A Volumetric Calculation of the Antarctic Ice Sheet

 

Lucas Diehm

Geo 326G-GIS & GPS in Applications in Earth Sciences

12/4/03

 

Figure 1-Antarctica

 

Figure 2-Antarctica (courtesy of http://terraweb.wr.usgs.gov/TRS/projects/Antarctica/AVHRR.html)

 

 

Introduction:

 

Antarctica is the most isolated continent on the planet, and with about 99.5 percent of its surface covered with ice all the time, one can see why it is such a mystery and interest too many people both in the scientific and civilian communities.  The main purpose of this project is to establish a procedure for calculating the volume and mass of ice that is stored at Antarctica.

In order to carry out this experiment, we must use DEM’s of the bedrock surface, the present elevation, and also the thickness of the ice sheet.  Several other data sets, including the coastline of Antarctica, the rock protruding above the ice sheet, and a contour map of Antarctica must also be utilized for this analysis.  The DEM’s will have to be manipulated by 3D analyst and spatial analyst in both ArcMap and ArcScene, in order to generate models that will illustrate the spatial relationship between the three layers being analyzed.  Once the layers have been modeled with 3D analyst, the volumes of the layers can be subtracted so that the volume of ice can be determined.

 

Data Collection:

 

            The data that is being used for this project was collected from the BEDMAP site at http://www.antarctica.ac.uk/aedc/bedmap/download/.  A consistent projection (stereographic projection of the South Pole), geoid model (WGS 1984), and geographic framework were used in accordance with the recommendations of the SCAR, during the construction of these data sets.

 

Data Preprocessing:

 

          All the data that I used for this project was provided to me by Dr. Helper, who has already preprocessed all the data.

 

ArcGIS Processing:

 

Constructing a General Map of Antarctica:

I first began this project by constructing just a general map of Antarctica, with several major features that are located upon the continent in order to provide a frame of reference for the reader.  The final product can be seen in figure 1 of this project.

 

I used a polygon shapefile (coast10 polygon) to begin my map (see figure 3), followed by changing the symbology by right-clicking on the layer of interest then selecting properties from the drop down menu (see figure 3a), which made it more presentable. 

 

Figure 3- Coastline polygon shapefile

 

Figure 3a-Changing the Symbology of the Layer

 

Next, within the layout view of ArcMap I added the text from the insert menu to label the main surface features, and finally I added a graticule to provide latitude and longitude for accurate positioning (see figure 4).

Figure 4- Antarctica with grid

 

In order to add the graticule I had to right-click the data frame and go to properties, and then I had to click on the grid tab, new grid, and then specify the parameters for the graticule I wanted to produce. (See figure 5)  

 

Figure 5-Setting a Graticule for Antarctica

 

Constructing a Present Elevation Map of Antarctica:

I then added the present surface elevation layer (surf_elev) into ArcMap, which was already in a raster model format, therefore I just had to change the symbology to show differences in elevation (see figure 6).

Figure 6-Present Surface Elevation of Antarctica

 

Constructing a Contour Map at 250m Intervals:

From the present surface elevation I constructed just a contour map by specifying 250 meter intervals for Antarctica, using Surface Analysis>contour under the Spatial Analyst menu in ArcMap. (See figure 7a)  

                 

 

Figure 7a-Setting parameters for the contour map

 

I changed the symbology of it a bit to make it more perceptible. (See figure 7b)

 

Figure 7b-Contour Map of Antarctica (250m intervals)

 

Constructing a 3D surface model of Antarctica:

I opened ArcScene and added the layer named surf_elev from my data set, in order to produce a 3D rendering of the surface of Antarctica via 3D Analyst.  After loading this layer into ArcScene I had to set the base heights for the cells of the raster so that they would exhibit three-dimensional characteristics.  To complete this step I right-click on the layer, and go to properties, then I clicked on the base heights tab, and choose the option “obtain heights for layer from surface”, and set the surface to surf_elev. (See figure 8)

 

Figure 8-Setting base heights for surface elevation layer

 

Following this step, I then had to set the vertical exaggeration for the data frame, by right-clicking the scene and going to properties>general tab, and choosing the “calculate from extent” button. (See figure 9)  However, the calculated exaggeration seemed too great so I set it to a lesser value of 100.

 

Figure 9-Setting the Vertical Exaggeration for the Scene

 

After that all I had to do was change the symbology of the layer to better show the differences in elevation, and viola, a three-dimensional rendering of the present surface elevation for Antarctica.  (See figure 10)

Figure 10-3D surface elevation model for Antarctica with Ice

 

Constructing a 3D model of Bedrock Elevation of Antarctica:

The next step in processing the data was to construct an elevation model for the underlying bedrock of Antarctica, so that the volume of ice can be calculated by the subtraction of these two layers using the volume function of the 3D Analyst.  This was done by adding the layer bed_elev to ArcScene, and again setting the base heights like the aforementioned layer, as well as changing the symbology. (See figure 11)

 

 

Figure 11-3D model of Antarctica’s Bedrock without Ice

 

Applying an Analysis Mask:

Before I can calculate the volume of the ice, I first have to make sure that the volume calculation is done based on the same area for each layer.  The quickest and simplest way to do this is to apply an analysis mask to the layers.  This is done by going to the 3D Analyst>Options menu in ArcScene, and after the options window comes up, I selected the general tab and specified the layer I wanted to use as my mask, which was the coast10polygon (see figure 12).  I also had to specify the extent of the mask, by selecting the extent tab and choosing the same layer for the analysis extent (see figure 12a).

 

Figure 12-Selecting an Analysis Mask

 

Figure 12a-Setting the Analysis Mask Extent

 

Calculating the Volume of Bedrock:

With the analysis mask, the next step was to begin calculating the volume of these two layers in order to establish the volume of ice, and I did this by using the area/volume option under 3D Analyst>Surface Analysis(see figure 13).

 

Figure 13-Using 3D Analyst to Calculate Volume

 

First, you must enter the input surface you want to use for the volume calculation, and in my case I used the bed_elev for the first volume (V1), which was the volume of Antarctica’s bedrock.  Second, I needed to set a height of a plane for reference for the calculation, because the program can either calculate above or below the reference plane.  For this project I set it to 0 or the elevation of sea level (see figure 15), as the height of my reference plane, and I wanted the volume above this plane to be calculated, so I also selected this option. (See figure 14)

 

Figure 14-Setting Parameters for Volume Calculation

 

Figure 15-3D model showing sea level reference plane

 

Calculating the Volume of Bedrock and Ice:

Next, I had to make another volume calculation (V2), so I followed the steps in the previous volume calculation but set the input layer to the surf_elev layer, which was the elevation of the bedrock and the ice, and used the same reference plane height of 0 and calculated the volume above the plane.(see figure 15) 

 

Calculating the Volume of the Ice:

Now that I had the volume of the bedrock and the volume of the bedrock and ice, so all I had to do was subtract the volume of the bedrock to give me the volume of the ice (V3), which can be seen in blue. (See figure 16; table 1)  So, I just used the equation V2-V1=V3.

 

Layer	Bedrock	Bedrock & Ice	Ice
Volume (m3)	4.02 X 1015	2.67 X 1016	2.27 X 1016

Table 1

Figure 16-3D model of ice sheet for which the volume was calculated

 

Calculating the Mass of the Ice:

The second goal of this project was to determine the mass of Antarctica’s ice.  For this procedure, the mass of the ice is easily calculated from the volume of ice contained within Antarctica’s main ice sheet.  The mass of the ice can easily be calculated with the equation “mass_ice= (Volume) (density)”, using the density of ice as 1000 kg/m³.

 

Mass_ice= (2.27 X 10¹⁶) (1000) =2.27 X 10¹⁹ kg

 

Conclusions:

 

The goal of this project was to develop a set of procedures that would enable a calculation of the volume and mass of ice that lies upon Antarctica to be made.  This goal has been met and the procedure and data needed to meet this goal have been presented in the most simple and straightforward manner so that any reader without knowledge of ArcGIS would be able to repeat this project if necessary.