Remote Sensing of Environment 99 (2005) 315 – 325 www.elsevier.com/locate/rse
Image-based atmospheric correction of QuickBird imagery of Minnesota cropland
Jindong Wu a,*, Dong Wang a, Marvin E. Bauer b
a Department of Soil, Water, and Climate, University of Minnesota, 439 Borlaug Hall, 1991 Upper Buford Circle, St. Paul, MN 55108, USA b Department of Forest Resources, University of Minnesota, St. Paul, MN 55108, USA
Received 3 March 2005; received in revised form 15 September 2005; accepted 15 September 2005
Abstract
High spatial resolution QuickBird satellite data have provided new opportunities for remote sensing applications in agriculture. In this study, image-based algorithms for atmospheric correction were evaluated on QuickBird imagery for retrieving surface reflectance (qk) of corn and potato canopies in Minnesota. The algorithms included the dark object subtraction technique (DOS), the cosine approximation model (COST), and the apparent reflectance model (AR). The comparison with ground-based measurements of canopy reflectance during a 3-year field campaign indicated that the AR model generally overestimated qk in the visible bands, but underestimated qk in the near infrared (NIR) band. The DOS– COST model was most effective for the visible bands and produced qk with the root mean square errors (RMSE) of less than 0.01. However, retrieved qk in the NIR band were more than 20% (mean relative difference or MRD) lower than ground measurements and the RMSE was as high h as 0.16. The evaluation of the COST model showed that atmospheric transmittance (Tk ) was substantially overestimated on humid days, particularly for the NIR band because of the undercorrection of water vapor absorption. Alternatively, a contour map was developed to interpolate h appropriate Tk for the NIR band for clear days under average atmospheric aerosol conditions and as a function of precipitable water content and h solar zenith angle or satellite view angle. With the interpolated Tk, the accuracy of NIR band qk was significantly improved where the RMSE and MRD were 0.06 and 0.03%, respectively, and the overall accuracy of qk was acceptable for agricultural applications. D 2005 Elsevier Inc. All rights reserved.
Keywords: Atmospheric correction; Image-based; Surface reflectance; QuickBird; Agriculture
1. Introduction radiometric resolution of QuickBird data has been increased to 11-bit digitization, which produces more discernible intensity Satellite remote sensing has developed rapidly in the last 30 levels (up to 2048 levels). years, but with limited application in field-scale agricultural However, like other satellite sensors, at a given illumination monitoring and management due to coarse spatial resolutions geometry, the apparent radiance of ground targets is affected by (Doraiswamy et al., 2004; Moran et al., 1997). The successful both surface characteristics and atmospheric conditions (Teillet, launch of high-resolution satellites, e.g., IKONOS and Quick- 1986). In order to fully utilize QuickBird satellite data for Bird, has provided new opportunities for remote sensing multitemporal analysis of seasonal changes in crop and soil applications in agriculture. The spatial resolution of QuickBird conditions, un-calibrated relative pixel values or image digital imagery data has been improved to 0.61 m for panchromatic numbers (DN) of each spectral band (k) have to be corrected and 2.44 m for multispectral images at nadir (DigitalGlobe, for atmospheric effects and converted to spectral reflectance at- 2002). QuickBird multispectral images have three visible surface (qk)(Kaufman, 1989; Moran et al., 1997). An improper bands (0.45–0.52 Am, 0.52–0.60 Am, 0.63–0.69 Am) and atmospheric correction could cause significant errors in the one near infrared (NIR) band (0.76–0.90 Am), which are retrieval of qk and affect the accuracy of the estimation of similar to the first four bands of Landsat TM data. But the agronomic variables, such as leaf area index (Rahman, 2001). A number of methods have been developed to remove or * Corresponding author. Tel.: +1 612 625 1798; fax: +1 612 625 2208. reduce atmospheric effects and retrieve qk. These methods vary E-mail address: [email protected] (J. Wu). from direct DN to qk transformation (Caselles & Garcia, 1989;
0034-4257/$ - see front matter D 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.rse.2005.09.006 316 J. Wu et al. / Remote Sensing of Environment 99 (2005) 315–325
Smith & Milton, 1999), image-based dark object subtraction of DOS and COST model were generally comparable to results atmospheric path radiance (Chavez, 1988; Vincent, 1972) and with RTM using in situ atmospheric measurements. Chavez cosine estimation of atmospheric transmittance (Chavez, 1996), (1996) justified the COST model by comparing the average h h to complex radiative transfer models (RTM) (Berk et al., 1998; cosine estimation of Tk across h with Tk derived from Tanre´ et al., 1990; Vermote et al., 1997). Many studies have atmospheric optical thickness and averaged across h and k. been made to refine these methods by integrating one with The author found that two estimates only differed by 0.01. another (Moran et al., 2001; Teillet & Fedosejevs, 1995), However, this did not hold true for an individual spectral band developing a simplified RTM (Gilabert et al., 1994; Rahman & or for a specific solar zenith angle because positives and Dedieu, 1994), or creating look-up tables (Fraser et al., 1992; negatives were canceled out in the comparison. Particularly for h Richter, 1990; Staenz & Williams, 1997). Several authors have TM band 4, Tk estimated with the COST model had the largest h compared the performance of these methods for Landsat TM deviation from concurrent measurements. The average Tk (Moran et al., 1992), AVIRIS (Airborne Visible/Infrared estimated with the COST model (0.80) was about 12% lower Imaging Spectrometer) (Farrand et al., 1994; Ferrier, 1995), than the average measurement (0.91), and the deviation could and other imaging spectrometer data (Dwyer et al., 1995). be up to 30% for relatively high zenith angles. It appears that Although qk retrieved from sophisticated RTM often have the COST model overcorrects the absorption effect of water relatively high accuracy, RTM requires in situ measurements of vapor for semi-arid areas like Arizona, where precipitable state and composition of the atmospheric profile at the time of water is often less than 2.5 cm. satellite overflight, e.g., spectral optical thickness of various Atmospheric scattering and absorption are highly wavelength atmospheric components (Berk et al., 1998; Vermote et al., dependent, and atmospheric transmittances are not equivalent 1997). For most potential users of QuickBird images, these across spectral wavelengths (Gaut et al., 1975). Moreover, for measurements are usually impossible to obtain in practice, and humid areas like Minnesota, where atmospheric water content is the procedures involved are too expensive to use operationally. relatively abundant (the average precipitable water is as high as For most agricultural applications, atmospheric correction 3 cm in summer) and also quite variable (precipitable water should be based on the acquired digital image itself and varies from 1 to 6 cm), the absorption effect of water vapor on requiring no atmospheric measurements during satellite over- NIR band may not be the same as in semi-arid areas or constant flight (so called image-based atmospheric correction). Dark over time. Thus, the DOS–COST model may behave quite object subtraction of atmospheric path radiance or DOS differently in humid environments. This study was intended to (Vincent, 1972) and cosine estimation of atmospheric trans- evaluate the accuracy of image-based DOS–COST atmospheric mittance or COST (Chavez, 1996) image-based models are correction for the retrieval of qk from QuickBird imagery data in such methods that have been proposed to simplify atmospheric a relatively humid environment. The evaluation was based on correction. The DOS model is based on the assumption that the comparison of retrieved qk with corresponding ground dark objects exist within an image and have zero reflectance measurements. To further investigate the performance of the (Gilabert et al., 1994; Moran et al., 1992). Consequently, the model, estimated spectral atmospheric transmittances with the radiance resulting from corresponding pixels is proportional to cosine approximation were evaluated by comparing with the atmospheric path radiance, and can be used to account for the simulated results using radiative transfer algorithms. A contour additive effects of atmospheric scattering. The pixel values are map was developed for average atmospheric aerosol conditions selected for each individual band with the histogram method and most water vapor conditions as an alternative to interpolate and subtracted from all pixel values for the corresponding band the appropriate atmospheric transmittance for the NIR band. The across an image. Thus, the path radiances determined in this apparent reflectance (AR) (Robinove, 1982) was also included way are spectrally uncorrelated. To explain the dependency of in the comparison to provide an insight of atmospheric effects on atmospheric scattering on wavelength, an improved DOS QuickBird images. technique was developed to estimate path radiances with selected relative atmospheric scattering models (Chavez, 2. Study area, satellite images, and ground data 1988). The estimated path radiances for all spectral bands with the improved DOS technique are spectrally correlated. 2.1. Study area and image acquisition The COST model was developed to account for the multiplicative effects of atmospheric scattering and absorption The study area was located on two agricultural farms near (Chavez, 1996). In the COST model, the cosine function of Becker, Minnesota. In the growing seasons of 2002, 2003 and solar zenith angle or satellite view angle (h) is used to 2004, corn (Zea mays L.) was cultivated on the first farm (a h approximate atmospheric transmittance (Tk ), to a first order, farmer-managed field) (45-23VN, 93-50VW) while potato (Russet for all spectral bands (spectrally independent). The DOS and/or Burbank) was cultivated on the other farm (the Sand Plain COST model has been evaluated by several authors in areas Research Farm of the University of Minnesota) (45-23VN, characterized by relatively low humidity (Chavez, 1996; Moran 93-53VW). Four QuickBird multispectral images covering both et al., 1992). Although the angular dependence of atmospheric fields and under clear sky conditions were acquired during the transmittance may be over-simplified by using a cosine summers of 2002–2004. These images were taken at off-nadir function, it was reported that atmospheric corrections per- angles (12–25- from nadir) with a pixel size of 2.4–2.8 m. The formed on Landsat-5 TM data with the combination of the basic specifications of satellite overflights are listed in Table 1. J. Wu et al. / Remote Sensing of Environment 99 (2005) 315–325 317
Table 1 separated from each other with a 3.1 m buffer of bare soil. Seven Illumination geometries and pixel sizes of acquired QuickBird multispectral measurements were made per plot, in which 4 measurements imagesa were centered over rows and 3 measurements were centered over s s v v Date DOY Time u h u h Pixel furrows. (deg) (deg) (deg) (deg) size (m) All reflectance measurements were then averaged for each 22 June 2002 173 12:16:20 145.2 25.0 351.1 24.7 2.8 sampling area to estimate a single reflectance value for each 20 June 2003 171 11:58:00 137.0 27.0 108.4 12.4 2.4 18 July 2003 199 12:07:39 141.7 28.6 287.5 15.5 2.4 pixel. The high spatial resolution of QuickBird data makes it 20 August 2004 233 12:09:50 150.6 36.1 105.2 6.2 2.8 possible to take corresponding ground measurements at the a DOY refers to day of calendar year; us and hs are sun azimuth and zenith pixel level. It is also reasonable to assume that land surfaces are angle, respectively; uv and hv are satellite azimuth and view angle, homogeneous within each QuickBird pixel. Compared with respectively. satellite sensors with coarse spatial resolution, problems with up-scaling point measurements at ground to pixel values of 2.2. Canopy spectral reflectance measurement images are negligible (Milne & Cohen, 1999).
Canopy surface reflectances were measured with a 16-band 2.3. Meteorological data multispectral radiometer (CROPSCAN MSR-16R, 0.46–1.72 Am) in both corn and potato fields for 2003 and 2004; for 2002, Meteorological data were taken from National Climate Data measurements were only made in the potato field. The band Center’s global surface hourly observations with high-level width of the spectroradiometer varies from 6.8–12 nm in the quality control. Climate normals were also obtained from the visible to 11–13 nm in the near infrared. Both irradiance and same data set. The data include air temperature, dew point radiance were measured simultaneously to derive canopy temperature, and sea level atmospheric pressure. Summer reflectance. The four multispectral bands of QuickBird data (June–August), as the major period of the growing season were simulated with appropriate CROPSCAN bands as weight- (May–September) for the study site, is characterized by warm ed averages (Table 2). The measurements were made either and humid weather. The average daily air temperature during concurrently with satellite overpass (20 August 2004) or around summer is about 21 -C while the maximum air temperature can noontime within 1–4 days before or after satellite overpass (26 be above 30 -C. Approximately 45% of annual precipitation June 2002, 17 June 2003, and 15 July 2003). The change of (about 770 mm) occurs during summer. The average daily canopy reflectances during a few consecutive days should be minimum relative humidity is over 50%. minimal (Pinter et al., 1990) and was neglected in this study, although ideally, only concurrent measurements should be used. 3. Methods To effectively evaluate retrieved qk from satellite imagery, ground data were collected with finer spatial resolution than 3.1. DOS–COST model that of QuickBird images. The view angle of the spectro- Within a limited range of illumination geometry with radiometer was constant by looking vertically downward with a relatively high solar elevation angles, it is reasonable to 28- field of view (FOV). Measurements were made at 1 m assume that a flat crop field with full canopy closure above crop canopies, which resulted in a projected view area of approximates a Lambertian surface (Forster, 1984; Lee & 0.2 m2 with a diameter of 0.5 m. All ground measurements Kaufman, 1986; Smith et al., 1980). If the sky irradiance is were taken at 0.7 m (corn) or 0.9 m (potato) interval with the further assumed isotropic and only atmospheric scattering and FOV centering over rows (mostly canopies) and furrows absorption are considered, the general equation for describing (mostly soil) alternatively in the fields. atmospheric interactions and retrieving surface reflectance can Three transects were set up across the corn field (about be expressed as (Moran et al., 1992): 500 500 m). Ten random sampling points were selected along s p the three transects. Each sampling point was located with the p LkðÞÀx; y Lk qkðÞ¼x; y v s o s d ð1Þ Ashtech Z-Surveyor of about 1 cm horizontal RMSE for the Tk TkDEkcosðÞþh Ek subsequent measurement of surface reflectance and extraction of where q (x, y) is the spectral reflectance at-surface for an corresponding image pixel values. With the increased heteroge- k image pixel at column x and row y; E o (W/m2 Am) is the neity of land surfaces due to the high spatial resolution of k QuickBird, it is critical to precisely geo-locate ground sampling Table 2 areas to ensure that the same locations are measured and QuickBird spectral bands simulated with multispectral radiometer extracted from satellite images. An area of 3.0 3.5 m around (CROPSCAN) each sampling point was measured in the corn field (Fig. 1a). QuickBird CROPSCAN spectral regions (Am) Multispectral reflectances were measured every 1 m along a row Band no. Band k (Am) or a furrow with 27 measurements per sampling area. Among 1 B 0.45–0.52 0.4566–0.4634, 0.5062–0.5139 them, 15 measurements were centered over rows and 12 2 G 0.52–0.60 0.5553–0.5647 measurements were centered over furrows. In the potato field 3 R 0.63–0.69 0.6540–0.6660 (70.1 m 3.7 m), surface reflectances were taken in 8 treatment 4 NIR 0.76–0.90 0.7545–0.7655, 0.8045–0.8155, plots with a size of 3.7 6.1 m (Fig. 1b). These plots were 0.8640–0.8760, 0.8935–0.9065 318 J. Wu et al. / Remote Sensing of Environment 99 (2005) 315–325
3.5 2.8 2.1 a 1.4 0.7 0.0 0.0 1.0 2.0 3.0
3.7 2.7 1.8 b 0.9 0.0 6.1 9.1 0.0 51.8 54.9 61.0 70.1 15.2 18.3 24.4 27.4 33.5 36.6 42.7 45.7 64.0
Fig. 1. Field sampling scheme of canopy reflectance at each sampling location in the corn field (a) (10 locations in total along 3 transects) and in the potato treatment plots (b). Dash lines indicate the evenly spaced center lines between crop rows in the fields; circles indicate where the measurements were made. The unit is in meters but the schematic is not drawn to scale.
p extraterrestrial solar spectral irradiance for wavelength k Atmosphere-scattered path radiance Lk was estimated with (Am) at the mean Earth–Sun distance; D is a correction a relative spectral scattering DOS model (kÀ2) under clear d 2 factor for the Earth–Sun distance; Ek (W/m Am) is atmospheric conditions (Chavez, 1988). Areas with clear downwelling atmosphere-scattered solar spectral irradiance; water in deep lakes were identified in images and used as s 2 Lk (W/m sr Am) is total spectral radiance received at-sensor dark objects. One-percent DOS techniques were applied to p 2 p within the sensor’s FOV; Lk (W/m sr Am) is path radiance estimate Lk in the blue band as the radiance from these dark or upwelling atmosphere-scattered spectral radiance within objects minus the radiance from surfaces with 1% reflectance s v p the sensor’s field of view; Tk and Tk are atmospheric (Moran et al., 1992). The estimated Lk in the blue band was p spectral transmittances at k in solar path with a solar zenith used as the starting values for the computation of Lk for angle hs and in view path with a satellite view angle hv, other bands of each image with the relative spectral p respectively. scattering model. The relative scattering model of Lk also o For the estimation of unknowns in Eq. (1), Ek was obtained normalized the effects of different Kk introduced by the from the revised solar spectrum for each band of QuickBird data imaging system. (Neckel & Labs, 1984); D was represented by a Fourier series The COST model was originally only used for the s v s (Spencer, 1971); the values of h and h were found in the image estimation of Tk (Chavez, 1996). In this study, we extended s v metadata files (*.IMD). Diffuse spectral irradiance requires this method to estimate both Tk and Tk by a cosine function of atmospheric measurements and is usually ignored in image- hs and hv, respectively: d s based atmospheric correction (Ek =0). The band-averaged Lk s s was calculated through the absolute in-flight radiometric Tk ¼ cosðÞh ð3Þ calibration of QuickBird data: v v Tk ¼ cosðÞh ð4Þ
KkDNkðÞx; y s v s where computed Tk and Tk varied with solar zenith angle and LkðÞ¼x; y ð2Þ Dk satellite view angle of different scenes, respectively, but were
2 constant for all QuickBird visible and infrared bands of a where Kk (W/m sr count) is the absolute radiometric specific scene. calibration factor for spectrum k with an effective bandwidth of Dk (Am) (Table 3). Kk accounts for the sensor status at 3.2. AR model the time of image acquisition (called K factor in 2002 and absCalFactor in 2003 by DigitalGlobe). The values of Kk With the assumption that the atmosphere does not influence were extracted from image IMD files. radiation transfer, no atmospheric correction was made in the AR model. Both atmospheric scattering and absorption were p s v neglected, i.e., Lk =0 and Tk =Tk =1.0. Thus, Eq. (1) was Table 3 simplified to the following form:
QuickBird effective bandwidth (Dk) and corresponding radiometric calibration p s coefficients (Kk) qkðÞ¼x; y o s LkðÞx; y ð5Þ 2 DEkcosðÞh Band Dk (Am) Kk (W/m sr count) B 0.068 0.0160412 where only solar zenith angle, solar spectral irradiance, and o s s G 0.099 0.0143847 sensor’s radiometric gains were corrected, and Ek , D, Lk,andh R 0.071 0.0126735 were obtained through the same way as in the DOS–COST NIR 0.114 0.0154242 model. J. Wu et al. / Remote Sensing of Environment 99 (2005) 315–325 319
3.3. Evaluation of the COST estimation of atmospheric Table 4 transmittance Precipitable water content (cm) as a function of air temperature and relative humidity - To compare performances of the COST model in relatively Relative Air temperature ( C) humidity (%) humid and arid environments, the COST approximation of 10 15 20 25 30 35 40 atmospheric transmittance was evaluated for Becker, Minne- 0 0.00 0.00 0.00 0.00 0.00 0.00 0.00 sota (45-23VN, 93-50VW) and Maricopa, Arizona (33-03VN, 10 0.21 0.29 0.39 0.52 0.68 0.89 1.15 112-59VW). The evaluation was performed for different spectral 20 0.42 0.58 0.78 1.03 1.36 1.78 2.29 h 30 0.63 0.86 1.16 1.55 2.04 2.67 3.44 bands, solar zenith, and view angles. The difference (DTk ) 40 0.84 1.15 1.55 2.07 2.72 3.55 4.59 between the COST estimation and actual atmospheric trans- 50 1.05 1.44 1.94 2.58 3.41 4.44 5.74 mittance at wavelength k can be expressed as: 60 1.27 1.73 2.33 3.10 4.09 5.33 6.88 70 1.48 2.02 2.72 3.62 4.77 6.22 8.03 h h 80 1.69 2.30 3.10 4.14 5.45 7.11 9.18 DTk ¼ cosðÞÀh Tk ð6Þ 90 1.90 2.59 3.49 4.65 6.13 8.00 10.33 h 100 2.11 2.88 3.88 5.17 6.81 8.88 11.47 where h is solar zenith angle or satellite view angle, and Tk is atmospheric transmittance at wavelength k in the corres- - ponding path. The computation was limited to h <60 , which 3.4. Modification of NIR band atmospheric transmittance is the practical range of solar zenith and view angle for the acquisition of satellite images. Also, for h <60-, the flat earth h As formulated in Eq. (7), Tk varies with both meteorological with a plane-parallel atmosphere is an adequate approximation conditions and atmospheric gas profiles. For the study area (Ricchiazzi et al., 1998) and a tenable assumption for the under clear sky conditions, the content of atmospheric perma- h following radiative transfer algorithms used to estimate Tk .For nent gases (nitrogen, oxygen, and argon) and ozone amount are h the Minnesota site, Tk was calculated with a simple radiative relatively constant over time and horizontally homogeneous. We transfer model for cloudless atmospheres—SPECTRL2 (Bird also found by examining AERONET observations in Sioux & Riordan, 1986) as follows: Falls, South Dakota that aerosol loading is relatively stable for this region around noontime on clear days of summer (June– T h ¼ T mT aT wT o ð7Þ k k k k k August) when the QuickBird images were acquired. In addition, m a w o atmospheric pressures only vary slightly during this period of where Tk , Tk, Tk , and Tk are atmospheric transmittances at wavelength k for Rayleigh scattering, aerosol attenuation, time. Thus, for a fixed solar zenith angle or view angle, the m a water vapor absorption, and ozone absorption, respectively. T m effects of Rayleigh scattering (Tk ), aerosol extinction (Tk), and k o was computed with a Rayleigh scattering equation (Kneizys et ozone absorption (Tk) tend to be relatively invariable. al., 1980) based on pressure-corrected relative air mass With the above assumptions, if the average atmospheric (Kasten, 1966). Because of the difficulties in making aerosol pressure (1971–2000) and average value of AOT at noontime measurements concurrently with QuickBird satellite overpass, (clear days of June–August) were used in Eq. (7) in order to a general continental aerosol optical thickness (AOT) model simplify computations where high accuracy is not required, the a only variables that may affect the magnitude of T h and DT h are (Gaut et al., 1975) was used to calculate Tk based on the k k comparison with the observations of the closest AERONET atmospheric water vapor content and solar zenith or view w angle. Water vapor is nearly transparent to radiance in visible station (Sioux Falls, South Dakota) (Holben et al., 1998). Tk was calculated with a water vapor transmittance equation wavelengths, but absorbs large parts of near infrared radiation (Leckner, 1978), where precipitable water content w (cm) was around 0.81–0.84 Am(Rodolfo & Rolando, 1984). Therefore, h integrated in a vertical column of atmosphere with a scale the variation of Tk with water vapor content would be height of 2.5 km by assuming water vapor density decreases negligible in the visible spectrum, but it cannot be neglected exponentially with height (Forster, 1984; Gaut et al., 1975) in the NIR spectrum. o We thus computed the variation of T h and DT h in the NIR (Table 4). Tk was computed with ozone absorption coefficients k k (Leckner, 1978) and ozone mass (Iqbal, 1983). The height of spectrum with precipitable water content (w) and solar zenith or maximum ozone concentration was assumed 22 km. view angle (h). The results were used to develop contour maps h of T h and DT h as a function of w (0–6 cm) and h (0–60-). The For the Arizona site, Tk was calculated with Eq. (8) for a k k plane-parallel atmosphere (Gaut et al., 1975). precipitable water content, w, was derived from a climatological look-up table of air temperature and relative humidity (Table 4), h ðÞÀsksecðÞh Tk ¼ e ð8Þ which can be easily obtained through operational meteorolog- ical observations. The solar zenith or view angle, h, which where sk is the normal atmospheric optical thickness at determines relative air mass of the atmosphere and optical wavelength k. sk, tabulated by Chavez (1996), was from thickness along a slant path, was derived from digital image ground measurements of Moran et al. (1992). The measured sk itself. Particularly for QuickBird satellite, most images were are for the following spectral regions: 0.45–0.52 Am, 0.52– acquired at an off-nadir view, and the atmospheric profile along 0.60 Am, 0.63–0.69 Am, and 0.76–0.90 Am, which are a slant solar or view path would be very different from that identical to QuickBird band 1 to band 4, respectively. along the zenith or nadir path. For each image acquired, an 320 J. Wu et al. / Remote Sensing of Environment 99 (2005) 315–325
h appropriate value of Tk was interpolated from the contour map 1975). On four different acquisition dates in this study, even all h based on atmospheric water vapor conditions and viewing with clear sky and similar summer atmospheric conditions, Tk geometries during satellite overflight. Surface reflectance was changed significantly across spectral bands: the shorter h h h recalculated for each image using the interpolated Tk as an wavelength the lower Tk (Table 5). TB was generally lower h m alternative to estimates of the COST model. than TNIR by 0.15–0.21. Particularly, Rayleigh scattering (Tk ) a and aerosol attenuation (Tk) were major components contrib- h m a 3.5. Evaluation of retrieved surface reflectances with uting to Tk . Large differences of Tk and Tk were found m ground-based measurements between shorter wavelength and longer wavelength, e.g., TB a m a and TB were lower than TNIR and TNIR by 0.13–0.16 and The most common method for evaluating atmospheric 0.10–0.12, respectively. With the general continental aerosol a correction is to compare qk retrieved from satellite images with model, we found that Tk was relatively stable for this particular ground-based measurements for a variety of targets. We thus study area in the summer daytime with a variation only on the compared qk retrieved with the image-based DOS–COST order of 0.02–0.04 depending on wavelengths. However, water model and the AR model from the QuickBird images with vapor absorption was quite variable even in the humid w ground-based reflectance measurements for all sampling areas. environment. It was found that TNIR varied about 0.08 on four Three different criteria were compared to evaluate the perfor- acquisition dates. mance of each model: linear regression through the origin, the With only one factor (i.e., solar zenith or view angle) being root mean square error (RMSE), and the mean relative considered in the COST model, the error in atmospheric difference (MRD) between retrieved qk and measured qk.All transmittance estimation with Eqs. (3) and (4) and the data points derived from each method and for each band were difference in performance between humid and arid environ- h first tested for normality with the Kolmogorov–Smirnov test ments are expected. For both Becker and Maricopa sites, DTk (SPSS, 1998). The slope of the linear regression through the varies with k and h (Fig. 2). The cosine function generally h origin is a direct indicator of any over- or undercorrections of qk overestimated or undercorrected Tk at lower h while it h under normal distributions. RMSE is the standard deviation of underestimated or overcorrected Tk when h increased to a absolute difference while MRD is the average of relative larger angle, hk. The values of hk decreased with increasing k, difference between retrieved qk and measured qk. These criteria but were not identical at two sites. For Maricopa, they were were computed for both the AR model and the DOS–COST around 50-,39-,31-, and 22- for bands 1, 2, 3, and 4, model for the four QuickBird bands. The same criteria were also respectively. As a result, at Maricopa, the cosine estimates were h applied to evaluate qk in the NIR band retrieved with the DOS closer to actual Tk in band 4 at lower h (< 25-), while the h model and the interpolated atmospheric transmittance. estimates were closer to band 1 Tk at higher h (> 45-). In the mid range of h (25- Table 5 h m a w o Atmospheric transmittance (Tk ) and its component of Rayleigh scattering (Tk ), aerosol attenuation (Tk), water vapor absorption (Tk ), and ozone absorption (Tk) for the four spectral bands Date Band Solar path View path m a w o h m a w o h Tk Tk Tk Tk Tk Tk Tk Tk Tk Tk 22 June 2002 B 0.822 0.746 1.000 0.992 0.608 0.834 0.762 1.000 0.993 0.631 G 0.897 0.784 0.989 0.969 0.674 0.904 0.798 0.990 0.971 0.694 R 0.946 0.821 0.996 0.979 0.757 0.950 0.834 0.996 0.980 0.773 NIR 0.978 0.864 0.901 1.000 0.761 0.980 0.874 0.905 1.000 0.775 20 June 2003 B 0.831 0.758 1.000 0.993 0.625 0.844 0.777 1.000 0.993 0.652 G 0.902 0.795 0.995 0.971 0.693 0.910 0.811 0.996 0.973 0.716 R 0.949 0.831 0.998 0.980 0.771 0.953 0.844 0.999 0.982 0.789 NIR 0.979 0.871 0.946 1.000 0.807 0.981 0.882 0.949 1.000 0.821 18 July 2003 B 0.828 0.755 1.000 0.992 0.621 0.842 0.774 1.000 0.993 0.648 G 0.901 0.792 0.993 0.970 0.688 0.909 0.809 0.993 0.973 0.711 R 0.948 0.829 0.997 0.980 0.767 0.952 0.842 0.997 0.981 0.785 NIR 0.979 0.870 0.926 1.000 0.788 0.981 0.881 0.930 1.000 0.802 20 August 2004 B 0.815 0.737 1.000 0.992 0.596 0.847 0.780 1.000 0.993 0.656 G 0.893 0.776 0.996 0.968 0.668 0.912 0.814 0.997 0.974 0.721 R 0.943 0.815 0.999 0.978 0.751 0.954 0.847 0.999 0.982 0.792 NIR 0.977 0.859 0.952 1.000 0.799 0.981 0.884 0.957 1.000 0.830 J. Wu et al. / Remote Sensing of Environment 99 (2005) 315–325 321 0.4 h a water). As a result, compared to Maricopa, Tk in the NIR band 0.3 was overestimated substantially (0.19 versus 0.07) for Becker. h 0.2 The contour map of DTk displayed the sensitivity of the h cosine estimation of Tk in the NIR spectrum to atmospheric water 0.1 vapor content and radiation path direction (Fig. 3). It should be θ λ T 0.0 ∆ noted that the COST model had the best performance in the NIR -0.1 spectrum if solar zenith and view angle were around 40-.Forh h h within 40-, the COST model overestimated Tk , and DTk -0.2 B increased with decreasing h and increasing w. Thus, the COST G -0.3 R model would not perform well if satellite images were acquired at NIR -0.4 nadir. Particularly under warm and humid weather conditions 0 102030405060 with air temperature higher than 30 -C and relative humidity over θ h (degree) 50%, i.e., w >3.5 cm (Table 4), Tk would be greatly over- h estimated (DTk >0.2). If h increases to more than 40 -,which 0.4 may rarely happen in practice, the COST model would b h 0.3 underestimate Tk . Particularly for very dry atmospheric condi- tions (w <1 cm)and h >50-, DT h would be as low as 0.2. 0.2 k À 0.1 4.2. Surface spectral reflectance θ λ T 0.0 ∆ -0.1 4.2.1. Visible bands Retrieved surface reflectances and corresponding ground -0.2 B measurements were compared for each band. Apparent reflec- G -0.3 R tances of the blue and red bands were much higher than ground NIR -0.4 measurements for not removing the effects of path radiance 0 102030405060 (additive effects) (Fig. 5a, c). The slopes of the correlations θ (degree) between retrieved and measured qk were much larger than 1.0 h (2.75 and 1.77 for the blue and red bands, respectively) (Table Fig. 2. Differences of spectral atmospheric transmittances (DTk ) in the blue (B), 6). The RMSE was as high as 0.06 for the blue band. This is not green (G), red (R), and near infrared (NIR) bands between the COST model and ground reference values at Becker, Minnesota (a) and Maricopa, Arizona (b), acceptable considering qk for vegetation in the blue band usually h and the variations of DTk with solar zenith or view angles h. The curves for only ranges from 0.02 to 0.05. The high apparent reflectances in Maricopa were derived using data from Moran et al. (1992); the curves for the red band indicated that atmospheric scattering still had Becker were derived with radiative transfer algorithms under an assumption of 3 cm precipitable water content. 6 5 0 0 5 0 1 0 5 0 0 . . . . 1 1 0 0 . . 0 conditions when most of satellite images were acquired 0 - - 0 0 0 h 2 (h <40-), the COST model generally overestimated Tk for all 5 0. h spectral bands (DTk >0). The magnitude of overestimation at Becker was greater than h 4 that at Maricopa. For Becker, DTk at h =0- were as large as 0.34, 0.28, 0.21, and 0.19 for bands 1, 2, 3, and 4, respectively; while the corresponding values for Maricopa were 0.24, 0.18, 3 0.12, and 0.07. The different performance of the COST model (cm) was possibly attributed to different atmospheric profiles at these w two sites, particularly aerosol loading and water vapor content. 2 An investigation of measured aerosol optical thickness (AOT) at 5 0 5 0 5 5 0 0 1 1 1 0 0 . . . Maricopa (Moran et al., 1992) showed that AOT was typically . 1 . . . 0 0 0 0 0 0 - - - 0 0 2 within a range of 0.06–0.18, 0.05–0.14, 0.04–0.11, and 0.03– 1 . 0 0.08 for QuickBird bands 1, 2, 3, and 4, respectively. These - AOT levels were considerably lower than those found at Becker, Minnesota (0.25, 0.20, 0.17, and 0.12 for bands 1, 2, 3, and 4, 0 respectively). The greater aerosol loading at Becker would lead 0 10 20 30 40 50 60 h to smaller atmospheric transmittance, so that DTk would θ (degree) increase in Minnesota (Eq. (6)). For the NIR band, the Fig. 3. Biases of the COST model in estimating spectral atmospheric overestimation was enhanced because of the undercorrection h transmittances (Tk ) in the near infrared spectrum (0.76–0.90 Am) and of increased water vapor absorption in the humid environment variations with precipitable water content (w) and solar zenith or view angel (sk of water vapor was 0.08 for an average of 3 cm precipitable (h) for Becker, Minnesota. 322 J. Wu et al. / Remote Sensing of Environment 99 (2005) 315–325 Table 6 Statistical evaluation of the performance of DOS–COST model and its modification for retrieving surface multispectral reflectancesa hb Statistic AR DOS–COST DOS–Tk qb qg qr qnir qb qg qr qnir qnir D* 1.39 1.20 0.93 1.23 1.15 1.26 0.88 0.89 0.88 a 2.75 1.21 1.77 0.67 0.94 0.96 1.06 0.77 0.98 t* 38.13 36.29 29.06 69.79 47.90 46.81 52.07 72.08 81.01 RMSE 0.06 0.03 0.03 0.22 0.01 0.01 0.01 0.16 0.06 MRD (%) 179.34 28.26 82.55 À 31.35 À 5.40 À 0.05 5.77 À 21.60 0.03 D* indicates a normal distribution of data points at p =0.05 (n =52). D values of ground measured reflectance are 1.23, 0.90, 1.39, and 1.09 for the blue, green, red, and near infrared bands, respectively, also indicating normal distributions at p =0.05. t* indicates t values are significant at a =0.001. a qb, qg, qr, and qnir are surface reflectances (qk) in the blue (qb), green (qg), red (qr), and near infrared (qnir) bands retrieved with the apparent reflectance model (AR) and the dark object subtraction and cosine transmittance function model (DOS–COST). D is the statistic of the Kolmogorov–Smirnov test for normality, a is the slope of regression between retrieved and measured qk, and t is the statistical test of the regression. RMSE is the root mean square error, and MRD is the mean relative difference between retrieved and measured qk. b k Atmospheric transmittance (Th ) was interpolated from the contour map (Fig. 4). significant contribution to path radiance in the longer visible cover QuickBird blue, red, and near infrared bands, but may spectrum. not be adequate for the green band. We applied the correction Errors of the AR model in the blue and red bands were factors to all bands, and as expected, not much change was significantly reduced with the DOS–COST model (Table 6). found in the blue, red, and near infrared bands. However, the The slopes of the correlations between retrieved and measured comparison showed that the retrieved green band qk with the qk were very close to 1.0 (0.94 and 1.06 for the blue and red DOS–COST model agreed well with corrected ground bands, respectively), and the RMSE and MRD significantly measurements. The correlation slope between retrievals and decreased to 0.01 and À5.4% for the blue band, and 0.01 and measurements was 0.96 (¨1.0), and RMSE was as low as 0.01 5.77% for the red band, respectively. (Table 6). With the correction, it was reasonable to find that the Retrieved qk in the green band with the AR model appeared green band qk retrieved with the AR model were much higher to be close to ground measurements, but the results with the than ground measurements, with the MRD>25%. DOS–COST model were about 15% lower than ground The DOS–COST model appeared to work well in retrieving measurements (figures not shown). However, this was likely qk in the visible spectrum (Fig. 5a, b, c), even though atmos- caused by factors other than atmospheric correction (Pinter et pheric transmittance was overestimated as discussed earlier. As al., 1990), such as possible errors in the ground measurement. indicated in Chavez (1996), one of the reasons that the DOS– One of the factors was the not-so-perfect match of the spectral COST model performed well could be partly explained by the bands of QuickBird and the spectral configuration of the mathematic operations in Eq. (1). While the omission of diffuse d spectroradiometer (CROPSCAN) used for ground measure- radiation Ek in image-based atmospheric correction tends to h ment, and thus the relative spectral responses differ between two make the denominator smaller, the overestimation of Tk with sensors (Steven et al., 2003). Particularly, the spectroradiometer the COST model makes the denominator larger. Therefore, has a narrower green bandwidth (0.5553–0.5647 Am) and it is errors associated with the algorithm may have canceled out. centralized in the ‘‘pure green’’ wavelength of QuickBird band 2 To further test the sensitivity of qk retrieval to the omission d h (0.52–0.60 Am) (Table 2). As a result, measured reflectances of Ek and the overestimation of Tk , we used SPECTRL2 (Bird with the spectroradiometer would be higher than the & Riordan, 1986) to calculate spectral diffuse irradiance under corresponding QuickBird measurements. a variety of cloudless atmospheres. The calculation indicated d Based on CROPSCAN measurements, we derived contin- that Ek was a large part of downwelling spectral irradiance, d uous average spectral signature curves for each crop type and even under clear sky conditions. The fraction of Ek was as numerically integrated qk over the spectral wavelengths of large as 30%, 25%, and 20% of total solar irradiance in the each QuickBird band. The integrated average qk was compared blue, green, and red wavelengths, respectively. The omission of d with the weighted average value to derive a correction factor Ek could increase qk by more than 20% (41% in blue, 25% in for each band. The integration and comparison were performed green, and 20% in red). On the other hand, the overestimation h individually for each sampling plot and for each sampling time. of Tk with the COST model could reduce qk by 38%, 28%, and The analysis showed that the values of the correction factors 23% in the blue, green, and red wavelengths, respectively. changed with spectral bands, but were generally close to 1.0 for Therefore, either of these two variables could cause consider- the blue, red, and near infrared bands. In contrast, the able errors in the retrieval of qk, but they tended to work correction factors for the green band were much lower than against each other and the errors were partly canceled out. 1.0 (0.84 for potato and 0.87 for corn on average), indicating measured qk with the CROPSCAN would be much lower if the 4.2.2. Near infrared band measurement was taken in QuickBird green band. It appears Without atmospheric correction, apparent reflectances in the that the CROPSCAN spectral configuration is sufficient to near infrared band were lower than ground measurements by J. Wu et al. / Remote Sensing of Environment 99 (2005) 315–325 323 6 0.16. But retrieved qk were still lower than corresponding ground 0 0 0 0 h . . . 0 6 0 . 7 6 measurements by about 20% because of the overestimation of T 7 . 6 k . 7 0 8 7 2 4 6 (multiplicative effect) as discussed earlier. The accuracy as such 5 0. 78 was not sufficient for most quantitative applications. One possible reason for the underestimation is that in the d 4 NIR spectrum, the omission of Ek may not be able to h compensate the effect of the overestimation of Tk . Compared d 0. to the visible bands, Ek in the NIR band was a relatively small 80 3 fraction of downwelling radiance (13%), and the effect of the (cm) d w omission of Ek on the retrieval of qk was minimal (qk h increased by about 2% on average). However, Tk in the NIR 2 band was overestimated substantially. The overestimation of 0 0 . 0 0. h . 7 . 7 6 7 72 Tk could reduce qk by more than 30%. 8 4 h 0 .8 We thus interpolated Tk for the NIR band through the contour 1 2 h d 0 map of Tk (Fig. 4), but Ek was still omitted because its effect .8 0.8 0 h 4 was minimal. With the DOS model and the interpolated Tk , the 0.86 accuracy of qk was significantly improved with only 0.03% 0 relative deviation from ground measurement. The slope of the 0 10 20 30 40 50 60 correlation with measurements increased to 0.98 (¨1.0), θ (degree) indicating very slight undercorrections. The RMSE decreased h Fig. 4. Atmospheric transmittances (Tk ) in the near infrared spectrum (0.76– to 0.06, which was nearly 65% less than for results with the 0.90 Am), as a function of precipitable water content (w) and solar zenith or COST model and 75% less than for results with the AR model. view angel (h), estimated with radiative transfer algorithms for Becker, Minnesota. 5. Conclusions more than 30% (Fig. 5d). The slope of the correlation was only The effects of atmospheric conditions on QuickBird 0.67 and the RMSE was as high as 0.22 (Table 6). Compared multispectral images were assessed and the DOS–COST with the AR model, the DOS–COST model produced better image-based atmospheric correction was evaluated by compar- results. The slope value increased to 0.77 and RMSE decreased to ing retrieved spectral reflectances with ground-based measure- 14 14 a b 12 12 10 10 (%) (%) g b ρ ρ 8 8 6 6 retrived 4 retrived 4 y = 1.21x 2 AR y = 2.75x 2 AR DOS-COST y = 0.94x DOS-COST y = 0.96x 0 0 0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14 ρ ρ measured b (%) measured g (%) 14 cd90 80 12 70 10 (%) 60 (%) r nir ρ 8 ρ 50 6 40 30 retrived 4 retrived AR y = 0.67x 20 2 AR y = 1.77x DOS-COST y = 0.77x 10 θ DOS-COST y = 1.06x DOS-T λ y = 0.98x 0 0 02468101214 0 102030405060708090 ρ ρ measured r (%) measured nir (%) Fig. 5. Multispectral surface reflectances (qk) measured at ground and retrieved with the apparent reflectance model (AR) and the dark object subtraction and cosine transmittance function model (DOS–COST) for the QuickBird blue (qb) (a), green (qg) (b), red (qr) (c), and near infrared (qnir) (d) bands. 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