1018 
6.2. Ratio between channels 
It is difficult to work with absolute values because many effects are not wellknown with a sufficient 
accuracy: slope, atmosphere, calibration. Working with ratios beween different channels instead of using 
each channel separately minimizes these effects: mainly slope effect because the slope is the same for each 
channel, atmospheric and calibration coefficient effects in a less important proportion because they don't 
influence the different channels in the same manner . An example of ratio between channels 4 and 5 is: R45 
- (TM4 - TM5) / (TM4 + TM5) where TM4 and TM5 are the ground reflectances measured by the 
Thematic Mapper. 
On Fig. 2-a is given the theoretical variation of this ratio R45 against grain size using the snow reflectance 
model. The bidirectional reflectances are computed for a nadir view and a sun position as at the time of 
the Landsat acquisition but for different slope angles: the azimuth is ranging between 0° and 315° and 
the zenithal angle is 0° (vertical) or 20°. 
On Fig 2-b are given the values of the same ratio for different sites against the measured mean convex 
radius of snow grains collected there. The ratios were computed from ground reflectance without 
atmospheric corrections and for horizontal surfaces as it could be done very easily in an operationnal way. 
The results are very similar after atmospheric correction. 
The comparison between theory and measurements is very hopeful. The same was done for other ratios: 
the ratio R25 is also satisfactory but the ratio R24 is not sensitive enough on the grain size and does not 
seem so useful. When doing this study we found that it is compulsory to use bidirectionnal reflectances and 
not to assume a iambertian surface. 
sphere radius (micrometers) mean convex radius (micrometers) 
Fig. 3: Variation of the ratio R45 against the grain size: 
a) from bidirectionnal model, the grains are spherical 
b) from Landsat data and mean convex radius measured on snow samples 
7 - CONCLUSION 
A large set of data was collected during three experiments on the snow reflectance in the Alps. The main 
interest is to have many ground truth measurements at the same time as remote sensing data acquisition. 
In particular on 11 December 1992, 4 different radiometers are available: 2 airborne, 2 spacebome. This 
is of great value in order to study the effect of grain size on the reflectance, to study the usefulness of