Experimental set-up

To measure the downwelling radiation fluxes in snow, a tunnel was dug with a base 3.5 m below the snow surface and an approximate height of 2.0 m, resulting in 1.5 mof undisturbed snow for investigation (see Fig. 1). From this tunnel the radiation sensor was inserted vertically into the snow by first drilling a hole with the diameter of the sensor (2.5 cm) and then placing the sensor facing upwards into the hole. The length of the hole was progressively increased and measurements taken until the top of the snow cover was reached.

Fig. 1. Snow tunnel to measure downwelling flux.The base of the tunnel is 3.5 m below the surface. 1.5 m of undisturbed snow are available for investigation. The length of the tunnel was progressively increased to ensure undisturbed snow on each measurement day.

At the same time, a reference sensor was placed on top of the snow cover to measure the incoming solar radiation. This insured that varying incoming radiation due to change in sun zenith angle and cloud cover could be accounted for.

The instrumentation consisted of an Analytical Spectral Devices FieldSpec Pro Dual visible/near-infrared (VNIR) spectrometer to which two sensor heads were connected via 4 m fibre-optics cables. The sensor heads have a diffuser with cosine response attached and collect radiation from one hemisphere. Data were then collected from both sensors simultaneously. The 340–1050 nm region of the spectrum is covered with a spectral resolution of 3 nm full width at half-maximum (fwhm) and a sampling interval of 1.4 nm.

Upwelling radiation in snow was measured by drilling a hole into the snow and inserting the sensor with the diffuser facing down. As with the measurements of the downwelling flux, the reference sensor was simultaneously measuring the incoming radiation.

In addition to the radiation measurements, weekly snow profiles to 1.5 m depth gave information on snow-cover stratigraphy. Snow-grain samples of the topmost layers were collected, stored in isooctane and photographed using macrophotography. These data are used to calculate the optical properties of snow and obtain parameters for a radiation transfer model.

Model description

The radiative fluxes in snow were calculated using the δ–Eddington radiation transfer model. The Eddington approximation describes the intensity in the radiation transfer equation by a linear polynomial and solves the resulting two equations for constant optical properties (each layer) (see Reference Shettle and WeinmanShettle and Weinman, 1970). Snow is an extremely forward-scattering material, i.e. a beam of radiation scattered by a snow grain does not change direction appreciably. The δ function accounts for this forward scattering by approximating the phase function by a Dirac δ function (Reference Joseph, Wiscombe and WeinmanJoseph and others, 1976). This then leads to a transformation of the optical properties and hence to an improved performance of the Eddington approximation (Reference Wiscombe and JosephWiscombe and Joseph, 1977).

The δ–Eddington model was applied to snow by Wiscombe and Reference Warren and WiscombeWarren (1980) and recently Reference Simpson, King, Beine, Honrath and ZhouSimpson and others (2002). Wiscombe and Reference Warren and WiscombeWarren (1980) compared albedo measurements with this model and concluded that the model-produced albedos are too high in the visible part of the spectrum. Their subsequent paper (Reference Warren and WiscombeWarren and Wiscombe, 1980) investigates the influence of snow impurities in the model output and concludes that, with impurities added, the model represents measured albedo also in the visible range. Reference Simpson, King, Beine, Honrath and ZhouSimpson and others (2002) present radiative flux measurements in snow from 300 to 422 nm and compare these with calculations using the δ–Eddington model. Instead of accounting for the layering of the snow cover, they calculated the optical properties from an average grain-size for the whole snow cover and achieved good agreement between measurements and model output when decreasing the single-scattering albedo due to an additional absorber in snow.

The model requires as input the incoming radiation conditions, properties of the snow cover and the optical properties of the snow grains.

Incoming direct and diffuse radiative fluxes along with the sun zenith angle and a ground reflectivity build up the surrounding radiation boundary conditions. The reference sensor measured the total incoming irradiance, hence direct and diffuse components have to be split and are estimated following Reference Perez, Ineichen, Maxwell, Seals and ZelenkaPerez and others (1991).

The layering of the snow cover comprises parameters such as number of layers and the height, density and grain-size in each layer. This information is gathered from the weekly snow profiles.

Optical properties of the snow grains are calculated for each snow layer using the Mie scattering theory for spheres. Assuming that the snow grains prevalent in Greenland are spheres, a single-scattering albedo ω (ratio of scattering to extinction), extinction efficiency Q_ext (ratio of extinction cross-section to geometrical cross-section) and asymmetry parameter g (mean cosine of scattering angle) can be calculated using for example the Mie scattering code of Reference WiscombeWiscombe (1980). These parameters have been shown to have a ripple structure which has its origin in the electromagnetic normal modes of spheres (see Reference Bohren and HuffmanBohren and Huffman, 1998). To avoid the ripple structure, calculations are averaged over a (log-normal) size distribution of snow-grain radii centred at the respective measured radius. In natural snowpacks, grain-sizes always vary around a mean grain-size, and hence the ripple structure is smoothed out naturally.

The output of the δ–Eddington model is the up and down fluxes at each layer boundary and hence also the albedo of the snow cover. Model calculations for the whole spectral range covered by the spectrometer, along with the measurements, are presented in the following section.

Transmission measurements in snow

The measurements on different days show similar patterns of the radiation field in snow throughout all measurement periods. The snow cover of Summit did not change very much during the period of the measurements. Only the topmost snow layers were affected by erosion and rare snow-melting events. In general, the snow structure is similar to very compact alpine seasonal snow. Grains ranged from small rounded ones with radii of 0.2 mmto large grains with radii of 1.5 mmwhich have undergone kinetic growth metamorphism. In the top layers densities ranged between 250 and 300 kgm^-3 and after a few centimetres reached values of 350–400 kgm^-3 and then remained in this range. An overview of a typical snow profile including grain-size, grain shape, snow hardness and temperature measurements is given in Figure 2.

Fig. 2. Snow profile taken on 22 July 2002. The ordinate represents the depth in snow. On the right side, grain shapes along with grain diameters in mm are shown. The lefthand side represents the hardness of the snow, and the line gives the snow temperature.

Atypical measurement of the downwelling irradiance is represented in Figure 3. The data show irradiance curves at several layers in the snow cover. Longer wavelengths are progressively removed from the spectrum. As an example the irradiances at wavelengths 660 and 730 nm are presented. The relative decrease of irradiance measured on 24 July 2002 at these wavelengths is summarized inTable 1. The percentage of the surface-level value is given for each depth. It can be seen that the far red portion of the spectrum disappears faster than the red portion. Hence, snow is acting as a spectral filter for radiation.

Fig. 3. Downwelling irradiance measured on 24 July 2002. The curves are the irradiances at levels 5, 10, 25, 43, 47, 57, 80, 103 and 112 cm. The two vertical lines indicate the wavelengths 660 and 730 nm respectively (phytochrome absorption peaks).

Calculated extinction coefficients were very high for the top layer and then reached lower values, as can be seen from Figure 4. In the top few centimetres, photons entering the snow cover are very likely to re-emerge out of the snow, causing a high extinction. Further inside the snowpack the asymptotic region is reached, where irradiance decreases exponentially according to the Beer–Lambert–Bouger law (Reference WarrenWarren, 1982).

Fig. 4. Extinction coefficient derived from data measured on 23 July 2002. Numbers in the legend represent levels for which the extinction is calculated, i.e. at 5, 8, 11, 18, 41 and 56 cm.

Irradiances over the snow depths at wavelengths 350, 450, 680 and 800 nm are shown in Figure 5. Linear regressions to the data points are also given. The reading at the first level in snow is excluded from the regression. The k values give the gradient, i.e. the extinction coefficient, of the regression lines. This figure illustrates the increasing extinction coefficient with wavelength and also indicates that the first reading in the surface layer of the snow does not fit an exponential decrease.

Fig. 5. Logarithm of the irradiance drawn against depth is shown as small triangles for four wavelengths. The lines are least-squares fits to the data points; the k values are the gradient, i.e. the extinction coefficient, of the regression lines.

Lines are cut off in deeper layers, as the measured signal dropped under the sensitivity limit of the instrument. Increasing wavelength leads to increase in extinction because of the absorption of ice, which is also shown in the graph (data taken from Reference Grenfell and PerovichGrenfell and Perovich (1981) and Reference Perovich and GovoniPerovich and Bovoni (1991)). The high-frequency variation of the extinction coefficients is a result of changes in grain-size.

Comparison to the model and sensitivity studies

Comparing the measurements with the model output shows that it is necessary, in order to obtain good agreement, to increase the absorption of the snow grains. Calculation of the single-scattering albedo ω of snow does not account for impurities, and hence the predicted value appears to be too high. Decreasing ω increases the absorption and leads to good agreement between model and measurements in the visible part of the spectrum. Longer wavelengths are less affected, since absorption is already high.

Impurity content of snow was not measured during this campaign, but it will be accounted for in further similar campaigns in the Swiss Alps. In this study, the model was fitted to match the measurements, and therefrom an impurity content deduced. Two approaches to model impurities in snow are common: the internal and the external mixture approach. In the internal mixture approach, impurities are thought of as being inside the snow crystals. The respective complex indices of refraction for ice and the impurities (e.g. soot) are averaged according to their weight fraction, and Mie calculations are done with this new index of refraction. The external approach assumes that the impurities are separate from the ice crystals and act as scatterers themselves. Optical properties for these impurities are calculated and then averaged (again by their weight fraction) with those of the ice particles. In this study we followed the external approach. Impurities were assumed to consist of soot particles with a complex index of refraction of m = 1.69 + 0.67i, a grain-size of 0.1 μm and a density of 1350 kgm^–3. Soot concentrations were varied until the model matched the measurements. Best agreement is found when a soot concentration of 0.3 ppmw is used for the top snow layers to 6 cm depth, and of 0.13 ppmw for the layers beneath. Reference Chýlek, Johnson, Damiano, Taylor and ClementChýlek and others (1995) found 0.02 ppmw of black carbon in Summit surface snow in 1989/90. In an earlier work, Reference Warren and WiscombeWarren and Wiscombe (1980) compared this model approach with albedo measurements of Reference Grenfell and MaykutGrenfell and Maykut (1977) in the Arctic basin and found values around 0.3 and 0.4 ppmw.

In Figure 6a a model run along with measurements taken on 26 July 2002 is represented. Grain-sizes and densities are taken from the snow pit from 22 July 2002 which is shown in Figure 2. The Mie-calculated values of ω are decreased by 0.000205 for the complete wavelength range and for all layers. At wavelengths below about 500 nm a good agreement between model and measurement can be observed. The difference at 6 cm depth in this wavelength range is most likely due to uncertainties in determining the sensor depth.

Fig. 6. Comparison of modelled and measured downward irradiance on 26 July 2002 at depths in snow at 6, 8 and 11cm. (a) Single-scattering albedo ω is decreased by 0.000205. (b) Grain-size scaled by 0.8, ω decreased by 0.00013. (c) Grain-size scaled by 0.8, asymmetry parameter g decreased by 0.03 and ω decreased by 0.0001.

An apparent disagreement between model and measurements must be observed at wavelengths above around 500 nm. Measurements indicate a much stronger extinction than the model predicts. In this spectral region the grain-size plays a key role in correctly modelling the fluxes. In fact, techniques have been developed to retrieve grain-sizes from reflectance measurements in this spectral region (Reference Nolin and DozierNolin and Dozier, 2000). Larger grain-sizes increase the likelihood of photons crossing through the grains to be absorbed. Especially in the spectral region where ω is already appreciably below unity, absorption has a predominant effect in large grains.

This feature shows that it is necessary when using Mie theory, which is valid for spheres only, that an equivalent or effective grain radius (see Reference Grenfell and WarrenGrenfell and Warren, 1999; Reference MitchellMitchell, 2002) is used, which is able to reproduce the measurements.

A first attempt is made here by scaling the measured grain-sizes by a factor of 0.8. This causes more scattering events (thus higher extinction) to take place, and hence ω needs only be decreased by 0.00013. The output is shown in Figure 6b. Now, longer wavelengths are slightly better represented but still not satisfactorily.

An additional explanation for the difference between model and measurement can possibly be found in the snow crystal shape. Approximating snow grains to be spheres may not be sufficient (even when using an effective grain-size). The phase function (which gives the average scattering angle) is especially sensitive to the shape of scatterers. The asymmetry parameter g used in this study is the first approximation of the phase function and therefore a parameter depending on the grain shape. Figure 6c represents a model run with g decreased by 0.03, ω decreased by 0.0001 and grain-sizes scaled by 0.8. A steeper decrease of irradiance at wavelengths above 500 nm compared to the other model runs can be observed.

Our adjustments of the parameters are made for all snow layers and for all wavelengths. This is certainly a shortcoming because effective grain-sizes have to be calculated separately for individual snow layers. Also g has to be adjusted for each layer with non-spherical grain shapes separately. Nevertheless, a qualitative description of the effect of the parameter variations could be obtained.