Citation
Calibration of a solar absolute cavity radiometer with traceability to the world radiometric reference

Material Information

Title:
Calibration of a solar absolute cavity radiometer with traceability to the world radiometric reference
Creator:
Reda, Ibrahim
Publication Date:
Language:
English
Physical Description:
viii, 80 leaves : illustrations ; 29 cm

Thesis/Dissertation Information

Degree:
Master's ( Master of Science)
Degree Grantor:
University of Colorado Denver
Degree Divisions:
Department of Electrical Engineering, CU Denver
Degree Disciplines:
Electrical engineering

Subjects

Subjects / Keywords:
Radiometers ( lcsh )
Radiometers ( fast )
Genre:
bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

Notes

Bibliography:
Includes bibliographical references (leaves 79-80).
General Note:
Submitted in partial fulfillment of the requirements for the degree, Master of Science, Electrical Engineering.
General Note:
Department of Electrical Engineering
Statement of Responsibility:
by Ibrahim Reda.

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Source Institution:
University of Colorado Denver
Holding Location:
Auraria Library
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
37767326 ( OCLC )
ocm37767326
Classification:
LD1190.E54 1996m .R43 ( lcc )

Full Text
CALIBRATION OF A SOLAR
ABSOLUTE CAVITY RADIOMETER
WITH
TRACEABILITY
TO THE
WORLD RADIOMETRIC REFERENCE
B.S.E.E., Military Technical College, Cairo, ARE, 1977
A thesis submitted to the
University of Colorado at Denver
in partial fulfillment
of the requirements for the degree of
Master of Science
Electrical Engineering
by
Ibrahim Reda
1996


This thesis for the Master of Science
degree by-
Ibrahim Reda
has been approved
by
Hamid Fardi
Miloje Radenkovic
V l /16
Date


Reda, Ibrahim(M.S., Electrical Engineering)
Calibration of a Solar Absolute Cavity Radiometer with
Traceability to the World Radiometric Reference.
Thesis directed by Assistant Professor Hamid Fardi
ABSTRACT
This thises describes the present method of
establishing traceability of absolute cavity radiometers to
the World Radiometric Reference (WRR) through the process
employed in the International Pyrheliometer Comparisons
(IPC). This method derives the WRR reduction factor for
each of the participating cavity radiometers. An
alternative method is proposed as a way to reduce the
uncertainty in the comparison process. The two methods are
compared using a sample of data from the recent IPC-VIII
conducted from September 25th to October 13th, 1995 at the
World Radiation Center in Davos, Switzerland. A description
of PM06 as an example of active cavity radiometers, and HF
as an example of passive cavity radiometers is included.
This abstract accurately represents the content of the
candidate's thises. I recomend its publication.
Signed:
Hamid Fardi
iii


ACKNOWLEDGEMENTS
There are a number of people I would like to thank who
made this project possible. First, I wish to thank my
professor, Dr. Hamid Fardi, who offered supportive guidance
from the beginning to the end of this entire project. A
debt of gratitude is extended to Chester Wells for his
infinite wisdom and continuous support. I would also like
to thank another colleague and friend, Tom Stoffel for his
trust and confidence in my abilities. I am also grateful to
John Hickey for his continuous support, and to Claus
Frohlich and Jose Romero at PMOD/WRC for their assistance
during IPC-VIII.
Additionally, I would like to extend my deepest and
sincerest thanks to all NREL staff that provided help with
this thesis specifically Jim Treadwell, Bev Kay, Mary Raye,
Mary-Margaret Coates and Penny Sadler.
My greatest gratitude goes to my wife, Mary Alice and
my family for their continuous support, patience and
encouragement.


CONTENTS
CHAPTER
1. Introduction ....................................... 1
1.1 The World Radiometric Reference .................. 1
1.2 Radiometry at the Physikalisch
Meteorologisches Observatorium Davos (PMOD). . 3
1.3 Organization and Sequence ........................ 4
2. PMO-6 Absolute Cavity Radiometer ................. 6
2.1 Description ...................................... 6
2.2 Operation......................................... 8
3. HF Absolute Cavity Radiometer ..................... 10
3.1 Description...................................... 10
3.2 HF Electrical Calibration Procedure and
Operation.........................................14
4. International Pyrheliometer Comparisons IPC-VIII 17
4.1 Introduction......................................17
4.2 Data Acquisition and Evaluation...................18
4.3 Calibration requirements ........................ 21
5. PMOD/WRC Method to Determine the WRR...............23
6. Proposed Method to Determine the WRR...............32
7. Calculation of WRR Reduction Factor of HF28968 . 40
7.1 PMOD/WRC method...................................40
7.2 Proposed method...................................51
8. Observations and Conclusions ...................... 63
References............................................79
v


FIGURES
Figure
2.1. The Detector System for PMO-6....................7
3.1. HF Sensing Element, Front View....................li
3.2. HF Sensing Element, Side View.....................11
3.3. Eppley Hichey-Frieden System Diagram ............ 13
4.1. Timing for Different Instrument Types
During IPC-VIII...................................19
5.1. PM02 Ratio to PM02................................26
5.2. PM05 Ratio to PM02................................26
5.3. CR0M2L Ratio to PM02..............................27
5.4. MK 67814 Ratio to PM02............................27
5.5. HF18748 Ratio to PM02.............................28
5.6. PAC3 Ratio to PM02................................28
8.1. WRR Reduction Factors........................... 66
8.2. Standard Deviations...............................67
8.3. Means of WRR reduction Factors for the WSG ... 68
8.4. Change of the M Factor with Irradiance
Calibration Levels and Time, 10/7/95 ............ 69
8.5. Change of the M Factor with Irradiance
Calibration Levels and Time, 10/11/95............70
8.6. Change of the M Factor Irradiance
Calibration Levels and Time, 10/12/95............71
8.7. Change of the Temperature with Time and
Irradiance Calibration Levels, 10/7/95 ......... 72
8.8. Change of the Temperature with Time and
Irradiance Calibration Levels, 10/11/95..........73
8.9. Change of the Temperature with Time and
Irradiance Calibration Levels, 10/12/95..........74
8.10. Change of M Factor with Temperature for 7, 11,
and 12 October 1995 ............................ 75
vi


8.11.
Irradiance Readings with Time and Irradiance
Calibration Levels.............................78
vii


TABLES
Table
7.1. PMOD/WRC Method..................................43
7.2. Proposed Method..................................53
8.1. WRR Reduction Factor for HF28968 ............... 64
8.2. Change of the M Factor for HF28968 ............. 76
viii


CHAPTER 1
1. Introduction
1.1 The World Radiometric Reference
The World Meteorological Organization (WMO) is an
intergovernmental organization sponsored by the United
Nations through which the United States and more than 160
other nations cooperate in meteorological and weather
related science and engineering. The WMO promotes the
development of reference instruments; conducts world wide
and regional field comparisons and evaluations; and
recommends test and calibration methods, and the
corrections applied. WMO sanctions the Physikalisch
Meteorologisches Observatorium Davos (PMOD) as its World
Radiation Center to establish, maintain, and propagate to
users the engineering measurement scale for solar radiation
measurements called the World Radiometric Reference (WRR).
This measurement scale is used by all nations that acquire
and report solar radiation measurement data for weather and
meteorological purposes, for solar energy and engineering
purposes, and for space research. The accuracy, precision,
and stability of the WRR is crucial for current scientific
and engineering activities. These activities include the
developing, testing, and using solar energy devices and
technologies; meteorological, weather and global climate
change measurements and research; and solar research from
space.1 WRR was established through special comparisons, in
1977, of 15 absolute cavity radiometers of 9 types. Since
WRR was established, the goal has been to ascertain and
l


maintain its stability, accuracy, and precision through the
World Standard Group (WSG) instruments.2 This is necessary
so that scientists and engineers have a common
internationally accepted reference for technical data and
can accurately measure trends, such as changes in the world
climate.
The following seven absolute cavity radiometers (three
from the United States and four from Europe) now form the
World Standard Group (WSG) that maintain WRR:
1. *PACRAD III: Built by and on indefinite loan from the
United States' National Aeronautics and Space
Administration.
2. *PMO-2: Built by and contributed by the Physikalisch
Meteorologisches Observatorium Davos, Switzerland.
3. PMO-5: Built by and contributed by the Physikalisch
Meteorologisches Observatorium Davos, Switzerland.
4. *CR0M-2: Built by and contributed and operated by the
Institute Royal Meteorologique de Belgique, Belgium.
5. *CROM-3: Built by and contributed and operated by the
Institute Royal Meteorologique de Belgique, Belgium.
6. TMI-67814: Built by Technical Measurements, Inc. (TMI)
and loaned from the National Renewable Energy
Laboratory, Golden, CO, USA.
7. HF-18748: Built and contributed by The Eppley Laboratory
Newport, RI, USA.
2


The four asterisked (*) instruments were part of the
original group of instruments that were used in the initial
development and definition of WRR; they have served as part
of the WSG ever since.1
1.2 Radiometry at the Physikalisch Meteorologisches
Observatorium Davos (PMOD)
The design and construction of absolute radiometers at
PMOD started in the early seventies. Due to their primary
use, the measurement of solar irradiance, these radiometers
are optimized to measure irradiances around 1 Kw/m2. The
first model built was the PMO-2, which is since 1975 one of
the World Standard Group (WSG) realizing the World
Radiometric Reference (WRR). Since then a more refined
version of the PMO radiometers (PMO-6) has been developed.
Such instruments are used for the solar constant
experiments of PMOD and for the subsistence of the World
Standard Group.2
In order to assess the uncertainties of this kind of
absolute radiometry more accurately, an important effort
was put into the development of independent laboratory
experiments. These are called characterization and consist
of the accurate determination of all deviations of the
radiometer from its ideal behavior.2
The calibration factor of absolute cavity radiometers
is a function of: radiation loss (ER) non-equivalence of
the radiative and electrical heating (ENB) scattered light
(Est) diffraction losses (ED) lead heating effect (ELS) and
area of the precision aperture. It is the uncertainty of
these factors that determines the accuracy of the
3


radiometer. The following accuracies were achieved in
characterizing the PMO-6 absolute cavity radiometers:
a) The precision aperture diameter is measured with an
accuracy greater than 0.5 fim (0.02 percent), and
roundness with accuracy greater than 0.2 fim.
b) The radiation loss is measured with an accuracy on the
order of 0.005 percent.
c) The non-equivalence between solar irradiance and
electrical heating is measured with accuracy 0.05
percent.
d) The scattered light is measured with accuracy 0.01
percent.
e) The leads heating is measured with accuracy 0.001
percent.
f) The diffraction losses correction is normally neglected
in solar measurements and as the different radiometers
have very similar corrections, this effect is left out.2
1.3 Organization and Sequence
This report is divided into eight chapters. Chapter 2
describes the PMO-6 absolute cavity radiometer as an
example of active cavity radiometers. Chapter 3 describes
first, the HF absolute cavity radiometer as an example of
passive cavity radiometers; second, its recommended
electrical calibration procedure during the outdoor
comparisons of absolute cavity radiometers. Chapter 4
4


contains the calibration procedure of the International
Pyrheliometer Comparisons IPC-VIII. Chapter 5 describes the
PMOD method used to derive the WRR reduction factors for
all the participating instruments, including those in the
World Standard Group (WSG). Chapter 6 describes the
proposed method to derive the WRR reduction factors in an
effort to reduce the random component. Chapter 7 contains
the calculations (using the two methods) of the WRR
reduction factors for, HF28968 absolute cavity radiometer
and each of the WSG instruments, using a sample of data
collected during IPC-VIII. Chapter 8 reports the
observations and conclusions.
5


CHAPTER 2
2. PMO-6 Absolute Cavity Radiometer
2.1 Description
The design of the PMO-6 absolute cavity radiometer is
based on the principle of an electrically calibrated
differential heat flux transducer with a cavity for the
efficient absorption of the radiation to be measured. The
cavity, which has an inverted cone inside a cylindrical
shield, is painted with a specular black paint and is tied
to a heat sink through a stainless steel thermal impedance.
For the measurement of solar radiation, a view-limiting
baffle mounted in front of the detector provides a full
field of view of 5 degrees (the detector system is shown in
Fig. 2.1). Only the primary cavity is used for radiation
measurements. The temperature difference across the thermal
impedance, sensing the heat flux, is measured with
resistance thermometers mounted on the two cavities and not
between the primary cavity and the heat sink. This
differential arrangement compensates for the sudden changes
in temperature of the heatsink and the rapid pressure
changes, as long as the thermal time constants of the two
cavity-thermal-impedance systems are equal.2
6


Field stop (J)
Fig.2.1 The Detector System for PMO-6
7


2.2 Operation
The instrument is operated in the "active" mode. That
is, the temperature difference between the two cavities,
the primary cavity and the compensating cavity, is kept
constant by an automatic control loop for the current of
the primary cavity's heater. Thus the difference in
electrical power during the reference phase (electrical
heating only) and during the irradiance phase (electrical
and radiative heating) is proportional to the incoming
radiation, S,
S
k(P,
p )
closed open'
(2.1)
where:
Peioaed = the electrical power (voltage times current)
applied to the primary cavity when no
radiation is applied to it and the primary
aperture's shutter is closed. This power is
always kept at equilibrium with the power
applied to the compensating cavity using a
current control loop
Popen = the power measured at the primary cavity when
the solar radiation is applied and the
primary aperture's shutter is open.
In equation (2.1), the parameter k is the calibration
factor,
8


r*R, rif &sTa ^D ^uf
(2.2)
Je
where:
Er = the radiation losses coefficient due to the
finite reflectivity and the infrared emission of
the heated black coating of the cavity
Eke = the non-equivalence coefficient due to the
effect of different temperature distributions
during electrical and combined radiative and
electrical heating
Est = the scattered light coefficient produced by the
light reflected from the precision aperture to
the baffle and back into the cavity
Ed = the diffraction losses coefficient due to
iffracted light in the cavity
Elb = the lead heating effect coefficient due to the
heating of leads feeding the current to the
cavity heater
Ap = the area of the precision aperture.2
9


CHAPTER 3
3. HF Absolute Cavity Radiometer
3.1 Description
The self-calibrating absolute cavity radiometer model
HF, manufactured by The Eppley Laboratory, has been a
reference standard level device since 1978. The sensor was
originally developed for measurements from satellites and
rockets. It consists of a balanced cavity receiver pair
attached to a circular wire-wound and plated thermopile
(Figs. 3.1, 3.2). The blackened cavity receivers are fitted
with heater windings which allow for absolute operation
using the electrical substitution method, which relates
radiant power to electrical power in SI units
(International System).
The forward cavity views the direct solar beam through
a precision aperture having an area of 50 mm2. The rear
receiver views an ambient temperature blackbody. The HF
radiometer element with baffle tube and blackbody are
fitted into an outer tube that encloses the instrument.3
The cavity radiometer is operated, and the required
parameters are measured, using an appropriate control box.
The cavity can be operated in either manual or automatic
mode. In the manual mode, the shutter can be controlled
remotely from the control box and the data from the digital
10


Fig. 3.3 Eppley Hickey-Frieden System Diagram


multimeter is logged manually. In the automatic mode, the
cavity is controlled through a computer program, normally
Quick Basic or Visual Basic. The program controls all
operations, calculates sensitivities and irradiance
results, performs first level statistical analysis, and
stores and backs up all data. The control functions include
shutter control, setting of the calibration heater power
level, activation of the calibration heater circuit,
selection of the signals to be measured, and control of the
digital multimeter measurement functions and ranges. The
measured parameters include the thermopile signal; the
heater voltage (approximately 2.0 to 2.7 V) ; and the heater
current (approximately 15 to 20 mA, which is measured as
the voltage drop across a 10 ohm precision resistor
connected in series with the heater). The instrument
temperature may also be measured using an internally
mounted thermistor. The digital multimeter resolution of
100 nV allows for a thermopile signal measurement with
resolution of 0.1 /iV which is equivalent to approximately
0.1 W/m2 (1 mV thermopile signal is equivalent to
approximately 1000 W/m2 of solar irradiance) (see simplified
function diagram in Fig. 3.3). The HF absolute cavity
radiometer can be run in either active mode (similar to the
PMO-6 discussed Chapter 2) or passive mode. Usually, the
cavity is used in the passive mode and that is how it is
calibrated and operated in all the International
Pyrheliometer Comparisons (IPC). In the passive mode, the
electrical power is applied only to the heater of the
forward cavity to calculate its sensitivity at certain
solar irradiance level (the calibration interval), and then
turned off during the solar irradiance measurement. But in
12


Fig. 3.1 HF Sensing Element, Front View
13


the active mode the electrical power is applied to both the
forward cavity and the rear cavity, and it stays on during
both the calibration interval and the solar irradiance
measurement.
3.2 HF Electrical Calibration Procedure and operation
The following procedure is recommended during the
comparisons of absolute cavity radiometers to reduce the
errors in measuring the cavity zero and TPe (thermopile
output voltage due to electrical power).
a) Mount the radiometer on the tracker, and adjust the
system so that the radiometer is perfectly aligned with
the sun's normal incidence.
b) Connect cable from the control unit to the radiometer,
turn on the control unit, and let the whole system warm
up for at least 1 hour to stabilize with the outdoor
environment.
c) On the radiometer, block the solar irradiance using the
metal beam plug provided, and close the shutter by
pressing the Shutter ON/OFF switch.
d) On the control unit, set the Function switch to TP
(Thermopile) position and Heater 1 and Heater 2 switches
to off (electrical power is turned off) with the
Low/High switches on Low positions.
e) Wait until the reading on the Digital Multimeter (DMM)
stabilizes (90 to 120 seconds), and record the reading
of the DMM as TP0 (Thermopile Zero) in mVDC.
14


f) Remove the metal beam plug from the radiometer, open the
shutter and wait for 30 to 60 seconds, and record the DMM
reading as TP8 (thermopile output voltage due to solar
irradiance) in mVDC.
g) Estimate the solar irradiance change during the solar
irradiance measurement interval, and record it as x in
mVDC.
h) Close the shutter, turn on Heater 1 and adjust Heater 1
control until the DMM reading equals TPe + x. Wait until
the DMM reading stabilizes (40 to 90 seconds), and
record the reading as TPe in mVDC.
i) Set the Function switch to VI position, wait until
heater voltage reading on DMM stabilizes (15 seconds),
and record the reading as in VDC.
j) Set the Function switch to II, wait until heater current
reading on DMM stabilizes (15 seconds), and record the
reading as VRI in VDC (measured as a voltage reading
because it is the voltage drop across a precision 10 ohm
resistor Rj that is connected in series with the heater
for accurate current measurement).
k) Calculate the multiplier factor at the solar
irradiance level being measured, M (W/m2/niV) ,
M =
V,
* (Vx*RC) *cf* 104
Ri
TPe-TPa
(3.1)
15


where:
Rc = the heater leads correction resistance,
which typically is 0.066 ohm
C£ = the calibration factor provided by the
manufacturer. Cf is approximately 2 because the
aperture area is 0.5 cm2 (value differs for
different radiometers).
l) Set the Function switch to TP, turn off Heater 1 and at
the same time open the shutter (to keep the thermal heat
of the cavity as close as possible to the solar
irradiance level through the transition).
m) To calculate the solar irradiance (W/m2) multiply each
TP reading taken from the DMM (mV) by the factor M
calculated during the calibration.
n) After taking a number of readings in a period of time
(usually that period is 10 to 30 minutes) perform the
calibration once again and note the M factor and cavity
zero readings. Then, linearly interpolate the M factor
and cavity zero values for each irradiance reading, then
recalculate the irradiance.
16


CHAPTER 4
4. International Pyrheliometer Comparisons IPC-VIII
4.1 Introduction
The Executive Council of the World Meteorological
Organization (WMO) authorized the 8th International
Pyrheliometer Comparisons (IPC-VIII) to be held at the
Physikalisch Meteorologisches Observatorium Davos, World
Radiation Center (PMOD/WRC) from 9/25/95 to 10/13/95. The
technical organization was delegated to PMOD/WRC, whereas
the overall responsibility for ratification and
dissemination of the final results rests with the WMO
Commission for Instruments and Methods of Observation
(CIMO) Working Group on Radiation and Atmospheric Turbidity
Measurements.4,5 Sixty five participants representing thirty
eight countries participated in the comparison. A WRR
reduction factor will be calculated for each participating
solar cavity radiometer. For a cavity radiometer to be
traceable to the World Radiometric Reference, each of its
irradiance readings will be multiplied by its WRR reduction
factor. The method of calculating the WRR reduction factor
described in this chapter has been used by PMOD/WRC for the
past several International Pyrheliometer Comparisons, and
it might be used for IPC-VIII.
17


4.2 Data Acquisition and Evaluation
a) Timing
The measurements are taken in runs lasting 21 minutes
with a basic sampling of 90 seconds. Voice announcements
before and buzzer signals during each event are used to
inform the participants about the sequence.6 The timing for
the different instrument types is shown in Fig. 4.1. For
nine instruments, of which HF28968 was one, the first
irradiance reading was at 90 seconds after T0, and a total
of 13 irradiance readings per run were recorded, which
resulted in a larger data sample than the other
participating instruments.
b) Acquisition
The analog data-acquisition system is based on eight
parallel DVM HP3478A with scanners and is used for WSG
instruments, the radiometers of PMOD/WRC, and the
auxiliary data. For the input data from the participants,
Burr-Brown types TM27 and TM2700 microterminals are used.
The whole system is controlled by an HP computer series
9200, which also stores and evaluates the data.6 For
HF28968 and a small group of other instruments, the data
were entered manually on a PC then copied to a floppy disk
at the end of each day.
c) Data evaluation
For each instrument the irradiance and ratio to PM02
is obtained with the corresponding evaluation procedure.
After each run, a summary of measured values and evaluated
irradiances is printed and distributed for checking by the
18


Fig. 4.1 Timing for Different Instilment Types
During IPC-VIII
90s
180s
270s
450s
990s 1080s 1170s 1260s
PM02
SRAD
PAC3
Heater
PAC3
Heater
HF
Shutter
HF
Heater
MKVI
ACTino
Angstrom
360s
Open OInsfi Pre-part Seq 1 Seq 2 Seq 3 Seq 4 Seq 5 r U Seq 12 Seq 13
T 1 T o ! t, f ] T 1 ! ] f l 13 Irrad.
Open " ' . v V-
i f T \ i J6 Irrad.
Open PJrkCO Zero Vth cal. Irrad! \ Irrad. fc
1 8 Irrad. 11 Irrad. 12 Irrad. 12 Irrad. 11 Irrad.
on H off H Open Close

Zero Vth cal. Jrrad. Jrrad. Irrad. Irrad Irrad. Irrad.

on H off H
1
Open Close Irrad. Irrad. Irrad. Irrad. Irrad Irrad. Irrad.

Open Zero t Irrad. Irrad. Irrad. Irrad. Irrad Irrad. ^ Irrad.
1
Left Riaht 1st. valid ^readlng_ _ A m
\ \ \ \ \ \ \L > CD > CD > C0 > J N W7 03 Dm Q.
A: Please shade and heat the right hand strip Reading
B: Please shade and heat left hand strip
End: Please check your zero point
C: The series is over


participants and, if necessary, the raw data are edited
for gross errors. Updated summaries with the mean values
of ratio and the standard deviation for each instrument
are made available during the course of the comparison.6
PM02 is used as the working reference instrument. The
irradiance values of PM02 are obtained with the algorithm
of the active cavity radiometers with Pcloee<1 as mean of the
closed readings (no sun irradiance) and after the current
open phase (sun irradiance) At the end of the open phase,
eight Popen readings are taken, separated by approximately
0.7 second. The first of these readings is used as
reference for the values entered by participants and the
WSG instruments at the appropriate time. The standard
deviation of these eight irradiance readings is also used
as a quality control parameter to judge the stability of
the solar irradiance for the data point to minimize the
effect of different time constants between different types
of instruments, so if the standard deviation is higher
than 0.3 percent of reading, the data point would be
rejected.6
d) Auxiliary data
The meteorological parameters are taken from the
automatic weather station of the Swiss Meteorological
Service located at PMOD/WRC. From this system 10 minutes
values are available which are averaged over the period of
a run. The values are air temperature, atmospheric
pressure, global irradiance, and sky radiation. Close to
the measuring benches, the wind speed and direction is
measured, not as a meteorological parameter, but as an
indication at the measuring site. Moreover, an instrument
20


temperature and the daily ozone values are also given.
Sunphotometer measurements are used to determine total
vertical optical depth.6
4.3 Calibration requirements
a) Radiation source:
- The radiation source is the sun, with recommended
irradiance level greater than 700 W/m2 during measurement
runs .6
b) Measuring equipment:
- Digital multimeters with at least 0.05% of reading
resolution, accurate and stable over at least 1 year,
including temperature drift, better than 0.1% of
reading. DMM should be protected from sun and wind and
it should be connected to signals using shielded low-
noise cabling.
- Sun tracker's admissible misalignment is 0.25 slope
angle.
c) Environmental variables:
- Wind speed should be low, particularly if blowing from
the direction of the sun's azimuth 30.
- Cloud cover should be less than 1/8, clouds at an
angular distance larger than 15, and Link turbidity
factor as low as possible.
21


Ambient air temperature and pressure changes, in
principle, have no influence on Absolute Cavity
Radiometers.6
22


Chapter 5
5. PMOD/WRC Method to Determine the WRR Reduction Factor
for Each of the Participating Instruments
The nomenclature used in this chapter has been
developed to clarify the PMOD/WRC procedure. Steps (a)
through (d) are used to establish the ratio of each
participating instrument in IPC-VIII (including the WSG
instruments) to PM02, which is the transfer instrument
for the whole procedure. Steps (e) and (f) are used to
compute the WRRIPCBi1c reduction factor for each instrument
in the WSG using PM02 as a transfer instrument. Steps (g)
through (i) are not used by WRC/PMOD but have been added
here to show that using the technique in step (f)
produces no difference between the means of the WRRIPCBjIt
and the WRRIPC7i1c reduction factors for the same WSG
instruments. Similarity of the means is the primary
assumption of this method. Step (j) is used to calculate
the WRRIPCBi)c reduction factor for each participating
instrument. Step (k) is used to show how well WRR is
defined by the WSG.
a) For each reading, calculate the ratio of the
irradiance reading of each participating instrument,
including the WSG instruments, to the irradiance reading
of PM02, Rjik,
23


(5.1)
J2-* L-
J.k r
h.k
j,PM02
where:
Ij;k = the jth irradiance reading of the kth
instrument (W/m2)
ij,PM02 = the jth irradiance reading of PM02 (W/m2) .
b) Calculate the mean of the ratios It,,* for each
participating instrument, R'k,

(5.2)
where N is the number of irradiance readings.
c) Calculate the standard deviation of the ratios R^ for
each instrument, SD'k,
sn'k
E N-l
(5.3)
d) Values of Rj,,, that deviate more than 0.3 percent from
the mean R'k are rejected, and a new Rk and SDk are
calculated using Equations 5.2 and 5.3.
24


e) In order to define the World Radiometric Reference
(WRR) for IPC-VIII, the results of the WSG are analyzed
by the Commission for Instruments and Methods of
Observation (CIMO). This commission then decides which
of the seven reference instruments will define WRR for
IPC-VIII. The reference instruments for IPC-VIII are
PM02, PM05, CR0M2L, CR0M3L and MKVI67814 only. PACRAD
III had an insect inside the cavity in April 1992. After
the instrument was cleaned, its ratio to PM02 decreased
from 0.99917 to 0.9975 and has stayed the same since
then. HF18748, which had an insect during IPC-VII, was
not considered for defining WRR for IPC-VIII. Both
instruments have not acquired enough measurement history
to show the stability of their ratios to PM02. Figs. 5.1
through 5.6 show the ratios of each of the WSG to PM02
since 1990.
25


Ratio PM02 Ratio PM02
World Standard Group
1.005
1.004
1.003
1.002
1.001
1.0
0.999
0.998
0.997
0.996
0.995
0.994
1990 1991 1992 1993 1994 1995 1996
Year
Fig.5.1 PM02 Ratio to PM02











1.005
1.004
1.003
1.002
1.001
1.0
0.999
0.998
0.997
0.996
0.995
0.994
1990



v/s(\ \Ay
V

1991
1992
1993
Year
1994
1995
1996
Fig.5.2 PM05 Ratio to PM02
26


Ratio PM02
1990 1991 1992 1993 1994 1995 1996
Year
Fig.5.3 CROM2L Ratio to PM02
1990 1991 1992 1993 1994 1995 1996
Year
Fig.5.4 MK 67814 Ratio to PM02
27


Ratio PM02 Ratio PM02
World Standard Group
1990 1991 1992 1993 1994 1995 1996
Year
Fig. 5.5 HF18748 Ratio to PM02
28


f) For each of the WSG instruments, calculate the WRRIPC8rX
reduction factor using the following procedure:
i. Calculate the ratios W1PC8flc/
^IPCB, k = WRRiPC7, k *
WRR
IPC7, PM02
(5.4)
where:
WRRIPC7i)c = the WRR reduction factor for the kth
instrument in the WSG during IPC-VII
R* = the mean of ratios of the irradiance
reading of the kth instrument in the
WSG to the irradiance reading of
PM02 for N readings (after rejecting
the outlier ratios)
WRRIPC7iPM02 = the WRR reduction factor of PM02
calculated during IPC-VII.4,5
ii. Calculate the mean of the ratios W1PC8iIc, M,
yi ^ipca,i
Ms =
Jc=l
n
(5.5)
where n is the number of WSG instruments that defines
WRR during IPC-VIII.
29


iii. Calculate the deviation of each WIPCBik from the mean
Me, DIPCBik,
D
IPCB.k
~ ^IPCB.k
(5.6)
iv. Finally, calculate the WRRIPCB(k reduction factor for
each instrument in the WSG,
WR^IPCB.k = WRRipc7 ,k~^iPCB,k
(5.7)
g) Calculate the mean, MIPCB, of the WRRIPCB(k reduction
factors of the WSG instruments,
y) WRRlPC8,k
Mjpcb = kn----------- (5'8)
h) Calculate the mean, MIPC7> of the WRRIPC7,k reduction
factors of the same WSG instruments that are used to
derive MIPCe,
IPC7
y! WRRlPC7,k
Jc=l__________
n
(5.9)
i) Calculate the change of the mean of WRR reduction
factors of the WSG instruments, D,
30


(5.10)
D should equal zero because the primary assumption
of this method is that the mean of WRR reduction factors
of the WSG is constant.
j) Calculate the WRRIPC0i)c for each participating
instrument,
WRR
IPC8,k
WRR
IPCB, PMQ2
Rk
(5.11)
k) Calculate the mean of WRRIPCS reduction factors for all
the participating instruments in IPC-VIII that have
WRRIPC7 reduction factors, including the WSG, to evaluate
how well WRR is represented by the WSG.4,5
31


CHAPTER 6
6. Proposed Method to Determine the WRR Reduction Factor
for Each of the Participating Instruments
This method is based on the fact that the standard
deviations of the WRR reduction factors of the WSG are
different. Thus, the influence of the instrument that has
larger standard deviation on determining the reference
irradiance at a specific time should be less than the
influence of the instrument that has a smaller standard
deviation.7 Step (a) divides the whole population of data
into different samples, each of which represent a
different group of instruments from the WSG. Steps (b)
through (j) are used to calculate the weighting factor
for each of the WSG instruments for each data sample.
Steps (k) through (m) are used to calculate the WRR
reduction factor and the standard deviation for each of
the WSG instruments for IPC-VIII. Step (n) is used to
recalculate the new weighting factor for each of the WSG
instruments for each data sample because the standard
deviations of the WRR(IPC8) reduction factors are
different from the standard deviations calculated in step
(f). Steps (o) through (r) are used to calculate the WRR
reduction factor and the standard deviation for each of
the participating instruments in IPC-VIII. Steps (s)
through (u) are used to evaluate the change in the mean
of the WRR reduction factors of the WSG. Step (v) is used
to evaluate how well WRR is represented by the WSG.
32


a) After determining the instruments from the WSG that
would define WRR for IPC-VIII, divide the whole
population of irradiance readings into samples. Each
sample should have at least three participating
instruments of the WSG and the participating instruments
should be the same in each sample.
b) Multiply each irradiance reading of each instrument of
the WSG by the instrument's WRR reduction factor from
IPC-VII,
Ij,k ^-j. k*^^lPC7, k (6.1)
where ij(k is the jth irradiance reading of the kth
instrument of the WSG (W/m2) .
c) Calculate the reference irradiance, for each
reading,
I
//
ref.
,j
E h.c
Jc=l
n
(6.2)
where n is the number of instruments from the WSG that
participated in the jth irradiance reading.
d) Calculate the ratio of the reference irradiance of
each reading to the original irradiance reading of each
instrument, R"jjk,
33


tH
-* lef. ,j
(6.3)
R
tt
j.k
i
j.k
e) Calculate the mean of all the ratios R".,,* for each of
the WSG instruments, R'\,
N
R"k =
E
N
(6.4)
where N is the number of irradiance readings of the kth
instrument in the whole population.
f) Calculate the standard deviation of the ratios R"jilt
for each of the WSG instruments using the whole
population, SD"*,
SD
n
k
If
E
-i=1
(tfV-R';,*)2
w-i
(6.5)
g) Reject all the ratios, R"jrk that deviate more than
0.3 percent from the mean R"k. It is most important to
reject also the irradiance reading from which that
rejected ratio was derived, because that irradiance
reading will affect the value of the reference
irradiance. Then, recalculate the ratios, R^,*, their
means, R'k, and their standard deviations, SD'k, using
Equations 6.3, 6.4 and 6.5.
34


h) Calculate the total bias error, Bk, for each
instrument of the WSG. The main source of bias errors is
the digital multimeter used to measure electrical
signals such as heater voltage, heater current,
thermopile voltage, and thermistor resistance.
Bk
\
3= 1
^g.k)\
(6.6)
where B3rIt is the gth bias error for the kth instrument.
i) Calculate the total uncertainty for each of the WSG
instruments, U'99ilc,
U'99k = BK+2*SD'k. (6.7)
j) Calculate the tentative weighting factor for each of
the WSG instruments for each data sample, W'n()c. The
number and type of participating instruments from the
WSG are going to be different for each sample, which
will result in different weighting factors for each
sample,
W
U
)
n,ic
99,1:
U 99,k
(6.8)
where n is the number of participating instruments from
the WSG in the sample.7
35


k) Recalculate the weighted reference irradiance of the
WSG for each irradiance reading, using WRRIPC7;lc reduction
factors, rr-f.,3#
I
/
ref.,j
n
E K'n.k*W&I?C7,k*ij.k'
(6.9)
1) Calculate the ratio of each of the weighted reference
irradiance to the original irradiance reading of each of
the WSG instruments, Rjilt,
R
J.k
ref.,j
h.k
(6.10)
where ijjk is the original irradiance reading (without
being multiplied by the WRR reduction factor) of the kth
WSG instrument (W/m2) .
m) Calculate the mean and the standard deviation of the
ratios Rj,* for the kth instrument of the WSG using
Equations 6.4 and 6.5. The mean is the WRRIPC8i)c reduction
factor for the kth instrument of the WSG and the
standard deviation is the SDIPC8()t for the same
instrument.
n) From the standard deviations in step (m) recalculate
the weighting factor, Wn>)t, for each of the WSG
instruments using Equations 6.7 and 6.8. Each data
sample will have different weighting factors.
36


o) Using the WRRIPC8ilc reduction factor for each of the
WSG, calculate the weighted reference irradiance for
each irradiance reading, lra£.(j,
ref. ,j
= 5^ Wn k*WRRIPC8 k*ij'k-
Jc1
(6.11)
p) For each of the participating instruments calculate
the ratio of the weighted reference irradiance to the
instrument irradiance reading, WRRIPCBij(lt,
WRR
IPC8,j,k
Lzef.,j
ij.k
(6.12)
q) Calculate the WRRIPC8iIc reduction factor for each of the
participating instruments,
r. MMiPcs.j.k
WRR-iPca.k = ^ (6.13)
r) Calculate the standard deviation for each
participating instrument, SDIPCe,k>
N
SD
IPC8, k

52 (WKRlPC8.k WWxPCS.j.k)
j= 1______________________
N-1
(6.14)
37


reduction factors for
s) Calculate the mean of WRRIPC8iJc
the WSG, MIPC0,
M,
IPCB
E
WRR
IPCB, k
Jc=1
n
(6.15)
where n is the total number of instruments from the WSG
that defines the WRR for IPC-VIII.
t) Calculate the mean of WRRIPC7iJc reduction factors for
the WSG instruments that define the WRR for IPC-VIII,
MIPC7,
M-
IPC7
- E
Jc=l
WRR
IPC7,k
n
(6.16)
u) Calculate the change of the mean of WRR, D,
D = MIPC8~MIPC7. (6.17)
D is the change of the mean of WRR that should be
monitored at every WSG comparison, and after a period of
time the two methods should be evaluated through a
comparison using an absolute cavity radiometer or a
group of absolute cavity radiometers that is more
accurate.
v) Calculate the mean of WRRIPC8i)c reduction factors for
all the participating instruments, including the WSG
instruments, that have WRRIPC7>lc reduction factors and
38


compare it with the mean of WRRIPCBi1c reduction factor for
the WSG instruments. This comparison allows one to
evaluate how well WRR is represented by the WSG
instruments for IPC-VIII.
39


CHAPTER 7
7. Calculation of WRR Reduction Factor of HF28968
Using the PMOD/WRC and the Proposed Methods
In this chapter, the WRR reduction factor for
HF28968 is calculated using the PMOD/WRC method and then
the proposed method. The data used in the calculations
are raw data that were collected during the comparison
(IPC-VIII) under clear skies and around solar noon. The
calculated WRR reduction factor in this chapter might
differ from the WRR reduction factor assigned by PMOD/WRC
due to using a small data sample. Tables 7.1 and 7.2 are
the printout of a spreadsheet software used for the
calculations.
7.1 PMOD/WRC method
The following rows, cells, or columns in Table 7.1
describe the sequence of the PMOD/WRC procedure used to
calculate the WRR reduction factor for HF28968.
a) Columns B through G contain the irradiance readings
for the WSG instruments and HF28968.
b) Columns H through L contain the ratios of each
irradiance reading to PM02.
c) Cells H137 through L137 contain the means of the
ratios to PM02 in their corresponding column (e.g., cell
40


H137 is the mean of the ratios in cells H2 through
H134) .
d) Cells H139 through L139 contain the standard
deviations of the means of the ratios in step (c).
e) Cells H152 through L152 contain the means of the
ratios to PM02 after rejecting the ratios that are 0.3
percent lower or higher than the mean.
f) Cells H154 through L154 contain the standard
deviations for the means in step (e).
g) Cells M3 through Q3 contain the WRR reduction factors
for the WSG Instruments from IPC-VII.
h) Cells M5 through Q5 contain the ratios calculated
using Equation 5.4.
i) Cell N6 contains the mean of the ratios in step (h).
j) Cells M8 through Q8 contain the difference between the
mean in cell N6 and each of the ratios in cells M5
through Q5 respectively.
k) Cells M10 through Q10 cotain the WRR reduction factors
for the WSG instruments from IPC-VIII, which are
calculated by subtracting cells M8 through Q8 from cells
M3 through Q3 respectively.
l) Cells 013 and 014 contain the means of the WRR
reduction factors of the WSG instruments during IPC-VII
41


and IPC_VIII. The two means should equal if the data
were processed properly.
m) Cells 017 and 018 contain the WRR reduction factor and
the standard deviation of HF28968.
42


A B C D E F G
1 Date/Time PM02 PM05 CROM2L CROM3R MK67814 HF28968
2 10/2/95
3 11:22:30 1023.9 1023.5
4 11:24:00 1022.2 1020.7 1019 1028.2 1022.9
5 11:25:30 1020.5 1022.4
6 11:27:00 1021.2 1020.3 1020.7 1029.8 1021.7
7 11:28:30 1020.1 1019.7
8 11:30:00 1018.6 1018.1 1019.1 1027.6 1019.1
9 11:31:30 1019.4 1021.4
10 11:33:00 1018.2 1017.8 1015.7 1018.5 1020.1
11 11:34:30 1018.8 1020.5
12 11:36:00 1016.9 1015.8 1013.6 1015.9 1017.7
13 11:37:30 1016.2 1017.6
14 11:39:00 1015.1 1013.4 1010.7 1011.2 1016.9
15 11:40:30 1016 1017.7
16 10/3/95
17 10:19:30 934.2 933.8
18 10:21:00 932.6 931.9 929.1 935.6 933
19 10:22:30 933.7 934.8
20 10:24:00 932.7 931.1 930 935.2 934.9
21 10:25:30 936.3 936.9
22 10:27:00 938 936.6 934.4 939.3 938.5
23 10:28:30 939.1 939.8
24 10:30:00 940.2 938.4 934.3 946.2 941.1
25 10:31:30 939.9 941.8
26 10:33:00 942.5 941 939.9 942.5 942.8
27 10:34:30 941.5 942
28 10:36:00 942 940.8 939.3 946.6 943.1
29 10:37:30 943.6 945.4
30 10/11/95
31 11:01:30 938.1 939.9
32 11:03:00 938.6 938 936.4 934.1 940.2
33 11:04:30 939.5 939.6 941
34 11:06:00 941.6 940.5 939.3 939.3 941.9 942.8
35 11:07:30 942.2 941.9 944.1
36 11:09:00 941.4 940.3 937.6 937.6 941.9 942.9
37 11:10:30 941.1 941.9 942.3
38 11:12:00 941.9 940.4 941.1 941.1 941.9 942.8
39 11:13:30 948.3 948.6 946.6
40 11:15:00 948.7 946.9 950 950 948.5 948.5
41 11:16:30 948.3 948.5 948.9
42 11:18:00 946.7 945.8 944.6 944.6 946.3 950
43 11:19:30 947 948.5 949.8
44 11:55:30 950.1
45 11:57:00 950.8 949.4 953.3 953.3 952.3
46 11:58:30 952.1 948.3 952.1
Table 7.1 PMOD/WRC Method to Calculate WRR Reduction Factor for HF28968
43


A B C D E F G
47 12:00:00 951.9 951.4 951 951 950.7 954.2
48 12:01:30 951.6 950.7 953.4
49 12:03:00 954.1 953.2 951.9 951.9 952.8 954.9
50 12:04:30 953.3 952.9 955.1
51 12:06:00 954.7 954.4 956.9 956.9 955.2 956.8
52 12:07:30 954.8 952.9 956.1
53 12:09:00 956.6 954.3 952 952 955.2 958
54 12:10:30 956.6 955.2 959.7
55 12:12:00 956.9 956.4 958.8 958.8 957.6 959.8
56 12:13:30 955.1 955.3 958.8
57 12:22:30 957.1 957.7
58 12:24:00 956.7 954.8 952.6 950.2 957
59 12:25:30 958.6 955.9 959.4
60 12:27:00 956.8 954.9 953.2 957.6 955.9 957.2
61 12:28:30 958.1 955.9 958.8
62 12:30:00 960.2 958.4 957.1 964.9 958.3 962
63 12:31:30 958.5 958.3 959.9
64 12:33:00 954.8 953.3 952.4 957 953.7 956.3
65 12:34:30 957.8 958.3 960.3
66 12:36:00 959 957.4 955.5 963.6 958.3 960.7
67 12:37:30 958.7 958.3 960.9
68 12:39:00 958 956.8 954.9 958.5 958.3 960.6
69 12:40:30 959.4 958.3 961.3
70 12:49:30 955.9 956.5
71 12:51:00 953.6 953.2 951.5 952.8 955.6
72 12:52:30 954.2 951.5 956.5
73 12:54:00 953.5 952.5 949.2 952.8 949.1 954.3
74 12:55:30 956.3 953.7 958.7
75 12:57:00 954.6 953.4 951.6 955.1 951.4 955.7
76 12:58:30 956.8 953.7 956.5
77 13:00:00 953.8 952.7 951.2 954.5 951.4 955.7
78 13:01:30 951.6 949.1 953.4
79 13:03:00 954 952.7 950.1 955.3 951.4 954.6
80 13:04:30 952 949.1 953.7
81 13:06:00 949.3 948.3 954.4 948 946.9 951.2
82 13:07:30 949.9 949.1 952.6
83 13:16:30 946.3 946.5
84 13:18:00 945.8 943.8 942.2 945.6 946
85 13:19:30 943.9 942.4 944.7
86 13:21:00 942.5 940.6 938.8 940.9 940.2 943.2
87 13:22:30 940.9 940.2 942
88 13:24:00 937.3 936.5 936 941.4 935.9 938.7
89 13:25:30 937.7 935.8 938.7
90 13:27:00 937.8 935.7 933.7 938.4 935.9 938.7
91 13:28:30 937 935.9 937.3
92 13:30:00 934.4 933.5 931.2 935.1 933.6 934.7
93 13:31:30 933.4 933.6 935.6
Table 7.1 PMOD/WRC Method to Calculate WRR Reduction Factor for HF28968
44


A B C D E F G
94 13:33:00 937.9 936 933.3 937.6 935.9 938.7
95 13:34:30 935.1 933.7 936.5
96 13:43:30 926.3 927.3
97 13:45:00 927.6 926.3 924.3 928.3 929.1
98 13:46:30 926.6 925.6 927
99 13:48:00 925.4 924.1 922.3 926.5 925.6 926.8
100 13:49:30 926.6 925.6 927.7
101 13:51:00 923.5 922.3 920.8 925.3 923.5 924.6
102 13:52:30 922.3 921.3 923.3
103 13:54:00 921.1 921 918.1 923.1 921.3 924.4
104 13:55:30 921.8 921.3 922.7
105 13:57:00 921 919.6 916.9 920.7 921.3 922.5
106 13:58:30 918.2 916.7 919.5
107 14:00:00 915.2 913.5 912.4 916.4 914.3 916.8
108 14:01:30 914.9 914.4 916.2
109 10/12/95
110 11:55:30 1000.2 1001.5
111 11:57:00 1000.6 999.7 997.9 1001.5 1001.9
112 11:58:30 1000.5 999.4 1002.1
113 12:00:00 1000.2 999.9 998.1 1002.3 999.3 1001.4
114 12:01:30 1001 999.4 1001.8
115 12:03:00 1001.4 1000.2 994.8 1012.3 999.4 1002.6
116 12:04:30 1002 999.4 1003.5
117 12:06:00 1003.1 1001.4 999.8 997 1001.4 1004
118 12:07:30 1002.2 1001.5 1003.1
119 12:09:00 1001.8 1000.8 998.9 1007 1001.4 1003.2
120 12:10:30 1001.1 999.5 1001.7
121 12:12:00 1000.7 1000.1 998.7 1005.6 999.5 1002
122 12:13:30 1000.4 1001.5 1001.8
123 12:22:30 999.3 1001.1
124 12:24:00 1000.6 999.5 998.3 1000.5 1001.9
125 12:25:30 999.5 997.2 1001.5
126 12:27:00 1000.4 999.6 997.5 999.1 999.2 1001.5
127 12:28:30 1000 997.2 1002
128 12:30:00 1000.3 998.9 999.9 999.8 999.2 1002.1
129 12:31:30 1000.1 999.2 1002.1
130 12:33:00 1000.5 1000.4 998.9 996.3 999.2 1002.6
131 12:34:30 1000 999.2 1002
132 12:36:00 998.9 997.4 995.4 1010.6 997.2 1001.7
133 12:37:30 999.5 997.2 1001.1
134 12:39:00 999.5 997.2 997.4 995.1 997.2 1001.1
135 12:40:30 998.7 997.2 1001
136
137
138
139
140
Table 7.1 PMOD/WRC Method to Calculate WRR Reduction Factor for HF28968
45


H I J K L
1 PM05/PM02 CR0M2L/PM02 CR0M3R/PM02 MK67814/PM02 HF28968/PM02
2 =R(j,PM05) -R(j,CROM2L) =R(j,CROM3R) =R(j,MK67814) =R(i,HF28968)
3 0.9996093
4 0.9985326 0.9968695 1.0058697 1.0006848
5 1.0018618
6 0.9991187 0.9995104 1.0084215 1.0004896
7 0.9996079
8 0.9995091 1.0004909 1.0088357 1.0004909
9 1.0019619
10 0.9996071 0.9975447 1.0002946 1.0018660
11 1.0016686
12 0.9989183 0.9967548 0.9990166 1.0007867
13 1.0013777
14 0.9983253 0.9956655 0.9961580 1.0017732
15 1.0016732
16
17 0.9995718
18 0.9992494 0.9962471 1.0032168 1.0004289
19 1.0011781
20 0.9982846 0.9971052 1.0026804 1.0023587
21 1.0006408
22 0.9985075 0.9961620 1.0013859 1.0005330
23 1.0007454
24 0.9980855 0.9937247 1.0063816 1.0009572
25 1.0020215
26 0.9984085 0.9972414 1.0000000 1.0003183
27 1.0005311
28 0.9987261 0.9971338 1.0048832 1.0011677
29 1.0019076
30
31 1.0019188
32 0.9993608 0.9976561 0.9952056 1.0017047
33 1.0001064 1.0015966
34 0.9988318 0.9975573 0.9975573 1.0003186 1.0012744
35 0.9996816 1.0020166
36 0.9988315 0.9959635 0.9959635 1.0005311 1.0015934
37 1.0008501 1.0012751
38 0.9984075 0.9991507 0.9991507 1.0000000 1.0009555
39 1.0003164 0.9982073
40 0.9981027 1.0013703 1.0013703 0.9997892 0.9997892
41 1.0002109 1.0006327
42 0.9990493 0.9977818 0.9977818 0.9995775 1.0034858
43 1.0015839 1.0029567
44
45 0.9985276 1.0026294 1.0026294 1.0015776
46 0.9960088 1.0000000
Table 7.1 PMOD/WRC Method to Calculate WRR Reduction Factor for HF28968
46


H I J K L
47 0.9994747 0.9990545 0.9990545 0.9987394 1.0024162
48 0.9990542 1.0018916
49 0.9990567 0.9976942 0.9976942 0.9986375 1.0008385
50 0.9995804 1.0018882
51 0.9996858 1.0023044 1.0023044 1.0005237 1.0021996
52 0.9980101 1.0013615
53 0.9975957 0.9951913 0.9951913 0.9985365 1.0014635
54 0.9985365 1.0032406
55 0.9994775 1.0019856 1.0019856 1.0007315 1.0030306
56 1.0002094 1.0038739
57 1.0006269
58 0.9980140 0.9957144 0.9932058 1.0003136
59 0.9971834 1.0008346
60 0.9980142 0.9962375 1.0008361 0.9990594 1.0004181
61 0.9977038 1.0007306
62 0.9981254 0.9967715 1.0048948 0.9980212 1.0018746
63 0.9997913 1.0014606
64 0.9984290 0.9974864 1.0023041 0.9988479 1.0015710
65 1.0005220 1.0026101
66 0.9983316 0.9963504 1.0047967 0.9992701 1.0017727
67 0.9995828 1.0022948
68 0.9987474 0.9967641 1.0005219 1.0003132 1.0027140
69 0.9988535 1.0019804
70 1.0006277
71 0.9995805 0.9977978 0.9991611 1.0020973
72 0.9971704 1.0024104
73 0.9989512 0.9954903 0.9992659 0.9953854 1.0008390
74 0.9972812 1.0025097
75 0.9987429 0.9968573 1.0005238 0.9966478 1.0011523
76 0.9967600 0.9996865
77 0.9988467 0.9972741 1.0007339 0.9974837 1.0019920
78 0.9973728 1.0018916
79 0.9986373 0.9959119 1.0013627 0.9972746 1.0006289
80 0.9969538 1.0017857
81 0.9989466 1.0053724 0.9986306 0.9974718 1.0020015
82 0.9991578 1.0028424
83 1.0002113
84 0.9978854 0.9961937 0.9997885 1.0002115
85 0.9984108 1.0008475
86 0.9979841 0.9960743 0.9983024 0.9975597 1.0007427
87 0.9992560 1.0011691
88 0.9991465 0.9986130 1.0043743 0.9985063 1.0014937
89 0.9979738 1.0010664
90 0.9977607 0.9956281 1.0006398 0.9979740 1.0009597
91 0.9988260 1.0003202
92 0.9990368 0.9965753 1.0007491 0.9991438 1.0003211
93 1.0002143 1.0023570
Table 7.1 PMOD/WRC Method to Calculate WRR Reduction Factor for HF28968
47


H I J K L
94 0.9979742 0.9950954 0.9996801 0.9978676 1.0008530
95 0.9985028 1.0014972
96 1.0010796
97 0.9985985 0.9964424 1.0007546 1.0016171
98 0.9989208 1.0004317
99 0.9985952 0.9966501 1.0011887 1.0002161 1.0015129
100 0.9989208 1.0011871
101 0.9987006 0.9970763 1.0019491 1.0000000 1.0011911
102 0.9989158 1.0010842
103 0.9998914 0.9967430 1.0021713 1.0002171 1.0035827
104 0.9994576 1.0009764
105 0.9984799 0.9955483 0.9996743 1.0003257 1.0016287
106 0.9983664 1.0014158
107 0.9981425 0.9969406 1.0013112 0.9990166 1.0017483
108 0.9994535 1.0014209
109
110 1.0012997
111 0.9991005 0.9973016 1.0008995 1.0012992
112 0.9989005 1.0015992
113 0.9997001 0.9979004 1.0020996 0.9991002 1.0011998
114 0.9984016 1.0007992
115 0.9988017 0.9934092 1.0108848 0.9980028 1.0011983
116 0.9974052 1.0014970
117 0.9983053 0.9967102 0.9939189 0.9983053 1.0008972
118 0.9993015 1.0008980
119 0.9990018 0.9971052 1.0051907 0.9996007 1.0013975
120 0.9984018 1.0005993
121 0.9994004 0.9980014 1.0048966 0.9988008 1.0012991
122 1.0010996 1.0013994
123 1.0018013
124 0.9989007 0.9977014 0.9999001 1.0012992
125 0.9976988 1.0020010
126 0.9992003 0.9971012 0.9987005 0.9988005 1.0010996
127 0.9972000 1.0020000
128 0.9986004 0.9996001 0.9995001 0.9989003 1.0017995
129 0.9991001 1.0019998
130 0.9999000 0.9984008 0.9958021 0.9987006 1.0020990
131 0.9992000 1.0020000
132 0.9984983 0.9964961 1.0117129 0.9982981 1.0028031
133 0.9976988 1.0016008
134 0.9976988 0.9978989 0.9955978 0.9976988 1.0016008
135 0.9984980 1.0023030
136 MEAN= R(k)'=
137 0.9987391 0.9974337 1.0009826 0.9988273 1.0013782
138 SD(k)'=
139 0.0005648 0.0020621 0.0037683 0.0011913 0.0008673
140 MEAN OF CR0M2UPM02, REJECTING READIN GS NUMBER 18,24,40,45,51,
Table 7.1 PMOD/WRC Method to Calculate WRR Reduction Factor for HF28968
48


H I J K L
141 55,81 AND 115= 8 READINGS=
142 0.9970142
143 0.0010445
144 MEAN OF CR0M3R/PM02, RE. JECTING READING NUMBER J4,6,8,14,24,28,
145 32,34,36,42,49,53,58,62,66,88,115,117,119,121,130,132 AND 134= 23 READINGS=
146 1.0006416
147 0.0012786
148 MEAN OF MK67814/PM02 AFTER REJECTING READING NUMBER K73=
149 0.9988669
150 0.0011865
151 MEAN= R(k)=
152 0.9987391 0.9970142 1.0006416 0.9988669 1.0013782
153 SD=
154 0.0005648 0.0010445 0.0012786 0.0011865 0.0008673
155
156 PM02 PM05 CROM2L CPOM3R MK67814
157 WRR(IPC7,K)=
158 0.9994370 1.0006300 1.0029400 0.9989010 1.0009400
159 W(IPC8,K)=
160 1.0000000 0.9999313 1.0005087 1.0001049 1.0003690
161 MEAN=M= 1.0001828
162 D(k)=
163 -0.0001828 -0.0002515 0.0003259 -0.0000778 0.0001862
164 WRR(IPC8,K)=
165 0.999619772 1.000881519 1.002614086 0.998978845 1.000753778
166 NOTE, INSTRUMENTS THAT H AVE MORE REA DINGS HAVE B GGER CHANGE
167 MEAN= M(IPC7)= 1.0005696
168 MEAN= M(IPC8)= 1.0005696
169 D= 0
170 WRR(IPC8,HF28968)= 0.99824402
171 SD(IPC8,HF28968)= 0.000867255
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
Table 7.1 PMOD/WRC Method to Calculate WRR Reduction Factor for HF28968
49


M N O P Q R S
1 PM02 PM05 CROM2L CROM3R MK67814
2 WRR(IPC7,K)=
3 0.9994370 1.0006300 1.0029400 0.9989010 1.0009400
4 W(IPC8,K)=
5 1.0000000 0.9999313 1.0005087 1.0001049 1.0003690
6 MEAN=M= 1.0001828
7 D(k)=
8 -0.000183 -0.000252 0.0003259 -7.78E-05 0.0001862
9 WRR(IPC8,K)=
10 0.9996198 1.0008815 1.0026141 0.9989788 1.0007538
11 NOTE, INSTRUMENT! THAT HAVE MORE F EADINGS HAVE LARGER
12 CHANGE IN THEIR W *R REDUC1 HON FACTOR
13 MEAN= M(IPC7)= 1.0005696
14 MEAN= M( PC8)= 1.0005696
15 D= 0
16
17 WRR(IPC8,HF28968)= 0.998244
18 SD(IPC8,HF28968)= 0.0008673
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
Table 7.1 PMOD/WRC Method to Calculate WRR Reduction Factor for HF28968
50


7.2 Proposed method
The following rows, cells, or columns in Table 7.2
describe the sequence of the proposed method used to
calculate the WRR reduction factor for HF28968.
a) Columns B through F contain the irradiance readings of
the WSG instruments; the whole population of data is
divided into seven samples. Rows 6 through 11, 13
through 25, 28 through 30, 34 through 48, 51 through 52,
56 through 58 and 61 through 83, are samples, 1, 2, 3,
4, 5, 6 and 7 respectively.
b) Columns G through K contain the ratios of irradiances
of the WSG instruments to a reference irradiance using
Equations 6.1 through 6.3.
c) Cells G86 through K86 contain the mean of ratios in
step (b) after rejecting the outliers.
d) Cells G88 through K88 contain the standard deviations
of the mean of ratios in step (c).
e) Cells G95 through K95, G97 through K97, G99 through
K99, G101 through K101, G103 through K103, G105 through
K105 and G92 through K92 contain the weighting factors
for each of the WSG instruments for samples, 1, 2, 3, 4,
5, 6, and 7 respectively. The weighting factor is
calculated using Equations 6.7 and 6.8.
f) Column L contains a reference irradiance calculated
using Equation 6.9.
51


g) Columns M through Q contain the ratios of the
irradiances in columns B through F to the reference
irradiances in column L.
h) Cells M86 through Q86 contain the WRR reduction
factors for the WSG instruments during IPC-VIII, which
is the mean of the ratios in step (g).
i) Cells M88 through Q88 contain the standard deviations
of the means in step (h).
j) The weighting factors are recalculated in the same
rows as in step (e) but using columns M through Q
instead of columns G through K.
k) Column R contains the reference irradiance calculated
using Equation 6.11.
l) Column S contains a sample of irradiance readings for
HF28968 during IPC-VIII.
m) Column T contains the ratio of column R to column 1.
n) Cell T86 contains the mean of the ratios in step (m),
which is the WRR reduction factor for HF28968 during
IPC-VIII.
o) Cell T88 contains the standard deviation of the WRR
reduction factor for HF28968 during IPC-VIII.
52


A B C D E F
1 Date/Time PM02 PM05 CROM2L CROM3R MK67814
2 WRR from (IPC7):
3 0.999437 1.00063 1.00294 0.998901 1.00094
4
5 10/2/95
6 11:24:00 1022.2 1020.7 1019
7 11:27:00 1021.2 1020.3 1020.7
8 11:39:00 1015.1 1013.4 1010.7
9 10/11/95
10 11:03:00 938.6 938 936.4
11 12:24:00 956.7 954.8 952.6
12
13 11:33:00 1018.2 1017.8 1015.7 1018.5
14 11:36:00 1016.9 1015.8 1013.6 1015.9
15 10/3/95
16 10:21:00 932.6 931.9 929.1 935.6
17 10:24:00 932.7 931.1 930 935.2
18 10:27:00 938 936.6 934.4 939.3
19 10/11/95
20 12:51:00 953.6 953.2 951.5 952.8
21 13:18:00 945.8 943.8 942.2 945.6
22 13:45:00 927.6 926.3 924.3 928.3
23 10/12/95
24 11:57:00 1000.6 999.7 997.9 1001.5
25 12:24:00 1000.6 999.5 998.3 1000.5
26
27 10/3/95
28 10:33:00 942.5 941 942.5
29 10/11/95
30 11:57:00 950.8 949.4 953.3
31
32
33 10/11/95
34 11:06:00 941.6 940.5 939.3 941.9
35 11:09:00 941.4 940.3 937.6 941.9
36 11:18:00 946.7 945.8 944.6 946.3
37 12:03:00 954.1 953.2 951.9 952.8
38 12:09:00 956.6 954.3 952 955.2
39 12:30:00 960.2 958.4 957.1 958.3
40 12:36:00 959 957.4 955.5 958.3
41 13:24:00 937.3 936.5 936 935.9
42 10/12/95
43 12:06:00 1003.1 1001.4 999.8 1001.4
44 12:09:00 1001.8 1000.8 998.9 1001.4
45 12:12:00 1000.7 1000.1 998.7 999.5
46 12:33:00 1000.5 1000.4 998.9 999.2
47 12:36:00 998.9 997.4 995.4 997.2
Table 7.2 Proposed Method to Calculate WRR reduction Factor for HF28968
53


A B C D E F
48 12:39:00 999.5 997.2 997.4 997.2
49
50 10/11/95
51 11:15:00 948.7 946.9 950 948.5
52 12:06:00 954.7 954.4 956.9 955.2
53
54
55 10/11/95
56 13:06:00 949.3 948.3 946.9
57 10/12/95
58 12:03:00 1001.4 1000.2 999.4
59
60 10/11/95
61 11:12:00 941.9 940.4 941.1 941.1 941.9
62 12:00:00 951.9 951.4 951 951 950.7
63 12:12:00 956.9 956.4 958.8 958.6 957.6
64 12:27:00 956.8 954.9 953.2 957.6 955.9
65 12:33:00 954.8 953.3 952.4 957 953.7
66 12:39:00 958 956.8 954.9 958.5 958.3
67 12:54:00 953.5 952.5 949.2 952.8 949.1
68 12:57:00 954.6 953.4 951.6 955.1 951.4
69 13:00:00 953.8 952.7 951.2 954.5 951.4
70 13:03:00 954 952.7 950.1 955.3 951.4
71 13:21:00 942.5 940.6 938.8 940.9 940.2
72 13:27:00 937.8 935.7 933.7 938.4 935.9
73 13:30:00 934.4 933.5 931.2 935.1 933.6
74 13:33:00 937.9 936 933.3 937.6 935.9
75 13:48:00 925.4 924.1 922.3 926.5 925.6
76 13:51:00 923.5 922.3 920.8 925.3 923.5
77 13:54:00 921.1 921 918.1 923.1 921.3
78 13:57:00 921 919.6 916.9 920.7 921.3
79 14:00:00 915.2 913.5 912.4 916.4 914.3
80 10/12/95
81 12:00:00 1000.2 999.9 998.1 1002.3 999.3
82 12:27:00 1000.4 999.6 997.5 999.1 999.2
83 12:30:00 1000.3 998.9 999.9 999.8 999.2
84
85
86
87
88
89
90
91
92
93
94
Table 7.2 Proposed Method to Calculate WRR reduction Factor for HF28968
54


G H I J K L
1 R"G,PM02) R"(j,PM05) R"(j,CROM2L) R"(j,CROM3R) R"(j,MK67814) l'(ref.,j)
2
3
4
5
6 0.999466 1.000935 1.002605 1021.54
7 1.000545 1.001427 1.001035 1021.19
8 0.998995 1.000670 1.003344 1014.17
9
10 1.000006 1.000645 1.002355 938.47
11 0.998907 1.000895 1.003207 955.69
12
13 0.999837 1.000230 1.002298 0.999542 1018.08
14 0.999147 1.000229 1.002400 1.000131 1016.24
15
16 1.000152 1.000903 1.003919 0.996945 932.49
17 0.999991 1.001710 1.002895 0.997318 932.24
18 0.999487 1.000981 1.003338 0.998104 937.39
19
20 0.999610 1.000030 1.001817 1.000450 953.40
21 0.998941 1.001058 1.002758 0.999152 944.77
22 0.999423 1.000825 1.002991 0.998669 927.01
23
24 0.999800 1.000700 1.002505 0.998902 1000.30
25 0.999601 1.000701 1.001904 0.999701 1000.15
26
27
28 0.999125 1.000718 0.999125 941.72
29
30 1.000040 1.001515 0.997418 950.37
31
32
33
34 1.000162 1.001332 1.002611 0.999843 941.44
35 0.999815 1.000985 1.003867 0.999285 941.09
36 1.000087 1.001039 1.002310 1.000510 946.55
37 0.999832 1.000776 1.002142 1.001196 953.81
38 0.998813 1.001221 1.003640 1.000277 955.43
39 0.999213 1.001090 1.002450 1.001194 959.35
40 0.999472 1.001142 1.003133 1.000202 958.36
41 1.000052 1.000906 1.001441 1.001548 937.13
42
43 0.999314 1.001010 1.002612 1.001010 1002.32
44 0.999911 1.000910 1.002814 1.000311 1001.54
45 1.000036 1.000636 1.002038 1.001236 1000.60
46 1.000236 1.000336 1.001838 1.001537 1000.64
47 0.999307 1.000810 1.002820 1.001010 998.18
Table 7.2 Proposed Method to Calculate WRR reduction Factor for HF28968
55


G H 1 J K L
48 0.999308 1.001613 1.001412 1.001613 998.52
49
50
51 0.999792 1.001692 0.998424 1.000003 948.14
52 1.000605 1.000919 0.998304 1.000081 954.97
53
54
55
56 0.999141 1.000194 1.001673 948.67
57
58 0.999270 1.000468 1.001269 1000.75
59
60
61 0.999911 1.001506 1.000761 1.000761 0.999911 941.56
62 0.999834 1.000359 1.000780 1.000780 1.001096 951.77
63 1.001406 1.001930 0.999422 0.999422 1.000674 957.57
64 0.999396 1.001385 1.003171 0.998561 1.000337 956.05
65 0.999981 1.001554 1.002501 0.997682 1.001134 954.43
66 0.999837 1.001091 1.003083 0.999315 0.999524 957.70
67 0.998385 0.999433 1.002907 0.999118 1.003013 952.43
68 0.999121 1.000379 1.002271 0.998598 1.002482 953.85
69 0.999435 1.000589 1.002167 0.998702 1.001956 953.26
70 0.999204 1.000567 1.003305 0.997844 1.001934 953.27
71 0.998551 1.000568 1.002487 1.000249 1.000994 941.33
72 0.998967 1.001209 1.003353 0.998328 1.000995 936.77
73 0.999668 1.000632 1.003103 0.998920 1.000525 934.07
74 0.998690 1.000717 1.003612 0.999009 1.000824 936.79
75 0.999897 1.001304 1.003258 0.998710 0.999681 925.09
76 1.000112 1.001414 1.003045 0.998167 1.000112 923.31
77 1.000372 1.000480 1.003641 0.998204 1.000155 921.34
78 0.999373 1.000894 1.003841 0.999698 0.999047 920.43
79 0.999649 1.001510 1.002717 0.998340 1.000633 914.63
80
81 1.000328 1.000628 1.002432 0.998232 1.001229 1000.36
82 0.999328 1.000128 1.002234 1.000629 1.000529 999.93
83 0.999889 1.001291 1.000289 1.000389 1.000990 999.95
84
85 RM(k)=
86 0.99962755 1.00089153 1.002527008 0.998940082 1.000789312
87 SD"(k)=
88 0.00055147 [0,00048267 0.000925781 0.000985592 0.000829701
89 (1/SD"(k))A2=
90 3288234.09 4292304.62 1166765.713 1029450.916 1452634.548
91 WF(k) WHE N ALL INSTRUMENTS FROM THE WSG ARE PARTICIPATING=
92 0.29282393 0.38223845 0.103902859 0.091674697 0.12936006
93 SUM= 1
94 WF'(k) WHE M PM02.PM05 AND CROM 2L ARE PARTICIPATING=
Table 7.2 Proposed Method to Calculate WRR reduction Factor for HF28968
56


G H I J K L
95 0.37591399 0.49070027 0.133385744
96 WF'(k) WHE IM PM02, PM 05, CROM2L AND CROM3R ARE PARTICIPATING=
97 0.33633184 0.43903161 0.119340791 0.105295763
98 WF'(k) WHE IM PM02, PM 05 AND CROM3R ARE PARTICIPATING=
99 0.38190918 0.49852611 0.11956471 |
100 WF'(k) WHEN PM02.PM05, CROM2L AND MK67814 ARE PARTICIPATING=
101 0.32237782 0.4208167 0.11438948 0.142416004
102 WF'(k) WHE N PM02, PM 05, CROM3R AND MK67814 ARE PARTICIPATING=
103 0.32677699 0.42655917 0.102304419 0.144359416
104 WF'(k) WHE N PM02, PM 05 AND MK67814 ARE PARTICIPATING=
105 0.3640176 0.47517129 0.160811102
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
Table 7.2 Proposed Method to Calculate WRR reduction Factor for HF28968
57


M N O P Q
1 R(i,PM02) RG.PM05) RU.CROM2L) RG.CROM3R) RG,MK67814)
2
3
4
5
6 0.999350345 1.00081897 1.002488639
7 0.999991421 1.000873507 1.000481277
8 0.99908749 1.00076348 1.003436936
9
10 0.999862214 1.000501784 1.002211313
11 0.9989412 1.000929039 1.003240653
12
13 0.999886904 1.000279864 1.002347983 0.999592387
14 0.999355319 1.000437511 1.002608942 1.000339033
15
16 0.999881785 1.000632849 1.003648426 0.996675665
17 0.999504203 1.001221749 1.00240599 0.996832304
18 0.999353094 1.000846895 1.003203341 0.99796998
19
20 0.999786282 1.000205832 1.001992852 1.000625734
21 0.998915587 1.001032382 1.002732288 0.999126863
22 0.999360263 1.000762798 1.002928248 0.998606679
23
24 0.999698868 1.000598867 1.002403735 0.998800487
25 0.99955379 1.000653849 1.001856679 0.999653696
26
27
28 0.999173745 1.000766477 0.999173745
29
30 0.999547174 1.001021122 0.996925893
31
32
33
34 0.999827056 1.000996445 1.002275265 0.999508606
35 0.999674386 1.000843844 1.003725967 0.999143717
36 0.999838763 1.000790185 1.002061568 1.000261394
37 0.999697818 1.00064172 1.002008286 1.001061805
38 0.998781059 1.001188264 1.003607102 1.000244934
39 0.999111965 1.000988428 1.00234804 1.001092882
40 0.999328499 1.000998569 1.002989043 1.000058469
41 0.999822352 1.000676445 1.001210994 1.001317972
42
43 0.999221154 1.000917455 1.002519244 1.000917455
44 0.999744442 1.000743387 1.002646894 1.000143781
45 0.999901088 1.000500969 1.001903494 1.00110157
46 1.000143013 1.000242987 1.001745004 1.00144424
47 0.99927689 1.000779712 1.002790521 1.00098043
Table 7.2 Proposed Method to Calculate WRR reduction Factor for HF28968
58


M N O P Q
48 0.999015746 1.001319934 1.001119148 1.001319934
49
50
51 0.999407759 1.001307573 0.998040148 0.999618493
52 1.000285064 1.000599487 0.997985317 0.999761464
53
54
55
56 0.999337763 1.000391583 1.001870671
57
58 0.999354327 1.000553312 1.001354235
59
60
61 0.999637419 1.001231907 1.00048718 1.00048718 0.999637419
62 0.999863574 1.000389044 1.000809817 1.000809817 1.00112563
63 1.000696422 1.00121958 0.998713398 0.998713398 0.999964918
64 0.999215976 1.001204153 1.002989767 0.998381209 1.000156759
65 0.999611824 1.001184694 1.002130795 0.997313865 1.000764778
66 0.99968485 1.000938636 1.002930241 0.999163366 0.999371895
67 0.998877003 0.999925693 1.003402046 0.999610855 1.003507768
68 0.999218435 1.000476105 1.002368556 0.998695339 1.002579271
69 0.999429041 1.000582995 1.00216087 0.998696091 1.001950199
70 0.999237509 1.000601011 1.00333921 0.997877717 1.00196824
71 0.998761241 1.000778726 1.002697561 1.000459634 1.001204499
72 0.998896999 1.001138833 1.003283288 0.998258318 1.000924891
73 0.999645283 1.000609054 1.00308049 0.998896965 1.000501877
74 0.998821489 1.000849011 1.003744427 0.999141077 1.000955951
75 0.999663256 1.001069557 1.003023287 0.998476392 0.999447253
76 0.999789637 1.001090458 1.002721253 0.997844731 0.999789637
77 1.000258837 1.000367443 1.003527301 0.998091664 1.000041696
78 0.999379858 1.000901315 1.003848674 0.999705495 0.999054433
79 0.999376273 1.001236086 1.002443188 0.998067618 1.000360018
80
81 1.000155056 1.000455133 1.00225938 0.99805955 1.001055827
82 0.999530556 1.0003305 1.002436459 1.000831116 1.000730953
83 0.999647673 1.001048721 1.000047572 1.000147597 1.000748166
84 WRR(IPC8)
85 PM02 PM05 CROM2L CROM3R MK67814
86 0.999516088 1.000779929 1.002419267 0.99883547 1.000676103
87 SD(k)=
88 0.00040699 0.00032042 0.000985037 0.001113079 0.000940421
89 (1/SD(k))A2=
90 6037150.257 9740021.616 1030610.526 807138.9198 1130720.495
91 WF'(k) WHEN ALL INSTRUME NTS FROM THE WSG ARE PA *TICIPATING=
92 0.322056205 0.519588591 0.054978674 0.043057417 0.060319113
93 SUM= 1
94 WF'(k) WHEN PM02,PM05 Ah D CROM2L ARE PARTICIPATI MG=
Table 7.2 Proposed Method to Calculate WRR reduction Factor for HF28968
59


M N O P Q
95 0.359187792 0.579494747 0.06131746
96 WF'(k) WHEN PM02, PM05, CROM2L AND CROM3R ARE PARTICIPATING:
97 0.342729334 0.552941534 0.058507813 0.045821318
98 WF'(k) WHEN PM02, PM05 AND CROM3R ARE PARTICIPATING=
99 0.364027805 0.58730337 0.048668825
100 WF'(k) WHEN PM02.PM05, CROM2L AND MH67814 ARE PARTICIPATING:
101 0.336547051 0.542967363 0.057452427 0.063033158
102 WF'(k) WHEN PMQ2, PM05, CROM3R AND M K67814 ARE PARTICIPATING1
103 0.340792526 0.549816789 0.045562376 0.063828309
104 WF'(k) WHEN PMQ2, PM05 A ND MK67814 AF IE PARTICIPAT NG=
105 0.357061077 0.576063616 0.066875307
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
Table 7.2 Proposed Method to Calculate WRR reduction Factor for HF28968
60


R S T
1 WRR(IPC8,j) i(j,HF28968) WRR(lPC8,j,HF)
2
3
4
5
6 1021.57 1022.9 0.99869913
7 1021.08 1021.7 0.999395947
8 1014.28 1016.9 0.997420162
9
10 938.52 940.2 0.998210065
11 955.75 957 0.998698127
12
13 1018.21 1020.1 0.998142998
14 1016.41 1017.7 0.998733845
15
16 932.47 933 0.999436578
17 932.10 934.9 0.997005415
18 937.41 938.5 0.998833462
19
20 953.56 955.6 0.99786098
21 944.81 946 0.998739203
22 927.05 929.1 0.997790334
23
24 1000.34 1001.9 0.998441457
25 1000.21 1001.9 0.998308727
26
27
28 941.83 942.8 0.998971806
29
30 950.31 952.3 0.997913256
31
32
33
34 941.31 942.8 0.998414529
35 941.03 942.9 0.998018196
36 946.48 950 0.996298439
37 953.82 954.9 0.998873456
38 955.42 958 0.997306988
39 959.35 962 0.997243484
40 958.31 960.7 0.997511224
41 937.12 938.7 0.998313301
42
43 1002.32 1004 0.998329325
44 1001.51 1003.2 0.998312875
45 1000.63 1002 0.998628461
46 1000.71 1002.6 0.998118944
47 998.22 1001.7 0.996523854
Table 7.2 Proposed Method to Calculate WRR reduction Factor for HF28968
61


R S T
48 998.43 1001.1 0.997329218
49
50
51 948.00 948.5 0.999469589
52 954.91 956.8 0.998024108
53
54
55
56 948.87 951.2 0.997548646
57
58 1000.90 1002.6 0.998300916
59
60
61 941.39 942.8 0.998507506
62 951.83 954.2 0.99752081
63 957.23 959.8 0.997317815
64 955.95 957.2 0.998694747
65 954.27 956.3 0.997879468
66 957.60 960.6 0.99687918
67 952.80 954.3 0.998431339
68 954.00 955.7 0.998216097
69 953.33 955.7 0.997515705
70 953.36 954.6 0.998705135
71 941.45 943.2 0.998146782
72 936.74 938.7 0.997915211
73 934.09 934.7 0.999343136
74 936.87 938.7 0.998055551
75 924.96 926.8 0.998012245
76 923.15 924.6 0.998430799
77 921.32 924.4 0.99667282
78 920.39 922.5 0.997717964
79 914.50 916.8 0.997491694
80
81 1000.34 1001.4 0.998938854
82 1000.07 1001.5 0.998571168
83 999.84 1002.1 0.997739958
84
85 MEAN, M(IPC8) WRR(IPC8,HF28968)
86 1.00 0.998103001
87 SD0PC8.HF28968)
88 MEAN, M(IPC7) 0.000697432
89 1.00
90 D= -124 ppm
91
92
93
94
Table 7.2 Proposed Method to Calculate WRR reduction Factor for HF28968
62


Chapter 8
8. Observations and Conclusions Drawn from the
International Pyrheliometer Comparisons IPC-VIII
a) Using the PMOD/WRC method, a single instrument, PM02,
is used as a transfer instrument through which all
instruments are compared to each other, resulting in a
larger random component of uncertainty than if that
transfer instrument were not interposed in the process.
b) Using the PMOD/WRC method, if an irradiance reading of
PM02 were out of tolerance, then all ratios to PM02
would be rejected for that irradiance reading, which
would result in rejection of good data.
c) The proposed method showed, independently, that PM02
has a small standard deviation. This finding supports
the PMOD/WRC choice to use it as a transfer instrument
for its stability during the comparison. The proposed
method also showed that PM05 has an even smaller
standard deviation than PM02, which makes PM05 a good
candidate for future considerations and that CR0M2L and
CR0M3R have the largest standard deviations of all the
WSG.
d) The standard deviation of the WRR reduction factor
derived by using the proposed method is smaller than the
standard deviation derived by using the PMOD/WRC method
(see Table 8.1).
63


e) The difference between the WRR reduction factors
derived by each method is much smaller than the standard
deviations (see Table 8.1). Thus, the results of both
methods are comparable.
Table 8.1 WRR Reduction Factor for HF28968
PMOD/WRC Proposed Difference
Method Method WRC Prop.
WRR 0.998244 0.998103 0.000141
SD 0.000867 0.000697 0.000170
f) Fig. 8.1 and 8.2 show the WRR reduction factors and
standard deviations calculated using the PMOD/WRC method
and the proposed method.
g) Fig. 8.3 shows the means of WRR reduction factors of
the WSG instruments.
h) Figs. 8.4 through 8.6 show the change of the M factor
with time and irradiance calibration levels, which is
the irradiance levels at which the HF28968 calibrations
are performed, on three different days. Figs. 8.7
through 8.9 show the change of temperature of the
sensing element, in degrees centigrade, with time and
irradiance calibration levels for the three days.
Fig. 8.8 shows that the temperature of the sensing
element decreased between 8:37 to 10:02; Fig. 8.5 shows
that the M factor increased during the same period. When
the temperature increased, during the period 10:02 to
64


13:12, the M Factor decreased. From 13:12 to 15:53, the
rate of temperature change was different, the M factor
changed in the same way, inversely proportional to the
change in temperature. The same trend is shown in Figs.
8.4, 8.6, 8.7 and 8.9 for two other days (see Fig. 8.10
for M factor against temperature). That shows the
importance of calibrating the absolute cavity
radiometers more often where there is large Change in
ambient temperature.
65


w
R
R
R
E
D
U
C
T
I
O
N
F
A
C
T
O
R
1.0030
1.0029
1.0028
1.0027
1.0026
1.0025
1.0024
1.0023
1.0022
1.0021
1.0020
1.0019
1.0018
1.0017
1.0016
1.0015
1.0014
1.0013
1.0012
1.0011
1.0010
1.0009
1.0008
1.0007
1.0006
1.0005
1.0004
1.0003
1.0002
1.0001
1.0000
0.9999
0.9998
0.9997
0.9996
0.9995
0.9994
0.9993
0.9992
0.9991
0.9990
0.9989
0.9988
0.9987
0.9986
0.9985
0.9984
0.9983
0.9982
0.9981
0.9980
f
c

1

I
I

I
I
11:1
:1
:!
I
-!
1
I

t
I

I
I;
I:

1
I

1

I

i
1


PM02 PM05 CROM2L CROM3R MK67814 HF28968
Participating Instrument
^ WRR(IPC8) Propo. M WRR(IPC8) PMOD ^ WRR(IPC7) PMOD
Fig. 8.1 WRR Reduction Factors
66


OOCD'tC'JOOOtD^l-CMOOOCD^tCNOOOCD-^-Cy|000(D'l-CNOCO(D' cNCMCMCMfM'*i<-T-oooooo50>0)0)0)eoeococoeor^ri^-r^is'COtocD(DCDininininiO'>tfT}"^"^-> tr-T-T-Tii-tii-t-trraoooooooooooaooooooooaooooocoooooooooooooooooooooo
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oppopooooooooooooopppoooopooooppooppooooooooooooopoooooooppppopop
ooooo'o'ooooooooo'ooooooooooooooo'ooooooocjoooooooooooooaooooooooooooo
CO I- D L1J >
PM02 PM05 CROM2L CR0M3R MK67814 HF28968
Participating Instrument
^ SD(IPC8) Proposed ^ SD(IPC8) PMOD
Fig. 8.2 Standard Deviations


2w ii. o a:
^ MEAN(WRR,IPC8) DU MEAN(WRR,IPC8) ^ MEAN(WRR,IPC7)
Fig. 8.3 Means of WRR Reduction Factors for the WSG
68


30HO>T1
M Factor For HF28968
7 October 1995
CALIBRATION LEVEL W/mA2
Fig. 8.4 Change of The M Factor With Different Irradiance Calibration Levels And Time
69


ilcoi-oq:
M Factor For HF28968
11 October 1995
CALIBRATION LEVEL W/mA2
Fig. 8.5 Change of The M Factor With Different Irradiance Calibration Levels And Time
70


M Factor For HF28968
12 October 1995
CALIBRATION LEVEL W/mA2
Fig. 8.6 Change of The M Factor With Different Irradiance Calibration Levels And Time
71


Hzmo
8:49 9:27 9:52 10:21 10:4711:1311:4012:0812:3513:0213:5714:2415:11 15:38
CALIBRATION TIME
10/7/95
Fig. 8.7 Change of Cavity Temperature with Time and Irradiance Calibration Levels
72


m d > n oizmo z mscH>7JmusmH -< h < > o
10/11/95
Fig. 8.8 Change of Cavity Temperature with Time and Irradiance Calibration Levels
73


23.5- Oft ft - / r-
Oft A - y| > \ X-7-
OO O 9 r.
OO 7 J >
/ oo c Ql 15''
OO ft / \
A OO A /
C 04 Q yi
A 4-1 .a- W 04 7 / r
V ^ 1 / 04 ft /
-i- 04 0 _ /
| ^ 1 .o w 04 4 9f [8
Y Z 1 1 Oft Q _ / f
-r Oft 7 _ /
| ^U. f r- Oft 5 _ / t
t ^U.j Ajf Oft ft _ j
Ivl ^u.o n Oft 4 _ Of i >o
C 4 Q Q _ JV r
D 40 7- /
K 1 57. / A 40 A _ /
M 1 w.3 T 40 ft _ /
II 40 4 - /
D 4 fl O . 40 nn
i\ 10.9 P 4ft 7 - 1U * JU
IOC. /
1 0.0 1 4ft ft j /
1 10.0 M 4 ft 4 J /
4 7 0- /
1 / . P. 4 7 7. nn7\ l//mA;
F 4 7ft- /
* i / .j N 17Q. /
T 171 . /
I 1RO. /
G 1R 7 - 9!
R 1ft R _ / >
A 1ft - /
D 1R 1 - /
E 1 ft Q - /
4ft 7 _ 91
4ft ft /
10.0 4ft ft / /
1 0.0 4ft io/ 9) n P
1 o. w 140 J )U-,_ r
4/7 _
14.5-
9:34 10:0 10:2 10:5 11:2 11:5 12:1 12:4 13:1 13:3 14:0 14:3 15:0 15:2 15:5
CALIBRATION TIME
10/12/95
Fig. 8.9 Change of Cavity Temperature with Time and Irradiance Calibration Levels
74


961.5
961.4
961.3
961.2
961.1
961.0
960.9
960.8
960.7
960.6
960.5
960.4
960.3
960.2
960.1
960.0
959.9
959.8
959.7
959.6
M 959.5
959.4
F 959.3
A 959.2
C 959.1
T 959.0
O 958.9
R 958.8
958.7
958.6
958.5
958.4
958.3
958.2
958.1
958.0
957.9
957.8
957.7
957.6
957.5
957.4
957.3
957.2
957.1
957.0
956.9
956.8
15 16 17 18 19 20 21 22 23 24
TEMPERATURE IN DEGREE CENTIGRADE
10/7/95 10/11/95 * 10/12/95
Fig. 8.10 Change of M Factor with Temperature for HF28968
75


i) Table 8.2 shows the calculated M factor when the
HF28968 is calibrated at three different irradiance
levels and temperature of the sensing element is at 18.9
C. The values are obtained using Figures 8.4 through
8.9.
Table 8.2 Change of the M Factor for HF28968
Date 10/11/1995 10/7/1995 10/12/1995
Irradiance 812 960 1000
Cal. Levels W/m2 W/m2 W/m2
Temperature 18.9 C 18.9 C 18.9 C
M Factor 958.7 959.3 959.6
If the HF28968 is calibrated at an irradiance level
that equals 812 W/m2, and the irradiance to be measured
is at 1000 W/m2, then an error of -0.9, (958.7 is
subtracted from 959.6), will be noticed in the
irradiance reading at 1000 W/m2. This error, which
appears because the output voltage of the thermopile
will be multiplied by 958.7 instead of 959.6, is on the
order of -0.09 percent of the irradiance being measured.
The change in the M factor is attributed to, the change
of the cavity sensitivity with the change in irradiance
levels, the change in barometric pressure and/or the
noise from, the Digital Multimeter, the control box and
signal connection from the control box to the DMM. Noise
can be minimized by using digital multimeters with less
noise and better zero stability, and also by using
thermal and electro magnetic interference (EMI)
insulated signal connection from the control box to
the DMM. Changing barometric pressure changes the
76


thermal impedance inside the sensing element; although
the changes are negligable, they should be characterized
in the future by monitering the barometric pressure
during the cavity calibrations (M factor calculations).
j) Fig. 8.11 shows the difference in the irradiance
readings during a run of 13 readings, when the
calibration is done at irradiance levels of 812 W/m2 and
908 W/m2. The difference is in the order of 0.07 percent
of the irradiance being measured. The temperature of the
sensing element is the same during both calibrations.
These results show the importance of calibrating the
HF28968 (calculating the M factor) using electrical
power that is as close as possible to the irradiance
level being measured during the comparisons of absolute
cavity radiometers.
k) The temperature dependancy of absolute cavity
radiometers shows the need to develop the cryogenic
absolute cavity solar radiometers to define the WRR with
a smaller uncertainty than 0.3 percent.
77


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00 r Q'ac _ V \
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ooo AAil _ \\
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AOA _ x i
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AOI _ w
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O I o A4 O - \ \ >
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UUJ AQA - X
AHA -
ouo Ano
801 -
4:30 6:00 7:30 9:00 10:30 12:00 13:30 15:00 16:30 18:00 19:30 21:00 22:30
TIME (90 SECONDS INTERVAL)
908W/mA2 821W/mA2
Fig. 8.11 Irradiance Readings with Time and Irradiance Calibration Levels
78


REFERENCES
1. Wells, Chester. (16 March 1993). Personal
Communication. "The NREL Reference Absolute Cavity-
Radiometer at the World Radiation Center in Davos,
Switzerland." NREL, Golden, Colorado, USA; 3p.
2. Frohlich, C.; Philipona, R.; Romero, J.; Wehrli, C.
(September 1995). "Radiometry at the Physikalisch
Meteorologisches Observatorium Davos and World Radiation
Center." Journal of Optical Engineering. Vol.34, no. 9;
pp.2757-66.
3. Karoli, Alton R.; Hickey, John R.; Frieden, Roger G.
(7-8 April,1983). "Self Calibrating Cavity Radiometers
at the Eppley Laboratory: Capabilities and
Applications." Proceedings of The International Society
for Optical Engineering. Vol.416, SPIE, Bellingham, WA,
USA; pp.43-50.
4. Swiss Meteorological Institute. (December 1985).
"International Pyrheliometer Comparisons IPC VI." Part I
of Working Report No. 137, Davos and Zurich,
Switzerland; p.4.
5. Swiss Meteorological Institute. (March 1991).
"International Pyrheliometer Comparisons IPC VII."
Working Report No. 162,Davos and Zurich, Switzerland;
p. 7.
79


6. Romero, Jos4. (September 1995). "Direct Solar
Irradiance Measurements with Pyrheliometers: Instruments
and Calibrations." IPC VIII, Davos, Switzerland; 16p.
7. Dieck, Ronald H. (Second Printing January 1995).
"Weighting Method for Multiple Results." Unit 6 in
Measurement Uncertainty: Methods and Applications. North
Carolina, Instrument Society of America; pp.117-24.
80