The Clouds and the Earth’s Radiant Energy System (CERES) instrument is a scanning radiometer for measuring Earth-emitted and -reflected solar radiation to understand Earth’s energy balance. One CERES instrument was placed into orbit aboard the Tropical Rainfall Measuring Mission (TRMM) in 1997; two were aboard the Terra spacecraft, launched in 1999; and two were aboard the Aqua spacecraft, launched in 2002. These measurements are used together with data from higher-resolution instruments to generate a number of data products. The nominal footprint size of the pixel at Earth’s surface is 16 km in the cross-scan direction and 23 km in the scan direction for the TRMM platform and 36 km in the cross-scan direction and 46 km in the scan direction for the Terra and Aqua platforms. It is required that the location on Earth of each pixel be known to 1–2 km to use the CERES data with the higher-resolution instruments on a pixel basis. A technique has been developed to validate the computed geolocation of the measurements by use of coastlines. Scenes are chosen in which the reflected solar radiation changes abruptly from the land surface to the darker ocean surface and the Earth-emitted radiation changes from the warm land to the cool ocean, or vice versa, so that scenes can be detected both day and night. The computed coastline location is then compared with the World Bank II map. The method has been applied to data from the three spacecraft and shows that the pixel geolocations are accurate to within 10% of the pixel size and that the geolocation is adequate for current scientific investigations.
The Clouds and the Earth’s Radiant Energy System (CERES) instrument is a scanning radiometer flown on a satellite for measuring the solar radiation that is reflected by Earth and the radiation that is emitted by Earth (Barkstrom 1990; Wielicki et al. 1996). The instrument has three channels, each with its own telescope, all mounted on a beam that rotates so as to scan across the full disk of Earth. The three channels are a shortwave channel, for measuring the reflected solar radiation (0.2–5.0 μm); a total channel, which measures radiation between 0.2 and 50 μm; and a third channel that measures radiation emitted in the 8–12-μm atmospheric window. At night, the total channel provides outgoing longwave radiance. During the day, the total channel measures outgoing longwave radiance together with the reflected solar radiance; this measurement is used with the shortwave channel to compute the daytime outgoing longwave radiance. Each pixel is used to compute the flux from the observed geolocation (i.e., the latitude and longitude of the measurement). To generate accurate maps of the radiation, it is necessary that the measurements be located accurately. This paper describes the coastline detection technique by which the accuracy of the computed geolocation is validated and presents results for the CERES instruments that have been flown to date. Validation requires demonstrating that the procedures for computing pixel geolocations give results that are sufficiently accurate for the scientific requirements.
The CERES instrument was developed from the Earth Radiation Budget Experiment (ERBE), the first instrument of which was launched in October 1984 aboard the dedicated Earth Radiation Budget Satellite (Barkstrom and Smith 1986). Hoffman et al. (1987) developed a technique for validating the geolocation of the measurements from the ERBE scanning radiometer. The present method was developed from their algorithm, taking into account the characteristics of the point spread function (PSF) of the radiometer.
The CERES protoflight model (PFM) was aboard the Tropical Rainfall Measuring Mission (TRMM), which was placed in orbit in November 1997 and became operational a month later. The orbit altitude of TRMM is 350 km, and the nominal CERES pixel size for this spacecraft is 16 km in the cross-scan direction and 23 km in the scan direction near nadir. Flight models 1 and 2 (FM-1 and FM-2, respectively) are on the Terra spacecraft, which was launched in December 1999, and the instruments were activated in February 2000. One instrument scans cross-track to map the geographic distribution of radiation fluxes, and the other instrument rotates in azimuth as it scans, so as to measure radiances in all directions to describe the directionality of the reflected solar radiation and the Earth-emitted radiation. Models of this directionality are required to compute fluxes from the measured radiances. CERES flight models FM-3 and FM-4 are on the Aqua spacecraft, which was placed into orbit in May 2002 and began Earth observations in June 2002. These two instruments provide additional temporal sampling of radiation. The Terra and Aqua spacecraft have orbit altitudes of 705 km, and the nominal footprint size of the CERES pixel aboard these two spacecraft is 32 km in the cross-scan direction and 46 km in the scan direction near nadir.
Data from the PFM were processed by using data from the Visible and Infrared Scanner (VIRS), which is also aboard the TRMM spacecraft, to compute cloud information within the CERES pixel. The VIRS has a pixel size of 2.11 km near nadir. For the CERES instruments aboard Terra and Aqua, MODIS data are used with CERES measurements to determine cloud parameters to compute radiation fluxes at the surface and within the atmosphere (Wielicki et al. 1998). MODIS pixels are spaced 1 km apart near nadir. To use these two data types together, the geolocation of the CERES must be validated to a high accuracy. CERES data are also used together with measurements of radiation at ground sites for validation studies (Charlock et al. 2003; Rutan et al. 2001; Velázquez Blázquez et al. 2006), again requiring precise knowledge of the footprint geolocations.
This paper describes the coastline detection algorithm that is used for validating the geolocation of the CERES pixel, after which results are shown for the CERES radiometers aboard the three spacecraft. Thomas et al. (2007) have recently used the moon as a target of known location to validate the 0.1° accuracy of pixel location of the CERES radiometers and their PSFs. That method serves as an independent check of these parameters. Poe and Conway (1990) reported a study of the geolocation errors of the Special Sensor Microwave Imager (SSM/I). That instrument was a scanning radiometer also, so the study was similar in general to the present study. Kroon et al. (2008) investigated the errors of the geolocation of the Ozone Monitoring Instrument, which is a “push broom” radiometer with 60 pixels aligned in the cross-track direction. The geolocation validation problem for a push-broom instrument is quite different from that for a scanning radiometer.
2. CERES measurements
The CERES geolocation is validated by use of the CERES measurements in a landmark analysis of coastlines. The shortwave channel measures radiation in the 0.2–5.0-μm range, which is reflected solar radiation, and the total channel measures radiation from 0.2 to 50 μ, which includes reflected solar radiation and Earth-emitted radiation. During daytime, the Earth-emitted radiance (i.e., longwave radiance) is computed by subtracting the shortwave radiance from the total radiance. The third channel measures radiance in the 8–12-μm range, corresponding to the atmospheric longwave window. Only the total channel is used for geolocation validation.
Each of the three channels consists of a telescope that collects radiation and focuses it onto a thermistor-bolometer. The three telescopes are mounted on a beam that scans in elevation angle from one limb of Earth to the other. This assembly is mounted on a table that permits it to rotate in azimuth. Figure 1 is a drawing of the CERES instrument. The instrument weighs 45 kg, fits within a 60-cm cube, and requires 47 W to scan in nadir and azimuth.
The CERES instrument scans from a position in which the detectors look inside the instrument to measure the internal calibration module (ICM) output, then scans to a space look, across Earth to nadir to space on the other side, and then scans back across Earth to the ICM. The instrument nominally scans at 63.5° s−1. The instrument data include the nadir and azimuth angles for the measurements, which are combined with the location and orientation information of the spacecraft to compute the pixel location on the surface of Earth. Further details of the calculations are given by Wielicki et al. (1998).
a. CERES point spread function
To locate the centroid of the pixel to a greater accuracy than the size of the footprint, it is necessary to take into account the PSF of the instrument, which describes the response of the instrument to radiance from a point as the radiometer scans over it. The PSF is determined by the field stop and the time response of the instrument (Smith 1994). A field stop at the focal plane of each telescope defines the field of view as a truncated diamond, or hexagon, as shown in Fig. 2. The width of the field stop is 2.6°. The detector has a 9-ms time constant, and the signal is processed through a four-pole Bessel filter, which suppresses electronic noise within the detector circuitry. The nominal PSF of the instrument is shown by Fig. 2. Because of the time responses of the detector and electronic filter, as the instrument scans over a point, the response of the instrument increases as a rounded exponential until the observed point is past the field stop, after which the PSF decreases exponentially. In Fig. 2, the diamond indicates the maximum value and the asterisk indicates the centroid (i.e., center of gravity) of the PSF. The total effects of the time responses are to move the centroid 1.51° behind the optical axis of the instrument, and the maximum value of the PSF is 1.36° behind the optical axis. In the data processing, the geolocation of the pixel is defined by the PSF centroid so as to minimize the blur of the retrieved radiation field relative to the original field. There are small variations from these nominal values among detectors, mainly because of differences among time responses of the detectors. The footprint, or ground pixel, is the PSF projected to the surface of Earth.
b. Host spacecraft
The CERES PFM was aboard the Tropical Rainfall Measuring Mission, which had a precessing orbit with an altitude of 350 km and an inclination of 35°. Smith et al. (1998a,b) discuss CERES on this mission and show the placement of the CERES PFM aboard the TRMM spacecraft so as to have an unobstructed view of Earth in all directions. At this altitude, the 2.6° width of the field stop projected to the ground gives a footprint width of 16 km and the root-mean-square length of the pixel projects to a length of 23 km. CERES FM-1 and FM-2 were aboard the Terra spacecraft in a sun-synchronous orbit with ascending node at 1030 LT at altitude 705 km. Smith et al. (1996) shows the placement of these instruments on the Terra platform. The Aqua spacecraft carried FM-3 and FM-4 in a similar orbit, except with an ascending node of 1330 LT. The footprint width for these instruments is 32 km, and the length is 46 km. All instruments are aligned to the spacecraft with an error of less than 0.1° along each axis.
3. Coastline detection algorithm
The geolocation of the CERES pixels may be validated by noting where the pixels scan across large variations of surface temperature or brightness whose locations are well known (e.g., coastlines). As the radiometer scans from a hot and bright desert onto sea, the shortwave radiance will decrease and the longwave radiance from the total and the shortwave channels will decrease as well. Such locations are the Libyan Desert coast with the Mediterranean Sea, Oman with the Red Sea, Baja California with the Pacific Ocean on the west coast and the Gulf of California on the east side, and northern Australia with the Pacific Ocean.
Figure 3 shows the radiances of the total channel of FM-1 as Terra flies from over Saudi Arabia, the Red Sea, and Egypt. The colors represent the radiances from the total channel. During each scan cycle, the instrument scans across Earth from one limb to the other. The scan cycles are delineated by the stripes between scans. There is much contrast between the land and the sea so that the coastline crossings are clear to the eye. The algorithm computes where these contrasts occur in the neighborhood of coastlines. The computed coastline crossing points are shown by black circles in this figure.
The algorithm of Hoffman et al. (1987) was modified to consider the CERES PSF (i.e., the effect on the measurement of a point source within the field of view and the geolocation process). The measurement as the radiometer scans across a step function is then computed as an idealization of scanning across a coastline.
a. Exclusion of cloudy pixels
In applying the method, it is necessary to exclude pixels that contain clouds, because clouds may have a strong contrast that may be mistaken to be cool water at night or bright land during day. Clouds are excluded by use of a scene identification algorithm that provides cloud information for analyzing the data (Wielicki et al. 1998). In simple terms, during the day clouds are bright against the darker surface and at night clouds are cooler than the surface. If clouds are present in the pixel, then the pixel is not used for validating geolocation. For a clear scene, scattering by the atmosphere of shortwave radiation is small so that the shortwave radiance at the instrument is from the point on the surface on the line of sight (i.e., not scattered by the atmosphere from another point on the surface). The contrast between the dark ocean and the relatively bright land is the basis for the shortwave part of the coastline algorithm. The broadband longwave radiance consists of radiance from the surface and from the atmosphere. For scenes that are useful for geolocation validation at night, there is a strong temperature contrast between the surface temperature of the land and that of the ocean, which gives a strong contrast between the radiances of the two surfaces. Within the 8–12-μm longwave window, this radiance contrast is observed at the instrument. Outside this window, the radiance is from the atmosphere, which has a relatively small horizontal variation above the planetary boundary layer (PBL). The temperature within the PBL varies with altitude from the contrasting temperatures of the land and ocean to the smooth temperature of the lower troposphere, and most of the radiance outside the longwave window is from above the PBL so that this part of the radiance outside the longwave window is smooth. The result is that the broadband longwave shows the contrast between the land and ocean. If optically thick aerosols are present, their effect will be to diminish the contrast in both the shortwave and longwave radiances so that the pixel would be rejected for use.
b. Geolocation computation
The first step in geolocating a pixel is to calculate the unit vector of the optical axis of the instrument in the spacecraft coordinate system, for which the z axis is toward nadir and the x axis is in the flight direction. The next step is to transform from the spacecraft coordinate system to an Earth-fixed Cartesian coordinate system. Earth’s surface is described by the World Geodetic System 1984 (WGS-84) ellipsoid model (NIMA 2000). The intersection of the optical axis vector with the Earth ellipsoid determines the geolocation of the measurement. The geocentric latitude ϕc and longitude λc are then computed by ϕc = a sin(Sz/|S|) and λc = a tan(Sy/Sx), where S is the position vector in Cartesian coordinates. The geodetic latitude ϕg is computed from tanϕg = (a/b)2 tanϕc, where a is Earth’s semimajor axis (6378.137 km) and b is its semiminor axis (6356.752 km). Further details of the geolocation computation are given by Green and Wielicki (1995).
c. Measurements across a step change
The radiance field as the radiometer scans across a coast may be considered to be a step change. For a unit step from sea to land, the measurement is the integral of the PSF over the land:
where ρ is the angular distance in the scan direction from the optical axis, σ is the angular distance in the normal direction, and D is the part of the field of view that is land. Figure 4 shows the PSF as the radiometer scans across a unit step as a function of distance in the along-scan direction, with the scan normal to the coastline and at angles to the normal in 5° increments up to 45°. The effect of the angle from the normal is to broaden the effect of the coast on the PSF. The maximum of the PSF is 1.36° behind the optical axis when the scan is normal to the coast and increases to 1.43° for θ = 45°. The centroid is at 1.51° and does not change significantly with the angle to the coastline normal over the range between 0° and 45°. Figure 4 also shows the integrated response to the step change (i.e., the measurement as the radiometer scans across the coast). The location of the inflection point of the response is the same as the maximum of the PSF and is not the location of the centroid.
The coastline location can be determined from the measurements by finding the inflection point of the measurement profile, which will be 1.36°–1.43° (depending on the angle of the scan to the coastline) after the optical axis. The centroid is 1.51° behind the optical axis. In the operational data processing, the geolocation is computed as the centroid location so that for the scan normal to the coastline the inflection point should be 1.51° − 1.36° = 0.15° ahead of the computed geolocation. The algorithm for validating the geolocation can now be described.
d. Algorithm description
The Hoffman et al. (1987) algorithm locates a coastline by fitting a cubic equation as it traverses a scan line; thus
where yi is the radiance and xi is the position of each measurement. A cubic is the simplest polynomial with an inflection point. The coefficients are given by
The inflection point is x = −b/3a. As the algorithm traverses the scan line, the inflection point will lie between x2 and x3. This location has two measurements on each side and is used for the coastline location computation. The location is taken to be a useful coastline crossing only if the change of radiance across the coast is sufficiently large. This procedure is illustrated by Fig. 5. This method worked quite well to validate the ERBE geolocation (Hoffman et al. 1987) and is used for validating the CERES pixel geolocations.
The geolocation validation uses data from the instrument in cross-track scan mode. There are two components to the geolocation error: in the cross-track direction and in the along-track direction. The error in the cross-track, or scan, direction is best measured by using coasts that are nearly normal to the scan direction so that errors in the along-track direction do not affect the result. To measure errors in the along-track direction, a coastline whose normal is at a large angle to the cross-track, or scan, direction is useful.
Currey et al. (1998) used the Hoffman et al. (1987) algorithm to compute the geolocation of individual crossings for a given scene and the distance of each computed crossing from the coastline indicated by the map. They used the (public domain) 1993 Central Intelligence Agency World Map database, or World Bank II, high-resolution map to compute elevation, whence coastline. The average distance for an ensemble of crossings was calculated and adjustments were made to latitude, longitude, and orientation for the scene to minimize the average distance, using a downhill simplex method (Press et al. 1988) until successive solutions are within the accepted tolerance. The resulting shift was the location error for the ensemble. From the errors in latitude and longitude, errors in the scan and cross-scan (or ground-track) directions were computed. The Currey et al. (1998) method was used for validation of CERES PFM aboard TRMM and was based on human selection of acceptable coastline crossings such as those noted at the start of section 3.
Spence et al. (2003) automated the process for application to CERES instruments aboard Terra and Aqua. Twenty consecutive scans across a coastline, with a gap of up to three scans permitted, are required to constitute an ensemble of coastline crossings. For a point to be considered to be a coastline crossing, the inflection point must be within 20 km of the computed coast. The total channel radiance is used to determine whether a coastline has been crossed. During day, the contrast must be at least 10 W m−2 sr−1. Scenes that are identified by the sun-scene-instrument geometry as having sun glint are not used. At night, the contrast must be at least 2 W m−2 sr−1. These threshold values were empirically determined to identify high-contrast scenes. Scenes that do not have these minimal contrasts in the total radiances are not used. Scenes that are rejected by this criterion include land and adjacent ocean with little temperature contrast at night and dark (vegetated) land next to ocean with little temperature contrast in day. Only coastline crossings near nadir are considered. The footprint grows with increasing nadir angle, decreasing the probability of the footprint being cloud free. Also, atmospheric effects increase as the zenith angle of the view increases with nadir angle.
e. Errors of geolocation and of validation method
The errors computed by the geolocation validation are due to two types of errors: errors of the geolocation and errors of the validation process. Error sources for geolocation include the computed spacecraft location and attitude, the direction of pointing of the instrument, and the description of Earth’s shape by the WGS-84 ellipsoid model. Errors of the validation include the use of a cubic to compute the location of the pixel centroid, the treatment of the coastlines as step functions, the spacing of the pixels, and the accuracy of the World Bank II map. The errors of the validation method are now discussed.
1) Errors due to use of cubic
This method approximates the PSF integrated over a step function by a cubic fit to compute the inflection point. An error is incurred by this approximation. If the PSF integrated over a step function were third degree over the interval for four points to compute the cubic, then the algorithm would provide the exact answer for the case of a straight coastline and no measurement error. This error in pixel location will be small relative to the distance between points x2 and x3. Also, the error is symmetric about the center between x2 and x3 as the scan goes from one direction to the other. Thus, this error will average out with inflection points being located randomly between x2 and x3 and will be a small random error with no expected bias.
2) Errors due to finite sampling rate
In the scan (or cross-track) direction, the accuracy is limited by the distance between data points and the shape of the PSF. The data spacing is 0.64° in the scan direction between pixels, or 4 km for the TRMM and 8 km near nadir for Terra and Aqua. Near nadir, the scans are about 26 km apart. However, information in the along-track direction is provided by the coastline not being normal to the ground track. If the coastline is not normal to the scan direction and the ground track is displaced from the nominal track, the coastline will appear too soon or too late in the scan, requiring an adjustment in the geolocation for the coastline crossing time to agree.
3) Errors due to irregular coastline
Any irregularities of the coastline that are large relative to the footprint (i.e., larger than 32 km) will appear as a movement of the coastline. Irregularities that are small relative to the CERES footprint (i.e., small relative to 32 km) will be averaged out by the measurement. Irregularities near 26 km in the along-track direction and 32 km in the scan direction will affect the measurements. These effects will be reduced by the averaging over the 17–20 scans that constitute an ensemble of coastline crossings. Rugged coastlines typically do not generate the contiguous datasets required for an ensemble of crossings and are rejected.
4) Errors due to reference map
The World Bank II map provides locations spaced approximately 3 km apart and is digitized at approximately 0.2-km resolution. Kroon et al. (2008) estimate the accuracy of the World Bank II map to be 1 km.
The error computed by the geolocation validation method is the sum of the geolocation error and the error of the validation process. The errors of the validation process are uncorrelated so that these errors are reduced by averaging. Also, the errors of the geolocation are uncorrelated with those of validation so that the variance of the error computed by the validation method is the sum of the variances of geolocation and validation. Because the results show that the geolocation errors of the footprints are an order of magnitude smaller than the footprint, no analysis of errors was needed.
This section presents the results obtained for the CERES instruments in orbit aboard the TRMM, Terra, and Aqua spacecraft. The results are summarized in Table 1. The results of application in Table 1 show that the standard deviation of error in the scan direction is about one-third of the pixel spacing, or approximately 2.4 km. There are a sufficient number of cloud-free coastline crossings that met the contrast criterion to give the sampling accuracy needed to validate the pixel location computation.
a. Results from CERES aboard TRMM
The CERES protoflight model collected data on the TRMM mission from December 1997 through August 1998. For PFM, the pixel geolocations were validated manually by use of a display system that permitted visual screening of clouds (Currey et al. 1998). Figure 6 shows the geolocation errors on Earth’s surface as cross-track and along-track errors for January 1998. For this case, the sample mean error is −0.58 km in the cross-track direction and 0.48 km in the along-track direction. The standard deviations for this sample are 1.11 km cross track and 1.08 km along track.
Figure 7 presents this information in the radiometer coordinate system. For points near nadir, the angles in the radiometric system are related to the surface errors by the TRMM spacecraft altitude of 350 km. The data points are clustered fairly tightly near the peak of the PSF. The mean of the geolocation is −0.095° in the scan direction (i.e., the location derived from the coastline method is 0.095° ahead of the location computed from the spacecraft navigation data). The mean error in the cross-scan direction is 0.078°. The standard deviation of the geolocation error is 0.182° in the scan direction and 0.176° in the cross-scan direction.
b. Results from CERES instruments aboard Terra
The geolocation validation algorithm was upgraded for CERES aboard Terra and Aqua to incorporate the scene identification as computed by a CERES algorithm using MODIS data. Scenes were selected between 70°S and 70°N so as to exclude the polar regions. Not using the polar regions avoided problems with snow and ice confusing the coastlines. Also, coastlines in those regions tend to be highly irregular.
Figure 8 shows scatterplots of the monthly-mean geolocation errors for FM-1 and FM-2, which are on Terra. Each monthly mean is based on 8–32 ensembles of coastline crossings, with a median number of about 16 ensembles. In each plot, the large symbol represents the grand-mean geolocation errors (i.e., the average of the monthly-mean errors over the 7-yr period of instrument operation to date). The scan-direction error for FM-1 is fortuitously small (0.01 km), and the along-track error is 1.24 km. The Terra and Aqua spacecraft operate at a nominal altitude of 705 km so that the geolocation errors for the CERES instruments aboard these satellites are expected to be 2 times those for TRMM.
Figure 9 shows the monthly-mean geolocation errors and the associated one-standard-deviation error bars for every six months, from March 2000 through March 2007 (84 months), for FM-1 and FM-2. The grand-mean geolocation error is within these error bars for each month. The scan-direction and along-track errors for each instrument do not indicate any trend (i.e., the grand-mean geolocation errors appear to be stable). These grand-mean errors and the root-mean-square standard deviations are listed in Table 1 for FM-1 and FM-2.
c. Application to Aqua
The CERES FM-3 and FM-4 instruments aboard the Aqua spacecraft began operating in June 2002. Figure 10 shows the comparison of geolocations computed by the validation algorithm and the positions given by the data products for FM-3 and FM-4 aboard Aqua. These results are similar to those shown in Fig. 8 for FM-1 and FM-2. Each monthly mean for Aqua is based on about 20 cases. For FM-3, the along-track geolocation error is 0.51 km, but the cross-track error is 1.88 km. For FM-4, both components of error are small: the scan-direction error is 0.22 km and the along-track error is 0.17 km. Figure 11 shows the history of geolocation errors for FM-3 and FM-4 for June 2002 through June 2007 (60 months). There is no apparent trend of geolocation error.
The histories of the geolocation errors for all five instruments show no trend, but the three-month averages appear to be random variations about a grand-mean value, or constant bias, in each case. Also, the bias is unique in each case, implying that there is no consistent cause for the bias from one model to the next. Table 1 shows that the accuracy of along-track errors is close to that for scan-direction errors.
The geolocation errors have been computed for pixels near nadir. These errors are due to angular displacements or, in the scan direction, possibly timing error, which can be expressed in terms of angles. For footprints at large nadir angles, the errors in terms of angles still apply. Thus, as the nadir angle increases, the footprint and the geolocation errors grow in proportion so that the geolocation error is the same fraction of footprint size.
A technique has been developed for validating the geolocation of Clouds and the Earth’s Radiant Energy System measurements by use of coastlines as accurately known locations with which to compare CERES measurements. The method uses a cubic fit that locates the maximum of the point spread function; the pixel location is 0.15° behind this point. For application to data from the CERES protoflight model, aboard the Tropical Rainfall Measuring Mission, an interactive environment was designed. Application of the method demonstrated that for the protoflight model of the CERES instrument aboard the TRMM, the mean geolocation error is within 0.6 km for the along-track and cross-track directions. The standard deviations of the errors are approximately 1 km for both directions. Experience from this use enabled the automation of the coastline detection process.
Use of the method demonstrated that, for CERES flight models 1 and 2 aboard the Terra spacecraft and for flight models 3 and 4 aboard the Aqua spacecraft, the geolocation errors of the pixels are less than an order of magnitude of the footprint size. In the scan direction the geolocation error is less than 2 km, and in the along-track direction the error is less than 1.3 km for all instruments near nadir. The geolocation errors will grow in proportion to the footprint with increasing nadir angle, remaining an order of magnitude smaller than the footprint. The geolocations are adequate for scientific applications of the measurements.
The authors gratefully acknowledge the support by the CERES Program, which is funded by the Earth Observation Office of the Washington, D.C., office of NASA, and by the Science Directorate of the Langley Research Center (LaRC). GLS is funded by contract between LaRC and the National Institute for Aerospace, and PCH is funded by contract between LaRC and Space Science Applications, Inc.
* Current affiliation: Planning Systems, Inc., Long Beach, Mississippi.
Corresponding author address: G. Louis Smith, Langley Research Center, Mail Stop 420, Hampton, VA 23681. Email: email@example.com