2.1. Description of Measurements and Models
 The required daily data for the Potsdam site (52°22′N, 13°5′E, 107 m a.s.l.), South-West of Berlin, were taken from the central data archive of the German Meteorological Service.
 Sunshine duration (SD) is defined as an accumulated time of bright sunshine during a specified period, here one day. Bright sunshine is defined as direct solar irradiance ≥120 W m−2. SD was measured with Campbell Stokes sunshine recorders. The time resolution of recorded values is one hour and the values are read-off to tenths between 0 and 1. All the values of one hour are summed up to hourly and then to daily sunshine duration. Horizon obstructions can be excluded for the Potsdam site. In the 99-year time series (01/1901 until 12/1999) only three complete months were missing (08/1998, 08/1999 and 09/1998). These gaps were replaced by 30-year climatological means, centered on each missing value.
 Daily column ozone data were taken from three sources: (a) modeled ozone from the CCM SOCOL [Rozanov et al., 2008], called model 1 hereafter (data available for the period from 1901 until 1999); (b) ozone reconstructed by a statistical model, hereafter model 2 [Krzyścin, 2008] (data available for the period from 1950 until 2003); and (c) ground based Dobson ozone observations available for the period from 1964 until 2003 [Spänkuch et al., 1999].
 Model 1: CCM SOCOL, the Climate-Chemistry Modeling tool for SOlar Climate Ozone Links studies is a combination of the general circulation model MA-ECHAM4 [Manzini et al., 1997] and the chemistry-transport model MEZON [Rozanov et al., 1999; Egorova et al., 2003]. CCM SOCOL is a spectral model with T30 horizontal truncation resulting in a grid spacing of about 3.75°. In the vertical direction the model has 39 levels in a hybrid sigma-pressure coordinate system extending from the surface to 0.01 hPa pressure height. The chemical-transport part treats 54 chemical species of the oxygen, hydrogen, nitrogen, carbon, chlorine and bromine groups. Their mixing ratios are determined by gas-phase, photolysis and heterogeneous (in/on aqueous sulfuric acid aerosols, water ice and nitric acid trihydrate) reactions. CCM SOCOL in version 2.0 [Schraner et al., 2008] was applied to simulate ozone and climate change during the entire 20th century. It was driven by prescribed time evolving sea surface temperature, sea ice distribution, greenhouse gases and ozone destroying substances, stratospheric sulfate aerosols, solar spectral irradiance, anthropogenic and natural sources of carbon monoxide and nitrogen oxides, as well as land use changes [Fischer et al., 2008]. A temporally invariant aerosol distribution with the aerosol parameters surface area density, extinction coefficient, single scattering albedo and asymmetry factor has been used for the troposphere. Last three parameters were defined separately for all spectral intervals of the model radiation code. The use of a temporally invariant aerosol distribution in the model disregards the seasonal variations of anthropogenic aerosol and could lead to higher uncertainties in the modeled ozone data. The output data were stored at 12-h intervals for all model grid cells. A spatial subset of 3 × 3 grid cells around Potsdam was extracted from the ozone data fields. Spatial means of daily averages were calculated. This averaging procedure was also applied for the ozone data set from model 2.
 Model 2: In the framework of the COST-Action 726,Krzyścin  presented a statistical model to reconstruct daily values of total ozone over Europe since 1950. The model was trained on the satellite derived total ozone over the period from 1979 to 2004 to select an optimal set of total ozone proxies from various indices of the atmospheric circulation, as well as from meteorological variables derived from the NCEP/NCAR reanalysis [Kalnay et al., 1996]. Model 2 parameterizes the long-term solar effects on total ozone using the so-called Penticton solar radio (10.7 cm) flux measured in Canada, since 1947. The 11-year solar signal in total ozone was found to be small in middle latitudes, ∼1.5% increase from the solar minimum to solar maximum [e.g.,Austin et al., 2008]. The COST-726 O3 database contains this ozone data set with a temporal resolution of one day (01/1950 until 12/2004) and a spatial resolution of 1° × 1° covering all of Europe from 25°W to 35°E and 31°N to 80°N (http://private.igf.edu.pl/∼jkrzys, last accessed 15.02.2012). The value of one grid cell represents an area of approximately 1500 km2 at the latitude of Potsdam.
 Ground-based ozone and UV observations: The daily mean values of the re-evaluated Dobson ozone measurements recorded at Potsdam from 1964 until 2003 had been re-evaluated bySpänkuch et al. . These measurements are based on direct sun and zenith sky measurements with Dobson spectrophotometers #64 and #71. For the period from 1987 to 2003, the few days with missing Dobson ozone values were filled by Brewer ozone measurements.
 UV irradiance was measured at Potsdam by Brewer spectroradiometers (#030 MKII, and #118 MKIII) once or twice per hour and is available for the period from 01/1995 to 12/1999. Regular on-site calibrations of the instruments were performed by 1000 W FEL quartz halogen lamps that had been calibrated according to the SI by the German National Metrological Institute Physikalisch-Technische Bundeanstalt with uncertainties of ±3% in the UV region. All measurements are corrected for the cosine error accounting additionally for changing cloudiness within the scan interval [Feister et al., 1997]. To account for short time variations of UV radiation, ratios between UV radiation and one minute values of global solar irradiance were used to determine hourly and daily totals of erythemal UV radiation. For further details and information about the instrument calibration see, e.g., Feister et al. . Spectral UV irradiance at Lindenberg (52°12′31″N, 14°7′17″E, 127 m a.s.l.) has been measured by Brewer spectroradiometer #078 (MKIV). The method of cosine correction applied to Brewer instruments at Potsdam could not be used, because the required concurrent broadband UV radiation data were not available Feister et al. . Therefore, the cosine correction method described by Bais et al.  that does not require additional measured input data was applied.
2.2. Neural Networks
 Artificial neural networks (ANN) consist of simple elements that operate in parallel. The most important common characteristic of biological and artificial neural networks is their capability to learn from examples. The neuronal network technology imitates the human brain's own problem solving ability to apply knowledge gained from past or previous experience to new problems by building a system of “neurons” that makes new decisions, classifications or forecasts. ANNs learn the relationship between the input and the output data by studying previously recorded data without knowing the physical relationships [López et al., 2001]. A function is set up by adjusting the values (weights) of the connections between the elements (nodes) during the training process. This function is iteratively adjusted until the network output matches the target with an adequate accuracy.
 This study estimates daily doses of UVER by a neural network approach using as standard predictors temporal information of the month and the day of the year (DOY), the minimal solar zenith angle of a day, which is for a given location a function of the DOY, and the sunshine duration. Depending on the network structure, total ozone is used as an additional predictor. In order to find the best ANN configuration several network architectures with up to three hidden layers and 32 nodes were tested. To evaluate the performance of the different networks the results were compared to independent measurements, which were not used to setup and train the model. Hence this setup allows us to reconstruct UVER despite the relatively short period of direct measurements of UV radiation, as ozone data is available through the modeling studies.