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A national laboratory of the U.S. Department of Energy

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NREL is operated by Midwest Research Institute ● Battelle Contract No. DE-AC36-99-GO10337 

A Case Study of the Application 

of a Modified Method to Measure 

Global Solar Irradiance 

F.P. Rael 

Technical Report 

NREL/TP-560-37184 

February 2006 
A Case Study of the Application 

of a Modified Method to Measure 

Global Solar Irradiance 

F.P. Rael 

Prepared under Task No. WUID.5600 and 

Inter-Agency Work Order No. 353926 

Technical Report 

NREL/TP-560-37184 

February 2006 

National Renewable Energy Laboratory 

1617 Cole Boulevard, Golden, Colorado 80401-3393 

303-275-3000 • www.nrel.gov 

Operated for the U.S. Department of Energy 

Office of Energy Efficiency and Renewable Energy 

by Midwest Research Institute • Battelle 

Contract No. DE-AC36-99-GO10337
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iii

Acknowledgments 

This research was supported by the Office of Biological and Environmental Research of the U.S. 

Department of Energy as part of the Atmospheric Radiation Measurement (ARM) Program. Solar 

radiation measurements from the ARM Climate Research Facility were essential to accomplishing 

this research. I would like to thank Afshin Andreas. The software he wrote was critical to this work. 

Mary Anderberg and Pete Gotseff made this work smoother by generously providing me with 

technical assistance and logistical support. Steve Wilcox, Daryl Myers, and Ibrahim Reda also were 

helpful advisors and great sources of information. Tom Stoffel oversaw and guided me through the 

entire endeavor. 
iv

Executive Summary 

Climate change research requires accurate measurements of downwelling, total hemispheric (global) 

solar irradiance. Until the performance of commercially available pyranometers can be improved, a 

better understanding of the radiometer response characteristics is needed to reduce the current 

measurement uncertainty levels of 5%–10%. The abilities of a pyranometer to respond equally to 

radiance from any part of the sky dome and to maintain thermal equilibrium under changing 

atmospheric conditions are important pyranometer design considerations. The resulting angular and 

zero-offset responses are currently the largest contributors to thermopile-based pyranometer 

measurement uncertainty. 

Fortunately, the calibration of pyranometers by the component summation method provides insight to 

the instrument-specific response characteristics that are important for reducing measurement 

uncertainties. Outdoor pyranometer calibration results show the variations of responsivity (μV/Wm-2) 

related to the solar zenith angle (Z) and the effective sky temperature. In this paper, we will describe 

the benefits of applying pyranometer responsivity (Rs) that varies as a function of solar zenith angle 

[Rs(Z)] compared with the traditional single-value pyranometer responsivity at 45° solar zenith angle 

[Rs(45)]. 

Using data from 23 measurement stations in the Southern Great Plains (developed for the 

Atmospheric Radiation Measurement [ARM] Program), we quantified the effects of applying a 

pyranometer responsivity function [Rs(Z)] to measurements taken between June 2003 and May 2004. 

We considered the effects of this technique on the corrected irradiance measurements (e.g., Wm-2) 

and on the changes to the automatic data quality assessments required for the ARM data. 

The improvements are greater for clear sky conditions when the direct beam solar irradiance 

dominates the pyranometer response. Our results suggest Rs(45) is adequate for cloudy sky 

conditions. The degree of data quality improvements varies with measurement station and the 

associated pyranometer in use at the time. 
v

Table of Contents 

Acknowledgments.................................................................................................................................iii 

Executive Summary .............................................................................................................................. iv 

Table of Contents................................................................................................................................... v 

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

Background ............................................................................................................................................ 2 

Field Instruments................................................................................................................................ 2 

Reference Radiometer Calibration ..................................................................................................... 3 

Calibration of Field Deployed Radiometers....................................................................................... 4 

Error Sources...................................................................................................................................... 4 

Data Quality Assessment ................................................................................................................... 6 

Flag Categories................................................................................................................................... 8 

Procedure................................................................................................................................................ 9 

Extra Steps for Data that Use Rs as a Function of Zenith Angle ..................................................... 11 

Results and Discussion......................................................................................................................... 12 

Conclusion............................................................................................................................................ 18 

References............................................................................................................................................ 18 
Introduction 

The Atmospheric Radiation Measurement Program (ARM) deploys about 100 pyranometers as part 

of a 23-station network in the Southern Great Plains (SGP) to study climate change. The study of 

climate change requires radiation measurements with an uncertainty below 2%. Thus, there has been 

a sustained effort to reduce this uncertainty. 

The outputs of unshaded global pyranometers depend on the incident angle of the direct beam 

component of the radiation being measured. Figure 1 shows a typical scatter plot for the calibration of 

The Eppley Laboratory, Inc. model Precision Spectral Pyranometers (PSPs) with Rs as a function of 

solar zenith angle. 

28403F3

7

7.5

8

8.5

25 30 35 40 45 50 55 60 65 70 75 80 85 90

Solar zenith angle

Responsivity (uV/(W/m2

) Figure 1. Component summation calibration data for PSP serial number 28403F3.

The most widespread method of making global solar radiation measurements is to use a pyranometer 

deployed with a constant Rs, namely Rs(45). Depending on the individual instrument, season, and 

time of day, errors introduced by using this single Rs method can be 5%–10%. 

A new method addresses the error from the use of Rs(45) by using a 49-order polynomial fit to the 

calibration Rs curve as a function of zenith angle for global pyranometers [1]. Two separate functions 

are associated with each pyranometer, one for the morning and one for the afternoon. This method is 

applied only to the readings of the global pyranometer. The functions are of the form: 

1
 Rs (Z) =∑ a =

n

i 0

i cosi

Zi (1)

Where 

Rs (Z) = Rs function of a pyranometer 

 N = number of data points used to solve the (n + 1)

th order equation 

ai = the i

th coefficient 

Zi = the i

th solar zenith angle 

Broadband Outdoor Radiometer Calibration (BORCAL) is the process used by ARM for calibration 

of the pyranometers it uses in the field. The BORCAL calibration report includes the Rs at each 2°

solar zenith angle (i.e. at Z = 0°, 2°, 4°, ..., 90°). The (n + 1) zenith angles and their corresponding 

Rs’s are substituted in Equation 2: 

 

 (2) 

The coefficients are then calculated with a series of matrix operations and manipulations as described 

in [1]. 

This new method is a major improvement over the Rs(45) approach for measuring clear sky data. 

Field conditions, however, are substantially different from the selected clear-sky controlled 

calibration conditions. 

The purpose of this report is to quantify the effectiveness of this method under field conditions. For 

this case study, data collected for all sky and ambient conditions for the entire Southern Great Plains 

(SGP) network from June 2003 to May 2004 were analyzed. An emphasis was placed on the three 

stations at the Central Facility and daytime data in which the solar zenith angle was less than 80°. 

Background 

Field Instruments 

The short wave radiometers deployed at SGP as part of the Solar and Infrared Radiation Station 

(SIRS) instrumentation are: 

2
3

• Eppley model Normal Incidence Pyrheliometers (NIPs), which measure direct normal solar 

irradiance. Direct radiation is defined as the radiation of the solar beam only as measured by a 

surface normal to the solar beam. 

• Eppley model 8-48 pyranometers, which measure diffuse horizontal solar irradiance. Diffuse 

radiation is defined as the sky-only radiation on a surface parallel to the horizon. 

• Eppley model Precision Spectral Pyranometers (PSPs), which measure global parameters. Global 

radiation is defined as the sky only plus the solar disk radiation on a surface parallel to the 

horizon. 

All three instruments use a thermopile detector. A more thorough description of how the instruments 

work is available on the ARM Web site at www.arm.gov/instruments. 

Reference Radiometer Calibration 

Pyrheliometers: Electrically self-calibrating Absolute Cavity Radiometers (ACRs) are used to 

calibrate the field NIPs are traceable to the World Radiometric Reference (WRR) developed and 

maintained by the World Radiation Center in Davos, Switzerland. The WRR is the only 

internationally recognized measurement reference for solar irradiance (Fröhlich, 1977; Fröhlich, 

1991, and Fröhlich et al., 1995). 

Pyranometers: There is no world standard for calibrating reference pyranometers. In the absence of a 

reference pyranometer, NREL uses commercial pyranometers with minimal zero offset 

characteristics to calibrate reference diffuse pyranometers. The reference pyranometer for measuring 

diffuse radiation is calibrated with a modified ASTM shade/unshade method (ASTM E913) 

developed at NREL (Reda et al. 2003). The shade/unshade method—modified or otherwise—

operates on the basis of the following equation: 

 Rs = (U-S)/ B cos Z (3) 

Where 

 Rs = responsivity [μV/(W/m^2)] 

 U = output voltage of unshaded pyranometer [μV] 

 S = output voltage of shaded pyranometer [μV] 

 B = direct beam radiation [W/m^2] 

 Z = solar zenith angle 

U and S are measured simultaneously with this method, which, of course, is impossible. NREL’s 

method, however, corrects for this necessary evil by using a continuously shaded control instrument 

to reference to the test instrument. This modification allows the engineer to calculate what the test 

instrument’s shade value would have been even as the unshaded irradiance is measured. The shaded 

measurement is achieved by using a simple ratio between the output voltages of the test and control 

instruments: 

 R = Stest/ Scontrol (4) 

Where 

 Stest = output voltage of shaded test instrument 

 Scontrol = output voltage of shaded control instrument 
4

The responsivity of reference diffuse pyranometers is determined from the shade calibration data 

taken at a 45° solar zenith angle. To account for responsivity variations caused by the relative solar 

azimuth angle, the calibration is performed at six pyranometer angles with respect to the sun: 0°, 60°, 

120°, 180°, 240°, and 300° azimuth angles. The resulting averaged responsivity at the 45° solar 

zenith is a good approximation for the average radiance of a diffuse pyranometer. That is, the 

pyranometer will respond in balance to the local horizon brightening caused by multiple scattering 

effects and circumsolar brightening near the solar disk due to forward scattering by the atmosphere. 

The 45° responsivity also accounts for the annual time-weighted average of solar zenith angles for 

mid-latitude measurement stations. 

Calibration of Field Deployed Radiometers 

The pyranometers deployed at SGP were calibrated with the ASTM standard G167 summation 

calibration method. Both the PSP and 8-48 model pyranometer were unshaded during calibration and 

compared to reference direct and diffuse radiation measurements. The global, direct, and diffuse 

radiation can be referenced to each other by using this equation: 

 Global = Diffuse + Direct [cos Z] (5) 

Where 

 Z = solar zenith angle 

This equation is at the core of calibration and data quality control for downwelling shortwave 

radiometer. The deployed pyranometers were calibrated under clear sky conditions during the 

summer when the minimum solar zenith angle is less than 45°. 

As mentioned earlier, the field-deployed NIPs are calibrated by comparing them directly to a WRRtraceable ACR. 

Error Sources 

Besides the cosine error response for a pyranometer, a multitude of areas throughout the data 

collection process introduce uncertainty. Reference 2 explains and quantifies the cumulative 

uncertainty in calibration of field-deployed pyranometers. It was determined that there is a 1.84% 

uncertainty in the calibration of pyranometers and a 1.59% uncertainty in the calibration of the 

pyrheliometer. The uncertainty results are duplicated in Table 1 for pyranometers and Table 2 for 

pyrheliometers. 
5

Table 1. Uncertainties in Individual Rs for PSP Summation Calibration.

TYPE A Statistical UNC (%) STD UNC (%) 

WRR Transfer 0.200 0.200 

Cos(z) (2° Z bin) 0.010 0.005 

Dif (2.5% D=>0.25% Ref.) 0.125 0.063 

Temperature (2° Z bin) 0.100 0.050 

Data Logger Precision 0.005 0.0025 

ACR (wind, T) 0.025 0.013 

Temp Chg (10°C) 0.250 0.125 

Diff Offset B&W 0.125 0.063 

UUT IR OFFSET 0.250 0.125 

EMI/Thermal EMF 0.010 0.005 

Subtotal 0.455 0.286 

TYPE B 

Logger Bias (9 uV/10 mv) 0.090 0.090 

WRR Std U95 0.300 0.300 

Cos(z); Z< 89o; 2o bin 0.010 0.005 

Temperature (2° Z bin) 0.100 0.050 

ACR Bias (M, wind, T) 0.025 0.013 

Temp B (event to event) 10°C 0.250 0.125 

Diff Offset B&W 0.125 0.063 

UUT IR OFFSET 0.625 0.625 

Spectral Error 0.500 0.250 

EMI/Thermal EMF 0.010 0.005 

Subtotal 0.910 0.872 

TOTAL 1.017 0.918

Effective Degree of Freedom >100 

Coverage Factor (k) 2 

Expanded Uncertainty 1.84%
6

Table 2. Uncertainties for 95% Confidence Interval for Individual Rs for Pyrhleiometer Calibration. 

Statistical UNC (%) STD UNC (%) 

TYPE A 

WRR Transfer 0.200 0.200

Temp Response UUT 0.500 0.050

Data Logger Precision 0.005 0.0025

Linearity (empirical) 0.200 0.100

ACR (wind, T) 0.025 0.013

Tracking Variations 0.250 0.125

Spectral (window) 0.500 0.500

EMI/Thermal EMF 0.010 0.005

Subtotal 0.802 0.615

TYPE B 

Logger Bias (9 uV/10 mv) 0.090 0.090

WRR Std U95 0.300 0.300

Temp Response UUT 0.500 0.250

ACR Bias (M, wind, T) 0.025 0.013

Temp B (event to event) 10° 0.250 0.125

Spectral Error 0.500 0.500

Tracking Bias 0.250 0.0125

EMI/Thermal EMF 0.010 0.005 

Subtotal 0.851 0.504

TOTAL 1.169 0.918 

Effective Degree of Freedom >100 

Coverage Factor (k) 2 

Confidence Interval 95% 

Expanded Uncertainty 1.59% 

In addition to uncertainty error introduced in the calibration, field conditions such as aging of the 

instrument, site maintenance issues, and variable ambient conditions introduce further uncertainty. 

Data Quality Assessment 

SERI QC is used to assess the quality of the solar ARM data (NREL, 1993). Most SERI QC test 

failures in the SGP SIRS data are three-component failures. The three-component test is essentially a 

normalized form of Equation 5: 

Kn = Kt + Kd (6) 

Where 

Kn = In / Io = direct beam transmittance 

Kt = It / (Io cos Z) = effective global horizontal transmittance 

Kd = Id / (Io cos Z) = effective diffuse horizontal transmittance 

 Io = extraterrestrial direct normal radiation 

 In = direct normal radiation at the Earth’s surface 

 It = total global horizontal radiation at the Earth’s surface 

 Id = diffuse horizontal radiation at the Earth’s surface 

 Z = solar zenith angle 
7

Operating in k-space is advantageous because it allows the engineer to see irradiance values as a 

percentage of maximum possible. Each global k-space value is compared with the summed direct and 

diffuse k-space values. Any discrepancies to Equation 6 are quantified and, based on the magnitude 

of the inequality, flags are assigned to each parameter. Table 3 presents the complete table for the 

SERI QC flagging system. The SERI QC suite includes one- and two-component tests in addition to 

the three-component test. However, “Because three-component tests are more reliable, threecomponent flags are retained regardless of previous one- or two-component results” (SERI QC 

Manual). A graphical description of the one- and two-component tests is provided in Figure 2. The 

criteria for both tests are set empirically. Kn, Kt, and Kd are merely normalized values of diffuse, 

global, and direct radiation measurements normalized to the concurrent extraterrestrial solar 

irradiance. 

Table 3. Flagging Convention for SERI QC.

Flag Description 

00 Untested (raw data) 

01 Passed one-component test; data fall within min-max limits of Kt, Kn, or Kd

02 Passed two-component test; data fall within 0.03 of the Gompertz boundaries 

03 Passed three-component test; data come within ± 0.03 of satisfying 

 Kt=Kn+Kd

04 Passed visual inspection; not used by SERI_QC 

05 Failed visual inspection; not used by SERI_QC 

06 Value estimated; passes all pertinent SERI_QC test 

07 Failed one-component test; lower than allowed minimum 

08 Failed one-component test; higher than allowed maximum 

09 Passed three-component test but failed two-component test by > 0.05 

10-93 - Failed two- or three-component tests in one of four ways. 

- To determine the test failed and the manner of failure (high or low), 

 examine the remainder of the calculation (flag + 2)/4. 

REM Failure 

 0 Parameter too low by three-component test (Kt=Kn+Kd) 

 1 Parameter too high by three-component test (Kt=Kn+Kd) 

 2 Parameter too low by two-component test (Gompertz boundaries) 

 3 Parameter too high by two-component test (Gompertz boundaries) 

 The magnitude of the test failure (distance in K-units) is determined from: 

 d = (INT (flag +2)/4)/100. 

94-97 Data fall into a physically impossible region where Kn > Kt by K-space distances of 

 0.05 to 0.10 (94), 0.10 to 0.15 (95), 0.15 to 0.20 (96) amd ± 0.20 (97). 

98 Not used 

99 Missing data 

Upon completion of automatic flagging, manual analysis begins. 
Figure 2. SERI QC data boundaries for two-element quality assessment. 

 

The horizontal and vertical blue lines in Figure 2 represent the limits for the one component test. Any 

data exceeding the maximum set value of either Kt or Kn will be flagged as unacceptable. The onecomponent test is the only test conducted at solar zenith angles of greater than 80°. Note that the red, 

blue, and green color scheme in Figure 2 has no relation to the ARM assigned colors for good, 

suspect, and unacceptable data. 

The polynomial curves are called Gompertz boundaries and further restrict the acceptable values for 

the global and direct components. All data must fall between the two curves to be acceptable. This is 

the 2-component test. 

It is important to remember that the three-component test is preponderant among the three tests. It is 

tighter than, and supersedes the one- and two-component tests. 

Flag Categories 

For the purposes of ARM data quality assessment, the SERI QC flags are divided into four different 

categories, as shown in Table 4. 

Table 4. Table of SERI QC Flags Categorized by ARM Color.

Color SERI QC Flags Description of Data

 

Green 1-6, 10-20 Good 

Yellow 21-41 Suspect 

Red 7, 8, 42-98 Unacceptable 

Black 99 Missing 

8
Procedure 

The ARM SGP SIRS data are reformatted, stored, and transferred many times between acquisition at 

the instrument to quality assessment at NREL. Figure 3 presents the flow of SGP SIRS data from 

collection to quality assessment. 

Figure 3. Electronic flow of SGP data. 

9
10

The output of the radiometers, referred to as raw data, is a milliVolt (mV) thermopile signal. This 

voltage is the input into the data logger where the constant calibration factor (Cf = 1/Rs) at 45° is 

applied to the output of the global pyranomter. The data are now in engineering units (W/m^2). 

SGP’s central facility downloads these data hourly from the data loggers at all the extended facilities. 

Pacific Northwest National Laboratory then ingests these data, flags them with SERI QC, converts 

them to NetCDF (Network Common Data Form), and stores them at the ARM archive. Because the 

ARM program collects and stores a huge amount of data, the NetCDF format was developed to give 

ARM a self-documenting and space-effective mode of storage. The ARM archive is the public access 

server for all ARM data. NREL has standing orders with the ARM archive for weekly delivery of the 

most recent available SGP/SIRS data. The weekly transfer of NetCDF data from a designated archive 

delivery area to a UNIX computer at NREL has been preprogrammed and is accomplished 

automatically. 

After an arbitrary time interval, the data—still in NetCDF—are manually sent via file transfer 

protocol (ftp) from the UNIX computer to a Windows PC at NREL for further processing. 

Once the data are on the PC, they are reformatted from NetCDF to ASCII by using an application, 

ARM NetCDF Data Extract (ANDX), developed specifically for ARM. ANDX converts the NetCDF 

file to an ASCII text file. ANDX also gives the user the ability to accept or reject any parameter he or 

she chooses from the data file being processed. 

The ARM archive offers various levels of processed data files. For example, one could order raw data 

files or highly processed data that are referred to as value added products (VAPs). NREL accesses the 

“b1” level NetCDF files stored at the ARM archive: the b1 indicates that the parameters are in 

engineering units and the data have been quality checked. They are one-minute data streams and are 

not VAPs. NREL ignores the flags and uses ANDX to extract only the six radiometer measurements 

from the NetCDF file, for which ANDX provides the capability. 

“In- house” software, called AftANDX, is then used after ANDX to reformat the date-time stamp into 

the Data Quality Management System (DQMS) compatible import format, comma separated variable 

(CSV) format, and to insert the individual site ID’s into the files. DQMS is software developed 

specifically for managing solar energy data. The data, now in comma separated variable (CSV) 

format with the appropriate site and date-time stamp are ready to be imported into DQMS. 

At this point two separate data sets are created for this study. The first data set will have global 

irradiance determined from the Rs(45). This is the data set that has been traditionally stored, quality 

assessed, and disseminated. The second data set will account for the global pyranomer’s Rs change 

with respect to the solar zenith angle (Rs(Z)). The description of the extra steps needed for applying 

the variable Rs to the global pyranometer readings follow. 
Extra Steps for Data that Use Rs as a Function of Zenith Angle 

Before these data are ready for import into DQMS, the raw data readings in millivolts must first be 

“backed out” with the Rs(45) calibration factor. The Rs(Z) function can then be applied to the data. 

All of this is accomplished with the Perl calculator, a Perl script program that can convert large 

amounts of data at a time by systematically backing out the constant Rs readings and applying the Rs 

function to the raw data. The inputs are the initial data file, the serial number of the global 

pyranometer being converted, the 45° Rs that applied to the input file, and the 49 coefficients for the 

Rs function. The output is a data file converted from the use of the constant Rs 45° to a file that 

applies the Rs function. The site ID is then changed to differentiate this dataset with that of the 

constant Rs. This is necessary to allow both datasets in DQMS simultaneously. 

Now both datasets can be imported into DQMS, which merely involves properly configuring the 

DQMS import drivers. The record definitions must also be modified in accordance with the proper ID 

stamps to accommodate the multiple datasets for each measurement site. 

Once the import is completed, automated testing by DQMS per the SERI QC test criteria is 

performed. This operation is also a trivial matter of configuration of test definitions and test drivers. 

According to Table 3, three flags are assigned to each one-minute data record, one for each 

downwelling shortwave SIRS parameter: direct, diffuse, and global. Figure 4 presents a typical view 

of a DataView plot, with time-series plots of upwelling longwave, downwelling longwave, and 

upwelling shortwave included in the image, in addition to the ARM data quality flag colors under the 

time axis for each of the three downwelling shortwave parameters. 

Figure 4. Typical DataView image with corresponding data in tabular form.

11
12

Results and Discussion 

Table 5 lists the performance of the entire SGP network for the time period beginning June 1, 2003 

and ending May 31, 2004, including nighttime data and daytime data that were recorded when the 

solar zenith angle was greater than 80°, where the three-component test is not applied. The first four 

columns of Table 5 show results of using Rs(45) for the entire test period. The next four columns 

show results of using Rs(Z) for the entire test period, and the last four columns show the difference 

between the two methods. 

The most notable change is the major reduction in the amount of the yellow, or questionable data. 

This is because the vast majority of yellow data are flagged because of three component failures at 

zenith angles approaching 80° (e.g., Equation 3 is not satisfied by the independent measurements), 

which is the area where the Rs function works best. 

There is little change in the number of red data, mostly because many nighttime empirical limit 

failures are caused by the known zero-offset characteristics of the Model PSP. Naturally, the data that 

are below empirical limits will have exceptionally low values and occur under cloudy sky conditions, 

where application of the Rs function is insignificant. Most daytime red data are below empirical 

limits as well. For daytime data to be below empirical limits Equation 8 must be satisfied.

DS < .05 ETR Cos (Z) (8) 

Where 

 ETR = I0 * ERV 

 I0 = solar constant = 1367 Wm-2

 ERV = (ro/ r)2 

 ro = mean sun-Earth distance 

 r = instantaneous sun-Earth distance 

Extraterrestrial radiation (ETR) is the amount of global radiation at the top of the atmosphere. 

The insignificance of the Rs function under cloudy skies is illustrated in Table 6. These data were 

taken from the three stations at the Central Facility: C1, E13, and BRS. The data constitute two 

consecutive hours from each site for each month during the test period. In other words, there were 72 

hours of data in this set before the data below empirical limits were removed. Each of the three sites 

contributed 24 hours; 2 hours for each month of the test period. Both Rs(45) and Rs(Z) data had to be 

flagged as below empirical limits for that data point to be discarded. All the data in this set were 

measured at least 2.5 hours after sunrise and 2.5 hours before sunset. Also, the direct measurement 

had to be less than 50 Wm-2 for the data to be considered cloudy and thus eligible for inclusion in this 

dataset. The first column categorizes all the data according to arbitrarily selected global irradiance 

values. The minimum and maximum global measurements in the data set were 41 and 487 Wm-2 and 

this is reflected in the first column of Table 6. The next three columns are averaged values. For 

example, the 77.1 Wm-2 is the average irradiance of the 1069 data points in the 41–100 Wm-2 bin. 

The 0.21 Wm-2 is the average change in global irradiance using Rs(45) instead of Rs(Z). The -0.019 

is the corresponding average change in SERI QC flag value. The averages were computed by 

averaging both data set together. A negative value in this column represents an improvement because 

the flag will have been reduced to a lesser magnitude. 
Table 5. Performance of the SGP Network, June 1, 2003 to May 31, 2004. 

Station Rs(45) Rs(Z) Change

Green Yellow Red Missing Green Yellow Red Missing Green Yellow Re

BRS 83.65 5.95 9.28 1.13 88.13 1.84 8.90 1.13 4.48 -4.11 -0C1 95.48 1.82 0.85 1.86 97.09 0.20 0.85 1.86 1.62 -1.62 0E1 93.39 2.14 0.85 3.62 95.22 0.31 0.85 3.62 1.82 -1.83 0E2 96.12 1.22 1.52 1.14 96.87 0.50 1.49 1.14 0.75 -0.72 -0E3 95.16 1.38 1.17 2.29 96.39 0.16 1.16 2.30 1.23 -1.23 -0E4 95.37 2.60 0.92 1.11 97.70 0.26 0.92 1.11 2.33 -2.34 0E5 95.19 1.89 1.81 1.11 96.66 0.47 1.76 1.11 1.46 -1.42 -0E6 95.94 0.90 0.87 2.28 96.59 0.24 0.87 2.30 0.65 -0.66 0E7 92.34 2.51 1.54 3.60 94.48 0.44 1.47 3.61 2.14 -2.07 -0E8 96.70 1.33 0.61 1.35 97.85 0.20 0.59 1.35 1.15 -1.13 -0E9 94.89 2.11 1.34 1.66 96.69 0.34 1.29 1.68 1.80 -1.76 -0E10 90.16 2.45 1.12 6.27 90.71 1.79 1.22 6.28 0.55 -0.65 0E11 95.92 1.87 0.71 1.50 97.49 0.31 0.71 1.50 1.56 -1.56 0E12 95.87 1.52 1.48 1.13 96.82 0.58 1.48 1.12 0.95 -0.94 0E13 93.62 2.17 0.71 3.51 95.50 0.28 0.73 3.50 1.88 -1.89 0E15 91.06 5.06 0.92 2.96 95.66 0.45 0.87 2.96 4.60 -4.61 -0E16 86.95 3.10 0.65 9.30 89.57 0.52 0.61 9.30 2.62 -2.59 -0E18 91.73 2.10 0.85 5.32 93.64 0.29 0.76 5.32 1.90 -1.81 -0E19 91.17 4.65 1.14 3.03 95.05 0.91 1.01 3.04 3.88 -3.74 -0E20 91.62 3.03 1.03 4.33 94.28 0.48 0.90 4.34 2.66 -2.55 -0E21 81.41 2.75 2.43 13.40 82.07 1.88 2.63 13.42 0.66 -0.88 0E22 95.25 1.00 0.74 3.01 95.97 0.28 0.74 3.01 0.72 -0.72 0E24 92.09 1.86 0.78 5.27 93.54 0.33 0.84 5.29 1.46 -1.53 0E27 94.17 1.48 1.30 3.04 94.51 0.95 1.49 3.05 0.34 -0.53 0

13
Table 6. Cloudy Data from the Central Facility. 

 Averages 

DS Irradiance (W/m^2) Irradiance (W/m^2) Change in Irradiance (W/m^2) Change in Flag Data Points in Bin

41- 100 77.1 0.21 -0.019 1069 

100- 200 141.9 -0.13 0.004 2049 

200- 487 290.0 0.15 0.015 1032 

*All data that had a flag of 7 were deleted and are not included in this table. 

One can also see the inconsequential effect of applying the Rs function under cloudy skies in 

Figure 5, a DQMS plot for C1 on April 23, 2004. Only the pink Rs(Z) global data are visible 

because both the Rs(45) global and diffuse are covered by it. At the bottom of the display, 

the change in flags was virtually nil. E70_E_GlobalFlag represents the flags for the Rs(45) 

data and E70_D_GlobalFlag represents the Rs(Z) data. 

Figure 5. Typical overcast day at SGP . 

his usually stands in stark contrast compared to the application of the Rs function on a clear 

t 

d data 

T

day, such as Figure 6, which is April 27, 2004 at C1, four days after Figure 5. There is a large 

change in absolute terms in the middle of the day and substantial improvement in flags at 

high zenith angles in the evening. This is due to the nature of Equation (3), and the fact tha

flags of 20 or less are still considered green, in accordance with Table 4. In the particular 

case of Figure 6 in the middle of the day, while the Rs(45) global data were flagged with 

SERI QC flags within the magnitude allowed by the ARM Green category, they were 

nonetheless improved to better SERI QC flags with RS(Z). So the Rs function correcte

that was too high around noon and data that was too low later that same day. This scenario is 

the most common concerning clear-sky daytime data. 

14
Figure 6. Typical sunny day at SGP, with Rs(45) data shown in grey and Rs(Z) shown in pink. 

BRS, C1, and E13

15th Day, JUN 03 thru MAY 04

0

200

400

600

800

1000

1200

-40 -30 -20 -10 0 10 20 30 40

Change in Global Irradiance (W/m^2)

Global Irradiance (W/m^2)

Figure 7. Scatter plot for data from the 15th of each month during the test period. 

Figure 7 shows how large the change in global irradiance can be in absolute terms in going 

from Rs(45) to Rs(Z). These data are from the three central stations only. They are all 

15
daytime data where the zenith angle was less than 80° from the 15th of all months of the test 

period. The y-axis is the average of the Rs(45) and Rs(Z) global data and the x-axis is the 

change from Rs(45) to Rs(Z).

BRS, C1, and E13 

15th Day, JUN 03 thru MAY 04

0

200

400

600

800

1000

1200

1400

1600

-31-29-27-25-23-21-19-17-15-13-11

-9-7-5-3-1

13579

111315171921232628

[Rs(Z) Flag] - [Rs(45) Flag]

Figure 8. Histogram of occurrences of the change in SERI QC flags.

Figure 8 uses the same dataset as Figure 7. Figure 8, however, is a histogram of the change in 

SERI QC flags from a global measurement that uses Rs(45) to one that uses an Rs(Z). 

Because some 65% of the data saw no change in their flag after going to a reading with 

Rs(Z), including these data in Figure 8 would have detracted from the resolution of the 

graph. They were, therefore, not included. Ten outlying data points are not shown in Figure 8 

to preserve resolution. 

16
Table 7. Same Data as in Figure 8, Except with ‘Zero’ Occurrences and Outliers Shown 

Bin Frequency Bin Frequency

-31 7 0 15471 

-30 0 1 20 

-29 0 2 1 

-28 2 3 0 

-27 27 4 172 

-26 0 5 5 

-25 0 6 11 

-24 19 7 586 

-23 78 8 241 

-22 0 9 6 

-21 0 10 2 

-20 170 11 6 

-19 152 12 99 

-18 1 13 5 

-17 0 14 0 

-16 396 15 0 

-15 341 16 59 

-14 3 17 2 

-13 3 18 0 

-12 572 19 0 

-11 720 20 19 

-10 5 21 0 

-9 0 22 0 

-8 1283 23 0 

-7 1435 24 10 

-6 3 26 0 

-5 2 27 0 

-4 1588 28 5 

-3 12 More 10 

-2 1 

-1 13 

The data in their entirety, however, can be seen in Table 7. Notice that there are over 15,000 

data points whose flags remained the same. Also since a smaller flag is an improvement, the 

negative change means the Rs function improved the data quality just as in Table 6. 

17
18

Conclusion 

Applying the Rs (Z) function to the global irradiance data reduces the measurement 

uncertainties due to variations of pyranometer angular response. In particular, the Rs (Z) 

function improves unshaded pyranometer measurement accuracies under clear sky conditions 

when compared with coincident observations of direct normal and diffuse horizontal 

irradiances. Overall, however, most daytime data quality flags remained unchanged for solar 

zenith angles much less than 80o. 

The greatest improvement appears for “questionable” (yellow data flag) data because these 

measurements typically occur during three-component consistency tests near 80o solar zenith 

angle when the Rs(45) would produce the largest discrepancies from ideal pyranometer 

angular response. 

Relatively little change was observed in the “failed” (red) data. No site saw an improvement 

greater than 0.37% or a degradation of less than 0.2%. The improvement could be partially 

attributed to three component failures of severe magnitude, flags of 11% error or more. The 

case where some sites actually saw their amount of red data increase—namely E21, E24, and 

E27—is harder to explain. It could be due to the different time-response characteristics of the 

PSP, NIP, and 8-48 radiometers and the resulting measurements under rapidly changing 

cloud conditions. Also, the Rs function does not consider ambient parameters such as 

longwave flux and humidity, which determine pyranometer thermal offsets . In any case, the 

number of red data fluctuations between Rs(45) and Rs(Z) analyses are minor. 

There are some small but notable changes in the black (missing) data. For the Rs(Z) dataset, 

some data were removed that were not removed from the Rs(45) dataset. This was done 

during instrument change outs to ensure that the correct Rs function was being applied to the 

instruments that took the reading. These omissions were very small. 

The Rs function had an inconsequential effect on cloudy sky data; when these data were not 

flagged as below empirical limits—which can be frequent—they were generally good 

(green), both with the Rs(Z) and the Rs(45). 

Each pyranometer behaves differently, so associated improvement with the Rs function 

depends heavily on the measurement characteristics of a particular instrument.

References 

1. Reda, I. (1998). Improving the Accuracy of Using Pyranometers to Measure the Clear 

Sky Global Solar Irradiance. Golden, CO: National Renewable Energy Laboratory. 24 

pp. Report Number: NREL/TP-560-24833. 

2. Myers, D.; Andres, A.; Reda, I.; Wilcox, S. “Optical Radiation Measurements for 

Photovoltaic Applications: Instrumentation Uncertainty and Performance.” Presented at 

the SPIE International Symposium on Optical Science & Technology, August 2–6, 2004, 

Denver, CO. 
19

3. Wilcox, S.; Myers, D.; Al-Abbadi, N.; Mahfoodh, M. B. (2001). “Improving Global Solar 

Radiation Measurements Using Zenith Angle Dependent Calibration Factors.” CampbellHowe, R., (ed.) Proceedings of Forum 2001 Solar Energy: The Power to Choose; 

Including Proceedings of ASES Annual Conference and Proceedings of the 26th National 

Passive Solar Conference, April 21–25, 2001, Washington, DC. Boulder, CO: American 

Solar Energy Society and Washington, DC: American Institute of Architects Committee 

on the Environment, pp. 267–271. 

4. The Eppley Laboratory Inc. Web site. www.eppleylab.com. Accessed June 24, 2004. 

5. Incpera, F.P.; DeWitt, D.P. (2002). Fundamentals of Heat and Mass Transfer. New York: 

J. Wiley. 5th ed. 981 pp. 

6. Reda, I.; Stoffel, T.; Myers, D. (2003). “Method to Calibrate a Solar Pyranometer for 

Measuring Reference Diffuse Irradiance.” Solar Energy vol. 74, no. 2, pp. 103–112. 

7. SIRS Instrument Logs. 

http://198.124.96.210/Instrument_logs/SIRSilog/sirs_ilog_list.htm 

June 1, 2004–August 17, 2004. Instrument change out dates. 

8. Maxwell, E.; Wilcox, S.; Rymes, M. (1993). “Users Manual for SERI QC Software.” 

NREL TP 463- 5608. 

9. Fröhlich, C., 1977, 'World Radiometric Reference', in: WMO/CIMO Final Report, WMO 

No. 490, 97-100. (PMOD/WRC intern: 545a) 

10. Fröhlich, C., 1991, History of solar radiometry and the World Radiation Reference, 

Metrologia 28, 111-115. (PMOD/WRC intern: 650) 

11. Fröhlich, C., Philipona, R., Romero, J., and Wehrli, C., 1995, Radiometry at the 

Physikalisch-Meteorologisches Observatorium Davos and the World Radiation Center, 

Optical Engineering 34, 2757-2766. (PMOD/WRC intern: 674) 

12. NREL, 1993. Users manual for SERI QC software: assessing the quality of solar 

radiation data., NREL/TP-463-5608. 191 pp. National Renewable Energy Laboratory, 

December. (Available from the Renewable Resource Data Center, 

http://rredc.nrel.gov/solar/#publications) 
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Case study that examines the application of a pyranometer responsivity function to data from 23 measurement 

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