# Ice sheet modelling

## What is an ice sheet model?

A quick search on Wikipedia for the word ‘model’ will give you a many different options, ranging from physical models that you can touch, to conceptual models of how a system works.  Here, we are considering a computer-based, numerical ice sheet model. This is where a mathematical formula which represents the way that ice behaves is converted into computer code and the code then used to simulate the ice sheet behaviour. The process of modelling. Modellers start with a physical process which can be described mathematically. This is turned into computer code where the equations are solved numerical for a 3D grid. The model is then applied to predict the behaviour of the ice sheet: here, applied to Pine Island Glacier (Gladstone et al. 2012).

## Why do we need a model?

There are two main reasons why we might want to use a numerical ice sheet model: 1) to make predictions (prognostic modelling) or; 2) to investigate behaviour of an ice sheet (diagnostic modelling).

### Prognostic (or predictive) modelling

Changes in the Antarctic Ice Sheet have a big influence on global climate and sea level.  For example, collapse of the West Antarctic Ice Sheet could raise average sea level by 3 metres (Bamber).  But what is the likelihood of this?  How long will it take?  Will it all collapse, or only part of it?  These are the sort of questions that policy makers need answers to, especially in low-lying coastal areas.  However, the Antarctic Ice Sheet is a complex system with interactions between the ice and climate, the ocean, and conditions at the base of the ice sheet.  The complexity of the system means that it is not straightforward to determine how one thing will affect another, hence, prediction requires a realistic numerical ice sheet model which takes into account all the important processes and how they interact.

Prognostic modelling can also involve reconstructing past ice sheets.  Understanding the behaviour of ice sheets in the past, in different climate settings, can help us understand what might happen in the future.

### Diagnostic modelling

Diagnostic modelling can be used to improve the understanding of the processes controlling the behaviour of a particular ice stream, or to study the importance of one or more physical process in an ice sheet in general.

Examples of the two approaches are given below in the examples section.

## Different types of model

Many ice sheet models are now freely available, for example, Elmer, Glimmer-CISM, ISSM, PISM, SICOPLIS, making it possible for a wider community to be able to use these models to answer a wide range of scientific questions.

The models vary in a number of different ways, for example: the way in which they break up the world into discrete elements to solve the equations; the representation of the physics of ice flow; the language the code is written in; whether they are solved on one or many computer processors.

Investigating the same question with different models allows us to compare the models and identify where models agree and where differences between the models lead to different answers to the same question.  A number of model intercomparison exercises have taken place, for example ISMIP and MISMIP.

## The process of modelling

### 1. Physical process

The starting point of modelling is a physical process, either from observation or from theory, for example: how ice “slides” over the underlying sediment or bedrock (e.g. Weertman et al., 1964, Tulaczyk et al., 2000).

### 2. Mathematical description

The relationship then needs to be converted to an equation that can be used to calculate, in our example, ice speed from our knowledge of conditions beneath the ice sheet.  However, this may require a greater knowledge of the system than we can ever have.   The base of the ice sheet is buried beneath kilometres of ice, so measuring it in great detail is almost impossible.  Therefore, we have to make certain simplifications to the equations and group together physical properties in model ‘parameters’ which represent the conditions at the base of the ice sheet.

### 3. Computer code

The equation is then solved over space and time in a computer program, this may require sophisticated numerical methods in order to solve complex equations.

### 4. Application

Once the computer code has been tested or verified against test cases, it can be applied to real world situations.  Inputs needed for a typical Antarctic ice sheet model are the elevation of the bed beneath the ice sheet, air temperature, snowfall and the heat input from the rock below (geothermal heat flux).  To consider change in the ice sheet over time, we also need to know how the inputs change over time.

### 5. Calibration

As mentioned in 2), we often have parameters which we need to assign a value to through calibration against observations.  For example, if we have a snapshot measurement of the ice velocity, we can infer the value of our basal parameter, i.e. the parameter that represents conditions at the base of the ice.

### 6. Validation

Once we have our model set up for our application, we need to determine whether the model is doing a good job of representing the real world.  This is done by comparison against observations.

### 7. Prediction

If the model is deemed to be valid, we can have confidence that our predictions are reliable.  The model is then either run into the future using scenarios of how the climate might change, or run in the past with a past climate reconstruction.

### 8. Sensitivity/uncertainty analysis

It is very important that we know how sensitive our predictions are to any uncertainty in input data or parameter values, so we can change values and investigate the impact on the predictions (see below).

## Examples

Pine Island Glacier (PIG) in West Antarctica is a good example of the value of both prognostic and diagnostic modelling in understanding and predicting ice sheet behaviour.

The video below shows how Pine Island (left) and Twaites glaciers have recently thinned (average ice elevation los of 6 meters per year). By NASA/Goddard Space Flight Center (Goddard Multimedia) [Public domain], via Wikimedia Commons.

### Diagnostic modelling

PIG has been accelerating and thinning over the past few decades (Joughin et al., 2003, 2010; Wingham et al. 2009); the reason for this signal was unclear.  It was generally believed that increased warm ocean water, in contact with the ice, was driving the changes (Shepherd et al., 2001).  However, the question was whether the changes at the front of the glacier could transmit quickly enough upstream to explain the pattern of acceleration and thinning.  This required a model with a full representation of all the forces involved in ice flow applied specifically to PIG: “A more detailed understanding of PIG’s departure from equilibrium flow will require an understanding of its particular stream mechanics” (Shepherd et al., 2001).

Application of complex ice flow models to PIG (Shmeltz et al., 2002, Payne et al., 2004) demonstrated that changes at the front of the ice stream could impact on the ice inland very quickly. As a result, the hypothesis that changes at PIG were being driven by the ocean was accepted.

### Prognostic modelling

Predicting the future

Once the driving force behind change at PIG was identified, future predictions could be made using different ocean condition scenarios, and the likelihood of significant retreat can be identified.

Joughin et al. (2010) applied a numerical ice sheet model to predicting the future of PIG, their model suggested ongoing loss of ice mass from PIG, with a maximum rate of global sea level rise of 2.7 cm per century.  Gladstone et al. (2012) also investigated the future of PIG, and they too found ongoing ice mass loss to be likely under a ‘business as usual scenario’ (IPCC), with full collapse of the main trunk of PIG during the 22nd century still a possibility.  They investigated using different parameter values in the model and exploring the variation in the result and found a great deal of variation in ice mass loss rates was possible.  This underlines the importance of being aware of the uncertainty in the predictions (see below).

Reconstructing the past

As well as using a model to predict the future, we can also use it to reconstruct ice sheets in the past, giving clues as to the behaviour of the ice sheet in different climate settings.  Ice sheet models can be run through many glacial cycles (i.e. cold glacial periods and warm interglacial periods).  See here for example.

## Uncertainty

By its very nature, a model is a simplification of reality, so the final step when we consider predictions made by numerical models is to assess the uncertainty in our predictions. This blog provides a good perspective on model uncertainty.

Any research involving ice sheet modelling will have a section on uncertainty in the model prediction, and may give a range of prediction values, rather than a single value.

Uncertainty comes from:

• lack of detail in the representation of the physical processes in ice sheet behaviour
• quality and quantity of the data that is input to the model.
• uncertainty in parameter values
• uncertainty in climate/ocean conditions input into the ice sheet model – any uncertainty in these, both present and future, will feed into uncertainty in the ice sheet model.

In order to reduce the uncertainty, further understanding and measurements of the Antarctic Ice Sheet are required.  Even with the best numerical model of ice flow available, if the data going into it is not accurate, then the predictions will not be reliable.  There are many huge challenges facing ice sheet modellers in reducing this uncertainty, which requires an interdisciplinary effort between glaciologists, geophysicists, oceanographers, climatologists, mathematicians, computer scientists…

This effort is going on, with major projects such as the EU funded Ice2sea project, which has brought together researchers across disciplines, from across Europe, in order to address the challenges faced in predicting the contribution of ice sheets to future sea level change.

Bamber, J. L., R. E. M. Riva, et al. (2009). “Reassessment of the Potential Sea-Level Rise from a Collapse of the West Antarctic Ice Sheet.” Science 324(5929): 901-903.

Gladstone, R. M., V. Lee, et al. “Calibrated prediction of Pine Island Glacier retreat during the 21st and 22nd centuries with a coupled flowline model.” Earth and Planetary Science Letters 333: 191-199.

Joughin, I., E. Rignot, et al. (2003). “Timing of recent accelerations of Pine Island Glacier, Antarctica.” Geophysical Research Letters 30(13).

Joughin, I., B. E. Smith, et al. (2010). “Sensitivity of 21st century sea level to ocean-induced thinning of Pine Island Glacier, Antarctica.” Geophysical Research Letters 37.

Payne, A. J., A. Vieli, et al. (2004). “Recent dramatic thinning of largest West Antarctic ice stream triggered by oceans.” Geophysical Research Letters 31(23).

Schmeltz, M., E. Rignot, et al. (2002). “Sensitivity of Pine Island Glacier, West Antarctica, to changes in ice-shelf and basal conditions: a model study.” Journal of Glaciology 48(163): 552-558.

Shepherd, A., D. J. Wingham, et al. (2001). “Inland thinning of Pine Island Glacier, West Antarctica.” Science 291(5505): 862-864.

Tulaczyk, S., W. B. Kamb, et al. (2000). “Basal mechanics of Ice Stream B, West Antarctica 1. Till mechanics.” Journal of Geophysical Research-Solid Earth 105(B1): 463-481.

Weertman, J. (1964). “The theory of glacier sliding.” Journal of Glaciology 5: 287-303.

Wingham, D. J., D. W. Wallis, et al. (2009). “Spatial and temporal evolution of Pine Island Glacier thinning, 1995-2006.” Geophysical Research Letters 36.

## One thought on “Ice sheet modelling”

1. Dredd on said:

Very informative presentation. Well worth a close read!

This site uses Akismet to reduce spam. Learn how your comment data is processed.