Solar Radiation Data Manual 

for Flat-Plate and 

Concentrating Collectors 
NOTICE 

This report was prepared as an account of work sponsored by an agency of the United States government. Neither the United States government nor any agency 

thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or 

usefuleness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein 

to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply iots 

endorsement, recommendation, or favoring by the United States government or any agency thereof. The views and opinions of authors expressed herein do not 

necessarily state or reflect those of the United States government or any agency thereof. 
National Renewable Energy Laboratory 

'16'17 Cole Boulevard 

Golden, Colorado 80401-3393 

A national laboratory managed 

for the U.S. Department of Energy 

by the Midwest Research Institute 

under Contract No. DE-AC02-83CH-10093 
Authors: 

Artists: 

Cover 

photographs: 

Editor: 

ii 

William Marion and Stephen Wilcox 

Joe Woodburn, Phyllis S. Kabins, and 

Jon Leedholm 

Warren Gretz 

Mary Anne Dunlap 
For designers and engineers of solar energy-related 

systems, the Solar Radiation Data Manualfor FlatPlate and Concentrating Collectors gives the solar resource available for various types of collectors for the 

United States and its territories. The data in the manual 

were modeled using hourly values of direct beam and 

diffuse horizontal solar radiation from the National Solar 

Radiation Data Base (NSRDB). The NSRDB contains 

modeled (93 %) and measured (7 %) global horizontal, 

diffuse horizontal, and direct beam solar radiation for 

1961-1990. 

This manual was produced by the National Renewable 

Energy Laboratory's (NREL's) Analytic Studies 

Division under the Solar Radiation Resource 

Assessment Proj ect Task No. RA310 102 and the 

Photovoltaic Solar Radiation Research Task 

No. PV360501. These tasks were funded and monitored 

by the Photovoltaics Branch of the Department of 

Energy's Office of Energy Efficiency and Renewable 

Energy. 

Approved for the 

National Renewable Energy Laboratory 

----------------------------------

4~)).~ 

Thomas D. Bath, Director 

Analytic Studies Division 

Daryl Myers, Project Manager 

Photo voltaic Solar Radiation Research Task 

Photovoltaics Division 

The authors would like to acknowledge Charles Gay 

(UNISUN), Dave Menicucci (Sandia National 

Laboratories), Tom Ross (National Climatic Data 

Center), Frank Vignola (University of Oregon), and 

NREL staff members Carol Riordan, Dave Renne, 

Roland Hulstrom, Daryl Myers, Martin Rymes, and Tom 

Stoffel for their contributions to the manual and for their 

review. 

In the early stages of developing the manual, we received 

suggestions and recommendations from more than 

70 people on what they would like the manual to contain. 

This group consisted of designers, installers, manufacturers, consultants, university and national laboratory 

researchers, utility engineers, meteorologists, and state 

energy office staff. We appreciate their efforts and hope 

that this manual meets their expectations. 

~?<:/ '- ----------------~ 

Carol Riordan, Manager 

Technology & Resource Assessment Branch 

c2 /- -----------~-~-------- Dave Renne, Project Manager 

Solar Radiation Resource Assessment Project 

Technology & Resource Assessment Branch 

iii 
Preface ....................................................................... iii 

Introduction ................................................................ 1 

Technical Background ................................................ 2 

Interpreting the Data Tables ........................................ 3 

Station Description ................................................. 3 

Solar Radiation Data for Flat-Plate and 

Concentrating Collectors ........................................ 3 

Solar Radiation Graph ............................................ 5 

Climatic Conditions ............................................... 5 

Other Data Formats .................................................... 6 

Data Tables ................................................................. 7 

Appendix - Methodology ....................................... 247 

National Solar Radiation Data Base 

Version 1.1 Revision........................................... 248 

Calculating Solar Radiation for Flat-Plate 

and Concentrating Collectors ............................. 249 

Estimating the Uncertainty of 

Solar Radiation Data .......................................... 250 

Deriving Climatic Data ...................................... 252 

Unit Conversion Factors ................... Inside back cover 

iv 
Designers and engineers of solar energy conversion systems need solar resource information for different locations and types of collectors. Solar resource information 

provides data on how much solar energy is available to a 

collector and how it might vary from month to month 

and year to year. 

This manual provides solar radiation values for common 

flat-plate and concentrating collectors for 239 stations in 

the United States and its territories. The solar radiation 

values are expressed as monthly and yearly averages for 

the period of 1961-1990. Minimum and maximum 

monthly and yearly averages are included to show the 

variability of a station's solar resource. 

MINOT 

. 

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V t . M.LIIOHM: ",/l.A...,." . \ •• ::\. .. 

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'>! I'AUI ISlAND ...... '\~ J<b ~" ~J /QKODIAK \\"V,\\ '! 

(' HONOLULU *j <~-'> KAHUlUI "'..- , 

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J,J-" .. CO~!)flAY \::,1" •• tP '.\, 

HAWAII 

_ HILO 

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In addition to the solar radiation data, this manual contains tables listing climatic conditions such as average 

temperatures, average daily minimum and maximum 

temperatures, record minimum and maximum temperatures, average heating and cooling degree days, average 

relative humidity, and average wind speed. 

The solar radiation and climatic data are presented in 

tables, with each station having its data presented on a 

single page. The pages are arranged alphabetically by 

the state or territory two-letter abbreviation, and within a 

state or territory the pages are arranged alphabetically by 

city or island. 

OTHER U.S. STATIONS: 

* GUAM. PACIFIC 

* SAN JUAN, PUERTO AICO 

of ... tAM1 

')·1 

I<IVW!ST .' 

Map showing the location of the 239 stations in the National Solar Radiation Data Base, whose data were used to calculate values for 

this manual. 

1 
The solar radiation data in this manual are based on the 

National Solar Radiation Data Base (NSRDB),Version 

1.1, which was completed in March 1994 by the National 

Renewable Energy Laboratory. Version 1.1 supersedes 

Version 1.0, which was completed in August 1992. 

Differences between the two versions are described 

briefly in the Appendix. The NSRDB contains hourly 

values of measured or modeled solar radiation and 

meteorological data for 239 stations for the 30-year period from 1961-1990. A complete description of the 

NSRDB and how it was produced is presented in its 

user'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, of 

which 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 measurements 

and have modeled solar radiation data that are 

derived from meteorological data such as cloud cover. 

They are designated secondary stations. Both primary 

and secondary stations are National Weather Service 

stations that collected meteorological data for the period 

of 1961-1990. 

Succeeding the older 1952-1975 SOLMET/ERSATZ 

data base, the NSRDB accounts for any recent climate 

changes and provides more accurate values of solar radiation for several reasons: 

2 

• More measured data 

• Better model for estimating values 

(More than 90% of the solar radiation data in both 

data bases are modeled.) 

• Improved instrument calibration methods 

• Rigorous procedures for assessing quality of data. 

A comparison of the old and new data bases provides the 

incentive for developing new solar radiation resource 

products such as this data manual. On an annual basis, 

40% of the NSRDB and SOLMET/ERSATZ stations are 

in disagreement for global horizontal radiation by more 

than 5 %, with some stations showing disagreement of up 

to 18% (Marion and Myers 1992). For direct beam 

radiation, 60% of the NSRDB and SOLMET/ERSATZ 

stations are in disagreement by more than 5 %; some 

stations show disagreement of up to 33%. Disagreement 

between the two data bases is even greater when compared on a monthly basis. Most of the disagreement is attributed to differences in the instruments' calibration 

procedures and models. 

This manual presents monthly and yearly average solar 

radiation values for various flat-plate and concentrating 

collectors to enable quick estimates of the incident solar 

energy for common collectors. The solar radiation 

values were computed using a model and NSRDB 

hourly values of direct beam and diffuse horizontal solar 

radiation. Climatic data were obtained from the NSRDB 

and from climatic data sets provided by the National 

Climatic Data Center, Asheville, North Carolina. The 

Appendix describes in more detail how this manual was 

produced. 

References 

NSRDB-Vol. 1 (1992). User's Manual-National Solar 

Radiation Data Base (1961-1990). Version 1.0. 

Asheville, NC: National Climatic Data Center. 

Marion, W.; Myers, D. (1992). A Comparison of Data 

from SOLMETjERSATZ and the National Solar 

Radiation Data Base, NREL/TP-463-5118, Golden, CO: 

National Renewable Energy Laboratory. 
For each of the 239 stations, a data page describes the 

station location, presents average solar radiation values 

for flat-plate and concentrating collectors, and gives average climatic conditions. Except for mean atmospheric 

pressure, 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 Description 

Information 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 and 

Concentrating Collectors 

For the period of 1961-1990, tables provide solar radiation data for flat-plate and concentrating collectors. 

• Monthly and yearly averages of solar radiation 

(kWh/m2/day) 

• Minimum and maximum monthly and yearly 

averages of solar radiation (kWh/m2/day) 

• Uncertainty of solar radiation data (± %). 

Minimum and maximum monthly and yearly averages 

are included to show the variability of a station's solar 

resource. The uncertainty of the data is presented in the 

table 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 tilt. 

Data are presented for five tilt angles from the horizontal: 0°, latitude minus 15°, latitude, latitude plus 15°, and 

90°. Data for a tilt of 0°, referred to as global horizontal 

solar radiation, show how much solar radiation is received by a horizontal surface such as a solar pond. 

Maximum yearly solar radiation can be achieved using a 

tilt angle approximately equal to a site's latitude. To optimize performance in the winter, the collector can be 

tilted 15° greater than the latitude; to optimize performance in the summer, the collector can be tilted 15° less 

than the latitude. Data for a tilt of 90° apply to collectors 

mounted vertically on south-facing walls and apply to 

south-facing windows for passive solar designs. 

w 

"" 

Flat-plate collector facing south at fixed tilt 

N 

3 
One-axis tracking flat-plate collectors with axis 

oriented north-south. Data are presented for four different axis tilt angles from the horizontal: 0°, latitude 

minus 15°, latitude, and latitude plus 15°. These trackers 

pivot on their single axis to track the sun, facing east in 

the morning and west in the afternoon. Large collectors 

can use an axis tilt angle of 0° to minimize collector 

height and wind force. Small collectors can have their 

axis tilted up to increase the solar radiation on the collector. Just as for the flat-plate fixed tilt collector, the yearly 

and seasonal solar radiation can be optimized by the 

choice 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 

4 

Two-axis tracking flat-plate collectors. Data for 

two-axis trackers represent the maximum solar radiation 

at a site available to a collector. Tracking the sun in both 

azimuth and elevation, these collectors keep the sun's 

rays normal to the collector surface. 

Axis of rotation ...... 

't/, 

///c:b~ 

S / / Axis of rotation I~ .. ~ E 

Two-axis tracking flat-plate collector 

Concentrating collectors. Direct beam solar radiation data are presented for four concentrators: one-axis 

tracking parabolic troughs with a horizontal east-west 

axis, one-axis tracking parabolic troughs with a horizontal north-south axis, one-axis concentrators with the axis 

oriented north-south and tilted from the horizontal at an 

angle equal to the latitude, and two-axis tracking concentrator systems. Direct beam radiation comes in a direct 

line from the sun and is measured with instruments having a field-of-view of 5.7°. These instruments see only 

the sun's disk and a small portion of the sky surrounding 

the sun. 
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 Graph 

A graph at the top of each data page shows the variability 

of monthly and yearly solar radiation for a flat-plate collector facing south with a tilt equal to the station's latitude. For each month and year, 30 data values 

representing each year of the NSRDB are plotted along 

with the 1961-1990 averages for the months and year. 

The graph shows how the minimum and maximum values compare with the 1961-1990 average. It also shows 

the distribution of data points with respect to the average, 

minimum, and maximum values. 

Climatic Conditions 

A table shows average climatic conditions by listing 

monthly 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 D C 

• Average cooling degree days (CDD), base lS.3 D C 

• Average relative humidity (%) 

• Average wind speed (m/s). 

Degree days indicate heating and cooling requirements 

of buildings. They are defined as the difference between 

the average temperature for the day and a base 

temperature. If the average for the day (calculated 

by averaging the maximum and minimum temperature 

for the day) is less than the base value, then the difference is designated as heating degree days. If the average 

for the day is greater than the base value, the difference 

is designated as cooling degree days. 

5 
The data presented on the data pages in this manual, with 

the exception of the solar radiation graph, are also available on floppy disks in ASCII format. These data can be 

imported into popular spreadsheet programs. Also available on floppy disks are averages of solar radiation for 

each of the flat-plate and concentrating collectors for 

each month during the period of 1961-1990 

(360 months). These data could be useful for identifying 

extended periods of low or high solar radiation or plotting graphs of monthly solar radiation for any of the flatplate and concentrating collectors. The printed manual 

includes graphs only for flat-plate collectors tilted at an 

angle equal to the latitude. 

To obtain either of these data sets on floppy disks, please 

contact 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. 

6 
AK (Alaska) ........................................................... 8 

AL (Alabama) ..................................................... 25 

AR (Arkansas) ..................................................... 29 

AZ (Arizona) ....................................................... 31 

CA (California) .................................................... 35 

CO (Colorado) ..................................................... 45 

CT (Connecticut) ., ............................................... 51 

DE (Delaware) ..................................................... 53 

FL (Florida) ........................................................ 54 

GA (Georgia) ....................................................... 61 

HI (Hawaii) ........................................................ 67 

IA (Iowa) ............................................................ 71 

ID (Idaho) ........................................................... 75 

IL (Illinois) ......................................................... 77 

IN (Indiana) ........................................................ 82 

KS (Kansas) ........................................................ 86 

KY (Kentucky) .................................................... 90 

LA (Louisiana) .................................................... 93 

MA (Massachusetts) ............................................. 97 

MD (Maryland) .................................................... 99 

ME (Maine) ........................................................ 100 

MI (Michigan) ................................................... 102 

MN (Minnesota) ................................................. 111 

MO (Missouri) .................................................... 116 

MS (Mississippi) ................................................ 120 

MT (Montana) .................................................... 122 

NC (North Carolina) .......................................... 131 

ND (North Dakota) ............................................ 137 

NE (Nebraska) ................................................... 140 

NH (New Hampshire) ........................................ 145 

NJ (New Jersey) ............................................... 146 

NM (New Mexico) ............................................. 148 

NV (Nevada) ....................................................... 150 

NY (New York) .................................................. 156 

OH (Ohio) .......................................................... 163 

OK (Oklahoma) ................................................. 170 

OR (Oregon) ............................... , ...................... 172 

PA (Pennsylvania) ............................................. 181 

PI (Pacific Islands) ........................................... 189 

PR (Puerto Rico) ............................................... 190 

RI (Rhode Island) ............................................. 191 

SC (South Carolina) .......................................... 192 

SD (South Dakota) ............................................ 195 

TN (Tennessee) .................................................. 199 

TX (Texas) ......................................................... 204 

UT (Utah) ................................... , ...................... 221 

VA (Virginia) ..................................................... 223 

VT (Vermont) .................................................... 228 

WA (Washington) ............................................... 229 

WI (Wisconsin) ................................................. 234 

WV (West Virginia) ............................................ 239 

WY (Wyoming) .................................................. 242 

7 















































































































































































































































National Solar Radiation Data Base 

Version 1.1 Revision ................................................................ 248 

Calculating Solar Radiation for 

Flat-Plate and Concentrating Collectors ................................ 249 

Estimating the Uncertainty of Solar Radiation Data .............. 250 

Deriving Climatic Data .......................................................... 252 

247 
This Appendix describes Version 1.1 revisions of the 

National Solar Radiation Data Base (NSRDB) and describes the method used to calculate the monthly and 

yearly averages of solar radiation for flat-plate and concentrating collectors. It also describes how the solar radiation data uncertainties were determined and how the 

climatic information was derived. 

National Solar Radiation Data Base 

Version 1.1 

This data manual is based on the NSRDB Version 1.1, 

completed in March 1994; the previous Version 1.0 was 

completed in August 1992. Version 1.1 corrects two 

types of errors discovered in Version 1.0: (1) for 23 

stations, the wrong time zones were used, and data values 

were mismatched with their time stamp by 1 or 2 hours, 

and (2) for 8 stations that measured solar radiation, from 

1 to 3 months per station had some hourly solar radiation 

values that were unrealistically low. 

Version 1.1 corrects time zone errors for the following 

stations: 

Anchorage, AK 

Annette, AK 

Barrow, AK 

Bethel, AK 

Bettles, AK 

Big Delta, AK 

ColdBay,AK 

Fairbanks, AK 

Gulkana,AK 

King Salmon, AK 

Kodiak,AK 

Kotzebue, AK 

McGrath,AK 

Nome,AK 

St. Paul Island, AK 

Talkeetna, AK 

Honolulu, HI 

Lihue, HI 

Evansville, IN 

South Bend, IN 

Louisville, KY 

Lewistown, MT 

Ely,NV 

Version 1.1 replaces erroneous measured solar radiation 

data with modeled data for the following stations: 

248 

Montgomery, AL 

Miami, FL 

Great Falls, MT 

Ely,NV 

Albany,NY 

Brownsville, TX 

Seattle, WA 

Lander, WY 
Calculating Solar Radiation for Flat-Plate 

and Concentrating Collectors 

The 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 from 

the surface in front ofthe collector (Ir): 

Ie = Ib cos 8+ Id + Ir 

where 8 is the incident angle of the sun's rays to the 

collector. The incident angle is a function of the sun's 

postion in the sky and the orientation of the fixed or 

tracking collector. Algorithms presented by Menicucci 

and Fernandez (1988) were used to compute the incident 

angles for the various collectors. For tracking collectors, 

these algorithms also were used to compute collector tilt 

angles from the horizontal. Direct beam solar radiation 

hourly values from the National Solar Radiation Data 

Base (NSRDB) were used to determine the direct beam 

contribution (Ib cos 8) for each hour. Except for the first 

and last daylight hour, incident angles were calculated 

at the midpoint of the hour. For the first and last daylight 

hour, incident angles were calculated at the midpoint 

of the period during the hour when the sun was above 

the horizon. 

The diffuse (sky) radiation, Id, received by the collector 

was calculated by an anisotropic diffuse radiation model 

developed by Perez et al. (1990). The model determined 

the diffuse (sky) radiation for the collector using hourly 

values (from the NSRDB) of diffuse horizontal and 

direct beam solar radiation. Other inputs to the model 

included the sun's incident angle to the collector, the 

collector tilt angle from the horizontal, and the sun's 

zenith angle. The model is an improved and refined 

version of their original model that was recommended 

by the International Energy Agency for calculating diffuse radiation for tilted surfaces (Hay and McKay 1988). 

The Perez model equation for diffuse sky radiation for a 

tilted surface is: 

where 

Idh = diffuse solar horizontal radiation 

F 1 = circumsolar anisotropy coefficient, function of 

sky condition 

F2 = horizon/zenith anisotropy coefficient, function of sky condition 

~ = tilt of the collector from the horizontal 

a o or the cosine of the incident angle, 

whichever is greater 

b 0.087 or the cosine of the solar zenith angle, 

whichever is greater. 

The model coefficients F 1 and F2 are organized as an 

array of values that are selected for use depending on the 

solar zenith angle, the sky's clearness, and the sky's 

brightness. The manner in which this is done is described 

by Perez et al. (1990). 

The ground-reflected radiation received by a collector is 

a function of the global horizontal radiation (Ih), the tilt 

of the collector from the horizontal (~), and the surface 

reflectivity or albedo (p): 

Ir = 0.5p Ih ( 1 - cos ~ ). 

Surface albedo was adjusted depending on the presence 

of snow cover, as indicated by the snow depth data in the 

NSRDB. If there was snow on the ground, the surface 

albedo was set to 0.6 (albedo for snow ranges from about 

0.35 for old snow to 0.95 for dry new snow). If no snow 

was indicated, the surface albedo was set to 0.2, a nominal value for green vegetation and some soil types. 

The concentrating collectors portrayed in the manual 

have small fields-of-view and do not receive diffuse 

(sky) radiation or ground-reflected radiation. 

Consequently, solar radiation for these concentrating 

collectors is solely a function of the direct beam radiation and the sun's incident angle to the collector. Solar 

radiation received by the concentrating collectors simplifies to 

Ie = Ib cos 8. 

For each station location, collector type, and collector 

orientation, hourly values of solar radiation received by 

the collectors were calculated. Monthly and yearly averages were then determined for the period of 1961-1990. 

For a few stations, monthly and yearly averages do not 

include data for 1989 or 1990 or both because NSRDB 

data did not include those station years. Stations with 

less than 30 years of NSRDB data, along with their period of record, are listed below: 

Tucumcari, NM 

Eagle, CO 

Minot,ND 

Miles City, MT 

CutBank,MT 

Burns, OR 

1961-1988 

1961-1988 

1961-1988 

1961-1989 

1961-1988 

1961-1988 

249 
Estimating the Uncertainty of Solar 

Radiation Data 

The solar radiation values presented in the manual were 

calculated 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 of 

Abernethy and Ringhiser (1985). This root-sum-square 

method defines an uncertainty, ±URSS, in which 95% of 

the time, the true value will be within plus or minus the 

uncertainty of the calculated value. 

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

where 

t = student's T distribution factor (equals 2 

for sample size greater than 30) 

R = random error 

B = bias error. 

Random and Bias Errors. The two types of errors 

that contribute to uncertainties are random errors and 

bias errors. Random errors usually follow statistical distributions and result in values both above and below the 

true 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 may 

use 10,800 hourly values (assuming 30 days per month 

and 12 hours of sunlight per day) to determine the 

average monthly solar radiation. The random error of the 

average is reduced by a factor of 10,8001/

2, or approximately 100. Consequently, random error sources do not 

contribute significantly to the uncertainty of 30-year 

monthly averages. 

Bias errors, however, are not reduced by averaging. Bias 

errors, which are often referred to as fixed or systematic 

errors, cause values to be in error by about the same 

amount and direction. The reason for bias errors, as well 

as their magnitude and direction, may be unknown; 

otherwise, corrections such as changes in the calibration 

factor can be made. When detailed information is not 

known about the bias errors, reasonable estimates of the 

bias error magnitude can be made using procedures 

similar to those described here. 

250 

For the monthly averages of solar radiation, we evaluated the three major bias errors: (1) errors in direct beam 

radiation incident on the collector caused by errors in 

NSRDB direct beam radiation data, (2) errors in diffuse 

radiation incident on the collector caused by errors in 

NSRDB diffuse horizontal radiation, and (3) errors in 

diffuse radiation incident on the collector caused by 

errors in modeling the diffuse solar radiation for the collector. Climate change could also bias monthly 

average solar radiation values but was not considered a 

major source of error for this work. 

The root-sum-square of the individual bias errors yields 

the 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, the 

uncertainty, ±URSS, can be expressed as: 

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

where 

Bb = errors in collector direct beam radiation 

caused by errors in direct beam radiation data 

Bd = errors in collector diffuse radiation caused by 

errors in diffuse horizontal radiation data 

Bm = errors in total collector radiation caused by 

errors in modeling the diffuse solar radiation 

for the collector. 

The bias errors for direct beam and diffuse horizontal 

radiation were extracted from the NSRDB daily statistic 

files for each station. The NSRDB daily statistic files 

include, among other information, 30-year averages and 

their uncertainties for direct beam and diffuse horizontal 

radiation. An integer number represents an uncertainty 

range. Examples of uncertainty ranges for the monthly 

averages are from 6% to 9%, from 9% to 13%, and from 

13% to 18% ofthe monthly average. 

For 30-year averages, most of the stations have direct 

beam radiation uncertainties in the 6 % to 9 % range and 

diffuse horizontal radiation uncertainties in the 9 % to 

13 % range. The remaining stations have direct beam radiation uncertainties in the 9% to 13% range and diffuse 

horizontal radiation uncertainties in the 13 % to 18 % 

range. For the purpose of extracting the bias errors from 

the daily statistic files, a single integer value near the 

midpoint of the range was used (8 % for the 6 % to 9 % 

range, 11 % for the 9 % to 13 % range, and 16 % for the 

13% to 18% range). 
The bias error for modeling the collector radiation is 

attributed to the diffuse solar radiation model because 

the direct beam component is considered an exact solution (Ibcos8). An evaluation of the original Perez model 

by Hay and McKay (1988) provided information 

whereby we estimated the bias error to be about 5 % of 

the total collector radiation for our applications. 

The uncertainty, ±URSS, can be expressed as a percentage of the total collector radiation by the following equation: 

URSS (±%) = 100 [(wbHb)2 + (wdhHd)2 + 

(wmHe)2 JI/2/He 

where 

Hb average monthly direct beam radiation incident on the collector 

Hd average monthly diffuse radiation incident 

on the collector 

He average monthly total radiation incident on 

the collector ( Hb + Hd ) 

wb percent bias unce11ainty of average 

monthly beam radiation 

w dh = percent bias uncertainty of average 

monthly diffuse horizontal radiation 

wm = percent bias uncertainty of the solar radiation modeling for tilted surfaces 

Uncertainty Values in Tables. Because of the large 

number of solar radiation values presented in the manual 

(546 per station), it was judged impractical with respect 

to space limitations to present uncertainty values for 

each solar radiation value. Rather, a simplifying assumption was made so that only one uncertainty value was 

presented for all flat-plate collectors. The assumption 

was that the direct beam radiation and diffuse radiation 

incident on the collector were of equal weight. The uncertainties ofthe diffuse horizontal and direct beam radiation have about the same value, so this assumption did 

not create large changes in calculated uncertainties for 

collector radiation. 

Over a range of direct-beam-radiation-to-diffuse-radiation ratios (30/70 to 90/10), the assumption yielded 

uncertainties within 1 % or 2 % of that when calculated 

using the exact proportions of direct beam radiation and 

diffuse radiation (e.g., uncertainty of 8% or 10% instead 

of 9 %). This was judged acceptable, considering that 

there are uncertainties associated with the uncertainty 

values used for the average monthly direct beam radiation, the average monthly diffuse horizontal radiation, 

and the solar radiation modeling for tilted surfaces. As a 

conservative measure, the calculated uncertainties were 

rounded to the next highest integer value. 

For most of the stations in the data manual, uncertainties 

of 9 % were assigned to the solar radiation data for flatplate collectors. The few stations with higher uncertainties for direct beam and diffuse horizontal radiation were 

assigned uncertainties of 11 %. 

A separate value was assigned to the uncertainty for the 

direct beam radiation for concentrating collectors, which 

is only a function of the uncertainty (wb ) of the average 

monthly beam radiation. For most of the stations in the 

data manual, uncertainties of 8 % were assigned to the 

solar radiation data for concentrating collectors. The few 

stations 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 the 

nearest tenth of a kWh/m2. Consequently, the data values 

presented are within 0.05 kWh/m2 of the calculated values. Because of the uncertainties of the data values, there 

is no benefit to expressing the data values to more than 

one significant figure. 

251 
Deriving Climatic Data 

The climatic data presented in the manual were derived 

using both data from the National Solar Radiation Data 

Base (NSRDB) and from climatic data sets provided by 

the National Climatic Data Center (NCDC), Asheville, 

North Carolina (704) 271-4994. 

Climatic data pertaining to average temperature, average 

daily minimum temperature, average daily maximum 

temperature, average heating degree days base 18.3°C, 

and average cooling degree days base 18.3°C were extracted from NCDC's data tape, "1961-1990 Monthly 

Station Normals All Elements." This data tape includes 

temperature and degree day normals for about 4775 

stations in the United States and its territories. The normals are averages computed by NCDC for the period of 

1961-1990. 

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. For 

one of the stations in this data manual, data were not 

available on NCDC's data tape. For this station, in 

Arcata, California, the averages were computed using 

NSRDB data, but no attempt was made to estimate missing data or to correct for other inconsistencies. 

NSRDB data were used to calculate average relative 

humidity and average wind speed. Record minimum and 

maximum temperatures were obtained primarily from 

NCDC's data diskette, "Comparative Climatic Data 

Tables-1991." This data diskette contains, among other 

useful parameters, record minimum and maximum temperatures for about 90% of the stations in this manual 

and spans periods of record back to 1948 and earlier. For 

the remaining 10% of the stations, record minimum and 

maximum temperatures are based on NSRDB data. 

252 

References 

Abernethy, R.; Ringhiser, B. (1985). "The History and 

Statistical Development of the New ASME-SAE-AIAAISO Measurement and Uncertainty Methodology." 20th 

AIAAjSAEjASME Joint Propulsion Conference (July 

1985). AIAA-85-1403. New York: American Institute of 

Astronautics and Aeronautics. 

Hay, J .E.; McKay, D.C. (1988). Final Report lEA 

Task IX -Calculation of Solar Irradiances for Inclined 

Surfaces: Verification of Models Which Use Hourly and 

Daily Data. International Energy Agency Solar Heating 

and Cooling Programme. 

Menicucci, D.; Fernandez, J.P. (1988). User's Manual 

for PVFORM: A Photovoltaic System Simulation 

Program for Stand-Alone and Grid-Interactive 

Applications. SAND85-0376, Albuquerque, NM: 

Sandia National Laboratories. 

Perez, R.; Ineichen, P.; Seals, R.; Michalsky, J.; 

Stewart, R. (1990). "Modeling Daylight Availability 

and Irradiance Components from Direct and Global 

Irradiance." Solar Energy, 44(5), pp. 271-289. 
To Convert Into Multiply By 

kilowatt-hours per square meter megajoules per square meter 3.60 

kilowatt-hours per square meter Btus per square foot 317.2 

kilowatt -hours per square meter Langleys 86.04 

kilowatt -hours per square meter calories per square centimeter 86.04 

meters feet 3.281 

meters per second miles per hour 2.237 

millibars pascals 100.0 

millibars atmospheres 0.0009869 

millibars kilograms per square meter 10.20 

millibars pounds per square inch 0.0145 

degrees Centigrade degrees Fahrenheit °C x 1.8 + 32 

degrees (angle) radians 0.017453 

degree days (base 18.3°C) degree days (base 65"F) 1.8 
National Renewable Energy laboratory 

1617 Cole Boulevard 

Golden, Colorado 80401-3393 

NREL is a national laboratory of the U.S. Department of Energy 

NREL/TP-463-5607 

DE93018229 

April 1994 

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