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

Impact of Aerosols on 

Atmospheric Attenuation Loss 

in Central Receiver Systems

Preprint

Manajit Sengupta and Michael J. Wagner 

To be presented at SolarPACES 2011

Granada, Spain

September 20-23, 2011

Conference Paper

NREL/CP-5500-52487

August 2011
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1 

IMPACT OF AEROSOLS ON ATMOSPHERIC ATTENUATION LOSS 

IN CENTRAL RECEIVER SYSTEMS 

Manajit Sengupta1 and Michael J. Wagner2

(1) Ph.D., Senior Scientist, National Renewable Energy Laboratory, MS 5202, 1617 Cole Blvd, 

Golden, CO 80401, USA, +1 303 275 3706, Manajit.Sengupta@nrel.gov 

(2) National Renewable Energy Laboratory, MS 5202, 1617 Cole Blvd, Golden, CO 80401, USA 

ABSTRACT 

Atmospheric attenuation loss between the heliostat field and receiver has been recognized as a 

significant source of loss in Central Receiver Systems. In clear sky situations, extinction of Direct 

Normal Irradiance (DNI) is primarily by aerosols in the atmosphere. When aerosol loading is high 

close to the surface the attenuation loss between heliostat and receivers is significantly influenced 

by the amount of aerosols present on a particular day. This study relates measured DNI to aerosol 

optical depths close to the surface of the earth. The model developed in the paper uses only 

measured DNI to estimate the attenuation between heliostat and receiver in a central receiver 

system. The requirement that only a DNI measurement is available potentially makes the model a 

candidate for widespread use. 

Keywords: DNI, Attenuation Loss, Heliostat, Central Receiver, Aerosols 

1. INTRODUCTION

Atmospheric attenuation loss between the heliostat field and receiver has long been recognized as a 

significant source of loss in Central Receiver Systems. Attenuation losses can potentially reach over 10% 

especially as distances between heliostats and receivers reach distances of a kilometer or more. Historically 

this loss has been represented by parametric equations that are functions of distance between heliostat and 

receiver [1],[2],[3][4][5] with separate equations for different levels of aerosol loading. Individual equations 

do not directly account for variability in aerosols, which is the primary source of DNI losses close to the 

surface where most of the transmission between heliostat and receiver occurs. It is therefore possible that a 

model that directly accounts for aerosol variability close to the surface will lead to a better estimate of 

attenuation losses between heliostat and receiver. In this paper we build a model that directly accounts for 

aerosol variability with the expectation that it will provide a more accurate representation of the attenuation 

loss. 

To get the most accurate estimate of attenuation between heliostat and receiver it is necessary to measure 

aerosol optical properties as well as water vapor mixing ratio profiles in the first few hundred meters from the 

surface where the heliostat and receiver lies. Such measurements are expensive and therefore generally not 

available. The other option is to obtain an estimate of aerosol optical depths close to the surface using 

available measurements. Making use of the fact that DNI measurements are generally available at central 

receiver system this study seeks to model attenuation loss close to the surface as a function of measured DNI. 

The theory and methodology behind this work is summarized in Section 2. Section 3 presents the results of 

the calculations and the model while Section 4 provides a brief summary and a description of future work. 

2. METHODOLOGY 

In clear sky situations, extinction of Direct Normal Irradiance (DNI) through either absorption or scattering is 

primarily from aerosols in the atmosphere. The ratio of absorption to scattering varies based on aerosol type. 

Accurate representation of that ratio is important for calculating diffuse radiation. On the other hand DNI loss 

estimation only requires knowledge of extinction and not the apportionment between scattering and 

absorption. The atmospheric constituents that impact solar radiation are the atmospheric gases and aerosols. 

Most atmospheric gases are well mixed and extinction of DNI resulting from those gases is easily calculated 

with minimal uncertainty. On the other hand the two most important variables that influence DNI but are not 

well mixed are aerosols and water vapor. For our study it is advantageous that aerosol and water vapor 

loading primarily lies in the lower troposphere with much lower concentrations generally existing above the 

boundary layer. As aerosol loading is high close to the surface the attenuation loss between heliostat and 

receivers is significantly influenced by the magnitude and variability of aerosol amount. Based on this 

understanding of aerosol distribution we build a model that relates attenuation losses close to the surface to 
2 

DNI measurements. This section is divided into three subsections. Section 2.1 outlines the theory used to 

develop a relationship between measured DNI and corresponding attenuation between heliostat and receiver 

in a central receiver system. Section 2.2 provides an outline of the radiative transfer model used in the 

calculations while Section 2.3 contains details about model inputs and the actual scenario used in this paper. 

2.1 Theory 

As previously mentioned we are concerned with DNI losses and do not require single scattering albedo (ratio 

of scattering to extinction) estimates. Therefore DNI at any height in the atmosphere can be represented as a 

function of the Top-of-Atmosphere DNI using the relationship. 

݁஺ை்ܫܰܦ ൌ ܫܰܦ

ି ఛ

஼௢௦ሺఏሻ ሺ1ሻ

where, DNITOA is the Top-of-Atmosphere DNI, τ is the extinction optical depth of the atmospheric column 

and θ is the solar zenith angle. We can then use Equation 1 to defining aerosol forcing F as 

 ൌ ܨ

௔ܫܰܦ

௕ܫܰܦ

 ൌ ݁

ିሺఛೌିఛ್ሻ

஼௢௦ሺఏሻ ሺ2ሻ

where DNIa represent the measured DNI in an atmosphere that contains aerosols while DNIb represents a 

baseline theoretically calculated clean atmosphere with no aerosols for the same sun position and therefore 

the same zenith angle and earth to sun distance. Using Equation 2 the difference in optical depth between 

DNIa (an atmosphere with aerosols) and DNIb (a “clean” baseline atmosphere with no aerosols) can be 

represented as 

ܺ ൌ ሺ߬௔ െ ߬௕ሻ ൌ െ logሺܨሻ ൈ ݏ݋ܥሺߠሻ ሺ3ሻ

Using a relationship similar to Equation 1 we can represent the DNI at the surface as a function of the DNI 

received at a layer Δz above the surface. This relationship is 

݁௜ܫܰܦ ൌ௙௖ ௦ܫܰܦ

ିఛ∆೥

஼௢௦ሺఏሻ ሺ4ሻ

where, DNIsfc and DNIi represent the DNI at the surface and a level Δz above the surface and τΔz represents 

the optical depth of the surface layer. Equation 4 can then be used to represent the optical depth of an 

atmospheric layer Δz that lies between the surface and any height z. The relationship is 

ܻൌ߬୼௭ ൌ െ log ൬ܦܰܫ௦௙௖

௜ܫܰܦ

൰ ൈ ݏ݋ܥሺߠሻ ሺ5ሻ

2.2 Radiative Transfer Model 

The radiative transfer model that we used in this study is based on the δ2 stream numerical algorithm 

presented by [6] and [7], which bears the acronym RAPRAD (Rapid Radiative Transfer) to signify its speed 

of computation. The model has 32 spectral intervals ranging from 0.24 μm to 4.6 μm in the shortwave and 

near-infrared, using absorption coefficients based on k distributions and a correlated-k approximation as 

explained in detail by [8]. 

The top of atmosphere spectral solar irradiance in the RAPRAD model is based on the solar irradiance of 

MODTRAN3[9] using the Kurucz database[10]. The RAPRAD model incorporates ozone, oxygen, carbon 

dioxide and water vapor absorption, as well as water vapor continuum absorption. The molecular scattering 

optical depth is computed using the Rayleigh optical depth calculation as shown in [11]. 

For RAPRAD model inputs based on high-quality measurements at the United States Department of 

Energy’s Atmospheric Radiation Measurement (ARM) Southern Great Plains (SGP) Cloud and Radiation 

Testbed (CART) site measurements, calculated surface fluxes are generally within 15-20 Wm-2 of surface 

flux measurements [12]. 
3 

2.3 Simulation Design 

The atmospheric layers in the RAPRAD model are arbitrary and can be set according to the requirements of 

the problem at hand. We set the top of atmosphere at 70 km and divided the atmosphere below 16 km into 

250 m thick layers. Above 16 km model layer thicknesses are set to increase with altitude. In the model 

simulations we use a surface albedo of 0.2 that is invariant with wavelength; this value is typical of the 

surface albedo of farmland in the mid-visible (e.g. Blythe, CA Typical Meteorological Year surface albedo 

from http://rredc.nrel.gov/solar/old_data/nsrdb/1991-2005/tmy3/). Clear-sky RAPRAD irradiance 

calculations require vertical profiles of pressure, temperature, water vapor, ozone, and aerosol particles. We 

used a mid-latitude summer atmospheric profile from MODTRAN [9] for pressure, temperature, water vapor 

mixing ratio and ozone profiles. Our baseline clean case contains no aerosols. For externally mixed aerosol 

we use mineral dust with the Angstrom exponent value [13] from [12]. The aerosol is taken to be evenly 

distributed in the lowest 1000 m of the atmospheric column. DNI is calculated for 0.5 degree increments with 

the zenith angle varying from 0-80 degrees. 

3. RESULTS 

Figure 1: DNI at the surface is shown for various times of the day. The green solid line having the highest 

DNI for a particular time represents the case of no aerosols. An aerosol optical depth of less than 0.1 can lead 

to a reduction of DNI by over 200 W/m2

. 

RAPRAD was run at 1-minute increments during the period of a day. For determining solar position during 

the time of the day we considered July 21 at Golden, CO. Calculations were done as previously mentioned 

for a mid-latitude summer atmospheric profile for a station assumed to be at sea level. The calculations were 

run for a baseline case with no aerosols as well as for various increasing levels of aerosol optical depths 

(AOD) ranging from 0.0125 to 0.1. RAPRAD produces DNI and Global Horizontal Irradiance (GHI) at the 

boundaries of every atmospheric model layer for each of the 32 spectral intervals. The broadband DNI is 

calculated by summing the spectral DNI. Figure 1 shows how the DNI varies during the day with each line 

representing various aerosol optical depths. It is seen that DNI can be reduced by around 200 W/m2

 for a 

change in AOD of 0.1. As all other atmospheric properties were held constant it is obvious that the reduction 

in DNI is a result of increase in AOD. 
4 

Figure 2: Attenuation of DNI in the lowest 250 m of the atmosphere for various aerosol optical depths. Note 

the low level of attenuation in the absence of aerosols as shown by the green solid line. 

While Figure 1 shows how the DNI changes for various AOD’s Figure 2 shows the attenuation in DNI in the 

lowest 250 m of the atmosphere where a power tower will operate. Effectively Figure 2 shows the difference 

in DNI at a level 250 m above the surface (not shown) and the surface (Figure 1). We can see that AOD 

difference of less that 0.1 can result in losses of around 40 W/m2

. 

As mentioned above the goal of this work is to relate the attenuation of DNI reflected towards the receiver in 

the layer closest to the surface to measured DNI in the presence of aerosols. To establish this relationship we 

relate X (the difference between the optical depth used to calculate a baseline DNI and the optical depth of 

the atmosphere for a measured DNI) and Y (optical depth of the layer closest to the surface) in Equation 3 

and Equation 5 respectively. 

Figure 3 shows the relationship between X (the total optical depth difference calculated in Equation 3) and 

the Y (optical depth of the lowest 250 m atmospheric layer). The colored lines show that the relationship is 

fairly constant for the whole range of zenith angles if the AOD is constant. The black line is a least square fit 

to the means calculated for each of the various colored datasets each representing fixed AOD but varying 

solar zenith angles. It is obvious from Figure 3 that the relationship with the means is robust. This is borne 

out of the fact that the coefficient of determination (Table 1) which is an indicator of the variance that is 

explained by the model is nearly 100%. Figure 3 shows that there is a zenith angle dependence on the 

relationship be X and Y. This primarily arises from some wavelength bands becoming saturated as the 

airmass increases with zenith angle. 

Using the relationship represented by the black line in Figure 3 we can determine the attenuation between 

heliostat and receiver if the distance between the two is known. The relationship in the case is represented by 

ܻ ൌ 0.2299 ൈ ܺ ൅ 0.002674 ሺ6ሻ

where Y is the optical depth of the bottom 250 m atmospheric layer. The intercept represents the in Equation 

5 represents attenuation in the 250 m atmospheric layer in the absence of aerosols. Therefore if the distance d

between heliostat and receiver is known the DNI at the receiver is 

݁௖௙௦ܫܰܦ ൌ௥௘௖ ܫܰܦ

ௗכ௒

ଶହ଴ ሺ7ሻ
5 

Table 1: The linear least squares fit shows that a robust relationship exists between the column optical depth 

difference when comparing the measured value to a clean atmosphere DNI and the optical depth of the lowest 

atmospheric layer (in this case 250 m). 

The relationship in equation 7 is dependent on the accuracy of DNI measurement at the heliostat. Typically, 

for well maintained sites, DNI accuracy is +/- 2.0% , or +/-20 W out of 1000 W full scale (for very well 

maintained measurements). It should be noted that DNIsfc in Equation 4 is the actual DNI reaching the surface 

while the DNIsfc in Equation 7 is the DNI that is reflected from the heliostats and factors in cosine losses, 

shading losses, blocking losses and reflectivity.

Figure 3: This figure shows how the optical depth of the lowest 250 m of the atmosphere is related to the 

difference in total optical depth between a clean atmosphere and an atmosphere with an aerosol optical depth 

represented in the legend. The black line represents the least square fit to the mean optical depth for each 

fixed AOD case 

4. CONCLUSIONS AND FUTURE WORK 

Equation 7 provides a model for attenuation losses between heliostat and receiver in a central receiver system 

that depends only on DNI measurements. As DNI measurements are generally available at any prospective 

CSP site or existing CSP plant such a model can be readily used in CSP production modeling. The model can 

be incorporated in available models such as the National Renewable Energy Laboratory’s Solar Advisor 

Model (SAM). 

This model relies on the fact that atmospheric constituents that are not well mixed but significantly influence 

DNI are primarily present close to the surface. This is especially the case of aerosols as they are primarily 

present below the atmospheric boundary layer. We have not investigated how sensitive the relationship we 

have derived is to other atmospheric profiles such as those present in the tropics. It is expected that the 

intercept in Equation 6 will vary to accommodate various levels of precipitable water vapor at the surface. 

We also have considered the case where the aerosols are uniformly distributed in the lowest 1000 m of the 

atmosphere. In future work our goal is to carry out the same modeling on a variety of atmospheric profiles 

Statistic Value 

P1 (slope of regression fit) 0.2299 (95% confidence bounds [0.2269, 0.2329]) 

P2 (intercept of regression fit) 0.002674 (95% confidence bounds [0.002223, 

0.003126]) 

Sum of squares of residuals 6.0907e-7 

Coefficient of Determination R2 0.9998 
6 

and aerosol distributions. Additionally surface elevation needs to be accounted for to make the model 

applicable at all locations. As a change in surface pressure due to elevation has a linear impact on the optical 

depth for well-mixed gases this scaling factor will be added to the baseline DNI to make the model applicable 

at all elevations. Finally as previously mentioned there is a small zenith angle dependence between DNI and 

attenuation close to the surface. This will also be considered in our future work. 

5. REFERENCES 

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