Three different methods are currently proposed to forecast solar radiation. The first is based on time series models, which use a series of the daily average of the measured solar radiation as input data. It has been shown in different papers that a RMSE of 5.1 % [7], 8.3 % [8], and 8.4 % [9] can be obtained, for local predictions using ANN — wavelet methods. Whereas in [7] and [8] the Continuous Wavelet Transform (CTW) is used, [9] employs the Discrete Wavelet Transform (DWT). The author of [8] uses the day number of the year and defuzzficated cloud cover information from the weather forecast service, as auxiliary information. These models are applicable for sites where the solar radiation was measured during one year [7], two years [8], or longer time intervals [7], [9]. The second method is able to forecast the motion of clouds using satellite imaging over the earth surface. It can forecast the solar radiation for any site or area, but the uncertainty related to the utilized models increases substantially over 22% to 30%, for forecast horizons larger than six hours, as reported by Lorenz [10]. The author obtained the former value for low and the latter for high cloud variability. The third method, used in the present article, is based on the NWP with its statistical correction MOS.

This study has been conducted within the Natural Park of Sierra Magina, in Southern Spain (37.6° N, 3.4° W) (Fig. 1). The area has a rough extension of 30 km x 48 km and shows a relatively complex topography, with a minimum height above sea level of 600 m and a maximum of 2150 m, with the 50% of the grids points above 800 m. The maximum surface slope is 56.94° and the 25% of the grids have a slope higher than 16.41°. The predominant surface orientation is around North. This aspects distribution benefits the existence of terrain patches with no direct solar beam along the year. The local climate is that of a typical middle and high Mediterranean mountainous environment, with dry hot summers, cold winters and relatively high precipitation during autumn and spring.

Located within the park, our research group have deployed a total of 11 radiometric stations (Figure 2). The radiometric stations are equipped, among other instrumentation, with HOBO (Onset Corporation) data-loggers that record the global irradiance registered by Licor 200-SZ radiometers. An annual calibration and inter-comparison of the sensors is carried out and the instrumental error is estimated to be less than 5%, typically 3%. The data set consists on data recorded on a 10 minutes basis and, for the purposes of this work, they were averaged to a hourly basis. In order to avoid the cosine error of the sensors, those data corresponding to a solar height below 7° were discarded. The location of the stations cover a range of elevations, slopes and aspects as wide as was possible. Table 1 shows the topographic features of the stations.

5

8

Mr

Fig. 2. Location of the stations. Results at stations 4, 5 and 11 are evaluated in this study.

Differences between global solar radiation interpolated from ground level measurements (Fig. 2 values) and published in [7] were shown on Fig. 6. As it is observed, a non-homogeneous distribution of significant relative differences (from +25 to -60 %) indicates the high dependence of solar radiation from the local conditions in every location. Therefore, it should be recommended a calibration of satellite data from a number of ground level measurements (ideally, from all of the available stations) that can represent these local effects.

2.2 Self-learning experience

From the 34 students registered in the Solar Radiation subject, 32 started their work selecting a meteorological station to process. 31 students passed the subject in the first attempt (including a written exam by 60 % of the total qualification); just one student required to repeat the written exam, in order to pass the subject. The other two students abandon the subject.

The interest of the students in this work was higher than the theoretical issues and practical problems of the subject. Specially, processing meteorological datasets from real stations selected by the students was an extra incentive. And, in addition, processed datasets result very useful to get a solar resource evaluation in the region over the studied period, as only minor revisions of students’ calculations were required.

3. Conclusions

In this work an estimation of the annual solar resource over Galicia was developed, in the framework of a self-learning experience with the collaboration of students of the MSc in Renewable Energies and Energetic Sustainability. This educational experience was very successful, as the interest of the students was very high and their results were very useful to achieve the solar resource maps.

From the solar global irradiation distribution, solar resource in this region is extremely connected to the local conditions (local cloudiness, rain, fog), that are very variable because of the changeable weather and complex topography of this region. Although the validity of these results is limited to an annual period, irradiation distribution shows the necessity to consider local conditions in the application of any methodology to estimate solar resources at Galicia.

As the main conclusion, satellite data processing has to be completed with a high number of ground level measurements. Other techniques, as Digital Terrain Models (DTM) [17], allow to estimating ground level irradiation considering topographic effects; these technique can help to cover complex terrain zones with lack of ground level data.

Acknowledgements

Meteorological dataset provided by MeteoGalicia (Xunta de Galicia) from its web page is acknowledged. Dataset processing was partially developed by the students of the MSc in Renewable Energies and Energetic Sustainability of the University of Santiago de Compostela (2007-08 academic year).

This work was partially funded by Galician regional R&D Programme (Xunta de Galicia) under project 07REM02CT.

References

[1] Vera Mella N. Atlas climatico de irradiation solar a partir de imagenes del satelite NOAA. Aplicacion a la peninsula iberica. PhD Thesis. Universitat Politecnica de Catalunya, Barcelona, Spain; 2005.

[2] Sharmer k. Towards a new atlas of solar radiation in Europe. International Journal of Solar Energy, 1994; 15: 81-87

[3] Baldasano J. M., Soriano C., Flores H. Atlas de radiacio solar a Catalunya. Institut Catala d’Energia. Barcelona, Spain; 2001.

[4] Alnaser W. E., Eliagoubi B., Al-Kalak A., Trabelsi H., Al-Maalej M., El-Sayed H. M., Alloush M. First solar radiation atlas of the Arab world. Renewable Energy 2004; 29: 1085-1107

[5] Font Tullot I. Atlas de la radiation solar en Espana. Instituto Nacional de Meteorologia, Ministerio de Transportes, Turismo y Comunicaciones. Madrid, Spain; 1984.

[6] Nrnez, M., Reyes, J. J., Marroquin, A., Ramiro, A. Mapas de valores medios mensuales de irradiacion solar estimados para Extremadura a partir de otros datos meteorologicos. XXVIII Jornadas Cientlficas de la Asociacion Meteorologica Espanola. Badajoz, Spain, 2004.

[7] Vazquez Vazquez M., Santos Navarro J. M., Prado Cerqueira M. T., Vazquez Rios D., Rodrigues Fernandes F. M. Atlas de radiacion solar de Galicia. Universidad de Vigo. Vigo, Spain; 2005.

[8] Rigollier, C., Lefevre, M. and Wald, L. The method Heliosat-2 for deriving shortwave solar radiation from satellite images. Solar Energy 2004; 77: 159-169.

[9] Pettazzi A., Souto J. A. Analysis of the incoming solar radiation and other significant parameters to estimate the solar resource at eight sites in Galicia (NW Spain), Proceedings of EUROSUN 2008, 1st International Conference on Solar Heating, Cooling and Buildings., Lisbon, Portugal, 2008

[10] Salson S., Souto J. A. Automatic weather stations network of the department of environment of Galicia: data acquisition, validation and quality control, Proceedings of the 3rd international conference on experiences with automatic weather stations, Torremolinos, Spain; 2003.

[11] Pettazzi A., Souto J. A., Salson S. EOAS, a shared joint atmospheric observation site of MeteoGalicia. Proceedings of 4th ICEAWS — International Conference on Experiences with Automatic Weather Stations, Lisbon, Portugal; 2006.

[12] Davies J. A. Validation of models for estimating solar radiation on horizontal surfaces. Report available from the IEA, Downsview, Ontario, Canada; 1988.

[13] Iqbal M. An introduction to solar radiation, Academic Press, San Diego, CA; 1983.

[14] Instituto Nacional de Meteorologia. Guia resumida del clima en Espana 1971-2000. Instituto Nacional de Meteorologia, D25.3, Ministerio de Medio Ambiente. Madrid, Spain; 2001.

[15] Batlles F. J., Martinez-Durban M., Miralles I., Ortega R., Barbero F. J., Tovar-Pescador J., Pozo — Vazquez D., Lopez G. Evaluation de los recursos energeticos solares en zonas de topografia compleja. XII Congreso Iberico y VII Congreso Ibero Americano de Energia Solar. Vigo, Spain; 2004.

[16] Martinez Cortizas A., Perez Alberti A. Atlas Climatico de Galicia, Xunta de Galicia, Santiago de Compostela, Spain; 1999.

[17] Tovar-Pescador J., Pozo-Vazquez D., Molina A., Batlles F. J., Lopez G. Mejora en la estimation de la irradiancia solar en zonas de topografia compleja mediante modelos digitales del terreno. XII Congreso Iberico y VII Congreso Ibero Americano de Energia Solar. Vigo, Spain; 2004.

The first step in any analysis of chaotic data is to reconstruct an attractor (defined as set of points in phase space visited by a signal trajectory after transients are gone) from the data. Taken [6] suggested a method of phase space reconstruction that is known as the method of delays. This method consists of embedding the time series into a d-dimensional space, ^d, which is equivalent to the original unknown phase space composed of all the dynamical variables. Figure 1a shows the lag space plot for the global solar radiation time series using a lag of one. Points are distributed around a 45° straight line denoting a periodic nonchaotic time series. This is also evidenced observing the correlogram showed in Fig. 1b. An annual cycle of 365 days is presented. This is an expected result as the daily values of solar radiation are mainly affected by the earth motion.

xt (MJ/m2) Lags (days)

Fig. 1. a) Phase space structure of the global solar radiation time series using lags of one; b) Correlogram for

the global solar radiation time series.

In order to remove periodicity and trend, a transformation of the time series is undertaken by differencing. The new data are arithmetic differences between pairs of observations using a lag of one day (Axt = xt+I — xt). The differenced time series is denoted as {Axt}. Figure 2a shows the phase space plot for the differenced time series. The periodic pattern shown in the above figure seems to be removed. This result is corroborated analysing the correlogram displayed in Figure 2b. Autocorrelation coefficients fall to within the random-like zone after the first lag and, for the most part, remain in that zone thereafter. It is thus assumed that periodicity is removed.

Although point distribution in Fig. 2a seems to be due to some non-random complex underlying behaviour, the presence of a chaotic attractor in that phase space is not clear. To search the
optimum time delay г we have used the method of mutual information [7]. Mutual information, like autocorrelation, tries to measure the extent to which values Axt+m are related to values of Axt, at a given lag. However, mutual information has the advantage of using probabilities, rather than a linear basis, to asses the correlation and thus, nonlinear correlations are taken into accounts. The software implementation of that algorithm (and of those used hereafter) is from the TISEAN package [8].

400

As a prescription, a good candidate for the time delay г will be where the first marked minimum of mutual information occurs. From Fig. 3 it is noted that the first minimum is for г = 3. Once the time delay is chosen, the next step is to select the embedding dimension. Kennel et al. [9] introduce the method called the false nearest neighbors, which calculates the minimal embedding dimension. Two points in a d-dimensional phase space are false neighbors, in the sense of some distance function, when the distance, ||xjd — x/||, is small but the distance ||xi+1d+1 — Xj+1d+1|| in a d+1- dimensional phase space is not. Given a distance function, the Euclidean distance in our case, and some threshold size, the percentage of false near neighbors becomes zero as the dimension of phase space goes to the minimal embedding dimension. Figure 4 shows the percentage of false nearest neighbors as a function of the embedding dimension d. The main characteristic is that the fraction of false nearest neighbors does not fall to zero as d increases. This implies that the differenced time series has residual ‘noise’ in it, and thus the existence of low dimensional chaos is to be discarded.

The comparison of the ordinary and the residual kriging models results, in terms of the validation dataset, shows several interesting features. Residual kriging provides better estimates for all the months, with relative improvement in RMSE ranging from 5% to 20%. The maximum

improvement is found for January, with (RMSE value of 0.46 versus 0.60, 23% for relative improvement). In June, relative improvement is about 5% and in October about 9%. Similar results are found for the MAE values, with relative improvements ranging from 5% to 20%. Particularly, the maximum improvement is found during December (MAE 0.31 versus 0.4, that is 22% of relative improvement). A slightly improvement is also found for the ME values, changing from a small underestimation using the ordinary kriging to almost negligible error values using the residual kriging. Finally, R2 values show an overall improvement, being particularly high for January, February and March.

Additionally, mean values are fairly reproduced by both ordinary and residual kriging methodologies, with a maximum error (overestimation) of about 0.5 MJ m-2day-1 (2.6%) during September. On the other hand, standard deviation estimation is considerable better reproduced by the residual kriging method than by the ordinary kriging. Maximum improvements are found for the winter months For instance, for January, the observed standard deviation is 0.99 MJ m-2day-1, while the value provide by the ordinary kriging is 0.62 MJ m-2day-1 (37% error) and the estimated using the residual kriging is 0.94 MJ m-2day-1 (5% error). For the summer months, residual kriging also provides better standard deviation estimates, but improvements are lower.

Regarding the maximum values, similar estimates are provided by both kriging methods during the summer months. On the other hand, residual kriging estimates are considerable better for winter months. As far as minimum values is concerned, residual kriging perform considerable better than the ordinary kriging method for all the months. Maximum differences are found for the summer months.

4. CONCLUSIONS

Overall, the ordinary kriging method is able to provide fair estimates of the solar resources in the area of the study, with RMSE values ranges from 0.63 MJ m-2day-1 (6.2%) in June to around 1.44 MJ m-2day-1 (11.2%) in October. Nevertheless, by the inclusion of external information in the interpolation procedure, the residual kriging estimates shows considerable lower errors.

Particularly, the inclusion as external explanatory variable of the semi-sky-view factor (which accounts for topographic shadows cast and is able to explain between 15% and 45% of the spatial variability) give rise to relative improvement in RMSE values ranging from 5% in the summer month to more than 20% in the autumn and winter months. Particularly, RMSE values of the residual kriging estimates ranges from 1.44 MJ m-2day-1 (5.5%) in the June to around 1.31 MJ m — 2day-1 (10.2 %) in October. Explained variance also shows a considerable improvement compared to the ordinary kriging method, with all month showing R2 values above 0.92.

REFERENCES

[1] J. Mubiru, K. Karume, M. Majaliwa, E. J.Banda, T. Otiti, (2006). Interpolating methods for solar radiation in Uganda. Theor. Appl. Climatol. 88, 259-263.

[2] I. O.Odeh, A. B.McBratney, D. J.Chittleborough, (1995). Further results on prediction of soil properties from terrain attributes. Geoderma, 67, 215-226.

[3] S. Ahmed, G. deMarsily, (1987). Comparison of geostatistical methods for estimating transmissivity.

Water Resour. Res. 23, 1717-1737.

[4] D. L.Phillips, J. Dolph, D. Marks, (1992). A comparison of geostatistical procedures for spatial analysis for precipitation in mountainous terrain. Agric. Forest Meteorol. 58, 1031-1047

[5] J. P.Delhomme, (1978). Kriging in the hydrosciences. Adva. Water Resour. 1, 251-266.

[6] Clark Labs, (2006). IDRISI Software, Clark University, MA, USA.

The SOLIS clear sky model [3] uses the radiative transfer model libRadtran [4] to calculate input parameters for a fitting function called the modified Lambert-Beer (MLB) relation. For this, only two radiative transfer calculations are needed for a given atmospheric state to get the irradiance for a full day. Since SOLIS can provide spectrally resolved irradiance data, it can be used for different applications. Beside improved information for the planning of solar energy systems, the calculation of photosynthetic active radiation, UV index, and illuminance is possible.

We use climatologies with monthly averages of AOD [5] and water vapour content [6] as input parameters for SOLIS and get the direct and global irradiance as output.

1.2. Direct model

We propose a new model [7] to calculate direct irradiance as a function of the clear sky index k* and the direct irradiance at clear sky conditions bciear. An appropriate clear sky model is the basis for this approach, see sec. 2.2.

For cloud events, described by k* < (1 — c(6)) (whith с(в) is a fit function), an exponentially rising parametrisation b(k*) for the direct irradiance was found empirically. It is given by

b(k*) = bdear k*P

with P as a fit parameter.

Situations where k* — 1 becomes smaller than c(6), are defined as clear sky situations and the parametrisation results in

b(k*) = bciear + (k*-1) a where a is a fit parameter.

If the clear sky index becomes greater than (1 + c(6)) we assume a special cloudy situation. In this case the global irradiance becomes more than Iciear in consequence of an increasing diffuse irradiance by reflection on clouds. The direct irradiance is then parameterised by

b(k*) = bdear / k*. (7)

In Fig. 3 the beam fraction as a function of clearsky index is given for satellite and ground derived values.

2. Analysis and results

The soil bidirectional reflectance can be expressed as (Rahman et al., 1993):

rs = r0 M Fhg H (3)

where r0 is an arbitrary parameter characterizing the intensity of the surface cover. The function H is characterised by a large reflection in the illuminating direction. M and FHG are the symmetric and asymmetric angular functions. The variation of this reflectance around the albedo can be greater than 0.1. In the specific case of oceans, the reflectance varies from zero to values greater than cloud reflectance, it also depends on wind speed (Lefevre et al. 2007). Thus, by considering the albedo instead of the bidirectional reflectance, one commits a significant error on irradiance reflected by the ground then backscattered by the atmosphere, thus contributing to the diffuse fraction of the SSI. This omission is very often made for operational reasons because of the lack of data describing the ground.

Very often, for operational reasons, the irradiance calculations are done under the assumption of a flat terrain inside the pixel. However, the cosine of the local incident angle 9 is:

cos9(P, a) = (cosracosScos^i + sinSsin^^cosP

+ cosracosSsin^icosasinP + sinracosSsinasinP — sinScos^icosasinP (4)

where a is the hour angle, S is the solar declination, ф is the latitude of the site, a and /3 correspond to the direction of the local slope, respectively in azimuth and tilt. Thus, the SSI of the pixel should be modified by the ratio:

R = Hpixelcos9(a(p),P(p))dp / cos9(0,0) (5)

2. Conclusion

We have quantified the influence of the different atmospheric properties on the SSI. Clouds (cloud optical thickness and type) are the most important variable for the SSI. They also exhibit high temporal (~ 30 m) and spatial (~ 10 min) variation (Rossow and Schiffer 1999). Aerosol loading and type, water vapour amount and atmospheric profile have a great influence on SSI, particularly in clear skies. Wald and Baleynaud (1999) demonstrate noticeable variation in atmospheric transmittance due to local pollution in cities at scale of 100 m. Ground albedo and its spectral variation have an important influence on diffuse part and spectral distribution of SSI. They exhibit very high spatial variation on a pixel basis and seasonal temporal variations. The influence of ozone amount is large in the ultraviolet range, but remains low on the integrated wavelength SSI.

Data availability of water vapour and aerosol loading is fairly low. We are expecting one value per day for a 50 km pixel. The error induced on the SSI depends on the variation of these parameters within the pixel. The clearer the sky, the greater the error. Comparisons of ground measurements of hourly means of SSI made at sites in Europe less than 50 km apart for clear skies show that the spatial variation in SSI, expressed as the relative root mean square difference, can be greater than 10 %.This result is in agreement with Perez et al. (1997) who stressed the large spatial variability of the SSI.

The influences of vertical position and geometrical thickness of clouds in the atmosphere are negligible. Thus, the solution of the RTM for a cloudy atmosphere is equivalent to the product of the irradiance obtained under a clear sky and the extinction coefficient due to the cloud. In particular, it means that the method Heliosat-4 may be composed of two distinct parts: the clear-sky part and the cloudy-sky part. In addition, given the fact that the cloud parameters may be known every % h and 3 km and the clear-sky parameters every day and 50 km, the adoption of the concept of "a model for the clear sky, another for other types of skies" saves time: the first model, which takes into account all other atmospheric parameters, focuses the bulk of computation resources.

The results of this work form the basis for the establishment of the method, called Heliosat-4, based on the exploitation of a RTM for the operational processing of satellite data to produce assessments of solar surface irradiance every 3 km and % h on Europe and Africa. The necessary inputs to Heliosat-4 have been identified; a gross assessment of the relative importance of their uncertainties on the final assessment has been obtained.

References

[1] Bernhard, G., Booth, C. R., Ehramjian, J. C., 2002. Comparison of measured and modeled spectral ultraviolet irradiance at Antarctic stations used to determine biases in total ozone data from various sources. In Ultraviolet Ground-and Space-based Measurements, Models, and Effects, edited by J. R. Slusser, J. R. Herman, and W. Gao, Proceedings of SPIE, Vol. 4482, 115-126.

[2] Cano D., Monget J. M., Albuisson M., Guillard H., Regas N., and Wald L., 1986, A method for the determination of the global solar radiation from meteorological satellite data. Solar Energy, 37, 31-39.

[3] Hammer, A., 2000. Anwendunsgspezifische Solarstrahlungsinformationen aus Meteosat-Daten. Dissertation, Carl von Ossietzky Universitat Oldenburg, Fachbereich Physik, Oldenburg, Germany.

[4] Ineichen, P., 2006. Comparison of eight clear sky broadband models against 16 independent data banks. Solar Energy, 80 (4), 468-478.

[5] Kato S., Ackerman T. P., Mather J. H., Clothiaux E. E., 1999. The k-distribution method and correlated-k approximation for shortwave radiative transfer model. Journal of Quantitative Spectroscopy & Radiative Transfer 62 (1999) 109-121.

[6] Kuhleman, R., Betcke, J., 1995. CloudS: A new parameterization of radiative transfer through clouds (summary of development and first validations). Heliosat-3 Reports, 21 p., http://www. heliosat3.de/documents/.

[7] Liou K. N., 1976. On the absorption, reflection and transmission of solar radiation in cloudy atmospheres. Journal of the Atmospheric Sciences vol.33 798-805.

[8] Liou K. N., 1980. An Introduction to Atmospheric Radiation. International Geophysics Series, volume 26, Academic Press, 392 p.

[9] Mayer B., Kylling A., 2005. Technical note: The libRadtran software package for radiative transfer calculations — description and examples of use. Atmospheric Chemistry and Physics, 5, 1855-1877.

[10] Mueller, R., Dagestad, K. F., Ineichen, P., Schroedter, M., Cros, S., Dumortier, D., Kuhlemann, R., Olseth, J. A., Piernavieja, G., Reise, C., Wald, L., Heinnemann, D., 2004. Rethinking satellite based solar irradiance modelling — The SOLIS clear sky module. Remote Sensing of Environment, 91 (2), 160-174.

[11] Perez R., Seals R., Zelenka A., 1997. Comparing satellite remote sensing and ground network measurements for the production of site/time specific irradiance data, Solar Energy, 60, 89-96.

[12] Perrin de Brichambaut C. et Vauge C., 1982. Le Gisement Solaire : Evaluation de la Ressource Energetique. Technique et Documentation, Librairie Lavoisier, Paris, France, 222 pages.

[13] Pinker R. T., Frouin R., Z. Li, 1995. A review of satellite methods to derive surface shortwave irradiance. Remote Sensing of Environment, 51 (1), 108-124.

[14] Rigollier, C., Lefevre, M., Wald, L., 2004. The method Heliosat-2 for deriving shortwave solar radiation from satellite images. Solar Energy, 77 (2), 159-169.

[15] Rossow W. B., Schiffer R. A., 1999. Advances in understanding clouds from ISCCP, B. Bulletin of the American Meteorological Society, 80, 2261-2287.

[16] Shettle E. P., 1989. Models of aerosols, clouds and precipitation for atmospheric propagation studies. In AGARD Conference Proceedings No. 454, Atmospheric propagation in the UV, visible, IR and mm-region and related system aspects.

[17] Stamnes, K., S.-C. Tsay, W. Wiscombe and K. Jayaweera, 1988. Numerically stable algorithm for discrete — ordinate-method radiative transfer in multiple scattering and emitting layered media. Applied Optics, 27,

2502.

[18] Vermote, E., Tanre, D., Deuze, J. L., Herman, M., Morcrette, J. J., 1997. Second simulation of the satellite signal in the solar spectrum (6S), 6S: An overview. IEEE Transactions on Geoscience and Remote Sensing, 35, 675-686.

[19] Wald L., Baleynaud J.-M., 1999. Observing air quality over the city of Nantes by means of Landsat thermal infrared data. International. Journal of Remote Sensing, 20, 5, 947-959.

In this study the generation of the variable which is going to be used to forecast future values of half daily solar global radiation is done taking into account gaussian and stationary properties needed in the time series to be used by predictive methods. This approach is based on “lost solar component” (Fig.

1.) defined previously.

Lost component time series presents higher variation in central months of the year due to higher solar radiation levels and bigger influence of cloudiness reflection and absorption on solar irradiance.

Elimination of the trend component is done differencing between successive time steps of lost component time series.

W/m2 half day

In the other side, synoptic predictions of future states of sky conditions by statistical post-processing models presents less uncertainty than direct output of global solar irradiance in numerical weather prediction models. The classification of sky conditions is done by national weather services in six levels Fig. 2. As sky condition variable wasn’t available directly from AEMet it has been simulated dividing measured solar radiation in six levels. Future variation of sky conditions is combined with the difference of lost component time series as input to predictive methods. Besides, pure statistical models have the advantage of limiting the upper error of prediction and improving predictions errors of persistence by making relations of patterns of past observations and future values. In the next sections, results of using and not using sky condition as input to neural network is shown.

The NWP models are able to provide the solution for seven atmospheric parameters, by solving the momentum, mass and energy conservation equations related to the motion of air and water vapor in the atmosphere. These models are also able to estimate the cloud cover, and incoming solar radiation [11]. By the model GFS (Global Forecasting System) [12], numerical modeling are performed in a (0.5 x 0.5)° earth surface grid with sampling interval of 3h. In order to improve the performance of local forecasts, the data of the global model are assimilated by regional NWP models. By using the hydrostatic model ETA with grid resolution of (0.4 x 0.4)°, Guarnieri [13] obtained a RMSE of 43.9 % and 43.6 % for the daily total of incoming solar radiation, for two different sites in Brazil.

The spatial configuration of the MM5 used in this work consisted in five nested domains and twenty four unevenly spaced sigma levels. The domains has an horizontal resolution of 71, 27,9, 3 and 1 km, respectively. The results of the last domain, of 1km resolution, were finally evaluated. Two-ways nesting was used to feed the information between domains. Atmospheric initial and boundary conditions were extracted from the analysis produce by the NCEP. The physical parameterizations used in the simulation were: the GRELL scheme for the cumulus parameterization, the MRF for the planetary boundary layer, the MIXED PASHED for the explicit moisture, the FIVE-LAYER SOIL for the soil model and the RRTM for the radiation scheme. This configuration is maintained for all the integrations. Finally, a 24 hours spin-up period was used in each 72-hours integration.

The simulations were carried out for a set of days selected along the year 2005. Particularly, four sets (one for each season of the year) of three consecutive days with clear-sky conditions were selected, one for each season of the year. As highlighted earlier, the aim of this work is to evaluate the ability of the MM5 to estimate the solar radiation in a complex topography area. To this end, two simulations were carried out for each season of the year. In one of the simulations (called hereinafter T, Topography), the solar radiation were computed using the MM5 subroutines OROSHAW and LEVSLP. These subroutines allows taking into account the effect of the slope, angle and shadow cast caused by the topography on the solar radiation estimates at the earth surface. In the second simulation, these subroutines were not used and, therefore, the MM5 solar radiation estimates do not account for these topographic effects. We will call these simulations as Not Topography (NT).

The MM5 estimates were evaluated in terms of the Mean Error (ME) and the Root-Mean-Square Error (RMSE). The ME quantified the overall bias and detected if the model is producing overestimation or underestimation, while the RMSE accounts for the spread of the error distribution. Al error estimates are computed using hourly values along the whole simulated period.

3. Results and conclusions

Table 2 to 5 shows the evaluation results for, respectively, winter, spring, summer and autumn,. The results are just presented for three representative stations: stations 4, 5 and 11. These stations have a important slope and represent different aspects (stations 4 aspect east, stations 5 aspect west and station 11 aspect south) (Table 1). Evaluation results present the comparison of the MM5 estimates using (T) and not using (NT) the topographic parameterization against the measured horizontal solar radiation (H). For instance, the NT-H notation in Tables 2 to 5 stands for the evaluation of the MM5 estimates not using topographic parameterization against the global horizontal radiation measured values.

Overall, the MM5 shows considerable skills in estimating the solar radiation under clear-sky conditions along the whole year, even for this complex topography area under study. Particularly, the lowest RMSEs are found in summer (~20%) and the highest during winter (more than 30%). Additionally, from the analysis of the ME values, it could be concluded the existence of a general tendency to overestimation in winter, spring and summer and to underestimation in autumn.

Regarding the topographic parameterization, tables 2 to 5 shows and overall improvement in the estimates, although this improvement strongly depends on the season of the year and the topographic characteristics of the location under study. Regarding the season of the year and as can be expected, the most important improvement takes place in winter (Table 2). The relatively low sun elevation angles during this seasons makes the topographic influence on the solar radiation measured ant the surface more important. The use of the topographic parameterization improves the MM5 estimates, in terms of RMSE, ranging from 10% of improvement in station 11 to less than 5% in the stations 4 and 5. This difference can be explained by the fact of that the station 11 has south aspect, while the station 4 has a west aspect and station 5 an east aspect. Therefore the station 11 receives more radiation than the other two and the potential improvement is higher. For the rest of the seasons, the improvement in the estimates provides by the MM5 topographic parameterization are lower than for the winter. Particularly, in spring and autumn, Tables 3 and 5, the improvement in the estimates in terms of the RMSE ranges from 1% to 7%. Particularly, the most important improvement (7%) is found during autumn and for station 5. Similar results are found in terms of the ME. During summer (Table 4), and as can be expected, the improvements in the estimates provide by the topographic parameterization are modest. The only important improvement (4% in terms of RMSE) is found for station 5.

RMSE (Wm-2) (%) ME (Wm-2) (%) Station NT T NT T 4 120.1 (23.4) 113.7 (22.1) -61.1 (-11.9) -68.0 (-13.2) 5 125.5 (22.4) 102.1 (19) -30.7 (-5.8) -44.8 (-8.4) 11 92.3 (17.5) 90.8 (17.3) -60.8 (-11.6) -63.6 (-12.1) Table 4. As in Table 2 but for summer.

RMSE (Wm-2) (%) ME (Wm-2) (%) Station NT T NT T 4 117.8 (279) 100.8 (23.7) 25.0 (5.8) 27.0 (6.2) 5 150.8 (37.6) 122.7 (30.6) CO CO 1.8 (0.4) 11 92.7 (21.2) 82.8 (18.9) -29.6 (-6.8) 25.8 (5.9) Table 5. As in Table 2 but for autumn.

REFERENCES

[1] G. A. Grell, J. Dudhia and D. R: Stauffer, (1994). A description of the fifth-generation Penn State/NCAR Mesoscale Model (MM5). Tech. Rep. NCAR/TN-398+STR, National Center for Atmospheric Research.