4.4. Cloud Optical Depth, Effective Hydrometeor Size, and Water Path
The standard COD, CER, and CWP products from CM4 and CERES MODIS Edition 2 have all been evaluated against various surface and airborne observations as discussed by [
16] and [
45], respectively. It is expected that those evaluations are applicable to the CV1S data, when the CV1S-CM4A differences are taken into account. For example, since
CERw(V) <
CERw(M), the biases in
CERw(M), found in some comparisons of CM4 retrievals with other data (e.g., [
16,
45,
46,
47,
48,
49]), will be reduced slightly because of the smaller values retrieved from VIIRS.
The mean CV1S-CM4A difference in
COD for both liquid and ice clouds is due to several factors. These include calibration disparities, slightly smaller VIIRS cloud fractions, discrepancies in the cloud phase selections, and the higher-resolution VIIRS pixels. Changes in the VIIRS data source and calibrations after 2015 produced a ~0.8 rise in nonpolar mean cloud τ for an average VIS-channel gain rise of 1.5%. The pre-2015 CV1S-CM4A VIS gain difference is ~0.3% compared to a mean
COD difference of ~1.1 for all nonpolar clouds. After 2015, the gain difference of ~1.4% is accompanied by a mean nonpolar
COD difference of ~1.5. This suggests that approximately one-third of the optical depth difference is due to unnormalized VIIRS calibrations. The gradual decrease in
COD from CV1S after 2018 in
Figure 11 results from a slowly decreasing VIIRS VIS gain relative to that of CM4A. Much greater differences in
COD are found for water clouds over polar regions. They are likely to depend more on the larger calibration discrepancies found in the VIIRS and MODIS 1.24-µm channels. This would give rise to larger
COD differences that would increase further because the mean
COD is already large compared to that over nonpolar areas and the surface albedo is quite large. Both of those factors enhance the change in
COD for a given change in reflectance (e.g., [
50]).
The higher spatial resolution of the VIIRS channels likely produces greater
CODs than for MODIS because average
COD decreases with rising pixel size. This is primarily true for liquid clouds, due to the heterogeneity of the internal structure and the non-linear relationship between τ and the reflectance. For example, [
37] found that the mean
CODw dropped from 20.2 for 1-km pixels to 18.9 and 17.6 for 2-km and 4-km MODIS pixels, respectively, while
CODi showed negligible changes with decreasing resolution. Thus, a significant fraction of the mean
CODw bias could be due to the resolution differences. This effect is evident in
Figure 13a, which shows the CV1S and CM4A liquid water curves diverging for VZA > 35°. The smaller cloud fractions for liquid water clouds could lead to a higher mean
COD if the missing cloudy pixels all had very low optical depths. Finally, discrepancies between the CV1S and CM4A phase selections might depend on
COD and, therefore, could result in systematic differences in the average
COD. This last possibility is probably only a small component of the overall
COD differences between the two datasets.
Although [
47] found good agreement between surface and CM4A retrievals of
CODw over Barrow, Alaska, the optical depths over most snow-covered areas in the polar regions from CM4A are probably too high, especially for thin clouds [
17]. This is due mainly to the uncertainty in the 1.24-µm clear-sky reflectance over snow, which is relatively high and quite variable. Thus, it is reasonable to conclude that the CV1S COD values, especially those for liquid clouds, are overestimated over snow/ice surfaces. Obtaining more realistic values over the full range of
COD could be obtained by applying a hybrid retrieval using reflectances measured at longer wavelengths for smaller optical depths and the 1.24-µm reflectances for optically thicker clouds.
In addition to being relatively consistent with the nonpolar CM4A retrievals of COD, on average, the microphysical properties are similar to those from other observations. For example, the CV1S nonpolar mean CODw is ~1.5 less than its CLDPROP counterpart of ~13.3, but CV1S CODi is approximately 1.5 greater than the CODi of 12.2 from CLDPROP. These differences could arise for a variety of reasons, including calibration, use of overcast pixels (non-edge pixels) only in the CLDPROP averaging, discrepancies in the ice cloud model optical properties, and possible differences in the phase selections for particular clouds.
The differences between the VIIRS and Aqua retrievals of CER are likely due to a variety of factors. For liquid clouds, the main discrepancy is the use of the new LUTs for VIIRS, which yield smaller values of CERw compared to those from the old LUTs. Another major source for the discrepancies is the inadvertent use of the smaller Aqua SIR solar constant for VIIRS. It produces a greater reflectance and, hence, yields a lower value of retrieved CERw. Using the correct VIIRS SIR solar constant accounts for about a third of the difference. The remaining difference is likely due to the LUT changes. For ice clouds, the small VIIRS-MODIS disagreement probably results from differences in ice cloud selection.
The VIIRS CLDPROP 9-y average nonpolar estimates of
CER from the VIIRS 3.74-µm channel are ~14.2 µm and ~23.0 µm for liquid and ice water, respectively. These means can be compared to the corresponding CV1S averages from
Table 6: 12.9 µm and 26.3 µm. The differences may be due to discrepancies in sampling, as only 70% of the pixels identified as liquid water by the CLDPROP algorithms had
CERw retrievals at 3.74 µm. For
CER2, the CLDPROP means are ~14.5 µm and ~30.3 µm for liquid and ice, respectively, compared to 17.1 µm and 33.8 µm from CV1S. The larger CERES values may be due to differences in the indices of the refraction used by the two algorithms, to different sampling, and errors in the retrievals, as discussed in the next section. In addition, for ice particularly, there are differences in the optical properties of the assumed ice crystal models used for the CV1S and CLDPROP LUTs. The CLDPROP results do not include
CER7.
Although the calibration of the 1.24-µm channel did not vary when the VIIRS data source changed in 2015,
CER7 and
CER2 both increased after 2015 (
Figure 16). This change is most likely due to the jump in
COD at the same time.
4.5. Hydrometeor Size Estimates from Alternate Wavelengths
Discrepancies in the patterns and, perhaps, the magnitudes of the three distinct VIIRS
CER averages in
Figure 12 and
Figure 15 may be due, in part, to differences among the cloudy pixels that yielded a
CER solution at a given wavelength. For example, over ocean, the mean
CER7w is based on 64% of the pixels having a
CERw retrieval. For ice clouds, that fraction reduces to 53%. Likewise, at 1.61 µm, those amounts are 59% and 77%, respectively. Thus, some of the differences in magnitude and pattern could be due to the alternative retrievals being successful for only a certain portion of the total sample.
To explore that idea further, histograms of
CER were generated from retrievals in all three channels for intervals of increasing
COD. Examples of those histograms are provided in
Figure S3 for liquid clouds, respectively, over
COD ranges of 1–2 and 16–32. For liquid water clouds, it was found that for all optical depths,
CERw has an almost log-normal distribution for both land and water scenes, whereas
CER7w and
CER2w are nearly linearly distributed with maxima near the high end over ocean and near the low end for land surfaces. As
COD increases, the maximum
CER7w and
CER2w gradually decrease, while the probability distributions slowly approach the log-normal shape and the fraction of alternative retrievals relative to the 3.74-µm retrievals increases. For
COD between four and eight and above, the histograms are essentially log-normal. Therefore, the data were plotted and averaged for
COD < 6 and for
COD ≥ 6.
The resulting histograms in
Figure 17 are similar to those in
Figure S3. At 1.24 µm, the
CERw distribution for
COD < 6 is relatively flat over water surfaces with a weak peak around 17 µm (
Figure 17a). For the greater
COD range (
Figure 17b), the maximum is near 11 µm and the distribution is nearly log-normal. The
CER2w histogram is less flat for the small
COD interval with a weak maximum of ~13 µm (
Figure 17c). This contrasts with the nearly log-normal histogram for the upper
COD range (
Figure 17d). The probability distributions for
CERw are nearly log-normal for the upper (
Figure 17f) and lower (
Figure 17e) ranges. For
COD < 6, the respective liquid
CER means for the 1.24, 1.60, and 3.74-µm channels are 18.8, 17.7, and 12.9 µm, compared to 13.8, 14.4, and 12.9 µm for the upper range. The fractions of the
CERw retrievals represented by those numbers are, respectively, 41 and 36.4% for
CER7w and
CER2w for the lower
COD interval, and 90 and 85% for the higher optical depths.
Similar results are found for ice clouds, although more reasonable values of
CER2i are found for lower optical depths than for those retrieved at 1.24 µm. Histograms of
CER for the same range of
COD as in
Figure S3, but for ice clouds, are presented in
Figure S4. At low optical depths,
CERi has a mostly log-normal distribution except for a significant bump around 10 µm, which is due to using a default value of
CERi in order to retrieve
COD. As
COD increases, the relative magnitude of the default maximum steadily decreases as the 3-channel retrievals become more successful. The probability distributions for
CER7i behave much like those for liquid water, but have more pronounced maxima in the lowest
COD ranges. At 1.60 µm, however, a more normal or log-normal type of distribution is found for some lower
COD intervals. Excepting the default maximum in 3.74-µm probability distributions, the histograms for 1.24 µm and 1.61-µm
CERi retrievals become increasingly like their 3.74-µm counterparts as
COD increases, although some significant differences remain for 1.24 µm.
This is borne out in
Figure 18, which shows that the histograms of ice
CERi for
COD ≤ 6 and
COD > 6 are somewhat different from those for water clouds, even after omitting the default peak for
CERi seen in
Figure 18e. Without that peak, the frequency distribution of
CERi in
Figure 18e would be similar to its
CER2i counterpart (
Figure 18c) in the low
COD range. This similarity does not extend to
CER7i in
Figure 18a. For the larger
COD interval, both the 3.78-µm (
Figure 18f) and 1.61-µm histograms (
Figure 18d) tighten up. The mode for the latter is less than that for the former. The
CER7i frequency distribution (
Figure 18b) takes on a more log-normal form, but has a longer tail than that seen for the other wavelengths. The
CER7i means are 47.5 and 36.7 µm, respectively, for the lower and higher
COD range, compared to 22.5 and 32.8 µm at 3.75 µm. The corresponding
CER2i averages are 34.8 and 29.3 µm. Relative to the number of 3.74-µm retrievals (including the default values), the fraction retrieved at 1.60 µm rises from 61% for
COD < 6 to 97% at the upper
COD end, compared to a rise from 41 to 89% for
CER7i.
These results suggest that the NIR retrievals at low optical depths are subject to significant uncertainties, a result found by [
51] for stratiform water clouds. These uncertainties include errors in surface and aerosol reflectances, which are less important as the cloud becomes opaque. The behavior of the reflectances at these wavelengths is also critical.
Reflectances ρ
7 at 1.24 µm (top) and ρ
2 at 1.60 µm (bottom) taken from the CSV1 water droplet LUTs are plotted against the VIS reflectance in
Figure 19 over a range of ρ
7 and
CERw values at SZA = 45.6° and VZA = 31.8°. The plots in each row are for different relative azimuth angles (RAZ) that increase from left to right. A relative azimuth angle of 0° is in the forward scatter direction, while 180° is in the backscatter direction. For a given value of
COD, the reflectances ρ decrease at both wavelengths in a mostly monotonic fashion with
CERw except at very low values of
CERw. In
Figure 19a–c, the ρ
7 curve for
CER = 2 µm falls below those for larger radii over most of the
COD range. Its drop increases as RAZ rises. Coincidentally, the separation of the curves for
CER = 4–8 µm also decreases with the rising RAZ, increasing the uncertainty in the retrievals for smaller radii. The separation between the curves for ρ
7 for all values of
CERw is smaller than that for ρ
2 (
Figure 19d–f), indicating that
CER2w should be less uncertain than
CER7w for a given retrieval. However, for both wavelengths, the curve separation is minimal for
COD ≤ 4, indicating that the retrievals at those optical depths will be highly uncertain, a conclusion borne out by the observations.
The behavior of the ice cloud curves (
Figure 20) is quite similar, but the reduced separation is more extreme at 1.24 µm for
COD < 8 (
Figure 20a–c). This would introduce even greater uncertainty into the ice retrievals, which could help explain the small fraction of retrieved pixels and larger average values for those pixels that were retrieved. The iteration used to solve for
CER and
COD simultaneously begins with the largest value of
CER in the LUT. If it finds a solution for a large
CER, and the error in the reflectance calculated from the assumed optical depth does not decrease significantly for a smaller
CER, then the iteration stops. When the reflectance curves are very close, or the dependence is not monotonic, the larger
CER value is more likely to be selected. For larger optical depths, the spread in curves is even greater than that seen for the water droplet model, especially for channel 2 (
Figure 20d–f). This greater range could explain why the
CER2i results yield a more normal histogram (
Figure 18c) than that for
CER2w (
Figure 17c).
From these analyses, it is clear that the
CER can be quite uncertain if the cloud is thin. A value of
COD > 6 is recommended as a conservative threshold for yielding an accurate retrieval for these alternate wavelengths. The exact
COD threshold value at either alternative wavelength depends on the phase, the angles, and likely, the surface characteristics. Retrievals at each wavelength correspond to a certain thickness at the top of the cloud. As the wavelength increases, the representative thickness decreases. Thus,
CER at 3.78 µm may correspond to the top 3–8 optical depth at the cloud-top. Depending on
CER and the viewing and illumination angles (e.g., [
52]),
CER2 can represent the true value for optical depths as great as 40 and 10–20 for liquid and ice clouds, respectively. The corresponding maxima for retrievals of
CER7 can be up to 64–128 and ~100. Thus,
CER7 probably provides little additional information about the effective radius, except when
COD exceeds ~20, the optical depths for which the retrieval is most accurate. Likewise,
CER2 does not provide much additional information about optically thin clouds, which are more suited for 3.74-µm retrievals. Thus, when carefully used, the three retrievals should be valuable for gaining an understanding about the cloud’s vertical structure for optically thick clouds.