an empirical method for the conversion of spectral uv irradiance measurements to actinic flux data

Atmospheric Environment 36 (2002) 4397–4404

An empirical method for the conversion of spectral UVirradiance measurements to actinic flux data

Ann R. Webba,*, R. Kifta, S. Thielb, M. Blumthalerc

aDepartment of Physics, University of Manchester Institute of Science and Technology, P.O. Box 88, Sackville Street,

Manchester M60 1QD, UKbFraunhofer Institut fur Atmospharische Umweltforschung, Angewandte Strahlungsphysik, Kreuzeckbahnstrasse 19,

D-82467 Garmisch-Partenkirchen, Germanyc Institute for Medical Physics, University of Innsbruck, Muellerstrasse 44, 6020 Innsbruck, Austria

Received 4 January 2002; received in revised form 25 April 2002; accepted 1 May 2002

Abstract

Routinely monitored radiation parameters, including those at UV wavelengths, most commonly refer to irradiance,

that is the radiation incident on a flat horizontal plate. However, in the study of atmospheric chemistry, where UV

radiation is a prime photochemical driver, the target molecules are approximately spherical and the actinic flux

(radiation on the surface of a sphere) is a better measure of the effective radiation. Unfortunately actinic flux

measurements (also known as scalar irradiance) are uncommon research measurements. The ability to convert

irradiance data to actinic flux data within a reasonable degree of uncertainty would provide an actinic flux database

mapped from existing irradiance databases, thus vastly increasing knowledge of actinic flux variability and climatology.

Synchronised spectral UV irradiance and actinic flux measurements have been made during the ADMIRA project, and

used to develop an empirical method for converting irradiance to actinic flux. With some prior knowledge of the sky

conditions during the irradiance measurements the actinic flux can be estimated to within a few percent. If no

knowledge of the sky conditions is available then the empirical method still returns actinic fluxes within 10% of those

measured at the site for which the conversion was developed.

r 2002 Elsevier Science Ltd. All rights reserved.

Keywords: Photochemistry; Aerosol; Photolysis rates; Scattering; Climatology

1. Introduction

Ultraviolet (UV) radiation is a significant driver of

atmospheric chemistry since photodissociation of sev-

eral important species occurs at these wavelengths. For

example, the photolysis rates of ozone and nitrogen

dioxide depend directly on the actinic fluxes in the

wavelength ranges responsible for these reactions

(roughly UVB and UVA, respectively). In the past

decade spectral UV radiation measurements, while not

commonplace, have become more readily available.

However, the vast majority of these measurements are

of spectral irradiance, that is the radiation incident on a

flat (usually horizontal) surface, i.e. the radiance

weighted with the cosine of the angle between the

incident direction and the normal to the surface, and

integrated over a hemisphere:

EðlÞ ¼Z 2p

0

Z p=2

0

Lðl; y; fÞ cos y sin y dy df; ð1Þ

where EðlÞ is the global irradiance at a specified

wavelength, L is radiance and y and f are zenith and

azimuth angles, respectively. However, the actinic flux,

F ðlÞ; required for calculating photolysis rates is the

radiation incident at a point, i.e. the unweighted

*Corresponding author. Tel.: +44-161-200-3917; Fax: +44-

161-200-3941.

E-mail address: [email protected] (A.R. Webb).

1352-2310/02/$ - see front matter r 2002 Elsevier Science Ltd. All rights reserved.

PII: S 1 3 5 2 - 2 3 1 0 ( 0 2 ) 0 0 3 1 9 - 9

radiance integrated over a sphere:

F ðlÞ ¼Z 2p

0

Z p=2

�p=2Lðl; y; fÞ sin y dy df: ð2Þ

While a few measurements of spectral actinic flux have

been reported (Hofzumahaus et al., 1999, 2002; Shetter

and Mueller, 1999), UV monitoring sites, some of which

now have datasets that exceed 10 years in duration,

measure irradiance. The use of these datasets could be

extended if a robust method of converting from

irradiance measurements to actinic fluxes with known

errors could be developed. The radiance distribution

Lðl; y; fÞ depends on the scattering that takes place

throughout the atmosphere, and thus on the three-

dimensional atmospheric composition plus the surface

properties, so it is necessary to define (measure or

assume) the state of the atmosphere in the vertical when

undertaking the E to F conversion.

Empirical relationships between irradiances and

actinic fluxes were first developed using broadband

measurements and the basic theory of transfer from flat

to spherical receiving surface (Madronich, 1987; Van

Weele et al., 1995), while more recent studies have

involved spectrally resolved measurements (Kazadzis

et al., 2000; McKenzie et al., 2002). The initial broad-

band relationship had an estimated uncertainty of 25%

(Van Weele et al., 1995), while photolysis rates

calculated from spectral measurements had uncertainties

between 10% and 20% depending on conditions

(McKenzie et al., 2002), since the irradiance to actinic

flux conversion factors depend on many variables

including solar zenith angle (SZA), aerosol optical depth

and cloud cover. Thus, there is the potential to use

historical records of irradiances to increase knowledge

of past photolysis rates at the surface, but further study

is needed to determine the errors involved in the

conversions under different conditions. This is the goal

of the actinic flux determination from measurements of

irradiance (ADMIRA, EVK2-CT-1999-00018), a pro-

ject within the Fifth Framework Programme of the

European Community.

The aim of the project is to develop algorithms to

enable the conversion of UV spectral global irradiance

measurements into spectral actinic fluxes, and quantify

associated uncertainties. The latter will depend to a large

extent on the additional information available about the

atmosphere at the time the irradiance measurements

were made. In the worst case there will be no additional

information. Approaches to developing the algorithms

are empirical and model-based, and both need a

comprehensive set of measurements as a starting point.

Such data were gathered during the ADMIRA cam-

paign of August 2000 (Webb et al., 2002). Further

synchronised spectral measurements of irradiance and

actinic flux were then made at four UV monitoring sites

in different surroundings and climates. These data were

supported only by the normal facilities at the monitoring

sites and not the full suite of ancillary measurements

available during the campaign. The derivation of an

empirical method of converting irradiance to actinic flux,

based first on the campaign data, is described below.

2. Experimental data

The ADMIRA campaign of August 2000 took place

in northern Greece and is fully described in Webb et al.

(2002). A brief description of the origins of the data used

in deriving the empirical conversion method is given

here. Further details on the spectroradiometers and their

performance characteristics can be found in Webb

(1997) and Bais et al. (2001).

Both the actinic flux and the irradiance were measured

by the University of Manchester Institute of Science and

Technology (UMIST) and Fraunhofer Institute (IFU),

respectively, using Bentham DTM300 scanning spectro-

radiometers, with either 2p actinic (FUMIST) or cosine

response (EIFU) input optics. Both angular responses

had been previously tested in the laboratory and were

close to the ideal response. The deviations of the actinic

response from ideal were estimated to give o3%

uncertainty in any measure of 2p actinic flux, while the

cosine response uncertainty in irradiance was o1%.

Although the scanning spectroradiometers were based

on the same hardware, they were used with different

options and modes of operation and therefore were not

directly equivalent in their characteristics. To overcome

some of the data features directly attributable to the

instrument characteristics the data were subject to the

SHICrivm process (Slaper et al., 1995) to correct any

wavelength errors in the data and map all the data onto

the equivalent measurement of a virtual instrument with

slit width of 1 nm FWHM. This removes much of the

instrument dependent structure seen in ratios of spectral

scans, though a small amount of residual structure due

to differing slit functions used in the original measure-

ments usually remains.

The two instruments were independently calibrated,

but the calibrations of both irradiance and actinic flux

were cross-checked between these and other spectro-

radiometers before and during the campaign. The

performance of both instruments proved very stable,

based on thrice daily checks throughout the 7 days of

the full measurement campaign. There was a consistent

wavelength independent difference between the calibra-

tions of the two instruments of 2–3% when both were

measuring either F or E: Applying this knowledge to the

ratios FUMIST : EIFU leads to a consistent overestimation

of the ratio by about 2%. The stability checks showed

diurnal variation between the two instruments of no

more than 71% at all wavelengths. The maximum

uncertainty in the underlying ratios of the measurements

A.R. Webb et al. / Atmospheric Environment 36 (2002) 4397–44044398

is therefore 3% (including the consistent, uncorrected

difference between the two instruments), while including

the residual structure after the SHICrivm process

(75%, peak to trough) gives a maximum uncertainty

at a specified wavelength of 7%.

Direct spectral UV measurements have also been used

in deriving the empirical conversion method, although

they are not necessary for application of the method.

The direct measurements were also made with both a

Bentham DTM300 spectroradiometer, fitted with a 1.51

field of view input optic mounted on a suntracker, and a

Brewer mark III spectrometer, the latter with a 31 field

of view. The discrepancy between the two direct sun

measurements was 9% (Brewer higher), and may be due

to different calibration methods or the different fields of

view. This difference was consistent to 75% during the

campaign. In deriving the empirical algorithms the data

from the Bentham instrument were used for direct

radiation. We calculate that a 9% uncertainty in direct

beam would give about 5% (or less) uncertainty in

calculated alphas, and so 5% or less additional

uncertainty in resultant calculations of actinic flux.

However, other evidence from Bentham measurements

suggests that the error is not this large.

Full datasets, including many ancillary measurements

(see Webb et al., 2002) were gathered on 6 of the 7

campaign days (days 217–219 and 221–223) while on

day 220 only global irradiance and actinic flux plus basic

meteorological data were measured, providing a situa-

tion much more representative of a monitoring station.

Conditions were fairly stable throughout the campaign

with consistent diurnal variations in temperature, ozone,

wind direction and boundary layer aerosol. Pressure

varied between 1005–1014 hPa and ozone changed from

301–320DU. Table 1 shows the range of values of

atmospheric properties important for radiative transfer.

Thus, while the campaign did not present any major

contrasts in weather it did provide a change in the

scattering characteristics of the atmosphere, which was

important since the ratio of actinic flux to global

irradiance is strongly dependent on the amount and

isotropy of scattering in the atmosphere. In terms of

other radiation parameters measured it depends on the

direct–diffuse partitioning of the radiation and the

radiance distribution. These in turn depend upon

wavelength, SZA (pathlength) and the number of

scatterers along the pathlength. In a clean, clear atmo-

sphere, Rayleigh scattering dominates and has a l�4

dependency, while scattering by aerosol and cloud

particles have a comparatively smaller dependence on

wavelength. The ratios of direct/global irradiance for the

2 days with most contrast (days 218 and 223) show a

clear difference in partitioning on the 2 days: the direct

contribution to global irradiance on day 223 is much less

than that on day 218 (Fig. 1). The differences in

scattering are also clearly visible in the ratios F:E for

the two days (Fig. 2). It is clear that these ratios are a

function of several interacting variables, and that other

values of the ratio might be expected in more extreme

cloud or aerosol conditions. Nevertheless, there is

enough variation here to assess whether, and how

successfully, a measurement of spectral irradiance can

be converted to spectral actinic flux in normal monitor-

ing or measuring conditions, i.e. without the benefit of

all the ancillary measurements available during the

campaign (Webb et al., 2002).

Table 1

Atmospheric parameters measured during the campaign

Day Ozone (DU) PWV (cm) AOD Alpha Clouds

217 30175 2.270.4 0.4570.1 1.370.1 No

218 30476 2.070.2 0.3570.1 1.470.1 No

219 31077 2.070.3 0.3570.05 1.570.1 No

221 31675 2.570.2 0.6070.1 1.370.1 Few Ci late p.m.

222 32078 3.270.3 1.3070.3 1.170.2 Ci a.m., hazy p.m.

223 318710 3.470.2 1.4070.2 1.170.1 Ci+Cs early a.m., hazy p.m.

PWV is precipitable water, AOD is aerosol optical depth and Alpha is the Angstrom alpha coefficient. The ranges given cover the

values measured during the radiation monitoring periods of each day.

300 350 400 450 5000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Wavelength (nm)

Dire

ct /

Glo

bal i

rrad

ianc

e

DAYDAY 218 218DAYDAY 223 223

Fig. 1. The ratio of direct to global irradiance on days 218 and

223 at SZA of about 471. The direct irradiance represents the

direct component incident on a horizontal surface.

A.R. Webb et al. / Atmospheric Environment 36 (2002) 4397–4404 4399

3. Derivation of empirical conversion

The actinic flux F ¼ F0 þ Fk þ Fm where F0 is the

direct beam component, Fk is the downward diffuse

component, and Fm is the upward diffuse component.

Similarly E ¼ E0 þ Ek: The ratio can then be written as

F

E¼ a 1þ

baA

� �þ

1

m� a

� �E0

E; ð3Þ

where a ¼ Fk=Ek; b ¼ Fm=Em; A is albedo and m is the

cosine of the SZA. The measurements were of 2p actinic

flux (i.e. downwelling only) but since measurements were

made close to a low albedo surface (AB0) this can be

considered equivalent to the 4p flux and Fm ¼ 0: Thenthe equation above reduces to

F

E¼ aþ

1

m� a

� �E0

E: ð4Þ

During the ADMIRA campaign all the variables except

a were measured, while in a basic monitoring situation

only E and m would be known, and the challenge is then

to determine F : Theory says that when the sky is

completely overcast, i.e. E0 ¼ 0; and if the radiation is

isotropic, then F=E ¼ a ¼ 2: Van Weele et al. (1995),

measuring broadband UVB and UVA, concluded that

F=E ¼ 2:070:5: The aim was to improve upon this

uncertainty for the more versatile spectral measure-

ments, thus enabling, for example, photolysis rates to be

estimated with reasonable certainty from measurements

of spectral irradiance.

The three determinants of F=E in Eq. (2) are a; E0=E;and m: The former two are functions of m; wavelengthand aerosol optical depth (AOD), the importance of mdecreasing as AOD increases and E0=E decreases (this

can be seen from Fig. 1). Since F ; E; E0 were all

measured during the campaign, and m is known from the

time of measurement, values of a have been calculated

for these data for all the 6 days (217–219, 221–223) for

the complete range of SZAs. Fig. 3 shows the range of

values of the ratio F=E on all 6 days for wavelengths of

310 and 360 nm, while Fig. 4 shows the spectrally

dependent mean values of a and the uncertainties (71

standard deviation) at three SZA, 241 (close to solar

noon), 491 and 721 (E0 still measurable). At high and

low zenith angles the standard deviations are between

2% and 6%, while in the mid-range of SZA, represented

by 491, the standard deviation is between 5% and 20%.

In both cases uncertainty increases with increasing

wavelength. The range of AOD experienced during the

campaign was 0.2–1.9 (at 350 nm) and is incorporated in

the figure.

The sensitivity of F=E to a has been calculated and is

illustrated in Fig. 5 as a function of E0=E: At one limit,

when there is no direct beam, F=E is a and their changes

are equivalent. At the other extreme if all radiation were

in the direct beam the ratio would be independent of a

300300 320320 340340 360360 380380 4004001

1.51.5

2

2.52.5

3

Wavelength (nm)Wavelength (nm)

Act

inic

flux

/ G

loba

l irr

adia

nce

Act

inic

flux

/ G

loba

l irr

adia

nce

DAY 218DAY 218

30300 32320 340340 36360 380380 404001

1.51.5

2

2.52.5

3

Wavelength (nm)Wavelength (nm)

Act

inic

flux

/ G

loba

l irr

adia

nce

Act

inic

flux

/ G

loba

l irr

adia

nce

DAY 223DAY 223

06:00 UT 06:00 UT

04:00 UT04:00 UT06:00 UT06:00 UT08:00 UT 08:00 UT 12:00 UT12:00 UT14:00 UT 14:00 UT 16:00 UT16:00 UT

08:00 UT08:00 UT12:00 UT 12:00 UT 14:00 UT 14:00 UT 16:00 UT 16:00 UT

Fig. 2. The ratio of actinic flux to global irradiance as a

function of wavelength and time of day for the two days with

most contrast in atmospheric conditions (day 218: clear, day

223: cloud and more aerosol).

1.01.21.41.61.82.02.22.42.6

20 30 40 50 60 70 80 90

SZA

AL

PH

A

305nm

1.01.21.41.61.82.02.22.42.6

20 30 40 50 60 70 80 90

SZA

AL

PH

A

3 6 0 nm

Fig. 3. Values of a as a function of SZA for all 6 full

measurement days for wavelengths of 305 and 360nm.


(the measured values of E0=E wereo0.7 at all times and

all wavelengths). Thus, if E0=E is known and a is

estimated from a comprehensive table of average a as a

function of SZA, then the uncertainty in F=E (and hence

F if E is known and assumed true) is no more than the

uncertainty in a:When E0=E is unknown, as might often

be the case, then there is a further cause of uncertainty.

E0=E depends on SZA, AOD and wavelength: it

becomes small at short wavelengths, large SZA and

large AOD. The ratio F=E is decreased by direct beam

radiation at small SZA (a > m�1), increased by direct

beam radiation at large SZA, and may be either

increased or decreased at mid-range SZA, depending

on the relative values of a and m: The maximum values

of E0=E can be assessed as a function of wavelength and

SZA, either from empirical experience at a given site, or

from a radiative transfer model for a pure Rayleigh

atmosphere. A default value of half the maximum would

give a maximum error in E0=E of 50%. The effect of this

on the ratio F=E is shown in Fig. 6 for combinations of

three SZA and two values of a: Only positive changes in

E0=E are shown in the figure for clarity: negative

changes are symmetrical about the horizontal axis.

The percentage change in F=E is independent of

wavelength for a fixed AOD, a and E0=E: However, for

a given set of atmospheric conditions the ratio E0=E will

change with wavelength, decreasing towards the shorter

UVB wavelengths. This means the uncertainties will

generally increase with increasing wavelength. In condi-

tions where a and 1=m are similar in magnitude (i.e. for

SZA in the region approximately 30–601 depending on

atmospheric conditions) the uncertainties are small. At

low and high SZA uncertainties increase, with 891 an

example of the extreme case, when however there would

be negligible direct beam radiation. In general, for

realistic values of E0=E in the UV the uncertainties

attributable to a 50% uncertainty in E0=E are o20%.

The uncertainties in F=E due to a and E0=E work in

opposition in that the SZA with uncertainties due to a(mid-range SZA) are those where the uncertainty due to

E0=E are smallest. Both uncertainties tend to decrease

with wavelength.

Now that a and E0=E can be estimated or measured,

F=E can be calculated and hence F is determined since E

is known. The resultant uncertainty in F will depend on

the amount of knowledge available to determine E0=E;and the degree to which the specific conditions match

those of the data used in determining a; i.e. whether theclimate matches that of the empirically derived values. It

will also depend on the starting uncertainty in E; but forthe purposes of this discussion E is taken as known and

true (negligible uncertainty). Day 220 of the campaign

produced measurements of irradiance and actinic flux,

but no supporting data, so this day, which was not

included in the derivation of a0s; was used as a test of the

conversion method. Since the day was in the middle of

the fairly stable conditions of the campaign, the

empirically derived values of a should be valid. No

measurements of E0 were available but the day was

known to be cloud free. Therefore the empirical

1.51.71.92.12.32.52.7

300 320 340 360 380 400

Alp

ha

Wavelength (nm)

SZA =49

SZA = 72

SZA = 24

Fig. 4. Average values of a as a function of wavelength for

three SZA: 241 (bottom), 721 (middle) and 491 (top). The

uncertainties (one standard deviation) are shown by the error

bars.

0123456789

10

0 0.2 0.4 0.6 0.8 1

Eo/E

% c

han

ge

in F

/E

Fig. 5. The calculated percentage change in F=E for a 10%

change in a; shown as a function of E0=E for two initial values

of a (1.5, — and 2.0 � � � � ) and four SZA: 101, 451, 701 and 891,

from top to bottom for each value of a:

-60.0-40.0-20.0

0.020.040.060.0

0.0 0.2 0.4 0.6 0.8 1.0E0/E

% c

han

ge

in F

/E

Fig. 6. The percentage change in F=E for a 50% change in

E0=E; plotted against the original E0=E: Values are for a ¼ 1:5;dotted lines, open symbols and for a ¼ 2:0; solid lines, closed

symbols. SZA are represented by squares (101), diamonds (451),

triangles (701) and circles (891). Positive and negative changes in

E0=E have effects that are mirrored about the x-axis. For

simplicity only positive changes are shown for a ¼ 1:5 and

negative changes for a ¼ 2:0:


conversion was run first using the values of E0=E from

day 218 (i.e. maximum values, and close to the real

situation) and then with half maximum E0=E to simulate

completely unknown conditions.

4. Results of application

The results of the conversions for the two values of

E0=E are shown in Fig. 7 for a SZA of 491. The

measured data retains some residual structure in the

ratio due to the spectral structure of the solar spectrum

and the characteristics of the two instruments, but it is

clear that the calculation using E0 from day 218 is a very

close match to a smooth line drawn through the data.

The site average E0 (half maximum) gives, in this case,

an overestimation of the F=E ratio, and hence of F :Table 2 shows the magnitude of the deviations from

smoothed measured values of F=E for all measurements

and both values of E0=E on day 220. A linear fit to the

measured values was compared with the calculated

values of F=E: In some cases the measured data would

have been better represented by a gentle curve, and this

can add marginally to the uncertainties especially at the

longer wavelengths, thus some of the values in Table 1

Table 2

Magnitude of the percentage difference between predicted and measured F=E on day 220 for different values of E0 and different

wavelengths

Time (UT) SZA Average, 300–366nm 305 nm 320 nm 340 nm 360nm

E0

04:30 78 2.0 +1.4 +1.9 +2.4 +2.8

05:00 71 5.1 �9.3 �6.0 �2.1 +1.2

05:30 66 5.0 �2.8 �0.8 +3.4 +1.2

06:30 56 9.9 +8.3 +9.4 +10.8 +12.0

07:00 49 1.6 �1.0 �1.4 �2.0 �2.5

07:30 44 6.5 �5.8 �6.3 �6.9 �7.5

09:00 29 2.2 �1.7 �2.0 �2.5 �2.9

11:00 25 2.5 �2.2 �2.4 �2.6 �2.7

13:00 41 2.7 �2.2 �2.5 �3.0 �3.6

14:30 57 2.7 �3.2 �2.8 �2.4 �2.0

15:00 64 3.1 +3.5 +3.3 +2.9 +2.6

Average 3.9 3.7 3.5 3.7 3.7

E0/2

04:30 78 2.1 +1.5 �0.3 �2.3 �4.0

05:00 71 7.7 �8.5 �8.0 �7.3 �6.7

05:30 66 4.5 +3.7 +2.8 +2.0 +0.2

06:30 56 1.3 +1.8 +1.5 +1.1 +0.7

07:00 49 3.4 +1.6 +2.8 +4.4 +5.9

07:30 44 1.9 �2.9 �1.4 +0.5 +2.4

09:00 29 7.3 +5.7 +6.7 +8.0 +9.5

11:00 25 7.2 +6.3 +6.9 +7.7 +8.5

13:00 41 4.6 +3.2 +4.1 15.4 �6.6

14:30 57 3.3 �5.0 �3.8 �2.4 �1.0

15:00 64 0.5 �0.02 �0.3 �0.7 �1.1

Average 4.0 3.6 3.5 3.8 4.2

The day was essentially cloud free and the solar disk was visible at all times. Positive values mean that the predicted F=E was greater

than the measured F=E: The average is the rms value and so positive by definition.

1.50

1.60

1.70

1.80

1.90

2.00

300 310 320 330 340 350 360

Wavelength(nm)

F/E

Fig. 7. Simulated and measured ratios of F=E for day 220 at

07:00UTC (SZA=491): measured and linear fit through the

measured data (—), simulated using E0 from day 218 (—) and

simulated using site average E0 ( � � � � ).


may be too large but only by about 1%. The ‘‘true’’

(measured) F=E is both overestimated and under-

estimated (i.e. the absolute values of the figures in Table

2 are both positive and negative) depending on the

selected value of E0 and the SZA at the time of

measurement. The mean magnitude of the uncertainty

(calculated so that positive and negative values do not

cancel out) is also shown for the whole day for each

value of E0=E as a function of wavelength. Although the

distribution of uncertainties changes with the selection

of E0; the average and extreme values are very similar in

both cases. This may be because the assumption that E0

was actually the same as on day 218 is incorrect and

there was more aerosol on day 220, leading to a

reduction in E0: Since either potential selection of E0

provides average uncertainties of o5% the method is

clearly robust and not very dependent on the exact

knowledge of the direct beam radiation.

Further illustration of the uncertainties in the algo-

rithm-determined actinic flux is given by Fig. 8. This

shows the diurnal change in measured actinic flux at 310

and 360 nm, with the ratio of the determined to

measured fluxes for day 219. The site values for a were

used (shown in Fig. 4) to calculate the actinic fluxes, and

day 219 was selected as the clearest day, and therefore

the most challenging to predict. It is clear that the

difference between derived and measured fluxes is

always o10%, and for much of the time is very close

to the measured value, especially at 310 nm.

The empirical deduction of spectral actinic fluxes

described here has proved successful in estimating

actinic fluxes to within 10% if nothing is known about

the sky conditions, and with similar outer limits but a

different distribution if the direct beam partitioning is

assumed. The derivation of the variables needed for the

conversion was based on a limited dataset, and the test

application was equally limited and performed on an

ideal dataset (one known to be similar to the derivation

data), thus giving a ‘‘best case’’ scenario for the test. It

should also be noted that the campaign was performed

at a relatively polluted, sea level site. At cleaner sites

(AOD50.2) and those at high altitude, where there is

less scattering and more direct beam radiation, higher

uncertainties in the derived values of F may be expected.

Nonetheless the results are very encouraging, improving

on previous estimates of actinic flux and providing

spectral data.

As with all empirical methods, this one will have its

limitations, and the values of a and E0=E derived here

will not be applicable to all situations and will have to be

independently derived for sites in different climatic

areas. The maximum values of E0=E can be modelled if

there are no data available to give the clear-sky maxima

for the site. Then, since direct spectral UV measure-

ments are not common, data from other radiation

instruments, e.g. a time series from a pyranometer, could

provide information about periods of the day when the

sun is free of cloud, and an estimate of the thickness of

the cloud. Thus simple ancillary instruments could be

used to assist application of the conversion method.

Determining the average a; and its variation, for a site is

less straightforward if no direct beam measurements are

available. However, the two extreme values (associated

with maximum E0=E for a given SZA, and E0=E ¼ 0)

can be found using the modelled E0=E referred to above,

and for a Rayleigh atmosphere model would be the same

for all low albedo sites. The mean of these values could

then be used as the average a: This fails to take account

of the frequency of these extremes and the intermediate

conditions at a site, but will provide a working value of athat could be modified based on local knowledge of

frequency of clear and complete overcast conditions, or

information about local aerosols to inform the modelled

E0=E:In conditions with high reflectivity, e.g. snow-covered

environment, the albedo cannot be neglected and the

empirical results are expected to be different to those

observed in low albedo situations. When there is

significant reflected radiation the 2p actinic flux mea-

surements no longer provide a reasonable representation

of the 4p fluxes. The downwelling radiation is also

increased by multiple reflection and scattering between

the ground and atmosphere, but for irradiance this

increase is completely included in the measurement.

During the ADMIRA project irradiance and actinic

flux have been monitored for several months at four

0.000.020.040.060.080.100.120.140.16

4:00 7:00 10:00 13:00 16:00

Time(UT)

Act

inic

Flu

x(W

/m2 ) 310nm

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.80.70.6

0.91.01.11.21.31.4

0.8

0.7

0.9

1.0

1.1

1.2

1.3

4:00 7:00 10:00 13:00 16:00

Time(UT)

Act

inic

Flu

x(W

/m

Act

d/A

ctm

Act

d/A

ct

2 ) 360nm

Fig. 8. The diurnal variation in measured actinic fluxes at 310

and 360 nm on day 219 ( � � � � ), and the ratio of derived to

measured fluxes at the same times (—, right-hand scale).


different sites in very different climates and surround-

ings, including Alpine sites with periods of snow cover.

It remains to test this empirical method of estimating

F=E on the data from all four sites, which also have

varying levels of supporting data.

5. Conclusion

An empirical method for converting UV spectral

irradiance data into spectral actinic fluxes has been

developed and tested on a limited dataset from a

comprehensive measurement campaign in Greece. With

partial knowledge of the spectral direct beam radiation

the actinic fluxes can be estimated with an average

uncertainty of o4% and a maximum uncertainty of

10% at all wavelengths. Note that these uncertainties

assume the irradiance to be true, they are in addition to

any uncertainty in the irradiance measurements. Results

are statistically very similar if there is no available

information about the direct radiation, but the distribu-

tion of uncertainties over time and wavelength are

different. The method must now be tested on data from

other sites with different climates and more complex

conditions, including snow cover.

Acknowledgements

This work was supported by the European Commu-

nity, Fifth Framework Programme, EVK2-CT-1999-

00018.

References

Bais, A.F., Gardiner, B.G., Slaper, H., Blumthaler, M.,

Bernhard, G., McKenzie, R., Webb, A.R., Seckmeyer, G.,

Kjeldstad, B., Koskela, T., Kirsch, P., Gr .obner, J., Kerr,

J.B., Kazadzis, S., Leszczynski, K., Wardle, D., Brogniez,

C., Josefsson, W., Gillotay, D., Reinen, H., Weihs, P.,

Svenoe, T., Eriksen, P., Kuik, F., Redondas, A., 2001. The

SUSPEN intercomparison of ultraviolet spectroradi-

ometers. Journal of Geophysical Research 106 (D12),

12506–12526.

Hofzumahaus, A., Kraus, A., Muller, M., 1999. Solar actinic

flux spectroradiometry: a new technique to measure

photolysis frequencies in the atmosphere. Applied Optics

38 (21), 4443–4460.

Hofzumahaus, A., Kraus, A., Kylling, A., Zerefos, C., 2002.

Solar actinic radiation (280–420nm) in the cloud-free

troposphere between ground and 12 km altitude: measure-

ments and model results. Journal of Geophysical Research,

submitted for publication.

Kazadzis, S., Bais, A.F., Balis, D., Zerefos, C., Blumthaler, M.,

2000. Retrieval of downwelling UV actinic flux density

spectra from spectral measurements of global and direct

solar UV irradiance. Journal of Geophysical Research 105

(D4), 4857–4864.

Madronich, S., 1987. Intercomparison of NO2 photodissocia-

tion and UV radiometer measurements. Atmospheric

Environment 21 (3), 569–578.

McKenzie, M., Johnston, P., Hofzumahaus, A., Kraus, A.,

Madronich, S., Cantrell, C., Calvert, J., Shetter, R., 2002.

Relationship between photolysis frequencies derived from

spectroscopic measurements of actinic fluxes and irradiances

during the IPMMI campaign. Journal of Geophysical

Research, in press.

Shetter, R., Mueller, M., 1999. Photolysis frequency measure-

ments using actinic flux spectroradiometry during the PEM-

Tropics mission: instrumentation description and some

results. Journal of Geophysical Research 104, 5647–5661.

Slaper, H., Reinen, H.A.J.M., Blumthaler, M., Huber, M.,

Kuik, F., 1995. Comparing ground level spectrally resolved

UV measurements using various instruments: a technique

resolving effects of wavelength shift and slit width.

Geophysical Research Letters 22, 2721–2724.

Van Weele, M., de Arrelano, J.V.-G., Kuik, F., 1995.

Combined measurements of UV-A actinic flux, UV-A

irradiance and global radiation in relation to photodissocia-

tion rates. Tellus 47B, 353–364.

Webb, A.R., 1997. Advances in solar ultraviolet spectro-

radiometry. Air Pollution Research Report 63. Office for

Official Publications of the European Communities, Lux-

embourg.

Webb, A.R., Bais, A.F., Blumthaler, M., Gobbi, G.-P., Kylling,

A., Scmitt, R., Thiel, S., Barnaba, F., Danielsen, T.,

Junkermann, W., Kazantzidis, A., Kelly, P., Kift, R.,

Liberti, G.L., Misslbeck, M., Schallhart, B., Schreder, J.,

Topaloglou, C., 2002. Measuring spectral actinic flux and

irradiance: experimental results from the admira (actinic

flux determination from measurements of irradiance)

project. Journal of Atmospheric and Oceanic Technology

19 (7), 1049–1062.


an empirical method for the conversion of spectral uv irradiance measurements to actinic flux data

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