Modelling solar UV radiation in the past: Comparison of...

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Modelling solar UV radiation in the past: Comparison of algorithms

and effects of the selected input data

Peter Koepke, Hugo De Backer, Alkiviadis Bais, Aleksander Curylo, Kalju Eerme, Uwe Feister,

Bjorn Johnsen, Juergen Junk, Andreas Kazantzidis, Janusz Krzyscin, Anders Lindfors, Jan Asle Ol-

seth, Peter den Outer, Anna Pribullova, Alois Schmalwieser, Harry Slaper, Henning Staiger, Jean

Verdebout, Laurent Vuilleumier, Philipp Weihs

1 Introduction

The knowledge of biologically effective UV radiation doses is important, since UV solar radiation plays

a role in many processes in the biosphere, including the influence on human skin and immune system,

and may be very harmful if UV exposure exceeds certain limits.

Thus to determine the geographical distribution of the UV-daily dose for whole Europe during the last

50 years, the COST action 726 “Long term changes and climatology of UV radiation over Europe”

(http://i115srv.vu-wien.ac.at/uv/COST726/Cost726.htm) has been established The methods and re-

sults derived in this Action will advance the understanding of UV radiation distribution under various

meteorological conditions, determine a UV radiation climatology for Europe and allow one to assess

UV changes. An intention is to develop detailed maps of biologically effective solar UV radiation over

Europe. These data will represent a basis for research on changes in UV dose regarding geographical

distribution and variable biological action spectra, and for investigations of skin cancer inventories and

other UV related questions.

2 Method

UV radiation in the past and at places without measurements can only be obtained by using models

running with the correct input data, i.e. values of the parameters which affect the solar UV radiation at

the surface. The astronomical parameters solar elevation and solar-earth-distance are known from

geographical coordinates and time, but to get proper values for the atmospheric parameters, like

ozone amount, cloud properties, aerosol amount and type, and regional surface albedo needs detailed

analysis. This is especially the case for the time many years back, where fewer parameters have been

measured and stored than today.

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Consequently a first objective of the Action was to record the available numerical models and algo-

rithms, the meteorological data needed to run these models, the availability of these data for different

places in Europe, and measured UV data that can be used to check the modelling results.

To do this in a practical way, UV radiation has been modelled for two years in the past for four stations

distributed over Europe, called the “Modelling Exercise”.

The quantity that has been modelled is the erythemal-weighted daily dose. Erythemal weighting has

been used since it is relevant for human health damage and is the quantity that has been measured

most frequently. Also from the modelling site it is the best spectral weighting since some algorithms

are focussed on UV Index, i.e. this type of weighting, but all spectral models easily can produce this

spectral weighting.

The daily dose as the final result was chosen as a compromise between the temporal resolution of the

available input data, on the one hand, and that needed to investigate biological UV-processes, on the

other hand.

The time interval for the test has been chosen as to be complete years, in order to check the widest

range of meteorological conditions. The results, as absolute and relative differences of modelled

against measured data, have been analysed on a daily basis. Thus the results for different time peri-

ods, e.g. because of the low UV-doses during winter time with low effects to human health, can be

analysed additionally.

To cover the geographical range in Europe, modelling has been done for the following sites:

-- Bergen (Norway, 60,4° N, 5.3° E, 45 m a.s.l.),

-- Potsdam (Germany, 52.4° N, 13.1° E, 107 m a.s.l.),

-- Davos (Switzerland, 46.8° N, 9.8° E, 1590 m a.s.l.)

-- Thessaloniki (Greece, 40.6°N, 23.0°E, 60 m a.s.l.)

The modelling exercise has been made for the years 1999 and 2002. These years have been chosen

as two different years with available measured UV doses.

For these two years and four sites, meteorological data which are useful for UV-modelling have been

made available by Woking group 1 of the Cost Action (Hugo De Backer et al.). These data have been

given into consistent format and should be the only basis to be used by the modellers. The data are

described in the next chapter.

3 Observational Data

To run the models, information is needed on ozone amount, on cloud properties, on aerosol amount

and absorption, and on regional surface albedo. Total ozone is taken from measurements by ground

based Dobson and Brewer spectrophotometers (Arosa for Davos, Potsdam (Spänkuch et al., 1999),

and Thessaloniki) that are used in WMO/GAW (www.wmo.ch) and NDACC (www.nadcc.org) observa-

tion networks, and satellite data (Bergen from TOMS, on board of Earth Probe satellite,

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jwocky.gsfc.nas.gov). Cloud information is contained in total cloudiness, cloudiness for different levels,

solar global irradiance and sunshine duration. Aerosol information is given as optical depth, visibility,

and aerosol type e.g. from spectral extinction, but these data are not routinely measured, so often

climatologic values or assumptions have to be used. Relevant information on surface albedo in the UV

spectral range can be derived from snow age and height. To check the results, measured daily doses

of erythemal-weighted UV are necessary.

As a consequence of these needs, and taking into account the availability of the data, the measured

data listed in the Tab. 3.1 have been made available as input data for the modelling exercise:

Tab. 3.1 List of meteorological, radiation and ozone data made available for the modelling exercise.

Meteorological and radiation data are from meteorological or synoptic observations. The in-

struments for ozone observations are mentioned in the table.

Bergen Potsdam Davos Thessaloniki

Cloud cover X X X X

(relative) sunshine duration X X X X

Diffuse solar radiation X X X

Global solar radiation X X X X

Visibility X X X X

Snow height X X X

Snow age X

Ozone TOMS Dobson

or Brewer

Dobson

(Arosa) Brewer

For verification of the models results comparison is made with UV observations at the same sites. The

UV-index data, which have been used to get the UV-daily doses used for the comparisons, are from

measurements with broadband Instruments or derived from spectral measurements as specified for

the stations in the following.

The UV-measurements for Bergen are based on a multiband filter radiometer, model GUV, serial

number 9270 from Biospherical Instruments Inc. The instrument is part of the national UV-monitoring

network. The radiometer has 5 detector channels in the UV with a spectral bandwidth of ca 10 nm

(FWHM). A linear combination of the output from different detector channels forms the basis for deriv-

ing CIE-effective doses. The absolute calibration is traceable to the Nordic Ozone Group international

intercomparison of global sky instruments in Tyløsand, Sweden, 2000. The instrument is once a year

calibrated against a travelling standard GUV operating side by side the network station instruments.

The calibrations are maintained by the Norwegian Radiation Protection Authority.

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In the framework of the Swiss Radiation Monitoring program (CHARM) of MeteoSwiss, UV erythemally

weighted broadband irradiance has been measured continuously at the World Radiation Center

(PMOD/WRC) at Davos since the end of 1995, using SolarLight 501A (SL501A). The instruments at

the WRC are ventilated and heated to keep the domes free of dew, snow and ice. In addition to this

external ventilation and heating, the temperature of the SL501A instrument body is stabilized to 25°C.

Measurements are performed automatically every 2 s, and 2 min averages are recorded.

The SL501A were initially calibrated, and had their spectral response determined by the manufacturer.

Thereafter, they have been calibrated annually by comparison with a Swiss reference SL501 at the

WRC. The accuracy of the Swiss reference is verified regularly at international intercomparisons. It

initially took part in the WMO/STUK intercomparison in Helsinki, Finland, 1995 [Leszczynski et al.,

1998]. It was also compared to spectroradiometers at Garmisch-Partenkirchen, Germany, 1997 [Phili-

pona et al., 2001], and participated in the COST 713 intercomparison at Thessaloniki, Greece, 1999,

as well as the COST 726 intercomparison at Davos in 2006. Philipona et al. [2001] estimated the ac-

curacy of SL501A radiometers used at Weissfluhjoch a station neighboring Davos. These instruments

are in a setting similar to those used at the WRC at Davos. They also undergo the same calibration

procedure. The absolute accuracy was estimated to be within ±10%. This uncertainty is also applica-

ble to the measurements of Davos.

Erythemal-weighted UV irradiance at Potsdam for the year 2002 was integrated from UV spectra

measured by a Bentham DM150 double monochromator that became operational in the year 2000.

The instrument measures UV spectra in the range from 290 to 450 nm with a spectral bandwidth

(FBHM) of 0.5 nm at time steps of 6 minutes between sunrise and sunset. For the year 1999 at Pots-

dam, measurements by Brewer spectroradiometer No 118 of the type MKIII (double monochromator)

in the spectral range from 290 to 363 nm have been used. All the Brewer spectra were cosine cor-

rected by the method of Feister et al. 1997, and spectral irradiance within the spectral range from 363

to 400 nm estimated by the method of Slaper et al. 1995. Calibration of both instruments has been

based on standard lamps of the FEL1000W type calibrated by the Physikalisch-Technische Bunde-

sanstalt (PTB) in Germany. Brewer instrument No 118 took part in the intercomparison of spectroradi-

ometers at Garmisch-Partenkirchen in 1997 (Seckmeyer at al. 1998), and in the QASUME campaign

in 2004 (Gröbner et al. 2004). As the typical number of Brewer spectral scans was only about 10 to 20

spectra per day, part of the variability of UV irradiance due to changing cloudiness between the spec-

tral scans has been accounted for by a method described by Feister and Junk (2006) that takes short-

term global irradiance variability into account for the calculation of hourly and daily UV irradiation.

The UV data for Thessaloniki were produced by an erythemal detector of type YES UVB-1, which is in

operation since 1991. Although spectral UV measurements are also available at the same location

from two Brewer spectroradiometers (Bais et al., 1996), the erythemal detector has better temporal

resolution (every 1 min) which allows more accurate calculation of the daily integrals required for this

study. The detector is regularly calibrated against the two Brewer spectroradiometers, and hence its

stability in time is sufficiently controlled to within about ±7%.

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4 Models and input data

4.1 Overview Sixteen models and algorithms took part in the modelling exercise. For each model a description is

given in the following paragraphs.

Tab. 4.1 Institutes and model versions

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Models using solar global irradiance

auth Aristole University Thessaloniki, Greece.

dwdk_day German Meteorological Service, Department “Climate and Environment”, Freiburg,

Germany. Model using solar global irradiance on a daily basis.

dwdk_acc German Meteorological Service, Department “Climate and Environment”, Freiburg,

Germany. Model using solar global irradiance on an hourly basis, accumulated.

dwdf German Meteorological Service, Department “Research and Development”, Meteoro-

logical Observatory Lindenberg – Richard Aßmann Observatory, Germany.

fmi Finnish Meteorological Institute, Meteorological Research Division, Helsinki, Finland.

gsas Geophysical Institute, Slovak Academy of Sciences, Bratislava, Slovakia.

igfpas Institute of Geophysics, Polish Academy of Sciences, Warsaw, Poland.

imwm Institute of Meteorology and Water Management, Warsaw, Poland.

jrc European Commission - Joint Research Centre, Institute for Health and Consumer

Protection, Ispra, Italy.

mim_cn4 Meteorological Institute Munich, Ludwig-Maximilians-University, Munich, Germany;

cloud neural network 4, directly using solar irradiance.

rivm National Institute for Public Health and the Environment, Bilthoven, The Netherlands.

tobs Tartu Observatory, Toravere, Estonia.

Models not using solar global irradiance

boku University of Natural Resources and Applied Life Sciences, Department „Water - At-

mosphere-Environment“, Vienna, Austria.

mim_cn1 Meteorological Institute Munich, Ludwig-Maximilians-University, Munich, Germany;

cloud neural network 1, using total cloudiness.

mim_wgt Meteorological Institute Munich, Ludwig-Maximilians-University, Munich, Germany;

using sun shine duration.

uvwm University of Veterinary Medicine, Institute of Medical Physics and Biostatistics, Vi-

enna, Austria.

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The way, how to use the available information from the observational meteorological data, is individual

by each modeller. This applies to the albedo, which is correlated to snow properties, and to the aero-

sol properties. To consider the influence of clouds, many of the models use so called Cloud Modifica-

tion Factors (CMF). These are defined as the ratio between the erythemal-weighted UV irradiance

under cloudy conditions against that resulting from the atmosphere with the same conditions, but with

no clouds (Borkowski et al., 1977; Blumthaler a. Ambach, 1994; Schwander et al., 2002).

The way how to use the available input information separates the models into two categories: Local

and general. “Local” models use regression constants, e.g. to get the CMF, which have been sepa-

rately derived for each station based on 1-year data. Thus it may be difficult to use such a model for

modelling over whole Europe. The “general” models, in contrast, take the information content of the

input data with general methods, which are independent from a station, and thus give results inde-

pendent of local properties.

The models are listed in Tab. 4.1, together with the acronyms used in this paper. They are separated

into two groups: The first combines models which use solar global irradiance as an input parameter,

the second one models without using this solar information.

4.2 auth model The main part of the methodology consists of the estimation of the cloud effect on UV and its relation

with the cloud effect on solar radiation. For this purpose it is tried to calculate the daily mean CMF for

both radiation quantities.

The daily integral of cloud-free solar radiation was calculated (in half-hour steps between sunrise and

sunset) by SBDART model (Ricchiazzi et al., 1998) using the two-steam radiative transfer solver. The

daily cloud-free UV erythemal dose was calculated with the same time step from UVspec model

(Mayer et al., 1997). The radiation transfer equation is solved with the two streams approximation.

The same vertical profile, alpha exponent (1.3) of Angstrom formula (τ=β*λ-α), single scattering albedo

(0.95) and asymmetry parameter (0.70) were used for aerosol in both models. Aerosol optical depth

values at 340 nm were assumed to be equal to 0.05 for Davos and Bergen, 0.3 for Potsdam and 0.55

for Thessaloniki. The US standard profiles for ozone, temperature and air molecule number density

were used in all model calculations (Anderson et al., 1986

Snow observations from all sites (except Thessaloniki, where surface is snow covered almost one day

per year) have been used in order to estimate surface albedo for UV and total radiation, according to

the values proposed by Schwander et. al. (1999). For snow-free days albedo values corresponding to

“open field” type of surface (0.02) were used.For all stations, the CMF for UV erythemal dose

(CMFUV) was estimated from the CMF for total solar irradiance (CMFTS ) with the empirical relation:

CMFUV = b*(CMFTS)a

Hence, the daily UV erythemal dose is calculated by multiplication of the empirically derived CMFUV

the corresponding modelled cloud-free values.

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4.3 dwdk-day model The modelling of the daily erythemal effective UV dose is based on DWD’s method in UV Index fore-

casting (Staiger and Koepke, 2005). To account for cloud modifications the method is adapted to ac-

cept as input standard synoptic observations and / or measured global radiation. The daily dose is

calculated by accumulating hourly values of the UV Index converted to the dimension of an hourly

erythemal effective UV dose.

The influence of snow albedo in the UV is determined applying the algorithm of Schwander et al.

(1999) to compute a factor accounting for regional increased UV albedo. In snow free cases the factor

is set to one corresponding to the albedo of 3 %, summer grass. In the case of Davos the factor is

calculated for the site itself and for Weissfluhjoch. Following, the both factors are averaged with the

weights 0.58 for the site and 0.42 for Weissfluhjoch.

The aerosol optical depth at 550 nm is taken from a “climatology (2000 – 2005)” derived from NASA

MODIS monthly averages (Staiger and Koepke, 2005). The single scattering albedo is derived from

the 5°· 5° longitude and latitude semi annual values of GADS (Koepke et al., 1997). According to the

reasons given by Lindfors and Vuilleumier (2005), the single scattering albedo from GADS appears

too low for an inner alpine site 1500 m a.s.l. and clearly contrasted to the lowlands. Thus, for model-

ling the required single scattering albedo at 300 nm is set to 0.9653 for summer and winter according

to the aerosol type “continental clear (cc)”.

To take the cloud effects into account, CMF has been used after den Outer et al. (2005).These have

been developed for daily erythemal effective UV doses by parameterizations based on the ratio RGR of

measured daily global short-wave irradiation and predicted clear sky sums. The latter are calculated

based on the algorithm of den Outer et al. (2000) depending exclusively on solar zenith angle (SZA).

The applied parameterizations algorithm requires as input RGR and the cosine of SZA. For a daily sum

the SZA at solar noon has to be taken to derive the parameter “p”. Thus, the daily erythemal effective

UV dose cloudy is the product of the daily CMF and the modelled daily erythemal effective UV dose

clear sky.

The SZA dependence of “p” is given by den Outer et al. (2005) in 6 bins. In the published version it is

restricted to SZA greater than 25.8°, since the algorithm is derived from measured global and UV irra-

diation in the Netherlands. To allow for lower SZA the given values of the bins thus are fitted by a sec-

ond order polynomial that can than be extrapolated for lower SZA. Based on the very good agreement

between published and fitted values, “p” is applied in the continuous form enabled by the polynomial.

The model version based on daily sums of clear sky UV doses and daily sums of measured global

irradiation is named “dwdk_day”.

4.4 dwdk-acc model The model behind version “dwdk_acc” is the same as used for dwdk-day, but on the basis of hourly

UVery doses that are accumulated to daily doses. Hourly resolved measured values of global irradia-

tion are available from the data base. The RIVM scaling of the measured daily sum of global irradia-

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tion by the predicted clear sky sum and its dependence on SZA let it furthermore consider possible to

apply the algorithm to calculate CMF’s for hourly values of erythemal UV. The solar zenith angle re-

quired to determine the value of the parameter “p” is that of the hour. The version based on an hourly

resolution should reduce uncertainties of the daily version accounting better for the SZA dependence

of the CMF’s.

4.5 dwdf model

Based on earlier work on statistical modelling of solar UV radiation into the past (Feister et al. 2002)

another statistical approach was developed to derive broad-band UV radiation from meteorological

predictors that are closely correlated to UV radiation. The model is an Artificial Neural Network ap-

proach (ANN) that is described by Feister and Junk (2006) and Junk et al.(2007). It uses meteorologi-

cal data such as global and diffuse irradiation, sunshine duration, column ozone and visibility to derive

broad-band UV irradiation. For the training of ANN, Brewer data have been used for the UV irradiance

within the period 1996 to 2001 without 1999, to check the model performance (1999 and 2002) with

data not have been part of the ANN training data sets. The ANN method has been applied to the sites

Bergen, Davos and Potsdam. ANN training and modelling for the Thessaloniki site was not finished in

the available time frame.

The respective input data at the sites have been selected by availability, i.e. not only the parameter

itself, but also a sufficient number of data (a few years) is needed for the ANN training. In addition to

the parameters global irradiation (G), sunshine duration (SD), column ozone (O3) and daily minimum

of solar zenith angle (SZA), also visibility (VIS) was used for Potsdam and Davos, diffuse irradiation

(D) for Potsdam , and snow cover (SC) for Davos (Tab. 4.2). The ANN can also be applied with a sub-

set of input data according to their availability.

Tab. 4.2 Input parameters to the Artificial Neural Network (ANN)

G D SD O3 VIS SC SZA

Bergen x - x X - - x

Davos x - x X x x x

Potsdam x x x X x - x

4.6 fmi model

The idea behind the UV reconstruction algorithm of FMI was to develop a method which is theoretical

and independent; independent of measurements in the sense that it does not rely on empirical rela-

tions, and also independent of location as far as possible. In order to achieve this goal, the method

was based on the theory of radiative transfer, that is, on physical relationships. The approach in prac-

tice was to use the libRadtran radiative transfer package [Mayer and Kylling, 2005] as a tool helping to

interpret this theory.

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The FMI method consists of three steps: (i) simulate clear-sky irradiances, both global and UV, using

libRadtran, (ii) based on measured global radiation, fetch the cloud modification factor of UV from a

pre-calculated cloud table, and (iii) using this information, calculate the estimated UV irradiance. When

simulating the clear-sky irradiances, the model was given as daily input the total ozone column, total

water vapour column (from the ERA-40 data set), surface albedo (one value for UV radiation, one for

global radiation), and the altitude of the location. For the aerosol properties, a constant yearly cycle

based on typical climatological values was assumed.

The cloud algorithm of the FMI method is based on simulations using libRadtran. By simulating the

cloudy atmosphere with varying cloud optical depth and varying solar zenith angle (SZA), a look-up-

table was produced, that describes the dependence of the cloud modification factor of UV radiation

(CMFUV) on the cloud modification factor of global radiation (CMFG). The cloud modification factor is,

as defined in section 4.1, the ratio of all-sky (including clouds) to clear-sky irradiance. This cloud table

can be expressed as function f in:

CMFUV = f (CMFG , SZA)

Hence, from this cloud table the UV cloud modification factor can be retrieved for any values of CMFG

and SZA. The simulation of the cloud table was done assuming a horizontally homogeneous water

cloud layer extending from 2 to 4 km in altitude with an effective cloud droplet radius of 10 μm. The

cloud optical depth was set at 550 nm, and its wavelength dependence follows the parameterization

by Hu and Stamnes [1993]. The Rayleigh scattering of the atmosphere is taken into account by the

model. Thus, the cloud model is realistic, and includes the main processes that influence the trans-

mission of UV radiation in a cloudy atmosphere.

4.7 gsas model

Reconstruction model of daily doses of solar UV radiation spectrally weighted by the weight function

CIE-UV defined by CIE (1987) consists of two parts. Radiative transfer model TUV – version V4.1b

(Madronich, 1993) was used for clear-sky daily dose modelling. Statistical model was created to model

relation between CMF of CIE-UV and CMF of global radiation (ratio between measured and maximal

daily dose of global radiation) for different solar zenith angles (SZA).

Discrete-ordinate radiative transfer scheme with assumption of pseudospheric atmosphere was used

for calculation of cloud-free CIE-UV irradiance (UVMAX). Time step of 0.5 h was applied for daily inte-

gral calculation. Geographical coordinates (including altitude), standard vertical profiles of atmospheric

components (U.S. atmosphere, 1976), daily average of total ozone, and snow-free surface albedo

(integral surface albedo for UV radiation A = 0.03) and spectral weight function were the most impor-

tant model information. Elterman’s (1976) vertical profile of aerosols was used in the TUV model.

Aerosol optical depth for radiation with wavelength λ = 340 nm (AOD340) was set to be 0.3 for Davos

and Bergen, 0.4 for Potsdam and 0.5 for Thessaloniki. AOD dependence on wavelength obeying

Ǻngström’s formula with exponent α = 1.3 was assumed. For all sites, except of Bergen, continental

sulphate aerosol with single scattering albedo ω = 0.95, asymmetry parameter g = 0.66 (for Bergen ω

= 0.99, g = 0.75) entered the TUV model. The modelled UVMAX values were corrected for assessed

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aerosol content and also for observed surface albedo, multiplying by two correction factors KAOD and

Ksnow.

Optical depth of the aerosol was assessed from information on horizontal visibility (VIS). Assuming,

that horizontal extinction at 1 km distance corresponds to vertical extinction of 2 km thick air layer,

total atmospheric extinction for visible radiation (λ= 550 nm) was calculated. Aerosol optical depth for

visible radiation (AOD550) was determined subtracting the optical depth of the Rayleigh scattering from

total atmospheric extinction. Aerosol optical depth in the UV range (AOD340) was derived from the

aerosol optical depth of visible radiation using Ǻngström’s formula with exponent α= 1.3.

Clear-sky CIE-UV radiation corrected for the assessed aerosol content in the atmosphere was then

modified with respect to surface albedo. The surface albedo parameter was determined using infor-

mation on snow cover presence and its properties at investigated sites and if available (Davos) also at

surrounding areas.

Daily doses of global solar radiation for cloud-less condition were constructed as an envelope curve of

all available measured global radiation daily doses. Effect of horizon complexity was involved in the

calculation of global radiation daily integral maxima by this way. Relative global radiation RG was ob-

tained as a ratio between measured and maximal daily dose of global radiation.

Dependence of the ratio between relative CIE-UV and relative global daily dose on atmospheric tran-

sitivity (for version M2a characterized by the RG) and also on SZA was assumed in construction of the

model equation for daily dose of CIE-UV radiation UVMOD :

UVMOD = UVMAX KAOD Ksnow RG (aX2+bX+c),

where a, b, c are 6 triplets of regression coefficients obtained from all available data and for selected

intervals of the SZA. X = RG for model version M2a. Separate model equations were created for 6

categories of the SZA: SZA <40º; SZA∈ ⟨ 40º; 50º); SZA∈⟨50 º; 60º); SZA∈ ⟨60º; 70º); SZA∈ ⟨70º;

80º) and SZA∈ ⟨80º; 90º⟩. The SZA was calculated for every investigated site at the time of daily solar

culmination.

4.8 igfpas model The igfpas model, UV Spectrum Reconstruction Model, belongs to the category of hybrid (analytical-

statistical) model. All-sky UV irradiance is derived as the clear-sky UV value from a radiative transfer

model simulation multiplied by CMF from a regression of the UV irradiance on various global charac-

teristics of solar radiation (Sun +sky irradiance, sunshine duration, direct to diffusive ratio, etc.). igfp

provides all-sky UV (290-400 nm) solar spectra. These spectra could be weighted by any action spec-

trum and integrated over the UV wavelength range to obtain biologically weighted dose rates. Finally

time integral of the dose rate yields the daily dose. According to the exercise objectives the recon-

structed UV spectra (with 5-minute resolution) are weighted by the CIE action spectrum.

Clear-sky UV spectra are calculated using a simple radiative transfer model (SMARTS Gueymard,

2001, 2006) assuming variable solar zenith angle, total ozone and setting constant aerosols character-

istics; 0.45, 0.92, 0.70 for aerosol optical depth, single scattering albedo, and asymmetry factor, re-

spectively. Lambertian surface albedo of 0.03 is assumed for the whole UV range. If the snow data

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over a site is available the surface albedo is changed to values (wavelength dependent) provided by

the SMARTS albedo data base for the snow conditions.

CMF is derived from a regression of the ratio between the measured and the hypothetical clear-sky

representatives of the spectrum intensity at selected wavelength on the clearness index (CI). CI is

defined as the ratio of the measured to the hypothetical clear-sky global (Sun+sky) solar irradiance

integrated over whole solar spectrum, thus providing an overall reduction of the solar radiation by

clouds. SMARTS (version 2.9.2) is used here to estimate the clear-sky value of the total solar irradi-

ances. The regression formula (polynomial of CI) is calculated for the following SZA ranges:

SZA<35°, 35°-45°, 45°-55°, 55°-65°, 65°-75°, and SZA>75°. Input to the regression model consists of

UV spectra over the 290-365 nm range and total ozone by the Brewer spectrophotometer, and global

irradiance by the Kipp-Zonen CM-21 pyranometer measured over Thessaloniki for the period 1993-

2002. CMF is calculated with resolution of 2.5nm and 5nm for UV-B (290-320 nm) and UV-A (320-400

nm) wavelengths, respectively (for more details see Krzyścin, 2005).

In the model exercise 1-hour or daily values of the clearness index are in our disposal because of the

resolution of the global radiation data provided by the stations. Clear-sky values of global solar radia-

tion are from SMARTS simulations assuming variable amount of column water vapour (from

NCAR/NOAA-Reanalysis-2 data base with 6-hour resolution), rural aerosols with constant or variable

optical depth (if hourly or daily visibility data were available for the site), grass or snow surface albedo

(wavelength dependent according to the SMARTS albedo data base), winter and summer vertical

profile of temperature and trace gases for the cold (November-April) and warm (May-October) sub-

periods of the year, respectively. Linear interpolation between 1-hour input values or constant daily

input is used to run the reconstruction model with 5-minute resolution.

4.9 imwm model Two radiative transfer models have been used to model UV and solar irradiance: UV model: Fastrt

(Engelsen, XXYY) and GR model: Streamer v.3.0 (Jeff Key, ZZXX). The results have been combined

after

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛=

modGRGRF

modUVUV

with UVmod , GRmod are UV and Global Radiation clear sky model results, and F is a function, depend-

ing on Julian day x, calculated to fit the relative differences between measured and reconstructed daily

doses for the fitting period 2002. This function is used to remove the observed yearly cycle of differ-

ences between modelled and reconstructed data. The data are given in Tab. 4.4

The aerosol properties have been taken from the EDUCE report (Gonzi et al., 2001) with aerosol

types varied with quarterly means (Tab. 4.3) : Ångström coeff. α, AOD440nm (Transformed to AOD at

UV and for Global Radiation/600nm/, respectively) .

Tab. 4.3 Aerosol properties

12

Dec – Feb Mar – May Jun – Aug Sep – Nov Station

α AOD440 α AOD440 α AOD440 α AOD440

Davos 1.26 0.11 1.26 0.11 1.26 0.11 1.26 0.11

Bergen 1.25 0.19 1.16 0.27 1.42 0.27 1.18 0.21

Potsdam 1.29 0.21 1.29 0.28 1.50 0.32 1.27 0.24

Thessaloniki 1.25 0.19 1.16 0.27 1.42 0.27 1.18 0.21

To get the albedo, for each station the UV model has been run several times with step by step chang-

ing albedo value until the coefficient of the fitted line between measured and modelled data is

1.00±0.02. These values of albedo have been used for Global Radiation model parameterisation.

Tab. 4.4 Values of albedo and fitting functions

UVmsr /UVmod = F(GRmsr/GRmod) Station

Albedo F

Davos 1 - no snow = 0.15

2 - snow = 0.65

0.23x3 – 0.7x2 + 1.56x

-0.80x2 + 1.74x

Bergen 1 - no snow = 0.03

2 = 0.4

3 = 0.6

0.60x3 – 1.6x2 + 2.06x

-0.76x2 + 1.68x

-0.76x2 + 1.68x

Potsdam 1 - no snow = 0.03

2 – snow = 0.35

0.66x3 – 1.8x2 + 2.09x

0.46x3 – 1.5x2 + 2.09x

Thessaloniki Assumed const = 0.03 0.43x3 – 0.9x2 + 1.40x

4.10 jrc model In principle, the model (version 01) consists in retrieving a daily average effective cloud density (effec-

tive because, in practice, it includes other effects) using hourly radiation measurements. This effective

cloud density is then used to estimate the daily erythemal dose by direct radiative transfer modelling.

The only input data are the global radiation and total column ozone; in particular the model does not

use any aerosol input data.

The processing is based on two Look Up Tables (LUT) generated with the UVspec code, included in

the libRadtran package (http://www.libradtran.org/). The GR LUT gives the global downwelling surface

irradiance with respect to six entries: solar zenith, cloud density, total column ozone, surface albedo,

horizontal visibility and ground altitude. All other parameters have default values, corresponding to the

US standard atmospheric profiles, a generic tropospheric aerosol type and background stratospheric

aerosols. The cloud density is the only variable cloud parameter, others are fixed, i.e. a water cloud in

the form of a layer extending from 1 to 2 km above the ground and with an effective droplet radius of

7 μm. The UV LUT gives the spectral downwelling surface irradiance in the wavelength range from

290 to 400 nm, with a spectral resolution of 0.5 nm. For the purpose of the COST modelling exercise,

it has been reduced to the erythemal radiation by integration with the CIE87 spectral action spectrum.

13

The entries of the UV LUT are the same as those of the GR LUT. For a given location and time, the

values of the entry parameters are in principle the same for the two LUT, except for the surface al-

bedo, which is markedly different in the UV and global spectral ranges. In this version of the model,

the UV albedo has been set to 0.03 in all cases.

The first processing step consists in generating global radiation daily doses from the hourly measure-

ments (taking into account missing data). The next step is to retrieve an average daily cloud density

that reproduces the observed global daily dose, according to the GR LUT. This inversion process

requires assigning values to all parameters except the cloud density. The altitude is known and the

GR albedo is assigned a constant value equal to the average surface albedo retrieved from the visible

band of METEOSAT/MVIRI images. In this version of the model, the aerosols are actually ignored

explicitly by setting the visibility to a high value (160 km) in all cases. The total column ozone is set

from the daily input data. At this point, for the times in the day corresponding to the available GR

measurements, the solar zenith is computed and the GR LUT is reduced to a function of cloud density

only. These functions are then summed to produce a modelled GR daily dose depending on the aver-

age cloud density, the value of which is determined by inversion to reproduce the measured GR dose.

Because the model ignores explicitly the aerosols, the retrieved value of the average cloud density will

actually include the attenuation by aerosols. In principle, the influencing parameter values for the GR,

and in particular the retrieved cloud density, can now be used to compute the UV downwelling irradi-

ance.

As such, the model was systematically underestimating the erythemal daily doses. Working on the

Thessaloniki 2002 data, it was however found that the bias could be eliminated with an empirical cor-

rection of the retrieved average daily cloud density; the logarithm of the corrected value being a linear

function of the logarithm non corrected value. Such a relationship suggests that the problem may

arise from a bad choice of the cloud droplet radius, leading to an inadequate spectral dependence of

the scattering by clouds. The empirical correction turned out to be valid for other stations and is part

of this version of the model, awaiting a possible re-calculation of the LUTs with a different droplet ra-

dius.

4.11 mim–cn4 model Cloud free UV irradiances are modelled with STAR (Ruggaber et al., 1994; Koepke et al., 2004), a one

dimensional model which allows a detailed description of the atmospheric parameters (e. g. variable

height distribution of components; aerosol properties depending on mixture of components and rela-

tive humidity; spectral surface albedo). This cloud free version of the model has been tested with good

results (Koepke et al., 1998). To reduce computer time a model version has been derived which uses

multiple scattering calculations only at 7 wavelengths and replenish irradiance for the other wave-

length by a neural network (Schwander et al., 2001).

For this modelling exercise the model version STARneuro has been used (Schwander et al., 2002),

which is based on a combination of spectral multiple scattering modelling with neural networks which

have been trained to derive cloud effects by UV data measured in Garmisch-Partenkirchen in a moun-

14

tain valley. Different versions of neural networks can be used, based on parameters that are taken to

describe the atmospheric conditions. For the version CN4, used here, the atmospheric conditions are

described by total cloud amount and broadband solar irradiance, in addition to solar zenith angle and

ground albedo. Thus global solar irradiance has been used directly and not a solar CMF has been

transferred to a CMF in the UV.

The results of STARneuro have been tested by comparison with UV irradiances from different sites in

Germany, with satisfying results (Schwander, 1999). But the results of the actual comparison with the

measurements from different countries show that the model results are systematically too high. This

will be explained by the reduction of the UV irradiances, which has been used to train the neural net-

work, due to the horizon. And this effect is shifted by the neural network also to the clear sky condi-

tions. This makes a difference against results of STAR, directly modelled for clear sky conditions, as it

is used e.g. for the dwdk modelling.

For the aerosol, the amount i.e. the aerosol optical depth, has been derived from visibility in combina-

tion with climatological values for the height of the boundary layer. Thus the aerosol amount shows

strong variations from day to day due to visibility, and partly very high values of aerosol optical depth.

The aerosol type is taken from OPAC (Hess et al., 1998) under assumptions on the general conditions

of the sites. The albedo is used to be 3% in snow free conditions (5 % for Davos due to the assump-

tion of rocks) and taken with increased values in case of snow, using an equation with snow age and

snow height (Schwander et al., 1999) adapted to the sites.

To get daily UV dose UV irradiance has been modelled for each hour with the available information on

atmospheric parameters, shifted to hourly doses and added to get the daily dose.

4.12 rivm model RIVM has used a generic approach for this modelling exercise based on its standard modelling as

described in den Outer et al. (2005). Adjustments to RIVMs standard model were incorporation of a

simultaneously performed height, cloud, and variable ground-albedo correction.

Clear sky daily UV-doses are integrations of clear sky UV irradiances using one-minute integration

steps. The clear sky UV irradiance is obtained from a look-up table for erythemal-weighted UV as a

function of ozone and SZA. The look-up table was produced by using the Tropospheric Ultraviolet-

Visible (TUV, Madronich, 1998) radiation transfer model in the pseudo-spherical 4-stream discrete

ordinates mode. The input for the TUV-model comprises a fixed set of atmospheric parameters

adopted from van Weele et al. (2000). The single scattering albedo (0.95) and the asymmetry parame-

ter (0.7) of the aerosols for the boundary layer are here also used above the boundary layer, as we

use the aerosol profile given by Deirmendijan et al. (1980). The scaling of the extinction cross section

is described by an Angström parameter 1.5, and the total optical depth is 0.4 at a wavelength of 320

nm. Daily variations in aerosol loading were not taken into account.

The bare cloud modification factor for the clear sky UV daily dose is derived from co-measured global

solar irradiation data following Den Outer et al. (2005). The adaptations of the clear-sky daily UV-

15

doses for clouds, ground albedo, and altitude were simultaneously performed as the impact of all

modifications depends on the overhead reflection properties of sky and clouds.

4.13 tobs model The reconstruction of UV doses for the past years is based on statistical relationships, a proxy-based

reconstruction using the climatic clear weather dose (Eerme et al., 2006). The daily climatic value here

means corresponding to the long-term average conditions of the atmospheric characteristics for each

calendar day. The smoothed climatic annual cycle of clear weather erythemal doses, corresponding to

climatic annual cycles of total ozone and aerosol optical depth has been interpolated from the ob-

served clear-sky values. The true all-weather ground-level daily erythemal dose D against the best

fitted clear-sky background can be expressed as

D = DclearKcloudinessKalbedoKozoneKturbidity.

In the equation Dclear is the smoothed climatic average clear-sky dose for the corresponding calendar

day, Kcloudiness is the daily cloud modification factor (CMF), Kalbedo is the factor accounting for the albedo

difference from the seasonal average, Kozone is the factor accounting for the deviation of total ozone

daily value from that of the climatic value for that particular day, and Kturbidity is the factor accounting for

the deviation of atmospheric turbidity from that of the climatic.

In climatic conditions of Northern Europe the major modulating factor of the daily erythemal doses as

well as the daily sums of broadband irradiance is cloudiness. From among the available cloudiness

influence related proxies, the daily sum of pyrheliometer-measured direct irradiance and the daily sum

of pyranometer-measured global irradiance were chosen as manifesting the best agreement of the

reconstructed daily erythemal doses with the measured values. The former turned out to be suitable

on partly cloudy and clear days and the latter on overcast days. The factor Kcloudineshas been ex-

pressed through its proxies X by a linear regression

Kcloudiness = aX/Xclear+ b.

The AERONET spectral aerosol optical depth data and the data of local broadband measurements of

atmospheric transparency confirmed that the aerosol influence in the erythemal radiation has been

proportional to that in visible and pyranometer-measured ranges. On these grounds it was assumed

that the value of broadband direct irradiance takes into consideration the aerosol attenuation devia-

tions from its climatic value. The large (small) average value of AOD during a certain period does not

mean that all values are systematically higher (lower). Usually both large and small values occur dur-

ing any period, and the average value depends on their relative frequency.

4.14 boku model

This model (Version sd1_BOKU) was designed to test the accuracy achievable using the sun shine

duration to determine the daily exposure of erythemal UV. Daily UV exposure is the integral of the

hourly exposures over the day.

16

Hdose =( Eclear * SD + Ecloudy * (1-SD) ) * 3600

Hdose is the hourly exposure, Eclear the clear sky ground UV erythemal irradiance, Ecloud the UV

erythemal irradiance under cloudy sky conditions and SD is the sunshine duration during one hour

(values between 0 and 1, 1= sun shine during 100% of the time)

If only an average sunshine duration over the whole day (SDmean) is available (like at station Thessa-

loniki) then SD is equal to SDmean. Assuming average aerosol and cloud optical depth for the whole

year the radiative transfer model SDISORT is used to calculate Eclear and Ecloudy. The average opti-

cal depth is obtained for each station by finding the best fit of absolute values of clear sky measure-

ments and model calculations. Cloud optical depth is determined by finding the best fit between abso-

lute values of cloudy sky (sunshine duration = 0 minutes) measurements and model calculations. The

same average optical depth is used for the whole year. When ground is snow free albedo is set to

0.03. In the event of a snow-covered ground the albedo amounts to 0.8 except for Potsdam where

albedo is set to 0.03 for whole year.

4.15 mim-cn1 model The UV irradiances have been modelled with the same algorithm STARneuro (Schwander et al.,

2002) and the same input parameters for aerosol and albedo as described in 4.11 for the mim-cn4

model, and thus the results will show the same problems already mentioned for mim-cn4.

The difference of cn1 against cn4 is the type of data used to describe the cloud effects. With respect

to the point that in older data global solar irradiance often is not be available and thus can not be used

as an input parameter, a version of the neural network (cn1) has been taken which describes the sky

conditions only by total cloud amount, again in addition to solar zenith angle and ground albedo

(Schwander et all., 2002). No global solar irradiance has been used and no information on the position

of the cloud with respect to the Sun, i.e. on shadow or not.

4.16 mim-wgt model In this model version the UV-dose is weighted with respect to sun shine duration. It is based on the

assumption that sun shine is one of the most dominant factors in UV irradiance. As a consequence,

the irradiance has been modelled, again with STARneuro (Schwander et all., 2002), for overcast con-

ditions and these results have been use for all the time when the Sun is masked by a cloud. For the

opposite condition, with the Sun is free of clouds, a sky with no clouds at all has been assumed and

the relevant data, again modelled with STARneuro, have been used. These two results have been

weighted by sun shine duration for each hour. Since both the irradiances for cloud free and for over-

cast conditions have been modelled with the neural network version of STAR, the results are affected

by the problems mention for model mim-cn4. The model mim-wgt does not use information on solar

irradiance or cloud optical depth.

17

4.17 uvwm model This model was developed at the Institute of Medical Physics and Biostatistics, University of Veteri-

nary Medicine, Vienna, in 1995 (Schauberger et al. 1996) as the core procedure of a world wide fore-

cast of the UV Index under clear skies. The model traces back to a suggestion of Diffey (1977) with

several improvements. The radiation model calculates the spectral irradiance at 17 discrete wave-

length between 297.5 nm and 400 nm with higher resolution in the UV-B than in the UV-A. Parame-

terization is done for the data base from Bener (1972) which was gained from spectral measurements

made over several years at Davos (46°48´N, 9°49´E, 1590 m above sea level). A detailed description

can be found in Schmalwieser et al. (2002). The model was validated in the past by a comparison to

other models (Köpke et al. 1998, Schmalwieser and Schauberger 2000, De Backer et al. 2001) as well

as by a comparison with measurements made at 4 continents for irradiance (Schmalwieser et al.

2002) and daily dose (Schmalwieser et al. 2005).

For clear sky conditions an aerosol pure atmosphere corresponding Bener’s data base was assumed.

Therefore, the amount of input parameters is restricted to date, time, geographical position, altitude,

TOC and the length of the day.

For real sky conditions the sun shine duration was applied without any site specific training. The daily

dose (H) was calculated by multiplying the clear sky daily dose (Hclearsky) by a modification factor for

sun shine duration (mf), whereas daily mean values of relative sun shine duration (sd) are used.

This modification factor mf is defined as:

mf = 0.60 + 0.40*sd

and applied as:

H = Hclearsky * mf

5 Results

5.1 Overview Figure 5.1 shows for each site (Bergen, Potsdam, Davos, Thessaloniki) and both years (1999, 2002)

the measured UV daily dose as function of the day. In addition the annual course is given as a curve

smoothed on the basis of local weighted regression (LOWES) using a window of 40 % of the days.

The figures show the annual course of UV dose, with high values in summer and low values in winter.

The maximum summer values increase with increasing solar elevation from Bergen to Thessaloniki,

but Davos shows the highest values due to high altitude and low aerosol amount. The large variability

from day to day, and between the two years, also clearly can be seen, which is due to variation in

cloudiness, but also in total ozone and the other atmospheric parameters.

18

5.1. The measured UV daily doses and their smoothed annual profile.

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19

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Thessaloniki 2002Correlation Coefficient (r)

In the following, the quality of the models is checked by comparing the modelled data against the

measured ones. Thus, it is assumed that the measured data are correct. But it should be kept in mind

that the uncertainty of UV irradiance measured with broad band instruments is at best in the order of

5 %, even in case of high quality assurance. Nevertheless, due to the use of measured data from

different sites, their uncertainty is of minor importance.

Measured daily UV-doses do not exist for all days, and also not all modeller calculated UV-doses for

all days, especially if one of the meteorological quantities used as input parameter was not available.

To perform the comparison of the modelled results on the basis of equal days, for the statistical analy-

sis and for the figures only those days have been used, which are available from all modellers. How-

ever, a comparison of the reduced data sets with data sets with all available data, individual for each

modeller, shows only very small differences in the statistical results.

To give an overview of the measured data, Fig. 5.1 shows the measured UV daily doses for all sta-

tions and the two years, together with their smoothed annual profile.

Figure 5.2 shows, as an example for the agreement between modelled and measured data, correla-

tion coefficients on a monthly base for Thessaloniki 2002.

Fig. 5.2 Thessaloniki 2002: Monthly distribution of the correlation coefficients modelled to measured

daily dose dependent on the model version

20

The values are given for all models and in addition for the assumption of persistence. For December

the correlation for persistence is not shown, because it is negative. But also for all the other months

can be seen that all models result are much better values than persistence and for other stations, with

more clouds than Thessaloniki, correlation for persistence even is worth than shown here. This is the

proof that modelling is necessary. Moreover can be seen already in Fig. 5.2 that the models using

measured values of solar global radiation result in better agreement with the measured UV data than

those models which do not use this information. This fact can easily be understood, since solar global

radiation contains information on the actual influence of clouds and aerosols, which only have to be

converted to the UV spectral range, while the other models use average values for the cloud effects.

This is the reason why a difference is made between these types of models, already in Tab. 4.1 and

again in the following presentation of the results.

5.2 Figures to compare modelled with measured daily doses To show the result of the modelling exercise, i.e. the agreement between modelled and measured

daily UV doses, the following type of figures have been made for each model, each station and both

years:

Scattering of modelled against measured data.

These data show the general agreement between modelled and measured UV data.

Absolute differences, modelled minus measured daily dose, as function of the day in the year

These values are of relevance with respect to the essential UV effects, because the dose is re-

sponsible for the impact of UV. The days with high UV dose during summer will dominate.

Relative differences, modelled minus measured divided by measured daily dose, as function of the

day in the year.

These values are of relevance for the quality of the models from the mathematical point of view.

Since here percentage deviations are considered, the winter values with low absolute values will

result in high deviations.

For all three versions used to present the agreement between measured and modelled UV doses, the

results are shown for each station (Bergen, Davos, Potsdam, Thessaloniki) and each year (2002,

1999) separately. Within the figures the results are presented for all models in the order given in

Tab. 4.1, starting with the 12 models using solar global irradiance and ending with the 4 models which

do not take this information into account.

21

5.3 Modelled against measured UV doses Figures 5.3.a to 5.3.h show modelled against measured data as green dots with bi-section line in

black and best fit straight line in red. The length of the cloud of dots represents the maximum dose at

the station, which increases from Bergen via Potsdam and Thessaloniki to Davos, as already shown in

Fig. 5.1.

The scattering of the points in Figs. 5.3 increases with increasing values, since the points show abso-

lute differences between measured and modelled doses. Another reason for scattering is cloudiness,

because here the largest variability occurs. This will be the explanation for the low scattering for Thes-

saloniki, even for high values during summer.

The results for 2002 and 1999 in general are similar, but differences can be seen for Bergen and for

Potsdam. For Bergen the agreement is worse for 2002 which may be explained by the degradation of

TOMS that has been used for the ozone data taken for modelling, and which was strongest for high

latitudes. The effect can clearly be seen at the highest doses for Bergen 2002, with deviations that are

nearly identical for all models. For Potsdam the agreement of the model dwdf_day is perfect for 1999

and much better than for 2002, but for all other models the agreement it is contrariwise. The reason

could be the UV_measurement at Potsdam. This has been made with a Brewer (See chapter 3) in

1999, and these data also have been used to train the neural network used by dwdf_day. In 2002 the

values used for comparison for Potsdam have been measured by a Bentham at shorter time steps and

thus better representativity of daily totals, with the consequences of different agreement mentioned

above.

Since the clear sky modelling generally is of high quality, besides uncertainties due to actual aerosol

and albedo properties, the agreement between measured and modelled data depends mainly on the

way how to take the cloud effects into account. Thus it is very good for the models that use solar

global irradiance as an input parameter to get a cloud modification factor CMF. Here both the effect of

shadow and cloud optical depth directly has been taken into account, which is not the case for models

that use cloud amount or sun shine duration. On the other hand, with respect to the time in the past

which should be modelled, the question arises whether cloud amount as an input parameter is more

easily available than global irradiance. The model mim_cn4 uses information of global irradiance as an

input parameter, but nevertheless shows systematically too high modelled doses. This effect can be

explained by the data used to train the neural network, which have been measured in an alpine valley

and apparently the effect of horizon has not been considered correctly. This also explains the effect

that the agreement of mim_cn4 is best for Davos.

22

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Fig. 5.3.a Modelled CIE-UV radiation daily dose as a function of measured value for Bergen 2002.

The red line represents linear dependence of modelled values on measured ones; black line repre-

sents ideal case when modelled values are equal to measured ones.

24

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Davos 2002daily CIE-UV doseimwm_day

UV

mod

( J /

m2 )

UVmeas ( J / m2 )

Davos 2002daily CIE-UV doseauth_day

UV

mod

( J /

m2 )

UVmeas ( J / m2 )

Davos 2002daily CIE-UV doseigfp_day

UV

mod

( J /

m2 )

UVmeas ( J / m2 )

Davos 2002daily CIE-UV dosefmi_day

UV

mod

( J /

m2 )

UVmeas ( J / m2 )

Davos 2002daily CIE-UV dosegsas_day

UV

mod

( J /

m2 )

UVmeas ( J / m2 )

Davos 2002daily CIE-UV dosedwdk_day

UV

mod

( J /

m2 )

UVmeas ( J / m2 )Davos 2002daily CIE-UV dosedwd_acc

UV

mod

( J /

m2 )

UVmeas ( J / m2 )

Davos 2002daily CIE-UV dosedwdf_day

UV

mod

( J /

m2 )

UVmeas ( J / m2 )

25

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UV

mod

( J /

m2 )

UVmeas ( J / m2 )Davos 2002daily CIE-UV doserivm_day

UV

mod

( J /

m2 )

UVmeas ( J / m2 )

Davos 2002daily CIE-UV doseboku_day

UV

mod

( J /

m2 )

UVmeas ( J / m2 )

Davos 2002daily CIE-UV dosemim_cn1

UV

mod

( J /

m2 )

UVmeas ( J / m2 )Davos 2002daily CIE-UV dosemim_wgt

UV

mod

( J /

m2 )

UVmeas ( J / m2 )

Davos 2002daily CIE-UV doseuvwm_day

UV

mod

( J /

m2 )

UVmeas ( J / m2 )

Davos 2002daily CIE-UV dosejrc_day

UV

mod

( J /

m2 )

UVmeas ( J / m2 )

Fig. 5.3.b Modelled CIE-UV radiation daily dose as a function of measured value for Davos 2002. The red line represents linear dependence of modelled values on measured ones; black line repre-sents ideal case when modelled values are equal to measured ones.

26

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Potsdam 2002daily CIE-UV doseimwm_day

UV

mod

( J /

m2 )

UVmeas ( J / m2 )

Potsdam 2002daily CIE-UV doseauth_day

UV

mod

( J /

m2 )

UVmeas ( J / m2 )

Potsdam 2002daily CIE-UV doseigfp_day

UV

mod

( J /

m2 )

UVmeas ( J / m2 )

Potsdam 2002daily CIE-UV dosefmi_day

UV

mod

( J /

m2 )

UVmeas ( J / m2 )

Potsdam 2002daily CIE-UV dosegsas_day

UV

mod

( J /

m2 )

UVmeas ( J / m2 )

Potsdam 2002daily CIE-UV dosedwdk_day

UV

mod

( J /

m2 )

UVmeas ( J / m2 )Potsdam 2002daily CIE-UV dosedwd_acc

UV

mod

( J /

m2 )

UVmeas ( J / m2 )

Potsdam 2002daily CIE-UV dosedwdf_day

UV

mod

( J /

m2 )

UVmeas ( J / m2 )

27

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UV

mod

( J /

m2 )

UVmeas ( J / m2 )Potsdam 2002daily CIE-UV doserivm_day

UV

mod

( J /

m2 )

UVmeas ( J / m2 )

Potsdam 2002daily CIE-UV doseboku_day

UV

mod

( J /

m2 )

UVmeas ( J / m2 )

Potsdam 2002daily CIE-UV dosemim_cn1

UV

mod

( J /

m2 )

UVmeas ( J / m2 )Potsdam 2002daily CIE-UV dosemim_wgt

UV

mod

( J /

m2 )

UVmeas ( J / m2 )

Potsdam 2002daily CIE-UV doseuvwm_day

UV

mod

( J /

m2 )

UVmeas ( J / m2 )

Potsdam 2002daily CIE-UV dosejrc_day

UV

mod

( J /

m2 )

UVmeas ( J / m2 )

Fig. 5.3.c Modelled CIE-UV radiation daily dose as a function of measured value for Potsdam 2002. The red line represents linear dependence of modelled values on measured ones; black line repre-sents ideal case when modelled values are equal to measured ones.

28

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Thessaloniki 2002daily CIE-UV doseimwm_day

UV

mod

( J /

m2 )

UVmeas ( J / m2 )

Thessaloniki 2002daily CIE-UV doseauth_day

UV

mod

( J /

m2 )

UVmeas ( J / m2 )

Thessaloniki 2002daily CIE-UV doseigfp_day

UV

mod

( J /

m2 )

UVmeas ( J / m2 )

Thessaloniki 2002daily CIE-UV dosefmi_day

UV

mod

( J /

m2 )

UVmeas ( J / m2 )

Thessaloniki 2002daily CIE-UV dosegsas_day

UV

mod

( J /

m2 )

UVmeas ( J / m2 )

Thessaloniki 2002daily CIE-UV dosedwd_acc

UV

mod

( J /

m2 )

UVmeas ( J / m2 )

Thessaloniki 2002daily CIE-UV dosedwdk_day

UV

mod

( J /

m2 )

UVmeas ( J / m2 )

29

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Thessaloniki 2002daily CIE-UV doserivm_day

UV

mod

( J /

m2 )

UVmeas ( J / m2 )

Thessaloniki 2002daily CIE-UV dosemim_cn4

UV

mod

( J /

m2 )

UVmeas ( J / m2 )

Thessaloniki 2002daily CIE-UV doseboku_day

UV

mod

( J /

m2 )

UVmeas ( J / m2 )


UV

mod

( J /

m2 )

UVmeas ( J / m2 )Thessaloniki 2002daily CIE-UV dosemim_wgt

UV

mod

( J /

m2 )

UVmeas ( J / m2 )

Thessaloniki 2002daily CIE-UV doseuvwm_day

UV

mod

( J /

m2 )

UVmeas ( J / m2 )

Thessaloniki 2002daily CIE-UV dosejrc_day

UV

mod

( J /

m2 )

UVmeas ( J / m2 )

Fig. 5.3.d Modelled CIE UV radiation daily dose as a function of measured value for Thessaloniki 2002. The red line represents linear dependence of modelled values on measured ones; black line represents ideal case when modelled values are equal to measured ones.

30

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Bergen 1999daily CIE-UV doseimwm_day

UV

mod

( J /

m2 )

UVmeas ( J / m2 )

Bergen 1999daily CIE-UV doseauth_day

UV

mod

( J /

m2 )

UVmeas ( J / m2 )

Bergen 1999daily CIE-UV doseigfp_day

UV

mod

( J /

m2 )

UVmeas ( J / m2 )

Bergen 1999daily CIE-UV dosefmi_day

UV

mod

( J /

m2 )

UVmeas ( J / m2 )

Bergen 1999daily CIE-UV dosegsas_day

UV

mod

( J /

m2 )

UVmeas ( J / m2 )

Bergen 1999daily CIE-UV dosedwdk_day

UV

mod

( J /

m2 )

Bergen 1999daily CIE-UV dosedwd_acc

UV

mod

( J /

m2 )

UVmeas ( J / m2 )

Bergen 1999daily CIE-UV dosedwdf_day

UV

mod

( J /

m2 )

UVmeas ( J / m2 )

31

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UV

mod

( J /

m2 )

UVmeas ( J / m2 )Bergen 1999daily CIE-UV doserivm_day

UV

mod

( J /

m2 )

UVmeas ( J / m2 )

Bergen 1999daily CIE-UV dosetobs_day

UV

mod

( J /

m2 )

UVmeas ( J / m2 )Bergen 1999daily CIE-UV doseboku_day

UV

mod

( J /

m2 )

UVmeas ( J / m2 )

Bergen 1999daily CIE-UV dosemim_cn1

UV

mod

( J /

m2 )

UVmeas ( J / m2 )daily CIE-UV doseBergen 1999daily CIE-UV dosemim_wgt

UV

mod

( J /

m2 )

UVmeas ( J / m2 )

Bergen 1999uvwm_day

UV

mod

( J /

m2 )

UVmeas ( J / m2 )

Bergen 1999daily CIE-UV dosejrc_day

UV

mod

( J /

m2 )

UVmeas ( J / m2 )

Fig. 5.3.e Modelled CIE UV radiation daily dose as a function of measured value for Bergen 1999. The red line represents linear dependence of modelled values on measured ones; black line repre-sents ideal case when modelled values are equal to measured ones.

32

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Davos 1999daily CIE-UV doseauth_day

UV

mod

( J /

m2 )

UVmeas ( J / m2 )

Davos 1999daily CIE-UV doseigfp_day

UV

mod

( J /

m2 )

UVmeas ( J / m2 )

Davos 1999daily CIE-UV dosefmi_day

UV

mod

( J /

m2 )

UVmeas ( J / m2 )

Davos 1999daily CIE-UV dosegsas_day

UV

mod

( J /

m2 )

UVmeas ( J / m2 )

Davos 1999daily CIE-UV dosedwdk_day

UV

mod

( J /

m2 )

UVmeas ( J / m2 )Davos 1999daily CIE-UV dosedwd_acc

UV

mod

( J /

m2 )

UVmeas ( J / m2 )

Davos 1999daily CIE-UV doseimwm_day

UV

mod

( J /

m2 )

UVmeas ( J / m2 )

Davos 1999daily CIE-UV dosedwdf_day

UV

mod

( J /

m2 )

UVmeas ( J / m2 )

33

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Davos 1999daily CIE-UV doserivm_day

UV

mod

( J /

m2 )

UVmeas ( J / m2 )


UV

mod

( J /

m2 )

UVmeas ( J / m2 )

Davos 1999daily CIE-UV doseboku_day

UV

mod

( J /

m2 )

UVmeas ( J / m2 )


UV

mod

( J /

m2 )

UVmeas ( J / m2 )Davos 1999daily CIE-UV dosemim_wgt

UV

mod

( J /

m2 )

UVmeas ( J / m2 )

Davos 1999daily CIE-UV doseuvwm_day

UV

mod

( J /

m2 )

UVmeas ( J / m2 )

Davos 1999daily CIE-UV dosejrc_day

UV

mod

( J /

m2 )

UVmeas ( J / m2 )

Fig. 5.3.f Modelled CIE UV radiation daily dose as a function of measured value for Davos 1999. The red line represents linear dependence of modelled values on measured ones; black line represents ideal case when modelled values are equal to measured ones.

34

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Potsdam 1999daily CIE-UV doseimwm_day

UV

mod

( J /

m2 )

UVmeas ( J / m2 )

Potsdam 1999daily CIE-UV doseauth_day

UV

mod

( J /

m2 )

UVmeas ( J / m2 )

Potsdam 1999daily CIE-UV doseigfp_day

UV

mod

( J /

m2 )

UVmeas ( J / m2 )

Potsdam 1999daily CIE-UV dosefmi_day

UV

mod

( J /

m2 )

UVmeas ( J / m2 )

Potsdam 1999daily CIE-UV dosedwd_acc

UV

mod

( J /

m2 )

UVmeas ( J / m2 )Potsdam 1999daily CIE-UV dosegsas_day

UV

mod

( J /

m2 )

UVmeas ( J / m2 )

Potsdam 1999daily CIE-UV dosedwdk_day

UV

mod

( J /

m2 )

UVmeas ( J / m2 )Potsdam 1999daily CIE-UV dosedwdf_day

UV

mod

( J /

m2 )

UVmeas ( J / m2 )

35

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Potsdam 1999daily CIE-UV doserivm_day

UV

mod

( J /

m2 )

UVmeas ( J / m2 )


UV

mod

( J /

m2 )

UVmeas ( J / m2 )

Potsdam 1999daily CIE-UV doseboku_day

UV

mod

( J /

m2 )

UVmeas ( J / m2 )


UV

mod

( J /

m2 )

UVmeas ( J / m2 )Potsdam 1999daily CIE-UV dosemim_wgt

UV

mod

( J /

m2 )

UVmeas ( J / m2 )

Potsdam 1999daily CIE-UV dosejrc_day

UV

mod

( J /

m2 )

UVmeas ( J / m2 )

Fig. 5.3.g Modelled CIE UV radiation daily dose as a function of measured value for Potsdam 1999. The red line represents linear dependence of modelled values on measured ones; black line repre-sents ideal case when modelled values are equal to measured ones.

36

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Thessaloniki 1999daily CIE-UV doseimwm_day

UV

mod

( J /

m2 )

UVmeas ( J / m2 )

Thessaloniki 1999daily CIE-UV doseauth_day

UV

mod

( J /

m2 )

UVmeas ( J / m2 )

Thessaloniki 1999daily CIE-UV doseigfp_day

UV

mod

( J /

m2 )

UVmeas ( J / m2 )

Thessaloniki 1999daily CIE-UV dosefmi_day

UV

mod

( J /

m2 )

UVmeas ( J / m2 )

Thessaloniki 1999daily CIE-UV dosegsas_day

UV

mod

( J /

m2 )

UVmeas ( J / m2 )

Thessaloniki 1999daily CIE-UV dosedwdk_day

UV

mod

( J /

m2 )

UVmeas ( J / m2 )Thessaloniki 1999daily CIE-UV dosedwd_acc

UV

mod

( J /

m2 )

UVmeas ( J / m2 )

37

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Thessaloniki 1999daily CIE-UV doserivm_day

UV

mod

( J /

m2 )

UVmeas ( J / m2 )


UV

mod

( J /

m2 )

UVmeas ( J / m2 )

Thessaloniki 1999daily CIE-UV doseboku_day

UV

mod

( J /

m2 )

UVmeas ( J / m2 )


UV

mod

( J /

m2 )

UVmeas ( J / m2 )Thessaloniki 1999daily CIE-UV dosemim_wgt

UV

mod

( J /

m2 )

UVmeas ( J / m2 )

Thessaloniki 1999daily CIE-UV doseuvwm_day

UV

mod

( J /

m2 )

UVmeas ( J / m2 )

Thessaloniki 1999daily CIE-UV dosejrc_day

UV

mod

( J /

m2 )

UVmeas ( J / m2 )

Fig. 5.3.h Modelled CIE UV radiation daily dose as a function of measured value for Thessaloniki 1999. The red line represents linear dependence of modelled values on measured ones; black line represents ideal case when modelled values are equal to measured ones.

38

The quality of the results of multiple scattering models dominantly results from the quality of the used

input parameters (Schwander et al., 1997). Besides the way to consider cloud effects, albedo and

aerosol are the relevant input parameters are. For aerosol very different methods have been used by

different models: climatological values, values measured at the site, values derived from visibility or

aerosol attenuation already has been taken into account by the retrieved CMF. The use of climatologi-

cal values for aerosol optical depth may result in a constant deviation, as it can be seen in the

dwd_acc results for Thessaloniki. Here an optical depth has been taken which is valid for a larger re-

gion and is lower than the value which seems to be valid for the measured data at the station in the

city, resulting in high modelled dose values.

5.4 Absolute differences Figures 5.4.a – 5.4.h show absolute differences, modelled minus measured daily doses, as function

of the day in the year. The figures are presented with respect to model, site and year, in the same

order than Fig. 5.3. If the value of the CMF is available, the data are separated by colour and symbol

for conditions with low (CMF > 0.75), medium (0.75 >= CMF > 0.50) and large attenuation due to

clouds (CMF<0.50). Values larger than 1000 J are presented close to the 1 kJ line and lower than –

1000 J close to –1 kJ, to have the same interval for all figures. The days 21 March and 21 September,

to separate the summer time, are shown with vertical lines.

As already mentioned, the possibility for large absolute differences increases with increasing daily

doses. Thus the differences for the winter time generally are lower, especially for Bergen and Pots-

dam, independent of the model. For Davos and Thessaloniki even in winter larger deviations occur, for

the first due to snow, for the latter due to rather high values due to higher sun even in winter. The dif-

ferent colour for different CMFs give the chance to look for wrong modelling of the cloud effects. The

strength and seasonality of the absolute deviations give additional possibilities to derive the reasons

for the deviations, which could be – beside general model problems – the use of wrong aerosol

amount and properties or a wrong albedo value. This has to be done by separating the results into

different categories, e.g. cloud free conditions, where specific effects may dominate.

39

Jan Feb Mrz Apr Mai Jun Jul Aug Sep Okt Nov Dez-1000

-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000

auth_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

UV

mod

- U

Vm

eas

(J /

m2 )

Bergen 2002daily CIE-UV dose

dwdk_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

UV

mod

- U

Vm

eas

(J /

m2 )


dwdk_acc

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

UV

mod

- U

Vm

eas

(J /

m2 )


fmi_day

all CMF

UV

mod

- U

Vm

eas

(J /

m2 )


gsas_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

UV

mod

- U

Vm

eas

(J /

m2 )


igfp_day

all CMF

UV

mod

- U

Vm

eas

(J /

m2 )


imwm_day

all CMF

UV

mod

- U

Vm

eas

(J /

m2 )


dwdf_day

all CMF

UV

mod

- U

Vm

eas

(J /

m2 )


40


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000

mim_cn4

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

UV

mod

- U

Vm

eas

(J /

m2 )


rivm_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

UV

mod

- U

Vm

eas

(J /

m2 )


tobs_day

all CMF

UV

mod

- U

Vm

eas

(J /

m2 )


boku_day

all CMF

UV

mod

- U

Vm

eas

(J /

m2 )


mim_cn1

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

UV

mod

- U

Vm

eas

(J /

m2 )


mim_wgt

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

UV

mod

- U

Vm

eas

(J /

m2 )


uvwm_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

UV

mod

- U

Vm

eas

(J /

m2 )


jrc_day

all CMF

U

Vm

od -

UV

mea

s(J

/ m

2 )Bergen 2002daily CIE-UV dose

Fig. 5.4.a Absolute differences between modelled and measured CIE-UV radiation daily doses calcu-

lated for Bergen 2002. If clear-sky CIE-UV radiation was available, the data points were sorted with

respect to cloud modification factor (CMF) calculated as a ratio between modelled and clear-sky CIE-

UV radiation daily dose.

41


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000

auth_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

UV

mod

- U

Vm

eas

(J /

m2 )

Davos 2002daily CIE-UV dose

dwdk_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

UV

mod

- U

Vm

eas

(J /

m2 )


dwdk_acc

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

UV

mod

- U

Vm

eas

(J /

m2 )


fmi_day

all CMF

UV

mod

- U

Vm

eas

(J /

m2 )


gsas_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

UV

mod

- U

Vm

eas

(J /

m2 )


igfp_day

all CMF

UV

mod

- U

Vm

eas

(J /

m2 )


imwm_day

all CMF

UV

mod

- U

Vm

eas

(J /

m2 )


dwdf_day

all CMF

UV

mod

- U

Vm

eas

(J /

m2 )


42


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000

mim_cn4

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

UV

mod

- U

Vm

eas

(J /

m2 )


rivm_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

UV

mod

- U

Vm

eas

(J /

m2 )


boku_day

all CMF

UV

mod

- U

Vm

eas

(J /

m2 )


mim_cn1

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

UV

mod

- U

Vm

eas

(J /

m2 )


mim_wgt

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

UV

mod

- U

Vm

eas

(J /

m2 )


uvwm_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

UV

mod

- U

Vm

eas

(J /

m2 )


jrc_day

all CMF

U

Vm

od -

UV

mea

s(J

/ m

2 )Davos 2002daily CIE-UV dose

Fig. 5.4.b Absolute differences between modelled and measured CIE-UV radiation daily doses cal-culated for Davos 2002. If clear-sky CIE-UV radiation was available, the data points are sorted with respect to cloud modification factor (CMF) calculated as a ratio between modelled and clear-sky CIE-UV radiation daily dose.

43


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000

dwdf_day

all CMF

UV

mod

- U

Vm

eas

(J /

m2 )

Potsdam 2002daily CIE-UV dose

auth_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

U

Vm

od -

UV

mea

s(J

/ m

2 )Potsdam 2002daily CIE-UV dose

dwdk_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

UV

mod

- U

Vm

eas

(J /

m2 )


dwdk_acc

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

UV

mod

- U

Vm

eas

(J /

m2 )


fmi_day

all CMF

UV

mod

- U

Vm

eas

(J /

m2 )


gsas_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

UV

mod

- U

Vm

eas

(J /

m2 )


igfp_day

all CMF

UV

mod

- U

Vm

eas

(J /

m2 )


imwm_day

all CMF

UV

mod

- U

Vm

eas

(J /

m2 )


45


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000

mim_cn4

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

UV

mod

- U

Vm

eas

(J /

m2 )


rivm_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

UV

mod

- U

Vm

eas

(J /

m2 )


boku_day

all CMF

UV

mod

- U

Vm

eas

(J /

m2 )


mim_cn1

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

UV

mod

- U

Vm

eas

(J /

m2 )


mim_wgt

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

UV

mod

- U

Vm

eas

(J /

m2 )


uvwm_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

UV

mod

- U

Vm

eas

(J /

m2 )


jrc_day

all CMF

UV

mod

- U

Vm

eas

(J /

m2 )


Fig. 5.4.c Absolute differences between modelled and measured CIE-UV radiation daily doses cal-culated for Potsdam 2002. If clear-sky CIE-UV radiation was available, the data points are sorted with respect to cloud modification factor (CMF) calculated as a ratio between modelled and clear-sky CIE-UV radiation daily dose.

46


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000

dwdk_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

UV

mod

- U

Vm

eas

(J /

m2 )

Thessaloniki 2002daily CIE-UV dose

auth_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

UV

mod

- U

Vm

eas

(J /

m2 )


dwdk_acc

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

UV

mod

- U

Vm

eas

(J /

m2 )


fmi_day

all CMF

UV

mod

- U

Vm

eas

(J /

m2 )


gsas_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

UV

mod

- U

Vm

eas

(J /

m2 )


igfp_day

all CMF

UV

mod

- U

Vm

eas

(J /

m2 )


imwm_day

all CMF

UV

mod

- U

Vm

eas

(J /

m2 )


47


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000

mim_cn4

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

UV

mod

- U

Vm

eas

(J /

m2 )


rivm_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

UV

mod

- U

Vm

eas

(J /

m2 )


boku_day

all CMF

UV

mod

- U

Vm

eas

(J /

m2 )


mim_cn1

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

UV

mod

- U

Vm

eas

(J /

m2 )


mim_wgt

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

UV

mod

- U

Vm

eas

(J /

m2 )


uvwm_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

UV

mod

- U

Vm

eas

(J /

m2 )


jrc_day

all CMF

U

Vm

od -

UV

mea

s(J

/ m

2 )Thessaloniki 2002daily CIE-UV dose

Fig. 5.4.d Absolute differences between modelled and measured CIE-UV radiation daily doses cal-culated for Thessaloniki 2002. If clear-sky CIE-UV radiation was available, the data points are sorted with respect to cloud modification factor (CMF) calculated as a ratio between modelled and clear-sky CIE-UV radiation daily dose.

48


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000

auth_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

U

Vm

od -

UV

mea

s(J

/ m


dwdk_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

UV

mod

- U

Vm

eas

(J /

m2 )


dwdk_acc

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

UV

mod

- U

Vm

eas

(J /

m2 )


fmi_day

all CMF

UV

mod

- U

Vm

eas

(J /

m2 )


gsas_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

UV

mod

- U

Vm

eas

(J /

m2 )


igfp_day

all CMF

UV

mod

- U

Vm

eas

(J /

m2 )


imwm_day

all CMF

UV

mod

- U

Vm

eas

(J /

m2 )

Bergen1999daily CIE-UV dose

dwdf_day

all CMF

UV

mod

- U

Vm

eas

(J /

m2 )


49


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000

mim_cn4

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

UV

mod

- U

Vm

eas

(J /

m2 )


rivm_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

UV

mod

- U

Vm

eas

(J /

m2 )


tobs_day

all CMF

UV

mod

- U

Vm

eas

(J /

m2 )


mim_cn1

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

UV

mod

- U

Vm

eas

(J /

m2 )


mim_wgt

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

UV

mod

- U

Vm

eas

(J /

m2 )


uvwm_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

UV

mod

- U

Vm

eas

(J /

m2 )


jrc_day

all CMF

U

Vm

od -

UV

mea

s(J

/ m


boku_day

all CMF

UV

mod

- U

Vm

eas

(J /

m2 )


Fig. 5.4.e Absolute differences between modelled and measured CIE-UV radiation daily doses cal-culated for Bergen 1999. If clear-sky CIE-UV radiation was available, the data points are sorted with respect to cloud modification factor (CMF) calculated as a ratio between modelled and clear-sky CIE-UV radiation daily dose.

50


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000

auth_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

U

Vm

od -

UV

mea

s(J

/ m


dwdk_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

UV

mod

- U

Vm

eas

(J /

m2 )


dwdk_acc

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

UV

mod

- U

Vm

eas

(J /

m2 )


fmi_day

all CMF

UV

mod

- U

Vm

eas

(J /

m2 )


gsas_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

UV

mod

- U

Vm

eas

(J /

m2 )


igfp_day

all CMF

UV

mod

- U

Vm

eas

(J /

m2 )


imwm_day

all CMF

UV

mod

- U

Vm

eas

(J /

m2 )


dwdf_day

all CMF

UV

mod

- U

Vm

eas

(J /

m2 )


51


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000

mim_cn4

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

UV

mod

- U

Vm

eas

(J /

m2 )


rivm_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

UV

mod

- U

Vm

eas

(J /

m2 )


boku_day

all CMF

UV

mod

- U

Vm

eas

(J /

m2 )


mim_cn1

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

UV

mod

- U

Vm

eas

(J /

m2 )


mim_wgt

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

UV

mod

- U

Vm

eas

(J /

m2 )


uvwm_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

UV

mod

- U

Vm

eas

(J /

m2 )


jrc_day

all CMF

U

Vm

od -

UV

mea

s(J

/ m


Fig. 5.4.f Absolute differences between modelled and measured CIE-UV radiation daily doses cal-culated for Davos 1999. If clear-sky CIE-UV radiation was available, the data points are sorted with respect to cloud modification factor (CMF) calculated as a ratio between modelled and clear-sky CIE-UV radiation daily dose.

52


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000

auth_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

UV

mod

- U

Vm

eas

(J /

m2 )


dwdk_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

UV

mod

- U

Vm

eas

(J /

m2 )


dwdk_acc

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

UV

mod

- U

Vm

eas

(J /

m2 )


fmi_day

all CMF

UV

mod

- U

Vm

eas

(J /

m2 )


gsas_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

UV

mod

- U

Vm

eas

(J /

m2 )


igfp_day

all CMF

UV

mod

- U

Vm

eas

(J /

m2 )


imwm_day

all CMF

UV

mod

- U

Vm

eas

(J /

m2 )


dwdf_day

all CMF

UV

mod

- U

Vm

eas

(J /

m2 )


53


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000

mim_cn4

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

UV

mod

- U

Vm

eas

(J /

m2 )


rivm_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

UV

mod

- U

Vm

eas

(J /

m2 )


boku_day

all CMF

UV

mod

- U

Vm

eas

(J /

m2 )


mim_cn1

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

UV

mod

- U

Vm

eas

(J /

m2 )


mim_wgt

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

UV

mod

- U

Vm

eas

(J /

m2 )


jrc_day

all CMF

U

Vm

od -

UV

mea

s(J

/ m

2 )Potsdam 1999daily CIE-UV dose

Fig. 5.4.g Absolute differences between modelled and measured CIE-UV radiation daily doses cal-culated for Potsdam 1999. If clear-sky CIE-UV radiation was available, the data points are sorted with respect to cloud modification factor (CMF) calculated as a ratio between modelled and clear-sky CIE-UV radiation daily dose.

54


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000

auth_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

U

Vm

od -

UV

mea

s(J

/ m


dwdk_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

UV

mod

- U

Vm

eas

(J /

m2 )


dwdk_acc

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

UV

mod

- U

Vm

eas

(J /

m2 )


fmi_day

all CMF

UV

mod

- U

Vm

eas

(J /

m2 )


gsas_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

UV

mod

- U

Vm

eas

(J /

m2 )


igfp_day

all CMF

UV

mod

- U

Vm

eas

(J /

m2 )


imwm_day

all CMF

UV

mod

- U

Vm

eas

(J /

m2 )


55


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000


-800

-600

-400

-200

0

200

400

600

800

1000

mim_cn4

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

UV

mod

- U

Vm

eas

(J /

m2 )


boku_day

all CMF

UV

mod

- U

Vm

eas

(J /

m2 )


uvwm_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

UV

mod

- U

Vm

eas

(J /

m2 )


mim_cn1

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

UV

mod

- U

Vm

eas

(J /

m2 )


mim_wgt

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

UV

mod

- U

Vm

eas

(J /

m2 )


rivm_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

UV

mod

- U

Vm

eas

(J /

m2 )


jrc_day

all CMF

U

Vm

od -

UV

mea

s(J

/ m


Fig. 5.4.h Absolute differences between modelled and measured CIE-UV radiation daily doses cal-culated for Thessaloniki 1999. If clear-sky CIE-UV radiation was available, the data points are sorted with respect to cloud modification factor (CMF) calculated as a ratio between modelled and clear-sky CIE-UV radiation daily dose

56

5.5 Relative differences Figures 5.5.a to 5.5.h show relative deviations, i.e. modelled minus measured daily dose divided by

measured daily dose, as function of the day in the year. Again the model, sites and years are given in

the same order than Fig. 5.3 and again the resulting values are separated for different ranges of CMFs

if this information is available. Values larger than 1 are presented near 1 and lower than –1 near –1.

The days 21. March and 21. September again are shown with vertical lines to separate the summer

time.

In general, in comparison with the absolute deviations, the relative deviations increase for winter time

and are reduced for summer. For some models and sites, the agreement mostly is better than 20%.

57

Jan Feb Mrz Apr Mai Jun Jul Aug Sep Okt Nov Dez-1,0

-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0

auth_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

(U

Vm

od -

UV

mea

s) /

UV

mea

sBergen 2002daily CIE-UV dose

dwdk_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


dwdk_acc

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


fmi_day

all CMF

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


gsas_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


igfp_day

all CMF

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


imwm_day

all CMF

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


dwdf_day

all CMF

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


58


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0

mim_cn4

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

(UV

mod

- U

Vm

eas)

/UV

mea

s


rivm_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


tobs_day

all CMF

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


boku_day

all CMF

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


mim_cn1

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


mim_wgt

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


uvwm_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

(UV

mod

- U

Vm

eas)

/ UV

mea

s


jrc_day

all CMF

(U

Vm

od -

UV

mea

s) /

UV

mea


Fig. 5.5.a Relative differences between modelled and measured CIE-UV radiation daily doses calcu-lated for Bergen 2002. If clear-sky CIE-UV radiation was available, the data points are sorted with respect to cloud modification factor (CMF) calculated as a ratio between modelled and clear-sky CIE-UV radiation daily dose.

59


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0

auth_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

(U

Vm

od -

UV

mea

s) /

UV

mea

sDavos 2002daily CIE-UV dose

dwdk_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


dwdk_acc

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


fmi_day

all CMF

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


gsas_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


igfp_day

all CMF

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


imwm_day

all CMF

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


dwdf_day

all CMF

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


60


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0

mim_cn4

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

(UV

mod

- U

Vm

eas)

/UV

mea

s


rivm_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


boku_day

all CMF

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


mim_cn1

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


mim_wgt

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


uvwm_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

(UV

mod

- U

Vm

eas)

/ UV

mea

s


jrc_day

all CMF

(U

Vm

od -

UV

mea

s) /

UV

mea


Fig. 5.5.b Relative differences between modelled and measured CIE-UV radiation daily doses calcu-lated for Davos 2002. If clear-sky CIE-UV radiation was available, the data points are sorted with re-spect to cloud modification factor (CMF) calculated as a ratio between modelled and clear-sky CIE-UV radiation daily dose.

61


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0

auth_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

(U

Vm

od -

UV

mea

s) /

UV

mea

sPotsdam 2002daily CIE-UV dose

dwdk_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


fmi_day

all CMF

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


gsas_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


igfp_day

all CMF

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


imwm_day

all CMF

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


dwdk_acc

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


dwdf_day

all CMF

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


62


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0

mim_cn4

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

(UV

mod

- U

Vm

eas)

/UV

mea

s


rivm_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


boku_day

all CMF

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


mim_cn1

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


mim_wgt

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


uvwm_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

(UV

mod

- U

Vm

eas)

/ UV

mea

s


jrc_day

all CMF

(U

Vm

od -

UV

mea

s) /

UV

mea


Fig. 5.5.c Relative differences between modelled and measured CIE-UV radiation daily doses calcu-lated for Potsdam 2002. If clear-sky CIE-UV radiation was available, the data points are sorted with respect to cloud modification factor (CMF) calculated as a ratio between modelled and clear-sky CIE-UV radiation daily dose.

63


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0

auth_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

(U

Vm

od -

UV

mea

s) /

UV

mea

sThessaloniki 2002daily CIE-UV dose

dwdk_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


dwdk_acc

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


fmi_day

all CMF

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


gsas_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


igfp_day

all CMF

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


imwm_day

all CMF

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


64


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0

rivm_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


mim_cn4

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

(UV

mod

- U

Vm

eas)

/UV

mea

s


boku_day

all CMF

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


mim_cn1

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


mim_wgt

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


uvwm_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

(UV

mod

- U

Vm

eas)

/ UV

mea

s


jrc_day

all CMF

(U

Vm

od -

UV

mea

s) /

UV

mea


Fig. 5.5.d Relative differences between modelled and measured CIE-UV radiation daily doses calcu-lated for Thessaloniki 2002. If clear-sky CIE-UV radiation was available, the data points are sorted with respect to cloud modification factor (CMF) calculated as a ratio between modelled and clear-sky CIE-UV radiation daily dose.

65


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0

auth_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


dwdk_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


dwdk_acc

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


fmi_day

all CMF

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


gsas_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


igfp_day

all CMF

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


imwm_day

all CMF

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


dwdf_day

all CMF

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


66


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0

mim_cn4

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

(UV

mod

- U

Vm

eas)

/UV

mea

s


rivm_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


tobs_day

all CMF

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


boku_day

all CMF

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


mim_cn1

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


mim_wgt

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


uvwm_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

(UV

mod

- U

Vm

eas)

/ UV

mea

s


jrc_day

all CMF

(U

Vm

od -

UV

mea

s) /

UV

mea


Fig. 5.5.e Relative differences between modelled and measured CIE-UV radiation daily doses calcu-lated for Bergen 1999. If clear-sky CIE-UV radiation was available, the data points are sorted with respect to cloud modification factor (CMF) calculated as a ratio between modelled and clear-sky CIE-UV radiation daily dose.

67


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0

auth_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

(U

Vm

od -

UV

mea

s) /

UV

mea


dwdk_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


dwdk_acc

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


fmi_day

all CMF

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


gsas_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


igfp_day

all CMF

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


imwm_day

all CMF

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


dwdf_day

all CMF

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


68


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0

mim_cn4

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

(UV

mod

- U

Vm

eas)

/UV

mea

s


rivm_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


boku_day

all CMF

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


mim_cn1

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


mim_wgt

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


uvwm_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

(UV

mod

- U

Vm

eas)

/ UV

mea

s


jrc_day

all CMF

(U

Vm

od -

UV

mea

s) /

UV

mea


Fig. 5.5.f Relative differences between modelled and measured CIE-UV radiation daily doses calcu-lated for Davos 1999. If clear-sky CIE-UV radiation was available, the data points are sorted with re-spect to cloud modification factor (CMF) calculated as a ratio between modelled and clear-sky CIE-UV radiation daily dose.

69


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0

auth_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


dwdk_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


dwdk_acc

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


fmi_day

all CMF

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


gsas_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


igfp_day

all CMF

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


imwm_day

all CMF

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


dwdf_day

all CMF

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


70


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0

rivm_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


mim_cn4

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

(UV

mod

- U

Vm

eas)

/UV

mea

s


boku_day

all CMF

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


mim_cn1

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


mim_wgt

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


jrc_day

all CMF

(U

Vm

od -

UV

mea

s) /

UV

mea


Fig. 5.5.g Relative differences between modelled and measured CIE-UV radiation daily doses calcu-lated for Potsdam 1999. If clear-sky CIE-UV radiation was available, the data points are sorted with respect to cloud modification factor (CMF) calculated as a ratio between modelled and clear-sky CIE-UV radiation daily dose.

71


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0

auth_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

(U

Vm

od -

UV

mea

s) /

UV

mea


dwdk_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


dwdk_acc

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


fmi_day

all CMF

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


gsas_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


igfp_day

all CMF

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


imwm_day

all CMF

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


72


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0


-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0

mim_cn4

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

(UV

mod

- U

Vm

eas)

/UV

mea

s


rivm_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


boku_day

all CMF

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


mim_cn1

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


mim_wgt

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

(UV

mod

- U

Vm

eas)

/ U

Vm

eas


uvwm_day

CMF > 0.75 0.75 > CMF > 0.50 CMF < 0.50

(UV

mod

- U

Vm

eas)

/ UV

mea

s


jrc_day

all CMF

(U

Vm

od -

UV

mea

s) /

UV

mea


Fig. 5.5.h Relative differences between modelled and measured CIE-UV radiation daily doses calcu-lated for Thessaloniki 1999. If clear-sky CIE-UV radiation was available, the data points are sorted with respect to cloud modification factor (CMF) calculated as a ratio between modelled and clear-sky CIE-UV radiation daily dose.

73

5.6 Statistics of modelled against measured UV doses To get detailed information with respect to the agreement of modelled and measured data, for each

site, each year, and each model version the statistical quantities have been calculated which are

shown in Tab. 5.1. The parameters standard deviation of measurements “st_deviat_x”, of model re-

sults “st_deviat_y”, and the correlation coefficient “r” allow to construct a Taylor diagram (Taylor 2001).

The definition of skill score 1 and 2 are taken from the description of the Taylor diagram. R0 is the

maximum, potentially realisable correlation, and is set to 1. Skill score 2 slightly increases the penalty

for low correlation. They result in different weighting of correlation coefficient and centred pattern root

mean square (≡ standard deviation of bias).

The results for all models and quantities mentioned in Tab. 5.1 are given in Tab. 5.2 to 5.10 for the

different sites and years. Tab. 5.2 to 5.9 summarize the results for each station (Bergen, Davos, Pots-

dam, Thessaloniki) and both years (1999, 2002) separately based on the absolute values. Tab. 5.10

combines all sites and the two years. Since the measured daily dose of a site depends on latitude and

the meteorological specifics in Tab. 5.10 both the measured and modelled absolute values are nor-

malized by the yearly average of the measured daily dose. This shall ensure a balanced weight of the

sites in comparison. The tables confirm the above derived results by statistical numbers.

74

Tab. 5.1 Statistical quantities

Symbol Definition Dimension

pair_number Number (n) of measured and modelled pairs of values 1

avg_meas__x Arithmetic average of measurements (xm):

xm = n-1 · Σ xi J m-2

st_deviat_x Standard deviation of measurements (σx):

σx = sqrt( (n – 1)-1 · Σ (xi – xm )2 ) J m-2

avg_meas_y Arithmetic average of modelled values (ym):

ym = n-1 · Σ yi J m-2

st_deviat_y Standard deviation of measurements (σy):

σy = sqrt( (n – 1)-1 · Σ (yi - ym )2 ) J m-2

bias__x-y Arithmetic average of difference measured – modelled value:

bias = n-1 · Σ (xi - yi) J m-2

st-dev_bias Standard deviation of bias (σb):

σb = sqrt( (n – 1)-1 · Σ ( (xi - xim )- (yi - ym ) )2 ) J m-2

rms__error Root mean square error (rms):

rms = sqrt( (n – 1)-1 · Σ (xi - yi )2 ) J m-2

corr_coef_r Correlation coefficient (r):

r = σx-1 · σy -1 · (n – 1)-1 · Σ (xi - xm ) · (yi - ym )

1

Linear regression : y = a + b · x

reg_coeff_a Regression coefficient « a » J m-2

reg_coeff_b Regression coefficient « b » 1

var_reduc_%

Reduction of variance compared to persistence:

var_reduc = 100 · [ 1 – (rmsmod / rmspers)2 ]

(pers = persistence = yesterday’s measurement)

%

skillscore1 skillscore1 = 4 · (1 + R) / [(σ0 + 1 / σ0 ) · (1 + R0)]

σ0 = σy / σx, R0 set to 1. 1

skillscore2 skillscore2 = 4 · (1 + R)4 / [(σ0 + 1 / σ0 ) · (1 + R0)4]

σ0 = σy / σx, R0 set to 1. 1

75

Tab. 5.2 Bergen 1999: Statistical comparison of measured and modelled daily erythemal UV doses based on equal days for all model versions

institute /

version p

airs

x =

ave

rage

mea

sure

d

sta

ndar

d

dev

iatio

n x

y =

ave

rage

mod

elle

d

sta

ndar

d

dev

iatio

n y

bia

s =

y-x

sta

ndar

d de

v.

bia

s

roo

t mea

n

squ

are

err.

cor

rela

tion

coe

ffici

ent

reg

ress

ion

coe

ffici

ent a

reg

ress

ions

coe

ffici

ent b

var

ianc

e

red

uctio

n

ski

ll so

re 1

ski

ll so

re 2

J m-2 J m-2 J m-2 J m-2 J m-2 J m-2 J m-2 J m-2 %

persistence 283. 1027.8 968.9 1024.3 965.1 -3.5 558.2 558.2 0.8334 171.05 0.830 0.0 0.9167 0.7062

auth_day 283. 1027.8 968.9 1058.5 961.0 30.6 96.8 101.6 0.9950 44.14 0.987 96.7 0.9974 0.9900

dwdf_day 283. 1027.8 968.9 1005.0 932.9 -22.9 99.1 101.7 0.9953 20.03 0.958 96.7 0.9962 0.9892

dwdk_day 283. 1027.8 968.9 1071.8 983.3 44.0 84.2 95.0 0.9964 32.51 1.011 97.1 0.9980 0.9926

dwdk_acc 283. 1027.8 968.9 1092.3 997.9 64.5 67.3 93.3 0.9981 35.84 1.028 97.2 0.9982 0.9953

fmi_day 283. 1027.8 968.9 1056.9 985.0 29.1 50.1 58.0 0.9988 13.22 1.015 98.9 0.9991 0.9974

gsas_day 283. 1027.8 968.9 1050.5 995.9 22.6 81.1 84.2 0.9970 -2.76 1.025 97.7 0.9977 0.9932

igfp_day 283. 1027.8 968.9 1014.9 951.6 -12.9 84.8 85.8 0.9963 9.23 0.978 97.6 0.9978 0.9922

imwm_day 283. 1027.8 968.9 981.7 894.4 -46.1 101.9 111.9 0.9972 35.63 0.920 96.0 0.9922 0.9881

jrc_day 283. 1027.8 968.9 1010.5 963.8 -17.4 103.3 104.8 0.9943 -6.13 0.989 96.5 0.9971 0.9886

mimg_cn4 283. 1027.8 968.9 1303.4 1162.0 275.5 217.4 351.3 0.9956 76.14 1.194 60.4 0.9655 0.9592

rivm_day 283. 1027.8 968.9 1000.1 935.7 -27.7 89.7 93.9 0.9962 11.34 0.962 97.2 0.9969 0.9911

tobs_day 283. 1027.8 968.9 1138.6 999.4 110.7 191.7 221.5 0.9815 97.99 1.012 84.3 0.9898 0.9626

boku_day 283. 1027.8 968.9 1021.1 974.7 -6.8 315.1 315.2 0.9475 41.41 0.953 68.1 0.9737 0.8989

mim_cn1 283. 1027.8 968.9 1373.9 1190.1 346.1 335.1 482.1 0.9725 146.04 1.195 25.4 0.9457 0.9073

mim_wgt 283. 1027.8 968.9 1133.4 1022.8 105.6 230.3 253.5 0.9747 75.90 1.029 79.4 0.9845 0.9476

uvwm_day 283. 1027.8 968.9 1004.5 832.2 -23.3 314.0 314.8 0.9505 165.37 0.816 68.2 0.9530 0.8840

76

Tab. 5.3 Bergen 2002: Statistical comparison of measured and modelled daily erythemal UV doses based on equal days for all model versions

institute /

version p

airs

x =

ave

rage

mea

sure

d

sta

ndar

d

dev

iatio

n x

y =

ave

rage

mod

elle

d

sta

ndar

d

dev

iatio

n y

bia

s =

y-x

sta

ndar

d de

v.

bia

s

roo

t mea

n

squ

are

err.

cor

rela

tion

coe

ffici

ent

reg

ress

ion

coe

ffici

ent a

reg

ress

ions

coe

ffici

ent b

var

ianc

e

red

uctio

n

ski

ll so

re 1

ski

ll so

re 2


persistence 322. 901.5 924.5 899.0 919.5 -2.5 566.3 566.4 0.8114 171.50 0.807 0.0 0.9057 0.6728

auth_day 322. 901.5 924.5 954.1 952.0 52.7 111.7 123.5 0.9933 31.99 1.023 95.2 0.9958 0.9859

dwdf_day 322. 901.5 924.5 908.0 920.0 6.5 98.7 98.9 0.9943 16.02 0.989 96.9 0.9971 0.9886

dwdk_day 322. 901.5 924.5 971.1 957.9 69.6 101.8 123.4 0.9948 41.97 1.031 95.3 0.9961 0.9884

dwdk_acc 322. 901.5 924.5 993.3 979.1 91.8 100.9 136.5 0.9960 42.42 1.055 94.2 0.9947 0.9888

fmi_day 322. 901.5 924.5 954.5 967.5 53.0 86.6 101.6 0.9968 14.11 1.043 96.8 0.9964 0.9917

gsas_day 322. 901.5 924.5 931.2 956.6 29.8 90.5 95.3 0.9959 2.22 1.031 97.2 0.9968 0.9908

igfp_day 322. 901.5 924.5 918.2 946.1 16.7 98.5 100.0 0.9947 0.56 1.018 96.9 0.9968 0.9889

imwm_day 322. 901.5 924.5 892.2 892.0 -9.2 87.1 87.6 0.9960 25.88 0.961 97.6 0.9967 0.9908

jrc_day 322. 901.5 924.5 892.4 916.7 -9.1 115.5 115.8 0.9922 5.49 0.984 95.8 0.9960 0.9844

mimg_cn4 322. 901.5 924.5 1181.6 1172.9 280.1 269.1 388.7 0.9951 43.63 1.262 52.9 0.9431 0.9362

rivm_day 322. 901.5 924.5 898.5 910.4 -3.0 95.3 95.4 0.9947 15.48 0.980 97.2 0.9971 0.9892

tobs_day 322. 901.5 924.5 963.4 931.5 61.9 173.4 184.1 0.9826 70.95 0.990 89.4 0.9912 0.9656

boku_day 322. 901.5 924.5 697.6 775.4 -203.8 331.1 389.0 0.9390 -12.30 0.788 52.8 0.9401 0.8567

mim_cn1 322. 901.5 924.5 1243.5 1210.2 342.0 341.6 483.8 0.9843 81.95 1.289 27.0 0.9236 0.9020

mim_wgt 322. 901.5 924.5 1010.1 1010.6 108.6 238.7 262.3 0.9735 50.79 1.064 78.5 0.9789 0.9405

uvwm_day 322. 901.5 924.5 901.4 844.5 -0.1 291.9 291.9 0.9495 119.47 0.867 73.4 0.9668 0.8955

77

Tab. 5.4 Davos 1999: Statistical comparison of measured and modelled daily erythemal UV doses based on equal days for all model versions

institute /

version p

airs

x =

ave

rage

mea

sure

d

sta

ndar

d

dev

iatio

n x

y =

ave

rage

mod

elle

d

sta

ndar

d

dev

iatio

n y

bia

s =

y-x

sta

ndar

d de

v.

bia

s

roo

t mea

n

squ

are

err.

cor

rela

tion

coe

ffici

ent

reg

ress

ion

coe

ffici

ent a

reg

ress

ions

coe

ffici

ent b

var

ianc

e

red

uctio

n

ski

ll so

re 1

ski

ll so

re 2


persistence 221. 2414.9 1583.4 2317.7 1585.9 -97.3 1093.2 1097.5 0.7621 474.41 0.763 0.0 0.8810 0.6025

auth_day 221. 2414.9 1583.4 2397.0 1556.9 -17.9 177.1 178.0 0.9938 37.26 0.977 97.4 0.9966 0.9873

dwdf_day 221. 2414.9 1583.4 2461.8 1593.1 46.8 224.1 228.9 0.9901 56.22 0.996 95.6 0.9950 0.9802

dwdk_day 221. 2414.9 1583.4 2353.1 1462.6 -61.8 190.8 200.6 0.9953 132.97 0.919 96.7 0.9914 0.9844

dwdk_acc 221. 2414.9 1583.4 2422.7 1525.2 7.8 120.4 120.6 0.9977 101.97 0.961 98.8 0.9974 0.9940

fmi_day 221. 2414.9 1583.4 2413.7 1540.2 -1.2 139.4 139.5 0.9964 73.16 0.969 98.4 0.9974 0.9921

gsas_day 221. 2414.9 1583.4 2360.3 1525.2 -54.6 222.0 228.7 0.9905 56.29 0.954 95.7 0.9939 0.9797

igfp_day 221. 2414.9 1583.4 2326.2 1490.5 -88.7 276.0 289.9 0.9857 85.46 0.928 93.0 0.9892 0.9681

imwm_day 221. 2414.9 1583.4 2376.3 1511.8 -38.6 190.4 194.3 0.9935 85.52 0.949 96.9 0.9946 0.9849

jrc_day 221. 2414.9 1583.4 1928.5 1279.9 -486.4 364.5 608.7 0.9900 -3.85 0.800 69.2 0.9512 0.9370

mimg_cn4 221. 2414.9 1583.4 2385.5 1600.0 -29.4 298.4 299.9 0.9825 -11.87 0.993 92.5 0.9911 0.9653

rivm_day 221. 2414.9 1583.4 2313.3 1507.1 -101.6 180.7 207.4 0.9944 27.64 0.946 96.4 0.9948 0.9864

boku_day 221. 2414.9 1583.4 2677.1 2016.0 262.1 731.3 777.1 0.9455 -230.20 1.204 49.9 0.9182 0.8452

mim_cn1 221. 2414.9 1583.4 2172.1 1562.6 -242.9 647.4 691.7 0.9154 -9.42 0.903 60.3 0.9575 0.8411

mim_wgt 221. 2414.9 1583.4 1981.4 1436.4 -433.6 490.7 655.5 0.9518 -103.80 0.863 64.3 0.9667 0.8985

uvwm_day 221. 2414.9 1583.4 2541.1 1641.9 126.2 539.6 554.2 0.9447 175.57 0.980 74.5 0.9711 0.8927

78

Tab. 5.5 Davos 2002: Statistical comparison of measured and modelled daily erythemal UV doses based on equal days for all model versions

institute /

version p

airs

x =

ave

rage

mea

sure

d

sta

ndar

d

dev

iatio

n x

y =

ave

rage

mod

elle

d

sta

ndar

d

dev

iatio

n y

bia

s =

y-x

sta

ndar

d de

v.

bia

s

roo

t mea

n

squ

are

err.

cor

rela

tion

coe

ffici

ent

reg

ress

ion

coe

ffici

ent a

reg

ress

ions

coe

ffici

ent b

var

ianc

e

red

uctio

n

ski

ll so

re 1

ski

ll so

re 2


persistence 261. 2283.8 1537.5 2192.0 1570.9 -91.7 947.0 951.5 0.8146 291.33 0.832 0.0 0.9069 0.6773

auth_day 261. 2283.8 1537.5 2299.7 1568.5 16.0 179.8 180.6 0.9935 -14.99 1.014 96.4 0.9963 0.9867

dwdf_day 261. 2283.8 1537.5 2300.0 1574.7 16.2 194.9 195.5 0.9924 -21.46 1.017 95.8 0.9957 0.9844

dwdk_day 261. 2283.8 1537.5 2253.5 1456.2 -30.2 159.3 162.1 0.9958 99.51 0.943 97.1 0.9950 0.9887

dwdk_acc 261. 2283.8 1537.5 2317.8 1512.8 34.1 112.4 117.5 0.9974 76.52 0.981 98.5 0.9984 0.9946

fmi_day 261. 2283.8 1537.5 2307.6 1529.7 23.9 133.7 135.8 0.9962 43.99 0.991 98.0 0.9981 0.9924

gsas_day 261. 2283.8 1537.5 2232.6 1511.2 -51.2 183.4 190.5 0.9929 3.79 0.976 96.0 0.9962 0.9856

igfp_day 261. 2283.8 1537.5 2064.4 1401.6 -219.4 303.5 374.7 0.9829 17.92 0.896 84.5 0.9830 0.9580

imwm_day 261. 2283.8 1537.5 2276.5 1523.9 -7.2 118.1 118.3 0.9971 19.53 0.988 98.5 0.9985 0.9941

jrc_day 261. 2283.8 1537.5 1878.0 1310.4 -405.7 309.0 510.6 0.9891 -47.27 0.843 71.2 0.9696 0.9538

mimg_cn4 261. 2283.8 1537.5 2485.6 1692.3 201.9 276.6 342.7 0.9899 -2.75 1.090 87.0 0.9858 0.9710

rivm_day 261. 2283.8 1537.5 2236.6 1525.1 -47.2 187.8 193.6 0.9925 -11.87 0.985 95.9 0.9962 0.9850

boku_day 261. 2283.8 1537.5 2162.6 1483.3 -121.1 330.4 352.0 0.9767 10.70 0.942 86.3 0.9871 0.9530

mim_cn1 261. 2283.8 1537.5 2261.5 1652.3 -22.2 449.5 450.0 0.9628 -101.61 1.035 77.6 0.9763 0.9229

mim_wgt 261. 2283.8 1537.5 2101.8 1537.1 -182.0 320.9 369.0 0.9782 -131.75 0.978 85.0 0.9891 0.9571

uvwm_day 261. 2283.8 1537.5 2441.9 1694.3 158.1 500.5 525.0 0.9566 34.30 1.054 69.6 0.9691 0.9075

79

Tab. 5.6 Potsdam 1999: Statistical comparison of measured and modelled daily erythemal UV doses based on equal days for all model versions

institute /

version p

airs

x =

ave

rage

mea

sure

d

sta

ndar

d

dev

iatio

n x

y =

ave

rage

mod

elle

d

sta

ndar

d

dev

iatio

n y

bia

s =

y-x

sta

ndar

d de

v.

bia

s

roo

t mea

n

squ

are

err.

cor

rela

tion

coe

ffici

ent

reg

ress

ion

coe

ffici

ent a

reg

ress

ions

coe

ffici

ent b

var

ianc

e

red

uctio

n

ski

ll so

re 1

ski

ll so

re 2


pers_day 214 1288.9 1235.2 1254.8 1222.5 -34.1 589.8 590.8 0.8849 125.97 0.876 0.0 0.9423 0.7888

auth_day 214 1288.9 1235.2 1317.6 1297.1 28.7 185.6 187.8 0.9904 -22.95 1.040 89.9 0.9929 0.9787

dwdf_day 214 1288.9 1235.2 1293.3 1243.8 4.4 46.4 46.6 0.9993 -3.69 1.006 99.4 0.9996 0.9986

dwdk_day 214 1288.9 1235.2 1161.6 1094.9 -127.3 212.8 248.1 0.9905 29.85 0.878 82.4 0.9810 0.9671

dwdk_acc 214 1288.9 1235.2 1185.1 1127.5 -103.9 186.1 213.3 0.9917 18.25 0.905 87.0 0.9876 0.9754

fmi_day 214 1288.9 1235.2 1211.7 1157.6 -77.2 142.9 162.5 0.9950 9.85 0.932 92.4 0.9933 0.9858

gsas_day 214 1288.9 1235.2 1214.6 1195.0 -74.3 170.3 185.8 0.9907 -20.81 0.959 90.1 0.9943 0.9805

igfp_day 214 1288.9 1235.2 1096.0 1132.2 -192.9 252.5 318.0 0.9810 -63.01 0.899 71.0 0.9830 0.9553

imwm_day 214 1288.9 1235.2 1155.0 1076.7 -134.0 222.7 260.1 0.9908 41.79 0.864 80.6 0.9769 0.9634

jrc_day 214 1288.9 1235.2 1190.1 1174.3 -98.8 182.3 207.4 0.9898 -22.84 0.941 87.7 0.9924 0.9773

mim_cn4 214 1288.9 1235.2 1458.9 1414.9 170.0 271.3 320.4 0.9882 -0.11 1.132 70.6 0.9760 0.9588

rivm_day 214 1288.9 1235.2 1192.9 1148.8 -96.1 159.1 186.0 0.9937 1.61 0.924 90.1 0.9916 0.9823

boku_day 214 1288.9 1235.2 988.8 1110.7 -300.1 285.4 414.6 0.9760 -142.35 0.878 50.7 0.9769 0.9421

mim_cn1 214 1288.9 1235.2 1416.2 1386.3 127.3 313.9 338.8 0.9779 1.57 1.098 67.1 0.9759 0.9439

mim_wgt 214 1288.9 1235.2 1390.9 1353.4 102.0 287.1 304.7 0.9795 7.57 1.073 73.4 0.9816 0.9517

80

Tab. 5.7 Potsdam 2002: Statistical comparison of measured and modelled daily erythemal UV doses based on equal days for all model versions

institute /

version p

airs

x =

ave

rage

mea

sure

d

sta

ndar

d

dev

iatio

n x

y =

ave

rage

mod

elle

d

sta

ndar

d

dev

iatio

n y

bia

s =

y-x

sta

ndar

d de

v.

bia

s

roo

t mea

n

squ

are

err.

cor

rela

tion

coe

ffici

ent

reg

ress

ion

coe

ffici

ent a

reg

ress

ions

coe

ffici

ent b

var

ianc

e

red

uctio

n

ski

ll so

re 1

ski

ll so

re 2


persistence 303. 1343.9 1118.8 1328.3 1112.4 -15.6 633.0 633.2 0.8390 207.22 0.834 0.0 0.9195 0.7149

auth_day 303. 1343.9 1118.8 1408.0 1193.1 64.1 140.8 154.8 0.9946 -17.41 1.061 94.0 0.9932 0.9852

dwdf_day 303. 1343.9 1118.8 1375.8 1139.0 32.0 231.3 233.5 0.9792 36.29 0.997 86.4 0.9893 0.9587

dwdk_day 303. 1343.9 1118.8 1297.1 1053.0 -46.8 138.9 146.6 0.9937 40.28 0.935 94.6 0.9932 0.9837

dwdk_acc 303. 1343.9 1118.8 1334.0 1093.8 -9.8 108.3 108.8 0.9955 26.23 0.973 97.0 0.9972 0.9904

fmi_day 303. 1343.9 1118.8 1369.2 1132.8 25.4 124.2 126.7 0.9940 16.71 1.006 96.0 0.9968 0.9879

gsas_day 303. 1343.9 1118.8 1367.0 1156.7 23.2 115.0 117.3 0.9954 -16.02 1.029 96.6 0.9966 0.9898

igfp_day 303. 1343.9 1118.8 1243.0 1096.9 -100.8 195.4 219.9 0.9846 -54.29 0.965 87.9 0.9919 0.9693

imwm_day 303. 1343.9 1118.8 1329.9 1062.8 -14.0 156.1 156.7 0.9911 64.75 0.941 93.9 0.9929 0.9797

jrc_day 303. 1343.9 1118.8 1327.4 1128.3 -16.4 121.4 122.5 0.9942 -19.87 1.003 96.3 0.9970 0.9884

mimg_cn4 303. 1343.9 1118.8 1659.6 1363.6 315.7 280.1 422.4 0.9939 31.60 1.211 55.5 0.9589 0.9502

rivm_day 303. 1343.9 1118.8 1350.8 1144.9 6.9 125.4 125.6 0.9941 -16.28 1.017 96.1 0.9965 0.9878

boku_day 303. 1343.9 1118.8 1150.5 1114.7 -193.4 225.4 297.2 0.9796 -161.11 0.976 78.0 0.9898 0.9599

mim_cn1 303. 1343.9 1118.8 1603.5 1324.3 259.6 315.7 409.0 0.9806 43.62 1.161 58.3 0.9627 0.9350

mim_wgt 303. 1343.9 1118.8 1516.9 1315.4 173.1 296.6 343.6 0.9832 -36.57 1.156 70.6 0.9661 0.9420

uvwm_day 303. 1343.9 1118.8 1354.6 1084.3 10.7 366.5 366.6 0.9451 123.64 0.916 66.5 0.9716 0.8938

81

Tab. 5.8 Thessaloniki 1999: Statistical comparison of measured and modelled daily erythemal UV doses based on equal days for all model versions

institute /

version p

airs

x =

ave

rage

mea

sure

d

sta

ndar

d

dev

iatio

n x

y =

ave

rage

mod

elle

d

sta

ndar

d

dev

iatio

n y

bia

s =

y-x

sta

ndar

d de

v.

bia

s

roo

t mea

n

squ

are

err.

cor

rela

tion

coe

ffici

ent

reg

ress

ion

coe

ffici

ent a

reg

ress

ions

coe

ffici

ent b

var

ianc

e

red

uctio

n

ski

ll so

re 1

ski

ll so

re 2


persistence 252. 2515.4 1463.7 2476.8 1497.9 -38.6 544.4 545.8 0.9327 75.78 0.955 0.0 0.9658 0.8715

auth_day 252. 2515.4 1463.7 2507.1 1430.6 -8.3 144.1 144.3 0.9953 59.99 0.973 93.0 0.9971 0.9901

dwdk_day 252. 2515.4 1463.7 2619.0 1418.7 103.6 157.4 188.6 0.9945 194.14 0.964 88.1 0.9963 0.9881

dwdk_acc 252. 2515.4 1463.7 2702.3 1477.3 186.9 139.3 233.4 0.9956 174.70 1.005 81.7 0.9977 0.9911

fmi_day 252. 2515.4 1463.7 2477.6 1367.0 -37.8 171.2 175.3 0.9950 140.00 0.929 89.7 0.9929 0.9855

gsas_day 252. 2515.4 1463.7 2530.7 1467.2 15.3 161.4 162.2 0.9939 24.49 0.996 91.2 0.9970 0.9879

igfp_day 252. 2515.4 1463.7 2471.2 1446.4 -44.2 205.6 210.3 0.9901 10.07 0.978 85.1 0.9949 0.9802

imwm_day 252. 2515.4 1463.7 2516.3 1442.4 0.9 125.8 125.8 0.9964 46.45 0.982 94.7 0.9980 0.9925

jrc_day 252. 2515.4 1463.7 2563.3 1430.3 47.9 149.4 156.9 0.9949 117.69 0.972 91.7 0.9969 0.9894

mimg_cn4 252. 2515.4 1463.7 2967.0 1714.9 451.6 346.2 569.8 0.9887 53.11 1.158 -9.0 0.9698 0.9535

rivm_day 252. 2515.4 1463.7 2662.8 1511.1 147.4 152.1 212.0 0.9953 78.07 1.028 84.9 0.9966 0.9896

boku_day 252. 2515.4 1463.7 2457.6 1532.8 -57.8 349.4 354.2 0.9739 -107.72 1.020 57.9 0.9848 0.9467

mim_cn1 252. 2515.4 1463.7 3062.6 1789.4 547.2 467.0 720.2 0.9786 53.04 1.196 -74.1 0.9504 0.9203

mim_wgt 252. 2515.4 1463.7 2681.9 1587.6 166.5 353.5 390.9 0.9764 17.91 1.059 48.7 0.9817 0.9474

uvwm_day 252. 2515.4 1463.7 2455.4 1329.3 -60.0 351.6 356.7 0.9729 232.92 0.884 57.3 0.9773 0.9381

82

Tab. 5.9 Thessaloniki 2002: Statistical comparison of measured and modelled daily erythemal UV doses based on equal days for all model versions

institute /

version p

airs

x =

ave

rage

mea

sure

d

sta

ndar

d

dev

iatio

n x

y =

ave

rage

mod

elle

d

sta

ndar

d

dev

iatio

n y

bia

s =

y-x

sta

ndar

d de

v.

bia

s

roo

t mea

n

squ

are

err.

cor

rela

tion

coe

ffici

ent

reg

ress

ion

coe

ffici

ent a

reg

ress

ions

coe

ffici

ent b

var

ianc

e

red

uctio

n

ski

ll so

re 1

ski

ll so

re 2


persistence 257. 2409.5 1334.5 2342.3 1389.2 -67.3 713.9 717.1 0.8633 176.72 0.899 0.0 0.9302 0.7522

auth_day 257. 2409.5 1334.5 2401.7 1311.4 -7.8 120.1 120.4 0.9960 43.21 0.979 97.2 0.9977 0.9918

dwdk_day 257. 2409.5 1334.5 2524.3 1289.9 114.8 138.2 179.8 0.9950 206.88 0.962 93.7 0.9964 0.9890

dwdk_acc 257. 2409.5 1334.5 2601.4 1338.2 191.9 135.7 235.3 0.9949 197.57 0.998 89.2 0.9974 0.9897

fmi_day 257. 2409.5 1334.5 2464.2 1269.5 54.7 154.4 163.8 0.9942 185.18 0.946 94.8 0.9946 0.9860

gsas_day 257. 2409.5 1334.5 2416.5 1347.9 7.0 130.6 130.8 0.9953 -5.80 1.005 96.7 0.9976 0.9906

igfp_day 257. 2409.5 1334.5 2378.0 1312.9 -31.6 228.9 231.0 0.9852 42.55 0.969 89.6 0.9923 0.9704

imwm_day 257. 2409.5 1334.5 2410.3 1327.2 0.7 121.8 121.9 0.9958 23.95 0.990 97.1 0.9979 0.9916

jrc_day 257. 2409.5 1334.5 2475.6 1323.2 66.1 125.2 141.6 0.9956 96.99 0.987 96.1 0.9977 0.9912

mimg_cn4 257. 2409.5 1334.5 3069.3 1544.9 659.7 303.2 727.2 0.9884 312.07 1.144 -2.8 0.9732 0.9564

rivm_day 257. 2409.5 1334.5 2551.7 1379.0 142.2 133.1 194.9 0.9957 72.33 1.029 92.6 0.9968 0.9904

boku_day 257. 2409.5 1334.5 2318.0 1436.8 -91.6 352.3 364.1 0.9704 -199.48 1.045 74.2 0.9798 0.9369

mim_cn1 257. 2409.5 1334.5 3169.5 1615.7 760.0 416.0 867.7 0.9782 315.75 1.184 -46.4 0.9538 0.9230

mim_wgt 257. 2409.5 1334.5 2726.3 1504.5 316.8 385.1 499.1 0.9703 90.45 1.094 51.6 0.9711 0.9284

uvwm_day 257. 2409.5 1334.5 2366.5 1193.5 -43.0 361.0 363.6 0.9653 286.16 0.863 74.3 0.9705 0.9209

83

Tab. 5.10 All sites and years summarised: Statistical comparison of measured and modelled daily erythemal UV doses.

Measured and modelled input has been normalised per site and per year to the yearly average of measurements.

institute /

version

pai

rs

x =

ave

rage

mea

sure

d

sta

ndar

d

dev

iatio

n x

y =

ave

rage

mod

elle

d

sta

ndar

d

dev

iatio

n y

bia

s =

y-x

sta

ndar

d de

v.

bia

s

roo

t mea

n

squ

are

err.

cor

rela

tion

coe

ffici

ent

reg

ress

ion

coe

ffici

ent a

reg

ress

ions

coe

ffici

ent b

var

ianc

e

red

uctio

n

ski

ll so

re 1

ski

ll so

re 2

1 1 1 1 1 1 1 1 %

persistence 2113 1.0000 0.8039 0.9794 0.8052 -0.0196 0.4588 0.4592 0.8374 0.14 0.839 0.0 0.9187 0.7124

auth_day 2113 1.0000 0.8039 1.0203 0.8216 0.0212 0.0987 0.1009 0.9929 0.01 1.015 95.2 0.996 0.9853

dwdf_day 1604 0.9988 0.8657 1.0051 0.8643 0.0063 0.1110 0.1112 0.9918 0.02 0.99 94.1 0.9959 0.9836

dwdk_day 2113 1.0000 0.8039 1.0079 0.7848 0.0088 0.1095 0.1099 0.9908 0.04 0.967 94.3 0.9948 0.9811

dwdk_acc 2113 1.0000 0.8039 1.0344 0.8073 0.0354 0.0988 0.1049 0.9925 0.04 0.997 94.8 0.9962 0.9850

fmi_day 2113 1.0000 0.8039 1.0106 0.8036 0.0115 0.0836 0.0844 0.9946 0.02 0.994 96.6 0.9973 0.9892

gsas_day 2113 1.0000 0.8039 0.9996 0.8133 0.0005 0.0917 0.0917 0.9936 0.00 1.005 96.0 0.9967 0.9872

igfp_day 2113 1.0000 0.8039 0.9549 0.7854 -0.0441 0.1324 0.1396 0.9864 -0.01 0.964 90.8 0.9927 0.9725

imwm_day 2113 1.0000 0.8039 0.9775 0.7618 -0.0216 0.1010 0.1032 0.9931 0.04 0.941 94.9 0.9937 0.9835

jrc_day 2113 1.0000 0.8039 0.9483 0.7797 -0.0508 0.1371 0.1462 0.9855 -0.01 0.956 89.9 0.9918 0.9704

mimg_cn4 2113 1.0000 0.8039 1.1933 0.9599 0.1943 0.2182 0.2922 0.9849 0.02 1.176 59.5 0.9619 0.9403

rivm_day 2113 1.0000 0.8039 0.9953 0.7920 -0.0037 0.0971 0.0971 0.9927 0.02 0.978 95.5 0.9961 0.9853

tobs_day 605 0.9974 0.9840 1.0841 1.0019 0.0868 0.1900 0.2089 0.9819 0.09 1.000 79.3 0.9906 0.9639

boku_day 2113 1.0000 0.8039 0.9173 0.7926 -0.0818 0.2650 0.2774 0.945 -0.01 0.932 63.5 0.9723 0.8943

mim_cn1 2113 1.0000 0.8039 1.1918 0.9758 0.1928 0.3075 0.3629 0.9586 0.03 1.163 37.5 0.9434 0.886

mim_wgt 2113 1.0000 0.8039 1.0527 0.8753 0.0536 0.2279 0.2342 0.9667 0.00 1.053 74.0 0.9763 0.9283

uvwm_day 1899 0.9990 0.7849 1.0069 0.7400 0.0079 0.2496 0.2497 0.9481 0.11 0.894 70.4 0.9707 0.8971

84

6 Evaluation of the Model Performance using Taylor Diagrams

Results presented in previous sections show that the models are able to mimic the measurements.

Objective of this section is to identify a group of models providing the best agreement between mod-

elled and measured UV daily doses. This has been done in terms of model-measurement correlation

together with equality of root mean square (RMS) values calculated from the modelled and observed

data, as it has been proposed by Taylor (2001).

The analyzed time series of UV daily doses have a strong annual course with the maximum in late

spring/early summer and minimum in winter (Fig. 5.1). Thus, any model simulating such behaviour will

yield a high correlations coefficient and close RMS value to observed one. As a consequence, for bet-

ter distinguishing between models’ performances the annual pattern has been removed from the ana-

lyzed time series. Therefore the smoothed annual course is extracted for each year and station meas-

ured data using the locally weighted scatter (LOWES) smoothing techniques, shown in Fig. 5.1 as red

curve. Next the deviations from the smoothed curves are calculated both for measured and each of the

modelled time series. These absolute deviations are equal to those already shown in Figs. 5.4, since

both for modelled and measured data the measured annual course has been subtracted. They still

have a seasonal course, as already discussed, since larger deviations (in absolute units) are possible

in seasons with normally high UV doses.

Also the relative deviations have been examined by Taylor diagrams. Here the values may be some

what different than the relative deviations shown in Figs. 5.5 since they are obtained by the normaliza-

tion of the absolute deviations using the smoothed annual values as the norm. Again the seasonality is

not completely removed from the time series of the relative variations as the model’s accuracy and

quality of the measurements are usually poorer in winter time. For the analysis of the relative devia-

tions, values of daily doses below 5 J/m² have been omitted. For lower values the smoothing proce-

dure may result in unrealistic results, division by zero becomes possible. Variation of this acceptance

criteria, e.g. to 1 J/m², may vary the correlation, but the differences are not significant.

The Taylor diagram (Taylor, 2001) has been developed for description and visualization of a corre-

spondence between various simulations of a measured variable. According to the methodology of Tay-

lor, a model performance relative to measurements is visualized by a point on a polar plot. The azi-

muth angle φ pertaining to this point is such that cos(φ)= correlation coefficient (coefficient of determi-

nation) between modelled and measured data. The distance from the origin is given as the ratio of the

standard deviation of the model values to that of the observed data. An ideal model (being in a full

agreement with measurements) is marked by the point with coordinates φ=0 and radius=1. It means

the correlation coefficient is equal to 1 and modelled and measured variations have the same ampli-

tude. Thus, in case many models have to be compared the best model is chosen as the model having

minimum distance between its point on the Taylor diagram and the ideal model point, (0, 1). Points

with the same distance to the point (0,1) are marked as blue circles in Figs. 6.1 to 6.3, which show the

results of the modelling exercise. The red lines give locations of models’ points with the same correla-

tion coefficients relative to the measured sample. The pertaining value of the correlation coefficient is

85

adjacent to this line. The red dashed circles give location of the models’ points with the same values of

the normalized standard deviation

The model performance (for each station and year) taking into account the absolute and relative devia-

tions is visualized in Fig. 6.1 and Fig. 6.2, respectively, with similar plots for all sites and both years. In

each figure always the resulting Taylor-points are given for all models, shown with the letter mentioned

in the figure. Similar pattern is to be seen in the plots. A group of points gathers closely to the ideal

model point (0,1) and some points appear away from this point. If figures 6.1 and 6.2 are inspected

separately, i.e. for each of the two data categories absolute and relative differences, the configuration

of the points remains practically unchanged for all sites. Usually the models not using global radiation

as a proxy for the cloud attenuation effects stay more away than other model points. Deviations for

specific models and stations already have been discussed with respect to Figs. 5.3. In general can be

seen that the deviations for 2002 for all sites are lower than for 1999, which could be a hint on im-

proved measuring quality or better quality of the input data ozone which has been used by all model-

lers.

But by detailed inspection of Figs. 6.1 and 6.2, differences can be seen between absolute and relative

deviations. For example models marked by letters B and C do not still belong to the group with the best

performance in Fig. 6.2. The results in Fig. 6.1a are mostly determined by spring/summer data be-

cause of large absolute (relative) deviations in that period, and the results in Fig. 6.2 by winter because

of larger deviations in this period.

86

Fig. 6.1 Taylor Diagrams for the absolute deviations

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.30.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

0.1

0.2

0.3

0.5

0.7

1.0

0.1 0.2 0.3 0.4 0.5 0.60.7

0.8

0.9

0.95

0.99

A BCD

EFGHI

J

K

L

MN

OP

Normalized Standard Deviation

BERGEN - 1999

Nor

mal

ized

Sta

ndar

d D

evia

tion

E - fmiF - gsas

J - mim_cn4K - rivmL - tobs

N - mim_cn1O - mim_wgtP - uvwm

A - authB - dwdk_dayC - dwdk_accD - dwdf

G - igfpasH - imwmI - jrc

M - boku

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.30.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

0.1

0.2

0.3

0.5

0.7

1.0

0.1 0.2 0.3 0.4 0.5 0.60.7

0.8

0.9

0.95

0.99A

BC

D

E

FG H

IJ

K

MN

O

P


DAVOS -1999

Nor

mal

ized

Sta

ndar

d D

evia

tion

E - fmiF - gsas

J - mim_cn4K - rivm




M - boku

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.30.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

0.1

0.2

0.3

0.5

0.7

1.0

0.1 0.2 0.3 0.4 0.5 0.60.7

0.8

0.9

0.95

0.99ABC

DE

FG

H

IJ

K

M

N

O

P


DAVOS -2002

Nor

mal

ized

Sta

ndar

d D

evia

tion

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.30.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

0.1

0.2

0.3

0.5

0.7

1.0

0.1 0.2 0.3 0.4 0.5 0.60.7

0.8

0.9

0.95

0.99ABC

D

EFGH I

J

K

M

NO

P


Potsdam - 2002

Nor

mal

ized

Sta

ndar

d D

evia

tion

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.30.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

0.1

0.2

0.3

0.5

0.7

1.0

0.1 0.2 0.3 0.4 0.5 0.60.7

0.8

0.9

0.95

0.99ABCEF

G

HI

J

K

M

N

O

P


Thessaloniki - 1999

Nor

mal

ized

Sta

ndar

d D

evia

tion

E - fmiF - gsas

J - mim_cn4K - rivm


A - authB - dwdk_dayC - dwdk_acc


M - boku

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.30.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

0.1

0.2

0.3

0.5

0.7

1.0

0.1 0.2 0.3 0.4 0.5 0.60.7

0.8

0.9

0.95

0.99A BCE

FG

H I

J

K

MN O

P


Thessaloniki - 2002

Nor

mal

ized

Sta

ndar

d D

evia

tion

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.30.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

0.1

0.2

0.3

0.5

0.7

1.0

0.1 0.2 0.3 0.4 0.5 0.60.7

0.8

0.9

0.95

0.99A BCDEFGH

I

J

K

L

MN

O

P


BERGEN - 2002

Nor

mal

ized

Sta

ndar

d D

evia

tion

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.30.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

0.1

0.2

0.3

0.5

0.7

1.0

0.1 0.2 0.3 0.4 0.5 0.60.7

0.8

0.9

0.95

0.99

ABC

D

EF

GH I

J

K

MN

O


Potsdam - 1999

Nor

mal

ized

Sta

ndar

d D

evia

tion

E - fmiF - gsas

J - mim_cn4K - rivm

N - mim_cn1O - mim_wgt



M - boku

P -uvwm (2002)

87

Fig. 6.2 Taylor Diagrams for the relative variations

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.30.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

0.1

0.2

0.3

0.5

0.7

1.0

0.1 0.2 0.3 0.4 0.5 0.60.7

0.8

0.9

0.95

0.99

A

BC

DE FG HI

J

K

LM

NO

P


BERGEN - 1999

Nor

mal

ized

Sta

ndar

d D

evia

tion

E - fmiF - gsas





M - boku

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.30.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

0.1

0.2

0.3

0.5

0.7

1.0

0.1 0.2 0.3 0.4 0.5 0.60.7

0.8

0.9

0.95

0.99

A

BCDEF

GH

I

J

K

L

MNO

P


BERGEN - 2002

Nor

mal

ized

Sta

ndar

d D

evia

tion

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.30.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

0.1

0.2

0.3

0.5

0.7

1.0

0.1 0.2 0.3 0.4 0.5 0.60.7

0.8

0.9

0.95

0.99

ABC

DEF

G

H

IJK

M

N

O

P


DAVOS -2002

Nor

mal

ized

Sta

ndar

d D

evia

tion

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.30.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

0.1

0.2

0.3

0.5

0.7

1.0

0.1 0.2 0.3 0.4 0.5 0.60.7

0.8

0.9

0.95

0.99ABC

D

EF

G

H IJK

M

NO

P


Potsdam - 2002

Nor

mal

ized

Sta

ndar

d D

evia

tion

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.30.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

0.1

0.2

0.3

0.5

0.7

1.0

0.1 0.2 0.3 0.4 0.5 0.60.7

0.8

0.9

0.95

0.99A

BCD

EF

GH

I

J

K

M

N

OP


DAVOS -1999

Nor

mal

ized

Sta

ndar

d D

evia

tion

E - fmiF - gsas

J - mim_cn4K - rivm




M - boku

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.30.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

0.1

0.2

0.3

0.5

0.7

1.0

0.1 0.2 0.3 0.4 0.5 0.60.7

0.8

0.9

0.95

0.99A

BC

E

FG

HIJ

K

MN O

P


Thessaloniki - 1999

Nor

mal

ized

Sta

ndar

d D

evia

tion

E - fmiF - gsas

J - mim_cn4K - rivm


A - authB - dwdk_dayC - dwdk_acc


M - boku

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.30.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

0.1

0.2

0.3

0.5

0.7

1.0

0.1 0.2 0.3 0.4 0.5 0.60.7

0.8

0.9

0.95

0.99A

BCE

F

GH I

J

K

M N O

P


Thessaloniki - 2002

Nor

mal

ized

Sta

ndar

d D

evia

tion

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.30.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

0.1

0.2

0.3

0.5

0.7

1.0

0.1 0.2 0.3 0.4 0.5 0.60.7

0.8

0.9

0.95

0.99

A

BC

D

EF

GH

IJ

K

M NO


Potsdam - 1999

Nor

mal

ized

Sta

ndar

d D

evia

tion

E - fmiF - gsas

J - mim_cn4K - rivm

N - mim_cn1O - mim_wgtP - uvwm (2002)



M - boku

88

The question remains if the Taylor diagram is able to provide the best model in term of the smallest

distance to the ideal case point, as it is, for example in the 1999 Davos data model C in both figures. A

group of other model points is not far away from this point. Thus, a test is necessary to evaluate how

significant are the differences between locations of the points of the different models in the diagram.

For estimation of the range of the model point distance to the ideal model point the resampling meth-

odology has been used. The distribution of the distance is obtained from the moving-block bootstrap

technique (Efron and Tibshirani, 1993). The bootstrap belongs to the category of nonparametric statis-

tical methods. It is able to simulate the probability distribution of any statistics without making any as-

sumptions related to the temporal or spatial covariance structure of the variables. The data simply are

resampled, with replacement, from the original record. The most challenging problem is to resample

the records in such way, as to preserve the temporal structure of the original time series. The time

series of absolute and relative daily deviations used here can be approximated as a simple autore-

gressive process with small serial correlations. Thus, sequences of 5-day data blocks will be approxi-

mately independent. Resampling of blocks of data is known as the moving-blocks bootstrap first intro-

duced by Kunsch [1989].

Radiation data show a large seasonality (spring/summer and winter maxima in the absolute and rela-

tive deviations data, respectively). So it is assumed that possible blocks for replacement are within ±1

month relative to the removed original block. It is rather an arbitrary assumption but gives ~ 1060 possi-

ble representatives of the original time series for each year. Both the original modelled and measured

time series are bootstrapped using the same sequences of the blocks. So a sample of 1000 pairs of

the annual time series has been analysed. For each model-measurement pair the data necessary for

the point on the Taylor diagram has been calculated. i.e. the normalized standard deviation and the

correlation coefficient and finally the distance to the (0,1). Sensitivity studies show that much larger

samples (10,000 and 100,000) provide similar results. The sample of the model-observation distances

is sorted in ascending order and point No. 25 and No. 975 define the 95% confidence range for the

distance calculated from the original data. The results are shown for all models and sites both for the

absolute deviations (Tab. 6.1 for 1999 and Tab. 6.2 for 2002) and the relative deviations (Tab. 6.3 for

1999 and Tab. 6.4 for 2002).

Analyzing the numbers in these tables show statistically significant differences between models’

performances for different stations and years. Even single model can behave differently for different

stations, which is especially the case for 1999. Many models using the global radiation data (auth,

dwdk_day, dwdk_acc, fmi, gsas, imgw, rivm) perform always better than those using other proxies for

the cloud effects.

89

Tab. 6.1 . Taylor model-measurement distance derived from the absolute deviations for selected sta-tion and model in 1999. The 95% confidence limit is shown in the parentheses.

Tab. 6.2. Taylor model-measurement distance derived from the absolute deviations for the selected station and model in 2002. The 95% confidence limit is shown in the parentheses.

Model Bergen Davos Potsdam Thessaloniki

auth 0.23(0.21,0.25) 0.27(0.23,0.32) 0.24(0.21,0.27) 0.21(0.16,0.26)

dwdk_day 0.21(0.18,0.24) 0.23(0.20,0.27) 0.24(0.21,0.27) 0.24(0.19,0.30)

dwdk_acc 0.21(0.17,0.24) 0.17(0.14,0.20) 0.19(0.16,0.22) 0.23(0.19,0.29)

dwdf 0.20(0.15,0.25) 0.28(0.24,0.33) 0.40(0.34,0.46) -

fmi 0.18(0.14,0.21) 0.20(0.16,0.24) 0.21(0.17,0.25) 0.26(0.20,0.34)

gsas 0.19(0.16,0.21) 0.27(0.23,0.31) 0.20(0.17,0.23) 0.22(0.18,0.28)

igfp 0.20(0.18,0.23) 0.44(0.40,0.48) 0.33(0.30,0.37) 0.39(0.31,0.48)

imwm 0.18(0.14,0.22) 0.18(0.15,0.21) 0.27(0.23,0.29) 0.21(0.16,0.27)

jrc 0.24(0.19,0.28) 0.45(0.39,0.52) 0.21(0.18,0.24) 0.22(0.18,0.27)

mim_cn4 0.53(0.48,0.59) 0.41(0.36,0.47) 0.47(0.43,0.52) 0.51(0.41,0.66)

rivm 0.20(0.17,0.22) 0.28(0.24,0.32) 0.21(0.18,0.25) 0.23(0.18,0.29)

tobs 0.35(0.30,0.41) - - -

boku 0.67(0.59,0.76) 0.48(0.42,0.53) 0.38(0.34,0.44) 0.59(0.45,0.78)

mim_cn1 0.68(0.61,0.77) 0.66(0.52,0.79) 0.53(0.47,0.61) 0.70(0.59,0.89)

mim_wgt 0.48(0.43,0.54) 0.47(0.42,0.54) 0.50(0.44,0.57) 0.65(0.48,0.85)

uvwm 0.59(0.52,0.65) 0.73(0.65,0.81) 0.61(0.56,0.67) 0.61(0.53,0.73)


auth 0.18(0.16,0.21) 0.22(0.19,0.26) 0.39(0.32,0.45) 0.31(0.26,0.39)

dwdk_day 0.16(0.13,0.18) 0.24(0.20,0.28) 0.44(0.36,0.52) 0.35(0.28,0.43)

dwdk_acc 0.13(0.10,0.15) 0.16(0.13,0.19) 0.38(0.31,0.48) 0.31(0.24,0.39)

dwdf 0.18(0.15,0.22) 0.28(0.23,0.32) 0.10(0.08,0.15) -

fmi 0.09(0.08,0.11) 0.18(0.15,0.22) 0.30(0.24,0.37) 0.37(0.30,0.47)

gsas 0.15(0.13,0.17) 0.28(0.23,0.34) 0.35(0.30,0.42) 0.35(0.30,0.41)

igfp 0.16(0.14,0.18) 0.35(0.30,0.39) 0.53(0.48,0.59) 0.44(0.38,0.54)

imwm 0.19(0.16,0.22) 0.24(0.20,0.28) 0.46(0.40,0.54) 0.27(0.23,0.34)

jrc 0.19(0.16,0.22) 0.45(0.40,0.53) 0.38(0.32,0.45) 0.33(0.27,0.41)

mim_cn4 0.40(0.34,0.48) 0.37(0.32,0.42) 0.56(0.45,0.67) 0.74(0.64,0.90)

rivm 0.17(0.14,0.19) 0.23(0.19,0.27) 0.33(0.27,0.40) 0.33(0.28,0.42)

tobs 0.37(0.28,0.46) - - -

boku 0.57(0.50,0.64) 0.89(0.79,1.01) 0.59(0.50,0.70) 0.75(0.62,0.91)

mim_cn1 0.61(0.50,0.74) 0.78(0.66,0.90) 0.64(0.54,0.76) 1.00(0.88,1.21)

mim_wgt 0.42(0.37,0.48) 0.60(0.52,0.71) 0.59(0.50,0.70) 0.76(0.64,0.93)

uvwm 0.57(0.52,0.64) 0.65(0.59,0.71) - 0.75(0.64,0.88)

90

Tab. 6.3. Taylor model-measurement distance derived from the relative deviations for the selected station and model in 1999. The 95% confidence limit is shown in the parentheses. Tab. 6.4. Taylor model-measurement distance derived from the relative deviations for the selected station and model in 2002. The 95% confidence limit is shown in the parentheses.


auth 0.26(0.19,0.30) 0.25(0.23,0.29) 0.47(0.40,0.55) 0.33(0.29,0.47)

dwdk_day 0.54(0.39,0.71) 0.36(0.32,0.45) 0.65(0.56,0.79) 0.65(0.56,0.80)

dwdk_acc 0.50(0.35,0.67) 0.30(0.25,0.39) 0.57(0.51,0.68) 0.58(0.51,0.72)

dwdf 0.24(0.20,0.27) 0.37(0.31,0.43) 0.12(0.11,0.22) -

fmi 0.21(0.15,0.25) 0.26(0.24,0.32) 0.45(0.37,0.55) 0.40(0.35,0.53)

gsas 0.19(0.14,0.27) 0.32(0.28,0.38) 0.40(0.35,0.48) 0.29(0.26,0.43)

igfp 0.32(0.27,0.35) 0.39(0.34,0.43) 0.63(0.56,0.71) 0.46(0.41,0.57)

imwm 0.20(0.17,0.22) 0.24(0.21,0.28) 0.43(0.37,0.53) 0.33(0.30,0.46)

jrc 0.22(0.19,0.26) 0.31(0.28,0.35) 0.50(0.41,0.61) 0.43(0.38,0.56)

mim_cn4 0.65(0.48,0.78) 0.45(0.37,0.51) 0.55(0.47,0.65) 0.41(0.36,0.52)

rivm 0.22(0.17,0.28) 0.26(0.23,0.30) 0.47(0.40,0.57) 0.36(0.32,0.49)

tobs 0.62(0.37,0.94) - - -

boku 0.83(0.73,0.89) 0.98(0.87,1.10) 0.80(0.71,0.90) 0.71(0.61,0.82)

mim_cn1 0.74(0.59,0.84) 0.76(0.65,0.85) 0.68(0.60,0.81) 0.59(0.53,0.69)

mim_wgt 0.69(0.55,0.85) 0.58(0.49,0.67) 0.74(0.64,0.86) 0.60(0.53,0.68)

uvwm 0.61(0.52,0.67) 0.63(0.56,0.69) - 0.71(0.66,0.79)


auth 0.28(0.25,0.33) 0.34(0.31,0.40) 0.26(0.23,0.30) 0.23(0.20,0.33)

dwdk_day 0.43(0.39,0.45) 0.41(0.38,0.49) 0.36(0.30,0.42) 0.40(0.38,0.49)

dwdk_acc 0.40(0.36,0.42) 0.35(0.32,0.42) 0.33(0.25,0.40) 0.37(0.35,0.46)

dwdf 0.24(0.20,0.32) 0.40(0.34,0.49) 0.49(0.42,0.56) -

fmi 0.16(0.11,0.22) 0.32(0.29,0.39) 0.20(0.17,0.23) 0.32(0.29,0.40)

gsas 0.14(0.11,0.21) 0.37(0.33,0.46) 0.21(0.17,0.24) 0.24(0.21,0.34)

igfp 0.38(0.33,0.45) 0.48(0.44,0.52) 0.53(0.48,0.58) 0.47(0.42,0.55)

imwm 0.20(0.16,0.23) 0.21(0.19,0.30) 0.23(0.20,0.26) 0.24(0.21,0.33)

jrc 0.18(0.14,0.26) 0.34(0.31,0.40) 0.24(0.19,0.28) 0.28(0.26,0.37)

mim_cn4 0.46(0.32,0.61) 0.34(0.30,0.40) 0.23(0.21,0.25) 0.43(0.37,0.52)

rivm 0.16(0.13,0.21) 0.30(0.27,0.37) 0.20(0.18,0.23) 0.24(0.22,0.34)

tobs 0.34(0.31,0.38) - - -

boku 0.78(0.72,0.85) 0.56(0.51,0.63) 0.72(0.64,0.81) 0.61(0.52,0.73)

mim_cn1 0.56(0.45,0.67) 0.67(0.57,0.76) 0.39(0.34,0.44) 0.58(0.50,0.68)

mim_wgt 0.45(0.37,0.61) 0.55(0.50,0.63) 0.44(0.39,0.50) 0.56(0.49,0.67)

uvwm 0.50(0.43,0.67) 0.77(0.70,0.85) 0.64(0.56,0.71) 0.59(0.53,0.66)

91

To gain additional insight into the model performance, for each model combination of all data (all sta-

tions and years the 95% confidence ranges have been calculated (Tab. 6.5) and Taylor diagrams

(Fig. 6.3) have been prepared. The number of daily doses contributing to these time series is about

2000 for the models which modelled all sites and years. The results confirm the previous finding ob-

tained from individual station and year data.

Tab. 6.5. Taylor model-measurement distance for the selected reconstruction model derived from all

available model-observation daily pairs representing:

Abs_Dev: the deviations from the smoothed annual profile (derived from the measured daily doses),

Rel_Dev: the deviations from the smoothed annual profile expressed in percent

95% confidence limit is shown in the parentheses.

Model Abs_Dev Rel_Dev

auth 0.25(0.24,0.27) 0.29(0.27,0.31)

dwdk_day 0.29(0.27,0.30) 0.50(0.45,0.57)

dwdk_acc 0.26(0.24,0.28) 0.47(0.41,0.53)

dwdf 0.28(0.25,0.30) 0.29(0.25,0.34)

fmi 0.23(0.21,0.25) 0.23(0.20,0.27)

gsas 0.26(0.24,0.28) 0.22(0.18,0.26)

igfp 0.39(0.36,0.41) 0.43(0.41,0.46)

imwm 0.25(0.24,0.27) 0.23(0.22,0.25)

jrc 0.47(0.44,0.50) 0.30(0.26,0.35)

mim_cn4 0.57(0.54,0.60) 0.58(0.51,0.66)

rivm 0.28(0.26,0.30) 0.24(0.21,0.29)

tobs 0.37(0.31,0.42) 0.49(0.33,0.67)

boku 0.69(0.65,0.72) 0.84(0.80,0.87)

mim_cn1 0.85(0.79,0.90) 0.75(0.69,0.82)

mim_wgt 0.66(0.62,0.70) 0.62(0.52,0.72)

uvwm 0.65(0.62,0.69) 0.59(0.53,0.66)

92

Fig. 6.3. Taylor diagrams from all available model-measurement pairs of the deviations (together all

years and stations); the absolute deviations- left, the relative deviations -right.

For application, the absolute doses are essential because they are relevant for human health. Thus the

main interest is for the results of the modelling exercise for the absolute deviations (Fig. 6.3, left).

Here, the models auth, dwdk-day, dwdk-acc, fmi, gsas, imwm, and rivm form the group with the best

correspondence to the measurements, which has no significant differences. It looks like that dwdf is

also a candidate to this group, but it requires further testing because the Thessaloniki data are not

analyzed and the model has to be tested yet for its use as a general model independent of site. The

other models show significant larger deviations. But again can be seen that the models igfp, jrc and

mim_cn4 form another group, with better results than the models which do not take into account the

global irradiance. The model tobs was run only for the Bergen data, so it cannot be classified at the

moment.

For the relative deviations (Fig. 6.3, right) the grouping is somewhat different. These relative devia-

tions are useful for modelling purposes, to see consequences if not adequate input data are used for

the modelling, like wrong aerosol amount or absorption. For these relative deviations, the group of best

models are given by fmi, gsas, imwm and rivm , with no significant differences. The next group is auth

and jrc and a third group consists of igfp, dwdk-day, dwdk_acc. and mim_cn4. The fourth group with

significantly lower results again is given by the models that do not use the global radiation data: boku,

mim_cn1, mim_wgt, and uvwm.

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.30.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

0.1

0.2

0.3

0.5

0.7

1.0

0.1 0.2 0.3 0.4 0.5 0.60.7

0.8

0.9

0.95

0.99


ABSOLUTE DEVIATIONSN

orm

aliz

ed S

tand

ard

Dev

iatio

n

E - fmiF - gsas



A BCDEF

GH

IJ

KL

M

N

O

P



M - boku

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.30.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

0.1

0.2

0.3

0.5

0.7

1.0

0.1 0.2 0.3 0.4 0.5 0.60.7

0.8

0.9

0.95

0.99


RELATIVE DEVIATIONS

Nor

mal

ized

Sta

ndar

d D

evia

tion

A

BC

DEF

GH

I

J

K

L

MN

O

P

93

7 Conclusion It should be noted that the classification of the performance of the models is based on their specific

statistical properties, i.e., a correspondence to the measured UV daily doses taking into account depar-

tures from the mean annual profile derived from the measurements. If more interest is put to analyses

of absolute values (daily doses) all models probably behave very similarly because of strong seasonal-

ity in the UV values. Nevertheless, groups of models have been found with significant differences both

for absolute and for relative deviations.

To decide, which of the models should be used for preparing the UV climatology for Europe, which is

the goal of the COST action, the problem has to be discussed, how the model requirements on input

parameters limit their use for a reconstruction of the UV doses in the past, when probably not all re-

quested input values are available.

An additional question is the algorithm to produce maps. How can such large data quantities be pro-

duced. Independent from the model is the question of the spatial resolution? Interpolation of the input

data or interpolation of UV doses with consideration of topography? Here also the question has to be

answered whether “local” models can be used in practice.

The modelling exercise was very successful. Models that are suitable to perform the COST action

have been identified.

And additionally to this main goal of the modelling exercise, now a large body of data is available which

can be used for many scientific questions: The data can be used to check the different algorithms to

describe aerosol amount and properties and the different ways to get albedo values. The cloud modifi-

cation can be compared, and even the basic model qualities some times may be improved. This is the

reason, why not only the Taylor diagrams have been presented, but all the detailed data for different

stations, astronomical and meteorological conditions.

94

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