Control de calidad de datos de radiación solar dentro de la red de medidas solar RMIB

7/27/2019 Control de calidad de datos de radiacin solar dentro de la red de medidas solar RMIB

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Available online atwww.sciencedirect.com

Solar Energy 85 (2011) 7286www.elsevier.com/locate/solener

Quality control of solar radiation data within the RMIB

solar measurements network

Michel Journe , Cdric Bertrand

Royal Meteorological I nstitute of Belgium, Avenue Cir culair e 3, B-1180 Brussels, Belgium

Received 20 April 2010; received in revised form 21 September 2010; accepted 30 October 2010Available online 30 November 2010

Communicated by: Associate Editor Frank Vignola

Abstract

Assessment of the solar resource is based upon measured data, where available. However, with any measurement there exist errors.Consequently, solar radiation data do not exhibit necessarily the same reliability and it often happens that users face time series of mea-surements containing questionable values though preliminary technical control has been done before the data release. To overcome such asituation, a major effort has been undertaken at the Royal Meteorological Institute of Belgium (RMIB) to develop procedures andsoftware for performing post-measurement quality control of solar data from the radiometric stations of our in situ solar monitoringnetwork. Moreover, because solar energy applications usually need continuous time series of solar radiation data, additional procedureshave also been established to fill missing values (data initially lacking or removed via quality checks). 2010 Published by Elsevier Ltd.

Keywords:Global, direct and diffused solar radiation; Sunshine duration; Quality control; Empirical models

1. Introduction

With the development of solar-based renewable energytechnologies national meteorological services are faced withincreasing demands for reliable solar resource data. Up-to-dateseries of these data are also being sought by archi-tects and

building services professionals for better design of buildings.Compared to measurements of other meteorologi-cal variables,the measurement of solar radiation is more prone to errors(Moradi, 2009). Younes et al. (2005) identified two major

categories ofpossible sources of problems or errors related to insitu measurement of solar radiation: (1) equip-ment error anduncertainty and, (2) operation related prob-lems and errors;with the most common sources of error arising from thesensors and their constructions (e.g., Muneer and Fairooz,2002; Younes et al., 2005). Because of the diffi-cultiesfrequently encountered when measuring solar radia-tion andthe resultant unknown quality of some solar

Corresponding author. Tel.: +32 2 3730598.E-mail address:[email protected](M. Journe).

0038-092X/$ - see front matter 2010 Published by Elsevier Ltd.

doi:10.1016/j.solener.2010.10.021

radiation data, it is crucial to perform a quality assessment ofthese data prior to their further processing (e.g., Hay, 1993).As an example Colle et al. (2001) have shown thatuncertainty in life cycle savings for solar thermal and photo-voltaic systems are linearly correlated with uncertainty insolar resource data.

Because quality control may be a lengthy and tedioustask, most of the customers and scientists are ready to usedata from meteorological offices in confidence without

performing an additional precise and fine control . A major

effort has therefore been recently undertaken at the RoyalMeteorological Institute of Belgium (RMIB) to developquasi-automated procedures and software for performing

post-measurement quality control of solar data in addit ionto the human data monitoring.

The usual solar radiation parameters measured onground are the global solar irradiance, the direct solarirradiance and the sunshine duration. We are currentlymeasuring various combinations of these parameters in14 automatic weather stations (AWS) in addition to themeasurements performed in our main/reference station in
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M. Journe, C. Bertrand / Solar Energy 85 (2011) 7286 73

Uccle (see Table 1 and Fig. 1). Since a few years, solarradi-ation data are integrated to bring them to a 10 min timestep (local mean time or clock time) in addition to the his-torical 30 min (solar time) time step.

Based on previously proposed procedures for qualityassessment of solar irradiation data (e.g., Maxwell et al., 1993;

Molineaux and Ineichen, 1994; Terzenbach, 1995; Geiger etal., 2002; Muneer and Fairooz, 2002; Younes et al., 2005; Shiet al., 2008; Moradi, 2009; Tang et al., 2010), we present inthis paper a new quality control scheme devel-oped for thesolar data measured within the RMIB solar radi-ationmeasurements network. In contrast to previously publishedquality control algorithms usually devoted to hourly or dailysolar radiation data, the new scheme is intended for sub-hourlydata (i.e., 10 min and 30 min averaged data). Since for solarenergy applications there is a need for continuous time seriesof solar radiation data to correctly assess the useful-ness of theparticular application and in its implementation, additionalprocedures have also been developed to provide users with an

estimation of missing solar values (i.e. data ini-tially lackingor failing the quality assessment criteria).

The paper is organized as follows: the new quality controlscheme is presented in the next section. Section 3 deals withprocedures to fill missing values in the data time series andtheir validation. Conclusions are given in Section 4. The mainnotations used in this paper are explained in Table 2.

2. Quality control of solar radiation and sunshine

measurements

The quality control of radiometric observations involvesvarious tests to establish boundaries or limits within whichacceptable data are expected to lie. These tests are guidedeither by physical reasoning (to detect physically impossibleevents) or by the statistical variability of the data (to detectvery rare and thus questionable events). Furthermore, they

either treat the various solar radiation parameters separately orcompare them to each other. Temporal dependence in the datacan eventually be taken into account. Finally, data frommultiple sites can be used to investigate spatial depen-dence.The proposed scheme for quality control of radiomet-ric data(see Fig. 2) involves several categories of tests that are

detailed in the forthcoming sections and summed up in Table3. While most of these tests can be used in a fully auto-matedmanner, some aiming at detecting specific error types (e.g.,misleading calibrations of the instruments as well as theimpacts of shadow and snow) require a decision taken by ahuman operator. Depending on the results of these tests, flagswith attribute eithervalid, suspicious orerrone-ousare set to inform the user of any departure of the data fromexpected values. All details on the rules followed to attributethe quality flags are provided in Table 4. Data that fail the testsare not deleted or modified but stored because they mayprovide valuable insight into the origin of failure.

Because the developed procedures can be applied to our

10 and 30 min averaged solar radiation data, solar irradi-ance values (in W m-2) are first converted in terms of solarirradiation data (in W h m-2). Sunshine duration values areexpressed in minutes. Finally, it is important to men-tionthat all threshold values used in these tests, except thosederived from physical reasonings, were established fromthe RMIB solar radiation data with the objective todiscriminate valid observations from erroneous ones. Thesevalues are thus representative of a low-altitude Europeanregion and might be adjusted for other regions.

2.1. Physical threshold tests

Physical limits on the solar radiation parameters arederived from the solar radiation at the top of the atmo-sphere (TOA) and at the Earths surface for both very clearskies and overcast skies.

Table 1Location of the ground stations involved in the RMIB solar radiation monitoring network, with the associated availability for the global horizontalradiation, the ground-reflected radiation, the diffuse horizontal radiation, the direct normal radiation and the sunshine duration.

Station code & name Lat. (oN) Long. (oE) Alt. (m) Global incident &reflected

Diffuse Direct &duration

6407 Middelkerke 51.198 2.869 3 x x6414 Beitem 50.905 3.123 25 x x6418 Zeebrugge 51.349 3.196 8 x6434 Melle 50.976 3.825 15 x x6439 St.-Katelijne-Waver 51.076 4.526 10 x x6447 Uccle 50.798 4.359 101 x x x6455 Dourbes 50.096 4.596 233 x x6459 Ernage 50.583 4.691 157 x x6464 Retie 51.222 5.028 21 x x6472 Humain 50.194 5.257 296 x x6476 Saint-Hubert 50.040 5.405 557 x x6477 Diepenbeek 50.916 5.451 39 x x6478 Bierset 50.646 5.452 176 x6484 Buzenol 49.621 5.589 324 x x

6494 Mont Rigi 50.512 6.075 673 x x


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74 M . Jour ne, C. Ber tr and/Solar Energy 85 (2011) 7286

5130'

6418

64646407

6439

5100'6414

6447

6478

6459

5030'

6472

6455

5000'

6484

0 50 100

4930' 4930'

6434

6476

6477

6494

5130'

5100'

5030'

5000'

230' 300' 330' 400' 430' 500' 530' 600' 630'

230' 300' 330' 400' 430' 500' 530' 600' 630'

Fig. 1. RMIB solar radiation measurements network. See Table 1 for the stations names and geographical coordinates.

Table 2Nomenclature.

E Extraterrestrial solar radiation on a horizontal surfaceG Global solar radiation on a horizontal surfaceD Diffuse solar radiation on a horizontal surfaceB' Direct beam solar radiationB= B'sin(h) Direct solar radiation on a horizontal surfaceh Solar elevation angleSD Sunshine duration (in minutes)SDmax Maximal sunshine duration, i.e., either 10 or 30 minR Ground-reflected solar radiationKt= G/E Clearness indexKn= B/E Beam transmittanceK= D/G Diffuse ratio

First, the global solar radiation on a horizontal surface atthe Earths surface, G, has to be less than the corre-sponding extraterrestrial value incident on a horizontalsurface, E. It is possible that solar irradiation at the surfaceis larger than at TOA for short time periods because of thediffusive effects of clouds that are not in the way of thesolar beam (Shi et al., 2008). This situation, which can bequite frequent in high altitude regions in case ofconvective clouds (Yang et al., 2010), is however notexpected for low-land areas except when the elevation ofthe sun above the horizon is small. We hence imposed thecondition G< Eto all data with a solar elevation anglegreater than 2. Because the global radiation accounts forcontributions of both the beam and the diffuse radiation,beam, B, and diffuse, D, radiation incoming on ahorizontal surface can-not be larger than E.

Second, because solar radiation at the surface is affectedby atmospheric absorbing gases, clouds, and aerosols themeasured values cannot exceed the maximum income ofsolar radiation with clear sky and high atmospheric

transparency, e.g., Gueymard (2004). As in Geiger et al.

Fig. 2. Flow diagram for the quality control of radiometric data. SeeTable 3 for the description of the labels used to denote the various testsand Table 4 for the rules followed to assign quality flag attributes(QCflag).

(2002), clear sky solar irradiations are assessed by means ofthe modified European Solar Radiation Atlas (ESRA)model. This model is based upon a parameterization for-

mula by Kasten (ESRA, 1984; Kasten, 1996) and has been


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M. Journe, C. Bertrand/ Solar Energy 85 (2011) 7286 75

G/Gcs61.1 ifh > 2G/Gcs62 ifh62

/Bcs61D/Dcs?... 1

G/E?... 10-4(h-10) ifh> 10 G?... 0 ifh610?... 0

l(G/E)?... 0.03

B/G?... 1R/G?... 0.7

< 0:75 if h(t)>

< 0:65 if h(t)> 2

< 0:35 if h(t)>

h(t) > 2B(t)?... G(t) andB(t-1) < G(t-1)

E(t)G(t)

G (t - 1)E (t -1)

E (t)B (t)

B (t - 1)E (t - 1)

E (t)D (t)

D (t - 1)E (t - 1)

k =

Table 3Quality criteria of radiometric data used in physical threshold tests (PT), step tests (S), persistence tests (P), quality envelope tests (QE), spatialconsistency tests (SC) and sunshine tests (SD).

Test Test description Quality criterialabe l

PT1 Comparison of surface solar radiation data against the extraterrestrial solar radiation G/E< 1 ifh > 2B/E< 1

D/E< 1 ifh > 2

PT2 Comparison of surface solar radiation values against the outputs of the modified ERSAmodel for clear sky

PT3a Lower bounds on G andB derived from heavily overcast conditions with low atmospherictransparency

PT3b Lower bounds on G derived from heavily overcast conditions with low atmospherictransparency. The daily mean l is derived from all data acquired from sunrise to sunset

PT4 Tests derived from the relation G =B +D B/G 60.95 ifh > 2B/G < 1 ifh 62D/G61

PT5 Test to detect snow-corrupted measurements of the global solar radiation. Special care hasto be taken when these two conditions hold simultaneously

S1 Bounds on the variations of the solar radiation parameters between two successivetimestamps

S2 Test to detect shadow obscuring the global sensor. Special care has to be taken when thesefour conditions hold simultaneously

E (t)G (t)

G (t -1)E (t -1) > 0:1

P1 Persistence tests. The daily mean l and standard deviation r are derived from all dataacquired from sunrise to sunset

G t -G t-1

B(t)-B(t-1) > 3 or


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surface solar irradiation are compared against the outputs ofthe model by means of the following thresholds:

The upper limit for G is set as 1.1 times the calculatedclear sky global solar irradiation value, Gcs.

The upper limit for the direct beam irradiation, B-L, is setas the calculated clear sky beam irradiance, Bc

-Ls.

Because diffuse irradiation usually increases with theatmospheric turbidity and cloud amount, the lower limitforD is set to its calculated value under clear-sky and

high atmospheric transparency condition,Dcs.

Following Geiger et al. (2002), the upper bound on Gneeds to be relaxed (i.e., G < 2Gcs) when the elevation ofthe sun above the horizon is small (i.e., smaller than 2)


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76 M . Journe, C. Bertr and/Solar E nergy 85 (2011) 7286

Table 4Decision rules for quality flag attributes of solar radiation and sunshine duration data. These rules follow the flow diagram in Fig. 2. See Table 3 for thedescription of the labels used to denote the various tests.

Fail ur e of semi-automated tests

Detection of a snow-corrupted value ofGby test PT5 The misleading value is flagged as erroneous.Detection of shadow contamination in the Gvalues by test S2 Misleading values are replaced by linearly interpoled values when possible or

otherwise flagged as erroneous.

Calibration error detected by test SC1 or by visual inspection ofscatter plots in K-Ktand Kn-Ktspaces

Fail ure of single parameter testsFailure of the physical threshold tests PT1, PT2, PT3a or the step

test S1

A compensation factor is applied to all misleading data when possible. Thesevalues are otherwise flagged as erroneous.

The misleading value is flagged as erroneous.

Failure of the physical threshold test PT3b All Gdata from sunrise to sunset are flagged as erroneous.Failure of the persistence test P1 All data from sunrise to sunset of the misleading solar radiation component are

flagged as erroneous.

Fai lur e of i ntra-parameter tests(only for {G,B} data that succeeded all previous tests)Failure of physical threshold tests PT4 or the quality code

resulting from the quality envelope tests QE1 and QE2 equals 2

The quality code resulting from the quality envelope tests QE1 andQE2 equals 3

The quality code resulting from the quality envelope tests QE1 andQE2 equals 4

The Bdata is flagged as erroneous, except if quality envelope tests indicate thatthe direct sensor is reliable and the temperature is negative. In the latter situation,the Gdata is flagged as erroneous.The Bdata is flagged as suspicious.

The Bdata is flagged as erroneous.

Fai lur e of sunshin e tests

Failure of sunshine tests SD1 or SD2 The SDdata is flagged as erroneous.

I n all other cases

Solar radiation data that succeeded these tests are considered as valid.Sunshine duration data that succeeded these tests are assigned with the same quality flag as the concurrent direct solar radiation data.

because of the instrumental precision and atmospheric phe-nomena like refraction that are present.

Regarding lower limits on Gand B, the opposite sky con-ditions need to be considered, i.e., heavily overcast condi-

tions with low atmospheric transparency. If under theseconditions the direct irradiance can be null, the diffuse irra-diance never reaches zero during day time. Geiger et al.(2002) proposed to set a lower limit on Gas 3% of the extra-terrestrial value incident on horizontal surface in the case ofhourly and daily cumulated data. Because this bound leads toexcessively large rates of rejection in the case of sub-hourlydata, we chose to replaced it by a less restrictive condition ofthe form: G/E10-4(h- 10) for all solar elevation angles, h,greater than 10 with the additional con-dition that thelower bound at 3% of the extraterrestrial radiation holds ondaily average for all global solar radia-tion data acquiredfrom sunrise to sunset.

Finally, because of the geometrical relation betweenglobal, direct and diffuse irradiance components, B+ D=G, the basic inequalities D Gand B Gmust be verified.Because the diffuse irradiance never reaches zero duringday time and is minimal under clear-sky and high atmo-spheric transparency condition, the upper limit on thedirect horizontal irradiation Bcan be further reduced to G-Dcs, which is well approximated by the condition B0.95Gwhen the solar elevation angle is not too small (i.e., greaterthan 2). Because global irradiance is mea-sured from afixed instrument while direct irradiance requires to trackthe sun, the latter quantity is the most del-icate to measure

precisely (Molineaux and Ineichen, 1994).

Hence, the values of direct solar radiation are the first to beconsidered doubtful when a lack of compatibility is identi-fied between B and G values, except when there issufficient insight to incriminate G rather than B. For

instance, the condition B< Gis usually not satisfied whenthe global sensor is covered by snow. Evidence for snow-corrupted G values can rely on measurements of theground-reflected solar radiation, R, that are available atmost stations of the RMIB solar measurements network(see Table 1). An underestimated value of Gleads to anoverestimation of the surface albedo (=R/G) that cannotexceeds certain lim-its. This snow test is optional and let tothe operators decision.

The threshold values used for the three components ofsurface solar irradiation are summed up in Table 3.

2.2. Step tests

Step tests check for a plausible rate of change from apreceding acceptable level (e.g., detection of unrealisticspikes or jumps in values, or dead band caused by blockedsensors).

First, the variations of the solar radiation measurementsbetween two successive timestamps cannot exceed certainlimits. Maximal variations of up to 800 W m-2 are usuallyrecommended for instantaneous (i.e., 1 min averaged) solarirradiances (Shafer et al., 2000; WMO, 2007). In the case of10 min data, we preferred to impose upper bounds on thevariations of the clearness index Kt= G/E, the beam trans-

mittance Kn= B/Eand the diffuse transmittance Kd= D/E,


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< 0.75 ,

< 0.65, 1

< 0.35,

G

B

D

2

AWS 6476 2009/01/11

4 00

350

300

2 50

2 00

15 0

10 0

5 0

1.5 1 0.5 0 0.5 1 1.5

AWS 6476 2009/01/30

EGB

400

300

200

10 0

1.5 1 0.5 0 0.5 1 1.510min.averagedsolarradiation[W.m

2]

10min.averagedsolarradiation[W.m2]450 600

50 0


G tEt1

B t

Et1

D t

Et1

where t1 and tare two successive timestamps. Because ofthe instrumental precision, the conditions (1) are consid-ered only when the solar elevation angle is greater than 2.

Second, the variations of the various solar radiationparameters need to be, in some sense, compatible with eachother, e.g., large fluctuations of the beam irradiance need tobe reflected in the time series of bothB and G. Although it isdifficult to set strict conditions for compatible rates of changein the overall case, a comparison of the G and B diur-nalevolutions is very useful to detect shadow contaminations in

the G data. In such a case, G exhibits large variations (i.e., arapid drop of the values followed by a sudden increase whenthe shadow disappears) that are either not reported or reportedwith a slight time delay in theB time series (see Fig. 3). Theratio GtGt1

BtBt1is large either in the positivedirec-tion (e.g., greater than 3) or in the negative direction(e.g., smaller than 1). In addition, a significant variationof theclearness index is observed, Gt

> 0 . 1 . A l t h o u g h t h i s Et Et1

situation is most often already identified by the non satisfac-tion of the compatibility conditionB(t) < 0.95G(t), compar-ingthe rates of change enables to further identify the origin of thefailure. The final attribution has however to rely on a visualinspection of the G and B time series. Because only a fewnumber of successive data are usually misleading, theerroneous data can often be replaced by linearly interpolatedvalues.

All threshold values used in these step tests are providedin Table 3.

2.3. Persistence tests

Persistence tests check the variability of the measure-ments. When a sensor fails, it often reports a constant

value, leading to a small standard deviation. The standarddeviation can even be null if the sensor is out for the entirereporting period. On the other hand, when an instrumentworks intermittently and produces reasonable values inter-spersed with misleading values, the variability can some-times be excessively high. Thus, data should be flagged for

further check when the standard deviation exceeds lowerand upper limits. Statistical quantities are computed fromall solar radiation data acquired over the day (from sunriseto sunset). For all three components of the solar radiation,the lower bound on the standard deviation, r, of the dailyseries of data is expressed as an increasing func-tion of themean l:

8lE G G 0 .35 ,

E 1 DW D0.2,6 l

E

rB 60.3,E

with the lower limitk

0 iflBE60.01,

21lE if 0.01


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Fig. 3. Time series of solar radiation data contaminated by shadow (contamination of the G data only (left panel) or both the G andB data (right-panel)).

(For interpretation to colours in this figure, the reader is referred to the web version of this paper.)

Solar hour angle [rad] Solar hour angle [rad]


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78 M. Journe, C. Bertrand/Solar Energy 85 (2011) 7286

dimensionless space are the clearness index Kt = G/Efor theabscissa and either the atmospheric transmission of the beamradiation as in Maxwell et al. (1993), Kn =B/E, or the diffuseratioK=D/G as in Younes et al. (2005). When no measure-ment of the diffuse solar radiation is available, the diffuseratio is estimated from the difference between the global and

the beam horizontal radiation, K= (G B)/G. In the case ofsub-hourly data, these tests are restrained to solar radiationdata acquired for a solar elevation angle greater than 2.Typical distributions of the data in the KtK and KtKnspaces are provided in the top plots of Fig. 5. Although thephilosophy is similar, the proposed approach differs fromYounes et al. (2005) and Maxwell et al. (1993) in theestablishment of the boundary shapes around the data.

The SERI QC quality control algorithm proposed byMaxwell et al. (1993) relies on the use of climatologicalboundaries established from scatter plots of historical goodquality solar radiation data in the KtKn space. Whenperforming data quality control, the boundaries are firstautomatically selected from a set of predefined empiricalboundary shapes using a criterion whereby the selection oftighter fitting boundaries results in a greater percentageincrease in errors than the percentage decrease in theacceptable data between the boundaries. The position of theselected boundaries are then manually adjusted such that upto 5% of the data lay outside the boundaries. This criterionwas based both on the assumption that some of the datawere in error and a desire to limit the acceptance oferroneous data to small percentages, while similarly lim-iting the rejection of good data.

Younes et al. (2005) proposed a statistical approach to

construct the KKt quality control envelopes on the ana-lyzed data. Basically, the Kt range of data is divided into nbands of equal width, within which the mean and standarddeviation of theKvalues, jii and ri, are calculated. The topand bottom boundary shapes are identified by fitting apolynomial through the points {jii + a ri}i = 1,...,n and {jiiari}i = 1, ...,n, respectively. Polynomial values are lim-itedbetween 0 and 1 to respect the physical limits of K.Finally, the cut-off points (the respective intersection ofthe upper and lower polynomials with the K= 1 andK= 0limits) are selected by visual inspection. The rejection ratelies usually between 2% and 6%.

The proposed method follows the statistical approach ofYounes et al. (2005) in the establishment of the boundaryshapes around the data, but does not require any manualoperation and can be used in both KtK and KtKnspaces. Moreover, our analysis uses recorded and simu-lated data, and considers both climatological envelopes asin Maxwell et al. (1993) and envelopes directly computedfrom the analyzed data.

Direct irradiance is the most delicate quantity to measureprecisely (Molineaux and Ineichen, 1994) and deficiencies inthe direct sensor may remain unseen in the absence of thedif-fuse component. Therefore, the procedure first starts byesti-mating the direct solar horizontal radiation, bB, from the

measured global horizontal solar radiation G using the

formulation of Skartveit and Olseth (1987) (see Section3.1). Although direct solar radiation is difficult to estimateprecisely, the accuracy of this G-to-B model is sufficient todetect gross deviations in the measurements. Both the mea-sured and the estimated direct solar radiation componentsare then plotted in the KtKand KtKn spaces (see Fig.4). For each distribution of points, a mean curve as a

function ofKt, ji(Kt) or^jiKt, is computed by dividingtheKt range in nbands and fitting a polynomial through themean of theK(orKn) values in each band (see the blue andgreen lines on the four panels in Fig. 4). The root meansquared distance between the two mean curves,

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1 XN D k 1jiKk

t ^jiKkt 2 ; N

is then evaluated, where N is the number of points in thescatter plots and Kk

t is the clearness index of the kth point.

Depending on the value of D with respect to a giventhresh-old (see Table 5), the direct sensor is consideredeither as reliable (see top plots ofFig. 4) or as deficient (seebottom plots of Fig. 4). In the former case, qualityenvelopes are directly constructed from the measured databy fitting polynomials through the points located at a fewstandard deviations above and below the mean in each bandto define the top and the bottom boundary shapes, as inYounes et al. (2005). The quality envelope width was set tofive times the standard deviation in each band, which is25% more than suggested by Younes et al. (2005). Thischoice was made to avoid as much as possible the rejectionof valid observations potentially related to rare events. In

addition to the fitted top and bottom boundaries, an upperlimit Kmaxt is set on the Kt values in such a way that Kmax

t isthe smallest value for which the right outliers (i.e., the datapoints such that Kt > Kmax

t ) are distant by more than 0.02 inKtvalues from the accepted data points.

When the direct sensor is found inefficient, a climatolog-ical quality envelope is used to filter the data. The climato-logical quality envelope was determined from two years ofdata (2008 and 2009) that succeeded all previous qualitycontrol tests. Examples of quality envelopes are provided inFig. 5.

Depending on the instruments reliability and the posi-

tion of the data with respect to the quality envelope, a qual-ity code ranging from 1 to 4 is given to each data pair{G,D} or {G,B}, as detailed in Table 6. When no measure-ment of the diffuse radiation is available, two quality codes(one for each of theKtKandKtKn spaces) are assignedto each pair {G,B}. Because these quality codes can differfrom each other, we retain the smallest value of them, i.e., asensor is considered as being deficient only if it found as itin both spaces.

Finally, it should be mentioned that a visual inspectionof the data distributions in the KtK and KtKn spacescan sometimes highlight failures in the global sensor. Thisis particularly under concern as the default assumption is to

attribute the wrong measurements to the direct sensor. Forinstance, a calibration error on one sensor is reflected


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.

.

.

.

.Kn

.

.

.

.

.

.

.

.Kn

.

.

.

o

Measured dataSimulated data

.

.

.

.

.

.

.

.

.

. . . . . . . . .

K t

to

.

.

.

.

.

.

.

.

.

. . . . . . . . .

K t

o

. . . . . . . . .

K t

to

. . . . . . . . .

K t

K

K

wi1/4

Fig. 4. Scatter plots and corresponding mean curves of solar radiation data in the KtKandKt~Kn spaces for reliable instruments (top plots) and in caseof a deficient instrument for the measure of the beam solar radiation B (bottom plots). (For interpretation to colours in this figure, the reader is referred tothe web version of this paper.)

Table 5Upper limits on the root mean squared distance A used in quality envelopetests to evaluate the overall reliability of the direct sensor when the modelofSkartveit and Olseth (1987) is used to estimate the direct solar radiation.The seasonal dependence reflects the larger dispersion of the data insummer because of the higher frequency of clear and partly clear skies.

Season KtKspace Kt~Kn space

Winter 0.085 0.050Spring 0.115 0.070Summer 0.125 0.075

Autumn 0.115 0.070

in the Kt K orKt~ Kn spaces by two distinct clusters ofpoints (see Fig. 6).

2.5. Spatial consistency tests

Data can be analyzed by comparing neighboring stationswith each other. Because the cloud cover can be highly var-iable even on small distances, spatial consistency tests haveto rely on cumulated data (at least daily values). As an alter-native, neighboring stations might be compared on periodswith concurrent clear sky. Finally, these tests should be

restained to sites with similar climate and geography.

Here, the approach proposed by Terzenbach (1995) isused to evaluate the spatial consistency between daily totalsof global solar irradiation data. In this method, the value ata station located in x0, G(x0), is compared against an esti-mation obtained through a spatial interpolation of themeasurements performed at nearby locationsxi, i.e.,

PNbGx0 1/4PN1 i1/41wiGxi, whereNis the number of sta-

i1/41wi

tions located within a given maximum distance R ofx0 andthe interpolation coefficients wi are a decreasing function ofthe distance dibe tween the locations x0 and xi, e.g.,

~ 2

1~di=R .The biasjbGx0~Gx0j is expected to stay

di=R

below certain limits. In practice, biases that are signifi-cantly larger (e.g., larger by more than 50%) than the meanbias over all sites are checked manually to attest whethertheir origin is natural or instrumental.

2.6. Sunshine tests

Sunshine duration values are first assigned with the same

quality index than the associated B data. Then, severaladditional checks are performed if theB value has


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80 M. Journe , C. Bertrand/Solar Energy 85 (2011) 7286

K

to to

0 . 8

0 . 7

.

.

.Kn

.

.

.

.

0 . 3

0 . 2

.

. . . . . . . . .

K t

AWS 6407 2008/05/01 to 2008/06/30

.

0 . 8

.

.

0 . 5

.

.

.

0. 1

0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 1

K t

K t

AWS 6407 2008/05/01 to 2008/06/30

. . . . . . . . .

K t

.

0 . 8

.

0 . 6

.

Accepted dataRejected data

K

.

.

.

.

0 . 4Kn

0 . 3

.

.

. . . . . . . . .

the root mean square error RMSE

Fig. 5. Quality envelopes in the KtKandKtKn spaces. In case of reliable instruments, these envelopes are directly computed from the analyzed data(top plots). Climatological envelopes are otherwise used (bottom plots, case of a deficient direct sensor). (For interpretation to colours in this figure, thereader is referred to the web version of this paper.)

Table 6Quality code information for quality envelope tests.

Quality code Status of the sensor Position of the data

1 Reliable Inside the quality envelope2 Reliable Outlier3 Deficient Inside the quality envelope4 Deficient Outlier

succeeded the quality assessment tests. Sunshine duration

values are to lie between zero and the sampling periodSDmax (i.e., 10 min or 30 min for the RMIB data set). Fur-thermore, in accordance with the WMO definition of thesunshine duration, the direct solar irradiance averaged onthe period SDmax cannot exceed 120 W m

2 ifSD = 0 and hasto be above the lower boundSD

SDmax 120 W m2.

3. Solar radiation modeling

Because the availability of solar radiation data in timeare important to assess the performance of solar energysystems, additional procedures have been developed to

provide users with an estimation of data initially lacking

or failing the quality assessment criteria. When two outof the three components of the solar radiation succeed thequality assessment checks, the remaining component canbe directly estimated from the relation D + B = G. Whenonly one solar radiation parameter is available, one canresort to empirical models to estimate one missing solarparameter from the available one and then use therelation D + B = G to derive the last parameter. Furthermodels enable to estimate the sunshine duration from theknowledge of the solar radiation parameters.

In this section we evaluate some empirical models basedon 2 years (2008 and 2009) of validated 10 min solar datawith a solar elevation angle greater than 2. Modelsperformance is quantified by means of the following statis-tical indices:

the mean bias error MBE E^x x,the mean absolute error MAE E^x x,

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffih iE ^x x 2 ,

the relativemean bias errorrMBE E ^xx,

xh i

the relative mean absolute error rMAE E^xx

and,x


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M. Journe, C. Bertrand/Solar Energy 85 (2011) 7286 81

AWS 6459 2009/10/01 to 2009/11/30

. . . . . . . . .

0 . 9

.

0 . 7

.

0.5

0 . 4

0 . 3

0 . 2

.

AWS 6407 2009/05/01 to 2009/06/30

. . . . . . . . .

>>>

>>>>>:

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiKn/0.09,

0.4

.

rMBE

.

0.4

.

0.8

Erbs et al. (1982)

Skartveit & Olseth (1987)

Maxwell (1987)Perez et al. (1992)

0 0 . 2 5 0 . 2 5 0 . 5 0 . 5 0 . 7 5 0 . 7 5 1 0 0 . 2 5 0 . 2 5 0 . 5 0 . 5 0 . 7 5 0 . 7 5 1

rRMSE

0 . 8

.

.

.

0

1

.

0

rMBE 0.1

.

0 . 3

.

.

rRMSE .

0 . 2

Clearness index

220 2035 3550 5065

Solar elevation angle

Clearness index

Solar elevation angle

observed for E82. This is not really surprising as this modeldoes not incorporate solar elevation as an input parameter.In overall, S87 and P92 appear as the bestmodels and exhibita rather equivalent performance. Missing or erroneous directsolar radiation within the RMIB data set are thereforeestimated by means of the model S87 that is conceptually

more simple.

3.2. Models for the global solar radiation

Sunshine duration was traditionally the main and oftenthe only measurement of solar radiation. Several modelshave been proposed to convert sunshine duration valuesinto global solar radiation values. The most widely usedmodel ofA ngstrom (1924) and Prescott (1940) propose alinear relationship between the clearness index G/Eand thesunshine fraction SD/SDmax,E = a +b SD

G , (3)SDmax

where the coefficients a and b are site-dependent. Morecomplex nonlinear models have been proposed in the liter-ature but without showing significant improvement withrespect to the linear formulation (3) (Almorox and Honto-ria, 2004). Although model (3) was initially proposed for

daily data, it is often used in the case of hourly data (see,e.g., Yang and Koike (2005)).

As an alternative, the global solar radiation can beinferred from the direct solar radiation by inverting themodels discussed in Section 3.1. In the case of E82 (seeAppendix A for the detailed formulation of this model), the

clearness index Kt can be expressed as a function of thebeam transmittanceKn =B/E,

if 0


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M. Journe, C. Bertrand/Solar Energy 85 (2011) 7286 83

0 0 . 2 5 0 . 2 5 0 . 5 0 . 5 0 . 7 5 0 . 7 5 1

r

.

.

.

.

0 . 2

AngstromPrescott modelInversion of Erbs et al. (1982)

. . . . . .

r

.

0.6

0 . 4

.

.

0

Table 8Comparison of the models described by Eqs. (3) and (4) that estimateglobal radiation against good quality 10 min data. The absolute errorstatistics MBE, MAE and RMSE are expressed in W h m-2.

Model (3) with site-specificcoefficients

Model (3) withaveraged coefficients

Model(4)

MBE -2.450 -2.446 1.314MAE 9.090 9.376 6.433RMSE 12.071 12.466 8.912rMBE 0.051 0.057 0.089rMAE 0.183 0.189 0.149rRMSE 0.286 0.299 0.264

ing comparison, one can expect, in view of the resultsdiscussed in Section 3.1, that the inverted version of S87may slightly outperform the model (4).

Because model (3) involves site-dependent coefficients,the RMIB data set was split randomly in two subsets of

equal size for each site to estimate the coefficients in a firsthand and evaluate the models on the other hand. In addi-tion, coefficients averaged over all considered stations (i.e.,a = 0.295 and b = 0.335) were used to evaluate the spatialsensitivity of the model. Although the site-specific coeffi-cients may vary by up to 16% with respect to the averagedvalues, the performance degradation of the averaged modelis rather small (e.g., the RMSEsee Table 8is increasedby 3.54%). Following the study ofAlmorox and Hontoria(2004), more complex polynomial regression models thatestimate global solar radiation values from sunshine dura-tion measurements were considered (although not reportedin Table 8), but we did not notice any improvement withrespect to the linear model (3). Hence, the model (4) that isbased on direct solar radiation measurements performssignificantly better than sunshine duration-based models toestimate global solar radiation values, i.e., all error indicesare smaller for this model, except the rMBE that is small forall models (Table 8). Sunshine duration values, which are

truncated from direct radiation values with

Clearness index

respect to the 120 W m-2 threshold, provide in fact a lessaccurate information on solar radiation.

As far as the impact of the sky conditions is concerned,both models (3) and (4) overestimate the global solar radi-ation for overcast sky and underestimate it for clear skies(Fig. 8). The model (4) exhibits the best agreement with the

measurements in case of intermediate and clear skyconditions (i.e., Kt > 0.25), while both models encounterdifficulties in overcast conditions.

In view of its overall better performance, model (4) isused to estimate missing and erroneous global solar radia-tion values.

3.3. Models for the sunshine duration

When measurements of the global solar radiation areavailable, sunshine duration values can be derived from thelinear relation (3). More complex polynomial regres-sion

model that rely on global and/or direct solar radiationmeasurements are in addition considered in this study (seeTable 9 for the formulation of these models). These modelsinvolve as input parameters either the clearness index Kt=G/E or the modified (i.e., elevation angle-indepen-dent)clearness indexK0tproposed by Perez et al. (1990a) and/orthe beam ratio B/G. In accordance with the physical limitsof the sunshine duration, the outputs of these poly-nomialmodels are truncated below at zero and above at SDmax. Asa consequence, the zero mean bias property of theregression models is lost.

As in Section 3.2, the RMIB data set was split in twosubsets to estimate the regression coefficients and comparethe models on distinct data. Average models over Belgiumhave been inferred in addition to the site-specific ones.Because the degradation in performance was small, the fol-lowing comparative study is focused on the average mod-els. When models that involve only one input parameter arecompared (SD1 to SD6), the smallest MAE and RMSE areobserved for those based on the beam ratioB/G (Table

Clearness index


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Fig. 8. Distribution of the relative mean bias error (rMBE) and relative root mean square error (rRMSE) between measured and estimated values ofglobal solar radiation as a function of sky conditions. The A ngstrmPrescott model refers to model (3) with the averaged coefficients, while theinverted version ofErbs et al. (1982) is model (4). (For interpretation to colours in this figure, the reader is referred to the web version of this paper.)


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84 M. Journe, C. Bertrand/ Solar Energy 85 (2011) 7286

Table 9Polynomial regression models to estimate sunshine duration values. Thesunshine fraction SD

SDmax is truncated below at zero and above at one. Theregression coefficients are computed on the basis of good quality data fromseveral sites in Belgium.

Model Model equation Coefficientlabel values

SDSD1 1/4 a0 a1Kt a0 = -0.266SDmaxa1 = 1.789

SDSD2 1/4 a0 a1Kt a2K2 a0 = 0.241SDmax ta1 = 1.612a2 = 0.214

SDSD3 1/4 a0 a1K0 a0 = 0.309SDmax ta1 = 1.608

SDSD4 1/4 a0 a1K0t a2K02 a0 = 0.194SDmax ta1 = 0.914a2 = 0.738

SD5 SDSiLx1/4 a0 a1 (1) a0 = -0.002a1 = 1.407

SD6 D 1/4 a0 a1BG

a2(c)2 a0 = -0.054a1 = 2.428a2 = -1.355

SDSD7 1/4 a0 a1K0 t a2 B a0 = 0.061

SDmax Ga1 = 0.519a2 = 1.033

SDSD8 1/4 a0 a1K0t a2K;2 a3 g a4 (c)2 a0 = -0.044SDmax

a1 = -0.175a2 = 0.562a3 = 2.104a4 = -1.277

10). When only the global solar radiation is available, theestimation is slightly more accurate when the modifiedclearness index is used instead of the usual one. The bestperformance is however obtained when both global anddirect solar radiation measurements are involved throughthe modified clearness index and the beam ratio (SD7 andSD8). Finally, quadratic models provide a significantimprovement with respect to their linear counterparts

Table 10Comparison of models to estimate sunshine duration against good quality10 min data. The error statistics MBE, MAE and RMSE are expressed inminutes. The model labels refer to the descriptions in Table 9. Thesubscripts B- and -G denote that estimations are used for eitherB or Ginstead of the actual measurement. These estimations are computed by themodel S87 (Skartveit and Olseth, 1987) forB- and by model (4) for-G.

Model label MBE MAE RMSE

SD1 0.088 1.372 2.034SD2 0.053 1.365 2.032SD3 0.169 1.333 1.981SD4 0.032 1.273 1.942SD5 -0.220 0.818 1.447SD6 0.109 0.716 1.281SD7 0.360 0.936 1.376SD8 0.077 0.663 1.179SD -0.198 0.871 1.685

SD8, B"8,e

0.133 0.671 1.230

(i.e., SD2,SD4,SD6,SD8 versus SD1,SD3,SD5,SD7,respectively).

As far as the impact of sky condition is concerned (Fig.9), the models overestimate the sunshine duration forovercast to intermediate skies (i.e., for 0 .., Kt < 0.5) andunderestimate it for clearer sky conditions (i.e., for 0.5 ..,Kt

< 1). All models perform almost equivalently for overcastconditions. Using measurements of the direct solar radiationis particularly beneficial for intermediate sky conditions. Inthe case of very clear skies, the best scores are howeverobtained by models that involve global solar radiationvalues (i.e., all models except SD5 and SD6).

Finally the performance ofSD8 was evaluated when oneof its both inputs is not available (Table 10). Although theuse of an estimation instead of the actual measurementdegrades the performance of the model (SD -B and SD8,-G

8,

versus SD8), the resulting MAE and RMSE are smallerthan those observed for models based on a single measure-

ments (SD - versus SD4 and SD - versus SD6). Hence,missing or8,Berroneous sunshine dllation values are esti-mated by means of SD8 and we resort to solar radiationmodels when one of the both inputs is not available.

3.4. Uncertainty of the filled data set

In addition to the limitations inherent to the empiricalmodels, uncertainty in filled solar radiation time series isalso function of the number of estimations they contain andthe time at which they are applied. To assess the reli-abilityof the filled data set, daily totals derived from time series of

G, B and SD data containing a varying proportion ofestimations were compared. Basically, we compiled a set ofcomplete daily time series of good quality 10 min data (i.e.,G, B and SD data were available over the entire day andsucceeded the quality assessment tests). Based on thesecomplete daily time series, new daily time series containingan increasing proportion of estimations were generated byreplacing at randomly selected timestamps measurements bythe corresponding estimations. Daily totals derived from theoriginal and the synthetic time series were finally comparedagainst each other. On average, the discrepancy between thefilled and the measured data appears to increase linearlywith the proportion of estimations included in the time series

but stays within reasonable lim-its (Table 11). For instance,when daily totals are derived from as much as 50% ofestimations and 50% of measure-ments, the RMSE amountsto 9%, 7.2% and 5.7% of the average of daily value for thedirect solar radiation, global solar radiation and sunshineduration, respectively. These results might be representativefor data acquired with iden-tical instruments in regions withsimilar climate.

4. Conclusions

This paper describes the procedures developed at the

Royal Meteorological Institute of Belgium for post-


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MBE

(minutes)

1

0.75

0.5

0.25

0

.25

0.5

. . . . . .

RMSE

(minutes)

.

.

.

.

SD1 ________ SD2 ____________SD3 __________ SD4 ____________SD5 __________ SD6 ____________SD7 ____________SD8

0 0 . 2 5 0 . 2 5 0 . 5 0 . 5 0 . 7 5 0 . 7 5 1

Clearness index

Clearness index

Fig. 9. Distribution of the mean bias error (MBE) and root mean square error (RMSE) between measured and estimated values of sunshine duration as afunction of sky conditions. The model labels refer to the descriptions in Table 9. (For interpretation to colours in this figure, the reader is referred to theweb version of this paper.)

Table 11

Comparison of measured daily totals against daily totals that contain a proportion p of estimations. The comparison indices are given in absolute value(i.e., in W h m-2 for the global and direct solar radiations and in minutes for the sunshine duration) as well as in relative value with respect to the averageof the measured daily totals.

p = 10 (%) p = 25 (%) p = 50 (%) p = 75 (%) p = 100 (%)

Estimation of direct solar radiation values by means of the model S87(Skartveit and Olseth, 1987)MBE -0.106 (-0.008) -0.022 (-0.002) -0.224 (-0.017) -0.304 (-0.023) -0.458 (-0.034)MAE 17.62 (1.32) 38.72 (2.91) 73.01 (5.49) 107.03 (8.04) 141.24 (10.62)RMSE 30.21 (2.27) 63.92 (4.80) 119.19 (8.96) 173.77 (13.06) 228.66 (17.18)

Estimation of global solar radiation values by means of model(4)

MBE -9.362 (-0.348) -23.291 (-0.865) -46.691 (-1.734) -69.870 (-2.595) -93.331 (-3.467)MAE 31.08 (1.15) 72.98 (2.71) 142.70 (5.30) 212.38 (7.89) 282.34 (10.49)RMSE 45.11 (1.68) 101.49 (3.77) 194.76 (7.23) 288.11 (10.70) 381.80 (14.18)

Estimation of sunshine duration values by means of the model SD8 ofTable 9

MBE 0.303 (0.113) 0.704 (0.263) 1.441 (0.538) 2.168 (0.809) 2.890 (1.079)MAE 2.57 (0.96) 5.52 (2.06) 10.33 (3.86) 15.15 (5.66) 19.88 (7.42)RMSE 4.08 (1.52) 8.37 (3.13) 15.36 (5.73) 22.39 (8.36) 29.33 (10.95)

measurement quality control of solar radiation data fromour radiometric stations. The data consists in measure-ments of the global, direct and diffuse solar radiations aswell as sunshine duration with either a 10 min or a 30 mintime step. The resulting quality control scheme is basedon previously proposed as well as new quality criteria. Itinvolves a set of optional semi-automated pro-cedures todetect specific error types followed by fully-automated

procedures. Because solar energy applications

need continuous time series of radiation data to correctlyassess the usefulness of the particular application and in itsimplementation, additional procedures have further-morebeen established to fill missing values (data initially lackingor removed via quality checks) in the time series of solarradiation data. These procedures rely on empirical modelsthat estimate missing solar parameters from avail-able ones.Several of such models, either found in the liter-ature or

proposed in this paper, have been evaluated on


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86 M. Journe, C. Bertrand/Solar Energy 85 (2011) 7286

the basis of 10 min data that succeeded the quality controlassessments. As far as the estimation of direct solar radia-tion is concerned, we selected the G-to-B model ofSkartveitand Olseth (1987), which exhibited a root mean square error(RMSE) of 10.2 W h m-2. The inverted version of the G-to-Bmodel ofErbs et al. (1982), which lead to a RMSE of 8.9 W

h m-2

, was chosen to estimate global solar radiation valuesfrom direct solar radiation measurements. A regressionmodel was also proposed to estimate sunshine duration frommeasurements of global and direct solar radiation (RMSEaround 1.2 min). The uncertainty of the filled data wasfinally observed to increase linearly with respect to theproportion of estimated values involved.

Acknowledgements

This study was supported by the Belgian Science Policyunder the research project: Contribution de lIRM audveloppement de lnergie renouvelable en Belgique.

Appendix A.

In this appendix, we provide the formulation of the G-to-Bmodel E82 proposed by Erbs et al. (1982) that underlies the

B-to-G model (4). The model E82 estimates the beam hor-izontal solar radiation as a fraction of the global horizontalsolar radiation, B = G where is an increasing function of theclearness indexKt,

8

>

>>:

=0.09KtifKt6 0.22,

=0.0489+0.1604Kt-4.388K2t+16.638K3t-12.336K4tif 0.22

Control de calidad de datos de radiación solar dentro de la red de medidas solar RMIB

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