Conference Paper

NREL/CP-3B0-46411

August 2009

Testing a Model of IR

Radiative Losses 

Preprint

Frank Vignola

University of Oregon

Charles N. Long

Pacific Northwest National Laboratory

Ibrahim Reda

National Renewable Energy Laboratory

Presented at Society of Photo-Optical Instrumentation Engineers 

(SPIE) 2009 Conference

San Diego, California

August 2-6, 2009
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Testing a model of IR radiative losses

Frank Vignola 

University of Oregon 

Department of Physics 

Eugene, OR 97403 

Charles N. Long 

Pacific Northwest National Laboratory

Ibrahim Reda 

National Renewable Energy Laboratory 

ABSTRACT

Thermopile pyranometers exhibit IR radiative losses that affect global and diffuse shortwave measurements made with 

first class thermopile based instruments. Pyrgeometers can be used to measure the sky temperature and are used to

calculate the pyranometer’s IR radiative losses. Few solar monitoring sites are equipped with pyrgeometers necessary 

to account for the IR radiative losses associated with the pyranometers. High quality data from the Solar Radiation 

Research Laboratory (SRRL) at the National Renewable Energy Laboratory are used to test and further develop a 

model for the IR radiative losses without the use of pyrgeometer data. The various methods for obtaining IR radiative 

loss values are compared and contrasted using the SRRL data. A simple scaling method is proposed and tested to 

adjust the non-pyrgeometer based correlation models to sites with different sky temperature characteristics. 

Keywords: Pyranometer, pyrgeometer, irradiance, IR, modeling, global, PSP

1. INTRODUCTION

Thermopile pyranometers exhibit IR radiative losses that affect global and diffuse shortwave measurements. 

Pyrgeometers are used to measure the downward long wavelength radiation (sky temperature) and hence can be used 

to estimate the pyranometer IR radiative losses1, 2. The IR radiative losses reduce the measured short wavelength 

irradiance and create a systematic error in the measurements. Adjusting the pyranometer measurements for this IR 

radiative loss creates more precise global and diffuse values that are very useful for a wide variety of objectives from 

studying climate characteristics to estimating the performance of photovoltaic systems. Systematic errors affect 

correlation models as the systematic errors get integrated into the correlation results. Diffuse measurements are 

especially affected as the IR radiative losses can be ten percent or more of the diffuse values on clear days.

Unfortunately the majority of sites that measure global and diffuse irradiance values do not have co-located 

pygeometer instruments. Therefore to remove the systematic errors from the sites without pyrgeometer data, it is 

necessary to develop a different method independent of the pyrgeometer measurements to correct for the systematic 

affect of IR radiative losses. 

In previous papers,

3, 4 a prototype model based solely on measured meteorological and short wavelength irradiance 

data was created to approximate the IR radiative losses for Eugene, Oregon. While the IR loss correction model can be 

used to estimate the IR radiative losses for Eppley PSP pyranometers in Eugene, this “Eugene” correlation model was 

not expected to work well in areas with completely different sky temperature characteristics. An examination of the IR 

1
radiative losses in Golden, Colorado, confirms this assumption, and it was necessary to develop a method to adjust the 

Eugene IR radiative loss model to the conditions in Golden, Colorado. While comparing the Eugene correlation model

with IR radiative measurement and other models, it was deemed useful to create an improved correlation-based model. 

Existing IR radiative loss models based on pyrgeometer measurements are also examined. 

In this article, the IR radiative losses are studied for atmospheric conditions experienced in Golden, Colorado. The 

National Renewable Energy Laboratory (NREL) operates a very high quality solar monitoring station at the Solar 

Radiation Research Laboratory (SRRL). Besides the pyrgeometer based models and the Eugene correlation model, the 

data from SRRL5 are used to develop an alternate non-pyrgeometer correlation model for the IR radiative losses at 

SRRL. All the IR radiative loss models are compared and contrasted. Sky temperatures in Golden are typically much 

colder than those in Eugene, and the Golden IR radiative losses are approximately three times larger than those values 

measured in Eugene. Just how well the model derived in Eugene works in Golden is examined and a methodology is 

developed to adjust the Eugene model to the Golden, CO climate. 

This article is organized as follows. The irradiance data from the Solar Radiation Research Laboratory at the National 

Renewable Energy Laboratory are briefly discussed. Next IR radiative loss models using pyrgeometer data are 

described. These models will be used in comparison with the Eugene and the Golden correlation-based IR radiative 

loss models. The method to adjust the Eugene model is then described. All the IR radiative loss models are then 

compared and contrasted. A summary of the work is presented along with suggestions for future directions.

2. THE SRRL DATA

NREL runs a very high quality solar radiation and meteorological monitoring station at SRRL in Golden, Colorado.

SRRL is the home of the largest collection of radiometers in continuous operation, and its 75 instruments contribute 

the surface meteorological measurements to the Baseline Measurement System. All data collected by SRRL since 

1981 are available to the public. The instruments are maintained on a daily basis, and calibration and maintenance 

records help ensure the quality of the data. A wide variety of solar monitoring instruments are utilized along with a 

comprehensive set of meteorological measurements. The one-minute data from this site can be downloaded from the 

SRRL website5

. 

The data used for this study are the raw global data from an Eppley Precision Spectral Pyranometer (PSP), the direct 

normal irradiance from the Eppley Normal Incident Pyrheliometer (NIP), the pyrgeometer data from an Eppley 

pyrgeometer along with the case and dome temperatures, and a series of meteorological measurements for ambient 

temperature, wind speed, relative humidity, and atmospheric pressure. The absolute accuracy of the solar irradiance 

measurements is the larger of 15 W/m2 or 2-3%5

. 

At SRRL, the PSP and the pyrgeometer are mounted on ventilators. In addition, the Eppley pyrgeometer is on a tracker 

that shades the dome from direct sunlight. This provides more accurate pyrgeometer readings.

3. CALCULATING THE IR RADIATIVE LOSSES

Using the pyrgeometer and meteorological data at the site, the IR radiative losses are calculated using the full 

Younkin, Long radiative correction model1

. This model uses the pyrgeometer measurements along with the case and 

dome temperatures to calculate the sky temperature. This information is combined with relative humidity 

measurements to calculate the IR radiative loss expected from a pyranometer. This model assumes that the IR 

responsivities of various Eppley PSP pyranometers are approximately the same. Also the broadband and the IR 

responsivities of a given PSP are proportional to one another. One part of the full correction procedure uses the 

measurements from the pyrgeometer detector. This part is called the detector only correction. This does not include 

other factors such as relative humidity that gives the full Younkin, Long methodology a broader range of IR radiative 

losses and reflect more of what is really seen by the first class thermopile pyranometers. These two methods will be 

referred to as the full correction and the detector only correction methods in this article.

2
In the SRRL dataset, the IR radiative losses are estimated by correcting the PSP measurements in a method similar to 

the detector only method. NREL uses the Net-IR responsivity of the PSP pyranometer to correct for the IR radiative 

losses. The Net-IR responsivity is derived by calibrating the PSP with a blackbody to simulate the ambient and sky 

temperature2

. The net downward IR flux is calculated by subtracting the pyrgeometer detector temperature 

measurements (σTdt

4

) from the pyrgeometer-measured downward IR flux. This radiative flux is then divided by the 

broadband responsivity of the instrument and multiplied by the instrument’s Net-IR responsivity. This SRRL method 

and the detector only method are similar to the SRRL method specifically designed for the pyranometer under study. 

This method will be referred to as the modified detector model.

4. NIGHTTIME IR RADIATIVE LOSSES

 

Nighttime is when the IR radiative losses from a pyranometer can be measured best. At night, there is no incident solar 

irradiance to affect the measurements. There are be small errors in measurement from the data logger and/or other 

external influences, such as rectification of radio waves, but these are small (1 W/m2 or less) in comparison to the IR 

radiative losses.

A series of comparisons of different IR Radiative Loss models with the PSP night values are made. In addition, a 

nighttime correlation using only meteorological variables developed for the Golden, Colorado data is studied. The 

nighttime correlation developed for the Eugene data is also compared with nighttime PSP measured values. The 

daytime comparisons will be made in the next section.

A sample of the nighttime irradiance values plotted in Fig. 1 shows the full correction and the detector only correction 

against the PSP nighttime readings. As expected, the full correction fits better than the detector only correction. The 

SRRL method, called the modified detector only model, is shown in Fig. 2. The mean value of the modified detector 

model is closer to the values obtained by the PSP measurements.

To see how well the PSP offset can be modeled, a nighttime correlation was created for the SRRL data. The 

correlation parameters for the coefficients found to be significant are given in Table 1. Also given are the standard

deviations of the uncertainty in each parameter. The table includes the average value of the parameter and the typical 

value of the parameter. Adding all the typical values together yields the typical IR radiative value of -10 W/m2

. The 

overall standard error for the nighttime correlation is ±1.1 W/m2

. 

Fig. 1. Comparison of the full correction and detector only 

IR radiative loss models during the night. The full 

correction model significantly improves on the 

estimated IR radiative losses when they are greatest 

(between -10 and -15 W/m2

). 

Fig. 2. Comparison between the full correction and the modificed 

detector correction for the IR radiative losses during the 

night. By measuring the pyranometer’s IR responsivity, an 

improvement in the estimated IR radiative loss can be 

achieved. While the difference at higher IR radiative loss 

values is smaller, it still exists. In addition there is a shift of 

many points to low estimated IR radiative loss values. The 

reason for this shift should be investigated.

3
Fig. 3. Comparison of the Golden nighttime correlation model 

and the Eugene nighttime correlation model with the 

measured PSP nighttime readings. The Eugene night 

correlation model significantly underestimates the PSP IR 

radiative reading, never getting smaller than about -4 

W/m2

. 

Fig. 4. Comparison of the adjusted Eugene nighttime correlation 

model and the Golden nighttime correlation model with the 

measured PSP nighttime readings. The Eugene nighttime 

correlation values were multiplied by 2.9, the ratio of the 

average PSP nighttime measurements and the average 

Eugene nighttime correlation results.

Note that the correlation did not use data from periods when the data was missing or marked bad. Also, when the 

change of variable with time was derived, periods that did not have previous data values were not used in the 

correlation data set. Time periods very near sunrise and sunset were not used as some sky brightening might affect the 

measurements.

 Table 1: Correlation parameters to the nighttime IR radiative loss fit

Parameter Coefficient % Standard deviation Average Typical Value

Intercept -9.2650608 -7.89% na -9.3

Ambient Temperature -0.0608274 -0.93% 282 K -17.2

Delta Temp. -7.4522427 1.09% 0 0

Relative Humidity 0.0786042 1.46% 50 % 3.0

RH2 -0.0003823 -2.57%

Wind Speed -0.6346762 -0.74% 2.6 m/s -1.4

WS2 0.0334419 1.28%

Delta WS -0.1993351 3.58% 0 0

Pressure 0.0182993 5.14% 815 hPa 14.9

The values for Delta Temperature and Delta Wind Speed were determined by subtracting the current value from the 

value obtained from the previous minute. The changes in relative humidity and pressure did not turn out to be 

significant variables. 

The Eugene correlation method used the hours from sunset as a parameter. This parameter was not used here because 

the number of hours from sunset changes from month to month and depends on location. Instead, the average value of 

five hours after sunset was used.

The comparison of the nighttime correlations from Eugene data and Golden data is shown in Fig. 3. The correlation 

parameters obtained from the Eugene data did not utilize the change in ambient temperature or the change in wind 

speed over time. The Golden nighttime correlation was developed from nighttime data in June, September, and 

December of 2007. March, 2007 data are utilized for comparison because the March data were not used in the 

correlation.

The nighttime Golden correlation obtained from June, September, and December shows a small bias when compared 

with the March data. Therefore the Golden correlation needs to be more thoroughly examined to determine the cause 

of this bias and to obtain an improved correlation model.

4
IR Radiative Loss Estimates

Golden, CO - March, 2007 Nighttime

0%

2%

4%

6%

8%

10%

12%

-20 -19 -18 -17 -16 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5

IR Radiative Loss Distribution (W/m2)

Frequency of Occurance (%)

Golden Correlation Night Eugene Correlation Night Adjusted

Modified Detector Correction Full Correction

Detector Only Correction PSP Offset

Fig. 5. Distribution of IR radiative loss values from the PSP 

measured nighttime values and the other models being 

studied. The plot represents over 20,000 one minute data 

points divided into 0.5 W/m2

 bins. 

As expected, the Eugene correlation was not close 

to matching the observed IR radiative losses seen 

in Golden, Colorado. The sky temperature at the 

high altitude site in Golden has different 

characteristics than the sky temperature around the 

low altitude site in Eugene. This difference in IR 

radiative losses accounts for much of the change in 

responsivity of the pyranometers observed in 

Eugene as opposed to the responsivities measured 

in Golden. 

The mean value of the Eugene correlation results is 

2.9 times smaller than the mean of the observed IR 

radiative losses in Golden. The effect of 

multiplying the Eugene correlation values by 2.9 is 

shown in Fig. 4. After normalizing the model to the 

observed nighttime IR radiative losses, the 

modified modeled values provide a much closer

match to the observed IR radiative losses.

Another way to look at the match between the PSP IR radiative losses and those predicted by the various models is to 

plot the frequency distribution of modeled IR radiative losses against the observed nighttime PSP values. The 

frequency distributions are given in Fig. 5. The full correction and the adjusted Eugene correlation give the best fits, 

for the March, 2007 data. The results should be compared with all the available data to see if the March data provides 

a typical comparison.

5. DAYTIME IR RADIATIVE LOSSES

The IR radiative losses during the day can be evaluated now that the nighttime IR radiative losses have been 

examined. Pyranometers also exhibit deviations from true cosine response, a measurable dependence on temperature, 

and possibly other minor systematic errors in addition to the IR radiative losses. The uncertainties associated with the 

measurement of incident radiation when combined with the systematic errors in the measurements make it very 

difficult to directly measure the IR radiative losses during daylight hours. Therefore, the full correction method that 

has been tested at a number of locations1 will be used as a segregate for the IR radiative losses during the daytime

hours. 

 Table 2: Correlation parameters to the daytime IR radiative loss fit

Parameter Coefficient % Standard Deviation Average Typical Value

Ambient Temperature -0.151056 1.44% 289 K -43.81

Delta Temp. -10.554729 1.61% 0 0

Relative Humidity (%) 0.253814 -1.14% 40 % 6.99

RH2 -0.001978 1.32% 0

Wind Speed -0.448232 1.55% 2.6 m/s -2.30

Delta WS -0.163556 11.59% 0

Pressure 0.029178 -2.80% 816 hPa 23.78

kb -56.094918 1.64% 0.2 -8.37 

kb

2 85.389791 -3.36%

kb

3 -71.101465 3.95%

Delta kb -5.158391 6.80% 0 0

kt 23.031028 -3.08% 0.52 6.50 

kt

2 -39.262094 4.80%

kt

3 34.940895 -3.67%

Cos(Z) -4.743173 5.42% 0.5 2.38 

Cos2(Z) 19.013970 -1.34%

5
Deviation from Full Correction

Golden, CO - March, 2007 Daytime

0%

1%

2%

3%

4%

5%

6%

-20 -15 -10 -5 0 5 10 15 20

Difference from Full Correction (W/m2)

Frequency of Occurance (%)

Delta Golden Correlation-Day Delta Modified Detector

Delta Eugene Correlation-Day Adjusted Delta Detector Only

Fig. 7. Distribution of the difference between the full correction model IR radiative loss values during the day from those of other 

models under study. Data from SRRL in March, 2007. Plot represents over 20,000 one minute data points divided into 0.5 

W/m2

 bins. 

As with the nighttime IR radiative loss examination, the months of June, September, and December 2007 were used in 

deriving a correlation for the Golden, Colorado data against the full correction IR radiative loss estimates. Table 2

gives the statistically significant correlation parameters and their coefficients along with the standard deviations for the 

model for estimating the IR radiative loss. Note that both the global and beam values were normalized by dividing by 

their relative extraterrestrial values, giving kt and kb respectively. The standard error for the correlation is 

approximately 3.4 W/m2

, which is a about a 1/3 of the estimated IR radiative loss values. 

The adjustment to the Eugene daytime correlation model is to multiply the calculated values by the 2.9 factor 

IR Radiative Loss Estimates

Golden, CO - March 2007 Daytime

0%

1%

2%

3%

4%

5%

6%

7%

8%

9%

-35 -30 -25 -20 -15 -10 -5 0 5 10

IR Radiative Loss Estimates (W/m2

)

Frequency of Occurrence (%)

Full Correction Modified Detector Correction

Golden Daytime Correlation Detector Only Correction

Eugene Daytime Correlation Adjusted

Fig. 6. Distribution of IR radiative loss values during the day from the models under study. The data are from SRRL in March, 

2007. The plot represents over 20,000 one minute data points divided into 0.5 W/m2 bins. 

6
determined from the ratio of measured nighttime PSP values and the estimated IR radiative losses using the Eugene 

nighttime correlation model. The comparison with the adjusted Eugene correlation model will help test whether a nonpyrgeometer based correlation developed in one area is scalable to different regions. The difference between the full 

correction model and the detector only, the modified detector model, the Golden daytime correlation, and the adjusted 

Eugene daytime correlation are shown in Fig. 6. March, 2007 data are used for the evaluation in Fig. 6 because March 

data was not used to develop the Golden correlation model.

The detector based models give approximately the right average IR radiative loss value, but do not show the 

distribution of values exhibited by the full correction. The modified detector model exhibits a peak at low IR radiative 

loss values, and it is uncertain why this occurs. Both the modified Eugene and the Golden calibrations seem to better 

match the distribution of the full correction values. However, while the distributions are similar they still deviate from 

the full correction.

Another way to compare the IR radiative loss predictions is to plot the distribution of the difference between the full 

correction model and the other IR radiative loss models. This comparison is shown in Fig. 7. The difference from the 

Golden correlation model appears to have a normal distribution. While March data were not used in the development 

of the Golden correlation model, it is expected that the characteristics of the IR radiative losses in March should 

behave similarly to those in other months for a given location. The distribution for the Eugene correlation is fairly flat 

and skewed to the higher average difference between the full correction model and the Eugene model. 

The detector model and parts of the modified detector model are incorporated in the full correction model and the 

predicted IR radiative loss values should be fairly similar as seen in Fig. 7. The modified detector model moves the 

peak of the difference closer to the full correction, but studies from more sites are needed before any firm conclusions 

can be drawn.

6. DISCUSSION AND CONCLUSIONS

A good model of the IR radiative losses from first class thermopile pyranometers such as the Eppley PSP would be 

useful in obtaining more accurate measurements of the total irradiance. This is especially true for diffuse 

measurements where the IR radiative losses can be between 10 and 20% of the clear day values. The use of 

pyrgeometers to model IR radiative losses has been demonstrated already1

. However there is a considerable amount of 

high quality pyranometer data from sites that do not have pyrgeometer data to correct for the IR radiative losses.

Therefore a model that corrects for IR radiative losses using pyranometer and meteorological data could prove useful. 

In early work3, 4 modeling the IR radiative losses using pyranometer and meteorological data were examined for one 

site (Eugene, Oregon). It is was found that a correlation model based on meteorological and short wavelength solar 

measurements could simulate the IR radiative losses obtained from pyrgeometer measurements. However it was 

evident that the model was site specific and that a method was needed to transform the model so that it could work at 

sites with different sky temperature characteristics. In particular, significant differences between the nighttime IR 

radiative losses in Eugene and Golden, Colorado, given similar meteorological conditions, were noted. 

In this article it was found that using the ratio of nighttime IR radiative losses, the meteorologically based IR radiative 

correlation models developed in Eugene could be scaled to simulate the IR radiative losses obtained by the 

comprehensive full correction IR radiative loss model. While the fit for the Eugene model was not perfect, it did show 

in principle that a well developed IR radiative loss model not requiring pyrgeometer data could be developed. 

In other words, the bulk of the difference between the IR radiative losses observed at different sites can be accounted 

for by the ratio of the nighttime IR radiative losses. This result holds for Eppley PSP pyranometers and assumes that 

the IR radiative losses for different PSPs are similar. The difference between the detector only and the modified 

detector model shows that there probably are some differences between instruments, but these differences are assumed 

to be small, and taking the nighttime IR radiative loss ratio will probably include some of this difference. 

The fact that the full correction model works for many locations shows that the pyrgeometer characterization of the 

sky temperature and the use of meteorological measurements that enhance the model can fairly accurately account for 

7
the IR radiative losses. This is clearly illustrated in Fig. 5, which shows the match between the IR radiative losses at 

night between the PSP measurements and the full correction model. This model has been tested using different PSP 

pyranometers and gives good results without specifying the exact IR profile of each pyranometer. This is probably 

because the IR profiles of the pyranometers are similar.

While the Eugene or Golden correlation models of IR radiative losses are useful prototypes for estimating IR radiative 

losses without pyrgeometer data, a full comprehensive model will require evaluation over a number of years and at a 

variety of sites. 

7. ACKNOWLEDGEMENTS 

The UO SRML Solar Monitoring Network and data analysis is sponsored by the Bonneville Power Administration, 

Eugene Water and Electric Board, the Energy Trust of Oregon, the National Renewable Energy Laboratory, Emerald 

People’s Utility District and the Salmon River Electric Cooperative. Dr. Long acknowledges the support of the 

Climate Change Research Division of the U.S. Department of Energy as part of the Atmospheric Radiation 

Measurement (ARM) Program.

8. REFERENCES

[1] Younkin, K. and C. N. Long, “Improved Correction of IR Loss in Diffuse Shortwave Measurements: An ARM 

Value Added Product,” Atmospheric Radiation Measurement Program Technical Report, ARM TR-009, 50 pp.,

(2004) Available via http://www.arm.gov/publications/techreports.stm. (2004)

[2] Reda, I., Hickey, J., Long, C., Myers, D., Stoffel, T., Wilcox, S., Michalsky, J.J., Dutton, E.G., and Nelson, D., 

“Using a blackbody to calculate net infrared responsivity of shortwave solar pyranometers to correct for their thermal 

offset error during outdoor calibration using the component sum method,” J. Atmospheric Oceanic Tech., vol. 22, pp. 

1531-1540, October 2005.

[3] Vignola, F., Long, C., Reda, I., “Evaluation of Methods to Correct for IR Loss in Eppley PSP Diffuse 

Measurements”, proceeding SPIE conference, San Diego (2007)

[4] Vignola, F., Long, C., Reda, I., “Modeling IR Radiative Loss from Eppley PSP Pyranometers”, proceeding SPIE 

conference, San Diego (2008) 

[5] NREL solar radiation data: http://www.nrel.gov/midc/srrl_bms/

8
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14. ABSTRACT (Maximum 200 Words)

Thermopile pyranometers exhibit IR radiative losses that affect global and diffuse shortwave measurements made 

with first class thermopile based instruments. Pyrgeometers can be used to measure the sky temperature and are 

used to calculate the pyranometer’s IR radiative losses. Few solar monitoring sites are equipped with pyrgeometers 

necessary to account for the IR radiative losses associated with the pyranometers. High quality data from the Solar 

Radiation Research Laboratory (SRRL) at the National Renewable Energy Laboratory are used to test and further 

develop a model for the IR radiative losses without the use of pyrgeometer data. The various methods for obtaining 

IR radiative loss values are compared and contrasted using the SRRL data. A simple scaling method is proposed 

and tested to adjust the non-pyrgeometer based correlation models to sites with different sky temperature 

characteristics.

15. SUBJECT TERMS

Pyranometer; Pyrgeometer; irradiance; IR; modeling; global; PSP

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