Weather data for building simulation574999/... · 2012. 12. 7. · Dynamic building simulation is...
Transcript of Weather data for building simulation574999/... · 2012. 12. 7. · Dynamic building simulation is...
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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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.
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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
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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
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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
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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
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SD Standard Deviation
BIM Building Information Modeling is a digital representation of physical and
functional characteristics of a facility
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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:
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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
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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)
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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
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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
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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
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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.).
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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.
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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%
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20%
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30%
35%
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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
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-10%
-5%
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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
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1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012
Direct Global Diffuse
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Lerwick direct Lerwick global Lerwick diffuse
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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.
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“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.
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[Accessed 24 9 2012].
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Norwegian Meteorological Institute, n.d. eKlima. [Online]
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tjanster/Fastighet/normalarskorrigering-under-var-sommar-och-host-med-smhi-graddagar-1.18575
[Accessed 22 10 2012].
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[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