1Grupo de FõÂsica de la AtmoÂsfera, Departamento de FõÂsica Aplicada, Universidad de Granada, Granada, Spain 2Grupo de FõÂsica de la AtmoÂsfera, Departamento de FõÂsica Aplicada, Universidad de MaÂlaga, MaÂlaga, Spain
On the use of a cloud modi®cation factor for
solar UV (290±385 nm) spectral range
I. Foyo-Moreno1, I. Alados2, F. J. Olmo1, J. Vida1, and L. Alados-Arboledas1
With 5 Figures
Received November 15, 1999 Revised September 11, 2000
Summary
Knowledge of ultraviolet radiation is necessary in different applications, in the absence of measurements, this radio-metric ¯ux must be estimated from available parameters. To compute this ¯ux under all sky conditions one must consider the in¯uence of clouds. Clouds are the largest modulators of the solar radiative ¯ux reaching the Earth's surface. The amount and type of cloud cover prevailing at a given time and location largely determines the amount and type of solar radiation received at the Earth's surface. This cloud radiative effect is different for the different solar spectral bands. In this work, we analyse the cloud radiative effect over ultraviolet radiation (290±385 nm). This could be done by de®ning a cloud modi®cation Factor. We have developed such cloud modi®cation Factor considering two different types of clouds. The ef®ciency of the cloud radiative effect scheme has been tested in combination with a cloudless sky em-pirical model using independent data sets. The performance of the model has been tested in relation to its predictive capability of global ultraviolet radiation. For this purpose, data recorded at two radiometric stations are used. The ®rst one is located at the University of AlmerõÂa, a seashore location (36.83N, 2.41W, 20 m a.m.s.l.), while the second
one is located at Granada (37.18N, 3.58W, 660 m a.m.s.l.),
an inland location. The database includes hourly values of the relevant variables that cover the years 1993±94 in AlmerõÂa and 1994±95 in Granada. Cloud cover information provided by the Spanish Meteorological Service has been include to compute the clouds radiative effect. After our study, it appears that the combination of an appropriate cloud-less sky model with the cloud modi®cation Factor scheme provides estimates of ultraviolet radiation with mean bias deviation of about 5% that is close to experimental errors. Comparisons with similar formulations of the cloud radiative
effect over the whole solar spectrum provides evidence for the spectral dependency of the cloud radiative effect.
1. Introduction
Ultraviolet radiation contributes relatively little energy to the solar spectrum, but affects human health (inmunosupression, carcinogenesis, eye cataracts), terrestrial plants, aquatic ecosystems, materials damage and the air quality in the lower troposphere (Feister and Grewe, 1995). This radiometric ¯ux is strongly affected by the presence of clouds. Clouds enhance the diffuse component of any solar radiative ¯ux whilst providing an effective reduction of the direct component if the cloud is in front of the sun. The sum of both components, the global component, suffers a subsequent modi®cation characterised by the modi®cation of its partitioning in direct and diffuse components and generally, an overall reduction averaging over time.
However, partly cloudy skies can either enhance or reduce UV depending on the geometry of the cloud cover and the relative position of the sun (Bodeker and McKenzie, 1996). Partly cloudy skies, not obscuring the sun, can enhance UV levels by up to 25% above cloudless sky values (Mims and Frederick, 1994). In this work, we focus on the cloud radiative in¯uence over ultraviolet radiation.
aerosol effect is the largest one, being charac-terised by a higher variability in both space and time. Findings in the parameterisation of cloudless sky ultraviolet radiation (Foyo-Moreno et al., 2000) and in the empirical modelling of this ¯ux (Foyo-Moreno et al., 1999) have been used in the present work to derive a model that estimates this radiative ¯ux under all sky conditions. For this purpose, we have de®ned a cloud modi®cation factor considering two different types of clouds: low and medium level (translucent) and high level clouds. Although this classi®cation could be simplistic it provides a ®rst distinction of cloud radiative effects and allows the derivation of a statistically signi®cant cloud modi®cation factor using the available data base. Different authors (Blumthaler et al., 1994; Davies, 1995; Kasten and Czeplak, 1980; Alados et al., 2000) have followed similar procedures in their analysis of the cloud radiative effect over the whole solar spectrum and over the UV and photosynthetically active spectral range.
Clouds refect, absorb and transmit the incoming solar radiation, modifying in this way the amount and spectral quality of the solar radiation reaching the Earth's surface. The cloud particles are res-ponsible for the scattering and absorption pro-cesses of solar radiation. Kylling et al. (1997) presented and interpreted measurements under a thin cloud, demonstrating that cloud scattering in combination with Rayleigh scattering may result in a distinct wavelength dependence of the cloud transmittance. Mayer et al. (1998) have showed that coupling of cloud scattering and molecular or particulate absorption can result in a strong enhancement of absorption which appears as a pronounced wavelength dependence of cloud attenuation. In fact, it tends to reduce UVB irradiance much more than UVA. However,
The data set used in this study came from two radiometric stations. The ®rst one is located at the University of AlmerõÂa, a seashore location (36.83N, 2.41W, 20 m a.m.s.l.). This
radio-metric station is located on the Mediterranean coast in south-eastern Spain and is characterised by a high frequency of cloudless days, and high humi-dity. Measurements include ®ve-minute values of various parameters. Solar global irradiance, Rs,
was measured using a Kipp & Zonen model CM-11 (Delft, Netherlands), while another Kipp & Zonen model CM-11 with a polar axis shadow-band was used to measure solar diffuse irradiance, Rd. The diffuse irradiance has been corrected
using the model developed by Batlles et al. (1995). Global horizontal ultraviolet solar irradi-ance has been measured by means of an Eppley TUVR. Air temperature and relative humidity at 1.5 m, are recorded. From this database, hourly values have been generated covering 1993±94.
A second station is located in the outskirts of Granada (37.18N, 3.58W, 660 m a.m.s.l.), an
inland location. Data collected at one-minute intervals during 1994±1995 has been used in the present study. The radiometric sensors are similar to those used at AlmerõÂa. Hourly values have been obtained for the radiometric and meteorological variables. Granada is located in the south-east of the Iberian Peninsula. Cool winters and hot summers characterise its inland location. Their diurnal temperature range is rather wide with the possibility of freezing on winter nights. Most rainfalls occur in spring and winter. The summer is very dry, with scarce rainfalls in July and August.
Considering the period used, a complete range of seasonal conditions and solar angles is included among the samples. Analytical checks, for
measurement consistency, were carried out to eliminate problems associated with shadowband misalignments, and other questionable data. Due to cosine response problems, we have limited our studies to cases with solar zenith angle less than 80. Calibration constants of the radiometric
devices used at AlmerõÂa and Granada have been checked periodically by our research team. Degradation of less than a few tenths per cent per year has been observed in the CM-11 pyranometers. The drift of the calibration con-stants of the TUVR sensors have been evaluated by ®eld comparison with measurements per-formed by a well-calibrated ®eld spectroradi-ometer (LI-1800). According to this devices manufacturer, measurements of solar global and diffuse irradiance have an estimated instrumental uncertainty of about 2±3% and the TUVR sensor has an instrumental uncertainty less than 5%. Figure 1 shows the spectral sensitivity of the TUVR sensor.
A common feature of parametric models such as SPCTRAL2 (Bird and Riordan, 1986) and SMARTS2 (Gueymard, 1995) are the required input data regarding ozone and aerosol character-istics in order to estimate UV global irradiance. The total ozone data frequently use the Dobson system. The precision of the Dobson instrument for measuring ozone ranges from 2 to 5%. The maximum error value of 5% in the ozone data, introduces an error in the output of the SPCTRAL2 and SMARTS2 models of 0.4 and
0.3% respectively. The aerosol information is generally introduced by means of the turbidity coef®cient , with associated errors up to 10%. This maximum error implies a relative error in the models output of 1.5% in SPCTRAL2 and 2.4% in SMARTS2. Bernhard and Seckmeyer (1999) have carried out a detailed analysis of measure-ment uncertainty of spectral solar UV irradiance.
The cloud information, cloud type and cloud amount, have been obtained from the Spanish Meteorological Service. At AlmerõÂa, the Meteor-ological Of®ce, where the cloud observations have been done, is located one kilometre away from the radiometric station; both places are located close to the coast. The frequency of the cloud observa-tions used in this study is two-hours. The registered information includes the cloud amount in octas for three different levels of clouds: low, medium and high. There is also information concerning the cloud type following the World Meteorological Organisation scheme.
At Granada the cloud observations have been done at the same location as the radiometric station. In this case, the observation frequency is lower, four observations per day, and the regis-tered information is the total amount of clouds and that of the lowest cloud layer. Thus, if there are three layers of clouds present the cloud amount for the lowest one is completely determined but this is not the case for the higher ones. Thus, it is necessary to de®ne a criterion to distribute the difference between the total cloud amount and
Fig. 1.Relative spectral response of the TUVR sensor
features (amount, location, type):
RsF Rso 1
Different authors have proposed empirical expressions for this function parameterised in terms of the type and amount of clouds (Atwater and Ball, 1981; Davies and Mckay, 1989; Degaetano et al., 1995; Davis, 1995; Alados et al., 2000). Usually this function is considered as a cloud modi®cation factor (CMF).
Considering the different radiative effects associated to different cloud types it seems convenient to de®ne a cloud modi®cation factor for the different cloud types. The overall cloud modi®cation factor will be the combination of the cloud modi®cation factor due to the different clouds present. Obviously, the contribution of a given cloud layer must depend also on its extension through the cloud amount term. In this work, we have considered the following expres-sion for the cloud modi®cation factor:
CMFYn
i1
CMFi 2
where CMFi represents the cloud modi®cation
factor associated to a given cloud layer. This factor is a function of the cloud amount,ci, associated to
this layer. The different radiative effects associated to different cloud types are captured through the differences in these functions.
To de®ne the cloud modi®cation Factor asso-ciated to each one of the three different types of clouds considered we have used the expression (1) adapted to the ultraviolet radiation:
UVCMF UVo
CMFlm clmCMFh chUVo 3
As a ®rst step, we have classi®ed the experi-mental cases in the AlmerõÂa database, considering
sky estimation of global ultraviolet radiation. This value has been combined with the measured ultraviolet radiation to de®ne the cloud modi®ca-tion factor for each experimental case. In a second step, these cases have been classi®ed according to the cloud fraction amount. The cloud amount has been characterised in terms of the fraction of the sky covered by the particular type of clouds. For each cloud type, eight different levels of fractional cloud coverage have been considered (due to the recording of these observations in octas). For each one of this cloud coverage, we have computed the mean cloud modi®cation factor and the associated standard deviation.
Figure 2 shows the behaviour of the cloud modi®cation factor for low-medium level clouds, as a function of the cloud fractional coverage. The size of the bar, representing the standard deviation, indicates the great spread of this CMF for a given fractional amount. This scatter is partly associated to the variety of clouds included under each one of the three categories considered in our rather simple classi®cation. On the other hand, the position of the clouds with respect to the sun, which we do not take into account, can be also responsible for this scatter. Nevertheless, considering the available data sets, searching on these aspects must be considered, in future studies with enlarged data sets. It is obvious that the mean value of CMF reveals the higher ef®ciency of overcast skies to reduce effec-tively the ultraviolet radiation. The dependence of the cloud modi®cation Factor deviates from the simpler linear function and thus we have tried to ®t this dependency through a potential function.
Figure 2 displays the ®tting function obtained by a weighted ®t using the standard deviation as weighting factor, the coef®cients that provides the best result for the2 statistic are:
blm 0:4800:018 alm1:740:11
The value obtained for the exponent alm reveals
that the ef®cacy of the partially covered skies to reduce the ultraviolet radiation does not increases linearly with the cloud fractional amount. Similar non-linear relations between the cloud radiative effect and the cloud coverage have being evidenced by other authors for the whole solar
spectrum (Kasten and Czeplak, 1980; Davis, 1995), for photosynthetically active radiation (Alados et al., 2000), for the thermal infrared emission of the atmosphere (Alados-Arboledas et al., 1995), and for the UV-B erythemal irradiance (Kuchincke and Nunez, 1999).
Finally, the high level cloud category has been considered. Figure 3 shows a less monotonic tendency than the previous ones. In this case, the values for the coef®cients are,bh0:1900:019
and ah 2:250:10, that reveal a lower
radia-tive effect of this last cloud category. It is interesting to note that these results illustrate the
Fig. 2.Cloud transmittance for low-medium level clouds. The square symbols represents the average values while the bars denote the standard deviation for each one of the cloud coverage considered
Fig. 3.Cloud transmittance for high level clouds. The square symbols represents the average values while the bars denote the standard deviation for each one of the cloud coverage considered
factor is:
CMF 1ÿ0:480c1:74
lm 1ÿ0:190c2h:25 5
In a next section, we will check this CMF expression using data acquired at the same location where the parameterisation has been developed. The validation data set includes the cases used in the development of the cloud modi®cation factor and additionally the cloudless sky cases and those cloudy conditions cases that include more than one cloud type. Anyway, in order to test against an independent data set we use the data registered at Granada.
The cloud modi®cation factor functions ob-tained for the ultraviolet radiation can be com-pared against similar functions developed for broadband solar radiation. Kasten and Czeplak (1980) and Davis (1995) have developed similar functions using data recorded at Hamburg
(Ger-dences that clouds transmit the shorter wave-lengths of the solar spectrum more effectively. For the low-medium level clouds the UV CMF is higher than that of the total spectral range (Kasten and Czeplack, 1980; Davies (1995)) under over-cast conditions. But for cloud coverage of low and medium level clouds less than 5±6 octas the cloud modi®cation factor is greater in the broadband solar radiation than in the UV range. Bodeker and McKenzie (1996) have obtained similar results. This last result can be explained considering that the UV global radiation presents usually a greater contribution of the diffuse component due to the spectral characteristics of the scattering process. In this sense under partially cloudy skies, for cases with the sun not-obscured by clouds, the direct beam contribution to the global component is proportionally greater for the whole solar spec-trum than for the UV region. This leads to greater
Fig. 4.Comparison among the different cloud transmittance functions proposed in this study and the broadband cloud transmittance functions proposed by Kasten and Czeplak (1980) and Davis (1995)
broadband cloud modi®cation factor for partially cloud covered skies.
4. Performance of models
As indicated the developed cloud modi®cation Factor function has been checked against experi-mental data in order to test their ef®cacy to estimate the global ultraviolet radiation in combi-nation with a cloudless sky model. Two different data sets have been considered for this task. The ®rst one is that registered at AlmerõÂa, that includes the data used to develop the cloud modi®cation Factor. Obviously, this data set also includes cases not used in the development of the CMF functions like the cloudless sky cases and those cases including a mixture of different cloud types. The second data set is that registered at Granada, where we have some limitation concerning the available information. As previously indicated the cloud information included in this data set is limited to the total cloud amount and that of the lower cloud type. Thus when there are three different types of clouds presents, according to our classi®cation, it is not possible to know exactly the speci®c amount of high and medium level clouds. We have solved this problem by considering that in such cases the difference between the total amount and that of the lower level clouds is partitioned equally between the high and medium level clouds.
The performance of the models was evaluated using different statistics, like the root mean square deviation (RMSD) and the mean bias deviation (MBD). The RMSD provides a term by term comparison of the actual deviation between esti-mated value and measured value, it is
representa-tive, therefore, of the magnitude of an individual error value. The MBD is representative of the systematic tendency of a model, positive values indicate over-estimation while negative values shows an under-estimation of the generated value. We have analysed also the linear regression between estimated and measured values, provid-ing information about correlation coef®cient, R, slope, a, and intercept, b. The ®rst one gives an evaluation of the experimental data variance explained by the model while the last two provide information about over or underestimation ten-dency, in a particular range.
The MBD and the RMSD have been presented as a percentage of the average value of the measured variable in order to facilitate the comparisons. Separated results are presented for the whole set of data and for those cases considered as cloudy skies. Table 1 shows the results for AlmerõÂa where we have also included the results for cloudless conditions obtained by using the cloudless empirical model. The MBD is lower than the experimental error and the RMSD is lower than 10%. The negligible intercept,a, and the slope,b, close to unity reveal that the cloudless sky model have a similar behaviour for the complete range of the ultraviolet solar radiation values. The goodness of this parameterisation is also evidenced by the value of the correlation coef®cient that is slightly lower than unity.
The combination of the cloudless sky model with the developed cloud modi®cation factor provides estimations under cloudy conditions with negligible MBD although there is an increase in RMSD with reference to the cloudless analysis.
It is interesting to note that under cloudy conditions the cloud radiative effect damps the
Table 1.Statistical results for the combination of the cloudless sky parametric model (Foyo-Moreno et al., 1999) and the cloud transmittance functions. AlmerõÂa data set. N represents the total number of cases in each analysed category. UVavecorrespond to
the average value of ultraviolet radiation for the indicated sky conditions. Other variables included in Table 1 are the linear regression statistics, intercept,a, slope,b, and correlation coef®cient,R. The Mean Bias Deviation (MBD) and the Root Mean Square Deviation (RMSD) are expressed as percentages of the average value UVave
UVave
Wmÿ2 aWmÿ2 b R MBD(%) RMSD(%)
Cloudless skies
N893 25.0 0.137 1.034 0.989 3.9 9.2
Cloudy skies
N1672 21.0 3.869 0.873 0.931 5.7 22.2
All Conditions
relative importance of other radiative contribu-tions. Thus, the good results obtained for cloudy conditions can be considered evidence of the goodness of the developed cloud modi®cation factor.
Concerning the results for all sky conditions as the statistics in Table 1 reveal the global behaviour is similar to that described both for the cloudless and cloudy conditions. That is, both components of the model perform adequately and thus the cloud modi®cation factor can be applied in combination with any other good parameterisation of the cloudless sky conditions to provide good estimates under all sky conditions.
Table 2 shows the results obtained for the Granada data set. This database has not been used in the development of the CMF function and thus this test can provide a independent veri®cation of the model validity. As in AlmerõÂa, Table 2
includes the results for the cloudless sky model. The consideration of cloudy conditions and all sky leads to MBD values less than the experimental error. The regression analysis presents a high regression coef®cient with slope close to unity. Figure 5 visualises the scatter plot of estimated versus measured values including all kinds of conditions. The symbols try to distinguish be-tween cloudy and cloudless conditions. As a general comment, we obtain a good agreement between estimated and experimental values. As the statistics in Table 2 reveal the global behaviour is similar to that described both for the cloudless and cloudy conditions. That is, both components of the model perform adequately and thus the cloud modi®cation factor can be applied in combination with any other good parameterisation of the cloudless sky conditions to provide good estimation under all sky conditions. The results
Fig. 5. Scatter plot of estimated versus measured values of ultraviolet global irradi-ance. Granada data set
obtained at Granada show that in spite of its simplicity the criterion followed in the separation of the cloud amount for the higher cloud layers seems acceptable. Obviously, the MBD and especially the RMSD values suggest the possibi-lity of additional improvements concerning the cloud categories considered or the possible in-¯uence of solar position. Nevertheless, this task will be accomplished when additional data are available.
5. Summary and conclusions
Cloud radiative effects over the visible part of the solar spectrum have been analysed in this study. The focus has been the ultraviolet radiation and the predictability of the cloud in¯uence over it. The cloud modi®cation factor has been de®ned for two different types of clouds, classi®ed according to their altitude into low-medium and high level clouds. This CMF has been computed by con-sidering the ratio of the actual global ultraviolet solar radiation to the cloudless sky value esti-mated by means of an empirical model.
Our study reveals that for low-medium level clouds the dependence of CMF on the cloud amount is far from linear. These results are similar to those obtained in previous studies for the whole solar spectrum, photosynthetically active spec-trum and the thermal infrared specspec-trum. For the high level clouds the relationship can be well represented by a simple linear equation. Fittings of the cloud modi®cation factor functions indicate that the Low and Medium level clouds affect more markedly the ultraviolet radiation than the high level clouds. This last type of clouds provides the lower radiative effect.
Comparisons with the results obtained by other authors in the whole solar spectrum suggest that clouds transmit more effectively the short-wave part of the spectrum. On the other hand, the cloud modi®cation factor for the broadband global region should be greater than for the UV region for partial cloudy skies with the sun not obscured. The parameterisations of CMF has been tested in combination with a cloudless sky empirical model for their predictive capability of the global ultraviolet radiation. For this purpose, we have used the complete database of AlmerõÂa that partially have been used in the development of CMF functions and an independent database
registered at Granada. The results of these tests indicate that the cloudless sky empirical model combined with the cloud modi®cation factor scheme can estimate the global ultraviolet radia-tion with a high con®dence level. Thus, the MBD present values about 5%. This good performance is obtained with both sets of data, indicating the applicability of the developed CMF scheme to different locations.
The behaviour of the cloud modi®cation factor suggests that additional re®nements can be done. Thus, different types of clouds can be considered in each one of the three categories used. On the other hand, a classi®cation concerning the sun elevation conditions can be used. This could be done if a larger database would be available.
Acknowledgements
This work was supported by La DireccioÂn General de Ciencia y TecnologõÂa from the Education and Research Spanish Ministry through the project NCLI-98-0957. We
are very grateful to the Armilla Air Base Meteorological Of®ce Staff and specially to Guillermo Ballester Valor, Meteorologist Chief of the Meteorological Of®ce for the maintenance of the radiometric devices. The Instituto Nacional de MeteorologõÂa kindly provided the cloud observation information for the two-radiometric stations.
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