Spatial, Spectral, and Radiometric

Spatial, Spectral, and Radiometric Characterization of Libyan and Sonoran Desert Calibration Sites in Support of GOES-R Vicarious Calibration Monica Cook Chester F. Carlson Center For Imaging Science Rochester Institute of Technology Frank Padula1 , Dr. John Schott2 , Dr. Changyong Cao3 August 2010 1

Integrity Applications Incorporated Rochester Institute of Technology 3 NOAA/NESDIS/STAR

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ABSTRACT Instrument calibration and data quality are central to mission success and practical use of quantitative satellite imagery products. Pre-launch and onboard methods are better established, but the use of invariant sites in vicarious calibration is becoming more popular with the changing design and demands of new instruments. Characterizing and understanding the invariant sites being used is key to successful vicarious calibration. This study focused on two common desert sites, the Libyan and Sonoran deserts, and three different parameters of region of interest (ROI) selection: spatial uniformity, spectral variability, and radiometric effects related to variability in the atmosphere. The spatial variability was explored by varying the size and location of the calibration ROI, the spectral variability was investigated by considering both temporal spectral variability and changes in spectral signature over a small region, and the radiometric effects were explored by using MODTRAN to simulate atmospheric changes within realistic environmental ranges. These results suggest that the Libyan desert is large and uniformly textured with high spatial uniformity; the sonora desert had high spatial uniformity but only in small areas because of the proximity of ROIs to various other land cover conditions. Both sites has extremely high spectral uniformity and only showed changes in magnitude or brightness rather than spectral shape, which suggest changes in illumination rather than physical changes on the ground. The radiometric investigation was difficult to interpret because the results are extremely spectrally dependent and therefore band and sensor dependent. It appears that there is slightly more variability in the winter than in the summer for both sites and meteorological variability is likely to be the largest source of variability. Ultimately the goal was not to select an optimal site or season but rather gain a better understanding of parameters under consideration when selecting an ROI because having a well characterized and known standard can decrease uncertainties in vicarious calibration.

1. INTRODUCTION The Geostationary Operational Environmental Satellite (GOES) program is an operational program operating two satellites simultaneously with a third always in storage orbit in case of failure. This program is a national asset because it is utilized hourly for numerical weather prediction, severe weather tracking, and aviation flight and ship route planning among other application. Heritage and current GOES satellites have only 5 bands, one of which is a visual band; this visual band is utilized mostly for qualitative or subjective analysis. However, the next generation imager, the Advanced Baseline Imager (ABI) to be launched on GOES 15 in approximately 2015, will have 16 bands, 6 of which will be visible bands (http://cimss.ssec.wisc.edu/goes/abi/). This increase in spectral resolution increases the ability to generate quantitative products, and quantitative products increase the emphasis on calibration. GOES-R will have an onboard solar diffuser, which is a new concept for the GOES satellites, but will also utilize various forms of vicarious calibration for post-launch monitoring and verification. 1

Instrument calibration and data quality is central to mission success and practical use of satellite imagery. Leveraging sensor output requires relating digital counts to a meaningful scientific quantity. Calibration relates the output digital number to the radiance reaching the sensor; therefore, generating calibration coefficients relies on knowing the radiance falling on the collection aperture of the instrument. Access to the instrument and well-known light sources can provide very accurate calibration coefficients. This pre-launch calibration is generally performed using an integrating sphere to fill the collection aperture of the sensor with varying known radiance. By observing the output of the system at a known radiance, and assuming the system is sufficiently linear, a linear regression model for the output digital counts as a function of incident radiance is developed using Equation 1. In this expression, DC is the digital count output by the sensor, g is the sensor gain term, L is the incident radiance, and b is the sensor bias term.1 DC = gL + b

(1)

Pre-launch calibration is generally accepted with high confidence but even assuming perfect characterization, the instrument will be launched and placed in the space environment; therefore even the best pre-launch characterization needs to be verified post-launch. Most sensors also have some form of onboard calibration for instrument characterization post-launch. Two common methods are solar diffusers or on-board lamps. Both require careful pre-launch characterization of the calibration mechanism, either the bi-directional reflectance function of the diffuser or the emitted radiance of the lamps. Post launch, onboard calibration is accomplished by imaging the solar diffuser or illuminating on-board lamps. A second point is obtained by collecting an image with the aperture closed (without the onboard lamps) or imaging deep space so that the radiance reaching the sensor is effectively zero. This provides two points for a two-point linear calibration using Equation 1.1 Similar to pre-launch, concerns exist for onboard calibration accuracy and degradation. The detrimental effects to the satellite from the launch, as well as the harsh conditions of space and the solar environment, can cause the instruments to degrade in ways that are difficult to predict and measure.2 These changes need to be assessed, and the error in both this monitoring and the calibration need to be tracked. These concerns lead to the desire for methods of vicarious calibration. Vicarious calibration includes any method that does not rely on the instruments onboard the satellite.3 Various methods of cross-calibration and lunar observation would also be included in this category, but vicarious calibration most commonly refers to the use of ground sites for instrument calibration. This requires very little information from the instrument but in-depth knowledge of the ground site. Vicarious techniques transfer the unknown of the calibration process from the instrument to the ground; the instrument need only be stable and capturing imagery. These methods are often useful for satellites when the onboard calibrators have failed or exceeded desired uncertainty due to degradation and post-launch changes. Onboard calibration can also be expensive and subject to space constraints of the instrument. As the uncertainty and confidence in vicarious calibration is better understood, it can be considered in the design and fabrication of future satellites to change the requirements of onboard calibrators in the design phase.2 Ground truth measurements from the test site can be propagated through the atmosphere using radiative transfer codes to predict the top-of-atmosphere (TOA) radiance, which can then be propagated to the satellite to calibrate the sensor.2 However, collecting ground truth can be costly, labor intensive, and difficult to correspond with satellite overpass. Pseudo-invariant sites eliminate the need for simultaneous ground measurements because their rate of change is slow enough that their characteristics can be known within an acceptable uncertainty without taking ground truth measurements. This methodology assumes stability in the sites being imaged so reoccurring ground measurements are not needed. Vicarious calibration using pseudo-invariant sites has become increasingly accepted as a method to monitor long term trending of satellite sensors and, as sites become better characterized, this methodology is growing as a post-launch calibration technique. There are several common desired characteristics of an invariant site. To be considered an invariant site, the location must be temporally stable such that ground measurements or known variables at one time can 2

Figure 1. Libya 4 Desert Calibration Site.

Figure 2. Sonoran Desert Calibration Site.

be assumed within some uncertainty at a later time. Because calibration requires averaging the signal from various pixels, spatial uniformity is also of utmost importance. The degree of spatial uniformity changes with the pixel size of the sensor and number of desired pixels in the calibration site. A relatively high surface reflectance (generally greater than 0.3) is desirable in order to increase the signal to noise ratio. The site should have a known reflectance and be approximately Lambertian or have a well characterized BRDF so that uncertainties due to viewing geometries are reduced. A flat spectral reflectance is desirable to eliminate dependence of measurements on different spectral bands; there should be little or no vegetation in a pseudo-invariant site as this would fluctuate seasonally and create a more variable spectral curve. Finally, it is desirable that the atmosphere is known and well-behaved, so there are various requirements to maximize atmospheric and aerosol uniformity, including high altitude, far from the ocean, far from urban and industrial areas, and in a generally arid region.4 There are several common sites used regularly because of their established spatial uniformity and temporal stability. One common site for vicarious radiometric calibration is in the Libyan Desert in Africa, referred to as Libya 4 (WRS-2 path/row 181/40), shown in Figure 1. It is centered at +28.55◦ latitude, +23.39◦ longitude.5 It is variable in intensity and color and is textured with sand dunes at multiple scales5 but has well established spatial uniformity and temporal stability through long term trending and analysis of large areas.6 Libya 4 is 118 m above sea level and it is generally acceptable that the site has no vegetation, reasonable spatial, spectral, and temporal uniformity and minimal cloud cover.7 A second site is a location in the Sonoran desert close to the Mexico and United States border (WRS-2 path/row 38/38), shown in Figure 2. This site is not nearly as well understood but is of interest because of its location; because it is on the opposite side of the globe from the commonly used Libyan desert, it is viewed at different times and falls within different fields of view. Centered at +32.35◦ latitude, -114.65◦ longitude, this site is 37 m above sea level, arid, and flat.5 It is partially vegetated, but in a uniform manner, and there are some concerns about the effects of the temporal variability of soil moisture on calibration. This site is much less established and not yet well trusted as an invariant site for radiometric calibration. Because the Libyan desert has been used and is well established, several assumptions about the uniformity and usability of this site are made during calibration. These assumptions cannot yet be made for the Sonoran desert. By exploring the importance of the selection of various parameters during vicarious calibration, the goal of this study is to verify these assumptions in the Libyan desert and leverage the same techniques to

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explore similar parameters in the Sonoran desert.

2. BACKGROUND AND MOTIVATION Better instruments are constantly being designed and built, each with higher accuracy, better performance, and more demanding requirements than the last. Improved instruments require improved calibration and uncertainty. Current standards for calibration of various research satellites are, on average, around 5% absolute and 2% relative.8,9,10 Future instruments and various research fields are projecting and requiring even lower uncertainties. Climate change is just one example of a developing field in remote sensing that has extremely stringent calibration standard due to the nature of the changes it is attempting to measure.11 These advances create higher standards for instrument monitoring and in-flight calibration and verification. With the use of invariant sites, this equates to a better understanding of the site and its characteristics in order to understand the uncertainty associated with such calibrations. Various sites, such as the Libyan and Sonoran deserts, have been identified, but the region of interest (ROI) within the scene to use as the calibration target is not yet a consensus. Different ROI selections will optimize different desired characteristics of an invariant site; for example, one ROI might have increased spatial uniformity but also have greater atmospheric effects, while another could be more temporally stable, but less spatially uniform. Perhaps most pertinent is the expected behavior of the ROI. Errors in calibration arise when the site does not behave as expected, which makes the understanding and selection of the ROI, within some given uncertainty, extremely important. This leads to the principle question of what parameters in ROI selection effect or change the expected or known behaviors of the site.

2.1 Spatial Uniformity The spatial uniformity of an invariant site is extremely important. Because the band averaged radiance is used to calibrate the satellite, the uniformity of the ROI can effect results. The uncertainty from this attribute can not always be considered negligible when tighter calibration specifications are required or when new sites are explored. Calibration with the Libyan desert site has largely operated with assumptions of high spatial uniformity such that any spatial variability in the scene would not change the calibration results. Such assumptions cannot yet be made with the Sonoran desert site; the spatial uniformity of both were explored such that techniques to verify the uniformity could be legitimated with the Libyan site and then used to explore the spatial uniformity in Sonora. Specifically, the effects of ROI size and location on the spatial uniformity were investigated. If a completely uniform target was available, ROI size would be irrelevant. However, even when centered at the same coordinates, ROIs of different size can produce different results. This is important to consider for different sensor characteristics. Different pixels sizes or resolutions can require different ROI sizes, and the sensor scan lines and collection areas can affect shape and size. Even if unlimited by the sensor, there are tradeoffs between using different size ROIs. Based on natural landscapes, it is more likely that a flat region without texture would only extend over a small area. Increasing the size of the ROI only increases the likelihood of including changes in landscape and therefore variability. However, with a large enough ROI, some of this variability can be integrated. One distinct feature in a small area can act as an outlier and skew the band averaged spectra but a number of features over a large area will not significantly skew the effective integrated response spectra of that larger target. The location of the ROI is also important. This refers not only to choosing the general area within the scene but also the accuracy with which this area needs to be specified and selected. If a good site size is established, this area will occupy a different number of pixels on different sensors. In general, the ROI location within the scene is well defined. What is unknown is the importance of the accuracy of this location (i.e. spatial registration between images). This initial investigation into spatial uniformity has the potential to raise a number of sensor or site specific questions. If the size of the ROI is relevant or the spatial variability in significantly changed with shifts in ROI location, further investigation and error propagation of uncertainty on a sensor specific basis

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would be necessary. However, if the the spatial uniformity of the site is well behaved, or at the very least well understood, it becomes less important to investigate on a sensor specific basis and makes it easier to use these sites for multiple calibration purposes. The spatial uniformity study investigated parameters that are nominally within user control due to the ability to select the ROI. Although the user does not have control of the spectral variability, discussed in the next section, it is still a parameter of importance in ROI selection and needs to be well understood.

2.2 Spectral Variability Invariant sites should generally have high and well known reflectance curves that are ideally flat and temporally stable. The high reflectance increases the signal to noise ratio and the flat spectral reflectance reduces band dependence. Although a band averaged spectra is used for calibration, a flat spectral dependence is desirable in order to reduce effects from the sensor specific spectral response functions or any on-orbit shifts of the spectral response functions. The spectral characteristics of the Libyan desert are well characterized. It is known that the spectral characteristics of the Sonoran desert are different but they are not as well understood or established. Specifically, the temporal spectral characteristics and the spectral variability within a small region were explored for both sites. For the Libyan desert in particular, the long term stability of calibration sites has been investigated and established. However, spectral variations over a one year cycle are also important. Seasonal cycles can affect the calibration results and modify the desert surface in complex ways. This creates uncertainties in the temporal stability that pose challenges to the overall uncertainty budget. Investigating the seasonal changes characterizes the spectral variability throughout the year. If there is significant variability, this can lead to further investigation into its origin. Changes in the spectral curve could indicate actual changes on the ground while variation in magnitude could be attributed to the bi-directional reflectance function (BRDF) or shadowing effects. The spectral variation within a small area is also important. It is accepted that the Libyan desert site has little vegetation and a constant spectral signature; this will be quantified by investigating the mean spectra. There are questions of sparse vegetation and soil moisture effects in the Sonoran desert site. It is important to determine how much the spectral signatures of pixels within a small neighborhood vary and if there are different materials on the ground or only illuminations changes. The spectral variability study investigated the spectral vectors of the calibration sites, but is closely tied to atmospheric effects due to the changes that can be seen in the spectral signature form changes in illumination. The following introduces the motivations of investigating radiometric effects, which in this study are largely due to the atmosphere.

2.3 Radiometric Effects Recall that ideal characteristics of desert sites include high altitude, far from the ocean, far from urban areas, and an in arid region. This criteria is primarily to reduce the atmospheric effects on the target site. The atmospheric effects on sensor derived data have been well documented but are hard to characterize in practice due to the remote locations of the desert sites; this can introduce uncertainties in the calibration. Therefore, atmospheric stability in a calibration region is important. It is possible, for example, that seasonal changes are atmospheric rather than physical changes on the ground. Predominant factors in atmospheric variability include aerosol number density, aerosol type, water vapor content and wind speed. The radiometric stability is not well understood for the Libyan or Sonoran desert; the goal with either site is to determine if the atmospheric variability is large enough to alter the calibration results. If so, the atmospheric parameters would need to be measured and the atmosphere modeled and accounted for in order to accurately calibrate. This may lead to an optimal time or location for calibration based on radiometric variability. This section addressed the importance of and motivation behind exploring each of the above parameters of ROI selection. The next section details the methodology and approach to these investigations. 5

Site WRS-2 Path/Row Dates of Acquisition

Libya 4 181/40 19 February 2004 12 July 2004 10 July 2009 19 February 2010

Sonora 038/038 9 February 2004 2 July 2004 1 August 2009 25 February 2010

Table 1. Summary of Landsat Images downloaded from the USGS Earth Explorer website.12

Site Dates of Acquisition

Libya 4 2 February 2009 20 April 2009 31 May 2009 24 July 2009 2 October 2009 5 December 2009

Sonora 18 May 2002 18 January 2005 17 November 2006

Table 2. Summary of Hyperion Images downloaded from the USGS Earth Explorer website.12

3. METHODOLOGY Although this study explores three separate aspects of ROI selection, there were various preparatory steps and analysis. This section details the methods for obtaining the necessary imagery, the data formatting and preprocessing and then the three step approach employed to investigate the spatial, spectral and radiometric variability.

3.1 Obtaining Imagery Landsat imagery was chosen for the spatial uniformity study and Hyperion imagery was used for the spectral variability study. Landsat imagery was leveraged for the spatial study because it is readily available and has the spatial and temporal coverage necessary for this study. In order to ensure the best results for the spatial uniformity study, images were chosen for two different years, five years apart, in both deep winter and deep summer, for each site. Also, in order to allow for comparison between the Libyan and Sonoran desert sites, images were chosen such that the dates of acquisition between the two sites were as coincident as possible, providing eight Landsat images to process and analyze [Table 1]. Hyperspectral imagery was used for the spectral study. Hyperion imagery was chosen because of it has high spectral resolution. However, note that Hyperion has significantly smaller spatial and temporal coverage with limited data availability that restricted performed analysis; this needed to be accounted for during the spectral processing and analysis. While Landsat has a repeat cycle of every 16 days, Hyperion only collects when tasked. Because the Libyan desert is a more commonly used calibration site, a number of Hyperion images are available in similar locations. To assess spectral characteristics temporally for each site, one cloud free image was chosen over the same area at a two month sampling rate; this ideally captured all seasonal scenarios. Unfortunately, Hyperion imagery for the Sonoran site was extremely limited. Because the spectral characteristics of the site were being considered, cloud free imagery was extremely important. Only three images, each in slightly different locations, were available in proximity to the calibration sites. These three images were processed in order to analyze the spectral behavior of the scene as best as possible [Table 2].

3.2 Top-Of-Atmosphere Reflectance Both Landsat and Hyperion images were obtained in digital number format. The images needed to be converted from digital number to radiance. Converting from digital number to radiance relies on the already 6

established calibration coefficients of the instrument. Landsat images are preprocessed and distributed in calibrated digital number; conversion from calibrated digital number to at sensor radiance required the rescaling factors, available in the metadata supplied with each image. The conversion from calibrated digital number, Qcal , to at sensor radiance, Lλ , for Landsat imagery is

Lλ =

! LM AXλ − LM INλ Qcal + LM INλ Qcalmax

(2)

where Lλ is the spectral radiance at the sensor aperture, given in Wm−2 sr−1 µm−1 , Qcal is the calibrated digital number, and Qcalmax is the maximum calibrated digital number, which corresponds to LMAXλ , the maximum spectral radiance in the images. Similarly, LMINλ is the minimum spectral radiance that is scaled to Qcalmin .13 The conversion from digital number to radiance for Hyperion is a simple scale factor. However, Hyperion is composed of two overlapping focal plane arrays; each array has a different scale factor and therefore the calibration for Hyperion is wavelength or band number dependent. The visible/near-infrared (VNIR) array has a scale factor of 40, and the short-wave infrared array has a scale factor of 80, as shown here VNIR Lλ =

DN DN , SWIR Lλ = 40 80

(3)

where Lλ is the at sensor radiance given in Wm−2 sr−1 µm−1 and DN is the digital number.14 For the spatial and spectral aspects of this study, top-of-atmosphere (TOA) reflectance was used. Working in TOA reflectance is generally used when considering atmospheric effects to be negligible because they are not accounted for. In order to obtain planetary reflectance values, atmospheric data and radiative transfer codes would need to be used to account for atmospheric effects. Major atmospheric variability over such a small area is unlikely, especially considering that largelycloud free imagery was chosen, so this study was performed using TOA reflectance, keeping in mind that the atmosphere was a possible source of variability in the results. TOA reflectnace, ρ, is the unitless reflectance at, effectively, the top of the atmosphere, calculated as ρ=

π·Lλ · d2 ESU Nλ · cosθs

(4)

where Lλ is the at sensor radiance, d is the Earth to sun distance in astronomical units, calculated from the julian day of the year that the image was captured, ESUNλ is the sensor specific mean solar exoatmospheric irradiance, and θs is the solar zenith angle in degrees. The at-sensor radiance is obtained from the above calibration equations. For both Landsat and Hyperion, the Earth to sun distance in astronomical units is interpolated from the set of points given in Table 3. The julian day of acquisition can be obtained from the metadata of each image. The exoatmospheric solar irradiances for Landsat were found in Chander and Markham’s paper in IEEE Transactions of Geoscience and Remote Sensing13 and the values for Hyperion were found on the USGS EO-1 Hyperion website.14 Finally, the solar elevation angle at acquisition is given in the image metadata, and from this the solar zenith angle can be calculated as shown in Equation 5. The data used is key to the validity and ability to perform any study. Obtaing imagery and preprocessing were important steps in order to assure the soundness of the images and only after this could the first investigation, exploring spatial uniformity, be outlined. θs = 90 − solar elevation angle

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(5)

JD 1 15 32 46 60

Dist 0.9832 0.9836 0.9853 0.9878 0.9909

JD 74 91 106 121 135

Dist 0.9945 0.9993 1.0033 1.0076 1.0109

JD 152 166 182 196 213

Dist 1.0140 1.0158 1.0167 1.0165 1.0149

JD 227 242 258 274 288

Dist 1.0128 1.0092 1.0057 1.0011 0.9972

JD 305 319 335 349 365

Dist 0.9925 0.9892 0.9860 0.9843 0.9833

Table 3. Earth-Sun Distances in Astronomical Units, JD = Julian Day

Location Area (km) Area (pixels) Center Lat/Lon

Libya 4 90 km x 90 km 3000 x 3000 28.9◦ N, 23.8◦ E

Libya 4 45 km x 29 km 1500 x 967 28.59◦ N, 23.5◦ E

Sonora 15 km x 15 km 500 x 500 32.35◦ N, 144.65◦ W

Sonora 5 km x 5 km 167 x 167 31.93◦ N, 114.39◦ W

Table 4. Details of the four typical calibration sites.

3.3 Spatial Uniformity As discussed in Section 2, methods and parameters for ROI selection is the principle motivation behind investigating these particular characteristics of invariant desert sites. Both deserts are already used in some capacity; therefore, investigating typical calibration sites produces more useful and meaningful results. A literature review was conducted and various sources were consulted to determine common ROI locations. Each was represented by a typical large and small ROI. The desert coverage and useable area in the Landsat scene containing Libya 4 is expansive. A bigger ROI covering a large portion of the scene can be used such that scene variations are integrated in the effective response, or a smaller ROI can be placed over a smoother area. Typically, a large 90 km x 90 km ROI is selected in the center of the scene.15 However, a smaller 45 km x 29 km ROI in the southwest corner is also used.3 The available area of the desert in the Landsat scene containing the Sonora desert calibration site is much smaller so ROI selection is limited; even the larger ROI is smaller than the smaller ROI in Libya. There is an extremely smooth area in the northwest corner of the scene, conveniently located near roads and a civilized area, which allows for easier access to ground measurements. However, the proximity to land cover other than desert limits the ability to vary size and location. The larger typical site in the Sonora desert is 15 km x 15 km in this very smooth area5 and the smaller typical ROI, which is 5 km x 5 km, is in a more remote area of the desert. Table 4 gives details for all four typical ROIs. The typical ROIs discussed above were used as the common or “truth” sites around which the size and location of the ROI was varied to explore the importance of such parameters in ROI selection. The frist step in the analysis was to determine how the size and location should be varied in order to provide meaningful and useful results. Because the sizes of the typical ROIs were so varied, the variations had to be specific to that ROI. Four sizes in equal increments were chosen based on each typical ROI as shown schematically in Figure 3. Whether the variations were larger or smaller depended on the size of the typical ROI. Figure 4 shows the four different sizes, summarized in the table below the images, for each typical ROI in the Libyan desert and their location in the Landsat scene. Figure 5 gives the same information for the Sonoran desert. In Figures 4 and 5, the rectangle shows the typical ROI and the circles are located at the corners of the size-varied ROIs, corresponding in color to the table below. The TOA reflectance image was subset via each ROI, such that there were four separate images, varying in size, for each ROI for each image. Statistics for each of these subsets were considered, including mean vectors, standard deviation per band, covariance matrices, and percent error to the typical ROI. To explore how the spatial uniformity changed as the ROI size changed, the standard deviation of each size ROI of each band was focused on. In a perfectly uniform ROI, all pixels would have the mean spectral vector. The standard deviation gives a measure, per band, of how the pixels vary from this mean and therefore is a good metric to understand changes in spatial uniformity. 8

Figure 3. Method for varying ROI size; each size was compared to the typical.

Figure 4. ROI Size Variability in the Libyan Desert.

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Figure 5. ROI Size Variability in the Sonoran Desert.

Figure 6. Method for varying ROI location; each shifted ROI was compared to the typical

The spatial variability as the location of the ROI changed was also explored. This is important for considering geolocational requirements as well as the amount of care that needs to be taken in selecting the ROI. These variations are very largely dependent on sensor resolution. A one pixel error on one sensor can equal a 5 pixel error on another. Therefore, shifts of various sizes were considered to encompass the footprints of multiple sensors. The typical ROI size in its original location was shifted north, east, southeast, south, west, and northwest, as shown schematically in Figure 6. Each typical ROI was shifted 3, 5, 10 and 20 pixels in direction, as well as some larger distance shift based on the typical ROI size. The pixel shifts are typical or reasonable errors in selection or geolocational accuracy and the largest distance shift was included for low resolution sensors and as an extremely limit for each site. This is summarized in Table 5. The TOA reflectance image was subset via each ROI such that there are six separate images to be analyzed for each ROI in each image. The same statistics were calculated for these subsets, including mean vectors, standard deviations per band, covariance matrices, and percent error to the typical ROI. For the locational study, the percent error in standard deviation between the shifted subset and the typical ROI was calculated per band and used as a metric to consider the importance of ROI locational accuracy. A modified percent error, as shown in Equation 6, was used without absolute value. It is important to note that standard deviations, rather than mean values, were used. Whether the number is positive or negative indicates if the standard deviation 10

Site Libya 4 (90 km x 90 km) Libya 4 (45 km x 29 km) Sonora (15 km x 15 km) Sonora (5 km x 5 km)

Shift (km) 0.09 (3 pix) 0.09 (3 pix) 0.09 (3 pix) 0.09 (3 pix)




Shift (km) 10 (333 pix) 5 (167 pix) 3 (100 pix) 1 (33 pix)

Table 5. Shifts for each ROI.

increased or decreased, which shows whether the spatial uniformity decreased or increased. %error =

σexperimental − σactual σactual

(6)

Currently, calibration corrections, such as BRDF corrections or atmospheric compensation, are not better than within 10% of the standard deviation of the site. This is a broad generalization of current methods for calibration improvement. The assumption for this study is that if locational changes do not improve or degrade the spatial uniformity by more than 10%, the change is small enough that it will not affect the calibration results within the achievable uncertainty. Therefore, as the metric of comparison for this investigation, when the percent error in standard deviation between the shifted and typical ROI was considered, 10% was used as a threshold and changes less than 10% were considered negligible. For example, if the standard deviation of a scene is 0.04, changes of less than 0.004 will not change calibration within current achievable uncertainties. This is approximately equivalent to changes between one percent or tenths of a percent in reflectance units (mean values).

3.4 Spectral Variability Hyperion is a pushbroom sensor collecting imagery in narrower swath widths than the Landsat 5 thematic mapper. New ROIs were selected in the coincident regions of the Hyperion and Landsat scenes due to data availability. In the Libyan desert, the Hyperion ROIs are smaller than but fell within the area of the typical ROIs [Table 4]. However, with the limited imagery available in the Sonoran desert, some ROIs had to be selected in the nearest possible adjacent region, and this needs to be considered when analyzing the results. Figure 7 outlines the Hyperion image, the typical ROI, and the selected Hyperion ROI overlaid on the Landsat scene in the Libyan desert. The almost vertical lines represent the boundaries of the Hyperion collect, the circles are located at the corners of the typical Landsat ROI, and the rectangles are the newly selected Hyperion ROIs. Figure 8 shows the same information for the Sonoran desert. The temporal spectral stability could only be evaluated for the Libyan desert due to data availability. The Hyperion imagery was subset based on the newly selected ROIs and the mean spectra for each ROI was calculated and plotted for each of the six images covering one full year. The spectral angle, as shown in equation 7, between each month’s spectral vector and the July spectral vector was also calculated for both ROIs in the Libyan desert. The spectral angle quantifies the separation of the vectors in spectral space and is invariable to brightness or magnitude. As shown schematically in Figure 9, vectors b, c, and d have different magnitudes but the same spectral angle separation to vector a. Vectors c and e have the same magnitude but different spectral angles to a. T a x θ = arccos = arccos(aTu · xu ) ||a|| ||x||

(7)

All of the Libyan and Sonoran images were subset via the spectral ROIs and each ROI was classified into five classes. A quick study was completed to determine an acceptable number of classes within an ROI. The mean spectral vector of each class for each image was plotted to investigate differences in brightness and magnitude. It was determined that a more quantitative analysis was necessary in order to draw further conclusions about the spectral variability within the scene. The spectral angle, expressed in Equation 7, 11

Figure 7. Hyperion ROIs in Libyan desert.

Figure 8. Hyperion ROIs in Sonoran desert.

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Figure 9. Schematics representation of spectral angle.

between each pixel vector and the mean spectral vector was calculated to investigate spectral variability within this small scene. For each image, the fraction of the image within some specified threshold of the mean spectral vector was calculated. A brief literature review was conducted to determine a reasonable threshold for spectral angle when determining significant spectral separability. This was applied to the temporal stability study and variability within the ROI. Spectral angle mapper is a common method for classification in which pixels are assigned to classes based on the spectral angle, and when the spectral angle is greater than some threshold, the pixels are unclassified. In one study for burnt area mapping, thresholds of 0.1, 0.2, 0.3, 0.4 and 0.5 radians were explored as a threshold and the study settled on 0.4 radians for optimal results for classification.16 This analysis requires tighter specification than a classification analysis; 0.1 radians (approximately 5 degrees) is a tight but reasonable threshold and therefore was used as the threshold for spectral variability in this study.

3.5 Radiometric Effects Radiative transfer codes, such as MODTRAN, are a generally accepted method of predicting TOA radiance, with known limitations.17 A solution is obtained every time the model is run, but the accuracy of the results depend on the accuracy of the input, and therefore correct parameters are extremely important.1 Accurate modeling requires temperature and water vapor distributions at specific times and locations and known surface properties for the ROI in question.18 Atmospheric radiometric effects were modeled using MODTRAN to obtain TOA radiance for each site at two different times of year; changes in radiance were analyzed as a single input variable was modified through a realistic range.19 Various inputs to MODTRAN needed to be obtained in order to obtain accurate output specific to each site for winter and summer. Pressure, temperature, and dew point temperature specific to the latitude and longitude center of each site was obtained to an altitude of 35 km from the Upper Air Gridded Climatology database.20 Data for each site for two different Julian days, one winter and one summer, were obtained. These were supplemented with MODTRAN’s typical mid-latitude summer to reach an altitude of 100 km. These data for Libya are shown in Figure 10 and for Sonora in Figure 11. Pressure, temperature, and dew point temperature were inputs to MODTRAN for the user defined atmosphere. The surface albedo for each site was also input. This was estimated by averaging the mean spectral vector in TOA reflectance for various Hyperion images at each site. TOA reflectance was used as a best estimator for surface albedo; this was an improvement, in sampling and accuracy, to the pre-defined MODTRAN desert albedo but it is important to note that this TOA reflectance value is still contaminated by the atmosphere. Besides the user defined atmosphere and site specific albedo, the altitude, Julian day of collection, latitude, longitude, and Greenwich Mean Time of collection were specified for Libya and Sonora for the two different seasons. These inputs are summarized in Table 6. In Figure 12, the black line is a radiance spectra from a Hyperion ROI in the Libyan desert collected in February, and the red line is the radiance spectra output by MODTRAN for the Libyan winter atmosphere with a desert aerosol, confirming the validity of the chosen inputs.

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Figure 10. Typical summer and winter atmospheres for the Libyan desert, derived from the Upper Air Gridded Climatology database and MODTRAN’s stantdard mid-latitude summer atmosphere.

Site Libya Libya Sonora Sonora

Season Winter Summer Winter Summer

Altitude 0.118 km 0.118 km 0.037 km 0.037 km

Figure 11. Typical summer and winter atmospheres for the Sonoran desert, derived from the Upper Air Gridded Climatology database and MODTRAN’s stantdard midlatitude summer atmosphere.

Julian Day 50 200 50 200

Lat, Lon 28.9◦ N, 336.2 ◦ W 28.9◦ N, 336.2 ◦ W 32.35◦ N, 114.65 ◦ W 32.35◦ N, 114.65 ◦ W

Time 8.35 8.35 18.00 18.00

Table 6. Inputs to MODTRAN for each site and season.

Figure 12. Comparing Hyperion derived and MODTRAN output at sensor radiance.

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Variable Aerosol Type Aerosol Number Density (Visibility [km]) Water Vapor [%] WIndspeed [m/s] ([mph])

Range Troposphere, Desert, Rural 1.0 to 50.0 by 5.0 0.5 to 1.5 by 0.1 0.0 (0.0 ) to 17.881 (40) by 2.2 (5)

Typical Desert Default Default 0 mph

Table 7. Realistic ranges for MODTRAN variables .

In order to determine the variability in the atmosphere over each site, aerosol type, aerosol number density, water vapor, and windspeed were varied across the realistic range. To develop a basis for comparison, a “typical” atmosphere for each site and season was developed by using the inputs in Table 6 and the typical values described in Table 7. Aerosol number density is varied in MODTRAN by changing the visibilty. In order to consolidate output and generate results for meaningful analysis, each variable was modified individually within the typical atmosphere. Aerosol type was only modified for no wind with the default water vapor and visibility; water vapor was only modified for the desert aerosol with no wind and default visibility; visibility was only modified with the desert aerosol with no wind and the default water vapor; and windspeed was only modified for the desert aerosol with default water vapor and visibility. Further analysis would confound variable effects and would sometimes be outside the scope of a realistic situation for these sites. For example, it would be uninformative for the Libyan and Sonoran desert to vary water vapor over the rural aerosol type. The default water vapor is dependent on input parameters so it is different for each site and season; these values are included for reference in Appendix D in Table 22. It was not only important to determine what variables were of interest, but also what a realistic range of those variables would be. Of the available aerosol types in MODTRAN, any that might pertain to the calibration sites, due to atmospheric conditions (troposphere and desert) or proximity (rural), were investigated. The range of visibility was determined by considering the extreme circumstances. The default visibility for the tropospheric aerosol in MODTRAN is 50 km; this was used as the upper limit. Various desert conditions, such as suspended dust, rising dust, and a dust storm, all create conditions of low visibility. Although there are differing definitions, visibility less than 1 km is generally considered to be a dust storm, so this was used as the lower limit.21 The water vapor column, as it is referred to in MODTRAN, is determined by the various atmospheric inputs. However, this can be modified relatively using a simple scalar, rather than attempting to input a range of absolute values. Therefore, the water vapor was modified from 50% of the default to 150% of the deafult. Finally, windspeed was also determined using desert meteorological conditions. Using no wind as an obvious lower limit, the upper limit was determined by the condition during a dust storm. During a dust storm, windspeeds generally range from 10.8 m/s to 20.7 m/s; this gives an upper limits of roughly 40 mph. Table 7 summarizes the ranges for each variable. MODTRAN was run at 0.01 µm resolution for the spectral response range of the Hyperion sensor. Radiance vs. wavelength was considered for each iteration through the realistic ranges. For these high resolution results, bands that would be removed in an atmospheric correction algorithm were set to zero in order to clarify results.22 The percent change to the typical output for that site and season was calculated and computed and percent error vs. wavelength was plotted for each iteration on a single plot. This shows the variability in the sensor-reaching radiance due to changes in atmosphere caused by a single variable. The high resolution MODTRAN results were also convolved with the simulated GOES-R ABI spectral response functions and these results were analyzed by radiance and percent change to the typical. This section addressed the methods used to investigate the three major aspects of ROI selection. The following section provides the visual and numerical results of this analysis.

4. RESULTS 4.1 Spatial Uniformity The spatial uniformity was investigated on a per band basis. Therefore, all plots concerning the spatial uniformity have six separate lines, each representing a different visible or near infrared band in Landsat 15

Figure 13. Legend for Landsat bands in spatial plots.

Figure 14. Variability in standard deviation for different size ROIs in the center of the Libyan desert for an image captured in February.

Figure 15. Variability in standard deviation for different size ROIs in the center of the Libyan desert for an image captured in July.

imagery. A legend for all plots in this section is shown in Figure 13. 4.1.1 ROI Size Although various statistics were calculated for each different size ROI, standard deviation was used a measure of the spatial variability. The larger the standard deviation, the further the pixels in the image are spread from the mean. Figures 14 and 15 show the results for the variation in size for the typical 90 km x 90 km ROI in the center of the Libyan desert; Figure 14 was an image captured in February (2010) and Figure 15 was an image captured in July (2009). There are four points on each line, one for each different ROI size including the typical. The different lines on the plot represent the different bands in the Landsat image, as explained in the legend in Figure 13. A flat line in Figures 14 and 15 signifies that there was no change in variability as the size of the ROI was changed. The flatter the line, the more stable the spatial variability around that typical ROI. Figures 16 and 17 show results in the same images for the variation in size around the typical 45 km x 29 km ROI in the southwest area of the Libyan desert. Numerical values for the results represented in Figures 14 and 16 are given in Appendix A in Table 10, and numerical values for the results represented in Figures 15 and 17 are given in Appendix A in Table 11. For all of the ROIs in both the Libyan and Sonoran deserts, the variability in the summer (July or August) demonstrated less variability than the winter (February). It is important to realize that the reflectance is much greater in the summer months and for some images, a large number of pixels, or even entire bands, are saturated. One example is band 5 in Figure 15; these values, as shown in Table 11 are zero or do not exist because all of the pixels are saturated. These seasonal effects are explored further in the radiometric study. The Libyan desert was shown to be very insensitive to changes in ROI size. This is reinforced by visually analyzing the image; the Libyan desert, while textured, is expansively uniform. There is an extremely large

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Figure 16. Variability in standard deviation for different size ROIs in the southwest of the Libyan desert for an image captured in February.

Figure 17. Variability in standard deviation for different size ROIs in the southwest of the Libyan desert for an image captured in July.

Figure 18. Variability in standard deviation for different size ROIs in the northwest of the Sonoran desert for an image captured in February.

Figure 19. Variability in standard deviation for different size ROIs in the northwest of the Sonoran desert for an image captured in August.

area with similar features. While there are smaller, more distinct features within the scene, the integrated effect for the larger ROI tends to reduce the sensitivity of spatial uniformity with size variability. Figures 18 and 19 show the results for the variation in size for the typical 15 km x 15 km ROI in the northwest area of the Sonoran desert for images captured in February (2010) and August (2009) respectively. Figures 20 and 21 show results in the same images for variation in size for the typical 5 km x 5 km ROI in the center of the Sonoran desert. Numerical values for the results represented in Figures 18 and 20 are given in Appendix A in Table 12, and numerical values for the results represented in Figures 19 and 21 are given in Appendix A in Table 13. For smaller ROIs in the northwest area of the Sonoran desert, the standard deviation or spatial variability is smaller than that in the Libyan desert. By studying the image, it can be seen that this area is extremely smooth, without the inherent texture in Libya or other parts of the Sonoran desert, but it is only smooth in a small area. Increasing the size of this ROI greatly increases the standard deviation; this is not due to changing characteristics of the desert but rather the inclusion of different types of land cover, such as roads or farming areas. For the ROI in the center area of the Sonoran desert, the standard deviation increases just slightly as size increases, and then levels off. This area is more similar to the Libyan desert than the other ROI in the 17

Figure 20. Variability in standard deviation for different size ROIs in the center of the Sonoran desert for an image captured in February.

Figure 21. Variability in standard deviation for different size ROIs in the center of the Sonoran desert for an image captured in August.

Sonoran desert; the area is textured but increasing to a large enough size can integrate the effects of these features. Libya is uniformly textured, and very large, so changing ROI size has little effect on the spatial variability of the ROI. Sonora is a more variable scene that has some areas with little texture and low spatial variability, but these regions are small and therefore selection of the ROI size becomes important. The same analysis was also performed on images acquired at corresponding times of the year in 2004 to verify that results were not dependent on individual image anaomolies or outliers and not significantly temporally dependent. Similar trends and results were found and therefore were not included to reduce redundancy. 4.1.2 ROI Location To study the importance of ROI location, a modified percent error, as shown in Equation 6, was used to determine how much the standard deviation changed when the area of which the typical ROI was shifted in various directions. Figures 22, 23, 24, 25, and 26 show the results for the 90 km x 90 km ROI in the middle of the Libyan desert for shifts of 3, 5, 10, 20 and 333 pixels respectively for an image captured in February (2010). The lines in these plots are described by the legend in Figure 13. A positive percent error represents an increase in standard deviation, and there increased spatial variability; a negative percent error represents a decrease in standard deviation and therefore decreased spatial variability. A flat line through zero would represent an area in which changing the location of the ROI has no affect on the spatial variability. There are two red lines on each plot at 10% and -10% to illustrate the thresholds for “significant changes” in spatial variability as discussed in Section 3.3. If all changes in standard deviation were below threshold, the plot ranges from 10% to -10% to show the relative magnitude of changes in that particular image. If the percent error in standard deviation varied beyond this range, the plot was modified to encapsulate the complete range of results, with the red lines showing the limits of the threshold. Figures 27, 28, 29, 30, and 31 show the results for the 45 km x 29 km ROI in the southwest of the Libyan desert for shifts of 3, 5, 10, 20 and 167 pixels respectively for an image captured in February (2010). For reference, the numerical values for Figures 22, 23, 24, 25, and 26 are given in Table 14 and the numerical values for Figures 27, 28, 29, 30, and 31 are in Table 15 in Appendix B. The numerical values for the same procedure performed on an image captured in July are shown in Table 16 and Table 17 in Appendix B for the center and southwest ROIs respectively. These values confirmed that other than the saturation issues in Landsat images in the summer, there was no major temporal dependence and therefore plots were omitted. Similarly, this analysis was performed on images captured in February

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Figure 22. Percent error in standard deviation for the ROI in the center of the Libyan desert shifted 3 pixels for an image captured in February.





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Figure 27. Percent error in standard deviation for the ROI in the southwest of the Libyan desert shifted 3 pixels for an image captured in February.





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Figure 32. Percent error in standard deviation for the ROI in the northwest of the Sonoran desert shifted 3 pixels for an image captured in February.




and July of 2004 for confirmation there results were not temporally dependent. Because long term temporal stability was not the focus of this study and these images provided the same findings for spatial uniformity, detailed results have been omitted. The changes in percent error in standard deviation for the Libyan desert, even for the largest shifts of more than 10% of the image width, were below the specified threshold. The area in the Libyan desert is large and uniformly textured so small shifts were negligible in the results. Figures 32, 33, 34, 35, and 36 show the results for the 15 km x 15 km ROI in the northwest of the Sonoran desert for shifts of 3, 5, 10, 20 and 100 pixels respectively for an image captured in February (2010). These results are given numerically in Table 18 in Appendix B. Figures 37, 38, 39, 40 and 41 show the results for the 5 km x 5 km ROI in the center of the Sonoran desert for shifts of 3, 5, 10, 20 and 33 pixels respectively for an image captured in February (2010). These results are given numerically in Table 19 in Appendix B. As with Libya, the same procedure was performed on an image captured in July; these numerical values are shown in Table 16 and Table 17 in Appendix B for the northwest and centered ROIs respectively. These values confirmed that other than the saturation issues in Landsat images in the summer, there was no major temporal dependence. Similarly, this analysis was performed on images of the Sonoran captured in February

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Figure 37. Percent error in standard deviation for the ROI in the center of the Sonoran desert shifted 3 pixels for an image captured in February.


and July of 2004 for confirmation there results were not temporally dependent; these images provided the same findings for spatial uniformity so detailed results have been omitted. The percent errors in the Sonoran desert were found to be greater than those for Libya. For the 15 km x 15 km ROI in the northwest of the image, these changes only become significant with the largest shift. For the 5 km x 5 km ROI in the center of the scene, these changes are of concern in the February image for shifts of 10 and 20 pixels as well as the largest shift but only for the largest shift in the July image. It is also interesting to note that even ROIs with the largest percent errors in the Sonoran image may have relatively small standard deviations in comparison to some of the Libyan ROIs. The areas are so smooth that even a small change can cause a large percent error. These large percent errors, even though the standard deviation is relatively small, are still important because the expected value is changing. It is also important to note that these errors in the Sonoran desert, unlike changes in size, do not correspond to including surrounding land cover types. By carefully considering the image, the magnitude of the shifts is not large enough to include nearby roads, farmlands, etc. Therefore, variability can be attributed to desert characteristics. In general, there are two main reasons the percent errors are smaller in the Libyan scene. Not only is the scene uniform across a more expansive region, but also the ROIs are bigger. A shift of three pixels changes a much smaller percent area in a large ROI than in a small ROI and therefore has a smaller impact on the 22




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Figure 42. Legend for different images in spectral temporal plots.

Figure 43. Mean spectral vectors throughout the year for the centered Libyan ROI.

Figure 44. Mean spectral vectors throughout the year for the southwest Libyan ROI.

expected standard deviation. This is one benefit of larger ROIs. The Sonoran desert is extremely smooth in some areas with very low standard deviations, but this is over a small area and this shows in the percent error when the ROI is shifted. Due the scene variability and small ROIs, location becomes important in the Sonoran ROIs where it is largely negligible with the Libyan desert.

4.2 Spectral Variability The spectral vectors and mean spectral vectors are more informative using Hyperion imagery. There was a tradeoff between data availability and spectral resolution that was made in order to perform this analysis. 4.2.1 Temporal Stability Due to data availability, the temporal analysis was only considered for the Libyan desert. Figure 43 shows the mean vectors for the centered ROIs for six months in the year at a two month sampling rate encapsulating the different seasonal changes. The lines in this image are described in the legend in Figure 42. Figure 44 shows the corresponding mean results for the ROI in the southwest part of the scene from the same images. As shown, although the winter months of December and February have lower reflectances, they have the highest standard deviations. However, even with these differences, the mean spectral vectors appear to be largely the same shape and varying only in brightness or magnitude. This was the motivation for computing the spectral angles. The spectral vector for July was used a reference or standard mean. The spectral angles between the seasonal spectral vectors is shown in Table 8. Although there are obvious differences in the magnitude of the reflectance, as shown by Figures 43 and 44, the spectral angles between the mean vector for the ROI in each image and the mean vector for the ROI for the image captured in July are below the predetermined threshold. This does not necessarily indicate that there are not spectral changes that are correlated with season but rather that these changes are below threshold. This would lead to the hypothesis that the differences in the reflectance spectra are in brightness or in atmospheric affects, rather than physical changes such as vegetation or land forms on the ground. 24

90 90 90 90 90 90 45 45 45 45 45 45

ROI km x 90 km x 90 km x 90 km x 90 km x 90 km x 90 km x 29 km x 29 km x 29 km x 29 km x 29 km x 29

km km km km km km km km km km km km

Acquisition Date 2 February 2009 20 April 2009 31 May 2009 24 July 2009 2 October 2009 5 December 2009 2 February 2009 30 April 2009 31 May 2009 24 July 2009 2 October 2009 5 December 2009

Spectral Angle to July 0.09001 0.06297 0.03553 — 0.01523 0.07261 0.08924 0.06651 0.04109 — 0.01286 0.07039

Table 8. Spectral angles between mean vectors for images throughout the year.

Figure 45. Mean spectral vectors for classes in centered ROI in Libya in a summer image.

Figure 46. Mean spectral vectors for classes in southwest ROI in Libya in a summer image.

4.2.2 Spectral Variability within the ROI As with the spatial uniformity study, there were many ways to investigate the spectral variability over the small region of the ROI. Rather than comparing mean vectors as with the temporal study, looking at the spectral variability within the ROI compares each pixel vector to the mean vector for that ROI. Unsupervised k-means classification, which uses the euclidean distance in spectral space, was used to classify each subset ROI. A quick investigation was completed in order to determine the optimal number of classes. Classifications of one ROI were implemented with three, five, and seven classes with the same number of maximum iterations. Increasing from three to five classes showed increased detail, but increasing from five to seven classes did not show any added value. Each ROI in each image was classified using five classes and the mean spectral vectors for each class were plotted. Figure 45 and Figure 46 show the mean spectral vectors for the classes for the centered and southwest ROIs in the Libyan images. Each line on the plot represents a mean spectral vector of a class; because the classes are arbitrary they are not distinguished by a legend. The same plots generated for a winter image showed similar results; they are included in Appendix C for reference. The ROIs in the Sonoran images were also classified with five classes. Figure 47 is a plot of the mean spectral vector for the different classes in a Hyperion Sonoran ROI. Figure 72 and Figure 73 are from two different ROI selections in the same image of the Sonora desert; these plots showed the same results and are included in Appendix C for reference.

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Figure 47. Mean spectral vectors for classes in Sonoran ROI.

Scene Sonora Sonora Sonora Libya Libya Libya Libya Libya Libya Libya Libya Libya Libya Libya Libya

Date 18 May 2002 18 Jan 2005 17 Nov 2006 2 Feb 2009 2 Feb 2009 20 April 2009 20 April 2009 31 May 2009 31 May 2009 24 July 2009 24 July 2009 2 Oct 2009 2 Oct 2009 5 Dec 2009 5 Dec 2009

ROI — — — Center Southwest Center Southwest Center Southwest Center Southwest Center Southwest Center Southwest

Spectral Angle Greater than Threshold (0.1 rad) 5.55 x 10−5 5.77 x 10−5 4.43 x 10−5 3.15 x 10−3 1.99 x 10−3 1.55 x 10−5 3.49 x 10−5 2.30 x 10−3 6.98 x 10−5 2.20 x 10−3 5.60 x 10−4 1.55 x 10−5 3.491 x 10−5 1.37 x 10−3 5.60 x 10−4

Table 9. Fraction of pixels greater than 0.1 radians from mean spectral vector.

Similar to the temporal analysis, the differences in the classes seems to be in magnitude rather than spectral signature or shape of the spectral vector. The spectral angle between each pixel in the ROI and the mean vector of that ROI was calculated; this was thresholded to determine the number of pixels greater than 0.1 radians from the mean spectral vector. These results are shown in Table 9. As shown, in all of the above ROIs, at least 99.6% or more of the pixels fall within 0.1 radians of the mean spectral vector. Therefore, it is likely that the differences between classes are due to changes in brightness; these could be BRDF or atmospheric effects but the spectral signature of effectively all of the pixels in the image is the same. Figure 48 is a grayscale representation of the spectral angles for all of the pixels in the ROI. As shown, the small percentage that falls beyond 0.1 radians of the mean vector could be attributed to noise in the Hyperion data, as illustrated by the one obviously noisy or dead pixel causing a stripe in the image because it is a pushbroom sensor.

4.3 Radiometric Effects Both radiance vs. wavelength and percent error vs. wavelength were plotted for each site and season from the output of the MODTRAN runs.

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Figure 48. Grayscale representation of spectral angles to mean vector for a single ROI.

Figure 49. Variation in radiance as a function wavelength for changing aerosol type in the winter.

Figure 50. Legend for different lines in plots with varying aerosol type.

Figure 49 shows the radiance output per wavelength as aerosol type was varied for both the Sonoran (dotted line) and Libyan (solid line) winter atmospheres. The different color lines on the plot are the different aerosol types, as detailed by the legend in Figure 50. The spread of lines in Figure 49 is better characterized by the percent error to the typical atmosphere (summarized in Table 7) for that site and season. Figures 51, 52, 53 and 54 show this percent change relative to the typical as a function of wavelength as 0.01 µm resolution. These four plots allow for comparison between site and between season. The desert aerosol is the typical, so the percent error is zero. The rural aerosol causes more variability than the tropospheric aerosol, as expected. This is noteworthy for the Sonoran site which is known to be in close proximity to some agricultural developments. It is interesting that the aerosols decrease observed radiance in the visible but increase observed radiance in the near IR.

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Figure 51. Percent error as a function of wavelength for changing aerosol type for Libyan atmosphere in the winter.

Figure 52. Percent error as a function of wavelength for changing aerosol type for Libyan atmosphere in the summer.

Figure 53. Percent error as a function of wavelength for changing aerosol type for Sonoran atmosphere in the winter.

Figure 54. Percent error as a function of wavelength for changing aerosol type for Sonoran atmosphere in the summer.

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Figure 55. Legend for different lines for plots with varying visibility.

Figures 56, 57, 58 and 59 show the same results for the percent change relative to the typical for varying visibility for the Libyan winter atmosphere, the Libyan summer atmosphere, the Sonoran winter atmosphere, and the Sonora summer atmosphere respectively. This graphic can be used to make a comparison between seasons by considering the plots horizontally and a comparison between sites by considering the plots vertically. In these plots, the blue line represents 1 m visibility, which is effectively a dust storm. This was included as an extreme case but is unlikely to be used for a calibration image and therefore can largely be ignored when considering the results. It is extremely difficult to draw concrete or overall conclusions from seasonal or site comparisons because the variability is spectrally dependent. For the visibility, it would appear that there are smaller percent changes in Libya than in Sonora for the same range of visibilities in the near infrared, but there are larger percent changes in Sonora than in Libya for the visible. In all cases, the visibility had to be as small as 10 km or 15 km to have a considerable effect. The water vapor results are shown in Figures 61, 62, 63, and 64. These results are particularly difficult to interpret. Notice that the water vapor is varied both above and below the default such that a water vapor scalar of 1.0 has zero percent change. In all cases, decreasing the water vapor increased the radiance and increasing the water vapor decreased the observed radiance. Finally, the results are presented for windspeed in Figures 66, 67, 68, 69. In MODTRAN, windspeed for the desert aerosol is used to control the visibility variable as well. Therefore, changing windspeed is effectively changing the visibility; notice that the windspeed results are similar but not as exaggerated as the visibility results. It is difficult with such small variability and the spectral dependence to make comparisons between the two sites and the two seasons. Increasing windspeed decreases the radiance, which is intuitive knowing that decreasing visibility generally decreased radiance values. The results for the MODTRAN output convolved with the ABI simulated spectral response functions are included in the Appendix D. It is interesting to note that the spectral dependencies are emphasized when integrated with the spectral response functions. Direct seasonal and site comparisons can be more easily made, but the conclusions may differ depending on the bands being considered. This section provided visual and numerical analysis for the analysis performed. The final section helps to summarize the work by drawing useful conclusions from these results.

5. CONCLUSIONS 5.1 Spatial Uniformity Unlike spectral or radiometric properties that are environmentally dependent, the user has some control over the spatial characteristics in the ROI selection. Carefully selecting a very specific ROI can be difficult and time consuming, but would be worth the cost if it greatly improved calibration results. Therefore, investigation into the variability of TOA reflectance as the size and location of the ROI changes is important.

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Figure 56. Percent error as a function of wavelength for changing visibility for Libyan atmosphere in the winter.

Figure 57. Percent error as a function of wavelength for changing visibility for Libyan atmosphere in the summer.

Figure 58. Percent error as a function of wavelength for changing visibility for Sonoran atmosphere in the winter.

Figure 59. Percent error as a function of wavelength for changing visibility for Sonoran atmosphere in the summer.

Figure 60. Legend for different lines for plots with varying water vapor.

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Figure 61. Percent error as a function of wavelength for changing water vapor for Libyan atmosphere in the winter.

Figure 62. Percent error as a function of wavelength for changing water vapor for Libyan atmosphere in the summer.

Figure 63. Percent error as a function of wavelength for changing water vapor for Sonoran atmosphere in the winter.

Figure 64. Percent error as a function of wavelength for changing water vapor for Sonoran atmosphere in the summer.

Figure 65. Legend for different lines for plots with varying windspeed.

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Figure 66. Percent error as a function of wavelength for changing windspeed for Libyan atmosphere in the winter.

Figure 67. Percent error as a function of wavelength for changing windspeed for Libyan atmosphere in the summer.

Figure 68. Percent error as a function of wavelength for changing windspeed for Sonoran atmosphere in the winter.

Figure 69. Percent error as a function of wavelength for changing windspeed for Sonoran atmosphere in the summer.

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Libya is a commonly used calibration site and it is generally assumed that this site is spatially stable; although there is obviously surface texture as shown in the both the RGB and classification images, this texture is uniform such that selection of a large area will average out the effects and create a stable signal. This was verified by investigating the standard deviation and change in standard deviation as the size of the ROI was varied about some typical area. As shown in Figures 14 and 15, changing the size of the large centered ROI has an insignificant effect on the standard deviation. Any of those four sizes could be used in calibration to obtain the same results. Even for a smaller ROI, as shown in Figures 16 and 17, changing the size of the ROI does not affect the spatial variability enough to change the calibration results. Therefore, size variability is not a parameter that is a concern for ROI selection in the Libyan desert. This verifies an assumption that was generally already being made when using the Libyan desert for vicarious calibration. Using the Libyan results as verification of the methodology, the same process was used to explore site variability with changing ROI size in the Sonoran desert scene. As shown in Figures 18 and 19, for the typical and smaller ROI sizes, the northwest calibration site in the Sonoran scene actually has less variabilty than the Libyan ROIs. This is confirmed by visual observation of the RGB and classified images, which show that this area is extremely smooth with little texture. However, increasing the area around this typical site increases variability due to proximity to other types of land cover, including rural and urban areas. Therefore, size is a parameter of interest when using this ROI, not because of variability in the desert surface, but because of limited availability of desert coverage in the region. The smaller typical ROI in the center of the Sonoran scene is less common but behaves more like the Libyan desert. This is a textured area so only the smallest selection has low variability; increasing the size increases the variability but only to a point at which is levels off due to the integrated effective response of the textured area. Size has some effect on the variability and is a more important parameter in the Sonoran than in the Libyan desert. ROI location is also a user controllable parameter. As shown in figures 22 through 25 and Figures 27 through 30, pixels shifts of 3, 5, 10, and 20 in all directions do not affect the spatial variability of either ROI in the Libyan desert. These pixels shifts would be around the expected uncertainties in geolocational accuracy for various sensor footprints. Even the largest shift, on the order of 10% of the ROI width, did not alter the spatial variability beyond the threshold set by the 10% error in standard deviation metric of comparison. The Libyan desert site has high spatial uniformity and the exact geolocational accuracy of the ROI selection is not a parameter of importance. As already illustrated by size, the available desert area in the Sonoran scene is limited. Therefore, it would make sense that the location of the ROI is more important. Related to this, the limited desert area inherently makes typical ROI sizes smaller in the Sonoran desert. A shift of the same number pixels changes a larger percent of the area of the ROI. As shown in Figures 32 through 35, small pixels shifts are still well below the threshold but shifts of 10 to 20 pixels begins to adversely change the spatial uniformity. This is also true for the centered Sonora ROI, as shown in Figures 37 through 40. For both ROIs, the largest pixel shifts, on the order of 20% of the ROI width, created significant changes according to the predetermined metric of comparison. Therefore, because of the inherently smaller ROI size and the limited desert surface within the scene, location is a parameter of importance in the Sonoran desert. The spatial uniformity in immediate areas surrounding typical ROIs is not as high, so it is important to place the ROI more carefully. It is important to relate these results to specific sensor characteristics. Because the ROI is determined by area on the ground, smaller ROIs will occupy fewer pixels on lower resolution sensors. Similarly, a locational error of one pixel on a high resolution sensor creates a much smaller change in area within the ROI than a locational error of one pixel on a low resolution sensor. For example, in the northwest Sonoran ROI, the largest shift was 20% of the typical ROI width; this was a shift of 3 km or 100 Landsat pixels. It is unlikely that the uncertainty for the geolocational accuracy of an image would be this high. However, for a low resolution sensor with 1 km pixels, this is only a three pixel error. Therefore, a larger ROI or highly accurately geolocated data would be needed to calibrate this sensor with lower uncertainty. Ultimately the Libyan site has more structure but but it is effectively more uniform over large areas and areas on the scale of the typical ROIs. Sonora has almost no texture over small areas but more variability

33

in land cover within the scene. Both has acceptable spatial uniformity with size variation, but the smaller ROIs in the Sonoran desert make ROI location a parameter of concern for this site.

5.2 Spectral Variability Spectral variability investigates the signature of the pixels within the scene; this cannot be controlled by the user but needs to be well understood in order to use an area for calibration. For calibration, stable and known spectral signatures are desired. This relates to both the temporal stability, variation in the spectral signature over time, and spatial stability, variation in the spectral signature between pixels within a scene. Through qualitative analysis of the temporal stability using Figures 43 and 44, it appears that there is only a seasonal change in magnitude but not in spectral shape for the Libyan desert. A more quantitative metric for spectral stability would reaffirm these observations, which is why spectral angle was utilized. Spectral angle is invariant to changes in brightness and only captures variations in the angle between vectors spectral space where each band is a dimension; this relates the changes in the shape of the spectral curve. As shown in Table 8, the spectral angle between any month and July was below the 0.1 radians threshold. This means there were only negligible changes in the shape of the spectral curve throughout the year. This leads to the speculation that the variation in spectral curve can be attributed to the brightness of the pixels, not the spectral signature. This means that while the illumination on the ground is changing, the material or physical make up of the area is constant. Because the sites are supposed to be invariant, it is encouraging that there are not annual physical changes on the ground. The changes in magnitude could be due to illumination effects, such as atmospheric attenuation and BRDF effects, which leads to further investigation into the radiometric effects for each site. Due to limited data availability, this analysis could not be performed for the Sonoran site. With the Sonoran site, due to the proximity to different types of landcover, there are more concerns with surface variation, such as soil moisture and vegetation, and with atmospheric variabiltiy, due to possible different aerosols and climate conditions. Therefore, this study would be extremely useful for the Sonoran site and should be performed when data becomes available. Classification was the first tool utilized to determine if there was spatial stability in the spectral signatures of the Libyan and Sonoran desert. Because K-means classification depends on euclidean distance in spectral space, difference in class spectra would indicate pixels with different spectral make up. Qualitatively considering the class spectra, as shown in Figures 70 through 73, the differences in the class spectra look very similar to the differences in the temporal spectra; there is obvervable variation in magnitude but not in shape. The spectral angle between each pixel and the mean vector was used to confirm that there was negligible variation between spectral signature. Therefore, differences between pixels can likely be attributed to brightness or illumination effects. Because it is unlikely that the atmosphere is varying rapidly enough to change the illumination of pixels within the small ROIs considered, it is likely these changes in illumination are due to BRDF effects. It is important to realize there were more samples for the Libyan desert. For the Libyan site, the spatial study shows that much of the variability is accounted for through the integrated effective response. However, with the smaller ROIs in the Sonoran scene, this may not be the case. Therefore, a better understanding of the BRDF of the surface would lead to more confidence when using the site for vicarious calibration. Ultimately, in both scenes there is negligible spectral variation within a small region. it appears that any temporal spectral variability is due to changes in magnitude of brightness, not changes in spectral signature. The radiometric study gives better insights to determine if these changes can be attributed to atmospheric effects rather than physical changes on the ground.

5.3 Radiometric Effects Stemming from the variation in magnitude of the spectral signatures, the radiometric effects due to changes in atmosphere were also explored. In order to avoid confounding variable effects, the effects of aerosol type, aerosol number density, water vapor, and windspeed were considered individually.

34

A large amount of information is contained within these plots and comparisons can be made between the sites and between the two seasons. However, the spectral dependencies of the variability makes it difficult to draw definite conclusions between site and between season. In general, for both sites, both the tropospheric and rural aerosols decreased the radiance from the desert aerosol. Because the Libyan site is extremely expansive and uniform, this is less applicable. However, the scene variability around the Sonora site makes different aerosols a larger concern. For both sites, it appears that the changes are slightly more exaggerated in the winter than in the summer. The variation in visibility cause the largest variability in atmosphere, but this was also the range with the largest extremes. It is important to note that the largest percent change in the blue line is for a visibility of 1 km which is effectively a dust storm. This was included as an extreme but is not an expected condition for calibration. In general, visibility of less that 10 km - 15 km begins to show larger separations from the typical, and even these are low and bordering extreme for a desert environment. Water vapor also had exaggerated results; even a ten percent change from the typical cause noticeable variability. It is important to note for these plots that the default water vapor for each site and season was different, and the changes in water vapor were by percent and not absolute. Unlike the other three variable, it would appear that the variability is larger in the summer than in the winter. Finally, because windspeed determines the visibility for the desert aerosol, the windspeed effects were similar but less exaggerated than the visibility effects. Even with windspeeds up to 30 mph, the variability was small and this made it difficult to make comparisons. Considering both the hyperspectral and ABI data emphasized the spectral or band dependency of these results. Conclusions about the magnitude of variability for each site and each season are largely dependent on the wavelength under consideration. Considering only the ABI results, it would seem that, in general, there is more variability in the Libyan site and definitely more variability in the winter. However, these same conclusions are not at all obvious from the hyperspectral. Therefore, concerns with the radiometric variability with respect to calibration are extremely band dependent and therefore need to be considered in a sensor specific fashion. Ultimately it was extremely difficult to draw conclusions from the radiometric study due to the band dependencies on the results. It appears, for the GOES-R ABI convolved results, that there is increased variability in the winter and slightly increased variability in the LIbyan scene, but these same conclusions are not seen with hyperspectral results. There is a great opportunity for further analysis of these results on a sensor specific basis and with a more complete investigation of surface characteristics.

35

APPENDIX A. VARIABILITY IN ROI SIZE DATA ROI Size 50 x 50 70 x 70 90 x 90 110 x 110 35 x 19 40 x 24 45 x 29 50 x 34

Band 1 0.0062 0.007 0.0076 0.0083 0.0076 0.0077 0.0077 0.0077

Band 2 0.0107 0.0119 0.0128 0.0136 0.013 0.0132 0.0132 0.0132

Band 3 0.0141 0.0156 0.0167 0.0176 0.0175 0.0176 0.0176 0.0176

Band 4 0.0169 0.0185 0.0198 0.0207 0.022 0.022 0.022 0.0219

Band 5 0.0163 0.017 0.0175 0.0181 0.0204 0.0204 0.0204 0.0204

Band 7 0.0204 0.0219 0.023 0.024 0.0285 0.0284 0.0284 0.0281

Table 10. Standard deviations for each band for each size ROI in Libya in February.

ROI Size 50 x 50 70 x 70 90 x 90 110 x 110 35 x 19 40 x 24 45 x 29 50 x 34

Band 1 0.0067 0.0074 0.0082 0.0092 0.0085 0.0086 0.0086 0.0086

Band 2 0.0102 0.0112 0.0121 0.0131 0.0126 0.0128 0.0128 0.0129

Band 3 0.0127 0.0138 0.0148 0.0157 0.0153 0.0155 0.0156 0.0156

Band 4 0.0142 0.0153 0.0162 0.017 0.0176 0.0178 0.0178 0.0178

Band 5 xxx 0.0001 0.0003 xxx 0 xxx 0 xxx

Band 7 0.0133 0.014 0.0146 0.0151 0.0179 0.0179 0.0179 0.0178

Table 11. Standard deviations for each band for each size ROI in Libya in July.

ROI Size 10 x 10 15 x 15 20 x 20 25 x 25 5x5 10 x 10 15 x 15 20 x 20

Band 1 0.0032 0.0034 0.0045 0.0073 0.0065 0.0087 0.0129 0.0149

Band 2 0.0048 0.0056 0.0095 0.0141 0.0127 0.0164 0.0194 0.0203

Band 3 0.0069 0.0088 0.0157 0.0225 0.0204 0.0255 0.0266 0.0268

Band 4 0.0077 0.0095 0.0167 0.0238 0.0277 0.0342 0.0342 0.0339

Band 5 0.0103 0.0129 0.0237 0.0349 0.0348 0.0428 0.042 0.0419

Band 7 0.0119 0.0151 0.0254 0.0363 0.0337 0.0419 0.0411 0.0421

Table 12. Standard deviations for each band for each size ROI in Sonora in February.

ROI Size 10 x 10 15 x 15 20 x 20 25 x 25 5x5 10 x 10 15 x 15 20 x 20

Band 1 0.0031 0.0033 0.0059 0.0075 0.0035 0.0065 0.0113 0.0144

Band 2 0.0044 0.0046 0.0076 0.0105 0.0055 0.0086 0.0137 0.0158

Band 3 0.006 0.0064 0.0104 0.0162 0.0086 0.0114 0.0149 0.0161

Band 4 0.0069 0.0073 0.0103 0.0166 0.0114 0.0142 0.0163 0.0172

Band 5 0.0083 0.0093 0.0149 0.0253 0.0151 0.0181 0.0193 0.0201

Band 7 0.0103 0.0115 0.0171 0.026 0.0149 0.0184 0.02 0.0205

Table 13. Standard deviations for each band for each size ROI in Sonora in August.

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APPENDIX B. VARIABILITY IN ROI LOCATION DATA Shift North, 3 East, 3 Southeast, 3 South, 3 West, 3 Northwest, 3 North, 5 East, 5 Southeast, 5 South, 5 West, 5 Northwest, 5 North, 10 East, 10 Southeast, 10 South, 10 West, 10 Northwest, 10 North, 20 East, 20 Southeast, 20 South, 20 West, 20 Northwest, 20 North, 10 km East, 10 km Southeast, 10 km South, 10 km West, 10 km Northwest, 10 km

Band 1 -0.0354 0.013 -0.0163 -0.0885 -0.1294 -0.106 -0.0252 0.0502 0.003 -0.1176 -0.1757 -0.141 0.0053 0.1238 0.0314 -0.1571 -0.3177 -0.2471 0.0511 0.2605 0.0982 -0.2285 -0.5977 -0.5276 4.3045 5.7055 3.3556 -1.1181 -4.3133 -1.4853

Band 2 0.051 0.0626 0.1342 0.0985 0.0928 0.0251 0.054 0.078 0.1337 0.0793 0.0645 0.0113 0.0844 0.0892 0.1015 -0.0007 -0.0125 -0.0785 0.1563 0.1497 0.0809 -0.1259 -0.2559 -0.1725 3.4118 3.31 0.2358 -2.8556 -2.3743 0.143

Band 3 0.005 0.0032 -0.0266 -0.0506 -0.0495 -0.02 0.0098 0.0128 -0.0358 -0.2011 -0.0675 -0.0271 0.013 0.008 -0.2119 -0.3589 -0.2726 -0.0577 -0.0011 -0.0053 -0.2773 -0.4338 -0.4979 -0.1418 3.1889 2.5709 -0.9931 -3.7208 -2.3273 0.7993

Band 4 -0.0145 -0.0789 -0.0612 -0.0713 -0.057 -0.0283 -0.0507 -0.0746 -0.0819 -0.091 -0.0683 -0.0246 -0.0062 -0.0859 -0.1511 -0.1274 -0.113 -0.0372 0.0412 -0.0501 -0.2682 -0.1502 -0.207 -0.0201 3.2082 2.4905 -0.4479 -3.5656 -1.9804 1.3614

Band 5 -0.0106 -0.0341 -0.0552 -0.1389 -0.1113 0.0026 0.074 -0.0105 -0.0757 -0.1412 -0.0579 0.0135 0.1528 0.0727 -0.1344 -0.1185 0.0026 -0.0311 0.18 0.0238 -0.2092 -0.059 0.0332 0.0384 1.898 -0.1904 -1.3296 -1.9744 1.0207 3.7717

Band 7 -0.1213 -0.1641 -0.1972 -0.2807 -0.3539 -0.1108 -0.1057 -0.1768 -0.2301 -0.4253 -0.356 -0.1818 -0.0558 -0.2523 -0.3515 -0.4964 -0.3906 -0.2969 0.0017 -0.2161 -0.4766 -0.5903 -0.4481 -0.2748 2.6458 0.5456 -1.6728 -3.4029 0.1917 3.7552

Table 14. Percent error in standard deviation for each band for each shift of the 90 km x 90 km ROI in Libya in February.

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Shift North, 3 East, 3 Southeast, 3 South, 3 West, 3 Northwest, 3 North, 5 East, 5 Southeast, 5 South, 5 West, 5 Northwest, 5 North, 10 East, 10 Southeast, 10 South, 10 West, 10 Northwest, 10 North, 20 East, 20 Southeast, 20 South, 20 West, 20 Northwest, 20 North, 5 km East, 5 km Southeast, 5 km South, 5 km West, 5 km Northwest, 5 km

Band 1 0.0355 -0.0117 -0.0406 -0.0542 -0.0508 -0.0009 0.0668 0.0034 -0.0497 -0.0811 -0.0444 0.0288 0.1306 0.0571 -0.0695 -0.1399 -0.0623 0.0838 0.2761 0.2493 -0.0514 -0.316 -0.1094 0.1869 3.9938 2.4773 -2.2703 -3.6977 -1.4038 2.0755

Band 2 0.0317 0.013 -0.0573 -0.0252 -0.0087 0.0242 0.0555 0.0065 -0.0589 -0.0245 -0.0129 0.0635 0.136 0.0668 -0.0489 -0.0811 -0.0103 0.1027 0.2678 0.1495 -0.0078 -0.1871 -0.0102 0.1994 3.1003 1.3483 -2.0627 -2.8571 -0.6854 2.0077

Band 3 0.0384 -0.0324 -0.0454 -0.0155 -0.0112 0.0303 0.0568 -0.0296 -0.0481 -0.01 -0.0285 0.0476 0.0655 -0.0129 -0.0718 -0.0636 0.0112 0.0664 0.168 0.0754 -0.0714 -0.1783 0.0106 0.1834 2.2932 0.4737 -2.1639 -2.3296 -0.0921 1.8757

Band 4 0.0059 -0.0652 -0.0884 -0.0257 -0.0245 0.0155 0.0216 -0.0689 -0.0653 -0.0048 -0.0023 0.0545 0.0305 -0.0416 -0.0803 -0.0443 0.0223 0.0629 0.104 0.0214 -0.0572 -0.114 -0.0172 0.1274 1.3725 -0.4426 -2.3417 -1.7935 0.5509 1.742

Band 5 0.022 -0.0414 -0.0448 -0.0117 0.0244 0.0304 0.0268 -0.0739 -0.0722 -0.0069 0.0178 0.0551 0.0182 -0.1532 -0.1292 -0.0048 0.0743 0.0733 0.0459 -0.2393 -0.2719 -0.0384 0.1272 0.2135 0.0951 -2.1337 -2.7558 -0.8349 1.8962 1.8609

Band 7 0.0071 -0.08 -0.0753 -0.0086 0.0227 0.0439 -0.0035 -0.1062 -0.0806 0.0111 0.0344 0.0714 -0.0372 -0.1517 -0.0863 0.0255 0.0653 0.0796 -0.0119 -0.1425 -0.1033 0.0074 0.051 0.0915 -0.0288 -1.9686 -2.5949 -0.8619 1.5315 1.4602

Table 15. Percent error in standard deviation for each band for each shift of the 45 km x 29 km ROI in Libya in February.

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Band 1 0.0629 0.0764 0.0202 -0.0676 -0.1017 -0.0221 0.0042 0.1263 0.0298 -0.0827 -0.1568 -0.137 0.0447 0.2537 0.1072 -0.2133 -0.3214 -0.2548 0.1763 0.3503 0.0346 -0.4114 -0.597 -0.4205 7.6091 5.5667 1.0651 -3.0732 -4.2368 1.4697

Band 2 0.0127 0.0419 0.0005 -0.0585 -0.0812 -0.051 0.0381 0.0718 0.0129 -0.083 -0.1174 -0.0612 0.0921 0.1424 -0.0789 -0.1483 -0.2385 -0.1215 0.1764 0.2543 -0.113 -0.3224 -0.5172 -0.2197 6.3458 3.8282 -0.9814 -4.0139 -2.917 1.91

Band 3 0.019 0.0365 -0.0162 -0.0648 -0.0746 -0.0354 0.0452 0.0476 -0.0224 -0.0901 -0.1034 -0.0361 0.076 0.096 -0.0355 -0.1222 -0.2025 -0.0997 0.1536 0.188 -0.108 -0.2875 -0.3483 -0.1854 6.0522 3.1275 -2.4642 -5.0235 -2.5265 2.1387

Band 4 -0.0391 -0.045 -0.0453 -0.0788 -0.0802 -0.0826 -0.0182-0.0333-0.0596-0.0725-0.0710-0.04000.0421 0.0251 -0.0673 -0.1278 -0.1438 -0.0386 -0.1535 -0.0508 -0.1553-0.2766-0.2883-0.05505.6859 2.5827 -2.7971 -4.827 -2.0434 2.7871

Band 5 -86.0868 -86.0868 -86.0868 -86.0868 -86.0868 -86.0868 86.0868 86.0868 86.0868 86.0868 86.0868 86.0868 -86.0868 -86.0868 -86.0868 -86.0868 -86.0868 -86.0868 86.0868 86.0868 86.0868 86.0868 86.0868 86.0868 -86.0862 -86.0868 -86.0659 -86.0659 -86.0868 -86.0862

Band 7 -0.2657 -0.315 -0.3591 -0.355 -0.3175 -0.2704 -0.2404 -0.3327 -0.4065 -0.3881 -0.3193 -0.2495 -0.1745 -0.3946 -0.5518 -0.4635 -0.3607 -0.2204 -0.0409 -0.423 -0.7391 -0.6259 -0.5281 -0.1539 4.5285 -0.1609 -4.4678 -4.9874 0.1181 5.1238

Table 16. Percent error in standard deviation for each band for each shift of the 90 km x 90 km ROI in Libya in July.

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Band 1 0.0304 0.0005 -0.0481 -0.0425 -0.0138 0.0023 0.0452 0.0181 -0.0608 -0.064 -0.0204 0.0184 0.1021 0.0698 -0.1057 -0.157 -0.0275 0.0874 0.2691 0.249 -0.1086 -0.3232 -0.1395 0.1738 3.9059 2.9495 -2.4517 -3.9884 -1.8109 1.3131

Band 2 0.0236 -0.0175 -0.0471 -0.0389 -0.035 -0.0028 0.0256 -0.0109 -0.0618 -0.0766 -0.0488 0.0069 0.0503 0.0287 -0.1195 -0.1545 -0.0433 0.0817 0.222 0.1514 -0.1443 -0.2626 -0.0953 0.1968 3.7128 2.4252 -2.081 -3.4782 -1.5381 1.4533

Band 3 0.0181 0.0257 -0.0487 -0.031 -0.0341 -0.0055 0.0429 0.016 -0.031 -0.0611 -0.0432 0.0102 0.1091 0.0655 -0.0827 -0.1357 -0.0095 0.1072 0.2715 0.1804 -0.0891 -0.2724 -0.0747 0.2176 3.5045 2.1069 -1.9582 -3.2555 -1.1297 1.7915

Band 4 -0.0299 -0.0049-0.0458-0.0234-0.0408-0.0105 0.0485 0.0144 -0.0434 -0.0479 -0.0282 0.0039 -0.1117 -0.0505 -0.0686-0.1323-0.0111-0.1011 0.2412 0.138 -0.0856 -0.2153 -0.0714 0.1946 -2.8165 -1.2915 -2.1264-2.8505-0.5075-1.9063

Band 5 98.7826 98.7826 98.7826 98.7826 98.7826 98.7826 -98.7826 -98.7826 -98.7826 -98.7826 -98.7826 -98.7826 98.7826 98.7826 98.7826 98.7826 98.7826 98.7826 -98.7826 -98.7826 -98.7826 -98.7826 -98.7826 -98.7826 97.8199 97.0268 97.0268 98.7826 98.7826 97.8199

Band 7 0.04 -0.0486 -0.0661 -0.0238 0.001 0.0413 0.0694 -0.0561 -0.0941 -0.0403 0.0097 0.0685 0.1137 -0.031 -0.1394 -0.1107 -0.013 0.1463 0.2172 0.0928 -0.1074 -0.1764 -0.0381 0.2304 1.795 -0.5686 -3.113 -2.4019 0.8262 2.5216

Table 17. Percent error in standard deviation for each band for each shift of the 45 km x 29 km ROI in Libya in July.

40


Band 1 -0.1943 0.0124 0.1617 0.1708 -0.0361 -0.2164 -0.3668 -0.0082 0.273 0.2899 -0.0242 -0.4028 -0.6705 0.1063 0.7044 0.6469 -0.0329 -0.7053 -1.1849 0.3472 2.2731 2.116 1.1521 0.0209 0.9363 3.6013 18.7701 33.0176 9.7692 2.3298

Band 2 -0.6941 -0.0489 0.4916 0.5557 -0.0021 -0.7193 -1.0885 -0.0789 0.8982 1.0271 0.0371 -1.1003 -1.9189 0.0345 2.1133 2.2269 0.236 -1.7979 -3.1485 0.6227 5.6956 5.6898 3.9599 0.5788 -5.7968 2.4711 22.9361 54.4901 21.0279 -2.9272

Band 3 -0.8161 -0.1752 0.4795 0.678 0.1526 -0.6939 -1.2968 -0.2814 0.9242 1.2587 0.2641 -1.0718 -2.2886 -0.4294 2.0514 2.6461 0.6842 -1.7264 -3.7314 -0.1844 5.7286 6.6276 5.1947 1.1952 -13.414 -2.4717 20.531 60.4677 25.3839 -7.331

Band 4 -0.6884 -0.1605 0.2511 0.4355 0.1234 -0.5878 -1.0827 -0.284 0.4981 0.818 0.2131 -0.8942 -1.8492 -0.532 1.014 1.7081 0.5694 -1.3837 -2.8632 -0.6443 3.4191 4.6852 6.7671 3.7551 -8.786 -4.4575 14.3725 55.5677 28.0685 -2.0703

Band 5 -0.8796 -0.3214 0.3661 0.722 0.3583 -0.5486 -1.4078 -0.5483 0.7159 1.33 0.5627 -0.8915 -2.5606 -1.01 1.5959 2.8931 1.2141 -1.5191 -4.2477 -1.3822 5.076 7.4807 6.976 2.3868 -19.7039 -7.3902 16.5118 70.3939 28.8222 -10.7333

Band 7 -0.8125 -0.2613 0.4418 0.7212 0.2916 -0.5297 -1.3042 -0.441 0.8602 1.3433 0.4682 -0.8572 -2.4024 -0.7597 1.9383 2.8953 1.0081 -1.4873 -4.1177 -0.8984 5.3457 6.937 4.8503 0.5416 -21.6374 -6.2176 17.1497 57.9996 22.1997 -13.5882

Table 18. Percent error in standard deviation for each band for each shift of the 15 km x 15 km ROI in Sonora in February.

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Band 1 -1.0026 1.09 2.6082 1.537 -0.5263 -1.5397 -2.0952 1.4788 4.3359 2.9098 -0.417 -2.5122 -3.7037 2.6628 8.791 6.2638 -0.5304 -4.1018 -8.0323 3.808 12.1357 9.4441 -0.248 -7.9696 -9.5697 4.4848 14.0842 12.7931 0.8763 -9.0244

Band 2 -1.2478 1.1307 3.0133 1.9134 -0.6479 -1.9424 -2.4871 1.5716 5.0233 3.5149 -0.6172 -3.1225 -4.394 2.9771 10.3539 7.6027 -0.8877 -5.1836 -9.7243 4.4163 14.3012 11.3225 -0.883 -10.3849 -12.3717 5.3812 16.5427 14.7411 0.1077 -12.8561

Band 3 -1.2776 1.1251 3.0292 1.9389 -0.7161 -2.0057 -2.5444 1.5339 5.0127 3.548 -0.7276 -3.2853 -4.5149 2.8701 10.2612 7.6475 -1.0528 -5.4525 -10.0208 4.493 14.393 11.3524 -1.1496 -10.9945 -13.0403 5.5572 16.7322 14.7316 -0.4467 -14.116

Band 4 -1.3505 1.1121 3.1316 2.0155 -0.7177 -2.0666 -2.5122 1.4859 5.061 3.6305 -0.722 -3.2405 -4.3802 2.7933 10.1561 7.5896 -1.1041 -5.3651 -9.9514 4.4121 14.2156 11.2042 -1.241 -11.0021 -12.7786 5.5063 16.4713 14.3474 -0.6041 -14.0134

Band 5 -1.3508 1.1686 3.0119 1.8712 -0.5682 -1.9309 -2.5629 1.5799 4.9789 3.4708 -0.5816 -3.1486 -4.4936 2.9471 10.1486 7.4749 -1.0382 -5.3937 -9.8757 4.6616 14.3028 11.1005 -1.1947 -10.9451 -12.7495 5.9645 16.6023 14.3068 -0.5487 -14.0297

Band 7 -1.4142 1.2572 3.1006 1.8757 -0.6143 -2.0408 -2.6395 1.6959 5.1569 3.5384 -0.6062 -3.2585 -4.5767 3.0001 10.4872 7.7708 -1.0309 -5.4952 -10.0122 4.805 14.8159 11.5208 -1.1334 -11.0553 -13.0884 6.0607 17.075 14.9827 -0.4182 -14.2606

Table 19. Percent error in standard deviation for each band for each shift of the 5 km x 5 km ROI in Sonora in February.

42


Band 1 -0.241 -0.09 0.2011 0.3001 0.0866 -0.16 -0.3967 -0.1231 0.3585 0.5022 0.1396 -0.265 -0.6646 -0.133 0.9666 1.1242 0.3379 -0.4036 -0.8501 -0.0054 2.835 2.5812 0.5581 -0.5982 5.6878 76.8998 42.4235 42.7369 12.9757 0.9449

Band 2 -0.0723 0.2661 0.3659 0.1048 -0.2789 -0.3615 -0.1058 0.4254 0.6003 0.1748 -0.4393 -0.5402 -0.1669 0.9395 1.5941 0.4444 -0.8957 -1.0743 0.0007 2.058 4.3094 1.6457 -1.8441 -1.9739 10.3897 65.0816 44.8984 25.0324 3.0199 6.4338

Band 3 -0.1651 0.0948 0.2647 0.1644 -0.1156 -0.2766 -0.2592 0.1361 0.4074 0.2613 -0.1895 -0.4432 -0.4613 0.3781 1.2533 0.5576 -0.4398 -0.91 -0.6111 0.8073 3.4271 1.9021 -1.0417 -1.6859 3.1247 45.5458 33.9131 23.6864 6.2922 6.4482

Band 4 -0.2042 -0.053 0.1548 0.2106 0.068 -0.1395 -0.3489 -0.1194 0.2204 0.3436 0.1224 -0.2281 -0.7085 -0.3473 0.8563 0.7863 0.1864 -0.5407 -1.1065 -0.75 2.8436 2.6714 0.2028 -0.9481 -1.7529 19.3798 23.0584 24.679 11.6499 7.1486

Band 5 -0.512 -0.2334 0.2305 0.4612 0.2897 -0.2227 -0.876 -0.4195 0.4016 0.8134 0.4844 -0.3847 -1.5731 -1.0154 1.1715 1.7028 1.0038 -0.6107 -2.4905 -1.9339 3.3478 4.2172 2.0201 -0.6371 -12.6097 15.2849 20.5252 34.7126 18.6564 -0.2596

Band 7 -0.5208 -0.2128 0.2615 0.4659 0.2708 -0.2467 -0.8689 -0.3567 0.4567 0.8078 0.445 -0.4264 -1.634 -0.7597 1.2235 1.6768 0.8667 -0.8289 -2.7053 -1.2985 3.3167 3.8162 1.8327 -1.0769 -11.5964 16.5437 24.1097 28.3714 12.7087 -2.4907

Table 20. Percent error in standard deviation for each band for each shift of the 15 km x 15 km ROI in Sonora in August.

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Band 1 -0.1512 0.158 0.382 0.2461 0.1265 -0.0997 -0.2747 0.4085 0.6899 0.3177 0.5016 -0.149 -0.2878 0.6073 1.8603 1.0866 -0.1176 -1.692 -1.2452 2.5055 7.1895 3.1545 -1.1001 -4.7274 -3.3623 4.3269 16.122 8.1433 2.2843 -5.3838

Band 2 -0.0473 0.1815 0.332 0.1772 0.4034 0.2463 -0.0603 0.4646 0.7056 0.3176 1.1267 0.5265 0.0847 0.0706 1.8991 1.477 0.7542 -1.2906 -1.0536 1.3587 8.6097 4.5839 -0.3675 -5.5789 -4.9423 4.7049 22.7932 12.8863 4.3376 -8.061

Band 3 0.0249 0.2401 0.3856 0.1867 0.502 0.3891 0.0215 0.433 0.718 0.3304 1.2805 0.7645 0.1906 -0.0166 1.9145 1.5811 1.1266 -0.8945 -1.1975 1.001 8.5975 4.7426 0.4592 -5.1768 -5.6893 4.6609 23.703 13.6044 4.903 -8.9836

Band 4 0.0239 0.3226 0.4902 0.2205 0.6792 0.5921 0.0338 0.5202 0.7812 0.3681 1.4277 0.9283 0.2253 0.0676 1.7296 1.4189 0.9566 -0.7665 -1.0751 0.602 7.9897 4.477 0.2816 -4.9055 -5.4123 4.0771 22.5901 12.9161 4.3766 -9.0626

Band 5 0.096 0.3021 0.3545 0.1413 0.6101 0.5409 0.0878 0.4071 0.5214 0.2925 1.2327 0.7629 0.3761 0.0217 1.2943 1.1601 0.6151 -0.8726 -0.5206 0.2087 6.6643 3.8571 0.4299 -4.1908 -4.526 3.3405 20.4036 11.8758 3.9669 -8.2343

Band 7 0.2435 0.2774 0.179 -0.0218 0.6533 0.7265 0.3552 0.3889 0.3332 0.08 1.4169 1.1736 0.6849 -0.2461 0.8538 0.9514 1.2111 -0.1402 -0.3157 0.1279 5.908 3.4732 0.8632 -3.7931 -4.5978 3.3601 19.9162 11.4895 4.8367 -7.6231

Table 21. Percent error in standard deviation for each band for each shift of the 5 km x 5 km ROI in Sonora in August.

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APPENDIX C. SPECTRAL VARIABILITY WITHIN A ROI

Figure 70. Mean spectral vectors for classes in centered ROI in Libya in a winter image.

Figure 71. Mean spectral vectors for classes in southwest ROI in Libya in a winter image.



APPENDIX D. RADIOMETRIC EFFECTS Site Libya Libya Sonora Sonora

Season Winter Summer Winter Summer

Water Vapor 1.33253 gm/cm2 2.34946 gm/cm2 1.78317 gm/cm2 3.27077 gm/cm2

Table 22. Default water vapors for each site and season.

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REFERENCES 1. John R. Schott. Remote Sensing: The Image Chain Approach. Oxford Uniersity Press, 2nd edition, 2007. 2. 4th Responsive Space Conference. On-Orbit Calibration and Focus of Repsonsive Space Remote Sensing Payloads, Los Angeles, CA, 2006. 3. Gyanesh Chander, Xiaoxiong Xiong, Taeyoung Choi, and Amit Angal. Monitoring on-orbit calibration stability of the terra modis and landsat 7 etm+ sensors using pseudo-invariant test sites. Remote Sensing of Environment, 114:925 – 939, 2010. 4. P.M. Teillet, J.A. Barsi, G. Chander, and K.J. Thome. Prime candidate earth targets for the postlaunch radiometric calibration of space-based optical imaging instruments. In James J. Butler, editor, Earth Observing Systems XII, volume 6677. SPIE, 2007. 5. CEOS Cal Val Portal. http://calval.cr.usgs.gov/. 6. Helene Cosnefroy, Marc Leroy, and Xavier Briottet. Selection and characterization of saharan and arabian desert sites for the calirbation of optical satellite sensors. Remote Sensing Environment, 58:101– 114, 1996. 7. Amit Angal, Xiaoxiong Xiong, Tae young CHoi, Gyanesh Chander, and Aisheng Wu. Using the sonoran and libyan desert test ties to monitor the temporal stability of reflective solar bands for landsat 7 enhanced thematic mapper plus and terra moderate resolution imaging spectroradiometer sensors. Journal of Applied Remote Sensing, 4, April 2010. 8. Xiaoxiong Xiong and William Barnes. An overview of modis radiometric calibration and characterization. Advances in Atmospheric Sciences, 23(1):69 – 79, 2006. 9. Jr. Robert E. Eplee, Wayne D. Robinson, Sean W. Bailey, Dennis K. Clark, P. Jeremy Werdell, Megnhua Wang, RObert A. Barns, and Charles R. McClain. Calibration ii. vicarious techniques. Applied Optics, 40(36):6701 – 6718, December 2001. 10. Stuart F. Biggar, Kurtis J. Thome, and Wilt T. Wisniewski. In-flight radiometric calibration of advanced land imager and hyperion sensors on eo-1 platform and comparisons with other earth observing sensors. In William L. Barnes, editor, Earth Observing Systems VII, volume 4814, pages 281–295. SPIE, 2002. 11. G.T. Fraser, S.W. Brown, R.U. Datla, B.C. Johnson, K.R. Lykke, and J.P. Rice. Measurement science for climate remote sensing. In James J. Butler and Jack Xiong, editors, Earth Observing Systems XIII, volume 7081. SPIE, 2008. 12. USGS Earth Explorer. http://edcsns17.cr.usgs.gov/earthexplorer/. 13. Gyanesh Chander and Brian Markham. Revised landsat-5 tm radiometric calibraiton procedures and postcalibration dynamic ranges. IEEE Transactions on Geoscience and Remote Sensing, 41(11):2674 – 2677, November 2003. 14. EO-1 FAQ Page. http://eo1.usgs.gov/hyperion.php, 2010. 15. Julia A. Barsi, Brian L. Markham, Dennis L. Helder, and Gyanesh Chander. Radiometric calibration status of landsat-7 and landsat-5. 16. George P. Petropoulos, Krishna Prasad Vedrevu, Gevriil Xanthopoulos, GEorge Karantounias, and Marko SCholze. A comparison of spectral angle mapper and artificial neural network classifiers combined with landsat tm imgery analysis for obtaining burnt area mapping. sensors, 10:1967 – 1985, 2010. 17. A. Berk, G.P. Anderson, P.K Acharya, H. Dother, M.W. Matthew, S.M. Adler-Golden, J.J.H Chetwynd, S.C. Richtsmeier, B. Pukall, C.L. Allred, L.S. Jeong, and M.L. Hoke. Modtran4 radiative transfer modeling for atmospheric correction. In Optical Spectroscopic Techniques and Instrumentation for Atmospheric and Space Research III, volume 3756, pages 348 – 353, Denver, Colorado, 1999. SPIE. 18. P. Dash, F.M. Gottche, F.S. Olsen, and H. Fischer. Land surface temperature and emissivity estimation from passive sensor data: tehory and practice - current trends. International Jounal of Remote Sensing, 23:2563 – 2594, 2002.

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19. A. Berk, G.P. Anderson, P.K. Acharya, M.L. Hoke, J.H. Chetwynd, L.S. Bernstein, E.P. Shettle, M.W. Matthew, and S.M. Adler-Golden. MODTRAN4 Version 3 Revision 1 User’s Manual. Air Force Reserach Laboratory - Space Vehicles Directorate, Air Force Material Command, Hanscom AFB, MA, February 2003. 20. Fleet Numerical Meteorology and Oceanography Detachment Ashville, 151 Patton Avenue, Asheville NC 28801. Database Description For Upper Air Gridded Climatology (UAGC) Version 1.0, July 1995. 21. Thomas T. Warner. Desert Meteorology. Cambridge University Press, 2004. 22. Dr. Richard Beck. EO-1 User Guide. Department of Geography at University of Cincinnati, Cincinnati, Ohio, 45221, July 2003.

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