Sensitivity of Spectroradiometric Calibrations in the 

Near Infrared to Variations in 

Atmospheric Water Vapor

Preprint 

March 2004 • NREL/CP-560-36037 

D.R. Myers and A.A. Andreas 

To be presented at the American Solar Energy 

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July 11–14, 2004 

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SENSITIVITY OF SPECTRORADIOMETRIC CALIBRATIONS IN THE NEAR 

INFRARED TO VARIATIONS IN ATMOSPHERIC WATER VAPOR

Daryl R. Myers 

 Afshin Andreas 

National Renewable Energy Laboratory, 

 1617 Cole Blvd 

Golden CO 80401 

daryl_myers@nrel.gov 

afshin_andreas@nrel.gov

ABSTRACT

Spectra of natural sunlight and artificial sources are 

important in photovoltaic research. Calibration of the 

spectroradiometers used for these measurements is 

derived from the response to spectral irradiance standards 

from the National Institute of Standards and Technology 

(NIST). Some photovoltaic devices respond in the near 

infrared, or NIR, so spectral measurements and 

calibrations are needed in this region. Over the course of 

several calibrations, we identified variations > 5% in 

spectroradiometer NIR calibration data for a certain 

spectroradiometer. Reviewing calibration procedures and 

historical data, we noted that the variations were seen in 

water vapor absorption bands. We used spectral 

transmission models to compute changes in atmospheric 

transmission (as a function of water vapor content) over 

path lengths occurring during calibration. The results 

indicate that the observed variations result from varying 

water vapor content. A correction algorithm for adjusting 

measured data was developed based on our analysis.

1.0 INTRODUCTION

1.1 Devices and Sources in the Near Infrared 

The spectral response of PV devices continues to migrate 

into the near-infrared (NIR) region of wavelengths > 

1000 nm (1). Figure 1 shows representative spectral 

response functions for some PV technologies. Figure 2 

shows natural (thin black line) and simulated (large area 

continuous Solar Simulator- (thick gray line) spectral 

distributions. 

The absorption bands between 1300 nm and 1500 nm and 

1800 nm to 1900 nm in the natural sunlight spectrum are 

due to absorption by water vapor in the atmosphere. The 

depths of these features vary only slightly with the 

Fig. 1: Representative spectral response functions for 

eight PV technologies, three of which respond at 

wavelengths > 1000 nm. 

Fig. 2: Natural sunlight (thin black line) and Solar 

Simulator (thick gray line) spectral distributions. 

0.0

0.50

1.0

1.5

2.0

300 8 00 1300 18 00 2300

Spectral Irradiance W m-2 nm-1

Wavelength nanometers
amount of water vapor. This means the bands always 

absorb strongly. The depth of the 820 nm absorption band 

increases as the water vapor content of the atmosphere 

increases, and the depth of this band can be used to 

estimate the water vapor content of the atmosphere. The 

natural sunlight spectrum is representative of absorption 

over the entire path length from the top of the atmosphere 

to the ground. Our investigations address the issue of 

absorption over shorter path lengths in the calibration 

laboratory. 

2.0 SPECTRAL STANDARDS AND CALIBRATIONS

Calibrations of spectroradiometers are the response of the 

system (input optic, monochromator, detector) to a 

known spectral distribution of a calibrated source (2). 

Spectral irradiance lamp standards are available from 

national standardizing laboratories, or from third parties 

transferring calibrations from reference to production 

lamps. There is additional uncertainty in third party 

lamps, due to uncertainties in the transfer process. Figure 

3 shows a typical spectroradiometer calibration setup. 

Fig. 3: Spectroradiometer (left) with NIST Spectral 

Irradiance Standard Lamp (right) and NIST tabulated 

spectral irradiance at 35 wavelengths (inset). Note the 

specified calibration distance is 500 mm. 

For each standard lamp, NIST gives 35 data points that 

"skip over" the water vapor bands at 720, 820, 940, 1120, 

1300 to 1500, and 1800 to 1950 nm as in figure 4. 

Fig, 4: NIST standard lamp data (points), interpolated data 

(black line), and (spiked gray line) spectral absorption 

coefficient of water vapor.

The result of a spectroradiometer calibration is the 

detector response R(λ) as a function of wavelength, λ. 

The response is defined as the ratio of a known radiant 

flux (from the standard lamp) E(λ) to the detector signal 

S(λ) at each wavelength; or R(λ)=E(λ)/S(λ). When a 

measurement is made, the unknown irradiance, I(λ), is 

the product of the signal from the unknown source, U(λ), 

multiplied by the response function: I(λ) = U(λ)*R(λ). 

Figure 5 is a plot of the response functions for three 

calibrations each of two NREL spectroradiometers in the 

region from 1000 to 2000 nm where water vapor 

absorption is strong, along with the water vapor absorption 

bands of interest. 

Fig. 5: Three response functions for a diffuser + fiber 

optic receiver system (top curves) and three response 

functions for integrating sphere receiver (lower curves) 

with water vapor spectral absorption curve (spiked light 

gray line). 

3.0 WATER VAPOR AND RESPONSE FUNCTIONS

In figure 5, the upper curves are for a spectroradiometer 

system with a diffuser and fiber optic input system. The 

lower curves are for a system with an integrating sphere 

input optic. Relative humidity in the laboratory where 

each of the responsivity functions were generated was 

22%, 23%, and 44%, for the Diffuser system, and 22%, 

26%, and 41% for the sphere system. 

Changes in the response function for the integrating 

sphere receiver system, (circled), are more apparent than 

in the diffuser-fiber optic system. 

All calibration files depicted above pertain to the same 

NIST lamp, power supply, and monitoring equipment, 

over a period of 18 months. It is apparent that the changes 

seen are inherent in the spectroradiometer system with 

the integrating sphere input. 

500 mm 
19 rays traced in 

sphere 8 cm 

Radius X 164 

Possible explanations for the variable response seen in 

the integrating sphere system are: a) the sphere coating 

absorbs water vapor; b) the path length from the lamp to 

the input slit of the monochromator for the sphere system 

is much greater, due to multiple reflections from the 

sphere walls before photons reach the sphere exit 

(monochromator entrance) port, or (c) some other 

component of the monochromator system is hygroscopic. 

Option (c) is rejected since replacing the sphere input 

optic with the diffuser/fiber optic input, variations in the 

response function in the water vapor absorption region 

are nearly negligible. Option (a) is not viable since the 

sphere coating is spectrolon, an inert compound 

(polytetraflourethylene) that is not hygroscopic. Thus, 

option (b) is the only remaining alternative. 

This led us to investigate the observed variations due to 

water vapor absorption over path lengths expected in the 

laboratory. If the variations seen in the calibration files 

are the result of variations in the water vapor content of 

the atmosphere in the laboratory, there will be errors in 

measurements made under different atmospheric 

conditions. We explored the relationship between water 

vapor absorption and path length using complex and 

simple atmospheric spectral transmission models. 

4.0 SPECTRAL MODELING

A “moderate resolution transmission” code, MODTRAN, 

developed by Air Force Geophysical Laboratory (AFGL) 

is a complex, rigorous radiative transfer model written in 

FORTRAN (3-5). AFGL has licensed MODTRAN 

through the Ontar Corporation (http://www.ontar.com). 

MODTRAN (ver. 4) code evolved over 30 years, and 

consists of about 52,000 lines of source code. The model 

uses a "band model" implementation of the HITRAN 

absorption line database (6-8). 

HITRAN contains over 1 million spectral absorption lines 

for 38 gaseous constituents of the earth's atmosphere, 

along with 27 additional molecules for which only 

absorption cross sections are given. HITRAN is 

considered an international standard database for 

atmospheric molecular spectroscopy. HITRAN contains 

23,406 water vapor absorption lines between 1000 nm 

and 2000 nm, as seen in figures 4 and 5. 

The MODTRAN band models are computationally 

efficient "transmission function" approximations that 

produce an "equivalent absorption" over the radiative 

transfer passband. The highest effective resolution in 

MODTRAN is quoted as 2.0 cm-1. This is a resolution of 

approximately 0.2 nm and 0.8 nm, at 1000 nm and 2000 

nm, respectively. We used MODTRAN 4.0 to look at the 

relative changes in calibration lamp spectral intensity by 

changing water vapor content by a factor of two over a 

path length of 1.0 meter. 

The are of an integrating sphere of radius 8 cm is 804 

cm2

. For an exit port area of 4.9 cm2, we estimate the 

number of reflections before a ray exits the port to be 164, 

the ratio of the total area to the exit port area. Using the 

radius of the sphere as the average path length of a 

reflection, the equivalent path length is 1.312 m. Ray 

tracing software would be a way to verify this estimate. 

An example of ray tracing software results in figure 6 

shows how 19 rays propagate "through" a sphere. With 

these assumptions, we set 1.0 meter as the path length in 

our MODTRAN model runs. Coincidentally, 1 m (0.001 

km) is the minimum path length MODTRAN accepts. 

Fig. 6: Ray tracing software example for 19 rays (entering 

from bottom) propagating in a sphere. 

4.1 MODTRAN Model 

Input parameters for our MODTRAN model runs were for 

a horizontal path of 1.0 m at the altitude of 1800 m (1.8 

km) above sea level (ASL). We used the 1976 United 

States Standard Atmosphere (USSA) with 330 ppm (parts 

per million) carbon dioxide loading (9). All other 

transmission parameters were automatically computed for 

the selected profile. The only parameter changed from run 

to run was the water vapor content. MODTRAN requires 

and input of equivalent atm-cm of water vapor. We used 

values of 1.5 atm-cm and 3.0 atm-cm of water vapor to 

study the effect of doubling water vapor content. 

At the 1.8 km altitude of our laboratory, these values are 

approximately the equivalent to relative humidity of 30% 

and 60%, respectively (10). MODTRAN runs were 

executed to produce the water vapor transmission data for 

800 nm to 2000 nm for each of the two water vapor 

conditions over the 1-meter path length. 

The resulting water vapor transmissions were then 

multiplied by the NIST spectral irradiance standard lamp 

curve, and the difference between the two resulting lamp 

spectra was computed. Figure 7 is a plot of the absolute 
difference, in Watt m-2 nm-1 between the 30% and 60% 

relative humidity cases. Note that the noise level of the 

spectrometer, when a dark scan is performed, is 2-

microwatt m-2 nm-1. 

These MODTRAN results show that, indeed, a doubling 

of the water vapor content in the laboratory can produce 

differences in absolute spectral irradiance that are two 

orders of magnitude above the noise equivalent power for 

the spectroradiometer system. 

Fig. 7: Absolute difference in spectral irradiance for 

NIST lamp with a factor of two change in water vapor 

content over a path length of 1.0 m at 1.8 km ASL. 

4. 2 SMARTS Spectral Model 

SMARTS, (Spectral Model for Atmospheric Transmission 

of Sunshine) is based on parameterizations of the different 

extinction processes in the atmosphere (11). The effective 

spectral resolution at each computed point is 5 nm in the 

NIR water vapor bands of interest. SMARTS incorporates 

ten widely used “reference” atmospheric profiles, 

including the 1976 USSA. The model accounts for 

Rayleigh, ozone, nitrogen dioxide, uniformly mixed 

gases, water vapor, and aerosol extinction properties, 

using individual parameterizations of MODTRAN 

components, or derived from analysis of multiple 

MODTRAN model results. Thus, SMARTS2 may be 

viewed as a "simplified" or "parameterized" MODTRAN 

model. 

We wished to see if SMARTS was accurate enough to 

reproduce the MODTRAN results presented above. While 

SMARTS can produce water vapor transmission directly 

as an output (among 24 other spectral parameters) for 

each model run, the only way to examine the variation in 

transmission with path length is to perform two model 

runs at different altitudes and compute the effective 

transmittance as the ratio of the two irradiance files. 

We computed the SMARTS direct normal spectral 

irradiance at our laboratory altitude of 1.800 km and at 

1.801 km, using water vapor of 1.5 atm-cm and 3.0 atmcm, the USSA atmosphere ,and an air mass of 1.0. All 

other atmospheric parameters unchanged between runs. 

The ratio of the irradiance at the lower altitude to the 

irradiance at the (1 meter) higher altitude should be the 

effective transmittance of the 1 meter path length with 

water vapor concentration equivalent to 30% and 60% 

RH, respectively. Figure 8 is a plot of the SMARTS water 

vapor transmission (black line) over 1.0 m at 60% RH 

compared with the MODTRAN direct computation of 

water vapor transmission over the 1.0 meter path (gray 

line). Similar results were obtained for the 1.5 atm-cm 

(30% RH) case. 

Fig. 8: Comparison of SMARTS (black line) and 

MODTRAN (gray line) derived water vapor transmission 

for 1.0 meter path length at 60% RH.

Differences between the SMARTS and MODTRAN 

results are primarily due to the difference in spectral 

resolution of the two models. The SMARTS model 

indicates the same relative sensitivity to changing water 

vapor as the MODTRAN results above. 

5.0 CORRECTING SPECTRAL DATA 

Multiple MODTRAN or SMARTS model runs at water 

vapor concentrations of 0.5, 1.0, 2.0, and 3.0 atm-cm of 

water, roughly equivalent to relative humidity levels of 

10%, 20%, 40% and 60% at the NREL laboratory altitude 

of 1.8 km provide data to show transmittance of the water 

vapor as a function of relative humidity at several 

wavelengths. Figure 9 shows the relationship between 

transmission and water vapor derived in this way for 

wavelengths of 1361, 1382, and 1829 nm. 

The correlation with water vapor content varies 

considerably from wavelength to wavelength and, 

therefore, across absorption bands. However, inspection 

of figure 7 shows that between about 1350 nm and 1380 
nm, adding a "linear" correction to measured data would 

reduce the error in data measured at 60% RH, when 

calibration was performed at 30% RH. Similarly, in the 

region from 1800 nm to 1950 nm, a "parabolic" correction 

function would appear to reduce the error in spectral data 

measured at 60% RH for calibrations at 30% RH. 

Fig. 9: Relationship between water vapor absorption at 3 

wavelengths with respect to varying relative humidity.

We derived linear and parabolic fits to the coefficients for 

the correlations of water vapor transmittance shown in 

figure 9. Resulting correction functions, Ti(λ), become: 

For 1360 nm < λ < 1380 nm; 

M1(λ) = 2.00056 • 10-07 • λ - 2.76735 • 10-04

and T1(λ) = M1(λ) • RH + 1.0. 

For 1800 nm < λ < 1900 nm; 

M2(λ) = 8.7584•10-10 • λ2 - 3.24061•10-6 •λ + 2.9954•10-03 

and T2(λ) = M2(λ) • RH + 1.0. 

Measured irradiance E(λ) can be modified to a corrected 

irradiance , Ec(λ), by computing 

Ec(λ) = E(λ) + ( 1-Ti(λ) ) • E(λ). 

Applying these corrections to a calibration file to correct 

to "zero" RH (or water vapor), the user would use the 

same algorithms to correct measured data taken at an 

arbitrary water vapor content (RH) to the equivalent with 

"no" water vapor. For outdoor measurements of natural 

solar radiation with an "RH=0" corrected calibration file, 

the measured irradiance in the water vapor bands will be 

more representative of the true irradiance. 

6.0 SUMMARY

We quantitatively correlated the variation in calibration 

response functions for spectroradiometer systems with 

integrating sphere input optics with the differences in the 

water vapor content of the atmosphere. MODTRAN and 

SMARTS spectral radiative transfer models are in 

reasonable agreement on the relative changes in 

atmospheric transmission over path lengths as short as 1 

meter. These models can be used to produce data for 

developing correction functions to reduce errors in 

measurements under varying water vapor concentrations. 

ACKNOWLEDGEMENT

This work was performed for the Department of Energy at 

the National Renewable Energy Laboratory under 

contract number DE-AC36-99GO10337. 

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"Spectral Irradiance Calibrations." National Institute of 

Standards and Technology, Gaithersburg, MD, 1987 

(3) Anderson, G.P., et al., "Reviewing atmospheric radiative 

transfer modeling: New developments in high and moderate 

resolution FASCODE/FASE and MODTRAN," in Optical 

Spectroscopic Techniques and Instrumentation for Atmospheric 

and Space Research II. Society of Photo-Optical Instrumentation 

Engineers, 1996 

(4) Anderson, G.P., et al., "History of one family of atmospheric 

radiative transfer codes," in Passive Infrared remote Sensing of 

Clouds and the Atmosphere II. Society of Photo-optical 

Instrumentation Engineers, 1996 

(5) Anderson, G.P., et al., "MODTRAN2: Suitability for remote 

sensing," in Atmospheric Propagation and Remote Sensing. 

Society of Photo-Optical Instrumentation Engineers, 1993 

(6) Rothman, L.S., "Update of the AFGL atmospheric 

absorption line parameters compilation." Appl. Opt. 17: pp. 

3517-3518, 1978 

(7) Rothman, L.S., et al., "The HITRAN molecular database: 

Editions of 1991 and 1992." J. Quant. Spectros. Rad. Trans. 48: 

pp. 469-507, 1992 

(8) Rothman, L.S., et al., "The HITRAN molecular 

spectroscopic database and HAWKS (HITRAN atmospheric 

workstation): 1996 edition." J. Quant. Spectros. Rad. Trans. 60: 

pp. 665-710, 1998 

(9) Anderson, G.P., Clough, S.A., Kneizys, F.X., Chetwynd, 

J.H., Shettle, E.P., "AFGL atmospheric constituent profiles (1-

120 km)." AFGL-TR-86-0110 Air Force Geophysical 

Laboratory, Hanscomb AFB, MA, 1986 

(10) Garrison, J.D., Adler, G.P., "Estimation of precipitable 

water over the United States for application to the division of 

solar radiation into its direct and diffuse components." Solar 

Energy, 44(4): pp. 22-241, 1990 

(11) Gueymard, C., "Parameterized transmittance model for 

direct beam and circumsolar spectral irradiance." Solar Energy, 

71(5): pp. 325-346, 2001 
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Sensitivity of Spectroradiometric Calibrations in the Near Infrared to Variations in 

Atmospheric Water Vapor: Preprint 

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D.R. Myers and A.A. Andreas 

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13. ABSTRACT (Maximum 200 words)

Spectra of natural sunlight and artificial sources are important in photovoltaic research. Calibration of the spectroradiometers 

used for these measurements is derived from the response to spectral irradiance standards from the National Institute of 

Standards and Technology (NIST). Some photovoltaic devices respond in the near infrared, or NIR, so spectral 

measurements and calibrations are needed in this region. Over the course of several calibrations, we identified variations > 

5% in spectroradiometer NIR calibration data for a certain spectroradiometer. A detailed uncertainty analysis did not reflect the 

observed variation. Reviewing calibration procedures and historical data, we noted that the variations were seen in water 

vapor absorption bands. We used spectral transmission models to compute changes in atmospheric transmission (as a 

function of water vapor content) over path lengths occurring during calibration. The results indicate that the observed 

variations result from varying water vapor content. A correction algorithm for adjusting measured data was developed based 

on our analysis. 

14. SUBJECT TERMS 15. NUMBER OF PAGES

Calibration of spectroradiometers; spectral irradiance standards; National Institute of 

Standards and Technology; photovoltaic research; Near Infrared; variations in water 

vapor 

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