Embed Size (px)
Citation preview
Notes for Remote Sensing of the Cryosphere
Nick Barrand School of Geography, Earth and Environmental Sciences
University of Birmingham RS 1: PRINCIPLES OF VISIBLE AND RADAR REMOTE SENSING AND SENSORS 1. Overview Over the past several decades, remote sensing has increasingly become a crucial resource for glaciologists. New technologies, algorithms, and processing methodologies, along with a coincident rise in the number and quality of Earth-‐observing sensors have revolutionised our ability to observe and to understand the cryosphere. The goal of this document (and of this series of lecture materials) is to introduce the topic of remote sensing of the cryosphere, and particularly remote sensing of glaciers. It will begin by introducing remote sensing (lecture 1: Principles of visible and radar remote sensing and sensors). The second section will describe the derivation of several important glaciological and physical parameters from remote sensing data (lecture 2: Deriving glaciological products from remote sensing). The final section describes the derivation of geodetic glacier mass balance from remote sensing data (lecture 3: Glacier mass balance from remote sensing). It is hoped that these materials will offer a primer in glaciological remote sensing, and that the references included herein will provide further comprehensive information to the reader. 2. Remote sensing: defined Remote sensing can be briefly defined as ‘The art and science of gathering information about an object without being in contact with it’ (David J. Schneider, MTU), or more technically as ‘the use of instruments or sensors to capture the spectral and spatial relations of objects and materials observable from a distance – typically from above them’. The components of a remote sensing system include: i) an energy source, ii) radiation and atmospheric interactions, iii) interaction with the target, iv) the energy recorded by the sensor, v) tranmission, recording and processing of that energy / signal, vi) interpretation and analysis, and vii) application of the information recorded (Figure 1)
Figure 1: Primary components of a remote sensing system
3. Electromagnetic radiation Remote sensing relies on transmitted and recorded electromagnetic radiation, energy derived from oscillating magnetic and electrostatic fields. Of particular importance is the electromagnetic spectrum (Figure 2), Each interval of the spectrum makes up a band, or channel, by a colour (if in the visible part of the spectrum), a descriptive label (e.g. near infra-‐red), or a specified range of wavelengths. Subdivisions of the spectrum have been established for convenience (e.g. microwaves, of wavelengths ~1 mm to ~1 m). Most remote sensing systems operate between wavelengths of 0.1 um to 1 m. The source of electromagnetic energy is either reflected solar radiation or the radiation emitted by objects (known as passive remote sensing), or a a system with it’s own energy source (known as active remote sensing – examples include radar, laser and flash photography). Energy interacts with the atmosphere, and the surface, being either absorbed, relflected or redirected. Different surface types have particular reflectance signatures, which describe how much energy is absorbed or reflected in different areas of the spectrum by the material. Fresh snow reflects most incident radiation, along a range of wavelength, while dirty glacier ice absorbs much more incident radiation. 4. Sensors Most remote sensing systems operating in the visible and near infra-‐red (VNIR) parts of the spectrum operate either as whiskbroom (across-‐track scanning) or pushbroom (along-‐track scanning) instruments (Figure 3).
Figure 2: The electromagnetic spectrum
Some sensors have the ability to point with offers advantages such as higher repeat frequency, and stereo viewing capability. Spaceborne sensor orbits include polar orbiting, sun synchronous and ascending / descending. Every satellite has a distinct orbit / repeat schedule. Sensor resolution refers to the ability to discriminate information and includes several aspects:
o SPATIAL : minimum separation at which objects appear independent and isolated
o SPECTRAL : number of sensor bands & associated spectral bandwidths o RADIOMETRIC : Sensitivity (range of values coded) of the sensor o TEMPORAL : Observation frequency
Figure 4 shows some typical sensors and platforms operating in the visible (and near visible) parts of the spectrum
Figure 3: Whisk and pushbroom sensors types
Figure 4: Common VNIR sensor systems
5. Common RS systems for observing the cryosphere The following sections introduce the most common remote sensing systems for observing the cryosphere. This list is not comprehensive and several more may be used.
1. Aerial photography Aerial photography is perhaps the most traditional and longest used system of remote sensing. It consists in the analogue form of a photochemical reaction of the exposure of silver halide crystal ‘grains’ in suspension, into metallic silver. Chemical development then results in a photo negative from which further processing is possible. In this instance the film is the detector and the film and filters determine the spectral response. Aerial photography is capable of very high geometric fidelity, and is increasingly digital.
2. Electro-‐optical visible and near infra-‐red Employs a similar spectral range (V to NIR) as air photos, but instead has a digital detection mechanism consisting of calibrated photodiode arrays. This supports a fully digital processing stream. This technology is commonly deployed from both aircraft and satellites. The ground resolution is limited by the detector resolution, and flying height. The majority of sensors operate in several spectral bands (multispectral), although some may operate in very many bands (hyperspectral). The field of view of such instruments, from spaceborne platforms, ranges from 10s and 1000s of km. The longest continously running program of electro-‐optical VNIR sensors is the Landsat program, which began in 1972 and continues to this day with the current Landsat 8. Other popular sensors include the SPOT constellation, ASTER, and MODIS.
3. Thermal infra-‐red Thermal infra-‐red radiation (~8 to 14 um) forms a major part of black-‐body radiation emitted at terrestrial temperatures. This make it useful for detecting Earth (& sea) surface temperatures. It does not detect reflected sunlight nor penetrate clouds yet tends to have coarser spatial resolution than VNIR imagery, at longer wavelengths. Both ASTER and MODIS have TIR capability yet the primary TIR imager is the Advanced Along-‐Track Scanning Radiometer (AATSR).
4. Laser ranging (altimetry) Laser ranging, or laser altimetry is an active remote sensing method for measuring Earth surface topography. It works by a system emitting a NIR pulse, a clock is started, the pulse travels, reflects, and returns, and is then detected by photodiode. The pulse detection stops an internal clock, with the propagation speed two-‐way-‐travel time, then means that range (or distance) to the surface can be determined. This method can achieve extremely high vertical resolution. Spaceborne sensors include the Geosciences Laser Altimeter System (GLAS) on ICESat (2003-‐2010), and the planned ICESat-‐2 (due for launch March 2016).
5. Radar altimetry Radar altimetry is conceptually similar to laser altimetry (LA) (being an active ranging method). This techniques however employs microwave radiation (~10 GHz frequency) with one key operational difference being its capability to observe through clouds (due to the wavelength of microwaves). TWTT and structure of returned pulse (waveform) are recorded, which include information on the surface roughness and/or scattering.
Dry surface snow may absorb radar energy and slope induced errors are of particular importance for this method. A 0.5° slope can result in up to 8 km error in x,y and 40 m in z from space.
6. Passive microwave Passive microwave remote sensing detects black-‐body radiation between wavelengths 3-‐6 mm. It is therefore able to penetrate through clouds – very useful! The longer wavelengths detected by its beam-‐scanning antenna results in coarser resolution data, usually on the order of tens of km per pixel. A 1 m antenna length (wavelength 2 cm) = 14 km ground resolution. Spectral resolution is typically low, 15-‐35 GHz, and the brightness temperature of surface emission is recorded. The method is veru sensitive to abrupt backscatter change resulting from phase change of water – useful for snowmelt monitoring. Figure 5 shows the details of some common passive microwave sensors.
7. Imaging radar Imaging radar utilises side-‐looking or multi-‐angled antennas to determine angular dependence of microwave backscatter. These systems are often known as ‘real-‐aperture’ or ‘side-‐looking’ radars. They utilise active ranging so are independent of illumination, and microwave so independent of clouds (& mostly, atmospheric effects).
8. Synthetic aperture radar Synthetic aperture radar (SAR) is defined by the relative motion between antenna and target. Long-‐term coherent signal variations are used to obtain finer spatial resolution imagery. A single antenna repeatedly targets a scene and then waveforms from different antenna positions are received, stored and processed. The following table (Figure 6) shows current, previously operating, and future planned SAR sensors.
Instrument Satellite Years Spatial res (km)
Frequency (GHz)
Swath width (km)
Max. latitude (deg)
SMMR SSM/I AMSR/E
Nimbus 7 DMSP Aqua
1978-‐ 1988 1987-‐ 2002-‐
136 x 89 87 x 57 54 x 35 47 x 30 28 x 18 70 x 45 60 x 40 38 x 30 16 x 14 74 x 43 51 x 30 27 x 16 31 x 18 14 x 8 6 x 4
6.6 10.7 18.0 21.0 37.0 19.35 22.24 37.0 85.5 6.93 10.65 18.7 23.8 36.5 89.0
780 1400 1445
84.2 87.5 88.3
Figure 5: Common passive microwave sensors.
RS2: DERIVING GLACIOLOGICAL PRODUCTS FROM REMOTE SENSING DATA 1. Overview These notes will describe how principle glaciological and physical variables are extracted from remote sensing data. While other variables are available, the focus of this section will be on derived outlines and glacier extents, structures, snow and ice facies, surface topography, albedo, surface temperature, accumulation and melting. Elevation changes (and subsequent geodetic mass balance) will be treated in greater depth in section ‘RS3: Glacier mass balance from remote sensing’. 2. Outlines and extents Glacier outlines can be produced with manual delineation, or automated and semi-‐automated approaches. Manual digitisation, by it’s very nature, is reliant on the skill level, judgement and experience of the user. Automated delineation aims to reduce the work necessary to produce outlines, and provide a more objective, rule-‐based outcome. Especially when using VNIR image, an image processing / display procedure called compositing is very useful. A composite image is the result of combining multiple image bands (3) to produce a single colour image. This is done in order to better discern features on the ground. How? Your computer uses R, G, B to show colours on the screen. Using different combinations of RGB, creates many different colour possibilities. The false-‐colour composite which works best for delineating snow and ice is (Landsat) bands 543, displayed in the red green and blue channels, respectively. Snow cover can be mapped using a normalised difference of 2 image bands known as the Normalised Difference Snow Index (NDSI). The normalised difference of these 2 bands (1 in V, 1 in NIR or SWIR) utilises the fact that snow is highly reflective in V, yet highly absorptive in NIR and SWIR.
Figure 6: Common SAR sensors
NDSI works by using the equation above, and a threshold approach (e.g. 0.4). It should be noted however, that this threshold is seasonably and regionally variable. The workflow to automated glacier mapping is summarised by Figure 7 (Paul, 2004). Overlaying of binary glacier, vegetation, and slope maps allows a coarse glacier classification resulting in classes for debris, glacier and debris not connected to the glacier. These sorts of approaches work reasonably well for glacier ice and snow covered glaciers but have difficulties with debris-‐covered ice. Further manual editing is usually required. 3. Structural glaciology Remote sensing data can greatly aid in structural glaciology due to its ability to image large, remote and inaccessible areas (e.g. crevasse fields). Figure 8 shows a satellite image of Wilkins ice shelf, Antarctic Peninsula, and the corresponding structural glaciological map of surface features.
Figure 7: Workflow for automated glacier mapping utilising NDSI, hue, image ratios, DEM slopes and accounting for debris cover (Paul, 2004).
4. Snow and ice facies The SAR backscatter from snow and glacier surfaces is dependent on various variables, including liquid water content, grain size and layering, surface roughness, wavelength, polarisation, incident angle, and more. The ability of radar band penetration into snow means that snow and ice surface facies may be mapped according to their corresponding ‘radar glacier zones’. The dry snow radar zone (-‐14 to -‐20 dB) corresponds approximately to the glaciological dry snow zone. The frozen percolation radar zone (0 to -‐8 dB) corresponds to the glaciological percolation zone, plus some of the wet snow zone. The wet snow and bare ice radar zone, correlate well with their glaciological counterparts. This discrimination of facies allows mapping of snow and ice zones over very large areas with imaging and synthetic aperture radar. 5. Topography
a. Photogrammetry: Photogrammetry is the process of determining the geometric properties of objects from photographic or stereo images. It can include interpretive, metric and stereo (3D) photogrammetry and involves reconstructing the geometric relationship between film, camera and ground at time of image capture. A 2D image space coordinate system is transformed to a 3D object space coordinate system utilising a mathematical back-‐calculations known as a bundle adjustment. This process is used to generate the image space coordinates of the camera centre, from known ground coordinates. In the case of satellite sensors with accurately known positions, ground space three dimensional coordinates are calculated through trigonometric calculations utilising the parallax between two images of the same scene taken from different positions.
b. Photoclinometry Photoclinometry provides an alternative to stereo photogrammetry for VIR imagery. It assumes a uniform Bidirectional Reflectance Function (BDRF) such that variations in radiance detected by the sensor are solely due to variations in viewing geometry. When
Figure 8: SAR image and corresponding structural glaciological map of Wilkins ice shelf (images courtesy of Matthias Braun).
the image illumintion (sun) is constant – variations in radiance are due to surface slope : surfaces facing the sun are brighter. This is expressed mathematically by D = A cosθ + B where D is image brightness, θ is angle between surface normal and solar direction, and A, B are constants derived from known ground points.
c. Altimetry Altimetry will be dealt with in more detail in RS3: Glacier mass balance from remote sensing. 6. Physical variables : albedo Remote sensing can be used to derive albedo by defining planetary reflectance as the ratio between radiance at sensor and solar irradiation in a given spectral band. planetary reflectance R is computed by where L is measured radiance, Esun solar irradiance, and θ sun zenith angle. This calculation should be corrected for atmospheric transmission effects, topography, and other effects. 7. Physical variable : surface temperature Surface temperature can be derived from thermal infra-‐red (TIR) data (e.g. from MODIS or AVHRR sensors). Following the form where T11 and T12 are brightness temperatures in each band, and a,b,c are empirical constants obtained by regression with surface measurements. This approach, however, should be corrected for atmospheric propagation, clouds may need to be filtered, and other algorithms developed for oblique viewing angles / multi-‐look techniques. 8. Physical variables : velocity a) Feature-‐tracking Feature tracking is posisble by locating and tracking the position of features in repeat imagery. This features may be crevasses, foliations, large boulders or moraines. It requires good image-‐to-‐image registration and can utilise manual or image cross-‐correlation. The methods work well for small glaciers which are relatively snow-‐free during summer so have good image texture, have exposed rock surrounding ice for image registration, and may be faster flowing glaciers, often heavily crevassed. The approach is less effective for large areas such as ice sheet interiors. Automated feature tracking uses algorithms designed to use image chips to search through image data; a chip size is selected, step size and previous filtering, then a correlation function is returned per chip. The process results in image motion in E-‐W, and N-‐S directions, magnitude, and angles. Also, a SNR image may be provided for quality judgement (see Figure 9).
b) Interferometric SAR (InSAR) InSAR exploits differences in phase of returned signal from 2+ sensor positions (e.g. Figure 10). Phase differences result from fraction of wavelength differences in pulse travel time which provide a parallax due to topography & shift in location of scatterers due to motion. The InSAR processing stream is characterised by two image pairs, exploitation of the phase difference in both image pairs to create an interferogram, removal of horizontal displacement by ‘double differencing’ one of the image pairs, to provide topography and
Figure 9: SAR image and components of feature-‐tracking algorithm (images courtesy of Matthias Braun).
Figure 10: Schematic diagram illustrating the principle of InSAR image acquisition (image courtesy of Matthias Braun).
vertical displacement. Combining with a DEM can remove the topographic signal, if desired. InSAR processing has the following, brief, advantages and disadvantages (among others): advantages
o Highly sensitive (m in z, cm-‐mm in x,y over large areas) o works in textureless areas o high density data o active radar so high-‐resolution data over large areas irrespective of solar
illumination or clouds limitations
o requires pulse coherence o decorrelation possible o requires starting point if areas of 0 movement o Penetration of SAR signal
c) Intensity and speckle SAR intensity tracking uses a similar procedure to feature-‐tracking in optical imagery. It utilises the intensity of radar backscatter to produce a direct 2D displacement field. This has the advantage of being computationally simpler than InSAR. Speckle-‐tracking uses image ‘chips’ and fringe rate or coherence to determine displacement. It works well in absence of visible features or fast-‐moving ice and can thus be considered complimentary to InSAR. 9 Physical variables : accumulation Accumulation from remote sensing data is based on the idea of an empirical relationship between thermal microwave emissivity and in situ accumulation rates. Authors have used AMSR-‐E radiometer data at 6.9 GHz (4.3 cm wavelength). Two channels measure horizontal and vert. polarisation and the polarisation ratio decreases as accumulation increases. 10. Physical variables : melt Microwave data can be used to derive snow facies (as shown previously). Due to the strong backscatter response due to phase change of water (solid – liquid), it can also be used to infer snowmelt conditions (Figure 11). 1-
7-20
001-
8-20
001-
9-20
001-
10-2
000
1-11
-200
01-
12-2
000
1-1-
2001
1-2-
2001
1-3-
2001
1-4-
2001
1-5-
2001
1-6-
2001
1-7-
2001
1-8-
2001
1-9-
2001
1-10
-200
11-
11-2
001
1-12
-200
11-
1-20
021-
2-20
021-
3-20
021-
4-20
021-
5-20
021-
6-20
02
-25
-20
-15
-10
-5
0
σ0 (d
B)
-50
-40
-30
-20
-10
0
10
T i (o C
)
Figure 11: Relationship between daily surface air temp and microwave backscatter through two melt seasons at Larsen C ice shelf, Antarctica.
This approach works by utilising daily microwave backscatter images (e.g. SMMR, SSMI, QSCAT). A winter mean normalised backscatter threshold approach is applied pixel by pixel e.g. where σ0 is daily pixel backscatter, is winter mean backscatter preceding each melt season, and b is a threshold constant (=3 dB). The approach identifies a ‘wet’ snowpack based on backscatter difference from reference ‘dry’ state, and can be used to derive spatial maps of melting, and when the time-‐series is long enough, correlate melting with atmospheric and climate variables. RS3: GLACIER MASS BALANCE FROM REMOTE SENSING 1. Overview The following notes describe the acquisition, processing and analysis of remote sensing data to measure glacier mass balance. Focus is primarily on the analysis of elevation data to calculate the geodetic (or map-‐based, or altimetric-‐) mass balance. The fundamentals of geodetic mass balance will be introduced, followed by platforms and methods of data collection, calculations of elevation change and corrections. The conversion of elevation change to volume change to mass change will be then be introduced, along with assumptions of the approach, errors, and methods of regional extrapolation. Why measure glacier elevation change?
o good spatial sampling o coarse temporal sampling o calculate volume change o ice dynamics o sea-‐level rise o proxy for climate change o can have small uncertainty bounds o independent measurement of mass balance
Some words of caution should be mentioned. It is possible to have:
o changes in volume without a corresponding change in mass o changes in ice discharge without corresponding changes in elevation, or volume.. o changes in mass without changes in sea level..
A change in volume may not equal a change in mass due to the concept of the ellipsoid and the geoid. The ellipsoid is a smooth elliptical model of the Earth’s surface, the geoid an equipotential surface that mean sea-‐level follows. As the height of geoid above (or
below) ellipsoid varies around the Earth, there are uncertainties in the reference frame of any elevation measurements. Glacio-‐isostatic adjustment (the viscous change in the Earth’s geoid is response to LGM glaciation can result in rapid uplift rate, control point errors and geoid / ellipsoid transformation errors. All must be accounted for prior to calculating elevation change of ice from geodetic data. 2. Fundamental of geodetic mass balance At a specific point where h-‐dot is the rate of change of ice surface elevation, b is the mass balance, and q is the ice flux per unit cross sectiob of the glacier. Glacier-‐wide mass balance is therefore where a(z) is the glacier’s area-‐altitude distribution function and Z is the elevation range of the glacier. Alternatively, where pi is the average material density required to obtain mass balance. h-‐dot and b, when integrated over the entire glacier basin, yield glacier-‐wide mass balance. This is because (the flux divergence term) sums to zero over the entire basin. 3. Platforms and data collection The following typically used platforms and methods of data collection are used in glaciology to derive geodetic measurements, and to further calculate geodetic mass balance:
a. Stereoscopic imagery Including air photos, SPOT and ASTER satellite data. Elevation information is derived from the parallax displacement of same object from different locations. To calculate 3D ground space coordinates, the position of the sensor is required relative to the reference plane. 3D coordinates of ground features are then back-‐calculated. The solution improves with GCPs, yet the method relies on surface texture for image matching
b. Laser altimetry The basic principles of laser altimetry are as follows (see also Figure 12). The distance between the sensor and surface is determined by the travel time of a laser pulse. The sensor position is known from either differential GPS (air) or star trackers (satellite). The attitude of the sensor is derived from an inertial navigation system (INS). Different altimeters include
o nadir-‐pointing vs scanning laser o scanning laser : different ways to distribute the measurement (conical, nutating
mirrors) o different scanning frequencies o first return, first-‐last, full waveform
Some common airborne laser altimetry (lidar) systems used in cryospheric remote sensing include the University of Alaska laser altimeter (20 Hz nadir laser (1993 – 2007), 10,000 Hz scanning laser (2009 – present), few hundred m altitude, ~1 m footprint), the NASA Airborne Topographic Mapper (ATM, 5000 Hz laser altimeter (1990s – present), Maximum 1 km altitude, 3 m footprint), the UK NERC Airborne Research and Survey Facility instrument (ARSF, Optech ALTM3033, ~1000 m flying height, swath scanning, 33000 Hz pulse rate, ~10 cm footprint), and the NASA Land, Vegetation and Ice Sensor (LVIS, swath scanning altimeter, high altitude (10 km), swath footprint (20 km)). NASA Geoscience Laser Altimeter System (GLAS) onboard ICESat (2003-‐2010) was the only spaceborne laser altimeter for observing the Earth’s surface (decimeter elevation accuracy, near-‐repeat-‐track profiles, can be differenced where slopes are low, steeper slopes (glaciers and ice caps) errors due to cross-‐track slope may be larger than elevation change signal). ICESat-‐2 is planned for launch in March 2016. 3. Corrections Prior to differencing elevation data, the following corrections may need to be applied:
1. Co-‐registration 2. Cross-‐track slope 3. Spatially-‐correlated biases 4. Elevation-‐dependent biases 5. Others
4. Elevation differencing 1. Altimetry vs map / DEM
Figure 12: Components of an aircraft laser altimetry system.
The following steps explain this process: 1) digitise glacier outlines, 2) difference elevations to calculate dh/dt, 3) extract glacier hypsometry using outlines and DEM (area per elevation bin), 4) parameterise dh/dt as a function of elevation 2. DEM vs DEM Two DEMsm from different times. Simple raster differencing of the two grids, provided that they are correctly geolocated. No extrapolation is required and volume change can be calculated from pixel summation, following: where B is total volume change, lp is the DEM grid spacing, A is the glacier area in the earlier DEM surface, and delta h is the difference model. 3. Altimetry vs altimetry This can be best described Figure 13 (courtesy A. Arendt) 5. Elevation change errors
Figure 12: Procedure for measuring elevation change from repeat altimetry data (A. Arendt)
Errors can be determined by examining the scatter in full geodetic map (DEM – DEM) of elevation change, as a function of elevation. This approach determines the statistics on extrapolation errors. Reasons for errors in centreline altimetry may include:
o glaciers do not thin in steps (or bins) o debris cover at the margins? o main glacier branch does not represent other branches? o advection of turbulent energy from valley sides?
6. Volume to mass change Volume – mass conversions are complicated by changes in near-‐surface density (Figure 13). In a dry snow zone accumulation and temperature are constant, so Sorge’s law holds true (that the density depth profile remains constant. However, this is rarely the case, and density must be measured, modelled, or assumed. For the ice sheets, small variations in density may mean large variations in mass balance. Densifications models require a physics-‐basis and coupling with regional climate models. 7. Regional extrapolation Regional extrapolation of elevation changes may be done by calculating an average thinning rate over elevation bands, upscaling that rate to the hyposometry of a larger glaciated area, and multiplying by the surface area of unmeasured glaciers to give a total regional volume change (e.g. Arendt et al, 2006). However, in regions with many different types of glaciers (land-‐terminating, lake / tidewater-‐terminating) it may be more appropriate to extrapolate area-‐averaged mass balance, rather than elevation changes (Arendt et al., 2006).
Figure 13: Changes in near-‐surface density profile between times t1 and t2, where t2 is warmer than t1 (image: A. Arendt).
REFERENCES Arendt, A. et al. (2006) ‘Updated estimates of glacier volume changes in the western Chugach Mountains, Alaska, and a comparison of regional extrapolation methods.’ J. Geophys. Res. doi:10.1029/2005JF000436. Cuffey, K.M. & Paterson, W.S.B., 2012. Physics of Glaciers. 4rd Edition, Elsevier Science Ltd. 480 pp. Lillesand, T., Kiefer, R.W. & Chipman, J. 2008. Remote Sensing and Image Interpretation. John Wiley & Sons, 768 pp. Paul, F., Huggel, C. and Kääb, A. (2004): Combining satellite multispectral image data and a digital elevation model for mapping of debris-‐covered glaciers. Remote Sensing of Environment, 89 (4), 510-‐518 Rees, W.G. 2005. Remote Sensing of Snow and Ice. CRC Press, 312 pp. WEBSITES http://arsf.nerc.ac.uk/ http://lvis.gsfc.nasa.gov/ https://airbornescience.nasa.gov/instrument/ATM http://fairweather.alaska.edu/chris/altimetry_text.html
