2.1. Wind velocity

The five-cup anemometers have a lower limit of 0.3 m s⁻¹ and a mean precision of approximately 0.05 m s⁻¹. Each wind-speed profile is obtained from three measuring points (0.5 m, 1 m and 2 m). In 1970, we provided for an additional point, ranging between 2 and 10 m.

2.2.Temperature and humidity

The apparatus used consists of a thermograph with digital remote indication (Reference Poggi, Schram and ThamsPoggi and others, 1967). The thermistors, protected by a series of double screens, are placed at 0.5 m 1 m and 2 m; in 1970, we added another one between 2 and 10 m. Their accuracy is about 0.05 deg.

The water vapour is calculated at 0.5 m and 2 m from the temperature difference between wet and dry thermistors placed at the same level:

where θ^’ is the temperature of the wet thermistor, θ the temperature of the dry thermistor, p the atmospheric pressure, and f_w ^’ the vapour pressure over water. This is computed from tables which gives f_w ^’ as a function of temperature.

Since the ventilation comes about naturally, we adapted the psychrometric constant A to the wind velocity according to Petit’s (1958) curves (Fig. 1).

Fig. 1. Variation of the psychrometric constant with wind velocity according to Petit.

2.3. Net radiation

The total radiation balance is measured directly by a thermopile with a telluride-copper thermocouple blackened on its two faces and placed at 1.5 m. Its sensitivity is 15.77 mV kW⁻¹ m³.

Largely due to poor stability with temperature of the apparatus, the absolute error is about ±10 W m⁻².

2.4. Run-off measurements

At 2 km from the meteorological station, a float recorder enabled us to follow the variations in height of the water of Rieu Blanc, a stream that collects the greatest part of melt water from the glacier. The calibration curve giving stream discharge is obtained from dilution techniques (Reference AndreAndré, 1964).

2.5. Complementary measurements

At 9.00h and 18.00h daily, we noted: atmospheric pressure, precipitation, nebulosity, and ablation at four stakes placed around the station.

This apparatus, largely conceived by the Laboratoire de Glaciologie, had the advantage of being easy to handle and not requiring much electricity,

3.1.In the Presence of a weak thermal gradient

When the surrounding air temperature is near 0^°C or when a sufficient wind assures good mixing in the lowest layer, the wind-speed profiles can be approximated by Prandtl’s semi-empirical law (Equation (2))

(2)

or by the more general Deacon’s empirical law (Equation (3)) which reduces to Equation (2) as ß →1 (Reference SuttonSutton, 1953):

(3)

where u_∗ is the friction velocity defined by the relation τ₀ = ρu_∗ ², τ₀ the surface shear stress per unit area, τ the air density, z₀ the roughness parameter, к is von Kármán’s constant, u the wind velocity, and z the height above the ice.

Table I gives the results of 18 profiles.

Table I. Profiles measured on 15 and 16 september 1969

Richardson’s number (Ri) (Reference PriestleyPriestley, 1959) interprets the ratio of the convective forces represented by the sensible heat flux to the shearing stresses represented by the flux of momentum:

(4)

where g is the acceleration due to gravity, T the air temperature, and θ the potential temperature. Richardson’s numbers were calculated at 1.08 m using the values of the velocities and temperatures at 0.5 m and 2 m. They vary from 0.013 to 0.004 and characterize a near neutral atmosphere.

The parameter z₀ is calculated from the logarithmic law (2) and ß from Deacon’s law (3):

With temperature inversion, (Ri) < 0.16, the logarithmic law again is a good approximation (Fig. 2).

Fig. 2. Wind-speed profiles fir winds blowing from the north-west, 5 September 1970.

3.2 In the presence of a strong thermal gradient: three days of glacier wind (18, 19 and 10 September 1970)

3.2.1. Wind-speed profiles.

The influence of stratification on the wind-speed profiles (Reference WebbWebb, 1970; Reference Grainger and ListerGrainger and Lister, 1966; Reference AryaArya, 1972) becomes more complicated on inclined surfaces because it also produces an acceleration of layers that are more dense (Reference Ellison and TurnerEllison and Turner, 1959,1960). If the stratification is sufficient, a katabatic flow appears on the glacier and follows the line of greatest slope: this is the “glacier wind” (Reference HoinkesHoinkes, 1954).

During three days without a dominating wind, we took advantage of the clear weather that permitted the surrounding air to reach elevated temperatures and the appearance of a strong stratification at the level of the glacier ((Ri) > 0.25). All of the wind-speed profiles are characterized by a maximum located between 1 and 5 m.

Reference PrandtlPrandtl’s analysis (1952) of winds of local origin and, notably, mountain and valley winds, leads to wind-speed profiles of the form:

(5)

where C and l are constants, and Z is the height above the inclined surface and measured perpendicular to it,

In our case, since the glacier has very little slope (7⁰) at the level of the measuring point, it will be considered that Z ≈ Z; the height z is taken vertically above this point.

Fig. 3. 20 September 1970. Fitting of a mean wind-speed profit by the equation:

u_z = 1.02 In (Z/0.045 m) exp – (z/6.53 m)

According to Equation (5), the velocity vanishes and the changes sign when Z = πl and the first maximum velocity is attained when

Thus, the height of vanishing wind is four times greater than the height of maximum velocity. This is not the case for the profiles we recorded since we found notable winds above 9 m, while the maximum is located between 1 m and 2 m (Fig. 3).

Among all the simple empirical laws that permit description of the recorded profiles, the one that is best suited is:

(6)

where A, a and b are constants. When the stratification diminishes, b → ∞ and we arrive again at the logarithmic law. Three measuring points are sufficient to calculate A, a and b. For instance, we have shown in Figure 3, the average profile calculated on 20 September 1970 from 8.00h to 17.00h

Taking into account only velocities above 1 ms⁻¹, we calculated the values of the parameters a, b and A for 50 profiles and traced their distributions (Fig. 4).

Fig. 4. Histograms if a, b and A distributions. Shaded zones characterize the “nocturnal” period and the white zone the “diurnal” period.

For a, the most abundant class is that which corresponds to the area of variation of z₀ in the case of logarithmic profiles (0.0016 m > z₀ > 0,0123 m).

The distribution of the parameter b has two maxima because it is necessary to separate the “diurnal” period (in white on Figure 4) from the “nocturnal” period (shaded on Figure 4). At night, the values for b are greater than during the day. This is probably due to the fact that the mountain wind that develops at this time blows in the same direction as the glacier wind and superimposes itself. Therefore, the ambient air is swept along by something other than the glacier wind which causes an augmentation of velocities and especially of the parameter b.

Table II shows the average values of the coefficients a, b and A during the “diurnal” period on one hand and nocturnal on the other hand.

Table II. Average values of the parameters a, b and a

3.2.2. Temperature profiles.

Taylor (mentioned by Reference SuttonSutton, 1953) studied the case where a hot air mass blows over a cold horizontal surface. If that surface stays at 0°C, which is the case of the glacier during the “diurnal” period, and if T₀ is the temperature of the hot air layer, the vertical temperature distribution fits the equation

where t is the time from the beginning of the contact between the hot air and the cold source, κ_h the turbulent heat exchange coefficient, and

We have attempted to fit the experimental profiles by the equation:

(7)

Temperature T₀ and с are calculated from the measured points at 1 m and 9 m. The fit is bad; for each of the profiles the temperature gradients are too strong between 0.5 m and 2 m (Fig. 5). This divergence seems to stem from the fact that Equation (7) characterizes a forced flow above a plane surface, while we were in the presence of a flow driven by density gradient above an inclined surface of average slope 7°.

Fig. 5. Fitting of a mean temperature profile (07.00 to 17.00 h 20 September 1970) by two equations:

(1)θ_z = 11.38 erf (z/1.31);

(2)θ_z = 2.49 ln (z/0.034) exp (-z/44.1).

In order to fit the experimental profiles we chose an empirical law similar to that for velocities:

(8)

The four parameters A^’, b^’, a^’ and θ₀ require four measuring points in order to be calculated, which prevents us from evaluating the quality of the fit. We will therefore limit ourselves to profiles for which the glacier surface is at 0°C (“diurnal” period) then θ= 0. Figure 5 shows the average values of “diurnal” temperatures (08.00h to 17.00h on 20 September 1970) fitted by Equations (7) and (8).

3.2.3. Inversion of temperature gradients.

In the hours after sunrise and while the weather is clear, two things contribute to a strong reheating of the air layer nearest to the glacier:

—at sunrise, the temperature θ₀ of the surface, up until now negative because of the radiation of the ice, goes back to o°C At equal ambient temperatures, there is therefore a reheating of the first decimetres of air and modification of the temperature profiles.

—with the beginning of melting the glacier surface constitutes a source of water vapour and it is thought that the absorbtion of the infrared leads to a selective reheating of the wettest, that is the lowest layers. A maximum appears in the temperature profiles and the sensible heat fluxes on the two sides of this maximum are of opposite sign (Fig. 6).

Fig. 6. Left: Heating of the lowest layer of air at sunrise. Right: Corresponding variations of radiation.

In the Nevacerrada pass in the Sierra Guadarrama northwest of Madrid, while studying the heat balance above the snow, Reference La casiniere deLa Casinière (1974) encountered this same inversion of sensible heat flux.

3.2.4 Correlations between wind-speed and temperature gradient.

The glacier wind results from a flow by density difference; it is normal to find a relation between the temperature gradients and the wind velocity that results from it.

In Figure 7A, we have used simultaneously the time evolution of the temperature gradient (θ_9.5 – θ_0.5) and the wind velocity at 0.5 m (u_0.s). 72 pairs of values shown in Figure 7B, give the linear correlation:

(9)

The correlation coefficient of 0.637 is very significant at the 0.01 level.

Fig. 7. A: Variation with time of wind velocity at 0.5 m and gradient of temperature between 9.5 m and 0.5 m. B: Correlation between wind-speed (v_0.5) and temperature gradient (θ._9.5–θ_O.5)

3.3. Regime changes

In an hour’s time, a “classical” regime with logarithmic wind-speed profiles can change suddenly into a glacier-wind regime. At equal ambient temperatures, we therefore observe a cooling of the first two metres. This cooling exceeded 2°C at 0.5 m as shown in Figure 8.

Fig. 8. Regime change over the glacier.

Transition periods can equally be observed during which the geostrophic wind is not strong enough to disperse completely the glacier wind. The curves in Figure 9A characterize the passage of a katabatic regime to a strong southerly wind. In Figure 9B, we have plotted the coefficients a and b calculated using Equation (6). At 19.00h the coefficient b becomes very large (b > 100 m); for the layer that interested us, the profiles can therefore be considered logarithmic. The mixing of air layers increases with this southerly wind (Fig. 9C).

Fig. 9. 7 September 1970. Transition between a glacier wind and a geostrophic wind blowing from south.

4.1. Calculation of average fluxes of sensible heat and water vapour

Prandtl’s theory on turbulent transfers leads to the following relations. For transfer of momentum:

(11)

where τ is the shear stress, and К_M the turbulent exchange coefficient of momentum.

For heat transfer:

(12)

where θ is the temperature, C_p the specific heat capacity, and К_H the turbulent exchange coefficient of heat.

For water-vapour transfer:

(13)

where m is the mass of water vapour, and К_E the turbulent exchange coefficient of water vapour.

Many workers have shown К_H/К_M = 1 for a neutral atmosphere and decreasing with stability. Reference Businger, J.A., J. C, Y. and E. F.Businger and others (1971) give К_H/К_M = 1.35 for a neutral atmosphere and diminishing as the stability increases. With conditions of strong enough stability that characterize our measures we assumed that:

We calculated hourly average fluxes of sensible and latent heat for a period extending from 30 August to 15 September 1969. For them, we considered the wind-speed profiles to be logarithmic and we computed К_M, Q and E, at 0.72 m if the glacier wind blows, that is below the maximum of the velocities, and at 1.08 m in all other cases.

KMis defined according to the Equation (11) and

Q, is simply calculated from the gradients of temperature (Equation (12)) and L_sE by Equation (13) using the conversion:

4.2. Analysis of the energy balance

For two days when the average fluxes exchanged between the ice and the atmosphere were particularly important (11 and 12 September 1969), a histogram of their variations has been made (Fig. 10). On this figure, the flow of the Rieu Blanc is also plotted. The delay that appears between the variations in flow and those of the total flux received by the glacier correspond to the flow time of the melt water down to the measuring point located at 2000 m from the meteorological station.

Fig. 10. Hourly heat fluxes and Rieu-Blanc run-off.

From 30 August to 15 September 1969, we plot on Figure 11 the daily balances and the mean melting measured at the four stakes (with ice density of 0.9 Mg m⁻³). In cutting off the quantity of heat necessary for the ice ablation, the end result must be zero. In fact, this is not always realized, because beside measurement errors and approximations, it is necessary to take into consideration that flux exchanged between the atmosphere and the glacier was neglected when the wind velocity fell below 1 m s⁻¹. Precipitation also upset the measurement of net radiation when it was deposited on the thermopile. This is particularly evident during the rainy episodes indicated in Figure 11.

Fig. 11. Daily heat fluxes compared with daily measured melting.

The daily average fluxes calculated on eleven days not disturbed by precipitation were:

radiation: 2.76 MJ m⁻² d⁻¹,

sensible heat: 2.09 MJ m⁻² d⁻¹,

latent heat: –0.30 MJ m⁻² d⁻¹.

The sum of the eleven daily fluxes leads to the comparison:

ablation from heat-balance measurement: 168 mm of ice,

ablation from direct measurement (stakes): 190 mm of ice.