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

Efficiency & Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

Contract No. DE-AC36-08GO28308

Quantitative Analysis 

of Spectral Impacts on Silicon 

Photodiode Radiometers 

Preprint

D. R. Myers

To be presented at SOLAR 2011

Raleigh, North Carolina

May 17–21, 2011

Conference Paper

NREL/CP-5500-50936

April 2011
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1 

QUANTITATIVE ANALYSIS OF SPECTRAL IMPACTS ON SILICON PHOTODIODE RADIOMETERS

Daryl R. Myers

National Renewable Energy Laboratory

1617 Cole Blvd. MS 3411

Golden, CO 80401

e-mail: daryl.myers@nrel.gov

ABSTRACT

Inexpensive broadband pyranometers with silicon 

photodiode detectors have a non-uniform spectral response 

over the spectral range of 300–1100 nm. The response 

region includes only about 70% to 75% of the total energy 

in the terrestrial solar spectral distribution from 300 nm to 

4000 nm. The solar spectrum constantly changes with solar 

position and atmospheric conditions. Relative spectral 

distributions of diffuse hemispherical irradiance sky 

radiation and total global hemispherical irradiance are 

drastically different. This analysis convolves a typical 

photodiode response with SMARTS 2.9.5 spectral model 

spectra for different sites and atmospheric conditions. 

Differences in solar component spectra lead to differences 

on the order of 2% in global hemispherical and 5% or more 

in diffuse hemispherical irradiances from silicon

radiometers. The result is that errors of more than 7% can 

occur in the computation of direct normal irradiance from

global hemispherical irradiance and diffuse hemispherical 

irradiance using these radiometers.

1. INTRODUCTION

The growth of interest in “bankable” solar resource data for 

the justification of solar energy conversion system financing 

has raised a question regarding the quality of measured and 

modeled solar radiation resource data. Inexpensive silicon

photodiode (PD) radiometers (pyranometers) for measuring 

total hemispherical solar radiation on a horizontal 

(“global horizontal”) or tilted (plane of array) surface are 

popular because of their low cost. These radiometers have a 

long history of characterization with respect to their 

response characteristics and accuracy in general (1, 2, 3). 

Here, the spectral response issue is specifically studied, as it 

has a fundamental impact on the performance of rotating 

shadowband radiometers. Rotating shadowband 

radiometers use measurements of two solar radiation 

components, total hemispherical radiation and diffuse 

hemispherical radiation on a horizontal surface, to compute 

direct beam irradiance. Each of these components has a 

distinct spectral distribution, which contributes to the 

overall errors in each reported solar radiation component. 

Mention of specific instrumentation does not imply 

endorsement or recommendations regarding such 

instrumentation. 

2. APPROACH

Because of their wide spectral response regime (typically 

300–2400 nm), pyranometers and pyrheliometers using 

thermal detectors have long been considered the most 

accurate instruments for measuring solar radiation (4, 5). 

Lower-cost silicon PD radiometers are popular for 

monitoring global hemispherical irradiance (GHI) and plane 

of array irradiance for solar conversion systems. PD 

radiometers also provide a relatively inexpensive means of 

estimating direct beam irradiance (direct normal irradiance, 

or DNI) using a rotating shadowband radiometer (6). 
2 

This analysis uses the spectral response for a typical PD 

radiometer (Li-Cor LI 200 SA pyranometer) in conjunction 

with modeled clear sky spectral distributions. The 

distributions are modeled using Gueymard’s SMARTS 

spectral model, version 2.9.5 (7). Spectral distributions representative of different atmospheric conditions and locations are used to compute the “effective irradiance” or actual 

irradiance sensed by the silicon PD. Effective irradiance is 

the integral of the convolution of the PD spectral response 

and the solar spectral distribution. (See Fig. 1.) 

By integrating the complete spectral distribution, the total 

irradiance available for a conversion system can be 

calculated. Typically, a “calibration” of a PD pyranometer 

compares the output, based on the effective irradiance, with 

the total irradiance measured with a thermal detector 

radiometer, such as an Eppley Laboratories Model PSP, 

Kipp and Zonen CM11, or other model pyranometer. These 

thermal detectors are calibrated to represent the total 

irradiance, or total integral of the prevailing spectral 

distribution. This analysis examines the relationship 

between the effective irradiance and total irradiance as a 

function of the changing spectral distributions during 

calibration and the routine measurement process.

3. SPECTRAL VARIABILITY AND EFFECTIVE 

IRRADIANCE

Fig. 1 shows the spectral response of the LI-Cor LI 200 SA 

pyranometer as obtained by digitizing Fig. 5 in (8). Also 

shown are sea-level GHI SMARTS spectra as a function of 

air mass (AM) as the atmospheric path length increases 

from AM 1.1 to am 5.0, with rural aerosol optical depth 0.1 

and total precipitable water 2.5 atm-cm.

Fig. 1: Spectral variations at sea level as a function of air 

mass with total precipitable water 2.5 atm-cm and aerosol 

optical depth 0.10.

In contrast, Fig. 2 shows the portion of the diffuse 

horizontal irradiance (DHI) spectral distribution not sensed 

by the silicon PD at sea level (lower set of thin curves) 

compared with the DHI at the National Renewable Energy 

Laboratory in Golden, Colorado, at an altitude of 1800 m, 

with a station pressure of 820 mB, aerosol optical depth of 

0.05, and precipitable water of 0.5 atm-cm.

Fig. 2: DHI not sensed by silicon PD at sea level (upper four

curves) compared with Golden, Colorado, at 1800 m.

The lack of sensitivity of the silicon PD radiometer to these 

spectral differences means the integrated energy beyond 

1100 nm cannot be deduced from a shaded PD radiometer. 

Corrections derived from King (2), Vignola (3), and others 

(9) are applied to shaded PD signals corresponding to where 

the sensor responds, but the corrections do not address these 

spectral differences. The spectral differences in the GHI are 

not as pronounced, as shown in Fig. 3, but are still apparent.

 

Fig. 3: GHI not sensed by silicon PD at sea level (thick 

curves) compared with Golden, Colorado (thin curves). 
3 

The reason for the spectral differences between the highelevation and sea-level spectra is the different atmospheric 

transmittance because of more or less atmosphere, aerosols, 

and water vapor. The water vapor absorption bands at 1100 

nm, 1400 nm, and 1900 nm are well outside the response 

region of the silicon PD radiometer. Variations in water 

vapor result in changes in the depth and width of these 

absorption bands that are not detectable by the silicon PD 

radiometer.

In contrast, Fig. 4 shows the effective GHI and effective 

DHI sensed by the silicon PD at AM 1.5 and AM 3.0 at sea 

level and the Golden, Colorado, site. By comparing the 

relative contribution of the integrated effective DHI and

GHI with the integrated total GHI and DHI for these sites

and a range of air mass and atmospheric conditions, it will 

be shown how the error in DNI derived from rotating 

shadowband radiometers measurement systems can vary.

Fig. 4. Effective GHI and DHI for sea level (thin lines) and 

Golden, Colorado, (thick lines) for AM 1.5 and AM 3.0 and 

conditions in Table 1.

4. 

Table 1 displays the conditions analyzed for the relative 

contribution of spectral error to GHI, DHI, and rotating 

shadowband radiometer computed DNI irradiances.

STUDY CONDITIONS AND ANALYSIS 

For each of the conditions, at each geometrical air mass 

specified in Table 1 (1.10, 1.25, 1.50, 1.75, 2.00, 2.50, 3.00, 

3.50, 4.00, 4.50, and 5.0), the following are performed:

• Integrate total GHI spectrum 300 nm–4000 nm

• Integrate total DHI spectrum

• Integrate effective GHI spectrum 300 nm–1100 nm

• Integrate effective DHI spectrum. 

TABLE 1. STUDY CONDITIONS

Site Golden, Colorado Sea Level 

Elevation 1800 m 0 m

Aerosol optical 

depth

0.05 0.1

Precipitable 

water atm-cm

0.5 2.5

Aerosol profile Rural Rural

Geometrical air 

mass

1.25 to 5.0 1.25 to 5.0

Using these integrals, the ratios of effective irradiances to 

total integrated irradiances are computed and plotted as a 

function of air mass, as in Fig 5.

Fig. 5. Ratio of clear sky effective GHI/GHI and effective 

DHI/DHI for sea level and Golden, Colorado, as a function 

of air mass. Note that the GHI curves are practically 

identical and the DHI curves are significantly different for 

the two locations. (TOTAL refers to the respective GHI or 

DHI total integral.) 

The important aspect of Fig. 5 is that the relative 

contributions of the effective diffuse irradiances to the total 

diffuse irradiance are significantly different at the two sites. 

The sea-level DHI ratio has a slightly greater nonlinear 

(more curvature) dependence on air mass than the Golden, 

Colorado, data. The relative error in “raw” DHI (shaded 

silicon pyranometer) for a sea level site is about 55%, while 

at the high-altitude Golden site, the relative error in “raw” 

shaded silicon detector data is only about 35%. The 

difference between any average correction factors needed to 

accurately estimate total DHI at each site is almost 60%.

To further emphasize differences in the relationship of the 

effective GHI and DHI irradiances to the total irradiances at 
4 

each site, Fig. 6 shows the ratio of the sea level to Golden, 

Colorado, effective to total ratios. For example:

[(DHIeff/DHI) at sea level] / [(DHIeff/DHI) at Golden].

Note the right (red) scale of Fig. 6 relates to the GHI ratios, 

and has a range of variation of only 1.4%. The ratio of GHI 

ratios at the two sites is nonlinear with air mass. However, 

the left scale (black) relates to the DHI ratios and has a 

range of variation of about 6%. The ratio of the DHI ratios 

appears to be linear with air mass. Empirical DHI 

corrections derived (e.g., by comparison with total diffuse 

measured with a thermal pyranometer) and applied at one 

site will generally not apply at the other. Also, corrections to 

GHI data applied to DHI data could be off by factors as 

large as 6 at higher air masses. 

Fig 6. Plot of the ratios of the effective to total GHI and 

DHI ratios at Golden, Colorado, and sea level ratioed to 

each other, as a function of air mass.

Given that there can be a 60% difference in a DHI 

correction factor of about 40% between a seal-level site and 

a high-altitude site such as Golden, Colorado, the net effect 

can be errors on the order of 0.6 x 0.4 or 0.25, or 25% in the 

corrected DHI data.

For clear skies, where DHI is about 10% to 15% of the GHI, 

rotating shadowband radiometer instruments compute DNI 

from (GHI-DHIcorrected) / cos(z). If there is a 1.5% “error” 

in GHI (e.g., as in Fig. 6) and a 50% error in DHI correction 

when the DHI is ~15% of the total, then the DHI 

contribution to the error in computing DNI, as a percentage 

of the total GHI, becomes 0.50 * 0.15 ~ 0.075 = 7.5% of 

GHI. The net result is that computed DNI may have a 

relative error of: 

(GHI ± 1.5%) – (DHI ±7.5% {of GHI}) ~ ±9%. 

Therefore, errors upwards of 7% to 9% can occur in the 

computation of DNI from GHI and DHI using silicon

radiometers. The lower bound results if DHI is a smaller 

fraction (e.g, 10%) of the total GHI. Of course, random 

cancellation of errors over longer intervals will help reduce 

the overall uncertainty in averaged data. But for high time 

resolution data, there can be a significant spectral impact on 

GHI and DHI measurements, depending on atmospheric 

conditions during calibrations and measurements.

GHI corrections for silicon radiometers derived by King (2), 

based on air mass, were empirically derived for a relatively 

high-altitude, clear Western site (Albuquerque, New 

Mexico) and are probably site- (and spectral-content) 

specific. Unless site-specific comparison measurements 

between broadband thermal detectors and narrow-band 

silicon detectors are used to develop site-specific corrections 

to silicon GHI and DHI data, larger uncertainties must be 

assigned to silicon radiometer GHI, DHI, and derived DNI 

data. Although relatively good performance of rotating

shadowband radiometers and GHI silicon photodectors is 

documented (9, 10), it is imperative to remember the units 

evaluted are generally calibrated and used for routine 

measurements at the same location.

5. SUMMARY

SMARTS 2.9.5 modeled relative spectral distribution of 

DHI sky radiation and total global hemispherical irradiance 

as seen by a typical silicon PD radiometer were analyzed. 

Spectra for a sea-level and a high-altitude site over a range 

of air masses and two atmospheric conditions (low aerosol 

optical depth and water vapor and high aerosol optical depth 

and water vapor) were modeled. Differences in the ratio of 

the effective solar irradiance to total solar irradiance ratios 

for each site are on the order of 2% in effective-to-total GHI

ratios and 6% or more in effective-to-total DHI irradiances. 

Empirical corrections derived at each of the sites, to arrive 

at a total DHI, can differ by up to 60%. The net result is that 

error of upwards of 7% to 9% may occur in the computation 

of DNI from GHI and DHI using silicon radiometers in 

rotating shadowband radiometers. Empirical corrections

(e.g., by comparison to thermal sensors measuring DHI) 

derived at one site may not be applicable at another, 

substantially different site.

6. NOMENCLATURE

Air mass (AM): The relative path length through the 

atmosphere, with respect to the vertical, of the direct beam 

radiation. AM equals the reciprocal of the sine (cosine) of 

the solar elevation (zenith) angle.

Aerosol optical depth: Dimensionless parameter 

representing transparency of the atmosphere as affected by 

small particles. The negative logarithm of relative amount of 
5 

direct beam radiation transmitted (not absorbed or scattered) 

in the beam path through the atmosphere. Usually with 

respect to the vertical path, or AM =1.

Diffuse hemispherical irradiance (DHI): Diffuse or total 

hemispherical sky radiation incident on a horizontal surface 

with the solar disk blocked in watts/square meter (Wm-2). 

Direct normal irradiance (DNI): Direct normal or direct 

“beam” irradiance. Radiation within a 5° field of view 

centered on the sun intercepted by a surface perpendicular to 

the surface (the “normal” vector) pointed at the center of the 

sun (Wm-2). 

Effective irradiance: For a detector with spectral response 

smaller than the total span of solar spectral irradiance, that 

portion of the total spectrum to which the detector responds, 

in units of integrated spectral power in Wm-2. 

Global hemispherical irradiance (GHI): Total 

hemispherical radiation on a horizontal surface, sometimes 

referred to as “global” horizontal radiation (Wm-2). 

Precipitable water: The total equivalent depth, in 

centimeters, of water vapor condensed from a vertical 

column in the atmosphere. Units of atmosphere-cm (atmcm).

Pyranometer: Radiometer for measuring GHI (unshaded) 

or DHI (shaded from direct beam radiation).

Pyrheliometer: Radiometer for measuring DN, sometimes 

referred to as “normal incident pyrheliometer.” 

Responsivity (Rs): The signal generated by a radiometer 

(generally microvolts, μV, or millivolts) per unit of incident 

radiation, e.g., μV/(Wm-2). The reciprocal of responsivity is 

the calibration factor, Cf, Wm-2/μV. 

Reference irradiance: High-quality solar irradiance, based 

on low-uncertainty instruments, or computed from lowuncertainty instruments, such as GHI from DNI and DHI.

Rotating shadowband radiometer: Instrument with an 

unshaded pyranometer to measure GHI and shaded with a 

rotating band to measure total sky DHI radiation, from 

which DNI is computed.

Silicon photodiode detector: Silicon-based solid state 

detector, typically operating in photovoltaic mode, 

generating a current proportional to the irradiance.

Spectral correction: An adjustment factor, usually 

empirically derived, to shift measured broadband data to 

account for spectral effects different from calibration 

conditions.

Spectral response: The variation in the output signal of a 

radiometer as a function of the wavelength of light being 

measured.

Thermal detector: Detector that absorbs optical radiation 

and produces a thermal signal (rise in temperature) that can 

be detected and recorded.

Zenith angle, Z: Angle between the foot of the local 

vertical (“zenith direction”) and the center of the solar disk. 

Complement of the solar elevation angle.

Zenith angle or angle of incidence correction: Correction 

to account for variations in responsivity, Rs, as a function of 

zenith and or incidence angle.

7. ACKNOWLEDGMENTS

This work was performed under DOE prime contract 

number DE-AC36-08-GO28308. 

8. REFERENCES

(1) Michalsky, J.J, Harrison, L., Lebaron, B.A., “Empirical 

Radiometric Correction of a Silicon Photodiode Rotating 

Shadowband Pyranometer,” Solar Energy 39(2): 87-96, 

1987

(2) King, D.L., Myers, D.R., “Silicon-Photodiode 

Pyranometers: Operational Characteristics, Historical 

Experiences, and New Calibration Procedures,” Proceedings 

26th IEEE Photovoltaic Specialists Conference, Sept. 29–

Oct 3, 1997, Anaheim, California, 1997 

(3) Vignola, F., “Removing Systematic Errors From 

Rotating Shadowband Pyranometer Data,” Proceedings of 

American Solar Energy Society Annual Conference July 9–

13, 2006, Denver, Colorado, 2006

(4) WMO, Guide to Meteorological Instruments and 

Methods of Observation, WMO No. 8. 7th Ed., World 

Meteorological Organization, Geneva, Switzerland, 2008

(5) Gueymard, C.A., Myers, D.R., “Evaluation of 

Conventional and High Performance Routine Solar 

Radiation Measurements for Improved Solar Resources, 

Climatological Trends, and Radiative Modeling,” Solar 

Energy 83, pp. 171–185, 2009

(6) Stoffel, T., et al., Concentrating Solar Power Best 

Practices Handbook for the Collection and Use of Solar 

Resource Data, National Renewable Energy Laboratory 

technical report, NREL/TP-550-47465, September 2010
6 

(7) Gueymard, C., “Parameterized Transmittance Model for 

Direct Beam and Circumsolar Spectral Irradiance,” Solar 

Energy 71(5): 325–346, 2001

(8) Anon., Li-COR Radiation Sensors Instruction Manual, 

Terrestrial Type SA, Li-COR Inc., Lincoln, Nebraska, 1991

(9) Geuder, N., Pulvermuller, B., Vorbrugg, O., “Corrections 

for Rotating Shadowband Pyranometers for Solar Resource 

Assessment,” Proceedings of SPIE Conference 7046, 

Optical Modeling and Measurements for Solar Energy 

Systems II, August 13–14, 2008, Society for Photo-Optical 

Instrumentation Engineers, Bellingham, Washington, 2008

(10) Wilcox, S.M., Myers, D., “Evaluation of Radiometers 

in Full-Time Use at the National Renewable Energy 

Laboratory Solar Radiation Research Laboratory,” National 

Renewable Energy Laboratory technical report, NREL/TP550-44627, December 2008