The

Radiative transfer models (RTMs) are often used to provide estimates of the
UV irradiance. One of the difficulties in the computation lies in taking
into account the gaseous absorption cross sections that are highly
wavelength dependent (Molina and Molina, 1986). For instance, the ozone
cross section changes by more than 2 orders of magnitude over the UV band
[280, 400] nm. The best estimate of the UV irradiance is made by a
spectrally resolved calculation of the radiative transfer for each
wavelength followed by integration over the UV band. However, such
spectrally detailed calculations are computationally expensive. Therefore,
several methods have been proposed to reduce the number of calculations.
Among them are the

For a spectral interval

The underestimation for these two bands can be explained by the fact that Kato et al. (1999) assume that the ozone cross section at the center wavelength in each interval represents the absorption over the whole interval. The ozone cross sections were taken from WMO (1985). Actually, the ozone cross section is strongly dependent on the wavelength in the UV region (Molina and Molina, 1986). Both KBs #3 and #4 in the UV range are large for considering only a single value of the ozone cross section.

In order to improve the potential of the Kato et al. method for estimating narrowband UV irradiances, in particular for the KBs #3 and #4, a new parameterization is proposed for the transmissivity due to the sole ozone absorption. Then, for each spectral interval, an assessment of the performance of the new parameterization in representing this transmissivity is made for a wide range of realistic cases against detailed spectral calculations. A short section describes how to implement this parameterization in the practical case of the RTM libRadtran 1.7. Finally, in each KB, the performance of the new parameterization is assessed when the direct normal, upward, downward, and global irradiances at different altitudes are computed.

The average transmissivity

A technique widely used for computing

In the Kato et al. method, only one exponential function (

Is there a single effective ozone cross section that may represent the
absorption over the whole interval? If so, this effective cross
section

Ozone cross sections at 203 K as a function of the wavelength.

Scatterplot between average transmissivity

The 10 000 simulations yield a set

Estimated transmissivities

Scatterplot between average transmissivity

In KB #4,

The new parameterization

Many solutions are possible. No systematic scan of possible solutions in

Sub-intervals, effective ozone absorption coefficient and weight in
each wavelength interval for computing

Statistical indicators obtained by using the new parameterization for
computing the transmissivity due to the sole ozone absorption in each Kato
band. No. is the number of KB,

Mean irradiances (left vertical axis), biases and RMSEs (right
vertical axis) at different altitudes in KB #3 and KB #4 for

To assess the performance of this new parameterization, reference
transmissivity

The file

Including the new parameterization needs two actions. Firstly, for KB #3
and KB #4, set the second column to 4 and the third column to

Statistical indicators of the performances of the new parameterization for computing the irradiances in Kato band #3 at different altitudes above ground level. Mean is the mean irradiance obtained from the detailed spectral calculations considered as reference.

Statistical indicators of the performances of the new parameterization for computing the irradiances in Kato band #4 at different altitudes above ground level. Mean is the mean irradiance obtained from the detailed spectral calculations considered as reference.

This section presents the errors made by using the new parameterization in
calculating irradiances in KBs #3 and #4. To that extent, a set of
10 000 atmospheric states have been randomly built following the marginal
distribution variables described in Table 2 of Wandji Nyamsi et al. (2014),
except for the solar zenith angle varying uniformly between 0 and
89

The deviations are summarized by the bias, RMSE and the correlation coefficient for each altitude and in each KB (Tables 3, 4). The biases and RMSE at each altitude are summarized in Fig. 4 for both KBs. The squared correlation coefficient is greater than 0.999, in most cases with a minimum at 0.992. This demonstrates that the new parameterization reproduces well the changes in irradiance in all cases.

The direct normal irradiance increases with altitude and exhibits negative
and positive biases in both KBs #3 and #4. The bias varies as a function
of the altitude. In KB #3 it reaches a minimum of

The downward irradiance decreases with altitude. The bias is positive in
both KBs #3 and #4. It is fairly constant with altitude in KB #3,
fluctuating between 0 and 0.007 W m

The upward irradiance is fairly constant with altitude in both KBs #3 and
#4. The bias and the RMSE are fairly constant with altitude in KB #3,
fluctuating respectively between

The global irradiance increases with altitude and exhibits negative and
positive biases in both KBs #3 and #4. The bias varies as a function of
the altitude. In KB #3, similarly to the case of the direct normal
irradiance, the bias exhibits a minimum of

A similar comparison was made by Wandji Nyamsi et al. (2014) with the
original approach of Kato et al. (1999) but for altitudes varying between 0
and 3 km. They reported relative bias, relative RMSE and

The present paper has shown the inadequacy of parameterization of the
transmissivity due to the sole ozone absorption based on a single ozone
cross section for the bands KB #3 [283, 307] nm and KB #4 [307,
328] nm in the

The authors thank the teams developing libRadtran
(