Of all the surface conditions, the extent of snow shows the largest spatial and temporal fluctuations. Over 50% of Eurasia and North America can be seasonally covered by snow (Robinson et al., 1993). Snow cover extent exhibits a strong seasonal cycle with a distinct interannual variability in the middle latitudes.

Snow cover extent has a strong influence on the Earth's heat balance, since a large part of the incoming shortwave radiation is reflected by the high snow albedo. The induced radiative cooling is reinforced by the high thermal emissivity of the snow cover which increases static stability in the boundary layer and consequently reduces turbulent fluxes. This effect is enhanced by a reduced roughness of snow covered vegetation when compared to snow free conditions.

Many studies have shown the importance of snow cover extent for weather forecasts as well as for climate simulations. For example, the sensitivity of the Indian monsoon to the extent of the Eurasian snow cover has been confirmed by several numerical experiments (e.g., Barnett et al., 1989). Walsh and Ross (1988) tested the sensitivity of 30-day forecasts to the presence of continental snow cover and found considerable sensitivity over Eurasia.

Snow extent is related to a number of feedbacks (Randall et al., 1994), the most obvious being the snow albedo feedback: A positive temperature bias leads to larger snow melt and favours rain over snowfall which leads to a decrease of surface albedo. This allows more absorption of solar radiation and therefore reinforces further warming.

Snow cover extent is measured by the snow cover fraction (SCF), which is the fraction of a surface element covered by snow. SCF data are obtained from snow depth (SDH) or snow water equivalent (SWE) data. For relatively thick snow covers, the SCF is obtained easily, for relatively thin snow covers, the computation of the SCF from SDH or SWE is more difficult: When the SDH decreases the exposed patches of ground and the transparency of the snow cover increase. Both cause the reflective properties of the underlying ground to affect the albedo (Kung et al., 1964). In climate models, SCF is diagnostically derived from the SWE, which is a prognostic variable in most models. A correct simulation of the snow cover fraction (SCF) is crucial for the computation of surface albedo during the winter season and the literature presents several parameterizations for use in GCMs

(Dickinson et al., 1993; Marshall et al., 1994; Sellers et al., 1996a; Yang et al, 1997).

In many GCMs, the parameterization of SCF is oversimplified. As a typical deficiency in GCMs, it is assumed that SCF is independent of the vegetation type. However, it is known that SCF over forests, e.g., depends on a number of parameters such as the density of the foliage and the snow intercepted by the canopy. The more closed the canopy, the less incoming solar radiation directly reaches the ground without being reflected at tree elements. In order to realistically compute SCF, it is thus crucial to account for varying canopy densities and the snow amount which is intercepted by the canopy.

As another typical deficiency, SCF in GCMs does not depend on orography, despite the fact that snow spreads more homogenously in flat areas compared to mountainous regions where steep slopes encourage redistribution of snow by wind and avalanches. Moreover, southern faced slopes (northern faced in the Southern Hemisphere) yield more rapid snow melt due to higher insolation when compared to horizontal plains. In addition, SCF depends on the height variation within the grid. As temperature usually decreases with height, the form of the precipitation and snow melting can differ within a single GCM grid element. The inclusion of the subgrid scale orography, i.e., the deviations of height within the grid square from the mean grid-box height, might thus yield more realistic SCF parameterization (Walland et al., 1996; Roesch, 2000).

For the above reasons, the SCF should include the effects of forests and mountainous regions in their parameterization. This paper provides a detailed investigation of SCF over forests as well as flat and mountainous areas and derives parameterizations which are tested in 3-D climate simulations (Section 4). As the main result, a compact formula for SCF is proposed in Section 4.4. The new SCF parameterizations are tested within the framework of 3-dimensional model simulations using the ECHAM4 GCM at T42 horizontal resolution (Section 5). Section 2 describes the model and Section 3 the data.

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