Characterizing the relative calibration of Landsat-7 (ETM+) visible

Remote Sensing of Environment 125 (2012) 167–180

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Characterizing the relative calibration of Landsat-7 (ETM+) visible bands with Terra (MODIS) over clear waters: The implications for monitoring water resources Nima Pahlevan a,⁎, John R. Schott b a b

Environmental, Earth, and Ocean Sciences, University of Massachusetts Boston, 100 Morrissey Blvd., Boston, MA 02125, USA Center for Imaging Science, Rochester Institute of Technology, 54 Lomb Memorial Drive, Rochester, NY 14623, USA

a r t i c l e

i n f o

Article history: Received 23 December 2011 Received in revised form 17 July 2012 Accepted 20 July 2012 Available online 12 August 2012 Keywords: Landsat-7 (ETM+) Over-water cross-calibration Terra-MODIS Water resources LDCM

a b s t r a c t Since its launch, the Enhanced Thematic Mapper plus (ETM+) onboard Landsat-7 has been continuously monitored via different calibration techniques to ensure it maintains the science requirements for demanding application areas. The majority of its applications, including agriculture and forestry, require a robust calibration for medium to high reflective targets. However, when imaging water resources, then the question becomes whether the calibration coefficients are valid for the dark end of the sensor's responsivity curve. Motivated by the Landsat Data Continuity Mission (LDCM) and its potential for providing long-term, robust water studies, in this effort, the calibration status of ETM+ visible bands are examined using a cross-calibration technique. The well-calibrated Terra-MODIS scenes (collection 5) of the past decade over relatively optically stable waters were chosen to evaluate ETM+ stability. The cross-comparison showed that the calibration instability of ETM+ reflective bands lie well within its radiometric uncertainty. The slight calibration differences were found to be less than 1.6%, 0.93%, and 3.2% for the blue, green and the red bands obtained for the period when the MODIS had been radiometrically stable. The NIR band of ETM+, however, exhibits, on average, 4.8% higher signals than those of MODIS. The error budget analysis for the calibration differences showed that 1.2%, 1.6%, 3.5%, and 6.5% errors are associated with the Visible-Near-Infrared (VNIR) bands, respectively. Using the results from the calibration study combined with simulations, it was demonstrated that ETM+ underestimates the retrieved diffuse surface reflectance (Rd) in the blue and the green bands as much as 12.2% and 4.4%, respectively, while the red band is overestimated 37%, on average, when studying slightly/moderately turbid. The uncertainties in the retrieval of Rd were applied in a water constituent retrieval framework where a physics-based model was utilized to obtain concentrations of chlorophyll-a (CHL) and total suspended solids (TSS) from a Landsat-7 dataset in slightly/moderately turbid waters. It was found that the calibration-induced errors in the retrieval of Rd yield, on average, 20% error in retrieval of these components. The results indicate that although ETM+ is well calibrated, its calibration status should be quantified rigorously for water studies when physics-based methods are employed for the removal of atmospheric effects. The over-water characterization of Landsat satellites will become more crucial when the LDCM becomes operational due to its increased capabilities for water resource studies. © 2012 Elsevier Inc. All rights reserved.

1. Introduction 1.1. Overview This study intends to evaluate the calibration status of the ETM+ sensor aboard Landsat-7, hereafter L7, with respect to Terra-MODIS over clear waters and to demonstrate how the calibration uncertainties affect the retrieval of surface reflectance and, as a result, concentrations of water constituents in optically complex waters, i.e., coastal/inland waters.

⁎ Corresponding author. E-mail addresses: [email protected] (N. Pahlevan), [email protected] (J.R. Schott). 0034-4257/$ – see front matter © 2012 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.rse.2012.07.013

Landsat has been recognized as a valuable means for monitoring earth resources over the past four decades. Obtaining physically realistic information from remotely sensed imagery is subject to accurate radiometric characteristics of the relevant imaging sensor. Although the stability of ETM+ over medium- and high-reflective targets has been properly investigated since launched (Chander et al., 2009), its calibration status has never been rigorously examined over dark targets. The Landsat satellite series, in general, has been widely used to empirically estimate water turbidity/trophic status of coastal aquatic environments, to obtain reasonable estimates of bathymetry and benthic cover, and to map and monitor fragile wetland ecosystems (Bustamante et al., 2009; Jensen, 2006; Lyzenga, 1981; Olmanson et al., 2008; Onderka and Pekárová, 2008; Palandro et al., 2008). The majority of the techniques used rely largely on empirically derived surface properties of water or simply discarding atmospheric effects by regressing digital numbers with in situ measurements. However, in

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more rigorous physics-based studies where radiative transfer codes are applied to account for the intervening atmosphere, a well-characterized imaging system is required. When sensing a body of water, the atmospheric interference is the major contributor to the total sensor-reaching radiance. Depending on the environmental conditions, such as wind speed, humidity, pressure, etc., and the optical properties of the waters under study, the atmospheric effects from more than 80% of the total signal (Gordon, 1998). Small calibration errors associated with the imaging instrument directly influence the retrieved remote sensing reflectance, which contains information about in-water constituents, their concentrations, and optical properties. Accurate radiometric calibration of the imaging system leads to a valid characterization of the atmosphere followed by an accurate retrieval of physical properties associated with the water body (Gordon, 1998; Wang and Gordon, 2002). Calibration uncertainties related to the NIR band also yield incorrect estimation of atmospheric parameters, which, consequently, introduce errors when retrieving the water constituents (Wang and Gordon, 2002). Landsat's continuing mission over the next decades in serving the science community enables a consistent, long-term monitoring of the earth. Motivated by the potential of a new generation of Landsat, Landsat data Continuity Mission (LDCM), for investigating water quality in coastal/inland waters (Gerace and Schott, 2009), this study addresses the calibration status of ETM+ over mesotrophic/oligotrophic waters for successful, long-term monitoring. In other words, ETM+ is used as a surrogate for LDCM to demonstrate the need for monitoring its stability over dark targets. The Operational Land Imager (OLI), which will operate onboard LDCM, has enhanced features that improve its capability for water studies when compared to the existing Landsat technology. The addition of a new short, blue band centered at 443 nm along with its higher Signal-to-Noise Ratio (SNR) and improved radiometric fidelity, i.e., 12-bit quantization, adds to the potential of LDCM relative to its predecessors (Gerace and Schott, 2009; Pahlevan and Schott, 2011). Although ETM+ has not been configured for water studies, if well calibrated, it can be utilized in conjunction with LDCM, as a tandem mission, for future coastal/inland water studies (LDCM will be placed in an orbit such that it images the same area seen by ETM+ with an eight-day lag). Furthermore, the availability of L7 imagery over the past decade may provide a valuable means for studying long-term trends in areas where other spatially, coarse resolution remote sensing systems are unable to resolve the desired spatial details. This paper builds upon the previous calibration research efforts made for both over-water characterization of MODIS and land-based monitoring of ETM+. It is demonstrated that the calibration status of L7 and its next generation (LDCM) have to be monitored over dark targets, i.e., clear waters, and that the calibration uncertainties can affect the retrieval of surface properties. Furthermore, an over-water cross-calibration methodology for comparing an ocean-color sensor with a land remote sensing system with different response functions is proposed. The following subsection (Section 1.2) presents background information regarding cross-calibration efforts between remote sensing systems. In Section 2, a description of the cross-calibration sites, including a mid-latitude lake, a low-latitude oceanic site, and tropical/ arid lake/sea waters, are given. This is followed by a detailed description of the proposed approach (Section 2.4). In order to ensure the robustness of our methodology, the procedure is also tested over a desert site for a limited number of scenes during 2008–2011. The results pertaining to the over-water historical trends of MODIS-ETM+ calibration are presented in Section 3.1 proceeded by the analysis over the desert site. In order to fully appreciate the sources of uncertainties in the proposed cross-calibration approach (Section 2.4), an error budget analysis is then detailed in Section 4. By treating the calibration differences derived from the trending study as bias-only errors associated with the ETM+ sensor, a series of simulations were conducted to evaluate the significance of such errors on the retrieved diffuse surface reflectance (Rd(λ)) (Section 5.1). In Section 5.2, it is demonstrated that

how errors in the retrieval of Rd(λ) would influence the retrieved concentrations of water constituents, including chlorophyll-a (CHL) and total suspended solids (TSS). 1.2. Cross-calibration of ETM+ with MODIS The calibration status of ETM+ has been monitored through its lifetime on a regular basis using onboard calibrators and vicarious calibration techniques. The ETM+ sensor has three onboard calibration devices, including a full aperture solar calibrator (FASC), a partial aperture solar calibrator, and an internal calibrator (IC), which is comprised of two lamps, to quantify the radiometric trending in its reflective bands. The pre-launch data coupled with the onboard calibrators facilitate a robust set of observations of medium- to high-level radiance (Markham et al., 1997). Markham et al. (2004) reported 0.5–2% change per year in the radiometric stability of ETM+ using the data from the FASC. However, based on vicarious calibration efforts, they speculated that this instability is related to the degradation of the solar diffuser after 6 years of operation. The sensor's low-level response, which represents a dark signal indicating the bias, is determined when the shutter obscures the focal plane from the earth light at the end of each scan line. Despite giving a measure of the gain and linearity for each detector, the two lamps are subject to degradation due to temperature sensitivity and contaminations over time (Markham et al., 2004). The L7 mission was planned to achieve a radiometric stability within ± 5% uncertainty for typical TOA radiance ranges, measured for 15–25% reflective ground targets, during the first 5 years of its lifetime (Chander et. al., 2010a). The MODIS sensor, on the other hand, was designed for large-scale, global monitoring of land and oceanic features. Onboard Terra and Aqua, the MODIS sensor has 36 spectral channels with 12-bit quantization rate making it superior to the Landsat satellite series (e.g. 8-bit for ETM+) when studying large bodies of waters. In addition, their frequent revisit cycle over a region has allowed for consistent monitoring of global primary production and carbon budget for the past decade. While Aqua has an equatorial crossing at 1:30 PM, Terra crosses the equator at 10:30 AM. The MODIS solar reflective bands are calibrated using onboard calibration devices, including a solar diffuser (SD), a solar diffuser stability monitor (SDSM), and a spectroradiometric calibration assembly (SRCA). Its solar reflective bands are also monitored through viewing the moon (Eplee et al., 2011) and deep space. The slight time difference between L7 and Terra-MODIS, i.e., 25 minutes on average, makes it possible to perform a cross-comparison between the overlapping scenes of a common target. The Terra and L7 satellites operate in a descending orbit with nominal altitudes of 705 km and nearly identical orbital periods, i.e., 98.9 minutes. Calibration stability of MODIS has been controlled through the onboard calibrators as well as vicarious calibration techniques (Franz et al., 2007). Although the present study assumes that MODIS is well characterized for dark targets (clear waters), inconsistencies in its blue bands have been reported after 2003 when the SD door failed to close causing significant degradation of the SD panel (Kwiatkowska et al., 2008). Since then, the Ocean Biology Processing Group (OBPG) and the MODIS Characterization Support Team (MCST) have made efforts to study the long-term trending of the sensor concerning its gain stability and polarization sensitivity. Kwiatkowska et al. (2008) used the SeaWiFS-derived ocean properties to cross-calibrate MODIS data collected until early 2008. Due to SeaWiFS remarkable stability over time, the method provided realistic corrections for degraded blue bands of MODIS. Although less significant, some corrections were also applied to the other visible bands. Hu et al. (2001) atmospherically corrected two ETM+ images using the SeaWiFS retrieved atmospheric parameters and compared the modeled TOA radiance with the TOA radiance measured by ETM+ for only two sample scenes. Although uncertainties, on average, less than 5% in units of TOA radiance for the visible bands were reported,

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their findings were restricted to a very limited signal level under specific environmental conditions. It should also be noted that ETM+ appeared to output higher values than those predicted via modeling (Hu et al., 2001). The vicarious calibration techniques, including cross-calibration methods, enable analyzing the radiometric stability of a system independent of the onboard calibration sources. The cost-efficient cross-calibration techniques over terrestrial objects have been well developed over the past decade. Teillet et al. (2001) calibrated L5 (TM) scenes with those of ETM+ over common targets of different spectral characteristics during L7's commissioning period. Using L7 imagery, TM was found to be within 2% (in counts) of relative radiometric accuracy. They also stated that dense vegetation and water bodies should not be used as calibration targets unless their spectral reflectances are available (Teillet et al., 2001). Thome et al. (2003) used ETM+ to validate the performance of the Earth Observing-1 (EO1) sensors, including the Advanced Land Imager (ALI) and Hyperion, Terra-MODIS, and IKONOS over the Railroad Valley Playa, Nevada (RVPN). The surface reflectance spectra obtained from ETM+ were propagated to the top of the atmosphere and were compared against what the other sensors “saw”. They concluded that, except Hyperion, the other sensors are relatively calibrated to better than 4.4% of ETM+ in all of the bands (Thome et al., 2003). Chander et al. (2004) evaluated radiometric fidelity of EO1-ALI imagery using coincident ETM+ data over desert sites and a grass field (Chander et al., 2004). The historical trends of the relative calibration of ETM+ and Terra-MODIS over desert sites were also presented in (Chander et. al., 2010a) and (Angal et al., 2010). In order to perform a robust vicarious calibration, a suitable site imaged nearly simultaneous with the two (or more) sensors has to be chosen. The selected site should exhibit stable radiometric properties, recognized as pseudo-invariant, which do not change over time. The corresponding target should also have near Lambertian properties, at least in the near-nadir viewing angles, and represent spatial uniformity throughout the calibration site. While the former minimizes its directional dependency, the latter ensures that the calibration site encompasses spectrally “pure” pixels (Thome, 2001). Over the past decade, several regions have been identified as calibration sites for validating remote sensing satellite systems. Among these sites are Railroad Valley Playa (RVPN) and Ivanpah, Nevada, USA, as well as a few other desert sites in Northern Africa (Chander et. al., 2010a). The relatively flat shape and high magnitude, i.e., ~ 30%, of the reflectance spectra associated with these sites make them ideal targets to calibrate the imaging systems designed for mapping and monitoring medium to high reflectance targets, such as soil, vegetation, and snow cover. However, not much effort has been put towards testing sensors, such as ETM+, over dark targets. In the following section, an approach dedicated to crosscalibrating a land sensor (ETM+) with an ocean color remote sensing system (MODIS) is proposed to examine the relative trend and the ability of the ocean system to predict the performance of the land sensor over the missions' lifetime. 2. Approach 2.1. The calibration sites For the purpose of this study, bodies of waters with relatively optically stable properties are utilized for evaluating ETM+ visible bands. Table 1 indicates the path-row, the site locations/elevations, the range of possible CHL concentrations (derived from MODIS products) and the total number of scenes used in the present paper. To a first order approximation, under ideal environmental conditions and near-nadir viewing angles, it is assumed that the water surface is nearly Lambertian. This is a valid assumption at near-nadir viewing angles and under normal environmental conditions (e.g. low wind speed). Moreover, it is desired that the corresponding site be situated

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Table 1 The specifications of the ETM+ scenes and the calibration sites. Sites

WRS-2 UTM Latitude, path/row zone longitude

Elevation Range of No. of (km) Chl (μg/l) image pairs

Lake Tahoe MOBY Lake Malawi Red Sea Striate of Hormoz

43/33 64/46 168/69 174/41 159/42

2.170 Sea level 0.777 Sea level Sea level

10 4 36 36 40

38.9 N, 120 W 20.85 N, 157.1 W 13 S, 34.6E 27.4 N, 34.3E 26 N, 57.1E

0.2–0.6 b 0.2 0.4–0.8 0.1–0.3 0.2–0.6

52 13 6 25 11

in an area where the effects of atmospheric gases and aerosols are minimal. Lake Tahoe, a high-altitude, mid-latitude lake located on the border of California-Nevada, USA, was found to satisfy the aforementioned conditions (Fig. 1). Due to its thermal stability and deep bathymetry, Lake Tahoe, (39°N, 120°W), has been used as a calibration/validation site for monitoring thermal channels of different flavors of remote sensing systems (Hook et al., 2005). Having a watershed area of 800km2, Lake Tahoe receives inputs from more than 60 river/streams among which the Upper Trukee River provides the largest stream flow into the southern lake areas, i.e., annual average of 10 m3/s (Schladow, 2011). Therefore, the southern parts of the lake were avoided in this study. Over the past decade, the NASA's Jet Propulsion Laboratory together with Tahoe Environmental Research Center has established collection sites to monitor the lake's physical/biological process. Among their observations, the water clarity and CHL concentration are of primary interest for this study. The Secchi depth of over 20 m and average CHL concentrations ofb 0.6 μg/l over the past 10 years indicate the lake's optical stability (Steissberg et al., 2010). Cloud-free image pairs most of which were acquired in late summer/early fall during the two missions' lifetime were used (Table 1). The main drawback of Lake Tahoe as a calibration site is its relatively limited spatial extent as opposed to the open waters that enable choosing areas with consistent atmospheric condition despite partial cloud contaminations. Since studying Lake Tahoe restricts our analysis to a limited range of signal levels, other sites situated in low-latitude areas, such as the marine optical buoy (MOBY) site and tropical–arid (Tr–Ar) lake/sea waters, are also investigated. The MOBY site established in 1997 in Lanai, Hawaii, is a NASA funded project for vicarious calibration/validation of ocean color products (Clark et al., 1997). The MOBY, which is equipped with an autonomous system to measure water-leaving radiance and total downwelled irradiance, has provided baseline optical measurements for SeaWiFS and MODIS datasets. This site was selected because of the availability of ETM+ imagery and its relatively clear atmospheric conditions. According to the published reports for this site, the average CHL distribution does not exceed 0.10 μg/l (oligotrophic waters) (Dong et al., 2009). Incorporating higher sensor-reaching radiances aids in quantifying the possible changes in the relative gain and offset between the two sensors. The brighter Tr–Ar sites include Lake Malawi in tropical east Africa, the northern Red Sea, and the strait of Hormoz in the Persian Gulf. Due to the climatic conditions, suitable scenes for MOBY and Tr–Ar were only available in late fall and winter periods. Although recognized as mesotrophic waters during this timeframe, the Tr–Ar waters exhibit less optical stability than Lake Tahoe and the MOBY site, and consequently, the concentrations of CHL have to be checked for anomalous scenes. Under ideal atmospheric conditions with low aerosol loading, the MODIS-derived CHL concentration maps provide a reasonable estimate of the sites' optical regime predominantly driven by CHL absorption/scattering properties. Furthermore, the atmospheric composition over such regions is temporally and spatially variable and is less known than that over Lake Tahoe/MOBY. The complex atmospheric condition reduces the number of successfully acquired image pairs for this study.

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Fig. 1. Lake Tahoe is located in the high mountains of the western US on Nevada–California border.

2.2. The criteria for image pair selection For the purpose of this study, the 500 m L1B calibrated Terra-MODIS products [W/m2 sr μm] from collection 5 (C5) are projected onto the UTM projection with WGS84 as the reference datum to maintain consistency with the L1T Landsat products (30 m ground sample distance). As in the previous cross-calibration studies of the two sensors, MODIS land bands, including B3, B4, B1, B2, B6, and B7 channels to represent the VNIR and Short-Wave-Infrared (SWIR) bands, are used to resemble ETM+ six reflective bands centered at 479 nm, 561 nm, 661 nm, 834 nm, 1650 nm, and 2207 nm (Chander et. al., 2010a). The ETM+ spectral band naming convention referred to as blue, green, red, NIR, SWIR-I, and SWIR-II is adopted for this study. The relative spectral responses (RSR) of the corresponding channels overlaid on an average sensor-reaching radiance (normalized with its maximum) over clear waters are shown in Fig. 2 (see also Table 2). Note the descending shape of the TOA radiance curve over the entire spectral range. The region-of-interests (ROIs) taken from the image pairs were situated in the near-nadir sensors' line of sight. It is highly desirable to choose a site imaged with a similar geometry by the two sensors. Both ETM+ and MODIS, for instance, observe Lake Tahoe at slight off-nadir scanning angles, i.e., b 3°. This similarity in the acquisition geometry mitigates artifacts introduced by the wide scanning angles of MODIS, such as increased polarization sensitivities. Moreover, the large scanning angles of MODIS cause significant differences in the path-lengths, the atmospheric conditions, and the BRDF effects that may invalidate the Lambertian assumption for bodies of waters. Although the ROIs satisfy very similar viewing geometry, the relative sun-sensor azimuth angles are slightly different due to the approximately 25-minute time difference. Such disparities are inevitable and assumed negligible owing to

the near Lambertian properties of the sites. The change in the solar elevation angles, however, is taken into consideration and is described in Section 2.3. The ROIs are rectangular areas of 1 km 2 containing four MODIS pixels equivalent to approximately 900 ETM+ pixels. The four MODIS pixels give sufficient number of samples while avoiding possible spatial heterogeneity due to atmosphere or water types and potential adjacency effects from the land. The area-averaged TOA radiance values calculated for ETM+ should mitigate the effects due to low SNR and quantization rate, glint, differences in wave facets, and whitecaps. It should be noted that the ROIs were drawn over spatially uniform waters and near-shore areas in the vicinity of discharges were avoided. This also minimizes the adjacency effects and possible mis-registration errors. The corresponding ROIs are also expected to exhibit minimum variability, i.e., low standard deviation. This condition minimizes the variability due to the inherent composition of the water bodies. To meet this condition, the coefficient of variation (CV), i.e., the ratio of standard deviation to mean value, was allowed to reach a maximum of 3%, 5%, 10%, and 17% for ETM+ VNIR bands, respectively. The corresponding values adopted for MODIS-derived ROIs were 0.2%, 0.7%, 0.6%, and 2%. Note that the larger variations in the ETM+‐derived values (particularly in the longer wavelengths) are due to its poorer SNR and coarser radiometric resolution when compared to those of MODIS. Moreover, the inverse of the CV values can be thought of the scene-derived SNRs associated with each dataset. Besides restricting the calibration sites according to the viewing geometry and the spatial uniformity, the atmospheric conditions between the two acquisitions were controlled by comparing the sensors' responses in the SWIR-bands. Following preliminary studies resulting from several simulations, it was found that under same imaging/environmental conditions, i.e., atmosphere, sun angle, and

Fig. 2. The relative spectral response functions of ETM+ (solid lines) and MODIS (dash lines) overlaid on an average modeled TOA radiance normalized to its peak value.

N. Pahlevan, J.R. Schott / Remote Sensing of Environment 125 (2012) 167–180 Table 2 Spectral configuration of ETM+ and MODIS together with their corresponding exo-atmospheric solar irradiances used in this study.

Blue Green Red NIR SWIRI SWIRII

Center wavelength [nm]

Nominal bandwidth [nm]

Exo-atmospheric solar irradiance [W/m2 μm]

ETM+

MODIS

ETM+

MODIS

ETM+

MODIS

479 561 661 834 1650 2207

469 555 645 858 1640 2130

70 80 60 120 200 260

20 20 50 35 24 50

1969 1840 1551 1044 226 82

2015.1 1859.1 1606.1 991.7 239.6 89.4

viewing condition, MODIS outputs, on average, 8% and 30% larger signals in the SWIR-I and SWIR-II bands, than those of ETM+. Therefore, it was decided to discard image pairs showing more than 8% and 30% differences in the SWIR-I and SWIR-II bands, respectively. Such a condition ensures consistency in the atmospheric states during the L7 and Terra overpasses. The approximately 20% average differences for the two bands give an estimate of the collective differences in the RSRs, the relative calibration, the BRDFs, the solar zenith angles (SZA), and the environmental conditions. Note that due to the relative MODIS-ETM+ spectral configurations for these bands (Fig. 2 and Table 2), MODIS always exhibits larger signals. With this strict requirement, out of approximately 150 image pairs over the sites, which were initially selected, nearly 35% (leaving n=99 scene pairs) were filtered out. It should also be noted that this criterion was not applicable for the most recent MODIS scenes, i.e., 2010–2011, over Lake Tahoe as negative values were recorded for most pixels in the SWIR bands causing them to be rejected. In addition to the calibration issues associated with MODIS, the limited number of photons reaching the sensor from a mid-latitude lake characterized with clear atmospheric conditions can explain the incorrect observation of the surface properties at the top of the atmosphere. The ROIs consisting of four MODIS pixels were drawn to obtain the basic statistics. The CV for each individual ROI was controlled to ensure the relative spatial uniformity and to avoid mis-registration errors. 2.3. Conversion to the TOA reflectance As Terra acquires imagery nearly 25 minutes after L7 overpass, the total solar radiation reaching the earth surface varies due to the change in the solar zenith angle (SZA). Moreover, the available solar radiation is different for different days of year (DOY) throughout the year. In order for a consistent analysis across all of the image pairs these factors were taken into account by applying the following equation, which transforms the observed TOA radiance quantity to the unitless TOA reflectance (ρ TOA):

TOA

ρλi

¼

2 π LTOA λi d

Eexo λi cosðθs Þ

ð1Þ

where ρλi TOA stands for the unitless TOA reflectance (planetary/apparent reflectance) at λi, Lλi TOA [W/m2 sr μm] is the TOA radiance for the same wavelength, d is the astronomical earth-sun distance [AU], Eλexo i [ W/m2 μm] is the band-specific exo-atmospheric solar irradiance, and θs is the SZA in degrees. The SZA was computed for each individual image at the location where the ROI was drawn. This is, in particular, important when determining the SZA for the MODIS-derived ROI. Two different solar models were used to represent Eλexo for ETM+ and the 0 MODIS sensors. For the ETM+ sensor, the Chance database (CHKUR) built in MODTRAN 4.0 (Berk et al., 1999) was used whereas the world radiation center (WRC) solar model was used for MODIS (Choi et al., 2008). Table 2 contains the effective exo-atmospheric solar irradiance values associated with the two sensors.

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2.4. Adjustments for the RSR functions As illustrated in Fig. 2, ETM+ RSR functions cover broad spectral regions relative to those of MODIS. This difference introduces significant inconsistencies when imaging a reference TOA radiance curve representing a large, band-to-band gradient (Teillet et al., 2007). This is most noticeable over dark targets when the signal is primarily dominated by the atmospheric interference. In order to take into account the differences in the band-specific RSRs of the two sensors, a model-based approach similar to that of Teillet et al. (2007) was adapted for this study. This technique relies upon hyperspectral TOA radiance spectra generated through simulations. Chander et al. (2010a) also proposed a similar method applying Hyperion measurements to estimate the RSR adjustment factors when imaging desert sites (Chander et. al., 2010b). Depending on the shape and the magnitude of the ground target and the atmospheric conditions, the effects of the differences in the RSRs would differ. If a dark target, such as water or dense vegetation, is considered as the ground target then the atmospheric condition must be estimated (see Section 2.4.2). 2.4.1. Modeling the site-specific diffuse surface reflectance (Rd) In this study, a radiative transfer code, i.e., MODTRAN (Berk et al., 1989), is employed to simulate the TOA radiance spectrum observed by the two sensors at a given time, which represents the mean overpass time of the two sensors. Given average CHL concentrations for each site (Table 1), the diffuse surface reflectance spectrum (Rd) were simulated using the Hydrolight code (Mobley and Sundman, 2008). Average Inherent Optical Properties (IOPs) of the sites were also provided to the Hydrolight code. For each site, three different Rd representing different CHL concentrations (increments of 0.2 μg/l in Table 1) were supplied to MODTRAN to simulate the TOA radiance for slightly different waters. The slight variations in the CHL concentrations account for the uncertainties in the estimated IOPs with which the reflectance properties are predicted for each site. The CHL concentration for several image pairs, however, was validated using MODIS-derived products. The variations of the CHL concentrations are carried out simultaneously with adjusting the aerosol properties described below. Note that the absorption due to the colored dissolved organic matter (CDOM) component of the waters is neglected in this study as ETM+ lacks the necessary band configuration to distinguish signals below 450 nm where CDOM is most influential. 2.4.2. Estimating the TOA radiance The modeled Rd of the calibration sites are propagated through the atmosphere to achieve the TOA radiance spectra for each image pair. For the simulations over Lake Tahoe, the MODTRAN code is provided with the modeled atmospheric profiles derived from North American Mesoscale Model (NAM) available from NOAA's National Center for Environmental Prediction (NCEP) office. An atmospheric profile, at 12 pm local time, for each DOY corresponding to a successful MODIS-ETM+ collect was obtained from the NAM model. For the MOBY/Tr–Ar sites, average upper-air atmospheric profiles were supplied to the code. The MODTRAN-derived TOA radiance curves were spectrally resampled to the RSR functions to reconstruct the multi-spectral curves as seen by ETM+ and MODIS. To do so, the following expression was applied ∫ Leff ðλ0 Þ ¼

LðλÞRSRðλÞdλ

bandpass

∫

RSRðλÞdλ

ð2Þ

bandpass

where Leff(λ0)is the band-average (effective) spectral radiance [W/m 2 sr μm] for the channel centered at λ0, L(λ) stands for the MODTRAN-derived spectral radiance spectrum and RSR(λ)is the normalized spectral response function.

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The aerosol type and visibility associated with each individual image pair is estimated via a spectral matching technique between the MODIS-derived TOA radiance curves and multiple MODTRAN simulations. While rural/urban aerosols were regarded to represent the dominant Lake Tahoe's aerosol content, maritime/rural aerosol types were adjusted for MOBY/Tr–Ar. The aerosol visibility is found by minimizing the root mean squared error (RMSE) calculated between the model outcomes and the reference curve across all of the seven bands, corresponding to the ETM+ reflective spectral channels. The RMSE represents the similarity of each individual simulated TOA radiance and the one observed at the TOA by the MODIS instrument. This process is repeated for each image pair for a certain DOY. It should be noted that ideally the exact shape/magnitude of the MODIS-derived curve is desired; however, the goal is to make an appropriate approximation of the ratio of the sensors' responses under an atmospheric condition that closely resembles the conditions at the time of imaging. In other words, it is not required to quantify the aerosol condition through this method and a reasonable estimate satisfies our objectives (see Section 4). 2.4.3. Applying the RSR adjustment and evaluate the MODIS-ETM+ disparity After approximating the aerosol contents for each MODIS-ETM+ image pair, the TOA radiances are passed through the sensors' RSRs Eq. (2) followed by conversion to the TOA reflectance for a mean SZA and d. As a result, the only contributor to the differences in the simulated band-specific TOA reflectance curves at each λi is the differences in the RSRs. Therefore, the following expression yields the RSR adjustment factor α λi ¼

ρMODIS TOA ρL7 TOA

ð3Þ

MODIS L7 and ρTOA correspond to the MODTRAN-derived TOA rewhere ρTOA flectances for MODIS and ETM+, respectively. Note that any slight differences caused by the use of different solar spectra (see Section 4.1) to calculate TOA reflectance are incorporated in the correction factor. The ETM+‐derived TOA reflectance values for targets of similar spectral shape in each band can then be adjusted by applying the RSR adjustment factor (αλi) as a multiplicative coefficient, i.e.,:

L7

L7

ρ′TOA ¼ α λi ρTOA

ð4Þ

The average RSR adjustment factors obtained for Lake Tahoe were found to be 1.1027, 1.0327, 1.0757, and 0.9055 for the blue, green, red, and NIR bands. The corresponding averaged coefficients for the MOBY/ Tr–Ar sites were 1.0949, 1.0342, 1.064, and 0.918. The largest disparity in the RSRs is observed in the blue and the NIR bands. However, the RSR functions exhibit rather high degree of similarity in the green bands as shown by approximately 3% adjustment factor (1.03). In general, for water targets, the greater the TOA radiances, the flatter the spectral shape and, therefore, the sensor-to-sensor disparity diminishes. The coefficients primarily vary with the change in the magnitude of the TOA radiance mainly driven by the atmospheric conditions. Nonetheless, depending on the atmospheric conditions, CHL concentrations can also slightly influence the coefficient associated with the blue band. These coefficients are applied to normalize the ETM+‐derived radiance values with respect to those of MODIS. The difference between two scenes for a specific DOY can be expressed as percent difference (PD):

.  L7 MODIS MODIS ρ′TOA −ρTOA ρTOA  100

.  L7 MODIS MODIS ρTOA  100 ¼ αρTOA −ρTOA

PD ¼

ð5Þ

which measures the disparity in the calibration of the two sensors. Eq. (5) can be further averaged for all the available scene pairs (n) per

year, i.e., PDY. To summarize, the following steps are to be followed to perform a cross-calibration task for an image pair over the water sites: 1. Geo-registration of the image pairs 2. Select the ROIs from the images based on the criteria described in Section 2.2 3. Calculate the mean values 4. Convert the image-derived TOA radiances to the TOA reflectances 5. Compute the RSR adjustment factor (αλi) through predicting the TOA reflectances by going through the following steps a. Provide the radiative transfer code with three different water types b. Configure the code for the mean time of the two acquisitions c. Find the best estimate for the MODIS-derived curve by simultaneously adjusting water types, aerosol types, and aerosol visibility d. Resample the matched TOA radiance curve to the ETM+ and MODIS RSRs Eq. (2) e. Convert to the TOA reflectance Eq. (1) 6. Apply the RSR adjustment factor Eq. (4) The adjustment for the differences in the RSRs, which normalize the responses of the two sensors in the TOA reflectance domain, is a vital part of the cross-calibration over clear waters. 2.5. Validation over a bright calibration site In order to validate the proposed approach for clear waters, the procedure was also implemented for the RVPN site over the recent years, i.e., 2008–2011. The RVPN is a desert calibration site situated at (39 N, 120 W), 1.35 km above sea level with typically clear atmospheric conditions (Thome et al., 2003). The site also represents a reasonably spatially homogenous area making it a suitable bright target. To examine the relative calibration of the sensors over this site, a handful (n = 11) of nearly coincident, cloud-free MODIS-ETM+ image pairs collected in 2008–2011 timeframe were utilized. Caution was taken to discard days with wild fire/smokes effects. An average surface reflectance of the site (Czapla-Myers, 2011) was input to the MODTRAN code. As expected, the αλiover the RVPN site are close to unity, i.e., 0.9935, 1.003, 0.9865, and 1.023, because of the relatively flat shape of the site's spectrum (Teillet et al., 2007). 3. Results The results of the cross-calibration of ETM+ with MODIS (C5) are presented in this section. While the cross-comparison over clear waters are given for the entire life time of the two missions, the MODIS-ETM+ relative calibration over the RVPN site is presented for only the very recent years, i.e., 2008–2011. The latter study aids in validating the findings over the dark targets in the above timeframe as compared to the recent studies (Czapla-Myers, 2011; Wang et al., 2012; Markham et al., 2012). 3.1. Over-water cross-calibration The historical trend study is obtained through calculating the annual percent differences (PDY) between the mean values corresponding to the ROIs throughout 2000–2011. Fig. 3 shows the long-term trends in the relative differences of ETM+ and MODIS obtained from annually averaged differences for all of the sites. The error bars indicate the uncertainty associated with the observations, i.e., n ≈9 made per year. The standard deviations are due to the cumulative impacts of inconsistencies in the atmospheric conditions and incorrect estimations of αλi (see Section 4). For completeness, the relative differences for the NIR band are also presented. The PDY is expressed in [%] of TOA reflectance [%], which translates into approximately similar percentage values in the TOA radiance domain. The average radiance values [W/m 2 sr μm]

N. Pahlevan, J.R. Schott / Remote Sensing of Environment 125 (2012) 167–180

173

Fig. 3. The historical cross-calibration trends of the relative differences Eq. (5) between ETM+ (L7) and MODIS (MOD) calculated by averaging the differences for all of the sites per year (PDY) expressed in [%]. The calibration differences in the blue and the green bands remain relatively stable during 2000–2007 and increase in 2008–2011. The solid horizontal lines exhibit average “decadal” difference while the error bars are one standard deviation per year. Note that the total number of image pairs are 99.

of the MODIS data for Lake Tahoe is 44.5, 19.8, 8.9, and 2.6 while the corresponding levels for the MOBY/Tr–Ar sites are 54.2, 26.4, 13.6 and 4.5 for the VNIR bands. It appears that ETM+ consistently exhibits higher outputs than MODIS in the red and the NIR bands over its entire lifetime whereas the signals, on average, are smaller during 2000–2007 for the blue and the green bands. ETM+ blue signal has been slightly lower, i.e., −1.6% on average (solid horizontal line in Fig. 3), during this timeframe, i.e., 2000–2007. However, the disparity in this band peaks in 2011 as much as +2.6%. The considerable change is related to the degradations associated with MODIS scanning mirror, which has resulted in increased sensitivity to polarization, and its onboard calibrators (Kwiatkowska et al., 2008; Xiong, 2011). The significant Rayleigh scattering in the blue portion of the spectrum leads to highly polarized signals at the top of the atmosphere. Therefore, such errors are expected to be less significant in the other visible bands (Kwiatkowska et al., 2008), although a discernable increase in the average differences in the green band is apparent as well. An average CV= 9.2% (mean standard deviation over the mean signal, i.e. σ =μ calculated for 2000–2007) in the blue band suggests high fidelity in the bias estimated during 2000–2007. The ETM+ green band exhibits a rather stable trend with an average relative difference of −0.93% in 2000–2007. Similar to the trends found for the blue band, the overall trend in bias shows a slight, gradual increase during 2008–2011. When compared to the blue band, higher uncertainties exist in the green band, i.e., CV= 18.6%. A fairly uniform bias, i.e., +3.2% from the post-lunch to the very recent years, was found for the ETM+ red band. However, there is a slight increase in PDY from the early mission to 2011, i.e., b1%. Due to the large uncertainties associated with the observations in the red band (CV = 43%), any degradation effects due to MODIS are not clearly captured. The primary reason inducing such uncertainties is believed to be due to inaccurate modeling of TOA radiance (Section 2.4.2) at such low signal levels (b 15 [W/m2sr μm]) as well as atmospheric inconsistencies between the two overpasses (see Section 4).

A +4.8% average bias was also observed in the ETM+ NIR band. Similar to the red band, the historical trend remains stable during the lifetime of the two sensors. That being said, the very low signal levels over water bodies in the NIR band diminish the ability to characterize the sensors' relative calibration stability. The noticeable annually averaged standard deviations (σ ≈3:9%Þ in this band (CV = 160%) verifies this speculation. Although the NIR band has no contribution in the water constituent retrieval, any mis-calibration artifacts can yield incorrect retrieval of atmospheric parameters (Ruddick et al., 2000; Wang and Gordon, 2002). The overestimation of the NIR output, for instance, would result in the overestimation of the atmospheric effects, and consequently, a failure to properly retrieve water-leaving radiance. In order to obtain better insights in regard to the relative gain and bias between the sensors' outputs in each spectral band, the scatterplots of the data points (n = 99) corresponding to the averaged ROIs in units of TOA reflectance [%] are analyzed (Fig. 4). The 1:1 slope and the root-mean-squared (RMSE) are also shown in Fig. 4. Given the large degradations in the MODIS performance (not accounted for in C5) in the recent years (Fig. 3), the data points from 2008 to 2011 were excluded for the blue and the green bands. This exclusion yielded n = 68. The data points include the ROIs taken from both Lake Tahoe and the MOBY/Tr–Ar sites. Linear regression models were fitted to the corresponding data points to find out inconsistencies between the two sensors over the dynamic range. This analysis also allows for investigating the spread of the data points in each band, i.e., precision error. The relatively high R 2, i.e., > 0.99, for all of the visible bands suggests a high predictability of MODIS data with ETM+ observations. As indicated by the slopes, there are slight signal dependencies in the visible bands, particularly in the blue and the red bands. While ETM+ underestimates the low signal levels in the blue band (Fig. 4-a), it overestimates the high signal outputs in the red band (Fig. 4-c). The most consistent trend is found for the green band with ~ 0.98 slope and RMSE = 0.05. The greatest change in the

174

N. Pahlevan, J.R. Schott / Remote Sensing of Environment 125 (2012) 167–180

Fig. 4. The band-specific scatterplots of the averaged ROIs derived from the corresponding L7-MODIS imagery in units of apparent reflectance [%]. The 2008–2011 timeframe is excluded for the blue (a) and the green (b) bands. The solid line represents the 1:1 slope.

characterized system for dark targets. This is accomplished through simulations under different atmospheric scenarios and water types. The calibration uncertainties are applied to several simulated TOA radiance curves to evaluate their effects on the retrieval of the diffuse surface reflectance (Rd) and the water constituents. 3.2. Over-land cross-calibration A similar procedure to that applied over clear waters was also implemented over the RVPN site. This case study aims at validating our methodology and demonstrating that the error levels lie within the ETM+ radiometric uncertainty, i.e., b5%, expressed in the TOA radiance domain. Fig. 5 shows the PDY (average percent differences Eq. (5)) for a limited number of image pairs acquired during 2008–2011. Although less significant over the RVPN site, i.e., b 2%, the degradations in the MODIS B3 (blue) band, which are perhaps due to the failure in accurately characterizing the degradations of the SD, have boosted the relative differences between the two sensors (Xiong et al., 2007). This uncertainty can be significant when analyzing bright targets or vegetations (Wang et al., 2012). The high error bar associated with this band refers to the uncertainties in the atmospheric conditions. The relatively small biases in the green, red, and 4

((L7-MOD)/MOD)*100

relative gain (slope) was obtained for the red band, i.e., slope of 0.94. As the signal-level rises in this band, the ETM+ output increases with a higher rate than that of MODIS. In contrast to the red band, the NIR band represents approximately a uniform disparity over a reasonably large signal range, i.e., slope of~ 0.99. Given the two forms of representing the relative MODIS-ETM+ outputs, it is inferred that the largest discrepancies in the blue band occur when imaging low signal levels while the red band shows the greatest relative differences for high signal levels. While MODIS-ETM+ signals are relatively consistent in the green band (R2 =0.998), the NIR band exhibits the largest spread across the dynamic range (R2 =0.987). As described, ETM+ tends to slightly underestimate the blue signal, i.e., 1.6%, and overestimates the red and the NIR outputs, on average, 3.2% and 4.8%. The relative errors for the green band, although very small, were estimated to be, on average, −0.93%. These uncertainties can be potentially due to non-linearity in the responsivity of the ETM+ sensor at the low signal levels. In addition to the non-linearity, the presence of straylight in the very low signal levels can add to the ideal signal levels. It is speculated that straylight may be the primary reason for the high signal levels in the red and the NIR bands. It should be noted that straylight is negligible when sensing medium to high reflective targets (see Section 3.2). The collective impact of these two factors, i.e., non-linearity and straylight, are thought to result in the small uncertainties found for such low signal levels. It is also believed that ETM+ polarization sensitivity over blue waters can add to the calibration uncertainties (Hu et al., 2001). Overall, it should be noted that calibrating an imaging system at low signal levels (particularly in the red and the NIR bands) is not an easy task. The large standard deviations (shown in Fig. 3) for these bands indicate this difficulty. Nonetheless, the relative differences between the two sensors found for these bands remain relatively stable during the 2000–2007 period, i.e., σ=0.6% and σ=1.4% (calculated for PDY values) for the red and the NIR bands, respectively. The corresponding variability for the blue and the green bands for the same timeframe was calculated as σ=0.7% and σ=0.4% (units of TOA reflectance). The stability found here is in agreement with the recent publication on the absolute calibration of ETM+ (Markham, et. al. 2012) wherein the long-term stability of gain and bias has been studied. In Section 5, the relative calibration uncertainties noted above are treated as bias-only errors in reference to MODIS as a well-

3 2 1 0 -1 -2 0

1

2

3

4

5

Bands Fig. 5. The average percent differences for the MODIS-ETM+ ROIs over the RVPN site. The error bars indicate the standard deviations associated with all of the ROIs.

N. Pahlevan, J.R. Schott / Remote Sensing of Environment 125 (2012) 167–180

the NIR bands, i.e., − 0.5%, − 0.6%, +0.5%, respectively, are well in agreement with the ETM+ radiometric uncertainty requirements. The degradations found in the green for bodies of water (Section 3.1) is minimal over such bright targets (Wang et al., 2012). The above-noted errors translate into +1.6%, − 0.4%, − 0.6%, and +0.5% difference in the TOA radiance domain whose average values for the RVPN site are 123.1, 133.2, 126.3, 93.7 [W/m 2 sr μm] for the VNIR bands. The above-noted values were found to be consistent with the recent calibration efforts, which indicate ETM+ high calibration stability (Czapla-Myers, 2011; Markham, et. al., 2012). 4. Error budget analysis In order to understand the robustness of the over-water crosscalibration technique, it is desired to investigate the uncertainties associated with different steps pursued in this study. To do so, the sources of errors have to be identified and accounted for in the processing chain. In the proposed methodology (Section 2.4), two primary steps were taken to obtain the sensor-to-sensor historical trend: a) estimating the RSR adjustment factor (αλi) and b) calculating the percent differences (PDY). While the former is primarily associated with modeling the TOA radiance described in Section 2.4.2, the latter is a function of the scene-derived (sensors') uncertainties. 4.1. Estimating αλi In the proposed approach, the main uncertainty corresponds to the estimation of the RSR adjustment factor (αλi) for each individual band (i) (Eq. (3)). Here, an error propagation analysis is carried out to evaluate how much error due to the assumptions/approximations made throughout the calculations is propagated through when estimating αλi. Based on the error propagation theory and considering Eq. (3) as the fundamental model (Beers, 1953): !2 !2 !12 ∂α i ∂α i MODIS L7 δρ þ δρ i i ∂ρL7 ∂ρMODIS i i !2 !2 !12  MODIS 1 −ρ MODIS L7 i δρ þ δρ   i i 2  L7 ρ  L7 ρ i i

δα i ¼ ¼

ð6Þ

where δαi represents the uncertainty associated with the RSR adjust MODIS  L7 ment factor for the channel i, ρ and ρ i i are site-specific mean TOA reflectance values computed from all of the ROIs used in this study (Table 1), δρiMODIS[%] and δρiL7[%] are band-specific errors committed when approximating the MODIS- and ETM+‐derived apparent reflectances (Section 2.4.2). By taking the partial derivative of Eq. (1) with respect to its individual components, i.e., LiTOA, Eiexo, and θ , that bear uncertainties, δρ can be decomposed as the following δρ ¼ πd

2

 2  2  2 !12 ∂ρ ∂ρ ∂ρ  100 δL þ δE þ δθ ∂L ∂E ∂θ

ð7Þ

where each term (in parentheses) is in units of sr −1 and δρ stands for the errors corresponding to the TOA reflectance computed for ETM+ and MODIS, and d is set to unity. The partial derivatives are further calculated as ∂ρ 1   ¼ ∂L E cos θ ∂ρ −L   ¼ ∂E E2 cos θ     ∂ρ L ¼ tan θ sec θ ∂θ E

ð8Þ

where constants are discarded. In order to quantify δρ, the errors committed when estimating L, E and θ (Section 2.4) also have to be

175

quantified. The term δL is caused by the cumulative effects of imperfect modeling of atmosphere and water-leaving reflectance (Rd), i.e., the best-match predicted through spectral optimization in Section 2.4. For each individual scene, there is a mis-match between the estimated TOA radiance and that derived from MODIS. An average δL can be defined as the absolute mean difference (Δ) computed for all of the scenes (Table 3). Relatively higher errors were estimated for ETM+ (δL) as MODIS-derived TOA radiance was applied in the spectral optimization. Table 3 contains the above-noted errors specific for each site along with the average propagated error (δα) for each spectral band. Analysis of δL  for each site indicates that relative to the average TOA radiance ( L) while the largest errors are associated with the Red Sea site, the MOBY site exhibits best predictions of the TOA radiances for all bands. This is related to the greater ability in modeling the clear atmospheric conditions over MOBY. The presence of aerosol loading over the Lake Tahoe site has resulted in relatively large δL. According to (Froehlich et al., 1995), the uncertainty associated with the measurements of exo-atmospheric solar irradiance (E) for the WRC model is b 0.1%. A similar error value (δE) is assumed for the CHKUR model used as a reference for the ETM+ instrument. Nevertheless, it is expected that the errors associated with the use of slightly varying solar models are minimal relative to δL. This is because the contribution from δE is diminished by the very small multiplicative factor of δρ/δE (on the order of 10−6 for all of the VNIR bands) (Table 2 and Table 3). Because SZA (θ) was calculated specifically for each ROI at a given (φ,λ), its associated error is regarded as minimal. However, different approximations used to calculate θ result in a slightly different angle. Therefore, for completeness, a maximum error for this component is estimated to be δθ ≈0.1∘ = 0.0019r for θ ¼ 32∘ and θ ¼ 42∘ for Lake Tahoe and the MOBY/Tr–Ar sites, respectively. The disparity in θ is due to the seasonal differences in the available scenes for each site, i.e., summer/fall for Lake Tahoe and fall/winter for the other sites. Table 3 contains band- and site-specific errors associated with each component as well as the total errors obtained in δρ and δα. As expected, the largest relative errors correspond to the NIR band (the average signal levels are given in bold). The largest contributions to δρ are from the uncertainties in predicting the TOA radiance (δL). This uncertainty results from a combination of errors in estimating Rd and atmospheric conditions. While the total errors (δαi) for the MOBY site are the lowest, the largest uncertainty corresponds to the Tr–Ar sites. This trend is related to the predominantly clear/troposphere atmosphere over MOBY and turbid atmospheric conditions (haze or dust) for the Tr-Ar site. It should be noted that 0.88 b αi b 1.15. The cumulative error propagated through the PDY calculation for the two sensors are further detailed in the following section. 4.2. Estimating annually averaged percent differences (PDY) After estimating the errors in RSR adjustment factor, it is desired to investigate the uncertainties associated with calculating the annually percent differences (δPDY) utilized in the historical trend study (Section 3.1). A similar procedure as described in the previous section applies here. The primary source of error in this analysis corresponds to the scene-derived L TOA. Here, the average standard deviations of the ROIs drawn from the ETM+ and MODIS scenes are considered as δL L7and δL MODIS (Table 4). The error associated with the SZA is assumed negligible due to relatively accurate knowledge of each ROI taken from each scene. To calculate the annually averaged error (δPDY), the partial derivative of Eq. (5) is derived as bellow  δPDY ¼

∂PD δα ∂α



2 þ

∂PD L7 δρ ∂ρL7

2

 þ

∂PD MODIS δρ ∂ρMODIS

2 !12

−1

n 2  100 ð9Þ

176

N. Pahlevan, J.R. Schott / Remote Sensing of Environment 125 (2012) 167–180

Table 3 The error analysis results associated with RSR adjustment factor (δα). Note that δθ (uniform across all of the bands) is not included for brevity. δL[ W/m2 sr μm]/L

Tahoe Tr–Ar MOBY Tahoe Tr–Ar MOBY Tahoe Tr–Ar MOBY Tahoe Tr–Ar MOBY

Blue

Green

Red

NIR

 δρ [%]/ρ

δE[ W/m2 μm]

ETM+

MODIS

1.7/37 2.15/45 0.60/40 0.76/18 0.82/22 0.32/18 0.87/8 0.62/9 0.45/8 0.24/3.5 0.51/4.3 0.26/2.6

1.1/45 1.02/52 0.38/49 0.45/20 0.71/24 0.22/20 0.7/9 0.60/10 0.59/9 0.25/3 0.48/3.9 0.20/2.3

ETM+

MODIS

2.0

2.1

1.8

1.9

1.5

1.6

1.1

1.0

 δα/α

ETM+

MODIS

0.31/9.5 0.39 0.11 0.15/4.6 0.16 0.06 0.20/2.5 0.15 0.10 0.08/1.2 0.18 0.10

0.19/9.5 0.18 0.06 0.09/4.6 0.14 0.04 0.16/2.5 0.14 0.14 0.09/1.2 0.17 0.09

0.038/1.1 0.046 0.014 0.038/1.03 0.047 0.017 0.09/1.06 0.065 0.076 0.095/0.89 0.192 0.090

where n ≈ 9 is the number of scene pairs available for each year (Y). Analogous to the steps taken in the previous section Eq. (8), δρ MODIS and δρ L7can be obtained. The only difference is that the uncertainty associated with L TOA is sensor/scene dependent. Larger errors are associated with the ETM+ sensor due to its low SNR and poor radiometric fidelity. Table 4 lists band-specific errors obtained for each component (L, ρ, and α) together with the total error propagated through the process. The values represent average values for each site. According to δPDY, it is found that, on average, 1.3%, 1.6%, 3.5%, and 6.5% errors are associated with the VNIR bands. This is consistent with the observed uncertainties shown in Fig. 3. It is clear that the errors associated with the proposed methodology are very signal dependent and are more significant over the sites with high atmospheric effects. By setting δL(λ) = 0 and then δα(λ) = 0 in Eq. 9, it was inferred that the process errors in the visible bands are primarily dominated by the uncertainties related to (δα) than those associated with δL. In contrast, δL has a larger contribution than δα in the errors corresponding to the NIR band, i.e., sensor-limited. Note that δLL7(834)> > δLMODIS(858). Needless to say that cross-calibrating sensors with high radiometric fidelity and SNR lead to more robust analysis in the NIR band.

targets and the slight mis-calibrations found in this study lie within the ETM+ radiometric uncertainty. Due to weak signals arising from a body of water together with ETM+ low SNR, the calibration errors, even though small, can contribute to erroneous retrieval of Rd. The calibration uncertainties introduce errors in the retrieved Rd only when physics-based models are used to remove atmospheric effects. Here, the band-specific bias-only errors, obtained for ETM+ in Section 3.1, are applied to approximate the errors when retrieving Rd. In order to generalize our study, four different water types (Table 5), representing Lake Tahoe and Lake Ontario, USA, waters, were propagated through the atmospheric columns (determined by relative humidity (RH)) commonly found over the two sites. Table 5 contains the range of the variables adjusted for Hydrolight simulations. The CHL and TSS indicate chlorophyll-a [μg/l] and Total Suspended Solids [g/m 3] concentrations. The modeled diffuse reflectance spectra (Rd) are illustrated in Fig. 6. For each water type, various aerosol models and concentrations, specified by the visibility parameter in the MODTRAN code, for different DOYs were included to capture a wide variety of signal levels and atmospheric conditions. The MODTRAN-derived total sensor-reaching radiances, Lt(λ), were then adjusted with the bias-only calibration errors as following:

5. Sensitivity analysis of the calibration uncertainties

L′t ðλÞ ¼ ½1 þ βðλÞLt ðλÞ

5.1. Retrieval of the diffuse surface reflectance (Rd) As described, in this section the relative calibration differences obtained for ETM+ are treated as absolute calibration errors. In order to evaluate to what extent such calibration uncertainties would impact the retrieved Rd, which carries information about the in-water components, a series of sensitivity analyses were conducted. This is a crucial part of this study as ETM+ is well calibrated for bright

Table 4 The error analysis results associated with the annual percent difference (δPDY).

Blue

Green

Red

NIR

Tahoe Tr–Ar MOBY Tahoe Tr–Ar MOBY Tahoe Tr–Ar MOBY Tahoe Tr–Ar MOBY

δL[ W/m2 sr μm]

δρ [%]

ETM+

ETM+

MODIS

0.15 0.17 0.17 0.12 0.14 0.14 0.14 0.17 0.17 0.18 0.20 0.12

0.021 0.029 0.028 0.018 0.023 0.022 0.016 0.019 0.019 0.011 0.013 0.013

MODIS

0.8

0.1

0.6

0.09

0.61

0.07

0.51

0.03

δα

δPDY[%]

0.038 0.046 0.014 0.038 0.047 0.017 0.09 0.065 0.076 0.095 0.192 0.090

1.4 1.7 0.8 1.6 1.9 1.2 3.9 3.5 3.2 5.4 8.3 5.8

ð10Þ

where β(λ) represents the band-specific biases found in Section 3.1 and L′t(λ) represents the un-calibrated TOA radiance. In other words, the simulated spectra, resampled to the ETM+ RSRs Eq. (2), were adjusted −1.6%, −0.93%, +3.2%, and +4.8% in the blue, green, red, and the NIR bands, respectively. Then, the governing remote sensing equation (Schott, 2007) was solved in the inverse mode (ignoring effects from sun glitter and whitecaps which were also ignored in the forward mode) to retrieve Rd: h i U U L′t ðλÞ ¼ Esλ cosðσ s Þτ1 ðλÞRd ðλÞ=π þ Ldλ Rd ðλÞ τ2 ðλÞ þ Luλ þ r f τ2 ðλÞLdλ ð11Þ Table 5 The variables applied for the MODTRAN simulation. The numbers in brackets denote the increments. Aerosol

DOY Lake Tahoe Lake Ontario

Visibility (km)

Type

5–80 (5)

Rural-Maritime-Urban

150–300 (30) Water Types (CHL = 0.3, TSS = 0) slightly turbid/mesotrophic (CHL = 1, TSS = 0.5 ) Moderately Turbid/eutrophic (CHL = 4, TSS = 4) Turbid/eutrophic (CHL = 10, TSS = 10)

N. Pahlevan, J.R. Schott / Remote Sensing of Environment 125 (2012) 167–180

177

Fig. 6. The modeled surface reflectance (Rd) for different water types.

where L′t(λ) denotes the total, un-calibrated TOA radiance [W/m2 sr μm], Esλ represents the exo-atmospheric solar irradiance [W/m2 μm], σs stands for the SZA, τ1 is the solar-earth path transmission, RdU(λ) is the un-calibrated unitless diffuse reflectance, Ldλis the downwelled sky radiance [W/m2 sr μm], τ2 is the sensor-earth path transmission, and Luλ indicates path radiance [W/m2 sr μm], which is the cumulative effects of Rayleigh and aerosol scattering. The last term is an additional component that takes into account the sky glint resulting from diffuse downwelled sky light reflected off the water surface. The Fresnel reflection coefficient is generally assumed constant for all of the spectral bands (rf ≈0.025). However, in this study, it is assumed that the modeled surface reflectance spectra, obtained from the Hydrolight code, are glint-free and , therefore, the sky glint component is ignored. All of the atmospheric components in Eq. (11) are obtainable via MODTRAN simulations. After applying the bias-only errors Eq. (10), Eq. (11) can be re-written to solve for RdU(λ), for each simulation. The retrieval errors are calculated using PD=|(RdU −Rd)/Rd|×100. Fig. 7 shows the retrieval errors (log10 space) for different aerosol types and visibility (VIZ) when Lake Tahoe (a) and Lake Ontario's (b) reflectance (visible) was retrieved. For brevity, the results from simulations with urban/maritime aerosol are not presented. The errors are shown for each individual band for different aerosol visibility. As seen, for all of the bands, the error curves exponentially decrease with the increase in VIZ (clearer atmosphere) up to 40 km and then remain relatively constant in the range 40–80 km. The −1.6% calibration error in the blue channel for a 2.5% water-leaving reflectance at 479 nm (Fig. 7) translates to~−10% error in the retrieved reflectance value at VIZ=25 km. In a similar fashion, ~2.5% and ~40% errors are obtained for the green and the red bands over Lake Tahoe. According to the additive/subtractive nature of the calibration uncertainties (bias), ETM+ always tends to underestimates Rd (479) and Rd (561) and overestimate Rd(661). As expected, a highly turbid atmosphere (low visibility) with significant aerosol content resulting in large L′t(λ) induces larger retrieval errors (Fig. 7). Although similar trends (magnitude/shape) in the retrieval errors are derived for the blue band, notable dissimilarities between the two sites are present in the trends of the green/red bands, i.e., larger errors are found for Lake Tahoe. This is, in particular, noticeable when retrieving Rd(661) where signal levels are lower six order of magnitudes (Fig. 7) over clear waters. The NIR band was excluded in this analysis because it solely carries information regarding the surface and is not commonly used for water constituent retrieval over water types examined in this study. Fig. 8-a illustrates the retrieval errors for different DOYs at Rd(661), which denote how the retrieval errors would change relative to the available solar irradiance in mid-latitude areas. As the solar radiation level decreases, which implies lower signal strengths from the water column, the retrieval errors increase. This indicates that the retrieval errors for the red channel at VIZ=25 km in mid fall is nearly 30% larger than those obtained in mid spring/summer. The error levels are clearly

Fig. 7. The band-specific retrieval errors [%] derived for Lake Tahoe (a) and Lake Ontario (b) for commonly found aerosol and water types (coastal waters for Lake Ontario).

much greater in turbid atmospheres. An average of 8% error is also derived for Lake Ontario's waters in mid spring/summer time for VIZ= 25 km (Fig. 8-c). This error level reaches 13% in mid fall when SZA is high. Fig. 8-b and -d show the input Rd(λ) into the MODTRAN code along with RdU(λ) retrieved after incorporating the calibration errors for urban aerosol in mid July, i.e., DOY=210. For Lake Tahoe, it is inferred that the slight calibration errors in Lt(479) and Lt(661) , i.e., −1.6% and +3.2% respectively, results in errors on the order of −10% and − 45% in the corresponding bands when Rd(λ) is retrieved. However, the −0.93% error for Lt(561) introduces~−4% error in retrieving Rd(561). Although smaller errors in the green/red bands were derived for turbid waters of Lake Ontario, i.e., 2.6% and 10.8%, the error levels for Rd(479) showed identical errors to that for Lake Tahoe due to relatively similar signal levels in this band. Table 6 summarizes retrieval errors associated with different types of waters for DOY=210 and rural aerosol with VIZ=25 km. The average errors of −10.8%, −3.8%, and +32% are derived in the blue, green, and red bands, respectively, for all water types. The associated values for eutrophic, waters (last two rows in Table 6), on average, are −10%, −2.8%, and +15% in the visible bands. Regardless of their direction, the small calibration errors, i.e., 1.9%, on average for the visible bands, amount to noticeable inconsistencies when retrieving Rd(λ). It should be noted that the Lake Tahoe's upper-air atmosphere is less humid than that in Lake Ontario. This implies that for identical water types higher retrieval errors are expected for Lake Ontario. The results presented here are well in agreement with (Gordon, 1998) wherein the errors in Rd(λ) are quantified to be more than five times greater than those in the TOA reflectance/radiance. Although remarkable errors, in the relative sense, were found for Rd(834) (Table 3), the large errors are due to the near zero reflectance

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Fig. 8. The simulation results for Lake Tahoe (upper) and Lake Ontario's waters (lower). The log(PD(661)) [%] for different times of the year with various aerosol visibility are shown in (a) and (c) whereas the reference and retrieved reflectance curves for DOY = 210 with urban aerosol are illustrated in (b) and (d).

in this band and are not applicable for the water constituent retrieval process in most water types unless turbid waters are considered. The noticeable calibration errors in the NIR band, however, would mainly influence the fidelity of the atmospheric compensation methods that entirely or partially rely upon characterization of the atmosphere/ aerosol through this band. 5.2. Retrieval of the concentrations of the water constituents A case study was conducted to analyze how the calibration bias-only errors (Section 3.1) ultimately influence the retrieval of the concentrations of optically active components of coastal waters. The purpose of this section is to investigate the relative impacts in the retrieval of CHL and TSS in coastal waters due to the sensor's calibration uncertainties. Therefore, absolute concentrations derived from ETM+ imagery are not of interest. To do so, an atmospherically corrected ETM+ imagery acquired over the Niagara River plume discharging into Lake Ontario was employed. The water-leaving reflectance and the ambient optical properties of the turbid waters as well as the environmental conditions were measured concurrent with the L7 overpass, i.e., row/path 30/18, at 11:53 am EST on October 19th 2010 (Pahlevan and Schott, 2011). The in situ optical measurements over the plume along with the simulated surface reflectance from the Hydrolight code for deep, clear waters allowed for implementing a linear regression correction, i.e., the empirical line method (ELM), to account for the atmospheric effects (Schott, 2007). Table 6 Band-specific PD (%) for different water types. Lake Tahoe

Lake Ontario

Blue

Slightly turbid Moderately turbid Turbid

Green

Red

NIR

−9.9

−4.2

+46.3

NA

−14.5 −10.7 −10.1

−5.6 −3.1 −2.6

+54.1 +19.2 +10.6

NA +88.1 +38.2

In order to examine the impacts of the mis-calibrations, the surface reflectance products was adjusted by applying Eq. (10) (in Rd(λ) domain) to simulate the un-calibrated ETM+ surface reflectance, i.e., RdU(λ). According to the range of concentrations in the study area, the average of the retrieval errors for the slightly turbid and moderately turbid waters (Table 6), i.e., −12.2%, −4.4%, +37% for the visible bands, were applied as bias errors (β(λ)) in Eq. (10). To retrieve the concentrations of CHL and TSS, a look-up-table (LUT) technique followed by a spectral optimization was employed as described in (Mobley et al., 2005; Raqueno, 2003). Briefly, an LUT of various concentrations of CHL and TSS was populated via many Hydrolight simulations to model different Rd(λ). The spectral reflectances are then resampled to the ETM+ visible RSRs. The ETM+‐derived surface reflectance associated with each pixel (Rd(λ) and RdU(λ)) is passed to the database where the best match with the pixel's spectral reflectance is found through an optimization. The matched reflectance curve for each pixel has a pair of components that specify that pixel's concentrations of CHL and TSS. As explained in Section 2.4.1, due to the insensitivity of ETM+ to the short, blue region of the spectrum, the third optically active component of turbid waters (CDOM), was set as a constant in this case study. As a result of this model-matching technique, the concentration maps derived from the original ETM+ (Rd(λ)) (Fig. 9-a and -b) and the un-calibrated ETM+ data (RdU(λ)) were produced. The ratio maps of the concentrations obtained from the originally observed ETM+ (O) and the un-calibrated data (U) are illustrated in Fig. 9-c and -d. The average CHL and TSS concentrations (C) over the plume area are 2.2 μg/l and 1.12 g/m 3, respectively. Overall, it was revealed that the current ETM+ data, if corrected for the atmospheric effects via physicsbased models, results in, on average, 20% uncertainty in the concentration retrievals (|(C U − C O)/C O| × 100). ETM+ with such small bias-only calibration errors overestimates the CHL concentration 19%, on average, whereas the TSS concentration is, on average, underestimated 22% over the plume area. In general, such a trend in

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a

CHL ( µg l )

4

179

TSS ( g m 3 )

b

2

3.5 3

1.5

2.5 1

2 1.5

0.5 1 0.5

c

CHL Ratio (O/U)

1 0.95

0

TSS Ratio (O/U)

d

1.5 1.4

0.9 1.3 0.85 1.2 0.8 0.75 0.7

1.1 1

Fig. 9. The Chl (a) and TSS (b) concentration maps derived from the originally observed L7 imagery showing the Niagara River discharging in the western basin of Lake Ontario, USA. The lower frames show the ratio of the concentration maps from the actual data and the un-calibrated data, i.e., O/U. The calibration errors cause overestimation and underestimation of CHL and TSS concentrations, respectively.

overestimation of CHL retrieval comes largely from the decrease in R (479) and, to a lesser extent, R (561). In spite of the 37% increase in the red channel's reflectance, the TSS concentration is underestimated. This is because of a) a non-linear correlation between the combination of R(561) and R(661) and TSS concentration and b) the uncertainty analysis in the concentrations is dependent on the retrieval approach (a spectral optimization technique over three visible channels was adapted). It is believed that retrieval techniques, such as those utilizing band ratios, which do not rely upon absolute spectral values, carry less errors when obtaining in-water components. The error levels attributed to the TSS concentrations in the non-plume waters, where the signal level in the red band is approximately 50% of that in the plume area, reach as high as 56% (see Fig. 9-d). In contrast, the relative differences in the derived CHL concentrations over the plume area exhibit similar values to those in clearer waters. It should be noted that the magnitude and the direction of the errors in the retrieval of concentrations are siteand approach-dependent. The impacts of the calibration errors in other water types characterized with different optical properties can dramatically change. The high correlation coefficient, i.e., > 0.98, between the concentration maps derived from the original ETM+ and the un-calibrated counterpart show that the spectral-dependent calibration uncertainties introduce only spatially uniform bias throughout the study area i.e., the relative spatial structure of the maps remain unchanged. The noisy nature of the concentration maps, particularly in the clear waters, is due to the poor radiometric fidelity of ETM+ and its low SNR. As the signal level rises, the unrealistic, spatial variations decrease. With the advent of the new generation Landsat (LDCM), it should be possible to achieve more accurate concentration maps with less artifact in both clear and turbid waters. 6. Conclusions In this paper, an over-water cross-calibration technique was conducted to examine the relative calibration of ETM+ with respect to Terra-MODIS, where MODIS was regarded as the reference sensor. This cost-efficient technique is scene-dependent and, with appropriate assumptions, does not require in situ measurements. The primary

impeding factor in performing this on-orbit cross-comparison is the lack of knowledge about the effects of the differences in the sensors' RSRs. These effects are significantly dependent on the atmospheric state and, to a lesser extent, on the water-leaving signal. A modelbased technique was used to account for such differences for each scene pair. In this method, several atmospheric conditions and multiple water types were simulated to estimate the closest TOA radiance curve observed by the MODIS sensor (C5) at each calibration site. After compensating for the differences in the sensors' RSRs, the annual percent differences averaged over different sites were analyzed. The historical trend studies verified Terra's significant degradations over the recent years, i.e., 2008–2011. It was found that, during 2000–2007, ETM+ has registered slightly lower signal levels in the blue and the green bands than MODIS. On the other hand, ETM+ tends to overestimate signals in the red and the NIR bands. The disparities, on average, were quantified as −1.6%, −0.93%, +3.2%, and +4.8% for the blue, green, red, and NIR bands. It is speculated that such small discrepancies, which remain very stable in 2000–2007 for all bands, at the low signal levels are primarily due to non-linearity and straylight. The latter particularly increases the signal levels at R(661) and R(834) while it is less significant at larger signal levels. The error budget analysis for the annually averaged PDs (PDY) showed that 1.2%, 1.6%, 3.5%, and 6.5% errors are associated with the VNIR bands, respectively. This trend demonstrates an increase in the uncertainties with the decrease in the signal level. In spite of the relatively small errors over clear waters, the recent relative calibration differences, i.e., 2008–2011, over the RVPN site showed even smaller errors, i.e., b 1% in magnitude, for all the VNIR bands, except for the blue band. The small over-water calibration errors, negligible when imaging most land targets, were further analyzed when retrieving surface reflectance and water constituents. This was accomplished by treating the calibration differences as bias-only errors and solving fundamental remote sensing equation in the inverse mode. The simulations under typical atmospheric conditions showed that the calibration errors, on average, lead to −12.2%, −4.4%, and +37% errors in the blue, green, and red bands when retrieving Rd for slightly/moderately turbid waters. The above-noted, mean uncertainties in the retrieval of Rd were further translated into errors in the retrieval of concentrations for a particular ETM+ scene with comparable turbidity

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levels. This study demonstrated that such errors introduce 20% uncertainty when retrieving the concentrations of water constituents. The bias-only errors cause overestimations in the predicted CHL concentration and underestimations in the TSS concentration. The uncertainties associated with the concentrations are deemed site- and approach-specific. The model-matching technique together with the spectral optimization may not particularly be generalized to all case scenarios; nevertheless, it gives insights into the uncertainties introduced by the sensor's mis-calibration. For a more robust analysis, different retrieval techniques have to be scrutinized. It is believed that various methods have different sensitivity to a sensor's calibration uncertainties. The calibration errors in the NIR band, although not significant when retrieving water constituents over most waters, can cause considerable errors in estimating the atmospheric conditions if physics-based models are utilized. The new generation of Landsat (LDCM) with its advanced technology is expected to outperform ETM+ when studying water resources. This new capability will require rigorous, over-water characterizations of its calibration stability to facilitate the use of physics-based techniques for atmospheric corrections and, consequently, reliable retrieval of bio-physical parameters. The Visible Infrared Imager Radiometer Suite (VIIRS) onboard NPOESS Preparatory Project (NPP), which has been placed in a higher altitude than that planned for LDCM, will permit a robust, relative characterization of the OLI sensor in the future. Acknowledgements The authors are grateful to Mrs. Nina G. Raqueno and the staff members of the Digital Imaging and Remote Sensing (DIRS) Lab at RIT for their support. We would like to thank Dr. Jack Xiong and the MCST for their insights and encouragements of this work. We also appreciate the Landsat/LDCM calibration team for providing us with thoughtful suggestions. The authors are also grateful to anonymous reviewers whose valuable comments have substantially enhanced the quality of the present paper. References Angal, A., Xiong, X., Choi, T. Y., Chander, G., & Wu, A. S. (2010). Using the Sonoran and Libyan Desert test sites 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. Beers, Y. (1953). Introduction to the theory of error. Reading, Mass: Addison Wesley Publisher. Berk, A., Anderson, G. P., Acharya, P. K., Chetwynd, J. H., Bernstein, L. S., Shettle, E. P., et al. (1999). MODTRAN4 user's manual. Air Force Research Laboratory (pp. 95). MA: HANSCOM AFB. Berk, A., Bernstein, L., & Robertson, D. C. (1989). MODTRAN: A moderate resolution model for LOWTRAN 7. Spectral Sciences. Bustamante, J., Pacios, F., Díaz-Delgado, R., & Aragonés, D. (2009). Predictive models of turbidity and water depth in the Doñana marshes using Landsat TM and ETM+ images. Journal of Environmental Management, 90(7), 2219–2225. Chander, G., Markham, B. L., & Helder, D. L. (2009). Summary of current radiometric calibration coefficients for Landsat MSS, TM, ETM+, and EO-1 ALI sensors. Remote Sensing of Environment, 113(5), 893–903. Chander, G., Meyer, D. J., & Helder, D. L. (2004). Cross calibration of the Landsat-7 ETM+ and EO-1 ALI sensor. IEEE Transactions on Geoscience and Remote Sensing, 42(12), 2821–2831. Chander, G., Mishra, N., Helder, D. L., Aaron, D., Choi, T., Angal, A., et al. (2010b). Use of EO-1 hyperion data to calculate spectral band adjustment factors (SBAF) between The L7 ETM+ and TERRA MODIS Sensors. 2010 IEEE International Geoscience and Remote Sensing Symposium, Honolulu, HI IEEE. Chander, G., Xiong, X. X., Choi, T. Y., & Angal, A. (2010a). Monitoring on-orbit calibration stability of the Terra MODIS and Landsat 7 ETM+ sensors using pseudo-invariant test sites. Remote Sensing of Environment, 114(4), 925–939. Choi, T. Y., Angal, A., Chander, G., & Xiong, X. X. (2008). Radiometric cross-calibration of the Terra MODIS and Landsat 7 ETM+ using an invariant desert site. Earth Observing Systems Xiii. SPIE. Clark, D. K., Gordon, H. R., Voss, K. J., Ge, Y., Broenkow, W., & Trees, C. (1997). Validation of atmospheric correction over the oceans. Journal of Geophysical Research-Atmospheres, 102(D14), 17209–17217. Czapla-Myers, J. (2011). Personal Communications. Dong, C., Idica, E. Y., & McWilliams, J. C. (2009). Circulation and multiple-scale variability in the Southern California Bight. Progress in Oceanography, 82(3), 168–190. Eplee, R. E., Sun, J. Q., Meister, G., Patt, F. S., Xiong, X. X., & McClain, C. R. (2011). Cross calibration of SeaWiFS and MODIS using on-orbit observations of the Moon. Applied Optics, 50(2), 120–133.

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