A New Method for Sub-pixel Snow-cover Mapping Using Hyperspectral Imagery – First Results

Most methods applied for snow-cover mapping classify each pixel into snow and no-snow. On the other side, a sub-pixel method classifies snow into several coverage classes or onto a continuous scale. If frequent mapping is required, only low and medium spatial resolution sensors are available (200-1000 m range). Classifying pixels into snow and no-snow only may be sufficient for largescale applications. The method presented here intends to solve the problems of the current linear reflectance-to-snow-coverage sub-pixel algorithm. It gives a fast and very accurate estimate for the actual snow cover at the sub-pixel level. The method is in particularly useful for hyperspectral data. The method predicts local end-member spectra for snow and bare ground for each pixel. Vegetation end-members are predicted using a vegetation map made from another satellite image and a vegetation development model. Furthermore, a local snow end-member-spectrum predictor is used to predict a spectrum, which matches the development stage of the snow. The predictors also compensate for terrain relief effects while generating the actual end-member spectra. The prior information and the predictors allow the number of possible end-members for each pixel to be very low. An iterative algorithm is proposed in order to unmix two and three class component spectra for the prediction of the areal contribution of each class. The method has been applied to field measured spectra. Further experiments are ongoing for airborne DAIS-7915 hyperspectral data covering the Heimdalen test site in Jotunheimen, Norway. The spatial resolution of the DAIS data is reduced to 250 m simulating a medium-resolution sensor. The preliminary results show that the new method gives higher accuracy and reasonable computation time. However, further assessment on larger data sets is necessary to make a full evaluation of the method. Introduction Seasonal snow cover has an extent during the winter months of 30-50 million km. This results in a substantial impact on climate processes, weather and the life in general of people living within this area. Seasonal snow cover is a significant water resource in many countries supplying electricity and freshwater. It is also a source of avalanches and floods. Its importance combined with its huge extent resulted very early in the history of remote sensing in snow-cover monitoring applications by satellite. A large range of methods has been used for snow-cover mapping. These include classical approaches applying statistical supervised classification (1 and 2) and unsupervised classification using clustering (e.g., see 3). Hybrid methods combining the two approaches have also been developed (4). An alternative approach is to apply physically-based methods (e.g., see 5). This is very common within meteorology (6), and has also been the approach when developing the MODIS algorithm (7), which is part of the USA's global climate monitoring system. All the above-mentioned algorithms are snow/no-snow methods classifying a pixel into either snow or no-snow. Alternatively, sub-pixel methods may be used, which classify each pixel into one of several coverage classes or onto a continuous scale. If frequent mapping is required, which is the usual case during the snowmelt season, only medium and low spatial resolution sensors are available (200-1000 m range). Classifying pixels into only snow and no-snow may be sufficient for large-scale applications, like global snow-cover monitoring for environmental applications. HowProceedings of EARSeL-SIG-Workshop Land Ice and Snow, Dresden/FRG, June 16 – 17, 2000 EARSeL eProceedings No. 1 256 ever, for medium and small-scale applications, like mapping catchments for hydropower production, or high-precision large-scale mapping, more exact information about the actual snow coverage inside a pixel is needed. The need for higher accuracy resulted in the invention, by Norwegian users, of a simple algorithm for sub-pixel snow-cover mapping using NOAA AVHRR data already in the beginning of the 1980ies (8 and 9). The method is based on the assumption that there is a linear relationship between snow coverage and measured reflectance. When this relationship is established, it is an easy task to classify each pixel into snow-cover percentage or a coverage category. In (9), four categories were used. The relationship is established by using training areas or interpretation of a histogram of the image. A population of 100% snow covered pixels is identified and determines the reflectance for 100% snow coverage. A corresponding procedure is followed for 0% snow coverage. The method has been applied operationally in Norway since it was developed, and has also been used in Canada (10). The method has later been extended with automatic training (11), automatic geocoding and automatic cloud detection. A relatively new approach to the problem of measuring snow at sub-pixel level is linear spectral unmixing. This is particularly suited for sensors having a high number of bands, imaging spectrometers, but it is also possible to use sensors like Landsat TM. Linear spectral unmixing assumes that a pixel is composed of several different classes, or end-members, and tries to estimate the aerial coverage of each class. Hence, the method does not rely on the assumption of one "background class" like the method described above. In (12), spectral unmixing for snow classification using a linear mixture model is introduced. The actual accuracy of the classification using spectral unmixing, was studied by (13) for an area in Mammoth Mountain in Sierra Nevada, California. The AVIRIS airborne spectrometer was used, and the actual snow cover was determined from aerial photography. The agreement between the snow cover map generated by spectral unmixing and the aerial photography was found to be 92% for areas of low relief and little shade. The agreement fell to about 71% in areas that were extensively shaded. A disadvantage of spectral unmixing, as applied in (12) and (13), is that the method is supervised. The spectral end-members have to be identified manually by training. In (15), a method for unsupervised spectral unmixing is proposed. The method determines end-members automatically and then compares them to a spectral library to estimate the mixture of each pixel. The first step is to use a classification tree to fragment the image into distinct land and cloud cover classes (16). The dimensionality and number of end-members are then determined for each fragment using principal component analysis. Each fragment is unmixed with all end-members sets located on its convex hull, and the best set is selected. The end-member spectra are corrected for the atmosphere using a radiative transfer model, and the end-members are then identified in a spectral library. The final snow cover is then determined from the best mixture model taking into account possible endmember impurities. The method was tested on Landsat TM data and found to have similar accuracy to aerial photography. • The motivation for the new method presented here is that: • Sub-pixel accuracy is a requirement for small-scale applications • Sub-pixel accuracy is an advantage for large-scale applications • The classical linear reflectance-to-snow-coverage method is far from accurate enough • Classical linear spectral unmixing is a supervised method needing manual intervention • The above-mentioned proposal for unsupervised classification is computationally demanding • Spectral unmixing may in general give very inaccurate results since many combinations of endmembers may give the same resulting spectrum The new method presented here intends to solve or limit the above-mentioned problems. The method is useful, in particular, for hyperspectral data. It applies a new iterative spectral unmixing algorithm in the last step. The number of spectra to unmix is limited to a minimum by a priori inProceedings of EARSeL-SIG-Workshop Land Ice and Snow, Dresden/FRG, June 16 – 17, 2000 EARSeL eProceedings No. 1 257 formation. Topographic effects are compensated for. The method applies local end-member spectra, which are generated for each individual pixel by special predictors for snow, vegetation and other bare-ground classes. The method has been tested on field-measured spectra and is currently evaluated on airborne DAIS7915 hyperspectral data covering the Heimdalen test site in Jotunheimen, Norway. DAIS 7915 (Digital Airborne Imaging Spectrometer) is a 79 bands spectrometer. Together with the airborne synthetic aperture radar EMISAR, these sensors comprise the European Airborne Sensing Capabilities (EARSeC) developed as an initiative by the European Union. The spectrometer was built by Geophysical Research corp. (GER), USA, and has been improved by Deutsches Zentrum für Luftund Raumfahrt e.V. (DLR), Germany. Due to requirements for very accurate calibration, a calibration laboratory was built at DLR. Two flight periods were accomplished in 1997 and 1998 as part of a European-wide campaign. The data were acquired in June 1998 as part of the DAIS-LSF’98 airborne campaign and cover most of a 100 km catchment. Very accurate snow-cover data were obtained at the same time from aerial photographs. A vegetation map was generated from Landsat TM data, and an accurate DEM was generated from the aerial photographs. Calibration end-member spectra were measured in the field using a FieldSpec portable spectrometer. The spatial resolution of the DAIS data was reduced to 250 m simulating a medium resolution sensor. The new method and the classical linear reflectance-to-snow-coverage method are applied to the data set. The Snow-Cover Classification Method A brief overview of the approach proposed will be presented followed by a detailed description. The method comprises five fundamental components: accurate prior data about the area to map, models for the spectral development of the end-members possibly present, radiometric correction for terrain effects, radiometric atmospheric correction and a new iterative spectral unmixing algorithm for the retrieval of the actual snow coverage within the pixel. The prior data comprises an end-member class map for the bare ground and a digital terrain model. The terrain model is only required when radiometric terrain correction is needed. The spectra for snow, vegetation and to some degree other bare ground classes change more or less all the time, with the largest changes present during the melting season when the snow metamorphosis develops fastest and the vegetation turns green. Predictors for the spectra have been developed, which limit the number of endmember spectra to decompose for a given pixel to a minimum. The decomposition is done by the new spectral unmixing algorithm. End-member Class Map The classical reflectance-to-snow-cover sub-pixel mapping algorithm assumes a single bare-ground spectrum for the whole image. The use of linear spectral unmixing by several authors compensates for this by assuming many possible classes present and tries to estimate the actual classes by spectral decomposition. However, due to the temporal development of the classes, an extreme number of end-members must be used to cover all the spectra that may be present. With very many spectra to unmix, there are often several solutions giving the observed spectrum. In particular, the snow area searched may be wrongly estimated. Here, it is proposed to use an end-member class map giving prior information limiting the number of classes to unmix for each pixel. By the term endmember class is here meant a group of end-members representing one thematic class, like the endmember class grass, which is represented by a set of different spectra all representing various development stages of grass. For the geographical area to monitor, an end-member class map has to be generated. The map, Me,, can be expressed as: Me(x, y) = {Sc | c is a class end-member at location (x, y)} (1) Proceedings of EARSeL-SIG-Workshop Land Ice and Snow, Dresden/FRG, June 16 – 17, 2000 EARSeL eProceedings No. 1 258 where (x, y) is the geographical position (covered by a pixel) and Sc is the set of all possible endmember spectra for class c. In order to reduce the total number of spectra, models will be used to generate the spectra in Sc for vegetation. Furthermore, Me is in practice implemented as a map of references to a spectral library of actual and model end-members (see Figure 1). In order for the method to be of interest for medium and large-scale operational applications, the end-member class map must be generated with minimal human intervention. The map may very well be made by classification of a satellite image of the same area acquired during snow-free conditions in the summer. This approach is actually much better than using a regular vegetation map made by other means because it is the spectral classes that are needed, not the actual vegetation classes. As long as two different vegetation classes have the same spectrum, they can be treated as one end-member here. Additionally, the usual generalisation present in a vegetation map is a deficit for this application. It is proposed to use an unsupervised classification method, preferably one that also does not need to know the number of classes to cluster. ISODATA (17) has shown to work well for the task given here. The clustering algorithm also takes into account the data distribution within a cluster to determine whether it is composed of more than one class. Spectral development model Spectral library Spectral class index Medium resolution pixel Clustering Me(x, y) = {Sc | c is a class endmember at location (x, y)} Figure 1: Conceptual overview of the spectral end-member class map.