’ which is based on the density of ice. For example a value of -1.0 m w.e. per year is the same as an annual glacier-wide ice elevation loss of ~1.1 m per year, as the density of ice is 0.9 times the density of water.

### DEMs of difference in the Himalaya

An example of using DEM differencing to understand glacier change is by King et al 13 in understanding mass loss of Himalayan glaciers since ~1974-2000, and 2000-~2015 in relation to glacial lakes.

King et al found that the rate of mass loss of Himalayan glaciers had change very little between these two time periods but had seen that after the year 2000 glaciers that had a glacier lake in front of them lost more glacial ice than those that did not. This can be seen in the figure below, where a glacial lake (blue outlines) is in front of a glacier there is substantially more melting (redder over the glacier).

## Understanding glacier mass and volume changes before the satellite era

Of course, since satellites have only really been around and used in scientific research since 1972, when LANDSAT 1 was the first open-access satellite for scientific use, and the use of stereophotography from limited missions, we have been able to fully observe glaciers globally. But what about for times before 1972? How do we know if glaciers have been losing mass slower, faster, or at the same rate as they are currently? Luckily, we have other sources and methods that we can use to fill in this ‘lost time’.

### Volume change using topographic maps

In countries where there have been extensive mapping expeditions to create topographic maps in regions where glaciers exist, we can use these to generate DEMs. This is very involved process that requires to use of a Geographic Information System (GIS) to transform a paper-based map into a raster image and DEM using contours (example of how this is done here).

When this done, we can then do a simple DEM differencing similar to the above. Another way we can understand mass loss since is by using the features glaciers have left to inform not only past glacial positions but thickness (or elevation).

### Volume Change using glacial features

One such study by Lee et al.14 was able to push back mass change rates within the entire Himalaya from ~1970s, to when glaciers started to retreat from their Little Ice Age extents (400-700 years ago). The Little Ice Age was one of the last known periods where, almost globally, glaciers advanced.

To do this, Lee et al14 mapped the glacial moraines in front of glaciers and reconstructed their glacial extents to these moraines. Moraines being a mass of rock and sediment that is carried and deposited by a glacier at its edges or frontal position and look like small ridges. Using these moraines, it can be assumed that the moraine crest (the top of the moraine ridge) can represent the thickness of the glacier, and if we assume this, we can interpolate between other moraine crests to generate a flat glacier surface to represent its former surface elevation. With this, we can then do a difference between a modern DEM with the interpolated surface elevation of the glacier.

With this, Lee et al. determined that glaciers across the Himalaya have lost at least 40% of their area, and 390-586 km3 of their glacier volume, with a mass loss of -0.011 and -0.020 m w.e. yr-1. When compared to studies looking are more resent mass loss within the Himalaya 15, this is ten-times lower then present day mass loss rates. This provides important context on the state of glaciers and their response to modern day climate change when the longer time context is taken into account.

I am a glaciologist that focuses on glaciological changes from past and modern climatic change. I use remote sensing to monitor and map glaciers and glacial geomorphology in order to reconstruct glacier extents, thickness and dynamics. Past research has focused on glacial changes within the Himalaya since the Little Ice Age (400-700 years ago).

More recently my PhD has been on determining the timing, nature, and extent of palaeoglacier advances in the tropical Andes, Peru. To do this I have used surface exposure dating, geomorphology and glacier modelling (PISM).

## References

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2.         Hugonnet R, McNabb R, Berthier E, Menounos B, Nuth C, Girod L, et al. Accelerated global glacier mass loss in the early twenty-first century. Nature 2021, 592(7856): 726-731.

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