3.1. Study Area
Snow survey and passive microwave airborne brightness temperature measurements were made across the Fosheim Peninsula, near the Eureka weather station on Ellesmere Island (~80° N; 84° W) between 13 and 22 April 2011 (Figure 1
). The region is cold and dry with an average annual air temperature at the Eureka weather station of −18.8 °C and total yearly precipitation of 79 mm (1981–2010), with almost 60% falling as snow [30
]. The snow survey study area centered on a previously studied inland drainage basin, Hot Weather Creek (HWC), approximately 30 km inland from the weather station [12
]. The HWC study area has been described as a polar oasis within the High Arctic polar desert because of its unique geography of being protected by surrounding mountain ranges resulting in less cloud cover and warmer temperatures and subsequent abundance of vegetation compared to the surrounding High Arctic environments [32
]. However, despite the greater presence and variety of tundra vegetation in this region relative to other regions of the High Arctic, the main controlling influence on the depth and distribution of snow across this region is local scale topography, as existing vegetation is extremely sparse (bare ground), or is very low-lying [31
]. The terrain of the study area is generally flat land consisting of upper plateaus, gently rolling hills and long slopes of varying aspects, accounting for approximately 90% of the study area, with the remain 10% made up narrow incised river/stream drainage channels draining into flat wetlands, lakes and valley bottoms [33
]. The Fosheim Peninsula is only approximately 75 km wide, but the extent of the generally flat terrain is large and far enough away from the coast to minimize the influence of the sea ice and surrounding mountain ranges on satellite-scale passive microwave swath data [34
], and includes the coverage of multiple re-sampled 25 km Equal-Area Scalable Earth Grids (EASE-Grids) [35
3.2. Airborne Data
Airborne Tb data were acquired from dual-polarized 19, 37 and 89 GHz microwave radiometers mounted on the Alfred Wegener Institute Polar-5 research aircraft. The radiometers were aft-viewing at a 53° incidence angle to simulate the earth-viewing characteristics of the satellite-based SSM/I and AMSR-E passive microwave sensors. The 19, 37 and 89 GHz radiometers all have the same 6° half-power beamwidth. After instrument calibration using warm and cold targets, the calibrated brightness accuracy was reported as <1 K for the 37 GHz and 89 GHz and <2 K for 19 GHz radiometers. The aircraft was based out of the Eureka weather station from 19 to 23 April 2011. Aircraft positional information was recorded using an AIMMS-20 system recording GPS data and platform attitude information which were used to precisely calculate the passive microwave radiometer footprint locations on the ground. All positional information was collected using the WGS 84 datum.
Three flight plans were devised to record multi-scale measurements of high Arctic tundra snow using passive microwave airborne radiometers. These multi-scale measurements include the following flights:
Local-scale grid (33 km × 6 km) low altitude flight (~350 m above ground level [a.g.l]), flown on 20 April.
Local-scale grid (33 km × 6 km) high altitude flight (~2900 m a.g.l.), flown on 21 April.
Regional-scale grid 48 km × 48 km high altitude flight (~2700 m a.g.l), flown on 21 April.
Flights 1 and 2 constitute the local scale analysis data set while Flight 3 constitutes the regional scale analysis. Observations taken from a KT-19 infrared surface temperature sensor mounted on the aircraft with the same incidence angle and orientation as the high frequency radiometer were used in the regional scale modeling analysis to estimate the snow surface temperature. Figure 1
shows airborne flight lines, snow survey locations, HWC location as well as EASE grid pixel boundaries.
The approach used in this analysis to spatially link ground snow depth measurements to airborne passive microwave footprints is similar to that used by [11
], where the IFOV of the airborne radiometer is calculated, and measured snow that falls within and around the bounds of this IFOV are linked to particular airborne measurement. The airborne radiometer’s IFOV dimension is dependent on the aircraft’s ground speed, altitude, roll, pitch and yaw, as well as the radiometer beamwidth, view angle, and integration time. The radiometer variables remain constant during data acquisition: beamwidth = 6°; view angle = 53°; and integration time = 1 s. The aircraft’s altitude above sea level remained stable along each flight line, however due to changes in terrain height, the height above ground varied, but on average was approximately 350 m above ground for the low altitude flights, and 2700 m (regional grid) to 2900 m (local grid) above ground for the high altitude flights. Variables such as aircraft heading and speed varied slightly during each flight, but overall was quite consistent at approximately 155 nautical miles per hour (~80 m/s). The aircraft’s roll, pitch and yaw varied substantially during turns, with the radiometer’s IFOV often pointed towards the horizon, rather than at the surface, and therefore these airborne measurements were removed from the analysis. If the airborne radiometer system was mounted on a stationary platform, the typical ground-projected IFOV for the low altitude flights would be approximately 100 m deep by 60 m wide. However, because the aircraft is moving, and the radiometer’s have a 1-s integration time, the IFOV between two observations is elongated in the along-track axis, producing a “smeared footprint” [13
]. The (smeared) footprint dimensions at low altitude were calculated as 120 m × 102 m (along-track × across-track).
The size of the footprints produced during the high altitude flights at ~2900 m above ground was approximately 850 m × 510 m. Figure 2
shows footprints in the Eureka low altitude flight grid. The flight lines were designed in this pattern to assist in the scaling up of Tbs from the airborne to the satellite scale and ensure complete coverage at different spatial resolutions of Tb products.
The lengthening of the radiometer footprint in the along-track axis is an important consideration when analyzing the high resolution, local-scale airborne data because the total number of snow measurements that fall within the radiometer’s IFOV varies depending on the size of the IFOV. This effect becomes less important when working with coarser resolution airborne data because the extent of the IFOV becomes larger than the distance traveled during the one second integration time and therefore adjacent Tbs are heavily overlapped, leading to an over-sampled dataset. To reduce computational time when working with the oversampled high altitude airborne data, the data were thinned by taking the average of every 10 airborne observations. Consequently, the dimensions of footprints for these filtered observations were based on the average flight height for all 10 measurements (Figure 2
3.4. Ground Based In Situ Data
Between 12 and 22 April, two types of snow surveys were conducted along the airborne radiometer flight lines. A regional-scale snow survey covering much of the Fosheim Peninsula was conducted via helicopter, with the purpose of evaluating the variability in snow properties at the 25 km EASE-Grid scale. The regional snow surveys involved snow depth transects and snow pits measuring snow properties including layering, density, temperature and mean geometrical maximum (Dmax
) grain size using a field microscope and a 2 mm comparator card, for 22 regional sites (these sites are presented by red crosses in the Figure 1
). The regional snow conditions were relatively homogeneous; there was minimal terrain influence (generally flat), and no emergent vegetation above the snowpack was visible [12
]. Snow depth was measured using a GPS enabled, self-recording snow depth probe [37
], called a MagnaProbe. Depth measurements were made at 5 to 10 m intervals along a 100 m sided-square centered on a snow pit. Total number of snow depth measurements made at each site ranged from 133 to 176 (average of 150) for a total of 2656 snow depths at all 22 sites. These measurements were used to determine the statistical distribution of snow depth at each site. An ESC-30 snow corer with a cross-sectional area of 30 cm2
] was also used to record bulk SWE and density measurements at each site three times, for a total of 66 times.
The second type of in situ
snow survey was conducted to characterize local-scale snow properties. The local-scale survey involved using a snowmobile to mark and set multi-kilometer snow depth/bulk SWE transects across the HWC study area, along the local grid airborne radiometer flight lines. A total of ten snow depth transects were surveyed, ranging in length from 2 to 15 km, with snow surveyors walking these lines and recording snow depths every 5–8 m and bulk ESC-30 SWE every 150–180 m. Eight of these lines were parallel, spaced approximately 900 m apart, creating a multi-kilometer snow survey grid. A total of 12,595 snow depths and 510 bulk SWE measurements were recorded within and around this grid. A total of 27 snow pits were measured along the local scale survey transects, following the same survey protocol used during the regional helicopter surveys [12
]. A summary of snowpack physical properties from the snow surveys is provided in Table 1
. The high coefficient of variation (CoV) of snow depth measurements confirms high spatial variability in the region that will contribute to higher uncertainties in evaluating the microwave emission modeling results in this region.
The data summarized in the Table 1
differ from the data presented by [12
] which reported exclusively on the regional-scale transects and snow pits. Table 1
gives the total summary statistics for all snow depth, snow density and SWE measurements from the Eureka field campaign used in this analysis. The measurements from the local scale transects were recorded mostly within a 33 km × 6 km grid while the regional-scale measurements were recorded across a larger 48 km × 48 km grid. An additional five snow pits were used in the generalization of snowpack characteristics analysis (see below). Table 1
illustrates that bulk snow density has the lowest coefficient of variation while the SWE has the greatest, indicating that the bulk density changes less over the study area than the depth (SWE is the product of depth and density). The conclusion from this feature is that any radiative transfer modeling should be driven by snowpack properties that likely have a low spatial variability (e.g., snow density) and high spatial variability (e.g., snow depth). It is necessary, therefore, to consider how the data can be effectively generalized while retaining the underlying statistical structural characteristics.
The average number of layers identified in all 49 snow pits was five but there was a variety of different snow types that were observed; including: recent, fine-grained (F.G.), medium-grained (M.G.), crust, soft slab (S.S.), medium slab (M.S.), hard slab (H.S.), slab-to-hoar (Slab-Hoar), chains of hoar (indurated) (CoHI), chains of hoar, depth hoar and icy hoar. Typically, the upper snow layers (recent, fine and medium grained and crusts) are the thinnest while the mid-pack slab layers have largest densities and the middle and lower layers have the largest grain sizes.
To undertake the DMRT-ML modeling, the snowpack characterization had to be generalized. An unsupervised K-means clustering [39
] of average grain size and snow density was conducted for 10 of the snow layer type classes (fine grained and icy hoar were excluded from the clustering because of the small sample size). The cluster analysis calculated five cluster means; this number of classes was set based on the average number of layers found in all pits. The hoar classes have cluster means that are low in density but have the largest grain sizes (and grain size range) while the recent and crust layers have the smallest grains and moderate density. The slab layers have the largest densities and the largest range of density values. Cluster 1 has very small layers with small grain sizes (top layer), while Clusters 2 and 3 have the largest densities (wind slabs) and Clusters 4 and 5 have the largest grain sizes (depth hoar).
For the DMRT-ML modeling, the upper cluster contained radiometrically insignificant layers since the layer thicknesses were small (~7% of total thickness) and the grains were also very small. Therefore, this class was removed from the analysis for further generalization. The effect of a layer with small scatterers on top of thick layers with medium-sized grains is simulated by [15
] where the 37 GHz Tb slope reversal was seen. They show that, when a snowpack is thick (~70 cm), a thin layer of new snow decreases attenuation of the ground emission, thus 37 GHz Tb increases, and, when a snowpack is shallow and composed of new snow, the emission (and Tb) decreases. It is noteworthy that, in all investigated cases discussed by Liang et al.
], a topmost layer of new snow, at least 10 cm in thickness, was present showing consistency with our study.
The remaining four classes are further combined into two layers: slab (Clusters 2 and 3) and hoar layers (Clusters 4 and 5). The combined statistics for the slab and hoar layers are shown in the layer temperatures and densities for both structures, were relatively consistent with low coefficient of variations while layer thickness and the grain sizes had high standard deviations. The summary of generalized statistics is presented in Table 2
For the model inputs, it is necessary to use in situ
forcing data (snow depth and snow pit) that are spatially coincident with the Tb observations. Tb observations represent snow emission from distributed areas across the radiometer’s IFOV whilst in situ
ground measurements are made at the point scale. To evaluate the spatial variability of the in situ
data (and determine the spatial representativeness of each in situ
measurement) semivariograms of the MagnaProbe snow depths were calculated. Semivariograms provide an unbiased description of the scale and pattern of spatial variation of snow depth, determining what the threshold distance (range) is beyond which snow depths are no longer spatially autocorrelated. Figure 3
shows the semivariogram fitted with a spherical model highlighting the range to be at ~58 m (range is identified where the variogram model line levels out). Snow depth (and snow structure from snow pits) separated by distances greater than the range value (58 m) are no longer spatially autocorrelated. To ensure a strong assumption of correlation between the in situ
snow survey data and the airborne radiometer measurements the 58 m range value was used as an inclusion/exclusion threshold, where snow survey data within 58 m of the calculated radiometer IFOV were likely to be spatially autocorrelated to the snow found within the IFOV and therefore were used in this analysis. For snow depth data from MagnaProbe measurements, the CoV (%) of snow depth measured within each individual footprint varied from 22% to 100%, suggesting the presence of high spatial variability within a single footprint. Therefore, only snow depth within IFOVs were used. After screening, 38 out of the total 49 snow pits and 12,671 MagnaProbe measurements were used in the DMRT-ML model analysis.