Simple Solar Spectral Model for Direct and Diffuse Irradiance on Horizontal and Tilted Planes at the Earth's Surface for Cloudless Atmospheres

TL;DR: In this paper, a simple model for calculating direct normal and diffuse horizontal spectral solar irradiance for cloudless sky conditions was described. But the model was developed using rigorous radiative transfer codes and limited outdoor measurements.

Abstract: In a previous work, we described a simple model for calculating direct normal and diffuse horizontal spectral solar irradiance for cloudless sky conditions. In this paper, we present a new simple model (SPCTRAL2) that incorporates improvements to the simple model approach and an algorithm for calculating spectral irradiance on tilted surfaces. The model was developed using comparisons with rigorous radiative transfer codes and limited outdoor measurements. SPCTRAL2 produces terrestrial spectra between 0.3 and 4.0 μm with a resolution of approximately 10 nm. Inputs to the model include the solar zenith angle, the collector tilt angle, atmospheric turbidity, the amount of precipitable water vapor and ozone, surface pressure, and ground albedo. A major goal of this work is to provide researchers with the capability to calculate spectral irradiance for different atmospheric conditions and different solar collector geometries using microcomputers.

Summary

INTRODUCTION

• In previous work [1] , the authors presented a simple model to calculate direct normal and diffuse horizontal spectral irradiance at the earth's surface for clear days.
• The authors present a new simple model that incorporates improvements in methodology as well as an algorithm to produce spectra for tilted surfaces.
• The goal of this work is to give researchers the capability to produce accurate terrestrial spectra using only a microcomputer.
• Refinements to the Justus and Paris model were based on comparisons with results of rigorous radiative transfer codes and with measured spectra.
• The new simple model and results are presented in the sections that follow.

ECTION 2.0 DIRECT NORMAL IRRADIANCE

• Minor modifications have been made to the methods the authors reported in [1] for calculating direct normal Lr r ad I anc e ,.
• The changes include the addition of an earth-sun distance factor, the use of Leckner's water vapor transmittance expression [2] with some modification of Leckner' s absorption coefficients, and the use of Robinson's ozone mass expression as given by Iqbal [6] .
• These changes and other minor adjustments are described in this section.
• A major segment of this spectrum that is of interest here was taken from the revised Neckel and Labs [8] spectrum.

2.2 AEROSOL SCA'lTKRING AND ABSORPTION

• For some types of aerosols, it may be important to separate the aerosol extinction into two or more segments, as the authors have done here for the rural aerosol model.
• The form of Eq , 2-6 allows the turbidity versus the wavelengths on a log-log plot to be nonlinear, which often occurs in the real atmosphere, as shown by King and Herman [14] .
• For the rural aerosol model [12] , this does not appear to significantly improve the accuracy of the modeled results since the function is approximately linear.
• Also, the approximate nature of this simple model approach sometimes masks the effect of refinements such as this.
• When a single value of a is used to represent the rural aerosol model, the value should be a = 1.140.

2.4 OZONE AND UNIFORMLY MIXED GAS ABSORPTION

• In addition, the authors examined different simple formulations for producing spectra on inclined surfaces.
• The authors obtained reasonable success with this effort and report their results here.

COMPARISONS OF THE NEW SIMPLE MODEL WITH RIGOROUS MODELS AND MEASUREMENTS

• Comparisons of the new, simple spectral model with results of rigorous radiative transfer codes and with measured data are given in this section.
• These comparisons give the reader some measure of the accuracy of the simple model.

4.3 COMPARISONS WITH MEASURED DATA

• A global horizontal spectrum was measured at 10:44 MST, a direct normal spectrum was measured at 10: 56 MST, and a global spectrum on a 40°south tilt was measured at 13: 42 MST.
• The atmospheric pressure was 832 mb for these measurements.
• The meteorological and geometrical parameters are shown in Table 4 -3 for these measurements.
• The agreement between the modeled and measured data is very good for these data sets.
• One has to keep in mind that the circumsolar scattered radiation within a 6°field-of-view (FOV) is included in the direct normal measurements.

Results of these comparisons are shown in

• Differences similar in magnitude but in the opposite direction have been observed in measured and modeled diffuse radiation.
• The circumsolar radiation is missing in the diffuse measurement, which causes the opposite effect.
• The agreement between modeled and measured data is not as good for this set of data.
• Justus and Paris have shown that the use of urban rather than rural aerosol parameters can account for differences of the magnitude and type shown in Figure 4 -11.

EXAMPLES OF THE APPLICATION OF THE NEW SIMPLE SPECTRAL MODEL

• The primary goal of this work on simple spectral models is to give researchers the capability to calculate spectral irradiance using microcomputers.
• The spectra can then be used in models to evaluate solar device performance.
• Spectra were calculated at 60-min intervals that are symmetrical about solar noon from sunrise to sunset.
• Of note in these spectra are the effects of high turbidity and air mass on the visible portion of the spectrum and the difference in spectral content at different times of the year due to differences in air mass values.
• These spectra can easily be converted to photon flux per wavelength or to photon flux per electron-volt if this format is more useful for particular applications.

Full text

Simple Solar Spectral Model
for Direct and Diffuse
Irradiance on Horizontal and
Tilted Planes at the Earth's
Surface for Cloudless
Atmospheres
R.
Bird
C.
Riordan
December
1984
Prepared
under
Task
No. 3434.10
FTP No. 460
Solar
Energy
Research
Institute
A Division of
Midwest
Research
Institute
1617
Cole
Boulevard
Golden,
Colorado
80401
Prepared
for
the
U.S.
Department
of
Energy
Contract
No.
DE-AC02-83CH
10093

NOTICE
This report was prepared as an
account
of
work
sponsored
by the United States Government.
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nor
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or process disclosed, or represents
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TR-2436
S=~I
I.
I-
----------------
PREFACE
This
report
documents
work
performed
by
the
Solar
Energy
Research
Insti
tute
(SERI)
Resource
Assessment
and
Instrumentation
Branch
for
the
Department
of
Energy
under
Task
No.
3414.10.
It
presents
a new
simple
model
for
direct
and
diffuse
spectral
irradiance
on
horizontal
and
til
ted
surf
aces
at
the
earth's
surf
ace
for
clear
days.
Approved
for
SOLAR
ENERGY
RESEARCH
INSTITUTE
Roland
Hulstrom,
Manager
Resource
Assessment
and
Instrumentation
Branch
j)~.~h~
Donald
Ritchie,
Director
Solar
Electric
Research
Division
iii

TR-2436
S=~I
:_ :
-----------
--J,;J~l.."lD
SUMKARY
Objective
To
present
a
new,
simple
model
for
direct
and
diffuse
spectral
irradiance
on
horizontal
and
tilted
surfaces
at
the
earth's
surface
for
clear
days.
Discussion
In
a
previous
report
(SERI/TR-215-1781),
we
described
a
simple
model
for
cal-
culating
direct
normal
and
diffuse
horizontal
spectral
irradiance
for
clear
days.
In
this
report,
we
present
anew,
simple
model
that
incorporates
improvements
to
the
simple
model
approach
and
an
algorithm
for
calculating
spectral
irradiance
on
tilted
surfaces.
The
goal
is
to
provide
researchers
with
the
capability
to
calculate
spectral
irradiance
for
different
atmospheric
conditions
and
different
collector
configurations/orientations
using
microcomputers.
Conclusions
A
new,
simple,
spectral
irradiance
model
has
been
formulated
that
produces
terrestrial
spectra
between
0.3
and
4.0
~
with
a
resolution
of
approximately
10
nm.
Inputs
to
the
model
include
the
solar
zenith
angle,
the
collector
tilt
angle,
atmospheric
turbidity,
the
amount
of
precipitable
water
vapor
and
ozone,
surface
pressure,
and
ground
albedo.

S
-
=
~
I ~;;~
~
In. 11 -- - - - - - - - - - - - -
--
- - - - - -
~~
/
TABLE OF CONTENTS
1.0
Introduction.e.
___
T_R_
-2436
1
2.0
Direct
Normal
Irradiance..............................................
2
2.1
2.2
2.3
2.4
Rayleigh
Scattering
••••••••••••••••••••••••••••••••••••••••••••••
Aerosol
Scattering
and
Absorption
••••••••••••••••••••••••••••
"
•••
Water
Vapor
Absorption
.
Ozone and
Uniformly
Mixed Gas
Absorption
•••••••••••••••••••••••••
2
4
4
5
3.0
Diffuse
Irradiance
•••••••••••••••
o....................................
6
3.1
3.2
Diffuse
Irradiance
on a
Horizontal
Surface
•••••••••••••••••••••••
Diffuse
Irradiance
on
Inclined
Surfaces
••••••••••••••••••••••••••
6
9
4.0
Comparisons
of
the
New
Simple
Model
with
Rigorous
Models
and Meas ur ement s
••••••••••••••••••••••
e 11
Com
parison
with
Dave
Rayleigh
Sc
atter
i ng
Data
••••••••••••••••••••
Comparisons
w
ith
BRITE
Code
Results
•
••••
8
••••••••••••••••••••••••
Co
mpar
isons
wi t h
Measured
Data.
e
•••••
e
•••••••••••••••••••••••
e
•••
11
11
14
580 E
xamples
of
the
Application
of
the
New
Simple
Spectral
Model
••
••••••••
20
6.0
Ref
ere
nceS ee
23
Appe ndi.x:
Pr o
gram
Li
s t i 11g
••
0
••
It c·
••
r)
~
e to 6) 6 • a •
~
• '" "
~
•••••••
.., c
Po
...
e ., t1
••••
c
•••••
v
26