JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 114, D00D20, doi:10.1029/2008JD011004, 2009
Surface insolation trends from satellite and ground measurements:
Comparisons and challenges
Laura M. Hinkelman,1 Paul W. Stackhouse Jr.,2 Bruce A. Wielicki,2 Taiping Zhang,3
and Sara R. Wilson4
Received 31 October 2008; revised 29 April 2009; accepted 11 May 2009; published 15 August 2009.
[1] 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 m2 decade1 dimming is found between 1983 and 1991, followed
by 3.17 W m2 decade1 brightening from 1991 to 1999, returning to 5.26 W m2
decade1 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 m2 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.
Citation: Hinkelman, L. M., P. W. Stackhouse Jr., B. A. Wielicki, T. Zhang, and S. R. Wilson (2009), Surface insolation trends from
satellite and ground measurements: Comparisons and challenges, J. Geophys. Res., 114, D00D20, doi:10.1029/2008JD011004.
1. Introduction
[2] 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
1
Joint Institute for the Study of the Atmosphere and Ocean, University
of Washington, Seattle, Washington, USA.
2
Climate Science Branch, Science Directorate, NASA Langley
Research Center, Hampton, Virginia, USA.
3
Science Systems and Applications, Inc., Hampton, Virginia, USA.
4
Department of Statistics, Virginia Polytechnic Institute and State
University, Blacksburg, Virginia, USA.
Copyright 2009 by the American Geophysical Union.
0148-0227/09/2008JD011004
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].
[3] Existing records of downwelling solar irradiance at the
surface are less common and shorter than surface temperature
measurements because of the greater technical skill required
to produce, calibrate, and maintain radiative instruments.
Although a few long-term records exist [e.g., Hatch, 1981;
Morawska-Horawska, 1985; de Bruin et al., 1995; Gilgen et
al., 1998], widespread measurements of surface insolation
first began in conjunction with the International Geophysical
Year in 1958. Since that time, various studies have analyzed
insolation variability at a regional scale [e.g., Russak, 1990;
von Dirmhirm et al., 1992; Liepert et al., 1994; Stanhill,
1995; Abakumova et al., 1996; Liepert, 2002; Dutton et al.,
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2006], often finding a decrease in downwelling solar irradiance in the latter half of the 20th century.
[4] Stanhill and Moreshet [1992] 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 m2 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. [1998]
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 [2001]
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. [2005] and Ohmura
[2006] found a reversal of this negative trend at many
locations beginning around 1990.
[5] 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 [2001] 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. [2005]
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. [2005]
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.
[6] 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 largescale 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
[7] 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
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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].
[8] 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 m2 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
[9] 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. [2006]. 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°
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Figure 1. Figures 1 and 2 from Evan et al. [2007]. (left) Raw (dotted line), deseasonalized (light solid
line), and smoothed (dark solid line) time series of infrared cloud amount from ISCCP between 60°S and
60°N after removal of El Niño signal. (right) Regression coefficients for smoothed average time series
(Figure 1, left) and corresponding time series from individual ISCCP grid cells.
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
[10] 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.
[11] In their Figure 1, reproduced here in our Figure 1
(left), Evan et al. [2007] 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. [2007] 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.
[12] 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 [2007] 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
[2007] 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.
[13] 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
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Figure 2. (left) Global mean anomaly time series and (right) their correlation to all-sky shortwave
downwelling flux time series from SRB version 2.8 on a 2.5° grid between July 1983 and June 2004.
(top) Total cloud fraction from ISCCP. (bottom) SRB version 2.8 all-sky shortwave downwelling flux
(ASWDN) at the surface.
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. [2005] or Hatzianastassiou et
al. [2005], 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
[14] 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.
[15] 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
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Figure 3. Comparisons of SRB and station measured all-sky shortwave downwelling flux time series at
surface measurement sites. A pair of plots is shown for each location. In each pair the top graph shows
raw flux values and the bottom graph shows flux differences (SRB-site) and their statistics.
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.
[16] The statistics in Table 1 indicate that, over all possible matches, the SRB flux bias is less than 10 W m2
while the standard deviation is below 25 W m2. As expected
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Table 1. Statistical Comparison of SRB and Site Monthly Surface Solar Flux Valuesa
Network
Period
Region
N
Bias
St. Dev.
RMS
CC
GEBA
BSRN
BSRN
BSRN
1983 – 2003
1992 – 2005
1992 – 2005
1992 – 2005
global
global
polar
nonpolar
82,977
2984
612
2372
3.10
7.49
15.66
5.38
22.86
22.05
36.03
15.98
23.07
23.28
39.27
16.86
0.96
0.97
0.96
0.98
a
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.
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 m2 and the standard deviation is greater than
35 W m2. 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.
[17] Of course, agreement of basic statistics to within 10–
25 W m2 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 m2 decade1.
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
[18] 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.
[19] Each time we fit a line to a monthly flux anomaly
time series, following Weatherhead et al. [1998], we assume
that the data fit a trend model of the form
Yt ¼ m þ wXt þ Nt ;
ð1Þ
where Y is the measurement variable, m is a constant term,
w 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
Nt ¼ fNt1 þ t ;
ð2Þ
where f is the lag one autocorrelation of Nt and the t are
independent random variables with zero mean and a common variance of s2 . We then estimate the trend, w, using a
standard least squares method and compute its standard
deviation according to equation (2) of Weatherhead et al.
[1998], namely
sN
sw 3=2
n
sffiffiffiffiffiffiffiffiffiffiffiffi
1þf
;
1f
ð3Þ
where n is the number of years of data in the series. This is
easily computed, given that
s2N ¼ s2 = 1 f2 :
ð4Þ
We likewise use Weatherhead et al. [1998]’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 jwj,
sffiffiffiffiffiffiffiffiffiffiffiffi#2=3
"
3:3 sN 1 þ f
n* :
1f
jw j
ð5Þ
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.
[20] 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
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Figure 4. Deseasonalized global mean all-sky downwelling shortwave flux at the surface from July 1983 to
June 2004 from the NASA/GEWEX SRB version 2.8 (top)
with single best fit line and (bottom) with best fit lines for
three segments.
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
[21] 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 m2 decade1.
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 confi-
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dence 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.
[22] The trend in the SRB time series for 1983– 2004 is
far smaller than the downward trends of 3 – 5 W m2
decade1 reported for surface measurements by Stanhill
and Moreshet [1992], Gilgen et al. [1998], and Stanhill and
Cohen [2001] over various periods in the middle to late
20th century. It is also smaller than the global trends of
+1.6 W m2 decade1 and +2.4 W m2 decade1 obtained
by Pinker et al. [2005] and Hatzianastassiou et al. [2005]
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 m2 decade1.
Even so, the trends obtained by both Pinker et al. [2005] and
Hatzianastassiou et al. [2005] 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.
[23] 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. [2005] or Ohmura [2006], it does
appear in the NOAA observations discussed by Dutton et al.
[2006] and the polynomial fit to the global satellite mean of
Hatzianastassiou et al. [2005]. 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.
[24] 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 m2
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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
Period
Source
Region
Trend
95% CI T
95% CI
July 1983 to June 2004
July 1983 to June 2001
1983 – 2001
1984 – 2000
SRB 2.8
SRB 2.8
Pinker et al. [2005]
Hatzianastassiou et al. [2005]
global
global
global
global
0.25
0.88
1.6
2.4
[0.08, 0.58]
[0.48, 1.28]
[0.41, 0.91]
[0.10, 1.66]
July 1983 to July 1991
SRB 2.8
SRB 2.8
October 1999 to June 2004
SRB 2.8
2.51
1.17
5.58
3.21
1.80
3.17
5.32
0.82
4.24
2.09
5.26
7.56
0.50
5.39
5.14
[3.62, 1.39]
July 1991 to October 1999
global
ocean
land
NH
SH
global
ocean
land
NH
SH
global
ocean
land
NH
SH
[4.68, 0.34]
[3.40, 1.06]
[8.19, 2.97]
[5.99, 0.44]
[4.81, 1.21]
[0.67, 5.66]
[1.80, 8.85]
[2.65, 1.02]
[1.72, 6.77]
[0.97, 5.14]
[9.89, 0.63]
[14.02, 1.10]
[4.35, 3.36]
[11.41, 0.62]
[13.03, 2.76]
[1.90, 4.43]
[7.87, 2.66]
a
Trend is the best fit slope of the data, in W m2 decade1; 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 m2 decade1.
decade1. 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 m2 decade1 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 m2 decade1
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.
[25] 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
[26] 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 rootmean-square difference between the global and oceanic
time series is 0.82 W m2, 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 m2, and the Southern Hemisphere
data correlate only slightly better with the global series than
the Northern Hemisphere data do.
[27] 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
[28] 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
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Figure 5. Mean deseasonalized NASA/GEWEX SRB
version 2.8 all-sky downwelling shortwave flux at the
surface for various regions over the period July 1983 to
June 2004, with piecewise linear fits as in Figure 4. (top)
Land, ocean, and all grid cells. (bottom) Northern and
Southern hemispheres and all grid cells.
examination of GEBA data from the 1950s through 1990,
Gilgen et al. [1998] 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 [2001] 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. [2005] were essentially the
same as those of Gilgen et al. [1998], 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
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‘‘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.
[29] 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. [2005].
In addition, the data extend to 2004, allowing us to look
beyond the 1990s.
[30] 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.
[31] 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. [2005]. 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.
[2005] 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.
[32] 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
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Figure 6. Time series of annual mean all-sky shortwave downwelling flux from SRB version 2.8
between July 1983 and June 2004 for each continent after subtraction of the overall mean value.
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Figure 7. GEBA measurement locations. White circles are all sites with data, 1919– 2003. Black circles
are sites with gaps no longer than 24 months between 1983 and 2003.
consistent with earlier findings. Stanhill and Cohen [2001]
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. [2005] 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 [2005] 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.
[33] Our results for Africa agree with the few observations discussed previously. Like Gilgen et al. [1998], 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. [2005]. 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
[34] 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
[35] 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.
[36] 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 deseason-
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Figure 8. GEBA-SRB data comparisons. (top) Matching
anomaly time series for an ensemble of 101 independent and
composite GEBA sites. (bottom) GEBA ensemble anomaly
time series and mean global anomaly time series from SRB
data with 11-point running means.
alized 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.
[37] 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 m2 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 m2 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,
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the GEBA time series is still far more variable than the SRB
global series, with an RMS value of 4.28 W m2 compared
with the global time series value of 1.61 W m2. This means
it would be significantly more difficult to detect a trend using
the GEBA versus the global flux data.
[38] 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 m2 decade1, in contrast to the value of
0.25 W m2 decade1 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 m2 decade1. 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.
[39] 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
[40] 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.
[41] 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.)
[42] 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
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Figure 9. Locations of BSRN measurement sites showing progress in regional coverage.
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 m2 (versus 1.61 W m2
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 m2 decade1 (BSRN) and 0.63 W m2
decade1 (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.
[43] 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.
Figure 10. Comparison of average downwelling shortwave flux anomaly time series: SRB global mean and
ensemble mean of SRB signals at the 35 BSRN sites with
data as of 2005. Fitted trends are indicated by the straight
lines. (top) Monthly data with 11-point running mean.
(bottom) Yearly data.
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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
Region
Std. Dev.
Std. Dev. Diff.
Globe
35 BSRN sites
43 BSRN sites
50 BSRN sites
1.61
3.39
3.07
2.81
–
3.06
2.78
2.52
Correlation
Results for Monthly Data
–
0.430
0.433
0.458
Globe
35 BSRN sites
43 BSRN sites
50 BSRN sites
1.03
1.68
1.42
1.31
–
1.42
1.16
1.02
Results for Annual Data
–
0.538
0.589
0.639
Trend
95% CI
Std. Years
0.63
0.37
0.58
0.65
[0.12,
[0.78,
[0.38,
[0.19,
1.37]
1.52]
1.53]
1.48]
21.6
29.1
25.7
23.5
0.81
0.78
0.91
0.99
[0.24,
[1.47,
[0.68,
[0.42,
1.86]
3.03]
2.49]
2.39]
26.0
43.2
34.2
31.6
a
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 m2 decade1; 95% CI is 95% confidence interval of the trend
accounting for correlation, in W m2 decade1; Std. Years is the number of years required to confidently detect a trend of 1.0 W m2 decade1 in a time
series with these characteristics.
5.3. Underrepresented Areas in Surface Networks
[44] 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
[45] 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 longterm sites are averaged together before deseasonalization, the
resulting time series has a root-mean-square difference of some
2.7 W m2 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.
[46] 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
Figure 11. Effects of missing data. (top) GEBA data from
101 GEBA sites deseasonalized before and after averaging.
(bottom) SRB data from 101 GEBA sites with and without
dropouts (deseasonalized by site before averaging.)
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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 m2 or approximately one third of the difference due to improper deseasonalization, with more variability evident in the series in which dropouts occur.
[47] 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 m2). 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
rffiffiffiffiffisffiffiffiffiffiffiffiffiffiffiffiffi
12 1 þ f
;
sw sN
n3 1 f
ð6Þ
where n is the number of years of data in the series and
sN and f are computed from the annual data. Likewise
equation (5) must be modified to
sffiffiffiffiffiffiffiffiffiffiffiffi#2=3 "
sffiffiffiffiffiffiffiffiffiffiffiffi#2=3
pffiffiffiffiffi
3:3 12 sN 1 þ f
11:4315 sN 1 þ f
n* ¼
:
jwj
jwj
1f
1f
"
ð7Þ
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 m2 decade1 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
[48] In this paper, we have addressed the ‘‘global dimming’’ problem using a satellite surface flux data product.
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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-ofatmosphere measurements. Together, surface and satellite
data sets permit a more rigorous analysis than either one
alone.
[49] 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.
[50] 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 m2 decade1, 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 m2 decade1 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.
[51] 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.
[52] 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
15 of 18
D00D20
HINKELMAN ET AL.: SURFACE INSOLATION TRENDS
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.
[53] 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.
[54] 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.
[55] 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
D00D20
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
[56] Weatherhead et al. [1998] 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
[57] Consider the linear trend model
Yt ¼ m þ wXt þ Nt ;
t ¼ 1; 2; ::; T ;
where m is a constant term, t is the index of yearly samples,
Xt = t represents the linear trend function, and w is the
magnitude of the trend per year. The noise Nt is assumed
to be AR(1), so that Nt = fNt1 + t where jfj < 1, and the
t are independent random variables with mean zero and
variance s2 . If Y = (Y1, Y2, .., YT)0 is the T 1 vector of
observations, this can be expressed in matrix form as
Y ¼ Xb þ N;
ðA1Þ
where X is a T 2 matrix comprising the constant and
trend terms, b = (m, w)0 or the coefficients of regression,
0
, N2, ..,
and N = (N
p1ffiffiffiffiffiffiffiffiffiffiffiffiffi
ffi NT) is the T0 1 vector of noise terms.
2
Let = ( 1 f N1, 2, .., T) , for which the covariance
matrix Cov( ) = s2 I. (Here I is the T T identity matrix.)
Since t = N t fN t1 , the noise vector N must satisfy
P 0N = , where the T T matrix P 0 is
2 pffiffiffiffiffiffiffiffiffiffiffiffiffi2ffi
1f
6 f
6
6
0
P0 ¼ 6
6
..
4
.
0
0
0
0
3
0
07
7
07
7:
7
5
0
1
f
0
0
1
..
.
...
...
...
..
.
0
0
. . . f 1
It then follows that N = (P0)1 and Cov(N) = Cov((P0)1 )
= s2 (P0)1 P1.
[58] Let us write the transformed equation
16 of 18
Y* ¼ P0 Y ¼ P0 ðXb þ NÞ ¼ P0 Xb þ P0 N ¼ X*b þ ;
ðA2Þ
HINKELMAN ET AL.: SURFACE INSOLATION TRENDS
D00D20
where
2 pffiffiffiffiffiffiffiffiffiffiffiffiffi2ffi
1f
6 1f
6
6
X* ¼ P0 X ¼ 6 1 f
6
..
4
.
1f
pffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1 f2
2f
3 2f
..
.
D00D20
Then the number of years T* of data required to detect a
trend of specified magnitude jwj = jw0j with 0.90 probability
is
3
7
7
7
7:
7
5
sffiffiffiffiffiffiffiffiffiffiffiffi#2=3
"
11:4315 s 2=3
11:4315 sN 1 þ f
T* ¼
1f
jw0 jð1 fÞ
jw0 j
ðA5Þ
T ðT 1Þf
Then the generalized least squares (GLS) estimator of b in
the model of (A1) is the ordinary least squares estimator
^ = (X*0X*)1
in the transformed model (A2). Thus b
0
X* Y* with
^ ¼ s2 ðX*0 X*Þ1 ¼ s2 h1
Cov b
h
2
h2
h3
1
;
where
h1 ¼ ðT 1Þð1 fÞ2 þ 1 f2 ;
using the expression for sN given in equation (4), where in
this case both s and sN must be values for yearly data.
[60] Acknowledgments. 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/).
References
1
h2 ¼ ð1 fÞ T ðT 1Þð1 fÞ þ T þ f ;
2
and
1
h3 ¼ T ðT þ 1Þð2T þ 1Þð1 fÞ2 þT 2 fð1 fÞ þ T f f2 :
6
^ ) is s2 times the (2, 2) element
It follows that Var( w
0
1
of (X* X*) , namely
^ Þ ¼ s2
Varðw
¼
h1
h1 h3 h22
12s2
:
T 3 ð1 fÞ þ6T 2 fð1 fÞ þ T 11f2 þ 2f 1 6fð1 þ fÞ
ðA3Þ
2
A simple approximation for the variance given by (A3) when
jfj 6 1 is
^Þ Varðw
12s2
T 3 ð1
fÞ2
:
ðA4Þ
A2. Number of Years of Data Required to Detect
a Trend
[59] The decision rule that a trend is significant at the
95% confidence level if j^
wj > 2sw^ is used here, as throughout the remainder of this paper. Tiao et al. [1990] established that there is at least a 90% chance of detecting a trend
of magnitude jwj = jw0j if jw0j > 3.3sw^ . Using the approximation for Var(^
w) given by (A4), we must have
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
12 s2
:
T 3 ð1 fÞ2
jw0 j > 3:3
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L. M. Hinkelman, Joint Institute for the Study of the Atmosphere and
Ocean, University of Washington, P.O. Box 355672, Seattle, WA 98195,
USA. ([email protected])
P. W. Stackhouse Jr. and B. A. Wielicki, Climate Science Branch, Science
Directorate, NASA Langley Research Center, 21 Langley Boulevard, MS
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S. R. Wilson, Department of Statistics, Virginia Polytechnic Institute and
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