At Uccle, Belgium, a long time series (1991–2013) of simultaneous measurements of
erythemal ultraviolet (UV) dose (

The discovery of the Antarctic ozone hole in the mid-1980s triggered an
increased scientific interest in the state of stratospheric ozone levels on a
global scale (

The possible increase in UV irradiance raises concerns because of its adverse
health and environmental effects. Overexposure can lead to the development of
skin cancers, cataract, skin aging and the suppression of the immune system
(

Physically, UV trends can only be detected from direct measurements on Earth.
Reconstructed data can be based on proxy data such as the abundance of ozone,
solar irradiance, sunshine duration or regional reflectivity of the
Earth–atmosphere system measured from space (

Not only stratospheric ozone influences the intensity of UV irradiance
reaching the surface of the Earth. Long-term changes in solar elevation,
tropospheric ozone, clouds, Rayleigh scattering on air molecules, surface
albedo, aerosols, absorption by trace gases and changes in the distance
between the Sun and the Earth can lead to trends in UV irradiance
(

At Uccle, Belgium, simultaneous measurements of erythemal UV dose, global solar
radiation, total ozone column and aerosol optical depth at 320.1 nm are
available for a time period of 23 years (1991–2013). The time series is long
enough to allow for reliable determination of significant changes (a minimum
of 15 years is required as shown in

In this study, the (all-sky) erythemal UV dose, (all-sky) global solar
radiation, total ozone column and (clear-sky) aerosol optical depth at
320.1 nm are investigated over a time period of 23 years (1991–2013). These
measurements are performed at Uccle, Belgium (50

In 1989, the Brewer spectrophotometer instrument #016, a single
monochromator, was equipped with a UV-B monitor (

The global solar radiation is a measure of the rate of total incoming solar
energy (both direct and diffuse) on a horizontal plane at the surface of the
Earth (

Total ozone column values (in Dobson Units, DU) are available from Brewer#016 direct sun
(DS) measurements. The instrument records raw photon counts of the photomultiplier
at five wavelengths (306.3, 310.1, 313.5, 316.8 and 320.1 nm) using a blocking
slit mask, which opens successively one of the five exit slits. The five exit
slits are scanned twice within 1.6 s, and this is repeated 20 times. The
whole procedure is repeated five times for a total of about 3 min.
The total ozone column is obtained from a combination of measurements at
310.1, 313.5, 316.8 and 320.1 nm, weighted with a predefined set of
constants chosen to minimize the influence of

Comparison of Brewer and Cimel aerosol optical depth values (2006–2013).

Improved cloud-screening procedure.

The initial cloud-screening algorithm, as described in

The cloud-screened

The advantages of the improved cloud-screening method are the removal of the
arbitrary maximum level of

Since most statistical analysis tests, such as linear regression and
change-point tests, rely on independent and identically distributed time
series (e.g.,

Linear trends are calculated for the monthly anomalies of

However, if the regression residuals are autocorrelated, the results of the
regression analysis will be too liberal and the original approach must be
modified. The method proposed in

The above-described linear trend analysis is also applied to the monthly anomalies of the extreme values (minima and maxima) of the variables. The extreme values are calculated by determining the lowest and highest measured value for each month. These trends will be studied together with the relative frequency distribution of the daily mean values. This distribution is determined by using the minimum and maximum values of the entire study period as boundaries and by dividing the range between the boundaries into a certain amount of bins of equal size. The daily values are distributed over the different bins, and the relative frequency in percent is calculated. This will be done for two different time periods: 1991–2002 and 2003–2013. Additionally, the medians for these periods are calculated. In this way, it is possible to investigate whether there is a shift in the frequency distribution of the variables from the first period to the second one. The results of the analysis of the frequency distribution will only be presented in case they show a significant shift in the data.

Change points are times of discontinuity in a time series
(

The goal of a MLR analysis is to determine the
values of parameters for a linear function that cause this function to best
describe a set of provided observations (

Trends of monthly anomalies at Uccle for erythemal UV dose (upper left panel), global solar radiation (upper right panel), total ozone column (lower left panel) and aerosol optical depth at 320.1 nm (lower right panel) for the time period 1991–2013. The blue lines represent the time series, whereas the red lines represent the trend over the time period.

The model will be developed based on data from 1991 to 2008. Data from 2009
to 2013 will be used for validation of the model. For the MLR analysis to
produce trustworthy results, the distribution of the errors of the model
should be normal. Non-normal errors may mean that the

The performance of the model and its parameters will be evaluated through
different statistical parameters. The adjusted

The mean bias error (MBE) and the mean absolute bias error (MABE) are also
calculated in order to evaluate the performance of the regression model. The
MBE (given in %) provides the mean relative difference between modeled and
measured values (

Seasonal trends of erythemal UV doses (1991–2013).

A significant positive trend (at the 99 % significance level) can be
detected in the time series of monthly anomalies of

A significant positive trend has been found in the monthly anomalies of both
the minimum and maximum values of

The values of

Seasonal trends of global solar radiation (1991–2013).

There is a clear difference between the trends of the monthly anomalies of
minimum and maximum values of

The monthly anomalies of

Seasonal trends of total ozone column (1991–2013).

Seasonal trends of aerosol optical depth at 320.1 nm (1991–2013).

Both the minimum and maximum

While the overall trends of

Relative frequency distribution of daily total ozone column values for the two time periods: 1991–2002 (in blue) and 2003–2013 (in red).

Relative frequency distribution of daily aerosol optical depth values for the two time periods: 1991–2002 (in blue) and 2003–2013 (in red).

There are no significant changes in the minimum and maximum

Trends of UV radiation at different stations from (a)

Long-term UV trends for different locations around the world have been the
subject of many research articles (e.g.,

Trends of total ozone column at different stations from (a)

Concerning the global solar radiation, many publications agree on the
existence of a solar dimming period between 1970 and 1985 and a subsequent
solar brightening period (

Ozone and its trends have been the subject of scientific research since the
discovery of ozone depletion. Many studies agree that ozone has decreased
since 1980 to the mid-1990s as a consequence of anthropogenic emissions of
ozone depleting substances. This period of decrease is followed by a
period of significant increase (

Absolute and relative trends of aerosol optical depth at different
stations from (a)

Trend analysis studies of long time series of aerosol optical depth are still
very scarce at the moment. Some studies, however, do report on aerosol trends
(Table 8).

According to the three tests (PMW, MWW and CST) of the change-point analysis,
there is a significant shift in the mean of the monthly anomalies of

A significant change point was detected (only by the PMW test) around January
2003 in the time series of

The black line represents the detrended time series of monthly anomalies of erythemal UV dose (1991–2013). The red (dashed) lines represent the (insignificant) positive trends before and after the detected change point. The grey lines represent the mean before and after the change point.

The black line represents the time series of monthly anomalies of total ozone column (1991–2013). The blue (dashed) line represents the (insignificant) negative trend before the detected change point, and the red (dashed) line represents the (insignificant) positive trend after the change point. The grey lines represent the mean before and after the change point.

All three tests confirmed the presence of a significant change point around
March 1998 in the time series of monthly anomalies of

According to the change-point analysis, no significant change was found in
the mean of the monthly anomalies of

The change points in the time series of

The change point in the

Before applying the MLR technique, it has to be
verified that the explanatory variables (

The MLR analysis has been applied to 1246 simultaneous daily values of
erythemal UV dose (

Performance of the seasonal regression models.

The adjusted

Scatterplot of the measured and modeled erythemal UV doses at Uccle
for the 2009–2013 validation period. The red line represents the regression
line of the data (

The data from 2009–2013 are used to validate the model (see Fig. 7). The
regression equation between the modeled and measured

Validation of the multiple linear regression equation: the upper panel shows the measured (in blue) and modeled (in red) erythemal UV values; the lower panel presents the absolute residuals.

Scatterplots of the measured and modeled erythemal UV doses at Uccle
for the 2009–2013 validation period for spring (upper left panel), summer
(upper right panel), autumn (lower left panel) and winter (lower right
panel). The red lines represent the regression lines of the data, and the
black lines are the

The multiple regression equations for the different seasons are presented below.

Spring:

Seasonal influence of the variation of

From Fig. 9 and Table 9, it can be concluded that the seasonal models perform
well in estimating the measured

Relative residuals
(= (measured

To determine the influence of the variation in the parameters on the
variation in UV, the standard deviation of each parameter is multiplied with
its corresponding regression coefficient, which is then divided by the
average

The influence of

Results of MLR analysis with only

It has already been shown that

Of the variables known to influence the UV irradiance that reaches the
ground, the variability of global solar radiation, total ozone column and
aerosol optical depth (at 320.1 nm) are studied by performing a trend
analysis, a change-point analysis and a multiple linear regression analysis.
This is done in order to determine their changes over a 23 year time period
(1991–2013) and their possible relation to the observed UV changes at
Uccle, Belgium.

The trend over the past 23 years was determined for each variable using their
monthly anomaly values. An overall positive trend was present in the time
series of

For both

The seasonal trends of the four variables were also studied and are similar
between

For

To investigate the influences of

All seasonal models perform rather well in explaining the variation in UV
irradiance, with adjusted

What is seen in reality (i.e., an increase in

The question that remains is whether

This research was performed under the project AGACC-II, contract SD/CS/07A, of the Belgian Science Policy. We thank Christian Hermans (Belgian Institute for Space Aeronomy, Belgium) for establishing and maintaining the AERONET site at Uccle. We would also like to thank the anonymous reviewers and the editor (S. Kazadzis) for their useful input.Edited by: S. Kazadzis