3.1.1. Relation between snow mass flux and data recorded by the acoustic sensor

The mass flux of drifting snow is one parameter in our numerical model. Up to now, the mass flux has been inferred from the wind speed by means of an empirical law (Reference Pomeroy and GrayPomeroy and Gray, 1990). In order to improve the model, however, we would like to obtain measurements of the flux. To this end, we plan to calibrate the acoustic sensor, in order to deduce the flux of drifting snow from the recorded signal. Therefore, we have performed experiments in which we compare the average mass flux during 15 min, and the average recorded signal.

The mass flux was determined using mechanical snow traps, called “butterfly nets”. These have a rectangular metal frame (15 cm × 2 cm) with an attached nylon bag. The traps, facing the prevailing wind direction, are fixed at different heights on a pole, next to the acoustic sensor. We obtain the drifting-snow flux by integrating the mass weight at each height. The collection efficiency of such mechanical traps depends on the wind speed and can be significantly below 100% (Reference FontFont, 1999). Lacking additional information, we applied no corrections.

The recorded signal is highly dependent on the snow depth. Therefore the acoustic sensor was fixed on a pole in a manner that allowed it to be raised during winter (Fig. 3). During the experiments for sensor calibration, the sensor was situated in an erosion zone with no snow on the ground. A plot of mass flux vs height with the output voltage as parameter is presented in Figure 5. The measurements correspond to two drifting-snow events (with and without snowfall). First of all, the data fit quite well with the values reported in Reference Mellor and FellersMellor and Fellers (1986) who did not distinguish the effect of snowfall in their experimental data processing (Reference Naaim-Bouvet, Naaim and MartinezNaaim-Bouvet and others, 1996). Here, however, the effect of snowfall is obvious: the mass flux above 1.3 m is constant and fairly substantial (8 gm–2 s-¹).

Fig. 5. Relation between the snow mass flux and the data recordedby the acoustic sensor for different wind speeds (ms–¹).

Moreover, we can compare the total measured mass flux (19–194 cm above the snow layer) and the sensor signal (Fig. 6). We notice a good correlation, but the low number of experiments prevents us from drawing final conclusions.

Fig. 6. Total measured mass flux (19–194 cm above the snow layer) vs the output voltage of the acoustic sensor.

3.1.2. Influence of snow-particle type on the acoustic sensor

Figures 7–9 illustrate the signal recorded by the acoustic snowdrift sensor (average signal over 15min vs the wind velocity) for various snowdrift episodes and thus for different snow types. In order to determine the snow type, we decided to rely on the SAFRAN (Reference Durand, Brun, Merindol, Guyomarc’h, Lesaffre and MartinDurand and others, 1993)/Crocus (Reference Brun, David, Sudul and BrunotBrun and others, 1992) model, for two reasons. Firstly, we were not always on our experimental site at the beginning of the drifting-snow event, so we have no other information about the snow type. Secondly, we are developing a connected model in which the output of SAFRAN/Crocus will be the input of our numerical drifting-snow model.

Fig. 7. Voltage (mean value over 15 min) from acoustic sensor No. 5 vs wind speed (mean value over 15min) for different drifting-snow events.

Fig. 8. Voltage (mean value over 15 min) from acoustic sensor No. 1 vs wind speed (mean value over 15 min).

Fig. 9. Evolution of snow depth near acoustic sensor No. 5 during winter 1998/99.

On 4 March 1998, we observed an episode with both snowfall and wind that appears as widely scattered data points in Figure 7. In this case, the mass flux was correlated with both the wind speed and the snowfall intensity, which was not constant. This scattering of data was always observed in episodes of snowdrift with snowfall during the winter (see Fig. 8).

The 8 March episode was characterized by drifting new snow, whereas the 17–20 March episode was characterized by rounded grains, and the episodes from 16–18 January and 3 March by faceted grains. The signal induced by rounded grains was higher than that generated by new-snow or faceted grains (see Fig. 7). However, we should keep in mind that this difference in signal might be caused by a shift of the signal due to the variation of the snow depth around the sensor during March. Figure 9 shows the evolution in time of the snow depth at sensor No. 5; the increase during March is caused by snowfall events without wind. The difference between signals for different types of grains was smaller for another sensor where the snow-depth variation was less (see Fig. 8). These observations confirm that a snow-depth sensor must accompany the acoustic sensor in an operational use. This will allow a correction of the data with regard to the ideal situation on which the sensor was calibrated (erosion area without snow).

As mentioned above, the 16–18 January and 3 March episodes were snowdrift events of faceted grains. These two graphs are relatively similar, with a recorded output voltage roughly proportional to the cube of the wind speed. Supposing that the mass flux is proportional to the cube of the wind speed, as predicted by some empirical formulations (Reference Dyunin and KotlyakovDyunin and Kotlyakov, 1980), led us to believe that the snowdrift flux might be proportional to the recorded signal on the acoustic sensor in these episodes. However, data on the calibration of the sensor are insufficient to confirm this hypothesis. On the other hand, preliminary laboratory studies on the acoustic sensor have shown that the signal generated by a quantity Q of sand falling from a height H was the double of the signal generated by a quantity Q/2 of sand falling from the same height within the same time (i.e. with the same speed).

3.2.1. Wind-gustfactor

Data obtained at La Muzelle was processed in three steps. Firstly, we filtered out data with a mean wind speed of < 4 m _s–1. For a wind speed weaker than 4 m s–¹, we considered that there was no drifting snow, or very little. Furthermore, a low wind speed often generates a high gust factor, which is of no interest for the present purpose. A gust factor of 5 produced by a mean wind of 0.5 ms–¹ and a gust of 2.5 ins”¹ is very different from the same gust factor with a mean wind of 5 m s–¹ and a gust of 25 m s–¹.

Secondly, winds were separated into four classes: northerly, southerly, easterly and westerly. As can be seen in Figure 1, the experimental site is a kind of natural cold wind tunnel with a north-south axis. Therefore, a northerly and an easterly wind will probably have different effects.

Lastly, gust factors were calculated both for 15 min average winds and for hourly mean wind speeds, in order to compare our results with previous works.

The obtained gust factors range from 1.1 to 8.8. Sometimes these gust factors were higher than in other experiments (e.g. Reference DeavesDeaves (1993) reported values of <4). However, we found only a few strong gust factors during the winter, and our average gust factor remained around 1.8. It should be mentioned that gust factors have often been investigated near sea level (Reference Beranger and PagesBeranger and Pages, 1958; Reference DeavesDeaves, 1993), whereas the present data were collected in a high-mountain environment. In addition, we used Young anemometers which are very sensitive (response time of Is), whereas Reference DeavesDeaves (1993) used different anemometers. The value of our gust factor also depended strongly on the wind direction. For northerly and southerly winds, the probability P of having a gust factor of > 2 is on the order of 10%, whereas it is much higher for easterly and westerly winds (>40%) (Fig. 10). This large difference is probably caused by the geometry of the Lac Blanc Pass, but there are fewer data available for easterly winds (only 53 hourly data) compared to northerly winds (1139).

Fig. 10. Overstepping probability for northerly and easterly winds.

The probability of a gust factor exceeding a given value G is called the overstepping probability. It is often greater for hourly data than for data collected every 15 min, and it follows a Fisher-Tippet distribution law (Reference DeavesDeaves, 1993). This can be written as:

where a is a scattering parameter and G₀ is a reference gust factor.

For most of our results (see Fig. 11), the data can be divided into two classes with different behaviours, i.e. data with gust factors < 5.5 and > 5.5. At 5.5 there is a kink in the data. Similar results were found by Reference DeavesDeaves (1993), even if the two classes of data were separated by a value of approximately 2.0 in his study.

Fig. 11. The Fisher- Ti_ppet law, for a northerly gust factor at La Muzelle.

Studying events that generate high gust-factor values brings out two different types of events. The first type covers events with no variation in wind direction and a gust factor of 3–4. They reflect a decrease in the mean wind speed during an increase or a smaller decrease in the maximum wind speed. The second type corresponds to events with variation in the wind direction. These events are often characterized by high gust factors of 5.5–8.8. The highest gust factors are observed during wind-direction changes from southerly to northerly. These different types may explain the kink in the Fisher-Tippet law (Fig. 11).

3.2.2. Drifting-snow gust factor

As shown above, the wind-gust factor can provide information on the non-stationary aspects of the wind. Similarly, the gust factor relating to the signal of the acoustic snowdrift sensor, defined as the ratio G_s = maximum signal of the acoustic sensor/average signal, can provide information about the snowdrift.

For this purpose, data from acoustic sensor No. 5 at the La Muzelle site were used. We first removed the offset of the sensor (50 mV). Then we filtered out the average signal < 5mV, because lower values do not correspond to snowdrift. The gust factor was then calculated every 15 min for the whole winter (scan rate of 1 s). We found that the gust factor did not follow a Fisher-Tippet law, but rather a polynomial law (Fig. 12).

Fig. 12. Polynomial law for snowdrift gust factors, based on data from snowdrift acoustic sensor Mo. 5 at the La Muzelle site (p is the overstepping probability).

The first scenario corresponds to areas 1 and 3 in Figure 13, and areas A and B in Figure 14. In the first case (area 1 in Fig. 13, and A in Fig. 14), high wind-gust factors were found, indicating very gusty winds, but very low average snowdrift signals and snowdrift gust factors were observed. Thus, this scenario does not show significant erosion, snowdrift and deposition. The second case (area 3 in Fig. 13, and B in Fig. 14) is characterized by gusty snowdrift episodes with sporadic wind gusts generating moderate snowdrift.

Fig. 13. The average snowdrift signal on acoustic sensor Mo. 5 at La Muzelle.

Fig. 14. The snowdrift gust factor recorded by acoustic sensor Mo. 5 at La Muzelle.

The second scenario corresponds to area 2 of Figure 13 and area C of Figure 14. Due to the limited output voltage of 5000 mV for the acoustic sensor, the maximum snowdrift gust factor is 50 for average signals of > 100 mV, causing the cut-off in Figure 14. This type of snowdrift occurs during more regular wind episodes characterized by low wind-gust factors.

This study of the snowdrift gust factor demonstrates that snowdrift is more substantial/voluminous when it is generated by a regular, sufficiently strong wind than when it appears with sporadic wind gusts. This important result allows us to somewhat simplify the numerical model presented in the next section.

4.2.1. Description of the event

In contrast to wind-tunnel experiments, all input parameters change during a real dnfting-snow event. We selected five important drifting-snow events during winter 1998/99. The wind direction stayed more or less constant in only two episodes and there was snowfall during both. Nevertheless we tried to reproduce the snowdrift at the La Muzelle site for the period 26 January-1 February (Fig. 15). There was snowfall on 4 days (26–29 January), totalling 1.20 m. For this period a wide scattering of data points can be observed in Figure 16 because the snow mass flux is not simply correlated with wind speed during snowfall periods.

Fig. 15. Wind speed and drifting snow, 26 January-1 February.

Fig. 16. Signal (mean value over 15 min) from acoustic sensor No. 5 vs wind speed (mean value over 15min), 26–31 January.

4.2.2. Modifications of the numerical model

The simulation of a real drifting-snow event must take into account the modifications of input parameters as a function of time. Initially, we planned to introduce the measured mass flux in the numerical model, but at the present state of development (section 3.1) the acoustic sensor does not assess the mass flux. Nevertheless, it provides the real duration of the drifting-snow event, so we will use the wind measurements during this event and make several approximations.

The numerical simulation of this long period using the fully coupled wind and snowdrift model was beyond our computer capacity. We thus simplified the problem by simulating the snowdrift phenomenon using the fully coupled model during the first hour of the drifting-snow episode. We used the topography, the initial snow cover given by Crocus, an average precipitation rate, and a logarithmic velocity profile represented by the friction velocity u* (x = 0, t = 0) at the upstream boundary. The outputs of this first calculation at t = t0 are the turbulent friction velocity u* (x, t = t₀) near the snow surface, the concentration field C(x,t = t₀) near the snow surface, and the mass flux exchange with the snow cover, M(x, t = t₀).

As the flow is turbulent with a fully developed turbulence, we assumed that if we changed the upstream friction velocity at the upstream boundary condition from u* (x = 0, t = 0) to u* (x = 0, t), the resulting friction velocity in each cell in contact with the snow cover, u* (x, t), may be determined by:

As presented in Reference Naaim, Naaim-Bouvet and MartinezNaaim and others (1998), the mass-exchange flux with the snow cover is a function of the concentration and the friction velocity near the ground.

According to Reference Pomeroy and GrayPomeroy and Gray (1990), the saltation mass flux is given by:

where u*_t is the threshold friction velocity.

In each bottom cell, the reference saltation mass flux is:

During the episode, in each bottom cell, the saltation mass flux is:

From the ratio between these two formulae, we deduce the concentration in each bottom cell:

By introducing the in situ measured wind velocity (Fig. 15) at the upstream boundary of the simulation area during the storm, we applied the snow-erosion and -deposition model (Reference Naaim, Naaim-Bouvet and MartinezNaaim and others, 1998) to this episode.

The results are illustrated in Figure 17. On the left vertical axis the altitudes before and after the event are reported. On the right vertical axis the accumulation values obtained by the numerical simulation and by the in situ measurements are reported. If we compare the numerical model results with the measured data, we can assert that the numerical model correctly localizes the snowdrift accumulation. However, we notice an error in the accumulation that can reach 30%. The error may be related to the strong hypothesis we adopted. This work will be continued in the future using the fully coupled model on the whole episode and using calibrated data from the acoustic sensor in order to improve the model.

Fig. 17. Numerical simulation of drifting snow (snow poles 13–16).