# Densification of Snow in Antarctica

- Malcolm Mellor

Published Online: 14 MAR 2013

DOI: 10.1029/AR002p0157

Copyright © 1971 by the American Geophysical Union.

Book Title

## Antarctic Snow and Ice Studies

Additional Information

#### How to Cite

Kojima, K. (1971) Densification of Snow in Antarctica, in Antarctic Snow and Ice Studies (ed M. Mellor), American Geophysical Union, Washington, D. C.. doi: 10.1029/AR002p0157

#### Publication History

- Published Online: 14 MAR 2013
- Published Print: 1 JAN 1971

#### Book Series:

#### ISBN Information

Print ISBN: 9780875901169

Online ISBN: 9781118669808

- Summary
- Chapter
- References

### Keywords:

- Densification of snow;
- Depth-density curve;
- Shallow pit densities;
- Sorge's law;
- Time-integrated load

### Summary

An attempt has been made to determine the relation between compactive viscosity factor η_{ c } and density ρ of snow in Antarctica from the density profiles observed at traverse stations and permanent bases. An observed density profile is transformed to the relation between density ρ and snow load σ. Assuming that the strain rate of densification is proportional to the vertical pressure exerted by the snow load and that the accumulation rate A is constant, a ρ ∼ σ relation provides the relation between ρσ (*d*σ/*d*ρ) = *A*η_{ c } and density. Plotting the values of log (ρσ *d*σ/*d*ρ) = log *A*η_{ c } against density, the relation between log η_{ c } and ρ can be obtained by subtracting the observed value of log A from log (ρσ *d*σ/*d*ρ) for various values of density.

The density is usually in the range 0.3∼0.4 g/cm^{3} at the surface and 0.5∼0.6 g/cm^{3} at 10-meter depth. A linear relation between log η_{ c } and ρ is found in the middle range of density; the intercept log *C* and the slope *K*′ are determined. The values of log η_{ c } for a density 0.50 g/cm^{3} are plotted against the reciprocal of absolute snow temperature *T**, and the relation between *C* and temperature is investigated. The empirical curves expressing log η_{ c } ∼ ρ relation deviate downward from the linear relation in the lower density range in almost all cases, and deviate upward from the linear relation at the density range greater than 0.50 g/cm^{3} in many cases. A density profile of snow is expressed as a load-density relation and a depth-density relation using the log η_{ c } ∼ ρ relation derived earlier.

To compare a theoretical depth-density curve with an observed one, a shallow pit density profile is first expressed by a straight line. This straight line is considered as a tangential line at the point of inflection of the theoretical curve, which is usually in the depth range 1∼2 meters. Two coefficients of the equation of the straight line pit density profile, which are the surface density ρ*so* and the vertical density gradient *B*, give the values of ρ*o* and (*AC*) for a definite value of κ (κ = 2.303 κ′).

Some examples show good agreement between the calculated and the observed density profiles, but at other stations the density profiles calculated from pit data give values to the densities in the lower part which are too small compared with observed values. It is possible to get good agreement between calculated and observed density profiles if appropriate values of κ, *AC*, and ρ_{ o } are selected. However, putting an observed value of *A* and the above-described values of *C* and κ into the equation of the density-depth curve does not always provide good agreement. To determine how the linear equation of a pit density profile varies with snow temperature, accumulation rate, and some other conditions, the relations between *B* and temperature, *B* and ρ_{ so }, *B* and *A*, and ρ_{ so } and temperature are studied from observed and theoretical values, where υ_{ƒ} =. κ ρ_{ƒ} and ρ_{ƒ} is the density at the point of inflection of a theoretical depth-density curve. The value of υ_{ƒ} is related to ρ_{ so } for a definite value of κ.

Observed and theoretical curves often show only poor correlation, but for many stations the plot of the averages of *B* against the average temperature shows a theoretically reasonable relation. The observed relation of *B* and ρ_{ so } is most clear for each traverse. The slope *dB*/ρ_{ so } so is found to be nearly 4.5×10^{−3} cm^{−1}. This empirical value is much larger than the theoretical value, especially in the coldest area. The relation of *B* and *A* has quite a poor resemblance to the theoretical one.

To study the local characteristics of density, the 10- and 15-meter densities are plotted against the 10-meter temperature, and the results are compared with the theoretical relations with different accumulation rates. It is found that the observed densities from most traverse stations can be explained theoretically, considering some errors in the estimation of accumulation rate. But the densities observed on the Ross ice shelf and at Byrd station are much lower than would be expected from theoretical considerations.