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This user's guide information, prepared in 1992 for the Pilot Land Data System, Goddard Space Flight Center, Greenbelt, MD, follows unedited for your convenience. Algorithms and description requiring special characters may be omitted. Contact NSIDC User Services with questions or to order data.
Nimbus-7 and the SMMR Instrument
Comparison with Other Data Sets
Display of Data Products
The Snow Microwave Data Set
Climate Modeling Studies
Snow Melt Runoff Studies
To study and understand the climatic and economic impact of snow, it is necessary to have long-term data bases of various snow parameters. Of particular interest to users of snow data are snow water equivalent, depth, and the area of snow cover. In November 1966, the first satellite-derived Northern Hemisphere Weekly Snow and Ice Cover Chart was produced by the National Environmental Satellite Data and Information Services (NESDIS) of the National Oceanic and Atmospheric Administration (NOAA). Since then, continental snow extent has been monitored on a weekly basis using NOAA satellites, thereby providing a data base with temporal and spatial continuity (Matson et al. 1986). Snow depth is reported regularly by stations in the World Meteorological Organization network and archived in various data centers (Crane, 1979). Unfortunately, most snow depth observations are limited to point measurements, and sparsely inhabited areas are poorly represented by conventional data.
Since November 1978, the Scanning Multichannel Microwave Radiometer (SMMR) on the Nimbus-7 satellite has been acquiring passive microwave data that can be used to measure snow extent and calculate snow depth on an areal basis (Chang et al., 1987). The capability to compute estimates of global snow storage, hence the depth of snow, was developed using an algorithm derived from microwave radiometric measurements of snow using ground-based, airborne, and spaceborne observations.
In the Northern Hemisphere, the mean monthly snow cover ranges from about 7 percent to over 40 percent of the land area, thus making snow the most rapidly varying natural surface feature. The mean monthly snow storage (excluding Greenland) ranges from about 1.5 x 10 g in summer to about 300 x 10 g in winter (Chang et al., in press). Snow cover is a sensitive indicator of climate change, with the position of the southern boundary of snow cover in the Northern Hemisphere of particular significance as it is likely to retreat northward because of sustained climate warming (Barry, 1984).
General circulation models (GCMs) suggest that the amount of snowfall by latitude may change because of changes in atmospheric moisture flux with a decrease in the frequency and occurrence of snowfall in the low and middle latitudes and an increase in the high latitudes (Barry, 1984).
Energy balance studies of the Earth-atmosphere system using satellite observations indicate a net radiative energy gain between the equator and 35 latitude and a net radiative energy loss poleward of this latitude. The Arctic region is influenced by the energetic subpolar systems transporting heat and momentum into the region and it, in turn, influences the general circulation of the atmosphere by being a heat sink for the global weather machine (Vowinckel and Orvig, 1970). For a better understanding of the heat transfer between the atmosphere, the snowpack, and the ground, snow depth and snow extent must be known.
The electromagnetic properties of snow vary as its structure and liquid content change. The snowpack as an electromagnetic medium is complex and requires rigorous quantitative evaluation. The snow medium is generally nonhomogeneous and stratified. It can contain snow in several different stages of metamorphism ranging from depth hoar near the ground-snow interface to melt-freeze layers near the snow-air interface. Snow grain size, shape, and density vary within the pack, usually from one stratigraphic layer to the next, which complicates the analysis of the electromagnetic wave/snowpack interaction. Liquid water content in the pack is seldom uniform. Depending on climatic conditions, liquid water content can be greatest at the surface, middle, or bottom of the pack (Jones, 1983).
Snow is a fine-grained material with a large, specific surface area. When snow exists near its melting point, as it often does, it is one of the most unstable natural substances. This instability permits drastic changes or metamorphism in crystals as soon as they are deposited. The temperature of the layer determines the rate of metamorphism, and the temperature gradient across the layer largely determines the type of metamorphism. If the process is not driven by the temperature gradient, but develops from the tendency of the snow to minimize its surface free energy, thereby simplifying its structure, the process is called equitemperature or destructive metamorphism. If the metamorphism is in response to a strong thermal gradient within the snowpack, the process is called temperature gradient metamorphism. When there is a steep temperature gradient, constructive metamorphism occurs, and large, angular, often hollow crystals of depth hoar grow in the warmer layers at the base of the pack. Depth hoar is common in snowpacks throughout the world, especially when snow remains on the ground for a month or more. A third type of metamorphism occurs when the snowpack temperature reaches 0 degrees C and surface snow layers undergo frequent melt-freeze cycles. Under these conditions, smaller ice grains in the surface layer melt during the day and the melt water refreezes at night. Repeated freeze-thaw cycles produce large, rounded clusters of ice grains by a process called melt-freeze metamorphism (Jones, 1983).
During the melt season, an ice layer may be found at the base of Arctic snowpacks. A basal ice layer forms when melt water, which percolates to the snow-ground interface, melts and refreezes. Water that percolates through a snowpack may freeze in layers and release heat to the lower parts of the snowpack. If the temperature of the substrate is below 0 degrees C when melt water reaches the bottom of the pack it will freeze. This ice may remain after the snowpack has melted. Hydrologically, runoff is delayed until formation of basal ice stops, but runoff may be prolonged as ice melts throughout summer.
Microwave remote sensing can be accomplished either by measuring emitted radiation with a radiometer or by measuring the intensity of the return of a microwave signal with a radar (Hall and Martinec, 1985). Microwaves can penetrate the snow and respond to variations in subsurface properties. Working in the microwave region also permits remote observation of snow under nearly all weather and lighting conditions. Often the areas that are most dynamic, such as boundaries of sea ice packs, are also the most difficult to measure with conventional instruments since the skies are often cloudy (Campbell and Gudmansen, 1981).
The equivalent temperature of the microwave radiation thermally emitted by an object is called its brightness temperature, TB. It is expressed in units of temperature (Kelvin) because for wavelengths in the microwave range, the radiation emitted from a perfect emitter is proportional to its physical temperature, T. However, most real objects emit only a fraction of the radiation that a perfect emitter would emit at its physical temperature. This fraction defines the emissivity, e, of the object. In the microwave region, e = TB/T, which is a basic equation of passive microwave radiometry (Zwally and Gloersen, 1977).
For many solids or liquids, microwave radiation emanates from only a thin surface layer. Since this layer is nearly isothermal, the emissivity in such a case is well defined. Also, if the solid is homogeneous and its dielectric properties are known, the emissivity can be readily calculated by considering the electromagnetic reflectivity at the surface of the material. For example, water has a low emissivity due to large reflectivity (0.6 to 0.7) and there is small penetration into the water body by microwaves.
The dielectric properties of a material are characterized by its dielectric constant, e (epsilon), which is a measure of the response of the material to an applied electric field. This response can be split into two factors: the first determines the propagation characteristic of the wave in the material, i.e., velocity and wavelength, and the second is a measure of the energy losses in the media. These two factors are represented by the real (e') and imaginary (e") parts of a complex dielectric constant. Thus e = e' - je"; where j = (-1)1/2. The ratio e"/e' is called the loss tangent for the material. In general, the values of e' and e" will be functions of temperature and frequency (Foster et al., 1984). It is the large contrast between the dielectric properties of water and those of most solids that makes the use of microwave radiometric techniques important for problems related to water resources (Schmugge, 1980a). The dielectric constants of water and ice are so drastically different that even a little melting causes a strong microwave response. In addition, the dielectric constant for snow is usually lower than that of dry soil, and since scattering further reduces the brightness temperature, there is sufficient contrast in the brightness temperature range for snowfield monitoring (Rango et al., 1979).
To understand features of the microwave emission, it is important to know the approximate depths from which the radiation emanates. For most materials the amount of external emission from a given depth below the surface tends to decrease approximately exponentially with depth. The optical or skin depth is then the thickness of the top layer, from which approximately 63 percent of the radiation emanates. At a wavelength of 1.55 cm, the optical depth is on the order of millimeters for water, wet soils, and first-year sea ice; centimeters for dry soils, wet snow, and multiyear sea ice; and meters for dry snow because of the small imaginary part of the dielectric constant for snow (Zwally and Gloersen, 1977). At a wavelength of 0.80 cm, the optical depth for snow is on the order of centimeters.
Microwave emission from a layer of snow over a ground medium consists of two contributions: emission by the snow volume and emission by the underlying ground. Both contributions are governed by the transmission and reflection properties of the air-snow and snow-ground interfaces and by the absorption or emission and scattering properties of the snow layer (Stiles et al., 1981).
A snowpack is a dielectric medium that can be described either as a collection of scatterers distributed within a lossy dielectric or as a continuous random medium with a large dielectric variation (Ulaby et al., 1978). The bulk dielectric properties of snow do not give an adequate prediction of the microwave response. For example, the dielectric constant of snow will be between that of air (e = 1.0) and that of ice (e = 3.2) and can be estimated as a function of snow density using the standard dielectric mixing formulas. For a snow density of .5 g/cm cubed, this yields a dielectric constant of 2. The resulting emissivity for a smooth surface would be approximately 0.98, and a TB very close to the physical temperature should be observed. Indeed, this is approximately observed for long wavelengths (> 10 cm) and thick snowpacks, e.g., permanent snow fields and glaciers. For shorter wavelengths, a different phenomenon is observed; volume scattering by the individual ice grains reduces the TB by scattering some of the radiation out of the sensor field of view. This has the effect of introducing some of the cold sky brightness temperature into the radiometer field of view, thus reducing the observed TB (Schmugge, 1980b).
As an electromagnetic wave emitted from the underlying earth surface propagates through the snowpack, it is scattered by the randomly spaced snow particles into all directions. Consequently, when the wave emerges at the snow-air interface, its amplitude has been attenuated. The dry snow absorbs very little energy from the wave; therefore, it also contributes very little in the form of self-emission. When the snowpack grows deeper, the wave suffers more scattering loss, and the emission from the snowpack is further reduced.
The intensity of microwave radiation emitted through and from a snowpack depends on physical temperature, grain size, density, and underlying surface conditions of the snowpack. Snow parameters significantly affecting microwave sensor response are as follows (from NASA, 1982): 1) liquid water content; 2) crystal size; 3) depth and water equivalent; 4) stratification; 5) snow surface roughness; 6) density; 7) temperature; and 8) soil state, moisture, roughness, and vegetation. With knowledge of these parameters, the radiation emerging from a snowpack can be derived by solving the radiative transfer equation, which usually serves as the starting point for electromagnetic modeling of snow (Chandrasekhar, 1960; England, 1975; Chang et al, 1976; Tsang and Kong, 1977).
The radiative transfer equation for an axially symmetric nonhomogeneous medium can be written in the form of an integrodifferential equation
(equation to come)
where the radiation intensity I(x,mu) is at a depth x and traveling in the direction toward increasing x, making an angle whose cosine is mu with the normal. The functions sigma(x), B(x), and P(x,mu,mu') are extinction per unit length, the single-scattering albedo, the source function, and the phase function, respectively. The snow grains scatter the electromagnetic radiation incoherently and are assumed to be spherical and randomly spaced within the snowpack. Although snow particles are generally not spherical in shape, their optical properties, both the scattering and the extinction effects, can be simulated as spheres by using the Mie theory (Chang et al., 1976). The scattering effect is more pronounced at the shorter wavelengths and for larger particle sizes and drier snow. Assuming a monodisperse distribution of the snow particles and a snow density representative of moderately packed snow, the extinction coefficient at 37 GHz is larger than at 19 GHz, and there is a drastic increase in extinction values for wet snow as compared to dry snow conditions (Burke et al., 1981). Using the above radiative transfer equations, one can calculate emerging brightness temperatures with different physical parameters (Chang et al., 1982).
When radiometric measurements of brightness temperature are made at more than one microwave wavelength or polarization, it becomes possible to deduce additional information about the medium. This potential, a consequence of the variation of the emissivity of a medium with the wavelength and polarization of the radiation, provides the rationale for the development of inversion techniques that calculate the desired physical parameters from the brightness temperatures measured at multiple wavelengths and polarizations (Gloersen and Barath, 1977).
An inherent advantage of the satellite passive microwave observations can be understood by describing the measurement method as an integrating technique rather than a resolving technique. With passive microwave observations, radiative emissions from snow-covered and snow-free land, for example, are integrated within the instantaneous field of view of the satellite sensor.
If the field of view of the sensor includes a mixture of two materials, with respective emissivities, ew and eI and physical temperatures Tw and TI, then the brightness temperature TB is approximately a linear combination of the two individual brightness temperatures (Parkinson et al., 1987). In cases of mixed pixels, multichannel signals may be used to determine the fractional ground cover (Hallikainen, et al., 1988).
The Nimbus-7 spacecraft was launched November 26, 1978, into a Sun-synchronous polar orbit with local noon (ascending) and local midnight (descending) equator crossings. The orbital period is approximately 104 minutes and the equator crossings are separated by 26.1 degree in longitude. The SMMR instrument (see pg. 5) is forward viewing and scans 390 km to either side of the orbital track (Table 1). It was operated every other day so that the entire globe was mapped twice every 6 days. The SMMR measured microwave radiation from Earth's surface and surrounding atmosphere at five frequencies (6.6, 10.7, 18, 21, and 37 GHz) in both the horizontal and vertical polarizations (Table 1). The band width at each frequency is 250 MHz (NASA, 1978). A combination of oval instantaneous fields of view (IFOVs) and the integration times of the radiometers yields roughly circular beam spots with the following diameters: 6.6 GHz-148 km, 10.7 GHz-91 km, 18 GHz-55 km, 21 GHz-46 km, and 37 GHz-27 km. The antenna beam scan lies along a conical surface with a 42 degree half angle so that the distance to the surface of Earth is constant over the scan. The angle of incidence at Earth's surface is approximately 50 degrees (Oakes et al., 1989). In 1987, the SMMR showed signs of instrument failure. From August 1987 until it was turned off in July 1988, the SMMR operated in a nonscanning mode.
By observing a hot and cold reference source, the instrument was calibrated in flight. An initial calibration was performed for every scan. A radio frequency termination at the ambient temperature serves as the hot reference, and deep space, viewed by a special antenna horn, provides a cold reference. This two-point reference system allows conversion of measured antenna counts to observed radiances. A gross check of the counts is used to filter out bad calibration counts. When the Sun shines directly on the cold horn, the radiometer is known to register abnormal cold calibration counts; therefore, during these periods, the calibration counts are labeled invalid. If there are no valid calibration data for a short period, the interpretation of calibration counts from the previous data are used. However, these values may not be the most up to date if there is a large data gap between them. Radiances are computed with a calibration equation of a radiometric signal from Earth's surface, hot and cold calibration counts, and several instrument temperatures in the SMMR microwave circuitry. This calibration equation was developed using prelaunch calibration data (Oakes, et al., 1989). The radiometer outputs are converted to antenna temperatures using the hot and cold sky reference measurements and then corrected for antenna pattern effects to obtain brightness temperatures.
The SMMR antenna scans from -25 degrees to +25 degrees off the velocity vector of the satellite during one half-scan period. However, the feed horn remains fixed. The two orthogonal polarizations of the radiation measured by SMMR are actually mixed with respect to the vertical and horizontal components. Furthermore, the possibility of leakage in the ferrite switches that separate the orthogonal inputs to the common radiometer, may cause additional mixing of the two components in actual measurements.
For the SMMR instrument, the different polarizations are sampled during successive half-scans for all frequencies except 37 GHz. This means that the IFOVs for the vertical and horizontal polarizations do not coincide. Assuming that the antenna temperatures vary smoothly over the extent of a cell, the collocated measurements can be approximated by interpolating the missing channel values from the FOV surrounding the subject FOV.
A detailed description of the correction for polarization mixing used here is given by Gloersen et al. (1980). The coefficients in the correction have been modified slightly as a result of additional analysis of the data since the publication of that paper. Details of this additional analysis are described by Han (1981).
The initial flight data were received by the Meteorological Operations Control Center (MetOCC). The user formatted output tape (UFO) from MetOCC was then transferred to and processed by the Science and Applications Computer Center (SACC). Two calibrated brightness temperature tapes, CELL-ALL and TCT (Temperature Calibrated Tape), were produced. CELL-ALL data were gridded according to SMMR spatial resolution while TCT data retained the footprint configuration. TCTs were used for the snow parameters. Each tape consists of six days' data.
Half-Degree TCT Map tapes contain 6-day averages (ascending and descending orbits separated) of TCT brightness temperatures for all channels mapped onto a 1/2 degree by 1/2 degree grid. Each tape contains one month's data.
Quarter-Degree TCT Map tapes contain 6-day averages (ascending and descending orbits separated) of TCT brightness temperatures of 37 GHz channels mapped onto a 1/4 degree by 1/4 degree grid. Each tape contains 3 months' data.
The above described data are available from the National Space Science Data Center (NSSDC), Goddard Space Flight Center, Greenbelt, Maryland.
Currently, several algorithms are available to evaluate and retrieve snow cover and snow depth parameters for specific regions and specific seasonal conditions. These algorithms have been derived from research using a combination of microwave sensors aboard satellites, aircraft, and trucks, as well as in situ field studies. A straightforward method to relate microwave radiometric data to snow cover and snow depth is to examine the differences between the brightness temperature observed for snow covered ground and that for snow free ground. The general form of a snow cover algorithm is:
(sigma)T(sub-)sc = F (sub-)sc - F (sub)sc = 0
sigma T change in brightness temperature sc snow covered terrain F(sub-)sc observed radiometric value for snow covered terrain F(sub-)sc=0 observed radiometric value for snow-free terrain
and where F may be either the brightness temperature at a single frequency or a more complicated expression involving the brightness temperature at several frequencies or polarizations (Hallikainen and Jolma, 1987).
Efforts have been made by several investigators to produce a reliable global snow algorithm (Kunzi et al., 1982; Hallikainen, 1984; Chang et al., 1987). The monthly snow cover and snow depth maps produced for this data set were generated by using the algorithm developed by Chang et al. (1987) that prescribes a snow density of 0.30 g/cubic centimeter and a snow grain size of 0.3 mm for the entire snowpack. The difference between the SMMR 37 GHz and 18 GHz channels is used to derive a snow depth-brightness temperature relationship for a uniform snow field. This is expressed as follows:
SD = 1.59 * (TB18H - TB37H)
where SD is snow depth in cm, H is horizontal polarization, and 1.59 is a 0constant derived by using the linear portion of the 37 and 18 GHz responses to obtain a linear fit of the difference between the 18 GHz and 37 GHz frequencies. If the 18 GHz TB is less than the 37 GHz TB, the snow depth is zero, and no snow cover is assumed.
An evaluation of the various derived algorithms shows that only algorithms including the 37 GHz channel provide adequate agreement with the manually measured snow depth and snow water equivalent values. It may also be noted that the T18H - 37H often gives better results than the 37 GHz channel alone. Use of the 18 GHz channel helps to reduce the effects of the snow and ground temperatures and the atmospheric water vapor on changes in TB.
Extensive validation of the SMMR-derived data on snow cover and snow depth is essential and will lead to the development of more accurate and reliable algorithms. The next step is to invert the algorithms that have been developed to model microwave emission so that the snow cover and snow depth may be calculated from the microwave TB. This appears to be possible in areas for which the relevant properties of the snowpack are well established (Foster et al. 1987).
There are, of course, complications that arise when one tries to apply an algorithm based on average snow conditions to specific regions where the climate, snowpack structure, and vegetation cover may differ. Studies using radiative transfer modeling and SMMR data demonstrate that snowpack structure significantly influences the microwave emission. Depth hoar, at the base of some snowpacks (Benson et al., 1975), consists of large snow grains that are effective scatterers of microwave radiation at the 37 and 18 GHz frequencies. These large grains cause a reduction in the microwave emission from the entire snowpack (Hall et al., 1986). Additionally, in dense coniferous forests the greater emission from the trees may overwhelm the emission from the underlying ground. Thus, the microwave brightness temperature of the snowpack is higher than if no trees were present (Hall et al., 1982; Hallikainen, 1984). Also, microwave radiation at 37 GHz is nearly transparent to shallow (<5 cm) dry snow, which results in underestimates of snow extent and snow volume in the vicinity of the snow boundary. These problems are being addressed and will lead to "fine tuning" of our current algorithm or to combining a number of regional algorithms into one general algorithm.
The SMMR instrument was not designed to last a decade. The characteristics of the SMMR instrument have been changing through the years. These changes in instrument behavior have affected the calibration of the SMMR measurements. To understand the long-term variations of the calibrated SMMR brightness temperatures, the monthly means and the standard deviations of the brightness temperatures over global ocean areas have been analyzed.
Brightness temperatures on CELL-ALL tapes were selected for each channel from all ocean areas between 60 degrees N and 50 degrees S and 600 km away from land masses. Daytime and nighttime data were separated. The means and standard deviations of the brightness temperatures for each month from January 1979 to October 1985 were calculated. The statistics of this analysis are available in Fu et al., 1988.
Along with the seasonal variations, the data show that the monthly mean brightness temperatures have systematic biases between daytime and nighttime for most channels. There are also patterns of increasing or decreasing monthly mean brightness temperatures throughout the first 48 months. Starting in the fifth year, some of these patterns changed.
Similar analyses were performed for the brightness temperatures over land. The statistics of the analyses are available in Fu et al., 1988. Plots of monthly mean brightness temperatures can also be found there. The averaged temperatures over land are mostly stable, although the standard deviations are, as expected, larger than those over the ocean because of the greater scene variability over land (Fu et al., 1988).
Seasonal and annual variability in snow extent have been measured from SMMR data as well as Advanced Very High Resolution Radiometer (AVHRR) data collected on the NOAA satellites, but the error bands are lacking for both products. The SMMR and NOAA products agree fairly well, but the SMMR data produce consistently lower snow covered area estimates than do the NOAA data. For example, snow covered area in the Northern Hemisphere for January 1984 is 39.3 x 10^6 km^2 and 45.5 x 10^6 km^2 as measured from the SMMR and NOAA data respectively, a difference of about 16 percent. The error in the SMMR-derived snow depths is more difficult to determine because there is no reliable data set with a spatially dense enough network with which to compare the SMMR-derived snow depths on a hemispheric basis. The only other data set available with which to derive global snow volume is the data set produced by the Rand Corporation. The monthly averaged Rand data set was constructed by using climatological averages from meteorological station data. But preliminary comparisons between the SMMR and the Rand data sets for snow volume in the Northern Hemisphere indicate that the data sets are comparable. For March, the snow volume is 290 x 10^16 and 364 x 10^16g as determined from the SMMR and Rand data sets respectively. This is a difference of about 20 percent. The error bands are unknown and may be large; however, this SMMR temporal data set is the only source of monthly snow volume currently available (Chang et al., in press).
Quick look images of monthly data collected by the Nimbus-07 SMMR for snow cover and snow depth are available in color image format for the Northern Hemisphere. The SMMR data were interpolated for spatial and temporal gaps and averaged on a monthly basis into microwave brightness temperatures and displayed in color-coded polar stereographic maps. The maps are based on six-day-average brightness temperature data from the middle week of one month. The data are placed into 1/2 degrees latitude by 1/2 degrees longitude grid cells uniformly subdividing a polar stereographic map according to the geographic coordinates of the center of the field of view of the radiometers. Overlapping data in a cell from separate orbits in the same six day period are averaged to give a single brightness temperature assumed to be located at the center of the cell. The polar stereographic projection provides a synoptic representation of the brightness temperature data. The maps are constructed by projecting points on Earth's surface onto a plane tangent to the surface at one of the poles, with the vertex of the projection being the other pole (Parkinson et al., 1987). A mask was constructed to remove brightness temperature data over oceans and bays so that only microwave data for land areas are displayed.
The color scheme used for the quick look microwave maps was chosen to be visually appealing as well as informative. Twenty-eight color increments in various shades of blue, green, yellow, brown, red, and violet represent different snow depths. Each color shade corresponds to a depth of about 3 cm. The shallowest depth used is 3 cm and the deepest is 84 cm, corresponding to brightness temperatures of about 240 degrees K and 160 degrees K respectively. Theoretically, it is possible to distinguish snow depths of about 2 cm, but in actuality it is probably not possible to differentiate between depths of less than about 5 cm. However, it should be kept in mind that these values are not meant to be indicative of a given locale, but are integrated over the entire 1/2 degrees by 1/2 degrees microwave pixel. So even though, for example, a given point may have a depth of 100 cm, it is unlikely that 100 cm of snow will cover an area on the ground the size of a complete pixel. Ice cap regions, like Greenland and Antarctica, are infinitely thick to microwaves and are shown in pink, which represents the deepest snow detectable with the algorithm used herein.
Although the broad patterns of snow accumulation and depletion are similar for Eurasia and North America, there are differences that may be attributable to differences in continentality and location of storm tracks (Foster, et al., 1983; Figures 1-10).
For both Eurasia and North America, snow cover in the source regions leads to intense surface cooling with subsidence (high pressure) and the formation of a low-level inversion. Because Eurasia is over twice the size of North America and has more of its surface area in northern latitudes, its snow cover is more extensive. As a result, the anticyclone found over Siberia is more pronounced and persistent than the corresponding high over northern Canada, which is far less regular and is comparatively a rather weak and unstable feature (Lockwood, 1974).
During early autumn in Eurasia, cold air intrusions moving down from the Arctic bring about widespread cooling into the central continent. By early October, generally, freezing temperatures are present over much of Siberia, and a cold wave progresses gradually from northeastern to southwestern Siberia (Lydolph, 1977).
As seen from microwave brightness temperature maps, the snow cover first becomes established in northcentral and northeastern Siberia between mid-September and mid-October. A shallow layer of cold air forms above the snow surface in response to radiative losses resulting from the increase in albedo of the expanding snow cover. By mid-October, the Siberian or Asiatic high has already become evident. If the snow cover forms early and becomes deep and extensive, then the air above the snowpack is likely to be colder than if the snow cover is late forming and does not cover as extensive an area. The refrigerated air overlying the snowpack is transported southward during late fall and winter, cooling much of the continent.
In October and November the snowpack increases in extent and begins to build in the Tiaga and tundra zones. Now, the Siberian high has become well-developed as a result of the extreme surface cooling and the constant feeding of fresh Arctic air into central Asia (Lydolph, 1977). This high is large enough to effectively prevent the incursion of maritime air or air from other source regions into the continental interior. In addition, numerous mountain ranges hinder advancing air masses from the south and west. By December, the snow covered area has expanded well into the Russian and Kazakh Soviet Republics. From December through March, the snowpack continues to increase in depth in the interior regions. Because of the strength and constancy of the Asiatic high, even during relatively mild winters, temperatures in the interior regions are rarely above freezing and so there is very little melting of the snowpack. In fact, the location of the snowline during winter in central Asia may be more of a result of moisture availability than of temperature. Year-to-year variations in the winter temperature are due not as much to the winter snow cover as they are to other factors such as the variability of the large-scale circulation.
In March, with increasing solar insolation, the snowline begins a rapid retreat northward. By mid-April the snowpack is typically confined to boreal forest and tundra areas. Because moisture is often scarce, much of the snow covered areas in the steppes and plains of interior Eurasia are quite shallow (<15 cm) and melt quickly in early spring. The snowpack, as seen from the microwave maps, shows a fairly constant regression in latitude from March through June, at which time the snow is relegated to the northernmost continental reaches and to those areas lying adjacent to the still very cold bays and inlets.
In North America, the north slope of Alaska is typically the first area to be snow covered, generally by mid-September. By the middle of October, the snow cover has become established throughout most of Alaska and northern Canada. As is the case in Eurasia, snow cover increases dramatically in North America during October and November. The snow cover and depth increase from the north and west to the east and south as observed from SMMR. As autumn progresses, temperatures in the Arctic regions fall rapidly with the decreasing amount and intensity of insolation, and the snow cover continues to expand southward. Anticyclones increasingly develop in the Arctic air masses over the interior of Canada, and sometimes they intensify to control the weather over the greater part of the continent. However, maritime air mass systems from the west (Pacific Ocean) periodically penetrate into the interior of North America during fall and winter.
The snow extent during winter in the interior of North America usually reaches approximately 40 degrees north latitude. However, in some winters the snowline may be positioned near the Canadian border (49 degrees north), whereas in other years the snowline may be located as far south as Oklahoma and Arkansas (33 degrees north). It appears that when the snow covered area in winter is extensive, the North American high is fairly strong; consequently, intrusions by air masses from other source areas are less likely to occur.
By April most of the snow is usually located north of the Canadian-U.S. border in nonmountainous areas. The deepest snowpacks are adjacent to the southern shores of Hudson Bay and in the boreal forests of the Northwest and Yukon Territories and Alaska. Since the storm tracks migrate north as spring progresses, it is not unusual for the snowpack to build in some areas north of about 60 degrees latitude throughout April. The snowpack recedes rapidly northward between mid-April and mid-May, and by mid-June most of the remaining snow lies along the Arctic coasts.
Even though nearly all of the SMMR analysis and validation has been performed in the Northern Hemisphere, because this is a global data set, snow cover observations for the Southern Hemisphere are included. However, there is very little variation in snow cover on an annual basis in the Southern Hemisphere. Over 99 percent of the snow is confined to the continent of Antarctica, which, except for coastal areas and the Antarctic Peninsula during the summer months, is always snow covered. Seldom are areas larger than an SMMR pixel completely snow covered in Australia and Africa. The South Island of New Zealand and western South America have numerous glaciers in the Southern Alps and Andes mountains, respectively, but the only extensive area of seasonal snow in the Southern Hemisphere is found in Chile and Argentina (Patagonia and Pampas regions). In 1980, the snow-covered area reached a maximum of over one million square kilometers in South America, and in 1979 the maximum was less than 700,000 square kilometers as measured from the NOAA satellites (Dewey and Heim, 1983). Thus, it is likely that the snow-cover area and variability are large enough to affect the weather and climate in nonequatorial areas of South America.
Fluctuations of snow volume and extent can be viewed in part as consequences of the varying large-scale circulation. The natural variability in snow extent and snow volume is imperfectly known because of the relatively short period of record, and several decades or more of such data may be needed to discern if trends exist. But no sustained trend in snow cover is observable from the AVHRR data (1967 to present; Barry 1985) or from the SMMR snow cover and snow depth record (1979 to 1987).
Other evidence indicates that changes in cryospheric features may already be in progress (Hall, 1988). Over the last century, a 2 to 4 degrees C rise in permafrost temperature has been measured in northern Alaska (Lachenbruch and Marshall, 1986) and the small glaciers of the world have generally retreated (Meier, 1984).
There is no apparent correlation between Northern Hemisphere snow cover conditions as observed from satellites and surface temperatures. However, even though these data sets do not fluctuate in synchrony, close attention should be paid to the warming signal detected by several climate researchers. Snow cover and snow depth increases may result if sufficient moisture is available, even if temperatures are above normal. It should be noted also that there is no direct association between sea ice extent and snow cover extent. This should not be surprising since the oceans have a much higher thermal inertia and heat capacity than do the continents, so time lags may mask any trends that exist. Even though satellite snow cover records are presently too short to determine definite trends, continued monitoring is essential and may provide an early indication of the onset of a warming signal or some other climatic fluctuation (Foster, 1989).
The establishment of the microwave snow data set has permitted a quantitative assessment of changes in global snow depth and volume, and has demonstrated that there exists considerable interannual variability in snow volume (Figures 11 to 19). But the Special Sensor Microwave Instrument (SSM/I) onboard the Defense Meteorological Satellite Platform (DMSP) launched in June 1987 is continuing the snow measurements begun in 1978 by SMMR. SSM/I operates in a Sun-synchronous, near-polar orbit at an altitude of 833 km with a period of 101 minutes. In contrast with SMMR, SSM/I provides near global coverage every day. SSM/I operates at four frequencies -- 19.35, 22.24, 37.0, and 85.5 GHz -- with orthogonal (horizontal and vertical) polarizations measured at each frequency except 22 GHz, which has only a vertical polarization channel (Cavalieri, 1988).
Thus far, the Southern Hemisphere snow data have not been analyzed as thoroughly as those of the Northern Hemisphere. The data record is too short to detect the presence of any trends that may exist, but preliminary analysis indicates that variations between South American and North American seasonal snow cover are poorly correlated. Figure 20 presents SMMR-derived snow data for both hemispheres during the winter months for the years 1979 to 1987.
Although the microwave snow products are not yet being used in an operational mode, several ongoing studies, described below, point out the potential uses of this microwave snow data set.
The mechanics of Earth's atmospheric circulation are highly complex and only partially understood, which makes numerical simulation difficult. Hence, it is difficult to describe rigorously the role of snow as it affects global climate, and it is hard to ascertain the causes of a particular deficiency in a model's climate simulation because of the complicated interactions that take place. In the case of snow, sorting out cause and effect can be particularly trying. Its existence depends on factors such as temperature, precipitation, and solar radiation, but once present, snow cover can influence each of these factors (Broccoli, 1985). Many global climate models (GCMs) have treated snow as a uniform feature; i.e., with a uniform albedo and a uniform coverage from year to year. This is not a good depiction of the physical situation. Snow cover and depth change rapidly over large areas during fall buildup and spring melt and, until recently, the capability did not exist to recognize these changes.
For over 25 years, efforts have been made to construct GCMs for use in both forecasting and climate modeling projects. During this period, great strides were made in improving the accuracy of numerical forecasts as well as in the quality of climate model simulations. To do this work, accurate snow and ice observations are needed to provide boundary conditions for atmospheric GCMs, to initialize forecast models, and to validate forecast and climate model simulations (Robock, 1980). At present, the most suitable snow cover record for validation of GCMs is the NOAA satellite-derived snow cover data base. This data base has been used to a limited extent in model validation (Kukla, et al., 1985).
Some GCMs also predict the mass of snow on Earth's surface from a snow mass budget equation that includes the processes of snowfall, snow melt, and sublimation. Generally, the snow layer is considered to have uniform properties over its entire depth within a model grid box, and the surface albedo is taken to be a function of the depth of snow and the type of underlying surface. GCMs calculate snow accumulation as the result of precipitation from clouds. In GCMs, snow ablation occurs only as a result of above-freezing temperature.
The observed water equivalent of snow is required to validate the surface snow mass simulated by GCMs. Such observations were made locally for Europe, North America, and elsewhere from climatological records and are archived in various reports. But passive microwave data from sensors such as SMMR and SSM/I may provide a more realistic synoptic representation of the snow water equivalent (Foster and Rango, 1989).
In addition, the snow extent data derived from passive microwave satellites may be useful for input to GCMs because the scale of the SMMR data is such that it can easily be made compatible with typical GCM grid scales, and data can be acquired through cloud cover and darkness. SMMR and AVHRR derived data on snow are being used in several different versions of GCMs to analyze the influence of snow on the global climate. Three of these models are the Goddard Laboratory for Atmospheric Sciences (GLAS) 4th Order GCM, the National Center for Atmospheric Research (NCAR) Community Climate Model (Dickinson, 1983), and the Goddard Institute for Space Studies (GISS) GCM (Hansen et al., 1983). Currently, realistic satellite derived values of snow extent and snow water equivalent are being used in the models to study interannual changes in the output of each GCM. Preliminary results for the Northern Hemisphere indicate that, as expected, there are some disagreements between the climatologically -derived and the satellite-derived snow distributions. However, overall patterns are basically the same.
Satellite microwave data have been used to evaluate the average areal water equivalent of snow cover in the mountainous Colorado River Basin in the western U.S. It has been shown that satellite microwave data, even at very poor resolution, can be used to obtain information about average basin snow water equivalent. The microwave approach has certain advantages including an all-weather observation capability, an ability to make areal measurements, and a data measurement capability in remote, inaccessible regions. Difficulties in using the microwave approach that arise from alternating dry and wet snowpack conditions are minimized by using nighttime data. In a study by Rango et al. (1989), an average snow water equivalent for a basin 3,419 km^2 in area was obtained using the difference in microwave brightness temperatures of the 37 and 18 GHz channels. In two test years (1986 and 1987), the microwave determined average basin snow water equivalent on April 1 was within 15 percent of the actual observed value as derived from stream flow measurements. The approach is not yet ready for true operational use because it needs additional tests in other years and in other basins. But as resolutions improve with future sensors, the advantages of the microwave measurements will be more significant, especially in data sparse regions. The improved microwave data could be used on smaller basins and for determining snow water equivalent of individual elevation zones. Such data could be used for selecting elevation zone snow cover depletion curves in particular years for use in snow melt runoff forecasts, or to directly provide areal water equivalent data to snow melt runoff models (Rango et al., 1989).
Any redistribution of water mass over Earth causes slight changes in Earth's rotation because of the exchange of angular momentum between the solid Earth and the hydrosphere. The buildup and disappearance of snow excites polar motion producing a shift in the position of the rotation axis relative to a fixed geographic axis. The polar motion consists mainly of an annual wobble and a 14-month Chandler wobble. The annual wobble is a forced motion caused primarily by seasonal changes in Earth's atmosphere and hydrosphere. In the course of the annual wobble, the rotational axis describes a somewhat elliptical path about the fixed geographic axis of perhaps four meters (Chao et al., 1987).
Until recently, monthly measures of polar motion and global snow volume were too inexact to be able to determine the effect of snow on Earth's rotation. However, with the launch of the Lageos satellite in 1976, which can measure polar motion accurately, and the Nimbus satellite in 1978 (SMMR), it is now possible to assess and monitor the effects of changes in the distribution of snow mass on Earth's surface. Chao et al. (1987) used the Lageos and Nimbus data sets to compute the snow load excitation of the annual wobble of Earth's rotation axis. It was found that the snow load excitation has an amplitude that is some 30 percent of the total annual wobble excitation, thus it represents a significant geophysical contribution (Chao et al., 1987).
There is potential for using passive microwave data to detect areas of winter kill. Winter kill results when grain crops planted in fall (e.g., winter wheat) are damaged or killed because there was insufficient snow cover to insulate the young plants from subfreezing temperatures. Winter kill is most often experienced in the Great Plains of the U.S. and Canada and in the steppe areas of the Soviet Union. With adequate snow cover the damage attributable to winter kill is minimized even during very cold winters. Microwave maps of North America and Eurasia are useful in discerning areas of meager snow cover and depth and thus may be used as an indirect means to assess winter kill losses (Goodison et al., 1986). In the future, microwave data on snow depth and snow cover may be included as an additional input to improve the performance of the models currently being used to forecast winter kill potential.
Monthly global snow maps are generated on an IBM 3081 computer. The tape format conforms to standard 9-track, IBM nonlabel tape. Each monthly map is one file. A simple sketch of the data structure is shown in Figure 21. The first record (720 bytes) is a header record, with ASCII characters, and contains the map's time period and comments. Records 2 through 341 are data records. Their contents can be expressed as follows:
Row 1 Row 1 Col 1 Col 720 84.5 to 85.0N 84.5 to 85.0N Rec 2 180 to 179.5W 179.5 to 180E Row 170 Row 170 Col 1 Col 720 0.0 to 0.5N 0.0 to 0.5N Rec 171 180 to 179.5W 179.5 to 180E
Each element is a one-byte unsigned integer.
Digital monthly global snow maps are archived through the NASA Pilot Land Data System (PLDS). They are available in 9-track 6250 bpi or 1600 bpi tape format. The logical record length (LRECL) is 720 bytes and the average block size is 30,960 bytes. The first seven blocks in each file equal 31,680 and the last block equals 23,760.
The tape contains 106 files of snow data from November 1978 to August 1987 (details are tabulated in Table 2). Each monthly map is one file on the tape. Each file contains 341 logical records. The first record is an ASCII character header. It contains the period of the map. The days that were used to create the maps are given as ranges expressed in Julian days, and for some maps also in calendar days. These are usually two ranges of days. The year is included as is the map number with the first map being "world map #1." This information is not given in the same sequence in each header file, so you will need to read the entire header. Examples of two different versions of header files are shown here -- there are others.
Header file examples
Table 2, Data File Number List
The rest of the map has the following specifications:
Top latitude 85 degrees North Bottom latitude 85 degrees South Left longitude 180 degrees West Right longitude 180 degrees East No. of columns (1/2 degree longitude/col.) 720 No. of rows (1/2 degree latitude/row) 340 Map grid data type unsigned 8-bit integer
Each map grid element may have the following values:
255 Water 254 Permanent ice 253 No data available or data failed quality filters 252 Unused 251 Unused 3 - 250 Snow depth in centimeters 0 No snow, or snow less than 2.5 cm
If you have questions or need assistance, please contact NSIDC User Services.
NSIDC User Services
National Snow and Ice Data Center
CIRES, 449 UCB
University of Colorado
Boulder, CO 80309-0449 USA
phone: +1 303.492.6199
fax: +1 303.492.2468
form: Contact NSIDC User Services
Barry, R. G. 1984. Possible carbon dioxide-induced warming effects on the cryosphere. In: Climate Changes on a Yearly to Millennial Basis. eds. N. A. Morner and W. Karlen, pp. 571 to 604. Hingham:D. Reidel.
Barry, R. G. 1985. Snow cover, sea ice, and permafrost. In Glaciers, Ice Sheets, and Sea Level: Effect of a CO2-Induced Climatic Change, pp. 241 to 247. Washington:Dept. of Energy.
Benson, C., B. Holmgren, R. Timmer, G. Weller, and S. Parrish. 1975. Observations on the seasonal snow cover and radiation climate at Prudhoe Bay, Alaska, during 1972. In \i Ecological Investigations of the Tundra Biome in the Prudhoe Bay Region, Alaska. ed. J. Brown, University of Alaska Special Report No. 2, pp. 13-50.
Broccoli, A. 1985. Characteristics of seasonal snow cover as simulated by GFDL climate models. In Glaciological Data Report GD--18, Snow Watch '85, pp. 241-248.
Burke, H. K., C. J. Bowley, and J. C. Barnes. 1981. Comparison of Theoretical and Actual Satellite Microwave Brightness Temperatures To Determine Snowpack Properties. Final Rep. A653-F. Concord:Environ. Res. and Technol. Inc.
Campbell, W. J., and P. Gudmansen. 1981. The application of microwave remote sensing for snow and ice research. In Proceedings of the IEEE International Geoscience and Remote Sensing Symposium Digest, ed. K Carver, pp. 951-957.
Cavalieri, D. J. 1988. NASA Sea Ice and Snow Validation Program. NASA Technical Memorandum 100706.
Chandrasekhar, S. 1960. Radiative Transfer. New York:Dover.
Chang, A. T. C., P. Gloersen, T. Schmugge, T. T. Wilheit, and H. J. Zwally. 1976. Microwave emission from snow and glacier ice. J. Glaciol. 16:23.
Chang, A. T. C., J. L. Foster, D. K. Hall, A. Rango, and B. K. Hartline. 1982. Snow water equivalent estimation by microwave radiometry. Cold Reg. Sci. Technol. 5:259-267.
Chang, A. T. C., J. L. Foster, and D. K. Hall. 1987. Nimbus-07 SMMR derived global snow cover parameters. Ann. Glaciol. 9:39-44.
Chang, A. T. C., J. L. Foster, and D. K. Hall. 1990. Satellite estimates of Northern Hemisphere snow volume. Remote Sensing Letters, International Journal of Remote Sensing 11:1:167-172.
Chang, H. D. 1982. User's Guide for Scanning Multichannel Microwave Radiometer (SMMR) Instrument First-Year Antenna Temperature Data Set. Washington:SASC.
Chao, B., W. P. O'Connor, A. T. C. Chang, D. K. Hall, and J. L. Foster. 1987. Snow-load effect on the Earth's rotation and gravitational field, 1979-1985. J. Geophys. Res. 92:9415-9422.
Crane, R. G. 1979. Inventory of snow cover and sea ice data. In Glaciological Data Report GD-7, World Data Center -A for Glaciology, pp. 1-3. Boulder:Univ. of Colo.
Dewey, K., and R. Heim, Jr. 1983. Satellite observations of variations in Southern Hemisphere snow cover. In NOAA Technical Report NESDIS 1, pp. 1-20. Washington:NOAA.
Dickinson, R. E. 1983. Land surface processes and climate surface albedos and energy balance. Advances in Geophysics 25:305-353.
England, A. W. 1975. Thermal microwave emission from a scattering layer. J. Geophys. Res. 80(32):4484-4496.
Foster, J. L. 1989. The significance of the data of snow disappearance on the Arctic tundra as a possible indicator of climate change. Arctic and Alpine Res. 21:1:60-70.
Foster, J. L., M. Owe, and A. Rango. 1983. Snow cover and temperature relationships in North America and Eurasia. J. Clim. Appl. Meteorol. 22:460-469.
Foster, J. L., D. K. Hall, A. T. C. Chang, and A. Rango. 1984. An overview of passive microwave snow research and results. Rev. Geophys. 22:195-208.
Foster, J. L., D. K. Hall, and A. T. C. Chang. 1987. Remote sensing of snow. Eos Trans. AGU 68:681-684.
Foster, J. L., and A. Rango. 1989. Advances in modeling of snowpack processes utilizing remote sensing technology. Geo Journal 19:2:185-192.
Fu, C. C., D. Han, S. T. Kim, and P. Gloersen. 1988. User's Guide for the Nimbus-7 Scanning Multichannel Microwave Radiometer (SMMR) CELL-ALL Tape. NASA Reference Publication 1210.
Gloersen, P., and F. T. Barath. 1977. A scanning multichannel microwave radiometer for Nimbus G and Seasat A. IEEE J. Oceanic Eng. OE-2:172-178.
Gloersen, P., D. Cavalieri, and H. V. Soule. 1980. An Alternate Algorithm for Correction of the Scanning Multichannel Radiometer Polarization Radiances Using Nimbus-7 Observed Data. NASA Technical Memorandum 80672.
Goodison, B. E., I. Rubinstein, F. W. Thirkettle, and E. J. Langham. 1986. Determination of Snow Water Equivalent on the Canadian Prairies Using Microwave Radiometry. IAHS Publ. 155, pp. 163-173.
Hall, D. K., J. L. Foster, and A. T. C. Chang. 1982. Measurement and modeling of microwave emission from forested snowfields in Michigan. Nordic Hydrology 13:129-138.
Hall, D. K., and J. Martinec. 1985. Remote Sensing of Ice and Snow. 189 pp. London:Chapman & Hall.
Hall, D. K., A. T. C. Chang, and J. L. Foster. 1986. Detection of the depth-hoar layer in the snowpack of the Arctic coastal plain of Alaska, U.S.A., using satellite data. J. Glaciol. 32:87-94.
Hall, D. K. 1988. Assessment of polar climate change using satellite technology. Review of Geophysics. 6:21:26-39.
Hallikainan, M., and P. Jolma. 1987. Development of algorithms to retrieve the water equivalent of snow cover from satellite microwave radiometer data. In Rep. ESA SP-254, pp. 611-616. Zurich:Eur. Space Agen.
Hallikainen, M. T., P. A. Jolma, and J. M. Hgyppa. 1988. Satellite microwave radiometry of forest and surface types in Finland. In IEEE Trans. GRS-26, pp. 622-628.
Hallikainen, M. T. 1984. Retrieval of snow water equivalent from Nimbus-7 SMMR data: Effect of land-cover categories and weather conditions. IEEE J. Oceanic Eng. OE-9:372-376.
Han, D. 1981. Offset of polarization rotation for the Nimbus-7 Scanning Multichannel Microwave Radiometer (SMMR). Washington:SASC.
Hansen, J., G. Russell, D. Rind, P. Stone, A Lacis, S. Lebedeff, R. Ruedy, and L. Travis. 1983. Efficient three-dimensional global models for climate studies. Models I and II, Monthly Weather Review lll:4:609-662.
Jones, E. B. 1983. Snowpack Ground-Truth Manual. NASA Contractor Report 170584.
Kukla, G., R. G. Barry, A. Hecht, and D. Wiesnet. 1985. Snow-Watch '85. In Recommendations, Glaciological Data GD-18, Snow Watch '85. pp. 1-18.
Kunzi, K. F., S. Patil, and H. Rott. 1982. Snow-cover parameters retrieval from Nimbus-7 scanning multichannel microwave radiometer (SMMR) data. IEEE Trans. Geosci. Remote Sens. GE-20:452-467.
Lachenbruch, A. H., and B. V. Marshall. 1986. Changing climate, geothermal evidence from permafrost in the Alaskan Arctic. Science 234:689-696.
Lockwood, J. G. 1974. World Climatology. New York:St. Martins Press.
Lydolph, P. E. 1977. Climates of the Soviet Union, World Survey of Climatology 7. Amsterdam: Elsevier.
Matson, M., C. F. Ropelewski, and M. S. Varnadore. 1986. An Atlas of Satellite-Derived Northern Hemisphere Snow Cover Frequency. Washington:Nat'l Weather Serv.
Meier, M. 1984. Contribution of small glaciers to global sea level. Science 226:1418-1421.
Nimbus-7 User's Guide, The. Washington:NASA. pp. 213-245.
Oakes, A., D. Han, H. Kyle, G. Feldman, A Fleig, E. Hurley, and B. Kaufman. 1989. Nimbus-7 Data Product Summary. NASA Reference Publication 1215.
Parkinson, C. L., J. C. Comiso, H. J. Zwally, D. J. Cavalieri, P. Gloersen, and W. J. Campbell. 1987. Arctic Sea Ice 1973-1976: Satellite Passive-Microwave Observations. NASA Spec. Publ. SP-489. 296 pp.
Rango, A., A. T. C. Chang, and J. L. Foster. 1979. The utilization of spaceborne microwave radiometers for monitoring snowpack properties. Nord. Hydrol. 10:25-40.
Rango, A., J. Martinec, A. Chang, J. Foster, and V. van Katwijk. 1989. Average areal water equivalent of snow on a mountain basin using microwave and visible satellite data. In IEEE Transactions on Geoscience and Remote Sensing 23:6:740-745.
Robock, A. 1980. The seasonal cycle of snow cover, sea ice, and surface albedo. Mon. Weather Rev. 108:267-285.
Schmugge, T. 1980 (a). Techniques and applications of microwave radiometry. In Remote Sensing in Geology, eds. B. S. Siegel and A. R. Gillespie, pp. 337-352. New York:John Wiley.
Schmugge, T. 1980 (b). Microwave approaches in hydrology. Photogramm. Eng. Remote Sens. 46:4:495-507.
Stiles, W. H., F. T. Ulaby, and A. Rango. 1981. Microwave measurements of snowpack properties. Nord. Hydrol. 12:143-166.
Tsang, L., and J. A. Kong. 1977. Theory for thermal microwave emission from a bounded medium containing spherical scatters. J. Appl. Phys. 48:8:3593-3599.
Ulaby, F. T., A. K. Fung, and W. H. Stiles. 1978. Backscatter and Emission of Snow: Literature Review and Recommendations for Future in Investigations. RSL Tech. Rep. 369-1. Lawrence:Univ. of Kans.
Vowinckel, E., and S. Orvig. 1970. The climate in the north polar basins. In Climate of the Polar Regions, Vol. 14 of World Survey of Climatology, p. 129-252. Amsterdam:Elsevier.
Zwally, J., and P. Gloersen. 1977. Passive microwave images of the polar regions and research applications. Polar Res. 18:431.