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Atmospheric Environment 39 (2005) 857–866

www.elsevier.com/locate/atmosenv

Photolysis rate coefficients calculations from broadband UV-Birradiance: model-measurement interaction

Gustavo G. Palancar, Rafael P. Fernandez, Beatriz M. Toselli�

Departamento de Fısico Quımica/INFIQC, Facultad de Ciencias Quımicas, Universidad Nacional de Cordoba, Ciudad Universitaria, 5000

Cordoba, Argentina

Received 15 May 2004; accepted 19 October 2004

Abstract

Broadband UV-B irradiance measurements (YES UVB-1) from a 4-year campaign in Cordoba City (311 240 S, 641 110

W, 454m a.s.l.) and the TUV 4.1 model were used to apply a new approach (exp-mod) to convert broadband irradiance

measurements at surface under clear sky conditions to actinic flux and then to J-values. The structure of the model was

used to split each measurement into its diffuse and direct component and, in turn, in wavelengths. The results for the

daily variation of JO3shows an agreement better than 5% for solar zenith angles (SZA) up to 651 and better than 10%

up to 701 compared against an 8-stream discrete ordinate method. The annual variation of JO3for clear sky days at

solar noon shows a general agreement better than 10%. The effects of the natural variation of ozone column and the

Cordoba meteorology on this agreement are analyzed. Empirical relations between experimental measurements and J-

values calculated with a 2-stream d-Eddington method are also presented.

r 2004 Elsevier Ltd. All rights reserved.

Keywords: Actinic flux; Radiative transfer calculations; Cordoba City; Broadband UV-B measurements; Diffuse ratio

1. Introduction

Photodissociation reactions are the driving force of

the atmospheric chemistry. These processes generate

highly reactive species, which are involved in many

mechanisms, and they are responsible for removing

most of the trace gases in the troposphere. As a

consequence of their importance for the chemical

behavior of the atmosphere, the rates at which

the photolysis reactions occur must be included

as input parameters in all photochemical models.

This is done by calculating the photolysis rate

e front matter r 2004 Elsevier Ltd. All rights reserve

mosenv.2004.10.033

ing author. Tel.: +54351 4334169;

4188.

ess: tosellib@fcq.unc.edu.ar (B.M. Toselli).

coefficients (J-values), also called photolysis frequen-

cies, as follows:

J ¼

ZjðlÞsðlÞF ðlÞ dl: (1)

In Eq. (1) jðlÞ is the quantum yield, sðlÞ is the

absorption cross section, and FðlÞ is the actinic

flux. As it can be seen from this equation, a J-value

is proportional to the actinic flux, which is defined

as the radiant flux density incident on a spherical

surface (e.g. Madronich, 1987; Lenoble, 1993; Rugga-

ber et al., 1993). Thus, the appropriate radiometric

quantity to calculate photolysis frequencies is the

actinic flux, and not the irradiance EðlÞ: Actinic

flux can be computed by integrating the radiance

Lðl; y;fÞ over all angles of both hemispheres of a

d.

ARTICLE IN PRESSG.G. Palancar et al. / Atmospheric Environment 39 (2005) 857–866858

sphere according to

F �

Zf

Zy

Lðy;fÞ sin y dy df; (2)

where y and f are the zenith angle and the azimuth

angle, respectively. The irradiance, on the other hand,

is the radiation received on a flat horizontal surface and

is calculated by integrating the radiance Lðl; y;fÞ overall angles of the upper hemisphere.

E �

Zf

Zy

Lðy;fÞ cos y sin y dy df: (3)

The irradiance expresses flow of energy and is the

radiometric quantity most frequently measured in the

atmosphere, e.g. with flat-plate radiometers. The factor

cos y which appears in its expression reflects the changein the projected area of the surface as the angle of

incidence is varied (Madronich, 1987). This is the

reason why irradiance is also known as cosine-weighted

irradiance.

The actinic flux can be either calculated by using a

radiative transfer model or directly measured. Actinic

flux detectors have been recently developed (Hofzuma-

haus et al., 1999; Shetter and Muller, 1999) but the

measurements are still experimentally complex and very

expensive. As a result, the current database of actinic

flux measurements is very limited. On the contrary, due

to its widespread use in chemical, biological, and

meteorological applications, a much more extensive

database of global irradiance exists (both broadband

and spectrally resolved). This kind of measurements

exists at several sites nearly all over the world and, at

present, more than a decade of data is available.

Although both radiometric quantities are closely related,

they are not equal and the usage of irradiance instead of

actinic flux to calculate J-values (e.g. O3 or NO2) leads

to errors of approximately 35% (McKenzie et al., 2002).

That is why a considerable effort has been devoted to

find a robust method to convert irradiance to actinic

flux. The theoretical formulation for this transformation

was outlined by Madronich (1987) and many researchers

have proposed empirical conversions for both broad-

band and, more recently, spectrally resolved measure-

ments (Van Weele et al., 1995; Kazadzis et al., 2000;

Webb et al., 2002; McKenzie et al., 2002).

An alternative method to obtain direct measurements

of the J-values is the use of the called J-radiometers or

chemical actinometers (Junkermann et al., 1989; Shetter

et al., 1992; Kraus and Hofzumahaus, 1998; Muller et

al., 1995). In this case each studied molecule requires

selective equipment and, consequently, only a reduced

set of reactions can be studied. Thus, the use of actinic

flux data has a big advantage over a J-radiometer: if the

corresponding cross sections and quantum yields data

are known, the photolysis frequency for any molecule

can be calculated by using Eq. (1). This fact means that

there is a potential to increase our knowledge about the

past photolysis frequencies at surface by using the world

wide historical data set of irradiance.

In this paper we present the results of applying an

approach for converting a set of experimental broad-

band irradiance data to J-values by using the structure

of a radiative transfer model. To show this approach we

will use the ozone (O3) and the formaldehyde (HCHO)

photolysis frequencies at the surface level although

many different reactions have been also tested (e.g. NO2,

NO3, HNO4, etc.). The converted J-values will be

compared against the results of a model which uses an

8-stream discrete ordinate radiative transfer method,

which will be used as a reference all through this work.

However, considering that the 2-stream methods and the

broadband irradiance measurements are the most widely

used tools throughout the world, an empirical relation-

ship between them will be also shown. The analysis will

be focused, on one hand, on the results of the daily

variation of the J-values and, on the other hand, on

their annual variation at midday, both of them at

surface.

The main advantage of this method is that the effect

of the variation of the ozone column along the day can

be included in the J-values calculations. To include the

effects of clouds or the variation of the aerosol loading

some other assumptions, concerning to the diffuse ratio,

should be formulated. In the future, these J-values

calculated at surface from irradiance measurements will

be used as input parameters of an atmospheric model to

assess the air quality and the tropospheric O3 formation

in Cordoba City.

2. Instrumentation and data gathering

The instruments used in this work were manufactured

by Yankee Environmental Systems, Inc. (YES). The

YES UVB-1 pyranometer measures broadband global

UV-B irradiance (280–315 nm) while the YES TSP-700

pyranometer measures broadband global total irradi-

ance (300–3000 nm). Due to the fact that the total

irradiance is quite sensitive to the cloud presence these

data have been used to assure the cloudless condition on

each day. Both instruments were mounted on a wide-

open area in the university campus in Cordoba City,

Argentina (311 240 S, 641 110 W, 454m a.s.l.). Basically,

the site can be described as an open semi-urban place

with some buildings, scattered trees and with different

kind of surfaces such as bare soil and grass. There are no

snow precipitations at any season in Cordoba City. A

more complete description of the characteristic and the

meteorology of the measurement site can be found in

Olcese and Toselli (1998) and Palancar and Toselli

(2002). The global UV-B and total observations were

recorded systematically as 5-min average values from

ARTICLE IN PRESSG.G. Palancar et al. / Atmospheric Environment 39 (2005) 857–866 859

March 1999 until September of the same year and

as half-a-minute average values from October 1999

onward.

3. Radiative transfer model

In the present work all the calculations have been

carried out by using the Tropospheric Ultraviolet and

Visible radiation model (TUV) version 4.1a (Madronich,

1993) developed at the National Center for Atmospheric

Research (NCAR, United States). A sensitivity analysis

was carried out on this model in order to establish the

appropriate setup and the best values for the most

important parameters for the calculations at surface in

Cordoba City (Palancar, 2003). According to this

analysis the surface albedo was assumed to be lamber-

tian, wavelength-independent, and with a constant value

of 0.05 throughout the year; the extraterrestrial irra-

diance values were taken from Van Hoosier et al. (1987)

and Neckel and Labs (1984); the wavelength grid ranged

from 280 to 735 nm with 1 nm intervals between 280 and

420 nm and with 5 nm intervals from 420 to 735 nm. A 2-

stream method (d-Eddington approximation) and an 8-

stream discrete ordinate method were used for the

calculations, both with no aerosols and cloudless sky

conditions. In all the calculations the scattering was

computed with a pseudo-spherical correction (Dahlback

and Stamnes, 1991). Although many studies using up to

32 streams have been done, it has been shown that the

differences with the irradiance calculated with 8 streams

are meaningless while the CPU time can increase by a

factor up to 4. Thus, the 8-stream method was used as a

reference against both the experimental measurements

and the 2-stream calculations. The d-Eddington approx-

imation was selected among nine 2-stream approxima-

tions (Toon et al., 1989) due to the good agreement

between its results and the results of the more

sophisticated methods using 8, 16, and 32 streams.

Due to the low levels of tropospheric UV-B-absorbing

pollutants like O3, SO2, and NO2 in Cordoba City

(Olcese and Toselli, 2002), they have not been con-

sidered in the calculations. Total ozone column values

were obtained daily by the Total Ozone Mapping

Spectrometer (TOMS) instrument onboard Earth Probe

spacecraft and were provided by the Ozone Processing

Team of the Goddard Space Flight Center of the

National Aeronautic and Space Administration (NASA,

United States).

4. Theoretical considerations

In this section will be described the formal process to

convert the broadband irradiance measurements at

surface into J-values, the necessary interaction between

the experimental measurements and the model, and the

different assumptions involved in this process.

In general, to convert the irradiance into actinic flux

the measured broadband global irradiance must be split,

in first place, into its direct and diffuse components.

Then, the contribution of each wavelength to both the

direct and diffuse components must be assigned

separately. Finally, the ‘‘spectrally resolved’’ direct and

diffuse irradiances can be converted into the correspond-

ing actinic flux quantity and in J-values.

If the direct part of the solar radiation is considered as

a collimated beam, essentially parallel, and originated

from a very small solid angle, the radiance ðLðl; y;fÞÞ inEqs. (2) and (3) may be taken as constant. Under these

conditions, the integrals in those equations can be

evaluated and the direct part of the actinic flux ðFdirÞ can

be obtained by dividing the direct part of the irradiance

ðEdirÞ by the cosine of the SZA (Madronich, 1987).

Due to the fact that the angular distribution of the

diffuse radiation is not known, no simple assumptions

can be made to relate the diffuse parts of the irradiance

ðEdif Þ and the actinic flux ðFdif Þ: As a consequence, the

relation between the two radiometric quantities is

usually established through the ‘‘diffuse ratio’’ rd (or

through the ‘‘diffusivity factor’’ ¼ 1/rd) defined as

rd ¼Edif

Fdif: (4)

The diffuse ratio depends on the wavelength, the SZA,

and other atmospheric parameters such as clouds and

aerosols. This factor has already been evaluated and

approximated under a range of conditions (Madronich,

1987; Ruggaber et al., 1993; Van Weele et al., 1995;

Hofzumahaus et al., 1999; McKenzie et al., 2002).

According to these studies, for isotropically scattered

radiation rd takes a value of 0.5 while for collimated

light incident from a SZA of 01 rd is equal to 1.

In this way, the total actinic flux at each wavelength

can be derived from the irradiance by using

F tot ¼Edir

cos yþ

Edif

rd: (5)

It should be pointed out that in the diffuse part of the

actinic flux the contribution of the reflection due to the

surface albedo (Fm) is usually included, although, from

the experimental point of view, in most cases this

component is not considered due to the low surface

albedo in the UV-B range.

Once the actinic flux at each wavelength is obtained,

the photolysis frequencies can be calculated by resolving

the integral in Eq. (1). Although this approximation is

widely used in many models, it should be taken into

account that in some specific conditions rd can take

values larger or smaller than 0.5, as for example at larger

SZA and longer wavelengths (horizon brightening),

leading to errors of considerable magnitude in the

ARTICLE IN PRESS

08:00 10:00 12:00 14:00 16:00 18:000.0

0.5

1.0

1.5

2.0

2.5

11/11/99

309 DU

Irra

dia

nce

(W

m-2

)

Local hour

Experimental Exp-mod Modeled

Fig. 1. Daily courses of the UV-B irradiance on 11th

November 1999. Direct measurements, model calculations

and calculations using direct measurements.

G.G. Palancar et al. / Atmospheric Environment 39 (2005) 857–866860

photolysis frequencies calculations. The accurate meth-

ods, like the n-stream discrete ordinate methods, avoid

these errors by computing the actinic flux directly. That

is the reason why all the calculations carried out through

formula (5) will be evaluated by comparing them against

an 8-stream method.

4.1. Methodology: model-measurement interaction

The TUV model in the 2-stream version calculates the

actinic flux, and then the J-values, from the previously

calculated irradiance values. These irradiance values are

calculated by using an unique value of ozone column

(the daily value provided by TOMS) for the whole day.

Thus, replacing the calculated irradiance values for the

experimental ones, the J-values calculations will show

the real variation of the ozone column along the day.

As it has been mentioned in the previous section, to

include the irradiance measurements in the model not

only the knowledge of the direct and the diffuse

fractions but also the irradiance values spectrally

resolved are required. Due to the lack of simultaneous

global and diffuse measurements, in order to distribute

the experimental irradiance in its direct and diffuse

components we used the distribution given by the TUV

model running an 8-stream discrete ordinate method.

This procedure is based on the excellent agreement

between the experimental and the modeled irradiance

values. It consists in calculating the broadband global,

direct, and diffuse irradiances with an 8-stream method

and, from these values, calculate the percentages of

diffuse and direct irradiances at each solar zenith angle.

Then, the corresponding broadband experimental irra-

diance values are divided into its direct and diffuse

components according to these percentages. A similar

process is carried out to assign the contribution of each

wavelength to the direct and the diffuse components of

the experimental values. Thus, the experimental irra-

diance values ‘‘spectrally resolved’’ are used as input in

the TUV model replacing the calculated ones. The

actinic flux at each wavelength is subsequently calcu-

lated from the spectral irradiance values using Eq. (5)

and the following equations:

F tot ¼ Fdir þ Fdif þ F"; (6)

F tot ¼ Fdir þ Fdif þ Fdir2A cos yþ FdifA; (7)

F tot ¼Edir

cos yð1þ 2A cos yÞ þ

Edif

rdð1þ AÞ; (8)

where A represents the surface albedo and the last two

terms in Eq. (7) represent the contributions of the

downward direct and diffuse radiation to the upward

diffuse radiation (Madronich, 1987). After carrying out

the actinic flux calculations the program follows the

usual steps (in the 2-stream version) to calculate the J-

values. From now on, the J-values obtained in this way

will be named as ‘‘exp-mod’’.

5. Results and discussion

The key factor to convert irradiance data to actinic

flux is the diffuse ratio. Ruggaber et al. (1993) have

evaluated the diffuse ratio at different wavelengths and

under different conditions. They have shown that for a

Rayleigh atmosphere with a defined ozone column, a

surface albedo of 0.05, at 300 nm, an altitude of 1 km,

and SZA up to 601 the diffuse ratio takes values very

close to 0.5 while at longer wavelength (700 nm), larger

SZA (751), and higher altitudes (10 km) it can take

values lower than 0.3. This change in the rd value is due

to the fact that not only the isotropy conditions (visible

light is less isotropic than the UV-B) but also the diffuse

fraction change considerably under these conditions.

Besides, Mckenzie et al. (2002) suggest that the errors in

the J-values calculated from irradiance data are

associated with departures from the isotropy of the

skylight (e.g. caused by clouds or aerosols) rather than

in calculating the diffuse fraction. In this work a

constant value of 0.5 was used for rd while, in order to

minimize the departures from the isotropy, the day

selected to show the daily variation of the J-values was a

cloudless day after a rain.

5.1. Daily variation

To verify the validity of the approach described in

Section 4 the output of the modified model and the

original broadband global measurements were plotted

along with the global irradiance calculated by using an

8-stream method. The results are shown in Fig. 1 where

it can be seen that the measurements and the output of

the modified model for 11th November 1999 present a

ARTICLE IN PRESS

08:00 10:00 12:00 14:00 16:00 18:000

1x10-5

2x10-5

3x10-5

4x10-5

0

1x10-5

2x10-5

3x10-5

4x10-5

J O3 (

s-1)

Local hour

Exp-mod Modeled

J HC

HO

(s-1

)

Exp-Mod Modeled

(a)

(b)

Fig. 2. Daily courses of the J-values for formaldehyde (a) and

ozone (b) photolysis calculated from experimental measure-

ments (exp-mod) and by using an 8-stream model.

G.G. Palancar et al. / Atmospheric Environment 39 (2005) 857–866 861

very good agreement. The differences between measure-

ments and a 2-stream d-Eddington method have been

analyzed for 29 clear sky days along 4 years in Palancar

and Toselli (2004a) where it was found a model-

measurement agreement better than 75% for SZA less

than 701.

In order to evaluate the conversion of the daily

variation of broadband irradiance to J-values many

reactions were analyzed. These reactions are listed in

Table 1. In order to show the results, reactions 2 and 8

were chosen. These reactions were selected due to their

well-known importance for the tropospheric chemistry

in the UV-B range. Fig. 2 shows the daily variation of

JHCHO (a) and JO3(b) calculated from the experimental

irradiance data. The J-values calculated with an 8-

stream discrete ordinate method is also shown in each

figure. Fig. 3 shows the differences between JO3

calculations. Here it can be seen that the agreement is

better than 5% for SZA up to 651 and better than 10%

up to 701. Beyond the 701 the differences show a steep

increase (in negative values) to reach 50% for a SZA of

801. However, these last differences are not critical

because they arise as a consequence of the low J-values

at sunrise and sunset and due to the well-known

problems for models and UV-B monitoring sensors at

these large SZA. Another important factor which can

also contribute to the differences at large SZA is the

departure from the isotropy. The differences for all the

other studied reactions are less than 20% at all SZA.

In Fig. 3 two important features should be remarked.

First, the spikes observed between 151 and 201 and also

at nearly 301 and 451 are consequences of the

instabilities shown in Fig. 2b. These numerical instabil-

ities, not present in the typical 2-stream calculations,

have appeared in the JO3exp-mod values. They are of

unknown origin but they were generated in the

calculation of the J-values because they were observed

neither in the irradiance (see Fig. 1) nor in the exp-mod

actinic flux values (not shown). The 8-stream results also

exhibit some numerical instabilities. This kind of

Table 1

Photolysis reactions of tropospheric relevance analyzed in this study

No. J Reaction

1 JO3O3+hn-O(3P)+O2

2 JO3O3+hn-O(1D)+O2

3 JNO2NO2+hn-NO+O(3P)

4 JNO3NO3+hn-NO2+O(3P)

5 JHONO HONO+hn-NO+OH

6 JHNO3HNO3+hn-NO2+OH

7 JHO2NO2HO2NO2+hn-NO2+HO2

8 JCH2O HCHO+hn-H+CHO

9 JCH2O HCHO+hn-H2+CO

10 JCH3OOH CH3OOH+hn-CH3O+OH

instabilities was previously observed in the TUV model

even by using 16 and 32 streams (Palancar, 2003) and

they usually affect only one wavelength. The irradiance

at this wavelength take a value either very high or very

low affecting the whole integral. Since these instabilities

are of random nature, only sporadic, and easily detected

(cf. Figs. 1 and 2b) they affect neither the analysis nor

the results of the present work. The second feature is

related to the observed changes in the J-values along the

day as a consequence of the natural changes in the

properties of the atmosphere. The daily variation of

many factors, which define the atmospheric conditions

(aerosol loading, contaminant levels, ozone column

content, etc.), is different for each day and it depends

Range (nm) Zone

315olo1200 Troposp., Stratosp.

lo315 Troposp., Stratosp.

lo420 Troposp., Stratosp.

lo580 Troposp., Stratosp.

300olo400 Troposphere

180olo330 Troposp., Stratosp.

190olo325 Troposp., Stratosp.

260olo360 Troposp., Stratosp.

260olo360 Troposp., Stratosp.

lo360 Troposphere

ARTICLE IN PRESSG.G. Palancar et al. / Atmospheric Environment 39 (2005) 857–866862

on the characteristics of each site. Hence, models do not

include the daily variation of the atmospheric properties,

and the calculations are only related to the SZA, that is

to say, at equal SZA, equal J-value, irradiance, or

actinic flux. This leads to the characteristic symmetry

(respect to the solar noon) between morning and

afternoon. Fig. 3 shows that, even though the sky was

cloudless throughout the day, the atmospheric condi-

tions have changed from the morning to the afternoon.

By using this method the changes along the day in the

properties of the atmosphere can be observed and

analyzed. In fact, for the particular conditions presented

in the analyzed day, the exp-mod JO3-values show

differences up to 7% for the same SZA (701) in the

morning and in the afternoon. These differences reach

10% for SZA up to 801.

The JHCHO calculations show a variation similar to

the JO3calculations. The agreement is better than 3% at

SZA less than 701 and better than 15% for SZA up to

10 20 30 40 50 60 70 80

-50

-40

-30

-20

-10

0

10

20

30

J O3

dif

fere

nce

s (

%)

Solar zenith angle (°)

Fig. 3. Percentage differences between 8-stream and exp-mod

calculations for ozone photolysis. The spikes are due to the

model instabilities. The differences between the morning and

the afternoon reveal the changing atmospheric conditions along

the day.

Table 2

Percentage differences between 8-stream and exp-mod calculations at

No. Reaction SZA

141 201

1 O3+hn-O(3P)+O2 3.1 3.1

2 O3+hn-O(1D)+O2 2.6 4.9

3 NO2+hn-NO+O(3P) 3.9 4.1

4 NO3+hn-NO2+O(3P) 4.1 4.3

5 HONO+hn-NO+OH 3.5 3.7

6 HNO3+hn-NO2+OH 2.3 1.6

7 HO2NO2+hn-NO2+HO2 2.1 1.5

8 HCHO+hn-H+CHO 0.0 0.0

9 HCHO+hn-H2+CO 1.5 1.6

10 CH3OOH+hn-CH3O+OH 2.1 2.0

801. As in the JO3case the best agreement is reached at

midday. Correspondingly, after 651 the calculations

using 2 streams (exp-mod) increasingly overestimate

those ones which use 8 streams. The differences between

morning and afternoon for the exp-mod JHCHO-values

are not as pronounced as in the JO3results. In this case

the maximum deviation is smaller than 4%.

Table 2 shows the variations of the differences

between the 8-stream and the exp-mod calculations as

a function of the SZA (during the morning) for all the

studied reactions. The minimum SZA (141) corresponds

to the solar noon. In this table two different trends can

be observed. In reactions 1, 3, 4, and 5 the exp-mod

calculations undervalue the 8-stream results at all SZA.

On the other hand, reactions 2, and from 6 to 10, show a

behavior in which for SZA greater than 65–701 the 2-

stream calculations overestimate the 8-stream ones.

With only one exception (reaction 2), all the exp-mod

results at solar noon undervalue the 8-stream ones.

5.2. Annual variation

As it can be seen from Fig. 3 and Table 2 the best

agreement between both methods is reached at solar

noon. Thus, in order to analyze the annual variation of

the J-values we plotted the results for the 4 years of

irradiance measurements at the SZA corresponding to

this time. Fig. 4 shows the annual and the interannual

variation of the J-values for reaction 2 calculated for 277

cloudless days by using the exp-mod method and the 8-

stream method. The J-values for the exp-mod method

range from 1.08� 105 s1 to 5.16� 105 s1 while for

the 8-stream calculations the results show a minimum of

1.01� 105 s1 and a maximum of 5.35� 105 s1. The

maximums are located between December and January

while the minimums are between June and July,

according to the seasonal variations of irradiance in

Cordoba City. As it was shown in Palancar and Toselli

surface for the photolysis reactions listed in Table 1

301 401 501 601 701 801

3.5 4.1 4.5 4.9 5.2 5.6

4.0 2.2 1.3 2.0 6.7 30.8

4.6 5.3 5.8 6.4 6.4 5.8

4.6 5.0 5.4 5.9 6.3 6.9

4.2 4.8 5.3 5.7 5.4 3.9

3.2 7.3 6.7 5.9 0.0 10.6

3.0 6.7 6.1 5.3 0.8 12.3

0.0 0.1 0.1 0.1 0.0 0.1

2.0 2.8 2.9 2.9 1.2 3.2

2.9 4.5 4.4 4.0 1.6 3.3

ARTICLE IN PRESS

10/15/1998 7/15/1999 4/15/2000 1/15/2001 10/15/2001 7/15/2002

0

2x10-5

4x10-5

6x10-5

J O3

O

(1D

) (s-1

)

Day

Exp-modModeled

↑

Fig. 4. Annual and interannual variation of the ozone photolysis at solar noon in Cordoba City. Exp-mod and 8-stream calculations

for cloudless days.

10/15/1998 7/15/1999 4/15/2000 1/15/2001 10/15/2001 7/15/2002

-40

-30

-20

-10

0

10

20

30

40

Dif

fere

nce

(%

)

Date

Fig. 5. Percentage differences between 8-stream and exp-mod calculations of J-values for ozone photolysis at solar noon in Cordoba

City. Only data for cloudless days were included (see Fig. 4).

G.G. Palancar et al. / Atmospheric Environment 39 (2005) 857–866 863

(2004b), the maximums do not agree with the summer

solstice but they are shifted toward January due to the

effect of the natural variation of ozone column. Fig. 5

shows the differences between both methods. In this

figure the full horizontal lines show the 720% limits

while the dotted lines show the 710% difference. For

nearly 84% of the days the agreement was better than

10%, in accordance with the results shown in Section 5.1

for 11th November 1999 (see Fig. 3). The rest of the

measurements shows an agreement up to 720% with a

few exceptions exceeding this value. However, note that

these differences of 720% take place periodically. The

+20% differences are originated in aerosol-loaded days,

due to the fact that the 8-stream calculations have been

done under cloudless and no-aerosol conditions. These

periodic increments in the aerosol loading occur in late

winter and spring, between August and November, due

to the particular meteorology of Cordoba City. The

ARTICLE IN PRESS

0.0 0.5 1.0 1.5 2.0 2.50

1x10-5

2x10-5

3x10-5

4x10-5

5x10-5

1x10-5

2x10-5

2x10-5

3x10-5

3x10-5

y= 1.90 x10-5 X - 1.4 x10-6

r2= 0.9661N= 277

J O

3 (s

-1)

UV-B irradiance (Wm-2)

y= -2.0 x10-6 X2 + 1.57 x10-5 X + 9.3 x10-6

r2= 0.9709N= 277

J H

CH

O (

s-1)

(a)

(b)

Fig. 6. Empirical relationship between calculated J-values for

formaldehyde (a) and ozone (b) photolysis, in units of s1, and

experimental UV-B irradiance measurements, in units of

Wm2.

Table 3

Fit parameters for the relationships between experimental UV-

B irradiance and J-values, in units of s1, calculated by using a

2-stream model. X represents the irradiance value in units of

Wm2

Jðs1Þ ¼ aX 2 þ bX þ c

a b c

JO3!Oð1DÞ 0 1.9� 105 1.4� 106

JO3!Oð3PÞ 8.6� 106 7.3� 105 3.1� 104

JNO2!Oð3PÞ 3.8� 104 2.6� 103 4.9� 103

JCH2O!H 1.8� 106 1.5� 105 9.7� 106

JCH2O!H22.6� 106 1.9� 105 2.0� 105

G.G. Palancar et al. / Atmospheric Environment 39 (2005) 857–866864

determining factors for this behavior are the strength of

the winds and the lack of rain (Palancar and Toselli

(2004b) and references therein). Aerosols not only

decrease the total radiation reaching the surface but

also they are one of the most important factors affecting

rd (Cotte et al., 1997). Thus, aerosols contribute to the

departures from the assumed isotropy condition causing

these higher errors. Besides, the 20% differences imply

that the experimental measurements overestimate the

model calculations. These differences are related to the

fact that TOMS can provide only one datum per day.

Thus, while the measurements reflex the real variation of

the ozone column along the day, the calculations have to

be done assuming a constant ozone column content. In

Palancar and Toselli (2004a) it has been shown that

although this assumption does not represent the reality,

in most cases (97%) this approximation leads to good

results because in Cordoba City the delta ozone between

two consecutive days is usually small (10% respect to an

average of 11 years). However, differences as large as 80

Dobson Units (DU) have also been registered between

consecutive days. A statistical analysis of the last 11

years of the ozone column content over Cordoba City

(1991–2002) showed that these large variations occur

systematically during the winter time. As these varia-

tions only affect the exp-mod results they lead to the

observed differences in the J-values determinations.

Due to the fact that the aerosols in Cordoba present

absorbing properties the 20% differences can only be

produced by ozone variations while the +20% can be

originated by either aerosols or ozone variations. Also in

this case the usage of the experimental values allows to

see the actual atmospheric conditions, which can be very

different from those assumed in model calculations.

5.3. Empirical relationships

The first attempts to relate irradiance with photolysis

frequencies have been done through empirical relation-

ships between broadband measurements at surface and

calculations carried out with 2-stream methods. Due to

the fact that these relations are highly dependent on the

particular meteorological conditions predominant in the

site where the measurements were taken their use to

compare with measurements in different places is very

limited. Nevertheless, they can be useful as a first step to

characterize the J variations at a specific site. To show

these relations we have used only clear sky days

(N ¼ 277) of a period of 4 years of measurements

(1999–2002) and a 2-stream method (d-Eddington).Within the reactions analyzed two different behaviors

have been observed: linear or quadratic relationships. In

order to show some examples reactions 1, 2, 3, 8, and 9

were selected. Fig. 6 shows the relationship found

between the broadband irradiance measurements

(Wm2) at solar noon and the calculated JHCHO (a)

and JO3(b) values (s1). From this figure it can also be

seen the minimum and the maximum values for the UV-

B irradiance along the year. Table 3 summarizes the fit

parameters only for the selected reactions. As it was

expected, for reaction 2 a linear relation was found. For

reactions 1, 3, 8, and 9 a quadratic relation was found.

These differences are related with the wavelength range

involving both the cross section and the quantum yield

of each molecule.

6. Summary and concluding remarks

Broadband UV-B irradiance measurements (YES

UVB-1) from a 4-year campaign in Cordoba City and

ARTICLE IN PRESSG.G. Palancar et al. / Atmospheric Environment 39 (2005) 857–866 865

the TUV model were used to apply a new approach

(exp-mod) to convert broadband irradiance measure-

ments at surface to actinic flux and J-values. In this

approach each broadband measurement was split in its

diffuse and direct components and, in turn, in wave-

lengths, based on the percentages given by an 8-stream

method. These data were used as input parameters of the

model to calculate the J-values. Clear sky days and a

constant rd value of 0.5 were used. The main advantages

of this procedure reside in that the J-values can be

calculated from the most common type of measurements

and that it allows to consider the random variations of

the atmospheric conditions along the day. It was shown

that these variations can lead to differences of up to

10% in the J-values for the same SZA (morning-

afternoon). According to the results showed in Section

5.1 for JHCHO and JO3the usage of this method to

calculate the daily variation of J-values leads to a good

agreement with more sophisticated methods (8-stream

discrete ordinate). The results for JO3show an agree-

ment better than 5% for SZA up to 651 and better than

10% for SZA up to 701 although for SZA larger than

701 the differences reached 50%. Therefore, this method

could be included in global atmospheric models to

calculate J-values with an acceptable accuracy and

without consuming as much CPU time as an 8-stream

method. Besides, this work showed that the widely

spread (geographically and temporal) database of

irradiance measurements could be used to extend the

database of either actinic flux or J-values measurements.

Although the method showed a good agreement against

more accurate calculations it should be also validated

against actual actinic flux or photolysis frequencies

determinations, which will be done in future works.

The annual variation of JO3was also analyzed. The J-

values for the exp-mod method ranged from 1.08� 105

to 5.16� 105 s1 while for the 8-stream calculations the

results showed a minimum of 1.01� 105 s1 and a

maximum of 5.35� 105 s1. The agreement for 277

days along the campaign was better than 10%. Some

deviations up to 20% were found although they were

originated by the natural variation of the ozone column

and by the meteorology of Cordoba City (aerosol

loading). Two kinds of empirical relations between the

irradiance measurements and the J-values calculated by

using a 2-stream d-Eddington method were found: linealand quadratic.

Acknowledgements

The authors would like to thank Fundacion An-

torchas, TWAS, CONICET, SeCyT (UNC), and the

Agencia Nacional de Promocion Cientıfica y Tecnolo-

gica (prestamo BID 1201/OC-AR No. PICT 06-06358)

for partial support of this work. G.G. Palancar thanks

CONICET for a post doctoral fellowship. R.P. Fernan-

dez thanks Agencia Cordoba Ciencia and CONICET

for a graduate fellowship. We are very thankful to Dr.

Sasha Madronich for his valuable help with TUV

model.

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