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Weather data for building simulation New actual weather files for North Europe combining observed weather and modeled solar radiation Lukas Lundström School of Sustainable Development of Society and Technology Subject: Building Technology Advanced level 15 credits Master program in Energy Optimization for Buildings BTA305 Supervisor: Robert Öman Examiner: Adel Karim Västerås, Sweden, 2012-12-07 DEGREE PROJECT, 15 ECTS School of Sustainable Development of Society and Technology, HST

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Weather data for building simulation

New actual weather files for North Europe combining

observed weather and modeled solar radiation

Lukas Lundström

School of Sustainable Development of Society and Technology

Subject: Building Technology

Advanced level

15 credits

Master program in Energy Optimization for Buildings

BTA305

Supervisor: Robert Öman

Examiner: Adel Karim

Västerås, Sweden, 2012-12-07

DEGREE PROJECT, 15 ECTS

School of Sustainable Development of Society and Technology, HST

2

Summary Dynamic building simulation is increasingly necessary for accurately quantifying potential energy

savings measures in retrofit projects, to compliant with new stricter directives from EU implanted

into member states legislations and building codes. For good result the simulation model need to be

accurately calibrated. This requires actual weather data, representative for the climate surrounding

the given building, in order to calibrate against actual energy bills of the same period of time.

The main objective of this degree project is to combine observed weather (temperature, humidity,

wind etc.) data with modeled solar radiation data, utilizing the SMHI STRÅNG model system; and

transform these data into AMY (Actual Meteorological Year) files to be used with building simulation

software. This procedure gives actual weather datasets that will cover most of the urban and semi

urban area in Northern Europe while still keeping the accuracy of observed weather data. A tool

called Real-Time Weather Converter was developed to handle data retrieval & merging, filling of

missing data points and to create the final AMY-file.

Modeled solar radiation data from STRÅNG had only been validated against a Swedish solar radiation

network; validation was now made by the author with wider geographic coverage. Validation results

show that STRÅNG model system performs well for Sweden but less so outside of Sweden. There

exist some areas outside of Sweden (mainly Central Europe) with reasonable good result for some

periods but the result is not as consistent in the long run as for Sweden.

The missing data fill scheme developed for the Real-Time Weather Converter does perform better

than interpolation for data gaps (outdoor temperature) of about 9 to 48 hours. For gaps between 2

and 5 days the fill scheme will still give slightly better result than linear interpolation. Akima Spline

interpolation performs better than linear interpolation for data gaps (outdoor temperature) in the

interval 2 to about 8 hours.

Temperature uncertainty was studied using data from the period 1981-2010 for selected sites. The

result expressed as SD (Standard Deviation) for the uncertainty in yearly mean temperature is about

1˚C for the Nordic countries. On a monthly basis the variation in mean temperature is much stronger

(for Nordic countries it ranges from 3.5 to 4.7 ˚C for winter months), while summer months have less

variation (with SD in the range of 1.3 to 1.9 ˚C). The same pattern is visible in sites at more southern

latitudes but with much lower variation, and still lower for sites near coast areas. E.g. the cost-near

Camborne, UK, has a SD of 0.7 to 1.7 ˚C on monthly basis and yearly SD of 0.5 ˚C.

Mean direct irradiance SD for studied sites ranges from 5 to 19 W/m2 on yearly basis, while on

monthly basis the SD ranges from 40 to 60 W/m2 for summer months. However, the sample base was

small and of inconsistent time periods and the numbers can only be seen as indicative.

The commonly used IWEC (International Weather for Energy Calculations) files direct radiation

parameter was found to have a very strong negative bias of about 20 to 40 % for Northern Europe.

These files should be used with care, especially if solar radiation has a significant impact of on the

building being modeled. Note that there exist also a newer set of files called IWEC2 that can be

purchased from ASHRAE, these files seems not to be systematically biased for North Europe but

haven’t been studied in this paper.

3

The STRÅNG model system does catch the trend, also outside of Sweden, and is thus a very useful

source of solar radiation data for model calibration.

Keywords: Energy, Building, Simulation, Model, Weather, Data, Actual, Historic, AMY, STRÅNG,

Solar, Radiation, Missing data, Data gaps, Fill scheme, Interpolation, Akima

4

Table of content

Summary .......................................................................................................................................................... 2

Table of content ............................................................................................................................................... 4

Terms and abbreviations .................................................................................................................................. 6

Introduction ............................................................................................................................................. 8 1

Objectives .............................................................................................................................................. 8 1.1

Limitations ............................................................................................................................................. 9 1.2

Methods ................................................................................................................................................. 9 1.3

1.3.1 Formulas used to estimate prediction power ................................................................................. 10

Background ............................................................................................................................................ 12 2

Weather data and energy balance calculation .................................................................................... 12 2.1

2.1.1 Hourly weather data files ................................................................................................................ 13

Solar radiation data by STRÅNG ............................................................................................................. 14 3

Validation ............................................................................................................................................ 14 3.1

3.1.1 Geospatial validation ....................................................................................................................... 15

3.1.2 Temporal validation ........................................................................................................................ 16

3.1.3 Correlation: direct, global and diffuse ............................................................................................. 17

“Real-Time Weather Converter”-software ............................................................................................. 19 4

Data retrieval ....................................................................................................................................... 19 4.1

Data conversion ................................................................................................................................... 20 4.2

4.2.1 Interpolation ................................................................................................................................... 21

4.2.2 Longer data gaps ............................................................................................................................. 21

4.2.3 Testing interpolation and fill schemes ............................................................................................ 22

4.2.4 Time shift ......................................................................................................................................... 23

4.2.5 Diffuse radiation .............................................................................................................................. 24

4.2.6 EnergyPlus and IDA ICE weather files .............................................................................................. 24

Weather data impact and uncertainty ................................................................................................... 26 5

Temperature ........................................................................................................................................ 26 5.1

Solar radiation ..................................................................................................................................... 27 5.2

Testing on an IDA ICE model ................................................................................................................ 31 5.3

ASHRAE IWEC weather files ................................................................................................................... 33 6

Conclusions ............................................................................................................................................ 35 7

Discussion .............................................................................................................................................. 36 8

References ..................................................................................................................................................... 38

5

Appendix A C# sample codes .......................................................................................................................... 40

Appendix A.1 C# method for filling missing data gaps ..................................................................................... 40

Appendix A.2 Part of the method used to load STRÅNG-data from file ............................................................ 41

Appendix B Tables .......................................................................................................................................... 42

Appendix B.1 Geospatial validation results ...................................................................................................... 42

Appendix B.2 Descriptive statistics: mean monthly temperatures [˚C] ............................................................. 44

Appendix B.3 Descriptive statistics: mean monthly solar radiation [W/m2] ..................................................... 45

6

Terms and abbreviations

Global radiation The total of direct and diffuse solar radiation received by a unit horizontal

surface. Also known as total radiation

Direct radiation Solar radiation received directly from the solar disk on a surface

perpendicular to the sun's rays, also known as beam radiation

Diffuse radiation Solar radiation energy falling on a horizontal surface from all parts of the

sky apart from direct radiation. Also known as sky radiation.

Irradiance Incident radiation energy per unit time and area [W/m2]

Irradiation Time integrated irradiance [Wh/m2]

AMY Actual Meteorological Year. Actual (historic) weather data for a specific

location and specific year.

TMY Typical Meteorological Year. Weather data for a specific location artificially

generated from a much longer period of time than a year. Selected so that

it presents the range of weather phenomena, while still giving annual

averages that are consistent with the long-term averages.

SMHI Swedish Meteorological and Hydrological Institute

IWEC International Weather for Energy Calculations weather data files, available

for free. Refers to the IWEC files created in 2000

IWEC2 A new set of International Weather for Energy Calculations weather data

files that can be purchased from ASHRAE

STRÅNG Model system by SMHI that produces instantaneous fields of solar

radiation related parameters

ISD Integrated Surface Database consists of global hourly and synoptic

observations compiled from numerous sources into a single database.

WRDC The World Radiation Data Centre

BSRN Baseline Surface Radiation Network

eKlima Web portal which gives free access to the climate database of the

Norwegian Meteorological Institute

MBD Mean Bias Difference

RMSD Root Mean Square Difference

MAD Mean Absolute Difference

7

SD Standard Deviation

BIM Building Information Modeling is a digital representation of physical and

functional characteristics of a facility

8

Introduction 1The buildings sector accounts for approximately 40 % of the total energy consumption in the

European Union (EU). Therefore, reduction of energy consumption and the use of energy from

renewable sources in the buildings sector are central measures needed to reduce the EU energy

dependency and greenhouse gas emissions. Increased energy efficiency in the EU is emphasized in

order to achieve a 20 % reduction in the EU energy consumption by 2020. In 2010 the EU adopted

the Energy Performance of Buildings Directive (EPBD) 2010/31/EU which is the main legislative

instrument that aims to reduce the energy consumption of buildings. In Sweden it is implemented in

the Swedish building code BBR where BBR 19 was adopted on 1 of January 2012.

In connection with the energy requirement in the Swedish building code a general advice was issued

(Swedish Building Regulation BFS 2011:26) that an energy balance calculation shall be made during

the design of a building, as to verify that the proposed building will meet the requirements. Any

uncertainty in the calculations should be handled by an appropriate safety margin applied so that

there is no risk that the energy requirements are exceeded. With reduced energy consumption due

to stricter legislation and regulation the necessary safety margin increases relatively. This in turn

leads to a need for more accurate energy balance calculations.

Building simulation software are tools that can be used to achieve the higher accuracy demand. To

get good results these software requires accurate weather data. Actual Meteorological Year (AMY)

files are needed for calibration of the building model. This weather data need to accurately represent

the climate surrounding the building during the time that data was collected.

This degree project studies how to obtain AMY-files by combining observed weather data from the

Integrated Surface Database (ISD) with modeled solar radiation data from the modeling system

called STRÅNG developed and run by SMHI (Swedish Meteorological and Hydrological Institute). The

degree project is made as a proof of concept: where a tool called Real-Time Weather Converter was

developed, consisting of following features:

Retrieving data from ISD and STRÅNG databases

Data extraction and merging of data

Data editing in tabular form

Interpolation and a fill scheme for missing data

Creation of AMY-files, supporting IDA ICE and EnergyPlus weather file formats

Generally temperature is the weather parameter with strongest impact on building simulation while

solar radiation has less impact. Observed temperature data exists for most urban locations while

ground observation of solar radiation, particularly direct radiation, is sparse. Using ISD for

temperature data and STRÅNG data for solar radiation gives weather files that will cover most of the

urban and semi urban area in Northern Europe while still keeping the accuracy of observed

temperature data compared to using interpolated values.

Objectives 1.1The main objective is to combine observed weather (temperature, humidity, wind etc.) data with

modeled solar radiation data (from SMHI STRÅNG model system), and to create AMY-files to be used

with building simulation software. To achieve this, following interim targets are set up:

9

Develop a prototype of a tool able to produce AMY-files from observed weather data and

modeled solar radiation from STRÅNG.

Test the tool.

Validate solar radiation data from STRÅNG modeling system for the whole covered

geographic area.

Study uncertainty and impact of weather data parameters on dynamic building energy

simulation.

Limitations 1.2This paper study hourly weather data that are required by dynamic building simulation software,

with focus laid on AMY-files. Other methods for calculating weather data impact on an energy

balance are not considered.

Validation is done on global radiation data from STRÅNG, direct radiation is not validated as there are

too few sources available of observed direct radiation. Validation is done on daily data because of

the “time shift” problem (Chapter 4.2.4) in the hourly data and because there are more sources of

observed daily data available than for hourly data. It is expected that the quality of the daily data also

reflects the quality of hourly data. There are many sources for error in the validation procedure:

Measured solar radiation data used for the validation origin from different sources, there can

be difference in how measurements are performed and how the data are processed.

The measured value is taken as the actual value, but the difference between a measured and

an actual value can in reality be significant. A radiation measurement can be erroneous e.g.

because of incorrect sensor leveling, complete or partial shading, electric field near cables,

station shut-down as well other uncertainty sources like dust, snow, dew and bird droppings.

The modeled values represent an average value of grid area (about 120 km2), while ground

observations are point values.

Other weather parameters from ISD are assumed to be of good quality and are not tested in any

way.

The Real-Time Weather Converter tool is developed as a prototype, meaning that many methods

can/need to be further developed.

Methods 1.3First the tool Real-Time Weather Converter was developed in the Visual Studio 2010 environment

using C# code. This tool was later used to acquire data from STRÅNG and ISD. A “fill algorithm” for

longer data gaps was developed and tested together with three interpolation schemes to determine

which method was best suited for different length of data gaps (Chapter 4.2.3).

For the validation of STRÅNG (Chapter 3.1) global radiation was chosen as there was most data

available for this solar radiation component. But building simulation software use the direct and

diffuse solar components, therefore the relationship between the different solar radiation

components were determined by a correlation study (Chapter 3.1.3). Building simulation software

usually use hourly weather data. But daily mean values were used for the validation because of the

“time shift” problem (Chapter 4.2.4) in the hourly data and because there are more sources of

observed daily data available than for hourly data. The year 2007 was chosen for the geospatial

10

validation as it was the year where there was most data available from all sources. Observed solar

radiation data was gathered from four sources:

Most of the global daily radiation origin from the World Radiation Data Centre (WRDC, u.d.)

using the html web archive for 2007 and earlier and the Java applet for data after 2007 . The

data is given as daily irradiation [J/cm2] and was transformed to daily irradiance [W/m2] by

( ) ( ) ( ) ( ). Quality flags were not considered, meaning that

also data of uncertain quality were included.

For Norway the eKlima (Norwegian Meteorological Institute, u.d.) web portal was used. The

data is given in hourly irradiation [Wh/m2]. Transformation to daily irradiance was done by

summing up all positive values per day and dividing with 24 [h]. Quality flags were not

considered.

For direct radiation component the Baseline Surface Radiation Network (BSRN, u.d.) was

used. Data was retrieved using the PANGAEA (PANGAEA, u.d.) Open Access library’s Data

Warehouse service, where data can be retrieved in minutely, hourly, daily, monthly or yearly

mean values [W/m2].

SMHI provided hourly solar radiation data for Norrköping for the period 2006 to 2007.

Daily and monthly STRÅNG data are arithmetic mean of hourly data acquired by using the Real-Time

Weather Converter tool. The validation calculation was done using formulas described in Chapter

1.3.1, within a Visual Studio C# Excel Workbook, which allowed automation of the otherwise quite

tedious procedure. Only data points where data existed for both observed and modeled data were

included.

As to establish the degree of significance of accurate actual solar radiation and temperature in a

building simulation calibration an uncertainty study was undertaken (Chapter 5), the IBM SPSS

Statistics software was used do acquire the descriptive statistics. Also a study of impact was started

but the real energy consumption data for the used IDA ICE model (Chapter 5.3) was too unreliable to

draw any general conclusion and should more be seen as a test.

In the progress of the work it was recognized that the ASHRAE IWEC files have strong negative bias,

to determine to what degree a short study was undertaken (Chapter 6).

1.3.1 Formulas used to estimate prediction power

Mean Bias Difference (MBD), more commonly known as Mean Bias Error (MBE). The word difference

is used instead for error as the measured (observed) value is not necessary a perfect reference.

∑( )

(1)

Mean Absolute Difference (MAD),

∑| |

(2)

11

Root Mean Square Difference (RMSD) is used to measure accuracy of the model. The difference

(error) occurs because of randomness or because the model doesn't account for information that

could produce a more accurate estimate. Since the difference ( ) is squared, large errors will

have a stronger impact.

[

∑( )

]

(3)

Relative MBD, MAD and RMSD are defined as normalized to the mean of the measured values.

[

∑( )

] [

] (4)

Calculated (modeled) value

Measured (observed) value

Number of counts

12

Background 2Calculations of the energy balance of buildings require a lot of input data that can be classified in

three groups1:

Technology. Building technology with thermal insulation, air tightness, heat capacity, size &

shape of the building etc. Heating and ventilations technology with air flows, heat recovery,

heat pump, time control, demand control, utilization of solar energy, waste heat, natural

heat etc. Efficiency regarding the use of electricity for different purposes in the building.

Human behavior. Has a very strong influence in many ways with different use of hot water

and electricity, different settings for the indoor temperature, different maintenance etc.

Weather data. Outdoor temperature, solar radiation, humidity, wind etc.

When calculating the energy balance there are a lot of uncertainties regarding input data within all

these three groups. This means that the difference can be significant when comparing the results

from calculations with the actual energy use from measurements (readings) of electricity and for

example district heating. All the three groups of input data are important for differences between

calculated and actual energy use.

Weather data and energy balance calculation 2.1There exist several methods to calculate an energy balance for a building that don’t require hourly

weather data. Two methods commonly used in Sweden, heating degree day and a method

developed at KTH (Royal Institute of Technology), are shortly described below:

Heating degree days are defined relative to a base (also called limit) temperature (17˚C is commonly

used the Nordics). This value refers to an imagined “limit” between active and passive heating where

active heating is assumed to reach 17 °C indoor temperature while passive heat on average adds 3 °C

so that 20 °C is achieved indoors. To account for the fact that solar radiation reduces the degree days

a threshold value for the outdoor temperature can be used, this value represents the temperature

above which no heating is needed. In Sweden following threshold values are commonly used: April

+12° C, May – July +10° C, August +11° C, September +12° C and October +13° C (SMHI, 2011). The

monthly heating degree days is calculated as the sum of the difference of the daily mean

temperature and the base value (17˚C), but just for days for which the mean temperatures reaches

below the threshold values.

A method developed at KTH to calculate solar radiation gain through windows by categorizing days

into three groups: clear, semi-clear and overcast days. Tables, based on 30 years of data, give the

amount of each type of day for every month. Expected solar radiation values for the three day types

are given in tables with a resolution of 2 latitude degrees, and for different angles and orientations.

These values are then multiplied with the amount of day type in question, which result in an estimate

of the solar radiation gain through windows in kWh/m2. (Höglund, et al., 1985). The same approach is

utilized in the Consolis Energy+ excel tool developed by Gudni Jóhannesson in 2005.

These two methods are fairly straight forward to use and give reasonable good result. But with

demand for reduced energy consumption in buildings, advances in computer technology and the

1 Personal communication, September 27, 2012, with Robert Öman

13

implementation of BIM the building industry is moving towards using building simulation software

for energy calculation more and more.

2.1.1 Hourly weather data files

Dynamic building simulation software (e.g. IDA ICE and EnergyPlus) uses weather files consisting of

parameter describing the weather, with a temporal resolution of at least one hour. Such a file would

then consist of 8760 rows for every hour of the year, and a number of columns with parameters

describing the weather. An IDA ICE weather file consist of following parameters: time, outdoor air

temperature, humidity, wind direction, wind speed, direct radiation and diffuse radiation. An

EnergyPlus weather file consists of 35 parameters, but not all are actually used and the parameters

above are enough for creating a usable weather file.

In the Nordics temperature is regarded as the weather parameter with strongest influence on an

energy balance followed by solar radiation (Jylhä & et.al., 2011). Humidity has impact mainly if the

outdoor air needs to be cooled under the dew point temperature, which seldom is the case in north

Europe. Local wind speed and wind direction around a building can be different from that of the

nearest observation station, but their influence on whole are considered relatively low2.

Whether data files can be classified in three main classes:

Typical Meteorological Year (TMY). Typical weather data representative of some specific site

over a longer period of time (e.g. 30 years) and consists of months selected from individual

years, concatenated to form a complete year. These weather data files are used for design

and performance conditions over the life of a building. For north Europe so called IWEC files,

produced by AHRAE in 2000, are commonly used.

Actual Meteorological Year (AMY). Actual weather data of a specific location and specific

year (also other time spans can be used). These are used for model calibration to actual

energy bills for the same period of time.

Future (forecast) weather data used for adaptive control of buildings.

This paper focus on AMY-data. There exist many stations observing temperature, humidity and wind

parameters but ground observation of solar radiation (particularly direct radiation) are limited to a

few station. Solar radiation data for a location that lack observed data can be acquired by:

Using data from a nearby station. Often nearest station is far away and/or at a site with

different geographical conditions.

Interpolate data from nearby stations. Difficult to account for differences in geographical

conditions.

Modeled using ground observation of cloudiness. Station network observing clouds have

been denser than solar radiation station networks.

Modeled using satellite data.

The STRÅNG model system calculates radiation by using cloud information acquired from ground

observation and satellite data, see Chapter 3 for more details.

2 Personal communication, September 27, 2012, with Robert Öman

14

Solar radiation data by STRÅNG 3Figure 1. Map of the geographic area covered in the STRÅNG model since June 2006, prior to that the deep green colored area was not covered. (SMHI, u.d.)

The STRÅNG model system produces

instantaneous fields of global-, photosynthetically

active- (PAR), UV- and direct radiation together

with sunshine duration at a horizontal resolution

of about 11 x 11 km and a temporal resolution of

one hour. Input data to the model are retrieved

from the mesoscale analysis system at SMHI

(Swedish Meteorological and Hydrological

Institute) called MESAN, a high resolution limited

area numerical weather prediction model (NWP)

called HIRLAM, an ice model for the Baltic Sea

(BOBA) together with satellite measurements of

total ozone (TOMS). Before 1 of June 2006 the

area coverage was smaller (colored area in Figure 1) and the spatial resolution was about 22 x 22 km.

Clear-sky condition is modeled with the spectral clear-sky model SMART2. The output is then

multiplied by a neural network function which captures the influence of clouds and precipitation. The

cloud information from MESAN is a synthesis of data from both polar (NOAA) and geostationary

(METOSAT) satellites as well as ground based observations. For more information about the STRÅNG

model readers are referred to (Landelius, et al., 2001) and (SMHI, u.d.)

Validation 3.1Table 1 shows the mean validation values for the period 1999 to 2009 at the 12 of the stations in the

SMHI radiation network, as presented on the STRÅNG homepage (SMHI, u.d.).

Table 1. Normalized relative MBD, MAD and RMSD at the 12 of the stations in the SMHI radiation network, for the period 1999-2009 (SMHI, u.d.)

Global radiation Direct radiation

Hourly MBD -0.2 % -0.4 %

Hourly MAD 2.1 % 3.5 %

Hourly RMSD 30 % 57 %

Daily MBD -0.2 % +0.5 %

Daily MAD 2.1 % 3.2 %

Daily RMSD 16 % 31 %

Monthly MBD +1.3 % +1.3 %

Monthly MAD 2.3 % 3.3 %

Monthly RMSD 8.9 % 14 %

To validate the model outside Sweden, a study was conducted comparing modeled data from

STRÅNG with observed data. Source of for the observed data are The World Radiation Data Centre

(WRDC, u.d.), Baseline Surface Radiation Network (BSRN, u.d.) and eKlima (Norwegian

Meteorological Institute, u.d.).

15

3.1.1 Geospatial validation

Daily global radiation from the STRÅNG model was compared with observed values; the year 2007

was selected as there was most data available for this year. To visualize the variation due to

geographical difference the result was mapped to Google Earth. Figure 2 shows relative MBD and

RMSD. The validation data are also available in more detail in Appendix B.1. The maps clearly shows

that there the accuracy and bias varies quite much geographically. Sweden got the best result

considering both MBD and RMSD. There are some areas (most of central Europe, east England and

south of Finland) where the model performs quite well when looking on the RMSD but with a

negative bias. Stations near the coast of the Atlantic and North Sea all show high RMSD values and

significant negative bias. The Baltic countries and northern part of Finland show the worst result with

all stations strongly negatively biased and a RMSD over 30%. High altitude stations also show worse

result.

Figure 2. Daily global radiation validation figure, year 2007. Relative MBD represented by white numbers and relative RMSD by purple. All values are in percentage. Note that some labels are overlapping resulting in that all values aren’t visible. The validation data are available in more detail in Appendix B.1.

16

3.1.2 Temporal validation

A few stations were selected for a long term validation. The selection was done based on data

availability and with the aim of getting a geographic spread.

Figure 3. Upper: Relative MBD for daily global radiation normalized on yearly basis. Lower: Relative RMSD for daily global radiation normalized on yearly basis. Both: Stations with similar geographical condition (subjectively considering both local conditions and in-between station distance) have same “line appearance” in the figure.

As can be seen in Figure 3 there’s a quite decrease in performance around year 2010, according to

Tomas Landelius3 at SMHI there was a problem with the analysis of cloud related parameters for the

period 2009 to 2011 (30/3). If this period is not considered it is clear that the Swedish station of

Stockholm shows the most consistent and reliable result. Also the Finnish stations of Jokionen and

3 Personal communication, August 28, 2012

0%

5%

10%

15%

20%

25%

30%

35%

40%

45%

50%

1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012

Stockholm Helsinki Jokioinen Særheim Praha Wien

Lerwick Aberdeen Cabauw De Bilt Toravere

-30%

-25%

-20%

-15%

-10%

-5%

0%

5%

10%

15%

20%

1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012

17

Helsinki shows reasonable consistent result but with an allover negative bias. In about 2005 the bias

seems to get more negative, especially for the Central European and British stations.

3.1.3 Correlation: direct, global and diffuse

Building simulations software like IDA ICE and EnergyPlus uses the direct and diffuse components of

solar radiation. But as there are few source of observed direct radiation the validation was conducted

on global radiation. A correlation study was made on a few stations with data available for all three

solar radiation components: direct, global and diffuse radiation.

Figure 4. Relative RMSD normalized on yearly basis for direct, global and diffuse radiation for Toravere. Visualizing how the solar radiation components correlate.

Figure 5. Relative RMSD normalized on yearly basis for direct, global and diffuse radiation for Lerwick and Cabauw.

As can be seen in Figure 4 and Figure 5 there’s a correlation between RMSD results of the different

radiations components. The correlation coefficient for global and direct radiation is 0.90, 0.72 and

0%

10%

20%

30%

40%

50%

60%

70%

1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012

Direct Global Diffuse

0%

10%

20%

30%

40%

50%

60%

70%

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013

Cabauw direct Cabauw global Cabauw diffuse

Lerwick direct Lerwick global Lerwick diffuse

18

0.24 for the stations Toravere, Cabauw and Lerwick respectively. And for global and direct radiation

it is 0.37, 0.76 and 0.56 in same order as above.

Figure 6. Relative RMSD normalized on monthly basis for direct, global and diffuse radiation for Norrköping.

The Norrköping station was studied by normalizing the RMSD on monthly basis. The correlation

coefficient for global and direct radiation is 0.73 for the studied period 2006 to 2007. And for global

and diffuse radiation the correlation is 0.43. It can also be seen in Figure 6 that the relative RMSD

gets much higher during the winter, which is expected as the monthly mean value used for

normalization gets lower during winter leading to a higher relative error.

0%

20%

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jan

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Direkt Global Diffuse

19

“Real-Time Weather Converter”-software 4As part of this degree project a tool was developed to demonstrate how locally observed weather

data can be merged with modeled solar radiation data to create AMY-files. The tool retrieves

weather data from Integrated Surface Database (ISD) and modeled solar radiation data from

STRÅNG. Supported weather file formats are EnergyPlus EPW and IDA ICE PRN formats. The tool is

programmed in C# making use of the .NET Framework. The tool features:

Retrieving data from ISD and STRÅNG databases

Data extraction and merging of data

Data editing in tabular form

Interpolation and a fill scheme for missing data

Creation of AMY-weather files, supporting IDA ICE and EnergyPlus weather file formats

Figure 7. Main user interface of the Real-Time Weather Converter tool. Tool version 1.6.

Data retrieval 4.1Actual metrological data are retrieved from ISD: air dry-bulb temperature, dew point temperature,

wind speed, wind direction and atmospheric pressure. ISD consists of global hourly and synoptic

observations compiled from numerous sources, into a database supported by The National Climatic

Data Center of USA. ISD data have been quality checked by algorithms checking for: proper data

format for each field, extreme values/limits, consistency between parameters, and continuity

between observations. (National Climatic Data Center, 2012).

3198 stations from the ISD are included, but not all of these stations have enough information to

make a useful weather file. There are differences from country to country; stations from some

1. Select ISD station

8. “Additional" data according to WMO resolution 40. For some countries this might make data allowable for commercial use.

2. Select station by WMO number

3. End date for available data according to last update

4. Link to interactive station map

5. Choose dates to retrieve, edit and convert data for

6. Starts retrieving STRÅNG using selected station geographic coordinates. This is time consuming, so be patient

7. Retrieves weather observation data from ISD for selected station

9. Start automatic conversion to IDA ICE or EnergyPlus weather file format.

10. Loads ISD and STRÅNG data for selected period for viewing, editing and conversion to desired format.

20

countries (e.g. Germany) lack recent data while other (e.g. Sweden and UK) have data from most

available stations. Stations are very roughly filtered with following criteria’s:

Geographic area (Figure 1 shows area that is included).

Only stations that have data in-between 1999 to current date are included.

Stations with missing information on longitude, latitude, date, WMO-number and FIPS are

excluded.

Modeled solar radiation data are retrieved from STRÅNG, see chapter 3 for more details. Figure 7

shows the main user interface of the tool (version 1.6) where the retrieval of data are handled,

Figure 8 shows the user interface where the merging and interpolation of data are done and AMY-

weather files created. The data are presented as tables and can be copied and pasted, allowing for

extraction of data insertion of data from other sources. Data can also be shown as monthly or daily

mean values.

Figure 8. User interface for data editing and creation of AMY-weather files.Tool version 1.6.

Data conversion 4.2Raw data from the ISD and STRÅNG is loaded into the software, adjusted to local time determined by

information from selected station. STRÅNG data can be loaded either raw as “on the hour” or shifted

(interpolated) half an hour backwards.

20. In the “Interpolated”-tab data are shown after has been interpolated. The time step is now evenly spaced.

21. Same as in “Raw Data”-tab but now interpolation is only done on selected columns.

23. Fill-scheme for longer data gaps: takes the trend of the first previous and/or next day that is valid and offset it by the values that surround the missing data to smooth the filled data. Suits weather parameters with a diurnal pattern.

22. Start conversion to EnergyPlus or IDA ICE weather file formats.

21

4.2.1 Interpolation

Data gaps are identified and interpolated by selected method. Supported methods are Linear Spline,

Cubic Spline and Akima Spline. For the actual interpolation algorithms the open source Math.NET

Numerics library is used (Math.NET, 2012).

Interpolation also serves the purpose of getting data to wanted timestamp (re-sampling). For

example if you have data for 12:20 and 12:50 (which often is the case for airports) you could

interpolate this to 12:00 or to 12:00 and 12:30.

4.2.2 Longer data gaps

If there are longer periods of missing data, these are filled by taking the trend of the first previous or next day that is valid and offset it by the values that surround the missing data to smooth the filled

data, see equation (5). A similar method is used by EnergyPlus Real-Time Weather Data website (Long, 2006). The idea is that many meteorological parameters have a diurnal pattern that this method is able to catch thus giving better result than simple interpolation.

( ) ( ) ( ( ) ( ))

(( ( ) ( )) ( ( ) ( ))

)

(5)

( ) is the time step to fill.

( ) ( ) are the values around the missing data points.

d is the offset back to or forward to previous valid day, that’s a …,-48, -24, 24, 48,… hour offset.

n is actual position.

Appendix A.1 shows the C# method used for filling data gaps taking the trend from the previous day.

Both forward and backward methods are run and then the result is mixed together to get one final

estimate. If one of the forward or backward methods fail due to missing data, the result from the

other one is used. Three different methods to mix (and no mixing) the values were tested and the

result is presented in Table 2, mixing 50/50 gives the best result and is therefore used in the tool.

Hard mixing:

( ) ( ) ( ) ( )

( )

( )

(6)

Soft mixing:

( ) ( ) ( ) ( ) ( )

(7)

50/50 (linear interpolation):

22

( ) ( ) ( )

(8)

N is the number of missing data points.

Table 2. Result from testing different mixing methods.

Data gap (hours)

N Hard, MBD

Soft, MBD

50/50, MBD

Non, MBD

Hard, RMSD

Soft, RMSD

50/50, RMSD

Non, RMSD

7-12 10651 0.0% 0.0% 0.0% -0.1% 20.19% 19.75% 19.3% 20.9%

13-24 17375 -0.5% -0.4% -0.3% -0.2% 27.8% 27.0% 26.3% 30.6%

25-48 25075 -1.3% -1.3% -1.1% - 41.1% 38.3% 37.8% -

49-72 19540 0.8% 0.8% 0.9% - 55.6% 52.2% 47.8% -

4.2.3 Testing interpolation and fill schemes

Three interpolation schemes from the Math.NET Numerics (Math.NET, 2012) open source library

were tested: Linear, Cubic and Akima Spline. Also the fill-scheme described in chapter 4.2.2 was

tested. Figure 9 shows graphically how the different schemes fill data gaps of 7 to 12 hours.

Figure 9. Missing data point filled by different interpolation and fill scheme methods. Data gaps are 7 to 12 hours. Original data is air dry-bulb temperature from springtime 2007 Stockholm/Arlanda.

Date used for the test was air dry-bulb temperature for Stockholm-Arlanda for the period 2007 to

2011. The testing was done by estimating artificial created data gaps, which were randomly

distributed over the dataset so that there was 25-28 hour of real data between the gaps, following

Mathlab function was used for the purpose:

function [Out,NaNs]= FillWithNaNs(Table,n1, n2) Out=Table; i=2; NaNs=0; while i<43824-(n2+3) % random number between n1 and n2 r=round(n1 + (n2-n1) * rand(1)); Out(i+1:i+r)=NaN; i=i+r;

0

5

10

15

20

25

Tem

pe

ratu

re (

˚C)

Time (hour)

LinearCubicAkimaFillReal temp

23

NaNs=NaNs+r; % random number between 25 and 28 r=round(25 + (28-25)*rand(1)); i=i+r; end end

Table 3 shows result of the first test, where data gaps are randomly selected between specified

intervals. In Table 4 data gaps are not varied in size, the purpose is to find the limits where different

schemes give best result. The result implicate that the Akima Spline interpolation is best suited for

temperature data gaps in the interval 2 to about 8 hours. For gaps of about 9 to 48 hours the fill

scheme clearly gives best result. For gaps between 2 and 5 days the fill scheme will still give slightly

better result than simple linear interpolation. As the fill scheme will preserve the diurnal

characteristics of meteorological parameters, e.g. temperature, it will most likely give a more

accurate result when used for dynamic building simulations than linear interpolation.

Table 3. MBD and RMSD for different schemes tested on artificially created data gap intervals

Data gap (hours)

N Linear, MBD

Cubic, MBD

Akima, MBD

Fill, MBD

Linear, RMSD

Cubic, RMSD

Akima, RMSD

Fill, RMSD

2-6 4512 0.4% 0.5% 0.5% 0.5% 12.1% 11.6% 10.7% 12.3%

7-12 10651 0.1% 0.0% 0.1% 0.0% 24.8% 21.4% 19.6% 20.2%

13-24 17375 -1.2% -0.4% -0.9% -0.5% 46.6% 46.2% 42.7% 27.8%

25-48 25075 -1.6% -2.6% -2.0% -1.3% 50.7% 99.4% 63.0% 41.1%

49-72 19540 -2.0% -7.5% -2.6% 0.8% 55.9% 153.7% 88.8% 55.6%

73-96 33207 1.1% -3.7% -0.6% -0.9% 56.2% 198.1% 107.8% 52.6%

97-120 35200 -3.5% - - -0.7% 58.7% - - 58.9%

121-144 36442 -2.0% - - 5.1% 62.1% - - 64.2%

Table 4. MBD and RMSD for different schemes tested on artificially created data gaps.

Data gap (hours)

N Linear, MBD

Cubic, MBD

Akima, MBD

Fill, MBD

Linear, RMSD

Cubic, RMSD

Akima, RMSD

Fill, RMSD

2 1594 0.1% 0.1% 0.1% 0.1% 6.5% 6.7% 6.2% 6.5%

3 3074 -0.4% -0.4% -0.3% -0.4% 8.1% 8.7% 7.7% 8.9%

8 10152 - - -0.5% -0.6% - - 18.5% 18.7%

9 10168 - - 0.0% 0.1% - - 18.6% 18.0%

11 12010 - - 0.0% -0.3% - - 22.5% 21.3%

4.2.4 Time shift

STRÅNG values are in irradiance [W/m2], with other words instantaneous, and refer to the full hour

(Landelius, et al., 2001). For weather data files used in building simulation software time integrated

irradiation [Wh/m2] values are used: amount of solar radiation during the number of minutes

preceding the time indicated (EnergyPlus, 2011). In other words the value for 14.00 o’clock refers to

the average value of the interval from 13.00 to 14.00 o’clock.

If trapezoidal integration is applied, and linear interpolation is used for getting the ( ) term, it will

turn out as a simple linear interpolation as can be seen in equation (9).

24

( ) ( ) ( ( )

( )

( )

)

( ) ( ( )

( ( ) ( ))

( )

)

( ) ( ) ( )

(9)

The effect of the time shift was tested on hourly global data from Wien Hohe Warte for the year

2007, source WRDC. The relative MBD was not affected by the time shift, relative RMSD changed

from 41.9 % to 36.3 %, the relative RMSD between shifted and unshifted (on the hour) STRÅNG data

was 27.0 %. Also using Akima Spline interpolation instead of linear interpolation in equation (10) was

tested, but did not give better result than linear interpolation. Table 5 shows the result as the

correlation between the tested methods.

Table 5. Correlation values of tested methods

Measured WRDC

STRÅNG On the hour

STRÅNG Shifted (linear)

STRÅNG Shifted (Akima)

Measured WRDC 1

STRÅNG On the hour 0.9675 1

STRÅNG Shifted (linear) 0.9754 0.9864 1

STRÅNG Shifted (Akima) 0.9754 0.9864 0.9999 1

4.2.5 Diffuse radiation

At present STRÅNG provides direct and global radiation, the diffuse horizontal radiation needed for

energy simulations is calculated by using the equation (10).

( ) (10)

The elevation of the sun is calculated from information about the local time, longitude and latitude.

Appendix A.2 shows a part of the C# method used to calculate diffuse horizontal irradiation, also the

linear interpolation to shift solar data with a half hour is included in that code sample. There will be

some error introduced at this point due to difference in methods for calculating the solar elevation.

The STRÅNG model does model the diffuse irradiance parameter as well but it’s not available at the

data extraction webpage at present time.

4.2.6 EnergyPlus and IDA ICE weather files

When data have been interpolated to right timestamp (re-sampled) and data gaps are filled,

conversion to EnergyPlus or IDA ICE weather files format is possible. For conversion to EnergyPlus

EPW file format the library file EPlusWth.dll supplied by EnergyPlus is used. Conversion to IDE ICE

PRN file format is done in the software. To calculate the relative humidity from dry-bulb and dew

point temperature following C# code, based on the Clausius-Clapeyron equation, is used:

public static double Humidity(double T, double Tdp) { // RH = relative humidity

25

// T = dry-bulb temperature in Celsius // Tdp = dew-point temperature in Celsius double E = 6.11 * Math.Exp(5417 * (0.003653 + 1 / (Tdp + 273.15))); double Es = 6.11 * Math.Exp(5417 * (0.003653 + 1 / (T + 273.15))); double RH = (Es / E) * 100; if (RH > 100) return 100; else if (RH < 0) return double.NaN; else return Math.Round(RH, 1); }

26

Weather data impact and uncertainty 5In Nordic countries outdoor air temperature is the most important factor for common building

energy simulations, but during summertime solar radiation has an equal influence (Jylhä & et.al.,

2011). Other parameters like humidity, atmospheric pressure and wind have much smaller impact on

the simulation result and therefore only temperature and solar radiation were studied.

Temperature 5.1Long timeseries of monthly mean temperatures were extracted from the ISD using the Real-Time

Weather Converter tool. Figure 10 shows the monthly and yearly mean temperatures and 2*

Standard Deviation (SD) for selected stations for the period 1981-2010. For northern stations Kevo-

Utsjoki, Stockholm and Tartu-Toravere the yearly SD is around 1˚C which is in line with what Lars

Jensen’s study (Jensen, 2010) resulted in using temperature data from 25 Swedish stations. These

northern stations also show the large monthly variation, especially for winter months. For the

southernmost stations Payerne, Camborne and Cabauw the yearly SD is much lower (0.5 to 0.8 1˚C)

and the monthly variation smaller.

A SD of 1˚C means that in two of three years the mean temperature will be in the interval Tmean ± TSD.

Using Tmean ± 2*TSD gives the mean temperature interval with a 95 % confidence, assuming normal

distribution around the mean value. With other words: to predict the mean temperature for January

for Tartu with a 95 % confidence would give -4.5 ± 8.2˚C, assuming normal distribution around the

mean value (which is not the case as the Skewness is -1.56 and Kurtosis is 2.28 indicating a long and

thin left tail in the distribution). While predicting January mean temperature for the coast near

Camborne with 95 % confidence would give 6.9 ± 3 ˚C, again assuming normal distribution (which is

almost the case with Skewness of -0.9 and Kurtosis of 0.1)

Appendix B.2 contains more descriptive statistics in tabular form for the selected stations. From this

table more trends can be seen. For example Skewness tends to be positive (right tailed) during

summer months and negative (left tailed) during winter months for all stations. This indicates that

there are winters when the mean temperature drops much under the mean and summers when the

mean temperature is much higher than the long term mean.

The outdoor temperature (or more exactly the difference between outdoor and indoor temperature)

is the driving force for heat transfer occurring in a building, and therefore outdoor temperature is

one of the parameters having the strongest impact on a dynamic building energy simulation. How

strong the impact is depends on what kind of building that is being modeled and of course of the

outdoor temperature itself. For example a residential house with low internal gains and high

envelope area volume ratio (Aenvelope/Vbuilding) the outdoor temperature will have large impact while a

large commercial building with high internal gains and low envelope area volume ratio the impact

will be relatively smaller.

27

Figure 10. Monthly and yearly mean temperatures (circles) and 2*standard deviations (bars) for the period 1981-2010.

Solar radiation 5.2Using measured solar radiation data from the BSRN, extracting monthly means using the PANGAEA

web portal (PANGAEA, u.d.), a study was made on a few stations with longer period of data. Figure

11 to Figure 15 shows the result as error charts giving the monthly mean and 2*SD values for all

three radiation components. The period studied is constrained to data availability and differs from

station to station, therefore making comparisons between stations problematic. Appendix B.3

contains a more detailed table with descriptive statistics for selected stations.

It can clearly be seen from the figures that the variation is much smaller for diffuse than for direct

radiation. The yearly SD for studied stations is in the range 1.0 to 1.9 W/m2 for the diffuse radiation

and 5.0 to 17.9 W/m2 for the direct radiation component, given in Relative Standard Deviation (RSD)

28

the values are 1 % to 4 % and 5 % to 9 %. In absolute values the SD is larger for summer month, as

expected as solar radiation is stronger during summer. But the relative SD (RSD) is actually slightly

larger for winter months, as can be seen in Figure 11 showing RSD for the direct radiation

component.

Figure 11. Monthly and yearly mean direct radiation RSD.

To predict the mean July direct radiation for Tartu with a 95 % confidence would give 223 ± 114

W/m2. While on yearly basis the direct radiation for Tartu can be predicted as 120 ± 11 W/m2 with 95

% confidence. With other words uncertainty is high on monthly basis while the yearly mean radiation

don’t vary that much.

Looking at Skewness and Kurtosis for all studied stations indicates that the solar fits a normal

distribution reasonable well, even though a slight tendency to negative Kurtosis on yearly basis for

direct radiation can be seen indicating that the observation cluster less and have thicker tails until

the extreme values of the distribution.

0%

10%

20%

30%

40%

50%

60%

70%

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Year

Lindberg Tartu-Toravere Cabauw Payerne

29

Figure 12. Monthly and yearly mean solar radiation (circles) and 2*standard deviations (bars). Tartu-Toravere 1999-2011.

Figure 13. Monthly and yearly mean solar radiation (circles) and 2*standard deviations (bars). Lindenberg 1994-2005.

30

Figure 14. Monthly and yearly mean solar radiation (circles) and 2*standard deviations (bars). Cabauw 2005-2012.

Figure 15. Monthly and yearly mean solar radiation (circles) and 2*standard deviations (bars). Payerne 1993-2009.

Impact of solar radiation on dynamic building simulation depends on what kind of building (i.e.

window area, solar energy applications, building heat capacity) is being modeled and at what

outdoor temperature the solar radiation occurs. Depending on the outdoor temperature the solar

radiation either contributes to the heating of the building, cause need for cooling or neither. Figure

16 shows the cumulative sum of yearly irradiation as a function of temperature for three selected

sites.

31

Figure 16. Cumulative sum of yearly irradiation [kWh/m2] as a function of temperature. Based on data for the period

2006-2007.

Testing on an IDA ICE model 5.3The IDA ICE model used for testing is based on a three story 1450 m2 office building located in

Västerås, Sweden. The building was built in 1982 and renewed in 1990 and is quite typical Swedish

office building with energy consumption in the lower end compared to other Swedish offices. It has

district heating, air-to-air cooling, central ventilation with heat recovery and 60 h/week operation

time. The building and the model is described in more detail in the report “Energy simulation of a

mid-sized office building” (Lundström, 2012).

Table 6. Comparison between climate files. The relative difference towards the TMY-file is given in the brackets.

Weather file Air tempera-ture [˚C]

Relative humidity [%]

Direction of wind [deg]

Wind speed [m/s]

Direct radiation [W/m2]

Diffuse radiation [W/m2]

TMY Stockholm (Arlanda), ASHRAE

6.5 78 - - 89 59

Stockholm-77 (Bromma)

6.2 (-5%) 78 178 3.3 106 (20%) 58(-3%)

AMY-2010 Stockholm (Arlanda)

5.1 (-22%) 81 192 3.1 131 (47%) 46 (-22%)

AMY-2011 Stockholm (Arlanda)

7.8 (20%) 79 202 3.4 135 (52%)

56 (-5%)

AMY-2010 Västerås 4.6(-29%) 80 186 3.0 113 (27%) 48 (-17%)

AMY-2011 Västerås 7.5 (15%) 76 200 3.6 120 (36%) 58 (-2%)

IDA ICE provides two weather files for Stockholm (about 80 km east of Västerås). A TMY based on

weather data from Arlanda airport, source being ASHRAE IWEC weather files which are the same files

32

that are provided by EnergyPlus. And a so called typical reference year weather file for Bromma

airport, the reference year being 1977. Four AMY-files were made with the Real-Time Weather

Converter tool, for the years 2010 and 2011. Table 6 shows mean yearly values for the weather

parameter in the files. From the STRÅNG-model validation chapter 3.1 it’s clear that the model has a

slight negative bias (especially for year 2010), so the real solar radiation will much likely be

somewhat larger than presented in the table. Note that the ASHRAE IWEC TMY weather file has a

very low direct radiation value. It’s clearly some fault with this file, Chapter 6 studies the IWEC

weather files in more detail.

Table 7. Comparison of results from simulations with different climate files. The relative difference towards the TMY-file is given in the brackets.

Electricity for cooling [kWh/m2]

Total electricity [kWh/m2]

District heating [kWh/m2]

Total energy Consumption [kWh/m2]

TMY Stockholm (Arlanda), IWEC

5.4 67.9 61.3 129.2

Stockholm-77 (Bromma)

5.5 (1.9%) 67.8 (-0.1%) 60.1 (-2.0%) 127.9 (-1.0%)

AMY-2010 Stockholm (Arlanda)

7.3 (35.2%) 69.6 (2.5%) 71.4 (16.5%) 141.0 (9.1%)

AMY-2011 Stockholm (Arlanda)

8.0 (48.1%) 70.3 (3.5%) 51.6 (-15.8%) 121.9 (-5.7%)

AMY-2010 Västerås 6.0 (11.1%) 68.3 (0.6%) 74.4 (21.4%) 142.7 (10.4%)

AMY-2011 Västerås 7.2 (33.3%) 69.5 (2.4%) 53.1 (-13.4%) 122.6 (-5.1%)

Table 7 shows results from simulations with different climate files. If we look at the simulations done

with the TMY and Stockholm-77 weather file we can see that the heating need is slightly less for

Stockholm-77, which most likely is caused by the slightly lower mean temperature. But the cooling

need is higher which most likely is caused by the lower mean solar radiation for the TMY file.

The differences in result for the AMY-file vs. the TMY-files are large, which to most extent can be

deduced to the fact that the year 2010 was an unusually cold year and 2011 was an unusually warm

year. Comparing result from the “AMY-2011 Västerås”-file with the “AMY-2011 Stockholm”-file

shows that heating demand was 3% higher and the cooling need 10% lower for Västerås. This shows

the impact the weather has, as the yearly mean temperature was 4% lower and the yearly mean

solar radiation was 10 % lower in the “AMY-2011 Västerås”-file. The total energy consumption,

however, stays quite the same as the two weather parameters in this case work in different

directions.

It’s difficult to draw general conclusion of the impact on the energy consumption from climate

parameters as they are interlinked and impact energy consumption in many ways depending on

circumstances. Impact will vary for building to building depending on design, location and season.

33

ASHRAE IWEC weather files 6The building simulation software IDA ICE and EnergyPlus provides so called IWEC4 (International

Weather for Energy Calculations) weather files and were produced by AHRAE in 2000. These are

TMY-files derived from up to 18 years of hourly weather data. The weather data are supplemented

by solar radiation estimated on an hourly basis from earth-sun geometry and hourly weather

elements. (EnergyPlus, 2011).

The radiation components of the IWEC files were compared against STRÅNG data because observed

direct radiation data sources are rare. Sites that are selected for the comparison are stations that

showed good bias- and RMSD-values in the validation made in Chapter 3.1. Comparison against

observed BSRN radiation data was also done for two sites, and also against the TRY2012 file for

Helsinki-Vantaa.

Table 8. Comparison of ASHRAE IWEC weather files yearly mean radiation with radiation from STRÅNG and BSRN. *1

BSRN data for Paris-Palaiseau 2004-2006. *2

BSRN data for Lindenberg 1995-2005, 50 km east of berlin. *3

TRY2012 for Helsinki-Vantaa (Jylhä, et al., 2011).

*4 This weather file don’t include all diffuse radiation (Jylhä, et al., 2011)

Site Difference ASHRAE STRÅNG 2007 STRÅNG

global MBD Direct Diffuse Direct Diffuse Direct Diffuse

Stockholm -33% 5% 88.9 59.6 132 57 1%

Helsinki -26% 16% 81.3 64.7 110 56 -8%

Göteborg -28% 12% 84.3 66.3 117 59 -1%

Karlstad -20% 10% 107 58.2 134 53 -5%

Östersund -26% 6% 88.9 58.2 120 55 -1%

Paris-Orly -25% 3% 77.5 76.3 103 74 -5%

Oostende -17% -5% 85.1 69.5 103 73 -2%

Berlin -24% -6% 80.3 66.8 105 71

Wien -30% -12% 93.1 71.6 133 81 5%

Hamburg -22% 7% 70.6 69.7 91 65 -3%

Aberdeen -37% 17% 55.1 70.3 87 60 -8%

Site Difference ASHRAE Other STRÅNG

global MBD Direct Diffuse Direct Diffuse Direct Diffuse

Paris-Orly*1 -39% 3% 77.5 76.3 127 74 -5%

Berlin*2 -27% 3% 80.4 66.9 110 65 -9%

Helsinki*3 -37% 32%*4 81.3 64.7 129 49

Table 8 shows the result from the comparison. Recall the STRÅNG validation in Chapter 3.1 that

showed that STRÅNG data also are somewhat negatively biased. STRÅNG data are only validated

against global radiation but as result presented in chapter 3.1.3 demonstrates there is a strong

correlation between errors occurring in STRÅNG global and direct radiation data. The STRÅNG data

are only for one year while the IWEC is TMY file constructed from 18 years of data which also affects

the result. The comparison against BSRN data is more reliable and shows even higher negative bias.

4 Note that there exist also a newer set of files called IWEC2 that can be purchased from ASHRAE, these files

seems not to be systematically biased for North Europe but haven’t been studied in this paper. See Chapter 8 for a short description of the IWEC2.

34

Taking all above mentioned in consideration it’s apparent that the IWEC files direct solar radiation

component has a strong negative bias, roughly ranging in-between 20 to 40 % for selected sites.

35

Conclusions 7The main conclusion is that solar radiation data from the STRÅNG modeling system are suitable for

calibration of building simulation models. For some areas the data would also be suitable for creation

of TMY-files and for other energy engineering applications.

For Sweden STRÅNG data are accurate and have low bias, both in long term and

geospatially.

Outside of Sweden the STRÅNG accuracy is in general poorer and bias higher. There exist

some sites (mainly in Central Europe) with reasonable good result for some time periods but

the result isn’t as consistent in long term as for Sweden.

It’s difficult to draw general conclusion of the impact on the energy consumption from climate

parameters as they are interlinked and impact energy consumption in many ways depending on

circumstances. Impact will vary for building to building depending on design and location. Weather

data uncertainty is, however, easier to study:

Uncertainty, expressed as SD, in yearly mean temperature is about 1˚C for the Nordic

countries. The SD gets smaller for sites at more southern latitudes and for coast-neat sites:

0.6 ˚C for Payerne, Switzerland, and 0.5 ˚C for Camborne, UK.

On monthly basis the variation in mean temperature is much stronger, especially for

northern and inland sites. The Nordic countries mean temperature SD ranges from 3.5 to 4.7

˚C for the winter months, while the summer months are more consistent with SD in the

range of 1.3 to 1.9 ˚C. The same pattern is visible in site at more southern latitudes but with

much lower variation, the cost near Camborne has a SD of 0.7 to 1.7 ˚C on monthly basis.

Mean direct irradiance SD for studied sites ranges from 5 to 19 W/m2 on yearly basis. While

on monthly basis the SD ranges from 40 to 60 W/m2 for summer months. However the

sample base was small and of inconsistent time periods and the numbers can only be seen as

indicative.

The fill scheme described in Chapter 4.2.2 is a fairly straight forward approach for dealing with longer

data gaps and gives reasonable good result. A few longer data gaps will not affect the quality of the

data too much if the data are to be used for model calibration against utility bills (usually done on

monthly or daily basis).

The fill scheme performs significantly better than interpolation for data gaps (outdoor

temperature) of about 9 to 48 hours. For example the 25-48 hour gap test with fill scheme in

Table 3 has 57 % of its temperature data taken away but still the average temperature of

6.99 ˚C for the whole period is just affected by -0.053 ˚C.

For gaps between 2 and 5 days the fill scheme will still give slightly better result than linear

interpolation.

Akima Spline interpolation performs better than linear interpolation for data gaps (outdoor

temperature) in the interval 2 to about 8 hours.

The commonly used and freely available IWEC files direct radiation parameter has a very strong

negative bias of about 20 to 40 % for Northern Europe. These files should be used with care,

especially if solar radiation has a significant impact of on the building being modeled.

36

Discussion 8The use of ISD data outside of the US might be restricted with respect to the WMO Resolution 40,

quoting the NOAA Policy:

“The following data and products may have conditions placed on their international commercial use.

They can be used within the U.S. or for non-commercial international activities without restriction.

The non-U.S. data cannot be redistributed for commercial purposes. …” (NOAA, 2012)

Norway, Spain, Netherlands, Slovenia, UK (ECOMET, u.d.) and soon Sweden (Morus konsult AB, 2012)

are European countries that have similar unrestricted data policy to that of US NOAA. Other

European countries do however restrict (to varying degree) the usage of their weather data. As long

as ISD data are utilized the resulting AMY-files should be used for research, education, and other

non-commercial activities. It is possible to insert data from other sources or from own local

measurements and then the resulting weather files can be used for commercial purposes.

Validation of the STRÅNG model system shows some inconsistence in accuracy outside of Sweden,

both in temporal and geospatial dimension. If these issues would be addressed it would be a very

interesting source of modeled solar radiation data to be used for different kinds of energy

engineering applications, requiring better quality on solar radiation data than calibration of building

simulation models does.

There are now IWEC2-files available from ASHRAE, covering over 3000 international stations. The

underestimation (for direct solar radiation) present in the old IWEC-files is not present in the IWEC2-

files for Stockholm and Helsinki5. Both the old IWEC and IWEC2 used the Zhang-Huang model that

derives global horizontal solar radiation from cloud cover, change in dry-bulb temperature over the

past three hours, relative humidity, wind speed and a set of regression coefficients. In the old IWEC a

single set of regression coefficients where derived using measured solar data for two Chinese cities.

In IWEC2 Köppen-Geiger climate classifications was used to group IWEC2 stations, using different

sets of regression coefficients for the Köppen-Geiger zones. Also a new model for splitting the global

horizontal to diffuse and direct normal solar radiation was used in the IWEC2-files.6

Deviation in STRÅNG values correlate quite well with nearness to ocean (UK, Norway and west coast

of Europe) and altitude (e.g. stations Poprad-Ganovce, Sonnblick and Löken i Volbu). Also vicinity to

mountains seems affect the STRÅNG model system negatively, e.g. Norwegian station Kise. The

strong underestimation at the Baltic stations is harder to explain as caused by climate differences,

the Baltic climate don’t deviate that much from the Swedish. The same goes for the two north

Finnish stations. This deviation at the Baltic and North Finnish stations need to be studied further.

Apart from the Baltic and North Finnish stations it seems very likely that adding one more input

parameter, describing the local climate/geography, to the STRÅNG “cloud function” would be

5 Personal communication, November 8, 2012, with Joe Huang contractor of the IWEC2 project. Reference:

AMY-weather files for North Europe. [Discussion Group]. Available at: http://tech.groups.yahoo.com/group/EnergyPlus_Support 6 Huang, J., n.d. (under review) ASHRAE Research Project 1477-RP.

37

beneficial for the STRÅNG model accuracy. The “cloud function” would also then need to be trained

(tuned) with solar data from stations outside of Sweden, so that all types of climate present in the

area covered by STRÅNG would be represented. For example a station at the Norwegian west coast

would most likely also represent the climate (from cloud formation point of view) of the west coast

of France, or at least does it better than a Swedish station do.

This paper has focused on creation of AMY-weather files. As the time span of the STRÅNG database is

growing (soon reaching 13 years) it would be possible to use a similar approach for creating TMY-

weather files with a good coverage rate of the urban and semi urban parts of North Europe.

38

References BSRN, n.d. Baseline Surface Radiation Network. [Online]

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mulna typdagar, Stockhom: Inst. för byggnadsteknik, Kungliga Tekniska Högskolan.

Huang, J., n.d. (under review) ASHRAE Research Project 1477-RP. s.l.:s.n.

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Institute.

Landelius, T., Josefsson, W. & Persson, T., 2001. A system for modelling solar radiation parameters

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[Accessed 8 2012].

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Available at: http://morus.se/2012/10/smhi-oppnar-data-intervju-med-marcus-flarup/

[Accessed 24 10 2012].

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[Accessed 8 2012].

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[Accessed 24 9 2012].

39

Norwegian Meteorological Institute, n.d. eKlima. [Online]

Available at: eklima.met.no

[Accessed 9 2012].

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Available at: http://www.pangaea.de/

[Accessed 2012].

Peel, M., Finlayson, B. & McMahon, T., 2007. Updated world map of the Köppen-Geiger climate

classification, s.l.: Hydrol. Earth Syst. Sci 11, 1633-1644..

SMHI, 2011. Normalårskorrigering under vår, sommar och höst med SMHI Graddagar. [Online]

Available at: http://www.smhi.se/Professionella-tjanster/Professionella-

tjanster/Fastighet/normalarskorrigering-under-var-sommar-och-host-med-smhi-graddagar-1.18575

[Accessed 22 10 2012].

SMHI, n.d. STRÅNG - a mesoscale model for solar radiation. [Online]

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[Accessed 8 2012].

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Available at: http://wrdc.mgo.rssi.ru/

[Accessed 8 2012].

40

Appendix A C# sample codes

Appendix A.1 C# method for filling missing data gaps private double[] FillMissingBackwards(int pos1, int pos2, int col) { int n_tot = (pos2 - pos1) - 1; // Total missing steps in gap int D = 24 * subHours; // Offset if (pos1 - D + subHours < 0 || n_tot < 1) return null; double[] repValues = new double[D]; double[] toReturn = new double[n_tot]; double f_t1 = Table.Rows[pos1].Field<double>(col); // Value at t1 double f_t2 = Table.Rows[pos2].Field<double>(col); // Value at t2 if (double.IsNaN(f_t1) || double.IsNaN(f_t2)) { return null; } double f_t2D; // Value at t2-d if (n_tot > 24 * subHours) { for (int t = 0; t < D; t++) // Values from offset point { repValues[t] = Table.Rows[pos1 + 1 - D + t].Field<double>(col); } f_t2D = repValues[D - 1]; // Value at t2-d } else { for (int t = 0; t < n_tot; t++) // Values from offset point { repValues[t] = Table.Rows[pos1 + 1 - D + t].Field<double>(col); } f_t2D = repValues[n_tot - 1]; // Value at t2-d } int count = repValues.Count(i => double.IsNaN(i)); if (count > 0) // If missing return null return null; double f_t1D = repValues[0]; // Value at t1-d int n = 0; double a = (f_t1 - f_t1D); double b = (((f_t2 - f_t2D) - (f_t1 - f_t1D)) / (n_tot + 1)); for (int t = 0; t < n_tot; t++) { toReturn[t] = repValues[n] + a + (n + 1) * b; n++; if (n == 24 * subHours) { a = (toReturn[t] - f_t1D); b = (((f_t2 - f_t2D) - (toReturn[t] - f_t1D)) / (n_tot + 1 - (t + 1))); n = 0; } } return toReturn; }

41

Appendix A.2 Part of the method used to load STRÅNG-data from file while (line != null) { dateStrang = DateTime.ParseExact(line.Substring(0, 8) + line.Substring(9, 2) + "00", "yyyyMMddHHmm", CultureInfo.InvariantCulture); if (dateStrang.AddHours(timeZoneOffset) > dateTo) break; dayNr = dateStrang.AddHours(timeZoneOffset).DayOfYear; if (dayNr > oldDayNr) { // Help variables to calculate solar time declination = Deg2Rad(23.45 * Math.Sin(2 * Math.PI * (284 + dayNr) / 365)); B = Deg2Rad(360 * (dayNr - 1) / 365); E = 229.2 * (0.000075 + 0.0011868 * Math.Cos(B) - 0.032077 * Math.Sin(B) - 0.014615 * Math.Cos(2 * B) - 0.04089 * (2 * B)); solCorrection = (4 * (longitudeTimeZone - longitudeLocal) + E); oldDayNr = dayNr; } // solarTime = hour + solCorrection, checks if solarTime is <=0 or >24 solarTime = dateStrang.AddMinutes(solCorrection+TimeZoneOffset*60).TimeOfDay.TotalHours; // Calculate hour angle from south, positive westward. // 12.5 shifts half hour, 12 if on the hour omega = (solarTime - 12.5) * Deg2Rad(15); // Solar elevation elevSun = Math.Cos(latInRad) * Math.Cos(declination) * Math.Cos(omega) + Math.Sin(latInRad) * Math.Sin(declination); // Parse data from file radDirekt2 = double.Parse(line.Split(';')[3], CultureInfo.InvariantCulture); radGlobal2 = double.Parse(line.Split(';')[2], CultureInfo.InvariantCulture); if (double.IsNaN(radDirekt1) == false) { radDirekt = (radDirekt1 + radDirekt2) / 2; radGlobal = (radGlobal1 + radGlobal2) / 2; // Calculate diffuse horizontal radDiffuse = Math.Round(radGlobal - radDirekt * Math.Sin(elevSun), 1); } radDirekt1 = radDirekt2; radGlobal1 = radGlobal2; // Load to table Table.LoadDataRow(MakeObject(dateStrang.AddHours(timeZoneOffset), new double[3] {radDirekt,radGlobal,radDiffuse}), LoadOption.PreserveChanges); line = sr.ReadLine(); }

42

Appendix B Tables

Appendix B.1 Geospatial validation results N Mean

Observation

Mean STRÅNG

MBD RMSD MAD Period Source Station Country WMO Id Latitude Longitude

362 101,8 93,9 -7,7% 20,3% 13,4% 2007 WRDC Aberdeen / Dyce Arpt

United Kingdom

30910 57,20 -2,22

363 122,7 104,0 -15,3% 25,8% 17,6% 2007 WRDC Aberporth United Kingdom

35020 52,13 -4,57

360 94,8 87,3 -7,9% 22,5% 15,0% 2007 WRDC Aviemore United Kingdom

30630 57,20 -3,83

364 136,9 134,7 -1,6% 19,8% 14,7% 2007 WRDC Basel Switzerland

66801 47,55 7,58

358 110,0 101,0 -8,2% 18,3% 12,5% 2007 WRDC Belfast / Aldergrove Arpt

United Kingdom

39170 54,65 -6,22

362 116,5 100,6 -13,7% 23,6% 15,8% 2007 WRDC Belmullet Ireland 39760 54,23 -10,00

365 127,2 106,4 -16,4% 27,7% 18,8% 2007 WRDC Belsk Poland 12471 51,83 20,80

358 90,4 85,2 -5,7% 19,1% 12,4% 2007 WRDC Bergen Norway 13160 60,40 5,32

365 110,2 93,4 -15,3% 25,9% 17,4% 2007 WRDC Birr Ireland 39650 53,08 -7,88

365 107,6 113,5 5,5% 19,9% 12,9% 2007 WRDC Borlange Sweden 24350 60,43 15,50

365 136,4 137,9 1,1% 16,9% 12,3% 2007 WRDC Bratislava -Koliba Slovakia 11813 48,17 17,12

363 118,2 109,3 -7,5% 18,3% 11,9% 2007 WRDC Braunschweig Germany 10348 52,30 10,45

365 138,3 135,2 -2,3% 16,9% 11,9% 2007 WRDC Bregenz Austria 11101 47,50 9,75

365 126,9 105,0 -17,3% 27,1% 19,0% 2007 WRDC Brest France 71100 48,45 -4,42

358 118,6 106,0 -10,7% 25,9% 16,5% 2007 BSRN Cabauw Netherlands

63480 51,97 4,93

365 119,6 110,4 -7,7% 20,9% 15,0% 2007 WRDC Caen France 70270 49,18 -0,45

365 127,2 111,9 -12,0% 21,4% 14,8% 2007 WRDC Camborne United Kingdom

38080 50,22 -5,32

182 186,3 148,8 -20,1% 30,7% 21,9% 2006 jun-nov

WRDC Cluj - Napoca Romania 15120 46,78 23,57

901 110,5 116,1 5,1% 19,4% 13,7% 2000-2002

WRDC Copenhagen / Taastrup

Denmark 61801 55,67 12,30

151 164,6 158,5 -3,7% 21,9% 17,1% 2006 jun-nov

WRDC Craiova Romania 15450 44,32 23,87

364 159,7 127,6 -20,1% 30,5% 22,2% 2007 WRDC Davos-Dorf Switzerland

67840 46,82 9,83

365 114,6 104,1 -9,2% 21,3% 14,4% 2007 WRDC De Bilt Netherlands

62600 52,10 5,18

365 125,6 104,3 -17,0% 29,6% 19,5% 2007 WRDC De Kooy Netherlands

62350 52,92 4,78

182 147,0 128,6 -12,5% 27,7% 20,1% 2007 WRDC Dobbiaco Italy 16033 46,73 12,22

358 127,7 117,6 -7,9% 18,1% 12,2% 2007 WRDC Dresden/Klotzsche

Germany 10488 51,13 13,75

363 103,9 99,2 -4,5% 19,9% 13,8% 2007 WRDC Edinburgh United Kingdom

31711 56,45 -3,07

361 96,6 85,8 -11,1% 22,1% 14,9% 2007 WRDC Eskdalemuir United Kingdom

31620 55,32 -3,20

365 112,7 101,3 -10,1% 21,0% 14,4% 2007 WRDC Eelde Netherlands

62800 53,13 6,58

365 108,6 108,0 -0,6% 17,2% 10,8% 2007 WRDC Goteborg Sweden 25130 57,70 12,00

361 108,5 105,8 -2,5% 16,5% 11,6% 2007 WRDC Hamburg Germany 10147 53,63 10,00

363 110,9 101,7 -8,3% 17,4% 11,2% 2007 WRDC Helsinki Arpt Finland 29740 60,32 24,95

365 133,4 124,6 -6,6% 17,7% 12,1% 2007 WRDC Hradec Kralove Czech Republic

11649 50,18 15,83

365 164,9 147,5 -10,6% 18,2% 13,0% 2007 WRDC Innsbruck Arpt Austria 11120 47,25 11,35

358 107,1 90,4 -15,6% 26,1% 17,4% 2007 WRDC Jokioinen Finland 29630 60,82 23,50

358 101,1 92,3 -8,6% 16,9% 11,1% 2007 WRDC Jyvaskyla Arpt Finland 29350 62,40 25,67

364 114,9 108,9 -5,2% 16,8% 10,9% 2007 WRDC Karlstad Sweden 24150 59,37 13,47

365 91,9 87,2 -5,1% 18,2% 11,6% 2007 WRDC Kiruna Sweden 20450 67,83 20,43

365 159,3 145,2 -8,9% 17,7% 12,5% 2007 WRDC Klagenfurt Austria 11231 46,65 14,33

365 116,3 102,8 -11,5% 23,3% 15,7% 2007 WRDC Kolobrzeg Poland 12100 54,18 15,58

365 135,8 126,2 -7,1% 16,2% 11,2% 2007 WRDC Kosetice Czech Republic

11628 49,58 15,08

43

365 141,5 141,0 -0,3% 11,7% 8,3% 2007 WRDC Kucharovice Czech Republic

11698 48,88 16,08

361 86,7 73,9 -14,8% 30,3% 19,2% 2007 WRDC Lerwick United Kingdom

30050 60,13 -1,18

363 126,7 116,0 -8,5% 15,4% 10,7% 2007 WRDC Lindenberg Germany 10393 52,22 14,12

365 100,8 95,8 -5,0% 15,7% 9,7% 2007 WRDC Lulea Sweden 21850 65,55 22,13

365 113,8 108,7 -4,5% 16,5% 11,3% 2007 WRDC Lund Sweden 26270 55,72 13,22

364 117,1 115,0 -1,8% 15,4% 10,8% 2007 WRDC Melle Belgium 64300 50,98 3,83

275 160,8 150,1 -6,7% 18,5% 12,7% 2007 WRDC Milhostov / Trebisov

Slovakia 11978 48,67 21,72

365 114,2 110,8 -3,0% 14,5% 9,7% 2007 WRDC Norrkoping Sweden 25710 58,58 16,25

360 123,1 113,8 -7,6% 17,7% 12,3% 2007 WRDC Odiham United Kingdom

37610 51,23 -0,95

365 122,0 120,0 -1,6% 15,9% 10,9% 2007 WRDC Oostende Arpt Belgium 64070 51,20 2,87

365 104,5 102,4 -2,0% 16,8% 11,5% 2007 WRDC Ostersund Sweden 22260 63,18 14,50

365 130,4 128,6 -1,4% 15,7% 10,9% 2007 WRDC Ostrava / Poruba Czech Republic

11790 49,82 18,15

365 124,5 118,9 -4,5% 20,5% 14,7% 2007 WRDC Paris / Orly France 71490 48,72 2,38

358 148,0 125,8 -15,0% 30,8% 22,0% 2007 WRDC Payerne. STRÅNG data from 20 km north

Switzerland

66100 46,82 6,93

189 134,2 117,9 -12,2% 25,5% 18,1% 2007 WRDC Poprad-Ganovce Slovakia 11952 49,03 20,32

365 129,3 129,2 -0,1% 14,1% 9,9% 2007 WRDC Praha / Karlov Czech Republic

11519 50,08 14,43

358 137,0 153,6 12,2% 21,6% 16,6% 2007 WRDC Puntijarka Croatia 13128 45,92 15,97

365 128,2 109,2 -14,8% 27,2% 18,2% 2007 WRDC Reims France 70700 49,30 4,03

356 123,5 99,4 -19,5% 30,4% 20,8% 2007 WRDC Rucava Latvia 26503 56,17 21,17

365 146,6 137,8 -6,0% 18,1% 13,5% 2007 WRDC Salzburg/Freisaal Austria 11350 47,78 13,05

363 89,6 67,1 -25,1% 39,9% 25,8% 2007 WRDC Sodankyla Finland 28360 67,37 26,62

269 122,8 135,1 10,0% 27,2% 20,5% 2007 WRDC Sofia Obs. STRÅNG data from 40 km north west

Bulgaria 15614 42,65 23,38

365 165,1 123,2 -25,4% 36,6% 28,0% 2007 WRDC Sonnblick Austria 11343 47,05 12,95

353 121,1 108,7 -10,2% 21,8% 15,1% 2007 WRDC St-Hubert Belgium 64760 50,03 5,40

365 111,7 112,7 0,9% 16,2% 9,8% 2007 WRDC Stockholm Sweden 24830 59,35 18,07

365 134,1 125,5 -6,4% 16,6% 11,2% 2007 WRDC Strasbourg France 71900 48,55 7,63

365 113,1 89,5 -20,9% 32,7% 21,9% 2007 WRDC Tartu / Toravere Estonia 26242 58,25 26,47

194 144,0 136,9 -4,9% 15,2% 10,8% 2007 WRDC Trier Germany 10609 49,75 6,67

365 113,9 119,5 4,9% 16,3% 12,0% 2007 WRDC Uccle Belgium 64470 50,80 4,35

179 148,4 141,6 -4,6% 18,5% 12,2% 2007. jun-dec

WRDC Udine / Rivolto Italy 16045 45,98 13,03

365 106,5 104,9 -1,5% 15,6% 9,8% 2007 WRDC Umea Sweden 22830 63,82 20,25

360 81,1 64,4 -20,5% 36,7% 22,2% 2007 WRDC Utsjoki Finland 28050 69,75 27,00

362 115,5 108,3 -6,2% 16,3% 11,1% 2007 WRDC Waddington United Kingdom

33770 53,17 -0,52

365 120,0 97,8 -18,5% 28,7% 20,0% 2007 WRDC Valentia Obs. Ireland 39530 51,93 -10,25

365 118,9 113,8 -4,3% 17,6% 12,0% 2007 WRDC Warszawa Poland 12372 52,28 20,97

360 121,8 111,2 -8,7% 18,9% 12,9% 2007 WRDC Wattisham United Kingdom

35900 52,12 0,97

365 107,2 102,7 -4,1% 15,7% 10,2% 2007 WRDC Vaxjo /Kronoberg Sweden 26410 56,93 14,73

363 142,6 136,3 -4,4% 15,7% 10,1% 2007 WRDC Weihenstephan Germany 10863 48,40 11,70

365 135,9 142,9 5,2% 13,2% 10,0% 2007 WRDC Wien / Hohe Warte

Austria 11035 48,25 16,35

335 116,5 112,9 -3,1% 16,1% 10,1% 2007 WRDC Visbyaerolog. Stn Sweden 25900 57,67 18,35

365 120,4 107,4 -10,8% 20,9% 14,5% 2007 WRDC Vlissingen Netherlands

63100 51,45 3,60

365 132,1 124,0 -6,1% 15,2% 10,3% 2007 WRDC Wuerzburg Germany 10655 49,77 9,97

352 155,5 152,9 -1,6% 15,3% 11,2% 2007 WRDC Zagreb / Horvatovac

Croatia 13129 45,83 16,00

365 124,6 112,9 -9,4% 27,6% 18,5% 2007 WRDC Zakopane Poland 126 49,30 19,95

199 147,2 117,3 -20,3% 32,2% 21,9% 2007 WRDC Zilani Latvia 26436 56,52 25,92

340 123,3 93,8 -23,9% 38,9% 26,1% 2007 WRDC Zoseni Latvia 26339 57,13 25,90

364 128,7 134,7 4,6% 25,4% 16,0% 2007 WRDC Zuerich / Kloten Switzerland

66700 47,48 8,53

359 109,3 93,0 -14,9% 26,3% 17,5% 2007 WRDC Boulmer United Kingdom

32400 55,42 -1,60

365 97,5 88,3 -9,4% 28,5% 18,2% 2007 WRDC Dunstaffnage United 31141 56,47 -5,43

44

Kingdom

365 102,8 89,8 -12,7% 30,9% 19,8% 2007 eKlima Kise Norway 12550 60,77 10,81

365 111,6 102,0 -8,6% 21,9% 13,9% 2007 eKlima Landvik Norway 38140 58,34 8,52

365 90,6 86,3 -4,8% 21,1% 13,3% 2007 eKlima Kvithamar Norway 69150 63,49 10,88

333 88,5 82,1 -7,2% 21,4% 13,5% 2007 eKlima Tromsø/ Holt Norway 90400 69,65 18,91

365 89,8 81,4 -9,4% 26,7% 15,8% 2007 eKlima Fureneset Norway 56420 61,29 5,04

365 83,8 83,6 -0,3% 21,8% 14,3% 2007 eKlima Trondheim - Voll Norway 68860 63,41 10,45

365 79,2 71,8 -9,3% 29,5% 18,2% 2007 eKlima Tjötta Norway 76530 65,83 12,43

361 89,1 78,6 -11,7% 25,8% 15,9% 2007 eKlima Bodö - Vågönes Norway 82260 67,2854 14,4515

365 98,2 89,4 -9,0% 30,1% 19,5% 2007 eKlima Östre Toten - Apelsvoll

Norway 11500 60,7002 10,8695

360 98,7 97,7 -1,0% 19,6% 13,1% 2007 eKlima Ås Norway 17850 59,6605 10,782

365 106,4 93,3 -12,3% 26,8% 17,5% 2007 eKlima Löken i Volbu Norway 23500 61,122 9,063

365 100,5 91,1 -9,4% 23,3% 15,2% 2007 eKlima Särheim Norway 44300 58,7605 5,6505

Appendix B.2 Descriptive statistics: mean monthly temperatures [˚C] Norrköping

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Year

Mean -1,7 -2,0 1,0 5,9 11,6 15,3 17,9 16,6 12,0 7,3 2,6 -0,9 7,2

Std. Error 0,6 0,7 0,4 0,3 0,3 0,2 0,3 0,3 0,3 0,3 0,4 0,5 0,2

Median -1,2 -2,0 1,5 5,9 11,8 15,3 17,8 16,8 12,0 7,5 2,4 -0,4 7,5

Std. Deviation 3,4 3,6 2,4 1,4 1,6 1,2 1,5 1,6 1,5 1,8 2,1 2,9 1,0

Variance 11,8 13,0 5,8 1,8 2,4 1,4 2,4 2,5 2,1 3,2 4,2 8,4 1,1

Kurtosis 0,1 0,3 0,1 -0,6 -0,6 0,7 0,0 0,9 0,3 -0,4 -0,3 0,2 0,1

Skewness -0,7 -0,4 -0,5 -0,5 -0,4 -0,5 0,1 -0,3 -0,4 -0,1 0,1 -0,6 -0,9

Range 14,2 15,8 10,6 5,0 5,8 5,1 6,8 7,1 6,5 7,1 8,5 12,6 3,8

Minimum -10,2 -10,9 -4,8 2,8 8,3 12,6 14,6 13,2 8,5 4,0 -1,6 -7,9 4,9

Maximum 4,0 4,9 5,8 7,8 14,0 17,7 21,4 20,4 15,0 11,1 7,0 4,7 8,7

N 29 29 29 29 29 28 28 29 29 29 29 29 28

Tartu-Toravere Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Year

Mean -4,5 -5,3 -0,9 5,7 11,5 15,2 17,9 16,4 11,2 6,1 0,4 -3,2 5,9

Std. Error 0,8 0,8 0,5 0,4 0,3 0,3 0,4 0,3 0,3 0,4 0,5 0,6 0,2

Median -3,1 -5,1 -0,9 6,1 11,9 15,1 17,4 16,4 11,2 6,3 0,4 -3,4 6,2

Std. Deviation 4,1 4,5 2,6 1,9 1,6 1,7 1,9 1,4 1,8 1,9 2,7 3,1 1,1

Variance 17,1 20,5 6,8 3,8 2,6 2,8 3,7 2,1 3,2 3,7 7,5 9,4 1,2

Kurtosis 2,3 -0,2 0,3 -0,5 0,1 1,3 -0,3 -0,6 0,6 0,6 2,0 -0,4 0,4

Skewness -1,6 -0,4 -0,2 0,1 -0,7 0,9 0,7 -0,1 -0,4 -0,7 -1,2 -0,1 -0,6

Range 17,7 18,5 12,2 7,7 6,5 7,8 7,1 5,6 8,1 7,9 11,2 12,8 4,7

Minimum -17,1 -16,0 -7,0 2,1 7,3 12,3 15,3 13,5 6,6 1,2 -7,3 -9,3 3,2

Maximum 0,7 2,4 5,2 9,9 13,8 20,1 22,4 19,1 14,8 9,2 3,9 3,5 7,9

N 30 30 30 30 30 30 30 30 30 30 30 30 30

Payerne Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Year

Mean 0,4 1,3 5,3 8,7 13,3 16,6 18,9 18,3 14,3 9,9 4,3 1,4 9,4

Std. Error 0,4 0,4 0,3 0,2 0,3 0,3 0,3 0,2 0,3 0,2 0,3 0,2 0,1

Median 0,5 1,1 5,3 8,8 13,6 16,6 18,9 18,2 14,2 9,7 4,1 1,2 9,5

Std. Deviation 2,1 2,4 1,7 1,3 1,7 1,5 1,5 1,3 1,4 1,3 1,5 1,3 0,6

Variance 4,3 5,9 3,0 1,7 2,9 2,4 2,1 1,7 2,0 1,6 2,2 1,7 0,4

Kurtosis 0,3 -0,4 -0,5 1,9 -0,2 5,5 0,1 2,0 -0,1 0,9 -0,3 -0,7 -0,4

Skewness -0,4 0,1 0,1 0,8 -0,8 1,8 0,4 1,0 -0,1 0,2 0,4 0,5 -0,3

Range 9,1 10,1 7,2 6,5 6,0 7,8 6,1 6,6 5,9 6,1 5,8 4,5 2,4

Minimum -4,8 -4,2 1,9 6,2 9,8 14,6 16,2 15,8 10,9 6,8 1,8 -0,6 8,1

Maximum 4,4 5,9 9,2 12,6 15,8 22,3 22,3 22,3 16,8 12,9 7,6 3,9 10,5

N 30 30 30 30 30 30 30 30 30 30 30 30 30

De Bilt Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Year

Mean 3,1 3,3 6,2 9,2 13,1 15,6 17,9 17,5 14,5 10,7 6,7 3,7 10,1

Std. Error 0,5 0,5 0,3 0,3 0,3 0,2 0,3 0,2 0,2 0,3 0,3 0,4 0,1

Median 3,5 3,0 6,4 8,9 13,3 15,8 17,6 17,4 14,3 10,7 6,9 4,1 10,4

Std. Deviation 2,7 2,6 1,7 1,4 1,6 1,2 1,7 1,2 1,3 1,6 1,8 2,0 0,8

Variance 7,1 7,0 2,8 2,0 2,6 1,4 2,7 1,5 1,7 2,4 3,2 4,0 0,6

Kurtosis -0,1 0,0 -0,5 1,2 -0,6 0,0 0,4 0,1 1,4 0,3 1,5 1,0 -0,5

Skewness -0,7 -0,4 -0,5 0,6 -0,6 -0,5 0,8 0,4 0,6 0,2 -0,8 -1,1 -0,8

Range 10,1 11,2 6,4 6,8 5,7 5,1 6,8 5,3 6,4 6,8 8,2 8,2 2,7

45

Minimum -3,0 -3,6 2,3 6,2 10,0 12,7 15,5 15,2 11,6 7,5 2,0 -1,2 8,5

Maximum 7,1 7,6 8,7 12,9 15,7 17,8 22,3 20,6 17,9 14,2 10,2 7,0 11,2

N 30 30 30 30 30 30 30 30 30 30 30 30 30

Stockholm/Arlanda Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Year

Mean -2,7 -2,9 0,1 4,9 10,7 14,7 17,7 16,4 11,5 6,7 1,9 -1,6 6,5

Std. Error 0,6 0,7 0,4 0,3 0,3 0,3 0,3 0,3 0,3 0,3 0,4 0,5 0,2

Median -2,2 -2,8 0,7 5,2 10,8 14,8 17,7 16,6 11,5 6,9 1,7 -0,9 6,7

Std. Deviation 3,6 3,7 2,3 1,5 1,5 1,4 1,5 1,7 1,6 1,9 2,1 2,9 1,0

Variance 12,6 14,0 5,1 2,3 2,1 1,9 2,3 2,8 2,5 3,4 4,2 8,4 1,0

Kurtosis 1,8 0,7 -0,4 -0,6 -0,7 -0,7 -0,8 0,4 0,2 -0,3 -0,7 0,1 0,5

Skewness -1,2 -0,6 -0,3 -0,3 -0,3 -0,2 0,3 0,0 -0,1 -0,4 0,1 -0,6 -0,9

Range 16,2 16,6 9,0 5,9 5,4 5,1 5,3 7,0 6,9 7,3 7,9 12,4 3,9

Minimum -13,4 -12,9 -4,8 1,8 8,0 12,1 15,4 13,0 8,0 2,8 -1,6 -8,1 3,9

Maximum 2,8 3,7 4,2 7,7 13,4 17,2 20,7 20,0 14,9 10,1 6,3 4,3 7,8

N 30 30 30 30 30 30 30 30 30 30 30 30 30

Kevo-Utsjoki Jan feb Mar Apr Maj Jun Jul Aug Sep Okt Nov Dec Year

Mean -13,9 -12,8 -8,2 -2,3 3,8 9,6 13,1 10,7 5,8 -0,5 -8,3 -12,2 -1,3

Std. Error 0,8 0,9 0,6 0,4 0,3 0,3 0,3 0,2 0,3 0,4 0,6 0,9 0,2

Medain -13,0 -12,5 -7,3 -2,0 3,1 9,4 13,2 10,8 5,6 -0,5 -8,0 -12,7 -1,1

Std. Deviation 4,2 4,7 3,1 2,1 1,5 1,7 1,4 1,3 1,4 2,4 3,4 4,8 1,1

Variance 17,7 22,4 9,5 4,5 2,3 2,9 2,1 1,7 2,0 5,8 11,4 22,6 1,2

Kurtosis -0,9 -0,3 0,0 -0,9 -0,2 0,1 1,0 -0,6 -0,2 3,6 -0,7 -1,1 -0,3

Skewness -0,5 -0,3 -0,5 -0,1 0,4 -0,5 0,8 0,0 -0,2 -0,7 -0,3 -0,1 -0,6

Range 13,9 18,9 13,2 8,1 6,6 7,0 6,2 5,2 5,3 13,3 11,8 15,5 3,9

Minimum -22,1 -22,6 -15,9 -6,6 0,8 5,4 10,8 8,2 2,7 -8,5 -14,5 -20,3 -3,6

Maximum -8,2 -3,7 -2,7 1,6 7,4 12,4 17,0 13,4 8,0 4,8 -2,7 -4,9 0,3

N 30 30 30 30 30 30 30 30 30 30 30 30 30

Camborne

Jan feb Mar Apr Maj Jun Jul Aug Sep Okt Nov Dec Year

Mean 6,9 6,6 7,7 8,7 11,2 13,6 15,5 15,8 14,3 11,9 9,4 7,6 10,8

Std. Error 0,3 0,3 0,2 0,2 0,2 0,1 0,2 0,2 0,2 0,2 0,2 0,2 0,1

Medain 7,1 6,7 7,8 8,8 11,2 13,6 15,4 15,7 14,4 12,0 9,4 8,0 10,9

Std. Deviation 1,5 1,7 0,9 0,9 1,0 0,7 1,0 1,1 0,8 1,1 0,9 1,2 0,5

Variance 2,3 2,8 0,8 0,9 1,1 0,6 0,9 1,1 0,7 1,3 0,8 1,5 0,3

Kurtosis 0,1 2,6 -0,6 3,0 -0,4 -0,9 0,2 1,3 2,6 0,0 1,8 1,7 0,2

Skewness -0,9 -1,2 -0,6 -0,6 0,1 -0,1 0,8 0,0 -0,9 -0,4 -0,6 -1,1 -0,7

Range 5,2 8,0 3,3 5,2 4,2 2,7 3,8 5,4 4,4 4,4 4,6 5,8 2,3

Minimum 3,5 1,0 5,6 5,9 9,1 12,2 14,0 13,1 11,6 9,3 6,8 4,0 9,4

Maximum 8,8 9,1 8,9 11,1 13,4 14,9 17,8 18,5 16,0 13,8 11,3 9,7 11,7

N 30 30 30 30 30 30 30 30 30 30 30 30 30

Appendix B.3 Descriptive statistics: mean monthly solar radiation [W/m2] Lindberg, direct radiation

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Year

Mean 42,3 62,8 94,1 138,1 180,7 171,2 169,3 166,1 136,4 81,8 43,6 30,5 109,7

Std. Error 3,1 6,1 8,1 12,6 12,5 11,6 16,8 9,1 14,8 6,4 5,2 3,2 4,2

Medain 42,5 55,5 86,5 140,5 183,5 149,0 165,0 157,0 154,5 79,5 44,0 28,5 108,7

Std. Deviation

10,8 21,1 27,9 43,6 43,4 40,3 58,2 31,5 51,1 22,1 18,1 11,0 14,7

Variance 117,5 444,6 781,2 1904 1886 1621 3383 993,5 2612 490,3 329,2 121,5 216,1

Kurtosis -0,3 3,3 -0,4 -1,3 1,1 -1,8 2,7 1,1 -1,4 2,5 -0,5 -0,1 -0,7

Skewness 0,3 1,6 0,5 -0,3 -0,7 0,4 0,7 0,1 -0,3 1,0 -0,1 0,9 0,5

Range 37,0 75,0 94,0 129,0 156,0 111,0 243,0 124,0 150,0 89,0 60,0 35,0 46,4

Minimum 26,0 42,0 52,0 64,0 84,0 125,0 63,0 103,0 56,0 46,0 12,0 18,0 90,2

Maximum 63,0 117,0 146,0 193,0 240,0 236,0 306,0 227,0 206,0 135,0 72,0 53,0 136,6

N 12 12 12 12 12 12 12 12 12 12 12 12 12

Lindberg, global radiation

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Year

Mean 30,7 57,7 104,5 168,3 217,3 232,1 218,3 195,5 136,3 74,9 35,7 22,3 124,5

Std. Error 0,9 1,9 3,5 5,8 7,0 6,0 9,8 5,2 5,7 2,7 1,4 0,8 1,8

Medain 31,5 57,0 104,0 163,5 221,0 224,5 211,0 192,5 145,5 75,0 36,5 22,0 123,5

Std. Deviation

3,1 6,6 12,3 20,1 24,1 20,7 34,1 18,1 19,8 9,3 4,8 2,8 6,2

46

Variance 9,7 43,0 150,3 403,1 582,4 428,1 1161 328,8 393,8 86,8 23,0 7,8 37,9

Kurtosis 0,7 1,4 0,7 -1,5 2,7 -0,8 1,0 0,3 -0,6 1,7 -0,8 -0,8 -1,0

Skewness 0,1 1,2 -0,6 0,3 -1,5 0,6 0,5 -0,3 -0,7 -0,1 0,0 -0,4 0,4

Range 12,0 22,0 44,0 53,0 84,0 66,0 127,0 63,0 63,0 38,0 16,0 9,0 18,9

Minimum 25,0 51,0 78,0 145,0 157,0 204,0 156,0 158,0 97,0 56,0 28,0 17,0 116,9

Maximum 37,0 73,0 122,0 198,0 241,0 270,0 283,0 221,0 160,0 94,0 44,0 26,0 135,8

N 12 12 12 12 12 12 12 12 12 12 12 12 12

Lindberg, diffuse radiation

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Year

Mean 20,8 36,8 61,2 87,1 103,9 118,8 108,1 92,3 67,2 42,7 23,8 15,9 64,9

Std. Error 0,5 0,9 1,4 1,3 2,1 2,1 1,8 1,4 1,6 1,1 0,3 0,3 0,4

Medain 21,0 36,5 62,5 86,0 105,0 120,0 108,5 93,5 68,5 42,5 24,0 16,0 64,5

Std. Deviation

1,7 3,2 5,0 4,5 7,4 7,2 6,3 4,9 5,4 3,7 1,0 1,2 1,3

Variance 2,8 10,4 25,1 20,3 55,2 51,2 39,4 23,7 29,1 14,1 0,9 1,4 1,7

Kurtosis 1,0 -0,5 -0,7 2,2 3,2 -1,5 2,4 -0,5 1,0 -0,5 0,3 -0,7 -0,5

Skewness -1,0 0,6 0,0 1,3 -1,5 0,0 -1,1 -0,5 -1,0 -0,1 -0,9 0,2 0,2

Range 6,0 10,0 17,0 16,0 27,0 21,0 24,0 16,0 18,0 12,0 3,0 4,0 4,5

Minimum 17,0 33,0 53,0 82,0 85,0 109,0 93,0 83,0 55,0 36,0 22,0 14,0 62,6

Maximum 23,0 43,0 70,0 98,0 112,0 130,0 117,0 99,0 73,0 48,0 25,0 18,0 67,1

N 12 12 12 12 12 12 12 12 12 12 12 12 12

Tartu-Toravere, direct radiation

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Year

Mean 21,0 55,0 114,8 175,4 227,2 227,8 223,4 171,0 124,0 60,0 19,3 15,9 119,6

Std. Error 2,7 7,7 8,1 10,5 11,5 12,3 15,8 11,0 10,2 7,7 2,1 2,7 3,0

Medain 19,0 43,0 115,0 170,0 225,0 236,0 224,0 167,0 114,0 49,0 20,0 13,0 115,8

Std. Deviation

9,6 27,7 29,1 37,7 41,3 44,3 56,9 39,6 36,8 27,7 7,5 9,6 10,6

Variance 92,5 767,3 845,2 1420 1707 1961 3240 1570 1353 766,3 56,7 92,4 113,3

Kurtosis 2,9 1,1 -0,6 -0,1 5,1 -1,1 -0,8 0,3 0,1 -0,1 -0,6 0,1 -1,6

Skewness 1,6 1,5 -0,4 -0,3 1,8 0,2 -0,3 0,3 0,6 0,8 -0,6 0,8 0,3

Range 35,0 87,0 95,0 137,0 162,0 137,0 180,0 151,0 124,0 92,0 23,0 31,0 30,8

Minimum 11,0 31,0 66,0 101,0 181,0 166,0 115,0 99,0 78,0 27,0 6,0 4,0 106,9

Maximum 46,0 118,0 161,0 238,0 343,0 303,0 295,0 250,0 202,0 119,0 29,0 35,0 137,7

N 13 13 13 13 13 13 13 13 13 13 13 13 13

Tartu-Toravere, global radiation

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Year

Mean 15,2 42,8 98,8 157,3 217,4 232,3 226,5 173,3 109,4 48,1 15,8 9,2 111,9

Std. Error 0,9 2,7 3,8 5,2 5,8 6,2 7,6 5,3 3,7 2,4 0,8 0,7 1,6

Medain 14,5 40,0 97,0 156,0 218,0 232,0 224,0 171,0 112,0 45,0 16,0 9,0 110,5

Std. Deviation

3,0 9,3 13,0 18,8 20,8 22,5 27,2 19,2 13,2 8,7 2,8 2,4 5,5

Variance 9,1 85,7 169,2 352,2 432,9 504,6 742,3 370,4 174,8 75,2 8,0 5,6 30,3

Kurtosis 3,9 -0,4 -0,5 -0,2 4,4 -1,7 0,1 1,1 -0,7 -0,8 -0,3 0,4 -1,0

Skewness 1,6 0,5 -0,1 -0,5 1,5 -0,1 -0,6 0,2 -0,3 0,6 -0,6 0,8 0,4

Range 12,0 31,0 44,0 60,0 84,0 59,0 95,0 78,0 44,0 27,0 9,0 8,0 16,4

Minimum 11,0 28,0 75,0 123,0 190,0 203,0 168,0 136,0 87,0 38,0 11,0 6,0 105,3

Maximum 23,0 59,0 119,0 183,0 274,0 262,0 263,0 214,0 131,0 65,0 20,0 14,0 121,7

N 12 12 12 13 13 13 13 13 13 13 13 13 12

Tartu-Toravere, diffuse radiation

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Year

Mean 11,8 28,0 53,0 69,4 89,3 99,9 96,8 81,0 55,1 29,3 11,9 7,3 52,7

Std. Error 0,5 1,1 2,0 1,2 1,7 2,4 2,1 1,4 0,9 0,4 0,4 0,4 0,5

Medain 12,0 29,0 52,0 69,0 88,0 99,0 96,0 81,0 56,0 29,0 12,0 7,0 53,3

Std. Deviation

1,8 4,0 7,4 4,4 5,9 8,7 7,6 5,1 3,4 1,5 1,3 1,4 1,9

Variance 3,2 16,2 54,5 19,8 35,4 76,4 58,4 25,8 11,6 2,4 1,7 1,9 3,5

Kurtosis -0,3 0,5 -1,5 0,7 -0,8 1,1 -1,1 -0,7 -1,0 -0,8 -0,8 -0,7 1,0

Skewness 0,0 -0,9 0,2 -0,4 0,1 -0,2 0,5 -0,4 -0,6 0,0 0,2 0,7 -0,9

Range 6,0 14,0 22,0 17,0 19,0 35,0 23,0 16,0 10,0 5,0 4,0 4,0 6,7

Minimum 9,0 19,0 42,0 60,0 79,0 81,0 88,0 72,0 50,0 27,0 10,0 6,0 49,1

Maximum 15,0 33,0 64,0 77,0 98,0 116,0 111,0 88,0 60,0 32,0 14,0 10,0 55,8

N 13 13 13 13 13 13 13 13 13 13 13 13 13

Cabauw, direct radiation

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Year

Mean 40,4 43,9 96,4 159,0 169,9 176,6 163,6 131,8 113,4 82,4 37,7 30,6 105,6

Std. Error 5,6 10,4 9,7 16,7 10,3 15,5 18,2 10,8 7,8 5,3 4,2 4,2 2,0

47

Medain 37,0 30,0 98,5 153,5 158,0 185,0 146,0 132,5 116,0 80,0 36,0 32,0 106,8

Std. Deviation

14,7 29,5 27,5 47,3 29,1 43,7 51,5 30,6 20,6 14,1 11,2 11,1 5,0

Variance 217,3 871,0 755,4 2239 844,4 1911 2648 939,4 426,3 198,3 124,6 123,3 24,5

Kurtosis -1,0 0,2 0,4 -0,4 0,2 -0,4 1,9 -0,4 0,3 -1,3 -1,0 -0,8 2,0

Skewness 0,6 1,3 -0,1 0,1 0,9 -0,4 1,5 0,1 -0,5 0,0 0,5 0,4 -1,4

Range 39,0 78,0 90,0 148,0 89,0 128,0 154,0 94,0 61,0 39,0 30,0 31,0 13,0

Minimum 25,0 20,0 51,0 86,0 134,0 113,0 116,0 86,0 78,0 62,0 23,0 17,0 96,6

Maximum 64,0 98,0 141,0 234,0 223,0 241,0 270,0 180,0 139,0 101,0 53,0 48,0 109,6

N 7 8 8 8 8 8 8 8 7 7 7 7 6

Cabauw, global radiation

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Year

Mean 30,0 50,1 107,0 182,5 214,4 230,6 215,1 176,1 129,3 77,4 34,4 22,7 122,8

Std. Error 1,8 3,3 3,1 8,5 5,4 8,2 10,1 7,2 4,0 1,8 1,5 0,9 1,2

Medain 29,0 44,5 109,0 178,0 216,5 238,5 203,0 175,0 131,0 77,0 34,0 24,0 123,0

Std. Deviation

4,8 9,2 8,8 24,0 15,1 23,3 28,7 20,3 10,7 4,8 4,0 2,4 2,8

Variance 23,3 85,0 78,3 574,3 229,4 542,8 821,3 411,0 114,6 22,6 16,3 5,9 8,1

Kurtosis -1,4 -1,7 -0,5 -0,2 -1,2 -1,1 0,5 -1,2 -2,0 3,2 -1,8 1,8 -0,7

Skewness 0,2 0,7 -0,4 0,0 0,2 -0,5 1,2 0,1 -0,2 1,5 0,4 -1,5 0,0

Range 13,0 23,0 26,0 76,0 42,0 64,0 80,0 58,0 27,0 15,0 10,0 7,0 7,8

Minimum 24,0 41,0 94,0 144,0 196,0 196,0 190,0 147,0 115,0 72,0 30,0 18,0 118,9

Maximum 37,0 64,0 120,0 220,0 238,0 260,0 270,0 205,0 142,0 87,0 40,0 25,0 126,8

N 7 8 8 8 8 8 8 8 7 7 7 7 6

Cabauw, diffuse radiation

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Year

Mean 19,6 34,9 62,5 93,6 109,5 120,0 113,8 99,1 72,1 44,9 23,7 16,1 66,9

Std. Error 0,6 1,1 1,8 1,8 2,3 2,3 2,4 1,7 1,0 1,2 0,5 0,7 0,4

Medain 20,0 34,5 62,0 91,5 108,5 121,0 114,0 99,5 72,0 45,0 23,0 16,0 66,8

Std. Deviation

1,6 3,2 5,2 5,0 6,6 6,6 6,8 4,7 2,7 3,2 1,4 1,9 1,0

Variance 2,6 10,1 27,1 24,6 44,0 43,7 45,6 21,8 7,1 10,5 1,9 3,5 0,9

Kurtosis -1,5 -0,4 -0,4 0,3 -0,6 -1,6 2,0 -0,5 -1,4 -2,1 -0,3 1,0 2,8

Skewness 0,3 0,1 0,2 1,1 0,6 -0,3 -1,1 0,3 0,1 0,1 0,7 -0,3 1,4

Range 4,0 10,0 16,0 14,0 19,0 18,0 22,0 14,0 7,0 8,0 4,0 6,0 2,8

Minimum 18,0 30,0 55,0 89,0 102,0 110,0 100,0 93,0 69,0 41,0 22,0 13,0 65,8

Maximum 22,0 40,0 71,0 103,0 121,0 128,0 122,0 107,0 76,0 49,0 26,0 19,0 68,7

N 7 8 8 8 8 8 8 8 7 7 7 7 6

Payerne, direct radiation

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Year

Mean 151,9 239,6 291,8 307,3 328,2 368,0 376,5 359,0 303,2 211,0 135,5 113,1 265,0

Std. Error 16,1 18,9 16,7 22,3 15,0 13,2 7,7 14,2 15,3 14,5 12,5 13,4 4,8

Medain 162,0 230,0 298,5 290,5 326,0 361,0 374,0 363,0 290,0 210,5 125,5 111,0 261,9

Std. Deviation

62,3 75,6 66,6 89,0 62,0 54,2 31,7 58,5 63,0 57,9 50,2 51,8 17,9

Variance 3887 5718 4435 7926 3849 2941 1002 3420 3966 3348 2515 2683 319,1

Kurtosis 0,2 -1,5 3,4 1,2 0,9 -0,7 -1,0 -1,1 -0,6 0,3 -0,9 0,0 -0,7

Skewness -0,3 0,1 -1,2 0,9 1,0 0,0 0,2 -0,2 0,3 -0,7 0,5 0,4 0,3

Range 231,0 231,0 303,0 355,0 238,0 181,0 102,0 179,0 213,0 219,0 159,0 189,0 58,8

Minimum 21,0 122,0 107,0 149,0 243,0 269,0 325,0 263,0 194,0 76,0 59,0 21,0 237,3

Maximum 252,0 353,0 410,0 504,0 481,0 450,0 427,0 442,0 407,0 295,0 218,0 210,0 296,0

N 15 16 16 16 17 17 17 17 17 16 16 15 14

Payerne, global radiation

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Year

Mean 43,9 80,4 135,8 181,8 223,3 259,9 247,2 209,8 153,5 90,2 49,9 33,7 142,9

Std. Error 2,0 2,7 4,2 6,5 4,8 5,6 3,6 4,3 4,5 3,0 1,8 1,4 1,4

Medain 44,5 80,0 137,5 177,0 225,0 256,0 243,0 210,0 154,0 92,0 51,0 33,0 143,1

Std. Deviation

7,9 10,9 16,8 26,8 19,8 23,2 14,9 17,8 18,5 12,2 7,3 5,6 5,5

Variance 61,7 119,5 283,8 718,0 390,2 540,1 223,4 317,9 340,8 149,7 53,9 31,2 30,8

Kurtosis 2,2 -0,9 2,6 0,4 0,0 -0,2 -0,3 0,2 -1,0 1,5 -0,5 0,1 0,8

Skewness -1,2 0,3 -0,7 0,9 0,2 0,4 0,4 -0,3 -0,1 -1,0 0,0 -0,5 0,6

Range 32,0 37,0 77,0 94,0 74,0 88,0 56,0 70,0 60,0 49,0 26,0 21,0 21,9

Minimum 23,0 63,0 92,0 149,0 191,0 218,0 222,0 170,0 120,0 58,0 37,0 21,0 134,3

Maximum 55,0 100,0 169,0 243,0 265,0 306,0 278,0 240,0 180,0 107,0 63,0 42,0 156,2

N 16 16 16 17 17 17 17 17 17 17 17 17 16