Spatial and Temporal Analysis of the Snow Line in the Alps Based on NOAA-AVHRR Data

Snow cover is an important feature of mountainous regions like the Alps. Depending on the latitude. the higher altitudes are completely covered by snow for several months a year. The high surface albedo of snow greatly influences the local climate, decreasing the sur¬ face net radiation and thus the energy transfer. In addition, snow cover is a relevant factor not only for the development of ecosystems, but also for human activities like hydropower generation or ski tourism. TTie snow line is an important indicator of snow cov¬ erage. Its spatial fluctuation reflects climatic behavior. indicating a tendency either towards cold and/or wet conditions or towards a warmer climate.


Introduction
Snow cover is an important feature of mountainous regions like the Alps. Depending on the latitude. the higher altitudes are completely covered by snow for several months a year. The high surface albedo of snow greatly influences the local climate, decreasing the sur¬ face net radiation and thus the energy transfer. In addition, snow cover is a relevant factor not only for the development of ecosystems, but also for human activities like hydropower generation or ski tourism. TTie snow line is an important indicator of snow cov¬ erage. Its spatial fluctuation reflects climatic behavior. indicating a tendency either towards cold and/or wet conditions or towards a warmer climate.
For many years now, satellite data has been widely used in snow hydrology at a regional to Continental scale (BAUMGARTNERet al. 1991;Carroll 1990;Ehrler & Schaper 1997;Kleindienst et al. 1999;Rango 1993;Ranzi et al. 1999;Pietroniro & Lecon iE 2000). How¬ ever, only few publications deal with the use of satellite data for assessing snow line elevation (e.g. Seidel et al. 1997). The major advantages of NOAA-AVHRR data are that a sufficiently high repetition rate is ensured and areas as large as the Alps are easily covered. The aim of this paper, therefore, is to show the applicability of NOAA-AVHRR data for analyzing the snow line level at an alpine scale.
2 Snow line derivation using satellite data 2.1 Definition of the snow line in satellite images Snow maps derived from satellite data are pixel-based representations of snow-covered areas. Due to a spatial resolution of between a few hundred meters and a kilometer, a pixel, although either classified as <snow> or <no-snow>, often consists of snow-covered and snowfree parts. In theory. the snow line defines the line separating snow-covered from snow-free areas. However, due to the patchiness of the snow cover edge, no dislincl line can be drawn. Instead, the snow line may be seen as a more or less narrow belt representing a zone of approximately 50% snow coverage (WMO -World Meteorological Organizationin Seidel et al. 1997). As satellite data inlcrpretation deals with mixed pixels, the above definition of the snow line is appro¬ priate.
Assuming that a pixel is classified as <snow> if 50% or more of the area it represents is covered by snow. those pixels found on the edge of snow-covered areas would represent the snow line belt. Figure 1 indicates which pixels in a slope-situation would be selected as snow line pixels. Taking into account the amount of NOAA-AVHRR data that has to be processed to analyze changes in alpine snow cover. an operational processing chain is necessary. As interactive processing does not meet with the Performance expeetations of processing tech¬ nology today, it cannot be considered an alternative.
The topography of the Alps with its high mountains and steep Valleys, as well as the wide-angle characteristic of the AVHRR sensor, are a challenge for remote sensing. These conditions require the development of special modules to process NOAA-AVHRR data preferably in a fully-automated manner. The following modules are part of our processing chain: Calibration of the data, which include a satellite intercalibration of NOAA-9 to NOAA-16 (Teillet &  atmospheric correction based on 5S (Rahman & Dedieu 1994); correction ofthe non-Lambert behavior of the surface using the Bidirectional Reflection Distribution Function (BRDF) (Wu et al. 1995) and Computing a cloud mask using the Cloud and Surface Parameter Retrieval (CASPR) of the University of Wisconsin-Madison (Key 2001) (Figure 2). The automatic pre-processing of a Single image covering the European Alps takes approximately 15 -25 minutes depending on the cloud cover.The thresholds for the modulc snow/ice are adapted automatically taking into account the time of the year (see Table 1).
The pre-processed NOAA-AVHRR data as described in section 2.2 and shown in Figure 2 form the basis for the generation of snow maps.

Snow map generation
Based on the Output of the processing chain. further analysis may be conductcd. The module SNOW/ICE (see Figure 2) allows the Classification of snow covered areas. Using an adapted algorithm. first presented in Gesell (1989). each pixel passes through a multi-step threshold scheme. which worksasa negative test. Table   1 lists the different tests and defines default values for each specific test.These threshold values were adapted manually to improve the snow Classification for each scene (Droz 2002).
In a first step. all pixels containing information other than snow were eliminated. The resulting bitmap-like snow map illustrates the snow coverage of a par¬ ticular day (Figure 3). In a next step, the elevation (meters a.s.l.) corresponding to each pixel describing the snow line is determined using a Digital Elevation Model (DEM) with a spatial resolution of 1 km. The GTOPO30 applied is a DEM with a horizontal grid spacing of 30 are seconds (approximately 1 kilometer) and available for free at the Earth Resources Obser¬ vation Systems Data Center run by the United States Geological Survey.
2.3 Inaccuracies in data processing Geo-coding In order to use satellite data in combination with other data sets. like for example a digital elevation model. the satellite data have to be transferred into a common geographical reference System. However, the error inherent in the so-called geo-coding process prevents the determination of the exact position of a spe¬ cific pixel. Generally, an accuracy of about 0.5 -1 pixel may be achieved, which means that NOAA-AVHRR data have an accuracy span of about 500 m at a resolu¬ tion of 1.1 km.
Assessing the snow line elevation of a specific slope, for example with an inclination of 45°, a horizontal dis¬ placement by as much as 500 m would lead to the same vertical error of the position of the snow line.
As a consequence, with the errors inherent in the under¬ lying satellite data, no aspect-dependent analysis of snow line elevation is possible. Only if the snow line ele¬ vation of complementary aspects is averaged. can the error caused by inaccurate geo-coding be levelled out.
Using hydrological basins as a basis for averaging the elevation data takes advantage of this behavior, since it can be assumed that within a hydrological basin, no aspect dominates. However, the size of the applied basins has to be large enough in order to ensure that a sufficient number of snow edge pixels can be used for Statistical analysis.
To be able to test the effect of geo-coding problems, the satellite data applicable for the snow line defini¬ tion is shifted northwards by one pixel, thus introducing an artificial error. Figure 4 shows that the effect of this manipulation on the snow line elevation distribu¬ tion is minimal.
Problems due to wrong Classification The original satellite data consist of digital numbers only, indicating the radiation energy received at the sensor. Using publicly available calibration informa¬ tion, these numbers can be transformed into values with a physical meaning, like albedo or brightness tem¬ perature. Classification procedures turn these values or numbers into thematic information, making use of the fact that certain surface types, such as Vegetation, water, snow or clouds have specific spectral proper¬ ties and, therefore, distinct relations between Channels with different wavelength sensitivity exist. Two major difficulties are encountered during the Clas¬ sification procedure. In the case of mixed pixels, which contain two or more surface classes, the assignment to a specific class is sometimes not easy This is par¬ ticularly the case for pixels close to the edge of the snow cover. The Situation is further complicated by the appearance of the pixels, the factors influencing the appearance being manifold, like the State of the atmosphere, the solar angle or shadow effects. Definition ofthe snow line elevation Once all the pixels representing the snow line have been marked, the elevation of each can be determined on the basis of a digital elevation model. However, as shown above, because of both the uncertainty of a Single pixel's location and the problems concerning snow Classification, a certain number of pixels is neces¬ sary if a reliable snow line is to be defined on the aver¬ age of all the pixels.
In order to tackle the problems mentioned above, river basins can be used as reference areas. Using walersheds for this purpose has the great advantage that most aspect classes are represented within the basin areas, leading to more reliable snow line ele¬ vation averages. It is important to note that the ref¬ erence areas have to be large enough if a sufficient number of snow edge pixels are lo be made available for a sound Statistical analysis. As a test, NOAA-AVHRR data with a spatial resolution of 1.1 km were plolled against IRS-WiFS data with 180 m res¬ olution, both data representing the Situation on 24,h March 1999. Thereby, two different sets of reference areas were applied, one with small basins averaging 145 km2, the other with basins combined to an aver¬ age of 2340 km2. The results shown in Figure 5 indi¬ cate that the size of the first set of reference areas (left plot) is too small. Where larger regions were targeted, an improved agreement between AVHRR and IRS-WiFS data could be achieved (right plot). The aver¬ age difference between AVHRR and IRS-WiFS based snow line elevations could be reduced from 141 m to 69 m.The maximum deviation improved to 183 m for the large basins, as compared to 669 m in the case of the small basins.

First applications and results
The NOAA-AVHRR sensor is well suited for snow cover monitoring. Its repetition cycle of less than a day allows the mapping of changes in snow cover extent with a sufficiently high temporal resolution. Rango et al. (1983) claim that the spatial resolution of 1.1 km is sufficient if large areas of more than 200-500 km2 are targeted. however. an area of 500-1000 km2 and more appears to provide a better Statistical data basis (cf. Figure 5). Consequently. our research focussed on the European Alps covering an area of approximately 290.000 km2 (Figure 3) as well as including further regions in Switzerland and Austria. Research, Davos but only for Switzerland. The ques¬ tion was whether the snow-conditions in Switzerland applied to the whole alpine area. We therefore processed and analysed the area of the Alps defined by the «Alpenkonvention». The three years defined above were selected to test the usefulness of NOAA-AVHRR data to analyse snow line elevation in a large area. Confection automatique ele cartes nivales au moyen d'une cheiine de processus et du module «snow/ice», avec des valeurs-seuils appropriees pour les divers mois de l'annee. L'exemple montre une vue NOAA-11 du 20 fevrier 1990 avec la carte nivale correspondanle.
As mentioned above, the selected years represent spe¬ cial situations, early ablation being observed in 1996 and heavy snowfall in 1999. As can be seen in Figure   6, major differences occur during the months of April and May. During these two months, the 1996 snow line was approximately 500m higher than in 1999. If the corresponding elevation is compared rather than the corresponding period. then it becomes obvious that snow ablation occurred earlier in 1996 than in 1999. Especially at elevations between 1500 m and 2500 m, snow ablation in 1999 look place approximately one monlh later.
It should be pointed out that the snow line behavior in early 1996 was dominated by snow cover in low eleva¬  1990 and 1996 did not see such marked changes in snow cover within short periods of time. This could be an indication of more homogeneous weather condi¬ tions prevailing throughout the Alps during these two years. A more detailed analysis of the variability of the snow line elevation is described in the next chapter (cf. Figure 9).  3.2 Spatial pattern of snow line behavior In principle, the analysis and Interpretation of the behavior of snow line evolution for the Alps as a whole is rather speculative due to the climatic differences between the western and eastern part of the Alps.
Consequently, we divided the alpine area into 55 subregions, the results of three of these regions discussed here (Figure 7). The first step was to compare the average snow line elevation of each region with the total alpine average for each day recorded by satellite. The elevation differences between the two scales were then averaged using data from all available observa¬ tions during the three years. However, the normative approach using alpine averages is not absolutely reli¬ able. Partial cloud cover over the Alps can cause a bias, particularly if clouds obscure a region with extraordinary high snow line elevations. This method is. there¬ fore, only an approximate way of defining regions with similar climatic conditions. The partition of the Alps was based on hydrological catchments taking into account that every sub-region should exceed the minimum of 3000 pixels to fulfil Statistical requirements (cf. Figure 5). The amount of pixels in the different catchments differs between 3200 and 8600 with a mean of 5911 pixels. The delimitation of the Alps was done according to the «Alpenkon¬ vention» and after Bätzing (1993). The focus on three sub-regions «Chablais» (exposed to north-west), «Aosta Valley» (a dry Valley in the central Alps) and «Pinzgau» (representative for the eastern part of the Alps) allowed for a more detailed look at climatic differences and therefore more precise Statements on snow line elevation. The analysis was done for the years 1990,1996 and 1999 (Figure 8).
As mentioned before, the snow line elevation of every subregion was compared with the evolution of the snow line of the whole alpine area. As can be seen in Figure 8, there are significant differences between the regions. On the whole, the snow line behavior of the L'evolution de la limite neigeuse dans les Alpes europeennes en 1990, 1996 et 1999. La basse altitude de la limite neigeuse de janvier ä mars 1996 et Tablation rapide de mars-avril sont clairement perceptibles.
in February, the Situation in the two regions was simi¬ lar. During the three years selected, fluctuation of the snow line according to the graph dots was less pronounced for the Aosta Valley than for Chablais and Pinzgau.
The snow line average of the Aosta Valley is significantly different to the rest of the Alps. During all three years the snow line was approximately 200 -300 m above the average, high irradiation and low local pre¬ eipitation rates being the main causes for the difference.
The high inter annual variability of the weather (Ranzi et al. 1999) certainly also plays a role.
In order to better understand the snow line behavior, maximum and minimum values (triangles) were added to the graphs (Figure 9). The circles indicate the mean values. As a result, the seasonality of the variability ränge was more apparent. Thus, this approach proved to be better suited for illustrating snow line elevation variability. For example, it became apparent that the variability is higher at the beginning of winter than during the ablation phase at the end of winter, espe¬ cially in the southern and eastern part of the Alps ( Figure 9).
Both snow cover and snow line are strongly influenced by different climate parameters. However, as individ¬ ual situations are influenced by Single snowfall events. they do not necessarily represent a general behavior. Figure 9 summarises the analysis of the snow line over three years.
Considering the importance of snow cover for alpine tourism, it should be pointed out that within a region. the differences between the ski resorts concerning snow line elevation can be very high, especially in the eastern pari of the Alps. The central Alps do not offer good skiing conditions under 2.400 m.
In addition. the high variability of the snow line eleva¬ tion in the Eastern Alps makes water management in this area difficult. Farming and hydropower genera¬ tion depend on snow cover as a source of waterthe unreliability of the source leading to greater financial risk. Abgrenzung gemäss Alpenkonvention sowie nach Bätzing (1993). Die Analyse auf subregionaler Ebene basiert auf den Regionen «Chablais» (randliche Nordwestalpen), Aostatal (inneralpines Trockental) und Pinzgau (Osialpen).

Discussion and outlook
The application of satellite data for snow line elevation assessment according to the method described above appears to be very promising. Figures 8 and 9 show that the temporal snow line signature can be used to identify regions with different snow line behavior.The experiences described in this article can, therefore, be seen as the first Steps towards creating a snow clima¬ tology of the Alps, advances in this field requiring the inclusion of further data and several more years of snow line monitoring.  Gesell (1989). Compared with results derived from distributed snow modelling (Weibel et al. 2002) and Landsat-TM data (Droz 2002), the snow covered area was underestimated. A further improvement can be obtained using atmos¬ pheric temperature at different levels to adapt the thresholds automatically to the daily atmospheric conditions. Furthermore, it will be necessary to test whether Statistical methods or GIS approaches should be applied to mask out those elevations defined as a result of misclassification.
In summary, the method presented describes an operational approach to deriving snow lines and their corre¬ sponding elevations using NOAA-AVHRR data. For the first time the temporal and spatial behavior of snow cover al the scale of the European Alps was investigated. The advantage of NOAA-AVHRR data for snow cover monitoring of large areas in complex terrain could be verified. Summary: Spatial and Temporal Analysis of the snow Line in the Alps Based on NOAA-AVHRR Data A method to derive the snow line elevation using NOAA-AVHRR satellite data in combination with a digital elevation model is presented. The AVHRR sensor enables the frequent Observation of snow cover with a sufficiently high temporal resolution.
The definition of the snow line and the impact of geocoding errors, as well as errors due to misclassification, are discussed. A comparison of the NOAA-AVHRR data with data from the higher resolution IRS-WiFS indicates that even at a spatial resolution of 1.1 km, a quantitative analysis of the snow line elevation is pos¬ sible.
The influence of different winter conditions in Switzer¬ land on the elevation of the snow line is reflected in satellite data from 1990,1996 and 1999. The results of the investigation were, firstly the presentation of the spatial pattern of the average snow line elevation, secondly the derivation of snow line signatures for three regions. These were then compared with the Overall alpine snow line signature. L'article presente une methode de determination de l'altitude de la limite neigeuse ä partir des donnees satellitales NOAA-AVHRR. en combinaison avec un modele d'altitude digital. AVHRR facilite une Obser¬ vation assidue de la couverture neigeuse dans une duree pertinente.