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Solar Energy 91 (2013) 102–110

Use of a clear-day solar radiation model to homogenize solarradiation measurements in Hawai‘i

Ryan J. Longman ⇑, Thomas W. Giambelluca, Michael A. Nullet

Department of Geography, University of Hawai‘i at Manoa, 2424 Maile Way, Saunders Hall 445, Honolulu, HI 96822, United States

Received 18 August 2012; received in revised form 29 January 2013; accepted 2 February 2013Available online 22 March 2013

Communicated by: Associate Editor Christian Gueymard

Abstract

The reliability of solar irradiance measurements is dependent on the calibration of the pyranometer used to make them. Internation-ally recognized standards for pyranometer calibrations require resources that may not be available to all observers. To fill this gap, wepropose a method of homogenizing hourly solar radiation time series based on comparison of clear-sky radiation observations againstestimates derived from a clear-sky radiation model. Inhomogeneities in the record are identified based on shifts in pyranometer responsein relation to the model estimates, and corrected to produce a homogeneous time series. This method was applied to the �23 year recordof hourly solar irradiance measurements recorded at three climate stations along a 870 m elevation gradient (2120–2990 m) on the slopesof Haleakala Volcano, Maui, Hawai‘i. Corrections resulted in changes in monthly solar radiation of as much as 6.8–7.4% among thethree stations.� 2013 Elsevier Ltd. All rights reserved.

Keywords: Solar irradiance; Pyranometer; Clear-sky radiation model; Sensor calibration; HaleNet

1. Introduction

1.1. Background

Long term records of global solar radiation, the totalflux of short wave radiation incident at a given point onthe Earth’s surface comprised of the direct and the diffusecomponents of sunlight, are used to assess the capacityand the variability of solar resources as well as anthropo-genic impacts on the Earth’s climate system (Riihimaki,2008). Measuring solar radiation incident at the surfaceusing a pyranometer is subject to some level of calibrationuncertainty. Instruments calibrated under ideal laboratoryconditions may experience a changed response whenmoved into the field environment (Gueymard and Myers,

0038-092X/$ - see front matter � 2013 Elsevier Ltd. All rights reserved.

http://dx.doi.org/10.1016/j.solener.2013.02.006

⇑ Corresponding author. Tel.: +1 808 956 8465; fax: +1 808 956 3512.E-mail addresses: rlongman@hawaii.edu (R.J. Longman), thoma-

s@hawaii.edu (T.W. Giambelluca), mnullet@hawaii.edu (M.A. Nullet).

2009). Instruments operated in the field for extended peri-ods of time are likely to experience additional calibrationshifts, producing results inconsistent with factory cali-brated standards, leading to inaccuracies and inhomogene-ities in data sets. Because erroneous solar radiation datamay lead to incorrect conclusions about environmentalphenomena, whenever possible, data should be correctedto account for sensor calibration errors (Allen, 1996). Datascreening procedures that detect and correct errors associ-ated with calibration uncertainty are necessary in order toinsure that representative, high quality data are made avail-able for further investigation.

The World Climate Research Programme (WCRP) hasinitiated a radiometric network where standardized calibra-tion and maintenance procedures have been established tofacilitate accurate assessment of long-term solar variationsWorld Climate Research Program (WCRP) (1991). Basedon these standards, several authors have proposedcalibration and correction techniques aimed at reducing

R.J. Longman et al. / Solar Energy 91 (2013) 102–110 103

measurement uncertainty (Dutton and Bodhaine, 2001;Myers et al., 2002; Reda et al., 2003; Lester and Myers,2006; Riihimaki, 2008). However the implementation ofthese techniques requires highly specialized and expensiveinstrumentation to measure the direct component of globalradiation and a consistent maintenance regimen to ensurethat sensors are serviced on an appropriate time interval.Operation of solar measurement networks constrained bylimited funding and use of existing data sets for whichthe calibration regime was not optimal require alternativemethods to correct calibration errors in order to producea homogeneous data set with reduced uncertainty.

This study was designed to improve the overall accuracyof measured solar radiation data by applying a newmethod for correcting instrument calibration errors. Allen(1996) suggested that calibration accuracy could be testedby comparing ground based measurements under cloudfree conditions with model-estimated clear-sky shortwaveradiation. In a previous manuscript we tested differentapproaches for parameterizing a clear-sky radiation modelin Hawai‘i (Longman et al., 2012). In this manuscript, wepresent a method for homogenizing long-term measure-ments of solar irradiance, in which modeled clear-sky radi-ation estimates are used to identify discontinuities in asolar radiation time series. Procedures for correcting thesediscontinuities are applied to long-term solar radiationdata sets from three high elevation stations in Maui,Hawai‘i.

1.2. Solar radiation observation sites and instrumentation

The climate stations in the HaleNet Climate Networkhave been recording microclimatic data since 1988(http://climate.socialsciences.hawaii.edu/HaleNet). Hale-Net consists of 11 individual climate stations on the slopesof Haleakala Volcano, Maui, Hawai‘i. Three of the elevenstations were selected for this analysis (Table 1). These sta-tions located on the leeward slope of Haleakala, cover an870-m elevation gradient (2120-2990 m) and representpoints near and above the mean trade wind inversion level(2200 m, Cao et al., 2007). Each station was equipped withan Eppley model 8-48 (Eppley Laboratory, Newport, RI,USA) thermopile pyranometer measuring global solar radi-ation, sampled at a 10 s interval and recorded hourly usinga Li-COR (Lincoln, NE, USA) Li-1000 data logger (beforemid-July 1999), and a Campbell Scientific, Inc. (Logan,UT, USA) CR10X data logger (after mid-July 1999).Beginning in January, 2011 a Hukseflux (Manorville NY,USA) model NR01 four-component net radiation sensor

Table 1HaleNet stations characteristics.

Sta. # Elev (m) Albedo Press. (mb) Lat.� Long.� Start date

HN-151 2190 0.07 789 20.763 156.25 June-88HN-152 2590 0.10 747 20.741 156.248 March-90HN-153 2990 0.05 713 20.713 156.259 March-90

was installed at each of the nine HaleNet stations currentlyin operation, now recording hourly data using a CampbellScientific CR3000 data logger.

Thermopile pyranometers sense incident radiation basedon the temperature difference between a hot junction, anabsorbing surface, and a cold junction, a surface with min-imal solar radiation absorption (Lester and Myers, 2006).The response of a pyranometer is quantified in terms ofthe voltage produced by 1 W m�2 of solar radiation (Riihi-maki, 2008). Pyranometers output a voltage proportionalto incident solar radiation, which is then divided by aresponse value determined by calibrating each instrumentagainst a known reference. The Eppley laboratory modelPSP (Precision Spectral Pyranometer) and the Eppley 8-48 black and white pyranometer are examples of thermo-pile pyranometers used to measure global radiation(direct + diffuse) on a horizontal surface. One differencebetween the two instruments is the way in which the volt-age produced by incident radiation is measured. In thePSP model, a wire-wound thermopile measures the temper-ature difference between a black painted surface disk thatabsorbs solar radiation and the instrument body (not incontact with the absorbing disk), which does not absorbradiation (Riihimaki, 2008). In the 8-48 models, the tem-perature difference between the black hot junctions andthe white reference cold junctions determines the measuredvoltage (Myers et al., 2002). The Eppley model 8-48 has acosine response of ±2% (Eppley Laboratory Inc., n.d.) andhas been shown to exhibit a low thermal offset (±1 W m�2)(Reda et al., 2003). Expanded responsivity uncertainty(standard uncertainty multiplied by a coverage factor),for a single model 8–48 has been reported as �2.2% to+3.31% National Renewable Energy Laboratory (NREL),2011. By comparison, the more highly-regarded EppleyPSP has a calibration uncertainty of 2–3% (Riihimaki,2008) and may experience a thermal offset of �30 W m�2

to �5 W m�2 (Reda et al., 2003).PSP thermopile pyranometer degradation is well known

but very little has been published with regards to the rate atwhich this degradation occurs (Riihimaki, 2008). Nelsonet al. (1994) have reported that PSP degrades at an averagerate of 1.9% per year and Wilcox et al. (2001) has reportedthat the PSP degradation is more affected by temperatureand irradiance exposure than it is by time in the field. Inaddition, Wilcox et al. (2001) has also reported that thedecline in the Eppley PSP response follows the same trendas a model used to predict the aging of paint. The PSPresponse has been shown to decline over time, thusunder-predicting actual solar radiation (Riihimaki, 2008).It is not known whether the Eppley 8-48 degrades at thesame rate as the PSP.

However given its design and painted surface it is likelythat some change in sensor response occurs over time. It ispossible that aside from the different measurement tech-niques employed by the two instruments the unequal dete-rioration of the two different colors on the 8-48 mightproduce different changes in responsivity than the PSP

104 R.J. Longman et al. / Solar Energy 91 (2013) 102–110

model. Dutton and Bodhaine (2001) has suggested that thewhite coating on black and white pyranometers has a ten-dency to spectrally darken which results in an overestima-tion of clear-sky diffuse radiation that increases over time.

Four-component net radiation sensors such as theHukseflux model NR01 measure the upward and down-ward fluxes of shortwave and longwave radiation sepa-rately. The shortwave downward component is measuredwith a thermopile pyranometer (type SR01) with a cosineresponse of ±0.5 percent and a maximum thermal offseterror of ±5% (Hukseflux Thermal Sensors). To our knowl-edge, no published studies are available on the rate of deg-radation of Hukseflux sensors.

1.3. Clear-sky radiation models

A clear-sky solar radiation model approximates atmo-spheric transmission through the atmosphere in whichextraterrestrial radiation diminishes as a result of severalabsorption and scattering processes (Leckner, 1978).Examples of this type of model include SPCTRAL2 (Birdand Riordan, 1986), SMARTS2 (Gueymard, 1995), andREST2 (Gueymard, 2008). SPCTRAL2 and SMARTS2can simulate solar irradiance under cloud-free conditionsover specific discrete wavelength bands or integrated acrossthe full spectrum, while REST2 uses only two discrete spec-tral bands. The models are semi-empirical and their perfor-mance relies heavily on the accuracy of input parameters(Utrillas et al., 1998; Foyo-Moreno et al., 2000; Tadroset al. 2005). To produce estimates of clear-sky radiation,these models have two primary tasks: accurately predictingthe cosine-adjusted extraterrestrial radiation, and estimat-ing the attenuation of incoming shortwave radiation as afunction of optical path length and atmospheric opticalproperties. Sun angle and optical path length, determinedby location on the Earth’s surface, time of day and timeof year, the geometry and timing of Earth’s rotation andorbit, and the variation in the angle between the Earth’srotational axis and the plane of the ecliptic, are well simu-lated in clear-sky models. Variation in prediction skill ismainly associated with how well atmospheric transmissionis simulated. We have chosen to adopt the SPCTRAL2clear-sky radiation model (Bird and Riordan, 1986) for thisstudy due to its simplicity and the success we had using it tomodel clear-sky radiation in Hawai‘i in a previous study(Longman et al., 2012). Other spectral clear sky radiationmodels use a more highly resolved spectrum and are some-what more accurate than SPCTRAL2 for specific wave-length ranges (Foyo-Moreno et al., 2000; Gueymard2001; Alados-Arboledas et al., 2000), However, SPC-TRAL2 has been shown to perform well for broadbandglobal solar radiation estimation (Jacovides et al., 2004;Longman et al., 2012). In other applications in Hawai‘i,we have used the two-band REST2 clear sky model andhave found its estimates to be very similar to those of SPC-TRAL2. The mean difference (SPCTRAL2 minus REST2)and RMSE between the model estimates for station HN-

152 (Table 1), for example, were �4 Wm�2 (�2.3%) and4.7 Wm�2 (5.9%), respectively.

2. Methods

2.1. SPCTRAL2 model applications

The SPCTRAL2 code was used to model hourly clear-sky solar radiation for the period of record at each of thethree HaleNet stations used in this analysis. Hourly valueswere computed as the average of sixty 1-min model esti-mates, each based on an integration of separate estimatesfor 122 wavelength ranges spanning 300–4000 nm selectedfrom the 10-nm resolution data set of Frohlich and Wehrli

(1981; as cited in Bird and Riordan, 1986). Integration isdone by weighting each spectral estimate by its bandwidth.Required input parameters include local geographic coor-dinates, atmospheric pressure, precipitable atmosphericwater vapor content, aerosol optical depth, Angstromexponent, surface albedo, and ozone concentration. Ouranalysis showed that horizontal variation in atmosphericparameters is negligible in Hawai‘i (Longman et al.,2012). Aerosol optical depth and the Angstrom exponentwere interpolated vertically from values measured at AER-ONET sites, Lana‘i (20 m elevation) and Mauna Loa(3397 m). The vertical profile of precipitable water wasderived from radiosonde measurements at Hilo, Hawai‘iIsland (Longman et al., 2012). The ozone optical depthdata was obtained from a Dobson Ozone Spectrometeroperated by the National Oceanic and AtmosphericAdministration at Mauna Loa Observatory (NOAA,2011). In a previous study, we analyzed the effects of tem-poral averaging of model atmospheric transmission param-eters (Longman et al., 2012). The results showed thatholding parameter settings at their mean values gave betterresults than using temporally varying (daily or monthly)estimates for prediction of clear-sky radiation at the Hale-Net stations used in the present study. Use of fixed param-eter values was also mandated for this study by the factthat measured atmospheric parameters were not availableat the two AERONET sites for the entire study period.While Hawai‘i has relatively small temporal variability inatmospheric transmission properties, in other locationswhere water vapor and aerosol loading are more variable,a fixed parameterization scheme may not be appropriate.SPCTRAL2 produces a stable baseline of clear-sky solarradiation against which solar radiation observed duringclear-sky conditions can be compared to assess how pyra-nometer response changes over time by comparing themodeled radiation to clear-sky measurements from theobservational record. To accomplish this, the seven peakhours of solar radiation (9 AM to 4 PM HST) were aver-aged to produce a single clear day modeled (CDMd,m,y)and clear day observed (CDOd,m,y) value for each clearday. The daily clear day ratio (CDRd,m,y) between the mod-eled and measured daily averages can be expressed as:

R.J. Longman et al. / Solar Energy 91 (2013) 102–110 105

CDRd;m;y ¼CDOd;m;y

CDMd;m;yð1Þ

The CDR may also be expressed as a monthly value(CDRm,y) by averaging all CDRd,m,y values within a givenmonth and as an annual value (CDRy) by taking the meanof all available months within a given year. We examinedtemporal variations in CDR to detect and adjust for incon-sistencies within a given data set. The assumption underly-ing this approach is that the CDR should be consistentover time and that any apparent shifts or significant trendsin the CDR time series indicate inhomogeneities in the dataset resulting from changing instrument sensitivity.Although CDR is estimated using only clear-sky observa-tions, it can be used to adjust to all observations, regardlessof sky condition.

2.2. Identifying clear days

To identify clear days within the solar record, the differ-ence between the modeled and measured radiation wastaken for each of the seven hours of peak insolation (9AM to 4 PM). For each day, the standard deviation (SD)of the hourly model-observed difference was calculated.Clear days were tentatively identified using an arbitrarilyselected criterion of SD < 10 W m�2. This first step nar-rowed down candidate clear days from the period ofrecord. Next, the selected days were manually screened toverify that cloud free conditions prevailed as indicated bya smooth, approximately sinusoidal shape in the hourlytime series. This method, which identified whole days withcloud-free conditions, was effective for a majority of thestudy period. When large gaps in the cloud free record wereidentified, solar radiation values were manually screened toidentify a minimum of three hours within partly cloudydays that followed the characteristic diurnal pattern forcloud free conditions. To facilitate this, hourly solar radia-tion was plotted over the 7-h daytime period for each dayand visually examined. Those hours judged to have fol-lowed the typical diurnal pattern for cloud free conditionswere selected. Modeled clear-sky radiation was used as areference as to the shape of the diurnal cycle; measuredradiation during clear periods matched the shape of themodeled radiation time series. Only differences in shape,not amplitude, between the modeled and measured radia-tion were used in the selection process. A statistical crossvalidation test showed that clear sky ratios calculated withdifferent subsets of 3–6 consecutive clear sky hours differednegligibly from that derived from the full 7 h.

2.3. Detecting changes in instrument sensitivity

Over the period of record at each station, instrumentcalibration coefficients used in data logger programs werechanged after calibration tests or sensor replacements,resulting in abrupt changes in apparent instrument sensitiv-ity (shifts). Between those events, sensitivity may have

changed gradually due to sensor degradation, withoutcompensation in the form of revisions to the calibrationcoefficient (drifts). In our analysis, we divided the recordat each station into periods delimited by known or sus-pected calibration coefficient changes and sensor replace-ment events. Within those periods, sensor drift wasevaluated by analyzing the CDRd,m,y record to identifyany significant temporal trends based on regressionanalysis.

Three distinct time periods were initially identified at allstations: T1, which represents measurements taken before anetwork-wide sensor intercalibration effort in July of 1999(Longman et al., 2012); T2, which represents measurementstaken after the intercalibration and before the installationof the Hukseflux radiometers in January of 2011; and T3,which represents measurements taken after the Huksefluxinstallation. Note that during a �3 month period the 8-48and Hukseflux sensors were operated simultaneously ateach station, providing for direct comparison between theold and new sensors. Time periods T1 and T2 were furthersubdivided at each station as needed on the basis of fieldnotes, voice transcripts, and calibration records, whichidentified times when pyranometers were either recalibrat-ed or replaced. CDRm,y values were calculated for all peri-ods, and CDRy values were also calculated for periods withmore than one year of data. In order to remove seasonalvariation in CDR, clear day anomalies (CDA), departuresof daily or monthly values from the respective long-termmonthly means, were calculated and used in the detectionof sensor drift. This was deemed necessary after an annualcycle in the value of CDR was found during initial screen-ing, with higher values occurring in the winter. Longmanet al. (2012) found that modeled clear-sky radiation under-estimated observed radiation by a greater margin duringthe summer months, which would explain higher CDRduring the winter. We do not know if the annual cycle isdue to model or measurement error. However, by usingthe anomaly time series (CDA) rather than CDR, biasesassociated with seasonally induced model errors or errorsdue to uneven distribution of clear days throughout a givenyear were considerably reduced.

Daily clear day anomaly (CDAd,m,y) values can beexpressed as:

CDAd;m;y ¼ CDRd;m;y � CDRM ð2Þ

CDRM is an average of all of the available CDRd,m,y val-ues for a given month (e.g. all the Januarys in the period ofrecord). Daily clear day anomaly values were averaged foreach month (CDAm,y), and monthly values were averagedto produce a clear day anomaly value for each year(CDAy). For time periods with less than 4 years of data,trends were analyzed using the monthly anomaly time ser-ies; for longer periods, the annual anomaly time series wasused.

Trends analyzed and tested for statistical significanceusing least squares linear regression of CDA vs. time,were evaluated with attention to the effects of temporal

Fig. 1. CDRd,m,y and CDRy values for the three HaleNet experimental stations plotted over time. Alternating colors and different symbols distinguishperiods between abrupt shifts in CDRd,m,y values corresponding to sensor recalibrations or replacements. Annual means (CDRy) are shown with tealcolored circles. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

106 R.J. Longman et al. / Solar Energy 91 (2013) 102–110

autocorrelation using the method of Santer et al. (2000).Trends for which p 6 0.05 were designated as significant.

2.4. Data homogenization

To homogenize solar radiation data, a reference CDRvalue was first determined for each station based on datafrom the period when new factory-calibrated Huksefluxsensors where in use. The mean CDR for this period ateach station was used as a reference value (CDRrp) toanchor the homogenization adjustments. All of the meanCDR values for each time period were corrected based

on this value. Note that we do not assume the model per-fectly simulates clear sky radiation, in which case CDRrp

would be assumed to equal 1. Instead we are examininghow the relationship between observations and modeledestimates changes over time. CDRrp was calculated as themean CDR for the �7 months of clear days available dur-ing the T3 time period. An adjustment factor (AFt) wasderived for each time period as:

AFt ¼CDRrp

CDRtð3Þ

where CDRt is the average clear day ratio within a giventime period. The number of adjustment factors for each

Fig. 2. Adjusted CDRd,m,y and CDRy time series for three HaleNet stations.

R.J. Longman et al. / Solar Energy 91 (2013) 102–110 107

station is dependent on the number of time periods identi-fied in the time series. Hourly solar radiation values aremultiplied by the corresponding AFt factor for their respec-tive time period at each station. The AF value was used toadjust hourly solar radiation (Kdh,d,m,y) measurements as:

AKdh;d;m;y ¼ AFt �Kdh;d;m;y ð4Þwhere AKdh,d,m,y is adjusted hourly solar radiation. Forperiods with a statistically significant trend in CDR, theregression equation was used to calculate a unique valueof CDAd,m,y for each day in the period, from which dailyvalues of CDRt were derived by adding the period meanCDR.

3. Results and discussion

3.1. Identifying abrupt changes

Using the methods described above, time series ofCDRd,m,y and CDRy were calculated and plotted for eachof the three field stations (Fig. 1). Unique time periodsare differentiated by different colors at each station. Theapparent scatter during each time period represents ran-dom measurement and model errors. Systematic errorsassociated with abrupt changes in instrument responsivityare identifiable at all three stations. The shifts can be seenmost clearly during the transition from T1 to T2, which

Fig. 3. Uncorrected (Kd) and corrected (KdA) monthly mean solarradiation values for the three HaleNet experimental stations.

Table 2Average and maximum adjustments of mean monthly solar radiationobservations for periods T1 and T2.

Sta. # T-1 (Before mid-July-1999) T-2 (After mid-July 1999)

Averagechange

Maximumchange

Averagechange

Maximumchange

(Wm�2) (%) (%) (Wm�2) (Wm�2) (%) (Wm�2) (%)

HN-151 16.8 7.1 28.1 7.4 2.1 0.8 5.0 0.9HN-152 20.0 7.4 29.7 7.4 8.2 3.0 13.6 2.2HN-153 20.2 6.9 35.6 6.8 16.1 5.4 21.0 5.5

108 R.J. Longman et al. / Solar Energy 91 (2013) 102–110

corresponds to the Eppley intercalibration event mentionedin section 2.4, and the transition from T2 to T3, which rep-resents the transition from the Eppley 8-48 to the Hukse-flux NR01.

3.2. CDR trends

To assess the significance of the trends in CDR withinthis clear day record, regression analysis and significancetesting were performed for all time periods with more than7 months of data. Of the four times periods at Station 151,four time periods at Station 152, and five time periods atStation 153, identified in Fig. 1, only time period T2 (15July 1999 to 22 January 2011) at Station 152 was foundto have a statistically significant (p = 0.01) trend. Becausethe clear-sky model parameters were held constant throughtime at each station, careful attention was paid to time peri-ods following high aerosol events such as that resultingfrom the eruption of Mt. Pinatubo in June of 1991, whichincreased the aerosol load in the atmosphere and decreasedatmospheric transmission of solar radiation for severalyears (Dutton and Bodhaine, 2001). Fortuitously, noknown calibration changes or sensor replacementsoccurred at the HaleNet stations around the time of thePinatubo eruption. The effects of the eruption can be seenas a sharp dip in the CDR time series at each stationbecause we held aerosol parameter settings constant inthe clear-sky model. Even if we had chosen to modelclear-sky radiation with time varying parameter settings,accurate parameterization of the model during this timewould not have been possible because AERONET mea-surements had not yet started. We avoided erroneouslyadjusting out the effects of the eruption at each stationby treating the time period including Pinatubo as a singleunit in the adjustment process,

3.3. Homogenizing solar radiation data

Using the homogenization procedures outlined above,the sensor shifts and significant calibration-related trendsidentified in the CDR record were corrected in the hourlysolar radiation time series. We checked our correction tech-nique by applying these methods to the CDR record aswell. Both CDRd,m,y and CDRy values have been homoge-nized by multiplying them by the appropriate AFt values(Eq. (4)) for each unique time period (Fig. 2). Fig. 2 showsthe CDR time series after being homogenized using thederived adjustment factors. Comparing this figure withFig. 1 illustrates the effects of the adjustments. Note thatwe do not correct for apparent errors indicated by randomscatter in the CDR time series. The homogenization proce-dure only corrects systematic errors associated with shiftsand drifts in the sensor response.

Mean monthly corrected and uncorrected solar radia-tion were compared visually (Fig. 3) and quantitatively(Table 2) to assess the magnitude of the adjustment. Over-all, solar radiation was adjusted on average from 4–6%

across the gradient. However, the magnitude of theseadjustments was unique for time periods before and afterthe 1999 sensor intercalibration. At the three stations, cor-rections resulted in changes in monthly solar radiationaveraging 16.8–20.2 W m�2 (6.9–7.1%), with individualmonthly values changing by as much 28.1–35.6 W m�2

(6.8–7.4%) during time period T1 (before the sensor inter-calibration). The magnitude of the adjustments was lesspronounced in time period T2 (after the sensor intercali-bration), in which average and maximum adjustments were2.1–16.1 W m�2 (0.8–5.4%) and 5–21 W m�2 (0.9–5.5%),respectively, among the three stations. The difference inthe average amount of adjustment needed for the two peri-ods confirms that sensor calibration was improved as aresult of the July 1999 intercalibration effort.

Comparing the magnitude of the adjustments to theinterannual solar radiation variability at each station pro-vides a means of gauging the importance of the corrections.The range in annual mean solar radiation is 28, 37, and

R.J. Longman et al. / Solar Energy 91 (2013) 102–110 109

33 W m�2 at stations HN-151, HN-152, and HN-153,respectively. The corrections of monthly means, averaging17–20 W m�2 are of a significant magnitude in relation tothe observed variability that failure to make these correc-tions would severely reduce the utility of this data set forassessing solar radiation changes, such as temporal trends.

The effect of the adjustments can also be evaluated dur-ing the brief (�3 month) overlap period at each stationduring which the Eppley and Hukseflux sensors were oper-ating simultaneously. Means of Eppley measured solarradiation after homogenization were in close agreementwith the means calculated from the Hukseflux measure-ments. Root mean square errors were reduced by 1–3 W m�2 after homogenization.

4. Conclusions

Infrequent calibration testing, sensor replacement, anddegradation in pyranometer response can contribute toinhomogeneities in long-term measurements of solar irradi-ance. Here, such inconsistencies found at three experimen-tal stations in Hawai‘i were detected and corrected using anew method based on variations in the ratio of observedradiation during cloud-free periods to simulated clear-skyradiation obtained with the SPCTRAL2 model. SPC-TRAL2 does a good job of providing a consistent baselinevalue of clear day solar radiation across the period ofrecord, against which observed radiation were evaluatedand adjusted. Abrupt changes in sensor response areclearly identifiable when using this method and correspondwell with known occurrences of sensor recalibration andreplacement events. The correction procedure employedhere aims to homogenize the data without removing anynatural variations within the record. Unaccounted shiftsand drifts in pyranometer calibration limit the utility ofsolar radiation data sets, especially for purposes of analyz-ing temporal variability and trends. The method presentedhere can be used to homogenize solar radiation data andprovides a tractable alternative in cases where WCRP stan-dards cannot be met.

Acknowledgments

This work was partially supported by the Pacific IslandClimate Change Cooperative (PICCC). Additional supportof HaleNet field observations and data management pro-vided through NSF EPSCoR 0903833. We thank the staffof Haleakala National Park and the Pacific Island Ecosys-tem Research Center (PIERC), USGS, for their long sup-port of the HaleNet system. Special thanks go to LloydLoope and Gordon Tribble of PIERC.

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