A thermodynamic rate of ablation for iceberg keels

Abstract

Glaciers melt in contact with seawater and this contributes to sea level change and affects water circulation, mixing, and hydrography. Estimating the rate of melting is therefore key to improving the representation of this input in global coupled circulation models. The goal of this project was to determine how fast vertical ice walls melt as a function of water salinity and temperature. Hitherto there was only one model that included both variables. Based on analytical fluid dynamics work from the 1970s, it is very expensive computationally and only applicable over a limited range of conditions. Several simple models are also available but they generally take the form of a power of temperature times the first power of a second variable that may or may not be broadly relevant. I collected experimental data from the literature, then used a benchtop-scale version of an experimental method first used in situ in Greenland in 1879 to conduct a more thorough investigation of the full domain of applicable temperature and salinity. I fitted a bivariate quadratic model which fit both my data and the legacy data. Finally I developed an easy model of glacier density and bubble pressure with depth to create a model iceberg, and applied my thermodynamic ablation model to the model iceberg with water conditions obtained from a reanalysis product. My main findings were that there is in fact an intrinsic thermodynamic rate of phase change, independently of fluid dynamics, and that it can be both measured and calculated very cheaply; but also that the bubbles in icebergs, when released by melting, add considerable buoyancy to the melt, which increases the rate of ablation by contributing additional energy to the ice interface as momentum flux. My model provides both a fast equation in salinity and temperature which can be applied anywhere in the sea, as required, but also an inexpensive model of the ice for more detailed descriptions at the level of an iceberg or ice face, and a basis for further work on the effects of pressure, stress, momentum transfer, the ice's thermal history, bubbles, solar radiation, and more.