Recent improvements of the Meteorological Radiation Model for solar irradiance estimates under all-sky conditions

Renewable Energy 93 (2016) 142e158

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Recent improvements of the Meteorological Radiation Model for solar irradiance estimates under all-sky conditions H.D. Kambezidis a, B.E. Psiloglou a, D. Karagiannis b, U.C. Dumka c, D.G. Kaskaoutis d, b, * a

Atmospheric Research Team, Institute for Environmental Research and Sustainable Development, National Observatory of Athens, 11810 Athens, Greece Collaborator of National Observatory of Athens on Contract to KRIPIS-THESPIA Programme, Greece c Aryabhatta Research Institute of Observational Science, Nainital 263 001, India d School of Natural Sciences, Shiv Nadar University, Tehsil Dadri 203207, India b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 19 October 2015 Received in revised form 17 February 2016 Accepted 19 February 2016 Available online xxx

This study presents the recent improvements of the Meteorological Radiation Model (MRM v6) against previous model versions for more accurate estimates of the solar radiation components, i.e. global, diffuse and direct. The MRM v6 follows a different approach for the simulation of the atmospheric conditions by selecting the most appropriate aerosol model (desert, urban, maritime or continental), and usage of look-up tables for the spectral variation of the aerosol optical depth (AOD) and single scattering albedo (SSA). Furthermore, the MRM v6 uses hourly data of sunshine duration in order to achieve better simulations under cloudy skies. The results show that the MRM v6 improves the estimates of the measured global, diffuse and direct solar irradiances at Athens, Greece since the Root Mean Square Error (RMSE) becomes 13.7%, 40.8% and 24.2%, respectively, against 18.0%, 44.5% and 34.1% for the MRM v5. A decrease is also found in Mean Bias Error (MBE), especially for the diffuse (from 26.2% to 19.5%) and direct (from
9.0% to
2.4%) irradiances, indicating that the inclusion of the aerosol properties in MRM v6 significantly improves the estimations. The MRM simulations are very satisfactory on monthly basis indicating that the model is suitable for solar energy applications. © 2016 Elsevier Ltd. All rights reserved.

Keywords: Meteorological Radiation Model (MRM) Solar radiation Model validation Aerosol Athens

1. Introduction Solar radiation is the main source of energy and the most important condition for life on Earth; it is also a determinant factor for climate change [58,78]. The increasing demand of energy over the globe due to the growing population and the major concerns of environmental protection, reduction of the greenhouse gases and mitigation of the climate change impacts shift the interest towards renewable energy sources and more specifically to solar energy [52]. The design of many solar conversion devices and photovoltaic cells requires the knowledge of solar radiation availability on horizontal and inclined planes [13,65,77] as well as solar maps at different spatial and temporal domains over the globe [62]. Mapping solar radiation over an area is essential for exploring the spatial variability of solar radiation and analyzing the solar energy

* Corresponding author. School of Natural Sciences, Shiv Nadar University, Tehsil Dadri 203207, India. E-mail addresses: [email protected], [email protected] (D.G. Kaskaoutis). http://dx.doi.org/10.1016/j.renene.2016.02.060 0960-1481/© 2016 Elsevier Ltd. All rights reserved.

potential, thus helping engineers in using solar energy systems [34]. Due to unavailability of a dense network for solar radiation measurements over the globe, solar radiation maps may be prepared using satellite retrievals, artificial neural networks, radiative transfer codes [62,63,72], or simple solar broadband radiation models that have been developed during the early 1970s (e.g. [10,11,15,20,22,51,65]. The main advantage of these radiative models is the estimate of solar radiation at specific places that are used for mapping solar radiation at regional to global scales. The atmospheric constituents attenuate solar radiation reaching the Earth's surface by the mechanisms of absorption and scattering [36,37], depending on multiple parameters like the amount, absorption capabilities, particle size and scattering processes of air molecules/aerosols/pollutants. Multi-decadal variations in the attenuation of solar radiation reaching the ground is a modulation factor for regional and global climate controlling the global dimming/brightening phenomenon [59,60,79]. Atmospheric aerosols play a very important role in the Earth's radiation budget [25,71] and, therefore, are very important in climate change. Thus, atmospheric turbidity is a major input parameter to radiative transfer codes [7,16,18,30,61], which has been replaced by more

H.D. Kambezidis et al. / Renewable Energy 93 (2016) 142e158

sophisticated expressions of the spectral aerosol optical properties [36,37]. Solar zenith angle (SZA) and cloudiness are the most significant factors affecting the variability of solar irradiance at the Earth's surface; SZA is readily estimated from astronomical functions [76,80], while cloudiness is characterized by a high variability in structure, thickness and composition, thus rendering the estimation of solar radiation under cloudy skies a real challenge [43,49,56]. Therefore, clouds play a fundamental role and may attenuate as much as 80% of the downwelling solar radiation reaching the Earth's surface, depending on cloud type, cloud optical depth (COD), and their distribution in the sky [1,12,66,68]. The COD is an inherent property of clouds and independent of SZA, surface albedo or aerosol loading [6,68]. An accurate determination of the COD and its spatial and temporal variation remains a serious concern in radiation and atmospheric studies, which implement different factors that relate atmospheric transmission with overcast skies [2,19,54,68]. In this respect, the Meteorological Radiation Model (MRM) was developed at the National Observatory of Athens (NOA) in the late 1980's [27e29,31] and has been under continuous improvements till its current version 5 (MRM v5) that has successfully been used for solar radiation estimates during the solar eclipse in Greece on 29 March 2006 [65]. On the other hand Gueymard [21], in an intercomparison study employing various broadband models found that MRM v4 did not perform so well compared to others. However, more recently Gueymard [23], checked the validity of 18 solar radiation models and classified MRM v5 in the 7th position after comparison with measured data from SURFRAD (Surface Radiation) network and usage of several statistical indicators. The MRM v5 is a simple radiation code based on meteorological parameters i.e. air temperature, relative humidity, barometric pressure and sunshine duration as inputs, which are easily available from many meteorological stations. Therefore, the main advantage of the MRM v5 against other simple radiation models is its easiness in being applied at any location over the globe. MRM v5 can be used for estimating solar radiation under different atmospheric conditions, for filling gaps in solar radiation data series and for solar-energy applications and engineering purposes. The various versions of MRM are described in detail in a book chapter [32] and in a study focusing on the accuracy of the latest version (MRM v5) in solar radiation simulations during the (almost total) solar eclipse conditions on 29 March 2006 over Athens, Greece [65]. The present work describes in detail the recent developments in the MRM v6 code, by inserting new techniques and functions for the aerosol transmittance by choosing the most appropriate aerosol model for representing the atmospheric conditions. The study provides comparisons of the MRM v6 solar irradiance (global, diffuse and direct) estimates with both real measurements taken at the Actinometric Station of NOA (ASNOA) during the period 2001e2005 and model estimates from the previous MRM v5. The model's performance is examined against SZA, sunshine duration and aerosol optical depth (AOD) in order to reveal the improvements of the solar radiation estimates that are attained in the new version. 2. Description of MRM v6 The MRM is a broadband algorithm for simulating solar irradiance on horizontal surface, using widely available meteorological parameters, viz air temperature, relative humidity, barometric pressure and sunshine duration as inputs. It is capable in performing calculations in various time steps dictated by the availability and temporal resolution of the meteorological input data, the majority of which are provided as hourly values. On the other

143

hand, the measured sunshine duration is usually given as a total daily or hourly value; the latter case leads to more precise calculations from MRM. In the following, we analytically describe the new developments in the MRM v6 code against its predecessor; a detailed description of the MRM can be found elsewhere [32,65]. 2.1. Direct radiation The direct beam irradiance, Ib, received on a horizontal surface under cloudless skies can be expressed as: Ib ¼ Iex cos qz Tw Tr To Tmg Taer

(1)

where qz is the SZA, Iex is the normal incidence extraterrestrial solar irradiance on the i-th day of the year; the term Tx stands for the broadband transmission functions for water vapor (Tw), Rayleigh scattering (Tr), absorption by ozone (To), absorption by uniformly mixed gases (CO2, CO, N2O, CH4 and O2) (Tmg) and aerosol total extinction (scattering and absorption) (Taer). The expression for Taer has changed in MRM v6, while the rest transmittances are kept the same as in MRM v5 (see analytical expressions in Ref. [65]. In MRM v5, the broadband Taer was calculated using the formula proposed by Yang et al. [81]: Taer ¼ exp{
m b [0.6777 þ 0.1464 m b
0.00626 (m b)2]
1.3} (2) € m turbidity coefficient and m the relative where b is the Ångstro optical mass. In the cases that b is not available from spectral radiation measurements it is estimated via the empirical Yang et al.'s [81] expression, which relates b to the geographical latitude, 4, and the altitude of the station, H, as:

b ¼ b0 þ db

(3)

b0 ¼ (0.025 þ 0.1 cos4) exp(
0.7H/1000)

(4)

db ¼ ±(0.02 e 0.06)

(5)

where b0 represents the annual mean value of turbidity and db the seasonal deviation from the mean, i.e. low values in winter and high values in the summer. For Athens (4 ¼ 37.967oN and H ¼ 107 m a.m.s.l.) b’ ¼ 0.09. It is well-known that the AOD and, thus, the aerosol transmittance are highly wavelength dependent due to different aerosol types that take place in the solar attenuation processes within the atmosphere [36,37]. Therefore, inclusion of spectral functions of AOD or transmittance can definitely improve the model simulations. However, MRM was built as a broadband code. Thus, in MRM v6 the broadband Taer is calculated by integrating the wavelengthdependent aerosol transmittance Taeri as:

Pl2 Taer ¼

i¼l1

Pl2

Taeri Iexti

i¼l1

Iexti

(6)

where l1, l2 are 280 and 3000 nm, respectively, i.e. the lower and upper limits of the solar spectrum. Iexti is the spectral extraterrestrial irradiance taken from SMARTS model, version 2.9.5 [22], with a spectral resolution of 0.5 nm between 280 and 400 nm, 1 nm between 400 and 1700 nm, and 5 nm between 1705 and 3000 nm. Taeri is the spectral aerosol transmittance: Taeri ¼ exp (
m0 AODi)

(7)

where m0 is the absolute air mass, corrected for the actual station

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pressure as m0 ¼ m(P/Po), where Po is the mean sea level pressure of 1013.25 hPa and P the measured pressure at the station. The air mass, m, in the code is obtained by the Kasten and Young's [41] formula for SZAs below 85 . In dealing with hourly data, MRM considers m or SZA at the middle of the hour interval, i.e. at 30 min before the hour given in the data-base. This constitutes a small bias since the measured radiation used for the model validation corresponds to the whole time interval of the 1 h, while all the astronomical calculations are considered at the middle of the 1h interval. AODi is the spectral AOD, calculated as: AODi ¼ RAOD550*AODki

(8)

where AODki is the spectral AOD for the kth aerosol model (k ¼ 1, 2, 3, 4 for DESERT_MIN, S&F_URBAN, S&F_MARITIME, SRA_CONTL, respectively) automatically chosen by the MRM code based on the relationship between AOD550 and fine mode (FM) (see Section 3). The aerosol models simulate different spectral AODs (Fig. 1a) due to the various size distribution of the aerosol particles that control the spectral extinction processes in the atmosphere.

RAOD550 ¼

AOD550 AODk550

(9)

RAOD550 is the ratio of the measured AOD at 550 nm (MODIS observations, see Section 3) to the value of AOD at 550 nm for the specific aerosol model (see Fig. 1a). The four aerosol models were run using a fixed AOD500 value of 0.3; their spectral distribution has been inserted as a look-up table in MRM v6. The RAOD550 ratio is used in order to normalize the standard AOD spectral distribution taken from the look-up table for each aerosol model to the real atmospheric conditions, i.e. the measured value of AOD550.

The term IexTwTmgToTaa represents the amount of solar radiation reaching the surface of the Earth after its absorption by the atmospheric constituents and aerosols; the second part, i.e. 0.5(1
TasTr), stands for the amount of solar radiation scattered forward (towards the surface) by air molecules and aerosols. The MRM v5 estimated the aerosol transmittance function due to absorption, Taa, using the expression by Bird and Hulstrom [8,9]: Taa ¼ 1e0.1 (1
m þ m1.06) (1
Taer)

where Taer is the aerosol transmittance due to both scattering and absorption. MRM v6 calculates Taa indirectly, via the aerosol transmittance due to scattering only (Tas) as: Taa ¼ Taer/Tas, where Tas ¼ exp (
m0 SSA AOD)

(12)

where SSA is the single scattering albedo of aerosol. For the broadband Tas we used an expression similar to Eq. (6) for integrating the spectral scattering aerosol transmittance Tasi in the wavelength range 280e3000 nm: Tasi ¼ exp (
m0 SSAki AODi)

(13)

The spectral SSAki differs for each aerosol model (k ¼ 1, 2, 3, 4) due to the different aerosol absorption (Fig. 1b), while the selection of SSAki is made automatically from the code according to the aerosol type. The diffuse component, Idm, due to the single reflection of Ib (Eq. (1)) and Ids (Eq. (10)) from the Earth's surface, followed by backscattering from the atmospheric constituents is modeled as:

Idm ¼ ðIb þ Ids Þ

2.2. Diffuse radiation

(11)

ag as 1
ag as

(14)

Under clear-sky conditions, the diffuse irradiance is assumed to be composed of a singly scattered part by the atmospheric constituents (molecules and aerosol particles), Ids, plus a multiple scattering component, Idm [3,64]:

where ag is the surface albedo taken here as 0.2, and as is the albedo of the cloudless sky, which is defined as the ratio of the radiation reflected back to space to the incident one. Under clear-sky conditions, as can be approximated as:

Ids ¼ Iex cos qz Tw Tmg To Taa 0.5 (1
Tas Tr)

as ¼ ar þ aa

(10)

(15)

where, ar represents the albedo due to molecular (Rayleigh) scattering, taken equal to 0.0685 [44]. MRM v6 introduces a small modification in the expression of aa ¼ 0.16 (1
Ta,1.66) [8,9], by replacing Ta1.66 (Ta,1.66 is the total aerosol transmittance calculated for m ¼ 1.66, i.e. for qz ¼ 53 ) with Taer corresponding to the real atmospheric conditions for each hour of the day and not being equal to the fixed value of m ¼ 1.66. However, this change causes negligible differences (<1%) in the diffuse component, since its fraction due to multiple reflections between the surface and the atmosphere is very low compared to the diffuse part due to the combined aerosol/cloud attenuation. Finally, the global irradiance, It, is calculated as the sum of the direct and diffuse irradiance components.

It ¼ Ib þ ðIds þ Idm Þ ¼

Fig. 1. Spectral distribution of AOD (a) and SSA (b) for the four aerosol models implemented in MRM v6. The spectral AODs correspond to a fixed value of AOD500 ¼ 0.3.

Ib þ Ids 1
ag as

(16)

It should be stressed here that no modification has been performed in the expressions used for the calculation of solar radiation under cloudy conditions. For this reason, these expressions are those mentioned in Ref. [65].

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3. Aerosol component in MRM v6 In contrast to MRM v5 that uses the empirical formula of Yang et al. [81] (Eqs. (2)e(5)) for Taer, MRM v6 uses measured values of AOD550, which are easily obtained at any location over the globe by various satellite sensors like MODIS, MISR, SeaWifs, etc. In the current work, AOD550 from Terra-MODS (C005.1) retrievals at 1 x 1 spatial resolution over Athens (38oN, 23oE) were used as inputs to the radiation code using the dark-target algorithm [46]. Several studies (e.g. [47,70] and references therein) resulted in a good agreement between MODIS and AERONET AODs besides the fact that ~75% of the MODIS AOD retrievals lie into the uncertainty bands (±0.05 ± 0.05AOD). However, a slight underestimation was observed in MODIS AOD retrievals especially for high AODs, which may bias aerosol and solar radiation simulations under turbid atmospheres. However, previous works [36e38,55,74] have shown that the spectral variation of AOD due to the presence of aerosols of different origin, size and chemical composition determines the spectral scattering and absorption processes and results in different solar radiation measurements, even for the same SZAs and atmospheric turbidity conditions. Thus, for a better simulation of solar radiation, and especially for its diffuse and direct components that strongly depend on the spectral attenuation processes in the atmosphere, spectral aerosol transmittance equations are used in MRM v6 as described in the previous section. On the other hand, except of the spectral AOD distribution, the relative influence of the absorption/scattering process is very important for the attenuation of solar radiation. Thus, more scattering aerosols enhance the diffuse spectrum, even under the same SZA and AOD values, while they theoretically leave unaffected the direct spectrum [4,38,55]. The critical parameter for determining the relative influence of the aerosol scattering and absorption processes is SSA, which takes values between 0 (pure absorbing aerosols) and 1 (absolute scattering). Therefore, there is a need for aerosol-type classification for better simulations of the solar radiation components. This classification was done in MRM v6 by using the scatter plot between AOD550 and FM fraction following previous works [38,39], since both parameters are available from MODIS sensor on near-daily basis over the globe. Based on AOD550 vs FM scatter plot the MRM v6 classifies four aerosol types: i) DESERT_MIN for AOD550 > 0.3 and FM < 0.6, ii) S&F_URBAN for AOD550 > 0.2 and FM > 0.7, iii) S&F_MARITIME for AOD < 0.2 and FM < 0.7 and iv) for the remaining cases the aerosol type is continental background (SRA-CONTL) of the IAMAP preliminary standard atmosphere [26]. These four aerosol models were selected from the nine included in the SMARTS ver.2.9.5 model [22] as having different optical and physical properties that define the spectral variation of AOD, SSA, asymmetry factor and refractive index. Fig. 1a, b shows the spectral dependence of AOD and SSA, respectively for an AOD500 value of 0.3. The Shettle and Fenn [69] Urban (S&F_URBAN), the DESERT_MIN and the continental (SRA_CONTL) models exhibit a similar spectral variation of

Table 1 Statistical parameters of the correlations between MRM 5and MRM 6 simulations with measured data for global, diffuse and direct irradiances at Athens in the period 2001e2005.

Fig. 2. Scatter plot of estimated vs measured global (a), diffuse (b) and direct (c) solar irradiances via MRM v5 and MRM v6 codes. The measured data were obtained at Athens during the period 2001e2005. The linear regressions for MRM v5 (blue) and MRM v6 (red) are given in the plots. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Radiation

Model version

RMSE

MBE

MAPE

NSE

Global Global Diffuse Diffuse Direct Direct

MRM MRM MRM MRM MRM MRM

18.0% 13.7% 44.5% 40.8% 34.1% 24.2%

2.9% 5.0% 26.2% 19.5%
9.0%
2.4%

19% 14% 30% 26% 331% 57%

0.90 0.95 0.37 0.43 0.82 0.91

5 6 5 6 5 6

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€m exponent (a) values of 1.0e1.1 [36], AOD due to similar Ångstro whereas the AOD spectral dependence is less for the S&F_MARITIME model due to low a (0.59) (Fig. 1a). The S&F_URBAN exhibits much lower SSA values due to the assumption of higher black carbon concentrations (this model is also suitable for regions influenced by seasonal biomass burning), whereas the SSA is very high (above 0.9e0.95) for the desert and maritime aerosol types indicating their strong scattering nature (Fig. 1b). Furthermore, the ozone amount in MRM v6 is now obtained from real-time satellite measurements, i.e. either from TOMS or OMI sensors at 1  1 or 0.24  0.24 spatial resolution, respectively around the measuring site (Athens). In the current validation, the TOMS-derived ozone concentrations were used during 2001e2005. In contrast, MRM v5 used the ozone amount as calculated via the Van Heuklon [75] formula, which is not representing the O3 column trends accurately anymore [35]. However, it was found that the ozone amount (either via the Van Heuklon estimates or the TOMS/OMI measurements) does not affect significantly the simulated solar radiation components, with the differences in the global radiation to be detected at the second decimal digit. It should be noted that on days with lack of satellite data, either due to cloud contamination and/or problems in the algorithm retrievals, the monthly-mean climatological values for AOD550, FM and O3 over Athens during the period 2000e2014 were used as inputs to the MRM v6 code. 4. Data collection and statistical analysis The measured solar irradiance data that have been used for the validation of the MRM v5 and v6 codes were obtained at ASNOA located in the hill of Pnyx (4 ¼ 37.967 N, l ¼ 23.717 E, H ¼ 107 m a.m.s.l.) near Athens city center [65]. The data consist of global and diffuse solar radiation (0.285e2.8 mm) on horizontal plane both measured by two Eppley PSP radiometers, one of them employing a shadow band for diffuse measurements. The solar radiation measurements in Wm
2 have been performed on continuous daily basis and the broadband global and diffuse irradiances, corresponding to hourly averages of 1-min recordings, have been obtained at the end of the hourly period (i.e. the average value given at 11:00 LST in the data-base corresponds to the period of 1-min measurements between 10:01 and 11:00 LST). Furthermore, a correction was performed for the diffuse radiation due to shadow-band effect following the procedure proposed by Littlefair, described elsewhere [17]. The direct irradiance on horizontal plane was calculated as the difference between global and diffuse irradiances. Before validating MRM, quality control was performed on the measured data by excluding: i) the cases that lead to negative values of direct irradiance (corrected diffuse irradiance larger than global), ii) cases with global irradiance less than 5 Wm
2, iii) solar altitude less than 5 , iv) cases with missing or zero values of global and/or diffuse irradiances and v) irradiance exceeding the extraterrestrial one. After this quality control, 16,923 data points were used for validation of the new MRM v6. It should be noted here that the measured radiation amounts correspond to the hourlyaveraged values, while the astronomical parameters used as inputs to the MRM code refer to the median of the time interval (i.e. 30 min before the hour given in the data-base); so does the estimated solar irradiance. Furthermore, there is a small difference

Fig. 3. Ratio of estimated/measured global (a), diffuse (b) and direct (c) solar irradiances against relative sunshine duration (time fraction of 60 min or 1 h). The model

simulations correspond to both MRM v5 (blue) and MRM v6 (red). The sunshine duration corresponds to observations taken at National Observatory of Athens during the period 2001e2005. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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147

between the astronomical daytime duration N and that considered as input to MRM, which excludes sun elevations below 5 ; therefore, the model's daytime duration is somewhat shorter than the theoretical one. The calculations of the solar position in the sky were performed using the modified SUNAE algorithm [76], incorporating all corrections introduced by Wilkinson [80], Muir [57], Kambezidis and Papanikolaou [28], and Kambezidis and Tsangrassoulis [29]. The meteorological data (air temperature, relative humidity, atmospheric pressure, sunshine duration) that have been used as inputs to MRM were obtained from the meteorological station of NOA located in the vicinity of ASNOA. All the meteorological data are hourly averages, while the satellite data are daily values (i.e. they are kept constant throughout the day). For checking the model's (MRM v5 and MRM v6) performance against solar radiation measured at ASNOA some common statistical indicators are used:



RMSE in Wm
2



sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi PN 2 i¼1 ðIm
Ic Þ ¼ N

  RMSE in Wm
2 ,  100 PN N i¼1 Im

RMSEðin %Þ ¼

(17a)

(17b)

where Im and Ic are the measured and model-estimated values of the irradiance components (in Wm
2) and N ¼ 16,923 is the number of available data points. The root mean square error (RMSE) is a measure of the average deviation from the measured value with lower values corresponding to better simulations. The mean bias error (MBE) of a sample of N measurements is defined as:

 PN ðI
I Þ  m c MBE in Wm
2 ¼ i¼1 N MBE ðin %Þ ¼

  MBE in Wm
2 ,  100 PN I N i¼1 m

(18a)

(18b)

MBE is a measure of the overall bias error or systematic error of a sample and gives a measure of underestimation or overestimation of the model against the measurements. The Nash-Sutcliffe Efficiency (NSE) and the Mean Absolute Percentage Error (MAPE) [48,50] are also used as criteria in evaluating the model performance:

PN

NSE ðunitlessÞ ¼

ðIm
Ic Þ2  2 PN i¼1 Im
Im i¼1

PN MAPEðin %Þ ¼

i¼1

jIm
Ic j Im

N

 100

(19)

(20)

where Im is the average value of the measured radiation. The lowest values of NSE and MAPE correspond to higher model efficiency. The statistical parameters have been applied in the whole set of measurements independently from season, sun elevation, sunshine

Fig. 4. Ratio of estimated/measured global (a), diffuse (b) and direct (c) solar irradiances against AOD at 550 nm (AOD550). AOD550 has been obtained from Terra-MODIS observations (Level 3, c005.1) centered over Athens, Greece.

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Fig. 5. Scatter plots of estimated vs measured global irradiance from both MRM v5 (blue) and MRM v6 (red) simulations for each of the four aerosol models. The linear regressions are shown in the plots, while N corresponds to the total number of observations during the period 2001e2005. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

duration and atmospheric conditions. 5. Results and discussion 5.1. Measured vs modeled radiations Fig. 2 shows the correlation between measured and simulated values of the solar radiation components for global horizontal (a), diffuse horizontal (b) and direct horizontal (c). The simulations were performed using both MRM v5 and MRM v6 in order to attain a direct comparison between the two versions. The measurements correspond to the period 2001e2005 (N ¼ 16,923) after excluding the questionable data according to the quality control. The results show that the new MRM v6 improves the model's performance on simulating the global solar radiation since the regression line is now closer to the 1-1 line; the slope approaches unity, the intercept approaches zero and the scatter of the data points has been reduced (R2 ¼ 0.95). The data points are close to the 1-1 line, but with a slight tendency of underestimation for the higher global irradiance values. This indicates that MRM v6 has some difficulty in simulating the peaks of the broadband global radiation likely due to uncertainties in the simulations of atmospheric aerosols and/or clouds. However, MRM v6 improves the simulations of global radiation and this is very important for atmospheric physical

sciences, like the filling of missing data in a solar radiation data series as well as for renewable energy applications like solar mapping, design and installing photovoltaic parks. The larger MBE (5.0%) value in MRM v6 against MRM v5 (2.9%) (Table 1) is attributed to the much lower scatter of the data points that overestimate the measured global irradiance (i.e. data points lying above the 1-1 line in Fig. 2a), thus resulting in larger overall underestimation of the global irradiance by MRM v6, without meaning that the model's performance is worst that the previous version MRM v5. In the meanwhile, the highly scattered data points at both sides of the 1-1 line for MRM v6 are somewhat self-canceled resulting in low MBE values. As far as the diffuse irradiance is concerned, the results show that the MRM v6 slightly improves the simulations (Fig. 2b). Besides that the model continues to be unable to follow the measurements for diffuse values above 200e250 Wm
2, a slight improvement is shown, since the linear regression is closer to the 1-1 line, as shown from the higher slope (0.49 for MRM v6 against 0.45 for MRM v5). However, the simulations of the diffuse radiation remain highly uncertain, since this component is very much sensitive on both aerosols and clouds. Thus, accurate parameterization of the aerosol optical properties is needed, since even for the same AOD and SZA the diffuse component may differentiate significantly due to the various aerosol types (highly or less scattering, large or

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149

Fig. 6. Same as in Fig. 5, but for the diffuse radiation.

small particles) as previous studies have shown [33,38,55,67]. The aerosol field was considered constant throughout the day based on the AOD550 and FM values at 10:30 LST (Terra-MODIS observations), thus being unable to follow the diurnal variation and sudden changes in aerosol loading due to arrival of turbid air masses (e.g. smoke or desert dust). Furthermore, the satellite data were not available on some days, when the climatological values of AOD550 and FM were used leading to higher uncertainties in the diffuse simulations. Thus, deviation in the optical properties of the four aerosol models used in MRM v6 from the real atmospheric conditions may lead to significant inaccuracies in the diffuse estimations. On average, the MRM v6 code underestimates global radiation by 24%, while a larger underestimation was found for MRM v5 (35% on average during 2001e2005) (Table 1). On the other hand, the diffuse radiation is very much sensitive to cloudiness, cloud cover, cloud thickness, cloud height, as well as optical and microphysical properties of clouds and the relative height between aerosols and clouds [2,14,45,53], rendering the diffuse simulation a real challenge [73,36]. Therefore, the simulation of solar radiation under cloudy skies includes high uncertainty due to difficult parameterization of the optical and microphysical properties of clouds as well as their interactions with atmospheric aerosols. Such simulations are usually based on empirical equations

between cloudiness and/or cloud modification fraction and clearness index [68]. However, any inaccuracy in the aerosol field cannot justify the large underestimates, even reaching above 100% for diffuse radiation values over 200e250 Wm
2. The analysis has shown that the diffuse simulations are improved (y ¼ 0.48x þ 40.06, R2 ¼ 0.55) for Sun elevations below 35 against those for Sun elevations above 40 (y ¼ 0.35x þ 92.16, R2 ¼ 0.46). It also seems that MRM v6 is unable to represent the peaks in the measured diffuse radiation usually observed in the data series around local noon, especially for periods with relative low sunshine duration, as in winter. Thus, a brief blockage of the Sun's disk by a fast-moving cloud and/or the presence of clouds near the Sun's field-of-view may increase the diffuse irradiance due to increase in cloud scattering and/or cloud reflection; this is nearly impossible to be accurately simulated almost in any solar radiation code due to the very short duration of the phenomenon. A sensitivity analysis showed that for relative sunshine durations of ~0.2e0.3 the estimated diffuse component is nearly independent of AOD. The same analysis revealed that for cloudless skies (relative sunshine above 0.9), the diffuse radiation depends strongly on variations in AOD increasing with it; for relative sunshine duration below 0.2 the simulated diffuse decreases as AOD increases, suggesting a higher dependence of diffuse on cloudiness.

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Fig. 7. Same as in Fig. 5, but for the direct radiation.

Thus, increasing turbidity under cloudless skies increases the diffuse radiation, which therefore, requires accurate parameterizations of the aerosol properties in order to attain a good simulation. On the other hand, extensive cloudiness decreases diffuse radiation as turbidity increases, suggesting that the influence of clouds is dominant. All the above suggest a difficulty in simulating the diffuse component due to contradictory influence of aerosols and clouds under clean and cloudless skies. It was also found that the simulations of the diffuse radiation depend strongly on SZA, with higher uncertainties for low SZA (high Sun elevations) because of the reasons discussed above. On the other hand, the sensitivity analysis revealed (not shown) that the MRM v6 performance slightly improves for cloudless rather than cloudy/overcast skies and for lower AODs, but the influence of these parameters (cloudiness and turbidity) is much lower compared to SZA. Despite all these difficulties, the MRM v6 improves significantly the simulations of the diffuse radiation compared to MRM v5, since the RMSE becomes 40.8% instead of 44.5% and the MBE is improved from 26.2% to 19.5%. Therefore, the detailed parameterization of the aerosol component in the MRM v6 by using spectral AOD and four models for the characterization of the different atmospheric conditions ameliorates the simulations. On the other hand, the MRM v6 shows much better simulations for the direct radiation (Fig. 2c) compared to those of MRM v5, as shown from the lower scatter (R2 ¼ 0.91), higher slope and lower

intercept that lead the linear best-fit curve to approach the 1-1 line. For low direct radiations, both MRM versions overestimate the measurements, while this overestimation is significantly lower for MRM v6. On average, MRM v6 overestimates direct radiation by 2% instead of 8% of the previous version; this leads to much lower RMSE and MBE values (Table 1). This improvement is attributed to the better aerosol parameterization and the usage of the relative sunshine duration instead of the daily one used in MRM v5. Thus, MRM v6 seems to follow better the gaps in direct radiation due to cloudiness during the day and, therefore, it reduces the RMSE and MBE parameters.

5.2. Model performance against sunshine duration Fig. 3a, b, c show the ratio of the estimated/measured radiation as a function of the sunshine duration for global, diffuse and direct horizontal components, respectively, in order to reveal possible trends of underestimation/overestimation in the irradiance components due to changes in cloudiness. It should be noted here that global irradiance values below 50 Wm
2 have been removed, since such values usually lead to very high ratios (especially for the direct irradiance since at several cases the measured and/or simulated values are close to zero, Fig. 2c). The results show that a decrease in sunshine duration (a consequent increase in cloudiness) leads to a higher degree of

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underestimation for both MRM v5 and MRM v6. In contrast, an opposite trend is shown for MRM v6 in the direct radiation with a tendency for overestimation for lower sunshine durations. All graphs agree that for cloudless skies (relative sunshine durations 0.9e1.0) the estimated to measured irradiance ratios exhibit the lowest values with averages close to 1.0. In the case of partly cloudy and overcast skies the range and the scatter increase significantly implying larger inaccuracies in the simulations of the radiation components. MRM v6 exhibits much better simulations compared to those from MRM v5 for the global irradiance, since the average ratio remains close to 1.0 nearly independently from the sunshine duration. In the diffuse radiation the MRM v5 seems to underestimate the measurements for any sunshine duration, while MRM v6 slightly improves the simulations under cloudless skies, but is incapable to reproduce the radiation for cloudy skies leading to underestimations. In contrast, a systematic overestimation is observed for low sunshine durations in the direct component for MRM v6, while for high sunshine durations the irradiance ratio values are much closer to 1.0 compared to those from MRM v5, indicating significant improvement in the simulations. 5.3. Model performance against atmospheric turbidity The respective graphs of the ratio estimated/measured radiation components as a function of atmospheric turbidity (expressed via AOD550) are shown in Fig. 4a, b, c for global, diffuse and direct, respectively. The MRM v6 shows a slight tendency of underestimation for the global irradiance at higher AODs, while the same tendency is observed for the direct component. In contrast, a slight tendency of overestimation in the diffuse is shown for AODs above 0.5. MRM v5 does not exhibit any trend in the global radiation simulations as a function of AOD, while it systematically underestimates the diffuse measurements at high AODs (and overestimates the direct) due to large uncertainties in reproducing the high AOD values via the empirical Yang et al.'s [81] formula. It was found that the Yang et al.'s empirical formula for Taer considers low AOD values (maximum 0.09e0.12), since for these AODs both MRM v5 and MRM v6 estimate very similar diffuse radiations. Therefore, for higher AODs, the MRM v5 underestimates (overestimates) the diffuse (direct) irradiance, as indicated in Fig. 4b, c, due to the consideration of more transparent atmospheres. 5.4. Model performance for various aerosol models As discussed in Section 3, depending on the AOD550 vs FM relationship different aerosol models are considered for the simulations of the radiation components in MRM v6. Therefore, the performance of the irradiance simulations is checked for each of the four aerosol models. Regarding global radiation (Fig. 5aed), the simulations are more or less similar independently of the aerosol model; this indicates that the global radiation is satisfactorily reproduced by MRM v6 under all atmospheric conditions. The improvement of the simulations from MRM v6 is significant for all aerosol models and more specifically for the S&F_URBAN model, since R2 has increased from 0.84 to 0.94. However, MRM v6 seems to have a worse performance for cases belonging to this aerosol type, since a systematic underestimation of the global radiation is observed. This is attributed to the very low SSA values (0.65e0.67) that the S&F_URBAN model encounters, which are much below the SSA values (0.88e0.95) for the typical Athens urban environment Fig. 8. Scatter plot between measured and estimated solar irradiance components: global (a), diffuse (b) and direct (c) for the hourly values of the monthly mean diurnal pattern per month for each year during 2001e2005 over Athens. The data correspond to clear-sky conditions (i.e. hourly sunshine duration ¼ 1). The linear regressions,

RMSE and MBE values are blue (red) for the MRM v5 (MRM v6) estimates. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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Fig. 9. Monthly mean diurnal variation of the global irradiance (measured and simulated via MRM v5 and MRM v6) for clear-sky days over Athens during the whole 2001e2005 period. Time is LST.

(see AERONET webpage, ATHENS_NOA station). The lower SSAs assumed by the model lead to higher absorption and less scattering of solar radiation; this reduces the diffuse component and, as a consequence, the global one leading to higher underestimation compared to the rest of the aerosol models. An underestimation of the global radiation is also shown for the DESERT_MIN model, while under clean maritime conditions the MRM v6 slightly overestimates the global radiation in contrast to MRM v5. The vast majority of the cases belong to the SRA_CONTL model where a correlation similar to that of Fig. 2a is shown. The four aerosol models used in MRM v6 slightly improve the diffuse simulations against the previous version (Fig. 6aed), although in all cases both MRM versions exhibit large underestimations for diffuse radiation values above 200e250 Wm
2 due to reasons discussed above. However, significant improvements in MRM v6 simulations are attained for the cases belonging to the DESERT_MIN and SRA_CONTL models. More specifically, despite the larger scatter (R2 ¼ 0.58 against R2 ¼ 0.69) for MRM v6 in Fig. 6a, the vast majority of the data points is much closer to the 1-1 line compared to MRM v5, where a significant and systematic underestimation is shown. The increased SSA for atmospheres dominated by coarse-mode particles of desert origin (transported dust from North Africa mostly during spring and summer,

Kaskaoutis et al. [39] enhances the scattering process and the estimated diffuse radiation, which is now closer to the measured values (Fig. 6a). In contrast, low SSA values encountering in the S&F_URBAN model lower the diffuse spectrum (due to lower scattering), thus resulting in significant underestimation and rather worse simulations by MRM v6 (Fig. 6b). In clean maritime conditions, the MRM v6 limits the overestimation shown from MRM v5 for diffuse radiation values below 120 Wm
2 (Fig. 6c), while for the rest of the cases (Fig. 6d) MRM v6 improves the estimates of the diffuse radiation. In synopsis, the results show that the usage of different aerosol models in MRM v6 for a more precise representation of the atmospheric conditions improve the estimates of the diffuse radiation, especially for values below 150e200 Wm
2. However, the larger discrepancies of the S&F_URBAN model indicate that the Athens atmosphere does not contain so large amounts of Black Carbon (BC) and, therefore, this model may be more appropriate for urban environments with larger amounts of fossil fuel combustion, biofuel burning as well as for sites affected by seasonal forest and agricultural fires with higher amounts of BC and lower SSA values (e.g. [5,24,40]. Theoretically, the spectral variation of SSA does not affect the direct radiation; according to the mathematical expressions used in the MRM v6, the SSA affects Tas, Taer and their spectral variation (see

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153

Fig. 10. Same as in Fig. 9, but for the diffuse irradiance.

Eq. (12)). Despite the fact that the spectral AOD for the three models (DESERT_MIN, S&F_URBAN, SRA_CONTL) is very similar (Fig. 1), MRM v6 improves the simulations of the direct irradiance, mostly by reducing the large scatter shown via MRM v5 simulations (Fig. 7aed). Nevertheless, larger discrepancies are shown in the DESERT_MIN model for the high direct-irradiance values with a systematic MRM v6 underestimation, while a large scatter is shown for the S&F_URBAN model. In the case of S&F_MARITIME, MRM v6 slightly overestimates the direct irradiance measurements, while the best performance is attained with the SRA_CONTL model. However, the influence of the aerosol types on the MRM v6 simulations of the direct radiation is much lesser than that on the diffuse (Fig. 6aed) since changes in spectral AOD and SSA mostly influence the diffuse rather than direct spectrum [38,55]. 5.5. Model performance under clear-sky conditions The model performance (for both MRM v5 and MRM v6) is further examined under clear-sky conditions as defined with hourly sunshine duration equal to 1.0. It should be noted here that the sunshine duration data correspond to 1-hr intervals implying that during this hour the Sun's disk was fully unblocked by clouds. However, this does not prevent cloud presence at any other part of the sky or even close to the Sun's field of view, thus affecting the

measurements and more specifically the diffuse irradiance. Using this criterion the analysis was limited to 10340 data (cloud-free, hourly averages) during the period 2001e2005. These data were classified for each month and averaged for each hour, thus providing the monthly-mean diurnal variation of the irradiance components. Fig. 8aec presents the scatter plots between the measured and simulated solar irradiances (global, diffuse and direct, respectively) for each month and hour during the period 2001e2005. Due to hourly averaging, the estimates of MRM v5 and MRM v6 have been improved compared to those in Fig. 2, while the MRM v6 presents better simulations for all irradiance components, except of a higher underestimation for the global irradiance (MBE ¼ 4.96 for MRM v6 instead of 2.82 for MRM v5). Finally, the monthly-mean diurnal variation of the measured and simulated (MRM v5 and MRM v6) global, diffuse and direct radiations are plotted (Figs. 9e11) and the statistical indicators RMSE and MBE via Eq. (17a, b) and (18a, b) are estimated (Tables 2 and 3). The diurnal variation of the global radiation on monthly basis is shown in Fig. 9 revealing a satisfactory agreement between measured and simulated irradiances, especially for MRM v6 whose performance is better compared to MRM v5 in nearly all the months except of January, while in July, August, October and November the two model versions exhibit similar RMSE values (see Table 2). MRM v5 systematically underestimates the monthly mean

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Fig. 11. Same as in Fig. 9, but for the direct irradiance.

Table 2 RMSE statistics for the MRM v5 and MRM v6 performance on the monthly-mean diurnal variation of the radiation components in Athens during 2001e2005. The RMSE is expressed in absolute (Wm
2) and percentage (%) values according to Eqs. (17a) and (17b). Global radiation

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Diffuse radiation RMSE (Wm
2)

Direct radiation

RMSE (Wm
2)

RMSE (%)

v5

v6

v5

v6

v5

v6

v5

v6

v5

v6

v5

v6

23.4 36.7 44.5 60.4 43.1 50.8 23.2 23.9 39.2 23.2 21.0 23.5

28.2 17.4 22.9 27.1 27.0 33.1 23.8 24.5 28.9 23.9 20.6 20.1

7.3 9.1 9.0 10.5 7.3 8.2 3.9 4.4 8.1 5.5 6.8 7.5

8.9 4.3 4.7 4.7 4.6 5.4 4.1 4.5 5.9 5.7 6.7 6.5

9.5 14.5 29.7 33.5 38.9 29.4 47.6 41.6 29.5 18.2 11.4 10.7

7.9 5.4 33.5 33.1 31.6 22.3 31.6 21.4 23.7 20.7 4.1 5.2

12.5 15.1 21.9 22.5 26.7 21.0 31.7 30.8 23.6 16.1 13.8 14.8

10.5 5.6 24.7 22.3 21.7 15.9 21.1 15.9 19.0 18.4 4.9 7.1

27.3 36.2 26.5 33.0 32.0 40.2 34.6 39.7 27.6 20.9 19.4 33.8

32.5 26.1 33.9 12.1 22.6 23.8 12.5 11.8 17.3 39.5 30.0 23.0

11.1 11.8 7.4 7.8 7.2 8.4 7.9 9.9 7.8 6.8 8.6 14.2

13.3 8.6 9.5 2.9 5.0 4.9 2.8 2.9 4.9 12.8 13.3 9.7

diurnal variation of the global radiation in all months (positive MBE values), whereas MRM v6 slightly overestimates it during the cold period (OctobereFebruary) of the year (negative MBE values in Table 3). Another characteristic is that both model versions reveal the largest underestimations (in absolute Wm
2 values) during the

RMSE (Wm
2)

RMSE (%)

RMSE (%)

noon hours in the MarcheJune period when global radiation takes its highest values (Fig. 9). The RMSE and MBE values are much lower considering simulations of the monthly means under cloudless conditions (Tables 2 and 3) compared to those of the whole dataset (Table 1). This indicates that the model performance

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Table 3 Same as in Table 2, but for the MBE according to Eqs. (18a) and (18b). Global radiation

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Diffuse radiation MBE (Wm
2)

Direct radiation

MBE (Wm
2)

MBE (%)

MBE (Wm
2)

v5

v6

v5

v6

v5

v6

v5

v6

v5

v6

v5

v6

15.0 27.6 27.8 47.9 25.2 29.7 12.7 3.9 23.1 9.3 15.9 21.8


21.9
7.9 12.3 19.8 13.4 17.1 18.6 15.3 17.9
15.4
17.7
18.9

4.7 6.9 5.6 8.3 4.2 4.8 2.2 0.7 4.7 2.2 5.2 7.1


6.9
2.0 0.3 3.4 2.3 2.8 3.1 2.8 3.7
3.6
5.7
6.1


5.0 12.4 28.0 32.3 37.6 28.9 45.8 39.3 26.4 17.3 7.5
10.1

5.9 2.3 29.3 28.7 28.5 20.5 27.9 17.9 18.1 18.2 2.3 0.8


6.5 12.9 20.6 21.7 25.9 20.7 30.5 29.1 26.2 15.4 9.0
14.0

7.9 2.3 21.7 19.3 19.6 14.7 18.6 13.2 14.5 16.2 2.8 1.2

19.9 25.4 3.9 15.5
12.4 0.8
33.1
35.4
8.2
8.1 13.6 32.0


27.6
20.3
23.8
8.9
15.1
3.4
9.4
2.5
5.1
33.6
38.8
19.7

8.1 8.3 1.1 3.6
2.8 0.2
7.5
8.8
2.3
2.6 6.0 13.4


11.4
6.6
6.7
2.1
3.4
0.7
2.1
0.6
1.4
10.9
17.1
8.3

MBE (%)

has improved under cloudless skies, while on monthly bases MRM can represent the diurnal patter of the global irradiance with high accuracy. More interesting results in view of the large monthly variability in the model performance are shown for the diffuse radiation. The diurnal plots (Fig. 10) and the RMSE values (Table 2) reveal a significant improvement in the accuracy of the simulations via MRM v6 in all months except for March and October; also a large underestimation in the diffuse radiation especially around noon from March to October is observed. This suggests an incapability of the model in representing the highest values of the diffuse irradiance during the summer period, which was also found to affect the global radiation (Fig. 9). The main reasons for this discrepancy have been discussed in the previous sections since bright cumulous clouds around the Sun's disk may increase significantly the diffuse radiation measured on the ground due to high reflectance, especially when the Sun is near to zenith. Furthermore, the increased aerosol loading during this period [38] enhances the diffuse component, which is more difficult to be represented by radiation transfer models [36,73]. On the other hand, under clear-sky conditions during NovembereFebruary, the model simulations show an excellent agreement with measured diffuse radiation at least for the monthly means. The discrepancy in simulations of the maximum diffuse radiation is the main issue in MRM v6 and a real challenge for resolving and improving the simulations in a future model version. As far as the direct irradiance is concerned (Fig. 11), the results are in general agreement with those presented for the global component (Fig. 9). The MRM v6 improves the simulations except for January, March, October and November when the model overestimates significantly the measured direct radiation. MRM v6 overestimates the diurnal pattern of the direct irradiance in all months (Fig. 11, Table 3), whereas MRM v5 overestimates it during the hot season (May, JulyeOctober) (Table 3). The RMSE and MBE values are in the same order of magnitude with those observed for the global radiation, implying a satisfactory agreement of the model in representing the monthly-mean diurnal pattern of the direct horizontal irradiance under clear skies over Athens. In synopsis, the RMSE and MBE values for the model simulations under clear skies are in similar magnitude to those reported by Gueymard [23] who examined the performance of MRM v5 at five locations over the globe. The satisfactory representation of the monthly-mean diurnal pattern of the irradiance components suggests that MRM constitutes a powerful tool for estimating the energy flux incident on the panels of a photovoltaic park; this parameter is very important for forecasting their performance. The capability of the MRM in

MBE (%)

reproducing the energy flux (Wh m
2) on monthly basis is examined in Fig. 12(aec) for all solar irradiance components. The energy fluxes were calculated from the daily integrals (trapezium method) using the daily mean for each month during the period 2001e2005. The results reveal a great performance of MRM (a little better for MRM v6, especially for the diffuse and direct irradiances). MRM v6 improves significantly the estimates of the monthly energy flux for the direct irradiance, which is overestimated via the MRM v5, but underestimates the amount of the global energy flux for values above 5000 Wh m
2. In synopsis, the whole analysis revealed that the inclusion of the aerosol properties in MRM v6 improves the simulations of solar irradiance, especially for the diffuse and direct components; however, on monthly basis and for energy purposes the two versions perform reasonably well indicating that MRM v5 may also be used in cases of unavailability of aerosol data. MRM v6 is an operational solar radiation model at any location over the globe with availability of meteorological and sunshine duration data and can be a powerful tool for atmospheric (solar radiation) and engineering (photovoltaic cells) applications. Testing of the model at many places over the globe will enhance its usefulness for the global community. 6. Conclusions This study described the recently updated version of the Meteorological Radiation Model (MRM v6) developed at the National Observatory of Athens with aim to improve the simulations of the solar radiation components, i.e. global, diffuse and direct, on horizontal plane. For the first time MRM v6 uses spectral distributions of the aerosol optical depth (AOD) and single scattering albedo (SSA) retrieved from different models implemented in SMARTS ver. 2.9.5 radiation transfer model for better simulations of the solar radiation components. Measured aerosols are inserted for the first time in MRM v6 through MODIS satellite observations of AOD and fine-mode (FM) fraction. Via the relationship of AOD vs FM and taking specific threshold values, four aerosol models were selected in MRM v6 (DESERT_MIN, S&F_URBAN, S&F_MARITIME, SRA_CONTL). The spectral AOD and SSA values of these aerosol models normalized for the measured atmospheric AOD are used in the code for better representation of the aerosol influence on solar radiation. Along with some other minor changes in the code, the better representation of the aerosol conditions in MRM v6 resulted in improving the simulations of the global, diffuse and direct radiation components. The validity of the MRM v6 was checked against ground-based radiation measurements taken at Athens, Greece during the period 2001e2005. In order to examine the degree of the

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improvement in model simulations, MRM v6 was also compared to its previous version (MRM v5). The results showed lower RMSE values for all radiation components (13.7%, 40.8% and 24.2%, for global, diffuse and direct, respectively) for MRM v6 against MRM v5 (18.0%, 44.5% and 34.1, respectively), also associated with lower scatter in the linear regressions between measured and simulated irradiances. Furthermore, the results showed a better simulation of the radiation components for lower AODs and higher sunshine durations. The analysis under clear-sky conditions (the Sun's disk to be unblocked by clouds) revealed a general satisfactory representation of the global and direct radiations, while an incapability of the model in representing the high diffuse values especially around local noon and during the MarcheOctober period was evident independently of the atmospheric turbidity, sunshine duration and aerosol type. This is the main drawback of MRM v6 in representing the diffuse radiation. The analysis revealed that the model is unable to follow the peaks in the diffuse irradiance in the cases of fastmoving clouds blocking the Sun or short-term reflections from clouds. For clear-sky days this phenomenon was more pronounced during the MarcheOctober period and maybe attributed to enhanced diffuse radiation via multiple scattering and reflection caused by bright cumulous clouds that maybe present in the sky or even near to the Sun's field of view. The further improvement of the MRM model targeting on better simulations of the peak diffuse irradiances constitutes a real challenge. However, the analysis revealed that MRM may represent the monthly energy fluxes with great accuracy (MRM v6 improves significantly the diffuse and direct energy fluxes) thus making MRM v6 a powerful tool for energy purposes and forecasting of solar irradiance for establishment of photovoltaic parks. Acknowledgments This study was supported by the EU-funded KRIPIS-THESPIA project. References

Fig. 12. Measured vs estimated energy fluxes for global (a), diffuse (b) and direct (c) irradiances in Athens, for the monthly-mean diurnal pattern for each month during 2001e2005. The linear regressions, RMSE and MBE values are blue (red) colored for MRM v5 (MRM v6) estimates. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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