Reflectance methods (Nianzeng et al. 1991; Staylor 1990; Teillet et al. 1990, 1988; Begni et al. 1986; Slater 1988; Slater et al. 1987) and radiance methods (Slater 1991 (Private discussion with P. N. Slater, 1991, University of Arizona, Tucson, Arizona.); Abel (Private discussion with P. Abel, 1991, NASA/Goddard, Greenbelt, Maryland.); Guenther et al. 1990; Slater et al. 1987; Smith et al. 1988; Kastner and Slater 1982) are used to make absolute indirect calibrations of space-based, visible-wavelength radiometers. Reflectance methods involve measuring the reflectance of a target surface from the ground, then using a radiation transport code and the solar irradiance to calculate the radiance at the aperture of the satellite radiometer. (Because reflectance measurements are made relative to the solar irradiance, they are not technically absolute methods. But, we include them here because the absolute solar irradiance is well known and its relative variation is small). Radiance methods involve measuring the radiance of a target from a high-flying aircraft so as to measure most of the atmospheric effects on the radiation transport directly. As with reflectance methods, a radiation transport code is then used to calculate the radiance at the satellite from the aircraft radiance measurements to account for the effects of the atmosphere between the aircraft and satellite. Thus, both methods require atmospheric corrections, but the corrections for the radiance methods are much smaller than for reflectance methods because of the smaller difference in intervening air mass between the reference radiometer and the satellite. Angular reflectance properties of the target, the state of the atmosphere, and the view and illumination geometries are important variables in making the radiation transport calculations. The view and illumination geometries are characterized as shown in Figure 1 (Frouin and Gautier 1987). Both radiance and reflectance methods can be further categorized as to whether field measurements or climatological values are used for the surface reflectance and the state of the atmos-phere data needed to make the radiative transfer corrections (see below).
The accuracy of indirect calibration depends on measuring the radiance of well-characterized and optically stable targets with surface uniformity over an area that exceeds the instrument spatial resolution (usually 4-9 pixels are averaged). Typically, radiometric response of the radiometer is assumed to be linear to within uncertainties that are small relative to other calibration errors. Thus, only two targets having different radiance are needed to generate a calibration line. A space view is measured frequently by most satellite radiometers and is taken as a practical zero radiance. Generally, this measured zero of radiance does not show much change over time or change from the prelaunch calibration (Staylor 1990). A second target is generally selected so as to span most of the range of Earth albedos measured by the satellite radiometer (Kaufman and Holben 1991).
Thus, the central problem in absolute indirect calibration is characterizing the radiance from a spatially uniform earth target, by measuring either the target's reflectance or radiance, then calculating the radiance at the aperture of the satellite radiometer.
The absolute accuracy of these methods is briefly summarized in Table 2 and given in more detail in subsequent sections below (see Table 3 and Table 4). The important point to note is that aerosol properties dominate the uncertainty of the reflectance methods. Reference radiometer calibration and co-alignment of the aircraft and satellite fields of view dominate the uncertainty of radiance methods.
Reflectance methods for visible-wavelength satellite radiometers have been reported by Frouin and Gautier (1987), Slater and Teillet et al. (1990), Teillet et al. (1988), Begni et al. (1986), Slater (1988), Slater et al. (1987), and Kastner and Slater (1982). These methods differ by way of the Earth targets used, details of the radiation transport calculations, and the degree to which climatological values are used to supplement field measurements for surface reflectance and for the state of the atmosphere. Field measurements improve the absolute accuracy of the calibration, but they are time-consuming and expensive. Thus, a practical trade-off between effort/cost and absolute calibration accuracy exists. Methods that do not require field meas-urements have the advantage in that they can be used retrospectively for data that have already been acquired, they require no advanced planning before calibration, and they are less expensive.
Frouin and Gautier (1987) report calibrations of AVHRR and VISSR/VAS using the dunes area of White Sands, New Mexico, that require no field measurements in addition to those normally recorded by nearby weather reporting stations. They estimate the reflectance of the dunes area based on previous field measurements of reflectivity, laboratory measurements of wet and dry White Sands soil, and climatological estimates for the soil moisture on days for which calibrations are determined. A radiative transfer code is then used to predict the radiance at the satellite, assuming standard atmospheric conditions. This approach produces absolute calibration accuracies of 8-13% for AVHRR and VISSR/VAS (Frouin and Gautier 1987).
Slater and Teillet et al. developed three methods (Teillet et al. 1990, 1988) for calibration of AVHRR. Method 1 relies on field measurements (including surface reflectance) in addition to data from another calibrated satellite sensor that acquired high-resolution imagery on or near the day of the AVHRR overpass. Method 2 makes no reference to another satellite sensor and is an extension of the reflectance-based method developed for TM and SPOT (Teillet et al. 1988; Slater et al. 1987). Method 3 achieves calibration by reference to another satellite sensor, but no surface reflectance and atmospheric measurements are needed on calibration day. One of the difficulties of implementing Methods 1 and 3 is that the two satellites used for calibration seldom view the same scene at the same time with similar view-ing and illumination geometries. Thus, finding suitable data sets for calibration is difficult [e.g., only 11 overpasses during a three-year period for NOAA-9 and -10 satisfy the selection criteria (Teillet et al. 1990)]. Estimated worse-case uncertainties are 7-8% (Teillet et al. 1990).
An approach developed by Justus (1988) and used recently to calibrate AVHRR on NOAA-11 (Abel 1991) is to measure cloud radiance on an overcast day and use a delta-Eddington cloud layer model to infer the irradiance incident on the cloud top images acquired by the AVHRR. RMS uncertainty of 10% is typical of this method.
Fraser and Kaufman (1986) use the radiance of sunlight scattered by the atmospheric gas above the oceans as a standard radiance source. This approach used for VISSR/VAS is possible under restricted conditions over oceans where the scatter from the atmospheric gas is comparable to that from aerosols and the ocean surface. This approach provides calibration of the lower 20% of the full-scale range of VISSR/VAS with uncertainties of 9%.
Radiance methods have been developed by Hovis, Smith and Abel et al. (Hovis et al. 1985; Smith et al. 1988; Kastner and Slater 1982; Abel et al. 1988), Slater and co-workers (Teillet et al. 1988; Begni et al. 1986; Slater et al. 1987), Justus (1988), and Fraser and Kaufman (1986). As with the reflectance methods, these methods differ in the earth targets used, details of the radiation transport calculations, and the degree to which climatological values are used to supplement field measurements needed for input in the radiation transport calculations. The radiance methods have the advantage over surface reflectance methods in that most of the effects of the atmosphere on the radiation transport are measured directly. Thus, the burden of calculating the radiation transport accurately is transferred to measuring the radiance accurately; which, in turn, depends on the accuracy of the airborne radiometer calibration and co-alignment of the fields of view of the satellite and airborne radiometers.
Hovis, Smith, and Abel use a calibrated radiometer mounted on a high-flying aircraft (ER-2 at 19,000 m above sea level) to calibrate AVHRR (Smith et al. 1988); AVHRR, VISSR/VAS, and TM (Abel et al. 1988). This followed earlier work calibrating the Coastal Zone Color Sensor (CZCS) (Hovis et al. 1985). Great care is taken to ensure that the field of view, viewing geometry, and viewing time of the aircraft radiometer coincide as closely as possible with that of the satellite as illustrated in Figure 2. White Sands, New Mexico, is used as the radiance target. Estimated absolute uncertainties are 6% (worse case) for the reference radiometer with an additional 3.5% associated with making the field measurements. This gives an RMS total uncertainty of 7%, but 5% is believed to be typical (Smith et al. 1988; Abel, Private discussions with P. Abel, 1991, NASA/Goddard, Greenbelt, Maryland.)
Slater and co-workers (Teillet et al. 1988; Begni et al. 1986; Slater 1988; Slater et al. 1987) use a high-flying helicopter (3,000 m above sea level) to make the radiance measurements at White Sands which is at 1200 m above sea level. They have provided calibrations for TM (Slater 1988), TM and CZCS (Slater et al. 1987), and SPOT (Begni et al. 1986) with this technique. Despite the lower altitude relative to the ER-2, the helicopter flies above most of the aerosol (Slater et al. 1987) that is concentrated in the lowest part of the atmosphere, primarily the planetary boundary layer (typically < 1000 m). They indicate a absolute accuracy of 5% for TM (Slater 1988) and 5.7% for SPOT (Begni et al. 1986).
Surface reflectance properties, radiation transport calculations with associated measurements, and target considerations affect the accuracy of both radiance and reflectance methods. The radiance method is additionally affected by the reference radiometer calibration. We now consider these issues in general, and in the following section discuss their impact on the accuracy of absolute indirect calibration.
Radiation transport calculations require as input the viewing geometry and properties related to the molecular and aerosol scattering and absorption. Fortunately, the molecular processes are separable from the aerosol processes, which greatly simplifies the radiation transport problem (Tanre et al. 1985).
Molecular scattering is due primarily to Rayleigh scattering and can be computed accurately from the wavelength of the light being scattered; Rayleigh scattering cross sections for the constituents of air; and the molecular density profile, which, in turn, can be estimated from the temperature profile and surface pressure.
Molecular absorption in the visible spectrum is due primarily to water vapor, ozone, carbon dioxide, and oxygen (in order of decreasing importance). So, absolute concentration profiles for these species are needed. Oxygen and carbon dioxide are generally well mixed in the atmosphere, so their profiles can be obtained from the molecular density profile. The water vapor and ozone profiles are more difficult to obtain. The ozone profiles may be obtained from ground-based solar attenuation measurements (Slater et al. 1987), or climatological values (Frouin and Gautier 1987) according to season and latitude. Water vapor profiles can be obtained from radiosonde measurements (Teillet et al. 1990) or extrapolated from surface relative humidity measurements (Slater et al. 1987). Another, more accurate approach for water vapor and ozone is to measure their total column concentration on calibration day and assume their profiles have the same shape as a standard atmosphere (Kneizys et al. 1983). Once the concentration profiles have been determined by one of these methods, radiation transport programs such as LOWTRAN (Kneizys et al. 1983) or the French "5-S" code (Tanre et al. 1990; Teillet et al. 1990; Fraser and Kaufman 1986) can be used to calculate the molecular atmos-pheric transmission.
In general, the accuracy of the radiation transport codes is good, provided that the state of the atmosphere is accurately known. The inherent model inaccuracies are typically <1% (Smith et al. 1988; Slater, Private discussions with P. N. Slater, 1991, University of Arizona, Tucson, Arizona.) In addition, as reported by Frouin and Gautier (1987) uncertainties in the water vapor amount (20%) and ozone amount (10%) produce proportionately smaller uncertainties in the calculated radiance at the satellite (0.2-1.2% and 0.1-0.7%, respectively) for Channels 1 and 2 of AVHRR. Similar results are reported by Kastner and Slater (1982) who indicate that 30% uncertainty in the water vapor content from its mean at White Sands leads to a 2% uncertainty in the TM band 5 radiance.
Aerosol scattering and absorption are determined from the aerosol number density, size frequency distribution, complex index of refraction, and scattering phase function (spatial aniso-tropy of the scattered light). These properties are most difficult to determine accurately for the purposes of indirect calibration and have various values, depending on the aerosol type (marine, continental, desert, etc.) and loading. Aerosol scattering has been determined from climatological properties and visibility (Teillet et al. 1990). Another approach is to measure the solar attenuation as a function of solar zenith angle (i.e., air mass). These data can be used to estimate the aerosol absorption and size frequency distribution (Slater et al. 1987). The complex index of refraction can be estimated by using it as an adjustable parameter in a radiation transfer code that computes radiance and then adjusting the complex index of refraction to minimize the difference between the computed radiance and that measured by an airborne radiometer (Slater et al. 1987). Once the aerosol properties are determined, the aerosol scattering and absorption can be computed with an appropriate code (Tanre et al. 1985; Kneizys et al. 1983; Dave 1969) which must take into account multiple scattering effects (Slater et al. 1987).
Errors in the aerosol loading and visibility lead to uncertainties in the calculated radiance. Errors of <5% are made for TM, Channel 1, with 50% uncertainty
in the visibility (over the range of 12.6 to 44-km visibility) (Frouin and Gautier 1987). Frouin and Gautier (1987) report a change of 30% in the visibility
produces a ~1% uncertainty in the radiance measured by VISSR/VAS and AVHRR. Uncertainties in the optical properties of the aerosols have a much greater affect
on the calculated radiance. A change of from 0 to 0.01 in the imaginary part of the index of refraction of the aerosol corresponds to a change of from 1 to
0.89 in the single-scattering albedo (
) and can change the radiance for TM, Channel 1, by 8% for a surface reflectance of 0.25 and 23-km visibility (Slater
1988). Uncertainties in aerosol optical properties are a major contributor to the uncertainty of radiance methods, and are therefore discussed in more detail
below.
The best calibration targets for indirect absolute calibration have 1) high reflectance (to calibrate the high end of the radiometer range), 2) have high spatial uniformity (to minimize co-registration errors between the reference radiometer and satellite radiometer), 3) are close to Lambertian reflectors (so any errors associated with differences in view geometry and illumination are minimized), 4) have generally clear skies (to minimize chances of cloud interference on calibration day), 5) have low aerosol loading (to minimize any errors in aerosol light scattering and absorption corrections), 6) have low humidity (to minimize any errors associated with water vapor absorption corrections), and are dry to minimize changes in surface reflectance with soil moisture. White Sands, New Mexico, with a reflectance of 0.5-0.85 located at 1200-m altitude above sea level is often selected as a calibration target because it meets most of the good-target criteria. Both the dunes and alkali flats areas of White Sands have been used for calibration (Teillet et al. 1990; Frouin and Gautier 1987). The Lybian Desert; Edwards Air Force Base, California (desert) (Teillet et al. 1988; Frouin and Gautier 1987; Slater et al. 1987; Kastner and Slater 1982; Slater, Private discussions with P. N. Slater, 1991, University of Arizona, Tucson, Arizona.) and marine stratus off the California cost (Justus 1988) have also been used. Snow at the poles has been used with less success, because the poles are illuminated only at low solar elevation angles which reduces the observed radiance and emphasizes any non-Lambertian properties of the surface (Slater[a]). Finding additional calibration targets is a topic of continuing research. One of the objectives of NOAA's Pathfinder Program (Mike Weinreb) is to upgrade AVHRR calibrations by locating suitable targets in the data that have already been acquired (Slater, Private discussions with P. N. Slater, 1991, University of Arizona, Tucson, Arizona.). In addition, work continues in developing the necessary algorithms to use marine stratus (Justus 1988). Deserts (Holben and Kaufman 1991; Teillet et al. 1988; Frouin and Gautier 1987; Slater et al. 1987; Kastner and Slater 1982; Slater, Private discussions with P. N. Slater, 1991, University of Arizona, Tucson, Arizona.) oceans (Holben and Kaufman 1991), clouds (Justus 1988; Slater, Private discussions with P. N. Slater, 1991, University of Arizona, Tucson, Arizona.) and air above oceans (Fraser and Kaufman 1986) are all targets currently under study for absolute indirect calibration.
The reflective properties of calibration targets are important because they determine the radiance observed by the radiometer for given atmos-pheric conditions and viewing geometry. The ideal target surface would be a perfect Lambertian diffuse reflector, having the same observed radiance independent of the solar zenith angle, viewing zenith angle and relative azimuthal angle. Such a surface would allow the greatest range of observing and illumination geometries. Unfortunately, most natural targets of sufficient size for indirect calibration are not very Lambertian.
However, the soil at White Sands, New Mexico, is nearly Lambertian for small viewing and solar zenith angles. Frouin and Gautier (1987) review the reflective
properties of White Sands soil (gypsum) and report an increase in reflectance of wet soil compared with dry soil because of an increasing specular component
for wet soil at azimuthal angles greater than 805. Dry soil shows a monotonic increase in reflectance of 0.70 to 0.85 for increasing solar zenith angle from
10
to 90. This is significant for the measured satellite radiance in that some of the satellite over- crossings occur at the time of large solar zenith angle
(particularly during the winter for sun- synchronous satellites with a late afternoon crossing, e.g., AVHRR), so are not usable for calibration. This is also
an important consideration for some of the reflectance methods, because the solar zenith angle changes significantly during the time required to measure the
reflectance of the target and reference panels (Slater et al. 1987) (~45 min). As a result, corrections must be made for any significant non-Lambertian reflection.
As with the radiation transport calculations, small viewing and solar zenith angles reduce the uncertainty in the calibration. This is particularly true of
the dunes area of White Sands because the dunes produce shade and reduce the observed radiance for large solar zenith angles (Frouin and Gautier 1987). Frouin
and Gautier report that a 1% uncertainty in surface reflectance leads to a 1.3-1.5% uncertainty in the radiance at the satellite (Frouin and Gautier 1987).
For radiance methods, accurate calibration of the reference radiometer is essential, as indicated in Table 2. Smith et al. (1988) estimate the absolute radiometric
accuracy of both the reference radiometer used in their study and the radiometer used for the NOAA-9 AVHRR prelaunch calibration at 
6%, RMS. More recent studies
indicate reference radiometer calibrations to 3.2% (Slater 1991, Private discussions with P. N. Slater, 1991, University of Arizona, Tucson, Arizona.) The
RMS calibration uncertainties accumulate in transferring the calibration of a reference lamp (which has typical absolute uncertainty of 1-2% and can change
by this amount on shipping [Hoyt and Zalewski 1991; Zalewski (Private discussions with E. Zalewski, 1991, Hughes Danbury Optical Systems, Danbury, Connecticut.)])
to an integrating sphere radiance source that uses the lamp. Two such steps typically occur in the calibration chain, one in the laboratory using a large integrating
sphere to calibrate the radiometer initially and one in the field to check the stability of the aircraft radiometer before and after the field measurements
(Smith et al. 1988). Current improvements are being developed and are reported below.
