solar radiation data manual

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Solar Radiation Data Manualfor Flat-Plate andConcentrating Collectors


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NOTICEThis report was prepared as an account of work sponsored by an agency of the United States government. Neither the United States government nor any athereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeneusefuleness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference hto any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or implendorsement, recommendation, or favoring by the United States government or any agency thereof. The views and opinions of authors expressed herein dnecessarily state or reflect those of the United States government or any agency thereof.


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Nat iona l Renewable Energy Laboratory'16'17 Cole BoulevardGolden, Colorado 80401-3393A nat iona l laboratory managedfo r the U.S. Depar tment o f Energyby the Midwest Research Ins t i tu teunder Contract No. DE-AC02-83CH-10093


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Authors:Artists:Coverphotographs:Editor:

ii

William Marion and Stephen WilcoxJoe Woodburn, Phyllis S. Kabins, andJon LeedholmWarren GretzMary Anne Dunlap


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For designers and engineers of solar energy-relatedsystems, the Solar Radiation Data Manualfor Flat-Plate and Concentrating Collectors gives the solar resource available for various types of collectors for theUnited States and its territories. The data in the manualwere modeled using hourly values of direct beam anddiffuse horizontal solar radiation from the National SolarRadiation Data Base (NSRDB). The NSRDB containsmodeled (93 %) and measured (7 %) global horizontal,diffuse horizontal, and direct beam solar radiation for1961-1990.This manual was produced by the National RenewableEnergy Laboratory's (NREL's) Analytic StudiesDivision under the Solar Radiation ResourceAssessment Proj ect Task No. RA310 102 and thePhotovoltaic Solar Radiation Research TaskNo. PV360501. These tasks were funded and monitoredby the Photovoltaics Branch of the Department ofEnergy's Office of Energy Efficiency and RenewableEnergy.

Approved for theNational Renewable Energy Laboratory

4 ~ ) ) . ~ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Thomas D. Bath, DirectorAnalytic Studies Division

Daryl Myers, Project ManagerPhoto voltaic Solar Radiation Research TaskPhotovoltaics Division

The authors would like to acknowledge Charles G(UNISUN), Dave Menicucci (Sandia NatioLaboratories), Tom Ross (National Climatic DCenter), Frank Vignola (University of Oregon), NREL staff members Carol Riordan, Dave RenRoland Hulstrom, Daryl Myers, Martin Rymes, and TStoffel for their contributions to the manual and for threview.In the early stages of developing the manual, we receisuggestions and recommendations from more th70 people on what they would like the manual to contThis group consisted of designers, installers, manufturers, consultants, university and national laboratresearchers, utility engineers, meteorologists, and stenergy office staff. We appreciate their efforts and hthat this manual meets their expectations.

~ ? < : / '-- - - - - - - - - - - - - - - - ~ Carol Riordan, ManagerTechnology & Resource Assessment Branch

c2 /-- - - - - - - - - - - ~ - ~ - - - - - - - -Dave Renne, Project ManagerSolar Radiation Resource Assessment ProjectTechnology & Resource Assessment Branch


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Preface ....................................................................... iiiIntroduction ................................................................ 1Technical Background ................................................ 2Interpreting the Data Tables ........................................ 3

Station Description ................................ ................. 3Solar Radiation Data for Flat-Plate andConcentrating Collectors ........................................ 3Solar Radiation Graph ............................................ 5Climatic Conditions ............................................... 5

Other Data Formats ................................. ................... 6Data Tables ................................................................. 7Appendix - Methodology ....................................... 247

National Solar Radiation Data BaseVersion 1.1 Revision........................................... 248Calculating Solar Radiation for Flat-Plateand Concentrating Collectors ............................. 249Estimating the Uncertainty ofSolar Radiation Data .......................................... 250Deriving Climatic Data ...................................... 252Unit Conversion Factors ................... Inside back cover

iv


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Designers and engineers of solar energy conversion systems need solar resource information for different locations and types of collectors. Solar resource informationprovides data on how much solar energy is available to acollector and how it might vary from month to monthand year to year.This manual provides solar radiation values for commonflat-plate and concentrating collectors for 239 stations inthe United States and its territories. The solar radiationvalues are expressed as monthly and yearly averages forthe period of 1961-1990. Minimum and maximummonthly and yearly averages are included to show thevariability of a station's solar resource.

.MINOT

" ' O M [ ~ J"-' " ' C G h ' A I I ~ i.. UfTHfI . G U L ~ A N A

V t . M.L I IOHM: ",/l.A...,." . \ ::\. ..'\ i / .,JJ " > - - ~ " ", K tNGSA l , , " ,ON : " " " - YAKUTAT ''>! I 'AUI ISlAND ...... ' \ ~ J


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The solar radiation data in this manual are based on theNational Solar Radiation Data Base (NSRDB),Version1.1, which was completed in March 1994 by the NationalRenewable Energy Laboratory. Version 1.1 supersedesVersion 1.0, which was completed in August 1992.Differences between the two versions are describedbriefly in the Appendix. The NSRDB contains hourlyvalues of measured or modeled solar radiation andmeteorological data for 239 stations for the 30-year period from 1961-1990. A complete description of theNSRDB and how it was produced is presented in itsuser's manual (NSRDB-Vol. 1, 1992).There are two types of stations in the NSRDB: primary(denoted by asterisks on the station map) and secondary(denoted by dots on the station map). Primary stations, ofwhich there are 56, measured solar radiation for a part(from 1 to 27 years) of the 30-year period. The remaining 183 stations made no solar radiation measurementsand have modeled solar radiation data that ar ederived from meteorological data such as cloud cover.They are designated secondary stations. Both primaryand secondary stations are National Weather Servicestations that collected meteorological data for the periodof 1961-1990.Succeeding the older 1952-1975 SOLMET/ERSATZdata base, the NSRDB accounts for any recent climatechanges and provides more accurate values of solar radiation for several reasons:

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More measured data Better model for estimating values(More than 90% of the solar radiation data in bothdata bases are modeled.) Improved instrument calibration methods Rigorous procedures for assessing quality of data.

A comparison of the old and new data bases provides theincentive for developing new solar radiation resourceproducts such as this data manual. On an annual basis,40% of the NSRDB and SOLMET/ERSATZ stations arein disagreement for global horizontal radiation by morethan 5%, with some stations showing disagreement of upto 18% (Marion and Myers 1992). For direct beamradiation, 60% of the NSRDB and SOLMET/ERSATZstations are in disagreement by more than 5 %; somestations show disagreement of up to 33%. Disagreementbetween the two data bases is even greater when compared on a monthly basis. Most of the disagreement is attributed to differences in the instruments' calibrationprocedures and models.This manual presents monthly and yearly average solarradiation values for various flat-plate and concentratingcollectors to enable quick estimates of the incident solarenergy for common collectors. The solar radiationvalues were computed using a model and NSRDBhourly values of direct beam and diffuse horizontal solarradiation. Climatic data were obtained from the NSRDBand from climatic data sets provided by the NationalClimatic Data Center, Asheville, North Carolina. TheAppendix describes in more detail how this manual wasproduced.ReferencesNSRDB-Vol. 1 (1992). User's Manual-National SolarRadiation Data Base (1961-1990). Version 1.0.Asheville, NC: National Climatic Data Center.Marion, W.; Myers, D. (1992). A Comparison ofDatafrom SOLMETjERSATZ and the National SolarRadiation Data Base, NREL/TP-463-5118, Golden, CO:National Renewable Energy Laboratory.


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For each of the 239 stations, a data page describes thestation location, presents average solar radiation valuesfor flat-plate and concentrating collectors, and gives average climatic conditions. Except for mean atmosphericpressure, given in millibars, Standard International (SI)units are used. To convert to other units, use the conversion factor table on the inside back cover.Station DescriptionInformation at the top of each page describes the station.

City and state in which the station is located Station Weather Bureau Army Navy (WBAN)identification number Latitude (degrees; north) Longitude (degrees; east or west) Elevation of station (meters) Mean atmospheric pressure of station (millibars) Type of station (primary or secondary).

Solar Radiation Data for Flat-Plate andConcentrating CollectorsFor the period of 1961-1990, tables provide solar radiation data for flat-plate and concentrat ing collectors.

Monthly and yearly averages of solar radiation(kWh/m2/day) Minimum and maximum monthly and yearlyaverages of solar radiation (kWh/m2/day) Uncertainty of solar radiation data ( %).

Minimum and maximum monthly and yearly averagesare included to show the variability of a station's solarresource. The uncertainty of the data is presented in thetable headings.The manual includes data for the flat-plate and concentrating collectors described in the next few paragraphs.

Flat-plate collectors facing south at fixed tiData are presented for five tilt angles from the horizotal: 0, lat itude minus 15, latitude, latitude plus 15, a90. Data for a tilt of 0, referred to as global horizonsolar radiation, show how much solar radiation isceived by a horizontal surface such as a solar pond.Maximum yearly solar radiation can be achieved usintilt angle approximately equal to a site's latitude. To opmize performance in the winter, the collector cantilted 15 greater than the latitude; to optimize perfomance in the summer, the collector can be tilted 15 lethan the latitude. Data for a tilt of 90 apply to collectomounted vertically on south-facing walls and applysouth-facing windows for passive solar designs.

w""

Flat-plate collector facing south at fixed tilt

N


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One-axis tracking flat-plate collectors with axisoriented north-south. Data are presented for four different axis tilt angles from the horizontal: 0, latitudeminus 15, latitude, and latitude plus 15. These trackerspivot on their single axis to track the sun, facing east inthe morning and west in the afternoon. Large collectorscan use an axis tilt angle of 0 to minimize collectorheight and wind force. Small collectors can have theiraxis tilted up to increase the solar radiation on the collector. Just as for the flat-plate fixed tilt collector, the yearlyand seasonal solar radiation can be optimized by thechoice of tilt angle. The data presented assume continuous tracking of the sun throughout the day.

One-axis tracking flat-plate collector with axis oriented north-south

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Two-axis tracking flat-plate collectors. Data fortwo-axis trackers represent the maximum solar radiationat a site available to a collector. Tracking the sun in bothazimuth and elevation, these collectors keep the sun'srays normal to the collector surface.

Axis of rotation...... 't/,

/ / / c : b ~ / I ~ .. ~ S / Axis of rotation ETwo-axis tracking flat-plate collector

Concentrating collectors. Direct beam solar radiation data are presented for four concentrators: one-axistracking parabolic troughs with a horizontal east-westaxis, one-axis tracking parabolic troughs with a horizontal north-south axis, one-axis concentrators with the axisoriented north-south and tilted from the horizontal at anangle equal to the latitude, and two-axis tracking concentrator systems. Direct beam radiation comes in a directline from the sun and is measured with instruments having a field-of-view of 5.7. These instruments see onlythe sun's disk and a small portion of the sky surroundingthe sun.


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Axis of rotation

""E

One-axis tracking parabolic trough with axis oriented east-west

Axis of rotation

w ~ " ' ~ / c : p ~

S / Axis of rotation E

Two-axis tracking concentrator

Solar Radiation GraphA graph at the top of each data page shows the variabilof monthly and yearly solar radiation for a flat-plate colector facing south with a tilt equal to the station's latude. For each month and year, 30 data valurepresenting each year of the NSRDB are plotted alowith the 1961-1990 averages for the months and yeThe graph shows how the minimum and maximum vaues compare with the 1961-1990 average. It also showthe distribution of data points with respect to the averagminimum, and maximum values.Climatic ConditionsA table shows average climatic conditions by listimonthly and yearly values for various parameters.

Monthly and yearly average temperature (DC) Average daily minimum temperature (DC) Average daily maximum temperature (DC) Record minimum temperature COC)

Record maximum temperature (DC) Average heating degree days (HDD), base lS.3 DC Average cooling degree days (CDD), base lS.3 DC Average relative humidity (%) Average wind speed (m/s).

Degree days indicate heating and cooling requiremenof buildings. They are defined as the difference betwethe average temperature fo r the day and a batemperature. I f the average for the day (calculatby averaging the maximum and minimum temperatufor the day) is less than the base value, then the diffeence is designated as heating degree days. If the averafor the day is greater than the base value, the differenis designated as cooling degree days.


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The data presented on the data pages in this manual, withthe exception of the solar radiation graph, are also available on floppy disks in ASCII format. These data can beimported into popular spreadsheet programs. Also available on floppy disks are averages of solar radiation foreach of the flat-plate and concentrating collectors foreach month during the period of 1961-1990(360 months). These data could be useful for identifyingextended periods of low or high solar radiation or plotting graphs of monthly solar radiation for any of the flatplate and concentrating collectors. The printed manualincludes graphs only for flat-plate collectors tilted at anangle equal to the latitude.To obtain either of these data sets on floppy disks, pleasecontact the NREL Technical Inquiry Service at(303) 275-4099. "Readme" files, which describe the contents of the data sets, are included on the floppy disks.

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AK (Alaska) ......................... ............................ ...... 8AL (Alabama) ............................. ........................ 25AR (Arkansas) ........................ ........................... .. 29AZ (Arizona) .......................... ............................. 31CA (California) ......................... ........................... 35CO (Colorado) ............................. ........................ 45CT (Connecticut) ., ............................................... 51DE (Delaware) ............................ ......................... 53FL (Florida) ............................. ........................... 54GA (Georgia) .............................. ......................... 61HI (Hawaii) ............................. ........................... 67IA (Iowa) ......................... ........................... ........ 71ID (Idaho) ......................... ............................ ...... 75IL (Illinois) ............................. ............................ 77IN (Indiana) ............................ ............................ 82KS (Kansas) ............ ......................... ................... 86KY (Kentucky) ........................... ......................... 90LA (Louisiana) ........................... ......................... 93MA (Massachusetts) ................................ ............. 97MD (Maryland) ........................... ......................... 99ME (Maine) ............................... ......................... 100MI (Michigan) ................................ ................... 102MN (Minnesota) ................................ ................. 111MO (Missouri) ................................. ................... 116MS (Mississippi) ................................................ 120MT (Montana) ............................. ....................... 122NC (North Carolina) ................................ .......... 131ND (North Dakota) ..................................... ....... 137NE (Nebraska) ................................ ................... 140NH (New Hampshire) ........................................ 145NJ (New Jersey) .............................. ................. 146NM (New Mexico) ............................................. 148NV (Nevada) ............................. .......................... 150NY (New York) ........................... ....................... 156OH (Ohio) ........................... ............................... 163OK (Oklahoma) ................................ ................. 170OR (Oregon) ............................... , ...................... 172PA (Pennsylvania) ............................................. 181PI (Pacific Islands) ................................... ........ 189PR (Puerto Rico) .............................. ................. 190RI (Rhode Island) .......................... ................... 191SC (South Carolina) .......................................... 192SD (South Dakota) ............................ ................ 195TN (Tennessee) .............................. .................... 199TX (Texas) ............................ ............................. 204UT (Utah) .......................... ......... , ...................... 221VA (Virginia) ..................................................... 223VT (Vermont) ............................ ........................ 228WA (Washington) ............................................... 229WI (Wisconsin) ........................... ...................... 234WV (West Virginia) ...................................... ...... 239WY (Wyoming) ........................... ....................... 242


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National Solar Radiation Data BaseVersion 1.1 Revision ........................ ............................. ........... 248Calculating Solar Radiation forFlat-Plate and Concentrating Collectors ................................ 249Estimating the Uncertainty of Solar Radiation Data .............. 250Deriving Climatic Data .......................................................... 252

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This Appendix describes Version 1.1 revisions of theNational Solar Radiation Data Base (NSRDB) and describes the method used to calculate the monthly andyearly averages of solar radiation for flat-plate and concentrating collectors. I t also describes how the solar radiation data uncertainties were determined and how theclimatic information was derived.

National Solar Radiation Data BaseVersion 1.1This data manual is based on the NSRDB Version 1.1,completed in March 1994; the previous Version 1.0 wascompleted in August 1992. Version 1.1 corrects twotypes of errors discovered in Version 1.0: (1) for 23stations, the wrong time zones were used, and data valueswere mismatched with their time stamp by 1 or 2 hours,and (2) for 8 stations that measured solar radiation, from1 to 3 months per station had some hourly solar radiationvalues that were unrealistically low.Version 1.1 corrects time zone errors for the followingstations:

Anchorage, AKAnnette, AKBarrow, AKBethel, AKBettles, AKBig Delta, AKColdBay,AKFairbanks, AKGulkana,AKKing Salmon, AKKodiak,AKKotzebue, AK

McGrath,AKNome,AKSt. Paul Island, AKTalkeetna, AKHonolulu, HILihue, HIEvansville, INSouth Bend, INLouisville, KYLewistown, MTEly,NV

Version 1.1 replaces erroneous measured solar radiationdata with modeled data for the following stations:

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Montgomery, ALMiami, FLGreat Falls, MTEly,NVAlbany,NYBrownsville, TXSeattle, WALander, WY


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Calculating Solar Radiation for Flat-Plateand Concentrating CollectorsThe total solar radiation received by a flat-plate collector(Ie) is a combination of direct beam radiation (Ib),diffuse (sky) radiation (Id), and radiation reflected fromthe surface in front ofthe collector (Ir):

Ie = Ib cos 8+ Id + Irwhere 8 is the incident angle of the sun's rays to thecollector. The incident angle is a function of the sun'spostion in the sky and the orientation of the fixed ortracking collector. Algorithms presented by Menicucciand Fernandez (1988) were used to compute the incidentangles for the various collectors. For tracking collectors,these algorithms also were used to compute collector tiltangles from the horizontal. Direct beam solar radiat ionhourly values from the National Solar Radiation DataBase (NSRDB) were used to determine the direct beamcontribution (Ib cos 8) for each hour. Except for the firstand last daylight hour, incident angles were calculatedat the midpoint of the hour. For the first and last daylighthour, incident angles were calculated at the midpointof the period during the hour when the sun was abovethe horizon.The diffuse (sky) radiation, Id, received by the collectorwas calculated by an anisotropic diffuse radiation modeldeveloped by Perez et al. (1990). The model determinedthe diffuse (sky) radiation for the collector using hourlyvalues (from the NSRDB) of diffuse horizontal anddirect beam solar radiation. Other inputs to the modelincluded the sun's incident angle to the collector, thecollector tilt angle from the horizontal, and the sun'szenith angle. The model is an improved and refinedversion of their original model that was recommendedby the International Energy Agency for calculating diffuse radiation for tilted surfaces (Hay and McKay 1988).The Perez model equation for diffuse sky radiation for atilted surface is:

whereIdh = diffuse solar horizontal radiationF1 = circumsolar anisotropy coefficient, function ofsky conditionF2 = horizon/zenith anisotropy coefficient, function of sky condition~ = tilt of the collector from the horizontal

a oor the cosine of the incident angle,whichever is greaterb 0.087 or the cosine of the solar zenith angle,

whichever is greater.The model coefficients F1 and F2 are organized as array of values that are selected for use depending on tsolar zenith angle, the sky's clearness, and the skybrightness. The manner in which this is done is describby Perez et al. (1990).The ground-reflected radiation received by a collectora function of the global horizontal radiation (Ih), the tof the collector from the horizontal ( ~ ) , and the surfareflectivity or albedo (p):

Ir = 0.5p Ih ( 1 - cos ~ ).Surface albedo was adjusted depending on the presenof snow cover, as indicated by the snow depth data in tNSRDB. If there was snow on the ground, the surfaalbedo was set to 0.6 (albedo for snow ranges from abo0.35 for old snow to 0.95 for dry new snow). If no snowas indicated, the surface albedo was set to 0.2, a nomnal value for green vegetation and some soil types.The concentrating collectors portrayed in the manuhave small fields-of-view and do not receive diffu(sky) radiation or ground-reflected radiatioConsequently, solar radiation for these concentraticollectors is solely a function of the direct beam radition and the sun's incident angle to the collector. Solradiation received by the concentrating collectors simpfies to

Ie = Ib cos 8.For each station location, collector type, and collectorientation, hourly values of solar radiation received bthe collectors were calculated. Monthly and yearly aveages were then determined for the period of 1961-199For a few stations, monthly and yearly averages do ninclude data for 1989 or 1990 or both because NSRDdata did not include those station years. Stations wiless than 30 years of NSRDB data, along with their priod of record, are listed below:

Tucumcari, NMEagle, COMinot,NDMiles City, MTCutBank,MTBurns, OR

1961-19881961-19881961-19881961-19891961-19881961-1988

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Estimating the Uncertainty of SolarRadiation DataThe solar radiation values presented in the manual werecalculated using improved models and data. The estimated data uncertainties assigned to the calculated values show how they might compare with true values.They were determined using the uncertainty method ofAbernethy and Ringhiser (1985). This root-sum-squaremethod defines an uncertainty, URSS, in which 95% ofthe time, the true value will be within plus or minus theuncertainty of the calculated value.

URSS = [(tR)2 + B2 ]1/2where

t = student's T distribution factor (equals 2for sample size greater than 30)R = random errorB = bias error.

Random and Bias Errors. The two types of errorsthat contribute to uncertainties are random errors andbias errors. Random errors usually follow statistical distributions and result in values both above and below thetrue values. Random errors tend to cancel when individual values are used to determine an average. For example, a 30-year monthly average of solar radiation mayuse 10,800 hourly values (assuming 30 days per monthand 12 hours of sunlight per day) to determine theaverage monthly solar radiation. The random error of theaverage is reduced by a factor of 10,8001/2, or approximately 100. Consequently, random error sources do notcontribute significantly to the uncertainty of 30-yearmonthly averages.Bias errors, however, are not reduced by averaging. Biaserrors, which are often referred to as fixed or systematicerrors, cause values to be in error by about the sameamount and direction. The reason for bias errors, as wellas their magnitude and direction, may be unknown;otherwise, corrections such as changes in the calibrationfactor can be made. When detailed information is notknown about the bias errors, reasonable estimates of thebias error magnitude can be made using proceduressimilar to those described here.

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For the monthly averages of solar radiation, we evaluated the three major bias errors: (1) errors in direct beamradiation incident on the collector caused by errors inNSRDB direct beam radiation data, (2) errors in diffuseradiation incident on the collector caused by errors inNSRDB diffuse horizontal radiation, and (3) errors indiffuse radiation incident on the collector caused byerrors in modeling the diffuse solar radiation for the collector. Climate change could also bias monthlyaverage solar radiation values but was not considered amajor source of error for this work.The root-sum-square of the individual bias errors yieldsthe total bias error. Because the random error is negligible, the total bias error is the same as the total uncertainty of the monthly averages. Consequently, theuncertainty, URSS, can be expressed as:

URSS = B=[Bb2 + Bi+Bm2 ]1/2where

Bb = errors in collector direct beam radiationcaused by errors in direct beam radiation dataBd = errors in collector diffuse radiation caused byerrors in diffuse horizontal radiation dataBm = errors in total collector radiation caused byerrors in modeling the diffuse solar radiation

for the collector.The bias errors for direct beam and diffuse horizontalradiation were extracted from the NSRDB daily statisticfiles for each station. The NSRDB daily stati stic filesinclude, among other information, 30-year averages andtheir uncertainties for direct beam and diffuse horizontalradiation. An integer number represents an uncertaintyrange. Examples of uncertainty ranges for the monthlyaverages are from 6% to 9%, from 9% to 13%, and from13% to 18% ofthe monthly average.For 30-year averages, most of the stations have directbeam radiation uncertainties in the 6 % to 9 % range anddiffuse horizontal radiation uncertainties in the 9 % to13% range. The remaining stations have direct beam radiation uncertainties in the 9% to 13% range and diffusehorizontal radiation uncertainties in the 13 % to 18 %range. For the purpose of extracting the bias errors fromthe daily statistic files, a single integer value near themidpoint of the range was used (8 % for the 6 % to 9 %range, 11 % for the 9 % to 13 % range, and 16 % for the13% to 18% range).


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The bias error for modeling the collector radiation isattributed to the diffuse solar radiation model becausethe direct beam component is considered an exact solution (Ibcos8). An evaluation of the original Perez modelby Hay and McKay (1988) provided informationwhereby we estimated the bias error to be about 5 % ofthe total collector radiation for our applications.The uncertainty, URSS, can be expressed as a percentage of the total collector radiation by the following equation:

URS S (%) = 100 [(wbHb)2 + (wdhHd)2 +(wmHe)2 JI/2/Hewhere

Hb average monthly direct beam radiation incident on the collectorHd average monthly diffuse radiation incidenton the collectorHe average monthly total radiation incident onthe collector ( Hb + Hd )wb percent bias unce11ainty of averagemonthly beam radiationwdh = percent bias uncertainty of average

monthly diffuse horizontal radiationwm = percent bias uncertainty of the solar radiation modeling for tilted surfaces

Uncertainty Values in Tables. Because of the largenumber of solar radiation values presented in the manual(546 per station), it was judged impractical with respectto space limitations to present uncertainty values foreach solar radiation value. Rather, a simplifying assumption was made so that only one uncertainty value waspresented for all flat-plate collectors. The assumptionwas that the direct beam radiation and diffuse radiat ionincident on the collector were of equal weight. The uncertainties ofthe diffuse horizontal and direct beam radiation have about the same value, so this assumption didnot create large changes in calculated uncertainties forcollector radiation.Over a range of direct-beam-radiation-to-diffuse-radiation ratios (30/70 to 90/10), the assumption yieldeduncertainties within 1% or 2 % of that when calculatedusing the exact proportions of direct beam radiation anddiffuse radiation (e.g., uncertainty of 8% or 10% insteadof 9 %). This was judged acceptable, considering thatthere are uncertainties associated with the uncertaintyvalues used for the average monthly direct beam radiation, the average monthly diffuse horizontal radiation,and the solar radiation modeling for tilted surfaces. As aconservative measure, the calculated uncertainties wererounded to the next highest integer value.For most of the stations in the data manual, uncertaintiesof 9 % were assigned to the solar radiation data for flatplate collectors. The few stations with higher uncertainties for direct beam and diffuse horizontal radiation wereassigned uncertainties of 11%.A separate value was assigned to the uncertainty for thedirect beam radiation for concentrating collectors, whichis only a function of the uncertainty (wb ) of the averagemonthly beam radiation. For most of the stations in thedata manual, uncertainties of 8% were assigned to thesolar radiation data for concentrating collectors. The fewstations with higher uncertainties for direct beam radiation were assigned uncertainties of 11%.Data values in the data manual are given to one significant figure by rounding the calculated value to th enearest tenth of a kWh/m2. Consequently, the data valuespresented are within 0.05 kWh/m2 of the calculated values. Because of the uncertainties of the data values, thereis no benefit to expressing the data values to more thanone significant figure.

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Deriving Climatic DataThe climatic data presented in the manual were derivedusing both data from the National Solar Radiation DataBase (NSRDB) and from climatic data sets provided bythe National Climatic Data Center (NCDC), Asheville,North Carolina (704) 271-4994.Climatic data pertaining to average temperature, averagedaily minimum temperature, average daily maximumtemperature, average heating degree days base 18.3C,and average cooling degree days base 18.3C were extracted from NCDC's data tape, "1961-1990 MonthlyStation Normals All Elements." This data tape includestemperature and degree day normals for about 4775stations in the United States and its territories. The normals are averages computed by NCDC for the period of1961-1990.For this data set, NCDC used procedures, when possible,to estimate missing data and to correct for other inconsistencies by using data from neighboring stations. Forone of the stations in this data manual, data were notavailable on NCDC's data tape. For this station, inArcata, California, the averages were computed usingNSRDB data, but no attempt was made to estimate missing data or to correct for other inconsistencies.NSRDB data were used to calculate average relativehumidity and average wind speed. Record minimum andmaximum temperatures were obtained primarily fromNCDC's data diskette, "Comparative Climatic DataTables-1991." This data diskette contains, among otheruseful parameters, record minimum and maximum temperatures for about 90% of the stations in this manualand spans periods of record back to 1948 and earlier. Forthe remaining 10% of the stations, record minimum andmaximum temperatures are based on NSRDB data.

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ReferencesAbernethy, R.; Ringhiser, B. (1985). "The History andStatistical Development of the New ASME-SAE-AIAAISO Measurement and Uncertainty Methodology." 20thAIAAjSAEjASME Joint Propulsion Conference (July1985). AIAA-85-1403. New York: American Institute ofAstronautics and Aeronautics.Hay, J .E.; McKay, D.C. (1988). Final Report lE ATask IX-Calculation ofSolar Irradiances for InclinedSurfaces: Verification ofModels Which Use Hourly andDaily Data. International Energy Agency Solar Heatingand Cooling Programme.Menicucci, D.; Fernandez, J.P. (1988). User's Manualfo r PVFORM: A Photovoltaic System SimulationProgram for Stand-Alone and Grid-InteractiveApplications. SAND85-0376, Albuquerque, NM:Sandia National Laboratories.Perez, R.; Ineichen, P.; Seals, R.; Michalsky, J.;Stewart, R. (1990). "Modeling Daylight Availabilityand Irradiance Components from Direct and GlobalIrradiance." Solar Energy, 44(5), pp. 271-289.


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To Convert Into Multiply By

kilowatt-hours per square meter megajoules per square meter 3.60kilowatt-hours per square meter Btus per square foot 317.2kilowatt -hours per square meter Langleys 86.04kilowatt -hours per square meter calories per square centimeter 86.04meters feet 3.281meters per second miles per hour 2.237millibars pascals 100.0millibars atmospheres 0.0009869millibars kilograms per square meter 10.20millibars pounds per square inch 0.0145degrees Centigrade degrees Fahrenheit C x 1.8 + 32degrees (angle) radians 0.017453degree days (base 18.3C) degree days (base 65"F) 1.8


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solar radiation data manual

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