1. Introduction
The changing masses of Greenland and Antarctica represent the largest unknown in predictions of global sea-level rise over the coming decades (
Dowdeswell, 2006). Recent analysis suggests that the contribution of the Greenland and Antarctic Ice Sheets to present-day sea level rise is more than 0.3 millimeters per year (
Krabill et al., 2000;
Rignot and Thomas, 2002;
Shepherd and Wingham, 2007). Changes in surface temperature on these large ice masses can affect the rate of ice deformation or basal sliding (
Zwally et al., 2002). Rapid increases in the extent and duration of surface melt have been detected using satellite imagery along the surface of southern Greenland and parts of Antarctica (
Jezek et al., 1992;
Ridley, 1993;
Zwally and Fiegles, 1994;
Abdalati and Steffen, 1995;
Mote and Anderson, 1995, and several others.)
Zwally et al. (2002) have demonstrated that ice flow speed increases during the summer melt season.
Rignot and Kanagaratnam (2006) have confirmed acceleration of ice flow over a large part of coastal Greenland between 1996 and 2000 from radar interferometry and attribute this to recent climate warming.
In recent years, observations of ice sheet physical properties and dynamic behavior have shifted from in-situ observations towards satellite techniques (
Lubin and Masson, 2006). The ability of satellite systems to acquire data over vast areas of remote terrain, during the day or night and in all weather conditions has facilitated this shift (
IGOS, 2007). A variety of satellite instruments sensitive to different parts of the electromagnetic (EM) spectrum provide rich data sets of elevation, motion, accumulation on ice sheets (
Bindschadler, 1998). Understanding the mechanism and features of the current approaches of modeling of ice sheet melt is critical to improve the assessment of melt dynamics over Greenland Ice Sheet (GIS). This work demonstrates a novel approach to improve the assessment of melt dynamics by expanding satellite derived estimates of melt from a binary measure of occurrence to melt magnitude or intensity.
2. Background
Snow is a mixture of ice, liquid water and air. The dielectric constant of snow is derived from a weighted average of the dielectric constants of these components (
Matzler et al, 1984). The real part of the dielectric constant of ice has a value of 3.17 throughout the microwave region. Specifically, microwave emission in dry snow is dominated by scattering (
Cumming, 1952;
Tiuri et al., 1984;
Rees, 2006). Consequently, liquid water in wet snow increases the dielectric constant of snow and thus enhances emissivity and absorption of microwave radiation (
Chang et al., 1976;
Tiuri et al., 1984;
Hallikainen, 1986). Given these relationships between microwave emission and ice properties, airborne and satellite based systems have been used successfully to map ice properties and assess surface and near-surface melt conditions. Active radar systems such as Synthetic Aperture Radar (SAR) provide high-resolution observations of microwave radar backscatter, and have been applied to study GIS surface and near-surface properties and ice dynamics (
Fahnestock et al., 1993). Ranging radars operating at 5.3 GHz and 13.3 GHz have been used and compared with in-situ data by
Jezek et al. (1994) to interpret melt-related processes on the GIS. NASA Scatterometer data (NSCAT) were combined with Seasat Scatterometer (SASS) data and ERS-1/2 Scatterometer data (ESCAT) to map ice sheet melt extent (
Long and Drinkwater, 1999). Due to its ability to penetrate into snow, normalized radar cross section (NRCS) measurements from C-band (5.3 GHz) scatterometers were used to monitor seasonal snowmelt on Greenland by
Wismann (2000).
Rapid increases in the extent and duration of surface melt on the GIS from 1978 to the present have been detected from passive microwave systems such as the Scanning Multi-channel Microwave Radiometer (SMMR) and the Special Sensor Microwave/Imager (SSM/I) deployed on several Defense Meteorological Satellite platforms (
http://cires.colorado.edu/steffen/).
The presence of liquid water has a dramatic effect on the microwave properties of snow. The Rayleigh-Jeans approximation for radiation in the microwave part of the EM spectrum is
where T
b is the brightness temperature,
ε is the microwave emissivity, and T is the effective physical temperature of the snow (
Abdalati and Steffen, 1997). Compared with dry snow, whose dielectric constant is a function of density only in the microwave region, the dielectric behavior of wet snow is a function of its physical parameters and frequency (
Hallikainen et al., 1986). Therefore, according to the Rayleigh-Jeans approximation, the emissivity is relatively constant over time for dry snow, in which case the T
b is approximately a linear function of T. When melt occurs, liquid water causes a large increase in the emissivity of snow and results in a corresponding increase in T
b (
Ashcraft and Long, 2003).
Changes in T
b at 19 and 37 GHz have been used as a metric for determining melt onset (
Zwally and Fiegles, 1994;
Ridley, 1993, and
Mote and Anderson, 1995).
Steffen et al., (1993) identified wet snow regions using AVHRR (Advanced Very High Resolution Radiometer), SMMR, SSM/I and in-situ data, based on the relationships between in-situ measurements and horizontally polarized 19 and 37 GHz observation. Specifically, the cross-polarization gradient ratio (XPGR) (
Abdalati and Steffen, 1995) approach was used to assess melt zones. XPGR indicates melt when the snow surface contains greater than 1% liquid water by volume. To study seasonal and inter-annual variations in snow melt extent of the ice sheet,
Abdalati and Steffen (1997) established melt thresholds in the XPGR by comparing passive microwave satellite data to field observations.
Ashcraft and Long (2005) studied the differentiation between melt and freeze stages of the melt cycle using the SSM/I channel ratios. In 2006, these authors assessed melt detection performance from SSM/I, SeaWinds on QuikSCAT (QSCAT), and the European Remote Sensing (ERS) Advanced Microwave Instrument (AMI) in scatterometer mode, and concluded that melt estimates from different sensors were highly correlated. The difference between ascending and descending brightness temperatures (DAV) (
Ramage and Isacks, 2002) measured either at 19.35- or 37- GHz by SSM/I was applied to map melt extent in Greenland, and the results compared with those obtained from QSCAT (
Nghiem et al., 2001;
Tedesco, 2007).
Although active and passive microwave systems have performed well in monitoring melt conditions over the GIS, they are limited in the amount of detail that can be either spatially or temporally resolved. Passive systems have relatively coarse spatial resolution and generally results from maintaining high radiometric resolution, while active systems demonstrate limited or lower temporal resolution (
Campbell, 2007). Active systems such as SAR in high-resolution observations of microwave radar backscatter have 16-day ground track repeat cycle, which is too infrequent to capture dynamic melt conditions.
Other parts of the EM spectrum offer potential advantages for monitoring melt over the GIS, and may augment the shortcomings of microwave systems. Data from optical satellites have been used to map surface dynamics related to the melt process over the GIS at higher spatial resolutions.
Hall et al. (1990) compared in-situ measurements with Landsat Thematic Mapper (TM)-derived reflectance on Greenland and concluded that Landsat TM was viable to obtain the physical reflectance of snow and ice. AVHRR visible and near-infrared radiances were used to derive surface albedo over the GIS and were validated by in-situ data (
Stroeve et al., 1997). Products from the Moderate Resolution Imaging Spectroradiometer (MODIS) were also widely used to retrieve snow albedo over Greenland, and have been compared with in-situ measurements and with other instruments such as Multi-angle Imaging SpectroRadiometer (MISR) separately (
Stroeve and Nolin, 2002a;
Stroeve et al., 2004).
Stroeve and Nolin (2002b) developed two different methods to derive the snow albedo over the GIS: one utilizing the spectral information from MISR and one based on angular information from the MISR instrument. Their results indicated that the accuracy of either of those two methods was within 6% compared of in-situ measurements.
Hall et al. (2004) compared MODIS with SSM/I-derived melt extent in summer of 2002 and concluded that the results are not, and should not necessarily be, the same. They also suggested that MODIS and SSM/I data were complementary in providing detailed information about the maximum snow melt on the GIS.
Satellite derived thermal information over GIS has been addressed over the past two decades (
Key and Haefliger, 1992;
Haefliger et al., 1993;
Comiso et al., 2003 and others). Specifically,
Hall et al. (2006) examined mean clear-sky MODIS derived surface temperature over GIS from 200 to 2005 during the melt season and have determined that during periods of intense melting, surface temperatures were highest in 2002 (-8.29 ± 5.29°C) and 2005 (-8.29 ± 5.43°C) relative to the 6-year mean (-9.04 ± 5.59°C). More Recently,
Hall et al. (2008) assessed the relationship between ice sheet mass balance and the spatio-temporal variability of MODIS retrieved surface temperature over GIS from 2000 to 2006. Daily, clear-sky MODIS land-surface temperature (LST) was compared to changes in mass concentration derived from the Gravity Recovery and Climate Experiment (GRACE) system and assessed that a mean LST increase (∼0.27°C per year) over this period was associated with an increase in melt season length and rapid mass loss during significant warming events, particularly at elevations below 2000 meters in 2004 and 2005.
Surface melt patterns and their duration are an important component of ice sheet mass balance, and have been successfully measured, however estimation of ice sheet surface melt amount is still underdetermined from passive microwave approaches. The missing link in improved modeling of ice sheet response to an increase in temperature is a full assessment of surface melt amount.
2.1. Optical and Thermal Radiative Theory
Surface albedo, which influences the amount of absorbed solar radiation, can vary due to several factors such as grain-size, emission angle, snow density, surface impurities, and liquid water content (
Dozier and Warren, 1982). Previous work has examined the strong relationship between snow spectral reflectance and grain-size, and modeled snow reflectance from the optical properties of snow and ice (
Bohren and Barkstrom, 1974;
Wiscombe and Warren, 1981;
Nolin and Dozier, 2000;
Painter et al., 2003). The optical properties of snow indicate high reflectance in the visible (0.4-0.7μm), and parts of the Near Infrared (NIR) (0.7-1.3μm) regions of the EM spectrum. Snow reflectance demonstrates substantial decrease in the Shortwave Infrared (SWIR) (1.3-3μm) due to increase in absorption.
In the visible and NIR regions of EM spectrum, the optical properties of snow depend, in large part, on the refractive index of ice (
Dozier, 1989). Absorption is due to variation in the imaginary part of the complex refractive index of ice given as:
where
n = real part of the refractive index,
k = imaginary part of refractive index. The absorption coefficient (i.e., the imaginary part of the refractive index) varies substantially in the wavelengths from 0.4 to 2.4 um. In the near-infrared region of EM spectrum, the reflectance of wet snow is lower than that of dry snow, but mainly because of micro-structural changes caused by the water (
Dozier, 1989).
Specifically, in wet snow with high liquid water content, heat flow from large grains causes smaller particles, which are at lower temperature, to melt and merge into larger clusters (
Colbeck, 1982;
Colbeck, 1989). As bulk grain cluster radius increases, an incident photon will have a high probability of being scattered when it transverses the air-ice interface, but a greater chance of absorption while passing through the ice grain (
Warren, 1982). Grain clusters optically behave as single grains, increasing the mean photon path length, subsequently increasing the opportunity for absorption and reduction in reflectance. Larger grains increase the degree of absorption, particularly in the shortwave infrared region, causing a substantial reduction in reflectance. The maximum sensitivity of reflectance to changes in grain size is in the shortwave (SWIR) region of the EM spectrum at approximately 1.1 um (
Nolin and Dozier, 2000).
The use of snow surface reflectance alone to track the surface melt process is not sufficient, because substantial decreases in reflectance are not due solely to grain enlargement associated with entrained liquid water. For example, small amounts of absorbing impurities can also reduce snow reflectance in the visible wavelength (
Warren and Wiscombe, 1981). As low as 0.1 ppmw (parts per million by weight) of soot concentrations are enough to reduce reflectance perceptibly, and the effect is significantly enhanced when the impurities are inside the snow grains, because refraction focuses the light on the absorber (
Grenfell et al., 1981;
Bohren, 1986). In this case, surface temperature can be used as a plausible mechanism in isolating the component in reduced reflectance that is due to the melt process.
Snow-cover melt dynamics in the thermal infrared region (8-14um) of the EM spectrum are a function of incident radiation as well as surface longwave emission, which is a function of snow surface temperature and emissivity (
Marks and Dozier, 1992). The relationship is given as follows:
where T
b is brightness temperature, which is defined as the temperature of a blackbody for a given wavelength that emits the same amount of radiation at that wavelength as does the snow; T is surface temperature;
ε is the emissivity of snow; λ is wavelength; and h, c, k are constants(
Dozier and Warren, 1982).
Therefore, the combination of optical and thermal signatures is an effective way to monitor the evolution of surface melt dynamics.
Lampkin and Yool (2004a) have evaluated MODIS visible and NIR bands for monitoring snowpack ripeness and suggested that couple optical/thermal measurements have the potential to detect snowpack evolution during the melt season. Furthermore,
Lampkin and Yool (2004b) have assessed surface snowmelt by developing a near-surface moisture index (NSMI) that uses optical and thermal variables.
5. Discussion and Conclusion
E-melt retrievals are heavily contingent on the accuracy of both MODIS derived surface reflectance and temperature products. An assessment of the maximum impact of accuracy from these products indicates relatively low errors. The errors increase from the earlier part of the melt season when the magnitude of melt is low to the warmer part of the season where the melt amount is higher. Additionally, errors due to the accuracy of the LST product are larger and become more important later in the melt season. Though late melt season variability in temperatures is lower than the early part of the season, the greater influence temperature has in E-melt retrievals later in the season are likely due to the fact that as surface temperature approach the melting point, significant error in LST can make the difference between melt and no melt conditions. Also, the relationship among temperature, reflectance and melt production can vary throughout the season. Early in the season, the correlation between surface reflectance and temperature can be high (∼ -0.8) at lower elevation and diminishes later in the season due more sustained negative sensible heat flux that stabilize and reduce temperature variability relative to surface albedo (
Veenhuis, 2006). Our linear retrieval model does not account for this dynamic and may exhibit seasonally dependent performance.
Point validation analysis, using meteorological data from GC-NET stations that were not used in the E-melt algorithm, indicates relatively good performance with E-melt retrievals within one standard deviation of the mean LWF derived from SNTHERM89 outputs for each point validation station except the South-D station. E-melt overestimated LWF at South-D by 4%. During the 161 period South-D demonstrates very low LWF and stable conditions with little variability. E-melt performed quite well at other stations that demonstrated low variability during the 8-day composite periods and very low mean LWF (approximately zero), therefore, retrieval performance at South-D could be the result of potentially contaminated pixels given the South-D station is bordering a region heavily obscured by cloud cover. Additionally, this bias might be due to the accuracy of the MODIS LST product.
High E-melt magnitudes tend to correspond to QSCAT wet zones, where the highest percentage of wet zones occupy between 10.5-12.0% LWF in composite period 145, and shift to 12.0-13.5% in composite period 153 and 161. Changes in the spatial patterns in wet and dry snow zones throughout the melt season show comparable changes in E-melt although some inconsistencies are apparent. There are dry snow zones near the ice sheet margin that do not correspond to low E-melt values. This may not be solely related to problems with the E-melt algorithm. This inconsistency may be attributed to how radiative information from the optical/thermal parts of the EM spectrum differs from the microwave region. Microwave derived backscatter radiation can be dominated by deeper ice structures such as lenses, pipes, and layers (
Baumgartner et al., 1999), while surface temperatures are heavily contingent on surface emission derived from no deeper than several centimeters. Additionally, backscatter can be dominated by subsurface depth hoar and coarse-grain firn (
Jezek et al., 1994). Ku-band scatterometers are very sensitive to increased wetness in firn surface layers, resulting in masking backscattering from deeper layers (
Nghiem et al., 2001). Therefore, wet snow zones corresponding to lower temperatures (
Figure 16) are likely indicative of subsurface melt. Performance issues in the E-melt retrieval may also be related to how the dynamic melt process was simulated in SNTHERM89. Though our model was initialized with a ‘glacier ice’ substrate with snow layers overlying, the melt infiltration and runoff process is not adequately represented in such simulations. SNTHERM89 does not have the capacity to partition melt into run and infiltration and has no specification for preferential flow paths characteristic of melt infiltration in nature.
This retrieval scheme does not take into account melt production during cloud covered periods where downward cloud-forced radiation may be significant in amplifying melt. To assess the impact of clouds on melt a more comprehensive analysis will have to be implemented and is currently under analysis through the use of mesoscale atmospheric model estimates of surface net cloud forced radiation and its relationship to melt extent and occurrence derived from passive microwave systems.
The strong relationship between melt production and surface temperatures may indicate that LST alone could be a suitable variable for this retrieval approach. Retrieval models using LST and reflectance as independent variables singularly were explored and it was determined that the model using coupled optical/thermal independent variables out performed those models that used only a single variable (
Peng, 2007).
This novel empirical retrieval scheme can provide valuable information about the spatiotemporal variability of surface melt dynamics that have a significant impact on the mass balance of the GIS. Assessments of melt extent have been informative but have failed to provide vital knowledge amount the amount of melt. This nascent approach can fulfill this need with additional work on validation and refinement. Comparison to traditional passive microwave melt extent and number of melt days will help provide insight into E-melt retrieval performance in addition to exploring application of this retrieval scheme to other years within the MODIS data archive.