The SCF of forests is difficult to assess since snow on the ground is strongly masked by the overlying canopy. In addition, snow intercepted on the canopy further complicates the SCF parameterization.

A detailed representation of the radiation fluxes within the canopy is a prerequisite for the computation of the total forest albedo. Numerous canopy models which focus on radiation transfer have been developed in the past (Dickinson, 1983; Sellers, 1985; Yamazaki et al., 1992; Joseph et al., 1996). They are usually based on the two-stream approximation and thus reduce the complex radiation transfer through canopies to a one-dimensional problem. The main deficiency of these rather sophisticated models arises from the need for further assumptions, such as randomly distributed leaves, and from the necessity to make those input data available on a GCM-grid.

Therefore, a second approach involving less assumptions and only available input data is used for the development of a new SCF parameterization. Various studies (Otterman, 1984; Barker et al., 1994; Yang et al., 1997) demonstrate that the SCF over forests is likely to differ from that over grass and agricultural lands. These studies suggest that over forests, an exponential relationship between SCF and SWE is more appropriate. However, these simple approaches neglect the structure of the forests. They consider neither variations in the leaf area index nor do they distinguish broad- and needle-leaf trees. They do not account for openings in the canopy where solar radiation reaches the (possibly highly reflective snow covered) ground without being reflected at tree elements. Furthermore, the process of snow intercepted by the canopy is neglected. Most of the above processes are considered in the Canadian Land Surface Scheme (CLASS, detailed in Verseghy, 1991). This parameterization is kept as simple as possible and does not require further surface boundary fields. As CLASS does not include the relevant processes leading to variations in the snow mass intercepted by forests, a simple snow interception model was developed. The relevant equations adopted from CLASS are briefly discussed in the next subsection.

4.4 Albedo of snow covered forests as in CLASS

CLASS computes the albedo of snow-covered forests using Eqs. 8, 9, 10, 11 and 12. Note that no other CLASS parameterizations (e.g., the computation of the snow albedo or the structure and heat conduction of the snow-pack) were adopted in ECHAM4.

CLASS allows for snow on the forest canopy. It is based on a simple algorithm, yet is dedicated to capture the principal relationships between the canopy albedo and snow water equivalent on both the underlying ground and the canopy.

The key parameter for the computation of the albedo of snow covered forests in CLASS is the sky view factor (SVF) which describes the degree of canopy closure. The SVF is related to the leaf are index by an exponential function:


(needleleaf trees) (broadleaf trees).

The total surface albedo of forests is computed as a =SVF-a +(l-SVF)-ac,

where ag is the albedo of the ground underneath the canopy and ac is the albedo of the closed canopy. The snow albedo on the ground is assumed to be the same as in the open area, which is in line with the findings of Pomeroy and Dion (1996). ac is given by ac = fsc '«sc +(l-0-fj-o c,snowfree '

where is the albedo of closed canopy with a maximal snow interception, and ac> Snowfree is the snowfree canopy albedo. asc is set to 0.20, from values given in the literature (e.g., Verseghy, 1991; Harding and Pomeroy, 1996; Pomeroy and Dion, 1996). The fraction of the canopy covered by snow, fsc, is defined as where Snc is the water equivalent of snow intercepted by the canopy and

Verseghy (1991) reports that Eq.12 works well for both rain and snow and for a wide variety of vegetation types and precipitation events. This means that for LAI = 5, an amount of snow equal to 1 kgnr2 (or 1 cm of fresh snow) is sufficient to fill the canopy storage capacity.

The computation of the albedo of snow covered forests using Eqs. 8-12 requires the snow water equivalent of the snow intercepted by the canopy. In CLASS, snow on the canopy is removed by sublimation only. Therefore, a model for must be developed. This will be assessed in the next section.

where Snc is the water equivalent of snow intercepted by the canopy and

4.5 Snow interception model

CLASS does not allow for the processes which are relevant for the snow mass intercepted by the canopy. In particular, it does not account for downloading of snow triggered by wind and temperature close to or above freezing point. Hence, as the current version of ECHAM4 sustains no reservoir for snow intercepted by the canopy a simple snow interception model was developed.

The prognostic variable Snc evolves according to the following equation:


Evaporation rate from the skin reservoir for intercepted snow [kgm'V1]

Snowfall rate per unit area intercepted by the canopy Snc Snow water equivalent of the snow intercepted by the canopy [kgm"2]

f(Tj) Function describing unloading of intercepted snow per time step caused by temperature at the lowest model level f(v) Function describing wind-induced downfall of intercepted snow per time step

Eq. 13 includes the major processes affecting the amount of snow intercepted by the canopy, i.e.:

(1) snowfall rate

(2) unloading due to temperature (melt/drip and slipping) (Eq. 14)

(4) sublimation of intercepted snow.

It is assumed that snow sublimation is at its potential rate. In order to keep Eq. 13 as simple as possible, f(Ti) is specified as a linear function in such that f (-3°C) = 0.0. The unloading rate due to melting is assumed to vanish for temperatures below Tj = -3°C. The value of the denominator allows for the unloading of half the intercepted snow during 12 hours at Tj = 0°C. For a temperature of 2°C, approximately 70% of the intercepted snow is unloaded during 12 hours. The considerable increase in unloading for air temperature above 0°C agrees with a rapid decrease of snow on trees after a snowfall caused by slipping and melt (Nakai et al., 1994). Eq. 14 is also in line with an exponential decrease of the crown-snow ratio with time, depending on the air temperature and wind speed (Yamazaki et al., 1996). According to this study, the response time t (reduction to -37% of initial value) of the crown-snow is about 1/2 day when the air temperature is below 0°C, and 1 - 5 hours when it is above 0°C. This is in reasonable agreement with the newly-developed model.

After snowfall, release of intercepted snow, triggered by branch movement due to wind influence, is generally observed. Unloading may also be caused by the atmospheric shear stress exerted by wind on the branches and snow. Betts and Ball (1997) analysed Boreal Ecosystem-Atmosphere Study (BOREAS) measurements from 1994 and 1995. They found that (winter) forest albedos above 0.3 correspond to days with low wind speeds of less than approximately 3 ms"1. Miller (1962) reports that snow interception considerably decreases when the wind speed during snowfall is larger than 2 ms-1. The equation for the wind induced unload of intercepted snow was assumed to be similar to that of temperature. In Eq. 15, v [ms"1] represents the wind speed at 10 m above the ground, which corresponds, to a first approximation, to the mean canopy height.

With this denominator 50% of the intercepted snow is unloaded within 6 hours for This interception model does not presume that the intercepted snow load approaches zero between each snowfall event as most simple interception models do (Hedstrom and Pomeroy, 1998).

4.6 Compact formula for the surface albedo of the entire grid-box

In the previous sections, improved SCF parameterizations have been separately derived for both non-forested and forested areas. In order to determine a closed formula for the surface albedo of an entire grid box, the formulae for SCF of non-forested areas will be combined.

Applying both Eqs. 6 and 7 produces an inhomogeneity as Eq. 7 approaches the current ECHAM parameterization (Eq. 2) for c z —> 0 . In order to fulfil the requests of both parameterizations, Eqs. 6 and 7 were merged:

Eq. 16 applies to non-forested (subscript "nf") areas.

The total surface albedo asfc can now be determined as an area-weighted sum of the surface albedo over non-forested (1-af [1-SVF]) and forested (af [1-SVF]) areas, respectively. The non-forested part consists of the two terms and as the canopy openings must be counted to the forest-

free part.

asfc = [1 - af(1 - SVF)} [fs,nf • as +(1- f5,nr)- asnfr ]+ af(1 - SVF). ac (n) where fractional forest area ac albedo of closed forest (Eq. 10) snow albedo albedo of unforested and snow free surfaces surface albedo for the entire grid box.

All other abbreviations are as in Eqs. 9 and 16.

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