Assessment of short-term irradiance forecasting based on ... - Wire 1002
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Assessment of short-term irradiance forecasting based on post-processing tools applied on WRF meteorological simulations A. Rincón (1), O. Jorba (1), J.M. Baldasano (1,2) and L. Delle Monache (3) (1) Earth Sciences Department, Barcelona Supercomputing Center (BSC-CNS), Spain. (2) Laboratory of Environmental Modeling, Technical University of Catalonia (LMA-UPC), Spain. (3) Research Applications Laboratory, National Center for Atmospheric Research (NCAR), USA. C/ Jordi Girona 29, Barcelona, Spain. 08034. [email protected] Abstract— Short-term irradiance forecasting is an important issue for many fields of solar energy applications. The use of numerical meteorological models in combination with statistical post-processing tools may have the potential to satisfy the requirements for up to several hours to days ahead of irradiance forecast. In this contribution, we present an assessment of a shortterm irradiance system based on the WRF-ARW meteorological model and two post-processing methods in order to improve the overall skills of the system for an annual simulation of the year 2004 over Spain. The WRF-ARW model is applied with 4x4 km of horizontal resolution and 38 vertical layers over the Iberian Peninsula. Ninety-five global irradiance stations located in the northeast of the Iberian Peninsula are used to assess the temporal and spatial fluctuations and trends of the system. Post-processes used are: Kalman Filter and Recursive method. The skills of the system are evaluated by means of statistical indicators: root mean square error, bias, correlation and normalized mean absolute error. The Kalman Filter shows an annual reduction of 8% of RMSE and 83% of bias, while the annual reduction using Recursive method is 2% by RMSE and 35% by bias. A previous evaluation of the WRF-ARW model without post-processing shows significant errors in spring and summer greater than 4 MJ·m-2·d-1. The evaluation points out an overestimation due to the lack of atmospheric absorbers different than clouds, e.g. aerosols, not considered in the meteorological model. When comparing stations at different altitudes, the overestimation is enhanced at coastal stations (less than 200m) up to 1000 W·m-2·h1 . These results allow us to analyze the strengths and weaknesses of the irradiance prediction system and its reliability in the estimation of energy production from solar devices.
I. NOMENCLATURE Global horizontal solar irradiance (GHI), Numerical Weather Prediction (NWP), Advanced Research Weather Research & Forecasting model (WRF-ARW), Kalman Filter (KF), Recursive Method (REC), Root Mean Square Error (RMSE), correlation coefficient (COR), normalized mean absolute error (NMAE) II. INTRODUCTION
T
he increased contribution of solar energy in power generation sources requires an accurate estimation of surface solar irradiance conditioned by geographical, temporal and meteorological conditions. The knowledge of the variability of these factors is essential to estimate the expected energy production. Therefore it may help to stabilize the
electricity grid and increase the reliability of available solar energy and its application in photovoltaic cells and solar thermal power plants. The modeling of solar irradiance has experienced a gradual progress over the last few decades, from the use of empirical formulations seeking the parameterization of the local physical conditions from available measurements as [1]-[2]-[3]-[4], to the development of radiative transfer parameterizations used within numerical weather prediction models (NWP) as MM5 model [5], HIRLAM model [6] and WRF model [7]-[8]. NWP models solve the atmospheric dynamics and physical processes in a nonlinear computing environment. Due to complex cloud microphysics and limitations in spatial resolution, clouds and their radiative properties are difficult to predict in numerical models. Consequently NWP models are expected to show inherent regional or global biases limiting forecast accuracy. Therefore, the use of NWP models in combination with statistical post-processing tools may have the potential to satisfy the requirements for solar irradiance forecasting. Preliminary efforts oriented to improve NWP direct model outputs were the Model Output Statistics (MOS) procedures. MOS techniques have been applied to improve forecast accuracy for several meteorological variables. Specifically, [29] established a regression model between solar irradiance measurements and available forecast variables. The forecasts of these variables were used as input to MOS, predicting GHI on a 6–30 h forecast horizon with a root mean square error (RMSE) of 13.2% of extraterrestrial radiation received. Similarly, artificial neural networks (ANNs) [30]-[31], recognize patterns in data and have been successfully applied to solar forecasting for a reduction of relative RMSE (rRMSE) of daily average GHI much as 15% on a 12-18 h ahead NWP forecast. Also, bias-removal post-process as Kalman filtering procedure were proposed in order to correct systematic errors of NWP models [33]-[34]-[35]. In this study, we evaluate the implementation and performance of bias-removal post-processes on an annual simulation of global horizontal solar irradiance (GHI) computed with WRF-ARW model [7]-[8]. A previous evaluation of GHI simulated by the WRF-ARW model showed an overestimation due to the lack of atmospheric absorbers (different from clouds) that are not included in the
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meteorological model [9] and do not contribute to the attenuation of solar radiation. Therefore, in this contribution we apply and evaluate the performance of two post-processes: Kalman Filter [10]-[32] and Recursive method [11] using a high-density network of global irradiance stations in the northeast of the Iberian Peninsula. III. METHODOLOGY A.
WRF-ARW meteorological mesoscale model The WRF-ARW model (v3.0.1.1) [7]-[8] is applied to compute the GHI over the area under study. It is an Eulerian non-hydrostatic mesoscale model with state-of-the-art physical parameterizations (microphysics, cumulus parameterization, surface layer, land-surface model, planetary boundary layer, and atmospheric radiation). The radiation schemes provide atmospheric heating due to radiative flux divergence and surface downward longwave and shortwave radiation for the ground heat budget. Longwave radiation includes infrared or thermal radiation absorbed and emitted by gases and surfaces. Shortwave radiation includes visible and surrounding wavelengths that make up the solar spectrum. Hence, processes include absorption, reflection, and scattering in the atmosphere and surfaces. Within the atmosphere the radiation responds to model-predicted cloud and water vapor distributions, as well as specified carbon dioxide, ozone and traces of gas concentrations. Table 1 summarizes the main characteristics of the parameterizations used by the WRFARW model as applied in this contribution. The WRF-ARW model is run on an initial regional grid of 12 x 12 km in space and 1 h in time, covering Europe. The European domain provides the boundary and initial conditions for the Iberian Peninsula domain with 4 x 4 km in space and 1 hour in time. The WRF-ARW is configured with 38 vertical layers (11 characterizing the PBL). The model top is defined at 50 hPa to resolve properly the troposphere-stratosphere exchanges. Initialization and boundary conditions are provided by the Final Analyses of the National Centers for Environmental Prediction (FNL/NCEP) with information provided each 6 h, at a spatial resolution of 1º x 1º. The simulation consists of 366 daily runs to simulate the entire year 2004. The choice for this specific year is based on the availability of ground measurements of global irradiance for this year. Post-processing description The Kalman Filter (KF) [10] and the Recursive Method (REC) [11] are linear, adaptive, fast and optimal algorithms which are used to estimate the systematic component of the forecast errors reducing the bias from recent past forecast and observations to produce an improved to future forecast. The bias-removal post-processes used are briefly described below.
bias using a linear relationship, given by the previous bias estimate plus a correction value between the difference of the present forecast error and the previous bias estimate. This approach adapts its coefficients each iteration, resulting in a short training period. However, KF is unable to predict a large bias when all the biases for the past few days have been small. KF is recursive because some of the iteration values of the KF coefficients depend on the values at the previous iteration. The filter estimates the systematic component of the forecast errors or bias, which are often present in forecasts. Once the future bias has been estimated, it can be removed from the forecast to produce an improved forecast. A detailed description of the filter algorithm is shown in [22]. Here only the definitions of the error variances are shown, because the ratio of these variances is an important parameter that affects the KF performance. TABLE I PARAMETERIZATIONS USED IN WRF-ARW MODEL FOR THE ANNUAL SIMULATION
B.
Fig. 1 shows a flow diagram of Kalman Filter. It uses a predictor corrector approach, starting with the previous estimate of the forecast bias xt at time t, by the previous true bias plus a white noise η term:
xt |t t xt |t 2 t 1. Kalman Filter The KF is a mathematical method that predicts the future
t t
(1)
Where t is assumed uncorrelated in time and normally
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distributed with zero-mean and variance ση2. The forecast error yt (forecast minus observation at time t), is assumed to be corrupted from true forecast bias by a random error term t :
yt xt t xt t
t t
t
(2)
Where t is assumed uncorrelated in time and normally distributed with zero-mean and variance σε2. Thus, the forecast error yt includes both the systematic bias plus random errors. Reference [10] shown that the optimal recursive predictor of the forecast bias xt (derived by minimizing the expected mean square error) can be written as a combination of the previous bias estimate and the previous forecast error:
xˆ
t t|t
x ˆt|t t
t|t t
( yt x ˆt|t t )
(3)
Then, the correction by the Kalman gain factor β of the difference between the previous bias estimate and previous observed forecast error (2) is used to estimate the future bias (3). Since there is a time lag, Δt = 24 hours is used, today‟s forecast bias is estimated using yesterday‟s bias, which in turn was estimated using the day-before-yesterday‟s bias, and so on. The difference between today‟s forecast error (2) and the portion of today‟s bias that was estimated yesterday, is weighted by the Kalman gain factor to give the correction that was „„learned‟‟ from previous errors. This correction is applied to yesterday‟s estimate of today‟s bias to produce today‟s estimate of the bias for tomorrow.
2 error ratio 2
If the ratio is too high, the forecast-error white-noise variance σε2 will be relatively small compared to the true forecast-bias white-noise variance ση2. Therefore, the filter will put excessive confidence on the previous forecast and the predicted bias will respond very quickly to previous forecast errors. On the other hand, if the ratio is too low the predicted bias will change too slowly over time. Consequently, there exists an optimal value for the ratio that is given by the forecast region, which can be estimated by evaluating the filter performance in different situations [28]. 2. Recursive method In this method the coefficients in the linear equation are determined in an iterative way and updated every time a new forecast is issued by comparing the last observed data with the corresponding forecast. Recursive method [11] combines the hourly irradiance forecast and measurements as follows. If D is the model issuing day, the irradiance forecast at time D+n days is calculated as:
Irradi (n) IrradWRF (i ) (n) corri
KF needs to set an optimal ratio value (4) that is given by the climatology of the forecast region. The error ratio is a key parameter which determines the relative weighting of observed and forecast records between the forecast-bias white-noise variance ση2 and the forecast-error white-noise variance σε2:
(5)
The first term on the right-hand side is the irradiance at forecast time D+n days, with n days. The second term is the correction term, which is updated recursively every day (the index i in corr indicates the iteration or equivalently the forecast issued). The implicit hypothesis in (5) is that the correction calculated on day D+1 is valid also on day D+n. The correction term is calculated as follows:
1 corri ( IrradOBS IrradWRF (1) corri1 ) 2 corro 0
Fig.1. Flow diagram of Kalman Filter, where the future bias (output) is estimate by means of the previous bias estimation (prediction). This is corrected applying a coefficient (Kalman gain factor) which corresponds with the difference between the previous bias estimates minus previous observed forecast error [22].
(4)
(6)
The first term in the square bracket is the ground station measurement of irradiance on D+1 day, the second term is the irradiance at forecast time D+1. The D+1 day is the issuing day of this forecast, while the forecast issuing day is D. The third term in the square bracket is the correction term calculated the day before the day i, corresponding to the previous forecast. The starting value of the correction term is zero. The factor 1/2 in (6) means that half the contribution to the correction term is given by the past corrections. The initial value of the additional correction corr is 0 and it is updated every day with each new model and new measurements. The correction thus includes the past relationship between the model and the measurements, but weighting it towards the last few days, as the first terms of these series is largest. The advantage of this is that, after a few days of iteration, the initial and erroneous value of zero contributes a negligible amount to
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the correction term. C.
Statistical indicators The model-to-data statistics bias, root mean square error (RMSE), normalized mean absolute error (NMAE) are selected for the present study, together with the correlation coefficient (COR). Annual, seasonal and daily mean statistics are computed, with seasons corresponding to winter (January, February and December), spring (March, April and May), summer (June, July and August) and autumn (September, October and November). IV. OBSERVATIONAL NETWORK
of ninety-five global horizontal solar irradiance (GHI) stations in the northeast of the Iberian Peninsula. Fig. 2 shows the geographical distribution of stations over an annual map of the averaged global irradiation on horizontal surface. The map is obtained from the latest revision of the Atlas of solar radiation of Catalonia with a dataset of 203 stations for the period 19712005 [23]-[24]. The current dataset used for the calibration and evaluation of the system provides observations with a measurement frequency of 5-minute, 30-minute and 24-hour; and the stations are distributed over a complex terrain area with station-elevation ranging from 1m to 1970m a.s.l. The full 2004 year is selected for the present work.
For the adjustment of post-processing methods in the annual simulation of the WRF-ARW model, we used measurements
Fig.2. Geographical distribution of the observational network used for post-processing on the annual averaged map of global irradiation obtained from the Atlas of Solar Radiation of Catalonia [23].
A. Quality treatment In order to analyze the quality of the available irradiance data, the quality limits of control methodology proposed by [25]-[26] has been applied. All stations have gone through a three quality treatment stages: 1. Filtering by sunrise and sunset To obtain the database of registered solar irradiance between sunrise and sunset, the records were deleted before sunrise and after sunset solar by 2004. These hours of sunset
and sunrise for all stations are calculated based on latitudelongitude coordinates of each station from the algorithms proposed by [27]. 2. Implementation of quality limits The QCRad Testing methodology [25]-[26] defines two ranges for physically and extremely possible limits. Such limits depend on the solar constant and the solar zenith angle. Then, the values correspond to levels of irradiance valid between rising and setting sun when the solar zenith angle is greater than 0 and less than 90 degrees. The parameters of the
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implemented quality standards are presented in Table 2. 3. Graphic validation From the records obtained from the former quality treatment, we performed a graphic validation of the annual evolution of global irradiation by day (in MJ·m-2·d-1) obtained from GHI in W·m-2. The GHI was evaluated comparing with the theoretical attenuation curve of extraterrestrial radiation in the top of atmosphere. TABLE II PARAMETERS OF QUALITY RADIATION FOR PHYSICALLY POSSIBLE LIMITS (Q1) AND EXTREMELY POSSIBLE LIMITS (Q2), APPLIED OVER THE OBSERVATIONAL NETWORK OF NORTHEAST OF IBERIAN PENINSULA [26]
computing time of the procedure is easy and very short. On the other hand, KF needs set an optimal ratio between the forecast-bias variance and the forecast-error variance. This value is estimated through the evaluation of filter performance with the change of seasons for several stations. Fig. 3 shows the ratio sensitivity for irradiance forecast of the WRF-ARW model over the seasons of the year 2004. To obtain an optimal value, ratios ranging from 0.005 to 0.2 (in x axis) were selected to produce forecasts for the full year and compute the RMSE and COR statistics (in y axis). A ratio value is identified for each season. Thus, the optimal ratio is the value of each station curve that minimizes the RMSE (minimum at 145.4 W·m-2) in fig.3a, and maximizes the correlation coefficient (maximum at 0.8) in fig.3b, given by the observation-WRF model relation. Overall, the optimal ratio for spring and summer is 0.015 and for autumn and winter is 0.03.
V. ANNUAL VALIDATION OF WRF-ARW DIRECT MODEL OUTPUT In a preliminary work, [9] presents a previous annual evaluation of GHI simulated by the WRF-ARW model over the Iberian Peninsula domain. Twenty-four global irradiance stations were used to analyze the model behavior (10 located at continental areas and 14 near the coast). The coastal stations present daily RMSE errors between 5-7 MJ·m-2·d-1 and 3-6 MJ·m-2·d-1 in summer. Moreover, the continental stations show lower errors, in this sense, the daily RMSE range between 3-6 MJ·m-2·d-1 in spring and below 3 MJ·m-2·d-1 in summer. Stations located on the coast with a high incidence of maritime air masses show the largest errors in the peak seasons of annual inrradiance. For sunny days, the WRF-ARW model overestimates the GHI due to the lack of atmospheric absorbers different than clouds, e.g. aerosols.
a
VI. IMPLEMENTATION AND ADJUSTMENT OF POSTPROCESSES The difference between KF and REC is the adjustment way, while KF is sensitive to the ratio between the variances of forecast-bias and forecast-error to adjust a gain factor, REC directly estimate the coefficients of the adjustment term which adds the day correction over the difference between the observed and forecast records per hour in the previous day. REC adjusts the adjustment term when values are updated, which allows the correction values to be easily adapted to seasonal variations. Once the WRF-ARW model is updated, the procedure needs only 2-3 days of iteration in order to adapt the correction to the model. Given the simplicity of formulas and the recursive way of calculating the correction term, the
b Fig.3. (a) RMSE and (b) Correlation coefficient variation depending to the Kalman Filter Ratio. A line per observational station is plotted. The optimal ratio is the value that minimizes the RMSE and maximizes the correlation coefficient given by the observation-WRF model relation.
VII. RESULTS A. Annual improvement The WRF-ARW direct model output, the KF post-process and the REC post-process are compared by means of statistical
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parameters. The annual statistics are computed for all stations and on an average over all stations. The Taylor diagram is used to depict the main differences produced when the postprocesses are applied. Fig. 4a shows the annual dataset results by KF and REC with respect to the WRF-ARW direct model output without post-processing. The impact of the postprocesses is observed in the standard deviation and slightly on the centered root-means-square difference. The KF results (red points) are located on the left side of REC (green points) and WRF-ARW results (blue points). Indicating a reduction of the standard deviation, but the correlation is maintained between the different approaches.
a
important improvement is observed on the bias, accordingly to the main characteristics of both post-processes. The KF is reduced from 35 W·m-2·h-1 to 6 W·m-2·h-1 with an 83% of improvement (only 48% for REC). As shown in fig. 4b, the differences in the correlation coefficients are negligible, while the percentage reduction of NMAE is 20% for KF respect to REC. Thus, on an annual basis the post-processes have a positive impact on the final model results, showing a clear increase in the accuracy of the irradiance forecast. TABLE III ANNUAL STATISTICS FOR THE 2004 WRF-ARW SIMULATION WITHOUT AND WITH POST-PROCESSES.
B. Hourly and daily improvement Fig. 5 shows the KF vs. observations plot from the hourly datasets for all available stations. The median, 25th/75th quantiles and 10th/90th quantiles are plotted. In the x axis, the histogram of observations is plotted with blue columns. The figure indicates the skills of the KF implementation to reduce the systematic bias of the system. The median line lies over the ideal line 1:1 for most of the values. Only on GHI observations over 850 W·m-2·h-1, the system with the KF presents a deviation from the observations with a clear overestimation of the values. These situations are associated to episodes with large diffuse radiation. Under such conditions, the nonlinearity of the process produces a strong bias on the KF results. It is important to note that this behavior is observed in stations below 200 m (not shown).
b Fig.4. Taylor diagram of WRF-ARW direct model output [blue], KF [red] and REC [green] post-processes. a) Points for each stations and b) station averaged point.
In order to better understand the impact of the postprocesses, Table 3 shows the annual statistics averaged over all the stations for GHI. The KF provides better results than the REC method. In this sense, the annual reduction of RMSE for the KF goes from 156 W·m-2·h-1 to 143 W·m-2·h-1, with an 8% of improvement (only 2% for the REC). The most
Fig.5. Comparison of KF post-process and WRF-ARW model in hourly adjustment of irradiance predicted against irradiance observed.
Furthermore, fig. 6 shows the hourly variability within a
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daily cycle of a specific station (Tarrega station) for the full 2004 year. The KF shows a better performance for sunshine hours during the year. For this station (located at 419 m a.s.l.), the better adjustment is applied over the maximum insolation hours from 8h to 18h UTC. The model overestimation during the first half of the day is corrected by the KF post-processes. The post-process is able to reduce the variability of the hourly measurement and corrects the shifts observed in the direct model output.
C. Seasonal improvement Fig. 7 plots the evolution of the daily statistics for 2004 computed from WRF-ARW direct model output (blue lines) and with the KF post-process (red lines). There is a large variability on the error of the model, but the KF is able to reduce such variability on several periods of the year. The KF shows a reduction of RMSE for summer and autumn, where an important removal of the bias is observed. This period comprises the seasons with larger insolation (spring and summer). It is also relevant the important improve on the correlation during autumn. In agreement with what has been observed before with the correlation, the KF do not improve the correlation over the year, but it produces an important improvement during autumn. Concerning the NMAE, the KF shows a consistent reduction overall the year. The episodes with large errors are substantially reduced by the KF algorithm. VIII. CONCLUSIONS AND OUTLOOK This contribution presents the assessment of short-term irradiance forecasting based on post-processing tools applied on WRF-ARW direct model outputs. The analysis is preformed on a full year meteorological simulation for 2004 over an Iberian Peninsula domain. The evaluation focuses on the capability of the post-processes methods to improve the forecast of solar irradiance, estimating and comparing their uncertainty.
Fig.6. Comparison of KF post-process and WRF-ARW model in the daily cycle for Tarrega station (altitude=419m) during the year 2004.
Fig.7. Seasonal distribution of statistical parameters: RMSE, bias, correlation coefficient and NMAE for comparison between KF and WRF-ARW model.
We apply and evaluate two statistical post-processes (KF and REC methods) on the WRF-ARW meteorological results in order to improve the irradiance predictions reducing the systematic error. The KF provides better results than the REC method, reducing the errors of WRF-
ARW model up to 83% of annual bias and 8% of annual RMSE. Also, the KF has a significant performance in the annual simulation specifically in spring and summer, where the WRF-ARW model showed the greatest errors. However, unusual irradiance peaks in stations below to
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200m are identified. The linear nature of the KF shows an irregular behavior with nonlinear peaks. Among the future developments of the work, we highlight the development and comparison of other postprocess including solar variables as solar zenith angle and solar constant, generation of surface energy maps allowing spatial visualization of the post-processing results, and validation of the prediction system through data of photovoltaic cells production.
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IX. ACKNOWLEDGMENTS The annual simulation has been made possible by the implementation of the model in the MareNostrum Supercomputer hosted by the Barcelona Supercomputing Center-Centro Nacional de Supercomputación (BSC-CNS). The work is partially funded by CGL2008-02818 project.
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cumulus convection in numerical models, K. A. Emanuel and D.J. Raymond, Eds., Amer. Meteor. Soc., 246 p, 1993. A.S. Monin and A.M. Obukhov. Basic laws of turbulent mixing in the surface layer of the atmosphere. Contrib. Geophys. Inst. Acad. Sci., USSR, vol. 151, pp 163–187 (in Russian). 1954 Z.I. Janjic. Nonsingular Implementation of the Mellor–Yamada Level 2.5 Scheme in the NCEP Meso model, NCEP Office Note, No. 437, pp 61, 2002. F. Chen, and J. Dudhia. Coupling an advanced land-surface/ hydrology model with the Penn State/ NCAR MM5 modeling system. Part I: Model description and implementation. Mon. Wea. Rev., vol. 129, pp 569–585, 2001. S.Y. Hong and H.L. Pan. Nonlocal boundary layer vertical diffusion in a medium-range forecast model, Mon. Wea. Rev., 124, 2322– 2339, 1996. E.J. Mlawer, S.J. Taubman, P.D. Brown, M.J. Iacono, and S.A. Clough. Radiative transfer for inhomogeneous atmosphere: RRTM, a validated correlated-k model for the longwave. J. Geophys. Res., 102 (D14), pp 16663–16682, 1997. J. Dudhia. Numerical study of convection observed during the winter monsoon experiment using a mesoscale two-dimensional model, J. Atmos. Sci., 46, 3077–3107, 1989. A.A. Lacis and J.E. Hansen. A parameterization for the absorption of solar radiation in the earth‟s atmosphere. J. Atmos. Sci., vol. 31, pp 118–133, 1974 L. Delle Monache, T. Nipen, X. Deng, Y. Zhou and R.B. Stull. Ozone ensemble forecasts: 2. A Kalman-filter predictor bias correction. J. Geophys. Res. Vol 111, 2006b. D05308, doi:10.1029/2005JD006311. J.M. Baldasano, O. Jorba, A. Rincón and E. Lopez, Atlas de radiació solar a Catalunya 1971-2005. Document tècnic: Versió preliminar. Universitat Politècnica de Catalunya, Barcelona, Espanya. 122 p, 2006. J.M. Baldasano, C. Soriano, and H. Flores. Atlas de radiació solar a Cataluña 1971-1997. Edició 2000, Institut Català d‟Energia, Barcelona, Espanya. 149 p , 2001 C.N. Long and Y. Shi. “The QCRad Value Added Product: Surface Radiation Measurement Quality Control Testing, Including Climatology Configurable Limits”. Atmospheric Radiation Measurement Program Technical Report, 2006. DOE/SC-ARM/TR074, available: http://www.arm.gov/publications/vaps.stm C.N. Long and E.G. Dutton. “BSRN Global Network recommended QC tests, V2.0.” BSRN Technical Report, 2002, available: http://ezksun3.ethz.ch/bsrn/admin/dokus/qualitycheck.pdf J. Meeus. Astronomical Algorithms. Willmann-Bell, Inc. 2nd ed, 1999. ISBN 0-943396-61-1. L. Delle Monache, J. Wilczak, S. Mckeen, G. Grell, M. Pagowski, S. Peckham, R. Stull, J. McHenry and J. McQueen. A Kalman-filter bias correction method applied to deterministic, ensemble averaged, and probabilistic forecasts of surface ozone, Tellus Ser. B, vol. 60, pp 238–249, 2008. doi:10.111/j.1600-0889.2007.00332.x. J. Jensenius and G. Cotton. The development and testing of automated solar energy forecast based on the model output statistics (MOS) technique. Satellites and Forecasting of Solar Radiation: Proceedings of the First Workshop on Terrestrial Solar Resource Forecasting and on Use of Satellites for Terrestrial Solar Resource Assessment. pp 22-29, 1981. D. Elizondo, G. Hoogenboom and R. McClendon. Development of a neural network model to predict daily solar radiation. Agriculture and Forest Meteorology 71 (1–2), 115–132, 1994. R. Guarnieri, F. Martins, E. Oereira and S. Chuo. Solar radiation forecasting using artificial neural networks. National Institute for Space Research 1, 1–34. 2008. S.M. Bozic. Digital and Kalman Filtering, 2nd ed., 160 pp., Jonh Wiley, Hoboken, N.J., 1994. A. Persson. Kalman Filtering. A new approach to adaptive statistical interpretation of numerical meteorological forecast. ECMWF Newsletters, n. 46., 1989 M. Homleid. Diurnal corrections of short-term surface temperature forecasts using Kalman filter, Weather Forecasting, vol 10, pp 689– 707, 1995. C. Cacciamani and C. Simone. Minimum temperature forecast at the regional meteorological service of the Emilia Romagna region
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Assessment of short-term irradiance forecasting based on post-processing tools applied on WRF meteorological simulations A. Rincón (1), O. Jorba (1), J.M. Baldasano (1,2) and L. Delle Monache (3) (1) Earth Sciences Department, Barcelona Supercomputing Center (BSC-CNS), Spain. (2) Laboratory of Environmental Modeling, Technical University of Catalonia (LMA-UPC), Spain. (3) Research Applications Laboratory, National Center for Atmospheric Research (NCAR), USA. C/ Jordi Girona 29, Barcelona, Spain. 08034. [email protected] Abstract— Short-term irradiance forecasting is an important issue for many fields of solar energy applications. The use of numerical meteorological models in combination with statistical post-processing tools may have the potential to satisfy the requirements for up to several hours to days ahead of irradiance forecast. In this contribution, we present an assessment of a shortterm irradiance system based on the WRF-ARW meteorological model and two post-processing methods in order to improve the overall skills of the system for an annual simulation of the year 2004 over Spain. The WRF-ARW model is applied with 4x4 km of horizontal resolution and 38 vertical layers over the Iberian Peninsula. Ninety-five global irradiance stations located in the northeast of the Iberian Peninsula are used to assess the temporal and spatial fluctuations and trends of the system. Post-processes used are: Kalman Filter and Recursive method. The skills of the system are evaluated by means of statistical indicators: root mean square error, bias, correlation and normalized mean absolute error. The Kalman Filter shows an annual reduction of 8% of RMSE and 83% of bias, while the annual reduction using Recursive method is 2% by RMSE and 35% by bias. A previous evaluation of the WRF-ARW model without post-processing shows significant errors in spring and summer greater than 4 MJ·m-2·d-1. The evaluation points out an overestimation due to the lack of atmospheric absorbers different than clouds, e.g. aerosols, not considered in the meteorological model. When comparing stations at different altitudes, the overestimation is enhanced at coastal stations (less than 200m) up to 1000 W·m-2·h1 . These results allow us to analyze the strengths and weaknesses of the irradiance prediction system and its reliability in the estimation of energy production from solar devices.
I. NOMENCLATURE Global horizontal solar irradiance (GHI), Numerical Weather Prediction (NWP), Advanced Research Weather Research & Forecasting model (WRF-ARW), Kalman Filter (KF), Recursive Method (REC), Root Mean Square Error (RMSE), correlation coefficient (COR), normalized mean absolute error (NMAE) II. INTRODUCTION
T
he increased contribution of solar energy in power generation sources requires an accurate estimation of surface solar irradiance conditioned by geographical, temporal and meteorological conditions. The knowledge of the variability of these factors is essential to estimate the expected energy production. Therefore it may help to stabilize the
electricity grid and increase the reliability of available solar energy and its application in photovoltaic cells and solar thermal power plants. The modeling of solar irradiance has experienced a gradual progress over the last few decades, from the use of empirical formulations seeking the parameterization of the local physical conditions from available measurements as [1]-[2]-[3]-[4], to the development of radiative transfer parameterizations used within numerical weather prediction models (NWP) as MM5 model [5], HIRLAM model [6] and WRF model [7]-[8]. NWP models solve the atmospheric dynamics and physical processes in a nonlinear computing environment. Due to complex cloud microphysics and limitations in spatial resolution, clouds and their radiative properties are difficult to predict in numerical models. Consequently NWP models are expected to show inherent regional or global biases limiting forecast accuracy. Therefore, the use of NWP models in combination with statistical post-processing tools may have the potential to satisfy the requirements for solar irradiance forecasting. Preliminary efforts oriented to improve NWP direct model outputs were the Model Output Statistics (MOS) procedures. MOS techniques have been applied to improve forecast accuracy for several meteorological variables. Specifically, [29] established a regression model between solar irradiance measurements and available forecast variables. The forecasts of these variables were used as input to MOS, predicting GHI on a 6–30 h forecast horizon with a root mean square error (RMSE) of 13.2% of extraterrestrial radiation received. Similarly, artificial neural networks (ANNs) [30]-[31], recognize patterns in data and have been successfully applied to solar forecasting for a reduction of relative RMSE (rRMSE) of daily average GHI much as 15% on a 12-18 h ahead NWP forecast. Also, bias-removal post-process as Kalman filtering procedure were proposed in order to correct systematic errors of NWP models [33]-[34]-[35]. In this study, we evaluate the implementation and performance of bias-removal post-processes on an annual simulation of global horizontal solar irradiance (GHI) computed with WRF-ARW model [7]-[8]. A previous evaluation of GHI simulated by the WRF-ARW model showed an overestimation due to the lack of atmospheric absorbers (different from clouds) that are not included in the
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meteorological model [9] and do not contribute to the attenuation of solar radiation. Therefore, in this contribution we apply and evaluate the performance of two post-processes: Kalman Filter [10]-[32] and Recursive method [11] using a high-density network of global irradiance stations in the northeast of the Iberian Peninsula. III. METHODOLOGY A.
WRF-ARW meteorological mesoscale model The WRF-ARW model (v3.0.1.1) [7]-[8] is applied to compute the GHI over the area under study. It is an Eulerian non-hydrostatic mesoscale model with state-of-the-art physical parameterizations (microphysics, cumulus parameterization, surface layer, land-surface model, planetary boundary layer, and atmospheric radiation). The radiation schemes provide atmospheric heating due to radiative flux divergence and surface downward longwave and shortwave radiation for the ground heat budget. Longwave radiation includes infrared or thermal radiation absorbed and emitted by gases and surfaces. Shortwave radiation includes visible and surrounding wavelengths that make up the solar spectrum. Hence, processes include absorption, reflection, and scattering in the atmosphere and surfaces. Within the atmosphere the radiation responds to model-predicted cloud and water vapor distributions, as well as specified carbon dioxide, ozone and traces of gas concentrations. Table 1 summarizes the main characteristics of the parameterizations used by the WRFARW model as applied in this contribution. The WRF-ARW model is run on an initial regional grid of 12 x 12 km in space and 1 h in time, covering Europe. The European domain provides the boundary and initial conditions for the Iberian Peninsula domain with 4 x 4 km in space and 1 hour in time. The WRF-ARW is configured with 38 vertical layers (11 characterizing the PBL). The model top is defined at 50 hPa to resolve properly the troposphere-stratosphere exchanges. Initialization and boundary conditions are provided by the Final Analyses of the National Centers for Environmental Prediction (FNL/NCEP) with information provided each 6 h, at a spatial resolution of 1º x 1º. The simulation consists of 366 daily runs to simulate the entire year 2004. The choice for this specific year is based on the availability of ground measurements of global irradiance for this year. Post-processing description The Kalman Filter (KF) [10] and the Recursive Method (REC) [11] are linear, adaptive, fast and optimal algorithms which are used to estimate the systematic component of the forecast errors reducing the bias from recent past forecast and observations to produce an improved to future forecast. The bias-removal post-processes used are briefly described below.
bias using a linear relationship, given by the previous bias estimate plus a correction value between the difference of the present forecast error and the previous bias estimate. This approach adapts its coefficients each iteration, resulting in a short training period. However, KF is unable to predict a large bias when all the biases for the past few days have been small. KF is recursive because some of the iteration values of the KF coefficients depend on the values at the previous iteration. The filter estimates the systematic component of the forecast errors or bias, which are often present in forecasts. Once the future bias has been estimated, it can be removed from the forecast to produce an improved forecast. A detailed description of the filter algorithm is shown in [22]. Here only the definitions of the error variances are shown, because the ratio of these variances is an important parameter that affects the KF performance. TABLE I PARAMETERIZATIONS USED IN WRF-ARW MODEL FOR THE ANNUAL SIMULATION
B.
Fig. 1 shows a flow diagram of Kalman Filter. It uses a predictor corrector approach, starting with the previous estimate of the forecast bias xt at time t, by the previous true bias plus a white noise η term:
xt |t t xt |t 2 t 1. Kalman Filter The KF is a mathematical method that predicts the future
t t
(1)
Where t is assumed uncorrelated in time and normally
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distributed with zero-mean and variance ση2. The forecast error yt (forecast minus observation at time t), is assumed to be corrupted from true forecast bias by a random error term t :
yt xt t xt t
t t
t
(2)
Where t is assumed uncorrelated in time and normally distributed with zero-mean and variance σε2. Thus, the forecast error yt includes both the systematic bias plus random errors. Reference [10] shown that the optimal recursive predictor of the forecast bias xt (derived by minimizing the expected mean square error) can be written as a combination of the previous bias estimate and the previous forecast error:
xˆ
t t|t
x ˆt|t t
t|t t
( yt x ˆt|t t )
(3)
Then, the correction by the Kalman gain factor β of the difference between the previous bias estimate and previous observed forecast error (2) is used to estimate the future bias (3). Since there is a time lag, Δt = 24 hours is used, today‟s forecast bias is estimated using yesterday‟s bias, which in turn was estimated using the day-before-yesterday‟s bias, and so on. The difference between today‟s forecast error (2) and the portion of today‟s bias that was estimated yesterday, is weighted by the Kalman gain factor to give the correction that was „„learned‟‟ from previous errors. This correction is applied to yesterday‟s estimate of today‟s bias to produce today‟s estimate of the bias for tomorrow.
2 error ratio 2
If the ratio is too high, the forecast-error white-noise variance σε2 will be relatively small compared to the true forecast-bias white-noise variance ση2. Therefore, the filter will put excessive confidence on the previous forecast and the predicted bias will respond very quickly to previous forecast errors. On the other hand, if the ratio is too low the predicted bias will change too slowly over time. Consequently, there exists an optimal value for the ratio that is given by the forecast region, which can be estimated by evaluating the filter performance in different situations [28]. 2. Recursive method In this method the coefficients in the linear equation are determined in an iterative way and updated every time a new forecast is issued by comparing the last observed data with the corresponding forecast. Recursive method [11] combines the hourly irradiance forecast and measurements as follows. If D is the model issuing day, the irradiance forecast at time D+n days is calculated as:
Irradi (n) IrradWRF (i ) (n) corri
KF needs to set an optimal ratio value (4) that is given by the climatology of the forecast region. The error ratio is a key parameter which determines the relative weighting of observed and forecast records between the forecast-bias white-noise variance ση2 and the forecast-error white-noise variance σε2:
(5)
The first term on the right-hand side is the irradiance at forecast time D+n days, with n days. The second term is the correction term, which is updated recursively every day (the index i in corr indicates the iteration or equivalently the forecast issued). The implicit hypothesis in (5) is that the correction calculated on day D+1 is valid also on day D+n. The correction term is calculated as follows:
1 corri ( IrradOBS IrradWRF (1) corri1 ) 2 corro 0
Fig.1. Flow diagram of Kalman Filter, where the future bias (output) is estimate by means of the previous bias estimation (prediction). This is corrected applying a coefficient (Kalman gain factor) which corresponds with the difference between the previous bias estimates minus previous observed forecast error [22].
(4)
(6)
The first term in the square bracket is the ground station measurement of irradiance on D+1 day, the second term is the irradiance at forecast time D+1. The D+1 day is the issuing day of this forecast, while the forecast issuing day is D. The third term in the square bracket is the correction term calculated the day before the day i, corresponding to the previous forecast. The starting value of the correction term is zero. The factor 1/2 in (6) means that half the contribution to the correction term is given by the past corrections. The initial value of the additional correction corr is 0 and it is updated every day with each new model and new measurements. The correction thus includes the past relationship between the model and the measurements, but weighting it towards the last few days, as the first terms of these series is largest. The advantage of this is that, after a few days of iteration, the initial and erroneous value of zero contributes a negligible amount to
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the correction term. C.
Statistical indicators The model-to-data statistics bias, root mean square error (RMSE), normalized mean absolute error (NMAE) are selected for the present study, together with the correlation coefficient (COR). Annual, seasonal and daily mean statistics are computed, with seasons corresponding to winter (January, February and December), spring (March, April and May), summer (June, July and August) and autumn (September, October and November). IV. OBSERVATIONAL NETWORK
of ninety-five global horizontal solar irradiance (GHI) stations in the northeast of the Iberian Peninsula. Fig. 2 shows the geographical distribution of stations over an annual map of the averaged global irradiation on horizontal surface. The map is obtained from the latest revision of the Atlas of solar radiation of Catalonia with a dataset of 203 stations for the period 19712005 [23]-[24]. The current dataset used for the calibration and evaluation of the system provides observations with a measurement frequency of 5-minute, 30-minute and 24-hour; and the stations are distributed over a complex terrain area with station-elevation ranging from 1m to 1970m a.s.l. The full 2004 year is selected for the present work.
For the adjustment of post-processing methods in the annual simulation of the WRF-ARW model, we used measurements
Fig.2. Geographical distribution of the observational network used for post-processing on the annual averaged map of global irradiation obtained from the Atlas of Solar Radiation of Catalonia [23].
A. Quality treatment In order to analyze the quality of the available irradiance data, the quality limits of control methodology proposed by [25]-[26] has been applied. All stations have gone through a three quality treatment stages: 1. Filtering by sunrise and sunset To obtain the database of registered solar irradiance between sunrise and sunset, the records were deleted before sunrise and after sunset solar by 2004. These hours of sunset
and sunrise for all stations are calculated based on latitudelongitude coordinates of each station from the algorithms proposed by [27]. 2. Implementation of quality limits The QCRad Testing methodology [25]-[26] defines two ranges for physically and extremely possible limits. Such limits depend on the solar constant and the solar zenith angle. Then, the values correspond to levels of irradiance valid between rising and setting sun when the solar zenith angle is greater than 0 and less than 90 degrees. The parameters of the
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implemented quality standards are presented in Table 2. 3. Graphic validation From the records obtained from the former quality treatment, we performed a graphic validation of the annual evolution of global irradiation by day (in MJ·m-2·d-1) obtained from GHI in W·m-2. The GHI was evaluated comparing with the theoretical attenuation curve of extraterrestrial radiation in the top of atmosphere. TABLE II PARAMETERS OF QUALITY RADIATION FOR PHYSICALLY POSSIBLE LIMITS (Q1) AND EXTREMELY POSSIBLE LIMITS (Q2), APPLIED OVER THE OBSERVATIONAL NETWORK OF NORTHEAST OF IBERIAN PENINSULA [26]
computing time of the procedure is easy and very short. On the other hand, KF needs set an optimal ratio between the forecast-bias variance and the forecast-error variance. This value is estimated through the evaluation of filter performance with the change of seasons for several stations. Fig. 3 shows the ratio sensitivity for irradiance forecast of the WRF-ARW model over the seasons of the year 2004. To obtain an optimal value, ratios ranging from 0.005 to 0.2 (in x axis) were selected to produce forecasts for the full year and compute the RMSE and COR statistics (in y axis). A ratio value is identified for each season. Thus, the optimal ratio is the value of each station curve that minimizes the RMSE (minimum at 145.4 W·m-2) in fig.3a, and maximizes the correlation coefficient (maximum at 0.8) in fig.3b, given by the observation-WRF model relation. Overall, the optimal ratio for spring and summer is 0.015 and for autumn and winter is 0.03.
V. ANNUAL VALIDATION OF WRF-ARW DIRECT MODEL OUTPUT In a preliminary work, [9] presents a previous annual evaluation of GHI simulated by the WRF-ARW model over the Iberian Peninsula domain. Twenty-four global irradiance stations were used to analyze the model behavior (10 located at continental areas and 14 near the coast). The coastal stations present daily RMSE errors between 5-7 MJ·m-2·d-1 and 3-6 MJ·m-2·d-1 in summer. Moreover, the continental stations show lower errors, in this sense, the daily RMSE range between 3-6 MJ·m-2·d-1 in spring and below 3 MJ·m-2·d-1 in summer. Stations located on the coast with a high incidence of maritime air masses show the largest errors in the peak seasons of annual inrradiance. For sunny days, the WRF-ARW model overestimates the GHI due to the lack of atmospheric absorbers different than clouds, e.g. aerosols.
a
VI. IMPLEMENTATION AND ADJUSTMENT OF POSTPROCESSES The difference between KF and REC is the adjustment way, while KF is sensitive to the ratio between the variances of forecast-bias and forecast-error to adjust a gain factor, REC directly estimate the coefficients of the adjustment term which adds the day correction over the difference between the observed and forecast records per hour in the previous day. REC adjusts the adjustment term when values are updated, which allows the correction values to be easily adapted to seasonal variations. Once the WRF-ARW model is updated, the procedure needs only 2-3 days of iteration in order to adapt the correction to the model. Given the simplicity of formulas and the recursive way of calculating the correction term, the
b Fig.3. (a) RMSE and (b) Correlation coefficient variation depending to the Kalman Filter Ratio. A line per observational station is plotted. The optimal ratio is the value that minimizes the RMSE and maximizes the correlation coefficient given by the observation-WRF model relation.
VII. RESULTS A. Annual improvement The WRF-ARW direct model output, the KF post-process and the REC post-process are compared by means of statistical
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parameters. The annual statistics are computed for all stations and on an average over all stations. The Taylor diagram is used to depict the main differences produced when the postprocesses are applied. Fig. 4a shows the annual dataset results by KF and REC with respect to the WRF-ARW direct model output without post-processing. The impact of the postprocesses is observed in the standard deviation and slightly on the centered root-means-square difference. The KF results (red points) are located on the left side of REC (green points) and WRF-ARW results (blue points). Indicating a reduction of the standard deviation, but the correlation is maintained between the different approaches.
a
important improvement is observed on the bias, accordingly to the main characteristics of both post-processes. The KF is reduced from 35 W·m-2·h-1 to 6 W·m-2·h-1 with an 83% of improvement (only 48% for REC). As shown in fig. 4b, the differences in the correlation coefficients are negligible, while the percentage reduction of NMAE is 20% for KF respect to REC. Thus, on an annual basis the post-processes have a positive impact on the final model results, showing a clear increase in the accuracy of the irradiance forecast. TABLE III ANNUAL STATISTICS FOR THE 2004 WRF-ARW SIMULATION WITHOUT AND WITH POST-PROCESSES.
B. Hourly and daily improvement Fig. 5 shows the KF vs. observations plot from the hourly datasets for all available stations. The median, 25th/75th quantiles and 10th/90th quantiles are plotted. In the x axis, the histogram of observations is plotted with blue columns. The figure indicates the skills of the KF implementation to reduce the systematic bias of the system. The median line lies over the ideal line 1:1 for most of the values. Only on GHI observations over 850 W·m-2·h-1, the system with the KF presents a deviation from the observations with a clear overestimation of the values. These situations are associated to episodes with large diffuse radiation. Under such conditions, the nonlinearity of the process produces a strong bias on the KF results. It is important to note that this behavior is observed in stations below 200 m (not shown).
b Fig.4. Taylor diagram of WRF-ARW direct model output [blue], KF [red] and REC [green] post-processes. a) Points for each stations and b) station averaged point.
In order to better understand the impact of the postprocesses, Table 3 shows the annual statistics averaged over all the stations for GHI. The KF provides better results than the REC method. In this sense, the annual reduction of RMSE for the KF goes from 156 W·m-2·h-1 to 143 W·m-2·h-1, with an 8% of improvement (only 2% for the REC). The most
Fig.5. Comparison of KF post-process and WRF-ARW model in hourly adjustment of irradiance predicted against irradiance observed.
Furthermore, fig. 6 shows the hourly variability within a
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daily cycle of a specific station (Tarrega station) for the full 2004 year. The KF shows a better performance for sunshine hours during the year. For this station (located at 419 m a.s.l.), the better adjustment is applied over the maximum insolation hours from 8h to 18h UTC. The model overestimation during the first half of the day is corrected by the KF post-processes. The post-process is able to reduce the variability of the hourly measurement and corrects the shifts observed in the direct model output.
C. Seasonal improvement Fig. 7 plots the evolution of the daily statistics for 2004 computed from WRF-ARW direct model output (blue lines) and with the KF post-process (red lines). There is a large variability on the error of the model, but the KF is able to reduce such variability on several periods of the year. The KF shows a reduction of RMSE for summer and autumn, where an important removal of the bias is observed. This period comprises the seasons with larger insolation (spring and summer). It is also relevant the important improve on the correlation during autumn. In agreement with what has been observed before with the correlation, the KF do not improve the correlation over the year, but it produces an important improvement during autumn. Concerning the NMAE, the KF shows a consistent reduction overall the year. The episodes with large errors are substantially reduced by the KF algorithm. VIII. CONCLUSIONS AND OUTLOOK This contribution presents the assessment of short-term irradiance forecasting based on post-processing tools applied on WRF-ARW direct model outputs. The analysis is preformed on a full year meteorological simulation for 2004 over an Iberian Peninsula domain. The evaluation focuses on the capability of the post-processes methods to improve the forecast of solar irradiance, estimating and comparing their uncertainty.
Fig.6. Comparison of KF post-process and WRF-ARW model in the daily cycle for Tarrega station (altitude=419m) during the year 2004.
Fig.7. Seasonal distribution of statistical parameters: RMSE, bias, correlation coefficient and NMAE for comparison between KF and WRF-ARW model.
We apply and evaluate two statistical post-processes (KF and REC methods) on the WRF-ARW meteorological results in order to improve the irradiance predictions reducing the systematic error. The KF provides better results than the REC method, reducing the errors of WRF-
ARW model up to 83% of annual bias and 8% of annual RMSE. Also, the KF has a significant performance in the annual simulation specifically in spring and summer, where the WRF-ARW model showed the greatest errors. However, unusual irradiance peaks in stations below to
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200m are identified. The linear nature of the KF shows an irregular behavior with nonlinear peaks. Among the future developments of the work, we highlight the development and comparison of other postprocess including solar variables as solar zenith angle and solar constant, generation of surface energy maps allowing spatial visualization of the post-processing results, and validation of the prediction system through data of photovoltaic cells production.
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IX. ACKNOWLEDGMENTS The annual simulation has been made possible by the implementation of the model in the MareNostrum Supercomputer hosted by the Barcelona Supercomputing Center-Centro Nacional de Supercomputación (BSC-CNS). The work is partially funded by CGL2008-02818 project.
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