1. Introduction

The sun is a very powerful emitter of radiation through the whole of the electromagnetic spectrum. The spectral radiance peaks at about 0.5 μm in the visible region, and although it falls off rapidly with increasing wavelength, radiation from the sun reflected by the sea surface contributes to the sea's blackbody radiation even in the infrared wavelength channels used by satellite radiometers for the measurement of sea surface temperature (SST).

The contribution is highest in areas where the sea acts as a specular reflector, in the so-called sun glint areas. The water surface, however, is almost never smooth enough for specular reflection in its purest form to occur as the sun is only partly the source of the reflected radiation, which is detected by a satellite instrument, even when the view is centered on the sun's image and the instrument's field of view is less than the angle subtended by the sun. Wind roughens the surface and the primary effect is that the “effective reflectivity” is much smaller than the theoretical value for a plane surface, calculated from the Fresnel equations. Sun glint can now also be present not just in an approximately elliptical area a few kilometers wide and tens of kilometers long but over thousands of square kilometers of the swath.

The magnitude of the surface roughness can be defined quantitatively by the variance in surface slopes, and this has been characterized as a function of wind speed by Cox and Munk (1954). The results of these authors have been used extensively in computing the change in surface emissivity, and hence surface reflectivity, caused by wind (see, e.g., Masuda et al. 1988; Watts et al. 1996). Saunders (1967) has also used the Cox and Munk equations to estimate the change in reflectivity, and hence the effect of sun glint on measurements made in the infrared over the open ocean.

Another approach, proposed by Cracknell (1993) and used by us in the present work, is to make use of the reflectivity measurements made at short wavelengths and coincident in space and time with the infrared results. In this case, as the effect of surface roughness is independent of wavelength, it affects the surface reflectivities by the same factor and hence knowledge of the actual wind speed is not required. The atmospheric absorption, however, is not the same in the two channels, and the ratio varies with the atmospheric water vapor loading among other things. Also, the reflected radiation from the surface is polarized for all viewing angles except the vertical, and if the satellite instrument is polarization sensitive, that has to be treated rigorously. Furthermore, the short-wavelength channel must be accurately calibrated.

Figure 1 shows the effect of sun glint on the measured 0.56-μm top-of-atmosphere reflectivities¹ and the very high values that can sometimes occur. Semiquantitative theoretical results for the increase in brightness temperature (BT) caused by sun glint are plotted in Fig. 2. Although the calculations were made for the simple case where the equivalent top-of-atmosphere reflectivity was the arbitrary value of 100% at all the wavelengths, it can be seen that, for this value, BT increases of about 0.3 K could be expected for wavelength channels in the 10-μm window. As both the reflectance of water and the atmospheric effects are wavelength dependent, and the weighting factors for the brightness temperatures in the SST algorithms are usually greater than unity, the errors in SST would not necessarily be smaller than this value even for this case.

For the above reason, and because measurements made by shipborne radiometers have shown increases of tens of kelvins [see, e.g., the results from the very high resolution thermal infrared camera described by Parkes et al. (2000)], doubts have sometimes been expressed about the validity of SST measured by the Advanced Very High Resolution Radiometer (AVHRR) instruments under glint conditions (Singh and Ferrier 1997; Nath et al. 1993; Brush 1993; Bhandari and Rakash 1996). The BT excesses observed in different wavelength channels, and attributed to reflected solar radiation were, however, not always consistent. In their study of sun glint effects observed in the 1.6-and 3.7-μm measurements from the second Along-Track Scanning Radiometer (ATSR-2), Závody et al. (1998, hereafter ZWSM) also used the 11- and 12-μm data, but they found no significant anomalies in these channels. Sun glint effects possibly as high as 0.5 K, however, would not have been noticed owing to the spatial variability in SST and atmospheric conditions.

Those ATSR instruments that have calibrated 1.6-μm channels—ATSR-2, Advanced Along-Track Scanning Radiometer (AATSR)—are ideal for studying sun glint effects for two reasons. First, because the 1.6-μm channel is accurately calibrated, the effective surface reflectivity for this channel, and hence for the 10-μm channels, can be deduced. Second, they make measurements at two angles—in the nadir view close to the vertical, and in the forward view at about 53°—and this allows BT view differences to be used, thereby largely removing the effects of spatial variability in surface temperature, surface reflectivity, and atmospheric characteristics. The sun's reflected radiation increases the BT measured in the glint region, hence the BT differences between the nadir-view and forward-view measurements—the latter shortened to “BT view differences” in the following—are expected to increase with glint strength when the glint occurs in the nadir view, and decrease with glint strength when it is in the forward view.

In the following, ATSR-2's 11- and 12-μm brightness temperatures are first examined for glint effects in section 2 and, using the same data, the expected temperature rises are computed in section 3. The results from the two methods are compared in section 4 and a correction scheme is proposed in section 5. The paper concludes with a brief discussion of the limitations and accuracy of the scheme.

2. Measured nadir-view minus forward-view brightness temperature differences in sun glint areas

In order to study the correlation between the BT view differences and the 1.6-μm reflectivities at the highest reflectivities, it is sometimes necessary to exploit the measurements made in the visible channels. This is because of saturation in the 1.6-μm channel. The 1.6-μm channel was designed for cloud detection and hence it was not thought necessary to give it the same large dynamic range as the visible channels, used for measuring reflected radiation over land. The 1.6-μm channel hence saturates in glint regions before the visible channels, of which the 0.56-μm was found to saturate last. The measurements made in the visible channels are, however, only received by the ground stations when ATSR-2 is operated in the so-called high rate mode close to the coast. This was the case for the Mediterranean image shown in Fig. 1, and the range of the 1.6-μm data could be almost doubled here as shown below.

In Fig. 3, the points below the horizontal dashed line show the measured short-wavelength reflectivities plotted against each other for cloud-free pixels in this image. The very high degree of correlation is clear, hence the slope and offset derived could be used to extrapolate the 1.6-μm values where this channel had saturated, as shown by the dashed line. The points above this line are computed values for the 1.6-μm channel, with top-hat noise of 5% added to the derived values in order to reduce overplotting. (Every tenth point is shown only, for the same reason.) The offset is due to the stronger Rayleigh scattering in the 0.56-μm channel.

The reflected radiation from the sun increases the measured BT; this increase for the 10-μm window channels, however, is small. Other effects, as pointed out in the introduction, can usually mask it. Using the BT differences for the two views reduces the importance of these, while the 1.6-μm reflectivities are, of course, directly proportional to the strength of the sun glint if the small contribution from atmospheric scattering can be neglected.

Attributing any correlation between the measured top-of-atmosphere 1.6-μm reflectivities and the BT view differences solely to sun glint would, however, be wrong. Owing to the local time of observations, 10:30 a.m., the highest reflectivities are always observed near the eastern edge of the swath, hence there is some correlation between them and the across-track distances. The scatterplot of Fig. 4, again using the measurements taken over the Mediterranean, demonstrates the above. The reflectivity values cover a large range even at the image's eastern edge; this is probably caused by different surface conditions. (N.B. It is clear from this figure as well that the 0.56-μm channel had saturated sometimes as the 1.6-μm reflectivities are limited to values below about 180%.)

The BT view differences, however, also correlate with across-track distances even in the absence of sun glint. The nadir path is longest and the forward path shortest at the edge of the swath, at about 250 km from the subsatellite track and hence, if other factors are the same, the differences will be smaller at the swath edge than at the center. Using the Rutherford Appleton Laboratory (RAL) atmospheric radiative transfer model (RTM) of Závody et. al. (1995), the differences have been computed for the midlatitude and high-latitude U.S. standard atmospheres given in McClatchey et al. (1972), and are plotted in Fig. 5. It can be seen that this primarily pathlength effect can be significant, amounting up to 0.5 K.

We have attempted to estimate the pathlength effect for the actual location of the measurements. This was done the same way as described by ZWSM, but is given here again for completeness. As a first step, the RTM was used to compute brightness temperatures for the U.S. standard mid-and high-latitude atmospheric profiles for a range of water vapor loadings, and for five sea minus air temperature differences in each case. Look-up tables were then generated for the following BT differences: 11-μm minus 12-μm, (nadir view); nadir-view 11-μm minus forward-view 11-μm; and nadir-view 11-μm minus forward-view 12-μm BT. These tables were used to find the scaling factor for water vapor and the sea minus air temperature difference that gave the best agreement between the precomputed BT differences and those measured. In order to reduce noise, averages were used for the measured values, calculated by using those measurements that were within 100 km of the subsatellite track. (Both the measurements and the examination of sun and satellite elevation angles showed that sun glint effects here were negligible.)

Owing to the combination of ATSR-2 viewing geometry—the viewing vector in the daytime orbits always had a southward component—and the dates of the acquisition of suitable products—between May and August regardless of the year—strong glint was always found to occur at midlatitudes in the nadir view, and at high latitudes in the forward view. Hence, for the cases when the strong glint was in the nadir view, the best water vapor scaling factor and sea minus air temperature difference were found for the (water vapor scaled) midlatitude atmosphere, and for the (scaled) high-latitude profile when the strong glint was in the forward view.

Once the most appropriate atmospheric profile and corresponding SST were determined, these were used as inputs to the RTM to compute the pathlength effect— defined as zero on the subsatellite track—for every across-track distance, and the appropriate correction was applied to all the measured BT view differences.

A total of 145 gridded brightness temperature (GBT) images were generated for this study. These were standard ATSR-2 BT image products, each of 512 km × 512 km area and with 1-km spatial resolution. The stipulated requirements were that they should be from areas where there was sun glint, and they had to be at least 30% cloud free, thereby reducing the need to inspect a large number of unsuitable products. These images, as well as the 15 used in the previous 3.7-μm sun glint work, and 3 others obtained from colleagues, were then examined in detail.

The images were checked first for the presence of substantial cloud-free areas in both the glint and nonglint areas, and also that the specularly reflected 1.6-μm radiation was relatively strong so that any correlation between it and increases in BT was meaningful. Only 15 image products were found to have a significant number of cloud-free pixels with 1.6-μm reflectivity values higher than about 50%. For this to happen, the surface wind speed has to be very low and, as shown by, for example, O'Brien and Mitchell (1988), this is an infrequent occurrence. This is the reason why images having a large number of clear pixels located close to the point of specular reflection were often found to be disappointing, with 1.6-μm reflectivities less than 20% or so.

The 15 images were examined for correlation between the 1.6-μm reflectivities in the view with the glint, and the nadir-minus forward-view BT differences for the 11- and 12-μm channels. An example of possible correlation in the nadir view is shown in Fig. 6, with the data from the same Mediterranean image as used previously.

The measured BT view differences have been plotted against the nadir-view 1.6-μm measurements in Figs. 6a,b. The differences have been pathlength corrected as described above. The input to the RTM in this case was the Air Force Geophysics Laboratory (AFGL) midlatitude atmosphere with the water vapor densities scaled by a factor of 0.62, and a sea minus air temperature difference of 0.15 K. Using only those values where the 1.6-μm reflectivities were higher than 50%, the slopes computed were 2.28 mK %⁻¹ for the 11-μm channel, and 2.33 mK %⁻¹ for the 12-μm channel. (The uncorrected data gave slopes of 1.94 mK %⁻¹ for both channels.)

In order to confirm that the differences were not affected by some unknown factor, the 11- and 12-μm BT differences in the forward view, again pathlength corrected, have also been plotted against the nadir-view 1.6-μm reflectivity values, and are shown in Fig. 6c. As the effect of sun glint on the forward view data was negligible, the correlation found—uncorrected and corrected slopes of 0.92 and 0.88 mK %⁻¹, respectively— was unexpected. It must be due to some other effect, which would, of course, also influence the BT view differences from which we have been attempting to isolate the effect of sun glint. This will be discussed further in the following sections.

Figures 7a–c show scatterplots where the sun glint occurred in the forward view. By using data with 1.6-μm reflectivities higher than 15%, the pathlength effect corrected slopes were found to be −2.61 and −3.22 mK %⁻¹ for the 11- and 12-μm channels, respectively. (Uncorrected values: −4.77 and −5.56 mK %⁻¹.) Notice, however, the slope in BT differences in the nadir view: −1.24 mK %⁻¹ (corrected) and −1.25 mK %⁻¹ (uncorrected). Again, reflected radiation from the sun cannot be responsible for this on its own.

3. Computation of the increase in brightness temperatures caused by sun glint

The results of ZWSM showed that the magnitude of the glint effect could be computed for the 1.6-μm channel by using 3.7-μm data. It follows that, in principle, the reverse is also possible, that is, the computation, and hence correction, of the glint contamination in the infrared data by using the measured 1.6-μm reflectivities. These theoretical results can then be compared with those deduced from the infrared measurements in the previous section.

As described above, the atmosphere was always characterized first for each of the BT images studied. We shall need the atmospheric characteristics again in order to compute the effective surface reflectivities from the measured 1.6-μm top-of-atmosphere reflectivities.

The reflectivities in Eq. (2) are weighted averages for the horizontal and vertical polarizations. The weighting factors would be the same if the measuring instrument were insensitive to the polarization of the incident radiation, or if the incident radiation were unpolarized. The ATSR instruments, however, are polarization sensitive and also the reflected radiation from the surface is polarized for all angles except the vertical.

In the previous work, ZWSM approximated the polarization effect by using the values appropriate for the subsatellite track, as most of the data in the forward view calculations were in this region. (Polarization is only marginally important for nadir-view data, owing to the near-normal incidence angles.) In this case, the reflectivity that would be measured in the absence of any atmospheric or wind effects, r₀, would be given by

View Expanded

where r_V and r_H are the Fresnel reflectances for vertically and horizontally polarized radiation, respectively, and S is the polarization sensitivity of the instrument.

As the results from the previous section show, the highest reflectivities occur near the edge of the swath, and hence it is important to use the correct angles for the apparent rotation of the polarization of the reflected radiation. As discussed by ZWSM, the polarization plane of the radiation incident on the focal plane assembly is rotated, with respect to the reference frame at the reflecting pixel, by angle ψ. The variation of ψ with across-track distance x is reproduced from their paper in Fig. 8, and fitting a second-order polynomial to the calculated values gives the analytical relationships

View Expanded

where ψ is in degrees and x in kilometers.

By resolving the reflected radiation, characterized by r_H and r_V, into their two components, one parallel and one orthogonal to the local vertical at the satellite, and bearing in mind that the way reflectivities have been used here they refer to power and not to electric fields, the general expression for the measured reflectivity can be obtained. It is given by

View Expanded

(The derivation is given in the appendix.)

The polarization sensitivity used for the 1.6-μm channel was 0.65, and (1/0.91) and 0.95 were used for the 11- and 12-μm channels, respectively; these figures were measured for AATSR (AATSR Project 1996). A value greater than 1 implies that the instrument was more sensitive to horizontal polarization than to vertical, and vice versa. Here r_V and r_H have been computed using the Fresnel equations with the appropriate angles for every measurement. The variation with incidence angle is shown in Fig. 9 for the 1.6-μm channel and, for completeness, also for the long-wavelength channels. Notice that for incidence angles 50°–55°, that is, measurements made in the forward view, the reflected radiation is almost fully polarized. It can be also seen that the reflectances are highest for the 1.6-μm channel (solid line) and lowest for the 11-μm channel (dot–dashed line). They are higher for the 12-μm channel than for the 11-μm channel, implying that the glint effect would be expected to be higher in the former; the higher atmospheric absorption at 12 μm, however, decreases the difference. The complex refractive indices used were taken from Hale and Querry (1973), and the band-averaged values were

View Expanded

As the reflectivities computed by using Eq. (5) are for the case of true specular reflection, these values are always greater than the absorption-corrected measured reflectivities given by Eq. (2). The ratio, however, is the same for all the channels and hence the effective surface reflectivities for the long wavelength channels can be calculated by using the 1.6-μm values computed from the 1.6-μm measurements, and the weighted Fresnel reflectivities for the long wavelength channels. The effective reflectivity for the 11-μm channel, for example, is given by

View Expanded

The intensity of the reflected long-wavelength radiation can be calculated next. It also suffers absorption on the sun–pixel–satellite path, and, as by ZWSM, the transmission spectra were computed by using the RTM with the appropriate atmospheric profile as input. With significant instrument sensitivity between frequencies ν₁ and ν₂ the intensity of the reflected radiation for the 11-μm channel is given by

View Expanded

where I_sun(ν) and τ_s–p–s(ν) are the spectral radiance of the sun and the atmosmpheric transmission at frequency ν, and ϕ₁₁ is the 11-μm channel's response function. The sun's radiance spectrum was again taken from The Infrared and Electro-Optical Systems Handbook (Zissis 1993), and the small seasonal variation was taken into account the same way as by ZWSM.

For the 12-μm channel, the temperature rises for that channel were obtained by using the appropriate 12-μm channel values in Eqs. (7)–(10).

Figures 10a,b show the computed BT increases for the data used previously in Fig. 6. The glint effect increases linearly with the 1.6-μm reflectivity and, as expected, the computed slope of 1.13 mK %⁻¹ for the 11-μm channel is slightly lower than 1.26 mK %⁻¹ for the 12-μm channel. The corresponding slopes deduced in section 2 from the measured infrared brightness temperatures were 2.28 and 2.33 mK %⁻¹ for the 11- and 12-μm channels, respectively.

The computed increases in brightness temperatures for the sun glint in the forward view are shown in Fig. 11, using the same measurements that had been used in generating Fig. 7. The scatterplots are similar to those shown for the nadir view. The slopes deduced for the 11- and 12-μm channels were 1.12 and 1.07 mK %⁻¹, to be compared with the magnitudes of the slopes of −2.61 and −3.22 mK %⁻¹ from section 2. The sign difference is due to the fact that, in this case, the observed BT differences between the nadir-view and forward-view measurements decrease as the 1.6-μm reflectivities increase, whereas the computed forward-view BTs increase with increasing 1.6-μm reflectivities, of course.

It will be instructive to see how the BT increases affect the computed SSTs. The SST retrieval algorithm used at present for the 1-km resolution SST, at the swath edge, is given by

View Expanded

The highest 1.6-μm top-of-atmosphere reflectivity derived for the nadir-view glint image shown in Fig. 1 was over 180%. Using this figure, the computed increases in BT were 0.200 and 0.224 K for the 11- and 12-μm channels, respectively. By substituting these values into Eq. (11), we get a change in SST of 0.49 K. For the forward-view glint, using the same data as in Figs. 7 and 11, the BT increases for the two forward-view channels were 0.078 and 0.075 K at 70% reflectivity, yielding a decrease in SST of 0.16 K. It is interesting, though it was to be expected, that the sign of the SST error is different for the two views. The changes in retrieved SST are about a factor of 2 greater than the values of the BT increases.

4. Comparison of the measured and computed glint effects

The results for the two cases shown above, and for others that were deemed suitable for deriving slopes, have been tabulated in Table 1.

The measured “glint effect” has been higher than that computed for nearly all the cases. We have every confidence in the technique used as it follows closely the method used in the 3.7-μm work where the agreement between measurements and theory was excellent. The data in the present case are really “stretched,” and the fact that there is significant correlation between the nonglint view 11- and 12-μm BT differences and the 1.6-μm reflectivities in the other view shows that there is another, so far unexplained, contributing cause.

If it is the atmospheric absorption that is increasing toward the eastern edge of the swath and therefore giving a correlation of, for example, the pathlength corrected forward-view channel differences and the nadir-view 1.6-μm reflectivities, then the magnitude of this can be used to compute a corresponding rate of change for the BT view differences. Using the RTM with the standard set of profiles, the relationships between the view-difference and channel-difference gradients with respect to the total columnar water vapor V, for across-track distances between 150 and 250 km, were found to be given by

View Expanded

where the superscripts NV and FV denote the nadir and forward views and the subscripts the channels. By multiplying both sides of the equations by dV/dx, the gradient of columnar water vapor with respect to across-track distance, it can be seen that the relationships between the BT gradients, this time with respect to across-track distance, remain unchanged.

Of course, the effect could also be caused by variation in surface emissivity. Slicks, for example, could cause the surface to be smoother thereby increasing the 1.6-μm reflectivity and, at the same time, changing the emissivities in the infrared. The “atmospheric” proportionality factors given above are all about 0.8 and, in the absence of other information, we assume that the same figures apply even if the anomalous correlation is caused by emissivity changes.

The sixth column in Table 1 gives the value of the anomalous channel difference versus reflectivity gradients, and the values of these can be used to make a first-order correction to the measured view difference versus reflectivity gradients. The corrected gradients are given in columns 7 and 8 for the 11- and 12-μm channels, respectively. Results for the observed slopes are given for only those cases where the data were judged to be good enough to yield meaningful correlations.

For the nadir-view and forward-view cases considered above—the best examples—these corrections certainly improve the agreement between theory and measurement, and statistically for the other cases as well. The fact that the measured glint effect seems to be higher than that computed strongly suggests to us that there is some other minor, so far unexplained, effect associated with measurements made in sun glint areas.

5. Improvements to SST retrieval scheme

The results show that strong sun glint occurs relatively infrequently, but when it does it can increase the 11- and 12-μm BT by 0.2 K or more. The magnitude of the contamination can be computed in the way described above; this is, however, not warranted as the theoretical results can be used to generate a computationally much less expensive empirical correction scheme.

The brightness temperatures were found to increase linearly with the measured 1.6-μm reflectivity. In order to isolate the atmospheric factor, the theoretically derived slopes for the 11- and 12-μm channels and nadir-view measurements have been plotted against the appropriate water vapor loadings in Fig. 12, and for the forward view in Fig. 13. The plots show that the rate of change in the value of the slopes is again approximately linear, and the constant of proportionality is different for the two views.

In section 2 the BT differences were used for finding the total columnar water vapor and hence the atmospheric profile closest to that over the measurement area, but in routine analysis it would be adequate to use a water vapor retrieval algorithm with the measured BT values:

View Expanded

where the brightness temperatures T are those close to the subsatellite track for cloud-free pixels, and the subscripts and superscripts denote the channel and the view.

The results from Eq. (13) need to be further corrected:

View Expanded

Using least squares fitting with the data plotted in Figs. 12 and 13, best fits can be derived and are shown by dashed lines in the figures. The offset and slope values found were 1.8 mK and −0.0340 mK kg⁻¹ m² for the 11-μm channel, and 2.1 mK and −0.0485 mK kg⁻¹ m² for the 12-μm channel, for sun glint in the nadir view. The temperatures by which the measured BT values should be decreased, δT (mK), are hence given for the nadir view by

View Expanded

and, for sun glint in the forward view,

View Expanded

where ρ_1.6 is the measured reflectivity at 1.6 μm, in percent. In view of the size of the effect, the seasonal variation in the sun's irradiance, about 3.5%, can be neglected.

6. Discussion and conclusions

The consistent variation of ATSR-2's nadir-view minus forward-view BT differences with the simultaneously measured 1.6-μm reflectivities shows that sun glint can indeed affect infrared radiometric measurements made over the open ocean. As the effect here is small, other factors, possibly correlating with the strength of the measured reflectivities, make it difficult to isolate and quantify. A small error may arise due to errors in the water vapor loading, as this was determined at the center of the swath whereas the glint effect is strongest at the eastern edge of the swath. It is not likely, however, that under the very calm conditions favorable to producing strong sun glint signals, large differences would exist over distances of a few hundred kilometers.

Instrumental noise and small differences in the atmospheric characteristics for the two propagation paths—fluctuations in aerosol concentration, for example—add random noise to the BT view differences. Bearing the above in mind, the agreement between the measured and the theoretically calculated glint effect is considered reasonable.

The correction algorithms also need the atmospheric water vapor loading as one of their inputs, and if this is not available from another source then the sea close to the subsatellite track has to be free of cloud. Simultaneously, the 1.6-μm data in the glint areas have to be valid; that is, their values have to be below the saturation value for that channel or, alternatively, must be recoverable from the measurements made in one of the other short-wavelength channels. It is recommended that no SST retrievals are attempted in sun glint areas where the reflectivities are saturated, just as if the data were cloud-contaminated.

Saturation of the 1.6-μm channel should be less of a problem for AATSR. This instrument is always operated in the high-rate mode and hence data from the visible channels are available everywhere. The range of the 1.6-μm measurements could be therefore extended by almost a factor of 2 by using the 0.56-μm data. For the accuracies required, it might be adequate to use the same intercalibration algorithm everywhere for converting 0.56-μm reflectivities into 1.6-μm values, but this would need to be confirmed. Watts et al. (1997) have found poor agreement between the measured and calculated reflectivities in forward-view glint data, caused principally by the polarization sensitivities being different for the visible channels. Nadir-and forward-view data will hence require their own algorithms.

Finally, the question arises whether the results could be applied directly to other satellite radiometers operating in the same or very similar spectral intervals, such as AVHRR, the Moderate Resolution Imaging Spectrometer, and the Geostationary Operational Environmental Satellite imagers. When the glint is viewed at angles within, say, 20° of the vertical, which is true for all of these instruments at least some of the time, then we believe that Eq. (15) would be a good approximation as the polarization of the reflected radiation is small and hence the polarization sensitivity of the radiometer is only marginally important. The substantial differences between the coefficients in Eqs. (15) and (16) show, however, that the viewing angles and the polarization sensitivities do affect the relationships and hence an analysis similar to the one performed by us for ATSR-2 would have to be carried out for the general case. For the above single-view instruments, however, the BT increases caused by sun glint would translate into very similar SST increases; the former would not be amplified in the way we found it for the two-view ATSR-2.