2.1.

Synthetic Landscape Development

To leverage data collected from the ground-truth campaign of the Algodones Dunes during 2015, DIRSIG was used to study factors that need to be considered when performing intercalibration over pseudoinvariant sites such as Algodones. The region used to perform the intercalibration introduced in this work is a $5\mathrm{km}\times 5\mathrm{km}$ area with the center pixel located at 32°53‘06“N and 115°00‘57“W. Leveraging the airborne and in situ measurements taken during the field campaign, DIRSIG was used to develop a synthetic, but realistic, landscape of Algodones. NASA Goddard’s LiDAR, hyperspectral, and thermal (G-LiHT) sensor was extensively used to image the Algodones Dunes.¹³ The Goniometer of the RIT (GRIT) was also used to collect ground-truth data over the scene of interest.¹⁴ Details of these instruments can be found in the summary article for the field campaign.⁵ Figure 1(a) shows the region within Algodones used to create the simulated scene, whereas Fig. 1(b) shows the GRIT instrument taking measurements on the ground with the NASA G-LiHT flying overhead during the 2015 field campaign.

Fig. 1

(a) The $5\mathrm{km}\times 5\mathrm{km}$ region of interest in the Algodones Dunes used to create the synthetic landscape for DIRSIG. (b) The image shows the GRIT instrument and the NASA G-LiHT taking measurement of the dunes system during the 2015 field campaign.

The synthetic scene of Algodones was created using the “scene construction tool” built into DIRSIG.¹⁵ This tool ingests various forms of image data to describe the terrain. Figure 2 shows the different sources of data/inputs required by the DIRSIG tool to describe the simulated landscape. High-resolution imagery by the National Agricultural Imagery Program (NAIP) dataset was used to classify the landscape and to describe its texture.¹⁶ The 2-m digital elevation model provided by G-LiHT was used to facetize the geometric properties of the terrain. Hyperspectral data collected by GRIT during the field campaign were used to assign spectral features to each of the classes (defined by the NAIP data) within the synthetic landscape. The BRDF properties were described from the MODIS BRDF product,¹⁷ which uses the Ross-Li model.^18–21 It should be noted that this is not the most appropriate model to describe the BRDF properties for sand as this kernel-based model does not adequately capture the hot spot (or the backscatter direction).²² Future work will focus on incorporating actual BRDF measurements from the Algodones campaign into DIRSIG.

Fig. 2

The various data sources required by the DIRSIG construction tool to describe the synthetic landscape (Algodones Dunes).

The DIRSIG simulation environment provides users with the ability to create sensor models at various focal lengths, sensor geometries, spectral responses, and platform motions, and to view through various atmospheres. This allows the creation of any airborne or spaceborne sensors to facilitate intercalibration studies. Figure 3 shows a nadir-looking image of the Algodones scene that was developed with the “scene construction tool,” and the subsequent top of atmosphere (TOA) radiance for an arbitrary pixel when imaging with a hyperspectral sensor model. The Algodones Dunes was imaged at a ground sample distance (GSD) of 10 m using a visible and near-infrared (VNIR) hyperspectral sensor (101 bands) over the 0.4-to $1.00\text{-}\mu \mathrm{m}$ spectral range.

Fig. 3

(a) A nadir-looking image of the Algodones Dunes at a GSD of 10 m and (b) the subsequent average radiance of the scene in the VNIR.

2.2.

Digital Imaging and Remote Sensing Image Generation Verification

DIRSIG’s potential to be used for intercalibration studies was performed by imaging the synthetic Algodones scene using different spaceborne satellite systems and comparing the TOA radiance to actual sensor data. The ability of DIRSIG to estimate/model TOA radiance of spaceborne sensors is dependent on an accurate representation of the scene and the atmosphere. Recall that the material properties of the scene were measured during the field-campaign so only a characterization of the atmospheric conditions is required to simulate the TOA radiance.

DIRSIG employs the radiative transfer algorithm moderate spectral resolution atmospheric transmittance model,²³ or MODTRAN, to simulate atmospheric conditions. In this verification study, atmospheric conditions are estimated for a fixed Aqua-MODIS geometry ($\theta =188.58\mathrm{deg}$ and $\varphi =31.64\mathrm{deg}$) using a standard midlatitude summer profile and a desert aerosol for several visibilities, which was compiled into a look-up-table (LUT). Then, to characterize (or estimate) the atmospheric conditions of Algodones for DIRSIG, actual MODIS data are compared to the LUT over an entire year for visibilities ranging from 20 to 50 km in 1-km increments. Note that the purpose of this study is to assess DIRSIG’s ability to model at-sensor satellite radiance. So, a rigorous characterization of the atmosphere was not performed.

The LUT is shown in Fig. 4(a). The minimum percent difference (PD) between real and simulated data was used to estimate the atmospheric inputs that provided the best match. The minimum difference was observed at a visibility of 41 km. Figure 4(b) shows the radiance measurement between the Aqua-MODIS and its simulation for the best fit. The root-mean-square error (RMSE) and PD for band 3, band 4, and band 1 were $12.23{\mathrm{Wm}}^{-2}{\mu \mathrm{m}}^{-1}{\mathrm{sr}}^{-1}$ ($\mathrm{PD}=1.26\%$), $9.19{\mathrm{Wm}}^{-2}{\mu \mathrm{m}}^{-1}{\mathrm{sr}}^{-1}$ ($\mathrm{PD}=5.14\%$), and $14.70{\mathrm{Wm}}^{-2}{\mu \mathrm{m}}^{-1}{\mathrm{sr}}^{-1}$ ($\mathrm{PD}=8.81\%$), respectively. The observed residuals are reasonable considering the use of Ross-Li and the nature in which the atmosphere was estimated.

Fig. 4

(a) Aqua-MODIS with sensor azimuth and zenith of 188.58 deg and 31.64 deg, respectively, imaging the Algodones Dunes simulated over 2015 at visibilities ranging from 20 to 50 km. (b) The best possible match of the simulated data with real measurements by the Aqua-MODIS. These measurements were observed at a visibility of 41 km.

With an estimate of the atmosphere in place, the TOA radiance for two spaceborne sensors was simulated: Aqua-MODIS and Terra-MODIS. Specifically, bands 1, 4, and 3 of the MODIS sensors were simulated and compared to real cloud-free data. The MODIS sensors were simulated for four different view geometries from 2012 to 2015, see Table 1.

Table 1

The different sensor view geometries of Terra-MODIS, Aqua-MODIS, and Landsat-8 being simulated in DIRSIG. The MODIS sensors are simulated from 2012 to 2015, whereas Landsat-8 is simulated from 2013 to 2017. These simulated measurements are then compared to measurements taken by the real sensors over the Algodones Dunes.

Figure 5 compares the average radiance of the scene between the actual and simulated Terra-MODIS for band 3, band 4, and band 1 (the RGB bands) of MODIS. The results for four different view geometries of Aqua-MODIS are shown in Fig. 6. The RMSE and PD between the simulated and original data are summarized in Table 2. DIRSIG primarily captures the at-sensor variability for all the simulated view geometries of Terra and Aqua. An exception to this can be seen in Fig. 6, where the predicted radiance is significantly higher for a particular sensor geometry ($\theta =184.73\mathrm{deg}$, $\varphi =59.35\mathrm{deg}$) of Aqua-MODIS. Considering that this is the longest slant path, this is likely due to the nature in which the atmosphere was estimated. The PD error was also significantly higher (greater than 50%) for a few particular days. By inspection, it was determined that the TOA radiance from these datasets was affected by the presence of clouds within the scene, which was not modeled in DIRSIG. Most of the deviation between the simulated and original data occurred during the middle of the year, where the sun is typically at higher elevation. This is likely due to the limitation of the Ross-Li model to account for the hot spot effect. The hot spot or the opposition effect results in a sharp increase in reflectance in the backscatter direction.^22,24 The original MODIS data have higher radiance during the middle of the year due to the hot spot effect, which the model does not capture with the Ross-Li input. Overall, the PDs are within a reasonable range for data to support the sensitivity studies presented in Sec. 3. However, future work will focus on driving down these errors to support intercalibration studies (presented next) by better characterizing the atmosphere and the BRDF of the Algodones Dunes.

Fig. 5

The mean radiance calculated over the scene of interest in the Algodones Dunes using the Terra-MODIS sensor from 2012 to 2015, which were compared to measurements simulated by DIRSIG. The radiance measurements were compared for the RGB bands of MODIS for four different sensor positions. The view geometries being simulated for the MODIS sensor is illustrated in Table 1.

Fig. 6

The mean radiance calculated over the scene of interest in the Algodones Dunes using the Aqua-MODIS sensor from 2012 to 2015, which were compared to measurements simulated by DIRSIG. The radiance measurements were compared for the RGB bands of MODIS for four different sensor positions. The view geometries being simulated for the MODIS sensor is illustrated in Table 1.

Table 2

The RMSE and PD with the DIRSIG simulations.

2.3.

Intercalibration Study with Landsat-8

The two MODIS sensors in Sec. 2.2 were used to verify the DIRSIG model’s capability to adequately simulate imagery of the Algodones Dunes system. The feasibility of DIRSIG to perform intercalibration studies between two sensors is evaluated here by simulating Landsat-8 using the aforementioned estimates of the material properties and the atmosphere from the MODIS sensor. Bands 2, 3, and 4 of Landsat-8 were simulated and compared to real cloud-free data over the Algodones Dunes. Landsat-8 was simulated for two view geometries from 2013 to 2017 (the sensor angles are reported in Table 1).

Figure 7 compares the average at-sensor radiance between the Landsat-8 sensor and the simulation for two view geometries for band 2, band 3, and band 4. The RMSEs and PDs are summarized in Table 2. There is, again, good agreement between the original and simulated data. Some of the high PDs are due to the presence of clouds in the Landsat imagery, while other errors can be attributed to the estimates of the atmospheric and BRDF inputs in the DIRSIG model.

Fig. 7

The mean radiance calculated over the scene of interest in the Algodones Dunes using the Landsat-8 sensor from 2013 to 2017, which were compared to measurements simulated by DIRSIG. The radiance measurements were compared for the RGB bands of Landsat for its two different looks of the dunes system.

This study was designed to assess the feasibility of using DIRSIG as a transfer mechanism to intercalibrate one sensor with another. While the absolute errors are quite high to justify performing intercalibration of Landsat-8 with MODIS-Aqua as described here, future work will assess the sensitivity of the atmospheric and BRDF inputs in intercalibration accuracy.

3.1.

Temporal Study

Due to the nature of the intercalibration process, there will always be a temporal offset between sensors. To assess the impact of temporal offset on intercalibration accuracy, an Aqua-MODIS image was simulated for June 14, 2014 at 20:40 UTC over the Algodones Dunes using DIRSIG (note that this date/time represents an actual MODIS overpass). Next, the synthetic Algodones Dunes landscape was imaged from 13:40 to 04:10 UTC (sunrise to sunset) using DIRSIG. The difference in radiance between each simulated time and the nominal time was calculated to assess the impact of temporal offset of image acquisition on at-sensor radiance, which can be used to set the requirements for a temporal constraint for intercalibration opportunities.

The PD in the at-sensor radiance measurement between the nominal and test collection time for band 1, band 4, and band 3 of MODIS is shown in Fig. 8(a). The general trend in the plot indicates that the PD naturally increases with elapsed time from the nominal collect. However, there seems to be a small window of time, $\sim \pm 1\mathrm{h}$ of the original flight, where the PD is $\sim 5\%$ or less for all three bands. Note that this time window is dependent on the amount of intercalibration accuracy required by the user’s application. This $\pm 1\text{-}\mathrm{h}$ time frame can potentially be used as a temporal constraint for intercalibration opportunities of the Aqua-MODIS with sensors on-board the ISS, while imaging the dunes system. The Systems Tool Kit (STK) from Analytical Graphics, Inc. was used to track the orbit of the ISS and find intercalibration opportunities over the 36-day period (May 29, 2014 to July 3, 2014) based on the temporal constraint. The Aqua-MODIS sensor typically images the Algodones Dunes between 20:00 UTC-21:35 UTC every 1 to 2 days, and based on the $\pm 1\text{-}\mathrm{h}$ time constraint there were several days where intercalibration studies could be performed over the time period. Figure 8(b) shows the ISS groundtrack with the intercalibration opportunities over the 36-day period.

Fig. 8

(a) PD in the observed at-sensor radiance to the original MODIS-flight from sunrise to sunset. The PD is shown for bands 1, 3, and 4 of MODIS. The PD is relatively low $\pm 1\mathrm{h}$ of the initial flight time. (b) Intercalibration opportunities of Aqua-MODIS using a sensor, on board the ISS, over a 36-day period in June of 2014 based on the time constraint.

3.2.

View Geometry Study

The view the geometry of a sensor has a significant effect on the at-sensor radiance measurements. The ISS and the Aqua platforms are in dramatically different orbits, and the likelihood of SOLARIS and MODIS having the same view geometries is low. Note that SOLARIS does have a three-axis gimble to minimize view angle differences, but they will still exist operationally.¹⁰ To quantify the impact of view geometry on the intercalibration accuracy, DIRSIG was used to simulate the Algodones Dunes at various geometries over a hemisphere ($\theta :0\mathrm{deg}$ to 360 deg and $\varphi :0\mathrm{deg}$ to 80 deg). The different view geometries used to image the Algodones Dunes for Aqua-MODIS sensor are shown in Fig. 9.

Fig. 9

DIRSIG is used to image the Algodones Dunes at various different view geometries for the Aqua-MODIS sensor. This was used to study the effect view geometry can have on the intercalibration process.

The PD in radiance of each view geometry from the nominal MODIS view was calculated for band 1, band 3, and band 4 for DOY165 (June 14, 2014), DOY169 (June 18, 2014), DOY174 (June 23, 2014), and DOY178 (June 27, 2014), where DOY is day of the year. The PDs are represented as polar plots in Fig. 10. The nominal MODIS view is shown in red, while the orbit of the ISS looking at the scene of interest within the Algodones Dunes is represented by the white curves within the polar plots.

Fig. 10

The polar-plot illustrates the PD in the view geometry of the MODIS sensor in bands 3, 4, and 1 for four different days in June 2014 (DOY165, DOY169, DOY174, and DOY178).

The maximum difference due to the sensor position is $\sim 10\%$, with no error when they have the same view geometry. Like the temporal study, sensor geometry constraints can be placed based on the user’s application. There are a few different intercalibration opportunities for a sensor on-board the ISS (white curve) on each of the days shown in Fig. 10, where difference due to view geometry is low (e.g., less than 1%) enough that it would not have had a significant effect on the calibration procedure. For example, in DOY169, there seems to be $\sim 12$ calibration opportunities between the sensor on-board the ISS and the Aqua-MODIS sensor. The PD is less than 1% at those 12 different view geometries (white curve), indicating that this was a potentially good opportunity to perform intercalibration between the SOLARIS and Aqua-MODIS sensor. DOY174 represents a poor case for intercalibration, as the sensor on-board the ISS would have been in positions where the PD was well over 8% in band 3 of MODIS.

3.3.

Changing International Space Station Orbit

The intercalibration opportunities in the two different studies were predicted based on dates in 2014, where both the orbits of ISS and Aqua-MODIS were known. Although, the orbit of Aqua-MODIS remains constant at an altitude of 705 km, the same cannot be said about the ISS.^25,26 The ISS resides in a lower earth orbit and experiences constant aerodynamic drag from the atmosphere.^26,27 The orbit of the ISS is constantly decaying due to microgravity and requires periodic reboost to maintain the correct altitude.^26,27 The reboosting maneuver is typically performed using thruster firings by the attached Progress M spacecraft, which makes frequent trips to resupply the space station.²⁷ The altitude profile of the ISS in 2016 over the Algodones Dunes, measured using the STK software, is shown in Fig. 11. The change in altitude of the ISS can be seen over the 1-year period; the negative slope is due to the orbital decay caused by the aerodynamic drag, whereas the sharp positive slopes are a result of the reboosting maneuvers. However, the ISS height changes only 12 km over the 1-year period, and the effect it has on the view geometry of a sensor, such as MODIS, is almost negligible. For all the view geometries of both Aqua- and Terra-MODIS, the biggest change in sensor zenith was 1 deg due to change in height of the ISS. A change in sensor zenith of 1-deg affects the TOA radiance by $\sim 2{\mathrm{Wm}}^{-2}\mu {\mathrm{m}}^{-1}{\mathrm{sr}}^{-1}$, which is quite negligible. So, the unpredictable nature of the ISS orbit should not influence intercalibration.

Fig. 11

The mean height (km) of the ISS in 2016 over the Algodones Dunes. The changes in height are due to the orbital decay of the space station and subsequent reboost to maintain the orbit.