The Characterization of the Railroad Valley Playa Test Site Using the DESIS Imaging Spectrometer from the Space Station Orbit

Abstract

The reflectance-based vicarious calibration approach uses measurements at well-understood test sites to provide top-of-atmosphere reference reflectance values suitable for inter-calibration approaches and does not require coincident views. The challenge is that results from such data may suffer from high variability from day to day. Data from high-quality sensors, such as the imaging spectrometers on the International Space Station (ISS) platform, provide an opportunity to use improved fine spectral information about the test sites with various sun/sensor geometries and site surface and atmospheric conditions to improve the test sites’ characterization. The results here are based on data from the DLR Earth Sensing Imaging Spectrometer (DESIS) instrument installed on the ISS since 2018 combined with output from the Radiometric Calibration Network (RadCalNet) site at Railroad Valley Playa (RRV) to decouple the effects of sun/sensor geometry from the RadCalNet predictions. The approach here uses the precessing orbit of the ISS to allow similar sensor view zenith angles at varying sun angles over short periods that limit the impact of any sensor changes and highlight the bi-directional effects of the surface reflectance and atmospheric conditions. DESIS data collected at (i) similar solar angles but varying view angles, (ii) similar sensor angles and varying solar angles, and (iii) similar scatter angles are compared. The DESIS results indicate that the top-of-atmosphere reflectance spectra for RRV at similar solar zenith angles but with varying sensor viewing angles provide more consistent data than those with varying solar zenith but with similar sensor viewing angles. In addition, comparisons of reflectance spectra of the site performed in terms of the sensor view scatter angle show good agreement, indicating that a directional reflectance correction would be straightforward and could offer a significant improvement in the use of RadCalNet data. The work shows that observations from imaging spectroscopy data from DESIS, and eventually Earth Surface Mineral Dust Source Investigation (EMIT), Surface Biology and Geology (SBG), and the climate-quality sensor CLARREO Pathfinder (CPF), provide the opportunity for the development of a model-based, SI-traceable prediction of at-sensor radiance over the RRV site that would serve as the basis for similar site characterizations with error budgets valid for arbitrary view and illumination angles.

1. Introduction

Understanding the Earth’s climate system requires integrating remote sensing data across time and space. Such integration requires ensuring inter-consistency between multiple sensors to create harmonized data sets, ideally traceable to the international system of units (SI). Past efforts at inter-consistency have forced agreement between sensor viewing test sites (i.e., calibration sources) viewed by the sensors at nearly the same time. The test sites are, however, often illuminated or viewed from different angles. Hence, systematic biases that are associated with the test sites’ dependence on directionality could exist. The approach used here can improve our understanding of the directionality dependencies of test sites and enable more accurate sensor inter-consistency studies. The improved understanding of the test sites supports model-based SI-traceable predictions of at-sensor radiance over selected sites.

The concept is that radiance from a well-characterized test site can be predicted for a given sun/sensor geometry under clear sky conditions with defensible error budgets. Such well-characterized test sites serve as a calibration source with a mainstreamed infrastructure to generate top-of-atmosphere radiance or reflectance spectra, allowing the accurate intercomparison of sensor data without needing coincident views. To achieve that, we would need to further our understanding of the dependencies of surface reflectance to illumination and viewing conditions and physical changes in the atmosphere and surface over time.

An airborne or satellite-based mapping of the spectral reflectance of the site can guide such efforts. Teillet et al. developed an approach to overcome minor differences in view and solar geometry by relying on an aircraft sensor to derive the surface reflectance of a test site both spatially and spectrally [1]. The derived surface reflectance is an input to a radiative transfer code, along with the coincident atmospheric data, which permits the prediction of the at-sensor radiance. The method was used to cross-compare data from various sensors viewing a test site at different times on the same date with varying view angles [2,3,4,5,6].

The characterization of a radiometric calibration test site can rely on in situ measurements, in which case the in situ measurements act as the transfer standard [7]. Alternatively, the characterization can be based on a model-centric approach, such as the models developed for desert scenes to study Advanced Very-High-Resolution Radiometer (AVHRR) sensors over time [8]. The SI-traceable model-centric prediction of at-sensor radiance over test sites is based on a physical understanding of the surface and atmosphere. Studying temporal effects from changing surface and atmospheric conditions will provide a better understanding of biases between sensors and produce more accurate results with documented SI traceability [9].

The challenge with the reflectance-based results such as those provided by the automated RadCalNet sites, as well as from collections performed with on-site personnel, is that the variability of the sensor calibration results is of a similar order to the absolute uncertainties [10,11]. Such variability makes it a challenge to understand the causes of outlier results in vicarious calibration because it can be attributed to issues with measurements of the surface properties, atmospheric conditions, or effects from the on-orbit sensor being calibrated. The ISS orbit allows for a range of sun/sensor geometries that can take place over short time periods.

This work characterizes the Railroad Valley Playa radiometric calibration site described in Section 3 by examining directional observations of the site using an ISS-based sensor viewing the site under various sun/sensor geometries. We aim to develop a better physical understanding of the site by studying spectral directional reflectance response characteristics of the site’s surface in both (i) an absolute sense, with reference to readily available in situ data for some of the DESIS scenes, and (ii) in a relative manner, with reference to a site-averaged top-of-atmosphere (TOA) reflectance spectrum chosen among the library of TOA reflectance spectra of the RRV site captured by DESIS. In addition, short-term and time-agnostic comparisons of the spectra are conducted to discuss long-term changes in the site and the sensor.

2. Orbital Characteristics of the International Space Station

DESIS was launched to ISS on 29 June 2018, by SpaceX-15 [12]. The unique orbital characteristics of the ISS make it an attractive Earth-observing platform to complement dedicated remote sensing satellites [13,14]. Many remote sensing satellites are placed in a high-inclination orbit where the satellite passes close to the poles. A sun synchronous orbit (SSO) in which the equatorial crossing time occurs for the same local mean solar time for all orbits is straightforward to achieve from these high inclinations. The advantage of an SSO is that sensor acquisitions will have similar surface illumination angles at a given location with significant changes in solar zenith angle occurring at seasonal time scales rather than weekly or monthly. The similarity in illumination reduces what can be a significant effect in understanding time series of surface properties.

The ISS, on the other hand, orbits the Earth in a near-circular orbit from west to east at an altitude of 375 to 435 km with an inclination of 51.6 degrees relative to the Earth’s equatorial plane [15,16]. The fluctuations in altitude are primarily due to atmospheric drag, which is compensated for by periodic boost maneuvers of the ISS. The mid-inclination orbit means that the ISS, unlike satellites in a near-polar orbit, never crosses the North or South poles and is (typically) limited to a latitude range between 52°N and 52°S. The mid-inclination orbit also means that a prohibitively large fuel usage would be needed to maintain an SSO; thus, the ISS has a range of equatorial crossing times. The result is that ISS-based Earth Observing (EO) missions sample the globe over a range of overpass times, including during the night, offering an opportunity to study the Earth under different solar illumination conditions over short time periods.

The ISS circles the Earth in about 90 to 93 min, depending on its altitude, completing 15.5 to 15.9 orbits daily. Due to the Earth’s rotation, each orbit shifts to the west by approximately 22.9 degrees longitude [13]. As the path of the ISS shifts westward with each orbit, it repeats the same orbital track roughly every three days. The ISS revisit frequency is not constant as can be the case for SSO satellites and the actual repeat depends on on-orbit maneuvers, but generally, it is within three- to five-day intervals.

The result is that an ISS-based sensor can image a particular site every three days but that imaging will take place at later times for each opportunity until orbital precession returns the ISS back to its original path. The whole process takes roughly 60 days. Thus, an imager on ISS will see a range of overpass times along with the corresponding changes in sun illumination geometry that repeats roughly every two months.

The approach here makes use of the precessing orbit described above to provide a range of varying sun/sensor angles over short periods of time. The varying geometry allows for studies related to bi-directional surface reflectance effects [17,18,19] and diurnally varying atmospheric and surface situations [20]. Barnsley at al. explored the BRDF sampling capabilities of several operational and planned satellite sensors in 1994 [17]. Wanner et al. describe the theory and the algorithm to be used in producing a global BRDF and albedo product of the moderate-resolution imaging spectroradiometer (MODIS) and the multi-angle imaging spectroradiometer (MISR) [18]. Jing et al. evaluate RadCalNet test sites using Landsat and Sentinel sensors, suggesting that the development of a site-specific BRDF correction would improve accuracy of their data products [19]. Wang et al. developed and performed atmospheric and BRDF correction using information in diurnal variability of geostationary observations [20]. The advantage to having the data collected over sub-seasonal time scales is that it helps to minimize influence of longer-term changes in the sensor calibration and the surface condition.

3. In Situ and Satellite-Based Data Products

3.1. RRV RadCalNet Test Site

The RRV, located east of Tonopah in Nevada at an elevation of 1435 m, is the site for this study. The site was initially chosen in 1995 for the vicarious radiometric calibration of MODIS because of nine characteristic criteria: (i) high surface reflectance, (ii) spatially uniform, (iii) flat spectral reflectance, (iv) temporal invariance and surface properties, (v) near-Lambertian surface, (vi) high elevation, (vii) large size, (viii) arid region, and (ix) accessibility [21]. The Remote Sensing Group at the University of Arizona designed nadir-viewing ground viewing radiometers (GVRs) to characterize the site. They operate an instrumented 1 km² area centered at [38.497, −115.690] with multiple automated GVRs, a meteorological station, and a sun photometer at 1435 m [22]. The site is designated as one of the Radiometric Calibration Network (RadCalNet) sites [10].

The playa contains clay-rich lacustrine deposits. The site’s surface stability is reasonably well understood under dry conditions [23]. However, the site receives periodic rain, snow, and salt deposits over the years and should be periodically studied. A study by Bruegge et al. presented a bi-directional reflectance distribution function (BRDF) for the RRV site using measurements from field instruments and satellite measurements from MISR and MODIS [24]. The study concludes that the most significant deviation of directional reflectance measurements from those of the nadir-view measurements is in the back-scatter principal plane and can reach up to 20% for wide view angles. Moreover, the results of the multispectral comparisons showed negligible spectral dependencies. More recently, Byford et al. studied temporal variation in directional surface reflectance of the RRV site [25]. The study concluded that the site was stable during the one-day campaign and that the surface reflectance anisotropy of the RRV site was more significant in the back-scatter principal plane, possibly due to its surface mineral compositions. The duration of the study was limited to 6 h during a vicarious calibration campaign conducted on 3 May 2018. To characterize long-term stability of the surface reflectance and the long-term directionality dependence of the surface, we need angular data from longer time periods (e.g., months and years).

The RadCalNet data from RRV offer an opportunity for such longer-term studies of bi-directional reflectance effects. RadCalNet relies on data supplied by site operators that collect and report bottom-of-atmosphere (BOA) reflectance spectra as part of a network that provides top-of-atmosphere (TOA) reflectance along with the associated absolute radiometric uncertainties according to standardized protocols formulated by the RadCalNet Working Group. In addition to the nadir-viewing BOA reflectance data, the site operator also provides atmospheric parameters, including the surface pressure and temperature, columnar water vapor, ozone, aerosol optical depth, and Angstrom coefficient that are used to determine the TOA reflectance. TOA spectra and their associated uncertainties are generated using a radiative transfer code and Monte Carlo simulations of input parameters to the radiative transfer code [11]. The data are freely available to the global community at RadCalNet’s website [https://www.radcalnet.org/; accessed on 1 January 2024].

3.2. Radiometric Calibration of DESIS

We use DESIS L1C imagery to generate TOA reflectance scenes of the RRV site captured under various sun/sensor geometries dictated by the ISS orbit. DESIS was calibrated pre-launch and includes a compact on-board calibration unit consisting of a Light Emitting Diode (LED) bank with nine different LED types. The pre-launch absolute radiometric calibration for spectral radiance of DESIS was performed using an integrating sphere [26].

DESIS does not have diffusers or integrating spheres on board for the uniform illumination of the detectors of its focal plane. Hence, radiometric calibration is mainly based on the pre-launch calibration of the instruments. Although the LED bank could be used as a calibration source, the non-uniform illumination of the focal plane poses challenges to its use for uniform radiometric calibration across pixel-wise sensors on the focal plane array. Therefore, DESIS mainly relies on various vicarious calibration methods on orbit to monitor and correct changes in the radiometric response of the sensors while relying on the LEDs to monitor spectral response changes and short-term relative radiometric calibration [27]. The vicarious calibration of DESIS uses observations of spectrally homogeneous scenes captured from CEOS Pseudo Invariant Calibration Sites (PICSs), TOA reflectance data products of RadCalNet sites [28], and cross-calibration using near-coincident scenes captured by the Landsat-8 Operational Land Imager [29] and Sentinel-2 Multispectral Instrument [30]. Since data from RVUS and GONA sites for RadCalNet have been used to update calibration coefficients of the instrument, agreements shown here between vicarious and space-borne data are not meant to validate the radiometric scale of DESIS. The radiometric coefficients calculated during the pre-launch characterization of the instrument were updated during the commissioning. After that, the DESIS calibration team has been generating regular radiometric calibration coefficient updates on at least five calibration periods [31,32].

3.3. Spectral Calibration of DESIS

DESIS covers solar reflected wavelengths at 400 nm to 1000 nm with a nominal spectral sampling distance of 2.55 nm, and Full Width Half Maximum (FWHM) of about 3.5 nm, and at 30 m spatial resolution. Seven LEDs in the LED bank are used to perform minor updates on its spectral calibration. The center wavelengths’ positions are vicariously validated and re-calibrated based on narrow atmospheric absorption features [33,34,35]. DESIS has an overall accurate and stable spectral calibration, but indications for minor wavelength shifts and uncorrected spectral smiles remain. The only update required on the spectral calibration was a global shift of 0.1 nm [35]. The absolute spectral response (ASR) of DESIS was extracted from the metadata of each scene in this study. By examining the trend of these spectra, we confirm that the ASRs are mostly the same from 2019 to 2023, with only the 0.1 nm minor shift.

3.4. Generating Top-of-Atmosphere Reflectance Data Cubes from DESIS Scenes

We identify the RadCalNet instrumented 1 km² region of interest centered at [38.497, −115.690] over available DESIS scenes of the RRV. Images of the playa that do not capture or only partially capture the 1 km² region are omitted. We extract the 34-pixel-by-34-pixel area from each scene, representing the 1 km² area (Figure 1).

As-downloaded DESIS images are stored as digital numbers ${\mathit{D}}_{\mathit{i},\mathit{j},\mathit{k}}^{\mathit{i}\mathit{n}\mathit{t}}$ (i and j representing spatial indexes and k representing spectral index) and are radiance-based values. Each image has an associated metafile containing a gain value ${\mathit{F}}_{\mathit{k}}$ and an offset ${\mathit{O}}_{\mathit{k}}$ for each band. The spectral radiance is calculated by

$${\mathit{L}}_{\mathit{i},\mathit{j},\mathit{k}}={\mathit{D}}_{\mathit{i},\mathit{j},\mathit{k}}^{\mathit{i}\mathit{n}\mathit{t}}.{\mathit{F}}_{\mathit{k}}+{\mathit{O}}_{\mathit{k}}$$

The spectral radiance, ${\mathit{L}}_{\mathit{i},\mathit{j},\mathit{k}}$, is converted to spectral reflectance, ${\mathit{\rho }}_{\mathit{i},\mathit{j},\mathit{k}}$, using

$${\mathit{\rho }}_{\mathit{i},\mathit{j},\mathit{k}}={\displaystyle \frac{\pi {\mathit{L}}_{\mathit{i},\mathit{j},\mathit{k}}{d}^2}{{\mathit{E}}_{\mathit{k}}cos{\theta }_s}}$$

where ${\mathit{E}}_{\mathit{k}}$ is the spectral solar irradiance at normal incidence and mean Earth–sun distance, $d$ represents the Earth–sun distance in astronomical units, and ${\theta }_s$ is the solar zenith angle at the time of image acquisition. Here, we use the Total and Spectral Solar Irradiance Sensor-1 (TSIS-1) Hybrid Solar Reference Spectrum (HSRS) version 2 as the spectral solar irradiance ${\mathit{E}}_{\mathit{k}}$ [36]. The TSIS irradiance scale is defined based on the average daily solar spectral irradiance observations from 1 to 7 December 2019 during the minimal solar activity period. The absolute uncertainty for the spectral solar irradiance is 0.5% in 400–460 nm and 0.3% in the 460–1000 nm spectral domain. We truncate (to the 400–1000 nm spectral domain) and resample (to 235 bands) the TSIS spectra to that of DESIS data.

In addition to the DESIS-based reflectance, we also use TOA reflectance data products of RadCalNet over the 1 km² region of interest as nadir-view reference spectra. The TOA data products from the RadCalNet database provide TOA and BOA reflectance spectra representing the surface reflectance of the 1 km² area. Figure 2 shows a sample DESIS radiance spectrum, its respective reflectance spectrum, and the associated RadCalNet reflectance spectrum generated based on the above-described procedure. We compute the arithmetic mean of the 1156 TOA spectral reflectance values in the RRV region of interest to calculate a single TOA reflectance spectrum representative of the TOA reflectance of the RRV site (Figure 2A).

Figure 3 shows the ratio of the two red lines in Figure 2. The dashed lines in the figure represent the absolute uncertainty (coverage factor k = 2) of the intercomparison, which is computed by

$$U_{ratio}=2\sqrt{U_{RCN}^2+U_{DESIS}^2}$$

where $U_{RCN}$ is provided for each RadCalNet spectrum and $U_{DESIS}$ is assumed to be 5%. The TOA reflectance spectra from DESIS and RadCalNet agree within the absolute uncertainty of the comparison. There are, however, two primary (high finesse) spectral features at 760 nm and 940 nm, in which the comparison spectra fall outside the k = 2 uncertainty boundaries. The 760 nm feature is due to oxygen absorption, and the 940 nm feature is due to the strong water vapor absorption. We will see similar features for other comparison spectra throughout this study due to the major atmospheric absorption of oxygen and water molecules. Besides those major spectral features, we generally see higher-frequency spectral features with small amplitudes that appear like noise in the comparison spectra. These high-frequency features are mostly in-phase from day to day and are attributed to systematic differences between the DESIS and RadCalNet’s BOA reflectance spectra.

4. Scene Selection

Figure 4 shows the daily orbit swaths for DESIS and the variation in the sun/sensor geometry of the ISS over the Railroad Valley calibration site in Nevada from December 2018 to December 2023. In addition, depending on the ISS’s orientation, the detectors’ tilt, and their optical components, the image view angle can also vary substantially. As a result, to accurately compare and harmonize remote sensing data from ISS with those acquired from satellites in SSO, one must correct for variations in sun and view geometries. Figure 4B shows a range of sun and view geometries for the DESIS instrument on board the ISS during its overpass of the Railroad Valley calibration site in Nevada from December 2018 to December 2023.

We found 59 DESIS scenes that captured the full 1 km by 1 km area of the RRV site and 15 matchups with RadCalNet that also coincided with clear sky conditions. The 15 matchups are used for intercomparisons similar to that shown in Figure 3. All 59 DESIS scenes were visually inspected for evidence of clouds and shadows, leading to the removal of 18 scenes, leading to 41 scenes that are used for relative comparisons.

For radiometric comparisons with TOA reflectance data products of RadCalNet, we omit images for which the difference between image capture time and RadCalNet surface reflectance collection time is larger than 15 min. Limiting the time difference in this way reduces effects from changes in atmospheric transmittance (e.g., due to intermittent clouds). Moreover, the solar angle changes over larger time scales can lead to significant differences between the DESIS data and RadCalNet products due to differences between atmospheric paths for the two data sets.

Sun/Sensor Geometries

The position of the sun with respect to the instrumented site is denoted by ${\theta }_s$ and ${\varphi }_s$, and the position of the sensor with respect to the instrumented site is denoted by ${\theta }_v$ and ${\varphi }_v$. Zenith angles are measured from the surface normal. The azimuth angles are measured clockwise from North, similar to the metadata convention of DESIS data products. Figure 5 shows the principal plane of the direct sun illumination and the sensor observation.

Figure 6 shows sun and sensor zenith angles for 41 DESIS scenes, capturing the RRV’s full view between December 2018 and December 2023. The notable feature in the plot is the range of solar zenith angles seen throughout the year as a result of the varying overpass times from the ISS orbit. The range of view angles seen in Figure 6 is an indication of the pointability of the DESIS instrument, allowing the sensor to see a test site such as RRV when a nadir pointing instrument would not. The advantage of such geometries is that we can investigate a range of geometries to isolate directional dependencies of the surface reflectance of the sites over short-term intervals and avoiding effects of long-term changes from the sensor and the surface that would occur if we needed to wait for seasonal change geometry as would be seen for an SSO.

The scattering angle $\Theta$ is defined as the angle formed between a first vector representing the direction of incoming photons originating from the sun and a second vector representing the direction of outgoing photons reflected from the site toward the observing sensor. The scattering angle is calculated by

$$\mathit{cos}\Theta =\mathit{cos}\left(\pi -{\theta }_s\right)cos\left({\theta }_v\right)+sin\left(\pi -{\theta }_s\right)sin\left({\theta }_v\right)cos(\Delta \varphi )$$

Figure 7 shows time-agnostic sun/sensor geometry (A) and temporal scatter angles (B) of the 41 DESIS scenes with a clear and complete view of the RRV between December 2018 and December 2023. From Figure 7A, we can identify time-agnostic clusters of scenes with similar sun and/or sensor geometries over the five years of DESIS data. Focusing on the time-agnostic clusters can isolate temporal dependencies of the surface and sensor by reducing effects from sun/sensor geometries.

Table 1. Sun and sensor angles of the analyzed matchups.

Scene Date	Time (UTC)	${\mathit{\theta }}_{\mathit{s}}$	${\mathit{\varphi }}_{\mathit{s}}$	${\mathit{\theta }}_{\mathit{v}}$	${\mathit{\varphi }}_{\mathit{v}}$	$\mathit{\Theta }$
6/14/2019	17.52	32.19	108.28	19.27	332.56	157.63
6/28/2019	18.91	18.90	139.73	3.35	238.58	161.33
8/4/2019	21.28	28.40	227.47	13.08	312.09	147.86
8/22/2019	21.11	32.08	218.42	1.16	9.59	148.93
10/29/2019	18.22	54.88	157.59	1.59	29.17	144.54
10/21/2020	20.71	52.35	202.62	18.68	44.18	124.39
12/19/2020	21.27	65.77	203.76	10.83	42.94	123.74
12/4/2021	19.90	61.05	185.00	7.97	313.81	131.14
2/19/2022	20.33	49.78	187.15	0.92	13.39	131.52
4/29/2022	17.20	40.98	115.22	16.64	44.00	167.40
6/7/2022	18.70	20.52	135.16	7.93	313.36	153.62
6/11/2022	17.09	37.29	102.52	13.73	313.68	153.19
6/18/2022	21.18	23.49	236.50	3.32	232.31	160.38
6/23/2023	18.74	19.99	134.25	0.44	281.33	154.87
8/4/2023	19.29	22.50	158.62	2.78	138.13	157.63

lists the analyzed matchups’ sun, sensor, and scattering angles. The minimum and maximum scattering angles attained from sun/sensor geometries of DESIS scenes from 2018 to 2023 are 123 and 167 degrees, respectively. Thus, the DESIS instrument on the ISS orbit primarily views back-scattered sunlight. This is, at least in part, because the DESIS scenes are captured under view angles smaller than 20 degrees (see Table 1).

5. Results

Figure 8 analyzes site-averaged TOA reflectance spectra of DESIS in three different ways. First (Figure 8A), absolute ratio spectra are generated by dividing the site-averaged TOA reflectance spectra of DESIS (${{\overline{\rho }}_{DESIS}}_{j,k}/n$) by the corresponding TOA reflectance spectra of RadCalNet ($\sum {{\overline{\rho }}_{RCN}}_{j,k}/n$):

Second (Figure 8B), relative ratio spectra are generated by dividing the site-averaged TOA reflectance spectra of DESIS by a reference site-averaged TOA reflectance spectrum of DESIS. Third (Figure 8C), relative double-ratio spectra are generated by dividing the absolute ratio spectra by a reference absolute ratio spectrum of 28 June 2019 (the blue spectrum of Figure 8A). This particular spectrum was chosen as the reference because of its near-nadir-view angle of 3 degrees, relatively small sun angle of 19 degrees, and small time difference of 5 min between the scene capture time and the in situ data collection time.

$${\displaystyle \frac{{{\rho }_{DESIS}}_i}{{{\rho }_{RCN}}_i}}={\displaystyle \frac{\frac{\sum {{\overline{\rho }}_{DESIS}}_{i,j,k}}{n}}{\sum {{\overline{\rho }}_{RCN}}_{i,j,k}}}$$

where $j,k$ represents two-dimensional pixels of the 1 km² site and $i$ represents the date of each space-borne or in situ data value. Figure 8A compares site-averaged TOA reflectance spectra of DESIS scenes, listed in Table 1, to corresponding RadCalNet spectra generated from automated in situ site measurements collected close in time (less than 15 min). The red line is the averaged absolute reflectance ratio spectrum calculated from the collective absolute reflectance ratio spectra of DESIS to RadCalNet. The dashed lines show the 95% confidence interval of the absolute radiometric uncertainty of the comparison using the same procedure as Figure 3. The averaged absolute reflectance ratio spectrum suggests that the consistency of the DESIS and RRV reflectance spectra is within 5% except for the spectral regions near the oxygen and water vapor absorption (760 nm and 940 nm) and below 450 nm, where the surface reflectance is lower. The DESIS instrument team previously reported rapid change in performance below 450 nm and large variation in calibration below 500 nm [38]. Those reports suggest that the short wavelength tails of the absolute ratios seen in Figure 8A are caused by a degradation of the coating on the mirrors of the instrument’s pointing unit.

Figure 8B compares each TOA reflectance spectrum of DESIS scenes of Table 1 to that of a reference DESIS spectrum (here chosen to be the scene captured on 4 December 2021) in a relative manner. The red line is the averaged relative reflectance ratio spectra. The relative spectra appear less noisy than the absolute ratio spectra because they are all DESIS-based results and, therefore, do not include systematic differences between DESIS and RadCalNet. These relative spectra are, however, more spread because temporal variabilities of the site and the sensor, in addition to differences in beam paths and the directional reflectance response of the surface, are included while these effects are removed in Figure 8A through the inclusion of the test site information from RadCalNet.

$${\displaystyle \frac{{{\rho }_{DESIS}}_i}{{{\rho }_{DESIS}}_r}}={\displaystyle \frac{\frac{\sum {{\overline{\rho }}_{DESIS}}_{i,j,k}}{n}}{\frac{\sum {{\overline{\rho }}_{DESIS}}_{r,j,k}}{n}}}$$

where $r$ represents the reference spectrum of 28 June 2019. Figure 8C compares the absolute ratio spectra of Figure 8A to a reference absolute ratio spectrum selected from those absolute ratio spectra. The red line is the average of the relative double-ratio spectra. The relative spectra do not have the high-frequency ripples of the absolute ratio spectra (Figure 8A) and are less spread out compared to the spread of the relative ratio spectra (Figure 8B). This is because each of the numerators and denominators of the relative double-ratio spectra include instrument-dependent terms. Therefore, relative ratios neutralize systematic spectral differences between small, uncorrected band-to-band calibration effects in the DESIS data as well as band-to-band differences from the spectral sampling differences between DESIS and RadCalNet data products. In addition, because each of the terms in the numerators and denominators initially compares a DESIS spectrum and a corresponding RadCalNet spectrum reported close to acquisition times, the relative double-ratio spectra reduce information about temporal variabilities of the site.

$${\displaystyle \frac{\left(\frac{{{\rho }_{DESIS}}_i}{{{\rho }_{RCN}}_i}\right)}{\left(\frac{{{\rho }_{DESIS}}_r}{{{\rho }_{RCN}}_r}\right)}}={\displaystyle \frac{\left(\frac{\frac{\sum {{\overline{\rho }}_{DESIS}}_{i,j,k}}{n}}{\sum {{\overline{\rho }}_{RCN}}_{i,j,k}}\right)}{\left(\frac{\frac{\sum {{\overline{\rho }}_{DESIS}}_{r,j,k}}{n}}{\sum {{\overline{\rho }}_{RCN}}_{r,j,k}}\right)}}$$

The ratio spectra display various spectral features, including broadband structures, spectral kinks, and spectral wiggles that are, in part, caused by spectral differences between the satellite-based and in situ data, the differences in view geometry, and the directional reflectance response of the surface. The spectral kinks can be attributed to the absorption features of the atmosphere, and the broadband structures to the surface directional reflectance and atmospheric scattering effects. The spectral wiggles are consistent in phase across the ratio spectra and can be attributed to systematic differences between the satellite-based and in situ sensors. Broadband structures and spectral kinks are present in all three comparison methods, but the spectral wiggles are more apparent in the absolute ratio spectra. The absolute ratio spectra compare reflectance values generated from different sensors with different radiometric and spectral calibrations. Therefore, systematic differences in the spectral calibration of the sensors can result in such consistent features. We can remove the spectral wiggles by dividing the DESIS spectra by another DESIS spectrum to reduce the effect of small band-to-band sensor differences.

Figure 9 shows the standard deviations of the mean curves from the three cases in Figure 8. The red line in Figure 9 corresponds to the mean shown in Figure 8A with the black and blue lines based on the means in Figure 8B,C, respectively. The smooth band-to-band standard deviation spectrum of the absolute ratio supports that the high-frequency fluctuations of the DESIS/RCN ratios are sensor effects.

The relative ratios have a more extensive spread across the five years of data. This is because, unlike the absolute ratio and relative double ratios, relative spectra include information about differences in the surface’s long-term temporal variability. Moreover, the spread of the relative ratio, unlike the absolute ratio and relative double ratios, largely depends on the choice of the reference absolute ratio spectrum of 28 June 2019 (the blue spectrum of Figure 8A). If the reference was chosen closer to the mean spectrum, the spread of the relative ratios would go down by about 1%.

5.1. Short-Term Studies

The orbit of the ISS allows us to examine similar sensor/sun angles at varying sun/sensor angles over short periods (within a month). Comparing such short-term observations limits the changes in the sensor and the site conditions and highlights the directionality dependence of the surface reflectance and atmospheric conditions. The rest of the plots and discussions in this section are about five such short-term studies. Dates, view zenith angles ${\theta }_v$, sun zenith angles ${\theta }_s$, view azimuth angles ${\varphi }_v$, sun azimuth angles ${\varphi }_s$, and scattering angles $\mathsf{\Theta }$ are shown in the legend tables for each plot in this section.

The short-term relative comparison of TOA reflectance spectra generated from four radiance-based DESIS observations of the RRV site captured in June 2019 is shown in Figure 10. The reference spectrum is generated from the image captured on 28 June 2019. The reference spectrum is selected for its smaller solar zenith angle and near-nadir sensor view angle compared to the sun/sensor geometry of the other three dates. Note that we do not need to correct these spectra for their cosine factor of the solar zenith angles because they were already taken into account in generating the TOA reflectance spectra, as described in Section 3.

Inspecting these spectra indicates that the data from the largest-solar-zenith-angle case of June 21 (blue line) have the largest difference from the June 28 data set. Changes in the sensor are unlikely to be the cause of this effect since that would necessitate two 20% changes in sensor response over a 14-day period and such behavior has not been noted by other users of the data or the DESIS sensor team. Similar 20% shifts in the reflectance of the surface are only seen in cases of large rainfall events, and on-site meteorological data and imagery from other sensors do not show such an event.

Thus, Figure 10 shows a clear example of the benefit of the lower-inclination orbit of ISS, leading to varying sun/sensor geometries over short time periods, meaning that the sites and sensor are not likely to cause such significant scene-to-scene differences because these scenes are captured within a month, and therefore, the site and sensor are under similar conditions. Notice that the three relative spectra of June 10, 14, and 21 show a similar spectra shape that is another indication that the effects seen in Figure 10 are caused by the changing sun/sensor geometries. These spectral trends are relative to the reference spectrum, and choosing a different scene as a reference would result in different spectral trends. A key point here is that the reflectance spectra for dates with the consistent scatter angles with values close to 160 degrees (black, red, and purple spectra) show excellent agreement.

Figure 11 shows another short-term relative comparison of TOA reflectance spectra generated from four radiance-based DESIS observations of the RRV site captured in August 2019. The August case is treated in a similar fashion to the June case shown in Figure 10. The geometry shown in the legend of Figure 11 shows that the sun/sensor geometry for these four cases covers a range view and solar zenith along with changes in relative azimuths, leading to a range of scatter angle cases. The reference spectrum chosen in this case is based on the data captured on 19 August 2019, and it is selected as the reference spectrum for its similarity of sensor view angles to two other spectra of this temporal window.

The relative spectra of 4 August and 22 August (blue and black lines), captured under similar illumination angles but different view angles, have very similar scatter angles. The two dates show remarkably similar relative ratio spectra in magnitude and spectral shape even with the 12-degree difference in view angle. Further evidence that the view angle plays a secondary role in the cause of changes in TOA reflectance for RVUS is the ratio for the September 6 date that has the same view angle as the August 19 reference. The 20% difference is similar to that seen in Figure 10 for which view angles are similar, but solar zenith angles are much larger than the reference spectra. We may infer from these two data clusters that the site’s top-of-atmosphere reflectance spectra at varying view sensor zenith angles provide more consistent data than those with varying solar zenith angles. The behavior with the view angle is one of the reasons that Railroad Valley was chosen as a reflectance-based calibration site. Early BRDF measurements at the site showed this behavior such that the site was seen to be within 5% Lambertian-wise for view angles out to 30 degrees [39,40]. The original work was collected under a limited range of view azimuths that corresponded with the cross-track direction of sun-synchronous sensors. Later work has shown that RRV displays greater non-Lambertian effects for specific sun/sensor view geometries [24,25,41] caused by small-scale surface features and shadow effects.

The results seen in Figure 11 are another of the utilities of the ISS orbit. The design of DESIS and its location on the ISS limits the range of sensor zenith angles for the DESIS data products. The orbit provides both a large range in solar zenith as well as a range of relative azimuth angles between the sensor view and solar principal plane. That provides a range of scatter angles that, again, lead to the reflectance spectra of the site being consistent with scatter angles (black and blue spectra), showing excellent agreement.

Figure 12 shows the cluster of DESIS data collected in October 2019 that allows for yet another short-term relative comparison of TOA reflectance spectra generated from three DESIS observations of the RRV site. The reference spectrum for this cluster is chosen for data captured on 29 October 2019 because of its near-nadir view. In this time cluster, the three observations were made under similar sun angles of 51 to 57 degrees and changing view angles from 1.6 to 17.6 degrees. We could infer that the site’s top-of-atmosphere reflectance spectra for oblique observations deviate more from that of the nadir-view reference spectrum with larger view zenith angles since the spectra from October 21 that have the largest view angle also show the largest difference from the reference.

However, the view angle inference overlooks two other factors. The first is that the larger solar zeniths coupled with larger view angles mean that differences in atmospheric conditions between the different dates could cause day-to-day effects. Section 6 provides a sensitivity of the ratio to atmospheric conditions based on surface measurements and radiative transfer simulations that take into account sun/sensor geometries for several specific cases.

The second factor to consider is the time of day of the overpass of these three dates corresponding to collections taking place prior to solar noon (ϕ_s = 158 degrees), near solar noon (ϕ_s = 187 degrees), and after solar noon (ϕ_s = 216 degrees). Thus, the solar principal plane is shifting relative to the wind-driven, small-scale structure of the surface. The change in solar azimuth, as well as the relative azimuth, can accentuate surface BRDF effects because of changes in surface shadowing.

Figure 13 shows the fourth short-term relative comparisons of TOA reflectance spectra generated from three DESIS observations of the RRV site captured in April–May 2022. The reference spectrum is generated from the data captured on 11 April 2022 because of the near-nadir sensor view angle, though it does correspond to the case with the largest solar zenith of all of the 14 cases examined in this section. In this time cluster, the three observations were made under different sun and different sensor angles. The red line, representing the relative ratio of the at-sensor reflectance response in the 29 April 2022 observation to that of the reference, has a larger deviation from the reference line than the blue line for the image captured on 3 May 2022. That is not a surprise because the magnitudes of the difference in the sensor and the sun angles ($\mathsf{\Delta }{\theta }_s=28.6$ and $\mathsf{\Delta }{\theta }_v=13.4$) are larger for the April 29 date (red line) than those for May 3 (blue line) ($\mathsf{\Delta }{\theta }_s=11.6$ and $\mathsf{\Delta }{\theta }_v=8.7$). Also of note is that the April 11 and May 3 dates have more similar scatter angles.

5.2. Time-Agnostic Study

The results of the above short-term studies point to directionality dependence of the site’s surface reflectance. Next, we study the changes in the site over time by comparing scenes with similar sun/sensor geometries captured over the five years of the DESIS data.

Figure 14 shows the ratio of site-averaged TOA reflectance spectra of DESIS observations of the RRV site captured under similar sun/sensor geometries relative to the reference site-averaged TOA reflectance spectrum captured on 28 June 2019. The set of spectra in each figure are spread over time and show variation in TOA reflectance characteristics of the site over five years, although they are captured under similar zenith angles. For example, in Figure 14, the TOA reflectance derived from the October 2019 image (black line) corresponds more closely to that of the June 2019 reference spectrum than do the other two data sets from four years later. That shows changes in the surface reflectance of the site over the course of four years. Such time-agnostic results isolate temporal dependencies of the surface and sensor by reducing effects from the difference between sun/sensor geometries. The observed changes in surface reflectance are mainly due to changes in the surface reflectance of the site over time because the sensor’s uncertainty is less than 5%. Differences in the atmospheric conditions under which these scenes are captured are an additional factor that contribute to the observed variations in Figure 14.

5.3. Absolute Studies

One way to reduce the difference in atmospheric conditions and changes in the natural variations in the surface over the years is comparing DESIS radiometric data with absolute precited radiometric data based on in situ measurements of RadCalNet. We use scenes captured under clear sky conditions to compare the TOA reflectance of satellite images and the TOA reflectance of RadCalNet ground site measurements. This process reduces DESIS scenes that we could use from 59 to 15. All the absolute comparison spectra were previously shown in Figure 8A. Here, those absolute spectra are clustered based on their view zenith angle in five degree increments: 0 < ${\theta }_{VZ}$ < 5, 5 < ${\theta }_{VZ}$ < 10, 10 < ${\theta }_{VZ}$ < 15, and 15 < ${\theta }_{VZ}$ < 20 (Figure 15). The absolute reflectance ratio can be thought of as spectral correction factors for BRDF correction. These results show that ratios of radiometric data of angular DESIS observations are more consistent with the nadir-view radiometric data of RadCalNet for a small view angle difference. The deviations of DESIS and RadCalNet data increase when the view angle differences are larger than 5 degrees.

6. Discussion

Radiometric calibration sites, such as the RRV site being studied here, are chosen to have a near-Lambertian reflectance response to minimize directional reflectance effects, and geometries used for calibration activities are chosen to minimize any non-Lambertian properties. Results of the above short-term studies of Section 5.1 from hyperspectral satellite observations support previous BRDF assessments of the site [24,25,41] and point to a noticeable directionality dependence of surface reflectance. The advantage of the work is that DESIS-captured hyperspectral data have been collected over a longer time frame and are at a spatial sampling that is more representative of what on-orbit sensors would see. In addition, the five years of DESIS data that provided enough data to conduct the time-agnostic studies of Section 5.2 under similar sun/sensor geometries suggest long-term variability of the surface reflectance response of the site. Finally, the absolute comparison of DESIS TOA reflectance with RadCalNet-predicted TOA reflectance made it possible to reduce differences caused by atmospheric effects and long-term changes in the surface. However, these results can be further strengthened by customizing the radiative transfer calculations of RadCalNet to account for specific observation angles of each scene. This section provides the method and results of such angle-adjusted radiative transfer computations.

6.1. Atmospheric Considerations

As described in the previous section, short-term temporal cluster studies can lead to inferences regarding the directional reflectance characteristics of a site because temporal effects from the sensor, site, and atmosphere can be mitigated. Of those three factors, it is the temporal changes in the atmosphere that typically attract the most attention as likely causes of uncertainties. Fortunately, test sites such as RVUS with reflectance values > 0.2 are not strongly affected by atmospheric variability [11].

Still, we consider the impact of atmospheric effects on the comparisons of the TOA reflectance spectra from nadir-viewing radiometers of the site to the directional observation of DESIS. Differences in TOA reflectance due to distance differences along the atmospheric path from the sun to the surface and then to the sensor will cause differences in scattering effects on the incoming sunlight as well as on the surface-reflected radiance. For instance, to illustrate the effect on incident solar irradiance, Figure 16 compares the direct and diffuse solar illumination of the surface for several solar zenith angles with an AOD of 0.028. The curves are peak-normalized to highlight the spectral shifts in solar and skylight irradiance reaching the surface.

At ${\theta }_s=0,$ the sun is directly overhead, and the atmospheric path is the shortest. The shape of the spectral solar irradiance at the surface is due to multiple factors. The first is that the overall spectral shape is a result of the TOA solar irradiance that peaks in the mid-visible portion of the spectrum. The strongly varying spectral structure in both the direct and diffuse irradiance curves at shorter wavelengths are primarily due to the spectral variability of the sun. Longer wavelength variability is due both to the solar irradiance as well as atmospheric absorption features. The second factor is that atmospheric scattering is much larger at shorter wavelengths due both to molecular gasses and aerosols. Thus, the peak of the transmitted solar irradiance at the surface will be at a slightly longer wavelength than the peak of the incident, TOA solar irradiance. The scattering effects of the atmosphere can also be seen in the spectral shape of the diffuse irradiance curve where there is more energy at the very shortest wavelengths in the curve relative to the peak.

Larger solar zenith angles result in a longer atmospheric path and larger impacts from scattering. The largest zenith angle in the figure highlights the effect for both the direct and diffuse terms. The spectral shape of the direct term (the deep red line for a solar zenith angle of 80 degrees) shows a shift in the peak irradiance to a much longer wavelength than the zero-degree case. The effect is caused by the attenuation due to scattering at the shorter wavelengths relative to longer wavelengths. Note that the solar irradiance for the 80-degree case will be significantly lower at all wavelengths than for the normal incidence case, but normalizing the irradiance highlights the spectral nature of the path length differences. At large illumination angles, there is a similar shift in the peak of the diffuser light to longer wavelengths. The effect here is more subtle in that there is an increase in downwelling irradiance due to greater scatter, but a fraction of that scattering is also lost to upward scattering out of the atmosphere as well as multiple-scattered light being absorbed by the surface. Ultimately, the relative spectral peaks of the direct, diffuse, and total illumination terms shift toward longer wavelengths.

In addition to the above-illustrated example of the effect of the sun angle on solar irradiance from the perspective of the surface, the view angle of the sensor can also introduce spectrally dependent effects on the observed radiance or reflectance, albeit with less magnitude because the view angles of DESIS are limited between 0 and 20 degrees. To account for any potential spectral effects due to the sun/sensor geometries, we predict TOA reflectance spectra by running radiative transfer code with an input file from in situ nadir-view surface reflectance data collected at the site, under the assumption of a Lambertian surface, but for the exact sun/sensor geometries of the DESIS scenes of Table 1. That is, we adjust the radiative transfer codes’ sun/sensor angles to match those reported for DESIS scenes to reduce radiometric differences due to directionality of the atmospheric radiative transfer. Figure 17 shows MODTRAN angle-adjustment correction factors computed by dividing predicted TOA reflectance of in situ measurements at an off-nadir sensor geometry by that of the nadir sensor geometry.

To evaluate typical levels of variability that could be associated with various DESIS cases, we conducted a sensitivity study of the TOA reflectance for the RRV site using a method like that used to generate the uncertainty look-up table for RadCalNet [11]. The sensitivity study makes use of typical atmospheric conditions seen for the site to evaluate expected variations in TOA reflectance due to a range of atmospheric cases for the given sun/sensor geometries shown above for DESIS. These radiative transfer code view angle adjustments result in less than a 0.5% shift between 600 nm and 1000 nm and gradually increase to 2% toward the shorter wavelengths. The sensitivity studies of the TOA reflectance spectra indicate that the variations seen in the TOA reflectance are much smaller by almost an order of magnitude than the variations shown above. Obviously, there are the possibilities of extraordinary atmospheric situations that could create an atmosphere-dominated situation, but as shown with the curves in Figure 16, there would be clear spectrally dependent effects that are not seen in these results. Thus, as is typically the case for vicarious calibration sites such as RVUS, the variations seen above are dominated by surface reflectance effects.

6.2. Directional Correction Factor

Extending the realization that the dominant feature of the DESIS-based data set is from the surface effects leads to the possibility of deriving a directional reflectance correction for RVUS. Such a correction applied to the nadir-view TOA reflectance from RadCalNet would reduce uncertainties for the calibration of large-view-angle cases. The approach developed here is an empirical directional reflectance correction factor, $CF$, calculated by taking the ratio of DESIS-observed TOA reflectance spectra to predicted TOA reflectance spectra from a Lambertian case assumption. The atmospheric conditions used in the radiative transfer calculations are taken from RadCalNet-provided data sets but rely on the specific sun/sensor geometries of DESIS observations. The predicted TOA reflectance values will be very similar to the output from RadCalNet except that the small atmospheric effects due to the off-nadir DESIS view are included. Then, $CF$ is calculated using

$$CF=100\times {\displaystyle \frac{{\sum }_{\lambda =400\mathrm{n}\mathrm{m}}^{\lambda =900\mathrm{n}\mathrm{m}}\left(\frac{{\rho }_{DESIS}\left({\theta }_s,{\theta }_v\right)}{{\rho }_{RRV}\left({\theta }_s,{\theta }_v\right)}\right)}{N_{[400\mathrm{n}\mathrm{m},900\mathrm{n}\mathrm{m}]}}}$$

where ${\rho }_{DESIS}\left({\theta }_s,{\theta }_v\right)$ represents DESIS-observed TOA reflectance at sun angle ${\theta }_s$ and sensor angle ${\theta }_v$, ${\rho }_{RRV}\left({\theta }_s,{\theta }_v\right)$ represents RadCalNet-predicted TOA reflectance, and $N_{[400\mathrm{n}\mathrm{m},900\mathrm{n}\mathrm{m}]}$ represents the number of spectral samples between 400 nm and 900 nm. Figure 18 shows the results in which the absolute ratio spectra are averaged over the spectral regions from 400 nm to 900 nm to calculate the empirical directional correction factor. The 900 nm to 1000 nm spectral region is avoided because of the large sensitivity of results to water vapor absorption in that domain.

Results of Figure 18 show that view zenith angles of larger than 10 degrees often lead to significant BRDF correction factors. One clear advantage of studying directionality dependence of the surface from on-orbit platforms compared to that of goniometric studies is that the resultant BRDF factors are collected at a wider variety of sun angles and surface area, and therefore are less prone to a bias dedicated by limited sun angles of the date and specific spot at which goniometric data were collected. On the other hand, on-orbit studies are disadvantaged because of natural variability of surfaces over the years. In this case, the 15 correction factors shown in Figure 18 are for scenes captured at a wide variety of sun/sensor geometries, albeit over the course of five years. Although we see outliers in the data, the statistics of the results collectively point to a zenith angle dependency. For example, if we divide the sensor zenith angles of the combined 15 scenes to four equally spaced sensor zenith angle clusters of Figure 4A, we obtain 0 < θ_v < 5, 5 < θ_v < 10, 10 < θ_v < 15, and 15 < θ_v < 20. The magnitude of correction factors for those clusters has an increasing trend, showing that correction factors in the order of 5% could be expected when view angles are >10 degrees. Individual outliers are expected because DESIS-observed data are collected over five years and different surface conditions.

We fitted a modified Rahman–Pinty–Verstraete physical (mRPV) model [42,43] to the correction factors of the 15 DESIS scenes shown in Figure 18. The RPV model is a three-parameter nonlinear semiempirical model based on three terms: (i) a combination of sun/sensor angles, (ii) a phase function of scattering elements, and (iii) a term to consider the sun hot spot. For each wavelength, BRF is computed by

$$BRF=r{\left(\cos {\theta }_v\cos {\theta }_s\left(\cos {\theta }_v+\cos {\theta }_s\right)\right)}^{k-1}\left(1+{\displaystyle \frac{1-r}{1+G}}\right)e^{-b\cos \xi }$$

$$G=\sqrt{{\tan }^2{\theta }_v+{\tan }^2{\theta }_s-2{\tan }^2{\theta }_v{\tan }^2{\theta }_s\cos \mathsf{\Delta }\varphi }$$

$$\cos \xi =\cos {\theta }_v\cos {\theta }_s+\sin {\theta }_v\sin {\theta }_s\cos \mathsf{\Delta }\varphi$$

where r, b, and k are fitting parameters to be optimized for the surface under study. Here, we compute those paramours for each spectral band and sun angle by minimizing a cost function computed based on the differences between output of the above model and the DESIS-observed BRFs. Figure 19 shows results of the computed mRVP model at four wavelengths of 440 nm and 550 nm, 660 nm, and 860 nm and for sun angle ${\theta }_s={20}^{\circ }$ and ${\varphi }_s={180}^{\circ }$. These results represent directionality dependence of the surface reflectance of the RRV site over the five years of DESIS data, showing that the surface is more reflective in the back-reflection geometry and less reflective in the forward-reflected geometry. Our DESIS-based BRFs match well with those of the 2018 goniometric measurements reported in [24]. We can estimate the uncertainty of the BRFs based on the propagation of uncertainties of contributing effects to the above-described algorithm. Effects include uncertainty of DESIS-observed reflectance (5%) and uncertainties in the observation and illumination angle (0.2%). The uncertainty in the BRF values computed using a Monte Carlo simulation of the model is 5%.

The BRFs of Figure 19 may be used to generate relative differences in the BRF map of each wavelength to their respective nadir-view BRFs to compute relative BRFs (denoted by $BR{F}^{\text{'}}$) shown in Figure 20:

$$BR{F}^{\text{'}}\left({\theta }_v,{\varphi }_v,\lambda \right)={\displaystyle \frac{BRF\left({\theta }_v,{\varphi }_v,\lambda \right)-BRF\left(0,0,\lambda \right)}{BRF\left({\theta }_v,{\varphi }_v,\lambda \right)}}\times 100$$

The advantage of relative BRFs is in ease of interpretation. The relative BRFs are magnitudes of correction needed for a sun/sensor geometry relative to the nadir view. These results confirm that the RRV still has near-Lambertian properties for view angles less than ${20}^{\circ }$. Nevertheless, the results clearly show directionality dependence on the site’s surface reflectance and the potential benefit of using BRDF corrections for improved accuracy of the RadCalNet data of the site.

7. Conclusions

Recent vicarious calibration activities have led to a greater understanding of the behavior of key test sites that are excellent candidates for Fiducial Reference Measurements (FRMs). We need to study the correlations of the surface reflectance of such sites with time, solar angle geometry, view angle geometry, spectral stability, and atmospheric behavior. Multi-angle data permit a greater understanding of surface directional reflectance effects. Taking advantage of the orbital precession of the ISS, multi-angle radiometric observations of DESIS enabled us to study the directional reflectance effects of the Railroad Valley radiometric calibration site.

In light of that, we studied DESIS-observed TOA reflectance spectra collected from the RRV test site for changing sun/sensor geometries over five years of DESIS data. Short-term analyses of DESIS-observed TOA reflectance spectra limit the effects from long-term surface and atmospheric changes over the test site. The analyses showed that

• The surface reflectance of the RRV site depends on the illumination and observation geometries;
• The dependence of the surface reflectance to the illumination and observation geometries shows weak spectral dependence;
• Data with consistent scatter angles show excellent agreement.

We deduce that variations in the RRV’s surface reflectance as a function of sun/sensor geometries are primarily due to the change in scattering angle. Therefore, generating a model to correct the site’s surface reflectance would be straightforward. A directional reflectance correction at this site (e.g., the mRPV fits shown in Figure 19 and Figure 20) would improve the use of RadCalNet data at this site, enabling calibration and validation studies of Earth observation missions that view the Earth at greater off-nadir angles. We also observed that data collected at similar solar angles, but varying view sensor angles, provide more consistent data than that with varying solar angles and consistent sensor zeniths, because variations in solar angles of the observations of DESIS from the ISS orbit are larger than their variations in the view angles. The current work is somewhat limited by the small pointing range and low duty cycle of the DESIS collections. Additional studies would benefit from wider sampling of both illumination and observation geometries, to separate surface effects from atmospheric effects, and to determine uncertainty associated with the derived correction factors.

Although the results of this set of short-term studies point to directionality dependence of the surface reflectance of the site, the sparsity of data limits our ability to confirm how directionality factors change over time or seasonally. Data from other hyperspectral sensors such as EMIT, EnMAP, HISUI, CLARREO Pathfinder, and TRUTHS are needed to improve the understanding of the test sites. Data from EMIT and CLARREO Pathfinder will also be from the ISS, allowing for increased sampling of sun/sensor geometries. The high accuracy and spectral sampling of CLARREO and TRUTHS will be vital to allow the separation of surface effects from atmospheric effects, permitting the development of the needed models for the at-sensor radiance prediction. The results shown here also make it clear that well-calibrated and -characterized ground-based instrumentation and airborne sensors will also play a key role in supplementing the data from on-orbit sensors to improve assessments of test sites such as Railroad Valley as well as others for both radiometric calibration and validation.