The interaction between relative humidity and circumsolar radiation and its effects on concentrating solar thermal systems in Australia (2006)

SCHOOL OF PHYSICS

HONOURS REPORT

2006

The interaction between relative humidity and circumsolar radiation and its effects on concentrating solar thermal

systems in Australia

Damien Scott Department of Plasma and Applied Physics

The University of Sydney

Abstract

The distribution and intensity of circumsolar radiation can be an important performance determinant

for optically concentrating solar thermal systems. Its characteristics are determined by the

composition and size distribution of atmospheric aerosols. Relative humidity has previously been

shown to significantly alter these aerosol size distributions particularly for values beyond 70%. A

model was developed to explore the relationship between circumsolar radiation and relative

humidity and was applied meteorological data from to nine Australian locations. Results confirmed

the increase in circumsolar radiation with relative humidity with the distribution highly dependent

on aerosol composition. Consideration of a minimum operational threshold at the 9 locations

suggest that the increased aerosol effects for relative humidity beyond 70% would rarely be

experienced. Average circumsolar ratios obtained by applying the model to locations data were

typically below 0.03.

Statements

Acknowledgments

I would like to thank my primary supervisor, Dr. Yonbai Yin, who - in addition to being responsible

for initially piquing my interest in solar energy - has provided guidance, an eclectic knowledge of

science, and many hours of discussion about all things related to climate change.

In addition I would like to thank Associate Professor Michael Box for very kindly agreeing to

provide guidance and advice on the meteorological aspects of the project.

The Australian Bureau of Meteorology provided the data used in this project in a most efficient and

helpful manner free of charge despite the cost exceeding the regular allowance for research

students. Finally I thank Craig F. Bohren for peppering his textbooks with personality and dry wit –

a welcome respite from the otherwise typically bland offerings.

Statement of Contribution of the Student

The majority of the work described in this report relates to the construction of computer simulations

and data analysis, all of which I carried out independently. Numerous different computer code

components and routines were required to fulfil the goals of this project, all of which I wrote and

tested in MATLAB. Many of the calculations required are well established and therefore source

code, typically in FORTRAN, is available. Thus some of the routines and functions are essentially

ports of algorithms with the necessary modifications to suit the purposes of this study. The

microphysical and aerosol optical data used was obtained from the electronically available Global

Aerosol Data Set. The Australian relative humidity and radiation data were provided by the

Australian bureau of Meteorology via a custom extraction routine and delivered in raw ASCII

format.

Statement of Originality

I certify that this report contains work carried out by myself except where otherwise acknowledged.

Signed

Date: 20 October 2006

Table of Contents

1 INTRODUCTION................................................................................................................................................... 1

2 LITERATURE REVIEW....................................................................................................................................... 2

3 THEORETICAL BACKGROUND....................................................................................................................... 6

3.1 SOLAR RADIATION............................................................................................................................................ 6 3.2 SCATTERING..................................................................................................................................................... 7 3.3 MIE SCATTERING ............................................................................................................................................. 8

3.3.1 Theoretical formalism................................................................................................................................. 8 3.3.2 Mie Computation ........................................................................................................................................ 9

3.4 THE ROLE OF RELATIVE HUMIDITY ................................................................................................................. 10 3.5 ATMOSPHERIC AEROSOLS ............................................................................................................................... 11

3.5.1 Sources and production methods .............................................................................................................. 11 3.5.2 Size Distributions...................................................................................................................................... 12 3.5.3 Vertical Distributions................................................................................................................................ 13

4 MODELLING AND DATA ANALYSIS............................................................................................................. 14

4.1 CIRCUMSOLAR CALCULATIONS FROM MICROPHYSICAL PROPERTIES .............................................................. 14 4.1.1 Limitations and assumptions..................................................................................................................... 16

4.2 ANALYSIS OF AUSTRALIAN RELATIVE HUMIDITY & RADIATION DATA ......................................................... 17 4.2.1 Description of available data.................................................................................................................... 17 4.2.2 Filtering and merging............................................................................................................................... 18

4.3 COMBINING CIRCUMSOLAR MODEL WITH RELATIVE HUMIDITY & RADIATION DATA................................... 19

5 RESULTS AND DISCUSSION............................................................................................................................ 20

5.1 CSR CALCULATION RESULTS.......................................................................................................................... 20 5.1.1 Results compared with previous work ...................................................................................................... 22

5.2 DATA ANALYSIS RESULTS............................................................................................................................... 23 5.3 COMBINING LOCATION DATA WITH THE CIRCUMSOLAR MODEL...................................................................... 26

5.3.1 Comparison with previous results............................................................................................................. 30 5.4 PREDICTION OF VARIABLES ............................................................................................................................ 30

5.4.1 Relative Humidity ..................................................................................................................................... 30 5.4.2 Aerosols .................................................................................................................................................... 31

6 CONCLUSION...................................................................................................................................................... 32

6.1 SUMMARY OF WORK....................................................................................................................................... 32 6.1.1 Implications for Solar Energy................................................................................................................... 32 6.1.2 Future work .............................................................................................................................................. 33

7 REFERENCES...................................................................................................................................................... 34

8 APPENDICES ....................................................................................................................................................... 37

8.1 APPENDIX A: ADDITIONAL EQUATIONS ......................................................................................................... 37 8.1.1 Local Time to Solar Time calculation....................................................................................................... 37 8.1.2 Computation of the Mie coefficients ......................................................................................................... 37

8.2 APPENDIX C: ADDITIONAL FIGURES............................................................................................................... 39

1

1 Introduction

Two of the key issues facing the world today are energy supply and climate change (IPCC Third

Assessment Report, 2001). The historical and current over reliance on fossil fuels and their

associated carbon emissions are the primary cause of anthropogenically induced climate change. As

a result numerous alternative sources of energy are being increasingly deployed or are in

development in an attempt to reduce carbon emissions and consequently slow or halt the progress of

climate change. Even without the pressing issue of climate change, the finite nature of fossil fuels

means that a shift to sustainable energy sources in inevitable in the long term. Two of the promising

long term candidates are wind and solar, with wind already established as a mature industry in

many countries already. Solar energy has yet to make a significant contribution to global energy

production, however due to the massive solar resource it has the potential to become a fundamental

component in the future. Both of these technologies are dependent on local weather conditions at

the site where they are deployed, thus the suitability of a region or location requires prediction of

the solar or wind resource over the estimated life of the installation. It therefore becomes necessary

to consider the reciprocal relationship between energy supply and climate change in that changing

localized weather induced by climate change may alter the energy supply derived from solar and

wind based renewables. As yet this relationship has not been considered in detail however the

implications for the wind industry are starting to be recognized (Hewer, 2006).

Concentrating Solar Thermal (CST) systems, as opposed to photovoltaic systems, have the potential

to provide large scale electricity generation in locations with high insolation such as many parts of

Australia (Carpenter, Kemp, Robillard, & Whittaker, 1999). A variety of designs have been built or

are in the design stages; however the technology and industry needs to mature before large scale

investment and deployment is possible (Quaschning, 2004; Sims, 2004). CST systems exhibit two

important characteristics uniquely relating their performance to local weather. Firstly CST systems

radiate heat from their absorbers setting an operational flux threshold on the incident radiation

below which they do not function. Secondly due to the optics of the concentration only light

incident with a specific angular range reaches the absorber. As a result CST systems can only

harness the radiation from the sun’s direct beam and the diffuse radiation in a small angular range

around it. This radiation is significantly stronger than diffuse radiation at other directions due to its

production method, scattering by atmospheric aerosols, having a strong forward scattering bias.

Relative humidity, a meteorological parameter which has the potential to be modified by climate

change, can significantly alter atmospheric aerosol size distributions and consequently their

scattering characteristics. This report is an attempt to investigate the relationship between

circumsolar radiation and relative humidity in the context of CST systems.

2

2 Literature Review

Not a great amount of attention has been paid to the possibility of the insolation arriving at a

potential CST site changing despite the fact that long term behaviour of direct insolation is not well

understood (Lohmann, Schillings, Mayer, & Meyer, 2006). Volcanic eruptions have been shown to

reduce annual productivity of CST installations by 30% (Michalsky, Perez, Seals, & Ineichen,

1994) further emphasizing the sensitivity of such systems to atmospheric changes. CST designs

have calculated to be economically viable in regions which receive direct insolation above

1700kWh/m2/year (Carpenter et al., 1999). Reductions in this value may cause a previously

economically viable system to be rendered unsustainable, underscoring the need for accurate

predictions of solar radiation.

Terrestrial solar radiation is typically broken up into a direct beam and a diffuse component. The

diffuse component is radiation which arrives at a surface having undergone any process in the

atmosphere which modifies its original vector, whereas the direct beam has not suffered any such

modification. CST systems are often assumed to only utilize the direct beam due to their

concentrating optics. This is not strictly true as many designs have angular acceptance angles

substantially larger than the angular size of the solar disc (Rabl & Bendt, 1982). The situation is

further complicated by the fact that the apparatus most commonly employed to measure the direct

beam, the Normal Incidence Pyrheliometer (NIP), has an acceptance half angle of 2.5º which is ten

times that of the angular size of the sun (Jeys & Vant-Hull, 1976). This results in an overestimation

of the true direct beam due to the capture of a portion of the diffuse component surrounding the

solar disc by the NIP. Were the diffuse radiation evenly distributed across the sky this would only

produce a minor error in measurement. Uniformity in diffuse radiation is known not to be the case

and the region surrounding the solar disc contains significantly more intense radiation than the rest

of the sky. This region – which is typically defined to extend from the edge of the solar disc

(~0.25º) to the angular limit of a NIP (typically 2.5º-3.5º) – is referred to as the aureole and the

radiation contained therein as circumsolar radiation.

The primary cause of the increased intensity in the region of the aureole is the scattering of part of

the direct beam by aerosol particles. When the scattering particle is larger than the wavelength of

the incident light, the interaction can be treated with Mie theory (Bohren & Huffman., 1998). The

scattered radiation under this regime is heavily biased in the forward direction with the specific

distribution being determined by the size and refractive index of the particle in question and the

wavelength of the incident light.

3

The ratio of the circumsolar flux,c

Φ , to the circumsolar and direct beam flux, b

Φ , is a useful

parameter often employed when dealing with circumsolar radiation and referred to as the

circumsolar ratio (CSR)

c

b c

χΦ

=Φ + Φ

(2.1.1)

The first major empirical investigation into circumsolar radiation was performed by a team from the

Lawrence Berkeley National laboratories. Custom equipment recorded the angular distribution of

solar profiles between 1976 and 1981 at various sites in the United States (Noring, Grether, & Hunt,

1991). The data obtained is referred to at the Lawrence Berkeley Reduced Data Base (RDB) due to

the exclusion of certain profiles after data quality control procedures. The LRRDB has formed the

basis for numerous examinations of circumsolar radiation and its impact on CST systems. One of

the first and most general was an analysis by Rabl & Bendt (1982). From the LBRDB they

generated a standard synthetic brightness distribution and proposed a model which would determine

the long term effect of circumsolar radiation on a CST system given the site’s average circumsolar

ratio. Buie (2003) conducted further analysis of the LBRDB and proposed a more detailed empirical

model of the angular brightness distribution and similarly only required as input the average

circumsolar ratio from a particular site.

Investigations into the performance effects of circumsolar radiation on specific CSP systems have

been found them to be significant. Schubnell (1992b) for example concluded that excluding

circumsolar radiation resulted in a 10% reduction in mean concentration ratio of a parabolic

concentrator at the Paul Scherrer Institute. Buie & Monger (2004) explored the effects of

circumsolar radiation on a line axis Fresnel CST system and reveal them to be significant for a

depending on the location’s average CSR values, with a range between 0.02 and 0.2 considered.

Such high CSR values are not necessarily relevant when the threshold of the CST system included.

Rabl & Bendt's (1982) analysis of the LBRDB data showed that for the majority of locations

considering a threshold insolation value of 500W.m-2

, the average monthly circumsolar ratio was

typically between 0.01 and 0.03.

The work of Rabl & Bendt (1982) and Buie (2003) provides a valuable tool to optimize the design

of a CST system at a given site by requiring only measurements of the circumsolar ratio, which is

much simpler to obtain than direct measurement of angular solar distribution profiles. The empirical

4

nature of the studies however did not allow for the investigation into the effects that variation of

aerosol composition and distributions would have.

An early model which allowed the simulation of circumsolar radiation was developed by Thomalla,

Kopke, Muller, & Quenzel (1983). The formalism allowed the circumsolar radiation to be

calculated from supplied aerosol optical depths, which is useful for locations were detailed aerosol

optical data exist. Another model was developed by Monger (1996) which allowed the CSR to be

calculated for a given location. The results of a simulation of the average CSR behaviour in Sydney

agreed with empirical data from climatically similar sites in the LRRDB with an average CSR value

of 0.07. In order to estimate aerosol size distributions, the model employed the average monthly

relative humidity which combined with historical records of visual range was used to infer an

aerosol size distribution described by the modified gamma distribution. While the modified gamma

distribution can be fitted well to observed aerosol populations its parameters lack physical meaning

(d'Almeida, Koepke, & Shettle, 1991). The use of average monthly relative humidity may be

problematic as the relative humidity variation from day to day can be substantial. By relying on

historical visibility data, this method suffers from the lack of ability to generalize to a location

where such data are not available. Using visibility to indirectly infer aerosol size distributions may

also suffer from the subjective nature of such measurements. Due to the reliance on site specific

data both of these models do not facilitate more general simulations or variations to specific

parameters of an aerosol model.

A more generic model does exist in the form of the Simple Model of Atmospheric Radiative

Transfer (SMARTS2) (Gueymard, 2001). This software package allows a variety of atmospheric

input parameters to be specified providing a comprehensive tool for a various of applications

involving atmospheric radiative transfer. The SMARTS2 model was compared with other available

simple - as well as more rigorous - radiative transfer models and claimed to be one of the most

accurate (Gueymard, 2003a, 2003b). SMARTS2 incorporates atmospheric aerosols by employing

one of Shettle & Fenn's (1979) standard aerosol models. The CSR’s generated by using this model

are much smaller than values quoted and considered by other authors. Even for aerosol optical

depths up to 0.5 the CSR value produced using the rural aerosol model was below 0.01. Previous

work by the author investigating atmospheric turbidity in Canada reported small average calculated

circumsolar corrections of the order 0.005 (Gueymard & Garrison, 1998). Commenting on the

markedly smaller values obtained compared with analyses of the LBRDB and Monger's (1996)

calculations, the authors suggest that the higher CSR values are not representative of clear sky

conditions and were most likely contaminated by thin cloud. This dichotomy of opinion regarding

5

CSR values suggests that there is a substantial difference in the analytical and computational

techniques involved. As a result of this discrepancy, the use of the SMARTS2 model for

investigating circumsolar radiation is limited.

Investigations into circumsolar radiation have also been conducted with the opposite objective;

using measured values to infer information about the aerosol properties. Box, Lo, & McKellar

(1977) examined the possibility of determining atmospheric turbidity from CSR but found it

necessary to know the aerosol particle size distributions.

Prior work has established the strong effect relative humidity has on atmospheric aerosols. Hanel &

Zankl (1979) provided one of the first simple models for the effect. This work was incorporated by

Shettle & Fenn (1979) to provide one of the first relatively comprehensive standard models of

tropospheric aerosols. The model and data were refined and added to by d'Almeida et al. (1991) and

then again by Hess, Koepke, & Schult (1998) who made the latest data available electronically.

Empirical field studies which have investigated relative humidity and its effects on atmospheric

aerosols have shown the rapid increase in radius for relative humidity values beyond 70% (Day,

Malm, & Kreidenweis, 2000) with similar effects being found at other locations (Fitzgerald,

Hoppel, & Vietti, 1982; Randriamiarisoa et al., 2006). Simulations using standard aerosol models

have also produced results which are in agreement (Kay & Box, 2000). The Hanel & Zankl (1979)

model does not take into account the hysteresis effect of aerosol growth and shrinkage under

changing relative humidity conditions that has been experimentally observed (Randriamiarisoa et

al., 2006).

Aerosol compositions themselves are of course the primary cause of circumsolar radiation however

due to their short lifetime, long term forecasts are difficult and can change rapidly (Twomey, 1977).

Relative humidity which is the most important external factor in altering existing atmospheric

aerosol’s optical characteristics is a much more stable and irreversible – if not well understood –

factor. Long term relative humidity data is sparse (IPCC Third Assessment Report, 2001) and in

some cases older equipment has been unreliable on a large scale (Wijngaarden & Vincent, 2005);

however localized increasing trends have been observed (Power & Goyal, 2003) in some locations.

The majority of general circulation climate models produce results indicating increasing absolute

humidity while marinating constant relative humidity (Pierrehumbert, Brogniez, & Roca, 2005).

6

3 Theoretical Background

Before discussing the design and implementation of a circumsolar model, it is necessary to briefly

outline some of the theoretical concepts employed.

3.1 Solar radiation

Emission of radiation by the sun approximates that of an ideal blackbody at an effective

temperature of between 5600K and 6300K (Thomas & Stamnes, 1999). The intensity of the this

radiation at the top of the earth’s atmosphere is referred to as the solar constant despite the actual

value varying by 3.3%± due to orbital eccentricity. Estimates of mean values have differed by a

few 2/W m , with 2

0 1368 .I W m−= being a typical value (Gueymard, 2001). Rabl (1985) points out

that the range of estimates is an order of magnitude smaller than the typical uncertainties of

terrestrial insolation data. This is due to the variety and variability of modifications which are made

to incoming radiation as it traverses the atmosphere.

From radiative transfer theory light traversing a medium may be attenuated by two processes:

scattering and absorption. In the case of absorption the incident energy is removed and usually

translated into kinetic energy. Scattering on the other hand removes energy from the original path

but then re-radiates it, typically at an angle distinct from the original direction of propagation.

Treatment of radiative transfer in the earth’s atmosphere frequently approximates it as plane parallel

which is sufficiently accurate unless large solar zenith angles are considered.

The intensity of radiation after traversing the plane parallel atmosphere is described by the Beer-

Lambert-Bouguer law:

( ) ( )0 exp ( )I I m αα

λ λ τ λ

= − ∑ (3.1.1)

where 0I is the intensity at a particular wavelength at the top of the atmosphere, I is the intensity

after traversing the atmosphere, m is the relative airmass and ατ the optical depth due to a particular

atmospheric process α . In the plane parallel or slab approximation, the optical depths, ατ are

defined for light incident perpendicular to a slab of atmosphere (when the sun is at a local zenith).

For cases other than this, there is the need to incorporate the increased path length traversed; this is

achieved by employing the relative airmass, m. Geometrically the relative airmass correction is

simply the secant of the zenith angle, however at increasingly large zenith angles, the plane parallel

approximation breaks down and a correction factor is introduced to the relative airmass

7

( )( )

1

1.253

0.15cos

93.885m φ φ

φ

−

= + −

(3.1.2)

where φ is the solar zenith angle in degrees.

The different optical depth terms in (3.1.1) are due to a number of processes which may be grouped

according to the class of process they represent. Broadly they can be grouped as follows

0 R g aτ τ τ τ= + + (3.1.3)

where R

τ is due to Rayleigh scattering (primarily due to molecular oxygen and nitrogen), g

τ is due

to all gaseous absorption and a

τ due to aerosol absorption and scattering ( , ,a a abs a scatτ τ τ= + ).

In situations where the aerosol optical depth is small, it is possible to determine the intensity and

angular distribution of scattered radiation by employing the single scattering approximation. This

approximation is achieved by expanding (3.1.1) to first order. Neglecting the contribution of

Rayleigh scattering this can be written as

( )0 0exp( )s a a

I I m mF pτ τ θ= − (3.1.4)

where 0τ is the total optical depth, a

F the effectiveness factor and ( )p θ the phase function. The

phase function defines the angular distribution relative to the original direction of propagation. The

effectiveness factor which describes the altitude dependence can be set to unity to remove the

dependence. This simplification has been shown to be acceptable for calculations where θ is small

(Box et al., 1977)

3.2 Scattering

Both scattering and absorption will attenuate incident light and thus will be relevant to the

determination of the intensity and spectral composition of light arriving at the earth’s surface.

Scattering processes however will re-introduce the light they removed from the original beam and

this will contribute – to some extent - to the resultant radiation received at the surface.

Scattering of light in the atmosphere often assumes the scattering particles are homogenous spheres

which is typically not true however it is possible to assign a non-spherical scatterer an effective

radius. The use of effective scattering spheres is sufficiently accurate for scattering in close to the

forward direction but becomes less accurate at larger scattering angles (Bohren & Huffman., 1998).

8

Scattering by homogenous spheres is divided into two distinct regimes: situations where the

scatterer is larger than the wavelength of the incident light and those where it is smaller. The former

(and more fundamental) conditions require solving the electromagnetic equations for a sphere.

While this is a complex task it has been rigorously explored by a number of authors including

Gustav Mie whose name is synonymous with the type of scattering. In the latter case

approximations and simplifications can be made to the Mie solution and this regime is referred to as

Rayleigh scattering. Rayleigh scattering is typically isotropic and therefore only a small amount of

scattered radiation delivered close to the original direction of propagation. As a result Rayleigh

scattering has been neglected as a contributor to the circumsolar radiation. In contrast to Rayleigh

scattering, Mie scattering is not isotropic and typically has a strong forward bias.

3.3 Mie Scattering

3.3.1 Theoretical formalism

As previously alluded to, obtaining a solution in the Mie regime it is necessary to solve Maxwell’s

equations in a sphere. Inclusion of a full derivation is to lengthy to include here, however a brief

summary of the relevant equations is provided and the reader is referred to Bohren & Huffman

(1998) for a complete treatment.

Three key parameters obtained from a Mie calculation are: the scattering cross section, the

extinction cross section and the phase function. The scattering and extinction cross sections are

larger than the geometric cross section and the ratio of the two defines the scattering or extinction

efficiency 2

, , /e s e sQ C rπ= . The extinction cross section is the sum of the scattering and absorption

coefficientse s a

C C C= + . The scattering cross section is given by

( )( )2 2

21

22 1s n n

n

C n a bk

π ∞

=

= + +∑ (3.3.1)

where / 2 /k cω π λ= = is the angular wavenumber. The extinction cross section, which is the sum

of the scattering cross section and absorption cross section, is given by

( ) ( )2

1

22 1 Ree n n

n

C n a bk

π ∞

=

= + +∑ (3.3.2)

In both preceding equations n

a and n

b are the scattering coefficients defined by

( ) ( ) ( ) ( )( ) ( ) ( ) ( )

( ) ( ) ( ) ( )( ) ( ) ( ) ( )

' ' ' '

' ' ' '

n n n n n n n n

n n

n n n n n n n n

m mx x x mx mx x m x mxa b

m mx x x mx mx x m x mx

ψ ψ ψ ψ ψ ψ ψ ψ

ψ ξ ξ ψ ψ ξ ξ ψ

− −= =

− − (3.3.3)

9

where /p s

m m m= the ratio between the refractive index of the scattering particle and the medium is

located in, n

ψ and n

ξ are the Ricatti-Bessel functions and x is referred to as the size parameter and

is given by

2 /x rπ λ= (3.3.4)

where 0 /p

mλ λ= is the wavelength inside the scattering particle.

The angular distribution of the scattered radiation which is referred to as the phase function

( ) ( )2 211 22

p S Sθ = + (3.3.5)

where 1S and 2S are the scattering amplitudes

( )

( )( )

( )( )

( )1 2

1 1

2 1 2 1

1 1n n n n n n n n

n n

n nS a b S a b

n n n nπ τ τ π

∞ ∞

= =

+ += + = +

+ +∑ ∑ (3.3.6)

where n

a and n

b are same scattering coefficients defined in (3.3.3) and n

π and n

τ are the angle

dependent functions given by

( )( )

( )( )1 1

sin

n n

n n

P dP

d

θ θπ θ τ θ

θ θ= = (3.3.7)

where ( )1

nP θ is the associated Legendre polynomial.

3.3.2 Mie Computation

From the preceding equations is evident that computation of the scattering and extinction cross

sections and the phase function requires (3.3.3) and (3.3.7) to be determined. Both of these can be

calculated using their recursive properties. Upwards recursion of the angle dependent functions

(3.3.7) is stable and straightforward. Calculation of the scattering coefficients (3.3.3) to sufficient

accuracy can require a large number of terms and may introduce error. One of the common methods

is the utilization of a logarithmic derivative described in Bohren & Huffman (1998) and briefly

outlined in Appendix A. Although the theory is well established, alternative techniques to improve

accuracy or reduce computational time continue to be investigated (Du, 2004). Figure 3.1 shows the

result of some typical Mie calculations performed using a MATLAB implementation of Bohren &

Huffman's (1998) algorithm.

10

0 20 40 60 80 100 120 140 160 18010

-8

10-6

10-4

10-2

100

102

104

Scattering Angle [Degrees]

Inte

nsity [

arb

. units]

r=1.0 [µm] n=1.5+0.01i lamda=0.4[µm]

r=1.5 [µm] n=1.6+0.1i lamda=0.4[µm]

r=4.0 [µm] n=1.5+0.1i lamda=0.5[µm]

r=1.0 [µm] n=1.5+0.1i lamda=0.4[µm]

r=2.0 [µm] n=1.5+0.1i lamda=0.4[µm]

r=3.0 [µm] n=1.5+0.1i lamda=0.4[µm]

Figure 3.1 Example of an angular dependent scattering plot produced by the MATLAB code for six different

parameter sets with 300 steps between 0º-30º and 150 steps between 30º-180º.

3.4 The role of relative humidity

Relative humidity is defined (Bohren & Albrecht, 1998) for a given temperature as the ratio of

vapour pressure, e, to the saturation vapour pressure, es, (of vapour in equilibrium with a flat surface

of water) expressed as a percentage

( )/ 100%sf e e= (3.4.1)

The composition of the aerosol will determine how it reacts to changes in relative humidity.

Hydrophobic particles are not affected by relative humidity while those that are hygroscopic can

respond either in a monotonic or deliquescent manner. In addition hysteresis effects have been

observed for certain aerosol types (Randriamiarisoa et al., 2006). Such effects are not considered in

this work

For hygroscopic aerosols increasing relative humidity has a twofold effect; increasing its radius and

modifying its refractive index. The exact nature of the relationship between relative humidity and a

particular scattering particle depends its composition and has to be determined experimentally.

11

Results from a variety of studies and the functional relationships exhibited were integrated by Hanel

& Zankl (1979). The relationship between the radius of a particle and relative humidity is

( )( )

1/ 3

0

0

1w w

w

m ar a r

mρ

= +

(3.4.2)

where ρ is the particle density relative to water, ( )wm a is the mass of condensed water, 0m is the

dry mass of the particle and w

a the water activity which is the relative humidity corrected for the

curvature of the particle surface

2

exp Ww

W

Va f

R Tr

σ −=

(3.4.3)

where σ is the surface tension, W

V is the specific volume of water, W

R the specific gas constant for

water and T the absolute temperature.

Using the modified radius, the effective complex refractive index is determined by a volume

weighted average of the refractive indices of the dry particle material, 0n , and that of water, w

n

( )3

00

( )w w

w

rn n n n

r a

= + −

(3.4.4)

3.5 Atmospheric aerosols

As has been established in section 3.3, given the effective radius and refractive index of a sphere it

is possible to calculate its optical characteristics at a particular wavelength. Equipped with this

calculation tool it is then possible to determine the scattering characteristics of atmospheric aerosols

provided that their composition and size distributions are adequately described.

3.5.1 Sources and production methods

Atmospheric aerosols come from a variety of sources and production methods. The production

source will determine the chemical composition of the aerosol and as such the refractive index and

interaction properties with water vapour. It is the production mechanism which generally

determines the size distribution and number densities (d'Almeida et al., 1991).

12

Once aerosols have been produced they have finite residence times, which depend on a number of

factors. The production intensity and the rate at which the aerosols are removed will give rise to the

ambient aerosol conditions. In order to perform meaningful calculations which represent the

aerosols in the atmosphere a sufficient method to describe the size distribution of a particular

particle species is required.

3.5.2 Size Distributions

Atmospheric aerosols span a wide range of sizes, the distribution of which is crucial in describing

the bulk optical properties. Various methods have been employed in an attempt to characterize

aerosol size distributions. Three such models are the Junge power-law, modified gamma

distribution and the log-normal distribution. While the Junge power-law and modified gamma

distributions can be fitted to measured distributions the log-normal distribution is the most

appropriate choice when using an aerosol model consisting of distinct components each with

differing distributions (d'Almeida et al., 1991). The log-normal distribution is described by:

( )

( )

2

2

log log( )exp

(log ) 2 log( ) 2 log

iMi i

i i

r rdN r N

d r π σ σ

− = −

(3.5.1)

Where M

r is the modal radius, logi

σ is the standard deviation of log r . Using this description ,

distributions of particles from different sources, i, can be combined to give a total distribution:

( ) ( )

(log ) (log )

i

i

dN r dN r

d r d r=∑ (3.5.2)

Figure 3.2 illustrates the different log-normal size distributions of some of the standard components

for both 50% and 95% relative humidity. It should be noted that as the relative humidity increases,

it shifts the modal radius without modifying the spread of the distribution.

13

10-2

10-1

100

101

102

10-20

10-15

10-10

10-5

100

radius [µm]

Norm

aliz

ed N

um

ber

density d

N/d

log(r

) [c

m-3

]

Soot

Sea Salt (acc., 50% RH)

Sea Salt (acc., 95% RH)

Sea Salt (coa., 50% RH)

Sea Salt (coa., 95% RH)

Sulfate 50%

Sulfate 95%

Water Soluble 50%

Water Soluble 95%

Figure 3.2 A selection of some of the size distributions described by (d'Almeida, Koepke, & Shettle, 1991)

3.5.3 Vertical Distributions

In addition to describing the size distribution of aerosols, a description of how their total number

density varies with height is also required. The model employed describes the vertical total number

density of aerosols as decreasing exponentially with height.

( )( ) (0)exp /N h N h Z= − (3.5.3)

where N(0) is the number density at ground level, h is the height above ground and Z is a scale

height. It is also assumed that the size distribution of aerosols does not itself vary with height.

14

4 Modelling and data analysis

Three separate steps were undertaken to examine the effect of relative humidity on circumsolar

radiation. Firstly a model which allows the circumsolar flux to be calculated from microphysical

properties was constructed. Secondly relative humidity and radiation data were obtained for

geographic variety of Australian locations then suitably manipulated and analysed. Finally the

microphysical model was used in conjunction with the obtained data to simulate localized

circumsolar behaviour.

4.1 Circumsolar calculations from microphysical properties

Determining the scattered flux in an angular range requires both a theoretical framework to describe

atmospheric aerosols and data to describe specific models. One of the first models providing both

the framework and relevant data was developed by Shettle & Fenn (1979). Further refinement and

additions were made by d'Almeida et al. (1991) and then again by Hess et al. (1998) in the form of

the Global Aerosol Data Set (GADS). By utilizing the framework and data provided by the most

recent of the above mentioned works it was possible to develop a model to perform circumsolar

calculations for a variety of atmospheric aerosol conditions.

MATLAB was the environment used to construct the model due to the modular flexibility, useful

included functions and advanced graphing tools. The variety of calculation steps were broken up

into discrete functions with a various of driver scripts used to call relevant functions with the

appropriate parameters and if required plot the results.

Firstly a set of functions to perform Mie calculations and return the scattering coefficients and

phase function were written. These were based on the

Fortran code of Bohren & Albrecht (1998) and Box

(2004). The result of some single calculations

performed using this code is illustrated in Figure 3.1.

In the GADS each aerosol component is defined in

terms of its wavelength dependent refractive index and

its size distribution, using the log-normal description,

for a range of relative humilities. The effects of

relative humidity on size distribution was achieved

Table 4.1 Primary aerosol models employed as

input with their components and associated

mixing ratios.

Name Component Mixing Ratio

Continental

Clean

Insoluble

Water Soluble

1.00

5.77E-5

Desert Water Soluble

Mineral (Nuc.)

Mineral (Acc.)

Mineral (Coa.)

8.70E-1

1.17E-1

1.33E-2

6.17E-5

Maritime

Clean

Water Soluble

Sea Salt (Acc.)

Sea Salt (Coa.)

9.87E-1

1.32E-2

2.11E-6

15

using the Hanel & Zankl (1979) method

described in section 3.4. This allows Mie

calculations to be performed for each

wavelength and across the size range.

Subsequent integration over the size

distribution produces the extinction and

scattering coefficients and the phase function.

These values are then normalized to 1 particle

per cm3 so that they can be multiplied by a

specific number density to retrieve the

corresponding coefficients and phase functions.

The results of Mie calculations to high accuracy

were available for the aerosol components

described by the GADS alleviating the need

perform them for the standard component size

distributions.

Aerosol models are then defined by their

relative number mixing ratios which allow the

constituent components to be appropriately

weighted and combined. The primary models

employed, their components and corresponding

number mixing ratios are shown in Table 4.1.

Using the exponentially decreasing number

density model described in equation (3.5.3) the

aerosol optical depth and aerosol scattering

optical depth are found by integrating the

corresponding optical coefficients over the

height distribution.

The scattered intensity was then calculated using the single scattering approximation described by

equation (3.1.4) provided a total optical depth and extraterrestrial spectrum are available. The

extraterrestrial spectrum as well as gas and Rayleigh optical depths were generated from the

SMARTS2 model using a standard atmosphere with no aerosols. The water vapour optical depth

0 0.5 1 1.5 2 2.5 3 3.5 40

500

1000

1500

2000

2500

Wavelength [µm]

Irra

dia

nc

e [

kW

.m-2

. µm

- 1]

Extraterrestrial spectrum

Blackbody @ 5600 K

Terrestrial spectrum

Figure 4.1 The SMARTS2 generated extraterrestrial

spectrum, a blackbody emission profile and the terrestrial

spectrum after attenuation due to gaseous processes.

Relative Humidity %

Airm

ass

50 60 70 80 90

1

2

3

4

5

6 500

600

700

800

900

1000

Figure 4.2 The DNI without aerosols as a function of

relative humidity and relative airmass using a standard

atmosphere at a constant temperature of 27º

16

was calculated for a range of relative humidity values with the surface temperature fixed at a

reference value of 27ºC. The extraterrestrial spectrum, terrestrial spectrum (after gaseous extinction)

and reference blackbody curve are show in Figure 4.1. The decrease in DNI solely due to gaseous

extinction values used as a function of relative humidity and relative airmass is shown in Figure 4.2

For a given relative airmass, the resultant scattered radiation was calculated. Combining this with

the phase function and integrating over the angular range from the solar disc to the edge of the

aureole the magnitude of the circumsolar radiation was calculated.

4.1.1 Limitations and assumptions

This model contains some important limitations and assumptions: the GADS models and size

distributions are average values and not necessarily representative of local conditions and the single

scattering approximation is typically only valid for optical depths in the order of 0.4 (Box &

Deepak, 1978).

The MATLAB m files which constitute this model are available online from

http://www.physics.usyd.edu.au/~dscott/csr/

17

4.2 Analysis of Australian Relative Humidity & Radiation Data

Relative humidity and solar radiation data were obtained from the Australian Bureau of

Meteorology for nine of their recording stations: Alice Springs, Broome, Darwin, Geraldton,

Learmonth, Mildura, Rockhampton, Tennant Creek and Wagga Wagga. The locations and average

daily number of sunshine hours of the nine stations are shown in Figure 4.3

Figure 4.3 Annual average sunshine hours from the Bureau of Meteorology and the location of stations where

relative humidity data was obtained.

The choice of stations was primarily determined by those where half hourly direct normal insolation

data were available. The nine locations are also geographically distinct and are subject to differing

weather patterns making for a good cross section of conditions.

4.2.1 Description of available data

The relative humidity data consisted of two measurements per day taken at 09:00 and 15:00 (local

time) and were available as far back as at least 1976 for all sites and further for others.

Detailed solar radiation measurements began in 1999 for all stations except Darwin which began in

recording in 2001. The direct normal insolation was measured by a pyrheliometer mounted on a

solar tracker with an acceptance half angle of 2.5º. Direct radiation data were supplied in MJ.m-2

for

18

a half hour period, with the end of the period specified in local solar time. In addition to the half

hourly data, the total daily direct energy was supplied.

There were gaps in both the relative humidity and radiation data due to a variety of causes, from

equipment malfunctions to maintenance.

4.2.2 Filtering and merging

It was assumed that the direct energy delivered over each half an hour was constant allowing the

instantaneous DNI value to be retrieved. This assumption may be contaminated due to transient

cloud cover and during mornings and evenings when the DNI value changes rapidly. In order to

compare direct radiation and relative humidity it was necessary to match solar time to local time

and select the closest half hour DNI value. For sites in states where daylight saving is observed

(Mildura and Wagga Wagga) this had to be corrected for. Then using the coordinates of each site,

the local time was converted to solar time using the algorithm of Rabl (1985), which is included in

Appendix A, and the closest matching DNI value was selected.

Utilizing the 9am relative humidity measurement presents some problems. As the measurement is

taken at 9am local time this will shift significantly closer to dawn and as such the corresponding

DNI measurement will experience a much larger relative airmass. The 3pm measurement, while

also experiencing variations in comparison to solar time over the course of the year will tend to be

more stable as the corresponding relative airmass variation is smaller. To illustrate; the relative

airmass corresponding to the morning measurement at Mildura ranged between 1.5 and 4.3 over the

course of the year compared with 1.1 and 2.6 for the afternoon measurement. The variation was

smaller at the sites which did not employ daylight savings. Calculations were therefore conducted

primarily using the 3pm reading.

The relative airmass corresponding to the two daily measurements at 09:00 and 15:00 local time

was calculated and added to the data. This was achieved by employing a MATLAB implementation

of the PSA algorithm (Blanco-Muriel, Alarcon-Padilla, Lopez-Moratalla, & Lara-Coira, 2001) for

calculating the solar vector and equation (3.1.2) to retrieve the corresponding relative airmass.

19

4.3 Combining Circumsolar Model with Relative Humidity & Radiation Data

The circumsolar model section 4.1 was adapted to allow the DNI, relative humidity and relative

airmass data from a particular site to be used as part of the input parameters to calculate the CSR,

the circumsolar intensity and the true beam intensity. The circumsolar model also requires an

aerosol model, total number density and gaseous optical depths to perform the calculations. The

choice of aerosol model could be arbitrarily selected and was typically selected dictated based on

the geographic location with a range of total number densities explored. This is an important

assumption as most locations will experience variation in aerosol loading which will likely result in

an overestimate of circumsolar radiation at high DNI as such measurements may correspond to low

aerosol loads. The gaseous optical depths were fixed using the standard atmosphere described in

section 4.1 with the exception of the water vapour which varied according to the measured relative

humidity and a reference temperature of 27ºC. This approximation will also introduce error as

gaseous optical depths can vary depending on location and time of year and the water vapour

present will depend on the site temperature. This simplification; however will still serve to

characterize the energy distribution of the solar spectrum after gaseous extinction.

As calculations were performed for a single time each day, the results are not necessarily

representative for the entire day.

A driver was written to perform the above integration with the inclusion of the ability calculate

include operational thresholds and to calculate average CSR, average power loss due to exclusion of

the circumsolar radiation.

20

5 Results and Discussion

5.1 CSR calculation results

The angular distribution of circumsolar radiation within the aureole is particularly relevant to CST

systems with acceptance half angles within the 0.25º to 2.5º range due to the typical acceptance half

angle of a NIP, therefore this angular range was considered. Figure 5.1 illustrates the nature of this

angular distribution and its variation depending on the aerosol model employed at a relative

humidity value of 50%. The maritime clean model exhibits the flattest distribution, followed by the

continental and urban models which have similar water soluble to insoluble component mixing

ratios. The desert model yields the most extreme variation across the aureole largely due to the

amount of large particles it contains.

0 0.5 1 1.5 2 2.50

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

Scattering Angle [degrees]

I s/I

b [

Sr-1

]

Continental Clean (2600cm-3) CSR:0.009 Ib 897W.m-2

Continental Average (15300cm-3) CSR:0.023 Ib 841W.m-2

Continental Polluted (50000cm-3) CSR:0.040 Ib 738W.m-2

Urban (158000cm-3) CSR:0.080 Ib 579W.m-2

Desert (1400cm-3) CSR:0.078 Ib 754W.m-2

Maritime clean (1520cm-3) CSR:0.021 Ib 865W.m-2

Figure 5.1 The angular distribution of intensity within the aureole and corresponding CSR values for six

standard models at typical number densities. Relative airmass and relative humidity are constant across models

at 1.5 and 50% respectively.

The shape of the aureole angular profile is markedly different between models when the relative

humidity is varied. This can clearly be seen in Figure 5.2 where a distinct difference between the

how the angular profile differs under increasing relative humidity for the continental clean and

maritime clean models is evident. As the relative humidity is increased the clean continental model

flattens its circumsolar distribution, whereas the maritime clean model shifts its distribution closer

to the small angle range. This difference can be explained by the differing dominant hygroscopic

component in each model. In the continental clean model the hygroscopic component is the generic

water soluble type with a dry modal radius of 0.021 mµ ; much smaller than the shortest wavelengths

21

of the solar spectrum. As a result a majority of

these particles will act as Rayleigh scatterers. As

the relative humidity is increased, the modal radius

is increased leading to more particles acting as Mie

scatterers. These particles that have transitioned

from Rayleigh to Mie scatterers will still be in the

lower Mie regime size limit and thus the forward

bias will not be as strong as larger Mie scatterers.

In contrast the maritime clean model has two

hygroscopic components, both with modal radii

larger than the minimum solar spectrum

wavelength. An increase in modal radius will

therefore increase the size of the majority of

particles already acting as Mie scatterers resulting

in a stronger forward bias. The desert model

exhibits only a small variation in its aureole

distribution due its largely insoluble composition

Figure 5.3 illustrates the behaviour of the

calculated CSR for the continental clean, maritime

clean and desert models as a function of total

number density and relative humidity. The

continental clean model exhibits a broader

dependence on relative humidity than the sharp

increase exhibited by the maritime model at high

relative humidity values. The desert model shows

only a minor dependence on relative humidity again due to its small hygroscopic component. The

CSR values for both the continental clean and maritime clean remain relatively small even as the

total number density is increased, provided that the relative humidity is below 70%. In contrast the

CSR value rapidly increases with number density in the case of the desert model.

0.5 1 1.5 2 2.510

-3

10-2

10-1

I s/I

b [

Sr-1

]

(a) Continental Clean

50%RH70%RH80%RH

90%RH95%RH98%RH99%RH

0.5 1 1.5 2 2.510

-3

10-2

10-1

100

Scattering Angle [degrees]

I s/I

b [

Sr-1

]

(b) Maritime Clean

Figure 5.2 The effect of relative humidity on the

angular distribution of aureole intensity for (a) the

continental clean model and (b) the maritime clean

model.

22

Re

lati

ve

Hu

mid

ity

[%

](a) Continental Clean

1000 2000 3000 4000 5000 600050

60

70

80

90

0.01

0.02

0.03

0.04

0.05

(b) Maritime Clean

1000 2000 300050

60

70

80

90

0.05

0.1

0.15

0.2

0.25

0.3

0.35

(c) Desert

1000 2000 300050

60

70

80

90

0.05

0.1

0.15

0.2

Total Number density [cm

-3]

Figure 5.3 CSR as a function of number density and relative humidity for three models (a) continental clean, (b)

maritime clean and (c) desert. Relative airmass is fixed at 1.5. Note that the CSR colour mapping is not uniform across

the figures.

5.1.1 Results compared with previous work

The SMARTS2 (Gueymard, 2001) model is a multipurpose software utility for which performs a

wide variety of calculations related to radiative transfer in the atmosphere. Early versions did not

consider circumsolar radiation however more recent revisions of the software introduce the option

to correct this. Running the model using the Shettle & Fenn (1979) rural aerosol model produces a

maximum correction due to circumsolar radiation of 1% for aerosol optical depths as high as 0.5.

Analysis of the SMARTS2 source code revealed the method of calculating the circumsolar

correction to the direct beam employed parameterized phase functions are defined for angles up to

10º by

( )2

1

a b cp

d

θ θθ

θ

+ +=

+ (5.1.1)

where a, b, c and d are constants derived from a MODTRAN simulation for particular wavelengths

and relative humidity values. SMARTS2 contains 20 sets of constants corresponding to five

wavelengths (0.3, 0.55, 0.694, 1.06 and 1.536 mµ ) and four values of relative humidity (0, 70, 80,

99 %) which select from a combination of 26 standard phase functions. Any intermediate values,

either for wavelength or relative humidity are arrived at via interpolation. While this approach may

yield usable results for the majority of applications, it would appear too coarse for an investigation

specifically into circumsolar radiation. It is thus difficult to ascertain where the discrepancy comes

in as the parameters used to run the MODTRAN results are unknown; however the strongly peaked

phase functions suggest the dominance of larger aerosols.

23

5.2 Data analysis results

Initial analyses were conducted on the relative humidity data in an attempt to detect long term

trends or patterns. Compiling annual averages over the years for which data existed for each

location produced no evidence of coherent trends. The inter-annual variability was typically in the

range of 20%, decreasing for those stations with higher average annual relative humidity values, a

plot of which is included in the appendix. Combining the monthly averages for all sites across the

years for which data were available provides a reasonable approximation of the annual relative

humidity behaviour of a particular site and is illustrated in Figure 5.4. The different sites exhibit

substantially different relative humidity profiles with Alice Springs, Learmonth, Geraldton, Mildura

and Wagga Wagga peaking in the winter months; Broome and Darwin and to a lesser extend

Tennant Creek and Rockhampton peaking in the summer months.

20

30

40

50

60

70

80

1 2 3 4 5 6 7 8 9 10 11 12

Month

Rela

tive H

um

idit

y

Alice Springs

Broome

Darwin

Geraldton

Learmonth

Mildura

Rockhampton

Tennant Creek

Wagga Wagga

Figure 5.4 Historical monthly average humidity values for all stations from 1976-2005.

With respect to solar energy those regions where relative humidity is high in summer have the

greatest potential to suffer performance losses from aerosol effects associated with increased

relative humidity.

The relationship between total daily DNI energy arriving at a site was examined for all sites by

sorting the sample days by DNI magnitude and plotting the corresponding daily relative humidity

value. Plots for three contrasting sites are shown in Figure 5.5. The other sites not shown exhibited

qualitatively similar relationships.

24

0

10

20

30

40

50

60

70

80

90

100

1 89 177 265 353 441 529 617 705 793 881 969 1057 1145 1233 1321 1409 1497 1585 1673 1761 1849 1937 2025 2113 2201

Sample Day

Re

lati

ve

Hu

mid

ity

(%

)

0

5

10

15

20

25

30

35

40

45

50

To

tal

Da

ily

DN

I (M

J.m

^-2

)

Alice Springs EnergyLearmonth EnergyWagga Wagga EnergyAlice Springs Avg. RHLearmonth Avg. RHWagga Wagga Avg. RH

Figure 5.5 Daily average DNI energy for Alice Springs, Learmonth and Wagga Wagga in increasing magnitude

with corresponding relative humidity (light shading) and moving average thereof.

It is clear that an inverse relationship between DNI and relative humidity exists. The dominant

cause of this relationship is most likely the increasing cloud cover and cloud optical thickness

associated with increasing relative humidity.

While a good marker of long term trends, the total daily DNI energy does not allow for

instantaneous effects on collector performance to be assessed. As outlined earlier; many CST

systems require a minimum DNI value to operate. Therefore at times when the DNI is less than the

operational threshold of a particular system, the relative humidity is of little concern. As the

simulations in section 5.1 clearly showed, when the relative humidity increases to values above

70% the effects on aerosols and consequently the bulk scattering behaviour of the atmosphere is

significantly altered. It is therefore important to determine how likely conditions where the DNI

threshold of a CST system is met and the local relative humidity is sufficiently high to modify

scattering behaviour. The percentage of samples when the afternoon relative humidity measurement

was above a particular value and the corresponding DNI measurement was also above a threshold

value is illustrated for three contrasting sites: Wagga Wagga, Broome and Tennant Creek, and is

shown in Figure 5.6.

25

Results for all sites at two different DNI and relative

humidity thresholds are summarised in Table 5.1. It is

immediately clear that even with a low threshold of

300W.m-2

only a small percentage of the sample

measurements occurred concurrent to relative humidity

values beyond 70% .For values beyond 90%, the

majority of locations did not experience any such

conditions. For an increased threshold this pattern is

repeated with further reductions. Darwin and Learmonth

are notable exceptions with a significant percentage of

measurements above the threshold experiencing

simultaneously high relative humidity conditions.

Broome also exhibits to a lesser extent these conditions

however in contrast to Darwin and Learmonth the

fraction drops to zero for relative humidity values above

90%.

These results are significant in that they illustrate

that when considering the threshold of CST systems the

relevance of the enhanced aerosol modifications which occur above 70%RH are only applicable to a

small fraction of days per year.

Rela

tivity h

um

idity (

%)

(a)

0 200 400 600 800 10000

10

20

30

40

50

60

70

80

90

10 20 30 40 50 60 70 80

Rela

tivity h

um

idity (

%)

(b)

0 200 400 600 800 10000

10

20

30

40

50

60

70

80

90

DNI Threshold (W.m-2)

Rela

tivity h

um

idity (

%)

(c)

0 200 400 600 800 10000

10

20

30

40

50

60

70

80

90

Figure 5.6 Percentage of sample days where the

direct insolation is above a threshold value and

above a relative humidity value for (a) Wagga

Wagga (b) Broome and (c) Tennant Creek.

Table 5.1 The percentage of daily measurements when

both the 15:00 DNI and corresponding relative humidity

is greater than a threshold value.

DNI

Threshold

300 Wm-2

DNI Threshold

500 Wm-2

Location To

tal

da

ys

da

ta

70% 90% 70% 90%

Alice Springs 2290 0.04 0.00 0.00 0.00

Broome 2297 5.88 0.00 4.79 0.00

Darwin 1335 4.49 0.75 3.37 0.52

Geraldton 2078 1.78 0.10 0.96 0.00

Learmonth 1860 3.44 0.65 3.33 0.65

Mildura 2233 0.76 0.00 0.54 0.00

Rockhampton 1932 0.21 0.00 0.05 0.00

Tennant Creek 2219 0.36 0.00 0.18 0.00

Wagga Wagga 2466 1.54 0.08 0.81 0.04

26

5.3 Combining location data with the circumsolar model

Application of the circumsolar model to site data was performed across all sites, using aerosol

models relevant to the particular site across a range of number densities. Figure 5.7 illustrates the

relationship between CSR and relative humidity for three sites and the difference that the inclusion

of a threshold DNI has.

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

1 501 1001 1501 2001

0

10

20

30

40

50

60

70

80

90

100

0

0.005

0.01

0.015

0.02

0.025

1 501 1001

0

10

20

30

40

50

60

70

80

90

100

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

1 501 1001 1501 2001

0

10

20

30

40

50

60

70

80

90

100

0

0.05

0.1

0.15

0.2

0.25

0.3

1 501 1001 1501 2001

0

10

20

30

40

50

60

70

80

90

100

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

1 501 1001 1501

0

10

20

30

40

50

60

70

80

90

100

0

0.01

0.02

0.03

0.04

0.05

0.06

1 501 1001

0

10

20

30

40

50

60

70

80

90

100

Figure 5.7 Relative humidity and corresponding CSR for three sites both with (right hand figures) and without

(left hand figures) a 500W.m-2

threshold considered. (a) & (b) Wagga Wagga (continental clean 2600 cm-3

); (c) &

(d) Tennant Creek (continental clean 1500 cm-3

) and (e) & (f) Geraldton (maritime 1500 cm-3

)

(a) (b)

(c) (d)

(e) (f)

CS

R

CS

R

CS

R

Rela

tive H

um

idity

Rela

tive H

um

idity

Rela

tive H

um

idity

CSR RH

27

Figure 5.7 shows the expected overall increase in CSR with increasing relative humidity and a

rapid increase when relative humidity passes 70% for all of the sites. Comparing Wagga Wagga’s

profile with and without inclusion of a threshold shows the exclusion of the majority of high

relative humidity values; however a CSR increase across the relative humidity mid range is

preserved. In contrast Tenant Creek exhibits a weaker correspondence and a much greater reduction

in the average magnitude when the threshold is considered.

Figure 5.8 on the following page shows the calculated circumsolar and direct beam

intensities for three sites; Alice Springs, Mildura and Learmonth. The desert model at two different

number densities was applied to Alice Springs, the continental clean to Mildura and both maritime

clean and continental clean to Learmonth. The circumsolar intensity for Alice Springs under the

desert model tends to peak along the upper range of direct beam values. The results from Mildura

under the continental clean model exhibits some important characteristics. The direct beam intensity

increases in an approximately linear fashion with the circumsolar intensity peaking at a direct beam

value of approximately 500W.m-2

, a typical CST threshold. Noting that a system which has an

acceptance half angle close to that of the angular size of the solar disc will exclude this circumsolar

radiation the possibility exists that the exclusion will result in the radiation received being under the

system threshold rendering it inoperable. Learmonth under a maritime clean model exhibits a

relatively constant circumsolar intensity profile, corresponding to its almost flat high insolation

plateau. Applying the continental clean model to Learmonth produces similar results.

Table 5.2 summarizes the effects of considering a threshold value of 500W.m2 for all sites

employing a variety of models and differing number densities. The resultant average CSR value,

average DNI reduction between systems accepting the circumsolar radiation and those that do not

and the number of days per year where systems accepting the circumsolar radiation would be above

the threshold and those that do not below it, are shown. Employing the continental clean model for

all sites shows average CSR’s typically below 0.02 even for high number densities. With the

exception of the desert model, the maximum number of days per year where the acceptance of

circumsolar radiation would determine if the operational threshold was met was 4.1 for Darwin. The

simulations based on the desert model show elevated effects, however it is likely that the number

densities will be significantly lower than those employed over a large timescale.

It should be emphasized that these results correspond to single measurements in the

afternoon at varying local solar times (due to the relative humidity measurements being taken at

local time, as discussed previously) therefore are not necessarily representative of the entire day.

The effects of falling below the threshold are potentially more complex than simply the

cessation of system operation due to the performance degradation experienced by many CST

systems during transient conditions.

28

0 500 1000 1500 2000 25000

5

10

15

20

I circum

sola

r [W

m-2

]

0 500 1000 1500 2000 25000

200

400

600

800

1000

(a)

0 500 1000 1500 2000 25000

10

20

30

40

50

60

0 500 1000 1500 2000 25000

200

400

600

800

1000

I beam

[W

m-2

]

(b)

0 500 1000 1500 2000 25000

1

2

3

4

5

6

I circum

sola

r [W

m-2

]

0 500 1000 1500 2000 25000

200

400

600

800

1000

(c)

0 500 1000 1500 2000 25000

2

4

6

8

10

12

0 500 1000 1500 2000 25000

200

400

600

800

1000

I beam

[W

m-2

]

(d)

0 500 1000 1500 20000

50

100

150

200

I circum

sola

r [W

m-2

]

0 500 1000 1500 20000

200

400

600

800

1000

(e)

0 500 1000 1500 20000

50

100

150

200

250

0 500 1000 1500 20000

200

400

600

800

1000

I beam [W

m-2

]

(f)

0 500 1000 1500 20000

5

10

15

20

25

30

I circum

sola

r [W

m-2

]

0 500 1000 1500 20000

200

400

600

800

1000

(g)

0 500 1000 1500 20000

5

10

15

20

25

30

35

0 500 1000 1500 20000

200

400

600

800

1000

I beam

[W

m-2

]

(g)

Figure 5.8 Circumsolar [red] and beam [blue] intensities for Alice Springs Desert model at (a) 300cm

-3 and (b)

900 cm-3

; Mildura clean continental model at (c) 1500 cm-3

and (d) 3500 cm-3

; Learmonth maritime clean model

at (e) 1500 cm-3

and (f) 2000 cm-3

; and Learmonth continental clean model at (g) 2600 cm-3

and (h) 3500 cm-3

.

29

Table 5.2 Average values for all sites using site relevant models and a range of number densities. A threshold

value of 500 W.m-2

was used for all calculations.

Location Av

era

ge

CS

R

Av

g.

DN

I

red

uct

ion

(W

.m-2)

Sa

mp

les

un

der

thre

sho

ld (

da

ys/

yr)

Av

era

ge

CS

R

Av

g.

DN

I

red

uct

ion

(W

.m-2)

Sa

mp

les

un

der

thre

sho

ld (

da

ys/

yr)

Av

era

ge

CS

R

Av

g.

DN

I

red

uct

ion

(W

.m-2)

Sa

mp

les

un

der

thre

sho

ld (

da

ys/

yr)

Continental Clean

1500 cm-3

2600 cm-3

3500 cm-3

Alice Springs 0.004 3.56 0.16 0.007 6.15 0.32 0.010 8.25 0.32

Broome 0.005 4.43 0.32 0.009 7.64 0.48 0.013 10.24 0.79

Darwin 0.004 3.12 0.82 0.008 5.38 1.09 0.010 7.22 1.64

Geraldton 0.005 4.27 0.00 0.009 7.37 0.53 0.012 9.88 0.70

Learmonth 0.005 4.04 0.39 0.008 6.98 0.78 0.011 9.35 0.78

Mildura 0.004 3.16 1.63 0.007 5.46 2.12 0.010 7.32 2.94

Rockhampton 0.005 4.20 0.94 0.009 7.25 1.51 0.012 9.72 1.70

Tennant Creek 0.004 3.31 0.49 0.007 5.72 0.99 0.009 7.67 0.99

Wagga Wagga 0.005 3.85 0.89 0.009 6.63 1.48 0.012 8.89 2.07

Desert

300 cm-3

900 cm-3

1500 cm-3

Tennant Creek 0.016 13.35 1.64 0.049 39.73 4.28 0.08 65.76 7.40

Wagga Wagga 0.019 14.33 3.11 0.056 42.38 8.44 0.09 69.32 19.39

Maritime Clean

1000 cm-3

1500 cm-3

2000 cm-3

Broome 0.014 11.72 0.95 0.022 17.54 1.43 0.029 23.34 1.91

Darwin 0.012 8.27 1.91 0.018 12.39 3.01 0.023 16.50 4.10

Geraldton 0.013 10.95 0.88 0.020 16.38 1.23 0.027 21.80 1.76

Learmonth 0.011 9.42 0.78 0.017 14.10 1.18 0.022 18.76 1.57

Rockhampton 0.012 9.70 1.70 0.018 14.53 1.89 0.025 19.35 3.59

Overall the results of this simulation indicate that the effects due to the inclusion or

exclusion of the circumsolar radiation will be small, yet non-negligible when averaged over the life

of a particular system. Coastal locations with a significant maritime aerosol component exhibit the

greatest effect.

30

5.3.1 Comparison with previous results

Previous experimental and simulation based investigations into circumsolar radiation and its impact

on CST systems considered average site CSR’s well beyond the 1-2% obtained in the above

simulation. Monger's (1996) model predicted an average CSR for Sydney, Australia of 0.0703.

Buie's 2003 analysis of the LBRDB data and subsequent calculations included CSR values up to

0.8. In both of the above mentioned works the large CSR values considered are most likely a result

of including CSR’s where the intensity is below the operational thresholds of many CST systems. In

Buie's (2003) analysis of the LBRDB data the criteria for a clear sky scan was that it could not

increase radially

( ) 0d

dφ θ

θ< (5.3.1)

allowing the inclusion of low intensity scans. An earlier analyses of the LBRDB by Rabl & Bendt

(1982) employed a threshold insolation value to filter the CSR data. For a 300W.m-2

threshold the

average monthly CSR values were typically between 0.02 and 0.05 with a few specific months at

one location reaching 0.1. Employing a 500W.m-2

threshold the majority of average monthly CSR

values fell to between 0.01 and 0.03 similar to the results obtained by the current simulation

5.4 Prediction of variables

5.4.1 Relative Humidity

Historical investigations have shown changing trends in relative humidity. Wijngaarden & Vincent

(2005) for example described a decrease in relative humidity in western Canada between 1953 and

2003, however the magnitude of the decrease had to be revised due the later discovered systematic

error introduced by the installation of new instrumentation by the Canadian Weather Bureau.

There is a general consensus the global temperature is set to rise however the magnitude of the

change is the subject of much debate and ranges from an increase of 1 degree to 7 degrees by the

end of the century (IPCC Third Assessment Report, 2001). This temperature increase will cause

increased evaporation from open bodies of water, however it will simultaneously increase the

saturation vapour pressure thus not necessarily leading to an increase in relative humidity

(Pierrehumbert et al., 2005).Models have however predicted drops in the relative humidity, albeit in

the upper troposphere as the surface temperature rises (Minschwaner & Dessler, 2004). While

global relative humidity may remain constant, climate change has the potential to drive localized

changes in weather patterns and thus alter both the average local relative humidity and its temporal

profile.

31

5.4.2 Aerosols

Due to the short lifetime of tropospheric aerosols, the diversity and variability of production

sources, long term prediction is extremely difficult. Anthropogenically produced aerosols, such as

sulphurous or soot particles from biomass and fossil fuel burning are within human control. This is

illustrated by the apparent reversal of the so called “global dimming” effect - the term given to the

decreasing trend in the amount of global solar radiation - when pollution controls were imposed in

the United States and Europe (Stanhill & Cohen, 2001). Another concerning, for solar energy at

least, and remotely plausible anthropogenic aerosol source is a result of a drastic plan to reduce

global warming. The idea entails the injection of sulphurous particles into the stratosphere to

increase Earth’s albedo (Crutzen, 2006). This would have disastrous effects for solar energy as was

evidenced by the 30% drop in output from the SEGS facility in Southern California after the

eruption of Mt. Pinatubo which injected a large amount of sulphur dioxide into the atmosphere

(Michalsky et al., 1994).

Aerosols derived from natural processes are potentially more variable and uncontrollable however it

is possible to speculate on the changes to naturally derived aerosols due to climate change.

Increasing the temperature will inject additional energy into the atmosphere which may result in

localized increases in wind velocity; a key determinant in the production of both terrestrial and

maritime aerosols. Increased desertification will expose more bare earth from which additional

aerosols may be produced. A combination of both increased desertification and increased wind

velocity could potentially have a substantial impact.

32

6 Conclusion

6.1.1 Summary of work

Previous investigations have illustrated that the amount of energy contained in the solar aureole is

both significant to CST systems and highly variable. The distribution and magnitude of the

circumsolar radiation depends the prevailing aerosol types and distributions. From the well

understood impact that relative humidity has on hygroscopic aerosol size distributions a model was

constructed to in order to investigate the relationship between circumsolar radiation and relative

humidity. Results showed that as expected high relative humidity significantly enhanced the amount

of circumsolar radiation, however the angular distribution within the aureole was highly dependent

on the aerosol model employed. The modelled distribution of circumsolar radiation was

significantly different from the SMARTS2 model, attributed to the highly forward peaked phase

functions it employed.

In order to assess the relevance of the calculated changes induced by modifications to relative

humidity, measured data from geographically and climatically distinct sites around Australia were

obtained. This data were appropriately manipulated, filtered and analysed. In conjunction with the

resultant data, the previously developed calculations were applied. It was found that at the majority

of locations, the effects of high values of relative humidity would have a minimal impact due to the

fact that during conditions of high DNI relative humidity was rarely above the critical value of 70%

- the value beyond which aerosol optical characteristics are significantly altered. It was evident

from the data supplied that at all locations there is an approximately inverse relationship between

relative humidity and DNI which is most likely due to its effect on cloud conditions.

6.1.2 Implications for Solar Energy

Assessment of the projected long term solar resource available at the proposed site of a CST system

is of utmost importance, both from a design choice and optimization perspective as well as an

economic one. For highly concentrating systems with acceptance half angles less than 2.5º this

assessment needs to take circumsolar radiation into account for two reasons. Firstly the majority of

direct beam data collected is done so using NIP’s with acceptance half angles between 2.5º and 3.5º

leading to a potential overestimate of available DNI from historical data. Secondly even if

historically accurate descriptions of the circumsolar radiation are available the system will be

sensitive to potential future variations.

33

The modelling and analysis described in this report suggests while high relative humidity does

significantly alter the aerosol size distribution and consequently the circumsolar radiation,

conditions where this would occur concurrent to operation of a CST system are rare, at least in the

Australian locations assessed. In situations where such conditions do prevail the aerosol type and

size distribution produce marked differences. Maritime derived aerosols, relevant for potential

coastal sites, exhibit a much tighter distribution around the solar disc under high relative humidity

conditions compared with continental aerosols.

6.1.3 Future work

It would be useful to further investigate the interaction between relative humidity and circumsolar

radiation by using more specific data about the aerosol composition of a particular site. This would

allow some of the assumptions employed in the current analysis to be avoided leading to more

accurate results. Another method of further investigation would be to combine detailed circumsolar

scans at a particular location with simultaneous measurements of relative humidity at sufficiently

small time intervals so as to allow daily variation to be considered.

The focus for CST related circumsolar radiation assessment should be on the measurement and

prediction of the specific aerosol cycles prevailing at a location. Relative humidity, while

contributing a non-negligible effect on circumsolar radiation, is likely to have its greatest effect on

the nature and frequency of clouds which will be significantly more important on the overall system

performance.

34

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37

8 Appendices

8.1 Appendix A: Additional Equations

8.1.1 Local Time to Solar Time calculation

Based on the details given in (Rabl, 1985) the change from the local time to the local solar time is

given by

4* ( )LSTM L

T EoTθ θ∆ = − + (8.1.1)

where EoT is the equation of time given by

9.87sin(2 ) 7.53cos( ) 1.5sin( )n n n

EoT B B B= − − (8.1.2)

where

360

( 81)364

nB N= − (8.1.3)

where N is the day number since January 1 of that year.

8.1.2 Computation of the Mie coefficients

One widely used approach (Bohren & Huffman., 1998) for calculating the Mie coefficients involves

the introduction of a logarithmic derivative:

( ) ( )lnn n

dD

dρ ψ ρ

ρ= (8.1.4)

Which allows the Mie coefficients (3.3.3) to be rewritten as

( ) ( ) ( )( ) ( ) ( )

( ) ( ) ( )( ) ( ) ( )

1

1

1

1

/ /

/ /

/ /

/ /

n n n

n

n n n

n n n

n

n n n

D mx m n x x xa

D mx m n x x x

mD mx m n x x xb

mD mx m n x x x

ψ ψ

ξ ξ

ψ ψ

ξ ξ

−

−

−

−

+ − =+ −

+ − =+ −

(8.1.5)

where the following recurrence relationships have been used to eliminate 'n

ψ and 'n

ξ

( ) ( )( )

( ) ( )( )

1 1' 'n n

n n n n

n x n xx x x x

x x

ψ ξψ ψ ξ ξ− −= − = − (8.1.6)

The logarithmic derivative (8.1.4) satisfies the following recurrence relationship

1

1

/n

n

nD

D nρ ρ− = −

+ (8.1.7)

and can therefore be calculated either by upwards or downwards recurrence.

38

Calculation of the angular functions n

π and n

τ is relatively simple and they are well behaved using

the following upward recurrence relationships:

( )

1 2

1

2 1

1 1

1

n n n

n n n

n n

n n

n n

π µπ π

τ µπ π

− −

−

−= −

− −

= − +

(8.1.8)

where cosµ θ= and with the initial values of 0 0π = and 1 1π =

39

8.2 Appendix C: Additional Figures

20

25

30

35

40

45

50

55

60

65

1975 1980 1985 1990 1995 2000 2005

Year

Rela

tive H

um

idit

y %

Darwin

Alice Springs

Broome

Geraldton

Learmonth

Mildura

Rockhampton

Tennant Creek

Wagga Wagga

Figure 8.1 Annual average relative humidity for the nine locations between 1975 and 2000.