This work presents a new field goniospectrometer developed at the Institute for Atmospheric and Climate Science (IAC) of the Swiss Federal Institute of Technology (ETH; Switzerland). The goniospectrometer was built to study the hemispherical directional reflectance factor (HDRF) of snow, but can also be applied to other surfaces with moderate surface roughness.
The IAC ETH goniospectrometer measures HDRFs with high spatial resolution. The goniometer is exclusively built of straight parts, thus ensuring a high pointing accuracy. The two robotic arms are controlled automatically with step motors, whereby the step size can be defined by the user. With the default grid size of 15° in zenith and azimuth, the time needed to collect one complete HDRF dataset is 11 min, corresponding to a change of less than 4° in solar zenith and azimuth angles.
The spectrometer comprises two probes. The first probe is equipped with a 3° foreoptic and is used for taking a spectrum of the reflected radiance; the second is placed on a tripod, has a 2π foreoptic, and simultaneously records a spectrum of the incoming irradiance. Both probes measure in the spectral range from 350 to 1050 nm, with a resolution of approximately 3 nm at around 700 nm.
The performance of the new goniospectrometer was tested at the Greenland Environmental Observatory Summit Station (72°35′N, 34°30′W, 3203 m ASL) during the summer of 2004.
The surface albedo is of great importance for understanding the energy balance of the earth's surface. Satellites provide an extraordinary means to measure reflected sunlight, especially in remote regions. However, the measured reflectances need to undergo complex data processing to account for the illumination conditions and the view angles of the airborne or space-based sensors relative to the target. The factor describing the angular distribution of reflected radiance is called the hemispherical directional reflectance factor (HDRF), where hemispherical incoming irradiance and directional outgoing radiance is considered. The HDRF is defined as the ratio of the radiance outgoing from a surface into a specific direction to the radiance outgoing from a Lambertian surface under the same hemispherically integrated incoming irradiance. The HDRF is a function of four angles: incoming (solar) zenith and azimuth (θi, ϕi, respectively) and outgoing (reflected) zenith and azimuth (θr, ϕr, respectively). Furthermore, the HDRF strongly depends on the physical surface properties (e.g., Warren 1982; Steffen 1987; Martonchik 1994; Warren et al. 1998; Pirazzini 2004; Kokhanovsky and Zege 2004).
With the advent of new satellite systems that offer hyperspectral resolution and off-nadir tilting capabilities, there is an increasing need for multidirectional and hyperspectral ground truth data (Sandmeier et al. 1998; Sandmeier 2000; Liang et al. 2000; Nolin and Liang 2000). In situ measurements of HDRF datasets consist of a combination of multidirectional and hyperspectral data, collected within a time period that is as short as possible to make changes in the solar illumination geometry negligible. As a consequence of these demands the existing database of experimental HDRF measurements is still small. Following are a few automated field goniometric instruments that have been utilized for snow HDRF measurements:
Complete instrumentation for HDRF measurements consists of a goniometer placing a radiometric sensor in the desired position on the hemisphere. While PARABOLA measures the radiance in eight spectral bands, FIGOS and ASG utilize high-resolution spectrometers similar to the one used for the measurements described in this study.
This work describes a field goniospectrometer that is capable of measuring HDRFs of surfaces with moderate surface roughness like snow, sand, soil, or pavement. The instrument was developed at the Institute for Atmospheric and Climate Science (IAC) at the Swiss Federal Institute of Technology (ETH). The main motivation was to study the HDRF of dry snow on the Greenland ice sheet and to investigate its influence on the surface energy balance and hemispherical albedo.
The IAC ETH field goniospectrometer measures the HDRF with high spectral and spatial resolution. It is fully automatic and the measuring program can easily be adapted in the field, allowing the appropriate sampling resolution for the HDRF measurements to be selected. The new instrument was designed for use in remote places, which gave rise to a construction that is easily transportable and set up, but nevertheless is very robust and adjustable. It was tested and utilized at the Greenland Environmental Observatory Summit Station (72°35′N, 34°30′W; 3203 m ASL).
The emphasis of this work is on the technical description of the IAC ETH goniospectrometer and its functionality. Necessary calibrations and data processing routines, including the investigation of measurements affected by self-shadowing, are also discussed.
A short theoretical overview on directional reflectance and the commonly used equations are given in section 2. Section 3 describes the hardware components of the new system, consisting of the IAC ETH goniometer and a portable spectrometer, FieldSpec Pro Dual visible/near-infrared spectrometer (VNIR) manufactured at Analytical Spectral Devices (ASD), in Boulder, Colorado. It also presents the utilized Spectralon reference panel along with the corrections needed to account for its departure from the ideal Lambertian reflector. Details of the hardware control, the data acquisition, and the data processing routines, as well a brief discussion of self-shadowing and an evaluation of the pointing accuracy of the goniometer, are also included in this section. Section 4 follows with first results, and a short discussion and some conclusions are provided in section 5.
2. Theoretical background
The directional reflectance properties of a surface can be described by a set of functions. Complete definitions of these functions are given in Nicodemus et al. (1977) and Martonchik et al. (2000). Relevant for the present work are the HDRF and hemispherical reflectance ρ (albedo).
It is well known that snow reflects solar radiation anisotropically and that snow surfaces are far away from being Lambertian reflectors (e.g., Bohren and Barkstrom 1974; Choudhury and Chang 1981; Warren 1982; Steffen 1987). The HDRF is thus defined as the ratio of the radiance reflected by a surface in a specific direction to that reflected in the same direction by a perfect Lambertian surface under ambient illumination (Martonchik et al. 2000). Assuming that the diffuse component of the incoming irradiance is isotropic, the HDRF can be expressed as
where Lλ denotes the spectral radiance; Lλ,Lamb the radiance of a Lambertian surface; Eλ,dir the direct incoming irradiance; Eλ,diff the diffuse incoming irradiance; θr and ϕr the reflection zenith angle and azimuth angle, respectively; θi and ϕi the incident zenith angle and azimuth angle, respectively; and μi the direction cosine of the incident solar beam.
With the appropriate instrumentation, HDRFs can be measured directly in the field. It is common to utilize a white reference standard, for instance, a Spectralon panel (see section 3c), as a Lambertian surface. However, commercially available panels are not perfect. Departures from a perfect reference are considered by introducing a spectral correction term Cλ,corr that accounts for the directional reflectance characteristics and for subunity in total reflectance:
As seen in Eq. (1) the HDRF is a function of the wavelength and four angles (Fig. 1). In experiments, HDRF datasets are measured under arbitrary illumination geometries. For easier comparability, however, the results are usually presented with respect to the solar principal plane (e.g., Steffen 1997; Sandmeier 2000; Painter and Dozier 2004). The solar principal plane is defined in such a way that the azimuth of the incident radiation is equal to 180° and the forward-scattering direction is equal to 0°. This reduces the number of relevant angles to three: θi, θr, and ϕi − ϕr.
In some earlier studies, researchers used the expression bidirectional reflectance factor (BRF; theoretically considering incoming and outgoing directional radiances) when talking about the HDRF. Obtaining the BRF through ground measurements is only possible by measuring the HDRF and applying corrections for the diffuse part of the incoming radiance (Sandmeier 2000; Bruegge et al. 2001).
By integration of the HDRFλ over the hemisphere, the spectral albedo ρλ can be determined as follows:
and by the integration over all wavelengths of the spectral albedo weighted by the spectral irradiance Eλ, the broadband albedo ρ can be calculated.
3. Instrument description
a. IAC ETH goniometer
The IAC ETH goniometer was designed for measuring the HDRF of relatively smooth surfaces. With this in mind, the radius of the measuring hemisphere was set to 1 m, defining a distance of 1 m between the sensor and target. To avoid disturbances of the surface the sensor arms were attached to an extended boom rather than placed in the middle of a large construction set on the surface, which is the case for most of the previous field goniometers.
Analysis of the motions necessary to let a point sweep a hemisphere—partly done with the aid of a computer-aided design (CAD) system—suggested that bent parts, as used on existing goniometers (FIGOS and ASG), are not needed. We thus use two straight arms of equal length, but different cross sections (the arms are reduced in mass by milling off statically unnecessary material). The first is attached under an angle of 45° to a horizontal boom and rotates about a vertical axis z. It carries the second arm, which folds back a full 180°, about an inclined axis k (Fig. 2).
Rotating these two arms individually by ϕr (motor I) and η (motor II) enables the sensor to be positioned on any point of the hemisphere above the target. The first angle is the same as the view azimuth of Eq. (1). The relation between η and the view reflectance angle θr can be derived either from Rodrigues' formula (Tsai 1999) or by using spherical trigonometry. It reads,
where a and b are the angles subtended by the two moving arms. With a = b = π/4, given by the instrumental geometry, one obtains
To move the two arms we chose stepping motors of an “intelligent” type, with integrated drive electronics. A gearbox was introduced as well to achieve the necessary torque. The possibility to adjust the motor's driving and halt forces individually made it unnecessary to use a clutch. First tests showed a rather small backlash of the gearbox that made the arm assembly oscillate for a short while after the top drive controlling the azimuthal position stopped. This problem was removed by introducing a disc brake for the top drive. Technical details of the motors are listed in Table 2.
The stepping motors offer a total of 20 356 counts per revolution. Obviously, not all steps in ϕr or η can be realized exactly with an integer number of counts. However, the rounding error is at most of one count. This corresponds to an angular accuracy of roughly 1′.
As seen in Fig. 3, the whole assembly consists of a vertical post, a horizontal boom fixed on that post, and two moving arms attached to the end of the boom. The horizontal boom of the goniometer can be rotated completely around the main vertical post. However, for the experiments at the Summit Station of the Greenland Environmental Observatory the boom was always aligned north–south, with the moving arms holding the radiometric sensor attached in the south. This guaranteed that consecutive experiments viewed the same surface area. The field deployment is shown in Fig. 4.
To ensure that the sensor is viewing the same target point on the ground at any time and from every position, (a) the instrument has to be level and (b) the sensor has to have an exact distance of 1 m from the target area in every position. Therefore, (a) a three-point leveling plate is mounted on the vertical post (Fig. 3) and (b) the vertical post can be extended with a fine-threaded screw located inside the vertical post. The distance to the target point on the surface is measured with a laser distance meter.
The IAC ETH goniometer is operated with a standard field spectrometer, FieldSpec Pro Dual VNIR, from ASD (see additional information online at http://www.asdi.com). This spectrometer comes with two 1.5-m fiber optics, which were replaced by two 4-m optics, given the size of the goniometer. The two 4-m optics were tested at ASD and were shown to have the same properties as the 1.5-m optics. The advantage of having two probes is that measurements of the incoming spectral irradiance can be taken simultaneously with those of spectral reflectance with the same instrument.
The utilized spectrometer covers a nominal spectrum between 350 and 1050 nm. The spectrum is measured with a 512-channel silicon photodiode array. Each channel, an individual detector itself, is geometrically positioned to receive light within a narrow bandwidth (1.4 nm). The VNIR spectrometer has a spectral resolution [full width half-maximum (FWHM) of a single emission line] of approximately 3 nm at around 700 nm.
For our measurements we attached a 3° field-of-view foreoptic to the fiber measuring the reflected radiance. A 2π foreoptic was mounted on the reference fiber measuring the incoming irradiance. While the target fiber is fixed along the goniometer arm, the reference foreoptic is put on a tripod and placed beside the goniometer (Fig. 4).
Accurate determination of absolute radiometric values depends to the greatest extent upon the accurate calibration of the utilized spectrometer. Both the 3° radiance and 2π irradiance foreoptic were calibrated radiometrically at ASD just before the instrument was deployed in the field. Information on the calibration procedure is available on the ASD Web site (online at http://www.asdi.com).
c. Spectralon panel
According to Eq. (1), the HDRF is defined with respect to a Lambertian reference. In our case, a near-Lambertian Spectralon panel from Labsphere (information available online at http://www.labsphere.com) was utilized. The Spectralon has been calibrated at the factory with an illumination angle of 8°. For each wavelength a calibration coefficient is provided that accounts for the subunity in the reflectance of the panel. The values of this coefficient lie between 0.982 and 0.988 for wavelengths in the range of 350–1050 nm. However, as shown by Sandmeier et al. (1998), even a calibrated Spectralon can show deviations of up to 10% from the perfect Lambertian behavior, depending on the angle of the incident beam. For this reason and given the fact that the anisotropy is nearly invariant for all Spectralon panels (Bruegge et al. 2001) we apply the correction algorithm of Sandmeier et al. (1998) to our data.
d. Control of the hardware, data acquisition
The motion of the goniometer is controlled with a Campbell CR10X datalogger. The datalogger is individually connected to the two motors of the goniometer and to the laptop, which controls the spectrometer. A default program for a standard sampling routine was stored on the datalogger. The program, however, can easily be modified in the field, in particular if a higher sampling resolution is needed.
A complete cycle starts with an optimization of the sensor on the actual reflectance of the Spectralon panel, followed by a nadir reflectance measurement on the Spectralon. The Spectralon panel is fixed on a turntable boom (Fig. 3). After turning the Spectralon panel away, a spectrum of the reflected radiance at nadir is taken. Then, motor II (Fig. 3) moves the lower arm to a new viewing zenith position. In this position the upper arm is turned counterclockwise around the vertical axis, providing a scan of all azimuth positions. After this first cycle, the lower arm moves to a new zenith position and the azimuth is now scanned clockwise. At the end of a complete hemispherical cycle the two arms are moved back into their home position and a second snow nadir and Spectralon reflectance sample are saved. Sometimes one of the measurements is outside of the optimization range defined at the beginning of each cycle. In this case, the program controlling the movement can be interrupted and a new optimization can be carried out.
Figure 5 shows the measuring path of a complete sampling cycle on a polar plot for the chosen sampling resolution of 15°. The time needed to sample one point is 5 s on average, including the traveling time to a new position. For a resolution of 15° the time required to complete a cycle is 11 min. At the location of the Summit Station at the Greenland Environmental Observatory, this corresponds to a change of less than 4° in the solar azimuth angle.
Each time the sensor arrives at a measuring position, a serial command is sent to the laptop controlling the spectrometer and a spectrum is saved. Spectra of the reflected radiance and incident irradiance are saved individually. The files are named automatically with consecutive numbers. A complete cycle results in a total of 296 files, each containing 701 values for the wavelength range between 350 and 1050 nm.
In summary, for a sampling resolution of 15° a full HDRF cycle consists of 148 measured positions, including 144 measurements distributed over the hemisphere (6 zenith angle positions and 24 azimuth angle positions), two surface nadir measurements, and two measurements on the Spectralon panel (nadir)—one at the beginning and one at the end of each cycle.
e. Pointing accuracy
The pointing accuracy of the goniometer was investigated with the aid of a laser pointer. The pointer was attached to the head of the lower arm (replacing the radiometric sensor), and a complete sampling cycle was carried out, recording the path left by the laser beam on the surface (Fig. 6). For the ideal distance of 1 m between the laser pointer and the target, the area covered by the laser beam was 1.4 cm in diameter, implying a pointing accuracy of roughly ±1 cm. Because the 3° field-of-view foreoptic results in an elliptical footprint with a major diameter of 5.2 cm at nadir and 31 cm at 80° (Fig. 7), this accuracy is considered satisfactory.
However, the pointing accuracy is very sensitive with respect to the distance. Our experiment revealed that changing the height of the horizontal boom by ±1 cm degrades the pointing accuracy by an order of magnitude, with the result that the laser beam spans an area of 15 cm in diameter at θr = 80°.
It is unavoidable that a shadow caused by the moving arm and the foreoptic of the instrument crosses the target area several times during a complete cycle. Occultation occurs when parts of the goniometer align with the sun and the target center. Examples of self-shadowing are shown in Fig. 8. These data were collected at 0836 and 1236 local time (LT) 26 June at solar zenith angles of 58° and 49°. In these examples, and for all other data collected during the 2004 field campaign, the measurements affected by self-shadowing are always in the 90°–180° quadrant after projection into the solar principal plane. Data points with low HDRF values resulting from self-shadowing are clearly recognizable in Fig. 8. In the course of the data processing, these shadowed data points are filtered and replaced with corresponding values from the other side of the solar principal plane, assuming symmetry along the solar principal plane. In general, knowledge of the instrumental geometry and the position of the sun are sufficient for determining the area affected by self-shadowing.
4. Performance of the IAC ETH goniospectrometer in the field
a. Experimental site
An extended set of HDRF data was collected in the summer season of 2004 on the Greenland ice sheet, at the Greenland Environmental Observatory Summit Station (72°35′N, 34°30′W, 3203 m ASL) (Ohmura 2001). Complete hemispherical cycles were measured on clear-sky days every 1 or 2 h for a total of 90 hemispheres. The largest solar zenith angle was 77° and the smallest was 49°. It was pointed out in the introduction that, in addition to the illumination geometry, the physical properties of the snow surface are important parameters influencing the HDRF of snow. Although the experimental site lies in the dry snow zone where no melting occurs, the snow surface properties vary significantly within a short time. During the summer of 2004, the relevant snow characteristics were measured in the field. These observations indicate that the occurring snow surfaces can be grouped in four classes: new snow with unbroken hexagonal snow crystals, wind-broken small snow grains, rounded snow grains from snow metamorphism, and coarse surface hoar growing during riming events.
Results of the experiments are presented in Figs. 9 –11. The datasets are plotted using the same format as in Fig. 8. For the data analysis and visualization the Interactive Data Language (IDL; information available online at http://www.rsinc.com/idl/) was utilized.
The HDRF shows a large variation across the solar spectrum. Figure 9 shows HDRF datasets, measured at 1835 LT 26 June 2004 at a solar zenith angle θi of 67°. The target area was covered with large crystals of surface hoar. Three wavelengths (400, 550, and 1000 nm) have been chosen to depict the variation of the reflectance with wavelength. The degree of anisotropy of the distribution of the HDRF is given by the anisotropy index (Anix), defined as the ratio of the maximum and minimum HDRF over the hemisphere for a given wavelength,
The Anix values for Fig. 9 are 1.75 (400 nm), 1.58 (550 nm), and 2.72 (1000 nm).
The HDRF also shows a strong dependence on the illumination conditions. Figure 10 shows the HDRF for four different solar illumination geometries for the wavelength of 550 nm. The datasets were collected in 2-h time intervals on 26 June 2004, starting at solar noon. The surface was again covered with hoar. The values of the Anix are 1.40 (θi = 49°), 1.48 (θi = 51°), 1.62 (θi = 58°), and 1.59 (θi = 67°).
Figure 11 shows the variation of the HDRF with changing snow properties. The two panels on the left show data collected on a snow surface of small wind-broken crystals, whereas the two panels on the right stem from of a snow surface covered with large crystals from surface hoar. As an example, two wavelengths of 550 and 1000 nm are displayed. Both datasets are collected at a solar zenith θi of 51°. For small crystals the value of the Anix is 1.42 (550 nm) and 1.60 (1000 nm), and for large crystals it is 1.13 (550 nm) and 1.28 (1000 nm).
In general, our preliminary results confirm findings from previous experiments. A strong forward-scattering peak is visible in the majority of all HDRF datasets (e.g., Steffen 1997; Aoki et al. 2000; Painter 2002). A weak backward-scattering peak is revealed at special conditions, for example, large illumination and measuring zenith angles. The Anix increases with increasing solar zenith angle and shows high values for surfaces covered with new snow.
A new field goniospectrometer is presented, including its technical details and functionalities. The hardware components, the control mechanisms, and the data acquisition procedure are described. The IAC ETH goniospectrometer was tested on the Greenland ice sheet in the dry snow zone at the Greenland Environmental Observatory Summit Station. A detailed data analysis of the described experiments is in preparation. With the IAC ETH goniospectrometer the variation of the HDRF with wavelength, changing illumination geometry, and snow surface characteristics can be measured with high accuracy.
The motion of the IAC ETH goniometer is controlled with a standard datalogger. A program was written to guide the radiometric sensor automatically through a complete cycle. With a default sampling resolution of 15° in zenith and azimuth, the program takes 11 min to collect a full HDRF dataset. The time needed for a complete cycle corresponds to a change of less than 4° in the solar zenith and azimuth. The spatial resolution of the samples can be increased, but at the cost of a prolonged assimilation time for completing a cycle. On average, the time needed for the collection of one data point is 5 s, including the traveling time to a new position.
The angular accuracy of the IAC ETH goniometer is very high, which results in a pointing accuracy of the sensor on the order of ±1 cm. The footprint size of the 3° foreoptic varies between 5.2 and 31 cm in diameter, depending on the view zenith.
With the spectrometer used in this study it was possible to measure incoming and reflected spectral radiance simultaneously. Having a continuous spectral reference of the incoming irradiance will be an advantage for the further analysis of the field data, allowing calculation of the HDRF with two different approaches.
The construction of the IAC ETH goniospectrometer is very robust and lightweight, which allows the instrument to be deployed in remote regions and to be left outdoors for several weeks.
The present study was supported by the Swiss National Science Foundation with Grant 200020-103558. The Swiss Federal Institute for Snow and Avalanche Research is kindly acknowledged for sharing the costs of the spectrometer. We would also like to thank VECO Polar Resources for the logistic support in Greenland, and Heinz Blatter for his help in solving geometric problems. We wish to express our gratitude to two anonymous reviewers for their helpful comments.
Corresponding author address: C. Saskia Bourgeois, Institute for Atmospheric and Climate Science ETH, Universitätsstrasse 16, 8092 Zürich, Switzerland. Email: email@example.com