In this article, temporal changes in the Multiangle Imaging Spectro Radiometer (MISR) and Moderate Resolution Imaging Spectrometer (MODIS) joint histograms of cloud-top height (CTH) and optical depth (OD) over the period 2001 to 2011 are examined. The analysis shows no significant trend in total cloud cover averaged over all oceans between 60°N and 60°S from 2001 to 2011. There are, however, significant trends in the amount of some CTH-OD histogram components or cloud types. In particular, there was an increase in the amount of cloud with intermediate optical thickness (23 > OD > 3.6) and a decrease in the amount of the most optically thick cloud (OD > 23) over this period. The total cloud amount shows no trend because the increase in the amount of intermediate optically thick clouds is nearly balanced by the decrease in the amount of the most optically thick clouds. This balance is not due to a simple shift toward optically thinner clouds in all regions but has a complex spatial pattern both regionally and vertically. An examination of the geographic distribution of the change shows that the decrease in the amount of the most optically thick cloud occurred primarily in the extratropics. International Satellite Cloud Climatology Project (ISCCP) observations are briefly compared with those from MODIS and MISR. The comparison shows that ISCCP-retrieved total-cloud fraction is reasonably robust, but changes in the ISCCP component cloud fractions sometimes show large deviations from those of MISR and MODIS.
 The Terra satellite was launched in December 1999 and began collecting Earth observations shortly thereafter. Data sets spanning more than 10 years are now available from the sensors on board Terra, including the Multiangle Imaging Spectro Radiometer (MISR) and the Moderate Resolution Imaging Spectrometer (MODIS). Among the data sets produced from MISR and MODIS observations are joint histograms of cloud-top height (CTH) and optical depth (OD). While there are some important differences, the MISR and MODIS CTH-OD data sets are conceptually similar to those produced by the International Satellite Cloud Climatology Project (ISCCP) over the past several decades based on observations from weather satellites. A detailed review of ISCCP, MISR, and MODIS CTH-OD data sets is given by Marchand et al. .
 Because top of atmosphere shortwave fluxes are strongly modulated by reflection of visible light from clouds (which is strongly related to the cloud optical depth) and longwave fluxes are modulated by the cloud temperature (which is strongly related to cloud-top height), joint histograms of CTH-OD provide insight into how clouds are affecting the Earth energy balance. Not surprisingly, analysis of temporal trends or changes in clouds based on ISCCP data sets has been a topic of significant research. For example, Clement et al.  analyzed time series of surface based observations and ISCCP retrievals of low-level cloud amounts in the North Pacific, finding that there is a positive cloud feedback in this region. That is, increasing sea surface temperatures are associated with a decrease in low-level clouds. Bender et al.  used ISCCP total cloud cover to show that midlatitude storm tracks have narrowed and shifted poleward over the past 25 years, in agreement with climate model predictions. There have also been numerous studies examining the correlation of cloud amounts with changes in tropical sea surface temperatures associated with the El Niño-Southern Oscillation (ENSO) [e.g., Klein et al., 1999; Norris, 2005].
 In section 2 of this article, temporal changes in the MISR and MODIS CTH-OD histograms over the period 2001 to 2011 are examined. This includes both changes in total cloud amount (clouds at all altitudes and all optical depths) as well as changes in component cloud fractions or, as they are sometimes called, cloud types. The analysis focuses on variations with time scales that are longer than annual. With regard to previous studies using ISCCP, there has been considerable concern over the stability of ISCCP-derived cloud fractions due to changes in the constellation of satellites used over time, as well as due to the significant uncertainty in the radiative calibration of these sensors [Klein and Hartmann, 1993; Rossow and Schiffer, 1999; Norris, 2000; Evan et al., 2007]. In section 3, ISCCP observations are briefly compared with those from MODIS and MISR, with conclusions and additional discussion in section 4.
2 Analysis of MISR and MODIS CTH-OD Data Sets
 All of the data analyzed in this article were obtained from globally gridded monthly cloud-top height optical-depth joint histograms, specifically, the ISCCP D1 data set [Rossow and Schiffer, 1999], the MISR L3 CTH-OD data set version V5 (file variable: “Cloud Top Height—Optical Depth Histogram (Best Camera)”) [Marchand et al., 2010], and the MODIS monthly MOD08 (for Terra) and MYD08 (for Aqua) collection 5 (C051) data sets (file variable: “Cloud Optical Thickness ISCCP Joint Histogram vs Pressure”) [Platnick et al., 2003].
 Figure 1 shows a time series of total cloud fraction derived from the CTH-OD histograms over ocean between 60°N and 60°S from the MISR instrument, the MODIS instrument on board the Terra platform (labeled MODIS), and the MODIS instrument on board the Aqua platform (labeled Aqua). The Aqua and Terra satellites are both polar orbiting satellites but collect observations at different times of day, with Aqua having an equator crossing time near 1:30 P.M. and Terra having a crossing time near 10:30 A.M. There is only one MISR instrument which is on the Terra platform. The total cloud fraction is obtained by summing the component cloud fractions for all height bins and across all optical-depth bins with an optical depth greater than 0.3. While MODIS produces CTH-OD histograms over both land and ocean areas, the MISR product is limited to ocean areas, and consequently all comparisons shown in this article are restricted to oceans.
 In order to make potential trends more obvious, the mean monthly cycle has been removed from these data. So, for example, the mean value for January (obtained from the 10 Januaries between 2001 and 2011) has been subtracted from all January values. The figure shows that there is a very strong correspondence between the MISR and MODIS total cloud fractions, with a linear (Pearson) correlation coefficient of better than 0.75. Given that both data sets rely on visible wavelength imagery with similar resolution, this is not entirely surprising. Nonetheless, these data sets are obtained using notably different algorithms from sensors that have very different swath widths and that have been independently calibrated.
 The mean value (obtained from the 120 monthly values between 2001 and 2011) are significantly different between the MISR and MODIS data sets. MISR has a mean CTH-OD-derived total cloud fraction of about 66% compared with 45% for MODIS. This large difference is primarily a result of the treatment of small (subpixel) clouds and cloud edges. This topic is discussed at length by Marchand et al.  and Pincus et al. . In brief, the MODIS retrieval for cloud optical depth also includes the simultaneous retrieval of cloud effective radius, and this retrieval is prone to significant error for small clouds or near the edges of large clouds. The MODIS team therefore chose not to calculate the optical depth of pixels that appear to be cloud edges (in MODIS collection 5). Unfortunately, cloud-edge pixels constitute a significant fraction of all pixels that are identified as cloudy. MISR and ISCCP CTH-OD histograms include cloud-edge pixels, in spite of the likely biases associated with these retrievals. To be clear, the MODIS cloud mask product (MOD35) identifies a similar amount of total cloud as MISR and ISCCP. There are simply no cloud optical properties for cloud-edge pixels, and so these pixels are not included in the MODIS CTH-OD histogram. In this sense, the MODIS total-cloud-fraction shown here might be called the total-OD-retrieval-cloud-fraction, although for simplicity the latter is used in this article. The consistency between the MISR and MODIS results in Figure 1 shows that changes in the total cloud fraction are remarkably insensitive to whether cloud edges are included in this calculation.
 The month-to-month variations in global (60°N to 60°S) total cloud fraction (from the monthly mean value) are less than about 2%. In spite of the seemingly small size of these changes, much of this variation represents real variation in the Earth's cloud cover rather than sampling noise. The error bars (blue for MISR and red for MODIS) show the sampling noise that one would expect if one assumes that each 400 km × 400 km area observed is equivalent to only one independent sample and the standard deviation in the cloud fraction is equal to the mean value. That is, the estimated uncertainty is the standard error given by the standard deviation divided by the square root of the number of samples; where the number of samples equals the cumulative swath area observed divided by 160,000 km2. For a bounded and always positive random variable (such as cloud fraction), the standard deviation is guaranteed to be less than the mean value. Thus, the true uncertainty in these measurements due to sampling is likely smaller than that represented by these error bars because we are overestimating the standard deviation and likely underestimating the effective number of independent samples (see Marchand  for a discussion of cloud occurrence correlation lengths). The error bar for MODIS is smaller than that for MISR, largely because the wider MODIS swath results in more total samples.
 In order to determine if the MISR or MODIS time series contains a trend or change in cloud amount on time scales that are longer than annual, two statistics are used. One statistic is the traditional slope found from a simple linear fit of the observations with respect to time, and the other is based on taking the difference in the mean value between the first half and the second half of the observed time series. I will refer to the former as the slope statistic and the latter as the Δmean statistic. While the slope statistic is commonly used in trend analysis, the Δmean statistic has some advantages. For example, because the Δmean statistic is a linear operator and the analysis window contains an even number of years, the Δmean statistic is completely unaffected by the removal of the mean monthly cycle. Also, all observations in the Δmean statistic have the same weight, whereas with the slope statistic values near the beginning or end of the time series influence the slope more than values near the middle.
 Figure 1 shows the linear fits to the observed data (nearly horizontal dashed lines). In order to test if the Δmean and slope statistics are significantly different from zero, a moving blocks bootstrap resampling hypothesis test was used [Wilks, 1995; Wilks, 1997], with a block length of 12 months and 1000 bootstrap resamples. The hypothesis is that these values are not significantly different from zero, and the moving blocks resampling method is used to determine the interval over which one might expect the slope or Δmean statistics to range (with 95% confidence) if this hypothesis is true. If the observed value of the slope or Δmean is outside of the hypothesis test interval (HTI), then there is likely a nonzero change, which hereafter will be called a trend, whether or not the change appears to be linear. In the case of total cloud fraction, the observed values fall within the HTI and so one cannot reject the hypothesis; there may well be no trend in the total cloud fraction.
 The results in Figure 1 are obtained from CTH-OD data sets, and (not surprisingly) comparisons of cloud cover obtained from the operational MODIS and MISR cloud masks likewise show little if any trend [Blunden and Arndt, 2012]. However, this is not true for all components in the MISR and MODIS CTH-OD histograms. Figure 2 compares the time series of cloud fraction for clouds with an intermediate optical depth (23 > OD > 3.6) in the top panel and for the most optically thick clouds (OD > 23) in the bottom panel. The data show an increase in clouds with intermediate optical depths and decrease in the most optically thick clouds. Both the slope and Δmean statistics show that these changes likely represent a significant trend over the period 2001 to 2011.
 As was the case for total cloud fraction (Figure 1), the MISR and MODIS data show a strong correspondence, especially with regards to intermediate optically thick clouds. In the case of optically thick clouds, the MISR and MODIS Terra (green line) data show a strong correspondence up through 2008. However, starting in 2009, the MODIS Terra results appear offset from MISR. The MODIS team has determined that there is a calibration problem with MODIS Terra (collection 5) data starting in 2009 (personal communication, Steve Platnick). The cause of this problem is not currently known, but it is known that the problem is view-angle dependent, and the MODIS team is working towards a correction. For comparison, the figure also includes results from the MODIS sensor on the Aqua satellite, which show a similar trend and match the MISR observations, including after 2008.
 Figure 3 shows the spatial distribution of the trends in the optically thickest clouds using the Δmean statistic. The dots in Figure 3 indicate those regions which have a trend that is significant at the 95% level of confidence. It should be stressed that when conducting a large number of comparisons, as is done here, one expects that there may be some false positives. That is, a few regions may appear to have a significant trend where no trend actually exists because there is still a 5% chance that an observed statistic can be outside the HTI when no trend exists. Nonetheless, the global results shown in Figure 2 constitute a field significance test, and the number of dots shown in Figure 3 exceeds the number that one expects is likely to result from false positives alone.
 Overall, Figure 3 shows that most of the reduction in the optically thickest clouds (OD > 23) occurred in the Northern and Southern Hemisphere extratropics. The time series for both the southern extratropical oceans (Figure 4) and the northern extratropical oceans (not shown) contain a linear trend that mirrors that shown in Figure 2. In Figure 3, the MODIS data show a somewhat larger change, especially in the southern ocean, than the MISR data. The larger change is due in large measure to the calibration issue discussed above. Nonetheless, Figure 3 shows that the MODIS and MISR data reveal a similar regional pattern.
 Figure 5 examines the situation in the Southern Hemisphere extratropics more closely. In this figure, the color represents the Δmean statistic for each MISR CTH-OD component with black dots denoting those components which are nonzero at the 95% level of confidence. The left panel shows results for the region between latitudes 30°S and 50°S, while the right panel shows results for the region between 50°S and 70°S. Both latitude bands show that the reduction in cloud with OD > 23 occurs for clouds with cloud-top heights at almost all altitudes. Much of the total reduction at OD > 23, including the most statistically confident trends, are occurring for clouds with cloud tops at middle and high altitudes. Nonetheless, when all clouds with an OD > 23 and CTH < 3 km are grouped into a single category, this category does show a statistically significant trend even though most of the individual components in this group are not significant at the 95% level of confidence, suggesting that the amount of optically thick low cloud is decreasing. The reduction of optically thick clouds in the Northern Hemisphere is likewise happening at almost all altitudes and is stronger in the North Atlantic than in the North Pacific (not shown).
 Figure 5 also shows that while both latitude bands show an increase in cloud with intermediate optical thickness above 7 km, in the 30°–50°S band there is a decrease in midlevel clouds, while in the 50°–70°S band there is an increase of midlevel clouds. The increase in clouds above 7 km is also larger in the 50°–70°S band. The net effect is an apparent shift in midlevel and high-level clouds toward higher latitudes. Figure 6 shows the regional distribution of the MISR Δmean statistic for high-level, midlevel, and low-level cloud tops. The decrease in midlevel clouds in the 30°–50°S latitude band is widespread, while the increase in the 50°–70°S latitude band is located primarily in the Eastern Pacific and Atlantic Oceans. MODIS results (not shown) reveal a similar pattern to that shown by MISR in Figure 6 but with some subtle differences due to differences in the cloud-top-height retrieval techniques (and to a small degree differences between pressure and altitude definitions of what constitutes a high, low, or midlevel cloud). MODIS uses a combination of CO2-slicing and IR-temperature techniques to determine cloud top height, while MISR uses a stereo-imaging technique. The largest differences in cloud top height occur for multilayer clouds where the upper level cloud is optically thin. In this situation, MODIS tends to identify the top of the upper level clouds, while MISR tends to identify the top of the lower level clouds [Marchand et al., 2010]. In regard to the shift in clouds between 30°–50°S and 50°–70°S, the MODIS data are similar but indicate that this change is occurring more at high levels than the MISR data, suggesting there may also have been changes in the occurrence of multilayer clouds in these regions.
 While Figure 6 includes clouds with an optical depth greater than 0.3, the spatial distribution of change shown in Figure 6 is predominately due to changes in intermediate optically thick clouds because the amount of cloud with OD > 23 is much smaller than the amount of cloud with 23 > OD > 3.6 (~7% compared with ~27%) and because there is little change in the amount of optically thin cloud (OD < 3.6; not shown). Figure 6 shows that the spatial distribution (both regionally and vertically) of trends in the amount of intermediate optically thick clouds has a more complicated pattern than that for the most optically thick clouds. Perhaps the most prominent feature in Figure 6 is the widespread decrease in clouds with cloud tops at high altitudes in the eastern half of the Pacific and a corresponding increase of clouds with cloud tops at low altitudes over much of this same region. Either a reduction in high clouds or increases in low clouds can be expected to decrease the mean cloud-top height. For the region off the coast of California, the MISR data show a reduction in the mean cloud-top height of approximately 258 m over this period. The increase in the amount of low cloud is larger than the decrease in the amount of high cloud. Therefore, the increase in the amount of low cloud cannot be due entirely to low clouds which already existed being uncovered (becoming visible to the satellite imagers) but must be due, at least in part, to an increase in low cloud amount.
 Unlike the case for optically thick cloud in the extratropics, which displays a linear trend (Figure 4), much of the temporal variability in the tropics and subtropics does not display a linear trend but rather shows large oscillations. For example, Figure 7 shows the time series of intermediate optically thick high cloud (23 > OD > 3.6; CTH > 7 km) amount over the Tropical Warm Pool region (ocean between 30°N–30°S and 100°E–160°E). These oscillations are strongly correlated with sea surface temperatures (SSTs) in the Tropical Central Pacific, that is, ENSO conditions. The orange line in Figure 7 shows observed SST anomalies for the Niño 3.4 region (5°N–5°S, 120°–170°W) as compiled at the National Center for Atmospheric Research [Trenberth, 1997], while the blue line shows a 3 month running mean of the MISR high cloud fraction. The correlation between these two quantities is about −0.8, meaning that warm SSTs in the Central Pacific are associated with a reduction in high cloud over the Tropical Warm Pool, while cold SSTs in the Central Pacific are associated with an increase in high cloud cover.
 There are equally obvious correlations in cloud amounts (especially high cloud amounts) in the Indian Ocean as well as the Tropical Western and Central Pacific (not shown). This result is not surprising as responses in cloud cover (and other cloud properties) to ENSO has been the focus of considerable study over the past decade [e.g., Norris, 2005, Zhu et al., 2007, Davies and Molloy, 2012] and extends to regions outside of the tropics [e.g., Klein et al., 1999; Park and Leovy, 2004]. The nonzero Δmean and slope statistics shown in Figure 6 for many tropical and subtropical regions are likely being driven by differences in the ENSO conditions, with more cold SST periods in the later part of the time series (2006–2011) and more warm SST periods in the early part of the MISR and MODIS time series (2001–2006). An analysis which attempts to characterize ENSO cloud responses or to separate ENSO variability from other potential trends is beyond the scope of the present work. However, these results certainly suggest that the MISR and MODIS CTH-OD data sets are well suited for these tasks.
3 ISCCP CTH-OD Data Set
 With regard to ISCCP, there has been considerable concern over the stability of ISCCP-derived cloud fractions due to changes in the constellation of satellites used over time, as well as due to the significant uncertainty in the relative calibration of these sensors. Overall, trends in ISCCP total cloud amount compare well to MISR and MODIS for the period 2001 through 2009, globally averaged and in most regions. Figure 8 (top panel), for example, compares MISR and MODIS total cloud fraction with ISCCP observations for the North Pacific (30°N–60°N, 160°E–140°W). In this figure, ISCCP results are given with and without satellite view zenith angle detrending, following Clement et al. . The purpose of the ISCCP detrending is to adjust the time series for biases due to changes in view angle from satellite to satellite used in the ISCCP processing. This detrending has little impact in the North Pacific or in the global average over the time period in question. The only region I examined where view-angle detrending had a noteworthy impact was in the Tropical Western Pacific, and even here it made only a small difference with regard to total cloud fraction.
 Unfortunately, while changes in the ISCCP total cloud amount track with changes observed by MISR and MODIS, this is not true of many of the component cloud fractions. For example, the bottom panel of Figure 8 shows that changes in the fraction of optically thick cloud (OD > 23) retrieved by ISCCP do not track the MISR and MODIS retrievals. In fact, the ISCCP data suggest there is a marginally significant positive trend in the amount of optically thick clouds, whereas the MISR and MODIS data show a small decrease between 2001 and 2009. In fact, the ISCCP data show anomalously increasing amounts of optically thick cloud throughout the Pacific (not just in the North Pacific), while it matches reasonably well in the Atlantic (not shown). The amount of optically thin cloud (OD < 3.6) likewise shows some large regional departures between ISCCP and either MISR or MODIS (not shown). These results support concerns over the stability of the ISCCP calibration across satellite platforms (which will affect the optical depth retrievals more than cloud detection) and suggest that analyses using ISCCP component cloud fractions in trend analysis should be undertaken with caution.
4 Summary and Discussion
 An examination of MODIS and MISR CTH-OD histograms shows no significant trend in total cloud cover averaged over all oceans between 60°N and 60°S from 2001 to 2011. There are, however, significant trends (or more precisely variations on temporal scales that are longer than annual) in the amount of some CTH-OD histogram components or cloud types. In particular, there is an increase in the amount of cloud with intermediate optical thickness (23 > OD > 3.6) and a decrease in the amount of the most optically thick cloud (OD > 23) over this period. While there are a few regions with discernable trends in the amount of optically thin cloud (OD < 3.6), perhaps most notably in the South Atlantic (not shown), there appears to be no significant trend in amount of optically thin cloud averaged over all ocean between 60°N and 60°S. The total cloud amount remains stable because the increase in the amount of intermediate optically thick clouds (Δmean statistic +0.27%) is nearly balanced by the decrease in the amount of the most optically thick clouds (Δmean statistic −0.30%).
 This balance is not due to a simple shift toward optically thinner clouds but has a complex spatial pattern both regionally and vertically, where reductions in the most optically thick cloud and increases in the amount of intermediately thick cloud are, for the most part, not happening in the same regions or at the same altitudes.
 An examination of the geographic distribution of the change in the amount of the most optically thick cloud shows that much of the change occurred in the extratropics where there was a reduction in the amount of optically thick cloud at all (cloud-top) altitudes. A recent analysis of ISCCP total cloud cover retrievals by Bender et al.  shows that midlatitude storm tracks have narrowed and shifted poleward over the past 25 years. I am inclined to speculate that the reduction in the most optically thick cloud found here is a manifestation of a narrowing storm track, and I expect this topic will be the focus of future research.
 The cloud optical depth retrieved by the MISR and MODIS projects have a variety of sources of error, and, in principle, it is possible that the trends in optically thick clouds discussed above are not due to changes in the cloud optical depth but could, for example, be due to errors in the sensor calibration or in the retrieved (or assumed) cloud phase or changes in cloud horizontal or vertical structure (because clouds are assumed to be single layered and horizontally homogeneous in the retrievals). However, it seems unlikely that these trends could be a result of calibration errors. Not only do the trends display significant regional variations (whereas one would expect an absolute calibration error to affect all regions uniformly), but the same trends are observed by MISR and MODIS sensors, which are independently calibrated. In fact, a previously unreported error in the MODIS Terra calibration after 2009 became apparent in the comparison. The consistency of the results between Terra and Aqua further suggests that the trends are not primarily due to calibration or shift in the diurnal cycle of cloudiness. I also think the trends are unlikely to be a result of errors due to the identification of cloud phase or three-dimensional structure because these errors are known to be most significant for optically thin clouds and yet there are no matching trends for optically thin clouds. While understanding the physical cause is an important topic for future research, it seems very likely that there was a decrease in the number of very bright pixels between 2001 and 2011.
 Comparisons with ISCCP suggest that ISCCP-retrieved total-cloud fraction (that is, cloud detection) is reasonably robust. On the other hand, the changes in the constellation of satellites used by ISCCP over this period have been relatively small compared to earlier periods, and restricting ISCCP analysis to periods and regions with small view-angle changes (as has been recommended by other studies) seems prudent. Unfortunately, even over the period examined here, changes in the ISCCP component cloud fractions show large deviations from those of MISR and MODIS. This suggests that cross-sensor calibration of the ISCCP data set (which one might expect to effect the consistency of optical depth retrievals more than cloud detection) remains a problem and that analyses using ISCCP component cloud fractions, especially trend analyses, should be undertaken with due caution.
 The results presented here include only ice-free oceans and are limited to the period 2001 to 2011. This is too short a time span to attribute the observed trends to climate change, and the changes may simply reflect low frequency variability in the climate system. Indeed, as discussed in section 2, many of the observed changes clearly are related to ENSO and likely represent a climate change response only to the degree that changes in ENSO over this period are themselves a climate change response. A more thorough understanding of the interactions between clouds and ENSO (for which the MISR and MODIS CTH-OD data sets are well suited) as a well as continued observations are certainly needed.
 Thank you to all those members of the NASA ISCCP, MODIS, and MISR teams who helped make this research possible, especially Catherine Moroney and Mike Smyth at NASA JPL who converted my research algorithm for MISR into operational programs. Special thanks also to Steven Platnick for the discussions and valuable insights. This research was supported by the MISR project at NASA Jet Propulsion Laboratory (under contract NMO710860).