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. 

Authors: 

Artists: 

Cover 

photographs: 

Editor: 

ii 

William Marion and Stephen Wilcox 

Jon Leedholm and Dean Armstrong 

Warren Gretz 

Mary Anne Dunlap 
For use by architects and engineers, the Solar Radiation 

Data Manual for Buildings provides solar resource information for common window orientations for the 

United States and its territories. This information was 

modeled using solar radiation and meteorological data 

gathered from 1961 to 1990 and will permit quick evaluations of passive solar and daylighting features for 

buildings. 

This manual was produced by the National Renewable 

Energy Laboratory's (NREL's) Analytic Studies 

Division under the Resource Assessment Program, 

which is funded and monitored by the U.S. Department 

of Energy's Office of Solar Energy Conversion. 

Approved for the 

National Renewable Energy Laboratory 

Thomas D. Bath, Director 

Analytic Studies Division 

The authors acknowledge Doug Balcomb and Ron 

Judkofffrom NREL's Buildings and Energy Systems 

Division. Their efforts were instrumental in establishing 

the content of the data manual. The authors also acknowledge the contributions and reviews of Steve 

Ternoey (Lightforms); Richard Perez (State University 

of New York); and NREL staff members Scott Crowder, 

Gene Maxwell, Steve Slazak, and Tom Stoffel. 

Dave Renne, Manager 

Resource Assessment Program 

iii 
Preface ........................................... " ..................... " ...... .iii 

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

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

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

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

Solar Radiation .......................................................... 3 

Solar Radiation Graph .............................................. .4 

Climatic Conditions .................................................. .4 

Illuminance ............................................................... .5 

Electronic Data ............................................................... 6 

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

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

Calculating Incident Solar Radiation ................... .248 

Calculating Transmitted Solar Radiation ............. .249 

Calculating Incident Illuminance ......................... .250 

Averaging Solar Radiation and Illuminance ......... .251 

Estimating Solar Radiation and Illuminance 

Data Uncertainty ................................................... .251 

Deriving Climatic Data ........................................ .253 

References .............................................................. 254 

Unit Conversion Factors ............................................ 255 

iv 
Architects and engineers use solar resource information 

to help design passive solar and day lighting features for 

bUildings. Solar resource information includes data on 

how much solar radiation and illuminance are available 

for different window orientations, and how they vary. 

This manual provides solar radiation and illuminance 

values for a horizontal window and four vertical windows (facing north, east, south, and west) for 239 stations in the United States and its territories. The solar 

radiation values are monthly and yearly averages for the 

period of 1961-1990. Included are values showing the 

solar radiation incident on the window and the amount 

transmitted into the living space, with and without exterior 

shading of the window. Illuminance values are presented 

for average diurnal profiles for 4 months of the year. 

In addition to the solar radiation and illuminance data, 

this manual contains tables listing climatic conditions 

such as average temperature, average daily minimum 

and maximum temperature, record minimum and maximum temperature, average heating and cooling degree 

days, average humidity ratio, average wind speed, and 

average clearness index. 

The solar radiation, illuminance, and climatic data are 

presented in tables. Data for each station are presented 

on a single page, and the pages are arranged alphabetically by the state or territory two-letter abbreviation. 

Within a state or territory, the pages are arranged alphabetically by city or island. 

Map showing the location of the 239 stations in the National Solar Radiation Data Base from which data were used to calculate values 

for this manual 

1 
The solar radiation and illuminance data in this manual 

were modeled using data from the National Solar 

Radiation Data Base (NSRDB) Version 1.1, which was 

completed in March 1994 by the National Renewable 

Energy Laboratory (NREL). 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. 11992) and the final technical report (NSRDB-Vol. 21995). The original version 

of the NSRDB, Version 1.0, was completed in August 

1992. Version 1.1 corrects two types of minor errors in 

Version 1.0 that affected about 10% of the stations 

(Rymes 1994). 

There are two types of stations in the NSRDB: primary 

(denoted by asterisks in the station map) and secondary 

(denoted by dots in the station map). Primary stations, of 

which there are 56, measured solar radiation for a part 

(from 1 to 27 years) ofthe 30-year period. The remaining 

183 stations, designated secondary stations, made no 

solar radiation measurements. Their data are modeled 

solar radiation values derived from meteorological data 

such as cloud cover. Both primary and secondary stations are National Weather Service stations that collected 

meteorological data for the period 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. The NSRDB data are more accurate for several 

reasons: 

• 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. 

2 

Results of a comparison of the NSRDB with the 

SOLMET/ERSATZ data base provide the incentive to 

develop new solar radiation resource products, such as 

this data manual. On an annual basis, 40% of the 

NSRDB and SOLMET/ERSATZ station values are in 

disagreement for global horizontal radiation by more 

than 5%; some station values show disagreement of up 

to 18% (Marion and Myers 1992). For direct beam radiation, 60% of the NSRDB and SOLMET/ERSATZ station 

values 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 solar radiation and illuminance 

values to enable quick estimates of the incident solar 

energy for common window orientations. The solar 

radiation and illuminance values were computed using 

models and NSRDB hourly values of direct beam, global 

horizontal, and diffuse horizontal solar radiation, and 

dew point temperature. 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 

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

from SOLMETIERSATZ and the National Solar 

Radiation Data Base. NRELlTP-463-5118, Golden, CO: 

National Renewable Energy Laboratory. 

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

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

Golden, CO: National Renewable Energy Laboratory 

and Asheville, NC: National Climatic Data Center. 

NSRDB- Vol. 2 (1995). Final Technical Report: 

National Solar Radiation Data Base (1961-1990). 

NRELlTP-463-5784, Golden, CO: National Renewable 

Energy Laboratory. 

Rymes, M. (1994). "Beyond the NSRDB Version 1.0." 

Proceedings of the 1994 Annual American Solar Energy 

Society Conference; June 25-30,1994, San Jose, CA. 
For each of the 239 stations, a data page contains a 

. description of the station location; presents average solar 

radiation and illuminance values for a horizontal window 

and vertical windows facing north, east, south, and west; 

and gives average climatic conditions. Standard 

International (SI) units are used for illuminance; otherwise, English units are used. To convert values 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 (feet) 

• Mean atmospheric pressure of station (pounds per 

square inch absolute) 

• Type of station (primary or secondary). 

Solar Radiation 

For the period 1961-1990, tables provide solar radiation 

data in units of Btu/ft2/day for five surfaces: a horizontal 

window and vertical windows facing north, east, south, 

and west. An estimate of the uncertainty (± %) of the 

solar radiation data is given in the table headings. The 

manual includes the solar radiation incident on the outside 

of the window and the solar radiation transmitted through 

the window into the living space. 

Incident solar radiation. For the five windows, monthly 

and yearly averages of incident solar radiation are given 

in terms of global radiation, clear-day global radiation, 

and diffuse radiation. 

Global radiation is the total radiation received by the 

window and is the sum of the direct beam radiation component, sky radiation, and radiation reflected from the 

ground in front of the surface. Clear-day global radiation 

represents the global radiation obtainable under clear 

skies. 

The diffuse radiation data in the tables do not include the 

direct beam radiation component. Diffuse radiation is the 

sum of sky radiation and radiation reflected from the 

ground in front of the surface. The ground-reflected 

radiation was calculated using a ground reflectivity or 

albedo of 0.2, a nominal value for green vegetation and 

some soil types. Values in the tables may be adjusted for 

other albedo values by using equation 4 from the 

Appendix. 

Standard deviations and minimum and maximum 

monthly and yearly values of global horizontal radiation 

are provided to show the variability of the solar resource 

at a station. These quantities pertain to monthly and 

yearly values, rather than to single days. 

Sky radiation 

Ground·reflected 

radiation 

~Transmitted LV radiation 

Incident global solar radiation includes direct beam, sky, and 

ground-reflected radiation 

Transmitted solar radiation. The solar radiation transmitted into a living space is less than the radiation that 

strikes the outside of a window because of losses associated with radiation reflected off of and absorbed by the 

glass. The manual presents data for windows with conventional, single-strength clear double glazing and a 

glass thickness of 0.125 in. (3.18 mm). 

Tables contain values for unshaded and shaded windows. 

Unshaded values are for windows with no external shading. 

Shaded values are for windows shaded by a roof overhang. The roof overhang and window geometry are 

shown at the top of each data page. The overhang width 

and the vertical distance from the window to the overhang are given in dimensionless units for a window 

height of 1.0. 

3 
For south-facing windows, the geometry balances the 

need for maximum heat gain during the heating season 

without creating unreasonable heat gain during the cooling 

season. The same shading geometry is used for all vertical 

windows for a station. The shading geometry is not 

applicable for the horizontal surface; consequently, 

shaded transmitted solar radiation values for a horizontal 

surface are not included. 

As described in the Appendix, the shading geometry is 

generally a function of the station latitude but consideration is also given to heating and cooling requirements. 

For example, Hawaii, Guam, and Puerto Rico have zero 

heating degree days; consequently, their shading geometry 

provides complete shading of south-facing windows at 

noon throughout the year. Alaskan stations, with no summer cooling loads, have shading geometries that do not 

shade south-facing windows at noon throughout the year. 

Solar noon 

on 11/17 

and 1/25 

no shading 

........p_~-.l 0.321 

1 

1.000 

Shading geometry and sun positions for 40° north latitude 

For south-facing windows, the shading geometries provide guidance for the appropriate dimensions of roof 

overhangs. However, situations may require a different 

geometry, depending on the balance between heating and 

cooling loads for the particular building and factors such 

as required window sizes and building practices. For 

east- and west-facing windows, overhangs are not particularly effecti ve in preventing unwanted heat gain. 

Additional shading strategies such as vertical louvers 

may be needed. 

4 

Solar Radiation Graph 

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

by month and window orientation, of the average 

amount of solar radiation transmitted through the windows into the living space. For the vertical windows, the 

graphs are based on the data values for transmitted solar 

radiation with external shading. The shading geometry is 

shown adjacent to the graph. 

Climatic Conditions 

The tables containing average climatic condition information list monthly and yearly values for the following 

parameters. 

.. Monthly and yearly average temperature (OF) 

.. Average daily minimum temperature (OF) 

.. Average daily maximum temperature CF) 

.. Record minimum temperature (OF) 

.. Record maximum temperature (OF) 

" Average heating degree days (HDD) , base 65°F 

.. Average cooling degree days (CDD) , base 65°F 

.. Average humidity ratio (lb water per lb dry air) 

.. Average wind speed (mph) 

.. Average clearness index, Kt . 

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 is greater than the base 

value, the difference is designated as cooling degree days. 

The clearness index (Kt

) is the station's global horizontal 

solar radiation divided by its extraterrestrial horizontal 

radiation. Because clouds decrease the amount of solar 

radiation reaching the earth, stations in cloudy regions 

will have lower values for Kt than stations in regions 

with fewer clouds. 
Illuminance 

The illuminance tables contain diurnal profiles of the 

average illuminance incident on five surfaces: a horizontal 

window and vertical windows facing north, east, south, 

and west. The illuminance profiles are given for 4 

months of the year (March, June, September, and 

December) and consist of two data values, separated by a 

slash, for each of the following hours: 9 a.m., 11 a.m., 

1 p.m., 3 p.m., and 5 p.m. The value before the slash is 

the average illuminance for mostly clear conditions (total 

cloud cover less than 50%), and the value after the slash 

is the average illuminance for mostly cloudy conditions 

(total cloud cover equal to or greater than 50%). 

The last line in the illuminance tables indicates the 

percentage of time during the hour that the station location was mostly clear (M. elr.). These values, along with 

the illuminance values, can be used to determine the 

average hourly illuminance: 

Average illuminance = 

[ (M. Clr . ) * (illuminance for mostly clear) 

+ ( 100 - M. Clf.) * (illuminance for mostly cloudy)] / 100. 

The illuminance data are given in units of kilolux-hours 

(klux-hr) and represent the illuminance received during 

the preceding hour. For example, data for 3 p.m. include 

the illuminance received from 2 p.m. to 3 p.m. The hours 

for March and December are local standard time. The 

hours for June and September are either local standard 

time or daylight saving time, depending on whether the 

station observes daylight saving time. Arizona, Hawaii, 

Indiana (except for Evansville), Puerto Rico, and Guam 

do not observe daylight saving time; consequently, the 

hours for June and September for these stations are local 

standard time. For all other stations, the hours for June 

and September are daylight saving time. An estimate of the 

uncertainty (± %) of the illuminance data is given in the 

table headings. 

5 
The data presented in the data tables, with the exception 

of the graph and shading geometry figure, are also available in ASCII format. These data can be imported into 

popular spreadsheet programs. 

To obtain the data set on floppy disk, please contact the 

NREL Technical Inquiry Service at 303/275-4099. A 

"readme" file that describes the contents of the data set is 

included on the floppy disk. 

The data set is available over Internet from NREL's 

Renewable Resource Data Center (RReDC). The 

Uniform Resource Locator (URL) address of the 

RReDC is ''http://rredc.nrel.gov.'' Users should have 

World Wide Web (WWW) browsing software, such as 

Mosaic or Netscape, to access the RReDC. 

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 















































































































































































































































Calculating Incident Solar Radiation ..................................... 248 

Calculating Transmitted Solar Radiation ............................... 249 

Calculating Incident Illuminance ........................................... .250 

Averaging Solar Radiation and Illuminance ........................... .251 

Estimating Solar Radiation and Illuminance Data Uncertainty ...... .251 

Deriving Climatic Data .......................................................... 253 

References .............................................................................. .254 

247 
This Appendix describes the methods used to calculate the 

monthly and yearly averages of incident and transmitted 

solar radiation and the illuminance diurnal profiles. It also 

describes how data uncertainties were determined and how 

the climatic information was derived. 

Calculating Incident Solar Radiation 

The incident solar radiation for a horizontal window and 

vertical windows facing north, east, south, and west was 

determined using models and hourly data from the 

1961-1990 National Solar Radiation Data Base 

(NSRDB). 

Global solar radiation. The incident global solar radiation (I) received by a surface, such as a window, is a 

combination of direct beam radiation (Ib), sky radiation 

(Is)' and radiation reflected from the ground in front of 

the surface (Ir)' The following equation can be used to 

calculate incident global solar radiation: 

(1) 

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

The incident angle is a function of the sun's position in 

the sky and the orientation of the surface. Algorithms 

presented by Menicucci and Fernandez (1988) were used 

to compute incident angles. Hourly values of direct 

beam solar radiation from the 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 sky radiation (Is) received by the surface was calculated using an anisotropic diffuse radiation model developed by Perez et al. (1990). The model determined the 

sky radiation striking the surface using hourly values 

(from the NSRDB) of diffuse horizontal and direct beam 

solar radiation. Other inputs to the model included the 

sun's in<;:ident angle to the surface, the surface tilt angle 

from horizontal, and the sun's zenith angle. The Perez et 

al. 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 following equation is the Perez et al. model for diffuse sky 

radiation for a surface: 

248 

where 

Idh = diffuse horizontal solar radiation 

Fl = circumsolar anisotropy coefficient, function of 

sky condition 

F2 = horizonlzenith anisotropy coefficient, function 

of sky condition 

~ = tilt of the surface from the horizontal 

a = 0 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. Perez et al. (1990) describe completely the 

manner in which this is done. 

The ground-reflected radiation (Ir) received by a surface 

is assumed isotropic and is a function of the global horizontal radiation (Ih), the tilt ofthe surface from the horizontal (~), and the ground reflectivity or albedo (p). 

Ir = 0.5 P Ih ( 1 - cos ~ ). (3) 

For the data in this manual, an albedo of 0.2 was used. 

This albedo is a nominal value for green vegetation and 

some soil types. The effect of other albedo values can be 

determined by adding an adjustment (Iadj) to the incident 

global and diffuse solar radiation values in the data 

tables: 

Iadj = 0.5( Pd - 0.2 )Ih( 1 - cos ~) (4) 

where 

Pd = desired albedo 

Ih = monthly or yearly average from data tables for 

incident global horizontal radiation. 

Diffuse solar radiation. The incident diffuse solar radiation (Id) received by a surface is the sum of the sky radiation (Is) and the radiation reflected from the ground 

in front of the surface (Ir)' both of which are considered 

diffuse. 

(5) 
Clear-day global solar radiation. Incident clear-day 

global solar radiation represents the global radiation 

obtainable under clear skies. It was calculated as above, 

but using clear sky values of direct beam and diffuse 

horizontal solar radiation. The clear sky values of direct 

beam and diffuse horizontal solar radiation were modeled using METSTAT (NSRDB-Vol. 2,1995), the same 

model used to model solar radiation for the NSRDB. 

Inputs to METSTAT included cloud cover values of 

zero; average monthly values of aerosol optical depth, 

precipitable water, albedo, and ozone; and the day of the 

month of which the solar declination equals the monthly 

average. Average precipitable water values were multiplied by 80% to compensate for expected clear-day 

precipitable water compared to the mean for all weather 

conditions. 

Calculating Transmitted Solar Radiation 

As solar radiation passes through a window, some of it is 

reflected or absorbed by the glass. Consequently, the 

solar radiation transmitted into the living space is less 

than the radiation incident on the outside of the window. 

The losses are dependent on the type of window. For this 

manual, the transmitted solar radiation data are for two 

layers of single-strength clear glass. Each glass is 3.18 mm 

(0.125 inch) thick and has an index of refraction of 1.526 

and an extinction coefficient of 32/meter (for glass with 

greenish appearance). 

Transmitted solar radiation values were determined for 

windows with and without external shading. 

Transmitted solar radiation for unshaded windows. For 

windows without external shading, transmittance coefficients were applied to the hourly values of incident solar 

radiation to obtain the transmitted solar radiation (It). 

La = transmittance for absorption of radiation 

Lr = transmittance for reflectance of radiation 

I = incident solar radiation. 

(6) 

As presented by Duffie and Beckman (1991), Bouguer's 

law can be used to determine the transmittance for 

absorption, and Fresnel equations can be used to determine 

the transmittance for reflectance. Both transmittance coefficients depend on the incident angle of the solar radiation. 

Because of their differences in incident angles, diffuse and 

direct beam radiation were treated separately when determining the transmitted solar radiation. 

If incident isotropic diffuse sky radiation is integrated 

over all angles, it has been shown to have an effective 

incidence angle of approximately 60° for vertical and 

horizontal surfaces (Duffie and Beckman 1991). 

Isotropic ground-reflected diffuse radiation for vertical 

surfaces also has an effective incidence angle of approximately 60°. To simplify the analysis, and because diffuse 

radiation from the horizon is a small part of the total 

radiation, it is treated in the same manner as isotropic 

sky and ground-reflected diffuse radiation. 

To determine the transmitted solar radiation, an incidence angle of 60° was used for all sky radiation (including 

diffuse radiation from the horizon but not circumsolar 

diffuse radiation) and ground-reflected radiation values. 

For direct beam and circumsolar diffuse radiation, the 

incident angle was the angle of incidence for the direct 

beam radiation. 

Transmitted solar radiation for shaded windows. 

Windows externally shaded by a roof overhang were 

treated differently than unshaded windows in two ways. 

First, the direct beam radiation component and the circumsolar diffuse radiation were reduced if portions of 

the window were shaded. Second, the isotropic diffuse 

sky radiation was reduced to account for the reduced 

field of view of the sky because of the roof overhang. 

The presence of the roof overhang was assumed to have 

no effect on the transmitted diffuse radiation from the 

horizon and on the ground-reflected diffuse radiation. 

The shading geometry selected for each station balanced 

the need for maximum solar heat gain for south-facing 

windows during the heating season without creating 

unreasonable solar heat gain during the cooling season. 

For each station, the same shading geometry was used 

for all vertical windows, and the roof overhang was 

assumed to extend an infinite distance with respect to the 

window width. 

Two angles (as and a w) describe the shading geometry. 

These angles determine the amount of shading of southfacing windows at solar noon throughout the year. If the 

sun elevation at solar noon is greater than as (summer), 

then the window is completely shaded. If the sun elevation at solar noon is less than as but greater than a w 

(spring and fall), then the window is partially shaded. If 

the sun elevation at solar noon is less than a w (winter), 

then the window is completely unshaded. 

249 
For most stations in this manual, as = 108° - latitude and 

a w = 71 ° -latitude. This shading geometry provides no 

shading of the south-facing window from November 17 

to January 25, and provides complete shading of the window (at solar noon) from May 12 to August 2. 

Stations in southern states can benefit from more summertime shading; therefore, the shading geometry was 

modified to accommodate a longer shading period. Their 

monthly heating degree day (base 65°F) requirements 

were examined to find the first fall month with a value 

greater than zero. If this month was October or later, then 

as = 92° -latitude and a w = 66.SO -latitude. 

For these stations, this provides no shading of the southfacing window only on December 21, and provides complete shading of the window (at solar noon) from March 

26 to September 18. 

. ' 

/os 

.y. ....... . 

Shading geometry described using as and aw 

Other exceptions to the shading geometry were also 

made. Hawaii, Guam, and Puerto Rico have zero heating 

degree days; consequently, their shading geometry provides complete shading of south-facing windows at noon 

throughout the year. Shading geometries that provide 

complete shading of south-facing windows at noon 

throughout the year were also used for stations that had 

more cooling degree days than heating degree days in 

December. This included stations in southern Florida. 

Alaskan stations, with no summer cooling loads, have 

shading geometries that do not shade south-facing windows at noon throughout the year. For the situations described in this paragraph, the roof overhang width was 

calculated using 1.0 for the window height and 0.2 for 

the vertical distance from the window to the overhang. 

250 

For each hour, the shading geometry and trigonometric 

relationships (ASHRAE 1993) were used to determine 

the fraction of window that was not shaded. This fraction 

was then multiplied by the transmitted direct beam component for unshaded windows to determine the transmitted beam radiation for shaded windows. Circumsolar diffuse radiation was treated in the same manner. 

The transmitted isotropic diffuse sky radiation was 

reduced to account for the reduced field of view of the 

sky because of the roof overhang. The fraction of the sky 

viewed by a vertical window with a roof overhang to that 

viewed by a vertical window without an overhang can be 

determined using methods presented by Iqbal (1983). 

These methods determine the configuration factors between inclined surfaces and the sky. This fraction was 

determined to be sina, where a varies from a w (top of 

window) to as (bottom of window). 

An average fraction for the window was calculated by dividing the window into 100 equal horizontal segments 

and finding the average sina, where a is based on the 

midpoint of each segment. This average fraction was 

multiplied by the transmitted isotropic diffuse sky radiation for unshaded windows to determine the transmitted 

isotropic diffuse sky radiation for shaded windows. 

Hourly values of the total transmitted solar radiation 

were determined by summing the transmitted component 

values for direct beam radiation, circumsolar diffuse 

radiation, isotropic sky diffuse radiation, horizon diffuse 

radiation, and ground-reflected diffuse radiation . 

Calculating Incident Illuminance 

Incident illuminance for the horizontal window and 

vertical windows facing north, east, south, and west was 

determined using equations 1,2, and 3 and inputs of 

global horizontal illuminance, direct beam illuminance, 

and diffuse horizontal illuminance instead of their solar 

radiation counterparts. When used to calculate the 

diffuse illuminance for a tilted surface, equation 2 uses a 

different array of values for model coefficients F 1 and F2 

than when it is used to calculate the diffuse solar radiation for a tilted surface. The input illuminance values 

were calculated using luminous efficacy models developed by Perez et al. (1990). Inputs to the luminous efficacy models are global horizontal radiation, direct beam 

radiation, diffuse horizontal radiation, and dew point 

temperature. 
Averaging Solar Radiation and Illuminance 

For each station location and window orientation, hourly 

values of solar radiation and illuminance for the windows were calculated. Monthly and yearly averages for 

solar radiation and hourly average profiles for illuminance for 4 months of the year were then determined for 

the period 1961-1990. Illuminance profiles were determined for mostly clear and mostly cloudy conditions by 

calculating separate averages for hourly illuminances 

when the hourly total cloud cover was less than 50% 

(mostly clear) and when the hourly total cloud cover was 

equal to or greater than 50% (mostly cloudy). 

For a few stations, the averages do not include data for 

1989,1990, or both because NSRDB data did not 

include those station years. The stations with less than 

30 years of NSRDB data and their period of record are 

listed below: 

Tucumcari, NM 1961-1988 

Eagle, CO 1961-1988 

Minot,ND 1961-1988 

Miles City, MT 1961-1989 

Cut Bank,MT 1961-1988 

Burns, OR 1961-1988 

Estimating Solar Radiation and Illuminance 

Data Uncertainty 

The solar radiation and illuminance values 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. 

(7) 

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 ,800 112, or approximately 

100. For the hourly averages of illuminance, each hourly 

average is based on approximately 900 hourly values. 

The random error of their average is reduced by a factor 

of 900112 , or 30. Consequently, random error sources do 

not contribute significantly to the uncertainty of the solar 

radiation and illuminance 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 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 in this section. 

For the solar radiation and illuminance averages, we 

evaluated the three major bias errors: (1) errors in direct 

beam radiation and direct beam illuminance incident on 

the window because of errors in NSRDB direct beam 

radiation data, (2) errors in diffuse radiation and diffuse 

illuminance incident on the window because of errors in 

NSRDB diffuse horizontal radiation, and (3) errors in 

diffuse radiation and diffuse illuminance incident on the 

window because of errors from modeling the diffuse 

solar radiation or diffuse illuminance for the window. 

Climate change could also bias monthly average solar 

radiation and illuminance values but was not considered 

a major source of error for this work. 

The analysis beginning in the next paragraph pertains to 

the solar radiation incident on the windows, but an 

analysis for incident illuminance would yield similar 

results because: (1) errors in the direct beam illuminance 

and the diffuse horizontal illuminance are predominately 

the result of errors in the direct normal radiation and 

diffuse horizontal radiation from which they are modeled, 

and the errors are the same relative magnitude, and 

(2) errors from modeling the diffuse solar radiation and diffuse illuminance for the window are approximately equal. 

251 
The root-sum-square of the individual bias errors yields 

the total bias error and, because the random error is negligible, is the same as the total uncertainty of the monthly 

averages. Consequently, the uncertainty, ±URSS , can be 

expressed as: 

(8) 

where 

Bb = errors in window direct beam radiation because 

of errors in direct beam radiation data 

Bd = errors in window diffuse radiation because of 

errors in diffuse horizontal radiation data 

Bm = errors in total window radiation because of 

errors in modeling the diffuse solar radiation 

for the window. 

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% of the 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 window 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 the bias error was estimated to be about 5% of 

the total window radiation for the applications. 

252 

The uncertainty, ±URSS , can be expressed as a percentage 

of the total window radiation by the following equation: 

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

(wmHe)2 ]1I2/He 

where 

(9) 

Hb = average monthly direct beam radiation incident 

on the window 

Hd = average monthly diffuse radiation incident on 

the window 

He = average monthly total radiation incident on the 

window ( Hb + Hd) 

wb = percent bias uncertainty of average monthly 

direct beam radiation 

wdb = percent bias uncertainty of average monthly 

diffuse horizontal radiation 

W m = percent bias uncertainty of the solar radiation 

modeling for tilted surfaces. 

Uncertainty values in tables. Because of the large number 

of solar radiation and illuminance values presented in the 

manual, it was judged impractical with respect to space 

limitations to present uncertainty values for each solar 

radiation and illuminance value. Rather, a simplifying 

assumption was made so that only one uncertainty value 

was presented for all windows. The assumption was that 

the direct beam radiation and diffuse radiation incident 

on the window were of equal weight. The uncertainties 

of the diffuse horizontal and direct beam radiation have 

about the same value, so this assumption did not create 

large changes in calculated uncertainties for window 

radiation. 

Over a range of direct beam radiation to diffuse radiation 

ratios (30/70 to 90110), the assumption yielded uncertainties within 1 % or 2 % of uncertainties calculated 

using the exact proportions of direct beam radiation and 

diffuse radiation (uncertainty of 8% or 10% instead of 

9%, and so on). This was judged acceptable, considering 

that there are uncertainties associated with the uncertainty values used for the average monthly 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 and illuminance data. The few stations with higher uncertainties 

for direct beam and diffuse horizontal radiation were 

assigned uncertainties of 11 %. 

Deriving Climatic Data 

The climatic data were derived using both data from the 

NSRDB and from climatic data sets provided by the 

National Climatic Data Center (NCDC), Asheville, 

North Carolina. 

Climatic data pertaining to average temperature, average 

daily minimum temperature, average daily maximum 

temperature, average heating degree days base 65°F 

(l8.3°C), and average cooling degree days base 65°F 

(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 hourly data were used to calculate the average 

wind speed, average clearness index, and average humidity ratio. The average humidity ratio was determined 

by first calculating the average station pressure (p) and 

average partial pressure of water vapor (Pw)' Partial 

pressure of water vapor values were determined using 

psychometric relationships (ASHRAE 1993) and 

NSRDB dew point temperatures. The humidity ratio (W) 

was then calculated using the following equation: 

W = 0.62918 Pw I( p - Pw)' (10) 

This approach gives a more accurate portrayal of the 

average water vapor content in the air than would be 

given by averaging hourly values of the humidity ratio or 

relative humidity (Linacre 1992). 

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 records 

back to 1948 and earlier. For the remaining 10% of the 

stations, record minimum and maximum temperatures 

are based on NSRDB data. 

253 
References 

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

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

AIAA/SAE/ASEE Joint Propulsion Conference (July 

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

Astronautics and Aeronautics. 

ASHRAE (1993). 1993 ASHRAE Handbook: 

Fundamentals. Atlanta, GA: American Society of 

Heating, Refrigerating and Air-Conditioning Engineers, 

Inc. 

Duffie, J .A.; Beckman, W.A. (1991). Solar 

Engineering of Thermal Processes. 2nd Edition. New 

York: John Wiley & Sons, Inc. 

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. 

Iqbal, M. (1983). An Introduction to Solar Radiation. 

New York: Academic Press, Inc. 

Linacre, E. (1992). Climate Data and Resources. New 

York: Routledge. 

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. 

NSRDB- Vol. 2 (1995). Final Technical Report: 

National Solar Radiation Data Base (1961-1990). 

NRELlTP-463-5784, Golden, CO: National Renewable 

Energy Laboratory. 

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. 

254 
To Convert Into Multiply By 

Btu per square foot kilowatt-hours per square meter 0.003152 

Btu per square foot megajoules per square meter 0.01135 

Btu per square foot Langleys 0.2712 

Btu per square foot calories per square centimeter 0.2712 

degrees Fahrenheit degrees Centigrade (OF-32)/1.8 

degree days (base 65°F) degree days (base l8.3°C) 0.5556 

degrees (angle) radians 0.017543 

feet meters 0.3048 

lux foot-candles 0.0929 

miles per hour meters per second 0.4470 

pounds per square inch atmospheres 0.06804 

pounds per square inch millibars 68.97 

pounds per square inch kilograms per square meter 703.1 

pounds per square inch kilopascals 6.897 

255 
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