Heard D.E. (editor) Analytical Techniques for Atmospheric Measurement
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468 Analytical Techniques for Atmospheric Measurement
(a) (b)
ϑ
φ
Figure 9.34 Polar diagrams of the relative angular response of radiation detectors for single-hemispheric
measurements. The solid curve in (a) (and the dashed curve in (b)) represent the response of an ideal
2 sr detector for actinic flux, while the solid curve in (b) represents the response of an ideal irradiance
detector (adapted from Hofzumahaus et al., 1999, used with permission of Optical Society of America).
100 2030405060708090
0.0
0.2
0.4
0.6
0.8
1.0
Normalized photon flux
Polar angle ϑ
max
/degree
e (ϑ
max
)
f
(ϑ
max
)
Figure 9.35 Normalised irradiance e = E
max
/F2 sr and actinic flux f = F
max
/F2 sr when the
field-of-view is restricted to polar angles = 0
−
max
. F2 sr represents the actinic flux from the full
hemisphere
max
= 90
. This example assumes an isotropically distributed sky radiance without direct
sunlight (adapted from Hofzumahaus et al., 1999, used with permission of Optical Society of America).
Here the first two steps constitute a calibration which depends on the availability of
absolute photolysis-frequency measurements as a reference. The resulting parametri-
sation is specific to a particular photolysis reaction and usually depends on the
individual radiometer properties.
9.6.2 Physical model–based methods
The theoretical foundation for the mathematical conversion of atmospheric irradiances
into actinic fluxes was outlined by Madronich (1987b) and Van Weele et al. (1995). The
working equation (see Equation A.10 in Appendix A.1) can be formulated as
Measurement of Photolysis Frequencies in the Atmosphere 469
F
E
=
E
1
cos
−r
dd
+r
dd
+r
du
A
s
where F
is the 4 sr actinic flux, E
is the downward irradiance,
E
means the fraction of
the direct irradiance, r
dd
is the ratio of the downward diffuse actinic flux to the downward
diffuse irradiance, r
du
is the ratio of the upward diffuse actinic flux to the upward diffuse
irradiance, and A
s
is the ground albedo. If one is mainly interested in the downwelling
actinic flux, for example because the ground albedo is small, the equation reduces to:
F
E
=
E
1
cos
−r
dd
+r
dd
(9.64)
According to this equation, downwelling actinic fluxes can be derived from measured
irradiances, if the parameters
E
and r
dd
are known. The problem is that the two
conversion parameters
E
and r
dd
have no unique values, but depend on many variables
including foremost the solar zenith angle, wavelength, aerosol abundance, and cloud
cover. At wavelengths below 320 nm, there also exists a dependence on the absorption
by atmospheric ozone.
The direct fraction
E
can be generally calculated as the ratio of the direct to the total
downwelling (global) irradiance (see Equation A.9). At some monitoring stations both
direct and global irradiance are measured routinely (e.g. Kazadzis et al., 2000). However,
when measurements of the direct component are not available,
E
must be obtained
from radiative transfer models (e.g. Cotte et al., 1997; McKenzie et al., 2002; Kylling et al.,
2003a). The model results are usually calculated as a function of wavelength and solar
zenith angle (see examples in Figure 9.36), and require first of all the column density
Figure 9.36 Ratio of the diffuse downward irradiance E ↓ to the global irradiance E
= E
0
+E ↓ from
measurements during clear-sky and low aerosol conditions in Boulder, Colorado, on 19 June, 1998.
Model values for different solar zenith angles are shown for comparison (adapted from McKenzie et al.,
2002, printed with permission from American Geophysical Union).
470 Analytical Techniques for Atmospheric Measurement
and scattering properties of the atmospheric aerosol as input parameters. When the sun
is blocked by clouds,
E
is set to zero. This condition applies in good approximation
when the ratio of the measured irradiance to the expected clear-sky value at 330–380 nm
is less than 0.8 (McKenzie et al., 2002; Kylling et al., 2003a).
The diffuse ratio r
dd
depends on the angular distribution of the diffuse downward
radiance (cf. Equation A.6; see also Figure 9.4) and is generally difficult to obtain
experimentally. In a first approximation it is often assumed that the downward diffuse
radiance is isotropically distributed, resulting in a value of r
dd
=2. Ruggaber et al. (1993)
investigated theoretically the dependence of r
dd
on various atmospheric parameters for
cloud-free conditions and came to the conclusion that the assumption of r
dd
=2 results in
errors up to 50% for the diffuse actinic flux. They noted that the ratio shows considerable
variability as a function of the solar zenith angle, wavelength, aerosol number density,
ozone profile, albedo, and height, and that no simple formula exists that can be used to
describe r
dd
. Thus, r
dd
values are usually derived from one-dimensional radiative transfer
models, which can simulate either clear-sky or completely overcast conditions (e.g. Cotte
et al., 1997; Kylling et al., 2003a; Kazadzis et al., 2004). Partial cloudiness, however,
cannot be treated explicitly owing to the one-dimensional character of the models and
the general lack of observed cloud input-data (see Section 9.7). In the particular case of
a completely overcast sky, the diffuse ratio was found to lie in the range 175 ±015 and
to have only a small variability with the solar zenith angle and wavelength for conditions
with a small surface albedo (Kazadzis et al., 2000, 2004). This experimental result is in
good agreement with corresponding model calculations (Van Weele et al., 1995; Kylling
et al., 2003a).
9.6.2.1 Accuracy
The conversion of UV irradiances into actinic fluxes was tested in a number of field
experiments, where spectral data of irradiances and actinic fluxes were measured by
synchronised spectroradiometers (McKenzie et al., 2002; Webb et al., 2002a; Kylling et al.,
2003a; Kazadzis et al., 2004). Equation 9.64 was used to convert the measured irradiances
into actinic fluxes, which were then compared to measured data of F
. Figure 9.37 shows
for example ratios of j-values that were determined from estimated and directly measured
actinic-flux spectra. Results are shown for three days with partial cloudiness (15, 16, 18
June, 2002) and one clear-sky day with very little aerosol (19 June, 1998). Values for
E
were obtained from a simple single-layer model (cf. Figure 9.36) and r
dd
was calculated
using a model-based parametrisation (McKenzie et al., 2002). Under clear-sky conditions
and at solar zenith angles less than 80
, the photolysis frequencies jO
1
D and jNO
2
derived from the estimated actinic-flux data show deviations up to 10% relative to j-values
derived from direct actinic-flux measurements (Figure 9.37). Under cloudy conditions,
the conversion errors can be larger. They are generally less than 20% for jO
1
D, but can
be larger for jNO
2
, which is attributed to the partial cloudiness causing departures from
the assumed angular distribution of the sky radiance (McKenzie et al., 2002).
Other field studies have obtained similar results. It was found that the assumption of
an isotropic diffuse radiance leads to an overestimation of the actinic flux by 10–15%
for clear-sky conditions (Kazadzis et al., 2000; Kylling et al., 2003a). When the diffuse
ratio and the fraction of direct radiation are calculated by a detailed one-dimensional
Measurement of Photolysis Frequencies in the Atmosphere 471
Figure 9.37 Ratios of j-values derived from measured spectral irradiances and measured spectral actinic
fluxes. The data were obtained at 1.6 km altitude in Boulder, Colorado, from 15 to 19 June, 1998 (adapted
from McKenzie et al., 2002, printed with permission from American Geophysical Union).
radiative transfer model, the uncertainty of the irradiance to actinic-flux conversion is
generally less than 10% on cloud-free days (Kazadzis et al., 2000; Webb et al., 2002a;
Kylling et al., 2003a). The conversion errors for a broad range of conditions, including
situations with and without clouds, were studied by Kylling et al. (2003a) for different
European monitoring sites. The ratios of the estimated to measured actinic fluxes were
found to vary around unity with a standard deviation in the order of 10% 1 over all
conditions, with a tendency to overpredict the actinic flux under clear-sky conditions
and to underpredict the actinic flux when clouds were present.
When photolysis frequencies are derived from estimated actinic-flux data, the resulting
total error has three main contributions. One is the error of the radiometer calibration and
another one is the uncertainty of the absorption cross sections and quantum yields. These
two error contributions are essentially the same as for actinic-flux spectroradiometry (see
Table 9.6). An additional error is caused by the conversion of the measured irradiance
data into actinic fluxes. This error is variable and depends on the ambient conditions,
like for example cloudiness, as discussed above.
9.6.3 Empirical methods
Different methods have been proposed to predict in a simple way photolysis frequencies
from measured irradiances by statistical methods, of which some will be mentioned here.
For example, an almost linear relationship was observed in Bonn, Germany, between
measured NO
2
photolysis frequencies and broadband (300–3000 nm) irradiances G,
which can be approximated by a linear regression (Bahe et al., 1980):
jNO
2
s
−1
= 133 ×10
−4
+887 ×10
−6
GW ·m
−2
(9.65)
472 Analytical Techniques for Atmospheric Measurement
Because of the constant offset, which has no physical meaning, the equation is useful
only for values of G>70W ·m
−2
for estimating jNO
2
from standard meteorological
measurements of broadband radiation. The surprisingly linear correlation is the result
of the accidental compensation of different spectral and geometrical dependencies of the
jNO
2
and irradiance measurement instruments. A similar regression was reported for
measurements on the Atlantic Ocean (Brauers & Hofzumahaus, 1992).
A nonlinear correlation was observed for jNO
2
measured by chemical actinometers
versus broadband irradiances (295–385 nm) measured by Eppley UV radiometers
(Harvey et al., 1977; Zafonte et al., 1977; Dickerson et al., 1982; Parrish et al., 1983;
Madronich et al., 1983). The nonlinearity is caused mainly by the different geomet-
rical responses of the instruments and less by the spectral radiometer sensitivity, which
matches approximately the wavelength range of the NO
2
photodissociation (Madronich
et al., 1983). Based on the physical model that leads to Equation A.12, Madronich
(1987b) developed a parameterisation that related measured jNO
2
values to the corre-
sponding broadband UV irradiances, E, measured by standard Eppley radiometers
W ·cm
−2
:
jNO
2
E
= C
1
J
cos +051 −
J
+2A
s
(9.66)
Here, C is an empirical factor 135 ±005cm
2
J
−1
for clear-sky conditions, is the
solar zenith angle, A
s
is the surface albedo, and
J
is the ratio J
0
/J
0
+J ↓, where J
0
and J ↓ represent the photolysis-frequency components caused by direct and downward
diffuse radiation, respectively. The relationship in Equation 9.66 has been used in
various field experiments to predict the jNO
2
values from UV measurements (e.g.
Shetter et al., 1992; Lantz et al., 1996). Its application requires
J
values that must
be calculated by a model and assumes that the upwelling and downwelling diffuse
radiances are isotropic. The parametrisation does not consider possible differences in
the spectral sensitivity of individual broadband radiometers and does not correct for
the spectral mismatch of the radiometer sensitivity to the photodissociation spectrum
of NO
2
. The accuracy of the relationship was tested against chemical actinometry
for a broad range of conditions at Mauno Loa (Hawai) (Shetter et al., 1992). The
estimated jNO
2
values were found to be accurate to within ±10% for clear skies and
independent of the solar zenith angle, and to ±20% for conditions with scattered clouds
(Figure 9.38).
Other empirical methods involve spectrally resolved irradiances to estimate the
photolysis frequencies of O
3
or NO
2
(McKenzie et al., 2002; Kazadzis et al., 2004).
These methods use polynomial statistical fits, but have the disadvantage that they
require narrow bandwidth UV measurements by a spectroradiometer for the prediction
of j-values. A technically more simple approach uses a multichannel filter radiometer
that measures UV irradiances at five different wavelengths with a bandwidth of about
10 nm (Seroji et al. , 2004). In this approach the photolysis frequencies of O
3
,NO
2
,
and HCHO can be derived from linear combinations of the spectral measurement
channels, which were calibrated against photolysis frequencies determined by actinic-flux
spectroradiometry.
Figure 9.38 Deviation of estimated jNO
2
values from direct measurements by a chemical actinometer. The estimated values were derived from broadband
UV irradiances obtained on Mauna Loa, Hawai, in May 1988. The left panel applies to periods without overhead clouds, but with lower lying valley clouds
in many cases. The right panel applies to periods with scattered overhead clouds (adapted from Shetter et al., 1992, printed with permission from American
Geophysical Union).
474 Analytical Techniques for Atmospheric Measurement
9.7 Modelling of photolysis frequencies
Photolysis frequencies are highly variable in space and time owing to the influences of
many varying atmospheric parameters. In situ measurements can provide data only in
a few places and times. For this reason, many atmospheric chemistry models rely on
photolysis frequencies that are derived from modelled radiation fields.
These are determined by means of radiative transfer (RT) models that use the extrater-
restrial solar spectrum as input, as well as vertical distributions of atmospheric parameters
(pressure, temperature, aerosol, ozone, clouds) and the earth’s surface albedo (see for
example Demerjian et al. (1980); Madronich (1993); Mayer & Kylling (2005)). The models
also require the absorption and scattering cross sections for the interaction of solar
radiation with atmospheric gases and aerosols. In a second step, photolysis frequencies are
calculated according to Equation 9.12, requiring the knowledge of the relevant parameters
and .
Radiative transfer models can differ significantly in the complexity of details describing
the transport of radiation in the atmosphere. For example, models can vary in the detailed
implementation of the atmospheric structure and composition, the spectral coverage
and resolution of the radiation spectrum, or the detailed treatment of the scattered
radiation (e.g. Bais et al., 2003). Most operational models are one-dimensional and treat
the atmosphere as a vertically inhomogeneous medium that is composed of a finite
number of homogeneous layers. This concept requires that absorbers and scatterers are
uniformly distributed over horizontal distances that are much wider than the thickness
of the respective model layers. In a realistic atmosphere, this is most likely the case
under cloud-free conditions, or when stratiform clouds extend across the sky. Despite the
limitation to a one-dimensional treatment, such models are widely used in atmospheric
chemistry and apply simplified parametrisations to handle broken cloud fields which
have horizontally inhomogenous properties (see e.g. Tie et al., 2003).
There have been attempts to simulate the transport of short-wave radiation in cloudy
atmospheres with two- and three-dimensional models (e.g. Los et al., 1997; Trautmann
et al., 1999). In practice, these models require too much computing time and lack
suitable input data, in order to be useful in current atmospheric chemistry models. In
some applications like global modelling, even one-dimensional RT models require too
much computer resources, because of the many wavelengths needed for the calculation
of photolysis frequencies. In these cases atmospheric models often apply parameterised
photolysis frequencies that have been precalculated with more sophisticated models as
functions of atmospheric input parameters.
Besides its use for predictions in atmospheric chemistry, RT models are also useful as
supporting tools for some kind of photolysis-frequency measurement methods, which
require some knowledge of the spectral or spatial distribution of the atmospheric
radiation. This is the case with actinic-flux filter radiometers, where the spectral compo-
sition of the actinic flux is needed for the development of an instrumental calibration
function (Section 9.5.3). Another example is the conversion of irradiances into actinic-
flux data, which requires the knowledge of the angular distribution of the diffuse
radiance (Section 9.6.2).
A detailed discussion of RT models is beyond the scope of this book. Details of the
theory of transport of solar radiation in the atmosphere can be found in text books,
Measurement of Photolysis Frequencies in the Atmosphere 475
for example by Goody and Yung (1989), Lenoble (1993), or Thomas and Stamnes
(1999). References to currently used models and a discussion of their ability to simulate
atmospheric actinic fluxes and photolysis frequencies can be found, for example, in Olson
et al. (1997); Bais et al. (2003); Shetter et al. (2003), and Hofzumahaus et al. (2004).
9.8 Sample applications
9.8.1 Photochemistry field experiments
Photolysis frequency measurements are an important integral part of any photochem-
istry field experiment. Atmospheric radical concentrations, ozone production rates, or
photochemical aging of emitted pollutants can only be understood quantitatively, if
the observation of trace gases is accompanied by photolysis-frequency measurements of
relevant compounds, like O
3
NO
2
, HCHO, etc. The important role of solar radiation in
tropospheric chemistry is illustrated in Figure 9.39. It shows the strong dependence of OH
radical concentrations on the solar UV, represented here by jO
1
D. The observed close
correlation between OH and jO
1
D is caused by the photochemical OH formation and
the short lifetime of the radicals, which respond immediately within seconds to changes
of their production rate (Hofzumahaus et al., 1996). Similar observations have been
0
2
4
6
8
10
12
04 06 08 10 12 14 16 18
0
2
4
6
8
10
12
[OH] /10
6
cm
–3
0.0
0.5
1.0
1.5
2.0
j (O
1
D)/10
–5
s
–1
17Aug.
Daytime/h (UT)
16 Aug.
0.0
0.5
1.0
1.5
2.0
Figure 9.39 Diurnal cycles of OH measured by laser-induced fluorescence and jO
1
D measured with a
filter radiometer. The data were collected at ground in North-East Germany on 16 and 17 August, 1994.
The fast variations seen in jO
1
D were caused by changing broken clouds (adapted from Holland et al.,
1998, with kind permission of Springer Science and Business Media).
476 Analytical Techniques for Atmospheric Measurement
reported from other field studies for OH (e.g. Eisele et al., 1997; Abram et al., 2000;
Brauers et al., 2001; Mauldin III et al., 2001; Berresheim et al., 2003; Holland et al.,
2003) and for peroxy radicals, HO
2
and RO
2
(e.g. Cantrell et al., 1992; Penkett et al.,
1997; Kanaya et al., 1999). The strong sensitivity of free radical concentrations to solar
radiation implies that photolysis frequencies must be measured (or modelled) first and
foremost with high accuracy, when photolysis data are to be used as model input for
reliable predictions of atmospheric photochemistry.
9.8.2 Temporal and spatial distributions
The distribution of photolysis frequencies over different temporal and spatial scales
can be simulated by radiative transfer models with different degrees of approximation
(see Section 9.7), but corresponding measured data are rather limited, in particular
over large scales. The temporal behaviour of photolysis frequencies was investigated
mostly for O
3
and NO
2
in the form of diurnal variations that were observed over time
periods of weeks or months in field campaigns (e.g. Shetter et al., 1992, 1996). Longer
time records are generally not available and may be obtained at present only from the
conversion of UV-irradiance data that are recorded at surface monitoring stations (see
Section 9.6).
Photolysis frequency measurements over large spatial scales are also rare. Figure 9.40
shows one example of the latitudinal distribution of jO
1
D that was measured
together with jNO
2
between 50
N and 30
S in early fall 1988 near-equinox condi-
tions (Hofzumahaus et al., 1992; Brauers & Hofzumahaus, 1992). The distribution was
recorded on a ship cruise along 30
W and shows superimposed diurnal variations. The
diurnal maxima show highest values in the tropics, where the solar zenith angles are
smaller and the stratospheric ozone layer is thinner than at high latitudes. A strong
reduction of jO
1
D was observed at 5
N in the innertropical convergence zone (ITCZ),
where thick cloud layers attenuated the solar radiation. Also shown are measurements of
ozone and water vapour, which were used together with jO
1
D to calculate the primary
production rate of OH, P
OH
, from the ozone photolysis. The figure indicates that the OH
production is largest in the tropics where water vapour and solar actinic flux are most
abundant.
Another important aspect is the vertical distribution of atmospheric photolysis
frequencies. Figure 9.41 shows as an example the measured actinic flux at selected
wavelengths between 120 m and 12 km altitude above the Agean Sea (Greece) for
cloudless-sky conditions (Hofzumahaus et al., 2002). The largest vertical gradients were
observed at short wavelengths in the lowest 3 km above the sea surface as the result of
ozone absorption and aerosol scattering. The observations agree well with model simula-
tions that were constrained by measurements of aerosol and ozone. Similar agreement
between measured and modelled radiation has been reported for cloud-free conditions
from another aircraft study that was performed in the same altitude range over the
western Pacific Ocean (Lefer et al., 2003).
Vertical (and horizontal) distributions of photolysis frequencies are much more
complex in the presence of clouds (Junkermann, 1994; Pfister et al., 2000; Früh et al., 2000;
Lefer et al., 2003; Kylling et al., 2005). The possible cloud impact can be seen for example
Measurement of Photolysis Frequencies in the Atmosphere 477
Latitude/degree
NS
[O
3
] (ppb)
[H
2
O] (hPa)
j (O
1
D) (10
–5
s
–1
)
P
OH
(10
6
cm
–3
s
–1
)
020–20 40
30
25
20
15
10
60
40
20
0
3
2
1
0
8
6
4
2
0
Figure 9.40 Latitudinal variation of jO
1
D, ozone and water vapour measured on board a ship over the
Atlantic from 18 September to 5 October, 1988. The latitudinal dependence of jO
1
D was superimposed
by diurnal variations while the ship cruised from North to South. Also shown is the primary OH production
rate P
OH
calculated from the ozone photolysis (adapted from Hofzumahaus et al., 1992, with kind
permission of Springer Science and Business Media).