Estimation of photosynthetically active radiation
under cloudy conditions
I. Alados
a, F.J. Olmo
b, I. Foyo-Moreno
b, L. Alados-Arboledas
b,∗ aDpto de F´ısica Aplicada, Universidad de Malaga, Malaga, SpainbDpto de F´ısica Aplicada, Universidad de Granada, 18071 Granada, Spain
Grupo de F´ısica de la Atmósfera Received 2 August 1999; accepted 16 December 1999
Abstract
Clouds are the largest modulators of the solar radiative flux 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 forcing is different for the different solar spectral bands. In this work, we analysed the influence of cloud radiative forcing over the photosynthetically active radiation. Knowledge of the photosynthetically active radiation is necessary in different applications, but due to the absence of widespread measurements of this radiometric flux, it must be estimated from available variables. Cloudless sky parametric models compute the global photosynthetically active radiation at surface level by addition of its direct beam and diffuse components. To compute this flux under all sky conditions one must consider the influence of clouds. This could be done by defining a cloud transmittance function. We have developed such a cloud transmittance function considering three different types of clouds. The efficacy of the cloud radiative forcing scheme has been tested in combination with a cloudless sky parametric model using independent data sets. For this purpose, data recorded at two radiometric stations are used. The combination of an appropriate cloudless sky parametric model with the cloud transmittance scheme provides estimates of photosynthetically active radiation with mean bias deviation about 4% that is close to experimental errors. Comparisons with similar formulations of the cloud radiative effect over the whole solar spectrum shows the spectral dependency of the cloud radiative effect. © 2000 Elsevier Science B.V. All rights reserved.
Keywords: Photosynthetically active radiation; Solar irradiance; Cloud radiative effect; Modelling; Parametric models; Estimation model
1. Introduction
Incident photosynthetically active radiation (400– 700 nm) is required to model photosynthesis, of single plant leaves to complex plant communi-ties. Photosynthetically active radiation is the
gen-∗Corresponding author. Tel.:+34-958-244024;
fax:+34-958-243214.
E-mail address: alados@ugr.es (L. Alados-Arboledas)
eral radiation term that covers both photon terms and energy terms. Photosynthetic photon flux
den-sity, Qp, is defined as the photon flux density
(1mol photons m−2s−1=6.022×1017 photons m−2s−1=1E m−2s−1). This radiometric flux is strongly affected by the presence of clouds. Clouds reflect, absorb and transmit the incoming solar radi-ation, modifying in this way the amount and spectral quality of the solar radiation reaching the Earth’s surface. The cloud particles are responsible for
tering processes that affect more markedly the shorter wavelengths in the solar spectrum, which include the photosynthetically active radiation spectral range. These phenomena produce an effective reduction of the global and direct components reaching the Earth’s surface through the enhancement of the diffuse radia-tion scattered both to the surface and to space. Clouds are also responsible for the absorption of solar radia-tion. This absorption affects the infrared wavelength of the solar spectrum, leaving unaltered the photosyn-thetically active spectrum. The cloud transmittance function analysed in this study tries to parameterise this effect in a simple and operational way.
In a previous paper (Alados et al., 1999) we anal-ysed parametric models that provide an estimate of the different components of solar photosynthetically active radiation under cloudless conditions. We have considered broadband models, which are physically based. These models use broadband transmittances of the extinction process that takes place in the atmo-sphere, obtained by means of a parametric approach. In order to improve the original models some mod-ifications have been introduced concerning the dif-fuse component parameterisation. It appears that for cloudless conditions the aerosol effect is the largest one, being characterised by a higher variability in both space and time. The findings in the parameterisation of the cloudless sky photosynthetically active radia-tion (Alados et al., 1999) have been used in the present work to derive a model that estimates this radiative flux under all sky conditions. For this purpose, we have defined a cloud transmittance function consider-ing three different types of clouds: low, medium and high level clouds. Although this classification is sim-plistic it provides a first distinction of cloud radiative effects and allows the derivation of statistically sig-nificant cloud transmittance function using the avail-able date base. Different authors (Kasten and Czeplak, 1980; Blumthaler et al., 1994; Davies, 1995) have fol-lowed similar procedures in their analysis of the cloud radiative effect over the whole solar spectrum and over the UV spectral range.
The cloud transmittance functions developed have been tested in relation to their predictive capability of global photosynthetically active radiation when they are combined with a cloudless sky parametric model. For this validation purpose, data recorded at two ra-diometric stations are used.
2. Data and measurements
The data set used in this study came from two radiometric stations. The first one is located at the
University of Almer´ıa (36.83◦N, 2.41◦W, 20 m
a.m.s.l.). This radiometric station is located on the Mediterranean coast in south-eastern Spain and is characterised by a greater frequency of cloudless days, and high humidity. Measurements include 5 min values of various parameters. Solar global ir-radiance, Rs, was measured using a Kipp & Zonen
model CM-11 solarimeter (Delft, Netherlands), while another Kipp & Zonen model CM-11 with a polar axis shadowband was used to measure solar diffuse irradiance, Rd. Photosynthetic active photon flux
den-sity, Qp, has been measured by means of a LICOR
model 190 SA quantum sensor (Lincoln, NE, USA). Another quantum sensor has been equipped with a polar axis shadowband in order to measure the diffuse photosynthetic active photon flux density incident on a horizontal surface, Qpd. Finally, air temperature
and relative humidity at 1.5 m, were recorded. Dif-fuse irradiance measurements have been corrected for the effect of the shadow-band following the method proposed by Batlles et al. (1995). This method has also been applied to correct the diffuse photon flux density. From this database, hourly values have been generated covering 1990–1994. The corrected diffuse horizontal values of both radiometric fluxes and the global horizontal fluxes are used to obtain the normal incidence direct beam components, both for the solar broadband irradiance, Rb, and the photosynthetically
active photon flux density, Qpb.
Rb=(R
whereθis the solar zenith angle. The broadband solar direct radiation has been used in combination with meteorological information for estimating the aerosol contribution through the computation of the Angstrom
coefficient for aerosol, β (Alados et al., 1999),
following the procedure proposed by Gueymard (1998).
location. Data collected at 1 min intervals during 1994–1995 has been used in the present study. The radiometric sensors are similar to those used at Almer´ıa. The diffuse irradiance, measured by a ra-diometer equipped with a shadowband, has been corrected using the previously cited model developed by Batlles et al. (1995). Mean hourly values have been obtained for the radiometric and meteorological variables. The Angstrom coefficient for aerosol ex-tinction,β, have been obtained following a procedure similar to that used at Almer´ıa. Granada is located in the south-eastern of the Iberian Peninsula. Cool winters and hot summers characterise its inland loca-tion. 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 con-sistency, were carried out to eliminate problems as-sociated 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 85◦. Calibration constants of the radio-metric devices used at Almer´ıa and Granada have been checked periodically by our research team. Degrada-tion of less than a few tenths per cent per year has been observed in the CM-11 pyranometers. The drift of the calibration constants of the Quantum sensors have been evaluated both by means of a calibrated standard lamp and by field comparison with measure-ments performed by a well-calibrated field spectrora-diometer (LI-1800). Measurements of solar global and diffuse irradiance have an estimated experimental er-ror of about 2–3%, while the quantum sensor has a relative error of less than 5%.
The cloud information, cloud type and cloud amount, have been obtained from the Spanish Mete-orological Service. At Almer´ıa, the MeteMete-orological Office, where the cloud observations have been made, is located 1 km away from the radiometric station, both places are located close to the coast line. The frequency of the cloud observations used in this study is hourly from 1990 to 1993 and every 2 h since 1993. The registered information includes the cloud amount in octas for three different levels of clouds: low, medium and high. There is also
informa-tion concerning the cloud type following the World Meteorological Organisation scheme.
At Granada the cloud observations have been made at the same location as the radiometric station. In this case, the observation frequency is lower, four obser-vations per day (at 9:00, 12:00, 15:00 and 18:00 hours GMT), and the registered 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 de-termined but this is not the case for the higher ones. Thus, it is necessary to define a criterion to distribute the difference between the total cloud amount and that of the lowest cloud layer between the medium and high level clouds. We divided this cloud amount equally between the two types of higher clouds.
3. Cloud transmittance functions
In order to define the cloud transmittance function we have considered the following expression that re-lates the solar global radiation under all sky condi-tions, Rs, to the cloudless sky radiation, Rso, being F a
function that depends on the cloud features (amount, location, type):
Rs=F Rso (3)
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; Davies, 1995; Degaetano et al., 1995). Usually this function is considered as a cloud trans-mittanceτc:
Rs=τcRso (4)
Considering the different radiative effects associated with different cloud types it seems convenient to define different transmittance for the different cloud types. The overall transmittance will be the combination of the transmittances 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 expression for the total transmittance due to clouds:
whereτl,τmandτhrepresents the cloud transmittance
associated with low, medium and high level clouds, respectively. This transmittance is a function of the cloud amount, ci, associated with each cloud layer.
The different radiative effects associated with different cloud types are captured through the differences in these functions.
To define the cloud transmittance function associ-ated with each one of the three different types of clouds considered we have used the Eq. (4) adapted to pho-tosynthetically active radiation:
Qp=τcQpo=τl(cl)τm(cm)τh(ch)Qpo (6)
where Qprepresents the photosynthetic active photon
flux density under all sky conditions and Qpo
repre-sents the same flux under cloudless sky conditions. As a first step, we have classified the experimen-tal cases in the Almer´ıa database, considering three categories. The first category includes those cases characterised by the presence of low level clouds with exclusion of cases with more than one type of cloud, this is the low cloud category. In order to have larger number of cases in the medium and high level categories we have included in these categories cases in which the nominal type of cloud is combined with only one octa of the remaining types of clouds.
It is obvious that the derivation of the cloud trans-mittance associated with a given experimental case needs knowledge of the cloudless sky estimate of the photosynthetically active radiation. For this purpose, we have used the models proposed in previous work (Alados et al., 1999), in this work it has been shown that the aerosols are responsible for the greatest ef-fect on the radiative flux under cloudless conditions. The cloudless sky model selected has been that called PARM that is based on a model proposed by Guey-mard (1989). This model includes some modifications in order to improve the parameterisation of the diffuse component of the photosynthetically active radiation and through this, of the global photosynthetically ac-tive radiation. Thus, in a previous work (Alados et al., 1999) some modifications suggested by Bird and Ri-ordan (1986) for the spectral code SPCTRAL2 have been included in the cloudless sky parametric model. As an additional modification step, the parameterisa-tion of the diffuse component by aerosol scattering has been modified in order to include the single scattering albedo as a multiplicative factor. For the selectable
parameters related to the aerosol optical properties we have used the values described in Alados et al. (1999). In our previous work (Alados et al., 1999), we have shown that the aerosol contribution has a marked influ-ence in the cloudless sky case. For this purpose the use of the parametric model requires the available infor-mation on the aerosol load, through the coefficientβ. Since the broadband procedure followed (Gueymard, 1998) for the derivation of this coefficient requires that broadband data were acquired under cloudless condi-tions, we have computed monthly average values of this coefficient from the available cloudless sky cases. Shorter period averages could be used, but monthly values seem appropriate if the interest is in the global flux.
Following the procedure described in the preceding paragraph, we have obtained for each hour the cloud-less sky estimation of global photosynthetically active radiation. This value has been combined with the mea-sured photosynthetically active radiation to define the cloud transmittance for each hour. In a second step, these cases have been classified according to the cloud fraction amount. The cloud amount has been charac-terised 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 (since the recording of these observations is in octas). For each cloud coverage level, we have computed the mean cloud transmittance and the asso-ciated standard deviation.
Fig. 1 shows cloud transmittance for low level clouds, as a function of the cloud fractional cover-age. The size of the bar, representing the standard deviation, indicates the great spread of this transmit-tance factor for a given fractional amount. In a next section we will consider the contribution of the solar zenith angle to this scatter. Part of this scatter is ob-viously associated to the variety of clouds included under each one of the three categories considered in our rather simple classification. It is obvious that the mean value of the cloud transmittance reveals the higher efficiency of overcast skies to reduce ef-fectively the photosynthetically active radiation. The dependence of the cloud transmittance deviates from the simpler linear function and thus we have tried to fit this dependency through a power function.
Fig. 1. Cloud transmittance for low level clouds. The square symbols represent the average values while the bars denote the standard deviation for each one of the cloud coverage categories considered.
Fig. 1 displays the fitting function obtained by a weighted fit using the standard deviation as the weighting factor, the coefficients that provides the best result for theχ2statistic are:
b1=0.334±0.016 a1=1.66±0.13
The value obtained for the exponent al reveals that
the effect of partially covered skies to reduce the
Fig. 2. Cloud transmittance for medium level clouds. The square symbols represent the average values while the bars denote the standard deviation for each one of the cloud coverage categories considered.
Our analysis of medium level clouds is shown in Fig. 2, with similar features to that of Fig. 1. After fitting to a power function
τm =1−bmcamm (8)
we obtain the following coefficients
bm =0.290±0.026 am=1.65±0.21
The corresponding function is included in Fig. 2. It is interesting to note that the differences between bland bm reveal a slightly greater radiative influence of low
level clouds, shown by other authors for the whole solar spectrum (Atwater and Ball, 1981). On the other hand, the decrease of the cloud transmittance with the cloud fractional coverage follows similar patterns for low and medium level clouds as the coincidence of the exponents al and amreveals.
Finally, the high level clouds category has been con-sidered in Fig. 3. In this case, after a first trial we have selected a linear fit
τh=1−bhch (9)
with a coefficient bh=0.104±0.012 that reveals a
lower radiative effect of this last cloud category. According to the previous results, for situations that are more complex we must consider a cloud transmit-tance that combines the effect of the different clouds
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 categories considered.
present in the sky. Thus the general expression for the cloud transmittance is:
τ =(1−0.334c1l.66)(1−0.290c1m.65)(1−0.104ch)
(10)
database into two categories with a similar number of cases.
When the separation in optical air mass is applied the transmittance functions obtained for the low level clouds are:
τl =1.0228cl1.27 form <1.56 (11a)
τl =1−0.376cl1.79 form≥1.56 (11b)
The behaviour of the new cloud transmittance function is presented in Fig. 4. It is evident that for higher solar elevation, lower optical air mass, low level clouds transmit the solar radiation in a more effective way for fractional coverage higher than 40%. Below this limit, there are no differences between both functions. This result is associated with the increase of the effective cross section of clouds for lower solar elevations.
For the medium level clouds we obtain the following set of functions:
τm =1−0.216cm1.00 form <1.56 (12a)
τm =1−0.313cm1.91 form≥1.56 (12b)
Fig. 4 shows the behaviour of these transmittance func-tions. In this case, we find a slightly greater efficiency of medium level clouds to provide radiative forcing for higher solar elevation in cases with fractional cov-erage below 50%. For fractional covcov-erage above this
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 Davies (1995). The variable m represents the optical air mass.
value, there is a greater radiative effect of these clouds for lower solar elevations. It is also interesting to note that for the lower solar elevations the behaviour of the low level and the medium level cloud transmittance function shows a close agreement. It seems that the geometric features of both cloud types provide similar blocking effects of the solar radiative flux for lower solar elevations.
Finally, for the high level clouds the differences in the unique adjustable coefficient reveal a lower effi-cacy for radiative forcing for lower solar elevations:
τh=1−0.143ch form <1.56 (13a)
τh=1−0.063ch form≥1.56 (13b)
In this sense, Fig. 4 reveals a negligible contribution of these clouds to the solar radiative forcing for lower solar elevations. This behaviour is opposite to the one encountered for the two other cloud types and shows the higher transparency of these clouds to solar radi-ation and the less thick configurradi-ation of these cloud layers.
(USA), respectively. In their studies, these authors proposed a unique transmission function for all kind of clouds following a functional dependence similar to that used in our study. Kasten and Czeplak (1980) obtained coefficients b=0.75 and a=3.4, while Davies (1995) obtained coefficients b=0.674 and a=2.854. Fig. 4 illustrates that these cloud transmittance func-tions despite the differences in the coefficients show a similar behaviour. The comparison with our results for the photosynthetically active radiation shows that clouds transmit more effectively the shorter wave-lengths of the solar spectrum. In a previous study (Alados et al., 1996, 1999; Alados, 1997) we have shown this fact by analysing the ratio of photosyn-thetically active radiation to broadband solar radia-tion. This ratio depends on the aerosol load, the solar zenith angle and the cloud coverage. Its increase for cloudy conditions is a result of the lower attenuation suffered by the photosynthetically active radiation in comparison with the whole solar spectrum.
4. Performance of models
As indicated the developed cloud transmittance function has been checked against experimental data in order to test their success in predicting the global photosynthetically active radiation in combination with a cloudless sky model. Two different data sets have been considered for this task. The first one is that recorded at Almer´ıa, that includes the data used to develop the cloud transmittance functions. Obviously, this data set also includes cases not used in the devel-opment of the cloud transmittance functions like the cloudless sky cases and those cases including a mix-ture of different cloud types. The second data set has been that recorded 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 present, according to our classification, it is not possible to know exactly the specific amount of high and medium level clouds. We have solved this problem 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 us-ing different statistics suggested by Willmott et al. (1985). These include the root mean square deviation
(RMSD) and the mean bias deviation (MBD). We have
analysed also the linear regression between estimated and measured values, providing information about correlation coefficient, R, slope, a, and intercept, b. The first one gives an evaluation of the experimen-tal data variance explained by the model while the last two provide information about over or under-estimation tendency, in a particular range. The root mean square deviation, RMSD, under certain
assump-tions can be separated into systematic (RMSDs) and
unsystematic deviations (RMSDu):
RMSD=
where Piand Oirefer respectively to the predicted and
observed values, N is the number of cases and Pave
represents the average of the predicted values.
The MBD and the different terms related to RMSD
have been presented as a percentage of the average value of the measured variable in order to facilitate the comparisons. In our analysis we have also included the index of agreement, d, that is a dimensionless in-dex bounded between 0 and 1. This inin-dex is a better measure of the model performance than the correla-tion statistics such as R and is defined as:
d=1−
where the term Oave represents the average of the
ob-served values.
Table 1
Statistical results for the combination of the cloudless sky parametric model PARM (Alados et al., 1999) and the cloud transmittance functions without explicit dependence on sun position — Almer´ıa data seta
Qpave(E m−2s−1) a (E m−2s−1) b R MBD (%) RMSD (%) RMSDs(%) RMSDu(%) d Cloudless skies
N=2936 1085 15 1.026 0.985 4.0 9.1 5.0 8.2 0.990
Cloudy skies
N=4396 1057 74 0.946 0.958 1.5 13.4 3.0 13.1 0.978
All conditions
N=7334 1068 50 0.979 0.968 2.5 11.8 2.8 11.5 0.983
aN represents the total number of cases in each analysed category. Q
pavecorrespond to the average value of photosynthetically active radiation for the indicated sky conditions. Other variables included in Table 1 are the linear regression statistics, intercept, a, slope, b, and correlation coefficient, R. The Mean Bias Deviation (MBD) and the Root Mean Square Deviation (RMSD) are expressed as percentages of the average value Qpave. The systematic, RMSDs, and unsystematic, RMSDu, parts of RMSD defined by Willmott (1984) are expressed as percentages. Finally, d means the index of agreement as defined by Willmott (1981).
use of an average value in spite of that estimated for each one of the experimental cases is responsible of a slightly degraded model behaviour. In any case the MBD is lower than the experimental error and the
RMSDis lower than 10% with a lower contribution of
systematic deviation. 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 photosynthetically active radiation values. The goodness of this parameterisation when monthly average values of the Angstrom coefficient for aerosol extinction are used is also shown by the value of the index of agreement, d, that is only slightly lower than unity.
The combination of cloudless sky model with the developed cloud transmittance functions is its simpler form, that is without consideration of solar position dependence, has been tested. Considering the coinci-dence of the low and medium level cloud exponents,
al and am, and the non significant difference between
the coefficients bland bm, due to the size of the
asso-ciated errors, we have tested the behaviour of a sim-plified cloud transmittance function:
τ=(1−0.317cl1.66)(1−0.317c1m.66)×(1−0.104Ch)
(18)
The use of this simplified transmittance function provides estimations under cloudy conditions with negligible MBD although there is an increase in RMSD
with reference to the cloudless analysis. It is interest-ing to note that the results obtained with this equation presents non significant differences with that obtained
using Eq. (8), that is using different coefficients for the low and medium level cloud transmittances. The relative contribution of RMSDs as quantified by the
ratio RMSDs2/RMSD2 is close to 4%. The index of
agreement shows the good behaviour of the model. It is interesting to note that under cloudy conditions the cloud radiative forcing damps the relative impor-tance of the aerosol radiative forcing. Thus, the good results obtained for cloudy conditions can be consid-ered as evidence of the goodness of the developed cloud transmittance functions.
Fig. 5 shows the scatter plot of estimated versus measured values including all kinds of conditions. The symbols try to distinguish between cloudy and cloud-less conditions. As a general comment, we obtain a good agreement between estimated and experimental values. As the statistics in Table 1 reveal the global be-haviour is similar to that described both for the cloud-less and cloudy conditions. That is both components of the model perform adequately and thus the cloud transmittance function can be applied in combination with any other good parameterisation of the cloudless sky conditions to provide good estimation under all sky conditions.
Fig. 5. Scatter plot of estimated, Qpe, vs measured values, Qpm, of global photosynthetically active photon density flux using the Almer´ıa data set.
differences between the results obtained with the cloud transmittance function including the sun position de-pendence and that excluding this dede-pendence are neg-ligible. There is a slight increase in MBD and RMSD,
being shown by an increase in the systematic compo-nent, RMSDs. The index of agreement also shows this
situation showing a slight reduction. Thus, from an operational point of view the simpler approach for the cloud transmittance function parameterised in terms of cloud amount and type seems good enough and con-venient.
Table 3 shows the results obtained for the Granada data set. This database has not been used in the devel-opment of the cloud transmittance function and thus this test can provide a independent verification of the model validity. In this case, we use the cloudless sky model, with the aerosol model adjusted to Granada
Table 2
Statistical results for the combination of the cloudless sky parametric model PARM (Alados et al., 1999) and the cloud transmittance functions with explicit dependence on sun position — Almer´ıa data seta
Qpave(E m−2s−1) a (E m−2s−1) b R MBD (%) RMSD (%) RMSDs(%) RMSDu (%) d Cloudy Skies
N=4396 1057 89 0.928 0.958 1.2 13.3 6.0 11.8 0.932
All conditions
N=7334 1068 59 0.968 0.968 2.3 11.8 5.2 10.9 0.946
aThe symbols used have been defined in Table 1.
Table 3
Statistical results for the combination of the cloudless sky parametric model PARM (Alados et al., 1999) and the cloud transmittance functions without explicit dependence on sun position — Granada data seta
Qpave(Em−2s−1) a (E m−2s−1) b R MBD (%) RMSD (%) RMSDs(%) RMSDu(%) d Cloudless skies
N=399 1261 −60 1.061 0.995 1.2 5.3 2.9 4.5 0.996
Cloudy Skies
N=1116 988 112 0.945 0.936 5.8 19.5 6.5 18.3 0.964
All conditions
N=1515 1060 78 0.970 0.954 4.3 15.9 4.6 15.2 0.975
aThe symbols used have been defined in Table 1. Table 4
Statistical results for the combination of the cloudless sky parametric model PARM (Alados et al., 1999) and the cloud transmittance functions with explicit dependence on sun position — Ganada data seta
Qpave(E m−2s−1) a (E m−2s−1) b R MBD (%) RMSD (%) RMSDs(%) RMSDu (%) d Cloudy skies
N=1116 988 130 0.916 0.936 4.9 18.9 12.2 14.6 0.889
All conditions
N=1515 1060 89 0.953 0.955 3.7 15.5 8.7 12.8 0.916
aThe symbols used have been defined in Table 1.
sets for the whole range of photosynthetically active radiation values under consideration. Also the results obtained at Granada are only slightly worse than those obtained at Almer´ıa. In this sense a separate analysis of the lower level clouds has shown that the criterion adopted in the separation of the cloud amount for the higher cloud layers can be improved. Nevertheless, this task will be accomplished when additional data are available.
Finally, as in Almer´ıa, the application of the cloud transmittance function depending on Sun’s position does not imply important changes as Table 4 shows. At this point, it is interesting to note that on some occasions simpler models are more appropriate than the complex ones, due to possible amplification of input parameter errors.
5. Concluding remarks
Our study reveals that for low and medium level clouds the dependence of the cloud transmittance on the cloud amount is far from linear. These results are similar to those obtained in previous studies for the whole solar spectrum and the thermal infrared spec-trum. For the high level clouds the relationship can
be well represented by a simple linear equation. Fit-tings of the cloud transmittance functions indicate that low and medium level clouds affect more markedly the photosynthetically active radiation than high level clouds. High level clouds provides the minor radia-tive effect. Comparisons with the results obtained by other authors for the whole solar spectrum suggest that clouds transmit more effectively the short-wave part of the spectrum.
additional dependence on sun position. For this pur-pose, we have used the complete database of Almer´ıa that partially have been used in the development of the cloud transmittance functions and an independent database collected at Granada.
The results of these tests indicate that the cloud-less sky parametric model combined with the cloud transmittance scheme can estimate the global photo-synthetically active radiation with a high confidence level. Thus, the MBD shows values about 4% and the index of agreement reveals the goodness of the modelling, showing values higher than 0.90 in all cases. The use of a simplified transmittance func-tion with same coefficients for the low and medium level cloud transmittances provides estimations close to that obtained using different formulations for this two cloud types. This good performance is obtained with both sets of data, indicating the applicability of the developed cloud transmittance scheme to different locations.
Acknowledgements
This work was supported by La Dirección Gen-eral de Ciencia y Tecnolog´ıa from the Education and Research Spanish Ministry through the project
N◦CLI-99-0835-C02-01. We are very grateful to
the Armilla Air Base Meteorological Office Staff and specially to Guillermo Ballester Valor, Meteo-rologist Chief of the Meteorological Office for the maintenance of the radiometric devices. The Instituto Nacional de Meteorolog´ıa kindly provided the cloud observation information for the two-radiometric sta-tions. The authors are indebted to the Regional editor Dr. J.B. Stewart, to Dr. Juhan Ross and the anony-mous referee who read the manuscript and made valuable suggestions.
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