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 Global “dimming” and “brightening,” the decrease and subsequent increase in solar downwelling flux reaching the surface observed in many locations over the past several decades, and related issues are examined using satellite data from the NASA/Global Energy and Water Cycle Experiment (GEWEX) Surface Radiation Budget (SRB) product, version 2.8. A 2.51 W m−2 decade−1 dimming is found between 1983 and 1991, followed by 3.17 W m−2 decade−1 brightening from 1991 to 1999, returning to 5.26 W m−2 decade−1 dimming over 1999–2004 in the SRB global mean. This results in an insignificant overall trend for the entire satellite period. However, patterns of variability for smaller regions (continents, land, and ocean) are found to differ significantly from the global signal. The significance of the computed linear trends is assessed using a statistical technique that accommodates the autocorrelation typically found in surface insolation time series. Satellite fluxes are compared to measurements from surface radiation stations on both a site-by-site and ensemble basis. Comparison of an ensemble of the most continuous Global Energy Balance Archive (GEBA) sites to SRB data yields a root-mean-square difference and correlation of 2.6 W m−2 and 0.822, respectively. However, the GEBA time series does not correspond well to the SRB global mean owing to its extremely limited distribution of sites. Simulations of the Baseline Surface Radiometer Network using SRB data suggest that the network is becoming more representative of the globe as it expands, but that the Southern Hemisphere and oceans remain seriously underrepresented in the surface networks. This study indicates that it is inappropriate to describe the variability of global surface insolation in the current satellite record using a single linear fit because major changes in slope have been observed over the last 20 years. Further efforts to improve the quality of satellite flux records and the spatial distribution of surface measurement sites are recommended, along with more rigorous analysis of the origins of observed insolation variations, in order to improve our understanding of both long- and short-term variability in the downwelling solar flux at the Earth's surface.
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 Solar irradiance reaching the Earth's surface is a key input to the climate system and the chief source of energy supporting life in the biosphere. It is also the main driver of the hydrologic cycle [Boer, 1993; Allen and Ingram, 2002]. Thus, the suggestion that insolation has decreased over the past decades at many locations worldwide has attracted the interest of the public as well as the global energy budget and climate research communities. Concern is great enough that a workshop to summarize the state of knowledge and prioritize future research plans was convened in February 2008 [Ohring et al., 2008].
Stanhill and Moreshet  first suggested that the frequently observed decreases in insolation might be a worldwide phenomenon. Using data from the World Meteorological Organization's “Solar Radiation and Radiation Balance Data” bulletin for the years 1958, 1965, 1975, and 1985 (ranging from 145 to 243 stations in a given year), they extrapolated a mean reduction of 9 W m−2 over the land surface of the Earth during this time period. Analyzing all insolation data in the Global Energy Balance Archive (GEBA) from the 1950s through 1990, Gilgen et al.  subsequently found negative trends over large portions of the Earth, with positive trends restricted to a few small regions. Continuing this line of research, Stanhill and Cohen  reviewed a range of shortwave irradiance measurements, concluding that “a worldwide spatially variable reduction in [surface insolation] has taken place during the last four decades.” More recently, Wild et al.  and Ohmura  found a reversal of this negative trend at many locations beginning around 1990.
 While detection of a significant long-term change in surface insolation over the globe could have serious implications for temperature trends, agriculture, and energy production, it is clear that the weaknesses of the global insolation measurement network limit our ability to draw broad conclusions from these data. Most importantly, surface radiation measurement sites number in the low hundreds with densities varying widely across the continents. For example, Stanhill and Cohen  made use of data for 1992 from 164 sites in Europe but only 4 in each of Africa and Antarctica. Now that the geostationary satellite-based surface solar flux record extends over 20 years, its global coverage gives it great potential to contribute to this discussion. Pinker et al.  briefly compared satellite surface flux records to ground measurements and found an upward trend in global mean insolation from 1983 to 2001. Hatzianastassiou et al.  have presented a more extensive study of the spatial and temporal variability of the shortwave surface energy budget using a similar satellite-based data set. Nevertheless, there remains much to be learned from further examination of the satellite data record. In particular, satellite data allow us to investigate ground-based insolation observations from a completely different point of view.
 In this paper, we use data from the NASA/GEWEX Surface Radiation Budget (SRB) data set to examine variations in surface insolation over the 21-year period from July 1983 to June 2004. We compare satellite retrieved values to measurements at ground stations to elucidate the advantages and difficulties in working with either system. In addition, we illustrate a number of statistical issues pertinent to insolation time series analysis. Finally, we present large-scale averages of downwelling surface fluxes from the SRB data set and relate these to previous observations from the surface stations.
2. Data Description
2.1. Surface Measurements
 Two surface flux measurement networks were examined in this study: the Baseline Surface Radiation Network (BSRN) and those sites with data in GEBA. GEBA [Gilgen and Ohmura, 1999; Ohmura, 2006], which is maintained under the auspices of the World Climate Research Programme (WCRP), is a database of monthly mean fluxes measured at approximately 1600 stations distributed around the world and dating back as far as 1919. Measurements are recorded by individual observers and transmitted to a central location for archiving. The GEBA data are stored at the Swiss Federal Institute of Technology in Zürich (ETHZ), under the care of the Institute for Atmospheric and Climate Science. The relative random error of the monthly shortwave downwelling irradiances in the GEBA archive is estimated to be about 5%, although larger random errors may occur at individual sites with special measurement issues [Gilgen et al., 1998].
 The BSRN, sponsored by the WCRP's Global Energy and Water Experiment (GEWEX), is a collection of surface measurement sites following a strict set of instrumentation and measurement protocols [Ohmura et al., 1998]. Both longwave and shortwave fluxes are recorded at temporal resolutions on the order of a minute. In general, data in the BSRN archive are expected to be of higher quality than the GEBA data; however, there are fewer BSRN sites (currently 35) and the BSRN record dates back only to 1992. BSRN data are currently housed at the Alfred Wegener Institute for Polar and Marine Research in Bremerhaven, Germany (http://www.bsrn.awi.de/). Barring significant data gaps or maintenance failures, the BSRN insolation measurements are expected to have an uncertainty of 5–15 W m−2 at the monthly time scale (E. Dutton, personal communication, 2004). This estimate includes contributions from both accuracy and precision, with most of the uncertainty being attributed to precision.
2.2. Satellite Data
 The satellite surface solar flux values used in this study are taken from the NASA/GEWEX SRB shortwave version 2.8 [Gupta et al., 2006]. This data set is produced from International Satellite Cloud Climatology Project (ISCCP) [Rossow and Schiffer, 1999] DX radiance and cloud parameters using an updated version of the University of Maryland flux algorithm [Pinker and Laszlo, 1992] with base horizontal and temporal resolutions of 1° and 3 h, respectively. Total column water vapor is obtained from the NASA Global Modeling and Assimilation Office Goddard Earth Observing System Data Assimilation System Version 4 [Bloom et al., 2005]. Ozone data blended from Total Ozone Mapping Spectrometer and TIROS Operational Vertical Sounder measurements are also employed. The SRB version 2.8 SW algorithm does not directly calculate the shortwave flux components via radiative transfer computations on the input data. Instead, it estimates the surface fluxes on the basis of the cloud fraction, atmospheric composition, background aerosol, and assumed surface spectral albedo shape, with the top of atmosphere measured cloudy and clear sky radiances acting as a constraint [see Pinker and Laszlo, 1992]. Version 2.8 of the SRB shortwave data product includes several improvements from version 2.0 [Stackhouse et al., 2004; Cox et al., 2006], which was evaluated by Raschke et al. . These include improvements to the TOA incoming solar irradiance, surface altitude corrections, and low sun angle integration. This data set runs from July 1983 through December 2005. Although the GEWEX SRB product is computed on a 1° pseudo equal-area grid, a version of the data averaged up to a 2.5° equal angle grid was employed in this study. For comparisons to measurements from surface sites, the values from the individual corresponding grid boxes were used directly. However, for large-scale averages, the fluxes were normalized by the area of the grid boxes for proper representation of the total surface area.
2.3. Quality of the NASA/GEWEX-SRB Data
2.3.1. Influence of ISCCP Trends on SRB Surface Fluxes
 Recently, trends in total cloud cover determined by ISCCP have been scrutinized closely. It has been suggested that the ∼7% decrease in mean cloud amount between 1986 and 2000 may be an artifact of satellite view zenith angle changes rather than a real trend [Evan et al., 2007]. Since ISCCP cloud fraction is an important input to the SRB calculations, we have analyzed the extent to which the SRB surface fluxes are influenced by the observed ISCCP trend. Determining whether this trend is real or an artifact is beyond the scope of this paper.
 In their Figure 1, reproduced here in our Figure 1 (left), Evan et al.  show the time series of ISCCP monthly mean total cloud amount from infrared measurements over the area 60° N–60°S in raw, deseasonalized, and smoothed formats after the Niño 3.4 index has been regressed out of the data. The coefficients of regression between the smoothed time series and the corresponding time series from individual grid cells from their Figure 2 are reproduced in our Figure 1 (right). Evan et al.  observe that the areas with high regression values, which are most responsible for the observed trend, correspond to the outer edges of the geostationary satellite fields of view, and argue that the trend is related to the satellite view zenith angles and therefore suspect.
 We have performed a similar analysis of the SRB surface solar flux data. For the reference time series, we used the total ISCCP cloud amount over the entire globe deseasonalized with respect to the entire time period of July 1983 to June 2004. This curve, shown in Figure 2 (top left), looks essentially the same as Evan et al.'s  Figure 1. (Note that, although we did not attempt to remove the El Niño signal, it is not obvious in Figure 2.) We then correlated this time series with the corresponding SRB downwelling shortwave flux in each 2.5° grid cell. The result, shown in Figure 2 (top right), has features very similar to those in Evan et al.'s  Figure 2, although opposite in sign. This indicates that the fluxes in these regions of high correlation rise and fall in synchronization with the questionable cloud signals in these areas. This is not surprising, given the inverse effect of clouds on surface insolation. However, it does not indicate whether the cloud trends dominate the global shortwave flux signal. To test this, we first plot the monthly mean deseasonalized global downwelling shortwave flux time series over the same July 1983 to June 2004 period in Figure 2 (bottom left) and note that this time series is not simply inversely proportional to the cloud amount time series. Although they are somewhat anticorrelated, with a correlation coefficient of −0.4, the flux time series is sometimes in phase with (instead of opposite) the cloud series (e.g., 1987–1991), and has a sharp peak in 1993 that is only faintly echoed in the cloud data. This lack of a strong connection between the two data sets stems from the fact that surface insolation is determined by many other factors in addition to cloud fraction, such as cloud optical depth, aerosol optical depth, and surface albedo. The fact that the SRB fluxes are constrained by the TOA radiance measurements also increases their independence from the ISCCP-determined cloud amount.
 As before, we then correlated the global SW flux time series with the corresponding time series in each 2.5° grid cell. The results are plotted in Figure 2 (bottom right) on the same scale as Figure 2 (top right). In this case, the correlation map features are much weaker than those in Figure 2 (top right). The regions of high correlation are more diffuse and located around the equator, in the southern oceans of the eastern hemisphere, in the northwest Atlantic, and just west of South America. These regions do not match the locations of the geostationary satellites nor are clear geometric features evident. This implies that the global insolation as represented in the NASA/GEWEX Surface Radiation Budget version 2.8 is not dominated by the questionable features in the ISCCP cloud amount time series. This does not, of course, indicate that any problems in the ISCCP data set are inconsequential to the SRB or any of the other flux data sets based on ISCCP cloud inputs, such as those discussed by Pinker et al.  or Hatzianastassiou et al. , only that the contributions of other variables and model assumptions to the SRB solar fluxes minimize the impact of the ISCCP cloud amount trends.
2.3.2. Comparison of Satellite and Surface Flux Values
 To further establish the reliability of the satellite data, we next compare measured and satellite retrieved all-sky downwelling flux values at individual surface sites. Time series for six of the GEBA and BSRN sites featured prominently in prior studies of surface insolation [Gilgen et al., 1998; Stanhill and Cohen, 2001; Wild et al., 2005; Dutton et al., 2006] are plotted along with matching SRB values in Figure 3. Statistics of the comparisons for all available GEBA and BSRN data are presented in Table 1. SRB data on their native 1° pseudo equal area grid are used for these comparisons.
Table 1. Statistical Comparison of SRB and Site Monthly Surface Solar Flux Valuesa
The bias, standard deviation (St. Dev.), and root-mean-square (RMS) values shown are for the flux differences, defined as SRB-site values. N is the number of samples, and CC is cross correlation. The polar region is defined as 60° to 90° north and south while the nonpolar region is 60°S to 60°N.
 Two plots are shown for each location in Figure 3. In the top plot of each pair, monthly values from each data set are presented to give a visual impression of the degree to which the signals track each other. In the bottom plot of each pair, a time series of the differences between the two records, defined as the SRB retrieval minus the surface measurement, is plotted. The top plots demonstrate clearly that the SRB captures the annual and interannual variability of each of the surface time series. The difference plots focus in on the systematic and seasonally dependent differences at each site. For instance, Strasbourg illustrates the good agreement typical of midlatitude sites in areas of relatively homogeneous surface conditions, while spatial scale mismatch between the surface and satellite measurements increase the differences at Locarno-Monti in the Swiss Alps. The subtropical/tropical island sites of Bermuda and, to a lesser extent, Kwajalein, tend to show a positive bias in the summertime, which may be attributable to a relative increase in cloudiness over the sites compared to the grid box averages. The SRB makes a transition from underestimation to overestimation during the spring snow melt season at Barrow, Alaska, while comparisons at the South Pole yield a smaller underestimate during the summer, also under snow cover conditions. The differences observed at these polar locations are most likely caused by the difficulty of detecting clouds over snow or ice surfaces from satellites, large aerosol loading imposed in the retrieval process owing to application of the constraint algorithm over these bright surfaces (which will be addressed in version 3.0 of the SRB shortwave product), and the highly oblique sun angles that dominate for large portions of the year. Together these sites illustrate a range of the various sources of uncertainty that can contribute to differences between the satellite estimates and the surface measurements.
 The statistics in Table 1 indicate that, over all possible matches, the SRB flux bias is less than 10 W m−2 while the standard deviation is below 25 W m−2. As expected for nondeseasonalized data, the correlation between satellite and surface values is very high. It is evident that the biggest discrepancies between the SRB and surface values occur in the polar regions, where the mean difference is about 15 W m−2 and the standard deviation is greater than 35 W m−2. However, even in these regions year-to-year variability appears to be well captured in the SRB despite algorithm biases at various times of the year. Given the difficulties outlined above and the large difference in the spatial scale represented by the two types of data (∼100 km grid box averages versus point measurements), we judge the satellite values to be in good agreement with the surface measurements.
 Of course, agreement of basic statistics to within 10–25 W m−2 does not guarantee that two time series include the same long-term trends, particularly when these trends are expected to be of the order of a few W m−2 decade−1. However, as we will demonstrate in section 5.1, SRB SW flux anomalies selected for locations matching an ensemble of GEBA locations correspond well to the mean anomalies from the surface sites. In addition, the two time series do not drift apart from each other over time. Similarly, the biases between the site measurements and SRB fluxes shown in the Figure 3 (bottom), while nonzero, appear largely stationary over the available time periods. This supports the use of SRB data in the analysis of long-term insolation variability.
3. Statistical Methods for Trend Analysis
 Autocorrelation, or dependence a given sample in a time series on previous samples, is common in geophysical data. The statistical impact of autocorrelation is to reduce the effective number of independent values in the time series, decreasing the significance of any detected trend [Wilks, 1995, pp. 125–129]. Since autocorrelation is evident in the surface solar flux anomaly time series presented in this paper, we apply a trend analysis formulation that specifically accounts for this autocorrelation.
 Each time we fit a line to a monthly flux anomaly time series, following Weatherhead et al. , we assume that the data fit a trend model of the form
where Y is the measurement variable, μ is a constant term, ω is the magnitude of the trend per year, t is the index of monthly samples, Xt = t/12, and Nt is the noise or the part of the time series not explained by the linear trend. Then, as is frequently the case for geophysical data, we assume that Nt is autoregressive of order one, or AR(1), such that
where ϕ is the lag one autocorrelation of Nt and the εt are independent random variables with zero mean and a common variance of σε2. We then estimate the trend, ω, using a standard least squares method and compute its standard deviation according to equation (2) of Weatherhead et al. , namely
where n is the number of years of data in the series. This is easily computed, given that
We likewise use Weatherhead et al. 's equation (3) to estimate the number of years n* of data needed to be 90% certain that we have detected a real trend (i.e., one with a 95% confidence level) with magnitude ∣ω∣,
The implication of these equations is that a trend is more difficult to detect with confidence when the noise on the signal is large or when the signal is highly autocorrelated, since the autocorrelation itself resembles a trend.
 The assumptions behind this analytical approach must be kept in mind when interpreting results of its application. We can easily verify that the appropriate conditions (e.g., the magnitude of the autocorrelation of the residual is less than 1 for a lag of one and approaches zero for lags greater than one) hold for a given time series before applying this analysis. It is more difficult to recall that the results will not be meaningful if the data do not follow the assumed model. For example, a best fit line can be computed for any time series, even when a polynomial or sine curve may fit better. In any measurement series, the true behavior of the observed phenomenon may be obscured by instrument errors that are not accounted for. More importantly, even given a time series with a clear linear trend, the desired confidence level will only be reached in n* years if the behavior of the time series does not change over this period. For geophysical processes such as the global energy balance, variations can occur on time scales up to thousands of years. Thus a “trend” observed in a short time series may prove to be a temporary fluctuation when a longer record is obtained. We bear these caveats in mind in the following analysis.
4. Large-Scale Trends Observed in the SRB Data
4.1. Global Trends
 Before further examining the relations between SRB and surface measured solar fluxes, we present the long-term time series of global mean SW flux from the SRB. Where does this data set weigh in on the worldwide trend in solar irradiance? The mean SW flux anomaly computed from the NASA/GEWEX Surface Radiation Budget data set is shown in Figure 4 (top), and a best fit line is indicated. This best fit line has a slope of +0.25 W m−2 decade−1. However, the 95% confidence interval, determined as the trend plus and minus 2 standard deviations, defined in (3) above, is [−0.41, 0.91], indicating that this trend is not statistically significant. (By standard definitions, a statistic is only significant at a given level if the corresponding confidence interval does not span zero.) Note that the 95% confidence level computed using the standard T test (i.e., without accounting for autocorrelation in the signal) is [−0.08, 0.58]. Thus use of standard techniques for time series with Gaussian noise statistics would lead to the erroneous conclusion that this trend approaches significance at the 95% level. Given the noise characteristics of this time series, we estimate that a total of 56 years of data with the same overall trend will be needed to be 90% certain that we have detected a trend with a 95% confidence level.
 The trend in the SRB time series for 1983–2004 is far smaller than the downward trends of 3–5 W m−2 decade−1 reported for surface measurements by Stanhill and Moreshet , Gilgen et al. , and Stanhill and Cohen  over various periods in the middle to late 20th century. It is also smaller than the global trends of +1.6 W m−2 decade−1 and +2.4 W m−2 decade−1 obtained by Pinker et al.  and Hatzianastassiou et al.  from similar satellite records. (See listings in Table 2.) However, the time periods under consideration were different for each of these analyses. If we restrict our attention to the period 1983–2001, similar to the period analyzed in the earlier satellite studies, the SRB shows a larger, statistically significant, increase of 0.88 W m−2 decade−1. Even so, the trends obtained by both Pinker et al.  and Hatzianastassiou et al.  fall at the margin or outside of our 95% confidence intervals. Although overall linear trends are not the best indicator of time series similarity, as we shall illustrate below, further investigation of these differences among related satellite data sets is recommended.
Table 2. Slopes of Best Fit Lines to Various SRB Version 2.8 Mean All-Sky Shortwave Downward Flux Time Series and Results From Other Global Satellite Studiesa
95% CI T
Trend is the best fit slope of the data, in W m−2 decade−1; 95% CI T is the 95% confidence interval of the trend from standard Student's T test; and 95% CI is the 95% confidence interval of the trend accounting for correlation, both in W m−2 decade−1.
 Closer examination of the SRB mean SW flux anomaly in Figure 4 reveals a clear decrease from the beginning of the record in 1983, changing to an increase sometime in 1991, followed by a second decrease after approximately 1999 rather than a simple linear change. This is in agreement with the general decline in surface SW irradiance from the 1950s until about 1990 observed at many measurement locations [Gilgen et al., 1998; Stanhill and Cohen, 2001; Liepert, 2002], which was followed by a reversal at the majority of these locations [Wild et al., 2005; Ohmura, 2006]. Although a subsequent decline in solar downwelling fluxes was not reported by Wild et al.  or Ohmura , it does appear in the NOAA observations discussed by Dutton et al.  and the polynomial fit to the global satellite mean of Hatzianastassiou et al. . Thus the NASA/GEWEX SRB supports the general trends that have been discussed in the “global dimming” literature. However, we must point out that this does NOT imply that these trends occur at all locations on the Earth, only that they have been observed in the global mean. Further analysis of fluxes obtained over various regions and climate zones is necessary to determine the prevalence of this pattern.
 Given the observed variability of the mean global SW flux anomaly, we believe it is more useful to characterize various time periods in the flux record separately than to fit the entire record with a single line. In Figure 4 (bottom), we have divided the SRB mean SW flux anomaly time series into three segments, with breaks at 1991 and 1999, and fitted a line to each segment individually. As listed in Table 2, the tendencies computed for these shorter intervals are much steeper than the slope for the entire time period, with values of −2.51, 3.17, and −5.26 W m−2 decade−1. Even accounting for autocorrelation in the residuals, each of these values is significant at the 95% level. While it may appear that the large spikes at and following the eruption of Pinatubo strongly influence the short-term tendencies, omitting this time period does not materially change the results of this analysis: For the period July 1983 to May 1991, the slope is −2.32 W m−2 decade−1 with a confidence interval of [−4.50, −0.14], while these values are 3.56 and [1.06, 6.05] for April 1994 to October 1999. We note that the decrease of −2.51 W m−2 decade−1 computed for the period 1983–1991 is still somewhat smaller than the declines observed in early “global dimming” studies, but lends credence to their suggestion of widespread decreases in surface insolation before the 1990s.
 At the beginning of the “global dimming” discussion, only a single downward trend had been observed. However, it is now apparent that the behavior of the solar flux at the Earth's surface is more complicated. Given the fluctuations observed in the SW flux signal to date, it is possible that in the future many more changes will occur, such that the data may become amenable to harmonic analysis to identify periodicities associated with various processes. Alternatively, a series of individual change points due to changes in a single process, such as output of anthropogenic aerosols, may be observed. This deviation from what was originally assumed to be a single linear trend should in any case serve as a reminder of how little we can conclude from a short record of a parameter influenced by many processes.
4.2. Trends by Surface Type and Hemisphere
 We next investigate the contributions of land and ocean and the Northern and Southern Hemispheres to the global mean trends. First, each of the 2.5° SRB grid cells is classified as ocean, land, or coastline and separate surface insolation time series are created for each set of pixels. (A land pixel must have less than 10% of its area covered by water and vice versa. All remaining pixels are categorized as coastal and excluded from the comparisons.) Northern and Southern Hemispheric mean time series are also constructed. Comparing the deseasonalized ocean and land time series to the global mean anomalies in Figure 5 (top), we confirm that the oceanic areas contribute more to the observed global pattern than the land areas do. The root-mean-square difference between the global and oceanic time series is 0.82 W m−2, less than half of that between the global and land surface series. The ocean data are also highly correlated to the global mean data, with a correlation coefficient of 0.93 versus the 0.48 correlation between the land and global mean data. As shown in Figure 5 (bottom), both hemispheres contribute equally to the global mean series, since they cover the same surface area. In both cases, the RMS difference between the global and hemispheric time series is 1.27 W m−2, and the Southern Hemisphere data correlate only slightly better with the global series than the Northern Hemisphere data do.
 Best fit lines are computed for all of the time series in Figure 5 over the three time periods used in the global analysis. The slopes and confidence intervals for these best fit segments are listed in Table 2. These values indicate that the decrease in the global mean anomaly for 1983–1991 is driven primarily by land, while the insolation increase during 1991–1999 and the subsequent decline over 1999–2004 correspond to large changes over the oceans. The slopes for the Northern Hemisphere are about double those from the Southern Hemisphere for the first two periods, while the two hemispheres behave similarly over 1999–2004. Thus all four areas contribute significantly to the observed global trends. However, the majority of all surface measurements are made in the Northern Hemisphere over land, leaving three of the four areas undersampled, as discussed below.
4.3. Regional Data Analysis
 Earlier studies using data measured at surface sites [Gilgen et al., 1998; Stanhill and Cohen, 2001; Wild et al., 2005] attempted to address insolation trends around the world on a continent by continent basis, but were limited by the paucity of sites in certain areas. For example, in an examination of GEBA data from the 1950s through 1990, Gilgen et al.  found that the shortwave irradiance decreased or remained constant “in large regions.” However, the bulk of the available measurements were from Europe, with the remaining stations concentrated in the former Soviet Union, North America, and southern Africa. The survey of Stanhill and Cohen  similarly focused on the former Soviet Union, Ireland, the Arctic and Antarctic, Australia, and Israel, although trends were also derived using all available data combined. A decrease of insolation was found in all of these locations except Australia, where no change was evident, and west Siberia, where increases were seen. The data analyzed were drawn from the period 1950–1994. The sites investigated by Wild et al.  were essentially the same as those of Gilgen et al. , with the addition of the high-quality sites of the Baseline Surface Radiation Network and the sites of the former NOAA Climate Monitoring and Diagnostics Laboratory. Some additional sites in China had also been added to GEBA by this time. This study found “indications for an increase in surface insolation since the mid-1980s at many locations, mostly in the Northern Hemisphere but also in Australia and Antarctica.” Continued decreases were identified in India and Africa. Very few sites in South America, Africa, and western and northern Asia contributed data to this analysis.
 To augment and assess the data presented in these earlier studies, we present in Figure 6 the annual mean shortwave downwelling flux anomaly time series for each of the seven continents from the SRB version 2.8. Given that the SRB record begins in 1983, these data cannot corroborate observations of declining insolation earlier in the century, but can be used to identify changes in trends beginning around 1990, as discussed by Wild et al. . In addition, the data extend to 2004, allowing us to look beyond the 1990s.
 Beginning with Europe, there does appear to be a decrease from the beginning of the record through 1990, after which an upward jump occurs, followed by leveling off and a slight decline since 1998. A roughly similar situation occurs in South America, with a somewhat downward tendency before 1992 (possibly extended by the eruption of Mount Pinatubo), followed by an upward jump, then a leveling off leading to a decline. In North America, we see a weak decline until 1995 followed by a 3-year rise before returning to a decline. In Asia, no strong trends are evident, although the time series could be read as a weak decline through 1995 followed by a leveling. Although the time series from these four regions are quite different, they each contain an upswing at some recent time, whether 1991 (Europe), 1993 (South America), 1996 (North America), or 1997 (Asia). However, given the overall variability of these signals, it is not clear that restricting consideration to any particular subdecadal period is meaningful. This is a problem for any analysis attempting to look for climatological norms or changes from a relatively short data record: It is difficult to know whether any individual variation is typical of the phenomenon's long-term behavior or an important deviation. Only extension of the data record, whether by continuing the measurements forward or finding proxy data to go farther back, can solve this problem.
 Of the regions that are less well-represented in the earlier studies, Australia shows the largest overall change in received solar flux in the 1984–2004 time period. The SRB exhibits a largely stable signal in Australia until 1993, followed by a significant decline until 2000, before a partial recovery. This decline stands in contrast to the upturn noted by Wild et al. . The greater coverage of the satellite estimates may be the cause of this difference, especially since several of the Australian sites used by Wild et al.  are in coastal areas, which were explicitly avoided in our averaging. (The regions selected to represent the continents are each a subset of the surface area previously classified as land versus ocean or coast.) However, it should also be noted that the SRB's surface flux retrieval algorithm sometimes has difficulty handling large surface albedos. Further analysis would be required to explain the observed difference definitively.
 For both Africa and Antarctica, the SRB time series decrease slightly, although there is some indication of greater downward movement before 1990. Depending on the exact time periods viewed, the results for Antarctica may be consistent with earlier findings. Stanhill and Cohen  described decreasing fluxes in Antarctica from 1950 to 1994. If the pre-1990 decrease evident in the SRB record began earlier in the century, an overall decrease to 1994 could easily have occurred. On the other hand, Wild et al.  found an increase in insolation after 1990 in the Antarctic, in contrast to the steady or slightly decreasing values evident in the SRB record. Once again, it is difficult to know which result is correct. The coverage provided by the satellite data is clearly far greater: Wild et al.'s  conclusions were based on only three stations, two on the coast and one in the interior of Antarctica, which may not be representative of the entire continent. On the other hand, these three stations belong to the high-quality Baseline Surface Radiation Network while satellite detection of clouds over the poles is notoriously difficult. Again, we cannot definitively state that one or other result more accurately characterizes the entire continent.
 Our results for Africa agree with the few observations discussed previously. Like Gilgen et al. , we do not see an increase (and possibly a decrease) in the solar downwelling flux until 1990. After this, the signal is largely flat, or possibly slightly decreasing, in line with the results of Wild et al. . However, fluctuations occur frequently and at a variety of time scales in the SRB insolation time series for Africa, making the identification of any long-term trends questionable.
5. Issues in the Use of Ground-Based Measurements to Assess Global Trends
 One clear advantage of satellite-derived radiation products is their excellent coverage of the Earth's surface. Being derived from ISCCP measurements, the SRB benefits from 3-hourly sampling of the entire globe from AVHRR and geostationary satellites. Since we have established that flux estimates from the SRB track the surface measurements quite well, we would like to use the SRB data to assess the degree to which available surface site measurements are representative of worldwide conditions. Unfortunately, this is extremely difficult. First, we would have to assume that the satellite fluxes are entirely accurate. Although we have shown that the SRB values are in general good agreement with surface measurements, we cannot conclude from this that they are equally accurate at all times and places. In fact, we know that certain surface types are handled better or worse by the SRB algorithms. In addition, the satellite data record is relatively short (on the order of 240 monthly values), providing a limited amount of data for comparison. Finally, there is the fundamental difficulty of proving a positive assertion. Finding a difference between two things demonstrates dissimilarity, but failing to find a difference is not sufficient to prove that they are the same. In particular, it does not imply that they will continue to behave similarly in the future. Nevertheless, we can still learn from comparisons of satellite and ground-measured surface flux data.
5.1. GEBA Measurement Site Distribution
 We begin by examining the Global Energy Balance Archive data set. This data set has been heavily used in prior studies of surface insolation variability [e.g., Gilgen et al., 1998; Wild et al., 2005; Ohmura, 2006]. As shown in Figure 7, this archive contains data from numerous locations around the world. For a long-term comparison, however, we limit our attention to sites missing no more than 24 consecutive monthly samples over the period July 1983 to June 2002. (After this time, not all of the available measurements have been reported or entered into the archive.) Unfortunately, only 121 sites meet this continuity criterion and these are concentrated mainly in Europe and Japan, with a handful in other Asian countries and Africa. (See the black circles in Figure 7.) Of these sites, several have fewer than 150 samples over the 19 years. Thus it is apparent that GEBA does not contain data that are globally representative over the most recent decades.
 In order to compare the mean signals from the two data sets, we determine the SRB grid cell in which each GEBA site falls. Because of the high density of surface sites in Europe, multiple GEBA sites sometimes fall within the same grid cell. To avoid having different numbers of sample points in the two time series or repeating SRB values, we combine the neighboring sites into “composite” sites, averaging the corresponding flux values together. The deseasonalized monthly flux values at the resulting 101 surface locations are then averaged together to create a single GEBA ensemble time series. SRB values for the times and locations where GEBA values are available are also deseasonalized and averaged to create a matched SRB time series.
Figure 8 shows a comparison between the matched SRB and GEBA time series (Figure 8, top) as well as a comparison of the GEBA ensemble series and the SRB global mean (Figure 8, bottom). From Figure 8 (top), we see that the SRB and GEBA yield very similar results for the 101 independent GEBA site locations, with an RMS difference of 2.58 W m−2 and a correlation of 0.82. This is not surprising given the agreement found at individual site locations earlier. The comparison of the GEBA ensemble and SRB global mean time series reveals much greater discrepancies. The RMS difference between the two series is over 4.5 W m−2 and the cross correlation is close to zero. The differences are obvious in the 11-point running means plotted for the two series, since these clearly do not track together. It is also worth pointing out that, even though it consists of data from over 100 surface sites averaged together, the GEBA time series is still far more variable than the SRB global series, with an RMS value of 4.28 W m−2 compared with the global time series value of 1.61 W m−2. This means it would be significantly more difficult to detect a trend using the GEBA versus the global flux data.
 Two additional points can be made on the basis of the data in Figure 8. The first is that changing the endpoints of a time series can have a large effect on fits to these data: The linear trend of the illustrated SRB global mean time series is 0.63 W m−2 decade−1, in contrast to the value of 0.25 W m−2 decade−1 obtained for the time series through June 2004. In this case, the difference in estimated trends stems from the fact that the slope of the time series is not constant, but this result can also occur when an end point differs from the rest of a time series owing to inclusion of a bad measurement or simply high signal variability. The second point is that time series that are quite different can exhibit rather similar linear trends. For example, the GEBA ensemble time series shown here has a fitted trend of 0.32 W m−2 decade−1. This is more similar to the trend of the 1983–2002 SRB global mean time series than the trend of the 1983–2004 SRB global time series is, even though the correlation between the two series is nearly zero. Thus trends are generally not good indicators of overall time series characteristics.
 To be fair, we point out that none of the long-term (greater than 10 years) trends presented in this paper is statistically significant at the 95% confidence level except that for the SRB global mean between July 1983 and June 2001 noted in section 4.1. This means that all the “trends” discussed above are effectively zero for the confidence criterion we have selected. Nevertheless, our point that caution is required in interpreting trends is still valid, since it is easy to be misled by the types of deceptive differences or similarities discussed here.
5.2. BSRN Measurement Site Distribution
 As discussed previously, BSRN is a network of radiation measurement stations adhering to high data quality standards. As this network has been assembled, emphasis has been placed on siting these stations at distributed locations covering a wide range of climatological conditions. For this reason, it is interesting to evaluate the representativeness of the BSRN system as it grows.
Figure 9 shows the distribution of the BSRN stations at various times. As of 2005, 35 stations had data in the BSRN archive. Although the locations of these stations were biased to Europe and the United States, sites in the Arctic, Antarctic, Middle East, Africa, South America, and western Pacific were also in use. As of 2008, 43 stations were operational. Four of the additional sites were located in Brazil, with others in eastern China, northern Australia, and Europe. Currently planned stations will add to the representation of the Arctic and Antarctic (Alert Bay, Greenland Summit, and the Dome C site) and the Indian Ocean (Cocos Island and the Maldives) as well as Europe (Jungfraujoch in Switzerland and a high insolation site in Spain.)
 Because even the oldest BSRN sites first became operational in 1992, we use SRB fluxes to investigate the expected performance of this network. As in the GEBA comparison, we select the SRB grid cells in which the surface sites fall to represent the sites themselves. We extract a time series for each location, deseasonalize them, and combine the resulting anomaly time series to yield a simulated average time series for the network. This was performed for the 2005, 2008, and currently planned network configurations as if they had been in operation for the entire period of July 1983 to June 2002. The resulting simulated time series for the 35 station configuration is shown along with the SRB global mean time series in Figure 10 (top). Like the GEBA ensemble time series, the variability of the simulated 35-site BSRN series is significantly greater than that of the global time series, with an RMS value of 3.39 W m−2 (versus 1.61 W m−2 for the global series.) However, the BSRN time series appears to better track the global signal: Their cross correlation is a modest 0.43. The trends computed for the two series are 0.37 W m−2 decade−1 (BSRN) and 0.63 W m−2 decade−1 (global), with a larger confidence interval for the BSRN data. (Neither of these trends is significant at the 95% level.) The statistics for the two time series are summarized in Table 3.
Table 3. Statistical Comparison of All-Sky Shortwave Downward Flux Time Series Consisting of SRB Version 2.8 Data Averaged Over the Globe and Various BSRN Site Configurationsa
Std. Dev. Diff.
Monthly data are analyzed over July 1983 to June 2002. Annual data is analyzed over January 1984 to December 2001. St. Dev. is the standard deviation of the individual time series. St. Dev. Diff. is the standard deviation of the difference between the time series and the global series. Correlation is between the time series and the global series. Trend is the best fit slope of the data, in W m−2 decade−1; 95% CI is 95% confidence interval of the trend accounting for correlation, in W m−2 decade−1; Std. Years is the number of years required to confidently detect a trend of 1.0 W m−2 decade−1 in a time series with these characteristics.
Results for Monthly Data
35 BSRN sites
43 BSRN sites
50 BSRN sites
Results for Annual Data
35 BSRN sites
43 BSRN sites
50 BSRN sites
 We do not present plots like that in Figure 10 for the other two BSRN configurations because the differences between these plots are difficult to detect by eye. However, statistics comparing the simulated ensemble mean time series for these arrangements are included in Table 3. These statistics indicate that the simulated ensemble BSRN time series more closely resemble the global mean series as additional sites are added. The standard deviation of the monthly anomalies, which was more than double the value for the global data when 35 BSRN sites were used, falls by 17% once the 15 new stations are included. This means that the overall noise level decreases as sites are added, making it easier to detect any trend that might occur in the data. This is reflected in the narrowing of the 95% confidence interval for the BSRN time series, until it is only 12% wider than the global mean time series trend confidence interval. At the same time, the standard deviation of the differences between the global and simulated BSRN time series drops about 17% and the cross correlation increases slightly. The slope of the best fit line is also seen to approach, then slightly overshoot, the global mean trend. Taken together, the observed changes are favorable indications that the BSRN is becoming more representative of the entire globe.
5.3. Underrepresented Areas in Surface Networks
 It is not possible to determine a specific network layout that would encapsulate most of the variability in the mean global insolation signal without further study. Still, the analysis of hemispheric, land, and oceanic mean trends support the obvious suggestion that the addition of sites in the Southern Hemisphere and over the oceans should be high priorities, since these poorly represented areas are important contributors to the global mean. Because the excess of measurement sites on the Northern Hemispheric land mass relative to the Southern Hemisphere is due to historical rather than technical reasons, this discrepancy is straightforward to remedy. However, the challenges of ocean-based radiometer deployment are much more serious. Until these are overcome, it is unlikely that the surface networks, however accurate, will be able to provide meaningful estimates of global radiative phenomena. Still, the addition of any oceanic surface measurement sites would be beneficial both to improve our understanding of global patterns of surface insolation and to provide satellite data providers with more varied data for the evaluation of satellite flux products.
5.4. Statistical Problems in the Analysis of Surface Measurement Data
 Missing data often occur in surface measurement records despite the best instrument maintenance efforts. We illustrate some of the effects of missing values using the GEBA and SRB data. The first problem is that erroneous results can be obtained if the data are not deseasonalized appropriately. If measurements from several sites, some having data gaps, are averaged together before deseasonalization is applied, the samples will include different combinations of locations depending on where missing values occur. If the entire series is subsequently used to define the seasonal cycle, the data points in this cycle will be representative of different locations. The curves in Figure 11 (top) illustrate how this artifact is passed through to the deseasonalized time series. When the GEBA data from the 101 long-term sites are averaged together before deseasonalization, the resulting time series has a root-mean-square difference of some 2.7 W m−2 from the series for which the mean was computed after deseasonalization independently by site. The correlation between the two series over 19 years is also only 0.83.
 Even if deseasonalization is performed properly, missing data can still significantly change a time series. Figure 11 (bottom) shows the mean time series for SRB data selected to match the sampling available in the GEBA database for the 101 chosen sites along with a similar time series obtained with continuous sampling of the SRB data at all of these sites. The two time series do not appear very different in character, but matching peaks often differ in magnitude. The RMS difference between the two series is about 0.76 W m−2 or approximately one third of the difference due to improper deseasonalization, with more variability evident in the series in which dropouts occur.
 Some investigators prefer to analyze yearly rather than monthly data because it obviates the need for deseasonalization and eliminates any artifact that may be caused by choices made in the application of this procedure. In addition, annual samples are much less noisy than monthly values. For example, the yearly BSRN time series shown in Figure 10 (bottom) has a standard deviation that is only half that of the corresponding monthly time series (1.68 versus 3.39 W m−2). However, this reduction in variability does not necessarily translate into better detection of long-term trends because of the concomitant reduction in the total number of sample points. Assessing the sensitivity of trend detection to the use of annual mean data requires minor modifications to equations (3) and (5) presented in section 3. Equation (3) becomes
where n is the number of years of data in the series and σN and ϕ are computed from the annual data. Likewise equation (5) must be modified to
The derivation of these modifications is presented in Appendix A. Applying these equations, the result of the competing effects of noise reduction and sample point reduction on trend detection can be seen from the “standard years” values listed in Table 3. This value is the number of years of data that would be required to detect a 95% significant trend of 1.0 W m−2 decade−1 in a time series with the characteristics of the given data with 90% certainty. Despite the large decrease in variability in moving from monthly to yearly values in the 35 BSRN site mean time series, the expected time to detect the standard trend increases by 50%. It should also be noted that the trend computed for a yearly time series can differ from the trend computed for the monthly version of the same time series. This is due to the sensitivity of least-mean-square fits to the particular structure of the time series, including endpoint behavior. In this case, six months of data was also removed from each end of the record when converting the monthly data to a yearly series, since the calendar year was used as the averaging period.
6. Summary and Conclusions
 In this paper, we have addressed the “global dimming” problem using a satellite surface flux data product. Although the ground-based measurement stations that supplied the data for early work on this topic provide direct flux measurements, their coverage of the Earth's surface is very limited. Satellites have much better areal coverage, but must rely on radiative transfer theory, external data sets, and flux retrieval algorithms to obtain surface values from top-of-atmosphere measurements. Together, surface and satellite data sets permit a more rigorous analysis than either one alone.
 The satellite fluxes used in this study were taken from the NASA/GEWEX Surface Radiation Budget data set version 2.8, which covers the entire globe from July 1983 through December 2005. Before using the SRB data in this analysis, several quality checks were performed. It is known that the ISCCP cloud cover data that serve as an input to the SRB shortwave flux algorithm contain artificial looking spatial patterns that correlate with surprisingly large temporal variations. A brief examination indicated that the SRB downward solar flux at the surface is not dominated by the questionable features of the ISCCP cloud amount data. In addition, agreement between SRB and measurements at individual surface sites was found to be relatively good.
 We next analyzed long-term trends in the SRB surface insolation data. In the global mean, the SRB downwelling shortwave flux at the surface appears to decrease from 1983 to 1991, increase between 1991 and 1999, and then decrease again. The overall trend between July 1983 and June 2004 is just 0.25 W m−2 decade−1, which is not significant at the 95% confidence level when autocorrelation is accounted for. Significant tendencies are found in this time series if it is divided into the three segments mentioned above. This includes a decrease of 2.5 W m−2 decade−1 between 1983 and 1991, when dimming was expected. However, this temporal pattern is not observed uniformly around the globe. The mean continental surface insolation time series from the SRB vary widely and clear trends are not obvious in these data.
 The SRB data indicate that the global mean insolation time series for land and ocean areas, and for the Northern and Southern Hemispheres, behave quite differently. For this reason, it would be advantageous to increase the number of high-quality surface flux measurement sites in currently undersampled regions such as the oceans and Southern Hemisphere.
 Although it is difficult to prove definitively whether a particular network samples the surface adequately to represent the entire globe, it is clear that the historical distribution of surface radiative flux measurement sites is quite limited. While the Global Energy Balance Archive includes data from sites where measurements have been made for periods as long as or longer than the satellite data record, the majority of these sites are located in Europe, with a few others in Asia and Africa. Thus although individual insolation values from the GEBA sites agree well with SRB data, the time series averaged over long-term GEBA sites is quite different from the SRB global mean series. The more recently founded Baseline Surface Radiometer Network, with an order of magnitude fewer sites than GEBA, has made a concerted effort to establish sites in a wide range of geographic locations. The comparisons between the SRB and simulated BSRN data illustrated here suggest that this strategy is paying off, with agreement between the mean SRB insolation aggregated over the BSRN sites and the SRB mean global shortwave flux improving as sites are added to the network. Nevertheless, we must emphasize that trends from the average of several surface sites are not necessarily representative of global trends even if similar trends are found at sites in different parts of the world. The variability of data from a combination of a limited number of surface sites (such as 20–100, as shown here) is also much greater than the variability of the global mean signal from satellite data, owing to the more extensive averaging incorporated into the global mean. This means that it is easier to detect trends in the less noisy global mean signal than in a composite of ground-based measurements. Still, the station data are extremely valuable as ground truth for the satellite products as well as in local process studies and as an independent check on satellite results.
 Examples described in this paper indicate that care must be used when investigating “trends” in surface insolation data. Like other geophysical data, surface solar fluxes generally do not conform to the assumption of negligible autocorrelation upon which standard time series analysis methods are based, and require the use of modified methods, such as we have illustrated here. Failure to use the appropriate analysis technique can lead to erroneous assessments of the significance of detected “trends.” The end points of a time series have greater influence on trends determined by least square error methods than intermediate points do. This means that trends computed for slightly different time periods can vary widely if the standard deviation between individual samples is high or if the series is not truly characterized by a constant slope. Missing data can also strongly affect trend analysis results. Likewise, two series that have similar slopes may be very different in terms of magnitude and timing of their variations.
 Additional analysis is needed to increase confidence in the SRB surface flux records. Comparisons to data from more advanced satellite instruments such as Clouds and the Earth's Radiant Energy System (CERES) and the Moderate Resolution Imaging Spectroradiometer (MODIS) are important to this effort. In particular, we note that preliminary results from CERES do not support the decrease in global mean insolation seen in the SRB record after 2000 (N. Loeb, personal communication, 2008). Careful examination of sources of error in the satellite retrievals is also essential. A more quantitative analysis of the variations in the insolation time series, including significance testing of selected segments, would help clarify the meaningfulness of the various shorter-term “trends” apparent in the regional data.
 The fact that insolation “trends” have been found to change dramatically depending on the time interval selected suggests that periods on the order of a decade are not sufficiently long to clarify tendencies in surface solar insolation. Use of regional rather than global averaging leads to additional variability. Most of the observed fluctuations are likely a combination of natural variations. To sort out natural variability from multidecadal trends such as anthropogenic effects on global radiative energetics, both longer records of well sampled and highly accurate radiation measurements and observations of the individual components that affect the radiation fields, such as aerosols, clouds, water vapor, and surface albedo, are needed. The three main issues in improving satellite surface flux data are instrument calibration, sampling (surface coverage and changing geostationary satellite viewing angles), and adequate knowledge of the variables affecting radiation. These issues can be addressed through better calibration of operational satellites, a broader network of BSRN quality surface sites, and more consistent control of weather satellite orbits, as well as continuing efforts to quantify the composition and variability of the Earth-atmosphere system.
Appendix A:: Derivation of Analysis Equations for Yearly Data
Weatherhead et al.  developed expressions for estimating the standard deviation of the annual trend estimate and the number of years of data necessary to detect an annual trend when modeling monthly time series data. Their methods are modified here for the case of modeling yearly time series data.
A1. Variance of the Trend Estimate
 Consider the linear trend model
where μ is a constant term, t is the index of yearly samples, Xt = t represents the linear trend function, and ω is the magnitude of the trend per year. The noise Nt is assumed to be AR(1), so that Nt = ϕNt−1 + εt where ∣ϕ∣ < 1, and the εt are independent random variables with mean zero and variance σε2. If Y = (Y1, Y2, ., YT)′ is the T × 1 vector of observations, this can be expressed in matrix form as
where X is a T × 2 matrix comprising the constant and trend terms, β = (μ, ω)′ or the coefficients of regression, and N = (N1, N2, ., NT)′ is the T × 1 vector of noise terms. Let = (N1, ε2, ., εT)′, for which the covariance matrix Cov() = σε2I. (Here I is the T × T identity matrix.) Since εt = Nt − ϕNt−1, the noise vector N must satisfy P′N = , where the T × T matrix P′ is
It then follows that N = (P′)−1 and Cov(N) = Cov((P′)−1) = σε2(P′)−1P−1.
 Let us write the transformed equation
Then the generalized least squares (GLS) estimator of β in the model of (A1) is the ordinary least squares estimator in the transformed model (A2). Thus = (X*′X*)−1X*′Y* with
It follows that Var() is σε2 times the (2, 2) element of (X*′X*)−1, namely
A simple approximation for the variance given by (A3) when ∣ϕ∣ ≉ 1 is
A2. Number of Years of Data Required to Detect a Trend
 The decision rule that a trend is significant at the 95% confidence level if ∣∣ > 2σ is used here, as throughout the remainder of this paper. Tiao et al.  established that there is at least a 90% chance of detecting a trend of magnitude ∣ω∣ = ∣ω0∣ if ∣ω0∣ > 3.3σ. Using the approximation for Var() given by (A4), we must have
Then the number of years T* of data required to detect a trend of specified magnitude ∣ω∣ = ∣ω0∣ with 0.90 probability is
using the expression for σN given in equation (4), where in this case both σε and σN must be values for yearly data.
 The authors thank Steve Cox of Science Systems and Applications, Inc., Peter Parker of the NASA Langley Research Center, and Betsy Weatherhead of the Cooperative Institute for Research in Environmental Sciences (CIRES) at the University of Colorado for their advice and assistance during the course of this project. We are especially grateful to Norman Loeb for many useful discussions and his involvement in the 2008 Global Dimming and Brightening Workshop held in Ein Gedi, Israel. This work was supported by NASA's Science Mission Directorate initiated through the EOS Interdisciplinary Science program (grant MDAR-0506-0383) and now continued under the Radiation Sciences Program (NNH06ZDA001N) and the CERES project. The NASA/GEWEX SRB data products are available through the NASA Langley Research Center Atmospheric Sciences Data Center (http://eosweb.larc.nasa.gov/).