Turbulent fluxes

For the calculation of the turbulent fluxes, the Monin-Obukhov similarity theory was followed, as formulated by Brutsaert (1982). This method calculates heat and vapour transfer from their gradients between surface and measurement heights, taking into consideration wind speed, air density, stability correction, and so on, and accounts for the surface roughness by introducing an aerodynamic roughness length, z0.

A standard approach for the computation of the roughness length for momentum is to extrapolate the profiles of wind speed under neutral conditions to the level at which wind speed equals zero (Stull 1988,

Munro 1989, Greuell and Smeets 2001). However, this procedure requires measurements at atleast two levels and is very sensitive to instrument errors. Therefore, the roughness for the lower site was selected from published mean values for melting snow (Marks and Dozier 1992, Morris 1989, Greuell and Smeets 2001), and it was calculated from microtopographical measurements for the upper site. This upper site is covered in large penitentes, sometimes over 1.5 m in height (Figure 3.3), which results in a very long roughness length. It was calculated as z0/ze = 0.5Xf, where ze is the roughness element height and Xf is the frontal area index or vertical silhouette area per unit ground area (Lettau 1969). Data from wind tunnel experiments and atmospheric observations shows that z0 /h increases linearly with X f for Xf < Xf max (Raupach 1992). The precise form of this function and the value of Xf max depends on the geometry of the roughness elements, but the above linear relationship was found satisfactory for very rough snow surfaces on Vatnajokull, Iceland, by Smeets, Duynkerke and Vugts (1999). For the present study, with an average penitente height of 1.35 m, separated about 0.8 m, the mean value of z0 was found to be 20 cm. The frontal area index will change depending on wind direction, and so will the surface roughness length, sometimes to a very large scale (Jackson and Carroll 1977), however, wind direction was observed to be fairly constant, either upvalley or downvalley, which justifies the selected profile. Values for turbulent fluxes plotted on Figure 3.5 correspond to this z0 value. The transfer mechanisms of momentum and of other scalar admixtures are different at the surface, and consequently the roughness lengths have different values for momentum, water vapour and heat, which were calculated following Andreas (1987).

3.5 MODELLING THE SURFACE MICROTOPOGRAPHY

To assess the effect of the surface ablation morphology on the interception of solar radiation and on the longwave radiative budget, a high-resolution digital elevation model of the surface with 1 cm grid cell spacing was created, and the solar radiative and long-wave models applied to it. The turbulent heat transfer was considered at the overall scale, but it is expected that sublimation and cooling are more intense on the peaks and on the wind side. Although some effort has been made in determining drag partition on rough surfaces (Raupach 1992), it was only for momentum transfer, and it would be desirable to get more detailed observations on real snow surfaces before extrapolating any modelling results.

The DEM was created according to measured penitente distribution and size, with an average height of 1.35 m and wavelength of 0.80 m. To add more realism, the base of the troughs was made flat, as there is frequent melting and even small water ponds in these areas. A smoothing filter was passed over the whole surface to avoid unrealistically sharp angles but it resulted in excessive flattening of the peaks. The ''virtual'' penitentes are concave and tilted 11° to the north, the sun direction in the southern hemisphere (note the arrows in Figure 3.7). As real penitentes have overhanging surfaces, these cannot be represented by a mathematical function, which requires a single z-value for every (x,y) pair. By rotating the reference system by an equivalent angle, we can build the DEM with no overhanging surfaces and then rotate the world according to this new reference system. For the calculation of solar irradiation on the penitentes surface (Figure 3.7), we only need to rotate the sun vector through the original reference system an opposite angle by applying the appropriate rotational matrices.

The sky view factor was computed for every grid cell as the finite sum:

where 6¡ is the local horizon angle, including the slope of the cell itself, for a given azimuth, y. This represents the ratio of the area of a projected circle, corresponding to the visible part of the hemisphere to the area of a circle of unit radius corresponding to the whole hemisphere. For a more detailed explanation, see, for example: Nuñez (1980), Dozier etal. (1981), Dozier and Frew (1990), or Corripio (2003b, 2003a)

The model calculated angle of incidence of the direct beam, shadows, diffuse reflected radiation and diffuse radiation from the sky. For a detailed discussion, see Greuell etal. (1997, appendix) and Corripio (2003b). Reflected radiation was computed for five multiple reflections, which accounts for more than 97% of the energy from this source. Only even reflections were computed, as odd reflections are ''reflected-out'' (Peterson et al. 1985). The modified incoming long-wave radiation is a function of the skyview factor, its value outside the penitentes layer and the long-wave emission of surrounding walls.

3.6 RESULTS AND DISCUSSION

The recorded meteorological variables are summarised in Tables 3.3 and 3.4. The most remarkable aspect is the very low relative humidity. High values were normally associated with the presence of clouds, sometimes enveloping the AWS. Relative humidity follows a diurnal cycle, with maxima due to nocturnal cooling and minima normally related to katabatic winds. Winds were light to moderate and fairly constant. Incoming solar radiation was very intense, with average values close to those of perfectly clear days and peaks exceeding 1700 Wm-2 at the upper AWS. These peaks were higher than the exoatmospheric radiation and were probably caused by enhanced downward flux because offorward scattering of light by large cumulonimbus. Albedo was fairly constant during the whole measurement period, and typically 8% lower on the upper station, where the site was completely

Table 3.3 Recorded meteorological variables and calculated dew point on both glaciers at different times of the day. Noon is about two hours around the daily peak of maximum short-wave radiation, sunrise and sunset are extended two hours after and before the respective events, and night correspond to the period where there is no incoming short-wave radiation. Note that although dew point is a function of temperature and humidity, the recorded variables, its calculated value is given to stress the meteorological conditions necessary for the formation of penitentes as pointed out by Lliboutry (1954b)

Juncal Norte Glacier (3335 m a.s.l.)

Table 3.3 Recorded meteorological variables and calculated dew point on both glaciers at different times of the day. Noon is about two hours around the daily peak of maximum short-wave radiation, sunrise and sunset are extended two hours after and before the respective events, and night correspond to the period where there is no incoming short-wave radiation. Note that although dew point is a function of temperature and humidity, the recorded variables, its calculated value is given to stress the meteorological conditions necessary for the formation of penitentes as pointed out by Lliboutry (1954b)

Juncal Norte Glacier (3335 m a.s.l.)

Time

Noon

Sunrise-set

Night

Min

Mean

Max

a

Min

Mean

Max

a

Min

Mean

Max

a

T°C

5.2

11.2

17.3

2.4

1.3

7.2

14.3

2.5

1.2

5.7

10.3

2.1

RH%

10.6

21.8

51.4

6.5

10.4

37.1

75.4

13.7

14.7

44.6

80.3

14.4

u m s-1

0.4

13.6

5.0

2.0

0.1

3.9

11.3

1.9

0.1

3.2

6.5

1.2

Dew Point ° C

-18.8

-10.4

-0.6

3.5

-19.3

-7.3

1.1

4.3

-16.5

-6.0

1.6

4.0

Loma Larga Glacier (4667

m a.s.l.)

T°C

5.2

11.2

17.3

2.4

1.3

7.2

14.3

2.5

1.2

5.7

10.3

2.1

RH%

10.6

21.8

51.4

6.5

10.4

37.1

75.4

13.7

14.7

44.6

80.3

14.4

u m s-1

0.4

13.6

5.0

2.0

0.1

3.9

11.3

1.9

0.1

3.2

6.5

1.2

Dew Point ° C

-18.8

-10.4

-0.6

3.5

-19.3

-7.3

1.1

4.3

-16.5

-6.0

1.6

4.0

Table 3.4 Short-wave radiation and derived albedo at Juncal Norte Glacier (3335 m) and Loma Larga Glacier (4667 m)

Juncal Norte Glacier

Loma Larga Glacier

SW|

SWf

Albedo

SW|

SWf

Albedo

Wm-2

Wm-2

%

Wm-2

Wm-2

%

Min

Mean

353

184

0.52

383

163

0.44

Max

1564

810

0.70

1727

737

0.65

covered in penitentes. The calculated dew point was well below zero, with very rare exceptions.

It should be pointed out that there were no reliable measurements of ablation in the area of study. This is not a simple task, as the volumetric change of the penitentes should be measured, besides their growth and lowering. However, to gain some confidence in the modelled data, the energy balance model was applied to the meteorological data recorded on the ablation area at the Haut Glacier d'Arolla, during the ETH summer campaign 2001. The modelled ablation was then compared to ablation measured by a sonic gauge. The results show good agreement, as illustrated in Figure 3.6.

It is interesting to point out the differences in the turbulent fluxes between the Alpine and the Andean glaciers. In the Alps, net turbulent flux was always positive: 16 Wm-2 mean value in the period corresponding to the plotted data, from 19 June to 5 July, with a standard deviation of 29.5. In general, large negative fluxes were associated to precipitation events, where sensible flux was also negative, while in the Andes large negative fluxes were associated with intense evaporation.

The energy balance model applied to the microto-pography DEM was run for several clear days with ten-minute time steps to assess the effect of penitentes on the interception of solar radiation. The results for day 37 are shown in Figure 3.7. The maximum total daily value is 490 Wm-2, while the mean value is only 207 Wm-2. The histogram of values shows a bimodal distribution with two peaks (248 and 156 Wm-2) corresponding to the north- and south-facing walls. The same day on a flat surface the modelled (and measured) radiation was 435 W m-2 (418). The mean values for the summer solstice (21 December) were 230 and 486 Wm-2 for the penitentes and a flat surface, respectively. Although not shown, an inspection of the results for diffuse and reflected radiation reveals that the latter

Ablation measured Ablation modeled Net radiation Net shortwave Q_sensible Q_latent

Ablation measured Ablation modeled Net radiation Net shortwave Q_sensible Q_latent

1200 1000

-200

1200 1000

-200

Jul, 2001

Figure 3.6 (Plate 3) Recorded solar radiation, estimated turbulent fluxes, and recorded and estimated snow ablation on the Haut Glacier d'Arolla from 19 June to 5 July 2001

Figure 3.7 (Plate 4) Insolation on penitentes for the 37th day of the year, corresponding to values in Figure 3.5. Superimposed is the histogram of cell values, clearly showing a bimodal distribution of insolation values corresponding to the north-facing and south-facing slopes. The reference system is rotated at an angle 9 so that the vertical is the direction of the sun at midday on the summer solstice

Figure 3.7 (Plate 4) Insolation on penitentes for the 37th day of the year, corresponding to values in Figure 3.5. Superimposed is the histogram of cell values, clearly showing a bimodal distribution of insolation values corresponding to the north-facing and south-facing slopes. The reference system is rotated at an angle 9 so that the vertical is the direction of the sun at midday on the summer solstice

Table 3.5 Energy penitentes (Wm-2)

balance

partition for

flat snow

and

SW|

SWnet

LWnet

Net turbulent flux

Total

Flat snow Penitentes (mean)

435 238

209 133

-77 -38

-17 -28

67

increases downwards and the former increases upwards, with a maximum at the peaks.

Net long-wave radiation increased its mean value from -77 Wm-2 on a flat surface to —38 Wm-2 on the penitentes, due to emitted radiation from the surrounding snow walls. Turbulent fluxes decreased their net value from —17 to —28 Wm-2 on average (Table 3.5). These values are averages for all grid cells, however, surface area is different according to the slope of the cell, and total area is increased on a rough surface, in this case by a factor of 2.8. On the larger scale, we have to assume the conservation of radiative fluxes, and therefore the main change in the overall energy balance is brought about by the increased turbulent fluxes due to increased roughness. This change represents about 2.85 mm of water equivalent melt (mmwe) decrease per day or 342 mmwe for the four principal months of the ablation season. The partition of the energy balance components on the altered snow surface is also important. Thus, the penitentes' walls receive about half of the incoming solar radiation with respect to a flat surface. This compensates for the increase in long-wave radiation and keeps the penitentes' walls generally frozen and dry, while melting occurs only at the bottom of the troughs. The localized melting favours percolation of water, with almost no supraglacial drainage, which in turn reduces loss of water by further evaporation. This corresponds well with the observed situation, although small streams may form lower down and later in the ablation season, as seen on the Horcones glacier on Aconcagua in a different year. Nonetheless, these streams are much smaller than supraglacial rivers observed in the Alps.

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