Testing and calibrating a global radiation model for the Netherlands

Bachelor thesis Earth Sciences

Testing and calibrating a global radiation

model for the Netherlands

_________________

Co-assessor: Dhr. dr. ir. E.E. van Loon Bachelor project coordinator: Dhr. dr. K.F. Rijsdijk

Words: 9.152

Abstract:

Global radiation plays an essential role in various meteorological and biological processes. This project tests and calibrates a global radiation model for application in the Netherlands on monthly and daily timescales using MATLAB R2012b.

The model is calibrated using data from five equally distributed stations of the KNMI. The model is validated using other KNMI stations that measure global radiation and results are interpolated for the entire area of the Netherlands. Cloud cover is used as input, combined with the date and the latitude and longitude of the location.

This research indicates that global radiation can be modelled on a daily timescale as well as on a monthly timescale. For days, the model has a standard error of 20%-25% and for months 5%-10%. These conclusions are in correspondence with results from previous research. Results are consistent for different input data.

Cross validation indicated that if the model interpolates measurements, it also produces valid results on locations where no measurements are conducted. This is one of the reasons that the model is widely applicable for further research based on limited data.

The model can easily be deployed for further research to calculate global radiation for a specific area within the Netherlands. Based on solely a visual interpretation of the cloud cover, reliable global radiation values can be produced.

Page 2 of 38

Table of contents

Page 3 of 38

Introduction

Global radiation is the part of the radiation that is transmitted by the sun that reaches the Earth’s surface. It is the primary energy source for all physical and biochemical processes on Earth (Meza & Varas, 2000) and plays an essential role in various meteorological and biological processes. Accurately estimating global

radiation contributes to a better understanding of these processes. One of these processes is photosynthesis which is essential for planth growth (Alados et al., 1996), but global radiation also has an important influence on the production of solar energy (Martín et al., 2010) and the climate (Marsh & Svensmark, 2003). Global radiation plays a crucial role in processes involving temperature changes, snow melt and wind intensity (Meza & Varas, 2000).

Due to these functions of global radiation, it is essential to know the amount of global radiation in an area where research is conducted or solar panels are situated

(Ehnberg & Bollen, 2003). However, detailed weather data is not always available and weather stations are not always equipped with a pyranometer which measures global radiation. It is therefore useful to use a model, preferably one that requires only little input and/or input that is easily collected.

Global radiation has been modelled in the past in various regions, including Chile (Meza & Varas, 2000), Spain (Almorox & Hontoria, 2004), various regions in Europe (Supit & van Kappel, 1998), Algeria (Chegaar & Chibani, 2001) and India (Reddy & Ranjan, 2003). The models calculated global radiation for hours (Reddy & Ranjan, 2003), days (Supit & van Kappel, 1998), months (Meza & Varas, 2000) and years (Ehnberg & Bollen, 2003). Some models used temperature as input (Meza & Varas, 2000), while others used cloud cover (Ehnberg & Bollen, 2003) and others combined them (Supit & van Kappel, 1998).The accuracy of these models was determined with different methods, for instance the coefficient of determination (Meza & Varas, 2000), the maximum mean absolute relative deviation (Reddy & Ranjan, 2003) and the standard error of estimate (Almorox & Hontoria, 2004) and mostly the models produced accurate results.

Van Boxel modelled global radiation for the Portofino area in Italy and the model was very accurate (Van Boxel, 2002). This model uses cloud cover as an input, combined with the Julian day number and the latitude of the location. As an output, it returns global radiation. Although this model was developed to calculate global radiation for months, it was also used in France and this research suggested that this model might also be able to accurately calculate global radiation on a daily timescale (Van Boxel, unpublished results).

De Boer (1960) modelled global radiation for the Netherlands, but this research is dated and only data from De Bilt and Wageningen was used. This casts doubt on the reliability of the model for calculating global radiation for every place within the Netherlands. Nowadays more data is available and it is easier accessible.

Page 4 of 38 The goal of this research is to calibrate the global radiation model of Van Boxel

(2002) for the Netherlands and to calculate monthly and daily global radiation values. Because this model is developed to calculate global radiation on a monthly timescale, the results should indicate that this is indeed possible in a reliable way. But how does this model behave when it is deployed to calculate daily values for global radiation for the Netherlands? The research question that this project focuses on reads as follows:

“To what extent can global radiation be modelled in a reliable way for the

Netherlands using cloud cover data from five equally distributed KNMI stations for the period 1985-2000?”

Results will come in the form of maps, plots and tables with global radiation values for different periods. The results are analysed using the standard error of estimate to determine whether the model actually produces reliable results. This is further elaborated on in the methods section.

Page 5 of 38

Theoretical framework

To understand how this model works, it is essential to know some background information about the various concepts that are processed in the model. The theoretical framework discusses these concepts shortly.

Extraterrestrial radiation

First, it is important to know how much radiation enters system Earth. This is the amount of radiation reaching the Earth’s atmosphere, known as extraterrestrial

radiation. It depends on the solar constant (1367 W/m²), the latitude of the research area and the elliptical track of the Earth (Van Boxel, 2002).

There are seasonal differences in the amount of radiation that reaches the atmosphere, mainly due to the zenith

angle in which the radiation reaches the atmosphere at a certain location (figure 1). This angle changes constantly and influences the amount of sunshine hours per day at the given location and the intensity of the radiation (Iqbal, 1983, p. 17).

Other factors are the track of the Earth, which is elliptical (figure 2) and the rotation of the Earth around its own axis. The distance between the sun and the research area on Earth also changes constantly. Although this is a minor effect, it should also be taken into account when global radiation is modelled.

Another fact for the amount of extraterrestrial radiation that reaches the atmosphere at a certain time, is that the solar time is not equivalent to the clock time. To approach the true solar time, two factors should be taken into account: the longitude of the location should be multiplied with four minutes and added to the clock time, and the equation of time has to be applied. This equation consists of the eccentricity and obliquity effect.

Direct radiation

Not all extraterrestrial radiation reaches the surface, because solar radiation is

scattered by clouds, aerosols and air molecules. The amount of radiation that reaches the Earth’s surface without being scattered is called direct radiation.

A factor that influences the amount of direct radiation is the transmission coefficient of the atmosphere. This depends on the mass of the atmosphere above a particular area and is related to the thickness of the atmosphere at that certain location. The elevation of the research area is therefore a necessary detail. The transmission

coefficient of the atmosphere is approached by using the transmissivity of a Rayleigh atmosphere, containing only air molecules that scatter solar radiation. Because this is solely a hypothetical situation, the actual transmissivity of the atmosphere is

approached using Linke’s turbidity factor. This is a parameter that is location-specific and represents how much radiation can penetrate the atmosphere without being scattered (Van Boxel, 2002).

Figure 2: The elliptical track of the Earth around the sun (Parker & Heywood, 1998).

Figure 1: The zenith angle in which the radiation reaches the atmosphere (Iqbal, 1983, p.60).

Page 6 of 38 Diffuse radiation

Part of the radiation that is scattered also reaches the Earth’s surface. This is called diffuse radiation (Liu & Jordan, 1960). Because not only clouds, but also aerosols and air molecules scatter global radiation, there is also diffuse radiation under an

unclouded sky.

The amount of radiation that is scattered with an unclouded atmosphere, depends on the turbidity of the atmosphere. The amount of diffuse radiation with a clouded atmosphere depends on the cloud type and thickness.

Global radiation

The global radiation is the sum of the diffuse radiation and the direct radiation; it is the total solar radiation that reaches the Earth’s surface. Therefore, it is important to know these different categories of radiation and in which proportion they are present on a certain moment. The next section of the report describes how global radiation is calculated.

Page 7 of 38

Implementation Calibration Validation Cross validation

Figure 4: Flowchart of how global radiation is calculated with this model.

Methods

This project mainly involved modelling, which consisted of four major tasks: the implementation, the calibration, the validation and the cross validation (figure 3). Each task is discussed separately.

Implementation

The model of Van Boxel (2002) is implemented in MATLAB R2012b. Figure 4 shows concisely how this model works.

The model uses the date, latitude, longitude and cloud cover as input. Various equations and parameters are used to approach realistic global radiation values as close as possible. Extraterrestrial radiation, direct radiation and diffuse radiation for a clear and a clouded sky are calculated. Then the model calculates global radiation, determined by the amount of direct and diffuse radiation based on cloud cover. To provide insight in the model, the equations and parameters that are used are now shortly described (adopted from Van Boxel, 2002). Only the equations for radiation on a horizontal surface are applied because the Netherlands are mostly flat and meteorological stations measure global radiation on a horizontal surface.

Equations

The extraterrestrial radiation (W/m2) is calculated using equations 1-4. Equation 1 calculates solar declination, using the Julian day number as input. The correction factor for the elliptical track of the Earth (2) also requires the Julian day number as input. For calculating the cosinus of the zenith angle (3) the solar declination and latitude are used, along with the true solar time which is calculated as described in the theoretical framework. When these three factors are multiplied, this results in the extraterrestrial radiation (4).

(1) Solar declination

Input

- Latitude & longitude - Julian day number

- Cloud cover Model - Equations - Parameters Output - Global radiation

Figure 3: The major tasks of this research.

Page 8 of 38

(2) Correction for elliptical track of

the Earth

(3) Zenith angle

(4) Extraterrestrial radiation

Then, the direct radiation (W/m2) under an unclouded sky is calculated using

equations 5-8. First, the mass of the atmosphere is calculated (5). Because the whole Netherlands have an altitude of around sea level, the relative optical mass of the atmosphere is considered equivalent to the absolute optical mass of the atmosphere (M). The optical mass of the atmosphere is then used to calculate the transmission of a Rayleigh atmosphere (6). The transmission of the real atmosphere is calculated by raising the Rayleigh transmission to the power of Linke’s turbidity factor (7). The direct radiation is calculated by multiplying the extraterrestrial radiation with the transmission coefficient of the atmosphere (8).

(5) Relative optical mass (=M)

(6) Transmission of a Rayleigh

atmosphere

(7) Transmission coefficient of the

atmosphere

(8) Direct radiation

Afterwards, the diffuse radiation for a clear sky (W/m2) is calculated with equations 9 & 10. First the turbidity coefficient is calculated by dividing the direct radiation by the extraterrestrial radiation and subsequently raise this to the power of 0.363 (9). Then the diffuse radiation for a clear sky is calculated by multiplying the direct radiation with a fourth degree polynomial in which the turbidity coefficient is used (10).

(9) Turbidity coefficient

(10) Diffuse radiation clear sky The diffuse radiation for a clouded sky (W/m2) is calculated from the direct radiation

under an unclouded sky as a measure of the amount of radiation that reaches the top of the cloud and the relative optical mass (equation 11).

(11) Diffuse radiation clouded sky

Eventually the global radiation (W/m2) is calculated with equation 12 & 13. The relative duration of sunshine is calculated by subtracting 1 with the cloud cover (12). Afterwards, the fraction of direct radiation, diffuse radiation for a clear sky and diffuse radiation for a clouded sky is used to calculate the global radiation using equation 13.

Page 9 of 38 Code Name 235 De Kooy 260 De Bilt 280 Eelde 310 Vlissingen 380 Maastricht Table 1: The calibration stations with their

corresponding code as used by the KNMI.

(12) Relative duration of sunshine

(13) Global radiation

To use these equations some constants are given, for instance for the solar constant. These constants are not changed, because their values correctly represent reality. However, some parameters have initially been given an arbitrary value based on a set of assumptions and those parameters might be not optimal for application of the model in the Netherlands. These parameters are Linke’s turbidity factor and a parameter for the average transmissivity of the clouds, which respectively have an initial value of T=2,7 and 0,40. In this project, those parameters are assessed an eventually adjusted.

Calibration

After implementation of the model in MATLAB, the model was verified by using the same model in Excel and checking whether the results of the MATLAB model were in correspondence with those of the Excel model. For this, test data was used of one year. The Excel model was independently produced by Van Boxel and thus not susceptible to programming errors that might have been present in the MATLAB model.

When the MATLAB model functioned correctly, it was calibrated. This was performed using five KNMI stations which are equally distributed over the Netherlands, to make sure that not all data was derived from a small area that would not have been representative for the

Netherlands as a whole. Data from the period January 1, 1986 until December 31, 2000 was used from the

stations De Kooy, De Bilt, Eelde, Vlissingen and

Maastricht (table 1). The locations of these stations are shown in figure 6.

The period 1986-2000 was chosen because a time span of 15 years seemed most appropriate given the time that is available for this research and the data processing it requires. Also, the method that the KNMI used for collecting cloud cover data has changed in 2002 (Klein Baltink et al., 2010) and to reduce inconsistency in the data, it seemed convenient to select a period before or after 2002. Because the cloud cover before 2002 was measured by a visual interpretation of an expert, the model will also be suitable for use with visual interpreted cloud cover. This makes the model broadly applicable and easy to use in the field. However, there is also a disadvantage because human deficiencies could cause inconsistencies in the data(figure 5).

Page 10 of 38 Figure 5: Frequencies of which the different cloud cover 0cta’s were measured with

equipment and by visual interpretation in De Bilt, 2000 (Klein Baltink et al., 2010).

For the calibration, the Excel model of Van Boxel was slightly adjusted to work with the exact longitude and latitude of the station locations. Also, the transmissivity of the clouds was made dependent of the cloud cover by adding an extra parameter (equation 14) and the Excel model was modified to handle this correctly.

Diffuse radiation clouded sky, using

(14) adjusted transmissivity of the clouds

parameters (a & b)

Calibration was performed by changing parameters T, a and b in such a way that the standard error of estimate was minimized. The standard error of estimate was calculated by equation 15, in which y is the measured global radiation and Yest is the modelled global radiation:

(15) The standard error of the estimate

By adjusting the parameters, the model was calibrated so that the standard error of estimate was minimal. This was done using the ‘Solver’ function in Excel. The only condition was that the first parameter of the transmissivity of the clouds was not allowed to exceed 0,5.

After the ‘Solver’ function chose the optimal values for the parameters, they were implemented in the MATLAB model and the standard error of estimate for each station was analysed. With these parameters, the model should produce results that approach the measurement values. However, to check whether the model also works on data for which it is not calibrated, the model needs to be validated.

Page 11 of 38 Validation

To validate the model, there was checked whether the model produced similar results for stations on which it was not calibrated. For these stations, the model also calculated the standard error of

estimate, following the same procedure as was applied to the calibration stations. The model also produced several tables and plots.

By comparing these results to those of the simulation with calibration stations, there was evaluated whether the model produced consistent results. This would indicate that the model could successfully be deployed for use with all stations of the KNMI.

Table 2 shows the stations that are used for validation with their

corresponding code. For validation, also data from the period January 1, 1986 until December 31, 2000 were used. These stations are also shown in figure 6.

These stations were chosen by downloading the measured global radiation and cloud cover data from all the KNMI stations for the given period. For all stations, the

completeness of the data was assessed and the stations that provided sufficient data were selected. The provided data were considered sufficient if measured global radiation as well as cloud cover data were available and the measurements started at January 1. Missing data were only considered a problem if more than the complete first two years were designated as missing data.

Figure 6: The locations of the calibration and validation stations. Figure is produced by the MATLAB model.

Table 2: The validation stations with their

corresponding code as used by the KNMI. Code Name 210 Valkenburg 240 Schiphol 270 Leeuwarden 290 Twenthe 344 Rotterdam 350 Gilze-Rijen 370 Eindhoven

Page 12 of 38 There was also simulated with both calibration and validation stations, resulting in various maps for modelled and measured global radiation and the corresponding residuals. These maps are compared to each other to identify differences in modelled and measured global radiation.

Cross validation

Also a cross validation is performed to indicate the accuracy of the maps. The modelled global radiation of the calibration stations was interpolated to produce these maps. The interpolated values at the coordinates of the validation stations are compared to the values that were measured at these coordinates. This can provide information about the validity of the interpolated global radiation and the maps. Analysis of the results

The model produces maps, plots and tables that are used to draw conclusions about the validity of the model. This will be further elaborated on in the next section of the report. Because the model produces a large amount of figures (>150), only those that provide general information regarding the research question are primarily analysed. If during this analysis remarkable results are observed, more specific tables, plots and maps will be engaged in the analysis to examine whether these can provide

explanations. The standard error of estimate is considered the decisive factor when assessing the validity of the model.

Page 13 of 38

The model

This section elaborates on how the model works and for what data analysis it can be applied. The main purpose of this model is contributing to this research and to supply sufficient information to answer the research question. However, because the model can simulate automatically and because during the implementation additional

applications of the model came to mind, the model has become a tool that also can be used for future research.

Requirements input data

This model is mainly suitable for data derived from the KNMI, using the interactive selection of data on hourly timescale (KNMI, 2015). The model is only suitable for data that starts at January 1 and ends at December 31 and all stations must have conducted measurements for the exact same period. The model can deal with missing data, but the length of the data for each station has to be the same size.

By default, the model is capable of simulating if the format of the KNMI is used as provided by the interactive selection; column 1 must contain the station numbers, column 2 must contain the date in YYYYMMDD, column 3 must contain the hours (UT), column 4 must contain the measured global radiation in J/cm² and column 5 must contain the cloud cover in octa’s (0-8 and a 9 indicating that the upper air was not visible). If data is imported in another format, columns can easily be adjusted at the top of the script. However, the units must be the same.

Although this is not elaborately tested, the model should be able to simulate all KNMI data and the user only has to fill in the correct name of the data file. For visualization purposes, it is advised to adjust the expected maximum global radiation values for months and days if necessary. The model relies on these values for setting the proper limits of its axes when visualisations are made. By default, the expected maximum global radiation on one day is 40 MJ/m² and 800 MJ/m² for one month.

Data processing

The model identifies the period for which the data is supplied and the leap years that occur in this period. It makes a variable with the corresponding day numbers and determines the amount of stations that are used. The exact coordinates of each station are assigned to the associated stations numbers to use for the calculation of the true solar time. Measured global radiation values are converted to W/m² and the cloud cover is divided by 8 to produce digits from 0 to 1 maximum. If the cloud cover data contained a 9, this was treated as if the upper air was fully clouded and thus converted to a 1. After these steps, the data is fully prepared to be used in the equations of the model as indicated in the methods section of this report.

After the calculations, negative global radiation values are set to zero. Also, missing data is detected and if data is missing for the modelled global radiation (due to

Page 14 of 38 missing cloud cover data) the modelled and measured global radiation are both set to zero and vice versa.

Global radiation was converted to MJ/m² for visualization purposes and afterwards it is summed to provide the daily sum of global radiation for each day. These daily values are then summed up to the monthly values and several tables, plots and maps are made based on this data. Before the production of these tables, plots and maps, the missing values are deleted. This should prevent that results are biased because of interference with technical problems.

Plots

For each station, several plots are made and saved in a subfolder. These include a line plot which shows the modelled and measured global radiation and a scatterplot with a regression line. Also, the residuals are calculated by subtracting the modelled global radiation from the measured global radiation. These residuals are also scattered against the measured global radiation and again a regression line is inserted. At last, a probability density plot is made to show the distribution of the residuals.

If there are missing values, this is visible in the line plot. The lines will not cover the entire length of the x-axis if data is missing. However this might seem sloppy at first sight, it is useful to identify periods in which the equipment failed and this can be considered when evaluating the results.

Plots will also be provided with some information from statistical tests. In the probability density plot, the result from a Lilliefors test are inserted, indicating whether the residuals are normally distributed or not. If the data is normally distributed, a paired t-test is performed on the data. If not, the non-parametric equivalent is performed: the Wilcoxon signed rank test. The line plot shows the outcome of one of these tests for means and the scatterplot will show the formula of the regression line and the standard error of estimate. In this project, the standard error of estimate is the main guidance and these tests are of minor importance. However, they do indicate certain characteristics of the data and provide a nuanced insight in the reliability of the conclusions.

Tables

The details of these plots are saved in a subfolder that is created by the model, along with several other tables that provide information about the global radiation for this simulation. These tables include: standard error of estimate for calibration stations, standard error of estimate for validation stations, the average global radiation in one day and in one month, tables in which the interpolated values are compared to the measured values at the same coordinates and the average global radiation for every station in every month.

Page 15 of 38 Also, for every station tables are made with the average monthly values in every month of every year (modelled, measured, residuals, residuals percentage). The same is done for the average day in every month of every year.

Tables are copied and pasted in Excel for the proper row- and column headers and are situated in the ‘Appendices’ folder.

Maps

If two or more stations are used, the model produces maps of the global radiation for the entire surface of the Netherlands. These are based on information from the tables as previously described. Contours used for these maps were provided by Van Boxel and were slightly adjusted to make them suitable for use in MATLAB. The maps are clipped so that only the surface of the Netherlands shows global radiation values. Maps are made for the average daily and monthly global radiation values for the entire simulation period and for each month separately. These maps are based on all stations that provide input data, but also maps are made that are based only on the calibration stations. These maps are saved in separate subfolders and are discussed separately further in this section.

For the maps, a grid of 401x501 grid points is used, ranging from a latitude of 50° to 54° and a longitude of 3° to 8°. For the interpolation, Inverse Distance Weighting is used with a distance weight of -1 and using all stations as neighbours.

Map visualizing location of the stations

A map is made which visualizes the locations of the stations and makes a distinction between validation and calibration stations if both are present. The codes of the stations are inserted in the map at the proper locations. An example is the map that is included in the methods section of this report (figure 6).

Maps using only calibration stations

If data is used that contains the measured global radiation and the cloud cover of the calibration stations and the timeframe ranges from 1986-2000, the model produces maps which interpolate the modelled global radiation for these five stations. The values at the coordinates of the other stations are automatically obtained from the grid and the values are stored in tables. Calibration and validation stations are visualized on the map with different colours. Maps of months and days for the same period of time are plotted next to each other.

The maps for cross validation are saved in a separate folder. The corresponding tables regarding the details of the cross validation are also saved in a separate folder.

Page 16 of 38

Maps using all stations

These maps use all input stations for interpolation. Only if at least two stations are used that provide data without NaN (missing data) for a map, this maps is actually made. If a particular stations does not provide data for January for example, it is not visualized on this map. But if the same station does provide data for February, it is visualized on the map of February because it does contribute to this particular map. On these maps, the locations of all stations that provide valid data are indicated with same colour on the map. To be able to conveniently compare measured and global radiation, the modelled and measured global radiation maps are visualized next to each other and the same colour scale is used. Residuals for days and for months are plotted alongside.

Additional applications of the model

If no measurement data is provided, the user is evidently not trying to compare the model to measurements, but intentions are probably to analyse collected data. Therefore the model performs a descriptive statistical analysis if only cloud cover is used as input; returning a table with the mean, median, modus, range, interquartile range, percentiles, variance, standard deviation, mean absolute deviation, skewness, kurtosis, geometric mean, the coefficient of variation and the amount of missing values. Also the result of a Lilliefors test is performed to indicate whether the data is normally distributed or not. A histogram, probability density plot, boxplot and a plot of the global radiation are also produced. Maps are also made based on this data, but only those of the modelled global radiation. Example results can be found in the ‘Appendices’ folder.

If data for this analysis is collected by individual measurements and is not derived from the KNMI, the latitude and longitude of the research location can be specified. This can be done at the top of the script where the data is also loaded. This can only be done for one station and therefore the model only performs the descriptive analysis and will not produce maps. Note that this has not been tested and that an error might occur.

Supplementary information about the model

To improve ease of use, the pop-up of figures is suppressed and instead figures are saved in subfolders that are created by this model. The openfig.m function of MATLAB was adjusted to make sure figures that are suppressed can still be saved. Also, the interpidw.m function is adjusted to make sure wait bars do not pop up. When the simulation is finished, the user is notified with three beeps. If the model is re-simulating, the previous results are overwritten and therefore it is important to change the name of the ‘results’-file after simulating. The full MATLAB model code is included in the ‘Appendices’ folder along with (test)results of the previous

Page 17 of 38 The model has a simulation time of about 15 minutes when both calibration and validation data are used. The simulation time is dependent on the amount of input data and if calibration data is included in the input data, the simulation time is considerably longer because cross validation is performed.

Page 18 of 38

Results

In this section the results of the simulations are described. First the results regarding the calibration task are examined, followed by the results regarding the validation task of the modelling phase.

Calibration

The ‘Solver’ function in Excel returned approximately 2,06 for Linke’s turbidity factor, 0,50 for the a-parameter of the transmissivity of the clouds and approximately -0,15 for the b-parameter of the transmissivity of the clouds. Using these parameter values, the model returned the standard errors of estimate as displayed in table 3. No patterns in relation to latitude and longitude were found and thus there was no further parameterization performed.

Validation

Several results are presented here regarding the validation of the model. Results with the calibration and validation data are included in the form of plots, tables and maps.

Plots

This section includes the plots of the stations that resulted in the smallest and largest standard error of estimate for days and for months for both the calibration and the validation data. These are visualized in figure 7 to 14.

When calibration data is used, the largest standard error of estimate amounts approximately 24% for days and approximately 9% for months. These values are respectively for De Bilt (figure 7) and De Kooy (figure 9). The smallest standard error of estimate amounts approximately for days 20% and 6% for months. These values are respectively for Eelde (figure 8) and De Bilt (figure 10).

When validation data is used, the largest standard error of estimate amounts approximately 24% for days and approximately 9% for months. These values are respectively both for Leeuwarden (figure 11 and 13). The smallest standard error of estimate amounts approximately for days 21% and 6% for months. These values are respectively for Rotterdam (figure 12) and Twenthe (figure 14).

Table 3: The standard errors of estimate for every station and for the model as a whole when using only calibration stations.

SEE day (MJ/m2) SEE day (%) SEE month (MJ/m2) SEE month (%)

235 De Kooy 2,47 23,76 29,67 9,39 260 De Bilt 2,29 24,11 16,79 5,80 280 Eelde 1,94 20,45 24,97 8,67 310 Vlissingen 2,48 23,62 25,01 7,83 380 Maastricht 2,31 23,20 22,14 7,32 Model 2,30 23,14 24,09 7,95

Page 19 of 38 Figure 7: Plots for station with the largest standard error of estimate for days if calibration data is used (De Bilt). Figure 8: Plots for station with the smallest standard error of estimate for days if calibration data is used (Eelde).

Page 20 of 38 Figure 9: Plots for station with the largest standard error of estimate for months if calibration data is used (De Kooy). Figure 10: Plots for station with the smallest standard error of estimate for months if calibration data is used (De Bilt).

Page 21 of 38 Figure 11: Plots for station with the largest standard error of estimate for days if validation data is used (Leeuwarden). Figure 12: Plots for station with the smallest standard error of estimate for days if validation data is used (Rotterdam).

Page 22 of 38 Figure 13: Plots for station with the largest standard error of estimate for months if validation data is used (Leeuwarden). Figure 14: Plots for station with the smallest standard error of estimate for months if validation data is used (Twenthe).

Page 23 of 38

Tables

The model produces several tables, in which the table with the standard error of estimate is most important in this research (table 3 and 4). Other tables that are included in the results are the tables with details of the plots (table 5 and 6) and the tables with the mean values for days (table 7 and 9) and months (table 8 and 10).

Note that the standard error of the estimate of the model is around 7% when validation data is used.

If the p-value in the fifth column of table 5 and table 6is smaller than 0,05, the test for means has indicated that there is a significant difference between the modelled and measured global radiation. This casts doubt on the validity of the model but these tests are not the main focus of this research. The concerning cells are highlighted in red. The fourth column indicates whether the residuals come from a normal

distribution or not.

SEE day (MJ/m2) SEE day (%) SEE month (MJ/m2) SEE month (%)

210 Valkenburg 2,24 21,45 22,55 7,13 240 Schiphol 2,16 21,67 16,63 5,55 270 Leeuwarden 2,38 24,17 25,78 8,62 290 Twenthe 2,20 23,26 15,90 5,55 344 Rotterdam 2,09 21,13 19,43 6,50 350 Gilze-Rijen 2,32 23,70 18,77 6,32 370 Eindhoven 2,27 23,20 21,77 7,32 Model 2,24 22,66 20,38 6,81

Details of the A-coefficient B-coefficient Normal distribution P-value of test for

plots for days regression line regression line residuals: Lillietest means: paired ttest scatterplot scatterplot (1=no, 0=yes) or signed rank

210 Valkenburg 0,90 0,61 1 3,88E-41 235 De Kooy 0,90 0,40 1 5,96E-91 240 Schiphol 0,95 0,56 1 6,92E-05 260 De Bilt 0,93 0,66 1 3,10E-01 270 Leeuwarden 0,88 0,55 1 1,67E-61 280 Eelde 1,00 0,40 1 5,58E-66 290 Twenthe 0,92 0,74 1 6,56E-03 310 Vlissingen 0,93 0,47 1 5,05E-11 344 Rotterdam 0,95 0,57 1 1,21E-02 350 Gilze-Rijen 0,92 0,69 1 1,69E-01 370 Eindhoven 0,96 0,61 1 5,64E-17 380 Maastricht 0,94 0,77 1 9,77E-11

Table 4: Table with the standard errors of estimate for validation stations.

Page 24 of 38 Table 7:Table with the mean daily values for calibration data.

Table 8:Table with the mean monthly values for calibration data.

Details of the A-coefficient B-coefficient Normal distribution P-value of test for

plots for months regression line regression line residuals: Lillietest means: paired ttest

scatterplot scatterplot (1=no, 0=yes) or signed rank

210 Valkenburg 0,97 -3,60 1 5,56E-21 235 De Kooy 0,95 -5,59 1 4,60E-32 240 Schiphol 1,02 -4,65 1 9,37E-01 260 De Bilt 1,02 -6,00 1 1,74E-02 270 Leeuwarden 0,96 -6,30 1 1,10E-28 280 Eelde 1,08 -9,34 1 2,62E-12 290 Twenthe 1,01 -3,56 1 4,82E-01 310 Vlissingen 1,00 -8,46 1 8,99E-09 344 Rotterdam 1,02 -4,50 1 3,37E-01 350 Gilze-Rijen 1,02 -6,09 1 3,12E-02 370 Eindhoven 1,04 -6,48 1 5,91E-03 380 Maastricht 1,03 -3,67 1 5,18E-02

Mean modelled Mean measured Residuals Residuals (%) global radiation global radiation (MJ/m2)

for days (MJ/m2) for days (MJ/m2)

235 De Kooy 9,70 10,38 0,68 6,55

260 De Bilt 9,47 9,51 0,04 0,42

280 Eelde 9,93 9,49 -0,44 -4,62

310 Vlissingen 10,20 10,49 0,29 2,72

380 Maastricht 10,09 9,94 -0,15 -1,55

Mean modelled Mean measured Residuals Residuals (%) global radiation global radiation (MJ/m2)

for months (MJ/m2) for months (MJ/m2)

235 De Kooy 295,30 316,00 20,71 6,55 260 De Bilt 288,12 289,34 1,22 0,42 280 Eelde 301,37 288,06 -13,31 -4,62 310 Vlissingen 310,58 319,28 8,69 2,72 380 Maastricht 307,28 302,58 -4,70 -1,55

The residuals for daily values of the calibration data have an absolute percentage of

0,42% to 6,55%, for months this is the same. Note that these are mean percentages, obtained from the entire period that the data was supplied. The model does not produce comparable percentages for one particular day or month. The largest

percentages of the residuals occur for De Kooy and Eelde. A more extensive insight in the results indicated that these differences are mainly caused between November and April for De Kooy and between April and September for Eelde.

Page 25 of 38

Based on Mean modelled Mean measured Residuals Residuals (%)

cloud cover global radiation global radiation (MJ/m2)

data for months (MJ/m2) for months (MJ/m2)

210 Valkenburg 302,17 316,39 14,22 4,50 240 Schiphol 300,24 299,62 -0,62 -0,21 270 Leeuwarden 280,44 299,11 18,67 6,24 290 Twenthe 286,25 286,65 0,40 0,14 344 Rotterdam 299,96 299,01 -0,96 -0,32 350 Gilze-Rijen 295,33 296,84 1,52 0,51 370 Eindhoven 303,03 297,47 -5,56 -1,87

Based on Mean modelled Mean measured Residuals Residuals (%)

cloud cover global radiation global radiation (MJ/m2)

data for days (MJ/m2) for days (MJ/m2)

210 Valkenburg 9,97 10,44 0,47 4,50 240 Schiphol 9,97 9,95 -0,02 -0,21 270 Leeuwarden 9,25 9,86 0,62 6,24 290 Twenthe 9,47 9,48 0,01 0,14 344 Rotterdam 9,90 9,87 -0,03 -0,32 350 Gilze-Rijen 9,75 9,80 0,05 0,51 370 Eindhoven 9,96 9,78 -0,18 -1,87

The residuals for daily values of the validation data have an absolute percentage of 0,14% to 6,24%, for months this is the same. The largest percentages of the residuals occur for Valkenburg and Leeuwarden. A more extensive insight in the results

indicated that these differences are mainly caused between January and May for Valkenburg and between October and April for Leeuwarden.

Note that day sums might be remarkably high in comparison to month sums, because month sums are also calculated if the months does not have measurements for every day in that month. Due to this fact, the day sum is not equal to the month sum divided by the amount of days in that particular month and the residual percentages of months and days do not always correspond. This could produce remarkable results but regarding this research question, this is not relevant because it is about the

relation between measured an calculated rather than investigating the amount of radiation in a certain month.

Table 9:Table with the mean daily values for validation data.

Page 26 of 38

Maps

The model produces several maps, of which the monthly (figure 15)and daily (figure 16) mean are included in this results section. The residuals are also visualized in figure 17. For these maps, the data from all input stations is used for interpolation.

Figure 15: Maps of the daily mean. The left map is based on the modelled results and the right map is based on the measured results.

Page 27 of 38 Figure 16: Maps of the monthly mean. The left map is based on the modelled results and the right map is based on the measured results. Figure 17: Maps of the mean residuals. The left map is based on the daily residuals and the right map is based on the monthly residuals.

Page 28 of 38

Based on Mean modelled Mean measured Residuals Residuals

interpolation of global radiation global radiation (MJ/m2) (%)

calibration stations for months (MJ/m2) for months (MJ/m2)

210 Valkenburg 298,49 316,39 17,91 5,66 240 Schiphol 296,19 299,62 3,43 1,14 270 Leeuwarden 298,53 299,11 0,59 0,20 290 Twenthe 299,91 286,65 -13,26 -4,62 344 Rotterdam 299,00 299,01 0,00 0,00 350 Gilze-Rijen 298,25 296,84 -1,41 -0,47 370 Eindhoven 299,54 297,47 -2,06 -0,69 Cross validation

The model also performs cross validation, comparing the interpolated values based on the calibration stations to the measured values of the validation stations. The interpolated values are obtained from the interpolated grid at the locations of the validation stations. The model produces several tables and maps, of which the most relevant are included. First, the tables are displayed (table 11 and 12) and then the corresponding maps are shown (figure 18).

As indicated in the tables, the residual percentages are not the same for days and for months if cross validation is performed. For days, the absolute percentages vary between 0,03% and 6,04%. For months, these percentages vary between 0,00% and 5,66%. The corresponding maps are shown below (figure #). Again, note that these are mean percentages, obtained from the entire period that the data was supplied. The largest percentages of the residuals occur for Twenthe and Valkenburg. A more extensive insight in the additional results indicated that the main part of these residuals are caused between January and April for Valkenburg and between June and September for Twenthe.

Based on Mean modelled Mean measured Residuals Residuals

interpolation of global radiation global radiation (MJ/m2) (%)

calibration stations for days (MJ/m2) for days (MJ/m2)

210 Valkenburg 9,81 10,44 0,63 6,04 240 Schiphol 9,73 9,95 0,22 2,20 270 Leeuwarden 9,82 9,86 0,05 0,50 290 Twenthe 9,86 9,48 -0,38 -4,05 344 Rotterdam 9,83 9,87 0,05 0,48 350 Gilze-Rijen 9,80 9,80 0,00 0,03 370 Eindhoven 9,84 9,78 -0,06 -0,63

Table 12: Cross validation table for months. Table 11: Cross validation table for days.

Page 29 of 38 Additional results

If calibration data combined with validation data is used as an input, the model produces >100 maps, about 50 plots and >150 tables. Therefore, not all the output is actually included in the results. Some of those results are quite detailed and for the conclusions only the more general information is relevant. A selection of the most relevant results that illustrate the establishment of the conclusions is shown here in the results and for a more extensive insight in the results, it is advised to consult the ‘Thesis results’ folder which is located in the ‘Appendices’ folder. Note that NaN means that the model was supplied with missing data for the concerning period and that some numbers at first sight appear to be incorrect due to rounding of the

Page 30 of 38

Discussion

In this section of the report, the results are discussed and the research is evaluated. How reliable are the results and what does this mean for the conclusions that eventually can be drawn? Weaknesses of the performed research are identified and the validity of the results is analysed. Also, the practical impact of this research is indicated and recommendations for future research are stated.

Discussion of the results

Calibration

The values for the parameters as returned by the ‘Solver’ function of Excel are mostly realistic values if related to the theory as provided in the theoretical framework. For the a-parameter of the transmissivity of the clouds, this is mainly due to the

restrictions that where imposed to the ‘Solver’ function. However, it is remarkable that the ‘Solver’ function chose the maximum value; this might indicate that the model tends to overestimate the global radiation. The negative b-parameter indicates that the transmissivity of the clouds decreases if the cloud cover is higher. The

parameter for Linke’s turbidity factor is slightly decreased compared to the initial situation, which might suggest that in the initial situation, the direct radiation was too low. It has resulted in a value that might even be too low to correctly represent reality. This could be caused by the fact that the ‘Solver’ function chose a set of parameter values that provided the best results for all calibration stations combined. It is possible that the experts at each calibration station systematically interpreted cloud cover differently and this inconsistency could be related to this low

T-parameter value.

Because no relation was detected between standard error of estimate of the stations and their latitude and longitude (table 3), no further parameterisation was

performed. This indicates that based on this data, no clear relation exists between for instance the turbidity factor of the atmosphere and the position of the stations

relative to the North Sea.

Regarding the standard error of estimate, values for the calibration stations are clearly higher when global radiation is modelled on a daily timescale instead of a monthly timescale (table 3). This is in correspondence with both the hypothesis and previous research. The relatively high standard error of estimate for days can

probably not be resolved, because the ‘Solver’ function has calibrated the model on the daily timescale and has already provided the optimal values for the parameters on a daily timescale.

Validation

If the results from the calibration and validation stations are compared (table 3 & 4), the standard error of estimate seems to be almost equivalent. The standard error of the estimate for the model is even smaller for the validation data than for the

Page 31 of 38 calibration data, which is remarkable because the model has been parameterised using the calibration data.

None of the stations provided data of which the residuals were normally distributed according to the Lilliefors test (table 5 & 6), so the test for means that is performed on each station is the Wilcoxon signed rank test. When comparing the results from these tests (table 5 & 6), it is remarkable that there is a significant difference between the modelled and measured global radiation in most cases. Also, the stations that have no significant difference for days, do have a significant difference for months and vice versa. This is also noteworthy and it implies that it is not possible to formulate an unambiguous statement based on the results of the Wilcoxon signed rank test. There can be various explanations for the fact that the means are generally not the same, for instance that there is inconsistency in the data from the several calibration stations. This could be due to differently calibrated pyranometers, experts that

interpret cloud cover differently or different cloud types that occur in various regions. However, it could also indicate that the model does not function correctly. Therefore, the results of these test are taken into consideration but the standard error of

estimate eventually serves as the decisive factor on which the main conclusions are based.

The slope of the regression lines is in all cases reasonably close to 1,0 and the offset is reasonably close to 0,0 (table 5 & 6), which indicates that the differences between the modelled and measured global radiation are minor. The scatterplots provide a clear illustration of this (figure 7-14). The regression and test for means results seem to be contradictory, which could be caused by the previously mentioned explanations. The model produces higher residuals in certain months for certain stations, but the months in which these residuals are larger differ for each station (additional results). This means that the model does not systematically produce higher residuals in

certain periods.

The maps indicate that the model produces results that mostly are slightly lower than the measurements (figure 15-17). This could be due to the fact that the model was calibrated using the standard error of estimate and not the residuals. Note that the colour bars of the residual maps have a small range and thus the residuals are quite low (figure 17). Also, the maps of the modelled and measured global radiation show different patterns on the maps (figure 15 & 16). This could however be due to the colour scale, which has set to a range so that all values from both maps can be shown on the map. This means for instance, that if the range of the modelled global

radiation map is 200-300 and the range of the measured global radiation is 100-400, the colour bar for both maps ranges from 100-400. In this case, the modelled global radiation map cannot show much detail because not the entire range of the colour bar is available and the colours can be flattened resulting in changing patterns. Therefore, it is difficult make solid statements about difference in the patterns based on the maps. What the maps do indicate, especially the residuals map (figure 17), is that the

Page 32 of 38 model tends to underestimate the global radiation because the residuals are

predominantly positive numbers.

Cross validation

The percentages of the residuals between the interpolated and measured global radiation values (table 11 & 12) indicate that, even though only five stations are used, the interpolated values are quite valid. For days and months the percentages are approximately equivalent and thus the model is in this case equally suitable for both. Regarding the cross validation, the model also produces higher residuals in certain months for certain areas and again there is no clear relation between higher residuals in certain months. Thus, the model does not systematically produce higher residuals in certain periods (additional results).

Large residuals for the cross validation can be due to missing data, because this can result in unrealistically low day and month sums for a certain station. The data of the calibration stations is complete, so the interpolated daily and monthly values might in that case be significantly higher.

The maps (figure 18) are quite valid. Again, note that the cross validation is based on mean percentages, obtained from the entire period that the data was supplied. The model does not produce comparable results for one particular day or month. Evaluation of the research

The research was quite successful; results were produced and those provide sufficient information to formulate an answer to the research question. However, there are also some aspects that should be reconsidered and might impose some points of

improvement.

The standard error of estimate was chosen as the main factor to rely on when answering the research question. With a value of approximately 20%-25% for days and approximately 5%-10% for months, it could be stated that the model is at least capable of producing reliable results for months. However, the Wilcoxon signed rank test suggests that the model produces results that are significantly different. This casts some doubts on the validity of the model and should be noted.

Whether the model produces reliable results or not, is also dependent on what the information is used for. For some processes within the context of Earth sciences, a standard error of estimate of 5%-10% is acceptable, while for others an error of this magnitude might significantly influence the underlying processes. The timeframe is also of importance; in various processes the monthly global radiation has a

significantly larger impact on system Earth than the daily global radiation.

Regarding the validation; note that the validation stations are not equally distributed over the Netherlands. This could imply that in the remaining parts of the

Page 33 of 38 Another remark regarding the cross validation is that some of the validation stations are situated on secluded locations relative to the calibration stations. For the

production of the maps, the model used extrapolation instead of interpolation to cover the areas in which these stations are situated. This might have caused less reliable results and might also explain the large percentage of residuals of Twenthe. The cross validation was performed with only five stations that provided

interpolation data, which is few relative to the amount of validation stations and the surface that these maps cover. The cloud cover can be very location-specific and interpolating a few point measurements of those stations over the entire surface of the Netherlands is not representative for reality. This casts doubt on the validity of the results but even with this method, the model seemed to validly estimate the global radiation.

One last remark is that in this research, altitude differences were not taken into account. Because the Netherlands is relatively flat, this was considered unnecessary. However, if the model seems to produce less valid results in an area where is

relatively much relief, this might be the explanation. Practical impact

These results demonstrate the usability of the model and provide an example of how this model can be applied. Scientists that investigate meteorological or biological processes in the Netherlands could use this model. If cloud cover data is available in a certain area where global radiation is not measured, this model can be used in the field to provide insight in the amount of global radiation in the area of interest and this can be related to the processes that are examined. This could be applied for instance when investigating whether there is correlation between global radiation patterns and patterns in vegetation within their area of interest.

But the model can also be used for commercial purposes, for instance to predict the yield of solar energy based on weather forecasts regarding cloud cover. Energy companies can anticipate on these predictions and reduce the production of non-renewable energy for periods that high solar radiation is expected. However, this demands that the model has slight deviations compared to the actual global radiation and the timescale on which this information is required is probably the daily

timescale. The standard error of estimate of 20%-25% indicates that the model is probably not capable of providing results that meet these criteria.

Despite this disadvantage, the model is widely applicable for other purposes. Cloud cover data can be measured with certain equipment but can also be based on visual interpretations of an expert and can thus easily be used in the field. However, one important remark is that this model is only calibrated for the Netherlands and for areas outside of the Netherlands the parameters might have to be adjusted again. Also, at this moment only maps for the Netherlands are implemented in the model.

Page 34 of 38 One major disadvantage that limits the possibilities that this model offers, is that the model only works with data that starts at January 1 and ends at December 31. This means that if a potential user decides to employ this model, there should be waited until January 1 before measurements can start, unless the measurements from January 1 until the start of the measurements are specified as missing data.

For understanding several meteorological and biological processes in a certain area, the model is probably suitable. Unless abrupt changes in ecosystems or weather patterns are investigated, expectancy is that data for at least a full year is used for the analysis, due to the timescale on which most changes within these systems occur. Also the monthly timescale, on which this model contends with an acceptable standard error of estimate, is probably be most relevant.

Further research

This research imposed new questions regarding global radiation and to which extent it can be modelled. Also, some recommendations came to mind for further research. Firstly, it should be stated that only Inverse Distance Weighting interpolation is used and other interpolation methods are not tested, while these might provide more accurate results. Inverse Distance Weighting interpolation using radius instead of numbers of neighbours might also decrease the standard error of estimate, or a fixed number of neighbours could be used. This requires more research.

Secondly, in this research, the maps are based on a maximum of 12 stations.

However, because also only the cloud cover can be used as input, stations that do not measure global radiation can also provide data for the maps. The maps can therefore be more detailed. This could also be realised by testing the model with more recent data, because nowadays more stations measure cloud cover and global radiation. However, if more recent data is used the model might behave differently because in this case, the cloud cover data is gathered using measurement equipment instead of visual interpretations. The model can also be tested to see how it performs with this data and optionally choose to calibrate the model again. If parameters are adjusted for this measurement equipment, the model might return a smaller standard error of estimate because human deficiencies are no longer causing potential disturbances. The model might also improve if it is calibrated on the validation stations rather than on the calibration stations as is done in this research. The model produced a smaller standard error of estimate for the validation stations than for the calibration stations, while the model was not specifically calibrated on these stations. If this calibration is performed, the standard error of estimate would probably further decrease. However, this might in general result in a less valid model because these stations are not

equally distributed over the Netherlands and it could be that the model produces better results at their locations by chance. The fact that the percentage of residuals for Leeuwarden is remarkably high supports this statement, but the fact that the

Page 35 of 38 percentage of residuals for Twenthe is relatively small opposes it. For a clear

conclusion about this issue, further research is needed.

The model could also be more extensively evaluated in future research. If for instance a pattern is observed where the model overestimates the global radiation for urban areas, it might indicate that there is a high atmospheric pollution in those areas. Aerosols might scatter a part of the radiation and thus less radiation reaches the surface. Local circumstances like these are not implemented in the model yet. The model can also be used to identify changes over time and for instance the

displacement of seasons due to climate change. Changing weather patterns can easily be related to the global radiation values for certain periods and this might lead to various conclusions.

Page 36 of 38

Conclusions

This research provides a clear impression of to what extent global radiation can be modelled for the Netherlands. Using optimized parameters that also represent realistic values, global radiation can be modelled on a daily timescale as well as on a monthly timescale. However, the degree to which reality is validly approached differs. For days, the model has a standard error of 20%-25% and therefore the model can probably not be deployed for all purposes as indicated in the discussion. For months, a standard error of estimate of 5%-10% has to be taken into account. Despite the adverse results of the Wilcoxon signed rank test, there can be stated that the model functions properly.

Based on the standard error of estimate that the model produced for the calibration and validation stations, it can be concluded that the model produces not only valid results, but that they are also consistent. The results for calibration stations are comparable to those of the validation stations. This indicates that he model probably produces similar results for data from other stations or timescales. Depending on the future research or the practical purposes for which the model is deployed, the model probably produces reliable results.

The maps that are produced by the model are also quite reliable. The differences between the interpolated and measured values amount 0%-6%, depending on the location of interest and the period of time that is researched. This indicates that the maps as well as the model provide a solid basis for further research.

The model can easily be deployed for further research to calculate global radiation for a specific area within the Netherlands. Based on solely a visual interpretation of the cloud cover, reliable global radiation values can be produced. However, the model can probably be improved if it is calibrated using data from more stations. For further calibration, also more recent data can be used that does not cope with human deficiencies, but this will make the model less suitable for use with visual interpretations.

Page 37 of 38

References

Alados, I., Foyo-Moreno, I., Alados-Arboledas, L., 1996. Photosynthetically active radiation: measurements and modelling. Agricultural and forest meteorology

78, 121-131.

Almorox, J., Hontoria, C., 2004. Global solar radiation estimation using sunshine duration in Spain. Energy Conversion and Management, 45 (9-10), 1529-1535.

Chegaar, M., Chibani, A., 2001. Global solar radiation estimation in Algeria. Energy

Conversion and Management, 42 (8), 967-973.

De Boer, H.J., 1960. A calculation of global radiation in the Netherlands with the aid of the relative duration of sunshine. Archiv für Meteorologie, Geophysik und

Bioklimatologie, Serie B, 10 (4), 537-546.

Ehnberg, J.S.G., Bollen, M.H.J., 2005. Simulation of global solar radiation based on cloud observations. Solar energy, 78 (2), 157-162.

Iqbal, M., 1983. An introduction to solar radiation. Toronto: Academic Press Canada.

Klein Baltink, H., Wauben, W., de Haij, M., 2010. Licht op wolken – toepassing van de LIDAR in de meteorologie. KNMI. Retrieved 04-05-2015 from:

http://www.knmi.nl/cms/content/83483/licht_op_wolken__toepassing_van _de_lidar_in_de_meteorologie

KNMI, Hour data from the weather in the Netherlands. Retrieved 08-05-2015, from: http://www.knmi.nl/klimatologie/uurgegevens/selectie.cgi

Liu, B.Y.H., Jordan, R.C., 1960. The interrelationship and characteristic distribution of direct, diffuse and total solar radiation. Solar Energy, 4 (3), 1-19.

Marsh, N., Svensmark, H., 2003. Solar influence on Earth’s climate. Space science

reviews 107, 317-325.

Martín, L., Zarzalejo, L.F., Polo, J., Navarro, A., Marchante, R., Cony, M., 2010. Prediction of global solar irradiance based on time series analysis: Application to solar thermal power plants energy production planning. Solar Energy 84, 1772-1781.

Meza, F., Varas, E., 2000. Estimation of mean monthly solar global radiation as a function of temperature. Agricultural and Forest Meteorology, 100 (2-3), 231-241.

Parker, J., Heywood, D., 1998. The Earth and beyond: developing primary teachers' understanding of basic astronomical events. International Journal of Science

Page 38 of 38 Reddy, R.S., Ranjan, M., 2003. Solar resource estimation using artificial neural

networks and comparison with other correlation models. Energy Conversion

and Management, 44 (15), 2519-2530.

Supit, I., van Kappel, R.R., 1998. A simple method to estimate global radiation. Solar

Energy, 63 (3), 147-160.

Van Boxel JH, 2002. Modelling global radiation for the Portofino area in Italy.

Report Institute for Biodiversity and Ecosystem Dynamics, University of Amsterdam, 21 pp.