Subgrid parameterisation schemes

Subgrid parameterisation I: topography

For the subgrid parameterisation of topography, each 8-km DTM cell is segmented into three subareas of equal size: the 64 pixels inside each cell are sorted, then the lowest pixels are assigned to a ''low'' subarea; the same number of highest pixels are assigned to a ''high'' subarea, and, consequently, the remaining pixels are assigned to a ''mean'' subarea. Then the mean altitude for the three subareas is calculated by simply averaging the pixel altitudes inside each of the three subareas. These are determined separately for each model cell and not necessarily coherent, in contrast to the elevation bands as derived by a conventional segmentation of an entire catchment. The resulting subarea altitudes are then used for the interpolation of the meteorological variables with SAFRAN.

Figure 4.3 shows the resulting mean subarea altitudes for the fifty 8-km cells in ascending order with altitude. It can be seen that the vertical extent between the subarea altitudes within one 8-km cell can reach more than 1000 m because of the steep relief. For cells with only few 1-km pixels inside (close to the watershed divide), the vertical extent is less. The geographical distribution of the standard deviation (sigma) of the pixel altitudes in the 8-km cells shows that the highest values can be found in the valleys of the rivers Durance and Guil and the summit region of the Ecrins massif, both being very steep. The smallest standard deviations are again found close to the watershed divide in cells that contain only few 1-km pixels, and in the comparably flat Queyras summit region (in the eastern part of the catchment).

Subgrid parameterisation II: forest climate

The meteorological conditions that affect the snow pack inside a forest canopy vary distinctly from those in

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10 20 30 40 50 60 % of catchment area

Figure 4.3 Hypsographic curve, altitudes of the three subareas (represented by the bar ends and the triangles) in the 50 model cells of 8-km resolution and geographical distribution of the standard deviation of the 1-km pixel altitudes in each 8-km cell

10 20 30 40 50 60 % of catchment area

Figure 4.3 Hypsographic curve, altitudes of the three subareas (represented by the bar ends and the triangles) in the 50 model cells of 8-km resolution and geographical distribution of the standard deviation of the 1-km pixel altitudes in each 8-km cell

the open. One of the goals of this study is to quantify the effects of the presence of a forest on the temporal evolution of snowmelt. These processes are considered in the model by modifying the meteorological variables as provided with SAFRAN and a variable albedo parameterisation in CROCUS taking into account the faster decrease of albedo inside the canopy. The main phenomena that affect the climatic conditions inside a forest are the following: shadowing effect of the trees for solar radiation (visible direct and diffuse as well as longwave), longwave radiation of the trees, increase of humidity, reduction of wind speed, reduction of temperature fluctuation amplitudes and interception of precipitation (including sublimation, melt and snow sliding from the branches). To characterise a forest, a certain number of parameters can be used: its density, the type and shape of the trees, their size or the LAI. However, for spatial applications at the scale as the one presented here it is necessary to define mean forest characteristics for the area to be modeled and not look at features of single trees. Here, the mean density of the forest, the mean tree height and the LAI are used.

The forest climate model used in this study was developed and validated by Durot (1999) at the Col de Porte station in the Chartreuse Massive in the French Alps. Since it has not been applied on a regional scale in combination with a distributed hydrological model before, it is described in detail in the following section. The model calculates the modified meteorological variables in a forest canopy, which are then used as input for CROCUS: direct, diffuse and longwave radiation, temperature, humidity, precipitation and wind speed. Thus, two snow covers are modeled separately in each grid cell: one for forest and one for open land conditions. The fraction of each cell that is covered by forest is derived from a landuse map.

The forest climate model

Generally, the reduction of the turbulent exchanges inside the canopy diminishes the sensible and latent heat fluxes, thus making the net radiation fluxes the principal energy sources for snowmelt. The radiative characteristics of a forest have a significant effect on the evolution of the snow cover. The albedo of the forest itself, usually between 0.1 and 0.3, changes considerably with the presence of snow under the trees. On the ground, the incoming radiative fluxes are diminished because of the vegetation cover. To describe this interception process, a wide range of models with different complexity has been developed. The model by Li and Strahler (1986, 1992) is the most detailed one but requires a large number of input parameters that can only be reliably provided for the plot scale. Monteith and Unsworth (1990) use the exponential decrease of the Beer-Bouguier law to describe the extinction effect, considering the LAI and a coefficient depending on the geometry of the trees as well as the incidence angle of the sun. A detailed historical overview of the different approaches is given by L'Homme (1991).

In this study, a simple formula assuming a linear dependence of the extinction with the forest density (Bowles et al. 1994) for both direct and diffuse radiation is applied:

Despite the attenuation of the incoming solar radiation, the canopy is also a source of longwave radiation by emitting part of the visible radiation absorbed like a black body in all directions. Thus, for the snow on the ground a new net balance of infrared radiation is calculated, taking into account the extinction of atmospheric radiation and emission of the vegetation:

Qiff = Qi • (1 - Df) + Df • £f • a • Talrf (4.3)

The emissivity of the forest depends on the tree type and can be represented by values close to a black body (Berris and Harr 1987). Here, it is assumed to be 0.97. For the radiation temperature of the trees, it is assumed that it is approximately equal to the measured temperature between the leaves (Davis and Hardy 1997), here represented by the estimated air temperature for the canopy. The latter has a vertical gradient that plays an important role for the heat exchange. Mostly during the day, the temperature in the canopy is higher than above, but it decreases rapidly downwards to the ground. During the night, the temperature can be very low outside the canopy, but inside it remains higher. As an effect, the forest temperature and particularly its daily amplitude is less pronounced than in the open. In the annual mean, the forest temperature is lower, but during winter it can be higher. Since it is usually measured directly, only few formulae exist to derive forest canopy temperature from standard observations. Here it is estimated using the model proposed by Obled (1971), which uses the mean daily temperature and a constant scaling parameter Rc = 0.8:

where Tmean = Tmax + Tnin) • 0.5 and AT = (Tmean -273.16)/3, with AT limited to the range -2°C < AT < +2°C. With Tmean and AT, respectively, the daily and seasonal effects on the temperature amplitudes are considered.

Generally, the humidity in the forest is increased because of the evapotranspiration from the trees (during summer). Durot (1999) conducted a series of measurements to evaluate the effect of the vegetation activity. In the mean, the humidity is approximately 10% higher inside the forest canopy (RHf = 1.1 • RH), but this increase is larger if the snow that is intercepted by the trees melts and falls down. In this case, it is estimated to be 20% (RHf = 1.2 • RH), which often leads to conditions close to saturation.

Wind speed is considerably reduced by a forest canopy, little in the corona layer and almost to zero close to the ground. The vertical wind profile depends on the forest type and its density (Jeffrey 1968). Bonan (1991) developed a model describing the wind speed inside the forest canopy depending on the height:

The parameter a was found to be equal to 3 for a wide range of conditions (Bonan 1991).

Solid precipitation is always partially intercepted if a vegetation cover is present, and then undergoes a more or less pronounced evaporation. Thus, a forest canopy can have a significant effect on the water resources of a basin. Numerous studies exist, investigating such consequences for the water balance of certain regions. Harding and Pomeroy (1996) found a loss of intercepted snow by evaporation of almost 30% in their study region in the United States. Schmidt (1991) investigated the sublimation of intercepted snow with an artificial tree. On the other hand, Jeffrey (1968) showed that the sublimation losses by interception in the canopy can often be neglected.

Those studies show that the interception phenomenon depends on the region and its climate. Extrapolation of interception rates into other geographical regions often leads to wrong results (Lundberg and Halldin 1994). Satterlund and Haupt (1967) concluded their study that no universal formula exists for the storage of snow and the interception loss because of the complexity of the processes involved after the deposition of snow on the trees.

In the model presented here, the precipitation as provided by SAFRAN is modified for the consideration of the interception processes according to

In the following, the derivation of I, Pc and Mt will be explained: the total interception is composed by the interception of solid precipitation (snow) and liquid precipitation (rain). Thereby, the snow interception is calculated considering the maximum snow interception, a cumulative precipitation of the snowfall event and a threshold precipitation:

Effectively, the values of Vmax and k depend on the density of the snow, being a function of the meteorological conditions and particularly the temperature and wind. For different conditions with low wind speeds and snow densities and for three different types of conifers, Schmidt and Gluns (1991) found Vmax = 5,P0 = 4 and k = 0.75 mm-1. They show that the difference of accumulation between various species of trees is less important than the one between different snowfall event types. Therefore, it is the meteorological conditions that mostly affect the process of interception. For low snowfall events (<2mm), the formula gives unrealistic results; then it is replaced by the simple linear parameterisation (Keller and Strobel 1979):

The amount of intercepted snow on the trees is reduced and, finally, removed from the storage by evaporation, melting, gliding or falling down to the ground, and redistribution by wind. Because of the comparably small height of the intercepted snow (app. 15 cm max.), it can be assumed that in the model the intercepted snow can be represented with a homogeneous snow cover (Durot 1999).

The evaporation of the snow is calculated as latent heat flux from the canopy allowing to introduce a parameter characterising the aerodynamic resistance of the canopy, after Monteith (1965):

Zm d zo

d is assumed to be 75%, and z0 10% of the tree height. Thus, the latent heat flux can be written as

_ Le-Pa 0.622 • e, • T^j ■ (RHf - 1) Ma ■ Pa Ra

Finally, the evaporation rate for the time step is given by

The interception of rain is distinctly different from that of snow. Again, a number of empirical or statistical formulas exist to quantify the evaporation losses ofwater intercepted by trees (e.g., Calder 1986,1990). According to the bibliographic synthesis of Msika (1993), the rain interception is in the range of 30-45% for pine, spruce and fir. For other species, it is less than 30%. Storage capacity is assumed to be 2.5 mm (Hutchings et al. 1988). During a rainfall episode, the interception reservoir is filled with a certain percentage b of the precipitation at every time step. If the storage is filled, the tree cannot intercept more water and the processes of drainage from the tree and evaporation start to reduce the intercepted amount of water:

Evaporation from the interception reservoir is estimated using the classical formula by Penman (1956).

The large amount of needles or leaves and particles falling down from the trees has an important effect on the albedo and its decrease with the densification and metamorphosis of the snow cover surface. Thereby, the reduction of the albedo under trees is faster than for open conditions and decreases to values of 0.45 at melting conditions (Barry et al. 1990). To take this effect into account, the ageing parameter for the albedo simulation in CROCUS is multiplied by two, and the minimum albedo is set from 0.7 (open land) to 0.45 for the radiation band 0.3 to 0.8 ^m. However, the modified albedo has only little influence on the energy balance of the snow inside the canopy because of the comparably small amount of solar radiation reaching the ground.

The simulated snow cover inside a forest canopy close to Col de Porte, calculated using the meteorological variables achieved with all these modifications, was compared with stake and pit measurements for several seasons; the results showed good agreement (Durot 1999).

The forest density was calibrated for the Col de Porte area and is taken here as spatially constant for the Durance catchment. Future investigations will concern a more physically based interpretation, for example, the derivation of vegetation parameters such as LAI or the normalised difference vegetation index (NDVI) from satellite images and the formulation of a mathematical relationship between the vegetation parameters and the forest density.

The landuse distribution in the upper Durance catchment

For the application of the forest climate model, the spatial fraction of forest in each cell or altitude subarea of a cell,

respectively, has to be determined. Therefore, a two-step analysis is performed: in a first step, the forest fraction per 8-km model cell is calculated for the experiment with the original 8-km resolution. Then the forest fractions for the three subareas inside each of the 8-km model cells are determined for the third experiment, which combines the altitude subareas with the forest climate model.

For all analyses, the landuse map derived from satellite images (NOAA/AVHRR and Landsat) and provided by the CORINE land cover database (Cornaert et al. 1996) with an original resolution of 250 m was used. The processing steps applied to the vegetation map include classification, geometrical rectification (rotation and compensation of distortion) and statistical aggregation. The result is illustrated in Figure 4.4. The ''forest'' fraction of the resulting 8-km resolution map (a) takes the ''coniferous forest'' class and half of the ''mixed forest'' class of the original map (b) into account, considering that only conifers, keeping their needles during winter, affect the meteorological variables as simulated by the model.

According to Figure 4.4, the higher fractions of forest cover can be found in the valley bottoms of the Durance and Guil. For the entire catchment, the forest cover is 26% (see Table 4.1).

4.4 RESULTS

The improvement of the modelling results as achieved with the transition from 8 km to 1 km resolution has already been quantified by Etchevers etal. (2001a). Here these 1-km resolution results represent the accuracy reference for the subgrid parameterisations as performed in this study.

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