Atmospheric and Climate Sciences, 2011, 1, 142-146
doi:10.4236/acs.2011.13016 Published Online July 2011 (http://www.SciRP.org/journal/acs)
Comparison of UV-B Broadband Brewer Measurements
with Irradiances from Surface-Based and Satellite-Based
Models
Jacqueline Binyamin1, John Davies2, Bruce McArthur3
1Department of Ge ography, University of Winnipeg, Winnipeg, Canada
2School of Geography and Earth Sciences, McMaster University, Hamilton, Canada
3Air Quality Research Branch, Meteorological Service of Canada, Toronto, Canada
Received May 1, 2011; revised June 13, 2011; accepted June 28, 2011
Abstract
UV-B irradiance can be estimated from surface meteorological data or from satellite measurements. This pa-
per compares irradiance estimates from the Davies surface-based radiation model and the Canada Centre for
Remote Sensing (CCRS) satellite model with Brewer spectrophotometer measurements for all sky conditions
at six Canadian stations (Edmonton, Regina, Winnipeg, Montreal, Halifax and Toronto). The Davies model
is applied with both the discrete ordinate radiative transfer (DISORT) and the delta-Eddington algorithms to
solve the radiative transfer equation.
Both models’ estimates are compared with instantaneous Brewer measurements. Both perform similarly
with mean bias errors within 6% of the mean measured irradiance for the measurement period and root mean
square errors between 25% and 30%.
Keywords: UV-B Irradiance, Brewer Spectrophotometer, DISORT, Delta-Eddington, TOMS,
Satellite-Based Models, Surface-Based Models
1. Introduction
Stratospheric ozone depletion increases the amount of
harmful UV-B (290 - 325 nm) irradiance reaching the
earth’s surface [1]. Instruments such as the Brewer spec-
trophotometer measure spectral irradiance [2], but meas-
urements in Canada and internationally are spatially s-
-parse and are generally of short duration. Radiation md-
els can estimate irradiance for locations and times with-
out measurements and can predict irradiances for possi-
ble changes in ozone concentrations.
Radiation models use either surface meteorological
data or satellite measurements. Models, which use sur-
face data, apply algorithms, which vary from simple ap-
proximations [3] to rigorous solutions of the radiative
transfer equation. The two most widely used radiative
transfer solutions are the discrete ordinate radiative trans-
fer (DISORT) model [4] and the delta-Eddington model
[5]. Since these use local data, they should represent
point conditions more accurately than the large area es-
timates from satellite.
Satellites measure reflected radiances at the top of the
atmosphere which, combined with radiative transfer cal-
culations or inversion algorithms, provide estimates of
the irradiance at the surface [6-8]. Although satellite meas-
urements provide extensive spatial coverage they usually
provide, unless they are sun synchronous, one measure-
ment each day, which prohibits the calculation of daily
total irradiance.
Comparisons of model calculations with measurements
are mostly restricted to data for a few cloudless days
[9-12]. Few studies have validated surface-based models
for all sky conditions [13-17].
This paper compares broadband irradiances (290 - 320
nm) from a surface-based model [16,17] and from the
Canada Centre for Remote Sensing (CCRS) Meteor-3/
total ozone mapping spectrometer (TOMS) satellite ba-
sed-model [6-8] with Brewer spectrophotometer meas-
urements in Canada.
2. Irradiance Measurements
Brewer spectrophotometer measurements for six Can

J. BINYAMIN ET AL.143
Table 1. Canadian UV-B monitoring stations used in the
study.
Station Latitude,
˚N
Longitude,
˚W
Elevation,
m
Years of
data
Edmonton (Alta.) 53˚33′ 114˚06′ 766 1993-1994
Regina (Sask.) 50˚13′ 104˚40′ 592 1994
Winnipeg (Man.) 49˚55′ 97˚14′ 239 1993
Montreal (Que.) 45˚28′ 73˚45′ 24 1993-1994
Halifax (NS) 44˚44′ 63˚40′ 31 1993-1994
Toronto (Ont.) 43˚47′ 79˚23′ 198 1993-1994
dian locations, for which there were simultaneous satel-
lite-based irradiances, are used in this study (Table 1).
This instrument allows for the calculation of daily ozone
depth and measures spectral irradiance for wavelengths
between 290 and 325 nm at a resolution of 0.5 nm. Ra-
diation measurements are made once or twice each hour
from sunrise to sunset at irregular times in GMT [18].
Following Krotkov et al. [12] and Wang et al. [19] the
Brewer values were increased by 6% to compensate for
the cosine error.
3. The Davies Model
The model developed by Davies et al. [16] and modified
by Binyamin et al. [17] is used in this study. Surface
irradiance is calculated as a linear combination of
clear and overcast sky irradiances weighted
with cloud fraction:
G
GG
C

1GCGCG

 .

(1)
G and are calculated spectrally at wavelength
interval of 1 nm using either the DISORT [4] or the
delta-Eddington [5] solutions to the radiative transfer
equation for a vertically inhomogeneous 49-layer, 120
km, plane parallel atmosphere, with cloud inserted be-
tween 2 and 3 km heights. The model uses spectral val-
ues of the extraterrestrial irradiance from the Solar Ul-
traviolet Spectral Irradiance Monitor (SUSIM) ATLAS-3
space shuttle mission (D. Prinz, personal communication,
2002), ozone absorption coefficients from Paur and Bass
[20], Rayleigh scattering cross sections following Elter-
man [21], aerosol optical properties from Shettle and
Fenn [22], a fixed cloud optical depth of 27 [17,23], and
a fixed surface albedo of 0.05 [24]. Hourly total cloud
opacity observations were obtained from the Meteoro-
logical Service of Canada.
G
4. The CCRS Satellite Model
The CCRS satellite algorithm for retrieving surface ir-
radiance [6] is based on a linear relationship between
TOA albedo at 360 nm and surface absorbed irradiance.
The surface irradiance is given by:


0 03360
cos1 0.1960.798
(1 )
d
sus
ST a
Ga


 
 (2)
where 0 is the extraterrestrial irradiance;S

the solar
zenith angle ;03 the band-mean transmittance due to
ozone absorption; 360
T

the albedo for the earth-atmos-
phere system at 360 nm;
s

surface albedo; and d
and u represent aerosol absorption for the downwel-
ling and upwelling irradiance.
a
a
The extraterrestrial irradiance was taken from Fröhlich
and London [25]. Total ozone amount was taken from
the TOMS data set. Surface albedo was assumed to be
0.04 for Toronto and 0.03 for other stations. Aerosol
optical depth a

measurements were available for To-
ronto [19] and a value of 0.31 was substituted for miss-
ing days. For Winnipeg and Edmonton a

was assumed
to be 0.2, and 0.1 for the remaining stations. Aerosol
single scattering albedo was assumed to be 0.95 for all
stations. The model can only be used for days without
snow cover.
5. Comparison of the Davies Model and
CCRS Model Results
The Meteor 3 reflectance measurements were made at
different local times, with usually once per day, with a
maximum of two values per day that matched the times
of Brewer measurements (Pubu Ciren, CCRS, personal
communication, 2007). Each CCRS model estimate is
compared with a simultaneous Brewer measurement and
a calculation from the Davies model using both the
delta-Eddington and DISORT methods. There is a small
difference in the spectral integration range used by
CCRS and the Davies model. CCRS presents irradiances
integrated over the 290 - 320.5 nm wavebands in 0.5 nm
steps while the Davies irradiances were integrated in 1
nm steps over the 290 - 320 nm range. In this section,
both models are compared with Brewer measurements
integrated to the upper wavelength limit appropriate to
the model.
Comparison of the Davies model broadband irradian-
ces and the simultaneous satellite-based results with Bre-
wer measurements made at six stations (Edmonton, Re-
gina, Winnipeg, Montreal, Halifax and Toronto) in 1993
and 1994 (Table 1) are presented in Figure 1. They rep-
resent 10 station years of instantaneous data mainly be-
tween May and September, with 605 data points in total.
Generally, the agreement between the three is visually
good for all stations. The MBE (mean difference) values
correspond to less than 0.04 W·m-2 on average for indi-
vidual stations and pooled data for both surface-based
and satellite-based methods.
Table 2 provides performance statistics for both indi-

J. BINYAMIN ET AL. 144
Figure 1. Comparison between Davies model calculations, CCRS satellite-based model calculations and measured UV- B ir-
radiances for all sky conditions for Edmonton, Regina, Winnipeg, Montreal, Halifax and Toronto. The dotted lines represent
linear regressions constrained to pass through the origin. A different symbol represents data for each station.
vidual stations and pooled data. For the pooled data, the
Davies model with the delta-Eddington and DISORT
methods and the CCRS model underestimate Brewer
measurements by less than 6% of the mean measured
irradiance. For the individual stations the relative MBE
values range between ±6% for the delta-Eddington me-
thod, between –10% and 0.2% for the DISORT method
and between –11% and 0.3% for the satellite-based me-
thod. These irradiance differences are smaller than dif-
ferences between near simultaneous measurements made
with different ground instruments ±10% [26-29]. The re-
lative RMSE values for the pooled data are similar (26%
and 29%) for the two methods. For the individual sta-
tions, relative RMSE values range from 24 to 34% for
the Davies model and from 20 to 40% for the satellite-
based model. This agrees well with the findings of Fio-
letov et al. [30] and Wang et al. [31] who found that dif-
erences between TOMS-estimated UV-B irradiances f

J. BINYAMIN ET AL. 145
Table 2. Summary of the Davies model and satellite-based method performance measures against Brewer measurements for
broadband irradiances (290 - 320 nm) for each satellite time for the period indicated for each station. is the number of
data points and N
M is the mean measured irradiance (W·m–2). MBE and RMSE are expressed as percentages (italic) of M.
Positive MBE values indicate model overestimation.
Irradiance results Edmonton
1993-1994 Regina 1994Winnipeg 1993Montreal 1993-1994
Halifax
1993-1994
Toronto
1993-1994 Pooled data
N 115 48 88 20 159 175 605
Davies model using delta-Eddington metho
M
1.16 1.20 1.54 0.66 1.19 1.13 1.21
MBE 6.22 –0.79 –4.97 2.13 –5.66 3.64 –0.29
RMSE 31.73 25.05 24.25 26.53 24.50 33.46 28.59
Davies model using DISORT method
MBE 0.15 –6.62 –10.06 –5.78 –10.28 –2.38 –5.80
RMSE 28.94 25.72 25.88 27.76 25.93 33.85 28.91
Satellite method
M
1.26 1.31 1.68 0.72 1.30 1.23 1.31
MBE 0.26 –5.14 –9.75 –10.86 –1.40 0.06 –2.73
RMSE 25.49 22.30 24.11 40.05 20.45 31.03 25.76
and Brewer observations range from 3 to 11% and can be
attributed to the Brewer angular response error.
6. Conclusions
This is the first study to compare the performance of
satellite-based model with ground-based model estimates
of UV-B irradiance. The two models perform almost i-
dentically. Differences in performance are within the
uncertainties in Brewer measurements. Different fields of
view of the TOMS instrument, the Brewer spectropho-
tometer and the Davies model seem to be inconsequen-
tial.
The satellite model can be applied virtually anywhere
and does not require other observations. However, it
does have two drawbacks. Firstly, because it cannot cal-
culate irradiance throughout the day, it cannot produce
daily totals. Secondly, it cannot be used over snow-cov-
ered surfaces because it is incapable of discriminating
differences between cloud and surface reflections. The
Davies model produces daily irradiance totals but its use
is currently restricted to stations with cloud observations.
Future work should examine the use of satellite cloud
data. The use of the delta-Eddington method is especially
appealing for calculating broadband irradiances since it
is computationally less demanding than DISORT
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