Parameterization issues of the turbulent exchange over snow and ice: from scalar roughness lengths to temperature-humidity correlation and similarity

The accurate determination of turbulent exchange over snow and ice surfaces constitutes a major challenge in boundary-layer meteorology, and specifically, turbulent sensible heat and latent heat fluxes have been recognized as important sources of a glacier's melt energy. The development of robust approaches to parameterizing both types of heat flux, therefore, is of common concern in the study of micro- and glacio-meteorology. Our presentation is based on a field investigation over a melting valley glacier on the Tibetan Plateau, and it is in the context of the stable atmospheric boundary layer that we work on two parameterization issues — one concerning the scalar roughness lengths for temperature and humidity, and the other concerning the turbulent temperature-humidity correlation and similarity. Separately for either issue, we summarize specific findings in the follows.

The scalar roughness lengths for temperature (z_0T) and humidity (z_0q) are key factors for the accurate estimation of turbulent sensible heat and latent heat fluxes using the bulk aerodynamic method, i.e. the most widely used approach in glacio-meteorological investigations. Their impact on heat-flux estimations is essentially realized through modulating the land-atmosphere coupling strength as described by the bulk transfer coefficients for temperature (C_T) and humidity (C_q). Following a strict quality control of eddy-covariance flux measurements over both snow and ice surfaces, we present a critical evaluation of three parameterization schemes of z_0T and z_0q in a glacial environment (viz. a setting not often addressed in previous evaluations). The three candidate schemes stem from Andreas (1987, Boundary-Layer Meteorol. 38:159–184), Yang et al. (2002, Q. J. Roy. Meteorol. Soc. 128:2073–2087), and Smeets and van den Broeke (2008, Boundary-Layer Meteorol. 128:339–355). The first scheme (i.e. by Andreas 1987) was originally proposed based on surface-renewal models and has been very extensively adopted in glaciated areas (such as sea-ice, valley glacier, and ice-sheet/ice-cap in the Polar regions); the second scheme (i.e. by Yang et al. 2002), in contrast, has never been applied over snow or ice surfaces, though it was validated previously over bare-soil of (semi-)arid regions; the third scheme (i.e. by Smeets and van den Broeke 2008) was proposed on the basis of the first one, for the sake of improved applications over rough-ice surfaces. We find in the present evaluation that the first and the third schemes are inclined to underestimate and overestimate turbulent heat/moisture exchange, respectively. Relative errors in sensible and latent heat-flux estimations can often reach about 30%, especially when the aerodynamic roughness length (z_0M) is higher than 10^-3 m or so (note that z_0M values were not fixed but varied on the order of 10^-4–10^-2 m during the glacier's ablation season). In comparison, the second scheme (i.e. by Yang et al. 2002) leads to relatively low errors in the heat-flux estimations, and this scheme hopefully emerges as a practically useful choice to parameterize z_0T and z_0q over snow and ice surfaces. Our efforts to present a critical evaluation of z_0T and z_0q parameterizations (see Guo et al. 2011, Boundary-Layer Meteorol. 139:307–332) should make available a useful source of reference for investigations on land-ice surface energy budget and mass balance, as well as for observational analyses or modeling over seasonal snowpack and sea-ice.

Turbulent scalar correlation and similarity is a research topic of widespread concern in micro-meteorology. It constitutes the rationale behind using indirect techniques for turbulent flux estimation, and specifically, temperature-humidity similarity is a working assumption for parameterizing the surface-atmosphere exchange of heat and moisture. An in-depth knowledge of the correlation and similarity between different scalars, therefore, is required in a wide range of micro-meteorological investigations. We seek to explore temperature-humidity correlation and similarity within the stably-stratified katabatic flow over a glacier. Because the uniform surface covers of snow and ice should create a fairly homogeneous source/sink distribution of heat and moisture, our measurements in a glacial environment should be advantageous to related analyses of scalar turbulence. First, we highlight the vital importance of making density effect corrections to the high-frequency fluctuations of scalar concentration (q′ for water vapor and c′ for CO₂), as originally suggested by Detto and Katul (2007, Boundary-Layer Meteorol. 122:205–216). These corrections are found to be particularly indispensable to derive meaningful turbulence characteristics of CO₂; an omission of the corrections can lead to spurious results, such as comparably high transport efficiency between water vapor and CO₂ (note that CO₂ fluxes are not significantly different from zero over this glacier). Second, temperature and humidity are found to be two closely correlated scalars, even when sensible heat and latent heat fluxes are in opposite directions (with negative Bowen ratio values). That is to say, the same direction of turbulent transport does not necessarily produce a notably higher temperature-humidity correlation. Third, the vertical transport efficiency of temperature is nearly always higher than that of water vapor, making their relative transport efficiency (λ_Tq) frequently higher than unity (absolute values). Recognizing such a dissimilarity and evaluating several λ_Tq parameterizations, we extend Lamaud and Irvine's (2006, Boundary-Layer Meteorol. 120:87–109) parameterization to the stable boundary layer (covering both positive and negative Bowen ratio values). We propose that the Bowen ratio (|β| > 1 in our dataset) is one governing factor of the temperature-to-humidity transport efficiency (λ_Tq) in stable conditions as well.