Estimating albedo from digital image pixels requires assumptions regarding the spectral reflectance of ice and snow and its relationship with the digital numbers of the image acquired by the camera. Our technique implicitly assumes that visible band (400–700 nm) digital imagery accurately captures the reflectance variability of surface types commonly found in glacier ablation areas. We evaluate this assumption by comparing albedo derived from the digital images to that obtained by a pair of Kipp & Zonen CM3 optical pyranometers (Section 3.3). We note that, at least for bare ice surfaces and snow with uniform grain size, most of the variability in reflected radiation lies in the visible band of the shortwave spectrum, between 350 and 695 nm (Wiscombe and Warren, 1980; Dozier et al., 1981; Cutler and Munro, 1996; Corripio, 2004) where a standard consumer-grade digital camera is most sensitive (e.g., Figure 1) (Jiang et al., 2013). In contrast, bare ice and snow albedo with uniform grain size does not display high variability in the near-infrared wavelengths (695–2,800 nm) (Warren and Wiscombe, 1980; Cutler and Munro, 1996).

We also assume there is a direct relationship between the digital numbers of the camera image, which represent brightness, and surface reflectance. We argue this assumption can be justified if the camera is suitably calibrated and corrected using the methodology presented in this study. Furthermore, previous studies have demonstrated that it is possible to retrieve albedo from digital images with accuracies of ±10% or less (e.g., Corripio, 2004; Rivera et al., 2008; Dumont et al., 2011; Garvelmann et al., 2013; Ayala et al., 2016). Based on these assumptions, a procedure (Figure 2) to obtain and process imagery suitable for conversion to albedo is described in Sections 2.2–2.6.

Here, an example instrument configuration is outlined for obtaining albedo data using digital camera imagery and broadband pyranometers mounted on a UAV. Instruments include a standard consumer-grade digital camera, a pair of broadband silicon pyranometers and a white reference target (specific instruments used in our application are described in Section 3). Digital images of the white Teflon reference target, assumed to be a near-Lambertian reflector, were used to convert downward radiation measured by the upward facing pyranometer into digital numbers. Because the reflected radiation measured by the downward facing pyranometer is used to correct the digital images, both sensors were mounted in close proximity to each other in order to minimize the differences between their respective ground footprints. The instruments may be mounted on a multi-rotor UAV, but they could equally be mounted on a fixed-wing UAV, kite, blimp (e.g., Carrivick et al., 2013), fiberglass rod (e.g., van der Hage, 1992), step-ladder or other handheld device depending on the required resolution and spatial extent of the investigation.

Upward and downward hemispherical reflectance were measured using broadband pyranometers, the ratio of which provides an estimate of the surface albedo. Downward radiation may be measured at a fixed ground station but if illumination conditions are rapidly changing, perhaps due to cloud cover, it may be more accurate to measure downward radiation from the aerial platform. In this case, we recommend using silicon pyranometers due to their low weight (~100 g per sensor) and rapid response time of 1 ms. The pyranometers must be precisely leveled with a clear view of the sky or surface to ensure accurate measurements.

The disadvantage of silicon pyranometers is that they are only sensitive to wavelengths between 300 and 1,100 nm, which excludes some of the solar energy contributing to the surface energy balance. We evaluate this source of uncertainty by comparing albedo derived from a pair of Apogee silicon pyranometers (https://www.campbellsci.com.au/sp-110) with albedo obtained by a pair of Kipp & Zonen CM3 optical pyranometers. The Kipp & Zonen pyranometers are based on carbon black thermopiles which have a flat spectral response for wavelengths between 300 and 2,800 nm and an accuracy of 2%. Comparison between the two sensors was made by simultaneously sampling 25 surfaces with an albedo of between 0.11 and 0.64 in a 20 × 20 m study area. The instruments were mounted on a 1 m aluminum rod and held 0.5 m above each surface for 1 min. Albedo was calculated as the mean of five 20 s samples. At this height, the pyranometers have a ground footprint of around 5.5 m in diameter. A root-mean-square difference (RMSD) of 3.6% between the two instruments justified that silicon pyranometers can accurately measure albedo of ice sheet surfaces between 0.11 and 0.64.

The Apogee silicon pyranometers were factory-adjusted to account for their partial spectral sensitivity under standard clear-sky atmospheric conditions. Therefore the upward facing pyranometer has an uncertainty of 5%, which includes a cosine-response error of 2% at solar zenith angles of 45°. The cosine-response error increases as solar zenith angle increases so we recommend acquiring measurements as close as possible to solar noon.

The digital images were acquired in RAW format with fixed exposure, ISO, and aperture. These settings are necessary to preserve linearity between RGB digital numbers acquired by the camera and the number of photons hitting the sensor. We recommend a relatively fast shutter speed to minimize image blur (when mounted on a moving UAV) and a low ISO and F-number to ensure that pixels do not saturate. Most software cannot read the RAW images so they should be converted to lossless 16-bit TIFF images using RAW decoding software such as dcraw (http://cybercom.net/~dcoffin/dcraw/) (Figure 2). When converting the RAW images it is important to use a fixed white level, or balance, and avoid using a gamma correction to ensure the reflectance histogram is not altered and the RGB digital numbers remain directly proportional to the brightness of the surface (Lebourgeois et al., 2008). A gamma correction is a non-linear function used to convert between the brightness measured by the camera's sensor and the output image pixel. In this study, we were only interested in the ratio between the total reflected and downward shortwave radiation and so the arithmetic mean of each pixel's RGB values was calculated.

Image brightness attenuation away from the center, vignetting, is inherent to all consumer-grade digital imagery and can be corrected by subtracting a vignette mask from the original image (Goldman, 2010). The vignette mask can be calculated by fitting a third-order polynomial function to multiple Gaussian smoothed images (e.g., Lebourgeois et al., 2008). The mean vignette polynomial function can then be applied to correct all the images from the survey. Finally, the geometric distortion of the images should be corrected to ensure that each image pixel represents the same ground sampling distance. We used Agisoft Lens 0.4.0 software and an on-screen checker board to automatically determine the camera calibration parameters and correct for this distortion. After vignette and geometric correction, the digital numbers of every pixel in the image are directly comparable.

The radiation recorded by an image pixel is not only related to the reflectance of the surface, but also to the downward radiation. The digital numbers in an image can be corrected for variations in illumination by including a leveled white Teflon reference target in every digital image (e.g., Hakala et al., 2010). An illumination corrected image can be produced from the ratio between the digital numbers of the ice surface pixels and the digital numbers of the white reference target, which are a proxy for downward solar irradiance. After applying an illumination correction, the digital numbers of pixels are comparable between images including those obtained under very different weather or illumination conditions.

If survey area is large, it may not be possible to include a white reference target in every image. Therefore, to facilitate the correction of UAV acquired imagery there is a need to quantify the relationship between downward radiation measured by an upward facing pyranometer and the RAW digital numbers of a white reference target. If linearity between the reflectance of the surface and digital numbers of the RAW images is preserved, then the relationship can be statistically represented by an orthogonal distance linear regression.

An example of this relationship between the digital numbers of a white reference target obtained by a Sony NEX-5N camera in RAW mode from the ground against the downward radiation measured by a static, upward facing silicon pyranometer with a clear sky view is presented (Figure 3). Here, the orthogonal distance regression fits the data well with a R² of 0.96 and an RMSD of 7.8%. The slope and intercept of the linear regression can subsequently be used to convert the downward radiation measured by the pyranometer to digital numbers. An illumination corrected image is then produced from the ratio between pyranometer to digital numbers.

The final stage in the workflow is to calibrate the image using coincident measurements of albedo obtained from upward and downward facing pyranometer measurements. Snow and ice reflect incoming radiation anisotropically such that a nadir measurement of reflectance actually underestimates albedo by between 1 and 5% between 530 and 610 nm (i.e., the visible band) (Knap and Reijmer, 1998; Klok et al., 2003). The pyranometers account for the reflectance anisotropy of snow and ice because they measure hemispherical reflectance so can be used to correct the bidirectional reflectance measurements of the digital camera. This was achieved by multiplying the image pixel numbers by a factor calculated by dividing the mean pixel value of the illumination-corrected image by the albedo recorded by the pyranometers.

This step introduces uncertainty since the rectangular footprint of the digital image does not completely coincide with the circular footprint of the downward facing pyranometer (Figure 4). We overcome this issue by comparing the mean image pixel within the circular pyranometer footprint to the mean image pixel outside the pyranometer footprint for 300 representative sample images obtained from 600 m above the surface of the ablation area of the Greenland Ice Sheet. The silicon pyranometer has a circular FOV of approximately 60° whereas the Sony NEX-5N camera, used to test this uncertainty, has a rectangular FOV of 53.1 by 73.7°. The significant, strong positive correlation (R² = 0.98; p < 0.01) between the mean pixel value inside and outside the pyranometer footprint, with an RMSD of 1.2%, demonstrates that the downward facing pyranometer can be used to correct the digital images over length scales in the order of hundreds of meters (Figure 4). We note that this relationship may not hold when there is a spatial trend at the scale of the image or extreme heterogeneity in the surface being measured.

The fixed-wing UAV used in this study was described by Ryan et al. (2015) and based on a Skywalker X8 airframe constructed from expanded polypropylene foam with a wingspan of 2.12 m (Figure 5). Autonomous control was provided by a Pixhawk autopilot module which utilizes an L1 GPS, two inertial measurement units (IMUs), a compass, and a barometer. A 30 Ah 14.4V lithium-ion battery pack provides power for the 715W electromagnetic motor, two servos, the receiver and the autopilot module. The UAV cruising speed is regulated by a digital differential airspeed sensor and targets 54 km h⁻¹. The weight of the UAV without the sensor package was 4.79 kg. The sensor package weighs 0.715 kg and includes a Sony NEX-5N digital camera (0.345 kg), a Hobo micro data logger stripped of its case (0.075 kg) and powered externally, two Hobo pyranometers (0.170 kg), a temperature/humidity sensor (0.065 kg) and a GoPro HERO4 (0.060 kg). In this configuration, the UAV had an all-up-weight 5.5 kg and a 140 km range dependent on conditions.

The upward and downward facing Hobo silicon pyranometers were aligned within the airframe (Figure 5) so that they were level when the UAV was in stable flight. Errors due to instrument tilting were limited by omitting radiation data recorded when the pitch or roll of the UAV exceeded 3°. According to Bogren et al. (2016), this introduces a maximum error of 8.1%. At a flight altitude of 600 m above the surface, a 60° FOV gives the pyranometer an estimated 700 m diameter footprint. The pyranometers were sampled by a micro data logger at 1 Hz and, before each flight, the data logger was synchronized to GPS time to ensure that upward and downward shortwave radiation data coincided with GPS and attitude data recorded by the PixHawk in post-processing.

Digital images were obtained by a downward facing Sony NEX-5N digital camera mounted in the UAV airframe (Figure 5). The camera was pre-set for a fixed exposure of 1/1,000 s, ISO 100 and F-stop of 8. The camera has a 16 mm fixed-focus lens (equivalent to 24 mm for a 35 mm film camera) which gives an FOV of 53.1 by 73.7° and yields a ground footprint of approximately 900 × 600 m at an altitude of 600 m above the ice surface. Vignetting was as high as 17.6% at the corners of the images and was corrected with a vignette correction mask (Section 2.4). Each image was tagged with the geographic location and attitude data recorded by Pixhawk's two IMUs and L1 GPS. The camera was triggered every 50 m of horizontal displacement (about every 3 s) which provided a forward overlap of 92%.

Gridded flight patterns over the ice sheet were planned and uploaded to the UAV using the Mission Planner ground station software (http://ardupilot.org/planner/). The UAV was programmed to maintain a constant altitude above sea level during missions and was targeted at 600 m above the surface. For the purpose of our study, this altitude was deemed an optimal trade-off between ground sampling distance and coverage. The distance between flight lines was set to 300 m which provided a 50% horizontal or side overlap between the aerial images.

The images were corrected and calibrated using the workflow described in Section 2 and mosaicked using Agisoft PhotoScan 1.3.0, herein PhotoScan, to produce UAV10A1. The images were imported into PhotoScan and automatically aligned based on the georeferencing information. This approach avoids the need for GPS-surveyed ground control points and reduces processing time because the software pre-aligns the images instead of performing global point matching to achieve accurate image alignment. The orthomoasaics were produced in the software's “mosaic” mode, meaning that the pixels in the centers of the image were preferentially used to provide the output pixel value. The orthomosaics were nearest-neighbor resampled to a pixel resolution of 20 cm and exported as GeoTIFFs for analysis.

Validation of UAV10A1 was undertaken by comparison with surfaces sampled by the Kipp & Zonen CM3 pyranometers (Section 2.3). Nine of the twenty five surfaces were identified in three images acquired when the UAV was close to the ground and a comparison, made by sampling pixels within a 5.5 m diameter circle in the images, indicates that the two measurements compared well with an RMSD of 4.9% and a bias of 4.1% (Figure 6). The slight underestimation of CM3 in comparison to UAV10A1 may be partly explained by the obscuring of reflected radiation by the observer holding the CM3 on the meter long rod (e.g., van der Hage, 1992). The difference between the range of wavelengths measured by the CM3 pyranometers (300–2,800 nm) and digital camera (300–700 nm) may be a source of error. For example, changes in snow grain size have less effect on visible wavelength albedo than in the near-infrared wavelengths (Wiscombe and Warren, 1980). The visible band digital camera is not sensitive to albedo variation in the near-infrared which likely introduces error when compared to CM3 albedo. Generally, UAV10A1 measures albedo of the ice sheet surface adequately between 0.11 and 0.64, and within our target accuracy of ±5%.

UAV10A1 was also compared to the satellite-derived MOD10A1 Collection 6 daily albedo product (300–3,000 nm) obtained from the National Snow and Ice Data Center (NSIDC) (Hall and Riggs, 2016). The daily temporal resolution of MOD10A1 reduces uncertainties that may arise due to changes in ice surface albedo between data acquisition. MOD10A1. The value of each MOD10A1 pixel represents the best single albedo observation in the day, based on cloud cover and viewing and illumination angles (Stroeve et al., 2006). Retrieving the time of the MOD10A1 albedo observation was not possible and so we note that there may be up to a couple of hours difference between UAV and satellite data acquisition which may lead to discrepancies between the two data sources if there is a significant diurnal albedo cycle caused by changing solar azimuth and zenith angles or ice and snow metamorphosis during the day (Stroeve et al., 2006; Bogren et al., 2016). Comparison between both products was achieved by mean resampling UAV10A1 to the same pixel resolution as the MOD10A1 product (~463 m) using the average pixel value of UAV10A1. Both products were then clipped to the same extent and 347 cloud-free samples were compared. The mean RMSD between the two albedo products was 3.7% which is within the 6.7–7.0% estimated uncertainty of the MOD10A1 product (Figure 7) (Stroeve et al., 2006; Wang et al., 2011; Ryan et al., 2016).

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.