How do Stability Corrections Perform in the Stable Boundary Layer Over Snow?

Abstract

We assess sensible heat-flux parametrizations in stable conditions over snow surfaces by testing and developing stability correction functions for two alpine and two polar test sites. Five turbulence datasets are analyzed with respect to, (a) the validity of the Monin–Obukhov similarity theory, (b) the model performance of well-established stability corrections, and (c) the development of new univariate and multivariate stability corrections. Using a wide range of stability corrections reveals an overestimation of the turbulent sensible heat flux for high wind speeds and a generally poor performance of all investigated functions for large temperature differences between snow and the atmosphere above (>10 K). Applying the Monin–Obukhov bulk formulation introduces a mean absolute error in the sensible heat flux of $6\,\hbox {W m}^{-2}$ (compared with heat fluxes calculated directly from eddy covariance). The stability corrections produce an additional error between 1 and $5\,\hbox {W m}^{-2}$, with the smallest error for published stability corrections found for the Holtslag scheme. We confirm from previous studies that stability corrections need improvements for large temperature differences and wind speeds, where sensible heat fluxes are distinctly overestimated. Under these atmospheric conditions our newly developed stability corrections slightly improve the model performance. However, the differences between stability corrections are typically small when compared to the residual error, which stems from the Monin–Obukhov bulk formulation.

Appendix

We used the following stability corrections (see also “Electronic Supplement Material” in Sharan and Kumar (2011) for further discussion and additional stability corrections) (Table 6):

Table 6 Stability correction functions for ${\psi }_m$ and ${\psi }_s$ used in the study