#
`thickness2freeboard` documentation

`thickness2freeboard` is part of Antarctic Mapping Tools for Matlab (Greene et al., 2017). Click here for a complete list of functions in AMT.

`thickness2freeboard` estimates freeboard height above sea level, from ice thickneess assuming hyrostatic equilibrium.

## Contents

## Syntax

F = thickness2freeboard(T) F = thickness2freeboard(...,'rhoi',iceDensity) F = thickness2freeboard(...,'rhow',waterDensity) F = thickness2freeboard(...,'rhos',snowDensity) F = thickness2freeboard(...,'Ts',snowThickness)

## Description

`F = thickness2freeboard(T)` estimatesfreeboard height height above sea level F in meters above the geoid from ice thickness `T` in meters.

`F = thickness2freeboard(...,'rhoi',iceDensity)` speccifies ice density in kg/m^3. Default ice density is 917 kg/m^3.

`F = thickness2freeboard(...,'rhow',waterDensity)` specifies water density in kg/m^3. Default water density is 1027 kg/m^3.

`F = thickness2freeboard(...,'rhos',snowDensity)` specifies snow density in kg/m^3. Default snow density is 350 kg/m^3, however the default snow thickness is 0 m, so the snow density value will only affect calculations if snow thickness is specified.

`F = thickness2freeboard(...,'Ts',snowThickness)` specifies snow thickness in meters. Default snow thickness is 0 m.

## Example 1:

An iceberg is 5 m thick and it's made of pure ice. How high is the iceberg's surface above sea level?

F = thickness2freeboard(5)

F = 0.54

## Example 2:

An iceberg is 4.83 m thick, including 40 cm of snow which has a density of 300 kg/m^3. How high is the iceberg's surface above sea level?

F = thickness2freeboard(4.83,'Ts',0.4,'rhos',300)

F = 0.80

And you can go back the other way too:

T = freeboard2thickness(0.8,'Ts',0.4,'rhos',300)

T = 4.83

## Example 3: A profile from laser altimetry

Imagine this elevation profile measured by a laser altimeter:

x = 0:1000; % A random profile: z = movmean(randn(size(x)),75); z(z<0) = 0; plot(x,z,'r.') xlabel 'distance along profile' ylabel 'elevation (m)' box off

Where's the ice base? It's the surface minus the thickness:

base = z - freeboard2thickness(z); hold on % Draw the ice: patch([x,fliplr(x)],[base,fliplr(z)],'b','facecolor',rgb('ice blue')) % Draw the water: yl = ylim; % y limits of the axis h = patch([xlim,fliplr(xlim)],[yl(1) yl(1) 0 0],'b',... 'facecolor',rgb('ocean blue')); uistack(h,'bottom') % sends "water" to the back

## Citing AMT

If this function or any other part of Antarctic Mapping Tools is useful for you, please cite the paper that describes AMT.

Greene, C. A., Gwyther, D. E., & Blankenship, D. D. Antarctic Mapping Tools for Matlab. *Computers & Geosciences*. 104 (2017) pp.151-157. doi:10.1016/j.cageo.2016.08.003.

## Author Info

This function was written by Chad A. Greene of the University of Texas Institute for Geophysics (UTIG), April 2017, for inclusion in the Antarctic Mapping Tools package.