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  • Zissis, G. J., Ed., 1993: The Infrared and Electro-Optical Systems Handbook. Vol. 1. Environmental Research Institute of Michigan, 373 pp.

  • View in gallery

    (a) Average nadir view 1.6-μm reflectances for cloud-free pixels plotted against across-track distance. (b) The corresponding 3.7-μm minus 11-μm brightness temperature differences. The area used was 512 km × 512 km in size and was centered at 34.7°N, 50.4°W. The measurements were made by ATSR-2 on 16 May 1995.

  • View in gallery

    Reflectivity of a flat water surface as a function of incidence angle at 1.6 (solid curves) and at 3.7 μm (dashed curves). (a) Horizontal polarization, (b) vertical polarization, and (c) random polarization.

  • View in gallery

    Ratio of reflectivities for 1.6 and 3.7 μm for a flat watersurface. (a) Horizontal, (b) vertical, and (c) random polarization.

  • View in gallery

    The 1.6-μm reflectivities computed by using the increase in the nadir-view 3.7-μm channel brightness temperatures. The data used were from the area centered at 24.9°N, 27.9°W (16 May 1995). Only every 10th point is shown.

  • View in gallery

    As in Fig. 4 for the area centered at 21.5°N, 53.9°W (16May 1995).

  • View in gallery

    Computed reflectivities at 1.6 μm using forward-view 3.7-μm channel brightness temperature data. The area used was centered at 73.2°N, 9.7°E (17 May 1995). All the points used are shown.

  • View in gallery

    Theoretical ratio of reflectivities from a flat water surface at 1.6 and 3.7 μm, as as would be detected by a polarization-sensitive instrument. The polarization sensitivity ratios used were 0.65 for the 1.6-μm channel and 0.97 for the 3.7-μm channel. Curves (a) and (b) are for the case when the sensitivities are higher for the same plane of polarization in both channels, and curves (c) and (d) are for the case when the channels sensitivities are in the opposite sense.

  • View in gallery

    As in Fig. 7 with the reflectivity ratios normalized by thereflectivity ratios for a nonpolarization-sensitive instrument.

  • View in gallery

    Angles made to the facet normals by the incident and reflected beams from the sun. The cases shown are for the pixels used in Fig. 4.

  • View in gallery

    Angles made to the facet normals by the incident and reflected beams from the sun. The cases shown are for the pixels used in Fig. 5.

  • View in gallery

    Angles made to the facet normals by the incident and reflected beams from the sun. The cases shown are for the pixels used in Fig. 6.

  • View in gallery

    Polarization rotation in ATSR plotted against pixel position on the swath. No rotation takes place for reflected radiation from the pixel on the subsatellite track in the forward view, and the rotation of the polarization plane is maximum for pixels close to the subsatellite point in the nadir view.

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A Novel Method for Calibrating the ATSR-2 1.6-μm Channel Using Simultaneous Measurements Made in the 3.7-μm Channel in Sun Glint

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  • 1 Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire, United Kingdom
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Abstract

Reflection of the sun’s radiation from the sea surface can give rise to abnormally high brightness temperatures in the 3.7-μm channel of the Along-Track Scanning Radiometer (ATSR-2). Using a radiative transfer model, this effect is used to calibrate the instrument’s 1.6-μm channel by first characterizing the atmosphere with the aid of 11- and 12-μm measurements and then calculating the surface’s effective reflectivity for radiation in the 3.7-μm channel. Scaling of this reflectivity by a factor deduced from the refractive indices of water at 1.6 and 3.7 μm allows, in principle, the calculation of the 1.6-μm channel reflectivity. This can be used directly to give a calibration factor for the 1.6-μm ATSR-2 channel. The polarization sensitivity of the ATSR-2 instrument requires a small correction to be made, and this can be derived by using measurements made in sun-glint areas in both the nadir and the forward views.

Corresponding author address: Albin M. Závody, RAL, Space Science Dept., Chilton, DIDCOT, Oxon OX11 0QX, United Kingdom

Email: albin@atsrsc.rl.ac.uk

Abstract

Reflection of the sun’s radiation from the sea surface can give rise to abnormally high brightness temperatures in the 3.7-μm channel of the Along-Track Scanning Radiometer (ATSR-2). Using a radiative transfer model, this effect is used to calibrate the instrument’s 1.6-μm channel by first characterizing the atmosphere with the aid of 11- and 12-μm measurements and then calculating the surface’s effective reflectivity for radiation in the 3.7-μm channel. Scaling of this reflectivity by a factor deduced from the refractive indices of water at 1.6 and 3.7 μm allows, in principle, the calculation of the 1.6-μm channel reflectivity. This can be used directly to give a calibration factor for the 1.6-μm ATSR-2 channel. The polarization sensitivity of the ATSR-2 instrument requires a small correction to be made, and this can be derived by using measurements made in sun-glint areas in both the nadir and the forward views.

Corresponding author address: Albin M. Závody, RAL, Space Science Dept., Chilton, DIDCOT, Oxon OX11 0QX, United Kingdom

Email: albin@atsrsc.rl.ac.uk

1. Introduction

The first Along-Track Scanning Radiometer (ATSR) was launched in 1991, and it has been described in Smith et al. (1994), Závody et al. (1994), with engineering details given in Edwards et al. (1990). The second instrument in the series, ATSR-2, was launched in 1995;it has three visible channels in addition to the infrared channels centered at 1.6, 3.7, 10.8, and 12 μm, which are common to all ATSRs.

The primary purpose of the ATSR instruments is the measurement of sea surface temperature to an accuracy of about 0.3 K. The three most important features that help in achieving this are 1) high sensitivity through actively cooled detectors, 2) two views of every point on the earth’s surface through different atmospheric path lengths, and 3) onboard calibrators to give a very high accuracy: 0.1 K or better for the three thermal infrared channels. In the case of ATSR-2, the three short wavelength channels, designed primarily for land applications and centered at 0.555, 0.660, and 0.865 μm, are also calibrated in flight to 2% in reflectivity (Read et al. 1991).

The main function of the 1.6-μm channel is cloud detection and for this, absolute calibration is only of secondary importance, hence there was no onboard calibration of this channel on the first ATSR. For ATSR-2, the calibrator for the visible channels can also be used to calibrate in flight the 1.6-μm channel but, owing to the low importance previously attached to having accurately calibrated 1.6-μm reflectances, the channel was not fully characterized before launch.

Accurately calibrated 1.6-μm data are required for the characterization of ground cover (see, e.g., Vogelmann and Rock 1988), the determination of the drop size and phase in clouds (Watts and Baran 1997), and for volcano monitoring (Wooster and Rothery 1997).

There are two traditional ways of checking the calibration or calibrating a visible or near-infrared channel in flight: by using data obtained over test sites like White Sands with in situ data from the same location (Slater et al. 1996) and by the use of other satellite instruments working in the same wavelength band either on satellites (Wooster 1996; Koelmeijer et al. 1998) or airborne instruments (Abel et al. 1993). All these methods rely on information from sources other than the instrument to be calibrated, and the quality of these is sometimes not proven and/or often there are differences in look angle, spatial resolution, or the time of the observations.

A possible way of calibrating a channel of a satelliteborne radiometer is to view the same calibration target by the uncalibrated and a calibrated channel. If the channel response functions are known, then using these with Planck’s radiation function the spectral radiance for the uncalibrated channel can be computed from that measured by the calibrated channel. After correction for the possible differences in the target emissivities and for atmospheric effects in the two channels, a comparison of the computed and the measured values can yield the calibration factor sought.

For channels in the near-infrared and visible wavelength regions, the blackbody emission is usually very small at temperatures normally encountered on the earth’s surface. The sun, however, is a very powerful source of radiation, and the maximum of the spectral power is in the visible region. If the radiometer can be pointed into space, then an extraterrestrial reflecting object (e.g., the moon; see Kieffer and Wildey 1996) could be used for both absolute and intercalibration of visible and near-infrared wavelength channels. A significant advantage in this case would be that no atmospheric correction is necessary; the disadvantage is that the reflectivity of the target has to be known.

Areas on the earth’s surface that partially reflect the sun’s radiation can also be used as targets, and water surfaces are ideal because values for its emissivity are readily available in the published literature. Both the 1.6-μm and the visible-channel signals can be very strong in regions of sun glint and can even saturate the ATSR instruments. Although in the 11- and 12-μm channel brightness temperatures no sun-glint effect has been observed, in the 3.7-μm channel the effect is very clear, as can be seen in the example shown in Fig. 1. Using data from this channel and the 1.6-μm channel is the basis of the calibration method to be described.

In the following, “nadir view” brightness temperatures–reflectances denote data obtained when the angle between the viewing vector and the local vertical on the surface was small (a maximum of 22° at the edge of the swath), and “forward view” refers to the slant path measurements when this angle was roughly 52°. Only measurements made over the clear sea, that is, pixels that have passed all the standard ATSR cloud tests in both views, have been used.

2. Theoretical model for calibration

The calibration coefficient for converting counts measured in the 1.6-μm channel into 1.6-μm top-of-atmosphere reflectances can be derived through the following steps:

  1. finding the increase in radiance at 3.7 μm caused by sun glint,

  2. characterizing the atmosphere in the glint region,

  3. computing the effective reflectivity of the sea surface at 3.7 μm,

  4. finding the 1.6-μm surface reflectivity, and

  5. calculating the 1.6-μm calibration coefficient.

a. Increase in radiance in the 3.7-μm channel caused by sun glint

It will be assumed in the following that the measurements are uncontaminated by clouds. In this case, the total upwelling radiance at satellite height Itot is the sum of terrestrial radiation from the surface and the atmosphere Iterr, radiation emitted by the sun and partially reflected by the surface Isun, and of radiation emitted by the sun and scattered back by the atmosphere Iscatsun. Here, Itot is hence given by
ItotIterrIsunIscatsun

Let us consider the third term on the right-hand side first. The ATSR-2 data show that, at 1.6 μm, the signal from nonsun-glint regions is equivalent to a reflectance of about 0.5%. As scattering aerosol particles are, on the average, much smaller than either wavelength, the ratio of the scattering cross sections at 3.7 and 1.6 μm is usually less than 1.0 and, for water-based aerosols, the ratio is less than 0.1 even for particles as large as 1 μm. The contribution of scattered radiation at 3.7 μm is hence about an order of magnitude smaller than that at 1.6 μm and, in comparison with the other terms, is negligible and will be neglected. (The results fully justify this approximation; further discussion is in section 5.)

Terrestrial Iterr can be estimated with the aid of the brightness temperatures measured in the 11- and 12-μm channels in the two views.1 To determine the relationship between the 3.7-μm brightness temperature and the corresponding brightness temperatures in the long-wavelength infrared channels, the Rutherford Appleton Laboratory (RAL) atmospheric radiative transfer model (RTM) of Závody et al. (1995) has been used to compute brightness temperatures for representative atmospheric conditions, and these were then used as input to a least squares fitting program. The procedure bypasses the retrieval of the true sea surface temperature and the following calculation of the 3.7-μm brightness temperature that would be measured at the satellite, and hence it gives a more accurate result.

The relationship is dependent to a small degree on the across-track position, but the simulated results from the model showed that the increase in the accuracy, that is, the decrease of the rms difference between “true” and recomputed 3.7-μm brightness temperatures, was not significant when this was taken into account. Across-track positions of 25 and 225 km were used for each of the profiles, and the standard deviation of the error for the combined dataset was 0.40 K, with a slightly higher value of 0.46 K for the forward view.

The relationships were found to be linear to a high degree. They are given by
i1520-0426-15-6-1243-e2
and, for the forward view,
i1520-0426-15-6-1243-e3
where the subscript in T signifies the central wavelength of a channel, and the superscripts NV, FV refer to the nadir-view and forward-view measurements,2 respectively.
The measured (sun-glint contaminated) and calculated (uncontaminated) 3.7-μm brightness temperatures, T3.7 and T3.7_calc, respectively, can then be converted into spectral radiances using a brightness temperature–radiance look-up table (LUT). The LUT was generated by integrating the Planck function over the channel’s frequency-response function. If P denotes the dependence of the radiance on temperature in this channel, then the radiance difference Isun_meas_3.7 is the increase in radiance due to reflection from the surface and is given by
Isun_meas_3.7PT3.7PT3.7_calc

b. Characterization of the atmosphere over the glint region

The atmospheric windows are not transparent even in the clear atmosphere, and hence the sun’s radiation is attenuated on the sun–surface–satellite path. The most significant absorbers in both the 1.6- and 3.7-μm channels are water vapor and carbon dioxide. Changes in the concentration of other gases have only a negligible effect on the total path attenuation for these wavelength channels and hence can be safely neglected in this analysis.

Carbon dioxide absorption is proportional to atmospheric pressure at sea level through its dependence on the total amount of CO2 present in the path and also varies slightly with location and season. These changes, however, affect the total absorption by less than 2%. Since other data were not readily available for comparison—and the effect is so small—the global average concentrations were used in the calculations.

Water vapor is highly variable with place and time, hence the water vapor and temperature profiles had to be estimated for each location, and this was done by using standard profiles of temperature and humidity. The profiles used were the U.S. Standard Atmospheres for tropical, midlatitude summer, and high-latitude summer conditions as given by McClatchey et al. (1972), and the choice was based on TNV11. If TNV11 was within the range of 280 and 295 K, then the profile was midlatitude summer; if below this range, then the profile was high-latitude summer; and if above 295 K, then the profile was tropical.

The water vapor loading in the chosen profile was scaled at all heights by the same factor so that the differences for the nadir-view 11-μm minus 12-μm channels, the nadir-view 11-μm minus forward-view 11-μm channels, and the difference for the nadir-view 11-μm minus forward-view 12-μm channels all approximated the corresponding average differences of the measured brightness temperatures, as computed by using the measurements from pixels within 100 km on either side of the satellite ground track.

The scaled total water vapor loading, to be used in computing the transmission for the 1.6-μm channel, was also calculated. In principle, it would have been possible to retrieve this from the measured brightness temperatures by a formula similar to SST retrieval algorithms;however, it was found that, even when this was done, further “tuning” of the scaling factor was usually still necessary before the differences of the modeled and measured brightness temperatures agreed. Direct retrieval of the water vapor loading was hence considered unnecessary.

For the the 1.6-μm channel, the total gaseous absorption is small. Using the latest high-resolution transmission molecular absorption database (Rothman et al. 1992), transmission computations have shown that the total absorption for a vertical path due to CO2 is about 2.2% with less than 0.05% variability caused by surface pressure changes, etc. Water vapor absorption varies between near zero for very dry conditions and about0.7% for humid, tropical atmospheres. The total one-way transmission for a vertical path was approximated by
τ1.62
where H2O was the total precipitable water (kg m−2) over the scene, estimated as described above.

For the the 3.7-μm channel, both water vapor absorption and CO2 absorption are much more important effects and they have to be allowed for more accurately. The chosen atmospheric profile was used in the RTM in computing the full transmission spectrum for a vertical path, which is in contrast to the single value given above for the 1.6-μm channel.

c. Effective reflectivity of the sea surface in the 3.7-μm channel

By using Eqs. (1)–(4) given in section 2a, the increase in radiance due to sun glint, measured at satellite height, can be derived. These values have to be corrected for atmospheric absorption before the effective reflectivity for the 3.7-μm channel can be obtained.

The radiation from the sun traverses the atmosphere twice. If the zenith transmission at a given frequency of ν is τzen, then, for sun and satellite zenith angles of θsun and θsat the sun–pixel–satellite transmission τs–p–s is given by
τs–p–sτ1/cos(θsun)+1/cos(θsat)zen
and it can be easily computed using the atmospheric model with the atmospheric profile and water vapor scaling factor in the way described in section 2b.
The solar irradiance shows less than half a percent variation from year to year (Kyle 1990) and, for the accuracy we require, can be considered as a constant. Owing to the ellipticity of the earth’s orbit, the incident flux reaching the earth changes during the year and this has been taken into account by scaling the spectral radiances by time-factor, given by
i1520-0426-15-6-1243-e7
where day_of_year is the day the measurements were made. The spectral irradiance data were taken from The Infrared and Electro-Optical Systems Handbook (Zissis 1993).
The intensity of the reflected upwelling radiation Isun_calc_3.7 can be computed in the standard way. For 100% reflectance, and with significant instrument sensitivity between frequencies ν1 and ν2, it is given by
i1520-0426-15-6-1243-e8
where Isun(ν) is the (scaled) spectral radiance of the sun at frequency ν and ϕ(ν) is the channel’s frequency response function.
The calculated intensity of the upwelling radiation is always less than the measured intensity owing to the surface reflectivity being less than unity. The effective surface reflectivity ρ3.7 is their ratio
ρ3.7Isun_meas_3.7Isun_calc_3.7
where Isun_meas_3.7 is given by Eq. (4).

d. Effective reflectivity of the sea surface in the 1.6-μm channel

Although the reflectivity of a rough-water surface cannot be calculated accurately, the effect of surface roughness is practically the same for wavelengths as close as 1.6 and 3.7 μm. (Possible errors due to foam and whitecaps will be discussed in section 5.) It follows that the reflectivity ratio is normally very close to that for a plain surface and can be easily derived by using Fresnel’s formula with the refractive indices of water given by, for example, Hale and Querry (1973).

The variation of reflectivity with the angle of incidence for a plain water surface is shown in Fig. 2. The shape of the curves are similar for 1.6 and 3.7 μm. Figure 3 shows the ratio of the reflectances at the two wavelengths and, similar to Fig. 2, the results for horizontal, vertical, and random polarization are all shown. For an instrument insensitive to polarization, or for angles of incidence close to zero degrees, it is valid to use the reflectivity averages of the two polarizations at the two wavelengths. This was done in the first instance in our analysis; it is a good approximation for data obtained in the nadir view. If the radiation to be measured is highly polarized and the instrument is polarization sensitive (the case for ATSR and forward-view data), then the analysis is more complicated. (Notice the rapid variation in the ratio for vertical polarization close to the Brewster angles at about 55°.)

Polarization effects will be discussed further in section 4.

3. Results

Sun glint occurs in the ATSR data over a wide range of latitudes in the Northern Hemisphere and, as has been shown in Fig. 1, its strength varies rapidly across the swath. Ideally, for this analysis, the 3.7-μm brightness temperatures for cloud-free pixels should be just below saturation at about 320 K for ATSR-2. Pixels with brightness temperature values less than this value, however, are also needed for determining any offsets caused mainly by scattered radiation from the atmosphere. Pixels with 3.7-μm brightness temperature increases of less than an estimated 5.0 K were not included as, in these cases, errors in the estimated glint-free 3.7-μm brightness temperatures could possibly lead to significant errors in the reflectivities.

Figures 4 and 5 show the 1.6-μm reflectances computed using the theoretical ratio and the 3.7-μm nadir-view reflectances. The measurement areas were centered at the latitudes of about 25° and 21°N, and the data were obtained on 16 May 1995. (The results are plotted for every 10th pixel only as showing all the points used would make these figures overcrowded.) They are from different orbits and the estimated total precipitable water vapor amounts are quite different: 21.2 and 41.7 kg m−2. (The corresponding average nadir-view 11-μm minus 12-μm brightness temperature differences were 1.20 and 1.73 K.) The computed reflectivities are plotted against nominal reflectivities; the latter are deduced by scaling the measured 1.6-μm channel counts by a figure deduced from the onboard visible calibration and auxiliary information (see Smith 1997). The excellent linear relationship is clear; the best-fit lines have slopes of 0.89 and 0.90, with the quadratic term making a maximum contribution of about 0.06% reflectance at nominal reflectivities above 10%.

Sun glint in the forward-view data occurs at high latitudes, and the advantage in this case is that here the brightness temperatures from the nonglint areas are quite low and hence much higher brightness temperature rises due to glint can be measured by the ATSR-2 instrument. These areas are, however, usually more cloudy and hence the number of suitable measurements is less than for the case of nadir-view glint.

An example of results deduced by using data from the forward view is shown in Fig. 6, and the computed reflectivities can be seen to be significantly lower than the nominal reflectivities. The lower slope from the regression is typical when forward-view data are used; in this case the slope calculated was 0.73.

A summary of the results is given in Table 1. In a few cases even though there was a significant number of usable cloud-free measurements, no good match of the measured and modeled brightness temperature differences could be obtained. For the nadir view, results are given when the match was better than 0.1K for all three differences, and the number of valid points was over 5000. In addition, for this view, the air–sea surface temperature difference in the simulations had to be less than the arbitrarily chosen threshold value of 2 K. It is self-evident that the difference cannot be large at midocean, hence, if the fit demands a large difference, the atmospheric profile used, and hence the computed water vapor loading is unlikely to be representative of the actual conditions. (This was indirectly confirmed in one case when the retrieved temperature difference was 3.3 K, and the retrieved slope of 0.84 was the lowest of all the cases examined.)

There were three cases when the fit criterion was not satisfied, and three cases when even though the fit was satisfactory, it was best for an air–sea temperature difference exceeding the 2-K threshold.

For the forward view, the number of valid points required was relaxed to 500, as the range of computed reflectances was always significantly higher and hence the uncertainty in the results was smaller than in case of the nadir view. As glint could only be observed in this view at high latitudes where the temperatures, and hence the total precipitable water amounts, were low, the possible range of water for the modeled atmospheres was also low. For this reason, and also as changing the modeled air–sea differences by as much as 4 K changed the total water by only 2–3 kg m−2, the air–sea temperature difference criterion was not applied in this case. The reason why the best match was often obtained for sea- minus air-temperature differences sometimes as large as +4 K is not known—it could be a genuine effect, or it is possible that the U.S. high-latitude summer profile was grossly unrepresentative of the atmospheric conditions prevailing at the time the ATSR measurements were made.

The incidence angle ranges given in the table are for the angles between the sun and the local vertical of the pixel facets reflecting, and they will be used in the next section.

4. Polarization effects

To fully interpret the results, the polarization sensitivity of ATSR-2 has to be considered, as mentioned previously. If we neglect the reflected sky radiation and, as explained in section 2a, its contribution of about 0.5% multiplied by the surface reflectivity of 2—10% is 1.5 to 3 orders of magnitude down on the total signal—the solar radiation reflected by the sea and detected by ATSR can be assumed to be randomly polarized before reflection. After being reflected, however, the reflected radiation becomes polarized for all elevation angles different from 90°, as was shown in Fig. 2.

For an instrument insensitive to polarization it would be valid to use the reflectivity averages of the two polarizations at the two wavelengths. The ATSR instruments are, however, polarization sensitive owing to the use of beam splitters and reflecting mirrors. Although the polarization sensitivities of the different channels of ATSR-2 had not been determined before launch, an indication of their magnitude is the figures measured for the Advanced Along-Track Scanning Radiometer (AATSR): about 97% for the 3.7-μm channel and 65% for the 1.6-μm channel (AATSR Project Document 1996).

If the sensitivity ratios of the ATSR-2 to the two polarizations are denoted by S1.6 and S3.7, where, by definition S = 1.0 shows no polarization sensitivity, then the observed ratio of reflectivities for the 1.6- and 3.7-μm channels, γ, is given by
i1520-0426-15-6-1243-e10
where the superscripts V and H denote vertical and horizontal polarization. (Note: The construction of the ATSR instruments is such that all the channels are most sensitive to either vertical or horizontal polarization in a reference frame on the ground.)

The sensitivity of the reflectivity ratio to polarization, as a function of incidence angle on the surface, is shown in Fig. 7. The polarization sensitivity ratios used were the values for AATSR, as quoted above. The two solid curves give the reflectivity ratio when the instrument is more sensitive for the same plane of polarization in both channels, and the dashed curves when the opposite is true. (The construction of the instrument makes the latter more likely.) The correction factor to be used on the reflectivity ratio for the average polarization, shown in Fig. 3, can be obtained by using this to normalize the dependencies shown in Fig. 7, and the results are plotted in Fig. 8.

The incidence angle for a reflecting pixel can be easily obtained by calculating the angle between the pixel–sun vector and the pixel–satellite vector and then halving this angle. Figures 9–11 show the reflectance angles corresponding to the pixels used in Figs. 4–6. The characteristics of these figures were typical for all the cases examined: for the nadir view, the incidence angle correlated with the value of the reflectance measured, and for the forward view, much higher incidence angles in a fairly narrow range.

The curves shown in Fig. 8 apply for a hypothetical instrument that would be bodily rotated along its vertical axis in order to view different parts of the swath. The ATSRs, however, achieve the scanning of the swath by using a rotating mirror, which reflects radiation from different parts of the swath into the focal plane assembly (FPA). The reflection from the mirror gives rise to an apparent rotation of the polarization, that is, say, radiation polarized vertically at the pixel is generally not parallel to the vertical axis of the FPA after reflection from the scan mirror. The angle of rotation, denoted by ψ, is plotted in Fig. 12 against across-track distance for both views. The figure shows that ψ is only zero for pixels on the subsatellite track in the forward view. The angle of rotation increases with this distance, reaching about 15° at the edge of the swath and, in the nadir view, it continues to increase as the across-track distance decreases until at the subsatellite point it reaches its highest value of 90°.

It follows from the above that the reflectance ratio for pixels away from the swath center is somewhere between the extreme cases shown in Fig. 8. If curve“a” is denoted as ratioa and curve “b” as ratiob, then a pixel with the electromagnetic field rotated at the FPA by angle ψ has a reflectivity ratio of
aψ2bψ21/2

For the nadir view, it can be seen from Table 1 that the incidence angles used were always less than 15°. Using the results shown in Figs. 7 and 12, it can be shown that even at this angle and at the edge of the swath, the change in the ratio values is less than 0.9% with respect to those shown in Fig. 8. For the forward view, owing to the glint pixels having much higher incidence angles, the polarization rotation effect can be larger and then the curves shown in Fig. 8 do not represent accurately the characteristics of radiation reflected by pixels away from the swath center. In the example shown, however, all the pixels having nominal 1.6-μm reflectances above 3% were within 120 km of the subsatellite track and hence, even in the worst case, the ratios plotted are accurate to better than 0.8%.

With these minor caveats, the results for the forward view can now be interpreted. Figure 8 shows that for a typical forward-view incidence angle of 50°, the computed 1.6-μm reflectivity would be over- or underestimated by a factor of 0.78–0.80. Multiplying the average nadir-view slope from the table, 0.92, by 0.78 gives 0.72, which can be compared with the average forward-view slope of 0.73. The agreement is excellent, making it very likely that the polarization sensitivities of ATSR-2 and AATSR are indeed similar. This is expected, given that the optical parts of the two instruments are of the same design.

Figure 7 can now be used to make a small correction to the nadir-view figures. As the highest reflectances in the nadir view have always been found at high-incidence angles, the variation in incidence angle itself would affect the slopes computed to a small extent. For incidence angles in the range of 4°–12°, this slope can be seen to be about 1%, hence the values given in the table have to be decreased by this figure to yield a final result of 0.91 ± 0.04.

5. Discussion

The consistent results obtained under very different atmospheric conditions, the tentative agreement between the nadir-view and forward-view derivations, and the close agreement with the nominal calibration give confidence in this method of calibrating the ATSR-2 1.6-μm channel. The highly linear relationship and the tight bunching of points around the best-fit line show that factors not fully considered are unlikely to have a significant effect. Possible sources of errors and their magnitude will be considered next.

The largest error is believed to be due to biases in the computed 3.7-μm attenuation, which are caused by errors in the water vapor profiles assigned to the different locations. As mentioned previously, the water vapor loading was deduced by matching the brightness temperature differences observed with those given by the atmospheric model for one of the scaled standard atmospheres. Although it was usually possible to get a near-perfect match for the three differences between nadir- and forward-view 11- and 12-μm channel brightness temperatures, it was still very unlikely that the attenuation characteristics of the atmospheric profile chosen agreed exactly with those from the measurement area.

By using different water vapor scaling factors on the McClatchey atmospheres, it was found that, for the case of measurements from the nadir view, an uncertainty of 10 kg m−2 in precipitable water was roughly equivalent to a 5% uncertainty in reflectance. The corresponding figure for the forward-view case was about 10%. The observed 8% range of slopes from the nadir-view analysis can be explained by random errors in the retrieved total precipitable water of up to ±8 kg m−2, a value consistent with the uncertainty from the water vapor retrieval simulations using U.K. Meteorological Office radiosonde profiles.

The uncertainty due to water vapor could be significantly reduced by using, for example, the water vapor results deduced from the microwave radiometer measurements. If, on the other hand, we had 100% confidence in the calibration of the 1.6-μm data, it would be the total precipitable water that could be accurately retrieved, and this could be the subject of a further investigation.

When computing the 3.7-μm reflectances, it was assumed that the reflectance of atmospheric aerosols was at least an order of magnitude lower in this channel than in the 1.6-μm channel. Even if this is not true, provided the scatterer density and the phase functions do not correlate strongly with across-track distance—and Table 1 showed that, for a given view, the range of incidence angles for the pixels used is small in any case—this would produce a constant offset. The measured 1.6-μm reflectances also have an aerosol contribution, using the argument above, that is also independent of pixel position etc. but larger, with a value close to the reflectance measured in nonsun-glint areas. The combined effect of aerosols is a net offset, with the nominal (i.e., measured 1.6 μm) reflectances being higher than those computed, owing to the higher atmospheric contribution at the shorter wavelengths. The numbers in the “offset” column of Table 1 confirm this hypothesis: the offsets in the nadir-view results are in the range of 0.2%–0.5% reflectance. These values are consistent with the 1.6-μm reflectances measured in nonsun-glint areas in this view (see Fig. 1).

The optical properties of sea foam and whitecaps are quite different from those of bulk water, and at wind speeds higher than about of 10 m s−1 the foam cover starts increasing rapidly (Ross and Cardone 1974). It might be thought at first that this could contaminate the results presented above. This is, however, unlikely for two reasons. First, the reflectance from the nonglinting part of the swath is small in all the cases studied, and the measured values can be wholly explained by aerosol effects. Second, as scattering from foam is close to isotropic, the extra contribution by foam to the upwelling radiance is almost independent of the pixel positions on the swath. It follows that, similarly to aerosols, foam could add a small offset to both the 1.6- and 3.7-μm reflectances, but it would not change the values of the slopes given in Table 1.

Finally, the slope derived could be affected by an incidental correlation of glint intensity with water vapor loading in the area. In the images examined, the relationship between the 11-μm minus 12-μm brightness temperature difference—a measure of precipitable water—and the angle of incidence was investigated for the cloud-free pixels. No significant correlation was found in any of the cases.

6. Conclusions

It has been demonstrated that it is possible to calibrate a satellite near-infrared channel by measurements made in an infrared channel, the latter having been calibrated to a high accuracy by using onboard blackbodies. The same technique can almost certainly be extended to the in-flight calibration of the visible channels of ATSR-2 and also to other instruments such as AVHRR. For the shorter wavelength channels, however, the effects of Rayleigh and aerosol scattering could become nonnegligible, and a correction for these effects would be required.

Both Rayleigh and aerosol scattering could be determined from a nonglint part of the swath or, in the case of the ATSR instruments, from the nonglint affected view. The result can then be used to correct the glint region data.

For ATSR-2, the agreement between the factors for converting measured 1.6-μm counts into 1.6-μm reflectances by using the simultaneously measured and accurately calibrated 3.7-μm brightness temperatures, and data obtained at tests on the ground and by other means, is good. The indications are that the nominal reflectances are 9% ±4% too high. Confirmation, or otherwise, of this by coincident measurements by the accurately calibrated AATSR instrument, to be launched on ENVISAT in 1999, are eagerly awaited.

Acknowledgments

The authors wish to thank the RAL ATSR data processing team for generating the data and helpful discussions with colleagues, especially J. Delderfield, P. Gray, and P. Read.

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Fig. 1.
Fig. 1.

(a) Average nadir view 1.6-μm reflectances for cloud-free pixels plotted against across-track distance. (b) The corresponding 3.7-μm minus 11-μm brightness temperature differences. The area used was 512 km × 512 km in size and was centered at 34.7°N, 50.4°W. The measurements were made by ATSR-2 on 16 May 1995.

Citation: Journal of Atmospheric and Oceanic Technology 15, 6; 10.1175/1520-0426(1998)015<1243:ANMFCT>2.0.CO;2

Fig. 2.
Fig. 2.

Reflectivity of a flat water surface as a function of incidence angle at 1.6 (solid curves) and at 3.7 μm (dashed curves). (a) Horizontal polarization, (b) vertical polarization, and (c) random polarization.

Citation: Journal of Atmospheric and Oceanic Technology 15, 6; 10.1175/1520-0426(1998)015<1243:ANMFCT>2.0.CO;2

Fig. 3.
Fig. 3.

Ratio of reflectivities for 1.6 and 3.7 μm for a flat watersurface. (a) Horizontal, (b) vertical, and (c) random polarization.

Citation: Journal of Atmospheric and Oceanic Technology 15, 6; 10.1175/1520-0426(1998)015<1243:ANMFCT>2.0.CO;2

Fig. 4.
Fig. 4.

The 1.6-μm reflectivities computed by using the increase in the nadir-view 3.7-μm channel brightness temperatures. The data used were from the area centered at 24.9°N, 27.9°W (16 May 1995). Only every 10th point is shown.

Citation: Journal of Atmospheric and Oceanic Technology 15, 6; 10.1175/1520-0426(1998)015<1243:ANMFCT>2.0.CO;2

Fig. 5.
Fig. 5.

As in Fig. 4 for the area centered at 21.5°N, 53.9°W (16May 1995).

Citation: Journal of Atmospheric and Oceanic Technology 15, 6; 10.1175/1520-0426(1998)015<1243:ANMFCT>2.0.CO;2

Fig. 6.
Fig. 6.

Computed reflectivities at 1.6 μm using forward-view 3.7-μm channel brightness temperature data. The area used was centered at 73.2°N, 9.7°E (17 May 1995). All the points used are shown.

Citation: Journal of Atmospheric and Oceanic Technology 15, 6; 10.1175/1520-0426(1998)015<1243:ANMFCT>2.0.CO;2

Fig. 7.
Fig. 7.

Theoretical ratio of reflectivities from a flat water surface at 1.6 and 3.7 μm, as as would be detected by a polarization-sensitive instrument. The polarization sensitivity ratios used were 0.65 for the 1.6-μm channel and 0.97 for the 3.7-μm channel. Curves (a) and (b) are for the case when the sensitivities are higher for the same plane of polarization in both channels, and curves (c) and (d) are for the case when the channels sensitivities are in the opposite sense.

Citation: Journal of Atmospheric and Oceanic Technology 15, 6; 10.1175/1520-0426(1998)015<1243:ANMFCT>2.0.CO;2

Fig. 8.
Fig. 8.

As in Fig. 7 with the reflectivity ratios normalized by thereflectivity ratios for a nonpolarization-sensitive instrument.

Citation: Journal of Atmospheric and Oceanic Technology 15, 6; 10.1175/1520-0426(1998)015<1243:ANMFCT>2.0.CO;2

Fig. 9.
Fig. 9.

Angles made to the facet normals by the incident and reflected beams from the sun. The cases shown are for the pixels used in Fig. 4.

Citation: Journal of Atmospheric and Oceanic Technology 15, 6; 10.1175/1520-0426(1998)015<1243:ANMFCT>2.0.CO;2

Fig. 10.
Fig. 10.

Angles made to the facet normals by the incident and reflected beams from the sun. The cases shown are for the pixels used in Fig. 5.

Citation: Journal of Atmospheric and Oceanic Technology 15, 6; 10.1175/1520-0426(1998)015<1243:ANMFCT>2.0.CO;2

Fig. 11.
Fig. 11.

Angles made to the facet normals by the incident and reflected beams from the sun. The cases shown are for the pixels used in Fig. 6.

Citation: Journal of Atmospheric and Oceanic Technology 15, 6; 10.1175/1520-0426(1998)015<1243:ANMFCT>2.0.CO;2

Fig. 12.
Fig. 12.

Polarization rotation in ATSR plotted against pixel position on the swath. No rotation takes place for reflected radiation from the pixel on the subsatellite track in the forward view, and the rotation of the polarization plane is maximum for pixels close to the subsatellite point in the nadir view.

Citation: Journal of Atmospheric and Oceanic Technology 15, 6; 10.1175/1520-0426(1998)015<1243:ANMFCT>2.0.CO;2

Table 1.

Main characteristics of the areas used and the results of the comparisons between nominal and computed 1.6-μm reflectances.

Table 1.

1

The 3.7-μm data from the second view were not included in the algorithm as the measured data showed that brightness temperatures measured in this view were also often elevated due to glint.

2

The agreement between the coefficients for the 11-μm view differences in Eqs. (2) and (3) is a coincidence. The fourth and subsequent decimal figures are different.

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