REMOTE SENSING OF POLLUTANTS
K. L. Sch wie sow
Environmental Research Laboratories
Boulder, Colorado
30 June 1971
NATIONAL TECHNICAL INFORMATION SERVICE
Distributed .., 'to foster, serve
and promote the nation's
economic development
and technological
advancement.'
U.S. DEPARTMENT OF COMMERCE
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SENSING OF POLLUTANTS
ANNUAL REPORT
June 30, 191$
N to .
Envi ronmental Protect! on
Air Pollution Control Offfofr
Research Triangle Park, North Carolina
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Dr. H. M. Barnes, Jr., Project Offi%r
Division of Chemistry Physics
tVon
National Oceanic and Atmospheric Administration
Environmental Research Laboratories
Boulder, Colorado
Dr. k. L. Schwiesow, Project Leader
Wave Propagation Laboratory
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NOTICE
THIS DOCUMENT HAS BEEN REPRODUCED FROM
THE BEST COPY FURNISHED US BY THE SPONSORING
AGENCY. ALTHOUGH IT IS RECOGNIZED THAT CER-
TAIN PORTIONS ARE ILLEGIBLE, IT IS BEING RE-
LEASED IN THE INTEREST OF MAKING AVAILABLE
AS MUCH INFORMATION AS POSSIBLE.
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L4. Title aDd 5aDcitie
Remote Sensing of Pollutants - Annual Report
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National Oceanic and AtmosphericAdministrat~on
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Environmental Research Laboretories
Boulder, Colorado
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12. Spoa.or~ Or,lIDizaUOD Name Md AcWreM'
Environmental Protection Agency
Ail' Pollution Control Office
Division of Chemistry Physics
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15. Supplemeot., Nace.
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3. Rec:ipient's Accession No.
S. Report Date
June 30.. 1971
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~ Petformm, Or,aoizacioD Repc.
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10. Pro;ect/Task/Work Unit No.
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13. Type of Report & Period
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14.
16. Ab8cracc8
) Research results obtained during FY 71 are sUTIIffiaI'ized on quantitative infrared spectra
of pollutant gases such as CO', 0;\ HCI, S(j~, NH3 J and HN03; on analyzing long path
infrared spectra by digital means for atmos.phe1'i,9 ga,s concentrations; on scattering
CI'OSS section measurements 'for S~ and NO; and 'On'literature search and consultative
services in atmospheric spectroscopy. Explanations and reviews of the particular
results are illustrated, bysamp-lea. of the voluminous: .transmission tables and graphs
supplied separately. Th~ developed infoI'ffiation ~s crucial for proper interpretation of
remote sensing field messUJ:'emen'ts'of pollutant 'c6i'ldentrcitions in both source and
ambient situations. (.) ':::;',~----~' . .
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17. ICe, Yard. and Doc_Dc A_I,.i.. . 170. De.cripcora
Air pollution
Infrared spectroscopy
Carbon monoxide
Ozone
Hydrochloric acid
Sulfur dioxide
Ammonia
Nitric acid
Data processing
Light scatte~ing
Nitrogen oxide (NO)
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52
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REMOTE SENSING OF POLLUTANTS
ABSTRACT
This report siimmarilis^research results obtained during FY 7Lon
quantitative infrared spectra of pollutant gases such as CO, 03, HC1,
SOgi NHg and HNO-; on analyzing long path infrared spectra by digital
means for atmospheric gas concentrations; on scattering cross section
measurements for SOg and NO; and on literature search and consultative
services In atmospheric spectroscopy. Explanations and reviews of the
particular results are illustrated by samples of the voluminous trans-
mission tables and graphs supplied separately. The developed information
is crucial for proper interpretation of remote sensing field measurements
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of pollutant concentrations in both source and ambient situations.
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REMOTE SENSING OF POLLUTANTS
1 0 Introducti~n and Sunmary .
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This report reviews support activities of the Atmospheric Spectroscopy
Group, ERL/NOAA, for the Air Pollution Control Office. EPA. for the year
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ending June 30, 1971. The :EPA funding for this cooperative effort was
. '
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$60;000, authorized by a letter of November 23, 1970 'from Dr. John T. Middleton,
EPA, to Dr. Wilmot Hess, ERL/NOAA.
The project study are~s include (1) quantitative infrared spectra of
atmospheric pollutant constituents. (2) least-squares fitting procedures to
, '
analyze infrared field data for constituent concentrations, (3) laboratory
laser scattering st~dies of pollutant gases, and (4) literature search and
consulting services.
Results of the studies have been transmitted to EPA
at various times throughout the year. These results are the significant end
products of the project, but are impractical to include in their entirety as
part of this annual report. because of their bulk. Samples of the generated
information are included as appendices to this report.
The data generated are important for the monitoring of gaseous air pollu-
tants by both 10n9 path infrared and Raman backscatter means.
In principle,
an infrared spectrum contains information. on the concentration of absorbing
molecules in the optical path.
In order,to extract this information, the
spectra of the molecules in the path, both natural and pollutant, must be
known, and one must have a method for fitting the known spectra to the field
spectrum.
This project ha~ generated essential information on reference
spectra and fitting programs. Similarly, to evalua:teand calibrate Raman
backscatter systems for monitoring source emissions, scattering cross
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sections and depolarization ratios for molecules of interest have been
measured during this project.
In the four stu~ areasoutlined~ the project has produced the follow-
ing infonnation:, (1) digit~zed 1 cm~l reso,lution infrared absorption
., ,
spectra, for three to five different representative concentrations, over
, the spectral ranges 740 to 1430 cm-l and 1824 to 3333 cm-l, for the gases
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H20. C02' CO. 03' N20. CH4': HC1, 502' NH3 And HN03 at 296 K and 760 torr
total pressure; (2) a least-squares spectrum fit~ngprogram successfully
tested 1n preliminary form on synthetic data; (3) Raman scattering cross
sections and depolarization ratios for 50iand NO at four'different incident
photon energies; and (4) a volume of selected 11 terature reprints on the
infrared absorption characteristics of pollutant gases and numerous written
proposal evaluations for APCO, Division of Chemist~ and ,Physics and the
Office of Research 'Grants.
These results are discussed in detail in the following sections.
2. Qu~ntitat1ve Infrared Spectra
A.
Introduction
Long path infrared spectra of the atmosphere contain information on the
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gaseous composition in the path. Particularly, spatially averaged pollutant
concentrations are in principle available, from this field data. ,In order
to analyze the field data APCO is now preparing to measure, quantitative
reference spectra for the gases in the path must be known at the instrumental
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literature are deficient in that they are taken at low total gas pressures
(not representative of the 'real atmosphere), they exhibit insufficient
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resolution used for the field spectra. Unfortunately, spectra in the
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resolution (lcm-,l resolution is to be used, in the field to increase
specificity of the measur~nt). and/or th'ey do not include quantitative
intensity information (required to determine concentrations).
The transmission. absorption coefficient and concentration of a
gas sample are related by t~e well-known expression,
T(y) = e-k~v)CL
, where T is the transmission~ k is the absorption coefficient. c is the
gas concentration in molecules/cm3 and L is the path length. If an
experimental measurement is made with an instrumental bandwidth wider than
the actual linewidth (which is less than approximately 0.1 cm-l at
atmospheric pressure) this expression no longer holds. ,Instrumentally
averaged absorption coefficient. £(v). then becomes an experimentally
unknown function also of the absorber den~itY cL.
The transmission at
a given wavenumber and 'the concentration are then related in a complicated
way. depending on the unresolved character of the spectral lines. Spectra
at various cL products are required as reference spectra.
Interpo lati on
for differing cL is approximately valid. but extrapolation is not.
Incidentally. if k(v) is established for five points in every resolution
element. extrapolation followed by five point averaging is approximately
valid.
For fitting field spec,tra. the spectrum of both natural and pollutant
gases must be considered.
B. Calculated Spectra
For the gases HZO; COZ' CO, 03' NZO, CH4 and HCl we have calculated
spectra for three to five concentrati on . path length products (i n units of
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molecules/cm2) at 296 K and: 760 torr to~lpre$sure. All known absorptions
have been included: for ,the regions 1824 to 3333 em-l and 740 to 1430 cm-l.
In the near infrared region. T(v) is sampled and 'recorded eyeryO.6 em-I.
For the mi ddle infrared. the sampHng i'ntetval is every 0.2 cm-1. This
data format is chosen to be compatible with the data format chosen by APeO
for the field data.
An instrumental bandwidth of 1 em-l was used for the calculated. spectra.
..
Appendix A shows samples of;graphical and tabulated data for short reg~ons
of CO, Hel and 03' The tab~lated data actually extends (on larger output
paper) to five concentrations, and is ~vailable on punched card and magnetic'
tape format as well. Complete volumes of graphical and tabulated data for
. '.
these gases have been supplied to Dr. Bames separately as part of this
project.
These spectral tab~lat1onsare'i.nput reference data for the field
analysis ,program. The digital data character is essential for the automated
processing, and is an additional advantage of the data developed during
thi s project. . .'
Line parameters for HCl35 and HCl37 in. natural isotope abundance were
computed as part of this project. The resulting spectrum (partially shown
in Appendix A) denonstrates the power an~ applicability of the line para-
meter appr9ach..
In Hel. for example. the computed line positions fit experiments to
. .
better than .Olem-l. and the intensity to better than 2%.': By comparing
the generated spectra to literature references (discussed later) it is
obvious that literature spectra are not directly applicable to the APeD
problem.
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c. Experimental Measurements
For 502' NHa andHNOa ,~e theoretical analyses are not sufficiently
developed to calculate transmissions. Data taken digitally with a 3/4
meter Ebert spectrometer with 1 em-l resolution (at 1000 cm-l) instrumental
bandpass is processed to the sampling interval and digital format discussed
under calculated spectra. This process includes digital filtering to
maximize signa1-to-noise, wavelength correction to eliminate scan system
. irregularities and conversion to an independent variable scale linear in
wavenutrber.
The data is taken at 296 K and 760 torr total pressure to be compatible
. ..
with the calculated spectra. Details of the experimental method, including
notes on equipment and data processing systems, are discussed in a previous
qua~terly report. Since these spectra are gro~nd state absorptions and
not "hot bands" (excited initial state), temper.ature variations of ~10% in
. .
the atmosphere have little effect on the spectra. A significant and accept~d
assumption at the low concentrations used, and at 1 cm~l instrumental band-
pass, is that self-broadening and nitrogen-broadening parameters are
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approximately the same for these gases. This allows simulation of a low
concentration, long path system by a higher concentration, shorter path
length laboratory absorption cell.
Samples of the digitized data for S02 and HNOa are also shown in
Appendix A. The complete set of graphs and printout is supplied to APCO
separately. Note that this data is in an identical format to the calculated
spectra, and that data is pvai1ab1e on magnetic tape and punched cards as
well.
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3. Field I)aU Analysis Program
A.
Introduction
The field infrared spe~trum is a compJicatedresult of the overlapping
absorption spectra of all ~e atmospheric molecules in th~ opti ca 1 path.
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An approach to deconvoluting the spectra is to perfonn a multi-dimensional
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least squares fit of the reference spectr~ to the f1eldspectrum. A total
transmission over a spectral interval isc~lculated using a best est1mate
of the atmospheric composition. The error matrix (from a cOfflP~risonof.
calculated and actual spectra) is analyzed to correct the constituent cOJl~
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centrati ons and 1 teratively determine the compos~tion of the field atmosphere.
Application of the program to real field data raises questions of
signal-to-noise in the field spectrum an~the effect of unkn~n gases for
which no reference spectrum exists. Even in the 8 to 12 ~ "window" water
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vapor has a significant continuum absorption for long path lengths.
. '
Fluctuations in water vapor content will introduce uncorrelated noise of
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a presently unknown magnitude. Similarly,' additional research is needed to '
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determi ne the effect of add; t; ona 1 unknown cons ti tuentS.. Instrumenta 1
(detector) noise may also adversely affect the fitting proced~re.
B. Results
The main fitting program is given in Appendix B. Operati.onal subroutines
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are not included in this brief example. A .preliminary version of the program
(with 2.5 cm-l data spacing) in card format, complete with annotated listing
and reference spectra, has been separately supplied to ApCO.This.program
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has successfully fi t a six-component trial spectrum made of ami xture of '
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reference spectra. The effects of noise on the s'pectrum have not been
sil11l1ated.
Appendix B also gives samples of total atmospheric absorption spectra.
taken with the sun as a source and normalized by the assumption of a 6000 K
thermal source for ,the solar spectral output. This digitized data is of
a format suitable for a test of the program. in absence of other field
data, but time limitations have prevented analysis of the spectrum yet.
The fitting program has subroutines for extensive checking of input
data and for output spectrum plotting if desired. The program has 'also
, ,
been modified to accept the newly generated reference data and fit on a
0.2 cm-l grid over 740 to 1430 cm-l and on a 0.6 cm-l grid over 1824 to
3333 cm-l. In general, the program relies on a gradient-projection method
of fitting.
The error functions discourage ~e1ectionof concentrations
outside a reasonable transmission range.
c. Summary
Although potential problems exist in the fitting of real, noisy data
to the reference spectra, the least squares fitting program developed during
this project period shows reasonabl;e promise (and more promise than any
other technique considered here) of analyzing infrared spectra for atmospheric
composition. Additional testing and refinement is indicated for next year.
4. Laboratory Laser Scattering Studies
A.
Introduction
Raman lidar, the optical analog of radar. maybe useful 'for monitoring
, source emissions and other air pollution detection applications where spatial
resolution is important. This is in contrast to long path absorption techni-
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ques which yield a spatial average, and to passiv~ infratedemission
techniques which lack the flexibili~ of an active illuminator and are
subject to interference problems.
Raman scattering cross sections are small, and field experiments so
far have at best had limited success. The laboratory scattering studies
of this project ana designed to (1) measure pollutant scattering cross
sections (relative to nitrogen as an internal standard) and (2) stu~
, .
photon energy dependent variations in relative cross section.
Quantitative cross section information is needed for feasibility
studies of Raman Lidar systems and as a calibration value to interpret
results of any field measurements in terms of actual amounts of pollu-
tants in the source sample. Energy-dependent cross section effects must
be understood to find pump wave numbers where, for a particular gas, the
cross section is relatively large so that range and concentration limits of
l1dar systems may be extended. This involves questions of resonance
Raman and atmospheric pressure fluorescence effects, if they indeed exist.
B. Analysis System
Considerable development has gone in~o a digital data analysis system
to rapidly and accu~ately compute relative Raman scatterin9 cross secti ons
. '
and depolarization ratios. The main program, less lengthy subroutines, is
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shown for example in Appendix C. This program is operational and has been
successfully checked against approximate hand calculations. ' Such an analysis
system permits consistent measurements of quantitative cross sections and
energy-dependent cross section effects.
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The analysis philosophy 1s shOiln in the "geocor" sketch of Appendix C.
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number to maximize Raman return for a particular constituent. Theoretical
understanding of the 'Raman effect is as yet insufficient to explain these
incident photon energy effects.
We are now prepared to analyze the. cross section behavior of other
interesting molecules, especially N02 and hydrocarbon vapors, which have
, '
shown promise 01 large scattering cross sections.
5. Literature Search and Consulting
A. Introduction
This cooperative research program benefits from and incorporates
, '
significant previous work i~ atmospheric absorption and scattering spectros-
copy. The Atmospheric Spectroscopy G~up maintains an extensive literature
file on the spectra of natural and pollutant gases. Over ~enty journals
are regularly scanned, as well as numerous reports, abstract services and
book lists.
Personnel from the Group also aid APCO/EPA in technical advice con-
cerning proposals from industry and general information on spectroscopic
prob 1 ems .
B. Resul ts
A volume of selected information from the literature has ,been sent
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separately., Spectra of C2H2' NH3' C6H6' HC1, H2S, HN03.' NO,.~02'
Peroxyacetyl Nitrate (PAN) and S02 were discussed in thesereferenc~s.
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These reported sources were chosen from many available because they
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contained the most useful information for APCO's purposes. The only
significant infonnation' since the date of the literature review volume is
that the C02 continuum in the 800'to1250 cm-l region is negligible at
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atmospheric partial pressures.
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Intercomparison .of the 11terature spectra and spectra dev,eloped
during this project .shows how the spectrum of a particular constituent
changes character as the instrumental resolution and buffer gas pressure
is varied. This emphasizes the need for quantitative reference spectra
taken under conditions simulating as closely as possible the field
experiment. The literature shows a surprising lack of data of the type
. needed by APCO for analysis of field data.
Literature information has been helpful for sample preparation techni-
ques and qualitative spectral information as a check of present results.
NOAA personnel have given written evaluations of industry Raman
sensing proposals and numerous university .grant applications through ORG
of APCO.
.6.
Future Project Direction
We expect that significant effort is required to test the field
data fitting program and train APCO personnel in the use of the program.
Experiments with various signal-to-noise ratios and components for which
no reference spectra exist are necessary to explore the performance,
envelope of the program and develop operational confidence.
Infrared reference spectra will be available to. A~CO based on line
parameter data only.
Experimental work is better .done on the APCO FTS-14
interferometric spectrometer than at NOAA. Details of expected line
parameters for NO and 502' as well as dev.elopment of a digital IIdegradell
program to modify high-resolution experimental data for particular field
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comparison, have been discussed in a separate memo to Mr. John Nader.
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Measu~d Relative Raman Cross Sections (oN = 1)
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Gas Laser Wavenumber. em-' Relative Cross Section Depolarization
S02 20 981 (416.5nm)' 5.1 .05
20 481 (488.0nm) 5.5 .06
20 135 (496.5nm) 5.8 .04'
19 430 (514.5nm) 6.1 .05
NO 20 981 .36 .11
20 481 .36 . 10
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19 430 .39 .08
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H20 20 981 2.5
20 487 1.9
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1301.0 0.5224141"
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12q5.~ 0.6196604
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1309.8 0.3947398
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1311.6 0.3623211
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1325.4 0.2523113
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1326.6 0.4229214
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1351.8 0.7596284
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1353.D 0.7965235
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1354.2 . 0.8329205
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1325.6 . 0.2130127
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1326.8 0.5008027
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1330.4 . G.5301507
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1363.8 O.95442QZ 136400 0.9566609
1364.4 . 0.9559040 1364.& 0.9574753
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1371.6 0.9799876 1371.8 0.9797896
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1372.8 0.9778629 1373.0 C.g79764y
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1329.8 0.4637676 1330.0 0,4627523
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1332.2 0.3853964 1332.4 C.37532B1
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134.0.6 0.1585266 134.0.6 0.1573123
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1343.Q 0.1102952 1343.2 O.10795~4
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1346.6 0.1065652 1346.8 0.1041953
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1347.8 0.1086505 1348.0 O.1D71~17
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1349.0 0.1012669 1349.2 O.10~2G2S
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1350.2 . 0.0968184 . 1350.4 C.OQB420C
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1351.4 0.1062112 1351.6 0.106&111
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1352.6 0.1198526 1352.8 C.1217151
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1353.8 0.139405.01354.0 O.14C2603
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1355.0 0.1502439 1355.2 u.1494714
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1356.2 0.1395140 1356.4 0.13816&5
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1357.4 0.121491c 1357.6 D.1197681
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1359.2 ,0.0926113, 1359.4 ~.0840119
---'-fi5-9. 6-'-'-'.-'-"--' o. !)65265i ---..--- -'----:---1360 ~O ..---,."-"'."'-" -0.0577132 -.--
1360.4 0.0444780 1360.6 t.0375S83
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1361.6 0.0475621 . 1~61.8 0.0781790
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1362.8 0.4748177 1363.0 0.5399328
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1364.0 0.5962220 1364.2 C.5762642
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1365.2 0.4602927 1365.4 0.4369466 .
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1366.4 0.32~0446 1366.6 0.3018246
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1370.6 0.0757696 1370.80.0713854
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1371.8 0..05994.03 1372.0 0.0572741
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1373.~ 0.0580362 1373.2 0..0554147
1373.6 0.0552215'. 1373.8 . 0.0563714
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1374.6 0.0565480 1375.D O.05~16~7
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1376.0 0.060645.0 1376.2 O.060213S
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1377.2 0.0656~21 1377.4 0.0672822
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1378.4 0.0735616 1378.6 ,C.0762831
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1380.6 0.1259191. 1381.~ t.1275601
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1393.4' O.8U06815 1393.6 O.80~6305
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1397.0 0.9346673 1397.2 C.9346793
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1398.2 0.9462791 1398.4 G.951186~
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. 1399.4 0.9546682 1399.6 D09712836
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1400.6 0.9915445 . 1400.8 0..9833760
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1401.8 0.9756918 1402.0 OG97674d8.
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1403.0 0.9799061 1403.2 0.9810226
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14Q4.2 0.9861268 14Q4.4 0.9869444'
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_2918...8.e -1.._0.0.Q_._-- ._.1..':'-0.0._..__-.-----... __.n'.--._. _...1'.000..
2g19.4Q 1.000 . 1.000 i.G~O
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292~.60 ~ 1.000 1.~Oa . 1.000
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29?'1.80 ~ 1.000 0.998 . ~.~96
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2 q 2 4 . 2. 0 . ~O. 9 g 8 0 . 9 q 2 fJ. q e .
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292~.40' ~ 0.997 O.98~ j.37~
__2926..0.0_- z: :"'__0_0_997 --_O.._9.88_.~_--_----_-:..._._--_!li. .3-/:\
2Q26.60 0.998 (J.ggl . OJ.g?£:.
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2927.80 ~.999 0.1<36 1.989
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2g3~.2Q l~OOO . 1.000 t.~~~
_2CJ3t ..8.Q 1...0.0.0 _..1_..(I.OQ-- .__.'._1...00Q
. 2q!1.4r 1.000 1.000.' 1.00G
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2Q32.&O. 1.000 1.000 t.oo~
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2Q3J.60. . 1.000 1.000 ~.cco
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TRANSMISSION SrECT~A' FOR 3 CONCENTRATIONS
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2 9 4 1 . 0 0 0 . 9 9 9 ,0 . 99 8 0 . 99'5
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2q~?.20 . 0.999' 0.994 0.'386
--2. 942. ..8 D....___----_!L...9..9.B. ...0.8_99 i n 6..97..7_-
294~.40 .' 0.9970.989 0.912
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2 9 4 4 . 6 0 .... -. a ~"9-9'6--'--~----'''-- ':0 ~"~H'5---"--'-'-" 0 . 9 62-
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2947.00 0.999 O.g~6. O~ge9 .
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2948.20 1.000 1.000 O..Q99
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2949.40 1.000 LU ,i. COO 1.000
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2g5G.60 1.000 ~ . 1.000 1.000
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2951.80 1.000' Q' 1.000 1..Q(1~]
29')2.40 1.000' ~ 1.000 1.000
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. 2')~4.20 1.000 6 1.~OO . 1.De
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2g5?40 1.000' i.COO 1.000
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?95~.6Q 1.000 1.000 1.000
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2g57.80 1.000 1.000 i.OOC
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29 ? g .0 D' 1 . 0 0 00 ~. 998 -... 0 . 99[.,
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2962.20 0.999 0.996 0.991
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.' .
APPENDIX B
I
! l
I .
I
,.
~
.'
B-1
~ -. - ..... .. . "
" I iJ
"tLt~ '.. '," ,.
'::":'1
-------
1
15
151
152
1521
2
21
22
221
3
31
319
35
36
38
4
41
42
43
44
45
46
47
471
4711
4712
4719
71 07 29
- .- -'--".--.' --"-""'~.'. ;.____--0- -.----.......-.- .~, -
,-' .
, " . r \ "" " t: It~. 1',:' " 1M I" .'1' 11 11 :'IN ~~ If. IT '" "IU U U JJ '" "'\ .u. 11 .,. .o" ill) U .. illS" ii' .. ....., ".\1 '.1 \4 ......" "" '\I MI "" 1.'..1 "4 ~\ ..to ." 1\11 ..., I" ., 1J 't I. ,", II " .~ ,', ...
PROGRAM NAPCA , '
DIMENSION S ( 5 ) ,KX e 10 ) , I OGAS ( 10) ,W (10 ) ,WI( 10) . WO ( 10) ,W I 0 ( 10 ) ,,"; , '
1 WIT(lO),ERReI60),XTMe160,11) "..'
DIMENSION ,TRAN(lOOO~10),NU(10),NW(iO),UR(lO,3),WR(lO,lO),TG(150)
1 U(150),CFe150),TC(150),WMelO),WHR~10),WW(lO).IPWelO)
COMMON TRAN ,NG,NU,Nw,UR ,WR,NT ,TG,U;,CF ,TC;,WM,WHR,WW, IPW.RMSTP ,RMST,
1 RMSW
EXTERNAL CALC, " , . '
CALL CONS T( S ,WM ,\'iHR ,WW, IPW"UMIN,UMf\X ,ZEPP"KX;,Q.,M,C..,Gl.6,CfM, IPRNT,
1 IPLOT) ; " "
IS=1 . , '
Z=THEOTRN (TRAN,NG, IOGAS,NU,.NW.UR,W,U '-'
IFCZ)152,2 ; ,
PRINT 1521 ~ ' , ,
FORMATe IHlt91H*****ERROR IN REAI)J_N~t, J.HE9RET.~AL VAl.UES OF TR
lANSMISSION***EXECUTION TERMINATED~*...1
CALL EXIT '
IPR=IPL=NM=O , ,"'-".. ,-..
RMSTP=I.EI00 '
CALL READALLCNG,S~UMIN'UMAX'WM,WHR~WW,I~W,ZEPO,KX,Q.GL8,MK,CFM,
1 IPRNT, IPLOT .W,WI .WO~WIOi;~J,TG,U.CFL ',.'~.. .-' . . .' ,
ZEPc:ZEPO
INC=O ' , '
CALL PRINTI C Q,GLB,CFM,MK, IPRNT. IPLOT;,VJ4,1~,'UMAX,lEf!,KX.NG, IOGAS,W,
1 WI,WM,WHR,WW,IPW,NT,TG.U,CF) , '
IF(KXel»221,221,3
INC=l '
KX(1)=XABSFeKX(I»)
CALL CALceW,~RR,RMS)
DO 319 K=I,NG
WITCK)=WI(K) , ,
CALL PR INT2 (NM,Q,GLB .MK,ZEP ,KX,RMS.RMST.RMSW,NG',lOGAS.WO,W,WI .WM,
1 WHR,WW,IPW,NT,TG,TC,U,CF,ERR) : :,' ',' '
CALL PLOTT(NT,TG,TC,U.NG:~W.IOGAS.N~"»' ':-.~- -, j'-" ....
IFCGLB-RMS)4,5,5 > , . ,
CALL M INMYZO C W ,W I T ,NG.CA~C ,ERR ,NG+~.T.~~p,!_~~-,~-,. .~~$:!XTM),
IPR=IPR+l ': ' ' , . i
IPL=IPL+l i ",,:: ' '
NM=NM+l ' . "
. ~ . ""'''''.-''r'~-_.'''-'--'. ~-
IFCIPR-IPRNTJ44,43,44 ! :;, "
IPR=O ,', . ,: , ' '
CALL PRINT2(NM,Q'GLB,MK,ZEP,KX,RMS~RMs;r.RMSW~NG.IOGAS,WO,w.wIT,WM,
. . ....... '.'" .. ,- -........ -.'~'-. ....","'_. .....'_. -, -. ....... - ."1" . ".
1 WHR,WW,IPW,NT.TG.TC,U,CF.ERR) :': ' :,'
IF( IPL-IPLOT)46,4:5,46 '
IPL=O , " ,:. ..
CALL PLOTT(NT,TG,TC,U,NG,W,10GAS,NM) ,
KX(4)=XABSF(KXe4»
ICXMIZ=CXMIZeKX,Q,GLB,MK-NM,RMS)
GO TO C4711,5,472).ICXMIZ .- '
IFC INC-I) GO T04
DO 4719 K=l,NG
WI 00 =.9*WI e K)
WITCKJ=WICKJ
GO TO 4
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B-2
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472
4721
5
6
609
,.
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.._._------._.__._.._.,.~----:...-..-.._~~~-._. -
, .
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, . 1.- ,. ': I I I. I:. t~ I'
II ,.. 1() 11 Jl n l' l' 2t 1J 11 lQ )0')1 )1 3] Ie U )6 31 )8 J9 080 .1 '2 .] U '!I .. "., d .9 )0 )1 U )] ). !Ii )6 )1 !of ), to 6' 1>1 63 U A~ ." ,., ". ''II 10 II n 1.1 .I. J~. ,'II
- ".. .--_....;... ,." -." -'" t ~..t" t......" -:>--..
PRINT 4721 !'! ; i ; :
FORMAT ( 1HO,8X,l15H******:tt******fIt*~****r S:INGULAR MATRIX; *** COMPUTA
I . ' I I I '" '. .
1 T ION HAL TED **.* NEX,T S,ET;- 9.f,_l)AJA:_.r,~~, e.Ei_BE,~P" il.~:-!~!,~!t-!~-*:»***********
2*) , 1" : ! : : ' ! i ~; : .". :
GO TO 6 . , :' Ii" . ,
CALL PR INT3 (NG, IOGAS,WO,W,WM,WHR,Ww:,]PWi,NT, TG',TC,Ui,CF,ERR,RMS.
. . t.. ~. ..-1. -,..- "..,.., ,-... - .-..- ,- 1-. ,. -'.
1 RMS T t RMSW) : .,.' ,
CALL PLOTT (NT, TG. TC.U ,NG;.W, IDGAS,-NM)
CALL PLOTDCNT,TGtTC.U,NG:.W,IDGAS) .
',. . ' .., ,," .., ""1
DO 609 K=l,NG \
WltK)=WITtK) ! . .
GO TO 2
END
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'1 07 29
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APPENDIX C
C-1
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~'IJ,) I}S~JL~-H~,\T[1-J .~~tIJ F'H G'~S~S. F'1L.;;:: /I'P'HI L5 !_FI');:i)
~'( ?nc.;:-)~q'~" ~n'H~:" ISIG/# -\\j!) Ii'BTI IS L1~')~"} -if 4;\\u.
. F'L~ST. :j use H~T EF"~:~5 TJ 3~'o'jr>L=:: (1) :)~~~P:;::<;;:'JC,;;: (~h =\-J)
S;;:Cl\j.) T'LH+V])"J~L (I> 1.~?~:~~LL~L (2) :'>~L~H?;=\Tl1~.
I F~~~~T(5~1~ i~4~L~# ~=3~11.~3 ~=3;;::11.51') .
2 f)i~\T(~Pli ~;;:~~<~'lJC~, ~=;=::11.~3 ~=~=::11.5/3
, 1~7.43 (;:,,:."'::(;T ..)-):» 512"; Ir;;::<-\TI~'B/)
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