Energy Balance, Monin Obukhov Theory, Stability Corrections and Snow Modelling

The Monin-Obukhov parameterizations for turbulent fluxes are used in a majority of numerical models, which represent surface exchange. Over snow and ice, stable conditions are often encountered and flux parameterizations are known to be difficult. This contribution discusses seven cryospheric data sets from diverse locations (Greenland, Antarctica, Alps) and assesses the performance of the most common stability correction functions. At all locations, high-resolution data from Sonic Anemometers allow a direct calculation of turbulent fluxes. A first assessment therefore is how well Monin-Obukov theory applies in these diverse settings. To this end, the stability corrections are calculated directly from the high resolution measurements. In a second step, the additional error that arises from the stability correction parameterization is assessed. It is shown that errors from the stability corrections are comparable to the errors by the Monin-Obukhov theory in the first place. Errors increase with wind speed and temperature gradient for all parameterizations. In general the parameterizations show different performance for different meteorological conditions. Therefore, as an additional assessment, the parameterizations are analyzed with respect to their influence on snow modeling and a correct representation of the total surface energy balance. We discuss the fact that a large turbulent flux error has more weight when the other surface exchange terms (mainly radiation) are small. Based on this it is shown, what turbulent flux modeling approach should be preferred when snow mass balance and/or internal snow structure are target variables. Special attention is given to rain on snow situations, which are often critical with respect to flood formation and rapid snow cover disappearance.