Introduction

Chapter 2 describes the complexity of snow physics. Most of the processes occurring inside the snowpack or at the snow-atmosphere interface can be represented in sophisticated snow models (see Sections 4.1 and 4.2) but not in snow param-eterizations developed for General Circulation Models (GCMs) (see Section 4.4) because of the necessary limitation of computation time. Some snow processes have little effect on snow-atmosphere energy and mass exchanges while others are critical. The first group can be neglected in snow parameterizations for GCMs while particular attention should be paid to the second group.

This section describes the sensitivity of snow models to different interfaces or internal parameters. The effects of surface heterogeneity are not considered here; they are discussed in Section 4.4. Following Loth and Graf (1998b), this investigation used a reference run of a snow model and compared it with runs with the same model where input parameters or parameterizations were changed. In this investigation, we used the snow model CROCUS (Brun et al., 1992) to compare simulated snow depth. Although snow water equivalent (SWE) is of greater interest and easier to interpret than snow depth in most applications, snow depth is better for assessing the performance of a snow model for the following two reasons: (1) it can be automatically measured with great accuracy, which means that daily and even hourly series of observed snow depth are available; (2) SWE is only sensitive to the energy and mass balance of the snow cover, while variations of snow depth also depend on the densification of the snow cover, which is a major process affecting the thermal properties of the snowpack. The CROCUS model runs cover the complete snow season 1993-1994 at Col de Porte (French Alps, 1320 m a.s.l.).

The sensitivity of the model's results to the following parameters has been investigated:

• liquid water retention;

• sensible and latent heat fluxes;

• rain-snow criterion;

other parameters also affect model results. That is particularly the case with snow emissivity but currently there is general agreement on its values, thus it is not necessary to investigate model sensitivity to it.

4.3.2 Sensitivity to albedo parameterization

Albedo is certainly the first physical property of snow that climatologists need to consider in climate simulations because it is considered as a major source of positive feedback (Randall et al., 1994). Since snow reflectance strongly depends on the size and shape of snow grains, a physically based calculation of albedo requires calculating the metamorphism of the different snow layers. Since it cannot be simply achieved, snow parameterizations designed for GCMs usually calculate snow albedo as a function of the age of the snow surface. This is meaningful because metamorphism generally induces grain growth when snow is ageing. Nevertheless, high temperature gradients prevailing in seasonal snowpacks may often create faceted grains (depth hoar), large grains but with small optical size because of their facets (see Sections 2.2.4 and 2.5.2). In such common cases, a calculation of snow albedo from the age of the surface snow can lead to a significant underestimation (Sergent etal., 1998).

- Measured snow depth

- - - Reference simulated snow depth

- - - CROCUS albedo without ageing effects --CROCUS albedo without grain effects

- Measured snow depth

- - - Reference simulated snow depth

- - - CROCUS albedo without ageing effects --CROCUS albedo without grain effects

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Figure 4.2. Sensibility to ageing and grain size in albedo calculation on snow depth simulations. (Plate 4.2.)

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Figure 4.2. Sensibility to ageing and grain size in albedo calculation on snow depth simulations. (Plate 4.2.)

To emphasize the sensitivity of snow modeling to the parameterization of the albedo, six simulations have been performed with CROCUS where only the calculation of albedo differs.

• The first using the original version of CROCUS where albedo is calculated on three wavelength bands ([0.3-0.8 x 10-6m], [0.8-1.5 x 10-6m] and [1.5-2.8 x 10-6m])and depends on grain size and shape and on the snow surface age. Ageing acts only on the first band. It is supposed to represent the deposition of dust at the surface.

• The second with the CROCUS dependence of albedo on the grain's size and shape on the three bands but without taking ageing into account.

• The third with the CROCUS dependence of albedo on the age of the snow surface but not on the size and shape of the grains.

• The fourth to sixth simulations with a constant value for the albedo respectively equal to 0.85, 0.725, and 0.60 in all bands. Generally, snow albedo varies between 0.85 and 0.60.

In all simulations, forcing shortwave downward radiation was split into three wavelength bands from pyranometer measurements according to a parameterization of the shortwave spectral distribution as a function of cloudiness and of the ratio between direct and diffuse radiation.

Figure 4.2 represents simulations one to three and shows that the effects of grain size on snow albedo and the effects of ageing of the snow surface are in the same

-Measured snow depth

--Constant albedo = 0.725

--Constant albedo = 0.6 (lower curve)

-Measured snow depth

--Constant albedo = 0.725

--Constant albedo = 0.6 (lower curve)

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Figure 4.3. Sensibility to albedo on snow depth simulations. (Plate 4.3.)

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Figure 4.3. Sensibility to albedo on snow depth simulations. (Plate 4.3.)

order of magnitude. Figure 4.3 represents simulations four to six and illustrates the sensitivity of the snow model to the albedo. With the two extreme values of 0.85 and 0.60, complete melting of the snow cover differs by about two months. With the average value of 0.725, the model gives reasonable results but it is compensating between a too active melting during the accumulation period (end of November, February) and a less active melting during the melting periods in March, April, and May. This clearly shows that despite the extreme sensitivity of snow models to the albedo, some simple parameterizations can give reasonable results (Essery et al., 1999).

4.3.3 Sensitivity to the parameterization of water retention

As seen in Section 2.4, wet snow retains a significant amount of immobile liquid water. Except in very high-latitude regions, the snowpack commonly undergoes diurnal melting-refreezing cycles during the melt season. A part of the liquid water produced during the day at the surface is retained by immobile saturation and may refreeze during the following night, typically under clear-sky conditions. If we consider a snow layer of 300 kg m-3 with a common immobile saturation of 5% of the pore volume, a common refreezing depth of 15 x 10-2 m corresponds to a

Effects of water retention

-Measured snow depth

- - - No immobile retention

Effects of water retention

-Measured snow depth

- - - No immobile retention

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Figure 4.4. Sensibility to water retention on snow depth simulations. (Plate 4.4.)

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Figure 4.4. Sensibility to water retention on snow depth simulations. (Plate 4.4.)

refreezing of about 5 x 10-3 m of liquid water, which corresponds to a release of latent heat equal to about 1.5 x 106 J m2. In such a case, this amount of refrozen water may represent about 30% of the snow water equivalent produced by melting during the previous day. This refrozen water will be available for a second melting during the following day or later, increasing the energy necessary for the melting of the snowpack. Most snow parameterizations for GCMs cannot take this effect into account because its physically based simulation requires multi-layering with numerous thin layers close to the surface.

To illustrate the sensitivity of snow modeling to the parameterization of this process, we ran two versions of the CROCUS model which differ only by the simulation of immobile saturation. To avoid feedback effects, the albedo was fixed to a constant value of 0.725 in both versions because suppressing water retention in the model had a strong impact on metamorphism and on albedo. Figure 4.4 compares the results of both versions. Focusing on the very active melting period extending from mid-February to the end of March, it is obvious that the melting rate is significantly increased when retention is not taken into account in the snow model. An apparently contrary effect is observed at the beginning of January. Indeed, the absence of retention affects the compaction rate of wet snow, which means that the wetting event following the heavy snowfall recorded at the end of December induces much less densification without retention than with retention. Therefore, the simulated snow depth during this period when water retention is not taken into account is greater.

The increase of the melting rate during melting-freezing cycles simulated when water retention is not taken into account would be enhanced at locations where diurnal cycles show large amplitudes. This is typical at high elevation in mid- or low-latitude regions where meteorological situations with intense solar radiation during the day and strong refreezing during the night are common. A snow model that does not take into account retention and the refreezing of immobile liquid water would calculate a water outflow at the bottom of the snowpack as soon as surface melting occurs. Indeed, a shift of one month between the onset of surface melting and the runoff of melting water is common at high elevations in alpine regions. At least for hydrological purposes, this process must be considered in snow models.

4.3.4 Sensitivity to the parameterization of turbulent fluxes

Sensible and latent heat exchanges significantly contribute to the energy and mass balance of the snowpack (see Section 3.2). A common feature of snow-covered regions is that the surface boundary layer is stable most of the time. Since the present knowledge of turbulent fluxes under stable conditions is still relatively poor, snow models can calculate these fluxes in different ways. In most parameterizations, stability and roughness length are key parameters that strongly affect the calculated fluxes. Large uncertainties still exist regarding the effect of high stability on the decrease of turbulent fluxes (Kondo etal., 1978; Musson-Genon, 1995) as well as on the roughness length of the different types of snow surfaces (Martin and Lejeune, 1998). To show the sensitivity of a snow model to both stability and roughness length, we have performed different runs with various versions of CROCUS, which use a parameterization of turbulent fluxes deduced from Deardoff (1968).

The effects of stability are calculated by using the ratio between the transfer coefficient under stable or unstable conditions and the transfer coefficient under neutral conditions. This ratio depends on the bulk Richardson number RiB (see Section 3.3.4). When RiB tends to 0.2, the transfer coefficient rapidly tends to 0 and then inhibits any turbulent flux; 0.2 is quite a common value for RiB above snow, and field observations show that turbulent fluxes cannot be neglected under such stable conditions (Martin and Lejeune, 1998). Figure 4.5 compares the results of three different versions of CROCUS. The first version uses Deardoff's parameterization (full effect of stability), which induces an obvious underestimation of the melting rate during spring. This is due to the underestimation of sensible heat fluxes during the relatively warm conditions prevailing in March. Indeed, since the snow surface temperature is limited to the melting point, RiB is generally larger than 0.2 in such

Effect of the stability of the boundary layer

-Measured snow depth

- - - Full effect of stability

— - Half effect of stability

No effect of stability (lower curve)

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Figure 4.5. Sensibility to the stability of the boundary layer on snow depth simulations. (Plate 4.5.)

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Figure 4.5. Sensibility to the stability of the boundary layer on snow depth simulations. (Plate 4.5.)

meteorological conditions and Deardoff's equations calculate negligible fluxes. The second version uses Deardoff's parameterization for unstable conditions but considers neutral conditions in the calculation when conditions are stable (no effect of stability). With this version, the melting rate is much more realistic. The third version is intermediate. It considers the effect of stability under stable conditions but it limits the decrease of turbulent fluxes to half of the turbulent fluxes calculated for neutral conditions (half of the effect of stability). The results are intermediate between both previous cases. This comparison shows that particular attention must be paid to the parameterization of the effects of the stability of the surface boundary layer on the calculation of sensible and latent heat fluxes. Because no completely suitable parameterization is presently available, numerous snow models neglect the effects of stability under stable conditions and consider that the conditions are neutral. However, GCMs take stability effects into account when calculating turbulent fluxes over snow-covered regions.

Under stable, neutral, or unstable conditions, the turbulent fluxes of sensible and latent heat depend on the roughness length zo of the surface. Even over homogeneous snow-covered surfaces, an accurate knowledge of the roughness length of snow surfaces is still lacking. The roughness length z0 of seasonal snow commonly ranges around 2 x 10-4 m but it varies over a large spectrum. Figure 4.6 compares the snow depth simulated with different versions of CROCUS where only z0 changes. To

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Figure 4.6. Sensibility to snow roughness length on snow depth simulations.

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Figure 4.6. Sensibility to snow roughness length on snow depth simulations.

emphasize the comparison, turbulent fluxes under stable conditions are calculated as under neutral conditions. It shows that the value given to z0 has a strong impact on the model results. The smaller the roughness length, the smaller the turbulent fluxes and consequently the smaller the melting rate because sensible fluxes are positive, i.e. downward most of the time. At Col de Porte, the best results are obtained when z0 is equal to 3 x 10-3 m. This rather high value for snow is partially due to the forest surrounding the test site.

4.3.5 Sensitivity to the snow-rain criterion

In nature, snowfall and rainfall occur over a range of temperatures. The temperature at which snow flakes melt and turn to rain drops depends on the vertical profile of temperature and humidity in the atmosphere and on the precipitation rate. In snow models and parameterizations, separation between snow and rain is generally deduced from the air temperature when direct observations of the precipitation type are not available. Several studies on the snow-rain criterion have been conducted but no universal criterion exists. For example, the criterion is different in regions of flat terrain where the surface boundary layer is well developed compared with the top of a mountain where meteorological conditions are closer to the free atmosphere conditions. To illustrate the sensitivity of snow modeling to the snow-rain criterion,

Effect of snow-rain criterion

-Measured snow depth

- - Snow-rain criterion = 0.5 °C -Snow-rain criterion = 1.0 °C

-Measured snow depth

- - Snow-rain criterion = 0.5 °C -Snow-rain criterion = 1.0 °C

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Figure 4.7. Sensibility to snow-rain criterion on snow depth simulations.

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Figure 4.7. Sensibility to snow-rain criterion on snow depth simulations.

we ran four versions of CROCUS where the unique change was a criterion based on the air temperature varying from 0 to 1.5 °C. Figure 4.7 compares the snow depth simulated with the four versions. At Col de Porte, during the season 1993/1994, most of the differences came from a rainfall event occurring at the beginning of January at a temperature close to the melting point. It is obvious that the sensitivity of snow models to the snow-rain criterion strongly depends on the prevailing climate of the considered region. In temperate regions, winter snowfalls often occur at relatively warm temperatures and model results should be very sensitive to the criterion. In contrast, in cold and continental regions snowfalls occur at relatively cold temperature and the transition from winter to summer and from summer to winter is short enough to predict that snow modeling should not be very sensitive to this criterion.

4.3.6 Conclusions

Snow models are very sensitive to the parameters that affect the energy balance of the snowpack. Therefore, particular attention should be paid to the choice of these coefficients or parameterizations. Fortunately, compensation for the effects of different processes often limits the consequences of a given parameterization, which means that different models may have similar results (Essery et al., 1999).

In addition to the choice of parameter values, choosing the number of computational layers is of major importance to the model results and the model costs. Boone and Etchevers (2001) have shown that a three-layer snow model can perform almost as well as a more sophisticated model, at least in terms of energy balance, surface temperature, and snow-water equivalent.

In order to provide scientists with relevant guidelines for designing snow models appropriate to their region of interest, the International Commission on Snow and Ice initiated a project called SNOWMIP (snow model intercomparison project) (Essery and Yang, 2001). The objective of this project was to compare snow models of various complexities at four sites belonging to various climatic regions. A total of 24 models from 18 teams were involved. The models varied from simple models designed for hydrology to sophisticated ones designed for snow physics research. The main conclusions of the first phase of the project are given below (Etchevers, et al., 2003).

• Some models showed a good ability to correctly simulate the snowpack features for all of the sites, whereas other models appeared to be more adapted to particular conditions. The high alpine site was the best simulated site, because the accumulation and melting periods are distinct.

• A detailed analysis showed that parameterization of the albedo was critical. A parameterization depending only on snow age gave less reliable results on the onset of snowmelt. Accounting for snow evolution in a better way (using a density evolution, or a grain size evolution as in detailed models) generally improves the models.

• The retention of water in the snow cover is also important. Bottom runoff usually began earlier in models without water retention. The water retention allows a part of the daily snow melt to refreeze during the night.

• This intercomparison based on data from open sites is now extended to forested sites. The second phase will be devoted to the representation of the interaction between snow and forest. At the end of this last phase, SNOWMIP will provide unique and comprehensive information on the ability of snow models to simulate various aspects of snow dynamics.

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