A new statistical approach for deriving global solar radiation from satellite images

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Solar Energy 83 (2009) 480–484 www.elsevier.com/locate/solener

A new statistical approach for deriving global solar radiation from satellite images Luis F. Zarzalejo *, Jesu´s Polo, Luis Martı´n, Lourdes Ramı´rez, Bella Espinar Energy Department, CIEMAT, Avda. Complutense, 22. 28040 Madrid, Spain Received 31 January 2007; received in revised form 12 September 2008; accepted 12 September 2008 Available online 16 October 2008 Communicated by: Associate Editor D. Renne

Abstract Solar radiation derived from geostationary satellite images has become an advantageous technique for solar resource characterisation over large areas. The simplest methods for estimate solar radiation from the satellite information rely on straight forward relationships between a normalised parameter of the solar irradiance (such as clearness or clear sky index) and the cloud index. This paper presents a statistical fit of this relationship (fitted and tested using data from 28 Spanish radiometric station) different from the approach used by Heliosat-2 method (Rigollier, C., Lefe`vre, M., Wald, L., 2004. The method Heliosat-2 for deriving shortwave solar radiation from satellite images. Solar Energy 77, 159–169), that includes local statistical measures of the cloud index distribution and the air mass. In particular, the inclusion of the local cloud index percentiles (median, first and third quartile) estimated from the whole series on each pixel improves clearly the model response, and is a way to account for the local climatological aspects of any location. The inclusion of the new explicative variables yield to practically unbiased results and the relative RMSE decrease to about 17% from the 21% result of the expression applied in the Heliosat-2 model. Ó 2008 Elsevier Ltd. All rights reserved. Keywords: Solar radiation; Satellite; Meteosat; Heliosat; Clear sky index; Cloud index

1. Introduction The knowledge of the solar resource at the earth surface, with enough accuracy, is essential for planning any solar energy system at a given location. However, ground measured solar radiation is scarcely available for a given site where a solar system is planned. In this regard, the use of satellite data, in conjunction with quality solar ground data sets and other meteorological data as well, has become an effective way of developing site-time specific solar resource assessment over large areas. In particular, geostationary satellites provide information of the earth’s atmosphere and cloud cover for a large area with high spatial and temporal resolution. *

Corresponding author. Tel.: +34 913 466 496; fax: +34 913 466 037. E-mail address: [email protected] (L.F. Zarzalejo).

0038-092X/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.solener.2008.09.006

Several algorithms and models have been developed during the last three decades for estimating the solar irradiance at the earth surface from satellite images (Pinker et al., 1995; Renne´ et al., 1999). They can be generally grouped into physical and pure empirical or statistical models (Hay, 1993; Noia et al., 1993a,b). Statistical models are simpler, since they do not need extensive and precise information on the composition of the atmosphere, and rely on simple statistical regression between satellite information and solar ground measurements. These simple models are based on deriving a cloud index from the satellite visible channel that can be correlated with either the clearness index or the clear sky index. Recent examples of these kind of methods can be found in Perez model for the GOES satellite (Perez et al., 2002) and Heliosat model for the Meteosat satellite (Beyer et al., 1996; Hammer et al., 2003; Rigollier et al., 2004). The accuracy of these models

L.F. Zarzalejo et al. / Solar Energy 83 (2009) 480–484

for hourly global radiation, in terms of relative RMSE, is around 20% for large data sets covering spread areas, although lower uncertainties can be found for some local estimations (Zelenka et al., 1999; Rigollier et al., 2004). This paper presents a set of new empirical fits of the relationship between the cloud index (n), calculated by Heliosat-2 method, and the clear sky index (KC) using groundbased pyranometric data of 28 meteorological stations in Spain. The new model responses are compared with the Heliosat-2 original method applied to the Spanish locations. 2. The method Heliosat-2 Various methods for deriving solar radiation from satellite images were developed during ’80. One of them was the method Heliosat-1 (Cano, 1982; Cano et al., 1986; Diabate´ et al., 1988) which could be one of the most accurate (Gru¨ter et al., 1986; Raschke et al., 1991). The method Heliosat-2 (Rigollier et al., 2001, 2004) integrates the knowledge gained by these various exploitations of the original method and its varieties in a coherent and thorough way. Both versions are based in the computation of a cloud index (n) from the comparison between the apparent albedo observed by the spaceborne sensor (q), the apparent albedo of the brightest clouds (qc) and the apparent albedo of the ground under clear skies (qg) n ¼ ðq  qg Þðqc  qg Þ1

ð1Þ

For the estimation of radiation at ground level the method Heliosat-1 uses an empirical adjusted relation between the cloud index and the clearness index (KT). The new Heliosat-2 method uses a relation between the cloud index and the clear sky index (KC) defined as the ratio of the global irradiance (G) to the global irradiance under clear sky (Gclear). KC ¼

G Gclear

ð2Þ

481

The Heliosat-2 method deals with atmospheric and cloud extinction separately. As a first step the irradiance under clear skies is calculated by using the ESRA clear sky model (Rigollier et al., 2000; Geiger et al., 2002), where the Linke turbidity factor is the only parameter required for the atmosphere composition. The following relationship between the cloud index and the clear sky index is then used for the global solar radiation determination (Rigollier and Wald, 1998) n < 0:2;

K C ¼ 1:2

 0:2 6 n < 0:8;

KC ¼ 1  n

0:8 6 n < 1:1; 1:1 6 n;

K C ¼ 2:0667  3:6667n þ 1:6667n2 K C ¼ 0:05 ð3Þ

3. Experimental data Simultaneous data of satellite derived cloud index and hourly global irradiance on ground-based stations are used for model development and assessment for 28 locations in Spain covering geographical areas corresponding to Mediterranean, Semi–Arid and Oceanic climate. The geographic information of the radiometric stations is listed in Table 1. The time period covered is from January 1994 to December 2004. In the cloud index estimations the HRI–VIS channel images of Meteosat are used. The spatial resolution is 2.5 km  2.5 km at nadir and the temporal resolution is 30 min (EUMETSAT, 2001). After an exhaustive quality analysis of the simultaneous data around 370000 h data pairs are available for fitting and assessment the new models (Zarzalejo, 2006). The whole data set is randomly separated into two groups, 80% for fitting the models and 20% for assessment. 4. New model proposals Fig. 1 shows the Box & Whisker plots of the clear sky and cloud indices for the 28 Spanish locations, over the

Table 1 Geographic information of the Spanish radiometric stations #

Station

Latitude

Longitude

Height (m)

#

Station

Latitude

Longitude

Height (m)

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Ca´diz Ma´laga Almerı´a (CMT) Huelva Murcia Badajoz Ciudad Real Albacete Ca´ceres Valencia Toledo Madrid Tarragona Salamanca

36.50°N 36.72°N 36.85°N 37.28°N 38.00°N 38.88°N 38.98°N 39.00°N 39.47°N 39.48°N 39.88°N 40.45°N 40.82°N 40.95°N

6.27°W 4.48°W 2.38°W 6.92°W 1.17°W 7.02°W 3.92°W 1.87°W 6.33°W 0.38°W 4.05°W 3.72°W 0.48°E 5.92°W

15 61 29 19 69 190 628 674 405 23 516 680 44 803

15 16 17 18 19 20 21 22 23 24 25 26 27 28

Barcelona Soria Zaragoza Le´rida Valladolid La Rioja Pontevedra Leo´n ´ lava A Vizcaya Guipu´zcoa Asturias La Corun˜a Cantabria

41.38°N 41.60°N 41.63°N 41.63°N 41.65°N 42.43°N 42.58°N 42.58°N 42.85°N 43.30°N 43.30°N 43.35°N 43.37°N 43.48°N

2.20°E 2.50°W 0.92°W 0.60°E 4.77°W 2.38°W 8.80°W 5.65°W 2.65°W 2.93°W 2.03°W 5.87°W 8.42°W 3.80°W

25 1090 250 202 740 365 15 914 508 41 259 348 67 79

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Fig. 1. Box & Whisker plots for the clear sky and cloud indexes.

whole time period, sorted in ascending values of the latitude. B & W plots show relevant information on distribution moments: 50% of population is contained inside the box (between 25th and 75th percentile) and the median value is marked into the box, non representative statistical values (outliers) are distinct as ‘+’. These plots give useful information on the distribution functions of both parameters for each location, and dependence with the latitude can be pointed out for both the clear sky index and the cloud index distributions according to the increase of the interquartile distance with the latitude. Therefore, the analysis of the information given in Fig. 1 suggests two ways for developing new models:  The use of a selective fitting technique to eliminate, as much as possible, the presence of outliers in the data set for model development. A technique for iterative filtering the data in statistical models is used for selecting the more representative data (Polo et al., 2006).  The use of additional independent variables, which allows take into account the intrinsic characteristics of each location. The new parameters selected for each location are the local median (n50), first quartile (n25), third quartile (n75), as parameters describing the distribution functions of the cloud index, and the air mass (mair) estimated by Kasten equation (Kasten and Young, 1989), as descriptor of atmosphere quality and time dependence.

The new models proposed are then K C ¼ a1 n þ a2 n50 þ b

ð4Þ

K C ¼ a1 n þ a2 n50 þ a5 mair þ b K C ¼ a1 n þ a2 n50 þ a3 n25 þ a4 n75 þ b

ð5Þ ð6Þ

K C ¼ a1 n þ a2 n50 þ a3 n25 þ a4 n75 þ a5 mair þ b

ð7Þ

The coefficients for the new fitted models are listed in Table 2. The values of the clear sky index in these expressions are forced to be limited to KC 2 [0.05, 1.2], as the range adopted by Rigollier, in order to impose physical limits. 5. Results Assessment of the new fitted models proposed is performed over the 20% of the radiation ground data separated for this purpose. Table 3 shows the accuracy of the new models compared with the results provided by the relation applied into the Heliosat-2 model, Eq. (3), in terms of relative MBE and RMSE vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u N N  0  X uX ðG  G0 Þ2 ðG  G Þ RMSE ¼ t ð8Þ MBE ¼ N N i¼1 i¼1 being N the population size, G0 the global hourly irradiance measured and G* the global hourly irradiance estimated. The improvement in the hourly global irradiance estimation is significant, as a consequence of the inclusion of local

Table 2 Coefficients for the new empirical proposed fits

Mod-1: Mod-2: Mod-3: Mod-4:

Kc = a1n + a2n50 + b Kc = a1n + a2n50 + a5mair + b Kc = a1n + a2n50 + a3n25 + a4n75 + b Kc = a1n + a2n50 + a3n25 + a4n75 + a5 mair + b

a1

a2

0.795 0.789 0.796 0.790

0.147 0.153 0.036 0.065

a3

a4

a5 0.025

0.601 0.534

0.014 0.019

0.023

b 0.976 1.010 0.961 0.996

L.F. Zarzalejo et al. / Solar Energy 83 (2009) 480–484 Table 3 Relative mean bias error and root mean squared error of the new fitted models compared to Heliosat-2 model

Eq. (3) Model Mod-1 Mod-2 Mod-3 Mod-4

MBE (%)

RMSE (%)

6.56 0.20 0.31 0.15 0.32

21.29 17.36 17.21 17.35 17.28

statistical parameters of the cloud index distribution and the air mass as well:  The new models offer, practically, unbiased results.  The relative RMSE decrease to about 17% from the 21% result of the reference model. The Kolmogorov–Smirnov Test has been used to compare the goodness of the new regression models fitted with the reference model. This test tries to determine if two datasets differ significantly. Among the several statistic tests and ways of evaluating the goodness of a model, the K–S Test has the advantage of making no assumption about the distribution of data, being thus non-parametric and distribution free (Massey, 1951). The test consists of comparing the distribution of a dataset to a reference distribution. This can be done by converting the set of data to an unbiased estimator, S(G*), of the cumulative distribution function (Press et al., 1998). The statistic DKS, defined as the absolute difference between two cumulative distribution functions DKS ¼ jSðG Þ  P ðG0 Þj

ð9Þ

483

where P(G0 ) is the cumulative distribution function of the ground reference data set. Thus, if the DKS statistic is lower than p a ffiffiffiffi threshold value (defined at 99.9% of confidence as 1:63= N ) the null hypothesis that the two datasets come from the same distribution cannot be rejected (Polo et al., 2006). The K–S test was used, therefore, to compare the goodness of the regression models fitted with the reference model showed in Eq. (3). Fig. 2 shows the evolution of DKS with the global irradiance for the different models, including a dotted line parallel to the x-axis indicating the K–S Test critical or threshold value. The results shown in the figure point out the significant improvement achieved with the new models in the hourly global irradiance estimation. The K–S Test results remarks the following aspects in the solar radiation estimations:  The median of the cloud index distribution is a key parameter that allows the inclusion of local climatological information in the model and thus it contribute to a global improvement of the estimation.  The other statistical measurements, first and third quartile, have a negligible contribution to the models responses.  The air mass inclusion, in conjunction with the median of the cloud index, yields to better results in the high solar radiation level (over 600 Wm2).

6. Conclusions The use of satellite images for deriving solar radiation values is a highly useful tool for solar resource analysis

Fig. 2. Kolmogorov-Smirnov Test results.

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over large areas. In particular, simple statistical models have the advantage of their simplicity, but even more, their capacity of being tuned with local data and applied on extensive data bases (i.e. Meteosat 1st Generation data base). The empirical relationship between the cloud index and the clear sky index, or any other normalised parameter for the solar global radiation, can be improved by the inclusion of local statistical measures of the cloud index distribution. These statistical parameters (such as the median and the quartiles) estimated just only from satellite images and Heliosat-2 application offer valuable information on the local climatological aspects. Local statistical parameters introduce, in fact, a local auto-adjust of the KC vs. n relationship: the local median of cloud index is a local constant that multiplied by his regression coefficient and added to the residual term could be interpreted as a ‘‘local residual” term. In addition, the inclusion of the air mass in the models yields to better responses in the range of high solar radiation levels. The new models were fitted and tested using data from 28 Spanish radiometric stations covering geographical areas corresponding to Mediterranean, Semi–Arid and Oceanic climates. Results show a reduction up to a 17% in relative RMSE and yield to practically unbiased results. The improvement in the hourly global irradiance estimation is significant. Taking into account the high variety of climate conditions inside the Iberian Peninsula, the results showed here point out that the inclusion of additional parameters concerning the cloud index probability distribution function (the cloud index median for instance) has statistical significance in the KC vs. n relationship and it contributes to a better model response. Future work will focus on (1) analysis of possible seasonal effects, particularly in Northern latitudes; (2) investigating other climates, particularly desert, subtropical and tropical areas. Acknowledgements The authors wish to thank the Spanish National Meteorological Institute (INM) for their collaboration with the ground-based measurements, and in particular to Jose´ Montero and Santiago Enriquez for their interest and help. References Beyer, H.G., Costanzo, C., Heinemann, D., 1996. Modifications of the Heliosat procedure for irradiance estimates from satellite images. Solar Energy 56, 207–212. Cano, D., 1982. Etude de l’ennuagement par analyse de se´quences d’images de satellite. Application a` l’e´valuation du rayonnement ´ cole Nationale Supe´rieure solaire global au sol. The`se 3e`me Cycle, E des Te´le´communications, Paris, France. Cano, D., Monget, J.M., Albuisson, M., Guillard, H., Regas, N., Wald, L., 1986. A method for the determination of the global solar radiation from meteorological satellite data. Solar Energy 37, 31–39.

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