HIGH TURBIDITY CLEAR SKY MODEL: VALIDATION ON DATA FROM SOUTH AFRICA

HIGH TURBIDITY CLEAR SKY MODEL: VALIDATION ON DATA FROM SOUTH AFRICA Pierre Ineichen 1 1 University of Geneva, Energy Systems Group ISE/Forel, 66 bd Carl-Vogt, CH 1211 Geneva 4, pierre.ineichen@unige.ch Abstract The simplified Solis clear sky scheme was developed in 2008 to be used in automatic on-line satellite irradiance evaluation processes. It is a fast analytical broadband version of the spectral clear sky model Solis developed within the Heliosat project. Its weakness was the divergence for high aerosol optical depths (aod > 0.45). A new model was developed that can be applied for aod values up to 7, even if these values are not realistic. This ensures that the irradiance based on the model remains coherent whatever the quality of the input values. The paper presents a validation of the model on data acquired in Geneva, in four turbid sites, and in Durban and Stellenbosch, Sauran network sites. Keywords: irradiance clear sky model; analytical fast model; model validation; large turbidity range value of 7 ( i.e. an aerosol optical depth aod700 = 0.44 for a 2cm water vapour column). The 2008 and 2010 versions of Solis diverge for high turbidity values as shown by Zhang [11] and illustrated in Fig. 1 where the normal beam irradiance Ibn is represented versus the aerosol optical depth for the Solis 2008 model and different solar elevation angles. 1. Introduction The clear sky Solis scheme was first developed within the Heliosat-3 European program whose subject was to support the solar energy community in increasing the efficiency and costeffectiveness of solar energy systems and improving the acceptability of renewables. In 2008, Ineichen published a broadband analytical version of the Solis model for rural aerosol type [1], and in 2010 a version in the form of an Excel tool [2] for the four types of aerosols as defined by Shettle and Fenn [3]. These versions were limited to aerosol optical depth values aod700 lower than 0.45. The anthropogenic heating and transportation activities resulted in a serious increase of the turbidity in countries like India or China. Looking into the limitations of the state of the art clear sky models, it appears that none is applicable for high turbidity. Indeed, for example, Gueymard CPCR2 model [4] is limited to Angström b turbidity values lower than 0.4 (which correspond to an aod700 of 0.64 for rural aerosol type, a = 1.3), Gueymard REST2 [5] is limited to b = 1 (aod700 = 1.6, rural aerosol), Bird s model [6] is defined for visibility values up to 23 km (which corresponds to an aod = 0.27) and the ESRA clear sky scheme [7-9] was developed for Linke turbidity values TL [10] not exceeding a Fig. 1. Behavior of the normal beam irradiance with the aerosol optical depth for the 2008 Solis version and different solar elevation angles This paper presents a validation of a new version of the analytical Solis scheme valid for the three radiation components, the global, the beam and the diffuse, and the four aerosol types, urban, rural, maritime and tropospheric. 2. Solis scheme basis The Solis clear sky scheme was developed within the Heliosat-3 European program which aim was to evaluate the solar irradiance components from the geostationary meteorological satellite Meteosat MSG by Müller et al [12]. It is a spectral model, based on LibRadTran [13] radiation transfer calculations and the Lambert-Beer attenuation equation: I "# = I % e )*+

where Io is the extraterrestrial irradiance, Ibn the normal beam irradiance reaching the ground, M the optical air mass and t the total atmospheric optical depth. The properties of the scattering process during the atmospheric transmission of the solar radiation lead to a slight modification of the attenuation equation for each component. At high aerosol load, Io has to be enhanced for the global and diffuse irradiance calculations, and a common modified Io irradiance is defined for the three radiation components. The equations take then the following form: sites of Jaipur, Ilorin, Solar Village and Xianghe, and the SAURAN network [19] for Durban and Stellenbosch. The latitude, longitude, altitude and acquired parameters are given on Table 1. I "# = I, % e.)/ 0 123 0 46 I 74 = I, % e.)/ 8 123 8 46 sin h I =4 = I, % e.)/ > 123 > 46 where Ibn, Igh and Idh are respectively representing the normal beam irradiance, the horizontal global and the horizontal diffuse components, h the solar elevation angle, tb, tg and td are respectively the beam, global and diffuse attenuation coefficients, and b, g and d the corresponding fitting parameters obtained from RTM calculations. The new Solis scheme is fully described in Ineichen [14] and an Excel tool is available for download [15]. 3. Ground measurements Data from seven sites are used to conduct a model validation. Sites acquiring simultaneously the irradiance components and the aerosol optical depth are very scarce, particularly in countries with high aerosol load such as China or India. For comparison purpose with the Solis 2008 scheme, we used the relatively low turbid site of Geneva, where the median aod value is around 0.1 with a maximum at 0.5. Furthermore, there are no aod measurements available in Geneva, so we used one of the best state of the art models, REST2 [5] to retrieve them by retrofit following a model described in [16]. We then used four sites with higher turbidity, Ilorin in Nigeria, Jaipur in India, Solar Village in Saudi Arabia, and Xianghe in China. The two sites in South Africa where the irradiance data and the aerosol values are simultaneously acquired are Durban and Stellenbosch. Durban presents slightly higher aod values than Geneva (median = 0.15 and maximum around 0.9); Stellenbosch is the clearest site with a median value at aod = 0.05. For all the sites except Geneva, the aerosol optical depth is provided by the Aerosol Robotic Network (AERONET [17]). The irradiance data are acquired by the University of Geneva, the Baseline Surface Radiation Network (BSRN [18]) for the Table 1 Latitude, longitude, altitude and acquired parameters of the sites The frequency distribution of the aerosol optical depth for the seven sites is given in Fig. 2. Fig. 2 Frequency distribution of the aerosol optical depth for the seven sites The effect of the atmospheric water vapor column w is of the second importance in the attenuation process. The development of the model was made for water vapor values up to 10 cm. Except for Ilorin where the median w content is 3.5 cm, all the other sites present median values between 1 and 2 cm. The

frequency distribution of occurrence of w is given in Fig. 3 for the seven sites. Fig. 3 Frequency distribution of the water vapor column for the seven sites The pertinence of the validation results is highly correlated to the quality of the ground data. Therefore, a stringent quality control (QC) has to be applied to the data. An on-line QC is normally applied by the institution in charge of the measurements so that acquisition failures, misalignment, sensor soiling, etc. can immediately be corrected. An a-posteriori QC has then to be applied to the data in order to assess the acquisition time, the sensor calibration, the components coherence, etc. An illustration of the components coherence is given in Fig. 4 where the closure equation is evaluated for the data of Durban. I 74 = I =4 + I "# sin h 4. Clear conditions selection In order to conduct the validation, only clear sky conditions have to be selected. To perform the selection, we applied the criteria defined in Ineichen [20]: If the three components are available, the closure equation has to be satisfied within -50 W/m 2-5% and +50 W/m 2 + 5%, If only two components are available, all the values are kept, The modified global clearness Kt (as defined by Perez et al. in [21]) calculated on the ground measurements is higher than 0.65, The stability of the global clearness index DKt is better than 0.01 (DKt is evaluated by difference of the considered hour and the average of the considered hour, the preceding and the following hour). This selection minimizes the cloud contamination, it is restrictive, but for the validity of the comparison, it ensures that only clear and stable conditions are selected. It shows its importance particularly for data from Xianghe where often the beam component is very low or missing in the middle of the day while the corresponding global component shows clear conditions (due to sensor saturation?). 5. Validation The first order statistics, i.e. the mean bias difference mbd between the model and the ground measurements (a positive value indicates an overestimation of the model), the standard deviation sd and the correlation coefficient R 2 are used to determine the accuracy of the model. A parameter dependence is conducted to visualise the behaviour with different parameters such as the aod or the season, and the frequency distribution of the bias is analysed to assess the validity of the first order statistics. In a first step, the validation is done for the site of Geneva on the same data set than for the Solis 2008 validation in [16]. The results are given in Table 2 Fig. 4 QC illustration: closure equation for the site of Durban. When all these control are fulfilled, the data can be considered as trustable and the validation procedure can be conducted. Table 2 Comparison of the validation results for the two version of Solis on Geneva s data

The comparison shows that the new version of Solis applied to data from Geneva gives slightly better results than the 2008 version. In Table 3 below, the validation results for the four turbid and the two South African sites are given in term of first order statistics. index (a), and the diffuse fraction against the global clearness index (b); the measurements are represented in green and the modelled values in blue. Table 3 First order statistics for the four turbid and the two South African sites From the table, the following comments can be made: Durban and Stellenbosch show good validation results, with negligible bias and low uncertainties, The high variability in the Ilorin climate induces a higher standard deviation, even if the bias remains very low, The high standard deviation for the site of Xianghe is certainly a result of the low quality of the normal beam data (see section 4), The daily values represent the sum of only the hourly values kept for the validation: it is not the daily integral (sum of all the values of the day). This is particularly the case during partly cloudy days where only a few hourly values are acquired during cloudless conditions. The consequence is that for example at Ilorin, where the sky conditions are highly variable and clear day from sunrise to sunset are very scarce, the average daily value is low. Fig. 5 Beam clearness index (a) and diffuse fraction (b) versus the global clearness index for the site of Durban Going into a more detailed analysis, the following observations can be done: Ground measurements and modelled values can be represented on the same graph in different colours. If the model reproduces faithfully the measurements, the envelopes of the data clouds should be similar. This is illustrated for the site of Durban in Fig. 5 where the beam clearness index is plotted against the global clearness Fig. 6 Global irradiance bias dependence with the aerosol optical depth The dependence of the model bias with the aerosol optical depth aod is analysed for the different components. No specific pattern could be pointed out. This is illustrated for the site of Durban in Fig. 6 where the global irradiance

model bias is represented versus the aerosol optical depth. We analysed the behavior of the model with the day of the year, this means the seasonal dependence of the model. The analysis is done in hourly and daily values, and for the three components. Here also, no significant pattern could be pointed out. The results for Durban are given in Fig 7 for the beam component. standard deviation value can be considered as representative of the uncertainty of the model. It is the case for all the distributions, except for the site of Ilorin, where the dispersion is high, probably due to the high variability of the climate. The representation for the site of Durban is given in Fig. 8 where the cumulative curve is also drawn. The corresponding graphs for Stellenbosch are given in the Appendix. 6. Conclusion Fig. 7 Seasonal dependence of the beam irradiance bias for the site of Durban When dealing with satellite images to derive the irradiance components on a large space scale and every 15 minutes, the computer time should be as short as possible. The analytical Solis scheme is valid for atmospheric water vapor w content from 0.01 to 10 cm, altitude from sea level to 7000 m, and aod up to seven, even if very high values are not realistic as an optical depth; it is probably more due to bigger particles like dust or sand, or in our countries, thin high altitude clouds. Nevertheless, contrary to other clear sky models, this permit to produce coherent irradiance values, even if the input values are out of range or questionable. The validation against ground measurements acquired in Geneva, Ilorin, Jaipur, Solar Village, Xianghe, Durban and Stellenbosch gives a mean bias difference less than ±4%, a standard deviation of 3 6% for the global component, and a mean bias difference less than ±3% with a standard deviation of 5 13% for the beam component. The 12 13% standard deviations are due to either the high variability of the sky conditions or the poor quality of the ground data. The validation results for South Africa are among the best. As it is very difficult to find ground measurements covering the complete range of validity of the Solis analytical scheme, it cannot be completely validated. However, the new version faithfully reproduces the RTM LibRadTran calculations. Nomenclature Fig. 8 Frequency of occurrence of the model bias for the beam and the global component The validity of the first order statistics can be verified by representing the bias frequency of occurrence distribution. If the shape of the distribution is near of normal, the

Appendix

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