Glacier winds and parameterisation of the related surface heat fluxes

Abstract

The katabatic flow over glaciers is studied with data from automatic weather stations (AWS). We analyse data from the Morteratschgletscher (Switzerland), Vatnajökull (Iceland) and West Greenland, and conclude that katabatic flow is very common over melting glacier surfaces and rarely disrupted by the large-scale flow. Over small and medium-size glaciers the height of the wind maximum is generally low (typically 10 m), and vertical temperature differences near the surface are very large (up to 15 K over 4 m). In glacier mass-balance models there is a great need for parameterisations of the surface heat flux. We develop a simple method to estimate the sensible heat flux F h associated with the glacier wind. It is based on the classical Prandtl model for slope flows. We set the turbulent exchange coefficient proportional to the maximum wind speed (velocity scale) and the height of the wind maximum (length scale). The resulting theory shows that F h increases quadratically with the temperature difference between the surface and the ambient atmosphere; F h decreases with the square root of the potential temperature gradient of the ambient atmosphere; and F h is independent of the surface slope.

Evaluation of different methods to model near-surface turbulent fluxes for a mountain glacier in the Cariboo Mountains, BC, Canada

“…Our results do not guarantee the validity of Eq. (30) but do demonstrate that the simple katabatic model of Oerlemans and Grisogono (2002) reproduces the basic characteristics of katabatic flow at our site. This model, when calibrated, can simulate the turbulent heat exchange more successfully than a common bulk method (C method).…”

“…C kat becomes smaller as the atmospheric boundary layer becomes more stable (larger γ ). As noted in Oerlemans and Grisogono (2002), this is a dynamic effect, which should not be confused with the effect of stratification on the exchange coefficients as predicted by the M-O theory. Our data are not suitable to adequately test this bulk method since we do not have the vertical profile observations of potential temperature needed to estimate s and γ .…”

“…Rather than integrating the flux-gradient relations with a chosen parametrization for K, Oerlemans and Grisogono (2002) derived a bulk approach for surface heat fluxes through a simplified scaling of the governing equations for heat and momentum balance in a 1-D katabatic flow model (Prandtl, 1942). Their basic assumption was that the katabatic flow is characterized by a well-defined wind maximum, setting the exchange coefficient for heat proportional to the maximum wind speed and to the height of the wind maximum.…”

“…If not otherwise stated, the roughness lengths are assumed to be constant in time and equal to the mean log value of the OPEC-derived 30 min roughness lengths observed only during the near-neutral conditions and when all the filters are applied to the OPEC data. The group of bulk methods derived from simple katabatic flow models consists of (5) C kat method -following Oerlemans and Grisogono (2002), and (6) K Int method -using an integrated varying eddy viscosity profile (Grisogono and Oerlemans, 2001;Parmhed et al, 2004). Details of each method (1)- (6) are provided in the sections that follow.…”

“…Using this "enhanced" Prandtl model, Parmhed et al (2004) found that modeled turbulent fluxes at a glacier surface compare well with the measured fluxes during katabatic flows. An alternative approach to incorporating the model for katabatic flow into the bulk method for turbulent heat fluxes was developed following the classical Prandtl model for slope flows (Oerlemans and Grisogono, 2002). The simple model only agrees in the overall pattern, which shows an increase in sensible-heat flux in response to an increase in air-surface temperature difference.…”