EPA-650/4-74-045-b
SELECT RESEARCH GROUP
IN AIR POLLUTION METEOROLOGY,
SECOND ANNUAL PROGRESS REPORT
VOLUME II
by
Select Research Group
Department oi Meteorology and
Center for Air Environment Studies
The Pennsylvania State University
University Park , Pennsylvania 16802
Grant No. R-800397
Program Element No. 1AA009
ROAP No. 21 ADO
Task No. 14
Project Officer: Kenneth L. Calder
Meteorology Laboratory
National Environmental Research Center
Research Triangle Park, North Carolina 27711
Prepared for
OFFICE OF RESEARCH AND DEVELOPMENT
ENVIRONMENTAL PROTECTION AGENCY
WASHINGTON, D.C. 20460
September 1974
-------
This report has been reviewed by the Environmental Protection Agency
and approved for publication. Approval does not signify that the con-
tents necessarily reflect the views and policies of the Agency, nor does
mention of trade names or commercial products constitute endorsement
or recommendation for use.
11
-------
Ill
TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing}
1. REPORT NO. 2.
EPA-650/4-74-045-b
4. TITLE AND SUBTITLE
Select Research Group in Air Pollution Meteorology,
Second Annual Progress Report: Volume II
7 AUTHOR(S)
Select Research Group
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Department of Meteorology and Center for Air
Environment Studies, The Pennsylvania State
University, University Park, PA 16802
12. SPONSORING AGENCY NAME AND ADDRESS
Environmental Protection Agency
National Environmental Research Center
Meteorology Laboratory
Research Trianqle Park, North Carolina 27711
3. RECIPIENT'S ACCESSIOI*NO.
5. REPORT DATE
Seot. 1974
6. PERFORMING ORGANIZATION CODE
8. PERFORMING ORGANIZATION REPORT NO.
10. PROGRAM ELEMENT NO.
1AA009
11. CONTRACT/GRANT NO.
R-800397
13. TYPE OF REPORT AND PERIOD COVERED
Annual Progress 6/1/73-9/30/74
14. SPONSORING AGENCY CODE
15. SUPPLEMENTARY NOTES
Issued as Volume II of 2 Volumes
16. ABSTRACT
Progress reports are included by the SRG task groups involved in: the
development of mesoscale air pollution related prediction models, modeling
of planetary boundary layer (PBL) turbulence and structure, the analysis of acdar
signals for wind and temperature measurements in the PBL, studies of atmospheric
aerosol properties and aerosol-atmosphere interactions, and airborne measurements
on the urban to mesoscale of atmospheric aerosol, turbulence and radiation.
17. KEY WORDS AND DOCUMENT ANALYSIS
a. DESCRIPTORS
Mesoscale Prediction Models
Boundary Layer Modeling
Pollutant Removal Processes
Acdar, Acoustic Sounding
Airborne Measurements
13. DISTRIBUTION STATEMENT
Unlimited
b.lDENTIFIERS/OPEN ENDED TERMS
19. SECURITY CLASS (This Report)
Unclassified
20. SECURITY CLASS {This page)
Unclassified
c. COS AT I Field/Group
21. NO. OF PAGES
22. PRICE
EPA Form 2220-1 (9-73)
-------
iv INSTRUCTIONS
1. REPORT NUMBER
Insert the EPA report number as it appears on the cover of the publication.
2. LEAVE BLANK
3. RECIPIENTS ACCESSION NUMBER
Reserved for use by each report recipient.
4. TITLE AND SUBTITLE
Title should indicate clearly and briefly the subject coverage of the report, and be displayed prominently. Set subtitle, if used, in smaller
type or otherwise subordinate it to main title. When a report is prepared in more than one volume, repeat the primary title, add volume
number and include subtitle for the specific title.
5. REPORT DATE
Each report shall carry a date indicating at least month and year. Indicate the basis on which it was selected (e.g., date of issue, date of
approval, date of preparation, etc.).
6. PERFORMING ORGANIZATION CODE
Leave blank.
7. AUTHOR(S)
Give name(s) in conventional order (John R. Doe, J. Robert Doe, etc.). List author's affiliation if it differs from the performing organi-
zation.
8. PERFORMING ORGANIZATION REPORT NUMBER
Insert if performing organization wishes to assign this number.
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Give name, street, city, state, and ZIP code. List no more than two levels of an organizational hirearchy.
10. PROGRAM ELEMENT NUMBER
Use the program element number under which the report was prepared. Subordinate numbers may be included in parentheses.
11. CONTRACT/GRANT NUMBER
Insert contract or grant number under which report was prepared.
12. SPONSORING AGENCY NAME AND ADDRESS
Include ZIP code.
13. TYPE OF REPORT AND PERIOD COVERED
Indicate interim final, etc., and if applicable, dates covered.
14. SPONSORING AGENCY CODE
Leave blank.
15. SUPPLEMENTARY NOTES
Enter information not included elsewhere but useful, such as: Prepared in cooperation with, Translation of, Presented at conference of,
To be published in, Supersedes, Supplements, etc.
16. ABSTRACT
Include a brief (200 words or less) factual summary of the most significant information contained in the report. If the report contains a
significant bibliography or literature survey, mention it here.
17. KEY WORDS AND DOCUMENT ANALYSIS
(a) DESCRIPTORS - Select from the Thesaurus of Engineering and Scientific Terms the proper authorized terms that identify the major
concept of the research and are sufficiently specific and precise to be used as index entries for cataloging.
(b) IDENTIFIERS AND OPEN-ENDED TERMS - Use identifiers for project names, code names, equipment designators, etc. Use open-
ended terms written in descriptor form for those subjects for which no descriptor exists.
(c) COSATI FIELD GROUP - Field and group assignments are to be taken from the 1965 COSATI Subject Category List. Since the ma-
jority of documents are multidisciplinary in nature, the Primary Field/Group assignment(s) will be specific discipline, area of human
endeavor, or type of physical object. The application(s) will be cross-referenced with secondary Field/Group assignments that will follow
the primary posting(s).
18. DISTRIBUTION STATEMENT
Denote releasability to the public or limitation for reasons other than security for example "Release Unlimited." Cite any availability to
the public, with address and price.
19. & 20. SECURITY CLASSIFICATION
DO NOT submit classified reports to the National Technical Information service.
21. NUMBER OF PAGES
Insert the total number of pages, including this one and unnumbered pages, but exclude distribution list, if any.
22. PRICE
Insert the price set by the National Technical Information Service or the Government Printing Office, if known.
EPA Form 2220-1 (9-73) (Reverse)
-------
ACKNOWLEDGEMENT
The Select Research Group gratefully acknowledges the
financial support? provided by research grant No. R800397 from
the office of Research and Development, Environmental Protection
Agency. The group also appreciates the financial support and
use of facilities from the Department of Meteorology and the
Center for Air Environment Studies of The Pennsylvania State
University.
An interdisciplinary research program such as the SRG effort
cannot possibly succeed without the contributions of the many
individuals who assisted on this project. The group wishes to
particularly thank the many faculty and staff members and graduate
students for their assistance.
-------
VI
TABLE OF CONTENTS
VOLUME II (of 2 Volumes)
Page
ACKNOWLEDGEMENTS v
CONTENTS OF VOLUME I ix
LIST OF FIGURES : xii
III TASK 1-C BOUNDARY LAYER MODELING 272
1.0 SUMMARY OF PROGRESS 273
2.0 SHORT-TERM FORECASTS OF TEMPERATURE AND MIXING
HEIGHT ON SUNNY DAYS, 275
3. 0 ATMOSPHERIC TURBULENCE MODELING 281
4.0 ATMOSPHERIC BOUNDARY LAYERS AND THE PRESSURE
GRADIENT-VELOCITY CORRELATION MODEL 284
5.0 NUMERICAL MODELING OF TURBULENCE FLOWS 289
6.0 MODELING TURBULENT FLUX OF PASSIVE SCALAR
QUANTITIES IN INHOMOGENEOUS FLOWS 293
7.0 EULERIAN AND LAGRANGIAN TIME MICROSCALES IN ISOTROPIC
TURBULENCE 304
8.0 NOTES ON TURBULENT FLOW IN TWO AND THREE DIMENSIONS 313
IV SRG ON AIR-POLLUTION METEOROLOGY 326
Part 1
1.0 ATMOSPHERIC EFFECTS ON PARTICIPATE POLLUTANTS 327
1.1 The sampling program 329
1.2 Chemical analysis of particulate matter 331
1.3 The numerical modeling program 334
1.4 Progress in field sampling of agglomeration 337
REFERENCES 341
Part 2
1.0 ATMOSPHERIC REMOVAL PROCESSES FOR AIR POLLUTANTS 349
1.1 Synopsis 350
1.2 Personnel 351
1.3 Accomplishments 352
1.3.1 Global Emissions and Natural Processes
For Removal of Gaseous Pollutants 352
1.3.2 Rock 416
1.3.3 SO Solubility 419
1.3.4 Rate of SO- absorption by sea water 426
REFERENCES 431
-------
Vll
Page
V OBSERVING SYSTEMS FOR URBAN AND REGIONAL ENVIRONMENTS 433
Part 1
Preface 434
1.0 TASK 1-D INTERPRETATION OF ACDAR SOUNDING OBSERVATIONS.. 437
1.1 Introduction 437
2.0 ANALYSIS OF DOPPER-SHIFTED MONOSTATIC ACDAR SIGNALS 441
2.1 System geometry 441
2.2 Surfaces of constant Doppler Shift 444
2.3 Horizontal wind 450
2.4 Antenna weighting 465
2.5 Total spectrum 468
2.6 With antenna weighting 475
2.7 Wind shear included 483
3.0 MONTE CARLO METHOD FOR EVALUATING ACDAR
SCATTERING VOLUMES AND SYSTEM FUNCTIONS 503
4.0 MEASUREMENTS OF SOUND REFRACTIVELY TRANSMITTED
IN THE PLANETARY BOUNDARY LAYER 510
4.1 Introduction 510
4.2 System description 510
4.3 Measurement of inversion layer temperature
gradients 517
4.4 Fluctuations of signal levels and possible
association with atmospheric gravity wave
motions 520
REFERENCES '. 526
5.0 TEMPERATURE PROFILE MEASUREMENTS IN INVERSIONS
FROM REFRACTIVE TRANSMISSION OF SOUND 527
6.0 ANALYSIS AND SIMULATION OF PHASE-COHERENT
ACDAR SOUNDING MEASUREMENTS 547
Part 2
1.0 AIRBORNE MEASUREMENT SYSTEMS 592
1.1 Introductory Remarks 593
2.0 PSU ISOKINETIC INTAKE FOR AIRBORNE AIR SAMPLING 594
2.1 Design of the PSU Model II Probe 595
2. 2 Sampler Performance 600
2.3 Conclusions 602
-------
Vlll
3.0 INSTRUMENTATION FOR MULTIWAVELENGTH AIRBORNE
PRECISION SPECTRAL RADIOMETER MEASUREMENTS .............. 604
3 . 1 The radiometers ............... • ................... 604
3 . 2 Radiometer mounting ................................ 610
3 . 3 Radiometer signal conditioning ..................... 612
3.4 Correction of radiometer outputs ................... 619
3.5 Data analysis ..... ................................. 621
REFERENCES [[[ 622
4.0 AIRBORNE MEASUREMENTS OF TURBULENCE IN THE
PLANETARY BOUNDARY LAYER ............. ................... 623
5.0 AIRBORNE MEASUREMENTS OF AEROSOL IN THE ST. LOUIS
URBAN AREA ............................ ................... 633
6.0 SURFACE MEASUREMENTS OF AEROSOL IN A RURAL AREA
USING DIFFERENT METHODS ............ ..................... 641
6 . 1 Introduction ................... ..................... 641
6 . 2 Instrumentation ............... .................... 641
6 . 3 Summary of a selected data ..... .................... 643
7.0 TECHNIQUES FOR THE "MESOSCALE" INTERPRETATION OF
AIRCRAFT MEASUREMENTS ................................... 651
VI OTHER CONTRIBUTIONS .......................................... 659
Part 1
1.0 A GENERAL APPROACH TO DIFFUSION FROM CONTINUOUS
SOURCES ................................................
1.1 Theory ............................................
1. 2 Analysis ..........................................
Part 2
2.0 THE NIGHT-TIME MIXING DEPTH AT PHILADELPHIA ............ 666
2 . 1 Introduction ...................................... 667
2 . 2 Analysis of observations ......................... 668
2.3 Results ........................................... 668
Part 3
3.0 SO CONCENTRATIONS AT KEYSTONE, PA. .................... 671
3.1 The purpose of the project ............... ......... 672
-------
TABLE OF CONTENTS
VOLUME I (of 2 Volumes)
Page
ACKNOWLEDGEMENTS V
CONTENTS OF VOLUME II ix
LIST OF FIGURES xii
I INTRODUCTION AND SCIENTIFIC OBJECTIVES 1
II THE DEVELOPMENT OF MESOSCALE MODELS SUITABLE FOR AIR
POLLUTION STUDIES : 6
ACKNOWLEDGEMENTS 7
1.0 INTRODUCTION 8
1.1 Potential use for regional and urban
dynamical prediction models 8
1.2 Some general considerations of the mesoscale
predictability problem 10
' 1.3 Overview of mesoscale modeling effort 14
2.0 THE REGIONAL MODEL 16
2.1 The basic equations in sigma coordinates for
a Lambert Conformal map projection 16
2.2 The horizontal and vertical grid structures 20
2.3 Finite difference equations 21
2.4 The two-dimensional analog 24
2.5 Kinetic energy budget equations for 2-D and
3-D models 25
2. 6 Lateral boundary conditions 28
2.6.1 Equations for mean motion over domain 29
2.6.2 Lateral boundary conditions for the 2-D
model 34
2.6.3 Lateral boundary conditions for the 3-D
model 36
2.7 Initial conditions 37
2.8 Two-dimensional flow across the Appalachian
terrain 38
2.8.1 Specifications of the 2-D experiments 39
2.8.2 Results with geostrophic initial
conditions 43
2.8.3 Initialization of the boundary layer winds
considering ''he effects of surface friction 49
APPENDIX - CHAPTER 2.0 57
-------
3.0 PRELIMINARY THREE-DIMENSIONAL EXPERIMENT USING
REAL DATA WITH AND WITHOUT TERRAIN 62
3.1 Synoptic Discussion on 12Z Oct. 16 -
OOZ Oct. 17, 1973 63
3.2 Initialization and verification analyses and
specification of time-dependent boundary conditions. 67
3.3 Specification of parameters 75
3.4 Qualitative discussion of results; 77
3.4.1 Low-level results 77
3.4.2 Middle level'results 82
3.4.3 Upper level results 84
3.5 Budget equations for the model domain and the
implications of the lateral boundary conditions 84
3.5.1 Mean kinetic energy budget for the 12-hour
forecast period 87
3.5.2 Time variation of the mean motion 89
4.0 NUMERICAL EXPERIMENTS WITH A TWO-DIMENSIONAL NESTED GRID. 97
4.1 The basic equations 98
4.2 The meshed grid system 99
4.3 Experimental results 103
4.3.1 Background experiment with uniform mesh 103
4.3.2 The treatment of the interface momentum
points in the meshed grid experiments 104
4.3.3 Meshed grid experiments with a mean wind
of 10 ms-1 110
4.3.4 Experiment with.mutually interacting grids
with the fine mesh moving through the
coarse mesh 112
4.4 Mesh grid experiments initialized with
Haurwitz waves 116
4.4.1 Initial conditions and the linear
solutions 117
4.4.2 Quantitative analysis of errors 123
4.4.3 Long-wave results: Exp. 1-5 125
4.4.4 Short wave results: Exp. 6-8 140
4.4.5 Mixed long and short wave results 149
5.0 INVESTIGATION OF SEMI-IMPLICIT MODELS 158
5.1 Advantages of semi-implicit models over
explicit models 158
5.2 Comparison of one-dimensional explicit and
"'semi-imp lie it shallow fluid model 160
5.2.1 Development of explicit model 160
5.2.2 Development of semi-implicit model 161
5.2.3 Initialization of models 165
5.2.4 Results 165
-------
XI
5.3 Comparison of two-dimensional explicit and
semi-implicit models
5.3.1 Development of the two-dimensional
S.I. model 171
5.3.2 Initialization 175
5.3.3 Results 176
5.4 Conclusions of preliminary tests of semi-
implicit models 186
APPENDIX - CHAPTER 5 187
6.0 DETERMINATION OF INITIAL DATA REQUIREMENTS 190
6.1 Development of Stochastic-Dynamic Equations-•• 192
6.2 Initialization Procedure 203
6.3 Energetics of the model 208
6.4 Interpretation of Predicted Variances 210
6.5 Pure gravity wave experiments 211
6.6 A Monte Carlo comparison 219
6.7 Synoptic Scale Error Compatability 224
6.8 Summary and Plans for Future Research 229
REFERENCES 232
7.0 EXPERIMENTS WITH SIMPLIFIED SECOND-MOMENT
APPROXIMATIONS FOR USE IN REGIONAL SCALE MODELS 234
7.1 Introduction 234
7.2 The "Poor Man's Method" 236
7.3 Semicomprehensive Methods 244
ACKNOWLEDGEMENTS 270
REFERENCES 271
-------
Xll
LIST OF FIGURES
VOLUME II
No. Title
CHAPTER III - Section 2
1. Forecast for April 15, 1971 276
2. Forecast for April 26, 1971 277
3. Forecast for July 11, 1971 277
4. Forecast for September 5, 1971 278
5. Forecast for October 12, 1971 278
6. Forecast for October 24, 1971 278
7. Initial Conditions for May 27, 1973 279
CHAPTER IV - Section 1
1. Particle surface area vs. particle diameter -
Altitude 1600 ft - St. Louis 103 342
2. Particle surface area vs. particle diameter -
Altitude 2600 ft - St. Louis 103 343
3. Particle surface area vs. particle diameter -
Altitude 6600 ft - St. Louis 103 344
4. Particle surface area vs. particle diameter -
Altitude 1700 ft - St. Louis 105 345
5. Particle surface area vs. particle diameter -
Altitude 3200 ft - St. Louis 105 346
6. Particle surface area vs. particle diameter -
Altitude 5000 ft - St. Louis 105 347
7. Particle surface area vs. particle diameter -
Altitude 3500 ft - Pittsburgh 102 348
-------
Xlll
No, Title Page
CHAPTER IV - Section 2
1. Uptake rates of different pollutants by an
alfalfa canopy 364
2. Aerosol formation and SO decay during the
photooxidation of SO ...7 372
CHAPTER V - Section 2
1. Illustration of coordinate system and basic angles
used in text 442
2. Lines of constant f when z = 0 445
3. When z « 0, lines are hyperbolas with z = 0
lines as assumptotes 447
4. Three dimensional depiction of lines of constant
Doppler shift with horizontal wind 448
5. Constant Doppler surface for vertically pointing
sounder with vertical wind 449
6. Doppler surface intersection with edge of
vertically pointing sounder with horizontal wind.... 451
6A. Horizontal wind and horizontal transmitter-
receiver 452
7. Primed coordinate system for horizontal wind
and sounder between the vertical and horizontal
axes 454
8. Over exaggerated view of hyperbolas due to a- and
circle subtended by transmitter-receiver cone.
Each hyperbola refers to a different a, and thus a
different f^ 459
-------
XIV
No. Title Page
9. Illustrating the actual relation of the hyperbola
to circle using a of 15°. The departure from a
straight line is quite small ......... '. ............. 460
10A. Head on view of circle subtended by transmitter
cone and illustrating component of u along r .......
10B. Side view of beam showing relation of a' to a.
a' is measured as positive in the clockwise
from the z axis ....................................
11. Depiction of lines of constant total shift as
well as f | lines and f(| ........................... 473
12. f( spectra with antenna weighting variation with
a (in radians). Note that calculations must be
carried out to a distance from bore sight at least
3 times the beam width to include the full spectrum
z, 1, u, , A = constant ........................... 478
13. f|| spectrum varying 4>. Note that, although spectra
overlap, the abcissa changes in each case. For
<(> = 0, f . = 58.5, f = 60. For (j) = 10,
fmin = 5' f x = 5' F°r * = 26' fmin = 51-05'
fm =52.4. Sfso note that the (j) = 0 curve
represents that which would be obtained from a
vertically pointing sounder with vertical wind,
a, z, 1, u, (f), X = constant ..... ..................... 479
14. f| spectrum for = — and horizontal wind of
10 m/sec ............ . ........... ..................... 480
15. Total spectra and variation with <)>. Note increase
in height occurs as <}> approaches 20° due to
inaccuracies in approximation. Also note the
change in shape as f dominates ( ~ 90°) and f
increases in contribution (4> -*• 0) ................... 481
16. Total f including antenna weighting and lobe
weighting for 0 = 45°, a = 5° ..... ................... 482
17. The CODOSS as they go through the scattering volume.
As wind shear increases, so does curvature .......... 496
18. Spectrum for wind shear and vertical sounder 497
-------
XV
No. Title Page
19. With sounder at 60° from horizontal and wind
shear varying (1): z = 0, k = .02, (2) z = 400,
k = .1 (3) ZQ - 450, fc = .2 ? 498
20. Spectrum for wind shear and vertical
sounder 499
21. With sounder at 30° from horizontal and wind
shear varying (1) z = 0, k = .02, (2) z = 400,
k = 0.1, (3) z - 4§0, k = .2 ? 500
o
CHAPTER V - Part 3
1. Instantaneous scattering volume for a.bistatic
acdar 504
2. System function as a function of range.
Comparison of analytic and Monte-Carlo schemes 507
3. System function as a function of range.
Comparison of analytic and Monte-Carlo schemes 508
CHAPTER V - Part 4
1. Transmitter diagram 511
2. "Phased Array" transmitter configuration 512
3. Comparison of measured and theoretical beam
patterns 514
4. Receiver block diagram 515
5. Comparison of raw and filtered received signals.... 516
6. Sound levels measured at various ranges on morning
of 7 July 1974 518
7. Maximum amplitude vs. range 519
8. Transport center record on morning of
21 August 1974 521
9. Electronic microbarograph trace from morning of
1 August 1974 523
10. Comparison of sounder and barograph observation for
morning of 13 July 1974 525
-------
XVI
No. Title Page
CHAPTER V - Part 5
1. Model temperature profile and refraction .
ray paths
2. Reduced travel time versus distance for H = 200 m. 541
The numbers under each curve give T ' in deg C/km.
3. Interpretation diagram to find T ' and T ' 542
H = 200 m .
4. Unfiltered and filtered received signal output, 543
showing signal onset. Range was 3-6 km
5. Caustic distance versus T~' 544
6. Interpretation diagram for determining T ' 545
computed for T ' = -3°C/km, but useful for full
range of T ' values. Dashed line example shows
an interpretation of T ' = 15° C/km for
measured R = 15 km and H. = 300 m
c 1
7. Reduced travel time versus range for ground based
inversion layer 546
CHAPTER V - Part 6
1. Two-dimensional equiphase surfaces in an isothermal,
windless atmosphere
2. Accumulated signal phase versus scatterer dis-
placement for a single scatterer moving horizontally
through the beam of a vertically pointing sounder.. 579
3. Cross section of bistatic link antenna and pulse
geometry 580
4. Intersection of transmit and receive antenna beams
on a surface of equitime or equiphase 581
5. Common volume as a function of range for pulse
lengths of 40, 80, 120, and 240 ms. a =1°,
3 = 2°, D = 100 m, = 10° 582
6. System function as a function of range and
transmitter-receiver separation. Pulse lengths
are 40 and 100 ms, a = 1°, 3-2°, and = 20°.. . 583
-------
xvii
No. Title Page
7. Combined amplitude weighting functions for
antenna pointing angles range from 0 to 9°
from zenith and cosine dependent scattering
angle dependence. Antenna beamwidth = 9° 584
8. Accumulated total phase from scatterers moving
into a vertically pointing beam, f, = A(j>/At 585
9. Comparison of mean Doppler frequencies computed
for multiply scattering layers of 246 and 123 m,
and for a single scatterer at 123 m and varying
distances from the zenith 586
10. Example of accumulated phase versus time ouput
of DS model 587
11. Example of signal amplitude versus time ouput
of DS model 588
12. Amplitude returns from "RP" model versus time,
with t subdivisions every 4At, where At is
determined from oiAt = .07 589
13. Doppler frequencies returns from "RP" model
versus time 590
14. Received power spectrum of -~- and input power
j i
spectrum. Units of -—• the same as for 591
at x
CHAPTER V - Part 2 - Section 2
1. Cross-section of air sampling probe 596
2. Cross-section of sampler air intake 597
3. Exhaust area ratio as a function of free stream
and sampler intake velocities 598
CHAPTER V - Section 3
1. Spectral response of Eppley Model 2 domes 605
2. Hemispherical view of (A) upward facing and (B)
downward facing radiometers when mounted on the
aircraft 609
-------
XVI11
No. Title Page
3. Basic two wire current transmitter circuit 615
4. Amplifier stability as a function of temperature... 616
5. Expander and positioning circuit 618
CHAPTER V - Section 4
1. Spectrum of vertical velocity fluctuations recorded
on 12 min run at = 1300 AGL, 0830 CAT,
17 August 1973 over St. Louis, Mo, 626
2. Calculated wavelengths as a function of altitude— 627
3. Arithmetic average wavelength as a function of
altitude. Bars denote standard deviation 628
4. Mixing length vs. altitude as predicted by
Blackadar model 630
CHAPTER V - Section 5
1. Vertical profile (all particles > .5y dia).
11 Aug. 1973 636
2. Vertical profile (all particles > . 5y dia).
18 Aug. 1973 636
3. Particle size spectrum, 18 Aug. 1973 638
4. Particle size spectrum, 15 Aug. 1973 638
5. Vertical profile of number concentration of
particles over St. Louis area on Aug. 5, 1974 640
CHAPTER V ,- Section 6
1. Sketch of the sampling line 642
2. Summary and typical schedule for surface
measurements 644
3. Comparison between the Nephelometer and the Mass
Monitor of the S-6 of Hardi 1974 645
4. Typical size distribution of March 5, 1974 648
5. The variations of the Nephelometer and the Royco
during a short time period 649
6. The variations of the Nephelometer and the Royco
(0.7 - 1.4u) during a short period of time 650
-------
xlx
No. Title Page
CHAPTER V - Section 7
1. Response functions of Martin-Graham and
bionomial filters 653
2. Mesoscale experiment flight path 655
3. Sample plot of unnormalized and pressure normalized
data 657
CHAPTER VI - Section 1
1. Normalized lateral spread as function of normalized
diffusion time at many locations (night) 663
2. Normalized lateral spread as function of lormalized
diffusion time at many locations (daytime. 66A
Section 2
1. h, VS. h+3 670
obs.
Section 3
1. Concentration isopleths as a function of insolation
and windspeed 674
2. Directional wind shear as a function of time 675
-------
Ill BOUNDARY-LAYER MODELING
Task 1C
-------
273
SECONV ANNUAL REPORT EPA-SR6
Ta&k 1C - tioundaAy-LayeA Modeling
SmmaAy o
H. Tennekes
Department of Aerospace Engineering
The task group is engaged in the development of model equations for
the description of turbulence and diffusion in atmospheric boundary layers.
Two major efforts are in progress. Under the direction of Dr. Lumley, a
complete set of second-order turbulence model equations is being developed.
Under the direction of Dr. Tennekes, simplified equations are used to
study the development of convective boundary layers and the daily cycle of
the mixing height. This latter work aims at improved boundary- layer
parameterization schemes for use in with regional computer model of the
Select Research Group.
The inversion-rise model developed by Tennekes during his sabbatical
leave at the Royal Netherlands Meteorological Institute (1972-3) appeared
to have the potential to produce short-term forecasts of temperature and
mixing height. In cooperation with one of the Dutch meteorologists, this
prospect has been explored. Very encouraging results have been obtained;
they were presented at the AMS-WMO Symposium on Atmospheric Diffusion* and
Air Pollution (Santa Barbara, September 1974) . A copy of the Santa Barbara
paper is included in this report (Section 2, page ).
This development suggested that a more detailed study of the convective
boundary layer and of the turbulence dynamics near the inversion capping the
boundary layer would be worthwhile. The mechanism of entrainment by which
a boundary layer grows into the stable air aloft requires a more thorough
analysis. It was decided to develop a computer program capable of reproducing
the results obtained by Dr. J. C. Wyngaard of AFCRL; this program forms the
foundation for further studies. The program has been developed by Otto Zeman;
it is now ready for the planned work on the entrainment mechanism. Mr. Zeman 's
progress report is given in Section 3 (page ) .
In his attempts to formulate the equations necessary for his computer
program, Mr. Zeman discovered that Rotta's simple model for the pressure-
gradient velocity terms in the momentum- flux equations was inadequate, and
that Lumley 's current model for those terms was too cumbersome for his
purposes. He developed an elegant and straightforward compromise; it is
described in Section 4 (page ) .
-------
274
In the system of equations developed by Dr. Lumley and Mr. Khajeh-
Nouri, there is a large number of coefficients that, have to be determined
from experimental data. A search program for the optimum values of those
coefficients in a plane isothermal turbulent wake was developed by
Mr. Alan Huber. The results of this work are described in Mr. Huber's
master's thesis (June 1974), of which copies have been sent to EPA. It
is worth mentioning that Mr. Huber joined EPA at Research Triangle Park
following his graduation.
Dr. Lumley and Mr. Khajeh-Nouri are continuing their development of
a complete system of second-order equations for turbulent flows. Dr. Lumley
has been on sabbatical leave in Europe during this past year; he has worked
also on thermocline erosion in the ocean (a paper on that subject is in
preparation), on the pressure-strain correlation, and on the turbulent flux
of passive scalars in inhomogeneous flows. Much of this past year has been
devoted to programming difficulties experienced with the simulation of a
plane isothermal turbulent wake. Mr. Khajeh-Nouri's progress report is
given in Section 5 (page ), and Lumley's paper on the turbulent flux of
passive scalar quantities is included here as Section 6 (page ).
This concludes the summary of last year's progress in the two main
areas of research. Other work included consultations with Dr. Anthes on
boundary-layer parameterization, discussions with the EPA-staff on a visit
to Research Triangle Park in December 1973, continuing discussions with
Dr. Panofsky on coherence measurements and turbulent eddy structures,
consultations on the design of the isokinetic aerosol sampling probe, and
studies of the differences between Lagrangian and Eulerian statistics of
turbulence. In this last area, which is crucial to the understanding of
turbulent diffusion in the atmosphere, an interesting discovery was made
concerning the shapes of the Lagrangian and Eulerian (sometimes called
quasi-Lagrangian) correlation functions and spectra. A paper by Tennekes
on this subject was accepted by the Journal of Fluid Mechanics; it is
included here as Section 7 (page ).
The research tasks of the Select Research Group encompass a great
range of scales, ranging from the turbulent microstructure to synoptic
scales of motion. Turbulence is generally analyzed with statistical
methods, but mesoscale and large-scale atmospheric motions are handled with
deterministic equations. The differences in approach make it difficult
to maintain effective communications between those who study the larger
scales and researchers concentrating on small-scale turbulence. In an
attempt to provide a better understanding of these problems, Tennekes
started a study of the similarities and differences between two-dimensional
turbulence (which is a crude model for large-scale atmospheric flows) and
three-dimensional turbulence. A first draft of a paper on this subject is
included here as Section 8 (page ).
-------
275
2 . SHORT-TERM FORECASTS OF TEMPERATURE AND MIXING HEIGHT ON SUNNY DAYS
H. Tennekes
The Pennsylvania State University
University Park, Pennsylvania 16802
and A. P. van Ulden
Royal Netherlands Meteorological Institute
De Bilt, the Netherlands
1. INTRODUCTION
The inversion-rise models that have appeared
in the literature recently (Betts 1973, Carson
,1973, Tennekes 1973) contain prognostic equations
for temperature and mixing height on sunny days
(without major advective changes. These equations
appear to be useful for short-term forecasts of
temperature, mixing height, and air-pollution
index. This paper reports on studies made at the
'Royal Netherlands Meteorological Institute since
the spring of 1973. In the first part of the
paper, the inversion-rise model of Tennekes
(1973) is used for forecasts pertaining to a
fairly large number of days in 1971; in the
second part, six representative forecasts are
idiscussed in detail, and in the third part,
progress in the determination of boundary
,conditions, initial conditions, and adjustable
numerical coefficients is reported.
The equations developed by Tennekes (1973)
do not account for advective changes, the
presence of moisture, and large-scale subsidence.
These effects can be incorporated if desired
(Deardorff 1972, Betts 1973) but it was felt that
a feasibility study such as this should
concentrate on the validity of the basic model.
The equations are
^=cl(ew)c
To"
3
. JC)
(«w)o - (6W)i = h f .
(1)
(2)
(3)
The symbols used here are defined as follows: h
is the height of the inversion base, A is the
temperature jump at the (idealized) inversion, 0
is the potential temperature in the mixed layer
(assumed to be independent of height), y is the
lapse rate of potential temperature above the
inversion base, (Sw^ is the turbulent kinematic
flux of sensible heat at the top of the mixed
layer (i stands for inversion base), (6w)o is the
turbulent kinematic flux of sensible heat at the
earth's surface, g/T0 is a buoyancy parameter,
and ut is the surface friction velocity.
This system of equations can be solved if
the initial conditions, the boundary conditions,
and the constants cj and C2 are specified.
Preliminary studies (Tennekes 1973) showed that
ci = 0.2 approximately. Also, the last term in
(1) can be ignored if the wind speed is
relatively low and the inversion height is
greater than about 100 m. Therefore, we put C2 =
0 for the first part of this study.
The initial conditions were taken from the
temperature profile of the midnight radiosonde at
De Bilt, the Netherlands. A minor adjustment was
made for the observed minimum temperature at
1.5 m; this changed the initial temperature
profile between 1.5 m and 50 m slightly, but it
had no appreciable effect on the results.
The equations require that the surface heat
flux be specified as a function of time of day
and season. In the absence of direct observa-
tions it was decided to use climatological data
on the annual cycle of the total amount of heat
entering the atmosphere between sunrise and sun-
set on sunny days. These data, which are used
for routine maximum-temperature forecasts by the
Royal Netherlands Meteorological Institute, are
readily available. The integrated heat flux
obtained this way was converted into a curve
representing the instantaneous heat flux by
fitting a half a sine wave between sunrise and
sunset such that the total area under the curve
was equal to the heat-flux integral on which the
operational maximum-temperature forecast is
based. Later in this paper, we present measure-
ments showing that these assumptions appear to be
insufficiently accurate for the description of
events during the early morning hours.
Calculations were performed for seventy-one
selected days in 1971. The selection procedure
discarded days with frontal passages, changes in
air-mass origin, days with less than 20% sun-
shine, and days suspected to be influenced
strongly by other advective effects. These trial
forecasts were of an exploratory nature, and no
attempt was made to account for subsidence, clouc
cover, radiational cooling, latent-heat fluxes,
and mechanical turbulence. The results of the
calculations were compared with the observed
temperature at 1.5 m in De Bilt, with the mixing
height indicated by the noon radiosonde, and with
the potential temperature in the mixed layer
observed by the noon radiosonde.
-------
276
2. STATISTICS
The observed maximum temperature at l.S m
was compared to the forecast potential tempera-
ture in the mixed layer at sunset. The mean
absolute value of the temperature difference,
computed over 64 days (seven days had to be
discarded because of computer program failure)
was l.3°C. The mean bias in the error was
insignificant (0.3°C). These results are
comparable in accuracy to those of the routine
maximum-temperature forecast at the Royal
Netherlands Meteorological Institute. This is
not surprising, because the same heat-flux
integral is involved. It should be noticed that
the maximum temperature at 1.5 m is a surface-
layer temperature, while the forecast temperature
is a potential temperature in the bulk of the
mixed layer. Also, the surface-layer temperature
reaches its maximum earlier in the afternoon than
'the mixed-layer potential temperature. However,
this inconsistency is ignored in the operational
forecasts, too. In all likelihood, the tempera-
ture drop in the surface layer in the late after-
noon approximately compensates the further
Cheating of the bulk of the mixed layer during
.that period.
The noon (1200 GMT) radiosonde leaves
>Dc Bilt at approximately 12:30 p.m. local time.
The observed potential temperature in the mixed
'layer at 12:30 p.m. was compared with the
predicted temperature. The mean absolute value
'of the temperature difference, calculated over
59 days (some days had to be discarded because
the radiosonde temperature profile did not show a
well-defined adiabatic layer, and some others
because of computer program failures) was 1.2°C.
The mean bias in the error was negligible (0.3°C),
showing that the method used does not introduce
significant systematic deviations between fore-
casts and observations.
The height of the mixed layer at 12:30 p.m.,
as determined from the radiosonde temperature and
humidity profiles, was compared to the forecast
value. The mean absolute value of the height
difference (calculated over 58 days) was 270 m;
the mean bias in the difference was very small
(11 m). The relatively poor accuracy may perhaps
be ascribed in part to the poor vertical resolu-
tion of the radiosonde data, but it should also
be kept in mind that the calculations did not
account for subsidence and other advective
effects. In order to obtain a preliminary
assessment of the influence of advection, a
subjective selection procedure was used to find a
subset of days on which advective effects were
small. This was done by comparing the tempera-
ture profile of the noon radiosonde with that of
the preceding midnight radiosonde, and keeping
all days in which the two soundings were nearly
the same for the air above the mixed layer. A
subset of sixteen days was found this way; the
error statistics for this subset showed a slight
improvement over those of the full set, except
for a much improved mixed-layer height forecast
at 12:30 p.m. (the mean absolute value of the
'error was 130 m for these sixteen days). This
seems to indicate that the accuracy of forecasts
of the height of the mixed layer can be improved
by accounting for advective changes in the
.temperature profile of the air aloft. It is
worth noting that for this subset of .sixteen
days, the average percentage of sunshine was 75%
far greater than that of the complete set.
3. SIX REPRESENTATIVE FORECASTS
From the subset of sixteen days with small
advective effects, six were chosen at random for
a more detailed comparison between forecasts and
observations. The predicted variation (with
time) of the potential temperature in the mixed
layer was compared with the temperature at 1.5
meter height as observed at De Bilt. The
observed temperature thus is a surface-layer
temperature. In convective conditions, the
potential temperature at 1.5 m in the surface
layer is higher than the potential temperature in
the bulk of the mixed layer. Radiosonde data at
De Bilt suggest that this difference is about 2°C
around noon on sunny summer days, and about 1°C
around noon on sunny winter days. This has to be
taken into account when comparing the predicted
curves with the observed ones.
The computed variation of the mixed-layer
height was compared with the height indicated by
the noon radiosonde and with the heights
estimated by drawing an adiabat from the observed
1.5 m temperature each hour and determining its
intersection with the temperature profile of the
nearest radiosonde. This, of course, is an
indirect estimate; however, no hourly data on the
height of the mixed layer were available. The
procedure followed here, incidentally, is
identical to the one used to determine the late-
afternoon height of the mixed layer from the
observed maximum temperature at 1.5 m and the
temperature profile of the noon radiosonde.
F-iut example:
fan Apiil 75, 1971
-ixx>
-500
04 10 12 14 K IB 2000
FIGURE 1: April 15, 1971
The temperature distribution at midnight on
this day is characterized by a strong ground
inversion, with a thickness of about 600 m. The
stability of the layer of air between 600 and
1600 m, however, is small. This causes a rapid
temperature rise in the morning hours and a very
slow increase in the height of the mixed layer.
Approximately 1,5:30 local time (MET), the mixed
layer passes the 600 m level; subsequently, the
height of the mixed layer increases - as
expected - quite rapidly, while the temperature
-------
277
increases very slowly. The observed maximum
temperature at 1.5 m is 20.6°C; the maximum mixed-
layer height estimated by drawing an adiabat from
the observed maximum temperature is about 13SO m.
The forecast height at the end of the day (sunset)
is about 1600 m; it differs about 250 m frpm the
estimated value.
Between 6:00 and 12:00 local time the differ-
ence between the observed temperature at 1.5 m and
the calculated potential temperature in the mixed
layer behaves approximately as expected; in the
afternoon, however, the calculated temperature
seems too high, even if the decreasing difference
between surface-layer temperature and mixed-layer
temperature is accounted for. In the late after-
noon hours, the observed temperature decreases
rapidly; this is (at least partially) a result of
the way in which the surface layer reacts to the
instantaneous heat flux (the surface heat flux
changes sign about one hour before sunset).
The large cross in the figure is the height
of the mixed layer as determined from the noon
radiosonde data. This is the only time of the
day on which a direct comparison between
predictions and observations is possible. The
mixed-layer height estimates based on late-
afternoon surface-layer temperatures are not
.plotted in the figure, as they would suggest that
the height of the mixed layer decreases after the
•maximum temperature is passed. Toward sunset,
the surface-layer temperature decreases much
faster than the temperature at higher levels
JFigure 8) .
•Second example;
ion. AP
-------
278
example:
ion September 5, J97I
-2000
-ISOO
-IOOO
MOO
FIGURE 4: September 5, 1971
Just like April 2b (Figure 2), this is a
case in which the initial conditions are
characterized by a shallow ground inversion and a
very stable layer between 1300 and 1600 m. The
stability of the layer in between, however, is
larger than it was on April 26. After the
nocturnal surface-based inversion has been filled
in (about 9:00 a.m. local time}, the height of
the mixed layer therefore does not increase quite
as fast as it did on April 26. In cases of this
kind, it is not hard to estimate the maximum
height of the mixed layer, because the pre-
existing inversion severely limits further growth
in the afternoon.
The temperature cycle on this day sees a
rapid increase during the filling of the
nocturnal inversion and a slower increase in the
following hours. The differences between
predicted and observed temperatures appear to
have reasonable values.
after 13:00 local time could not be used to
estimate the subsequent growth of the mixed layer.
Nevertheless, the calculated maximum height of the
mixed layer agrees well with the height estimated
with the aid of the observed maximum temperature.
The differences between temperature forecast
and observations are appreciable. The origin of
this discrepancy is not clear. Possibly the
prediction method is more sensitive to errors and
inaccuracies when the total heat input is small.
exompte (toMc.cu,t (jo* Ocstob&i 24, 1971
TT '
JOOO
ISOO
-1000
Of
10 12
It 2000
example:
{,01 OcJobeA. M, 1971
FIGURE 6: October 24, 1971
This is a day with an appreciable likelihood
of serious air pollution. An inversion of 16°C,
with a thickness of 400 m, characterizes the
initial conditions. The heat supply is not
sufficient to relieve this situation. Days such
as this one are also marked by a large amplitude
of the diurnal temperature cycle: at 8:00 local
time, the temperature is 5°C, while the maximum
temperature is 19°C. Such a large increase,
notwithstanding the small heat supply, is made
possible because the height of the mixed layer
stays small.
-1000
1000
-900
FIGURE 5: October 12, 1971
The midnight radiosonde data for this day
show a ground inversion up to 350 m; above that
level, the air is less stable. Approximately
13:00 local time, the ground inversion has
disappeared; after that, the height of the mixed
layer increases rapidly. The observed tempera-
ture reaches its maximum fairly early in the
afternoon, so that the temperatures observed
4. FURTHER STUDIES
The instrumented 200-meter mast of the Royal
Netherlands Meteorological Institute became
operational in October 1972. It is located at
Cabauw, 25 km SW of the Institute's headquarters
in De Bilt. The mast has thermometers and
anemometers at ten levels between 20 and 200 m;
also, net radiation is measured at 2 m. The
temperature measurements at the mast make it
possible to determine the potential-temperature
profile in the lowest 200 m; this provides
accurate initial conditions. Also, there are
several thermometer levels above the surface
layer, so that the predicted potential temperature
in the mixed layer can be compared with the
potential temperatures observed at the higher
levels on the mast. This procedure avoids the
problems inherent to comparisons between observed
surface-layer temperatures and predicted mixed-
layer temperatures.
Radiation measurements taken at Cabauw during
the first half of 1973 showed that a sine-wave
approximation fits the daytime variation of the
incoming net radiation very well on sunny days.
-------
279
The curve, however, does not change sine at sun-
rise and sunset, but approximately one hour after
sunrise and one hour before sunset (roughly when
the sun is 10° above the horizon). We assumed
'that the upward flux of sensible heat at the
surface is a constant fraction of the net
radiation flux. After a number of trial fore-
'casts, in which the constant of proportionality
was varied over a wide range, it was determined
that a factor of 0.43 gave the best overall fit
.between the forecasts and the observations.
The good vertical resolution of the tempera-
ture profile in the lowest 200 m allows an
accurate determination of the initial values of A,
0, and h. One example is presented in Figure 7.
The values ho, Ao, and Oo at the beginning of the
calculation are chosen in such a way that the
initial inversion is represented in the best
possible way. Figure 7 pertains to the initial
'conditions on May 27, 1973; moderately high wind
;speeds (3-4 m sec"1) maintained a low-level
frictional inversion that night.
FIGURE 7: Initial Conditions for May 27, 1973
Further calculations were performed for 11
days in the period March-June 1973. These days
were selected on basis of the following criteria:
sunshine more than 65%, no rain or fog, and
stationary large-scale weather conditions (in six
cases), or clearly defined subsidence or advection
effects (in five cases). For the five days with
subsidence or advection, the initial conditions
were adjusted to account for the trends associated
with those effects. The adjustment procedure gave
satisfactory results. Advective processes can be
incorporated into the model without undue effort;
however, the recognition of th«se processes
remains a source for concern.
Various choices for the constant cj in (1)
were tried. This constant determines the heat
flux at the inversion base as a fraction of the
surface heat flux in conditions with light winds.
A satisfactory correlation between the predicted
and observed mixing heights (the latter based on
i the noon radiosonde data) and between the
predicted and observed potential temperatures in
the mixed layer could be obtained only for ci =
0.5. The use of ci = 0.2 (as in the first part
of this paper) did not change the agreement
between observed and predicted temperatures
appreciably, but it caused the mixing height to
be underestimated by some 10 to 50%, depending on
initial conditions. Apparently, the use of ci =
0.2 is permissible only in the context of the
heat-flux integral data employed in operational
maximum-temperature forecasts. The source of this
discrepancy has not yet been determined; we
suspect that compensating errors are involved.
Because the early morning hours contribute
relatively little to the growth of the mixed
layer, the value cj = 0.5 should be representative
of conditions during the middle of the day. This
disagrees with the estimates made by Tennekes
(1973) and Ball (1960), but it is in agreement
with Carson's estimate. The latter (Carson 1973)
is based on O'Neill data. We note that the
frictional inversion-erosion term in (1) was
neglected in all calculations reported here; it
seems likely that the estimate cj = 0.5 will have
to be revised downward if the frictional term
(with a realistic value of ca) is carried along
in the calculations. The effect of the frictional
term increases roughly as the cube of the wind
speed; in a windy country such as Holland it may
be necessary to include that term.
Comparisons between observed and predicted
temperatures for ten days in 1973 are presented
in Figure 8; they show that the agreement between
forecasts and observations generally is quite
good. For all cases, the forecast mixing height
at 1200 GMT was within 200 m of the mixing height
determined from the noon radiosonde; on six days,
the difference was less than 100 m. For these
calculations, we used cj = 0.5, cz = 0.
In the early morning hours, the forecasts
provide a good fit to the data on days with low
wind speeds. In the mornings of March 22 and 23,
May 26, and June 25 the wind speed at 10 m was
less than 3 m sec"1; for those days the predicted
curve stays very close to the observed one. For
the other six days significant deviations are
found, which cannot be explained by possible
errors in the initial conditions or in the heat-
flux estimate. For all of these six days, the
wind speed at 10 m was more than 3 m sec, for
May 17 and May 28, it was about 6 m sec"1.
Clearly, the mixed layer was not in a state of
free convection during the early hours of these
days. Mechanical turbulence caused a larger
downward heat flux at the inversion base, and a
more rapid increase of temperature in the mixed
layer. The effects of faster entrainment were
visible in the shapes of the observed temperature
profiles along the mast.
During the late afternoon the predicted
temperature generally is higher than the measured
one. This seems to suggest that the surface heat
flux may decrease to zero somewhat earlier than
the observed net radiation. In two cases, an
alternative explanation can be given. On June 23
and June 25, wind direction changes were large;
during the afternoons of these days, northerly
winds advected cooler air toward the mast.
-------
280
5.
CONCLUSIONS
-8
- 4
— fa
Ten days in 1973
Ocu>he.d tinu: Xoi.eca6.fcs
fa 8 10 12 14 16 GMT
I I I
On days without major advective changes, the
simple inversion-rise model used here appears to
be able to describe the essential features of the
daytime development of convective boundary layers
quite well. The model requires a very limited
input of data, and the computer calculations
require only about a second per day. Operational
use of a model such as this would seem to be
feasible.
Several problems remain, however. In
practice, relatively few days are characterized
by stationary large-scale weather conditions;
many more days throughout the year are affected
by advective changes. Such changes can be
incorporated into the model, but at this time it
is not clear that this can be done successfully
on an operational basis. This problem is
particularly pronounced during the winter months,
when the daily cycle of the surface heat flux
plays only a minor role in the development of the
boundary layer, so that a state of free convection
does not occur all that often.
Another problem is that these forecasts
cannot be made before the midnight radiosonde data
are available. This limits the forecasting period
to about 18 hours. In operational applications,
however, forecasts of pollution-related para-
meters often have to be made for a 24-hour period;
it is not clear whether the use of an estimated
initial temperature profile would give
sufficiently accurate results.
Acknowledgments
The computer calculations presented in this
paper were programmed and executed skillfully by
Mr. H. Daan. Partial support from the U.S.
Environmental Protection Agency, through its
Select Research Group in Air Pollution Meteorology
at The Pennsylvania State University, and from the
Atmospheric Sciences Section of the U.S. Natjonal
Science Foundation is acknowledged. This paper is
published with permission from the Director-in-
Chief of the Royal Netherlands Meteorological
Institute.
References
Ball, F. K. (I960) Control of Inversion Height by
Surface Heating. Quasvt. J. Koy. Me.te.oti.. Soc.
86, 483-494.
Betts, A. K. (1973) Non-Precipitating Cumulus
Convection and Its Parameterization. QaafLt.
J. Roy. MittOI. Soc. 99, 178-196.
Carson, D. J. (1973) The Development of a Dry,
Inversion-Capped, Convectively Unstable
Boundary Layer. Qua.n£. J. Koy. Me-teo'i. Soc..
99, 450-467.
Deardorff, J. W. (1972) Parameterization of the
Planetary Boundary Layer for Use in General
Circulation Models. Mem. lile.autke.'i Reu. 100,
93-106.
Tennekes, H. (1973) A Model for the Dynamics of
the Inversion Above a Convective Boundary
Layer. 3. kbno*. Set. 30, 558-567.
-------
281
3. ATMOSPHERIC TURBULENCE MODELING
Otto Zeman
Development of the Computer Program
As a prerequisite for detailed studies of the erosion of an inversion
layer capping a convective boundary layer, a computer program was developed
that simulates mean flow and turbulence in atmospheric boundary layers.
The program utilizes time-dependent ensemble-averaged equations for
mean momentum, enthalpy, and turbulent fluxes. The DuFort-Frankel leapfrog
method is used. This method has been successfully applied to a great number
of fluid-dynamics problems and is well suited to the solution of non-linear
differential equations in two independent variables (time and space). The
solution proceeds from arbitrary initial conditions specified on the vertical
axis between two boundaries at time t=0. As long as the initial values are
reasonably well behaved, the time dependent solutions at time t > 0 converge
to the desired steady-state solution, that is independent of the initial
values. The rate of convergence is usually determined by the degree of
turbulent diffusivity throughout the boundary layer.
Presently, the program is capable of predicting an entire neutral
boundary layer or a convective layer capped with a rigid lid. The convective
layer solution converges rapidly to its steady state. It requires only two
CPU's on an IBM/370 to run a convective layer program at medium lid height
to a Monin-Obukhov length ratio (z/L) = - 20. The neutral layer solution
converges relatively slowly, due to the large response time T, which is on
the order of the inverse of the Coriolis parameter f (T ~ 1/f).
The program has a built-in flexibility to allow for incorporation of
a variety of model equations, subsidence, moisture flux equations, etc.
At present the program is being prepared for study of the convective
layer-inversion interface. Further, the program shall be put to use for
the verification of the modeled terms in the turbulent flux equations.
Turbulence Model Equations, Boundary Values
In the case of a dry convective layer, a total of 15 equations have to
be solved; in the case of a neutral layer, these reduce to nine equations.
The upper boundary values are set at zero for all second moment turbulent
quantities and for the mean velocity and temperature gradients. The upper
boundary has to be placed high enough so as not to affect the solution below.
The lower boundary is placed at a height where a neutral, constant stress
layer is still existent. In other words, the ratio z/L has to be sufficiently
small. Experimental constants and lower boundary values for all the
quantities are in principle those used by Wyngaard (2).
-------
282
The transport terms are modeled by gradient transport with an eddy
viscosity proportional to the product of the kinetic energy and a turbulent
time scale. The equation for the kinetic energy dissipation was adopted
from Lumley (3).
Modeling of the Pressure Gradient-Velocity Term
The pressure gradient-velocity term (further PG-V) is represented in
the equations of the present model by a single nonlinear return-to-isotropy
term as proposed by Rotta:
- - 26
Although the model in this form can reproduce all the main features of the
atmospheric boundary layer, it suffers from a serious shortcoming. The
constant of proportionality of the return-to-isotropy terms has one value
for the stress equation and another for the kinetic-energy component equations.
It seems reasonable to require that the constants should be the same for all
terms of the tensor A-y . Furthermore, the model does not allow for differences
in component energies in the cross-stream and vertical directions. It is
known, however, from the experimental data that in the log-law region of
neutral boundary layers, the cross-stream energy component is larger than the
vertical one.
The fact that the single non-linear return-to-isotropy terms alone are
not sufficient to represent the PG-V's has been long recognized by a number
of researchers. The Poisson equation for the turbulent pressure fluctuation
suggests that the mean shear be present in the PG-V model. Lumley (3)
proposed terms which represent the effect of mean vorticity on the return-to-
isotropy. Presently, there is a great number of PG-V models available. Most
of the models suffer from either one of the following drawbacks:
a) An excessive number of undetermined constants.
b) Too many constraints imposed on the turbulent stress
distribution.
In an attempt to avoid these pitfalls, we have developed two terms to
be added to Rotta1s original model, which include the effect of the mean
strain rate and of the mean vorticity. Because in the neutral surface layer
all transport terms become negligibly small, the equations for the turbulent
second moments can be reduced to a set of three independent equations. With
the known stress distribution, these equations allow for determination of
the three unknown constants in the PG-V model. Details of the development of
the new PG-V model are described in the next section ("Atmospheric Boundary
-------
283
Layers and the Pressure Gradient-Velocity Correlation Model"). The new
model allows for one numerical value of the constant GI of the return-to-
isotropy terms in all equations and lends to the proposed model the
desired universality.
Similar ideas will be applied to the heat flux equations.
Future Work
1) Incorporation of the proposed PG-V model in the turbulent boundary
layer computer program.
2) Development of a quantitative model of the erosion of the inversion
by a convective layer.
3) Study of details of the erosion layer using the computer program.
4) Study of large scale eddy transport in convective layers.
5) Computer simulation of the inversion rise.
References
1. Roache, P. J., "Computational Fluid Dynamics", Hermosa Publishers,
1972.
2. Wyngaard, J. C., "Modeling the Atmospheric Boundary Layer",
Second IUTAM-IUGG Symposium, Charlottesville, Va., 1973.
3. Lumley, J. L. and B. Khajeh-Nouri, "Modeling Homogeneous Deformation
of Turbulence", submitted to Physics of Fluids, 1974.
-------
284
ATMOSPHERIC BOUNDARY LAYERS AND THE PRESSURE
GRADIENT-VELOCITY CORRELATION MODEL
by
Otto Zeman
A pressure gradient-velocity (PG-V) model has been developed that
gives realistic values of the turbulent stress components in the surface
layer. The model consists of three terms: a nonlinear return-to-isotropy
term (Rotta's model), a mean vorticity term, and a mean strain-rate term.
In the neutral surface layer, the turbulent stress equations can be
reduced to three independent equations. For a given turbulent stress
distribution, a unique set of three constants can be determined. The
return-to-isotropy constant appears to be relatively insensitive to a
variety of turbulent stress distributions.
Approach
If only Rotta's model is used, the turbulent stress equations in the
neutral surface layer reduce to the following set:
r 2, _ 9u Cl , 2 1 2, 2 _
[u]: -2uw— - — (u - y q ) - y e = 0
[v2]:
[w2]:
1 , 2 l
_ (v . _ q
1 , 2 1 2, 2 n
- T (w - - q ) - - e = 0
[uw] : - w - - — uw = 0 .
(1)
(2)
(3)
(4)
It can be shown that the set of equations (1) through (4) represent three
independent equations. The turbulent equations in this form cannot
reproduce the experimental data if the constant C± is to be the same for
all four equations. Furthermore, v^ = w2, so that the model does not
allow for unequal values of the vertical and lateral component energies.
-------
285
It is apparent that the equations in the surface layer can accommodate
two additional terms with two undetermined constants. The additional terms
were sought to possess the following properties:
1) To be of the same or the next higher order as compared to the original
return-to-isotropy term and to be a function of the departure-from-
isotropy stress tensor.
2) To reflect "the effect of mean strain rate on the return to isotropy.
3) To reflect the effect of the mean vorticity on the return to isotropy.
The turbulent stress equations contain explicitly certain terms in
which the Coriolis parameter occurs. These terms influence the
distribution of the normal stresses and the shear stress levels. It
appears logical to represent the earth's rotation effect in the
pressure gradient-velocity model.
4) The new terms have to have the correct tensorial properties, i.e.,
they have to be symmetric with zero trace.
5) There can be as many undetermined constants in the model as the number
of independent equations allow, i.e., 3.
In view of the foregoing, we have selected additional terms as follows.
Both have the proper symmetry and invariance properties.
a) A tensor that contains accounts for the effects of the mean strain rate
s 7
A. . E b. S . + S. b . - |- (Sb) 6. . ,
IJ IK KJ IK KJ 3 *• ' IJ
b) A tensor representing the effects of the total vorticity
v
A. . = ft. b . - ft .b.
13 IK KJ KJ IK
Here, b. is the departure-from-isotropy tensor
1 2,
b. = u.u - •=- q 6 .
IK IK 3 n IK
S. is the mean strain rate tensor
IK
3U. 8U
c = _ + !£.
•i iy ~ ^v Ci-v
IK oX dX-
K 1
-------
286
. = vorticity tensor, defined by
1 K
-»• R
R
o,? = relative vorticity vector, defined by
T = " 31 ' al
C
o = earth rotation vector, defined by
C
uin = (0, 2 o)cos<|), 2 cosing}
The entire pressure gradient-velocity term is thus
12
_
A..E - — (u.u. -^-
ij T *• i j 3
where GI, a, y are undetermined constants. Nondimensionalizing the turbulent
stress equations in the surface layer by u*3/KZ, we obtain the following set
of equations:
2(l-a/3-Y) - (bu/q2)C1/3 - | = 0 , (1*)
4/3 a - (
- 2/3 a + 2Y - (
q
= 0
3. 3.
The equations (1 ) through (4 ) can be solved with C,/g, a, and y as unknowns.
The constant 3 relates to the time scale used by Lumley (3 = Te/q2) . For each
set of ratios iJZ/q2, w^/q2, u*2/q2, there is a unique set of constants =
Ci/3, a, Y- The constants were calculated for six cases, representing
experimental and arbitrary turbulent stress distributions. In all cases
presented, the value of the constant GI is relatively insensitive to the
stress distribution. Adopting Lumley 's numerical value of 3, which is
0.312, the value of GI is in the proximity of unity. The values of the
constants a and Y seem reasonable; they are always positive and smaller than
unity.
-------
287
2. 2
U /q
T, 2
V /q
w2/q2
«.2/q2
a
Y
Cj/B
#1
0.53
0.25
0.22
0.13
.291
.3705
3.32
#2
0.48
0.38
0.14
0.12
.653
.1225
4.45
#3
0.57
0.28
0.14
0.16
.393
.215
2.65
#4
0.53
0.33
0.13
0.13
.50
.152
3.59
#5
0.65
0.23
0.12
0.113
.23
.04
3.46
#6
0.565
0.34
0.695
0.117
.515
.1025
3.45
O f\
#1 An arbitrary stress tensor with (v -w )/q2 « 1,
based on a modification of Wyngaard's data
(reference 4)
#2 Cramer's data (reference 5)
#3 Mellor's data (reference 1)
#4 An arbitrary stress tensor with b22 = 0
#5 Comte-Bellot's data (reference 2)
#6 Hinze's data (reference 3)
-------
288
REFERENCES
1. Mellor, G. L. 1973: J. Atmos. Sci., Sept. 1973, p. 1061.
2. Comte-Bellot, G., "Ecoulement Turbulent Entre deux Parois Paralleles",
Publications Scientifiques et Techniques, 1964, No. 419.
3. Hinze, J. 0., "Turbulence", McGraw-Hill, pp. 522-523.
4. Wyngaard, J. C., 1973, "Modeling the Atmospheric Boundary Layer",
Second IUTAM-IUGG Symposium, Charlottesville, Virginia, 1973.
5. Monin, A. S. and A. M. Yaglom, "Statistical Fluid Dynamics: Mechanics
of Turbulence", Vol. I, The MIT Press, 1971, p. 519.
-------
289
5: NUMERICAL MODELING OF TURBULENT FLOWS
B. Khaj eh-Nouri
The first part of the year was spent in trying to find the reasons
behind multiple roots for solutions to the turbulent shear equations. This
multiplicity was first noticed when Mr. Huber's program for finding constants
by trial and error kept giving different values. This program is based on
finding the best set of constants to give the smallest mean square difference
between the experimental and theoretical values. After writing a number of
programs that could give themselves new and random starting positions in the
space defined by the constants, it was possible to find a definite relation-
ship among them. After this work the smallest (in terms of absolute value)
values of the constants were used in the turbulent shear program.
During the first part of 1974, work was resumed on the equations of the
turbulent shear program. The basic new assumption was that the amount of
energy returned into a given direction must come from a direction rotated
backward by the same amount that the flow has rotated. This means that the
return to isotropy term in the turbulent shear equations is now expressed as
(1 + 711) ~ 2
- T bij1
where 2
T = —-*— is the time scale,
e is dissipation of turbulent energy,
2222
q =u + v + w is the total turbulent kinetic energy,
b.. = u.u. - q 6. ./3 is the rotated component, and
ij i J ij
II is the second invariant b..b...
Here, b-jj has its eigenvector rotated each by an amount depending on its
original location. The total amount of the rotation cannot exceed 180°.
The characteristic time T was expressed as t = wT where u is a constan
The search for this constant and the use of the rotated bjj's was not very
fruitful. However, it was an indication toward the next technique that was
tried.
It was decided that the rotation cannot be expressed simply in terms
of the rotation tensor ftjj , because the shear flow is a large distortion.
Therefore, the whole expression for the expansion was redone using the
whole U-j -j term.
-1- > j
The expansion up to third order is
-------
290
(i + AII + 2E.fi a ){b.. + v.(b. n . + b. n .)
*• 1 pK
-------
291
3b. . 6.. 6b 2_2 <5b.. 6..
2b..
where a is a constant taken to be of order one. The derivatives are
intrinsic and depend on the deformation of the fluid system. Therefore the
program for the deforming turbulent flow of Tucker and Reynolds changed
also.
For a quasi-steady homogeneous flow, the derivatives become
6b
-57*- = - U. b . - U. b. ,
Ot 1,K KJ J , K IK '
62b..
= U. U »b». + U. U -»b.» + 2U. U. »b
The return- to- isotropy terms for deforming flow then become
2
All= ' V OAD){bu+ f
A22= - V d+ADHb22- | YST(bn- b33) + f
A33= - SL (l+AD){b33- f YST(2b33+bn) + |
2
D = b. -b.. S = strain rate A = constant
U J1
Y = new constant to be determined.
The return to isotropy terms for turbulent shear flow become
2
All= - V d+ADMb11+ YTU' | b12 + f YVul2b22} ,
2
A22= " V (1+ADMb22- f YTU'b12- | Y2T2Ul2b22) ,
(l+AD){b33-
2
S_
-------
292
Because of these changes, y and the time constant c in the expression,
T = cq2/e, become the only constants to be searched for. When these changes
were put into the respective programs, the deforming turbulent flow would
not work for any value of y or c. However, the shear flow did work but for
strange values (not near one) of gamma. Realizing that the shear program did
work gave a clue as to the direction one should take in trying to solve the
problem.
This was to realize that q2 is transported like a scalar in a boundary
layer. To represent this we must deal with uiuj and not u.u.. Hence, we
should have """
d+cll) * aT!^+aV 1^
T Lbj fit 2 fit2 J '
The contravariant indices do not matter to us as we are in Cartesian ^
cpordinates but the signs of the terms do. Thus in this case since U ^ and
b* are in the same principal axes, both derivatives
6bX
6I1 and
are identically equal to zero.
This means all of the equations in the deforming turbulent flow stay
exactly the same. The turbulent shear terms now become
2
An = - ^r (l+AD)[bn
A22 = - (l+AD)[b22 - YTU'b12] ,
A33 = - ci+AD) b33
12J
The value of gamma was searched for in the seeker program and was
found to be + .25. This produced very good results in all of the component
energies but the uv graphs were 1/3 less than the experimental values.
The work is now at this point. Obviously new values for the uv term
must be found from modifications of the theory. This is now in progress.
-------
293
6- MODELING TURBULENT FLUX OF PASSIl/E SCALAR
£UAWTITIES IW IWHOMOGENEOUS FLOWS*
by
**
John L. Lumley
Summasuj
It is suggested that, in an inhomogeneous turbulent flow, the flux
of a passive scalar admixture should be modeled to first order by a linear
combination of gradient transport and convective transport, where the
convective transport coefficient is proportional to the QM.die.nX. of the
(gradient)-transport coefficient. A simple model is presented which allows
determination of the coefficient of proportionality.
This work was supported in part by the U.S. Environmental Protection
Agency through its select research group in Meteorology, in part by the
U.S. National Science Foundation, Atmospheric Sciences Section, under
Grant No. GA-35422X, in part by the Delegation Generale a la Recherche
Scientifique et Technique (France), and in part by the John Simon
Guggenheim Memorial Foundation.
**
Evan Pugh Professor of Aerospace Engineering, The Pennsylvania State
University, on leave at the Laboratoire de Mecanique des Fluides,
Ecole Centrale Lyonnaise.
-------
294
It is common in semi-empirical schemes for computation of turbulent
flows (see Monin and Yaglom, 1971) to model the turbulent flux of a
passive scalar admixture C = C + c, c~ = 0, by simple gradient transport
even in -cn/iomogc.nc.ou4 situations. That is, one writes in an inhomogeneous
flow
(cu^^ = - (KijCj)^ (2)
The transport coefficient KJJ may be variously determined from local or
global turbulent quantities.
The form (1) or (2) is strictly correct even in kinetic theory only
in a homogeneous situation, and it is not a pAxCO-'u. clear that retaining
K-ji inside the divergence in (2) gives the proper lowest-order correction
for inhomogeneity . In fact, we shall attempt to show that it does not.
First, let us present an argument of Kolmogorov (Monin and Yaglom,
1971, p. 610). As originally presented, this argument related specifically
to a Markov process, having anisotropic transport coefficient. We will
For a general discussion of application of gradient transport forms to
turbulent transport, see Corrsin (1974). We are concerned here not
with their general inapplicability, but with finding the correct kinetic
theory form in inhomogeneous situations. Corrsin discusses these
questions also, and beginning from a form somewhat less general than
(3), he finds something similar to (9), but lacking several terms.
-------
295
present a simplified one-dimensional generalization of the argument,
which is not dependent on the Markov assumption.
Suppose that, at t = 0, each point K on a line has an indelible
concentration C(<,0). The points begin to move under the action of some
agency, and at time t the point originally at K,0 is found at X,t. Let
P(X,t/K,0)dX be the probability that a point beginning from <,0 is found
at time t between X and X+dX. Then the proportion of the line segment
(K,K+d<) to arrive between X and X+dX is P(X,t/K,0)dXdK. Now, at the
time t, the total number of points which have crossed to the right of an
arbitrary point, KO, will be those which have positions on the right at t,
but were on the left at 0. The net integrated flux to the right will be
the difference between those that have moved to the right and those that
have moved to the left. The mean net integrated flux of contaminant will
be given by weighting each point by its corresponding concentration, thus:
F = d< C(K,0)P(X,t/K,0)dX - d< C(K,0)P(X,t/K,0)dX
Ko
Ko Ko
The flux at time t can be obtained by taking the time-derivative after the
expression has been evaluated. We may make a change of variables to
K-KO = Z, X-K = c (4)
and reverse the order of integration to give
-------
296
oo 0
F = J d£ J dZ C(Ko+ZfO)P(Ko+Z+5,t/ico+Z,0)
0
0
J dc J dz C(Ko+z,0)P(Ko+z+;ft/Ko+zfo)
Now, the integrand may be considered as a function of Z, and expanded
in a Taylor series about KO (presuming that it is suitably well behaved):
,0) =Z rZ --jj. [C(Ko,0)P(Ko+C,t/Ko,0)j (6)
n=0 ' 9<
So that the integrated flux may be written as
00 f-nn an f+C° n+i
F = Z feTTTr -^ [C(K ,0)
(7)
i n »n rT+-1
The flux is given by the time derivative -
n
This is a generalization of the form given by Kolmogorov, which stops at
second order -
-------
, 297
*•
This clearly reduces to the classical form in a homogeneous situation.
It might be thought that (9) could be obtained more simply by using the
fact that C(X,t) = C(K,0), and expanding in series. However, this gives
expressions which are easy to evaluate only in homogeneous (reversible)
situations .
We must pause for a moment to discuss the relation between C(KO,0)
and C"(K,t). In fact, C(K0,0) = C"(
-------
298
be restarted, so that F always depends on C at a time earlier by the
(integral) time scale. Thus, in replacing (T by the current value, we are
supposing that (DC/Dt)T « C (where T is the time scale); this is true in
kinetic theory, but of course, not true in turbulence. It is, however,
consistent with the complementary assumption that the length scales of
the dispersion process are small relative to those of the C distribution.
Monin and Yaglom (1971) compare (9) with the more usual form
2 9< dt
o
and conclude that
•
t = \ a|- ^ (11)
O
It does not appear that this reasoning can be correct, since it results
from comparison of, effectively, the form (9) specialized to a homogeneous
situation, and the full form. We shall show, however, that a form similar
to (11), with a different coefficient, may well be correct.
First, we must discuss the possible value of ^ in a homogeneous flow.
Let us consider, for example, vertical transport in an incompressible,
horizontal homogeneous shear flow, without gravity. The flow must be
* '3~
symmetric about horizontal planes, and hence T, £' , etc., must vanish.
If gravity is introduced, with density fluctuations within the Boussinesq
approximation (Tennekes and Lumley, 1973), we might expect to find
-------
299
dissymmetry. However, we would expect to find the direction of the
dissymmetry to change sign with the sign of the gravity. However, if
both the sign of the density fluctuations and the sign of gravity are
reversed, the equations remain unchanged. Since the entire detailed
velocity field remains unchanged, the sign of t, cannot change. Hence it
must be zero. Hence, f must be zero in a homogeneous flow, as expected.
This suggests that an expression for £ may be obtained by considering
the departure from homogeneity represented by, for example, expressions
such as (11), which will vanish when the field becomes homogeneous.
It is very instructive to consider a somewhat restricted case. Let
f(t) be a stationary random function with zero mean and finite, non-
vanishing integral scales (Lumley 1972). Let £(K,t) be the dLl>p£.(ic.ejne.n£
at t of the point initially at K. Suppose that the moving point is
governed by
(12)
F(Z) = aZa , 0 < a. < 1
That is, the Lagrangian velocity can be reduced to a stationary function
by renormalization. This is by no means the most general form - we
could, for example, consider a case in which not the amplitude of the
velocity, but the time scale, were stretched according to the location.
This does not give a solvable case, however. The most general case, of
course, is that in which the position and time effects are not separable.
If we define K+L. = Z, and
-------
300
T = f(t')dt' (13)
0
we can write
1
= - K + K[l + -] 1
J
<
" " a(l-a)
where, for large time, T is a Gaussian variable (Lumley, 1972)
T £ 2f' tT, T = 0 (15)
where T is the integral time scale of f, and f is its variance. Expanding
the binomial in (14) we have (with n = 1/1-a)
2 2
y
(16)
2
2 2 T
= K n
P
Since 1-a > 0, y is monotone increasing in K; the series (16) proceed in
inverse powers of n, and hence, for larger values of K, higher order
terms are less important. As <->•<*>, the leading term is
C17J
-------
301
^..e. - for very large <, when the situation is almost homogeneous, we
have
t - i £ 7 (18)
and this is true regardless of the value of a (so long as 0 < a < 1).
The series (16) of course, terminates if 1/1-ot = n is an integer. For
example, if a = 1/2, we have
2
_ _ ,2f'2 r
2 ^T - a f T
(19)
f = ^T
while if a = — ,
- a
T = K - 2 f'2 T
_ 2 (20)
-i so ^ 2 12 -1/3
C + 27 at T £ K
a = 1/2 is the only value for which both £ and HV9K are constant in time,
For all others there is also a time limitation - roughly translated as
requiring that total dispersion must remain small enough for the
inhomogeneity across the dispersed material to remain weak.
If we accept (18) as a general value, then (9) should be
To lowest order.
-------
302
That is: there is, in addition to the gradient transport form, even
within the framework of kinetic theory, a convective transport term in
inhomogeneous situations. In turbulence modeling, the form (21) provides
a means for estimating the convection velocity; such a term has been
suggested by many authors (e.g. Townsend, 1956), but without useful
suggestions for estimating the form of the term.
Equation (21) of course may be generalized to several dimensions as
i — a •
L r(if tl fr r 1 (T.T\
A ^ LK» LJ ^\ L^-^-J L^^J
4 *• ' ^ 9K. *• i i''
-------
303
BIBLIOGRAPHY
1. Corrsin, S. (1974) "The Second Twenty-Five Years of Turbulent
Transport" in Advance* i.n Ge.opkyt>-icjt> , Vol. 18 (New York, Academic
Press; Landsberg, et al . , eds.).
2. Lumley, J. L. (1972) "Application of Central Limit Theorems to
Turbulence Problems" in S&Lt6io£enc.e
Cambridge, The M.I.T. Press).
-------
304
7. EULERIAN AND LAGRANGIAN TIME MICROSCALES IN ISOTROPIC TURBULENCE
(accepted by Journal of Fluid Mechanics)
H. Tennekes
Abstract
In isotropic "box" turbulence without a mean flow, the Lagrangian
frequency spectrum extends to frequencies of the order (e/v)1'^ (e is
dissipation rate of kinetic energy per unit mass, v is the kinematic
viscosity of the fluid). This leads to an estimate that makes the rms
value of du/dt of order (e3/v) 4. The Eulerian frequency spectrum,
however, extends to higher frequencies than its Lagrangian counterpart;
this is caused by spectral broadening associated with large-scale advection
of dissipative eddies. As a consequence, the rms value of 3u/at at a
fixed observation point is (apart from a numerical factor) R^1 times as
large as the rms value of du/dt (R^ is the turbulence Reynolds number
based on the Taylor microscale). The results of a theoretical analysis
based on these premises agree closely with data obtained by Comte-Bellot
and Corrsin. The analysis also suggests that the Eulerian frequency
spectrum has a uT5' 3 behavior in the inertial subrange, and that it is
not governed by Kolmogorov similitude.
1. Introduction
The study of turbulent diffusion requires that the distinction
between Eulerian statistics (those obtained by sensors at fixed locations)
and Lagrangian statistics (pertaining to the motion of fluid particles,
aerosols and pollutants) be kept in focus at all times. Diffusion is a
Lagrangian process, and there is no one-to-one correspondence between
Lagrangian variables and their Eulerian counterparts. This paper reports
on the distinctive differences between Eulerian and Lagrangian frequency
spectra.
The shapes of the Eulerian and Lagrangian frequency spectra in
isotropic "box" turbulence without mean flow have been subjects of some
speculation over the years (Inoue 1951, Corrsin 1963, Tennekes and Lumley
1972). Both spectra are assumed to obey Kolmogorov scaling; this leads
to forms which are proportional to eoT2 in the inertial subrange (e is
the dissipation rate of kinetic energy per unit mass, oj is the angular
velocity).
Comte-Bellot and Corrsin (1971) measured the Eulerian time correlation
function (in a frame of reference moving with the mean flow) of isotropic
wind-tunnel turbulence. From their experimental results, they calculated
-------
305
the Eulerian time raicroscale. The calculated value, however, was five
times as small as the one derived from the hypothetical similarity between
the Eulerian and Lagrangian frequency spectra. This discrepancy suggests
that the assumptions involved in the theoretical models should be reexamined.
In this paper, the results of an alternative theoretical approach are
presented.
The highest frequencies characterizing the dynamics of turbulence
occur at the smallest length scales. The Kolmogorov microscale is
(v3/e)1/lf, the Kolmogorov frequency of dissipative eddies is (e/v)1'2,
and the kinetic energy of the dissipative eddies is of order (ve)1/2 per
unit mass. It appears reasonable to postulate that the position of the
viscous cut-off in the Lagrangian frequency spectrum is determined by
the parameters v and e.
An Eulerian observer of "box" turbulence, however, will on occasion
encounter appreciable energy at frequencies much larger than (e/v)1/2.
Random advection of the dissipative structure past the observation point
causes spectral broadening, which is not unlike a Doppler effect. The
highest frequencies that will be observed must be associated with the
advection of dissipative eddies past the observation point by the most
energetic eddies. The frequencies involved must be of order q/n, where
1/2(q2) is the mean kinetic energy per unit mass and n is the Kolmogorov
microscale (v3/e)1/'t. A simple calculation, based on the assumption that
e ~ q3/£ (where t is an integral scale). shows that q/n is larger than
(e/v)1/2 by a factor proportional to R£//4 = (q-t/v)1/4.
In turbulence at high Reynolds numbers, therefore, the dissipative
eddies flow past an Eulerian observer in much less time than the time
scale which characterizes their own dynamics. This suggests that G. I.
Taylor's "frozen-turbulence" approximation should be valid in the analysis
of the consequences of large-scale advection of the turbulent microstructure.
Since Eulerian frequencies larger than (e/v)1/2 can be generated only by
advective spectral broadening, and since the rms value of 9u/8t is
determined by the position of the viscous cut-off in the Eulerian frequency
spectrum, it appears reasonable to postulate that the Eulerian time
microscale is determined by large-scale advection of dissipative eddies.
This hypothesis serves as the starting point for further analysis.
2. Analysis
If Taylor's hypothesis governs the advection of dissipative eddies
past a fixed observation point, we can write
8u 8u 8u 3u
= — 11 — V — W
at 8x V 8y 9z '
If we assume that the microstructure is statistically independent of the
-------
306
energy-containing eddies, we obtain for the mean-square value of (1) in
isotropic turbulence without mean flow
In isotropic turbulence, we have (Batchelor, 1953)
rt-i
u = v = w , (3)
Therefore, (2) reduces to
In isotropic turbulence, the following relation holds (Tennekes and Lumley
1972): . _
e = 15v (|^)2 (6)
Also, the Taylor microscale X is defined by
-ax'
Therefore, (5) may be written as
3u 2 1 2 e
or as _ —
A
Comte-Bellot and Corrsin (1971) define the Eulerian time microscale
through the relation
TE
2 '
(10)
Substitution of (9) into (10) yields
20
-------
307
In the experiments by Comte-Bellot and Corrsin, the value of T£ was
determined from the Eulerian time correlation behind a two-inch grid, with
the origin of the time delay chosen at the point x/M = 42 (M is the mesh
size of the grid). Their experimental value for Tg was 6^2 milliseconds.
At the reference position, X was equal to 0.484 cm and (u2)1/2 was 22.2 cm
sec"1. Substituting these values into (11), we find that the predicted
value of Tg is 14 milliseconds.
If TE is estimated on basis of the hypothetical similarity between
the Eulerian and Lagrangian frequency spectra (Corrsin 1963), a value of
approximately 30 milliseconds is obtained (Comte-Bellot and Corrsin 1971).
It appears that calculations based on the advection hypothesis are
more realistic than calculations based on the Eulerian-Lagrangian similarity
nypothesis. It should be pointed out, however, that the low Reynolds number
grid turbulence used in the Comte-Bellot and Corrsin experiments is not an
ideal test case for the advection hypothesis. At low Reynolds numbers, the
advective spectral broadening is not very pronounced, and the validity of
Taylor's hypothesis is questionable. Still, the relatively good agreement
between the prediction based on the advection hypothesis and the experimental
result is sufficiently encouraging to attempt an alternative analysis of the
Eulerian frequency spectrum in "box" turbulence.
3. The Eulerian Frequency Spectrum
The frequency spectrum observed at a fixed point in isotropic turbu-
lence without a mean flow is strongly affected by advective spectral
broadening. At a frequency corresponding to the viscous cut-off in the
Lagrangian time spectrum for example, fluctuations are observed which are
related to the passage of eddies in the inertial subrange. Some qualitative
estimates will help to illustrate the issue. Large-scale advection of
eddies of size r (where r is taken to be in the inertial subrange) creates
frequencies of order q/r. In order to find the value of r that contributes
most to the energy at the cut-off frequency (e/v)1'2 of the Lagrangian
spectrum, we have to put
q/r ~ (e/v)1/2 . (12)
This yields /
r ~ q(v/e) ' . (13)
If r relates to an eddy in the inertial subrange, its kinetic energy may
be estimated as (Tennekes and Lumley, 1972)
12 2/32/3
i- u (r) - e ' r ' . (14)
The contribution of these eddies to the kinetic energy at the Eulerian
frequency (e/v)1'2 is therefore
-------
308
1 2 l/2 */3 2/3 1/3
u {r, (e/v) } ~ e q v . (15)
at
In the absence of advection by large scales, the kinetic 'energy
frequency (v/e)1/2 would be
1 2 V2 I/2
j u {n, (e/v) } - (ve) . (16)
The ratio of (15) and (16) is
ju2{x, (e/v)1/2> q2 1/3
1~2~. , . ,1/2. ~ ( .i/J •
j u {n, (e/v) } (ev)
1/2
Here, (ev) is the kinetic energy of the dissipative eddies. Clearly,
the advective contribution outweighs the quasi -Lagrangian one, at least if
the Reynolds number of the turbulence is large enough.
We conclude that the high-frequency end of the Eulerian time spectrum
must be dominated by the Doppler shifts in frequency caused by random
advection by the energy- containing eddies. This generalization of the
advection hypothesis permits us to obtain a probable form of the inertial
subrange (obviously better referred to as the inertial-advective subrange)
in the Eulerian frequency spectrum.
If the dominant contribution to the kinetic energy at a frequency u>
in the inertial-advective subrange is made by large-scale advection of
eddies in the inertial subrange of the wave-number spectrum, we have
<«> - q/r , (18)
and
1 2, -, 2/3 2/3 ,irn
j u (co) - e r . (19)
Substitution of (18) into (19) yields
1 2 2/3 2/3 -2/3
j u (u) ~ e q a) . (20)
The Eulerian frequency spectrum is defined as the kinetic energy per unit
frequency. We obtain
2/3 2/3 -5/3
«E(u) = 3Ee • q u , (21)
where Pg is an unknown constant, which presumably is of order one.
The inertial-advective subrange in the Eulerian frequency spectrum
thus does not obey Kolmogorov scaling, and is markedly different from the
inertial subrange in the Lagrangian frequency spectrum. The latter is
(Inoue 1951, Corrs?.n 1963, Tennekes and Lumley 1972)
-------
309
4, (u) - gjEco . (22)
Li Li
Let us compare (21) and (22) at the lowest frequency for which they might
give a reasonable representation. That frequency is oo ~ q/£ (£ is an
integral scale), and we find
(23)
•*LW+-J ML
2
Since e ~ q /-£., the values of $g and $L at the large-scale end are of
comparable magnitude. In the absence of high Reynolds number data on these
spectra, we cannot determine if the Eulerian spectrum is likely to have a
co~2 shape at frequencies below those in the inertial-advective subrange,
but it seems fair to speculate that such a small difference in spectral
slope would be extremely hard to verify experimentally. One point appears
to be clear, however: since the spectral "smearing" caused by random
advection tends to remove discontinuities in the spectral slope, the inertial-
advective spectrum proposed here may well be a valid approximation at
frequencies near those characteristic of the large-scale structure.
2
The spectra given by (21) and (22) can, after multiplication by oj ,
be integrated to obtain estimates for the mean-square values of 9u/9t and
du/dt:
T9ITT f 2 . . . f. 2/3 2/3 1/3
=
ppe q co dco
0 0 (24)
2/3 2/3
WE,D •
and
;du,2 _ i 2
tU ir, i \M i vj-wj — i i_j
0 0 (25)
Here, oog ^ is the frequency of the viscous cut-off in the Eulerian spectrum,
and WL Q is its Lagrangian counterpart. According to the advection
hypothesis,
a 1/t -3/4
COE D = 3- = qe v , (26)
while the highest Lagrangian frequency is
1/2
co = (e/v) . (27)
L , L)
-------
310
In (26) and (27), unknown numerical coefficients have been ignored.
Substitution of (26) into (24) yields
()= CEq(^) ; (28)
The value of Cg can be estimated by comparing (28) with (8); this yields
CE = 1/3, because q2 = 3 u2 .
Substitution of (27) into (25) yields
The value of CL can be estimated from the data given by Shlien and Corrsin
(1974). They define the Lagrangian time microscale by
— 2
, cm, 2 _ 2u
TL
Substitution of (30) into (29) gives
l/2 "2, 1/2
U)
For (u2)1/2 = 22.2 cm sec"1, e = 0.4740 m2sec"3 and v = 15 x 10"6
Shlien and Corrsin found TL = 76 x 10~3 sec. Substitution of these values
into (31) gives CL = 4/9 approximately.
The ratio between the Eulerian time microscale and its Lagrangian
counterpart thus is given by (note that Corrsin1 s definition of Tg, given
in (10), involves a factor 4, whereas his definition of TL, given in (30),
involves a fac.tor 2) :
4 (e ^ (32)
3 <
Here we have used CE = 1/3, CL = 4/9.
The velocity (ev) occurring in (32) is the Kolmogorov velocity of
the dissipative eddies. Since the ratio (ev^/Vq is proportional to
^£~1 = C^/v)" > this result confirms that the Eulerian time microscale
must be appreciably smaller than its Lagrangian counterpart if the Reynolds
number of the turbulence is large enough. The comparison also shows that
the approximate equality of TE and TL predicted by Corrsin 's (1963)
Eulerian-Lagrangian similarity hypothesis is bound to produce unrealistic
-------
311
values of T£. The values of Tg and TL obtained in the experiments by
Corrsin and his co-workers prove that the advection hypothesis is
justified, even at relatively low Reynolds numbers.
4. Discussion
The consequences of the advection hypothesis are rather embarrassing
in a personal sense. The section on time spectra in Chapter 8 of Tennekes
and Lumley (1972) treats the Eulerian spectrum on basis of the similarity
hypothesis; if the analysis presented in this paper proves to be reliable,
that section will have to be revised before a new edition goes to press.
The advection-dominated Eulerian spectrum strongly suggests that the
evolution of turbulence in wave-number space is best computed on a
Lagrangian basis. Large-scale advection of the small-scale structure
creates Eulerian Fourier components at frequencies that are higher than
the angular velocities characterizing the internal evolution of the scales
being advected, and calculations of the temporal evolution at the points
of an Eulerian grid would tend to get overwhelmed by these spurious advection
effects. From this point of view, models such as Kraichnan's Lagrangian-
history, direct-interaction approximation obviously are to be preferred
above their Eulerian counterparts.
This research was supported by the Atmospheric Sciences Section of
the U.S. National Science Foundation (Grant GA-35422X). Partial support
was received also from the U.S. Environmental Protection Agency, through
its Select Research Group in Air Pollution Research at The Pennsylvania
State University.
-------
312
REFERENCES
1. Batchelor, G. K., 1953, The Theory of Homogeneous Turbulence,
Cambridge University Press.
2. Comte-Bellot, G. and Corrsin, S., 1971, "Simple Eulerian Time
Correlation of Full- and Narrow-Band Velocity Signals in Grid-
Generated, Isotropic Turbulence," J. Fluid Mech. 48, 273-337.
3. Corrsin, S., 1963, "Estimates of the Relations Between Eulerian and
Lagrangian Scales in Large Reynolds Number Turbulence," J. Atmos. Sci.
20, 115-119.
4. Inoue, E., 1951, "On Turbulent Diffusion in the Atmosphere," J. Met.
Soc. Japan 29, 246-252.
5. Shlien, D. J. and Corrsin, S., 1974, "A Measurement of Lagrangian
Velocity Autocorrelation in Approximately Isotropic Turbulence,"
J. Fluid Mech. 62, 255-271.
6. Tennekes, H. and Lumley, J. L., 1972, A First Course in Turbulence,
MIT Press, Cambridge, Massachusetts.
-------
313
NOTES ON TURBULENT FLOW IN TWO AND THREE DIMENSIONS
by
H. Tennekes
1. Introduction
These notes contain the core material for a paper that will be
submitted for publication in the near future. Though the issues taken up
in these notes do not pertain directly to the atmospheric diffusion
modeling tasks of the Select Research Group, it is felt that the analysis
presented here contributes to the study of some of the problems we face
in our research.
The dispersion of atmospheric pollutants is affected by motions on
all scales, ranging from the turbulence microstructure in the mixed layer
to mesoscale and synoptic-scale flow patterns. The study of three-
dimensional turbulence needs to be related to that of the quasi two-
dimensional "turbulence" of the synoptic eddies, if only to obtain a
more profound insight into the extremely difficult task of modeling meso-
scale motions, for which neither the assumptions used in turbulence theory
nor the approximations employed in synoptic analysis are valid.
This material is based on lectures in the author's turbulence course;
it was presented also at a seminar for the Department of Meteorology given
in the spring of 1974.
2. Statement of the Issue
What do a turbulence theoretician and a numerical modeler of atmospheric
motions have in common? It would seem that there is not much that unites
them. The turbulence researcher ordinarily takes a statistical approach to
his flows, but the forecaster treats his flows in a deterministic way. What
is it that makes the turbulence community prefer statistics? And what
happens when you think of an ensemble of synoptic flow fields as a kind of
turbulence? A forecaster identifies "eddies" (such as a low-pressure
system) on the weather map with great confidence, but the turbulence researcher
has a hard time recognizing individual eddies. Why is that so? Is it the
limited spatial resolution of a synoptic analysis that makes a weather map
so clean-looking, or do synoptic flows in fact have much less microstructure
than the kind of flow that is found in the atmospheric boundary layer?
Questions such as these can be answered only if one is willing to
study the "primitive equations". These provide a common foundation, and
-------
314
we trust that they are capable of providing pertinent insight. In our
exploration, we shall emphasize the role of vorticity, since it holds a
key position both in turbulence dynamics and in dynamical, meteorology.
We restrict the analysis to incompressible flows. By doing so we cannot
do justice to the energetics of atmospheric flows; however, we can take
a close look at major kinematical aspects. The generalization of the
equations of motion to stratified fluids in an environment exposed to the
acceleration of gravity is discussed in textbooks on dynamical meteorology
(for example, Haltiner and Martin).
3. The Equations of Motion
For our purposes, it is useful to write the Navier- Stokes equations
in such a way that the role of vorticity is emphasized. The formulation
we select is (Tennekes and Lumley, p. 77)
8ui 13,1 , 9\
at" = - p 3x~ (p + 2 pujV + e - ve - C1
In vector notation, this reads
-JL = _ 1 y (p + T pu • u) + uxw - vVxu . (1 )
dt P~ z. ~ ~ ~~ -~
Local accelerations apparently are caused by the gradient of the stagnation
pressure (the validity of Bernoulli's equation in steady flow without
vorticity is evident here) , by the "vortex force" u x oj, and by the viscous
force (the last term of (1) , which shows that in solid-body rotation the
viscous force is zero) .
The most interesting of these forces is the vortex force u x co. Since
its direction is normal to the velocity vector, this force does not perform
work; therefore, the vortex force does not affect the kinetic energy of the
flow in an explicit way. Nevertheless, the vortex force plays a dominant
role in the evolution of many flow fields.
Equation (1) is written for an inertial frame of reference. If it is
to be used in a rotating coordinate system, the vortex force has to be
replaced by
u x co = uxu) + 2u x ft . (2)
** ~a ~ ~r ~ ~
Here, co is the "absolute" vorticity, wr is the "relative" vorticity, and
Q is the angular velocity of the coordinate system. The factor 2 in the
last term occurs because vorticity is defined as twice the angular velocity
of a small fluid element. In the conversion to a rotating frame we also
should include the centrifugal force,, but that can be incorporated in the
definition of the pressure p (see, for example, Greenspan's book).
-------
315
One major difference between turbulence and synoptic flows is that for
large-scale atmospheric motions the "external" vortex force (the Coriolis
force) tends to control the evolution of the flow field, while in fully
three-dimensional flows such as turbulence the "internal" vortex force plays
a major role. For example, the shear-stress components of the Reynolds
stress tensor in turbulence are associated with the contributions of turbulent
velocity and vorticity fluctuations to the average vortex force acting on the
mean flow (Tennekes and Lumley, p. 79).
In a two-dimensional flow field evolving on a horizontal plane, the
vertical component of the velocity is zero and so are both of the horizontal
components of vorticity. Defining v as the horizontal wind speed vector, V^
as the horizontal gradient operator, C as the relative vorticity, f as the
vertical component of 2Q (f is the Coriolis parameter), and k as the vertical
unit vector, we find that (1) reduces to
It"= " £ Vp + \ PY * Y) + Yx -^ + ~ x ~£ • (3)
In this equation we have ignored the viscous force.
The geostrophic wind vg is defined by
"*o
- - V, p = - v x kf . (4)
p ~h^ ~g
With this relation, (3) may be rewritten as
= ' PY • Y) + Y * k£ + (Y-Y) x kf • (5)
4. Order-of-Magnitude Estimates
For large-scale motions in the_earth's atmosphere, the two terms of
equation (4) are of order 10"3 msec 2:
i -3 -2
- V, p and v x kf ~ 10 msec . (6)
p ~hF ~g v
The terms of (5), however, generally are one order of magnitude smaller:
— 4 — 2
-zf- , YV.CT v*v)> v x k£, (v~v ) x kf ~ 10 msec . (7)
ot n £ - - ~ - ~ ~g
These estimates imply that the relative vorticity £ is about 10 times as
small as f, so that its order of magnitude is 10"5 sec"1. Also, the
ageostrophic wind component v - vg is implied to be about 10 times as small
as Vg. With Vg ~ 10 msec"1, this means that v - vg ~ 1 msec"1.
-------
316
What would be the orders of magnitude of the various terms in the
equations of motion if they were used to describe a three-dimensional
turbulent flow with the same velocity and length scales? In 3D turbulence,
most of the vorticity resides at very small scales, and the mean-square
vorticity (twice the "enstrophy") is given by
oo.UK = a) • a) = e/v , (8)
IX "* ***
where e is the mean dissipation rate of kinetic energy per unit mass, and
v (as before) is the kinematic viscosity of the fluid. The dissipation
rate may be estimated as (Tennekes and Lumley, p. 20)
e ~ u3/L , (9)
where u is a velocity characteristic of-the large-scale eddy motion, and L
is the length scale (for simplicity defined as a quarter wavelength) of the
large eddies.
In order to make a fair comparison between 3D turbulence and synoptic
flows, we select u = 10 msec"1 and L = 106m (= 1000 km). This choice is
consistent with equations (6) and (7), because it makes the relative
vorticity of the large eddies of order 10~5 sec"1 and the internal vortex
force of order 10"1* msec"2 if the same values of u and L are used in the
equations for large-scale atmospheric flows.
With u = 10 msec'1 and L = 106 m, we obtain e - 10~3 m2sec"3, and,
with v = 15 x 10"6 n^sec"1 for air at sea level, we obtain the following
estimate for the order of magnitude of the vorticity fluctuations:
u - 10 sec"1 . (10)
Since u - 10 msec"1, we conclude that the internal vortex force, u x u ,
is of order 100 msec"2, which is six orders of magnitude larger than in
the two-dimensional reference case.
This estimate for u x to, however, is dominated by the contributions to
the vortex'for'ce made by large-scale advection of small-scale vorticity
fluctuations. The smallest eddy size in 3D turbulence is n = (v3/e); using
the same numbers as before, this gives n ~ 10"3 m (1 mm). Advection of
those eddies past a fixed observation point with velocities of order 10
msec"1 gives rise to angular velocities of order 10^ sec"1. This is three
orders of magnitude larger than the angular velocities of those small eddies
themselves (see equation (10)). If the reciprocal of 01 is taken as the
smallest dynamically significant time scale in the turbulence, it would seem
that it isn't really necessary to carry events at smaller time scales along.
If we filter all angular velocities greater than 10"l sec"1 away, we remove
the fluctuations associated with the large-scale advection of small-scale
features without doing harm to the evolution of the flow. This procedure is
valid only if the large-scale advection of small-scale features is governed b
-------
317
~
+ (u£ • V) ys = 0 . (11)
Here, us is the small-scale velocity and u_£ is the large-scale velocity.
Equation (11) is the "frozen-turbulence approximation", proposed originally
by G. I. Taylor.
If these advection effects are removed by filtering, we still need to
consider the vortex force arising from small-scale advection of small-scale
vorticity. This requires that the characteristic velocity of the small-scale
structure of 3D turbulence be used in estimating u x w. The velocity of the
smallest eddies may be estimated as (ve)1/^ (Tennekes and Lumley, p. 20);
with v = 15 x 10~6 m2sec~1 and e = 10~3 m2sec~3, this gives 10~2 msec'1.
Therefore, the order of magnitude of u x to in 3D turbulence with the same
velocity and length scales as synoptic flows is, when large-scale advection
effects are filtered out,
-1 -2
u x u ~ 10 msec . (12)
These effects occur at angular velocities of order 10 sec"1 (eddy sizes near
10~3 m advected at relative velocities of about 10~2 msec"1). Therefore,
the limiting frequency corresponding to to _ 10 sec"1 does not need to be
changed.
The estimate presented in equation (12) can be supported by estimates of
some of the other terms in the equations of motion. The mean- square value of
du/dt in 3D turbulence is estimated from the Lagrangian time spectrum (Tennekes
and Lumley, p. 279) as
du 2 e3 1/2
S - (— ) • (13)
dt v
A different kind of calculation (Batchelor, p. 183) gives for the pressure-
gradient fluctuations in turbulent flows:
1 - 2 e3 1/2
(^V p)Z ~ 3(^-) . (14)
If we continue to use e ~ 10~3 m2sec"3 and v = 15 x 10~6 m^sec"1, we find that
^ ~ 10"1 msec"2 , (15)
- Vp ~ 10"1 msec"2 . (16)
These numbers are comparable with the estimate given in equation (12) .
If large-scale advection of small-scale fluctuations had not been
filtered out, we would have, from (10) and (11),
|£ ~ 102 msec"2 . (17)
-------
318
Comparing this with (15), we see that it indeed is fair to use the frozen-
turbulence approximation in (11).
The Coriolis force in this turbulent flow is of order 10"3 msec"2
(u ~ 10 msec"1, f = 10~4 sec"1). This suggests that, the Coriolis force
plays an altogether insignificant role in the temporal evolution of 3D
turbulence. In all fairness, however, it should be pointed out that the
role of the Coriolis force in the evolution of the large-scale features of
3D turbulence is not necessarily small. In order to recover the large-scale
dynamics, the equations of motion have to be filtered in such a way that the
rapid changes associated with the small-scale structure are removed. This
is at the heart of the issues mentioned in the introduction. In 3D turbulence,
the temporal changes in the flow field are dominated by the dynamics of the
smallest scales of motion; if one is primarily interested in the evolution
of the larger scales, one has to remove the small scales by averaging.
However, as soon as averaging is performed, say over a grid with relatively
coarse spacing, new unknowns are introduced into the equations of motion.
These unknowns are the average subgridscale eddy forces, which make the
system undetermined (the "closure problem" of turbulence). The only way to
solve this problem is to employ parameterization techniques for the sub-
gridscale effects. In a Lagrangian frame of reference (which removes the
troublesome advection effects), the temporal rate of change of 3D turbulence
with the same length and velocity scales as synoptic flows is 1000 times as
rapid as that of its two-dimensional counterpart. For large-scale atmospheric
flows, v ~ 10 msec'1 and dy/dt ~ 10~^msec~2, so that the characteristic time
of temporal changes is of order 105 sec (the reciprocal of the relative
vorticity £). This implies that in a numerical prediction scheme the time
step could be at least lO1* sec (a few hours). This estimate also suggests
that, generally speaking, there is no need to draw weather maps more often
than every three hours.
- 2
In the corresponding 3D flow, du/dt - 10"1 msec ~. Again using u -
10 msec"1, we find that the time scale becomes of order 102 sec (about two
minutes). This is not a fair estimate, however, because du/dt is greatest
for the smallest eddies. The vorticity of those eddies is of order 10 sec'1
(equation (JLO)>, and if we want to include their evolution we have to use a
time step of order 10"2 sec, and a grid spacing of 10~3 m. Clearly, the
drawing of weather maps for 3D turbulence is an insurmountable task!
5. The Effects of Scale
The obviously quite dramatic differences between large-scale atmospheric
flows and their three-dimensional counterparts can be illustrated further
by a study of the effects of scale on the equations of motion. In this way,
we should be able to find answers to such problems as the validity of using
the equations of motion for atmospheric flows without including subgridscale
forces associated with the averaging processes that are used in practi..
We restrict our analysis to eddy sizes that are small compared to tue
-------
319
dimensions of the large-scale motion. This restriction allows us to use
the relatively simple formulations that have been developed for the "inertial
subranges" of two- and three-dimensional turbulence.
In the inertial subrange of two-dimensional turbulence, the kinetic
energy spectrum drops off as the inverse third power of the wave number (see
e.g., Charney, 1971). This behavior implies that an eddy of size X (where
X « L and L is the scale of the large eddies) has a characteristic velocity
which is proportional to X. Later in this paper we shall show that a fair
estimate for the velocity v(X) of a 2D eddy of size X is
v(X) ~ (L/a)fX . (18)
Here, a is the earth's radius. For X -> L, equation (18) becomes v(L) ~
(L/a)fL, wnich is of order 10 msec"1 if L/a ~ 10"1, f ~ KT4 sec'1 and
L ~ 106 m. Therefore, (18) is consistent with the numbers we used earlier.
The corresponding relative vorticity at scale X can be estimated as
v(X)/X. This yields
C(X) - (L/a)f . (19)
This indicates that in the inertial range of two-dimensional turbulent flows
the vorticity is independent of eddy size. We note that equation (19) is
consistent with the numbers used earlier: the relative vorticity is of
order 10~5 sec"1 at all scales in this range of scales.
Eddies of scale X thus make a contribution to the Coriolis force which
(v x kf)x ~ (L/a)2f2X . (20)
may be estimated as
This decreases with decreasing eddy size. The geostrophic balance, equation
(4), thus is not affected strongly by the presence of small eddies. This
implies that the definition of the geostrophic wind does not need to be
corrected for subgridscale effects if the grid size is reasonably small (say,
a few hundred kilometers).
Let us now assume that the near-cancellation of pressure gradient and
Coriolis force holds also in the inertial range. This assumption amounts
to stating that the ageostrophic wind component ya = v - vg depends on X as
"* *** &
va ~ A- (L/a)fX . (21)
The Coriolis force of the ageostrophic component at scale X becomes
{(v - vg) x kf}x ~ -^ (L/a)f2X . (22)
At X ~ L this term is of order lO"1* msec~2, but at X ~ 0.1 L (corresponding
to wavelengths of about 400 km) this term is of order 10"5 msec"2. Therefore,
subgridscale eddies make small contributions to the Coriolis force on the
-------
320
flow field, and there is no need to represent subgridscale Coriolis forces
by some kind of model if the grid size is of order 100 km. Formally
speaking, this need does not exist anyhow, because the Coriolis force is
linear in velocity, and the mean value of subgridscale fluctuations is zero
by definition.
The advective terms do not possess this feature, since they are non-
linear. Linear estimates of nonlinear effects are tricky; in this context,
they involve interactions between eddies of various sizes. The vortex
force at scale X, for example, includes large-scale advection of A-scale
vorticity, A-scale advection of large-scale vorticity, A-scale advection of
A-scale vorticity, and many other combinations.
Small-scale (A-scale) advection of A-scale vorticity scales as
y(A) x kC(A) - (L/a)2f2A . (23)
At a scale A = 100 km (wavelengths of 400 km), this effect is of order 10~5
msec"2, which is 10% of the overall vortex force. Therefore, this term may
be ignored if no great precision is required.
Small-scale advection of large-scale relative vorticity behaves in the
same way as (23):
v(A) x kc(L) ~ (L/a)2f2A . (24)
This is due to the fact that the vorticity is independent of scale.
Evidently, all small-scale advection may be ignored in the formulation of
approximate equations of motion.
Problems arise, however, when the large-scale advection of small-scale
vorticity is considered. This is estimated as
y(L) x k£(A) ~ (L/a)2f2L . (25)
This contribution is independent of the size of the A-scale eddies; it is
of order 10"1* msec"2 at all scales because the vorticity is independent of
scale in the inertial range. Strictly speaking, therefore, the equations
of motion should contain a term representing the average subgridscale vortex
force.
Filtering of high frequencies appears to be a suitable solution of
this dilemma. Contributions of the type expressed by equation (25) generate
angular velocities at the observation point that are of order v(L)/A. For
A = 105 m (100 km) and v(L) = 10 msec"1, the "frequency" is of order 10"1*
sec"1, which is one order of magnitude larger than the angular velocity in
all eddies (the latter is £ ~ 10"5 sec"1). It would seem that careful
removal of these higher frequencies would alleviate the problem.
If the same analysis is applied to the other part of the advective
term (the dynamic-pressure gradient in the equation of motion), the conclusions
-------
321
obtained above do not change. Apparently, if large-scale advection of
small-scale features can be handled somehow, all other contributions to
the rate of change of the flow field decrease with decreasing scale. In
other words, the evolution of the flow field is dominated by the evolution
of its large-scale features. This means that equations of motion without
subgridscale eddy terms may describe the evolution fairly well. It also
means that numerical prediction methods do not have to be extremely
concerned about the limited spatial resolution of the observational network.
In three-dimensional turbulence, on the other hand, the situation is
altogether different. In the inertial subrange of 3D turbulence, the kinetic
energy spectrum is proportional to the inverse five-thirds power of the wave
number, and the characteristic velocity of an eddy of size A is estimated as
0-, i1/3 flf.-\
u(A) ~ e A . (26)
The vorticity at scale A is therefore given by
u(X) ~ e1/3 A~2/3 . (27)
Here, the Coriolis force also decreases with decreasing eddy size, though
not as rapidly as in the atmospheric counterpart:
(u x kf). ~ fe1/3 A1/3 . (28)
~ ~ A
The vortex force corresponding to A-scale advection of A-scale vorticity,
however, increases as the scale decreases:
u(A) x u(A) ~ e2/3 A'1/3 , (29)
and the vortex force corresponding to large-scale advection of A-scale
vorticity increases fairly rapidly with decreasing eddy size:
u(L) x u)(A) ~ u(L) e1/3 A'2/3 . (30)
This latter term can be filtered out however, because at a fixed observation
point it generates frequencies that are much larger than tu(A) .
We need not search further, because (29) - a term which cannot be
removed by filtering - increases as the scale decreases. This shows that
the temporal evolution of 3D turbulence is dominated by its small-scale
structure. Terms such as (29) cannot be ignored, because the subgridscale
contributions may be larger than the contributions made on the resolvable
scales. A statistical approach seems inevitable. If the grid size is A,
the equations of motion have to include the average contribution to the
vortex force made by all subgridscale eddies. Fortunately, this averaging
process removes the large, rapid fluctuations associated with eddies much
smaller than A, so that the proper estimate is
,2/3 -1/3
(u x co), - e ' X ' . (31)
*" •" A
-------
322
The task of finding appropriate models of the various components of (31) is
a major issue in turbulence theory; here we will restrict ourselves to a
numerical estimate. For e ~ 10~3 m2sec~3 and X = 10s m (numbers we used
before) , we obtain _
(U x UJ)A ~ 2 x 10"1* msec'2 „ (32)
This is only a factor of two larger than the vortex force at the large-scale
end (where L = 106 m is the eddy size) . The time step required in numerical
computations, however, becomes fairly small, because it has to be geared to
the dynamic time scale of1 of the A-scale eddies. For A = 105 m, o> ~ 4 x
10~5 sec'1, which is four times as fast as the evolution of the L-scale
structure.
In numerical work along these lines (Deardorff, 1970 - present) the grid
size is nevertheless taken as small as possible, consistent with the computer
facilities available. The reason for this approach is that the modeling
(parameterization) of average subgridscale contributions becomes easier as
the grid size decreases.
6. Vorticity Dynamics
One of the most pronounced differences between 3D-turbulence and quasi-2D
atmospheric flows is the magnitude of the vorticity fluctuations. In large-
scale atmospheric flows the relative vorticity is of order 10" 5 sec"1 at all
scales down to a few hundred kilometers, while in the 3D counterpart the
vorticity fluctuations are of order 10 sec"1 (for conditions with the same
large-scale velocities and the same large-eddy size) .
This suggests that the study of the vorticity equation should be worth-
while. For an inertial frame of reference, the vorticity equation is
d • V)u + W uj . (34)
The first term on the right-hand side represents two kinds of effects: (a)
turning of the vorticity vector direction caused by shear (off-diagonal
components of the velocity gradient), and (b) amplification or attenuation
of the vorticity amplitude by streaming motions ("stretching" or "squeezing",
respectively) .
For our analysis, vortex stretching is the most important of these
effects. However, in an exactly two-dimensional flow there is no vortex
-------
323
stretching at all because to then is at right angles to the gradient operator
(which lies in the plane of the flow) . Therefore, we must allow some
vertical motion in order to keep the stretching term.
In an approximately 2D flow, the vertical component of u is by far the
largest. If we call that component £a (we are still in an inertial frame
of reference), and if we ignore viscous diffusion, (34) may be approximated
a 8w
diT = Ca3l '
In incompressible flow, we have
3w 3u 8v, „
87 = ' (8l + 1y} = " ~h ' Y '
where V^ • v is the horizontal divergence of the horizontal wind field. If
we substitute (36) into (55) , we obtain
dCa
= - tVh - v . (37)
For a rotating system, this equation does not change; one common form is
(Haltiner and Martin, p. 350)
•^ U + f) = - (C + f) Vh • v . (38)
This states that the absolute vorticity is amplified in regions with
horizontal convergence, and that it is reduced in regions with horizontal
convergence. Convergence leads to convergence of angular momentum,
divergences spreads angular momentum over larger areas. Generally speaking,
vortex stretching is not at all pronounced on synoptic scales; in hurricanes
and tornadoes, however, vorticity amplification leads to destructive
concentrations of vorticity and of kinetic energy.
At levels at which the horizontal divergence generally is small (such
as the 500 millibar surface, the "middle" of the atmosphere), equation (38)
reduces to
-^ U + f) = 0 . (39)
This states that the absolute vorticity is conserved along fluid trajectories.
This equation plays a key role in simple models of atmospheric motion and in
short-term prediction schemes. It can be generalized to more realistic
models by taking it to describe the evolution of such quantities as the
pseudo-potential vorticity (Charney, 1971) .
Equation (39) implies that vorticity changes are due solely to advection.
Now, the Coriolis parameter f does not depend on time or longitude, but it
does change as the latitude (y) varies. In a "B-plane approximation" (which
uses df/dy = g, a constant), e.g. (39) may be written as
-------
324
+ (Y • YhK - - vft . (40)
At any fixed observation point, the only source of relative vorticity
(apart from mere advection) is transport of Coriolis rotation in the
latitudinal direction. Therefore, at middle latitudes, the relative vorticity
level may be estimated as
£ ~ pL , (41)
where L is the distance over which transport of angular velocity is effective,.
If we put
n _ df _ f
e - dy- - I '
where a is the earth's radius, we obtain
C - (£) f • (43)
This is the foundation for the estimates we used earlier. Because L/a = 1/6
if L = 1000 km, the relative vorticity in synoptic flows is nearly an order
of magnitude smaller than the absolute vorticity.
Does equation (39) imply that nothing at all happens to the absolute
vorticity, except for the obvious advective changes? No; two-dimensional
flows are capable of increasing vorticity gradients. For incompressible,
two-dimensional flow in an inertial frame of reference, the evolution of
9co/9xi is governed by
d ,9m . U 3u _ 3 .3t» .
_
dt x 9Xi 3x- " 3x,9x. x '
The second term on the left hand side tends to amplify vorticity gradients,
much as the stretching term in the vorticity equation tends to amplify
vorticity.
Two-dimensional flow conserves vorticity, but it amplifies vorticity
gradients. Since the increasing gradients cannot be associated with
increasing vorticity, they must be associated with decreasing scales of
motion. The net effect of (44) must be that vorticity is carried to smaller
scales. This amounts to a spectral flux of vorticity. The average flux
must conserve enstrophy (mean square vorticity) , so simple similitude
suggests that the vorticity at any scale X smaller than L is independent of
scale. This leads to the k~3 spectrum and to the scale relations we used
in Section 4.
We can be brief about 3D turbulence. Vorticity dynamics in 3D turbu-
lence is covered in Section 3.3 of Tennekes and Lumley; it is completely
dominated by vortex stretching (something like complex interactions among
tornadoes at all scales), and leads to extremely high enstrophy levels.
Atmospheric flows are gentle compared to turbulent flows, because they do
not possess a mechanism for the nearly unlimited increase of vorticity
fluctuations. This makes it a lot easier to predict the evolution of
-------
325
synoptic flows than the evolution of their 3D counterparts. Statistical
techniques are a necessity in 3D turbulence; fortunately, this is not so
for large-scale atmospheric flows.
This research was supported by the U.S. Environmental Protection
Agency through its Select Research Group in Air Pollution Meteorology,
and by the Atmospheric Sciences Section of the U.S. National Science
Foundation.
-------
326
IV SRG ON AIR-POLLUTION METEOROLOGY
Part 1
TASK 2
W. J. Moroz
-------
327
SECOND ANNUAL REPORT
IV. SRG on Air-Pollution Meteorology
TASK 2
1.0 Atmospheric Effects on Particulate Pollutants
The objectives of Task 2 are to:
1. Select and establish operating procedures for instruments capa-
ble of providing quantitative values to establish particle number size
distributions in the atmosphere;
2. Establish chemical analytical procedures which would permit
particle identification in the atmosphere in order to establish mass
continuity (including loss or addition by difference) for the atmos-
pheric burden of particles;
3. Collect data establishing particle number size distributions
applying to selected chemical species which can be used as tracers in
following a cloud of particles from a specific urban source; make ob-
servations using aircraft in a spatial grid network (horizontal and
vertical) to establish particle characteristics and changes in physi-
cal characteristics of the particles during their travel time in the
atmosphere;
4. Study the behavior of the size distributions as functions of
time, location, underlying terrain and pertinent meteorological varia-
bles;
5. Initiate development of a model capable of predicting par-
ticle behavior in time and space, relative to the source emission, in
-------
328
terms of particle-number concentrations and size distributions; field
observations, suitably processed, will serve as input for the pre-
diction model.
The rationale underlying the above objectives is that information
regarding particle-number concentrations and size distributions in
the atmosphere is essential to an understanding of the following
fundamental processes:
(a) particle removal mechanisms; e.g., fallout, agglomeration,
surface deposition, particle growth by moisture condensation;
(b) effects of absorption and scattering of electro-magnetic
radiation, especially with regard to visibility and modification of
solar radiation. Number-size distributions of particles, total con-
centration, shapes, (by inference if particle growth by condensation
is significant) indices of refraction and surface states of the in-
dividual particles (by inference) all contribute to these effects;
(c) potential health effects due to particles at some distance
from the point of generation.
Since information describing number-size distributions of parti-
cles in the lowest 3000m of the atmosphere over and downwind from
urban areas is scarce at the present time, the data our research team
is gathering will constitute valuable information in its own right.
Particle agglomeration, breakup, nucleation, diffusion and removal
are allied problems to be considered and/or resolved in Task 2.
-------
329
1.1 The Sampling Program
The effort of the second year has focused heavily on the develop-
ment of a sampling and analysis system capable of identifying the
chemical species of particles collected in microgram quantities.
Techniques for size distribution analysis described in the first annual
report have been used and have proved to be adequate. The CAES optical
particle counter was used to size particles in four size ranges and has
a lower size limit of 0.4 microns. An Environment-One Condensation
Nuclei Counter (CNC) with a diffusion-denuder provided information on
particle concentration and responds to particles 0.003 microns and
larger. Precise particle counts and sizes were measured using electron
microscope pictures. Grids were placed in a Bendix Model 959 electro-
static precipitator (ESP) and particles equal to and larger than 0.05
microns were sized using optical counting methods. The CNC and the
CAES counters are essentially instantaneous point readings and are used
to establish the location of the plume and to give general particle
size data. Manual counting of the particles collected by the ESP is
the primary method of analysis for particle size data. The CAES
counter is calibrated using a generated aerosol of polystyrene latex
spheres. The Whitby 3000 was used to calibrate and establish count-
ing efficiencies for the Environment-One CNC and the Bendix ESP.
The site selected for field investigation was the area downwind
from Pittsburgh. This site was chosen because of proximity but,
even more, because it is a steel production center which would be a
strong, identifiable particle source. Further, the particles emitted
-------
330
at this source would contain a high concentration of iron and other
specific metals which would serve as chemical tracers for following
and identifying the plume from a diffuse urban source.
In the initial stages of the work the particles collected by the
Bendix ESP were used for chemical analysis. Gold coated teflon was
used as the collection surface to avoid interference from collection
surface contaminants. Nitric acid was used as the solvent of the
metals and atomic absorption spectroscopy as the analytical technique.
Numerous attempts were made to analyze the microgram quantities collected
in this way. While initial results were promising, calibration
routines indicated the technique yielded erratic data. A new procedure
has been selected after a series of experiments described in the section
of this report entitled "Chemical Analysis of Particulates."
A routine flight plan has been established to permit intercom-
parisons between flights. A regular forecasting service is provided
by the University Meteorology Department and when the selected
meteorological conditions exist, a flight is made in one of several
directions from the urban source which minimize the local interferences.
Wind speed is specified as 5 to 10 knots blowing constantly from the
same direction for a 10 to 12 hour period beginning sometime in the
morning hours. These conditions are needed to establish a uniform
plume down wind from the urban source. Tight and specific constraints
have severely restricted the number of flights which could be made.
In the field program a preliminary survey is conducted immediately
preceeding entry into the "flight plan". Passes are made upwind and
downwind of the city and using particle detection instrumentation and
-------
331
wind direction data the position of center line of the plume is
estimated. Flight paths are chosen at right angles to the plume
center line at 12 1/2 kilometer intervals to 100 kilometers from
the source center. Each path is 10 minutes in length, the center
line is crossed at approximately the 5 minute mark, and an ESP sample
is taken over that 10 minute interval. The instantaneous particle
counters show the particle concentration in the plume during the
sampling on a given flight path. As time and weather conditions
permit, this "flight plan" is repeated at other altitudes within the
surface mixing layer.
The aircraft is equipped with instrumentation to record on
magnetic tape every second of the time, the coordinates of the
location of the aircraft, the altitude, the temperature, the ground
temperature, the relative humidity, the wind speed and direction,
the readings on the four channels of the CAES particle counter and
the CNC reading. Computer programs have been written to reduce and
to present these data.
1*2 Chemical analysis of partieulate matter
Since erratic results were being obtained using the initial
chemical analysis techniques substantial efforts have been directed
toward refinement of the sampling and chemical analysis procedures
necessary to interpret the very small masses of particles obtained
during short sampling periods. This refinement is critical for
aircraft sampling at higher altitudes because of the decrease in
sample mass relative to a similar ground level sample. Further, it
is essential to establish a sampling analysis scheme which will
-------
332
provide a "blank" (a sampling surface on which no particles have
been collected) level which is as low as possible, and at the same
time provide for efficient collection of small particles (d > 0.1 torn)
P
in a form readily amenable to analysis by flameless atomic absorption
spectroscopy which provides the analytical precision required.
The initial chemical analysis system tested was a modification
of the Varian Techtron Model 63 Carbon Rod Atomizer (CRA). It con-
sisted of a small disc of type MF Millipore filter (MF) which was
inserted directly into the CRA Carbon Cup furnace. Five holes were
drilled through the bottom of the cup to provide air flow through the
MF, and the sample was collected in this unit.' Although the system
is quite efficient in its sampling ability, it was found to be much
less than satisfactory for analysis of certain metals; particularly
Fe, Zn, and Mg due to a high level of these metals as an impurity in
the filter matrix. Thus, a very high, undesirable concentration of
metals in the blank was the result. The problem is compounded by the
very sharp "flash point" of the MF when subjected to ashing in the
CRA. It was necessary to modify the procedures to meet the requirements
of the field sampling program.
The carbon cups are now available commercially in porous form.
This porous graphite appeared to be an efficient matrix for trapping
particles and was substituted for the MF system described previously.
As before, air filtration was quite efficient,, and low volume (low
mass) samples seemed adequate. However, we observed definite decreases
in filtration efficiency upon successive atomizations in the CRA and
only one determination could be allowed per cup, substantially increasing
-------
333
operating costs. It also reduced to one the number of elements which
could be determined per sample, and eliminated the possibility of
duplicate determinations on any one sample.
It became obvious that a much more desirable filtration-analysis
scheme should involve a larger filter assembly which would allow higher
volumes of air in shorter time periods to obtain larger sample masses
and to make it possible to perform multi-element analysis on single
samples. We decided to further study the MF filter because of its
efficiency for particle removal. The plan was to sample with a 47mm
MF filter, and dissolve the MF and the particles in nitric acid.
Experiments using one 47mm disc of MF in 10ml nitric acid (40%) yielded
low blanks for Mn, Cu, Co, Ni, and Cr but much higher blanks (contami-
nation) for Fe, Zn, and Mg; three metals of primary interest in the
industrial emissions from a steel manufacturing center. The high
background in the blank was contributed partly from impurities in
Reagent grade nitric acid, as well as contamination in the filter
matrix.
Preliminary tests with Nuclepore filters (NF) showed promise with
respect to filter stability in strongly acidic solutions. A 5 minute
NF soak in concentrated nitric acid showed effective removal of Fe,
Mn, Mg, Co, Cu, Cr, Ni, and Zn contaminants which are found in the
commercial NF. (Although NF contaminants are present in lower levels
than in the MF, the NF contaminants can be removed with acid treatment
prior to sampling. This is not possible with the MF.) After sampling,
previous experience suggested particles could be removed from the NF
using the nitric acid solution. Field sampling was undertaken to test
the existing system.
-------
334
Preliminary samples were taken at the Tussey Mountain fire tower,
which is a remote site free of particles from man-made sources simulating
upper level atmospheric particle concentrations. The filters used had
pore diameters of 0.05 and 0.10 microns. The conclusion from these
field experiments was that the individual samples showed poor correlation
between sample volumes and weights of metallic impurities detected
chemically. With the use of Ultrapure nitric acid (ULTREX, J. T. Baker),
significant decreases in blank levels were observed for Mg, Cu, Al,
Mn, Cr, Zn, and Fe and further sampling at the Tussey Mountain Site
was undertaken. Filter cleaning procedures have been modified (use
aqua regia as particle solute and ultrasonic cleaning of filters to
assure all particles are removed from filters) further on the basis
of field experience.
In summary, the development of this method for low-volume sampling
of particulates is in the final stage. An optimum filter medium
(Nuclepore filters) which is amenable to a necessary chemical decon-
tamination step prior to sampling has been chosen and we have found
a suitable means for processing these particulate samples into a
solution form which is readily analyzed with high sensitivity using
flameless atomic absorption spectroscopy.
1.3 The Numerical Modeling Program
The objective of this aspect of the task 2 is to develop numerical
methods which will allow the prediction of changes in particle con-
centration on a size distribution basis, as the air containing particles
-------
335
travels downstream from the particle source. A mesoscale model of
dimensions comparable to the width of a large city or travel distances
between two large cities (about 100 km) is postulated.
The configuration of the model is shown in the following figure.
The concentration distribution of particles on the grid points
at the first cross section downstream from the city is assumed to be
Gaussian and is computed from the following equation.
n(r,t) = Q (r.t)
2Tv a a u
y z
2 a
-
-------
336
where n (r,t) is the number concentration of the particles of radius
r, Q (r,t) is the total source strength for particles of radius r,
ys and z are the co-ordinates of the source and the rest of the
symbols are conventional.
The particle concentrations at the grid points are calculated
using a finite difference form of the particle diffusion equation.
8n (r,t) 8n 3n . - 32n . _
+ u. -^— = - V -r + K. + C
3t J 8xj s ** ~J 3x.2
where u^, u2 and u are the conventional three dimensional velocities
u, v and w and x , x and x are x, y and z respectively.
v is the Stokes fall velocity for particles with a Cunningham
5
correction factor and molecular "slip" factor applied as appropriate
for small particles. (See Fuchs, p27.)
"K is an atmospheric diffusivity which is calculated as a function
X
of atmospheric variables. (As in Sheih and Moroz, 1973.)
and C is a coagulation term following Friedlander (1960).
A program for this model has been written and is currently being
"debugged." Dr. Sheih is continuing to work with us on development
of this model despite his transfer to Argonne National Laboratories
because of his personal interest in the activity.
-------
337
iii Progress in Field Sampling of Agglomeration
A total of twenty field trips have been made in addition to the
three reported in the first annual report. Thirteen ground level
operations and seven aircraft flights were conducted. Of the flights,
five were made in St. Louis in connection with the RAPS program in
August 1973 and two flights were centered around the Pittsburgh urban
area in January and February of 1974.
For the most part the ground level trips were designed for
instrument check out and for gathering samples to perfect the chemical
analysis techniques. As was noted in the section on chemical analysis,
this has been a difficult and time consuming part of this work.
Aircraft sampling has been delayed by unsuitable meteorological
conditions and by the availability of the airplane. In order to
observe the behavior of particles downstream from an urban complex
it is necessary to have persistent meteorological conditions and a
minimum of interference from terrain and from particulate input from
other sources. Analysis of data obtained during the St. Louis flights
indicated that the wind was light and variable during field experiments.
The plume downwind of that urban area was not well defined. Results
from flights in the Pittsburgh area indicated that interference from
terrain and other major sources in the area resulted in distorted
interpretations. Analysis of the data did provide preliminary
information which are presented as tentative.
-------
338
Table I shows particle number and mean diameter (corrected to sea
level) obtained using the Rich 100 CNC. Particle concentrations do
decrease as one moves away from the center city and as the altitude
increases from 2600 to 6600 ft. above sea level, as expected. The
mean diameter readings are not sufficiently precise to be truly
meaningful but are presented as a matter of interest.
TABLE I
Particle Concentrations (Particles/cc) and Mean Diameters (Microns)
Downstream from St. Louis at Three Levels Calculated from Rich 100
Condensation Nuclei Counter (Flight 103, August 17, 1973). All
observations are below the top of the base layer.
Downstream Position (km) in Direction of Mean Wind
Upstream 25 50 75 100
A. Level 1500 MSL
Particle Cone.
Mean Diameter
B. Level 2600 MSL
Particle Cone.
Mean Diameter
C. Level 6600 MSL
Particle Cone.
Mean Diameter
34,600 14,000 14,600 5,900 3,900
0.008 0.0085 0.014 0.006
450 16,400 14 ,,100 6,500 5,100
0.007 0.005 0.014 0.009 0.014
340 7,100 6,800 950 2,300
0.01 0.0045 0.005 0.013 0.0075
-------
339
After looking at the data in a number of ways, it was determined
that plots of dS/d (log D), where S is particle surface area calculated
assuming spherical particles and D is particle diameter, were most
sensitive to small changes in particle number and characteristics.
In this type of presentation the area under the curve is proportional
to the surface area in a given size range and an aerosol containing
larger particles will have a smaller total particle surface area than
an aerosol containing the same mass of smaller particles. Data from
St. Louis flights 103 and 105 are presented in Figures 1 through 6.
Figures 1, 2 and 3 are from flight 103 and represent samples collected
at three altitudes. The distributions were obtained using the Bendix
electrostatic precipitator. The distributions are generally bi-modal
or tri-modal. In all three figures there is a shift in the diameter
corresponding to the peak concentration as one moves away from the
center of the city and at the same time there is a decrease in the
area under the curve. Comparing Figures 1 to 2 and 2 to 3 one notes
that as the altitude increases the distributions at various distances
from the source become more alike. These same observations hold for
Figures 3 through 6 which present a similar set of data from Flight
105. Unfortunately the Pittsburgh flight labeled 102 was made at
only one altitude. Figure 7 is the data presentation for that flight.
Again the same trends appear as in the other two data sets.
Tentatively, the following conclusions may be drawn from these
data:
1. As one moves away from the urban center, the maximum concen-
tration of particles in a given size range decreases. At the same
-------
340
time the size for which maximum concentration occurs shifts to larger
particles indicating significant agglomeration. This effect is
contrary to that which would be expected if only particle removal by
fallout is considered.
2. As one moves away from the earth's surface the particle
surface area analysis shows a shift toward uniformity. This may
suggest that as agglomeration precedes, the fall velocity of particles
becomes significant in determining the particle distribution in the
atmosphere; that is, larger agglomerated particles with higher fall
velocities are not diffusing to upper levels.
Gaussian diffusion models may yield incorrect concentrations at
both upper and lower levels if these tentative results are further
confirmed.
It was determined after the analysis of the Pittsburgh data that
the terrain and strong, outlying particle sources in the area surrounding
this urban center introduced variables which made analysis very difficult
and reduced confidence in conclusions. Recognizing that a relatively
flat area with no outlying particle sources is most desirable for field
studies we are considering other experimental sites. Currently we are
trying to obtain permission from the Canadian Government to fly in the
Hamilton, Ontario region. Hamilton has a large steel complex so all
currently developed techniques are fully applicable; it is located on
Lake Ontario and is situated so that prevailing winds from the west and
southwest carry the plume over the lake. It is within easy flying
distance and offers the same advantages, with respect to logistics,
which Pittsburgh has. Alternatives to Hamilton are Buffalo and New
York City.
-------
341
References
Fuchs, N. A., 1964; "The Mechanics of Aerosols", Pergamon Press,
N. Y., 408 pp.
Sheih, C. M. and W. J. Moroz, 1973; "A Lagrangian Puff Diffusion
Model for the Prediction of Pollutant Concentrations over Urban
Areas", Proc. 3rd Int. Clean Air Congress, Dusseldorf.
Friedlander, S. K., 1960: "Similarity Considerations for the Particle-
Size Spectrum of a Coagulating, Sedimenting Aerosol" J. of
Meteor., 479-483.
WJM
10/1/74
-------
342
o
o
T3
3
LTI O LO Q
cs m r^ 3
I I I l
< O D x
§
Q
3
oo
p
V
o
J
o
ro
O
W
•r-l
3
O
-b-
O
o
o
o
o
fsl
-------
343
s s s
g
o
o
03
a
oo
3
ro
O
01
•H
3
O
e
00
-------
344
o
o
0)
13
3
o
o
I III
o on x
O.
<~1
01
oo
•i-t
o
o
-------
345
o
o
u~l O ""I O
CNI m r- o
I I I I
T3
Q
O
O
o
c/3
Q
in
3
60
m
o
en
•H
3
O
p 5b
o
o
co
-------
346
o
o
og
CD
T3
3
o "~i o
in r--. o
I I I I
O
CJ
o
hJ
Q
CO
Q
CO
3
60
u-i
O
3
O
_J
3.
C
O
3
OC
o
o
o
o
o
o
-------
347
o
o
o
CD
•a
in o
O
O
I I I I
< on*
o
o
o
fj
o
UJ
3
DO
O
v£)
tu
M
•H
-fcr
o
c-g
-------
348
o
o
01
"O
3
n)
Q
O
O
J
O
W
Q
3
Xl
(ft
a
a
e>o
cf
CO
I
o
r
o
a 8oTp/SP
o
Csl
-------
349
IV ATMOSPHERIC REMOVAL PROCESSES FOR AIR POLLUTANTS
Part 2
TASK 3
R. L. KABEL
-------
350
IV- Atmospheric Removal Processes for Air Pollutants
Part 2
Task 3
R. L. Kabel
This first portion of the Task 3 annual report presents the
intended timetable for the anticipated five year project duration.
Brief status statements are included at this point. Extended
discussion of accomplishments follow.
1.1 Synopsis
The first year and a half were devoted to a literature review
in which potential natural processes for pollutant removal
were identified. Background levels as well as natural and man-made sources
were also included for perspective. The relevant data on rates of
removal by the various mechanisms were assembled. The few quantitative
models were scrutinized. The results of the survey are an EPA Grant
Report (Rasmussen, Taheri, and Kabel, 1974) and a much abbreviated
version of the full report which has been accepted for publication in
Water, Air and Soil Pollution. Since the lengthy report is already in
the hands of the EPA, the paper is included here as an indication of
the work in the first phase of Task 3.
The second and third years are planned for preliminary modeling.
Very few documented quantitative data are available in the literature
for natural modes of pollutant removal. Still fewer mathematical models
exist with demonstrated predictive or even correlative capability.
Work is already underway in this area as illustrated later in this report.
-------
351
Experimental work in the field or laboratory may be taken up in
the third and fourth years as appropriate. It is expected that
information available in the literature will be inadequate for the
development of reliable models. Information gaps will have to be filled
or tolerated. The Task 3 budget for experimental work will suffice
for no more than a few brief, simple laboratory investigations. Only
limited planning has occurred so far in this area. A research proposal
to seek funding for such work is in the very first draft stage.
In the fourth and fifth years refined modeling and integration
of these models into the comprehensive SRG air pollution-meteorology
model are anticipated. The only step taken toward this goal is the
decision to focus on sulfur dioxide. The bases for this decision are:
1) the importance of SC>2 as a pollutant,
2) the consequent greater extensiveness of data
and understanding available for SC>2 and
3) the fact that SC>2 exhibits more of the various removal
mechanisms to a significant extent than do most other pollutants.
1.2 Personnel
With the completion of the first phase of Task 3, the task force
has been altered somewhat corresponding to the shift in emphasis
toward quantitative modeling. The task leader is Dr. R. L. Kabel,
a chemical engineer with interests in reaction kinetics, adsorption,
transport phenomena, and mathematical modeling of naturally occurring
processes. Continuing are faculty consultants Dr. D. D. Davis, a
plant pathologist active in pollutant - vegetation interactions,
-------
352
and Dr. R. G. de Pena, a meteorologist with interests in atmospheric
chemistry and pollutant washout by rain or snow. Also continuing is
Mr. L. B. Hausheer, a chemical engineering graduate student. Leaving
the task force are Dr. F. E. Wickman, a geochemist who has returned to
his home in Sweden;Dr..M. Taheri, who has completed his sabbatical
leave from Pahlavi University in Iran; and Miss K. H. Rasmussen, who
has completed the requirements for the degree of Master of Science in
Geochemistry. Joining the team this fall is Mr. R. A. O'Dell, a
graduate of Rensselaer Polytechnic Institute in Environmental Engineering.
Mr. O'Dell is supported by an Air Pollution Traineeship through the
Center for Air Environment Studies and seeks a Master of Science degree
in Environmental Pollution Control.
1.3 Accomplishments
1.3.1. The literature survey phase phase is covered by the
following paper which will appear in Water, Air, and Soil Pollution, an
international journal of environmental pollution.
-------
353
GLOBAL EMISSIONS AND NATURAL PROCESSES
FOR REMOVAL OF GASEOUS POLLUTANTS
by
Karen H. Rasmussen
Department of Geochemistry
The Pennsylvania State University
University Park, Pennsylvania 16802
Mansoor Taheri
Department of Chemical Engineering
Pahlavi University
Shiraz, Iran
Robert L. Kabel*
Department of Chemical Engineering
The Pennsylvania State University
University Park, Pennsylvania 16802
All associated with the
Center for Air Environment Studies
The Pennsylvania State University
University Park, Pennsylvania 16802
May 13, 1974
CAES Publication No. 361-74
to whom correspondence concerning this paper should be addressed.
-------
354
ABSTRACT
This review attempts to briefly illustrate what the "state of the
art" is in the recognition of the various sources and natural sinks of
gaseous pollutants. The removal mechanisms include absorption by vege-
tation, soil, stone, and water bodies, precipitation scavenging, and
chemical reactions within the atmosphere. The nature and magnitude of
anthropogenic and natural emissions of the gases discussed (H2S, S02,
N20, NO, NC>2, NHa, CO, 03, and hydrocarbons), along with their ambient
-background concentrations and information on their major sinks identi-
fied to date, are discussed.
-------
355
INTRODUCTION
The last decade has witnessed an unprecedented interest and con-
cern in the development of mathematical models for predicting air
pollutant concentrations. The aim of such models is to define the com-
plicated relationship between air quality and emission rates. The in-
terest in air pollution modeling is based on its potential value in near-
ly all practical problems involving quantitative consideration of air
quality relative to the source location and emission rates. These in-
clude the forecasting of undesirable levels of pollution, abatement
strategies, long range air resource management programs and urban planning,
Because of energy shortages and use of lower quality fuels it is
now more urgent that we develop a much better ability to forecast the
consequences of increased pollutant emission. While considerable effort
has been devoted to characterizing emissions from anthropogenic sources
and their turbulent transport and convection, very little has been done
to determine the extent of emission from natural sources and to character-
ize the processes that clean the atmosphere. Therefore, for a more real-
istic air pollution model, it is necessary to quantify natural emissions
and removal mechanisms. The purpose of this study is to provide quan-
titative information on source and removal mechanisms so that a real-
istic air pollution model can be constructed.
Pollutants may be emitted to the atmosphere from many diffuse
natural and anthropogenic sources. The natural sources of many gases as
shown in Table I far exceed the anthropogenic sources on a global basis.
However, because such gases are usually well distributed throughout the
atmosphere their concentration, known as the background concentration,
-------
356
is extremely low. Anthropogenic sources of many pollutants are centered
near urban complexes and therefore, their local pollutant concentrations
are high and pose a major threat to the urban environment.
The removal of air contaminants from the atmosphere can take place
by various mechanisms. A review of these mechanisms and their signifi-
cance was given by Robinson and Robbins (1968) and more recently by Hidy
(1973). The important mechanisms are:
(1) precipitation scavenging in which the pollutant is removed
via two modes. The first is termed "rainout" which involves
absorption of gases in the cloud. The second is called "washout"
which involves both absorption and particle capture by falling
raindrops;
(2) chemical reactions in the atmosphere including the stratos-
phere which produce either aerosols or oxidized products such as
carbon dioxide and water vapor;
(3) dry deposition which involves absorption by aerosols and
subsequent deposition on the earth's surface; and
(4) absorption by various substances at the earth's surface in-
cluding vegetation, soil, stone, and water bodies.
This report presents an analysis of various sources and natural
removal processes which should be reflected in the results obtained
by air pollution mathematical modeling. Consideration of natural sources
and more importantly removal processes in the mathematical modeling not
only will yield more accurate results, but will provide a basis for
determining the possibilities of expanding local air pollution models
to regional or global scales. This study has considered various pollu-
-------
357
tants including sulfurous compounds, nitrogenous compounds, carbon monox-
ide, ozone, and hydrocarbons. The analysis is presented in a similar form
for each compound including data on ambient concentrations, sources, and
mechanisms of removal. An overview of this paper is provided by Table I.
The quantitative information given in this paper has, in most in-
stances, been subject to conversion of units. The conversions were made
to attain some consistency among the data and with the International Sys-
tem (SI) of Units.
-------
358
O
03
ti
X
ex.
CO
o
I
u.
o
I
CJ
I
Q
O
OS
Z
o
CO
CO
CO
UJ
u
c;
3
o
CO
u,
o
CD
J)
Major
Identified Sinks
•o o
C -H
3 4->
O OM
J-l 1-4 £
CO 4-> -^
,ii C CM
OOP.
CO O
O
ogram |
r-t
• H
^
•
C
o
1/1
tn
'e
UJ
-O
O
+J
rt
•H
t/1
UJ
.ource
t/j
0
2:
rt
3
cO
2:
o
• H
C
CJ
00
o
ex
o
•~
^
•<
Natural
o
c
o
00
o
p.
1 An thro
5
03
3
*~H
o
ex
c
o
4-> c
0 0
;ing; Chemical rea
d surface water
ion; Dry depositi
CQ C 4J
C CS P.
O r<
> -< 0
CO -H in
O O J3
cn co co
.pf
^
en
O
X
CM
c
o
•H
+J
•T3
•H
X
0
f>
o
CTl
O
PH
X
o
o
*"*
Ol
o
p-t
x
tn co
Volcanoe
Biologic
decay
i
ca
.. 0)
1/1 ^
p- 4 O *-*
co tn
Chemic
proces
Sewaae
to
CN
X
1
0
o! -a
ssociation in str
Surface water an
sorption
•3 o a
0 P<
*-> CD p^
O ^ -H
j= a, o
ex in t/i
o
CJ!
t
0
i£
O
p-4
X
o
O)
m
0
c
0
rt
o
GO *
O 0
H CD
CQ -U
C
o
z
0
CN
z
OJ
o
o
4->
e
o
• H
4-»
•3
X
O
u")
CN
O
emical reactions;
on to nitrate;
ing
JS .H CX
cj +-> C
O CO O
+-> -a >
O -H CO
-C X CJ
a. o to
CN
CN
O
X
00
*o
r~
CTl T3
O 4)
—l C pC
X J3 .H O
S 3 Z
to 0
m o
O 1 **H
•rj 0 0
CO 2 C CN
CX -H O
— < *-> Z
rt .- co
•H p-4 -H T3
r< -H o e
o o o o
CJ in O
rt c -p< CN
a TH -a z
e
0
•H
tn
3
O
CJ
c
5 i
•H CO
O .M
CO X
0 0
^ z
Bacteria
in soil;
tion of
c:
0
•H
Comb us
(SI
o
•z.
c
o
•H
n with SO • Oxidal
ate; Scavenging
0 ^
•H +-»
O C
CO
o o
oi *->
*
0>
0
,_^
X
o
1— 1
CTl
O
i— 1
X
CO
Biologic
decay
c
CD
BO g
c -.y
•H M CO
C CU CD
i— ( 4J 4-)
cO ^ tn
O (U co
cj 1^ a
-r;
sorption; Chemica:
on
cs v
O
r-« T3
•H -H
O X
C/l O
o
o
CTl
O
P_4
x ;^_
0
o
o
'
CTt
O
pH
X
o
i CM
0 0
*-• in
1-1 0 C c
o j= o a
CX 'p4 4-* O
C +-> in cj
O •* co o o
•p4 CU -H FH
4-> C CJ O ••>
co co o u, in
^3 -C 10 ,ft CD
X O -H O -H
O S "3 CJ m in
O J o
o _a cj
4-" -3 E O
3 C o -<
<; co o cx
o
tn
cu
ti
emical reactions;
ion by land surfai
nd vegetation) ;
water
_C »-> CO O
U CX CJ
O P4 -1 «
4J O -H t+-t
o m o s-i
£1 < v_ C
•H O
U L4
CO CO
CD O
a: o
c -a
0 X
Z JS
!
o
•H
4-1
-J
X
o
f— (
CJ
o
o
o
HZ
V
CTl
O
X
LA
r^_
t-«
CTl
O
r-f
^
CN
c:
• H
r— <
CO 1O
Biologic
procc.sse:
forests
.,
to
ci o
rC -H
X •*-*
si'3
3 o Uj
< -J o
tn
c
o
O J-t
> rt
w o
U V-4
-------
359
SULFUR CONTAINING GASES
The two primary sulfur containing gases present in the atmosphere
are hydrogen sulfide (HaS) and sulfur dioxide (SOa). Hydrogen sulfide,
the most reduced form of sulfur, is not considered to be an air pollu-
tant per se, for its primary modes of origin are natural processes. Its
importance arises from the nature of the chemical reaction it is subject
to once it has been released to the atmosphere. That reaction is its
rapid oxidation to sulfur dioxide. As such, H2S has oi'ten been thought
of as a "natural" source of S02.
Accurate measurements of the background concentration of hydrogen
sulfide in the atmosphere are not as yet available. Measurements over
Bedford, Massachusetts, and New York City performed by Junge (1963] found
values ranging from 2-20 yg/m3 (1.4 - 14 ppb). Robinson and Robbins
(1968) estimate HaS concentrations in clean air to average 0.3 yg/m3
(0.2 ppb). The National Center for Atmospheric Research (NCAR) (as cited
in Kellogg et_ al_., 1972) has shown these measurements to be unreliable
because they were made using liquid scrubbers. These scrubbers are faulty
in that they allow both the oxidation and loss of significant quantities
of H2S.
Because of early recognition of sulfur dioxide as a primary pollu-
tant capable of inflicting severe illness or even death on humans, exten-
sive research has increased our knowledge of the sources and sinks of
this gas far more than any other pollutant. Background concentrations of
sulfur dioxide seem to range between 1 and 4 yg/m3 (.4 - 1.5 ppb). Georgii
(1970) found concentrations over the Atlantic Ocean ranging from 1-4 yg/m ,
and over Colorado from 0.5-2.0 yg/m3 (.2-. 8 ppb). Cadle et_ &!_. (1968) found
values over Antarctica ranging from <1.0 to 3.2yg/m3(<.4-1.2 ppb).
-------
360
HYDROGEN SULFIDE
Sources
The primary source of H2S is decaying vegetation in swamps, bogs,
and other land areas. Very little is known about annual rates of H2S
from these regions though, and up to this time estimates that have been
made are only the result of balancing suggested sulfur budgets. Esti-
mates of this H2S source strength range from 58 x 109 kg/yr (Friend, 1973)
to 112 x 109 kg/yr (Eriksson, 1960).
The oceans have been suggested as an additional source of sulfides
to the atmosphere (Eriksson, 1960). Measurements though have not been
conclusive and so estimates on the magnitude of this flux [see Table IV]
have been made by determining the value needed to balance a particular
portion of the sulfur cycle and equating that value with the flux of S~
from the oceans to the atmosphere. H2S is also released by volcanoes
but the quantity is far less than the amount of SQ2 released. Only rela-
tively minor amounts of H2S are released from anthropogenic sources.
Removal Mechanisms
Hydrogen sulfide is relatively insoluble in water; at 20°C and 1
atmosphere, the solubility is only 0.385g/100g H20. It therefore will
not be readily absorbed by vegetation or bodies of water, nor will it be
involved in liquid state reactions in the atmosphere. In fact, the only
real mode of "removal" is the oxidation reactions it so readily becomes
involved in.
H2S can be oxidized by ozone (Os), molecular oxygen (02) or atomic
oxygen (0). Cadle and Ledford (1966) have shown that although the
oxidation of H2S by ozone proceeds quite slowly in a gaseous atmosphere,
the reaction is catalyzed by the presence of aerosols. Hales et al.
-------
361
(1969) have given a rate equation for the change in S02 concentration
with time as a function of the concentration of both H2S and ozone.
Oxidation of H2S by atomic oxygen will probably be significant only
in photochemical smog and the stratosphere; the reason being that only
in these environments are significant quantities of atomic oxygen avail-
able due to the photolysis of ozone. The reaction to proceed first
would be:
H2S + 0 -> OH + HS
This is then followed by a reaction chain producing S02, SO 3, and sulfuric
acid (Liuti et_ a.\_., 1966). As a result of its rapid oxidation, H2S has
a very short residence time in the atmosphere, probably about 2 days
(Hidy, 1973).
SULFUR DIOXIDE
Sources
Industrial growth has caused a significant increase in the production
and ultimate release of sulfur dioxide to the atmosphere. Robinson and
Robbins (1968) estimated anthropogenic activity as the source of 146 x
109 kg S02 each year. A study on anthropogenic S02 production by the
Study of Critical Environmental Problems (SCEP) (M.I.T., 1970) concluded
that globally 93 x io9 kg S02 were produced in the year 1967-1968. Kel-
logg et_ al. (1972) point out that this estimate may be low because the
"emission factor" used for this global estimate is probably applicable
only in the United States and will be higher in other nations which rely
more heavily on fossil fuels with high sulfur contents such as coal.
Kellogg et_ al. believe an estimate of about 100 x io9 kg S02 per year
would be much more reasonable; of this, almost 94% is emitted in the
Northern Hemisphere alone. Friend (1973) has estimated anthropogenic
-------
362
emissions of S02 at 130 x 109 kg per year.
There are, of course, natural sources of sulfur dioxide as well but
the total amounts derived from these sources are extremely difficult to
quantify. It is believed that most natural S02 is released by volcanoes.
Kellogg et_ al. estimate that the quantity released by volcanoes is about
two orders of magnitude less than the amount they estimated to be a result
of man's activities (1.5 x 109 kg/yr vs. 1.0 x 1011 kg/yr). There is,
as the authors point out, a good deal of uncertainty in their estimate.
Stoiber and Jepsen (1973) estimated annual volcanic emissions of S02 to
be 15 x 109 kg, an order of magnitude greater than the estimate of Kel-
logg et_ al.
There are no other widely accepted natural S02 sources. Kellogg
et_ al. have pointed out that despite the fact that S02 is so very soluble
in water, sea water might be a source rather than a sink if the right
physicochemical conditions prevail. Without further convincing evidence
on this subject, one should probably contend that sea water would,
in toto, provide only relative minor amounts of S02 to the atmosphere,
if any at all.
Removal Mechanisms
Sulfur dioxide is very soluble in water; at 20°C and 1 atmosphere
the solubility is 10.8 g/100 g H20. It is also very chemically reactive
and either oxidizes to sulfate or photochemically reacts with other at-
mospheric contaminants. Therefore, sulfur dioxide is removed from the
atmosphere by various mechanisms involving water or other compounds. The
major identified sinks for this gas are: precipitation scavenging, chem-
ical conversion, and absorption by soil, water, stone, and plants. The
lifetime of sulfur dioxide in the atmosphere is estimated to range between
-------
363
20 minutes and 7 days (Nordo, 1973). Following is a discussion of the
various mechanisms mentioned.
Vegetation: A portion of the much needed sulfur used by plants in
metabolic processes has been shown by Fried (1948) to be attributed to
the direct absorption of S02 from the atmosphere, especially in areas
where the soil is sulfur deficient. The ability of the plant to utilize
this sulfur effectively without damage is dependent upon the rate of
absorption of 862 and the rate of production of sulfites.
Studies by de Cormis (1969) suggested that the extent of S02 absorp-
tion is directly proportional to the atmospheric S02 concentration and
is not influenced by the amount of sunlight. Hill (1971) investigated the
uptake rates of several gases by an alfalfa canopy. His results [see
Figure 1] confirmed those of de Cormis. Hill found that S02 was absorbed
with a deposition velocity of 2.8 cm/sec, given a wind velocity of 1.8-2.2
m/sec as well as a number of other fixed variables. He did note that, in
general, those gases readily absorbed by the alfalfa were those with the
greatest solubility in water [see Table II].
Table II. SOLUBILITY IN WATER AND UPTAKE RATE OF POLLUTANTS
Pollutant
CO
NO
03
NO 2
SO 2
Uptake Rate
in Alfalfa*
(mol/m2 sec) x 109
0
2.1
34.7
39.6
59.0
Solubility
at 20° C
g/100 g
0.00234
0.00625
0.052
decomposes
10.8
Concentration of the gas in the chamber was 2x10 mol/m .
-------
364
0
I 2 3
Pollutant Concentration
(mol/m3)Xl06
Figure 1, Uptake rates of different pollutants by an alfalfa canopy.
-------
365
Factors which influence pollutant uptake by plant canopies have
been discussed by Bennett and Hill (1973). In a more recent communication
Bennett et_al. (1973) present a model simulating pollutant transfer
between leaves and the free air surrounding it. This model is based on
the rate of exchange via a series of external and internal leaf mass trans-
fer resistances. The model indicates the importance of gas solubility
within the leaf.
Estimates of the amount of S02 removed each year by vegetal absorp-
tion vary greatly. Eriksson's (1963) cycle estimates 75 x 109 kg S02-S
are removed in this manner. Junge (1963) estimates 70 x 109 kg S02-S,
Robinson and Robbins (1968) estimate 26 x 109 kg S02-S, Kellogg et al.
(1972) estimate 15 x 109 kg S02-S, and Friend (1973) also estimates that
15 x 109 kg S02-S are absorbed by vegetation each year. The designation
"S02-S" expresses the mass of sulfur existing in the S02 form.
Soil: Various studies have shown that soils are capable of absorb-
ing significant amountsof sulfur dioxide (Vandecaveye, 1936; Bonn, 1972).
Terraglio and Manganelli (1966), in studies of two soil types, found not
only that SOa was more readily absorbed by soil with a higher moisture
content, but that the reaction also appeared to be dependent upon the pH
of the soil, more S02 being absorbed in the soil where the pH was greater.
The degree of absorption is also dependent upon such factors as the min-
eral and organic content of the soil, soil structure, ion-exchange capa-
city and porosity (Faller, 1968; Seim, 1970; and Smith et_ al_., 1973).
Both Seim and Smith et_ al. suggest that the SO? absorbed is oxidized to
sulfate which may then be subject to leaching and/or plant uptake.
Deposition velocities have often been used to determine the removal
-------
366
of S02from the air above soils and vegetation. From the data available
in the literature deposition velocities for soils are in the range of
0.2 - 0.7 cm/sec, which seem to be less than those for vegetation (Cham-
berlain, 1960; Spedding, 1969a; and Owers and Powell, 1974).
Estimates on the amount of S02 that is absorbed by soils are lacking
and, for the most part, missing from most sulfur cycles that have been
compiled. Unless this process has been taken into account in estimating
the total sulfur deposited by dry deposition on the land surface then one
must conclude that there is an obvious omission in the cycles. Eriksson
(1963) estimated that 25 x 109 kg S02-S per year are directly absorbed
by the soil. Abeles _et_ al_. (1971), based on experiments they themselves
ran, concluded that soils of the United States are capable of removing 4 x
109 kg of S02 per year (2 x 109 kg S02-S).
Stone: Sulfur dioxide in the atmospheric environment has caused in-
estimable damage to frescoes, monuments and other edifices throughout the
world. The damage is a result of enhanced weathering rates caused by the
attack of sulfuric acid (S02 + 1/2 02 + H20 -> H2SOit) on the carbonate ma-
trix of limestone and sandstone. Spedding (1969b) showed that the S02 up-
take rate is dependent upon the moisture level in the atmosphere. The
H2SOi+ reacts with the carbonate matrix to form gypsum as follows:
CaC03 + H2S04 + H20 -> CaS(V2H20 + C02
(Luckat, 1973). Because the resulting salt is more soluble in water than
the carbonate, the gypsum would be more readily leached out from the stone.
The stone would also be subject to physical disintegration because of the
volume expansion that accompanies the mineral change (Luckat, 1973) .
Luckat also points out that the extent of weathering varies with the
porosity of the affected rocks as well; a rough, porous, lime-cemented
-------
367
sandstone would weather faster than a smooth and dense limestone.
Luckat (1973) and Spedding (1969b)provide values for S02 removal by
stone of 6 - 200 and 50 - 200 mg/m2'd, respectively. Luckat's data were
obtained in highly industrial sections of Germany and Spedding had a con-
centration of 360 yg S02/m3 (100 times the world-wide background level)
in his experiments. Taking 5 mg/m2-d as the lower limit of these data,
the total earth's surface of 5 x lO14 m2, and an estimate that one percent
of the earth's surface is stone capable of removing S02, the annual remov-
al rate is calculated to be 4.5 x 109 kg S/yr. By comparison to Table IV
this rate is considerably smaller than any of the estimated rates for the
other natural S02 sinks.
Water Bodies: Theoretical discussions in support of the contention
that sea water is capable of absorbing significant quantities of sulfur
dioxide from the atmosphere first appeared in a paper by Liss (1971). He
showed that the exchange of S02 across an air-liquid boundary is control-
led by the resistance of the gas-phase and is a function of the pH of the
aqueous solution.
Liss and Slater (1974) elucidated and modified the theory suggested
by Liss (1971). Liss and Slater used the mass transfer coefficient for
water vapor to calculate the overall mass transfer coefficients for a
number of gases crossing the air-sea interface. The results are given in
in Table III. To calculate the SOa flux across the air-water interface,
one must know the S02 solubility. An equation to predict this parameter
at low S02 concentrations is now available (Hales and Sutter, 1973).
Estimates of the amount of S02 absorbed annually by the oceans indi-
cate the importance of this sink. Liss and Slater (1974) estimate this
-------
368
Table III. MASS TRANSFER COEFFICIENT FOR A NUMBER OF GASES
CROSSING THE AIR-SEA INTERFACE
k\f
f\
Gas ^
cm/ sec cm/ sec H
S02 0.45 9.6 3.8 x 10~2
N20 0.53 0.0055 1.6
CO 0.67 0.0055 50
CHu 0.885 0.0055 42
H20 0.833 °°
r /r^ K*
cm/ sec
573 0.45 (g)
6.6 x 10-3 0.0055 (£)
1.7 x 10-" 0.0055 (£)
1.5 x 10"1* 0.0055 (£)
0.83 (g)
*The overall exchange constant, K, is expressed on either a gas (g) or
liquid (£) phase basis.
S02 flux at 1.5 x 1011 kg/yr based upon their own calculations. Their
estimate is in good agreement with those of Eriksson (1963) (2 x 1011 kg/
yr) and Robinson and Robbins (1968) (0.5 x 1011 kg/yr), but is lower than
that determined by Spedding (1972) (9.6 x 1011 kg/yr). Liss and Slater
explain that this discrepancy is due to a 3 yg/nT' difference in the mean
atmospheric S02 concentration used by each and because Spedding's value
for the total resistance of the gas phase (1/K ) was much lower. As noted
O
earlier, Kellogg e^ al^. (1972) consider the net flux of S02 from air to
sea to be negligible, based on observations made by Pate et al. (personal
communication to Kellogg et_al_.) that in some areas, where the equilibrium
vapor pressure of S02 in surface waters exceeds the partial pressure of
S02 in the air above it, the ocean might actually be a source of S02.
Washout and Raimout of S02: The major portion of S02 present in
the atmosphere is probably removed by the processes known as rainout and
washout. Rainout involves the scavenging of S02 and sulfate particles
within the clouds while washout is the removal of these sulfur compounds
-------
369
below cloud level via precipitation. The S02 scavenged will undergo a
series of reactions,some catalytic, and ultimately form H2S04 drops or a
sulfate salt. From the time S02 is absorbed by cloud droplets it is both
ionized and oxidized by the reaction sequence suggested by Scott and
Hobbs (1967).
Because the oxidation of S02 in the liquid phase does not occur at
a rate fast enough to account for the sulfate content found in rain, in-
vestigations were undertaken to find an effective catalyzing agent. Ex-
periments have shown that of all the metals found in the atmosphere, Mn
salts were the most effective in promoting S02 oxidation (Junge and Ryan,
1958; Johnstone and Coughanowr, 1958; Matteson et al., 1969). Although
Mn salts are the best known catalyst for S02 oxidation, the concentration
of these salts in the atmosphere is still not great enough to account for
the sulfate content in rain. Recent investigations have shown that
when ammonia is present the rate of sulfate production in solution is
greatly enhanced (van den Heuval and Mason, 1963; Scott and Hobbs, 1967;
Miller and de Pena, 1972)
Field investigations by Beilke and Georgil (1968) indicated that the
absorption of gaseous SOa by rainout and washout accounted for 75% of the
sulfate content in rain water and that scavenging of sulfate particles
contributed only 25%. The model formulated by Miller and de Pena contra-
dicts those measurements of Beilke and Georgii. Miller and de Pena show
that the sulfate content of rainwater is much more dependent on the sca-
venging of particles rather than S02. In their model, the sulfate content
of rain water near a highly concentrated S02 plume of only moderate par-
ticle concentration showed that the contribution of S02 to the total sul-
fate concentration was 4 times less than that of sulfate particles.
Appreciable effort has been devoted to the analysis of S02 scavenging
-------
370
by rain (Engelmann, 1968; and Fuquay, 1970). Field measurements of S02
washout (Hales e_t_ aJL , 1971) have demonstrated that there is a signi-
ficant accumulation of S02 in the water drops.
A comprehensive analysis of reversible washout based on the inter-
action of raindrops with atmospheric contaminants has been presented by
Hales (1972). This analysis indicates the use of overall mass transfer
coefficients for determining the washout. From this analysis, it is ap-
parent that the degree of success in determining washout rates depends on
estimating mass transfer coefficients and solubility data. Further study
(Hales et_al_., 1973a and Hales et_ al_., 1973b) has led to the development of
a mathematical model for predicting ground level concentrations in the rain
as a function of location beneath a plume under stable meteorological
conditions.
Atmospheric Reactions Involving S02: Reactions involving S02 in the
dry state, not unlike those discussed above for S02 in the wet state, are
very complex. The most important reaction involved here is the photochem-
ical oxidation of S02 which takes place in polluted atmospheres.
Early measurements of the rate of photo-oxidation of S02 made by
Gerhard and Johnstone (1955) seem to be the most widely quoted. They
found the rate of S02 oxidation to proceed from 0.1-0.2%/hour. Renzetti
and Doyle (1960) and Cox and Penkett (1970) have suggested that the rate
of photochemical aerosol formation (the end result of the photo-oxidation
of S02) is greatly accelerated in the presence of olefinic hydrocarbons
and nitric oxide. Endow et_ al_-> (1963) and Harkins and Nicksic (1965)
have shown that the resulting aerosols consist almost entirely of sulfuric
acid droplets when the relative humidity is greater than or equal to 50%.
Cox and Penkett (1971a) have given experimental evidence to support
the hypothesis that low concentration olefinic hydrocarbons and nitric
-------
371
oxide can greatly affect the rate of S02 photo-oxidation in air. Results
of their experiments can be easily observed from Figure 2.
Although the rate of S02 oxidation by ozone alone is quite slow, Cox
and Penkett (1971b) found that when S02 was injected into a chamber con-
taining ozone and olefins the oxidation rate was greatly enhanced. They
also found that the oxidation rate, or aerosol formation, was dependent
upon the nature of the olefin.
As little as is known about the oxidation of S02 in the troposphere,
still less is known about its oxidation in the stratosphere. Kellogg et
al. (1972) have suggested a possible 3-body reaction with atomic oxygen
for removal within the stratosphere:
S02 + 0 + M -> S03 + M
where M is a molecule of 02 or N2, which acts to carry off the excess
energy, thereby preventing prompt reversal of this reaction. The 863
formed reacts almost immediately with H20 vapor to form H2SOi+ which then
combines with more water to form droplets of H2SOi, solution which are then
removed by precipitation. This reaction is thought, by the authors, to
be responsible for the layer of H2SOit or sulfate particles found at an
altitude of approximately 18 km.
Perhaps the best way to summarize the possible reactions involving
S02 in the atmosphere would be by repeating the summary made by Robinson
and Robbins (1968). "It seems that in the daytime and at low humidity,
photochemical reaction systems involving S02, N02 and hydrocarbons are
of primary importance in the transformation of S02 into essentially an
H2SOit aerosol. At night and under high humidity or fog conditions, or
during actual rain, it seems that a process involving the absorption of
SOi; by alkaline water droplets and a reaction to form SOJ within the
-------
372
1000.
fO
E
X.
CP
3.
en
100.
I
c
O
o
o01
O
O)
O
^J-
I
10
o S02 concentration
Aerosol concentration
Inject
NO(.3xlO"4mol/m3)
2Pentene (.4I6XlO'4mol/m3)
t I
100 200
Time(min.)
300
Figure 2, Aerosol formation and SCL decay during the photooxidation of SO ,
-------
373
drop... can occur at an appreciable rate to remove SOa from the atmosphere."
Environmental Sulfur Cycle
Table IV summarizes the estimates made by Eriksson (1960), Junge
(1963), Robinson and Robbins (1968), Kellogg et_ al_. (1972) and Friend
(1973) in compiling their respective sulfur cycles. It should be kept in
mind that while all the values given are only estimates, the degree of
uncertainty in some is greater than that in others. For instance, there
are no measurements upon which estimates of the quantity of H£S or S~
emitted by decaying land and sea biota can be based. Also, there are no
specifications of the form of the sulfides (i.e. H2S, HS~, or S=). These
estimates have therefore been arrived at by the authors' balancing of
particular portions of their cycles; the difference needed to balance each
section has then been set equal to the flux of HaS or S~ from the land and
sea to the atmosphere, respectively.
-------
374
/_4
cd
O
X
fa
0>
£L«
to
60
r»
O
rH
rj[
•r-l
> — '
CO
W
u
u
oi
U.
~- i
to
CO
o
rH
f*S
<
•z
1— 1
a
>
o
rH
CO
>2
»— )
^"j
JL,
u
1— (
ATMOSPHER
^
I-H
a>
Ctf
•a ,--.
c *o
CD f-.
•rH Oi
f-l rH
C*U **~s
bO • ^-N
WJ r-ta CN
O cd| i*^
i-H O^
r-4 -4-*! rH
(U QM V— /
i^
(/)
C
C -H
O ,O ^™N
in ,0 oo
C O vO
•rH O£ CTl
J3 i-H
O *O *-— '
02 §
r~*
60 vO
§s
C '-x
0 0
in o»
•H N— '
t|
tu
in vo
\O in'd-TtrH + rHfMOOfMt->i-l (N'S-OOIO
CM tS rH
in in
i g * •
Oi-to*OTt mrj- inivootMto iiii
in OTI-OO -f rH i oo i— t t^ eO 1111
^ y "^ rH rH
O lOOO'fCS \OTJ- vOinoOrHfM i—trfoOlO
r**- i \o to Tj" rH o*j CM CM r^ CM r** I-H rH »-H TT f^
(M + CM
J 1 1 1 -
o i o o i o 01 oovomorH mom
^f i P** \o i ^^ tO i t^- r^* in *-H \o f^- CM P^ cTi
rH CM 1 • CM » -v- '
x * \
o 10000 om m o m o o oinmo
rf IrHr^^tVO r- 1 t-~O^OO*tf' 1-HrHinOO
rH rH tO I I-l* ,. 'i-H tO
/— V
in /— »
TJ fl) II ^ S
§o o /— \ «
o , . to -o o
rH V- ' UJ X C O^
II +-> rH «Mil-« M
to to aJ O t " •* J*-1
CM OJ C CO n* O *H
-fj OfnO CMCMtO O
e a> •> m oo cc
«« rt+J4-»^-> COCO'—N- O3
XX rHfirJ /-^"O- -iHr*
Ojrt Ctf.HO4-> "-T3CPH •!-»
CM CvIO Ull'* X) ft,^ CJCCrtOJ cd rO
•P 0) cd in P+J^-^X rH M. H c
. ,^H rH« Xif-lG P inin-H-PT3 3J H
a> cGObop, nx:«aci)
bo cdoom a>4->r«x cdcdcdincd in a> +•> f-i >
QOrHrH CtdOJCd 4->O 3MOJO.H
P,rH r-l O O Cd » ' XIrH rHO-iHft- O -H 4) XI M
OtdO'H-Htt) P-lftl Cd-HPiOP. CU rH^Pi
Jnf-i>xixiin +-> win +JC-H-O-H C -H inr-j
j- 3 M O cDrtO o cd-u^ocd
<>»P OE«J MOCOXO) rHfnOT3-l-»
0) C rt • • • • P.PO Cl)OfHr H H cdxi to tdxiU'oof-" S rtxiU'Ta
• * * *
HH t-H rH >
rH rH rH
rH
v
a>
TJ
3
O
c
•H
j n
q
(fl-
ed
o
rH
O
x
0
0
^_)
c
o
•M
rH
cd
in
cd
in
iw
o
4J
O
CD
MH
4^
CD
CD
(4
O
«w
CD
f.
*k
X
^H
c
0
r4
rH
3
in
in
tn
o
o
ncerned ex
0
o
rH
CD
1
-W
60
-------
375
CARBON CONTAINING GASES
CARBON MONOXIDE
Each year more carbon monoxide is released into the atmosphere than
any other pollutant (excluding carbon dioxide), and, each year the quantity
released increases. One would therfore expect a gradual increase in ambi-
ent CO levels, yet one finds that the background concentration of this gas
in the atmosphere has not fluctuated the last few decades. There must then
be one or several major active sinks for CO within the troposphere. Until
just a few years ago though, investigations on possible sinks had only
turned up additional sources of CO. This dilemma, as a result, came to
be known as the "CO sink anomaly".
Background concentrations of CO range from 50-200 yg/m3 (0.04-0.20
ppm) (Jaffe, 1973). Robinson and Robbins (1968)indicate that a mean con-
centration of 100-yg/m3 (0.1 ppm) is found in the northern hemisphere,
while concentrations less than 60 yg/m3 (0.05 ppm) would probably be more
common in the southern hemisphere.
Sources
Carbon monoxide is the product of incomplete combustion of fossil
fuels containing carbon. With the advent of large scale industrialization
and the tremendous increase in the use of the automobile, great quantities
of CO have been emitted into the atmosphere. Recent investigations for
CO sinks to explain why the ambient CO concentration has not been increa-
sing have resulted in the discovery of new natural sources of CO whose to-
tal quantity far exceeds the total mass of CO produced as a result of man's
technology (Stevens et_ al_., 1972).
By far the greatest single anthropogenic source of CO is motor
-------
376
vehicle exhaust. Jaffe (1973) estimated a total anthropogenic CO emis-
sion source in the United States in 1970 of 132.6 x 109 kg and 359 x 109
kg on a global scale. He notes that whereas the level of CO produced
by man in the United States appear to be leveling off, globally it is on
an increase. Underdeveloped nations, which are undergoing increased tech-
nological development, are not as yet concerned with the resulting pollu-
tion as much as the economic gains and so their emission levels are on
the rise.
The most widely recognized natural source of CO is forest fires
n
which have been estimated as releasing 11 x 10 kg CO into the atmos-
phere each year (Robinson and Robbins, 1968). This is, by no means, the
only major natural source of CO. Minor amounts of CO have been found to
be released from volcanoes and marshes (F]ury and Zernik, 1931). CO can
also be formed during electrical storms (White, 1932) and by the photodis-
sociation of C02 in the upper atmosphere (Bates and Witherspoon, 1952). Cal-
vert et al. (1972) has suggested the photodissociation of formaldehyde as
a possible source of CO and recently, Swinnerton et_ al. (1971) have found
CO to be present in rain water in rather high concentrations. Galbally
(1972) has offered a hypothesis wherein the CO in rain is a product of
the photodecomposition of aldehydes in the rain water by sunlight.
The ocean was first suggested as a major source of CO by Swinnerton
et al., (1970). Linnenbom et_ al_., (1973) have estimated the oceans can
produce up to 220 x 109 kg each year } whereas Liss and Slater (1974)
have estimated this flux at 43 x 109 kg per year. Robinson and Moser
(1971) have suggested that plants could indirectly be the source of about
54 x 109 kg CO by the oxidation of released terpenes. Finally, McConnell
et al., (1971) suggested that approximately 900 x 109 kg CO are produced
-------
377
each year by the oxidation of methane.
In light of this new source information, Stevens et_ al. (1972) be-
lieve that natural sources of carbon monoxide could yield about 10 times
more CO than all anthropogenic sources in the northern hemisphere. Up to
this time it has been assumed that anthropogenic activity released far
more carbon monoxide than nature. It will be interesting to follow the
outcome of this contradiction over the next few years.
Removal Mechanisms
Carbon monoxide can be regarded, for all intents and purposes, as
being insoluble in water; its actual solubility being only 0.00234g
CO/lOOg H20 at 20°C, Therefore, wet processes such as washout and rain-
out can be regarded as playing an insignificant part in the removal of CO
from the atmosphere. Experiments on the absorption rate of CO by an al-
falfa canopy (Hill, 1971) showed that, virtually no CO was absorbed and
therefore, vegetation can be disregarded as a sink. Absorption of CO by
the oceans can now be disregarded as well because it has recently been
shown (Swinnerton et^ al., 1970) that the oceans actually constitute a sig-
nificant natural source of carbon monoxide. It seems then that the major
sinks for CO are gas-phase reactions in the troposphere and stratosphere
and soil fungi (Inman et_ a_l_. , 1971; and Inman and Ingersoll, 1971). Esti-
mates of the residence time of CO in the troposphere range from about 0.1
year (Weinstock, 1969) to about 2.7 years (Robinson and Robbins, 1968).
Soil: Experiments by Inman and Ingersoll (1971) showed that both
potting soils and natural soils absorbed from 2-20 mg C0/m2-hr. They ob-
served that, in general, soils with the highest uptake activity were those
with higher organic content and lower pH. Inman e£ al. (1971) also noted
that if a soil was autoclaved (sterilized) removal of CO by the soil was
-------
378
inhibited. This suggested that the removal was due to biological activ-
ity in the soil.
In late 1972 Ingersoll published the results of a more extensive
study on the uptake of CO by soils. Here he measured the in situ uptake
at various locations throughout North America. He found that:
1) The total amount of CO destroyed by various soils ranged from
7.5 to 109.0 mg CO/hr-m2, the spectrum ranging from tropical soils which
were the most active down to desert soils which were the least active.
Although there were many exceptions, more CO tended to be destroyed by
soils with low pH and moderate moisture content O20%) than others.
2) The rate of CO uptake decreased as the concentration of CO de-
creased in the air, with maximum removal with ambient concentrations of
100,000 ug/m3 (100 ppm)•
3) Given the same soil, CO uptake was far greater when vegetation
was growing than when the soil was under cultivation. Ingersoll suggests
this is because the amount of organic matter present in soils being cul-
tivated is substantially lower than that present in soils actively growing
crops.
4) Soils that were removed from their site of origin and tested in
the laboratory showed greatly reduced uptake ability. The magnitude of
decrease was not uniform from one soil sample to the next.
Based upon data he had collected which he corrected for temperature
and uptake variations, Ingersoll (1972) estimated the CO uptake potential
of the conterminous United States and the world. His estimates of 505 x
109 kg and 14.3 x 1012 kg CO per year for each, respectively, are based
on ambient CO levels of 100,000 ug/m3 (100 ppm), three orders of magnitude
-------
379
greater than average ambient CO levels. Ingersoll noted that
Seller (1972) had found soil CO uptake rates to be one-tenth of those
Ingersoll had measured when these soils were exposed to ambient CO
levels (200-1000 ug/m3) rather than concentrations of 100,000 yg/m3.
On the basis of this information, Ingersoll reduced his estimates of the
total capacity of soils to consume CO in the United States and the world
to around 50 x 109 kg and 1.4 x 1012 kg per year, respectively.
Earlier, Inman and Ingersoll (1971) had estimated that soils of
the continental United States were capable of removing over 500 x 109 kg
CO per year.
Results of recent experiments by Smith et_ al. (1973) support earlier
findings that soils are capable of effectively removing CO from the atmos-
phere. They also found though that when moist soils were placed in the
chamber with air containing 100,000 yg CO/m3 (100 ppm), the concentration
of CO in the chamber rose, in one case tripled, before it was reduced to
zero. This effect was found to be more pronounced in sterilized soils
than unsterilized soils. They surmise that the evolution of CO from the
soils is a nonbiological process, but made no attempts to identify the
processes responsible.
Atmospheric Reactions Involving CO: Recently it has become appar-
ent that the stratosphere constitutes a sink for carbon monoxide. The
significant reaction seems to be the reaction of CO with the hydroxyl
radical (Weinstock, 1969; Pressman and Warneck, 1970; and Pressman et al.,
1970) as follows:
OH + CO + C02 + H
A rate constant for this reaction is available (Schofield, 1967). The
series of reactions which follow not only provide for the regeneration
-------
380
of the OH radical needed but possibly for the reaction of CO with the
hydroperoxyl radical as well (Westenberg and de Haas, 1972; and Davis
et_al. , 1973).
Vertical CO profiles of the atmosphere have recently been carried
out by Seiler and Junge (1969), and Seiler and Warneck (1972). These re-
ports both found a sharp decrease in the CO mixing ratio when crossing
the tropopause into the stratosphere. The mixing ratio is defined as the
mass of gas per unit mass of dry air. It seems obvious from vertical pro-
files such as these that there is a significant decrease in the CO concen-
tration above the tropopause, thus rendering valid the conclusion that
the stratosphere is a sink for carbon monoxide.
Quantitative estimates of the amount of CO destroyed in the stratos-
phere by this reaction mechanism have not been made. Pressman and Warneck
(1970) believe that virtually all CO entering the stratosphere is des-
troyed in that manner. Therefore, the size of the stratospheric sink is
dependent upon the transport rate of CO rich air through the tropopause into
the stratosphere. They have estimated this flux at 1.3 x 10~3 mol/m2*sec
but admit the degree of uncertainty in this estimate is very high due
to insufficient data. Based on this flux and recent estimates of the
total CO reservoir in the troposphere, they estimated that about 11-15%
of the total CO inventory in the troposphere is destroyed in the stratos-
phere.
Although the reaction sequence mentioned above has been recognized
as a major sink in the stratosphere, only recently has it been suggested
to be a significant destructive reaction in the troposphere (Weinstock,
•
1969). Recent investigations (Levy, 1971;and McConnell et_ al_. , 1971)
have shown that great enough concentrations of hydroxyl and hydroperoxyl
-------
381
radicals also exist in the troposphere to provide a mechanism for the
oxidation of carbon monoxide there too.
Carbon Monoxide Cycle
Over the last several years we have witnessed an explosion of inter-
est in the problem of defining natural sources and sinks of carbon monox-
ide. While several researchers have confirmed that soil and the reaction
of CO with hydroxyl and hydroperoxyl radicals in the stratosphere and pos-
sibly the troposphere constitute major sinks for CO, other researchers
have been finding additional natural sources of this gas. These sources,
oxidation of methane, oxidation of terpenes,and the oceans to name just a
few, are now thought to contribute more CO to the atmosphere than that
emitted as a result of anthropogenic activity. This is an outright con-
tradiction of what only two years ago was thought to be the final word;
i.e., anthropogenic CO emissions are many times greater than natural CO
emissions.
Table V compares recent estimates of the strength of CO sources and
sinks. It is obvious from this table, if these estimates are at all rea-
sonable, that soil and gas-phase oxidation in the stratosphere and tropo-
sphere might be capable of consuming all the CO that nature and man pro-
duce. If this is the case, it is understandable why the background con-
centration of CO has not increased over the last several decades, and we
might suggest that there no longer exists a "CO sink anomaly".
-------
382
Table V. ATMOSPHERIC FLUXES OF CARBON MONOXIDE (in 109 kg/yr)
I. Sources
a. anthropogenic 359 Jaffe (1973)
b. natural
1. oceans 43-220 Liss and Slater (1974) -
Linnenbom ejt al_. (1973)
2. oxidation of terpenes 54 Robinson and Moser (1971)
3. oxidation of methane 900 McConnell et_ al_. (1971)
4. other 1_
TOTAL 1356-1533
II. Sinks
a. soil 67-1400 Heichel (1973) -
Ingersoll (1972)
b. gas-phase oxidation
1. stratosphere 52-71 Pressman and Warneck (1970)
2. troposphere ?_
TOTAL 119-1471
-------
383
NITROGEN CONTAINING GASES
Although the most abundant oxide of nitrogen in the lower atmos-
phere is nitrous oxide (NaO), it does not play an important part in air
pollution chemistry. The two nitrogen oxides which are important are
nitric oxide (NO) and nitrogen dioxide (N02) for they play a prominent
role in the generation of photochemical smog.
Measurements of the background levels of nitrous oxide seem to con-
sistently average out to about 460 - 490 yg/m3 (0.25 - 0.27 ppm) (Schiitz
et_ a_l_., 1970). Ambient levels of NOa are much lower, probably around
2 yg/m3 (.001 ppm) (Robinson and Robbins, 1968) to 2.6 yg/m3 (.0014 ppm)
(Junge, 1963). Too few accurate measurements have been made of ambient
concentrations to obtain a meaningful average but Lodge and Pate (1966)
found concentrations up to 11 yg/m3 (.006 ppm) in Panama. The background
level of NO is approximately the same as that of N02.
The other nitrogen compound considered is ammonia. Although ammonia,
per se, is a relatively unimportant air pollutant, it does play am impor-
tant role in atmospheric chemistry for its part in the formation of aero-
sols. Ambient concentrations of ammonia seem to average about 4 yg/m3
(.006 ppm) (Robinson and Robbins, 1968).
NITROGEN OXIDES
Sources
Nitrous oxide (N?.0), which is the most abundant nitrogen compound
present in the atmosphere, is produced as a result of the decomposition
of other nitrogen compounds within the soil by bacteria. Arnold (1954)
was the first to study the production of NaO by soils. He found that the
one factor most conducive to increased NaO evolution is a high soil mois-
ture content, especially if a nitrogen source, such as nitrate or ammonia,
is present. An estimate of the flux of NaO from soils into the atmosphere
-------
384
has recently been made by McConnell (1973), who estimates that 1.1 x 1010
kg N20 - N (1.73 x 1010 kg N20) are released each year; Schiitz et^ al^. (1970)
declined to extrapolate the data they collected on three soil samples to at-
tain a global rate. Their measurements though showed a flux on the order of
10~8 g N20/m2-sec, an order of magnitude which, if maintained globally, would
necessitate an NiO residence time of about 70 years. This is the same resi-
dence time they had estimated based on the photodissociation rates of N20 in
the troposphere and stratosphere. Goody and Walshaw (1953) estimated the N20
global production rate to be about 100 x 1012 kg/yr and Robinson and Robbins
(1970) estimated that soils produce about 59.2 x 1010 kg N20 each year by
this biological action; of this about 55.4 x 1010kg (35.3 x 1010 kg N20-N)
are reabsorbed by the soil and about 3.8 x 1010 kg N20 (2.4 x 1010kg N20-N)
travels up to the stratosphere where it is destroyed. It is the latter rate
that is shown in Table VI.
Craig and Gordon (1963) raised the possibility that the ocean might be
a source or a sink of N20. Bates and Hays (1967) concluded that the uptake
of N20 by the oceans in areas where upwelling waters are deficient in N20 is
of negligible importance. Based upon the difference between the mean N20
concentrations of oceanic surface waters and the air about it and an estimate
of the total liquid phase resistance, Liss and Slater (1974) estimated the
flux of N20 from the ocean to the atmosphere at 1.2 x 1011 kg/year. This flux
is based entirely on theory and not measurements, but it does indicate that
the oceans could conceivably release significant quantities of N20 to the at-
mosphere. Laboratory and field experiments should be undertaken to provide
an answer as to whether or not the ocean is a source of N20.
Production rates of NO and N02 by soils are much more difficult to
measure and estimate, and good data are lacking. McConnell (1973) recently
summarized a few of the problems involved in obtaining an estimate for the
amount of nitrogen oxides produced by soil. It is his contention that
-------
385
this soil source is small compared to the production resulting from the gas
phase oxidation of atmospheric ammonia by OH which he estimates produces
7 x 1010 kg NO - N per year. McConnell though offers alternative reaction
A.
sequences for NHs in the atmosphere; one reaction sequence provides a con-
stant source of NO, the other a sink. If the latter is shown to occur in
the atmosphere, then an additional or enlarged source of NO must be found
in order to account for the amount of NO known to be in the atmosphere. If
this is the case, McConnell concedes that the soil might actually constitute
a significant source of NOX, on the order of 1011 kg/yr.
Nitric oxide is also produced as a result of the photolysis of N20
in the stratosphere as follows:
N20 + hv •> NO + N
The photolysis rate for this reaction is less than or equal to 7.4 x 10 9
sec"1 (McElroy and McConnell, 1971). Whereas these authors estimate the
production of about 3 x 108 kg NOX - N per year in this manner, Bates and
Hays (1967) estimated that 3.5 x 1010 kg NO are produced annually by this
photolysis reaction.
The other primary source of nitrogen oxides is anthropogenic, pri-
marily combustion processes. Estimates of production rates for NO and N02
are included together because emission data available rarely distinguish
between these two forms. Robinson and Robbins (1970) recently estimated
that each year 18 x 109 kg NOX - N are emitted into the atmosphere as a
result of man's activities. An earlier estimate by these same men in
1968 states that 53 x 109 kg of N02 were emitted annually (here again N02
includes both NO and N02 production).
In toto, natural emissions of NO2 (including NO) are approximately
15 times greater than anthropogenic emissions (768 x 109 kg vs. 53 x 109k
-------
386
N02) (Robinson and Robbins, 1970). Therefore anthropogenic emissions
play only a minor part in the total circulation of nitrogen compounds in
the atmosphere.
Removal Mechanisms
At 20°C, the solubility of N20 in water is 0.121 g/lOOg H20. Upon
release from soils, an unknown portion is believed to be removed by vege-
tation, soil and water. No information is available on these processes
though. The major portion of the released N20 is destroyed by photodisso-
ciation in the stratosphere and upper troposphere. Because under normal
tropospheric conditions N20 is chemically inert, it partakes in no other
chemical reactions in the troposphere. The residence time of nitrous ox-
ide is probably around 70 years if there is no removal by the biosphere
(Robinson and Robbins, 1968), but could be reduced to about 1-3 years if
there is a biologic loss mechanism. Hidy (1973) has estimated the resi-
dence time as 4 years.
Nitric oxide is rather insoluble in water. At 20°C its solubility
is 0.00618 g/lOOg H20. Nitrogen dioxide, on the other hand, immediately
dissociates when in water to form HN03 and HN02. For this reason, no
real value for the solubility of N02 in water exists.
Nitric oxide is either oxidized to N02 or photolyzed to N2. The N02
is then removed primarily by precipitation, more often than not in the
form of nitric acid (HN03). N02 can also be absorbed by vegetation and
soils or participate in photochemical reactions to form aerosols. Due to
their reactivity, the residence times of NO and N02 are 'relatively short,
probably around 5 days (Hidy, 1973). Nitrogen oxides are removed from
the atmosphere by the following mechanisms.
Vegetation: Vegetation has been shown capable of removing significant
-------
387
amounts of NOa and NO from the atmosphere. Tingey (1968) showed that
alfalfa and oats absorbed NOa from the air in excess of 100 x 10 12 mol/
m2*sec when exposed to an atmosphere containing 460 yg NOa/m3 (or ^ 1 x
10"5 mol/m3).
Hill (1971) found in his experiments on the uptake rate of gases by
an alfalfa canopy that NO was absorbed with a deposition velocity of 0.1
cm/sec, and NOa with a velocity of 2 cm/sec when present in the air of the
chamber at a concentration of 2 x 10 6 mol/m3 (or 96 yg/m3).
Soil: Nitrogen oxides (especially N20) have long been known to be
produced by biological action in soils. Recently though, Abeles et a_l.
(1971) found that soils could absorb nitrogen dioxide from the atmosphere
as well. Extrapolating the results of their experiment, the authors suggest
that the soils of the United States might be capable of removing 60 x 1010
kg of N02 per year from the atmosphere, an amount they point out to be a
bit under 20 times the total annual production of N02 in this country
(3.3 x 1010 kg).
Nelson and Bremner (1970) point out that the N02 that the soil ab-
sorbs will ultimately be oxidized to nitrate. These nitrates eventually
decompose and result in the production of nitrogen dioxide again. The
rate of NOa production by nitrate decomposition in soils is 2 x 10 "* g
N0a/m2-hr (Marchesani et_ al_. , 1970; and Makarov, 1970, as cited in Bohn,
1972). This NOa production rate is dependent upon the nitrate content
of the soil and does not proceed during darkness.
Nitric oxide may also be absorbed by soils, but upon absorption is
oxidized almost immediately to N02 (Mortland, 1965; and Bremner and Nel-
son, 1968). Mortland has also discovered that when transition metal ions
-------
388
are present in the soil, absorption of NO is promoted. If the soil is
saturated with alkaline earth cations though, absorption of NO is halted.
Sundareson £t al. (1967) found though that alkaline-earth zeolites read-
ily absorb NO and released it as NOX and HNOa when heated. To date, the
role organic matter plays in the absorption of nitrogen oxides by soil
remains a mystery. Ganz £t a.l_., (1968, as cited in Bonn) found that upon
passing NOX-contaminated air through 1 meter of peat, all nitrogen compon-
ents were removed. Organic matter is such an important component of soil
that to not be fully aware of its affects on a gas could only hinder full
understanding of the mechanism of absorption by the soil. Obviously, more
research is needed in this area.
Water Bodies: There are very little data available on the amount of
nitrogen oxides absorbed by the oceans. Craig and Gordon (1963) first
suggested that the oceans might constitute a sink for NzO when they found
that the sea water at depth was depleted in NaO compared to the surface
waters which they found to be in equilibrium with atmospheric concentra-
tions. The depletion they determined could not be explained by tempera-
ture variations with depth. Based on the mean upwelling speed of the
ocean's waters, estimated by Bowden (1965) as ranging from W~k to 10 5
cm/sec, Bates and Hays (1967} estimated the potential sink strength of
the oceans for NaO as ranging between 6 x 10~ and 6 x 10~
kg/m2.yr. Liss and Slater (1974), on the other hand, concluded that the
flux of N20 was from the sea to the air. They calculated a flux rate of
3.2 x 106 kg/m2*yr based upon an NzO concentration gradient across the
air-sea interface measured by Junge and Hahn (1971). The total flux of
NzO from the sea to the atmosphere, as.suming this flux is constant over
•
the entire oceanic surface, is 1.2 x 10n kg/yr. With such an obvious
-------
389
contradiction as to the direction of the N20 flux, there is a real need
for additional research in this area.
Washout and Rainout: The major sink identified thus far for nitrogen
oxides (NOX) is the solution of soluble species in cloud and rain droplets
with subsequent removal by precipitation. Different schemes of N02 hydro-
lysis have been proposed by Haagen-Smit and Wayne (1968), Georgii (1963)
and Robinson and Robbins (1968). However the hydrolysis reaction pro-
ceeds though,the outcome is the same in all cases; the nitric acid formed
is absorbed onto hygroscopic particles or reacts with atmospheric ammonia
to form nitrate salt aerosols (NHi^NOs for instance). It is then either
removed by precipitation, or if vaporization of the droplet occurs, by
dry deposition.
McConnell (1973) estimates that 2 x 1010 kg N03 - N is removed from
the atmosphere each year by precipitation, and an additional 7 x 1010kg
NOX - N is removed by dry deposition, the major portion of this probably
being HNOs.
Atmospheric Reactions Involving Nitrogen Oxides: Although more ni-
trous oxide is released to the atmosphere, than any other nitrogen oxide
it does not play a major or very complex role in atmospheric reactions.
Because it is chemically inert in the troposphere, its sink lies in the
stratosphere where it is transported by vertical mixing. In the stratos-
phere it is destroyed by photolyzing reactions.
Bates and Hays(1967) indicate that the most significant reactions are:
o
N20 + hv -> N2 + 0 (*D) ; X < 3370 A
N20 + hv -> NO + N ('*S) ; X < 2500 A
-------
390
The latter reaction they believe to be responsible for about 20% of the
total dissociation in the stratosphere.
Nitric oxide can be removed from the atmosphere by several reactions.
The primary reaction is its oxidation by ozone to form N02. In the
upper atmosphere, NO can be photolyzed and the resulting atomic N may re-
act with other NO molecules to form N2 (Schofield, 1967;and Callear and
Pilling, 1970).
Nitrogen dioxide also engages in a number of reactions. It may be
oxidized to N03 (Schofield, 1967), or it may form nitric acid by its re-
action with hydroxyl radicals (McConnell and McElroy, 1973). The nitric
acid that is formed would be removed by precipitation. For further ela-
boration, the reader is referred to McConnell and McElroy's article.
The importance of NO and N02 as pollutants is a result of their par-
ticipation in photochemical reactions. In polluted atmospheres they react
with S02 and hydrocarbons to form aerosols. Probably the most important
photochemical reaction involving N02 is its photodissociation as
follows:
0 o
N02 + hv (2900 A < X < 3800 A) £ NO + 0
This atomic oxygen then is free to react with molecular oxygen to form
ozone.
Peroxyl radicals (ROO-), formed by the reaction of reactive free
radicals (R) with 02, can react with NO and N02 to form alkyl nitrates or
peroxyacyl nitrates. These secondary reaction products are then targets
of further photochemical attack (Haagen-Smit and Wayne, 1968). Be-
cause it would not serve the purpose of this paper to elaborate on photo-
chemical reactions involving nitrogen oxides, the reader is referred to
Altshuller and Bufalini (1971), Cadle and Allen (1970), and Leighton (1961)
for more detail.
-------
391
Environmental NOX Cycle
The circulation of nitrogen oxides in the atmosphere is a complex
problem and, as yet, not well understood. The global NOX cycles that
have been formulated, those of Robinson and Robbins (1968) and McConnell
(1973), have made it clear how very little good quantitative data exist.
The holes in these cycles are obvious and major ones(see Table VI). We
need, for instance, a better idea of how much NO and N02 is released from
the soil, how much NHs is oxidized to NO , and how much NO and N02 is des-
X
troyed by photochemical reactions. And, we need to know why such a dis-
crepancy exists between estimates that have been made and in ways they are made
For example, McConnell bases his estimate of NO removed by dry deposition
on soil data, the nitrogen content of precipitation and a deposition velo-
city factor. Robinson and Robbins, on the other hand, use the deposition
velocity function to estimate gaseous deposition, a removal mechanism
McConnell makes no mention of. Inconsistencies like these indicate again
the need for further study in this area.
AMMONIA
Sources
The primary source of atmospheric ammonia appears to be the result
of bacterial decomposition of organic material on the earth's surface.
The factors which affect the emission of this NH3 from the soil are its
nitrogen content, pH, and moisture content (McConnell, 1973;and Georgii,
1963). NH3 is more readily released from dry soils than moist ones, and
is more readily released when the pH of the soil is greater than or equal
to 6. Junge (1963) also suggested that the oceans may contribute some
NH3 to the atmosphere, but to date there has been no accurate measurement
made upon which to base an estimate of the source strength. McConnell
-------
392
10
Table VI. ATMOSPHERIC FLUXES INVOLVED IN VARIOUS NO CYCLES (in 10'° kg N/yr)
Robinson and
Robbins*
(1968)
Robinson and
Robbins
(1970)
McConnell
(1973)
I. Sources
a.
b.
c.
d.
e.
anthropogenic; NO, N02
biological; N20
biological; NO, N02
oxidation of NHs
stratospheric transport;
1.5
1.2
30.4
N.E.
NO, N02 ---
1.6
1.2
23.4
N.E.
1.8
1.1
?
7
0.07
26.2 9.97
II. Sinks
a. rainout 112.9 7.5 2
b. dry deposition 27.1 1.9 7
c. oxidation of N20 + NO (strat.) 0.2 0.2 0.03
d. photolysis of N20 + N2 (strat.) --- --- (1.07)
e. gaseous deposition 10.7 4.5 —
TOTAL 150.9 14.1 (10.1)
N.E. = Mechanism recognized but no estimate made.
*NOTE: Friend (1973) has pointed out that due to an error in converting units
of kilograms per hectare to tons per square meter, much of Robinson
and Robbins' nitrogen compound cycle is invalid. Friend though, gives
no indication as to which values are wrong. Due to lack of information,
their cycle is nonetheless shown for comparison.
-------
393
has estimated that these biological sources release about 17 x 1010 kg
NHa - N each year, whereas Robinson and Robbins1(1968) nitrogen cycle
calls for the release of NHs on the order of 1012 kg NH3 each year (see
Table VII).
Anthropogenic NHa emissions result primarily from the combustion of
coal. Robinson and Robbins (1970) estimated that the atmospheric ammonia
burden due to man's activities is 0.4 x 1010 kg NHa - N per year, less
than 2 1/2% of the estimated NHs burden due to biological emissions
(17 x 1010 kg).
Removal Mechanisms
Ammonia is extremely soluble in water. At 20°C its solubility in
water is 62.9 g/lOOg h^O. From the data available, the residence time of
ammonia in the atmosphere is probably around 7 days (Hidy, 1973).
Water Bodies, Vegetation, Soils, Atmospheric Reactions: Due to
ammonia's solubility in water it can be readily absorbed by
water bodies (Hutchinson and Viets, 1969; and Calder, 1972) and vegetation
(Hutchinson et_ a_l_. , 1972;and Porter et^ aJL , 1972). Ammonia has also
been shown to be readily absorbed by soils, especially acid soils (Malo
and Purvis, 1964; DuPlessis and Kroontje, 1964; and Hanawalt, 1969a £ b).
It is also destroyed by its reaction with hydroxyl radicals in the atmos-
phere to form nitric oxide (McConnell, 1973).
Rainout and Washout: Probably the most important removal mechanism
for ammonia is its solution in rain water along with S02 or other gases
to form aerosols. Once dissolved NHs ionizes to NHi* as follows (Robinson
and Stokes, 1959):
NH3-H20 £ NH4+ + OH"
-------
394
Ammonia has been shown to be an important catalyst for the oxidation
of SOa and N02 in solution (van den Heuval and Mason, 1963). Both Scott
and Hobbs (1967) and Miller and de Pena (1972) have shown that as the par-
tial pressure of NHs in the atmosphere increases, greater concentrations
of SOa can be dissolved and oxidized in solution to form sulfate particles.
The resulting aerosols, if evaporated, are composed largely of
particles with probably minor amounts of NH^HSOa, NH^HSOit and
(Miller and de Pena, 1972). In the case where NH3 is co-absorbed with
the resulting particles would be composed primarily of NHJ^lOs.
It has been estimated (Robinson and Robbins, 1968) that almost 75%
of atmospheric ammonia is removed from the atmosphere by conversion to NH*
ions which condense in cloud droplets or particles and may form aerosols
upon evaporation of water. McConnell (1973) has estimated that of a total
source strength of about 17.4 x 1010 kg NHs - N/yr, approximately 3 x 1010 kg
of this ammonia are removed each year by rainout. He points out that
this is a very conservative estimate and "may be low by as much as a fac-
tor of 3." Earlier, Robinson and Robbins estimated that 280 x 1010kg NH3-N
are removed each year by precipitation. On the whole, quantitative
estimates are rather sparse and show a great discrepancy.
Environmental Ammonia Cycle
Relatively little quantitative information is available on the
strengths of both sources and sinks of ammonia. In fact, research into
possible atmospheric oxidation reactions is so recent that any estimates
made would certainly be subject to great uncertainty. Separate atmospheric
ammonia cycles have never been constructed; its cycle is always considered
together with that of nitrogen oxides. Because not very much is even known
about the nitrogen oxides cycles, the uncertainty involved in the combined
cycle is probably very high.
-------
395
To date the only nitrogen compound cycles devised are those of Robin-
son and Robbins (1968, 1970), McConnell (1973) and an overall geochemical
nitrogen cycle of Rasmussen et al. (1974). The first three cycles are com-
p'ared in Table VII. The discrepancy in source and sink estimates among the
three is immediately obvious. More research must be undertaken to provide us
with a better understanding of the part ammonia plays in atmospheric chemis-
try and to quantify possible sources and sinks such as the oceans, soil, and
vegetation.
Table VII. ATMOSPHERIC FLUXES INVOLVED IN VARIOUS AMMONIA CYCLES
(in 1010 kg N/yr)
Robinson and Robinson and
Robbins* Robbins McConnell
(1968) (1970) (1973)
I . Sources
a. anthropogenic — .35
b. biological 670± 95.7
TOTAL 670 96.05
II. Sinks
a. precipitation 280 18.6
b. dry deposition 70 4.9
c. oxidation to NO (troposphere) N.E.
X
d. oxidation § photolysis to NOX N p
(stratosphere)
e. gaseous deposition 90 74.9
TOTAL 440 98.4
0.4
17
17.4
3
7
7
0.04
17.04
N.E. = Mechanism recognized but no estimate made.
*NOTE: (see note in Table VI)
± Source strength here was adjusted by R. § R. to provide an additional
amount of nitrogen needed to balance other portions of their nitrogen
compound cycle.
-------
i96
OXIDANTS
OZONE
The problems involved when significant amounts of ozone are present
in the atmosphere have come to light probably more as a result of the
photochemical pollution problem in Los Angeles than from any other single
factor. While background concentrations of ozone probably range from
about 20-60 yg/m3 (0.01-0.03 ppm), in urban centers like Los Angeles, it is
not unusual to have 03 present at levels greater than 500 yg/m3 (.25 ppm).
Ozone levels up to 400 yg/m3 (0.2 ppm) usually will not cause any dele-
terious effects (Masters,1971), but at concentrations of 600 yg/m3(0.3 ppm)
ozone causes irritation of the mucous membranes in the nose and throat.
At somewhat higher levels, it can cause coughing, choking and severe fa-
tigue. When present at relatively high levels, such as those that occur
in severe photochemical smogs, ozone causes bronchial irritation and inter-
feres with normal lung functioning, causing breathing difficulty and chest
pains. For reference sake, the highest ozone concentration detected in
the Los Angeles atmosphere was 2,000 yg/m3 (0.99 ppm) in 1956 (Chambers,
1958, as cited in Tebbens, 1968).
Sources
Because the wavelengths of the ultraviolet radiation that pene-
trate the troposphere are too long to cause photodissociation of oxygen,
it has long been accepted that the presence of ozone in the troposphere
is due primarily to the transport of ozone down from the stratosphere.
The amount present in the troposphere would then be related to the injec-
tion rate through the tropopause, estimated as ranging between 1.9 and
7.5 x 103 kg/yr (Junge, 1962).
-------
397
Recently, Chameides and Walker (1973) proposed a model wherein both
seasonal and diurnal variations in the tropospheric ozone density are
assumed to be caused by photochemical changes rather than a change in the
flux of stratospheric ozone-rich air into the troposphere. Their model
calls for the production of Oa by the methane oxidation scheme suggested
by Crutzen (1973). The oxidation of methane produces hydroperoxyl radi-
cals which react with nitric oxide to form nitrogen dioxide which in turn
is photodissociated to NO and 0. This atomic oxygen then reacts with 02
to form ozone.
Removal Mechanisms
Ozone is relatively insoluble in water; at 20°C its solubility is
0.052 g/lOOg HaO. Therefore, removal of ozone from the atmosphere by wash-
out and rainout can be disregarded. There is evidence though that ozone
is removed by the oceans to some extent (Aldaz, 1969). Ozone is also ab-
sorbed by vegetation (Hill, 1971; Hill and Littlefield, 1969; and Rich ert
al. , 1970), and soil (Junge, 1962; Kroening and Ney, 1962; Aldaz, 1969;
and Turner et_ al_., 1973). Aldaz (1969) has shown that soil and vegeta-
tion probably represent a major sink for this gas. He estimated the sink
strength of the earth's surface to lie between 1.3 and 2.1 x 1012 kg 03/yr.
Due to its nature as a strong oxidizing agent, ozone participates in
a number of atmospheric reactions, especially in polluted atmospheres; name-
ly the photooxidation of hydrocarbons in the presence of nitrogen dioxide.
The initial oxidation of olefins by ozone, for instance, can lead to a long
series of reactions which produce ketones, aldehydes, organic acids and
nitrogen-containing compounds such as peroxyacetylnitrate (PAN). The pre-
sence of these compounds in the atmosphere has been shown to be the
cause of considerable eye irritation (Schuck and Doyle, 1959). Rate con-
stants for the reaction of ozone with numerous hydrocarbons have been
-------
398
summarized by Altshuller and Bufalini (1971) and Bufalini and Altshuller
(1965). Because the reactions of ozone in polluted atmospheres are so
numerous and have been the subject of extensive investigation and review,
it would not serve the best interest of this paper to review these reac-
tions here. For additional information the reader is referred to Hecht
and Seinfeld (1972), Dutsch (1971), Ripperton and Vukovich (1971), Stephens
(1969), Altshuller and Bufalini (1965),and Leighton (1961). Junge (1962)
has estimated the tropospheric residence time of ozone to range between
3 and 4 months.
-------
399
HYDROCARBONS
Hydrocarbons constitute a major group of air contaminants which can
be subdivided into reactive and non-reactive classes. The more important
reactive hydrocarbons include the olefins and aromatics. Paraffinic hy-
drocarbons are classified as non-reactive.
REACTIVE HYDROCARBONS
Because of their role in photochemical reactions in polluted atmo-
spheres, reactive hydrocarbons have been the subject of great interest.
These photochemical reactions produce smog which is associated with eye
and respiratory tract irritation, reduced atmospheric visibility, and
plant damage.
Limited ambient data from Point Barrow, Alaska (Robinson and Robbins,
1968) indicate that ethylene, the most abundant hydrocarbon of this group,
is present at a concentration of less than 1 yg/m3 (less than 1 ppb). In
the absence of other ambient measurements one might consider the concen-
tration of ethylene measured at the above location to represent the upper
limit of the background concentration for components in this group.
Sources
A variety of hydrocarbons are released to the atmosphere as a result
of both anthropogenic activity and natural processes. The most important
anthropogenic source of hydrocarbons, resulting from the incomplete com-
bustion of fuel, is motor vehicle exhaust. Robinson and Robbins (1968)
estimate that the total annual emission of olefins and aromatics resulting
from the combustion of various fuels is 27 x 10a kilograms. A bibliography
of various emission sources has been compiled by the U.S. Department of
Health, Education and Welfare (1970).
-------
400
Plant species also release appreciable quantities of volatile organic
substances to the surrounding air. The major reactive hydrocarbons emit-
ted by trees are ethylene, monoterpene (Cio), and isoprene (C5). In a
recent study, Rasmussen (1972) concluded that the forests represent a
global natural source of 175 x 109 kg of reactive hydrocarbons each year.
This emission rate is 6 times greater than that estimated for reactive
hydrocarbons of anthropogenic origin.
Removal Mechanisms
Hydrocarbons in general are not water soluble, and therefore, they
cannot be directly removed from the atmosphere by wet processes such as
washout and absorption by surface waters. Various studies have shown that
photochemical reactions are important in removing reactive hydrocarbons,
although the products formed may cause detrimental side effects such as
eye and throat irritation. Hydrocarbons of this class, upon their emis-
sion into the atmosphere, undergo rapid chemical transitions in the pre-
sence of: atomic oxygen and ozone (Bufalini and Altshuller, 1965); oxides
of nitrogen (Shuck, 1961; and Alley et_ al_., 1965); ozone and sul-
fur dioxide (Cox and Penkett, 1971b) and; nitrogen dioxide and sulfur di-
oxide (Schuck and Doyle, 1959).
The basic kinetic mechanisms of hydrocarbon reactions in the atmos-
phere are given by Hecht and Seinfeld (1972). These authors have present-
ed a 15-step mechanism for photochemical smog formation, with rate con-
stants and stoichiometric coefficients chosen according to the particular
hydrocarbons involved in the reactions and the initial reactant ratios.
The state of the art of photochemical reactions is analyzed by Dodge
(1973) and Seinfeld, Hecht and Roth (1973).
-------
401
Quantitative data on the rates of these atmospheric reactions are
rare. The limited data available as reported by Hidy (1973) suggest
that 1-10% by weight of the reactive hydrocarbons emitted into the atmos-
phere are converted to aerosol and eventually are removed by scavenging
or deposition. The remaining hydrocarbons are eventually oxidized to car-
bon dioxide and water vapor.
Smith et_ al. , (1973) investigated the capacity of soils to absorb
ethylene and acetylene. They concluded, as did Abeles et_ al. (1971) in
an earlier experiment on ethylene uptake by soil, that the sorption of
both ethylene and acetylene is due to microbial activity in the soil.
Smith et_ al. found that the soils they tested removed ethylene at
average rates ranging from .14-.97 x 10 9 mol per gram of soil per day
(mol/g'd) and acetylene from .24-3.12 x 10~9 mol/g'd.
NON-REACTIVE HYDROCARBONS
This group, which consists of methane and the higher saturated hydro-
carbons, has been found to be much less involved in photochemical reactions
and smog formation than reactive hydrocarbons. By far the most abundant
paraffinic hydrocarbon in the atmosphere is methane. Methane's background
concentration is about 1000 Ug/m3 (1.5 ppm), while the background concen-
tration for heavier gases in this class is less than 1 pg/m (less than
1 ppb) (Robinson and Robbins, 1968).
Sources
The anthropogenic source of paraffinic hydrocarbons is the incomplete
combustion of fuel in motor vehicles. The annual emission of paraffinic
hydrocarbons is estimated to be 60 x 109 kilograms (Robinson and Robbins,
1968).
Among natural sources approximately 310 x 10 9 kilograms of methane
-------
402
is produced annually in swamps and various water bodies as a result of
bacterial decomposition. The relatively high concentration of methane in
the atmosphere compared to other organic gases is related to this natural
process.
Removal Mechanisms
Because they are so insoluble in water, paraffinic hydrocarbons can
not be removed from the atmosphere by wet processes. The primary sink for
methane in the troposphere is its oxidation by hydroxyl radicals to form
carbon monoxide. The initial reaction is as follows:
CHi* + OH -> CH3 + H20
The rate coefficient for this equation equals 5.5 x 10"12 exp (-1900/T)
(Greiner, 1970). For a complete development of this oxidation scheme the
reader is referred to Levy (1971), McConnell et_ al^. (1971) and Levy (1972,
1973a). Based upon density profiles of CHi^ and hydroxyl radicals in the
troposphere, and the rate equation given above, Levy (1973b) was able to
calculate the average daily loss of methane at a particular altitude. The
total column loss rate for methane was found to be 7.48 x 10 8 mol/m2 sec.
•
This results in a tropospheric residence time for methane of 2 years.
Rasmussen e£ al. (1968) and Robinson and Robbins (1968) have also
suggested that the volatile organic components of the atmosphere are re-
moved by bacteriological processes and vegetation. However, quantitative
data and rate equations for these removal mechanisms are nonexistent in
the literature.
-------
403
RECAPITULATION
1. Hydrogen sulfide, sulfur dioxide, nitrous oxide, nitric oxide,
nitrogen dioxide, ammonia, carbon monoxide, ozone, and some hydrocarbons
have been surveyed regarding their sources and sinks because of their
importance as gaseous atmospheric pollutants.
2. In recent years vastly increased information on pollutant
sources, sinks, and background levels has become available. Sheer
speculation is being replaced by documentation. Still the current
state of understanding is changing so fast that there emerge regularly
whole new concepts which alter our thinking by orders of magnitude and
even in direction.
3. The comprehensive search for natural pollutant removal
mechanisms lead to the identification of the following processes:
absorption (often accompanied by chemical reaction) by vegetation,
soil, water bodies, and natural stone; precipitation scavenging; and
chemical reactions in the atmosphere. The relative importance of
these processes depends on the particular pollutant and on environmental
circumstances. Quantitative modeling of most of these removal processes
was found to be in its infancy.
4. For clarity and brevity many details of interest only to a
limited audience have been omitted from this article. Such peculiar
details as well as extended discussion of conflicts among the
available information are presented in a separate report by Rasmussen,
Taheri, and Kabel (1974).
-------
404
ACKNOWLEDGMENTS
The authors wish to acknowledge the technical advice of W. J. Moroz,
R. G. de Pena, F. E. Wickman, and C. M. Sheih. Also thanks are due to
many staff members of Penn State's Center for Air Environment Studies for
their support in a variety of ways.
Special appreciation is extended to the Environmental Protection
Agency for its financial support of this project via Grant No. 800397,
administered through the Center for Air Environment Studies and the
Department of Meteorology of The Pennsylvania State University.
-------
405
REFERENCES
Abeles, F. B., Craker, L. E., Forrence, L. E., and Leather, G. R.: 1971,
"Fate of air pollutants. Removal of ethylene, sulfur dioxide and
nitrogen dioxide by soil." Science, 175(4000):914-916.
Aldaz, L.: 1969, "Flux measurements of atmospheric ozone over land and
water." J. Geophys. Res., 74 (28):6945-6946.
Alley, F. C., Martin, G. B., and Ponder, W. H.: 1965, "Apparent rate
constants and activation energies for the photochemical decomposition
of various olefins." J. Air Poll. Control Assoc., 15(8):348-350.
Altshuller, A. P. and Bufalini, J. J.: 1965, "Photochemical aspects of
air pollution: A review." Photochem. § Photobiology, 4_:97-146.
Altshuller, A. P. and Bufalini, J. J.: 1971, "Photochemical aspects of
air pollution: A review." Environ. Sci. Technol., 5CL):39-64.
Arnold, P. W.: 1954, "Losses of nitrous oxide from soil." J. Soil Sci.,
5_: 116-128.
Bates, D. R. and Hays, P. B.: 1967, "Atmospheric nitrous oxide."
Planetary Space Sci., 15:189-197.
Bates, D. R. and Witherspoon, A. E.: 1952, "The photochemistry of some
minor constituents of the earth's atmosphere. Mon. Notic. Roy.
Astron. Soc., 112:101-124.
Beilke, S. and Georgii, H.: 1968, "Investigation on the incorporation
of sulfur dioxide into fog- and rain-droplets." Tellus, 20(3):
435-442.
Bennett, J. H. and Hill, A. C.: 1973, "Absorption of gaseous air pollu-
tants by a standardized plant canopy." J. Air Poll. Control Assoc.,
25_: 203-206.
Bennett, J. H., Hill, A. C., and Gates, D. M.: 1973, "A model for gaseous
pollutant sorption by leaves." J. Air Poll. Control Assoc., 25(11):
957-962.
Bohn, H. L.: 1972, "Soil absorption of air pollutants." J. Environ.
Quality, 1(4) :372-377.
Bowden, K. F.: 1965, "Currents and mixing in the ocean." Chemical
Oceanography, Vol. 1, J. P. Riley § G. Skirrow, eds., Academic
Press, New York.
Bremner, J. M. and Nelson, D. W.: 1968, "Chemical decomposition of
nitrite in soils." Int. Congr. Soil Sci., Trans. 9th (Adelaide)
2_:495-503.
Bufalini, J. J. and Altshuller, A. P.: 1965, "Kinetics of vapor phase
hydrocarbon-ozone reactions." Can. J. Chem., 45:2243-2250.
-------
406
References
Cadle, R. D. and Allen, E. R.: 1970, "Atmospheric photochemistry."
Science, 167(3916):243-246.
Cadle, R. D. and Ledford, M.: 1966, "The reaction of ozone with hydrogen
sulfide." Int. J. Air Water Poll., 10:25-30.
Cadle, R. D., Fischer, W. H., Frank, E. R., and Lodge, Jr., J. P.: 1968,
"Particles in the Antarctic atmosphere." J. Atmos. Sci., 25_: 100-103.
Calder, K. L.: 1972, "Absorption of ammonia from atmospheric plumes by
natural water surfaces." Water, Air 5 Soil Pollution. 1(4):375-380.
Callear, A. B. and Pilling, M. J.: 1970, "Fluorescence of nitric oxide,
Part 6. Predissociation and cascade quenching in NO D2!"1" (v=o)
and NO C2II (v=o), and the oscillator strengths of the e(0,0) and
6(0,0) bands." Trans. Faraday Soc., 66^:1886-1906.
Calvert, J. G., Kerr, J. A., Demerjian, K. L., and McQuigg, R. D.: 1972,
"Photolysis of formaldehyde as a hydrogen atom source in the lower
atmosphere." Science, 175:751-752.
Chamberlain, A. C.: 1960, "Aspects of the deposition of radioactive and
other gases and particles." Int. J. Air Poll., 3_: 63-88.
Chambers, L. A.: private communication (1958) to Tebbens (1968).
Chameides, W. and Walker, J.: 1973, "A photochemical theory of tropospheric
ozone." J. Geophys. Res., 78(36):8751-8760.
deCormis, L.: 1969, "Absorption of sulfur by plants subjected to an atmos-
phere containing SOa.". Air Pollution, Proc. European Congress, 1st,
22-27 April, 1968 (Publ. 1969): 75-78.
Cox, R. A. and Penkett, S. A.: 1970, "The photo-oxidation of sulfur
dioxide by sunlight." Atmos. Environ., 4_: 425-433.
Cox, R. A. and Penkett, S. A.: 1971a, "Photo-oxidation of atmospheric
S02." Nature, 229:486-488.
Cox, R. A. and Penkett, S. A.: 1971b, "Oxidation of atmospheric S02 by
products of the ozone-olefin reaction." Nature, 230:321-322.
Craig, H. and Gordon, L. I.: 1963, "Nitrous oxide in the ocean and marine
atmosphere." Geochimica et Cosmochimica Acta, 27:949-955.
Crutzen, P. J.: 1973, "Gas-phase nitrogen and methane chemistry in the
atmosphere." Physics and Chemistry of the Upper Atmosphere, B. McCormac,
ed., D. Reidel Publ. Co., Dordrecht, Netherlands.
-------
References 407
Davis, D. D., Payne, W. A., and Stief, L. J.: 1973, "The hydroperoxyl
radical in atmospheric chemical dynamics: Reaction with carbon
monoxide." Science, 179;280-282.
Uodge, M. C.: 1973, "Workshop on mathematical modeling of photochemical
smog." Summary of the proceedings, U.S. Environmental Protection
Agency, EPA-R4-73010.
DuPlessis, M. and Kroontje W.:1964 "The relationship between pH and
ammonia equilibria in soil." Soil Sci. Soc. Amer. Proc.,
28^:751-754.
Dutsch, H. U.: 1971, "Photochemistry of atmospheric ozone." Advanc.
Geophys., 15^219-222.
Endow, N., Doyle, G. J., and Jones, J. L.: 1963, "The nature of some
model photochemical aerosols." J. Air Poll. Control Assoc.,
13_: 141-147.
Engelmann, R. J.: 1968, "The calculation of precipitation scavenging."
Meteorology and Atomic Energy, D. H. Slade, ed., U.S.A.E.G.
68-60097.
Eriksson, E.: 1960, "The yearly circulation of chloride and sulfur in
nature; meteorological, geochemical and pedological implications."
Tellus, 12^:63-109.
Eriksson, E.: 1963, "The yearly circulation of sulfur in nature."
J. Geophys. Res., 68:4001-4008.
Faller, N. N.: 1968, Der Schwefeldioxydgehalt der Luft als Komponente
der Schwefelversorgung der Pflanze. Diss. Doktorgrades, Inst.
Pflanzenernahrung, Justus Liebig Univ., Giessen, 120 pp.
Flury, F. and Zernik, F.: 1931, Schadliche Case, Dampfe, Nebel,
Rauch und Staubarten, pp. 195-196, Springer, New York.
Fried, M.: 1948, "The absorption of sulfur dioxide by plants as shown
by use of radioactive sulfur." Soil Sci. Soc. Amer. Proc.,
13^:135.
Friend, J. P.: 1973, "The global sulfur cycle." Chemistry of the
lower atmosphere, S. I. Rasool, ed., Plenum Press, New York.
Fuquay, J. J.: 1970, "Scavenging in perspective." Precipitation
Scavenging, R. J. Engelmann § W. G. N. Slinn, ed. coord.
-------
408
References
Galbally, I. E.: 1972, "Production of carbon monoxide in rain water."
J. Geophys. Res., 77(56):7129-7152.
Ganz, S. N., Kuznetsov, I. E., Shlifer, V. A., and Leiken, L. I.: 1968,
"Removal of nitrogen oxides, sulfur dioxide, and sulfuric acid vapor
and spray from waste gases by alkaline peat sorbents under industrial
conditions." (Chem. Abstract, 69_:12755n) Zh. Prikl. Khim, 41_: 720-725,
Georgii, H. W.: 1965, "Oxides of nitrogen and ammonia in the atmosphere."
J. Geophys. Res., 68(15):5965-5970.
Georgii, H. W.: 1970, "Contribution to the atmospheric sulfur budget."
J. Geophys. Res., 75(12):2565-2571.
Gerhard, E. R. and Johnstone, H. F.: 1955, "Photochemical oxidation of
sulfur dioxide in air." Ind. Eng. Chem., 47:972-976.
Goody, R. M. and Walshaw, C. D.: 1955, "The origin of atmospheric
nitrous oxide." Quart. J. Roy. Meteorol. Soc., 79:496-500.
Greiner, N. R.: 1970, "Hydroxyl radical kinetics by kinetic spectroscopy,
4, Reactions with alkanes in the range 500-500°K." J. Chem. Phys.,
.55:1070.
Haagen-Smit, A. J. and Wayne, L. G.: 1968, "Atmospheric reactions and
scavenging processes." Air Pollution, 2nd ed., vol. 1, A. C. Stern,
ed., p. 149-186, Academic Press, New York.
Hales, J. M. : 1972, "Fundamentals of the theory of gas scavenging by
rain." Atmos . Environ., 6_: 655-659.
Hales, J. M., Dana, M. T., and Wolf, M. A.: 1975a, "Advances in the
theory and modeling of pollutant gas washout." Proceedings of the
5rd Int. Clean Air Congress. VD1 - Verlag GmbH, Dusseldorf, B-92.
Hales, J. M., and Sutter, S. L.: 1975, "Solubility of sulfur dioxide in
water at low concentrations." Atmos. Environ., ]_: 997-1001.
Hales, J. M., Thorp, J. M., and Wolf, M. A.: 1971, "Field investigation
of sulfur dioxide washout from the plume of a large coal-fired
power plant by natural precipitation." Final Report to the Environ-
mental Protection Agency No. CPA22-69-150.
Hales, J. M., Wilkes, J. 0., and York, J. L.: 1969, "The rate of
reaction between dilute H2S and 03 in air." Atoms. Environ.,
5^:657-667.
Hales, J. M., Wolf, M. A., and Dana, M. T.: 1975b, "A linear model
for predicting the washout of pollutant gases from industrial
plumes." A.I.Ch.E. Journal, _19:292-297.
-------
409
References
Hanawalt, R. B.: 1969a, "Environmental factors influencing the sorption
of atmospheric ammonia by soils." Soil Sci. Soc. Amer. Proc.,
33_: 231-234.
Hanawalt, R. B.: 1969b, "Soil properties affecting the sorption of
atmospheric ammonia." Soil Sci. Soc. Amer. Proc_., 53:725-729.
Harkins, J. and Nicksic, S. W.: 1965, "Studies on the role of sulfur
dioxide in visibility reduction." J. Air Poll. Control Assoc.,
15(5);218-22l.
Hecht, T. A. and Seinfeld, J. H.: 1972, "Development and validation
of a generalized mechanism for photochemical smog." Environ. Sci.
Technol., 6(l):45-57.
Heichel, G. H.: 1973, J. Environ. Quality 2(4), 419-423.
van den Heuval, A. P. and Mason, B. J.: 1963, "The formation of
ammonium sulphate in water droplets exposed to gaseous sulfur
dioxide and ammonia." Quart. J. Roy. Meteorol. Soc., 89:271-275.
Hidy, G. M.: 1973, "Removal processes of gaseous and particulate
pollutants." Chemistry of the lower atmosphere, S. I. Rasool,
ed., Plenum Press, N. Y.
Hill, A. C.: 1971, "Vegetation: A sink for atmospheric pollutants."
J. Air Poll. Control Assoc., 21(6):341-346.
Hill, A. C. and Littlefield, N.: 1969, "Ozone: Effect'on apparent
photosynthesis, rate of transpiration, and stomatal closure in
plants." Environ. Sci. Techno 1., ,3:52-56.
Hutchinson, G. L., Millington, R. J., and Peters, D. B.: 1972,
"Atmospheric ammonia: Absorption by plant leaves." Science,
175(4023) -.771-772.
Hutchinson, G. L. and Viets, Jr., F. G.: 1969, "Nitrogen enrichment
of surface water by absorption of ammonia volatilized from
cattle feedlots." Sciejice, 166(5904) :514-515.
Ingersoll, R. B.: 1972, "The capacity of the soil as a natural sink
for carbon monoxide." Stanford Research Institute, Menlo Park,
Calif. SRI LSU-1380 CRC A PRAC CAPA 4 68 6, 43 pp.
Inman, R. E. and Ingersoll, R. B.: 1971, "Note on the uptake of carbon
monoxide by soil fungi." J. Air Poll. Control Assoc.. 21f101'
646-647. —*—'
Inman, R. E., Ingersoll, R. B., and Levy, E. A.: 1971, "Soil: A
natural sink for carbon monoxide." Science, 172:1229-1231.
Jaffe, L. S.: 1973, "Carbon monoxide in the biosphere: Sources,
distribution and concentrations." J. Geophys. Res., 78(24):
5293-5305.
-------
410
References
Johnstone, H. F. and Coughanowr, D. R.: 1958, "Absorption of sulfur
dioxide from air. Oxidation in drops containing dissolved
catalysts." Ind. Eng. Chem., 50(8) :1169-1172,.
Junge, C. E.: 1962, "Global ozone budget and exchange between
stratosphere and troposphere." Tellus, 14(4):565-377.
Junge, C. E.: 1963, Air Chemistry and Radioactivity, p. 72,
Academic Press, New York.
Junge, C. E. and Hahn, J.: 1971, "N20 Measurements in the North
Atlantic." J. Geophys. Res., 76(35):8143-8146.
Junge, C. E. and Ryan, T. : 1958, "Study of the SO;, oxidation in
solution and its role in atmospheric chemistry." Quart. J.
Roy. Meteorol. Soc. , 84_:46-55.
Kellogg, W. W., Cadle, R. D., Allen, E. R., Lazrus, A. L., and
Martell, E. A.: 1972, "The sulfur cycle." Science, 175(4022):
587-596.
Kroening, J. L. and Ney, E. P.: 1962, "Atmospheric ozone."
J. Geophys. Res^, 67:1867-1875.
Leighton, P. A.: 1961, Photochemistry of air pollution, Academic
Press, New York.
Levy, H., II.: 1971, "Normal atmosphere: Large radical and
formaldehyde concentration's predicted." Science, 175(3992):
141-143.
Levy, H., II.: 1972, "Photochemistry of the lower troposphere."
Planetary Space Sci., 20_: 919-935.
Levy, H., II.: 1973a, "Photochemistry of minor constituents in the
troposphere." Planetary Space Sci., 21:575-591.
Levy, H., II.: 1973b, "Tropospheric budgets for methane, carbon
monoxide, and related species." J. Geophys. Res., 78(24):
5325-5332.
Linnenbom, V. J., Swinnerton, J. W., and Lamontague, R. A.: 1973,
"The ocean as a source for atmospheric carbon monoxide."
J. Geophys. Res., 78(24) :5333-5340.
Liss, P. S.: 1971, "Exchange of S02 between the
atmosphere and natural waters." Nature, 233:327-329.
Liss, P. S. and Slater, P. G.: 1974, "Flux of gases across the
air-sea interface." Nature, 247:181-184.
Liuti, J., Dondes, S., and Harteck, P.: 1966, "The reaction of
hydrogen sulfide and atomic oxygen." J. Amer. Chem. Soc.,
88:3212-3215.
-------
411
References
Lodge, J. P. and Pate, J. B.: 1966, "Atmospheric gases and participates
in Panama." Science, 153(5754):408-410.
Luckat, S.: 1973, "Die Wirkung von Luftverunreinigungen beim Steinzerfall."
Staub-Reinhalt. Luft, 55J7): 285-285.
Makarov, B. N.: 1970, "Liberation of nitrogen dioxide from soils."
Soviet Soil _Sci., 1_: 20-25.
Malo, B. A. and Purvis, E. R.: 1964, "Soil absorption of atmospheric
ammonia." Soil Sci., 97:242-247.
Marchesani, V. J., Towers, T., and Wohlers, H. C.: 1970, "Minor sources
of air pollutant emissions." J. Air Poll. Control Assoc., 20:19-22.
Massachusetts Institute of Technology: 1970, Man's Impact on the
Global Environment, M.I.T. Press, Cambridge, tables 1.2, 5.6, 7.2,
7.3 and 7.5.
Masters, R. L.: 1971, "Air pollution - human health effects."
Introd. Sci. Study Atmos. Pollut., B. M. McCormac, ed., Reidel
Publ. Co., Dordrecht, Neth., p. 97-150.
Matteson, M. J., Stoeber, W., and Luther, H.: 1969, "Kinetics of the
oxidation of sulfur dioxide by aerosols of manganese sulfate."
Ind. Eng. Chem. Fundam., 8^:677-687.
McConnell, J. C.: 1975, "Atmospheric ammonia." J. Geophys. Res.,
78(53):7812-7821.
McConnell, J. C. and McElroy, M. B.: 1973, "Odd nitrogen in the
atmosphere." J. Atmos. Sci., 50(8):1465-1480.
McConnell, J. C., McElroy, M. B., and Wofsy, S. C.: 1971, "Natural
sources of atmospheric CO." Nature, 255:187-188.
McElroy, M. B. and McConnell, J. C.: 1971, "Nitrous oxide: A
natural source of stratospheric NO." J. Atmos. Sci., 28:1095-1098.
Miller, J. M. and de Pena, R.: 1972, "Contribution of scavenged sulfur
dioxide to the sulfate content of rain water." J. Geophys. Res.,
77(20): 5905-5916.
Mortland, M. M.: 1965, "Nitric oxide adsorption by clay minerals."
Soil Sci. Soc. Amer. Proc^, 29:514-519.
Nelson, D. W. and Bremner, J. M.: 1970, "Gaseous products of nitrite
decomposition in soils." Soil Biol. Biochem., 2^:203-215.
Nordo, F. J.: 1973, "Mesoscale and larger scale transport of air
pollutants." Proceedings of the 3rd Int. Clean Air Congress.
VDL-Verlag Gmbh, Dusseldorf, B-105.
-------
412
Reference
Owers, M. J. and Powell, A. W.: 1974, "Deposition velocity of sulphur
dioxide on land and water surfaces using a 35S tracer method."
Atmos. Environ., 8(1):63-67.
Pate, J. B., Sheesley, D. C., and Wartburg, A. F.: unpublished data.
Porter, L. K., Viets, Jr., F. G., and Hutchinson, G. L.: 1972, "Air con-
taining Nitrogen-15 ammonia: Foliar absorption by corn seedlings."
Science, 175:759-761.
Pressman, J., Arin, L. M., and Warneck, P.: 1970, Mechanisms for removal
of carbon monoxide from the atmosphere. U. S. Public Health Service,
NAPCA-CKS. Final Report, Contract No. CPA22-69-36.
Pressman, J. and Warneck, P.: 1970, "The stratosphere as a chemical sink
for carbon monoxide." J. Atmos. Sci., 27(1):155-163.
Rasmussen, K. H., Taheri, M., and Kabel, R. L.: 1974, "Sources and
natural removal processes for some atmospheric Pollutants," Environmental
Protection Agency Grant Report No. EPA-650/4-74-032, 121 pp.
Rasmussen, R. A.: 1972, "What do the hydrocarbons from trees contribute
to air pollution." J. Air Poll. Control Assoc., 22(7):537-545.
Rasmussen, R. A., Hutton, R. S., and Garner, R. J.: 1968, "Factors in
establishing microbial populations on biologically inert surfaces."
Biodeterioration of Material, A. H. Walters § J. J. El Phick, eds.,
Elsevier, London, pp. 79-98.
Renzetti, N. A. and Doyle, G. J.: 1960, "Photochemical aerosol formation
in sulfur dioxide-hydrocarbon systems." Int. J. Air Water Poll.,
2:327-345.
Rich, S., Waggoner, P. E., and Tomlinson, H.: 1970, "Ozone uptake by bean
leaves." Science, 169(5940):79-81.
Ripperton. L. A., White, 0., and Jeffries, H. E.: 1967, presented before
the Division of Water, Air, and Waste Chemistry, 154th American
Chemical Society Meeting, Chicago, 111., September 10-15.
Ripperton, L. A. and Vukovich, F. M.: 1971, "Gas phase destruction of
tropospheric ozone." J. Geophys. Res., 76:7328-7335.
Robinson, E. and Moser, C. E.: 1971, "Global gaseous pollutant emissions
and removal mechanisms." Proceedings of The Second International
Clean Air Congress, edited by H. M. Englund and W. T. Berry, Academic
Press, New York, pp. 1097-1101.
-------
413
References
Robinson, E. and Robbins, R. C.: 1968, "Sources, abundance and fate of
gaseous atmospheric pollutants." Final Report, SRI, Project PR-6755.
Robinson, E. and Robbins, R. C.: 1970, "Gaseous nitrogen compound pollutants
from urban § natural sources." J. Air Poll. Control Assoc., 20:505-506.
Robinson, E. and Stokes, R. H.: 1959, Electrolytic Solutions, Buttersworth,
London, 559 pp.
Schofield, K.: 1967, "An evaluation of kinetic rate data for reactions of
neutrals of atmospheric interest." Planetary Space Sci., 15:645-670.
Schuck, E. A.: 1961, "The nature of eye irritants in smog." Stanford
Research Institute, South Pasadena, 8 pp.
Schuck, E. A. and Doyle, G. J.: 1959, "Photo-oxidation of hydrocarbons in
mixtures containing oxides of nitrogen and sulfur dioxide." Rept.
No. 29, Air Pollution Foundation, San Marino, Calif.
Schiitz, K., Junge, C., Breck, R., and Albrecht, B.: 1970, "Studies of
atmospheric N20." J. Geophys. Res., 75(12):2250-2246.
Scott, W. D. and Hobbs, P. V.: 1967, "The formation of sulphate in water
droplets." J. Atmos. Sci., 24:54-57.
Seller, W.: 1972, "Carbon monoxide in the atmosphere." Symposium on
Sources, Sinks and Concentrations of CO and CH^ in the Earth's
Environment, St. Petersburg Beach, Florida.
Seiler, W. and Junge, C.: 1969, "Decrease of carbon monoxide mixing ratio
above the polar tropopause." Tellus, 21(5):447-449.
Seller, W. and Warneck, P.: 1972, "Decrease of the carbon monoxide mixing
ratio at the tropopause." J. Geophys. Res., 77(18):5204-3214.
Seim, E. C.: 1970, "Sulfur dioxide absorption by soil." University of
Minnesota, Ph.D. Thesis.
Seinfeld, J. H., Hecht, T. A., and Roth, P. M.: 1975, "Existing needs in
the experimental and observational study of atmospheric chemical
reactions." U. S. Environmental Protection Agency, EPA-R4-75051.
Smith, K. A., Bremner, J. M., and Tabatabai, M. A.: 1975, "Sorption of
gaseous atmospheric pollutants by soils." Soil Sci., 116(4):515-519.
Spedding, D. J.: 1969a, "Uptake of S02 by barley leaves at low SOa concen-
trations." Nature, 224:1229-1250.
-------
414
References
Spedding, D. J.: 1969b, "S02 uptake by limestone." Atmos. Environ
3_:683. - -
Spedding, D. J.: 1972, "Sulfur dioxide absorption by sea water."
Atmos . Environ . , 6:583-586.
Stephens, B. D.: 1969, "Chemistry of atmospheric oxidants." J. Air
Poll. Control Assoc., ^
Stevens, C. M., Krout, L., Walling, D., Venters, A., Engelkemeir, A.,
and Ross, L. E. : 1972, "The isotopic composition of atmospheric
carbon monoxide." Earth Planet. Sci Lett., 16:147-165.
Stoiber, R. E. and Jepsen, A.: 1973, "Sulfur dioxide contributions to
the atmosphere by volcanoes." Science, 182:577-578.
Sundaresen, B. B., Harding, C. I., May, F. P., and Henrickson, E. R.:
1967, "Adsorption of nitrogen oxides from waste gas." Environ.
Sci. Technol., 1_: 151-156.
Swinnerton, J. W. , Lamontagne, R. A., and Linnenbom, V. J.: 1971,
"Carbon monoxide in rainwater." Science, 172:943-945 .
Swinnerton, J. W., Linnenbom, V. J., and Lamontagne, R. A.: 1970,
"The ocean: A natural source of carbon monoxide." Science,
167 (3920) : 984-986 .
Tebbens, B. D.: 1968, "Gaseous pollutants in the air." Air Pollution,
Vol. 1, 2nd ed., A. C. Stern, ed., Academic Press, New York, pp. 23-45,
Terraglio, F. P. and Manganelli, R. M. : 1966, "The influence of moisture
on the adsorption of atmospheric SOa by soil." Int. J. Air 5 Water
Poll. Nov. -Dec., 783-791.
Tingey, D. T.: 1968, "Foliar absorption of nitrogen dioxide." Dept. of
Botany, Univ. of Utah, M. A. Thesis.
Turner, N. C., Rich, S., and Waggoner, P. E.: 1973, "Removal of ozone by
soil." J. Environ. Qual . , 2(2) : 259-264.
U. S. Dept. Health, Education and Welfare: 1970, Hydrocarbons and air
pollution: An annotated bibliography. Part I, Categories A to E.
Environ. Health Service, Raleigh, North Carolina.
Vandecaveye, S. C., Homer, G. M., and Keaton, C. M.: 1936, "Unproduc-
tiveness of certain orchard soils as related to lead arsenate spray
accumulations." Soil Sci., 42:203-215.
-------
415
References
Weinstock, B.: 1969, "Carbon monoxide: Residence time in the atmosphere."
Science, 166:224-225.
Westenberg, A. A. and de Haas, N.: 1972, "Steady-state intermediate
concentrations and rate constants. Some HOa results." J. Phys.
Chem., 76(11):1586-1595.
White, J. J.: 1932, "Carbon monoxide and its relation to aircraft."
U. S. Nav. Med. Bull., 30:151.
-------
416
The kind of preliminary quantitative modeling which has been
done so far is shown by the following three examples concerning
removal of SC>2 from the air at rock and ocean interfaces.
1.3.2. Rock: Living matter has a threshold limit of tolerance to
pollutants, below which no injury will occur, and, in fact, the
substance might actually benefit from the presence of that pollutant.
Rock reacts with pollutants such as SC>2, at all concentrations. The
results of these reactions may not be visible for quite some time,
for the effects are cumulative. The extent of breakdown of the rock
is therefore less a product of the momentary concentration of the
pollutant than the uptake per unit time on a unit area of the material
(Luckat, 1973).
The effects of 502 on frescoes, monuments and other edifices
have been most pronounced over the last century, especially in Europe
where high-sulfur coal and oil are used as heating fuels. The basic
destructive reaction is that of sulfuric acid (SC>2 + 1/2 C>2 + I^O-*
H^SO^) on the carbonate matrix of limestone and sandstone in the
presence of moisture. Spedding (1969) has shown that as the relative
humidity in the air increases, the S02 uptake rate by oolitic limestone
increases significantly (Table I) .
Table I. UPTAKE OF S00 BY OOLITIC LIMESTONE
Relative
Humidity
%
11
13
79
81
S02
concentration
yg/m3
360
280
100
370
Time of
exposure
min.
20
40
48
10
'Uptake
yg S02/cm2
of surface
0.069
0.061
0.24
0.28
Uptake
rate
yg/cm^'d
5.0
2.2
7.2
40.3
-------
417
The product of the reaction between sulfuric acid and the
carbonate matrix is gypsum if sufficient evaporation occurs:
f
CaC03 + H2S04 + H20 -»• CaSO^'2E20 + C02
Because the calcium carbonate is slowly being replaced by gypsum, the
rock would be subject to increased weathering rates due to:
(1) an enhanced chemical disintegration caused by the much
greater solubility of gypsum in water than calcium
carbonate. The newly formed mineral would be subject
to dissolution in water with accompanied leaching out
of the rock, and
(2) an enhanced physical disintegration caused by the almost
two-fold volume expansion in the rock accompanying the
formation of gypsum.
Other properties such as the density and porosity of the rock
are also important and affect the amount of weathering to be expected
in a rock per unit uptake rate; a rough, porous, lime-cemented
sandstone would be expected to weather faster than a smooth, dense
limestone (Luckat, 1973).
To determine wheather the absorption of S02 by sedimentary rocks
would constitute a significant sink for S02, a number of assumptions
were made:
(1) Knowing that approximately 30% of the total earth's surface
area of about 5 x 10-*-^ m^ was land (Holmes, 1965), and
assuming that perhaps 5% of the land surface had exposed
rock (F, E. Wickman, 1974), and of this approximately 75%
is sedimentary (Leet and Judson, 1965), it was calculated
that about 1% of the total earth's surface was covered
with rock capable of absorbing S02.
-------
418
(2) Luckat (1973) and Spedding (1969 ) found S02 absorption
rates ranging from 5-200 mg/m2«d in sandstone and limestone,
respectively. Luckat1s measurements were taken in a highly
industrialized region of Germany; Spedding's measurements
were made with S02 concentrations approximately 100 times
greater than the average world-wide background concentration.
For this calculation, the lower limit of 5 mg/m2-d was used.
From these values it was calculated that approximately 9 x 10^ kg
or 4.5 x 10^ kg S/yr could be removed by stone under these
optimal and exaggerated conditions. Comparison of this value with
those in Table IV of the paper included earlier in this report shows
this value to be considerably smaller than that of any other natural
S02 sink.
There are many problems related with making any such estimate as
was done above. First of all, any estimate of the total percentage
of the earth's surface which has exposed rock is entirely speculative
at this time because geological maps are not available for all parts
of the world. Then again, there is the problem of defining an outcrop
and mapping it in its strictest sense; that is, mapping the outcrop
without magnification and without the inclusion of soils or detritus
as part of the outcrop. There is also the fact that not all the
sedimentary rock that is exposed is sandstone or limestone; much of
it is shale or mudstone or something of similar density which would
probably not absorb S02 to any extent. Finally, the areas where most
of the rock does outcrop would be in areas where the 862 level would
probably be quite low. It can therefore be assumed that rock constitutes
a negligible sink for S02 on a global scale.
-------
419
1.3_3. jto Solubility; Most data on SO,, solubility in the literature
have been determined when atmospheric S02 concentrations in the
experimental chambers far exceeded those found in ambient air. Hales
and Sutter (1973) worked towards closing this obvious gap by running
a number of experiments to help "quantify the relationships between
S02 solubility, concentration, and hydrogen-ion impurity at levels
normally encountered in nature." The dissolution of SC>2 was assumed
to proceed according to the reactions set forth by Falk and Giguere (1958) :
S02 + H20 £ S02 + H20
g aq
S02 + 2H20 J H30+ + HS05 (2)
aq
H20 J H30+ + S0§~ (3)
The second ionization (reaction 3) was assumed to be negligible.
Based upon the first two of the above reactions, Hales and Sutter
derived an "extrapolation equation, relating the concentration of total
dissolved S00 in water (C,,,. ) to airborne concentration and solution
L bUo
acidity" as follows:
CS02 =
= [S02]g -[H3°+]ex +
H 2
where those terms bracketed are concentrations in moles per liter and
[H30+]ex is the "excess" hydrogen ion concentration, defined as the
concentration of hydrogren ion in solution present due to sources other
-------
420
than the dissolving of S02. K-. is the equilibrium constant for
reaction (2) and H is the Henry's law constant. Extrapolation of 862
solubility data from Johnstone and Leppla (1934) down to low ambient
S02 concentrations show deviations ranging from 0.7 to 21.2% of those
by Hales and Sutter. In general, the percent deviation increased
as the concentration of S02 in the gas phase decreased. The authors
suggest that even though this deviation does exist, the ability of
equation (4) to predict low SC>2 concentration solubility appears
excellent and they recommend its use whenever low concentration solubility
data are needed.
A more exact equation for determining the total dissolved S02 in
water can be derived based on the solution equilibria involved. The
resulting equation not only takes into consideration the pH of the
solution and the atmospheric partial pressure of the gas, POQ , but applies
2
to different aqueous phase conditions, including both sea water and
rain water. Also, it eliminates the use of the often confusing and
now outdated hydronium ion (HoO+). The dissolution and dissociation
reactions for S02 in water are more correctly written (Scott and
McCarthy, 1967)
S00 + H90 £ S09-H90 (5)
£, <£ & L.
S02-H20 J H+ + HSO^ (6)
H+ +S0 (7)
-------
421
In the equations which follow the activity, a, of the aqueous
species is denoted by brackets [ ] . The activity and the molality of
a species are related by the activity coefficient, a = my. In dilute
solutions the molality (moles/lOOOg 1^0) of a species is approximately
equal to its molarity (moles/£ H~0) . Rigorously the activity is
dimensionless but for calculational purposes it may be taken to have
the dimensions of molality or molarity with the activity coefficient
being dimensionless.
Johnstone and Leppla (1934) and Scott (1964) show that reaction (5)
follows Henry's law for dilute solutions up to concentrations of at
least one molar. Thus,
[S02-H20]
H = - - (8)
so2
where [SO 'H...O] is the activity of solvated sulfur dioxide and PQ_ is
L 2. oU«
the SO,, partial pressure in atmospheres. The defining equations for
the ionization constants are:
[H+] (9)
[S02-H20]
(10)
-------
422
Using equations (8), (9), and (10), a molal mass balance for the
system can be written
EmSO = mso + "nqn- + m^n=
ou. ? nbU» oO_
aq
wherein,
Hpso2
"s\q" ^r
CtU ^
aq
Kl H PSO
X U2 and (13)
K» KI H ?„
= 1 °2 (14)
Substituting the values for the molality for each of these species
into equation (11), the following general formula for the concentration
of dissolved SOo is derived:
-------
423
aq
The definition of pH is
pH = -log [H+]
Therefore, by convention, in equations the activity of the hydrogen ion
can be written [H ] = 10 " as desired.
For use in predicting SO solubility, equation (15) requires values
for H, KI, K? and the three activity coefficients in addition to the
pH and the SO partial pressure. Scott and Hobbs (1967) give H = 1.24,
o
K., = 0.0127, and K = 6.24 x 10 at 25°C. Corresponding data at other
temperatures are given by Johnstone and Leppla (1934). One case of
considerable interest is the absorption of S0« in sea water. Activity
coefficients of aqueous sulfite species, SO-'H?0, HSO,, and S0~ in sea
water are not available. However, Reardon (1974) determined activity
coefficients for the analogous carbonate species and a]so sulfate ion in
sea water. From a point of view of similarity of species and coherence among
the variables, the sulfate activity coefficient is rejected in favor of
use of the carbonate species activity coefficients. Hence,
- vr1-19
aq
- = °:67
-------
424
By substituting these values into equation (15) , and assuming that sea
water has a pH of 8.1, equation (15) reduces to
where the amount of dissolved S02 is seen to be a linear function of tlv_
atmospheric partial pressure of SO,,.
The minimum background concentration of S07 is 1 yg/nf which
1 /"*
corresponds to 3.3 x 10 atmospheres SO partial pressure. Fron
equation (16) the amount of S0? dissolved in sea water at equilibrium
_2
would be 3.2 x 10 mo]/£. As an upper limit one might consider ambienL
S09 concentrations found by Luckat (1973) in highly industrialized
sections of Germany. The observed 360 yg/m is equivalent to P =
-7 2
1.4 x 10 atm. In equilibrium with such an atmosphere sea water
would absorb 11.6 mol S09/Jl. This molarity is an order of magnitude highc:
than that where Henry's law is known to hold. Thus, the predictive
equation might fail under these circumstances.
When the dissolution of S0« takes place in rain water, the activity-
coefficients required for equation (15) may be assumed equal to unity
because the ionic strength of rain water (a measure of the interionic
effect resulting primarily from electrical attraction and repulsions
between the various ions) would be very low, probably on the order of
10" . Therefore, equation (15) 7-educes to
_ 9 -in
(, ., 1.58 x 10 9,83 x 10 \
"SO, - V (^ ' — l^p— ) (17,
-------
425
In this case the hydrogen ion activity is dependent upon the amount
of SO absorbed and cannot be specified a priori. The charge balance
for the dissolution and dissociation reactions of S02 in water is
[H] = [HSO~] + 2[SO] + [OH"]
By substituting in the respective expressions for the [HSO ] and [S0_]
J «5
as given by equations (8, 9, and 10), and setting [OH~] = ICf /[H+],
an expression is derived for the partial pressure of SO,, as a function of
[H ] as follows:
P [H+]3 - IP"14 [H+]
PSO = ^2—* ^9 (18)
U2 1.58 x 10 [H'] + 1,97 x 10
Choosing an initial value for the [H ], and substituting that value
into equation (18)»a corresponding value for Pcn (atm) cen be found.
2
These values for ?„,, and [H ] are then in turn substituted into
O VJ rt
equation (17) ^o find the amount of total dissolved S0~,
In pure rain water the pH is 7.0. Any SO which dissolves would
produce an acid solution and a drop in pH. Thus, for pH = 7, Pcn =
bU2
Em = 0, For a pH of 5, Pcn and 2mc are calculated to be 6.3 x 10
oU« oU_ oU—
atm and 1.0 x 10*" mo I/'A, respectively. For a pH of 3, P = 6.35 x
bu
-5 -3
10 atm and £mc_ = 1.1 x 10 mol/£. Clearly as Pcn increases, the
so2 so2
amount of dissolved S0_ increases and the pH decreases. The dissolved
£*
S0? predicted by equations (17) and (18) agree excellently with the
experimental data of Hales and Sutter (1973) and Terraglio and
Manganelli (1967),
-------
426
1.3.4. Rate of SO^ absorption by sea water; The solubility of SCL in
sea water as discussed in the preceding paragraphs is only the
equilibrium limit of the absorption process. It is much more complex to
quantitatively model the rate of absorption. A parameter commonly used
in such quantification is the deposition velocity. Kabel (1973) showed
the relation between the deposition velocity, v_, and the mass transfer
coefficient, k . He showed how a simple extension of the Reynolds
o
analogy could be used with a boundary layer characterization of the
fluid mechanics to predict the deposition velocity for ammonia
absorption. The following example illustrates a somewhat different
approach which is carried through to the determination of the distance
polluted air must travel over the ocean to have a specified proportion
of the S09 removed. It should be kept in mind in following this example
that many alternative models and assumptions are possible.
For correlation of mass and momentum transfer , Perry, et. al.
(1963) give
(19)
where f is the friction factor, v is the average velocity, p is the
inert component mass density, and Sc is the Schmidt number. For flat
surfaces the friction factor can be estimated from various correla-
tions (Schlichting, 1968; Sherwood, 1950; Schnautz, 1958). However,
perhaps the most promising and applicable route to the friction factor
-------
427
is via models which predict wind velocity profiles over various sur-
faces. One such well established model, for an adiabatic lapse rate,
is (Pasquill, 1962)
Z = lnl- (20)
v* k zo
where VA is the friction or shear velocity, v the wind velocity at
height z, and z0 is a roughness length characteristic of the ground
surface (for smooth sea Schnautz (1958) gives z0 - 2 x 10 ** m).
Von Karman's constant k is taken to be 0.4. The friction velocity
is related to the ground level shear stress, T0, by (Sutton, 1949)
The friction velocity can be obtained from equation (20) by measuring
the velocity vi at height za. With v^ known, equation (20) provides
the velocity profile which can be integrated over the range of height,
z=0 to z=H, to give the average velocity as
- 'nvdz 'n^ln- ^
v = J2 = -^ ^— (22)
/«dz
Knowing v the friction factor can be obtained from equation (21) and
equation (19) can be solved directly for k_.
-------
428
The removal of SO- from air, Sc=1.28 at 0°C, 1 atm (McCabe and
Smith, 1967), over a natural surface such as sea water can now be
estimated. For the case of v. = 5m/s at z = 2m, v. is found to be
i i *
0.216 m/s and v (up to an inversion height of 100 m) = 6.6 m/s.
Scorer (1968) discusses inversion heights for a variety of cases.
The friction factor is then 0.00228 and kn is 7.53 g/m2s. For a
(j
very small equilibrium vapor pressure of S02 over sea water, the
deposition velocity can be calculated from the mass transfer coeffi-
cient by dividing k by the air density, hence v =k /p . =0.64
Cr D (j air
cm/s. This result is comparable in magnitude to literature values.
Now one can crudely estimate the effects of this removal mech-
anism downstream of a line source of the pollutant. Neglecting end
effects and assuming that all fluid motion is between ground level
and an inversion height of 100 m and that the logarithmic velocity
profile is adequate, the rate of mass transfer per unit length of
source can be expressed by a mass balance about an element of height,
H, and thickness, dx, as
HvdC = v Cdx (23)
where x is the distance downwind of the line source. The boundary
condition is C(x=0) = CQ. Solving equation (23) leads to
V X fi
In £i*l = _5_ = 9.65 x 10~ x (24)
C0 vH
-------
429
From equation (24) one can calculate that 90 and 99% of the SO- would
be removed at downstream distances of 238 and 476 km, respectively.
It might be noted that the height H strongly affects the distance
required to remove a fixed proportion of the pollutant; however, values
of v, f, v , etc. are little changed.
The foregoing analysis is based on several simplifying assump-
tions. First, it is assumed that the logarithmic velocity profile is
valid. This assumes that an adiabatic lapse rate exists, an assump-
tion inconsistent with those used in the calculation of concentration
downwind of a line source under an inversion. Note that the complete
air pollution meteorology model should provide a velocity profile and
this contradiction will not occur.
To allow for the fact that the zero velocity may occur at a point
other than the actual earth interface, this equation can be modified.
For example, z can be replaced by z+d0 where d0 is a displacement
factor to designate the point of zero velocity. However, for trans-
fer to sea water do« z. There is also some uncertainty in the
estimate of the roughness length over water. It is also assumed that
the velocity profile is unchanged downwind of the source.
Another assumption made is that the Reynolds analogy holds and
that the molecular dispersion of pollutants is negligible. It was
further assumed that the equilibrium vapor pressure of the pollutant
at the ocean interface is very small at all times (i.e. the sea is a
perfect sink). This restriction is readily removed by use of the SO-
solubility correlation presented earlier. And the S02 concentration
-------
430
is taken to be uniform in the vertical direction. In the line source
calculation, the assumption was made that all unabsorbed pollutant
was held between the sea and the arbitrarily chosen inversion height.
Many of these assumptions are arbitrary and can be varied at will.
It is possible to approach the problem of mass transfer at the
interface differently. One could deal with dispersion coefficients
instead of mass transfer coefficients. In this case the rate of
removal would be expressed in terms of the dispersion coefficient
and concentration gradients. The dispersion coefficient can be ob-
tained from the velocity profile information. Such an approach will
be considered in further work.
-------
431
REFERENCES
Falk, M. and P. A. Giguere. "On the nature of sulfurous acid."
Can. J. Chem. , _36_:1121 (1958).
Hales, J. M. and S. L. Sutter. "Solubility of sulfur dioxide in
water at low concentrations." Atmos. Environ., ^:997-1001 (1973).
Holmes, A. Principles of Physical Geology. Ronald Press Co. , New
York, 1288 pp, 1965.
Johnstone, H. F. and P. W. Leppla. "The solubility of sulfur dioxide
at low partial pressures." J. Am. Chem. Soc.. J56_: 2233-2238 (1934),
Kabel, R. L. "Atmospheric Removal Processes for Air Pollutants (Task
III)," First Annual Report to the Meteorology Laboratory of the
U. S. Environmental Protection Agency, Grant R-800397, 1973.
Leet, L. D. and S. Judson. Physical Geology, 3rd edition, Prentice-
Hall, Englewood Cliffs, New Jersey, 406 pp, 1965.
Luckat, S. "Die Wirkung von Luftverunreinigungen beim Steinzerfall."
Staub-Reinhalt. Luft, 33(7):283-285 (1973).
McCabe, W. L, and J. C. Smith. Unit Operations of Chemical Engineer-
ing, 2nd edition, p. 990, McGraw-Hill Book Co., New York, 1967.
Pasquill, F. Atmospheric Diffusion, p. 71, D. van Nostrand Co., Ltd.,
New York, 1962.
Perry, R. H., C. H. Chilton, and S. D. Kirkpatrick. Chemical Engineers'
Handbook, 4th edition, p. 14-15, McGraw-Hill Book Co., New York,
1963.
Rasmussen, K. H., M. Taheri, and R. L. Kabel. "Sources and natural
removal processes for some atmospheric pollutants," Environ-
mental Protection Agency Grant Report No. EPA-650/4-74-032, 121
pp, 1974.
Reardon, E. Thermodynamic properties of some sulfate, carbonate and
bicarbonate ion pairs, Dept. of Geosciences, The Pennsylvania
State University, unpublished Ph.D. Thesis, 1974.
Schlichting, H. Boundary Layer Theory, p. 599, McGraw-Hill Book Co.,
New York, 1968.
Schnautz, J. A. Effect of Turbulence Intensity on Mass Transfer from
Plates, Cylinders, and Spheres in Air Streams, Ph.D. Thesis,
Oregon State College, Corvallis, Oregon, 1958.
-------
432
Scorer, R. Air Pollution, ch. 3 and 4, Pergamon Press, New York, 1968.
Scott, W. D. Ph.D. Thesis, University of Washington, Seattle, Wash-
ington, 1964.
Scott, W. D. and P. V. Hobbs. "The formation of sulphate in water
droplets." J. Atmos. Sci., J24:54-57 (1967).
Scott, W. D. and J. L. McCarthy. "The system sulfur dioxide-ammonia-
water at 25°C." Ind. Eng. Chem. Fundam.. 6^:40-48 (1967).
Sherwood, T. K. Ind. Eng. Chem.. _42:2077-2083 (1950).
Spedding, D. J. "SO- uptake by limestone." Atmos. Environ., J3:683
(1969).
Sutton, 0. G. Atmospheric Turbulence, p. 103, Methuen & Co., Ltd.,
London, 1949.
Terraglio, F. P. and R. M. Manganelli. "The absorption of atmos-
pheric sulfur dioxide by water solutions." J. Air Poll. Control
Assoc., 17:403-406 (1967).
Wickman, F. E. personal communication, May 8, 1974.
-------
433
V OBSERVING SYSTEMS FOR URBAN AND REGIONAL ENVIRONMENTS
Part 1
INTERPRETATION OF ACDAR SOUNDING OBSERVATIONS
-------
434
OBSERVING SYSTEMS FOR URBAN AND REGIONAL ENVIRONMENTS
Preface
,•
Measurements-oriented research activities within the SRG are
included in both the Department of Meteorology (DM) and Center for Air
Environment Studies (CAES). Within the DM, studies are concentrated
in two specific problem areas. They are, as defined in the scope of
work in the original SRG propsal (18.1.72), to:
a) Task ID
"Perform studies relating to the comparative applicability
of various remote sensing instrumentation systems for
economically providing the data required for evaluating and
applying numerical air pollution simulation models".
and
b) Task 4
"Modify the PSU aircraft for use in air pollution field
measurements needed for providing initial conditions for numerical
models and for verifying them. Particular emphasis will be placed
on the installation and testing of equipment for gaseous and
particulate air pollution sampling."
For air pollution and urban-to-mesoscale meteorology related measure-
ments, acdar and lidar systems continue to yield some of the most dramatic
and useful observations of atmospheric structure and dynamics, and aerosol,
respectively. The wider (and more quantitative) application of acdar systems
depends upon "theoretical-physical" research regarding techniques for
processing and interpreting the received acdar signals. This has been the
focus of research conducted by members of Task Group ID.
-------
435
In particular, the research to date has been concerned with numerical
simulation of received signals and analysis of the capabilities and limita-
tions of acdar systems (of many different configurations) for tropospheric
temperature, wind profile and turbulence measurements. To the extent
required for checking theoretical work in progress, experimental acdar
systems have been developed and used in field measurements at Penn State.
Rather than undertake theoretical studies, such .as that of the well
known "inversion" problem regarding the interpretation of lidar data,
we noted the lack of suitable airborne systems for obtaining direct
measurements of atmospheric aerosol at heights greater than those of
instrumented towers. Consequently, the research effort related to the
evaluation of lidar systems has for all practical purposes been integrated
into Task 4. That is, we have undertaken and have, now, nearly completed
the development of a comprehensive airborne instrumentation package capable
of obtaining direct aerosol measurements in the regions probed by existing
lidar systems. Thus, during cooperative aircraft-lidar experiments, we have
a unique capability for obtaining data for direct-indirect intercomparison
studies.
Under the auspices of the SRG grant, in Task Group 4 we have
developed, and used for a variety of experiments, what is probably the
most comprehensive university-based airborne meteorological and aerosol
instrumentation system in the world. A complement of nearly 40 individual
sensors and instruments output data from which diverse meteorological,
turbulence, aerosol, and radiation quantities are derived. Extraordinary
-------
436
care has been taken in, for example, designing and fabricating the
isokinetic sampling tube and radiometer mounts to insure that data will
be non-biased and have the highest possible signal/noise ratio.
Only recently completed, the reconfigured aircraft has not only
been extensively used for individual SRG in-house research studies,
but also been flown more than 100 hours in conjunction with other EPA
measurement programs in the St. Louis Regional Air Pollution Study (RAPS)
The following pages summarize some of the individual efforts which
have contributed to the overall progress made by Task Groups ID and 4.
-------
437
1.0 TASK ID-INTERPRETATION OF ACDAR SOUNDING OBSERVATIONS
1.1 Introduction
A propagating pulse of acoustic energy emitted by an acdar trans-
mitter is refracted by "average" spatial gradients of temperature and
wind and scattered by local turbulent velocity and temperature fluctua-
tions. One may choose to measure the received power, P(r), as a
function of range which may be related to the acoustic refractive index
2 2
structure functions, CL, and C or the signal Doppler shift f, which
may be related to mean and turbulent atmospheric motions.
In their fundamental form the defining equations appear deceptively
simple.
A A (• Scat. _ r Rec.
P(r) = P -f- -£ L • e a(r) dr • B(0,r) • e a(r) dr (1)
° \ RZ V J Trans. J Scat.
where P = peak transmitted power
A = area common to transmitter and receiver beams
c
A,^ = area of transmit antenna
A = area of receiver antenna
r
R = range along L
L = length of scattering volume to space
a(r) = extinction coefficient
B(Q,r) a scattering angle dependent volume scatter coefficient
-------
438
The Doppler spectrum S(f) is given by
S(f) df = G(a,4>) W() da (2)
where G(a,cj>) is related to the distribution of energy within the antenna
beams and the antenna pointing angle, and W(cj>) is the scattering angle
dependent volume scatter coefficient, B(0,r), expressed in terms of the
antenna pointing angle. But in practice quantitative evaluation of the
equations is difficult due to the complicated terms which are used to
parameterize the system geometry and atmospheric conditions. Furthermore,
it is clearly quite a different problem to evaluate P(r) given all the terms
on the right hand side of equation (1) than a(r).
and 3(0,r) given a series of P(r) measurements. Precise determination
of atmospheric motions is also difficult since the observed Doppler
spectrum depends upon the integral of combined atmospheric and system
dependent functions.
Clearly, if acdar systems are ever to be used on an operational
basis for inputing, for example, vector wind and intensity of turbulence
as a function of height data into a running regional or urban-scale
predictive model, schemes for objectively, and automatically, processing
the return signals will be essential. The data reduction procedure
currently used by most acdar research groups involves post-experiment
subjective-objective evaluation of vertical time sections generated using
a facsimile to identify structural features and, if Doppler data is
available, analysis of computed spectra to estimate winds.
-------
439
It is our (Task Group ID) thesis that if we can precisely define the
acdar "system" functions for any specified operating sounder, and
adequately model the refraction and scattering of acdar signals in the
atmosphere, many experiments which are critical to improving our under-
standing of acdar measurements can be performed using a numerical
simulator in which the system parameters and the atmospheric conditions
(the independent variables) can be precisely controlled.
Thus, one aspect of the theoretical work in the group consists,
basically, of the analysis of the acdar and Doppler equations. The magnitude
of the power and the characteristics of the Doppler spectrum as a function
of range as they depend upon both the properties of the sounding system and
the highly variable physical state of the atmosphere are being quantitatively
dissected and modeled.
A second area of theoretical study concerns the analysis of refractive
propagation of sound in surface-based and elevated temperature inversions.
When such inversions exist it is, at least theoretically, possible to infer
the temperature gradient up to the top of the inversion by using sound
refractively propagated over an - 3 to 20 km path. We are presently
attempting to establish, using our own field measurements, the utility of
the technique.
In general, experimental work by the group has been limited to that
minimally necessary to check the theoretical work in progress. One section
of this report summarizes field measurements currently underway.
-------
440
The last section consists of copies of two papers submitted by
members of the group to the Journal of Geophysics Research during
the past year. Both papers have been accepted for publication, presumably
in late 1974.
-------
441
2.0 ANALYSIS OF DOPPLER-SHIFTED MONOSTATIC ACDAR SIGNALS
R. L. Coulter, Ph.D. Research in Progress
2.1 System Geometry
In any monostatic indirect sensing system, the basic geometry is
as described in Fig. (1), where = elevation angle, 3 = azimuth angle
and R = distance from the transmitter-receiver to the target.
Generally, a target will have motion along all three perpendicular
axes, but for a monostatic system and Doppler frequency shift consid-
erations, the only velocity that really matters is the radial velocity,
i.e.
Vr>= v Sin 3 Cos - v Cos 3 Cos - v Sin
R x y z
But
Sin 3 = —-zr—r , Cos g = =-% -r ; Sin a = f
R Cos <(> R Cos <{> R
Thus
xv + yv + z vr
R R
where the coordinates of the scatterer are (x,y,z).
To a high degree of accuracy, the Doppler shift due to a scatterer
in motion is given by
-------
442
X
UJ
Q
UJ
co
CO
UJ
o
CO
<
CO
Q
Z
UJ
H-
co
>
CO
UJ
I-
<
Z
o
QC
o
O
O
O
tr
i-
co
UJ
(E
-------
443
-2V
f = R 2 ,
D —7— = - -r—- (xv + y v + z v )
X X R x J y z
xv +yv + z v
/ 2 , 2 -L. 2.1/2
(x + y + z )
If there is an integer number of wavelengths between transmitter
and target, we can determine the equiphase geometry by
2R = nX 3>4(x2 + y2 + z2) = (nX)2
, 2 2 . 2 nX.2
(x + y + z = (y-)
i.e., the equiphase surfaces, disregarding phase velocity changes
with wind speed and/or temperature structure are a series of concentric
spheres of radius -r- .
The normal to the equiphase surfaces in the y-z plane is given by
z/y, i.e., any st. line from the center through a point is the normal. Thus,
when the wind is along the normal, we have a maximum doppler shift:
v
z _ z^
v y
y
seen in the x-y plane as
v
v x
X
and in the x-z plane as
-------
444
v
X X
V Z
z
2.2 Surfaces of Constant Doppler Shift
In order to evaluate the spectral broadening due to different
scatterers within a transmitted beam, a weighting function must be devised
which accounts for different scatterers producing the same Doppler shift.
Thus, in order to determine this weighting, we must determine the surfaces
in space with constant Doppler shift (CODOSS).
First, assume v = 0 = v and we are at z = 0, looking at the x-y
y z
plane. In this case, for f = constant we have
2x v 2v
x
D A R X , 2 . 2.1/2
(x + y )
2 + 2 4 Vx 2
x +y = -—x
and
*°±y(, \ >1/2^±f; *2^<^>2-i
•x. _ D
X fD
i.e., at z = 0 we have straight lines of slope — = — (Fig. 2).
Of course z = 0 is not of interest, so we set z = z . Now:
2x v
f =-
D , , 2 , 2 2.1/2
X(x + y + z )
-------
445
(OllO
-I& roco
o -Yi
n
N _
o
n
CM
O
|00
II
UJ
X
V)
z
o
o
V)
UJ
CM
UJ
tr
-------
446
2.2. 2 4 Vx 2 2 y2 Zo
X + y + Zo = TTTT x * x 2 + ~
X f a a
or
22 2
3 X
2 2
z z
o o
which is the equation for a hyperbola of asymptote x = + ^ and inter-
— a
z
section with the x axis (y = 0) at x = + —- (Fig. 3).
3.
Thus, when J»z we tend to straight lines, and when y > z the surfaces
at a height z are sharply curved. In three dimensions, this appears as in
Fig. 4 for a given f , A, and v = v =0.
Similar results hold for v = v = 0 and v = v =0, except that
x z y x
the hyperbolas are rotated 90 degrees. That is, when there is vertical
motion only, the hyperbolas are around the vertical axis with asymptote
z = H . At a constant z = z with vertical motion only we have
a o J
2 x2 y2 2 2 vz 2
z = —;r + -^r- where now a = (T—-=—') - 1
o 2 / A r
a a D
i.e., in the x,y plane we have a circle of radius a z . (Fig. 5)
When v and v are both non-zero, the same hyperbolas are obtained
x y
by rotating the axes through an angle
_1 v
0 = Tan -2-
v
x
-------
447
co
o
CD
IE
UJ
0.
> CO
X
UJ CO
Z CO
_l
CO
o <
II CO
N UJ
to
UJ
cr
:D
o
u.
N
3-
-------
448
(ft
or
LU
_l
o.
Q.
O
Q
V)
z
o
(J
U.
O
LU
Z
U.
o
z
o
E 3:
z
1 ^
W Q-
z d
LU
LU
IT
3
O
-------
449
-------
450
And, if v ^ 0, after rotating through 0, rotating through a vertical
-1 Vz
angle, to the horizontal. (Appendix I)
2.3 Horizontal Wind
For simplicity, align the x axis with the horizontal wind. As shown
above, no generality is lost. First, consider a transmitter-receiver
pointing vertically (Fig. 6). Since the x intercept at any height x is
given by x = + z/a (the minus sign applicable to the negative shifts which
are symmetric in this case to the positive ones), the straight lines (in
the y = 0 plane) x = z/a determine the closest point at any height z that
any given CODOSS comes to the axis of the transmit beam. We can, therefore,
determine the maximum and minimum shift for this situation simply by setting
this slope equal to the slope of the edge of the conical beam
= a = etna (a= beam width)
dx ,.
surface
,2 „
V - 1 = ctn a
f = (___) = |v 1 ,1/2 = |v
max A .... 2 A 2 A
1 + ctn a cos 1
mm 0" T j.
sin '
which is precisely what is to be expected from a scatterer at the edge of
the beam and moving horizontally toward the axis.
-------
451
§1
uj o —
w a. is
tr
5>i
°V x
K°t
Q. Q OC
O W Uj
O O
-11
UJ
cc
-------
452
CJ
z
o
M
tr
o
Si
UJ
tr
LU
S|
cr <
CO
UJ
-------
453
Now point the antenna horizontally (or, have a vertical wind only)
(Fig. 6A). At any given value of x, the CODOSS is the edge of a circle
given by
2 . 2 22
y + z = a x
Thus, setting the radius equal to the beam edge
ax = x Tan a
4 v 2
= 1 + Tan a
2v
= + -r— Cos a
— A
where now the plus or minus refers to the beam pointed into the wind
or with it, i.e., if we are pointing into the wind, the minimum f is
rt
T — Cos a while the maximum is given by ax = 0,
A
A f
When the transmitter is pointed between 0 and 90° with respect
to the horizontal wind, analysis is not quite so simple. Assume the
transmitter has a boresight at an angle with respect to the horizonta
wind axis (x axis). Now, as in Figure (7), we change our coordinate
-------
454
\
o
M
I UJ
I
CE H
O
H- Z
UJ
UJ *
h- h-
cn uj
>- m co
CO UJ
tr x
UJ UJ *t
h- Q
< Z _|
? 2 <
Q O H
cr OT z
o o
O O N
O Z £
^<1
2°
£ z Q
tc — z
Q. S <
h-
UJ
-------
455
system such that the x' axis points along the boresight of the transmitter-
receiver and the x' axis is perpendicular to the boresight, i.e., we
TT
rotate about the y axis by an angle - -x-.
The horizontal wind (u) can be broken up into components u , = u cos <}>
z
and u , = u Sin 4>, and there will be two'contributions to the Doppler
spectrum, one arising from u , (denoted parallel) and another from u
Z X
(denoted perpendicular)
Parallel
The parallel contribution is due to that component parallel to the beam axis
and it leads as before to hyperbolas about the z1 axis (along the beam)
governed by
2 ,2 ,2 ,2
z - y = x
o
where now
,2 29
2 _ uz' _ 4 u Cos
a" ~ ~~2 2" 22 ~
f A f AZ
Just as with the horizontally pointing beam, then, the minimum values
of f are determined by the value of a..., such that the asymptote matches the
edge of the beam, i.e.,
x1 x'
= z' = -—;—. a = Tan (a)
a(( Tan (a)
-------
456
f . = T— Cos d) Cos a
mm A. r
f = T— Cos
max A
22 2 2
Perpendicular (ax x1 - y1 = z' )
For this component we have the vertically pointing sounder with
horizontal wind. The maximum and minimum frequencies are determined
by the intersection point (y = 0) of the hyperbola at a given distance
,2
z' Tan a = —
i, = ctn a -> f = H Sin <|> Sin a
1 ~ A
u _. 2 , -
^ Sin cp-1
In order to calculate the spectrum, the total area of each CODOSS
within the volume bounded by the transmitter beam and the instantaneous
scattering length along the beam axis (i.e., Lnst. scattering length
V T
,v = speed of sound, T = pulse length (sec.)) must be found.
At a given range (z1 in the rotated coordinate system) the parallel
component is determined by
2 ,2 ,2 2
a,, z1 - x' = y
or
,2^2 2,2
x' + y = a|( z'
-------
457
which, at any given range z' is a circle; and within the whole volume,
is the surface of a truncated rt. circular cone with apex at the
coordinate origin (i.e. radius -> 0 as z' ->• 0) , not including the area of
the base.
So the length of the line at distance z' is S = 2fra z' and the
surface area is given by
A = | Sdl = |S r dz'
dl = 1 = 1 = rx_x ,a/2 , 21/2
dz Cos Y , ,. 2 . ,2,1/2 ^ 2J ' n U'1 ;
z / (x + z ) _., z y=0
.Z2
I 2 1/2 2 1/2 2 2
-> A = 2ir -> aM z(al( +1) dz = IT a,, (au + 1) (z - z1 )
Zl
but
z2-zi = f=¥; A = i£a (a
9 1/2
a,, (a
,
where z is the middle of the volume.
m
This weighting factor would be the only areal one for the case of a
vertically pointing antenna with a vertical velocity alone. Given a Doppler
shift, a is specified and, thus, so is the weighting function in an atmosphere
with no horizontal wind and no change of vertical velocity with height.
This is, without a doubt, oversimplified, but at least provides a starting
point .
-------
458
In the case of a., things are not so simple. The problem is to
determine the length of the hyperbola within a circle of a given radius
(Fig. 8), i.e., the hyperbola intersects the circle at points determined
2 _,_ 2 2^2
x + y - z Tan a
and
222 2
^ x - y = z
combining
x2 = z2 (1 + Tan2 a)/(I + ax2)
Thus, there are two intersection values of x, corresponding to f
greater than, or less than, zero. And for each value of x,
2 2 2 2,T 2 (1+Tan2 a), 2 / + a± Tan a,
y = r - x = z (Tan a - -) = z ( — )
(1 f a/) 1 + a/
The length of the line is twice the length of the line from
22 2
x1(y = 0) to x? = z (1 + Tan a)/(I + aL ). At any point, the
infinitesimal length of the line is
ds = (1 + Or*-)''")"1'''" dx where y = a. x - z
„ , _ 2 , dy 2x 2 x
9.y dy = 2aL xdx; ^ = a^ - - ax —^ 2-^72
x -
-------
459
CO
CD
o
cr uj
UJ O
a. z
UJ
z
UJ
cr
UJ
Pjjjt
00 z 5
o co
O nT
UJ
UJ
cr
UJ
co
X _
UJ O
cr
UJ UJ
o!e
CE m
"S£
Q o: uj
-------
460
LU
UJ
O 3
QC O
O
CO
UJ
z
o
03 K-
Q: i
LiJ O
CO
UJ
X <
o
u or
CC <
-J UJ
< Q
u
CD
ID
CO C3 -I
:D z -i
.j - <
.j co 5
— ^ to
-------
461
0 42
2 ax x ,
S = 2 (1 + —5—0 o-) dx
t £- £• £- •.
, (aA x - z )
z /aj. o
Rather than attempt this integral, it is easier (and perhaps
more instructive) to try and approximate the hyperbola by a straight
line, noting that the asymptote x1 = + — y has a slope
-
dx
which has a minimum value ctn a (i.e, at x ~ r). Even if a were as large
as 15°, ctn a ~3.7 which is quite large and thus the hyperbola itself, even
though it has slope changing from °° to 4, hasn't curved much by the time
it reaches the edge of the circle. More precisely, compare the value of
x and x '•
,1 + Tan2 aq/2 _ _ „ 2
^.; x,? = z( - - - ) ; Def. Tan a = w
2
w 3 w w , Z/T 1/1 rr,2
2+7^-8---^ "•> ~I4.(1- 2 (— - Tan
8aj_ 4aj. *• aL
-------
462
zl ? X2 X1 ~ 1 1 2
£j /-L m^p\ &• J.J-/J. m *" \
C2 - VST (~: -Tan a) " —r—= 2 (~2 -Tan a)
aju2 aj.
and, percentagewise, x2 - x.. is quite small.
There are two approximations to straight lines available; one uses
the length between x~ and x ; the other the length of the line
perpendicular to the x axis at z /a and intersecting the circle at
2 2.2
y = r - z /a .
It can be shown that the first approximation yields
S. = ((x, - x,)2 -1- y -, - 2
1 2 1 2 (1 + a/)
- (— - aA Tan2 a)2 + a/ Tan2 a + 1} 1/2
The second, obviously is
.2 . __2Nl/2 /rn 2
S2 = ((x2 - X;L) + y) = y = z(Tan a
Either case is easily integrated
Z2 22
A 9 f c dl ^ 9Q n + ! ^1/2 ^2 Z;L
A = 21 S — dz = 2S (1 + —2) (^ 2"
z &i
Z
1 1/2 1 1/2
i.e., ^ = Hzm (1 +-^2) (Tan2 a - -^) '
-------
463
11 9999
zm (-^~ (— - a. Tan a) + aA Tan a +
IQ . £, 3. *
Using A we can summarize
2 1/2
A,, = TT&Z a „ (a,, + 1) ; 0 < a,, < Tan a
—
A = &z_ (1 + -^r'" (Tan2 a) - -^)*'fc; ctn a < * - < °°
where
2 4u2 Cos2 4> . 2 4u2 Sin2
ai, = —^—^ - -1; ai. = —
X2
Ajy is a maximum when a ,j is a maximum, namely Tan a. A. is a maximum
when aa is 00. The ratio of the maxima then is
£z Tan a
m _ Cos a
A,/ 7f£z
m Cos a
i.e., not including antenna weighting, the contribution at = 45° due
to the areal weighting o£ the parallel component has a peak about 3 times
as great as that from the perpendicular. The — factor is due to the ratio
of the circumference of a circle to the diameter and the Cos a is due to the
parallel contribution integration at maximum being along the outside surface
of the cone while the perpendicular is along the axis (i.e., at an angle of a
to the parallel integration).
-------
464
The frequency range of the two contributions is not, in most
cases, coincident. In the perpendicular case, the max and min are given
by
f\
f= + - Sin Sin a
while in the parallel case they are
f .. = T— Cos
II max X
r\
f,, . = T— Cos d) Cos a
" mm A
Thuss for overlap
Cos Cos a < Sin > ctn a
Tan cj> > Tan (y - a) •* (f) > j - a
which would require ~ y if a were small, i.e., almost a vertically
pointing antenna.
-------
465
In an obvious extension, if the transmitter-receiver were pointed
off the wind axis, there would be a third component to the spectrum. All
previous results hold with the redefinition
2 u Cos 6 Cos .. 2 u Cos 9 Sin
a" = 2—2 1; a = 2—2
fZ XZ JT XZ
and now
1 _ ,1/2 2 u2 Sin2 9
2} ; aL2 =~T72
aJ.2
2.4 Antenna Weighting
Any signal received has another variable intrinsic to the system which
affects the Doppler spectrum. The power output of the antenna system
drops off as one moves away from the boresight (axis of beam) . As a general
form for this effect, we shall assume it to be Gaussian
Thus when a' = a the power incident on that portion of space is about
.6 what it was on the beam axis. This term is a function only of the distance
from the center. Thus for the parallel contribution, it is easily incorporated.
We define the weighting function
Wn (z,r) = S(z,r) P(z,r)
-------
466
a'2
= 2* (a,, z)
Now a' Is determined by the radius of the circle defined by a , i.e.,
,2 ,T -1 r,2 f -I x2 + y:\l/2 2 x2 + y2
a' = (Tan —) = (Tan ( 2"' ' ~ 2~
z z z
but
2^2 22
x + y = a(, z
2
a/:
Wu = 2ir(a,, z) P e "(T
So, integrating in z:
2
_ a
~(
W,. = 2TT P_ I a z e 2 dz
= 2TT
TT Po a,, (a,,2 + 1)
For the perpendicular contribution, things are not quite so simple,
but are straight forward. At a constant z,
-------
467
W ' (z,a) =
S • Pdy = 2P
a
'2
22
e . 2 dy = 2P e \ 2 2 'dy
2a 7 o I 2a z
= 2Pe .2 2 e 0 2 2 bee. x = — in this case.
o 2a aj. I 2a z z
2 fy -u2
erf(y) = — e du
Define
= u2 -> i- dy = 2u du; y = /2 az du
2a z
a z
2u (g2 z2) du
dy = — — r— - - =
/2 azu
,
az du
v
W = 2/2 P e 2a2 a 2 az e U du;
0
2 z_vl/2 2 1 ,1/2
- p (Tan a )
v =
v/2
az
a
W = /2TT P e 2 2 az erf(v)
Integrating in z, then,
-------
468
Wj. (aj.,01) = /y PQ e"^ 2}a erf(v)
2.5 Total Spectrum
The complete spectrum due to scatters filling the scattering volume
of a monostatic sounder is not just the simple combination of V, and U^.
Any given scatterer will at any instant have a total Doppler shift equal
to the sum of f,, and fx . Thus, the contour must be established such that:
fp + fx = const, and its area calculated.
This is not to say that f(l and f^ are not useful, for they are the
limiting cases, and very important ones at that. When ^ = — there is no
Doppler shift due to a parallel component because the wind is horizontal -
thus, the only spectrum is that due to fA and we have the case of no vertical
wind with a vertically pointing monostatic sounder. If tj> = 0, the spectrum
due to fA is zero because the wind is directly along the beam axis.
Naturally, no acoustic sounder points horizontally, but the solution to this
case (f jj only, = 0, horizontal wind) is precisely that of a constant
vertical wind with a vertically pointing sounder.
Let us consider now the total spectrum with a monostatic sounder
pointed off the vertical, but in the plane of the wind vector, whose
magnitude and direction is constant with height. At any point, the Doppler
shift is
„ U Z + U X
2 z x
A 2 2 2 1/2
(x + y + z )
-------
469
where now z refers to the direction along the beam axis and x is the
direction perpendicular to this axis; y is perpendicular to the
horizontal wind vector. Rewritten, at a constant z:
f = f (r) + g(r) Sin 8
where r refers to the radial distance perpendicular to the beam axis and 6
is an angle defined in this plane originating at the y axis as in
Fig. (10A). In other words, f is the shift due to the parallel
component and f_ is that due to the perpendicular component. We can
write f as
,. ~2u Cos (fr _ ,
f.. = r Cos a'
-L A
where a' is an angle taking on values between a and -a (Fig. 10B) and
r 2u Sin 4> _. ,
f2 ^ Sin a'
The total change in f.. across the plane is, in most cases, much
less than the change in f~ because Cos a' changes from Cos (0) to Cos (a)
while Sin a' changes from -Sin (a) to + Sin a and Sin a changes much more
rapidly as a' varies about 0. The only point where this doesn't apply is
when 4> approaches TT/2, and Cos <{>-»• 0 and the f ' variation becomes small.
With this in mind, then, we will try as a curve of constant Doppler shift a
-------
470
UJ
UJ
"ou.
E O O
o
f - Q.
UJ 5 5
— CO O
> Z o
s*s
UJ h-
I Q CO
uj rs
Q _J w
a
UJ
cr
OQ Q O
^ Z -1
CO < <
-------
o
471
to <
UJ
UJ (O
CD —
CO
o
_l
o
UJ
UJ o
> I-
iu
Q
CO
° > to
zt $
o co
UJ
cr
o
CO
UJ CO
LU
-------
472
straight line (Fig. 11). In order to determine the slope we set the total
Doppler frequency at y = 0 equal to that at y(r) where r is the radius
of the beam at any given z. At this point we shall use, rather than a
circle of radius z Tan a, one of radius Ztan(3a). The reason for this will
become apparent later, but suffice it to say that in the final result, one
may replace 3a with a and the results will be equally correct so far as
calculating the equation of the straight lines is concerned.
Thus
_, . f( .
f(y , o ) = f(r)
- -r^ (Cos Cos a' + Sin Sin a')
= - Y^ (Cos <{> Cos 3a + Sin Sin 3a Sin 6)
A
The left side is
2u , , z . ,,. , x
- T— (Cos cp —^ 0 -, /0 + bin
-------
473
CVJ
ro
«*-
+
ro
? /-/- / / -
< r f-/.--
M~ \
CO
CO ^
§5
li.
o
CO
CO
LU
_ UJ —
*
o S
CL
UJ CO
Q <
S2
u.
-------
474
2 1/2 Cos ^ + ~2 I/? S*n ^ = Cos $ Cos 3d
L > (1 + aj. )
+ Sin cf) Sin (3a) -—-
(1 + a/)
z Tan (3a)
2.1/2 (aJ. Cos * + Sin *> - Cos * c°s (3d) = - Sin $ Cos
Thus
aj. ct + 1
x(r,a ) = z { ? . ctn 0}
(1 4- Sj. ) ' Cos (3a)
The slope of the line is then
aj. ctn + 1 ,-i 1
-^-o 1/2 ctn *} ~ T
(ax + 1) 7 Cos (3a) 3j
a^ ctn (() + 1 2 1/2
[Tan (3d) - { = ctn *} ^
(ax + 1) Cos (3a)
and we can easily find its length. One should note, however, that the
Doppler frequency to which this line corresponds is not that associated
with aj_, but rather the f calculated from
f = Y^ (Sin Sin a' + Cos cj) Cos a')
where a' is determined by a,.
-------
475
Rather than calculate step by step the area for a given CODOSS without
the antenna weighting included, the result is just given
A = {Tan2 (3d)
where
ctn + I/a
= Sec (3a) - -^ -ctncf> =
r-i , -i I A '
(1 + 1/aj. )
2.6 With Antenna Weighting
ds = 2 dy (1
+
-------
476
W = 2Pn f exp ( -- \—^ {(f- + ay)2 + y2}) (1 + aV/2 dy
J • *A
By completing the square, we may rewrite the exponential term as
UU H- a2]1'2
Defining
YV + 6 - Y dy , ^ , a/2
-LZ - = u, -1 - •*- = du -> dy = — — du
~ ~ Y
i (1 + a2)
= (1 + a2)172 . __ a
' 2
2
ax (1 + a) a (1 + a)
we can write
R2 ?9
9 I Ir) _/P \ f £ i „
W = 2P (1 + az) ' e 2 2; exp (- -^ (yy + 6) )
Jy 2a
Then
and
2
,. . 2.1/2 3 fU2 2
W = 2^ Pa (1a) e * 2 e -u du
where
-------
477
1 a/2 a^ (a2 + 1)1/2 a/2
Yy2 + 6 n + 2,1/2 a2
u9 = = (l + a ) n 9~777 ;
a 72 aj_ (1 + a )i/^
2 21/2
y2 = z (Tan (3d) - n ) '
Thus, noting the definition of J,
sL
W = /2~TT a e 2a2 z {erf (u2) - erf(U;L)}
Integrating in z we get
2
_ D
W = /| a e~(^T){erf(u2) - erf (U;L)} £zm a
Spectra for varying cf^, a;L are depicted in Figures ((12) - (15)) as
calculated from the previous equations. It is in the calculation of these
spectra that the necessity to include scatters out to 3a rather than just
to a in order to include enough of the wings of the spectra arises. Of course,
in addition to the antenna weighting, contributions from the side lobes should
be considered. The easiest method for calculating lobe effects is to use
step functions; i.e., assume each lobe has constant power up to a certain
angle (a) , and then cuts to zero for the same angle, etc. etc.. If one does
this and recalculates the spectrum, the result is
-------
478
"M
-------
479
< -
W *• ~
— N O
<-> 10 ,
CD «
< II ~
Q.
UJ
'E <
«»F UJ O
X .-
s;^"
^*s <
UJ I-
> cr
°?u *
H
o
CO
<~> Q o
a » 8 " "
w g-i £ u
^J^X
s * • s ^
? od *. • =
H « CM uj -
^ „ » CD N"
< .E „ r
ur - S3 •
H- p -i a
^o—BE
H .. »- * *
QC
O
Ul
ii
J
tr
UJ
ii
^ X
< o
> <
LU
Z
3
tr
o
UJ
CO
^^i
CO
UJ
o
<
H-=O
cc
o
0)
10
REPRESI
RVE
ce
ui
o
•z.
o
CO
e>
** n "• *"
-X c O Z
-~O »? O —
ro
-
-------
480
u
O)
<
O
U.
O
Q
z
z
O
N
CC
O
I
O
z
IE
O
13
cr
H-
o
UJ
Q.
Ll_|
-------
oo — .
.
KJ K> od on
— 10 in
481
o a
x
O
or
a.
UJ
en z
< ~
UJ
en
UJ
Z
o
o
•e-
x
H
£
0
h-
<
cr
<
>
a
<
<
tr.
^_
a
a.
en
_j
<
h-
O
H-
0
\—
Ul
3
Q
O
O
CM
en
UJ
X
0
<
o
tr
a.
a.
<
-©-
en
<
en
C5
0
o
en
<
UJ
a.
<
X
en
z
UJ
Cfl
z
X
o
UJ
X
1-
UJ
o
•yr
O
en
_i
<
0
-e-
^-
z
o
i-
3
03
tr
i-
z
o
o
z
en
UJ
en
<
Ul
a:
o
z
_
«»^~
a:
Z)
o
o o o o
o m o o
C7> ^ IO CM
II II II II
-e-e-e--©-
-------
482
x
C£
UJ
UJ
00
o
Q
z
I
C
<
Z
<
II
o K
Q o
-, in
a:
O
<
o
ccl
z>
-------
483
W(z,ct) - / PQ e 2Q2 £zma {erf^) + erf (y2) - erf(u2) - erf(U;L)}
where
2 _ Tan2 a' - 32 2 _ Tan2 (2ct') - g2
" 0 2 ; U2 . 2
2a 2a
2 = Tan2 (3a') -
2
2a
An example of this is shown in Fig. (16). Now, we see the possibility
of more than one peak appearing in the spectrum. The reason, of course,
is the cutting out of part of the input spectrum between a and 2a.
2.7 Wind Shear Included
The inclusion of wind varying with height is not a trivial problem,
Analytically, things rapidly get out of hand and some simplifying assumptions
are required. Although an alternate approach is, of course, to use a computer,
this does not yield a comparable understanding of the physics of the problem.
Parallel Component
We go back to the equation
22 2 . J
z = x + y
where
2
^- -r «_*. >^v/o CD -
a-i = ~J72 1
iii "
-------
484
only now u is a function of z, and therein lies the problem. Let
u = kh; h = height above ground
and
n 2 - ^k2 COS2 4)
c" 2~2
f2 X2
(c,, 2 h2 - 1) z2 - x2 + y2
Now
h = z Sin <{> - x Cos <{>
Then
{c,, 2 (z2 Sin2 (j) + x2 Cos2 <|> - 2xz Sin $ Cos <)>) - l}z2 - x2 + y2
and things have rapidly become much more complicated. Note, however,
that the maximum absolute value for x is z Tan a which becomes for narrow
beams (a < 5°) x £ .lz. So, in order to simplify things write
h ~ z Sin
222 22?
(*• ^"* *-i « *" ± -i \ *" i £•
c,, z Sin 4>-l)z =x +y
This, again is the form for a circle of radius
22 2 1/2
z(c,, z Sin 4> - 1) '
-------
485
and we can write, for the length of the CODOSS at a given z:
s = 2irz (c,, 2 z2 Sin2 $ - 1)1/2
Now, if we use, as before,
dl = 1 = 1 ((x.2 .1/2
dz Cos y // 2 . 2.1/2 VV 'y=0
z/(x + y )y=Q
229 1/9
= (c z Sin <|> - 1 + 1) ' = c,,
Sin
This form for -r— is not exactly correct. In full form, it turns out
dz
to be
42 4
dl r 2 2 2 c,, z Sin (j) 2 2 ,1/2
^ = {c(/ Z z SinZ 0 + ^-^r + 2c,, Z z SinZ (J)}1^
dz z. z. _. ^ , -
cl( z Sin - 1
We have, thus far, kept only the first term. This has had consequences
mainly for thos CODOSS which are near the axis of the transmitter.
Continuing:
Z9
f 2 2 7 2 1/9
A = 2ir cn Sin - 1) ' dz
Zl
-------
^
J r , 2 _ 1 1/22 1
2 1Z2 U2 " 2 2 "/ (X2 22 }
c,, Sin (p 2c^i Sin '(j
zi(zi
Sin 41 2c,, Sin
2 2 1/7
z + (z - c,f Sin 4>) '
ln (_J - 2 - . --
2C"
Zl + (z,
2 c- 2 A
c,, Sin - 1)]
2a
zl
222 2 1/2
z (cu z Sin 4> - 1) dz
_
2ir | 22 2 1/2 2 22 2
e 2a x (x + 1) dx where x = c .z Sin 4> - 1
— n \ ^- *-\Jd A \^V I O,/ VJ. A V* AH— i. %_ -Ti. I <
c it Sin 4> •*
Xl
2 2
0 £ x <_ a
2
If one assumes 0
-------
487
A /2TT3 a2 (1 + a2) , , . X2, _ xl.
A = - r - - - '- {a (erf (— ) - erf (— )
*- f, . ^- i Ut> H
c t) Sin
2 2
Xl X2
2 _ /—i—N 2
n , l 2a /n , X2 e 2a2 Xl
X (1 + - = - ) - X (1 + - r - ) }
a (1 + a ) 7 2 (1 + a )
Perpendicular Component With Wind Shear
Again, we have
22 2^
^ x = z + y
2 Au Sin 0 . ^ __ -> , 2 U2
a. = —r—z *• - 1 •* 7 , b h - where
A f2 X U = ^
2 = 4k2 Sin2
22
f A
Once again,
h = z Sin ~ z Sin
222 22?
(b z SinZ <}> - 1) x = z + y
or
-------
488
22? 2
2 ,bZ ZL SinZ d> - 1 / _
x i. ; - - I
which is another hyperbola at constant z with assymptote
x = + (b2 z2 Sin2 - 1)1/2 y
and x intercept (y=0)
22 2 1/2
(b z Sin 4> - 1) '
For a circle of radius r = z Tan a, we get a value of x = z Tan a when
y = 0, where
Tan a =
,,2 2 _. 2 .
(b z Sin
-------
489
, , 2 2.1/2 1 r 2 1/2 2 ,22 .
^ 1 r (a - u ) _ 1 1 ,[a - u] - a. -, d z - 1
[a - u] + a
1
u, = —
, u r T ,
d [a - u] + a
A2 2 i
d z - 1
222
d = t> Sin
with
a = Tan <(>
Including Gaussian antenna weighting leads to some difficulties,
but an answer can be obtained:
2
z
9 29
r2 (d2 z2 - 1)2
r 1-4-
S = 2PQ exp ( £ {^—2~2~^ = 4Po 6Xp ^~
J 9r« ^
2a z 2a (d2 z2 -1)
un 2
1 ~u j
e du
0
where
(Tan2 a -
d z - 1
Then
fZ2 1 1
A - 2/F Pa z exp {- -^- (-—^ )} erf (u. (z))
' 20L d z - 1 X
-------
490
Expanding erf(u..) in a McLaurins series and integrating (App. IT)
A ~- {5 l-L_ + ( _ a ) (ln u _ ^ u + I (_L
d u 2a i 2a Z 2u
(2'3) 2a2
2 A2 2 1
1 v3 3 . u d z - 1
) u +...)}
1 A2 2 1
d z - 1
The applicability of the last two derivations as they stand is rather
limited. This last one is strictly valid only for a vertically pointing
sounder. At any other angle the sum of A|(and A^_ must be considered once
again. A,, is really not valid anywhere, because the only time we have A,,
only is when = 0. At this point the approximation h = z Sin + x Cos 4>
= z sin prohibits any variation across the beam of the wind. This case in
no wind shear conditions was equivalent to the vertical wind, vertical
pointing case, but is no longer. Thus AJ( cannot be used by itself for any
computations. A separate study of this case for w varying with height
could and should be done.
Combined Spectrum
In order to try and come to some expression for the total Doppler
frequency spectrum, we must go back to essentially the same point from which
we started the no shear case.
fT = f (r) + g (r) Sin
-------
491
Constant f.. circles at a constant z are defined by
2 ,2, ,2 _. 2 , 1N2 2 4k2 Cos2
-------
492
2u Cos (j) Sin
"X "
Whence
Cos <|> Cos (3a) + Sin Sin (3a) Sin 9(r) = ——— -7- (Cos + — Sin ')
x
z Tan(3a)
We have, here, made the implicit assumption that: h = z Sin 4> because
we have cancelled out the u on both sides of the equation while they are
not necessarily equal because u changes across the face of the beam.
This leads to
= - ctn d> + ,„.. (ctn ) ]
from which we get the slope
-------
493
(— + ctn cj))
Sec(3a)n , 2,1/2 - ctn cf> - ^~
(1 + l/bj_ ) bj_
Ay (Tan3(3a) - [Sec(3a)(ctn (J) + ^-) ^ r-rr- - ctn
Q x -. t -L \ -L/ ^-
2 21/2
(Tan (3a) - 3 ) '
This is exactly the same form as previously used. However, now 3 and
b are functions of z. Since they are functions of z and not x or y, we can
follow exactly as in the no shear case to the result at constant z:
R 2
^1 1 2
2 fy2 2 (Y1 y + V
W (z,a,(j)) = 2PQ (1 + b2)172 e 2a I e 2a dy
2
= / P e 2a a {erf C
with
]_ , (1 + b2)172
2 2 ' y 7
Z Z
? 1/? ' l 21/9 ,—
(1 + b )x/z -1 b (1 + b^)177 / 2
21/9 9 9
u2 = (1 + b ) '^ (Tan (3a) - 3 )
-------
494
where $ = r| with aA replaced by bx.
Inasmuch as Q , u«, and u.. are rather complicated functions of z,
the integration in the z direction was carried out numerically. Before
this is done, a calculation similar to that for determining the straight
line at constant z must be carried out.
At each level along z, the point at which the Doppler frequency remains
the same, will determine a new a1 (See Fig. 17), which in turn determines
a new b • and thus, the length of the line at the new level along z. This
value is then used in the calculation for the next level and so forth.
Specifically, we set the Doppler frequency at level 1 equal to that at level
2 at the point ® I /2.
2u (z2) 2u (z )
—r—— (Cos a ' Cos<}>+ Sin a ' Sin } = —r {Cos a.' Cos
A i t- A 1
+ Sin a ' Sin <(>}
or
2 1/2 X 2u (Z1)
Cos(a2) Cos + (1 - Cos (a2)) ' Sin <}> = 2u (z ^ — ^ -
Cos
because f is the same on both sides.
Then
Cos(a2') ctn
-------
495
2
Cos2(a ') (1 + ctn2 ) - Cos(a ') (2£ °S
-
Sin <(> Sin
Simplifying
2 29
Cos (a ') - (2e Cos cj>) Cos (a') + e - Sin = 0
Solving
2 1/2
Cos (a ') = e Cos + Sin cf> (1 - e )
i.e.
_ , ,, Af Cos j) _ ^ _. , ,. , _ Xf
C°s(a > = ± Sln * (1 - (
2 2k(z2 - z Sin cj> 2k(z2 - ZQ) Sin
But
Using this, then, a new a' is calculated at each new level of z. Now
, ,4k2 Sin (j) , .2 _. 2 . ..1/2
bA = ( 9—9 (z - z ) Sin ij> - 1) '
f X
f, = |^ Sin (j> Sin a' -> b,. = ( \ l)1/2= ctn2 a1
A Sin a'
Thus, the calculation of a_ leads to bj^which gives a length of line
at the new height z_ and the integration can be performed throughout the
volume.
-------
496
(£>
Z
LU o
XW
co"
I LO
O <"
ID <
O LU
tr o:
x u
I- Z
o
o tr
LU
X
1-
LU
I
CO
co —
< 5
CO co
s<
Q
O .
O LU
LU
I
LU
tr
tr
rs
o
LU
o:
=>
C£
Lu
-------
497
UJ
O
CO
O
I-
£T
UJ
o
z
<
rr
UJ
o
i
tr.
o
o
u
Q.
CO
UJ
oc.
-------
498
-------
499
0
II
o
IM
UJ
z
0
1
O
^4.
Q:
E
O
o
in
II
^£
E
0
0
II
o
N
UJ
i
"g-
o
z
§
E
O
o
II
^
g
o
II
o
N
UJ
_ z
0>
(A
o
tr
E
O
m
II
^
I I l i l i i i i i I
\
o
CO
a:
UJ
a
z
UJ
I
CO
i
CL
s
tr
o
UJ
a.
co
o
CM
UJ
a:
3
(9
M
-------
500
o
O
ro
n
-e-
CM
O
e
CD
Z
cc
cr
UJ
en
d
z
o
N
E
o
O if)
tr TJ-
"- n
ro
Q "
z ->=
X
i- o
_ N
^ ^
CM
Ul
K
3
CD
-------
501
Care must be taken when a' = + 3a. When a' > |3a'|, contributions
are ignored. A sketch of the CODOSS as calculated in this manner is shown
in Fig. (17). As can be seen, because of the wind shear, the CODOSS can
enter and leave the defined volume as z increases. The exponential weighting
causes the contribution at a' > |3a'| to be negligible, however, care
must be taken to count those lines which enter the volume above z .
Figures (18) - (21) show the results of integrating in the previously
discussed manner. The figures show the spectra at cj) varying from 90° to
30°, each with varying wind shear and z. The three wind shear cases are
picked in each case in a manner such that the wind speed at z = 500 m is
10 m/sec. This is done so that they may be compared to the no wind shear
case which has wind speed 10 m/sec and the middle of its scattering volume
at 500 m.
The wind shear case with z = 0 and k = .02 is the closest to the
o
no wind shear case and a comparison of the two yielded quite close results,
which is only as it should be, but encouraging nonetheless.
As would be expected, as the shear is increased, there is a greater
contribution to the wings of the spectrum and a decrease in the maximum
height. In addition there is a slight shifting of the peak as the shear
increases. This is due to the changing slope and curvature of the CODOSS
with height and wind shear for at greater heights in the volume, the contributions
near the beam center will be greater than at smaller heights.
-------
502
The most noticeable effect, however is the occurrence of a linear
portion of the spectrum near the peak with an increase of wind shear and/or
decrease of . Thus far, the actual cause of this effect is unknown.
Further study on this is now underway.
-------
503
3.0 MONTE CARLO METHOD FOR EVALUATING ACDAR
SCATTERING VOLUMES AND SYSTEM FUNCTIONS
R. J. Greenfield
Thomson and Coulter (1974) discussed the importance of careful
analysis of the system function of an acdar system if sounding is to
be used to obtain quantitative information on the state of the atmosphere.
Expressions were given for evaluating such quantities as the scattered
power arriving at the receiver and the volume common the source and
receiver beams. To obtain numerical volumes for these quantities, it is
necessary to carry out some sort of a volume integration. Their evalua-
tion which was performed for uniformly weighted beams clearly showed how
radically the system function normally changes with range.
To carry out the required integrations analytically is complex even
for the constant weighted beam as discussed by Thomson and Coulter, In
more realistic transmitter and receiver beam patterns, when, in addition,
scattering loss, and angular dependent scattering coefficients are
considered, an analytic solution for the evaluation of the system function;
will not normally be possible.
As a convenient alternative, a Monte Carlo evaluation of the
numerical integration is under investigation. The desired integrals
are of the form
I = dV • W(r) (1)
vol
-------
504
Volume VB
ISV
Transmitter Receiver
FIGURE I : INSTANTANEOUS SCATTERING
VOLUME FOR A BISTATIC ACDAR .
-------
505
where r is the position vector and W(r) is a position dependent
weighting function.
As a specific example of such an integral we evaluate the
instantaneous scattering volume (ISV), the volume within a range gate,
of a bistatic acdar system. The ISV for a pulse of length I = C • T
is the volume common to the transmitter and receiver beams which
contributes to the energy arriving at the receiver at some instant
of time. Here T is the time duration of the pulse, and C is sound
speed. Thus for a point to be in the ISV, as well as being in both
beams, the travel time T = (R + RR)/C must obey 2'R._
-------
506
between two planes normal to the transmitter axis. The position of
the planes is chosen large enough to contain the whole of the
instantaneous scattering volume. The value of A is found by randomly
generating points in the volume V . As the number of points goes to
i
infinity the fraction of the random points for which W(r) = 1
approaches A. Even for a finite number of random points, we obtain a
good estimate of A. The volume of V is readily calculated analytically
since it is the volume of a truncated cone. Thus equation 2 can be used
to estimate the ISV.
The results of the Monte Carlo calculation of the ISV were
compared to analytic results given by Thomson and Coulter. Comparisons
are shown in figures 2 and 3. In figure 2, T = 80 ms, C = 320 m/s,
D = 100 ms, the transmitter beam width, $, == 2°, and the receiver beam
width, a, = 1°. The transmitter axis is vertical, and the receiver
tilted at <}>= 10° from the vertical, towards the transmitter. The
calculation was made generating 3000 random points and required
approximately 15 seconds of computer time (System 360). We consider
the accuracy of the Monte Carlo results to be satisfactory.
Also shown on figure 2 is a calculation of the ISV when the
responses of transmitter and receiver beams are dependent on the angle
from the beam axes (non-uniform beam weighting functions). Antenna
TT TT
pattern power factors of exp {- 50 • To7T~ ®T>^ an^ exP {~ 25 • on 0_}
±oU* K. lol) * 1
-------
104
fO
102
\ I Thomson and Coulter I -
o. I—— . 1
Weighted Beam |
Q Monte-Carlo |
400 500 600 700 800 900 1000
RA(m)
FIGURE 2 « SYSTEM FUNCTION AS A FUNCTION OF
RANGE. COMPARISON OF ANALYTIC AND
MONTE-CARLO SCHEMES.
-------
,0-
?
^•^
c
o
c
£ 10-5
E
0
1/>
(fl
i i i
A D=1OOm
-------
509
have been applied. Here 0 and 0T give the angle, respectively,
K. 1
from the receiver and transmitter axes. All other parameters are
the same as in the previous example. The antenna pattern has, of
course, an effect equivalent to narrowing the beam widths. This
calculation of the ISV for the beam weighted bistatic configuration
would be extremely difficult by analytic methods.
An additional calculation made to further compare Monte Carlo
results for the system functions with analytic results of Thomson
and Coulter is shown in figure 3. For these calculations a = 1°,
3 = 2°, T = 100 ms, = 20°, and the D values are given on the figure.
*
2» 1
The expression for W(r) for the system function is r—r- when the
VT V
_,
point is in the ISV and 0 elsewhere. This W(r) leads to the system
function given by Thomson and Coulter. S is the solid angle of the
receiver beam.
-------
510
4.0 MEASUREMENTS OF SOUND REFRACTIVELY TRANSMITTED
IN THE PLANETARY BOUNDARY LAYER
M. Teufel, M.S. Thesis Research in Progress
4.1 Introduction
A bistatic acoustic probing system for studying temperature inversions
within the planetary boundary layer (PEL) has been constructed and used
to transmit sound to receivers located at distances ranging from a few
to more than 10 km. The system consists, basically, of a 200 Hz acoustic
transmitter, a fixed receiver station at which a micro-microbarograph is
also located, and a second truck-mounted mobil acoustic receiver.
The system is being used in two types of studies. The first is to
evaluate a scheme (Greenfield et al, 1974) for estimating temperature
gradients in PEL inversions. The second study consists of an examination
of the statistical properties of the fluctuations in the received acoustic
signal level.
4.2 System Description
The transmitter consists of a 200 Hz CW source, and a variable tone
burst generator which drives a series of 4 power amplifiers (Fig. 1).
The 200 Hz operating frequency was chosen because of its relatively low
attenuation under expected relative humidity and temperature conditions.
In order to be able to vary the antenna beamwidth, a "phased array" trans-
mitter configuration was chosen (Fig. 2). Each power (60 CW watts)
-------
FIGURE I • TRANSMITTER DIAGRAM
51]
AMPLIFIER
(DYNACO MARK IE)
SPEAKER
UNIT
SINE WAVE
GENERATOR
(GR I3IO-B)
TONE BURST
GENERATOR
(GR 1396-B)
AMPLIFIER
AMPLIFIER
SPEAKER
UNIT
SPEAKER
UNIT
AMPLIFIER
SPEAKER
UNIT
-------
REFRACTION CONFIGURATION
E
o
ro
~i~
o o o
o o o
o o o
CO
cc
Ul
I-
UJ
CO
to
o oo
o oo
o oo
o oo
o o o
o oo
\\\\\\\\\\ \ \ \ \
SIDE VIEW
o o o
o oo
o o o
FIGURE 2 "PHASED ARRAY"
TRANSMITTER CONFIGURATION
-------
513
amplifier drives a separate speaker enclosure. Each enclosure is equipped
o
with nine 8" woofers. The separation of the approximately 1 m enclosures
may be varied to adjust the acoustic beamwidth from essentially that of an
isotropic source to one of only a few degrees beamwidth. Measurements
of the total transmitted acoustic power (- 12 watts) show the emitted
patterns are in agreement with theory, at least to within the experimental
error resulting from ground reflections. Fig. 3 shows the emitted pattern
for three different power levels superimposed with the theoretical pattern
for the speaker enclosure configuration previously shown in Fig. 2.
One receiving unit is van mounted. Since a directional antenna at
200 Hz cannot be made readily portable, an omidirectional" microphone is
used as an antenna-receiver. The received signal is preamplified, filtered
in an active bandpass filter (CF = 200 Kz, BW = 10 Hz) and both the filtered
and unfiltered outputs recorded on a multi-channel analog tape recorder
(see Fig. 4). The filtered signal is also envelope detected, averaged on
an integrating RMS volt meter and then displayed as "signal strength"
on a strip chart recorder.
Fig. 5 is an example of typical unfiltered and filtered signals ob-
tained at approximately 5:30 a.m. on the morning of September 13, 1974 at a
range of 3.6 km.
In addition to the van-mounted receiver, a second acoustic receiver
was placed at a fixed base station (University Park Airport) 4.7 km from
the transmitter. This was done to allow continuous monitoring of the signal
as atmospheric conditions changed. A recording micro-microbarograph was
constructed and positioned at this station.
-------
FIGURE 3 •• COMPARISON OF MEASURED AND
THEORETICAL BEAM PATTERNS
-------
515
RECEIVER DIAGRAM
TAPE
RECORDER
MICROPHONE
(GR 1560-9531)
MICROPHONE
PREAMPLIFIER
(GR 1560-P62)
200 HZ
AMPLIFIER
ACTIVE FILTER
(BW =8HZ)
INTEGRATING
RMS VOLTMETER
(DISA 55D35)
CHART
RECORDER
(HEATH EU-20B)
FIGURE 4 » RECEIVER BLOCK DIAGRAM
-------
o
0)
V)
E
O
o
o
UJ
UJ
O
UJ
cc
o
UJ
a:
LJ
u.
Q
I
-------
517
4.3 Measurement of Inversion Layer Temperature Gradients
A method for measuring the temperature gradient, T.', in an elevated
inversion layer has been developed. A paper describing the method has
been accepted for publication in the Journal of Geophysical Research
and a preprint is included as Section 4 of this report.
Briefly, the method requires two quantities to be measured. First,
the height of the base of the inversion layer must be determined. This
will be done with a monostatic sounding system which is presently being
constructed and tested. The second quantity needed to resolve T ' is
the distance to the caustic. It can be determined either by a high sound
level or by the smallest distance at which sound is detected.
For an elevated inversion layer sound rays transmitted at a low angle
to the vertical will initially bend upward, then return to the surface.
The caustic is then the minimum distance at which the sound rays will
return (distances less than the minimum will be referred to as the zone
of silence).
Preliminary measurements have been made to determine the ability to
locate the caustic. The following are two examples of these measurements.
Data was collected on July 7, 1974 with the fixed acoustic receiver
at the airport and the van-mounted receiver roving from location to locatior
Fig. 6 shows several sections of the record from the truck mounted re-
ceiver. From this data a plot (Fig. 7) of maximum amplitude versus range
was made. The amplitude decreases with increasing range from the airport.
However, the amplitude is lower at the SA station than at the airport.
-------
-------
519
36
33
30
27
24
o
.0
UJ
§ .8
a.
5
2
x
15
12
SIGNAL CLIPPED
0
0 EARLY ARRIVALS 3:30-4 = 58 A.M.
• LATE ARRIVALS 4=58-6:42 A.M.
©
NOISE LEVEL
(SIGNAL BELOW NOISE) \
i 1 i 1 i 1 , 1
L 1 1
D 2 4 6 8 10
RANGE (Km.)
FIGURE 7 : MAXIMUM AMPLITUDE VS. RANGE
-------
520
Thus the amplitude is not a monotonically decreasing function of range.
We believe that the lower sound level at the SA station was due to
scattered energy (Wiener and Keast, 1959) while the arrivals from the
airport outward were actual refracted arrivals. Thus the zone of
silence ends somewhere between the SA and airport stations.
Data taken on August 21, 1974 may be an example of arrivals from a
raised inversion. Fig. 8 shows the sounder record at the TC station
(6.4 km). The first section was received at approximately 6:00 am and
has a peak amplitude of 31.7 ubars. The second section received at 6:35 am
shows a greatly reduced signal level, 4.4 ubars which is practically
buried in noise. The signal amplitude at the TC station decreased con-
siderably as the rising sun destroyed the inversion layer.
After sunrise, the sounder record at the fixed airport station (4.7 km)
was also reduced to a level below the noise.
These two examples suggest that the zone of silence from the source
to the caustic distance has been observed. When the monostatic sounder
is in operation later this fall, it will be possible to much better establish
the existence and the height of the inversion layer. Thus, we will be more
confident of the zone of silence observations.
4.4 Fluctuations of Signal Levels and Possible Association with
Atmospheric Gravity Wave Motions
In the course of our experimentation with the long baseline acoustic
sounder we have regularly observed apparently periodic fluctuations in the
signal amplitude (Figures 6 and 8). The fluctuations appear to have periods
-------
521
5=58 6'00
6:02
EOT
6:04 6:06 6:08
632
6:36 6:38 6:40
EOT
FIGURE 8 : TRANSPORT CENTER RECORD ON MORNING OF
21 AUGUST 1974.
-------
522
on the order of minutes and over extended periods, a sinusoidal pattern
with periods varying from 15 to 30 minutes is also frequently evident.
It should also be noted that most of the data has been collected on mornings
when there were clear skies overnight and winds were calm (conditions
commonly associated with high pressure systems).
For refractively propagated signals, changes in signal strength are
due to one of two causes. The first possibility is that the sound reaching
the receiver follows a single ray path. Then the amplitude fluctuations
simply reflect changes in the geometric spreading of the ray. The second
possibility is that the amplitude fluctuations are caused by some type of
multipath phenomenon. Energy arrives along two or more ray paths, and gives
a large signal when the individual rays tend to be in phase and a
low level signal when the individual rays destructively interfere.
The above observations led us to investigate the possibility that the
fluctuations might be associated with gravity waves. Observed (e.g.,
Gossard, E. E. and W. H. Munk, 1954) for many years using microbarographs,
these waves have periods of approximately 5-30 minutes and amplitudes
on the order of tenths of millibars. In order to confirm our hypothesis,
a micro-microbarograph was constructed earlier this summer and located
at the airport station.
Figure 9 shows a portion of one barograph record received in the
early hours of the morning of August 1, 1974. The sinusoidal character
of the gravity waves is obvious; the waves have a period of approximately
45 minutes and a fairly uniform amplitude of .34 mbar. Although sound data were
-------
en
CD
IO
CM
ID
2
o:
o
o
o:
u.
o
<
cr
x
a
o
a:
<
CO
o
a:
CJ
o
a:
h-
o
en
en
-------
524
also obtained, no obvious correlations between the sound level
and pressure fluctuations were evident.
Both the barograph and sounder (fixed station) data of July 13, 1974,
are shown on a reduced time scale in Fig. 10. On this particular morning,
the signal to noise level for the acoustic record was quite high (- 10).
Again, no obvious correlation is evident.
Work is presently underway to objectively analyze the fluctuation data.
Power spectra are being computed for the sounder microbarograph records.
Further, data will be taken to establish the spacial correlation properties
of the sounder amplitude fluctuations.
Modeling or signal amplitude based on ray tracing in atmospheric models
which are not horizontally layered is also being conducted. Such models
may be used to represent layered structure perturbed by a gravity wave.
The modeling of signal amplitudes will examine both geometric spreading
and multipath interference effects.
-------
525
OD 5
CJ a
O E
in
-------
526
REFERENCES
Wiener, F. M. and D. N. Keast; Experimental Study of the Propagation
of Sound Over Ground, J_. Acoust. Soc. Am. , 31., 724-733, 1959.
Gossard, E. E. and W. H. Munk; On Gravity Waves in the Atmosphere,
J. Meteor., 11, 259-269, 1954.
-------
527
5.0 Temperature Profile Measurements in Inversions
from Refractive Transmission of Sound
R. J. Greenfield1, M. Teufel1
D. W. Thomson2 and R. L. Coulter2
The Pennsylvania State University
University Park, Pa. 16802
Department of Geosciences
M
Department of Meteorology
-------
528
Abstract
A method is described for estimating temperature profiles in the
lower troposphere during conditions including a surface-based or elevated
inversion layer. The method uses acoustic energy transmitted over paths
on the order of ten kilometers in length. Measurements are made at
approximately one kilometer intervals extending radially outward from
the transmitter. The vertical temperature profile is modeled as two
constant temperature gradient layers. The first layer extending from the
surface to height Hj has a temperature gradient Tj' (usually negative
upward). The second layer temperature gradient T2' is strongly positive
upward. For temperature profiles of this type, ray paths arrive with a
high intensity at a caustic, and no rays return to earth between the
source and the caustic. The method requires that Hj be determined by yome
other means such as vertical acdar sounding. Tj' and T2' are then simul-
taneously determined by measuring the range to the caustic and the wave
propagation time. Even if the propagation time can not be measured,
useful estimates of T2' can be obtained from observations of Ha and the
caustic distance. For a ground-based inversion no caustic occurs. However,
the temperature profile can be determined by measuring the wave propagation
time. Since horizontal wind shear produces the same effect on ray paths
as a vertical temperature gradient, the proposed method obtains the sum
of the effects of the wind shear and the temperature gradient. In conditions
including significant wind shear, corrections for it must be made.
-------
529
I. Introduction
Atmospheric refraction of sound has been recognized for more than
fifty years to be the consequence of particular atmospheric temperature
and wind profiles. In fact, some of the earliest estimates of stratospheric
temperatures were made using explosion sound observations. Recently, the
development of various acdar systems has revived interest in using acoustic
signals for, in particular, low-level atmospheric sounding. Observations
of planetary boundary layer structure, winds, gravity waves and turbulence
have been made by a number of research groups (see, e.g.: McAllister, 1968;
Little, 1969; Beran et al., 1971; Beran and Clifford, 1972; Cronenwett
et al., 1972; Hooke et al., 1973; and Bean et al., 1973).
The amplitude of received acdar signals depends upon the intensity
of scattering or partial reflection of sound in regions of turbulent
temperature and wind fluctuations. The altitude of a scattering re£,icr.
is determined using the elapsed signal travel time and atmospheric velocities
are inferred from the properties of the Doppler spectrum of the received
signal (see e.g.: Brown, 1972; Brown and Clifford, 1973; Thomson and Coulter,
1974).
Most acdar systems are either monostatic, that is the same antenna
is used for both transmitting and receiving, or "short-baseline" bistatic
in which the transmitter and receiver are separated by, at most, only a
few hundred meters. With these systems it is now possible to monitor more-
or-less continuously the altitude of many structural features and the
vector velocity at selected levels. The systems are not suited, however,
for measurements of the vertical temperature profile.
-------
530
The technique described in this paper for determining temperature
gradients of surface-based and elevated inversions within the planetary
boundary layer requires a monostatic sounder estimating the height of the
inversion base and a "long-baseline" bistatic sounder for measuring the
characteristics of refracted signals. The refracted signals are measured
at distances ranging from about 3 to 15 km.
In a windless atmosphere, refraction arrivals will return to the
ground only if temperature at some level exceeds the surface value.
Fortunately, because the analysis of refraction measurements is so greatly
complicated by wind, the surface and elevated inversions, which we are
measuring because of their effect on the dispersion of pollutants, occur
most frequently during calm or light wind conditions. The nocturnal
surface (or slightly elevated) inversions are strongest in large high
pressure weather systems in which clear skiee enable the surface to ef-
ficiently cool by radiation. When light winds are present, they frequently
are of the "drainage" type and, thus, dependent upon local terrain conditions.
In many areas the lowermost elevations are enveloped in ground fog.
Several previous studies have discussed the "ducting" of sound in low
level inversions (Ingard, 1953; Weiner and Keast, 1959; Kriebel, 1971; and
Lyon, 1973). Chung (1972) studied wind and temperature variations in the
boundary layer using infra-sonic, bistatic techniques,
II. Model for Ray Paths in the Lower Troposphere
We assume a two or three layer model for the planetary boundary layer
which is analogous to tnose frequently employed for studies of propagating
gravity waves (Muller, 1969; Stilke and Mu'ller, 1972, Stilke, 1973). Below
-------
531
the inversion layer the upward temperature is assumed to be small and
negative, within the inversion the gradient is positive and relatively
large and in the atmosphere above it is again negative. From the surface
to a height H , the temperature gradient Tj' is negative and less than the
adiabatic (Figure 1). Within the inversion layer T ' is positive and may
be as much as 20°/km. Above the inversion layer (z > H2) the temperature
gradient T2' is again negative and its magnitude less than Tj". If the
inversion is a surface inversion, H: = 0. But in urban environments the
inversion may be somewhat elevated during the same conditions in which in-
versions are surface based in rural areas (Panofsky, 1969).
Ray paths for waves refracted in an inversion layer are also shown
in Figure 1. A zone of silence extends from the source to the arrival
distance of ray B. In the vicinity of the closest arrival at the "caustic"
distance, RC, th? co«and level is high due to refractive focusing. Individual
rays arriving beyond the caustic do have different arrival angles and phases.
Thus, they may either constructively or destructively interfere. When the
incidence angle on an inversion exceeds a certain critical angle, such as
for ray E, rays will no longer be sufficiently refracted to return to the
surface.
Ray paths and travel times for the two or three layer models were
computed using the standard method for constant velocity gradient profiles
(see e.g.; Officer, 1958). The slight nonlinearity in the sound speed
profile for a constant temperature gradient was neglected. For the nearly
horizontal rays with which we were concerned, the formulation given by
Chung (1972) would also have been suitable. Chung's method is useful when
significant horizontal wind is present. For this the effective sound speed
-------
532
profile is defined by
Ce(z) = C(z) + Vx(z) - Vx(o)
where C is the sound speed, Vx the component of the wind along the
transmitter-receiver line and z is height.
III. Methods for Estimating the Vertical Temperature Profile
In order to determine the atmospheric parameters T ' , T2 ' and H.,
we assume first that the height Hj of the base of the transition layer
may be determined using a vertically pointing monostatic acdar. The
caustic is located using either a mobile receiver or in a permanent
installation using an array of receivers spaced at 500 m to 1 km intervals
stretching outward from the transmitter. Either the boundary of the so
called zone-of-silence or the characteristics of the high intensity zone
may be used to identify R . Some sound may be present in the zone-of-
silence due to scattering (Weiner and Keast, 1959) but its level is,
normally, very low. If possible it is also advantageous to measure the
signal travel time, tc, from the source to a receiver located near the
caustic.
The values of Tx' and T2' may be estimated from Hj, RC and tc< Let
t(R) be the reduced travel time
t(R) = t(R) - f-
uo
where C is the sound speed at the surface
and' R is the source to receiver distance,
Figure 2 shows t versus R for various combinations of Tj' and T2' with
*.
H! = 200 m. Figure 3 illustrates an interpretation diagram based on tc
-------
533
the reduced travel time at the caustic, and RC. To use the diagram the
^
measured values are plotted with RC and tc as abscissa and ordinate,
respectively. Then Tj ' and T2f can be interpolated from the plotted
/*.
curves. As an example, a measurement of RC = 12 km, tc = 40 msec is shown.
Temperature gradients of -1.5°/km and 14°/km are, thus, estimated for
below and within the inversion layer. To assess the error, 6T2 ' , of T2 '
we write
2 3H i 3R c 9 c
where 6Hj , 6R and 6t are the errors in the measured values. To obtain
typical numerical values consider an atmosphere with T ' = -3 deg/km,
1
T2' = 10 deg/km and H = 200 m. For this atmosphere ^- = .04 deg/km/m,
dHj
J\rri I /^T '
7—2- = 1 • deg/km2 and ~^~ ~ -04 deg/km/sec.
c c
To demonstrate the measurement accuracies v:hich these values imply,
assume an experiment in which only one of the measured parameters Hj, RC, or
tc is in error. If a resultant error of 1 deg/km in T2' is acceptable,
it requires that if Hj is the parameter in error, that its error be
6H < 25 m; if RC is in error that 6RC ^ 1 km; or if tc is in error, that
6tc < 25 msec.
Monostatic acdar measurements may be used to locate layer boundaries
to within ranging errors of less than about 25 m. Thus, a satisfactory
estimate of H. is not a problem. The error in RC depends upon the distance
between measuring stations.
The determination of tc is more difficult. Measurements we have taken
(Figure 4) indicate that the error in estimating arrival time is on the
order of 10 msec. This is sufficiently precise. However, the total travel
-------
534
time for a distance of 10 km is only about 30 sec. Thus an error in tc
of even 25 msec is approximately only .1% of the travel time. In fact,
the limiting factor in determining tc is probably not the signal to
noise ratio but rather inhomogeneities in the horizontal temperature field.
We do have, however, aircraft observations which indicate that the maximum
/s
standard deviation of tc variations due to horizontal temperature variations
will in many cases be less than 5-10 msec.
Fortunately, an estimate of T2' can be made without using tc. Figure 5
shows RC plotted versus T2' for three values of Tj'. From the figure it is
apparent that if the curve for T ' = -3 deg/km is used to make the interpreta-
tion based on the measured value of Rc, the error in T2' will be on the
order of .5 deg/km if 0 > T1' > -.6 deg/km. In Figure 6 a second diagram
for making this estimate of T2' is presented. This diagram may be used
for any valnp<* nf T ' *nH H .
Travel time measurements may also be used to estimate the temperature
gradient, T1, for a ground-based inversion layer. In this case signals
are received at all distances. Figure 7 illustrates the reduced travel
time versus distance curves for a surface-based inversion.
IV. Techniques for Field Measurements
Refraction observations made to date have been obtained using a bistatic
system operating at 200 Hz over distances ranging from about 1.5 to 10 km.
The transmitter consists of a 200 Hz CW source, and a variable tone
burst generator which drives a series of power amplifiers. In order to be
able to experiment with variable antenna beamwidths, a "phased array"
transmitter configuration was chosen. Four 60 watt (CW) power amplifiers
-------
535
drive four separate woofer enclosures, each with nine 8" woofers. The
separation of the approximately 1 m3 enclosures may be varied to adjust
the acoustic beamwidth from essentially that of an isotropic source to one
of only a few degrees beamwidth. Measurements of transmitted acosutic
power (- 12 watts) show the emitted patterns to be in agreement with theory
at least to within the experimental error resulting from ground reflections.
The mobile receiving unit is van mounted. Because a directional
antenna at 200 Hz cannot be made readily portable, an "isotropic" sensitive
microphone is used as the antenna-receiver. The received signal is pre-
amplified, filtered in an active bandpass filter (CF = 200 Hz, BW = 10 Hz)
and both the filtered ard unfiltered outputs recorded on a multi-channel
analog tape recorder. The filtered signal is also envelope detected,
averaged on an integrating RMS voltmeter and then displayed as "signal
strength" on a strip chart recorder.
Figure 4 is an example of typical unfiltered and filtered received
signals obtained during one experiment during fall of 1973. Experiments
to date have focused on examining the signal behavior as a function of time
of day at different ranges. Fluctuations in signal strength, fadin^, appear
to be strongly dependent on the inversion dynamics. Periodic variations
which could be associated with propagating gravity waves are evident and
the signal scintillation markedly increases as radiative heating breaks
up the nocturnal inversion. Whenever inversions are present, the signal
to noise ratio does appear to be adequate for temperature profile estimates.
Field measurements during summer of 1974 will include acoustic
measurements of the caustic distance and travel time, aircraft or digital
sonde measurements of the vertical temperature and wind profiles, and
electronic micro-microbarograpL recordings of atmospheric gravity waves.
-------
536
ACKNOWLEDGEMENTS
Support for this research was provided by the Meteorology Laboratory
of the U.S. Environmental Protection Agency (Grant R-800397) and the
Pennsylvania State University Center for Air Environment Studies. W. Benson
and J. Breon have assisted in the design and fabrication of the field
measurement system.
-------
537
REFERENCES
Bean, B. R., A. S. Frisch, L. G. McAllister and J. R. Pollard,
Planetary Boundary-Layer Turbulence Studies from Acoustic
Sounder and In-Situ Measurements, Boundary Layer Meteorol.,
£, 449-474, 1973.
Beran, D. W. and S. F. Clifford, Acoustic Doppler Measurements
of the Total Wind Vector, Second Symp. on Meteorol. Obs.
and Inst., 100-109, Amer. Meteorol. Soc., San Diego, Cal.,
27-30 March 1972.
Beran, D. W., C. G. Little and B. C. Willmarth, Acoustic Doppler
Measurements of Vertical Velocities in the Atmosphere,
Nature, 230, No. 5290, 160-162, 1971.
Brown, E. H., Acoustic-Doppler-Radar Scattering Equation and
General Solution, J_. Acoust. Soc. Am. , 52, No. 5 (part 2)
1391-1396, 1972.
Brown, E. H. and S. F. Clifford, Spectral Broadening of an
Acoustic Pulse Propagating Through Turbulence, J. Acoust.
Soc. Am., 54, No. 1, 36-39, 1973.
Chung, A. C., The variabilities of wind and temperature
structures in the lower troposphere as revealed by an infra-
sonic wave probe, Ph.D. thesis, Dept. of Earth and Planetary
Sciences, M.I.T., Cambridge, Mass., June 8, 1972.
Cronenwett, W. T., G. B. Walker and R. L. Inman, Acoustic
Sounding of Meteorological Phenomena in the Planetary
Boundary Layer, J. Applied Meteorol., 11, pp. 1351-1358,
1972.
Hooke, W. H., F. F. Hall, Jr. and E. E. Gossard, Observed
Generation of an Atmospheric Gravity Wave by Shear Instability
in the Mean Flow of the Planetary Boundary Layer, Boundary-
Layer Meteorol. , 5_, 29-41, 1973.
Ingard, V., A review of the influence of meteorological conditions
on sound propagation, J_. Acoust. Soc. Am. , 25, 405-411, 1953.
Kriebel, A. R., Refraction and attenuation of sound by wind
and thermal profiles over a ground plane, J_. Acoust. Soc.
Am. , 5J^, 19-23, 1971.
Little, C. G., Acoustic methods for the remote probing of the
lower atmosphere, Proc. IEEE, 57, 571-578.
-------
538
Lyon, R. H., Propagation of environmental noise, Science/
179, 1083-1090, 1973.
McAllister, L. G., Acoustic sounding of the lower troposphere,
J. of Atmospheric Terrest. Phys., 3£, 1439-1443, 1968.
Mxiller, H., fiber schwerewellen in der unteren atmosphare,
Technische Mitteilungen aus dem Institut fur Radiometeorologie
und Maritime Meteorologie an der Universitat Hamburg, Institut
der Fraunhofer-Gesellschaft und dem Meteorologischen Institut
der Universitat Hamburg, Nr. 4, 1969.
Officer, C. B., Sound Transmission, McGraw-Hill, New York, N.Y.,
1958.
Panofsky, H. A., Air Pollution Meteorology, Amer. Scientist,
57_, 2, pp. 269-285, 1969.
Stilke, G., Occurence and Features of ducted modes of internal
gravity waves over Europe and their influence on microwave
propagation, Boundary-Layer Meteorology, 4_, 493-509, 1973.
Stilke, G., and H. Miiller, Observations of Gravity Waves
Propagating in Ground Based Temperature Inversion Layers,
Berichte des Instituts fur Radiometeorologie und Maritime
Meteorologie an der Universitat Hamburg Institut der
Fraunhofer-Gesellschaft, Nr. 22, 1972.
Thomson, D. W., and R. L. Coulter, Analysis and simulation
of phase coherent acdar sounding measurements, submitted
to J. Geophys. Res., 1974.
Wiener, F. M., and D. N. Keast, Experimental study of the
propagation of sound over ground, J. Acoust. Soc. Am.,
31, 724-733, 1959.
-------
539
FIGURE CAPTIONS
1. Model temperature profile and refraction ray paths.
2. Reduced travel time versus distance for Hj = 200 m. The
numbers under each curve give T2' in deg C/km.
3. Interpretation diagram to find TI* and T2'. H: = 200m.
4. Unfiltered and filtered received signal output/showing
signal onset. Range was 3-6 km.
5. Caustic distance versus T2'.
6. Interpretation diagram for determining T2' computed for
*
Tj ' = -3° C/km, but useful for full range of Ta' values.
Dashed line example shows an interpretation of T2' = 15°
C/km for measured RC = 15 km and Ha = 300 m.
7. Reduced travel time versus range for ground based inversion
layer.
-------
540
CO
UJ UJ
h- Z
Z O
— N
X
e>
UJ
O
CO
o
o
en
o
z
g
_J
CM
X
1H9I3H
UJ
(T
o:
UJ
a.
UJ
-------
541
80-
in
E
LJ
2
LJ
£
c:
h-
o
LU
o
r>
o
LU
OC
R(km)
FIGURE 2
-------
542
(OliSnVO IV) 3IAII1 13AVdi Q30nQ3d
-------
o
0>
0)
E
O
_L
T
LL
543
W
ttl
ED
O
-------
544
25.
20.
15.
Rr (km)
(deg/km)
10.
= 200m
5.
0.
10.
20.
30-
T2' deg/km
FIGURE 5
-------
545
VD
w
PS
"H
-------
546
w
03
(oes uj) 3WI1
030na3d
-------
547
6.0 ANALYSIS AND SIMULATION OF PHASE-COHERENT
ACDAR SOUNDING MEASUREMENTS
D. W. Thomson and R. L. Coulter
Department of Meteorology
The Pennsylvania State University
University Park, Pennsylvania 16802
-------
548
3790 Instruments and techniques
ANALYSIS AND SIMULATION OF PHASE-COHERENT ACDAR
SOUNDING MEASUREMENTS
D. W. Thomson (The Pennsylvania State University,
Department of Meteorology, 506 Deike Building,
University Park, Pennsylvania 16802)
R. L. Coulter
The phase-surface geometry and its dependence
upon system and atmospheric parameters for both
monostatic and bistatic acdar sounders is discussed.
The observed Doppler frequency shift is shown to be
a consequence of the motion with respect to the
equiphase surfaces of many distributed atmospheric
scatterers. Because acdar measured average Doppler
frequencies and Doppler spectra are integral func-
tions of system-related and atmospheric structure-
dependent weighting functions, application of simple
models which assume signal scattering only along the
antenna beam axis may result in significant wind
velocity measurement errors. It is further shown
that accurate quantitative estimates of Cj and Cy
for thin turbulent layers require detailed analysis
of the bistatic acdar common volume. Two tech-
niques, based on distributed scatterers and random
phasors, respectively, are used for simulating acdar
signal phase and amplitude fluctuations.
-------
549
Abstract
The phase-surface geometry and its dependence upon system and atmos-
pheric parameters for both"monostatic and bistatic acdar sounders is
discussed. The observed Doppler frequency shift is shown to be a con-
sequence of the motion with respect to the equiphase surfaces of many
distributed atmospheric scatterers. Because acdar measured average Doppler
frequencies and Doppler spectra are integral functions of system-related
and atmospheric structure-dependent weighting functions, application of
simple models which assume signal scattering only along the antenna beam
axis may result in significant wind velocity measurement errors. It is
2 2
further shown that accurate quantitative estimates of CT and Cv for thin
turbulent layers require detailed analysis of the bistatic acdar common
volume. Two techniques, based on distributed scatterers and random phasors,
respectively, are used for simulating acdar signal phase and amplitude
fluctuations.
-------
550
I. Introduction
If the Doppler frequency shift measured with a phase-coherent acdar
system resulted from signal, scattering by a single point target, the
observed Doppler shift would depend only upon the acdar operating fre-
quency, the transmitter-receiver separation, the vector velocity of the
scatterer and the line integral of the transmitter-scatterer-recei^er
acoustic ray path. In general, however, the received signal is the
resultant or sum of many components. Although the acoustic scattering
may be relatively more efficient within a given layer or region smaller
than the volume defined by the combined transmit and receive antenna beams,
individual moving point scatterers, much as raindrops in a cloud, are
randomly distributed in space. Thus, the received signal from which one
can derive a Doppler spectrum and an average Doppler frequency, represents
an integral space-time average. The Doppler spectrum will depend not only
upon the system frequency and geometry but also upon the antenna beam-
width (s) and the distribution of energy within the transmitter beam. The
t
atmospheric variables which influence the shape of the Doppler spectrum
include the mean vertical temperature and vector wind profiles, the 3-
dimensional turbulent velocity and temperature fields and, finally, the
angular dependence of the scattering coefficients of all the individual
scatterers which contribute to the total received signal.
Acdar Doppler measurements have been used to study thermal plume ve-
locities (Beran et al., 1971a; Beran et al., 1971b), winds in the planetary
boundary lay;er (Beran and Willmarth, 1971; Beran and Clifford, 1972;
Mahoney et al., 1973), gravity waves (Hooke et al., 1973; Beran et al.,
1973), and boundary layer turbulence (Bean et al., 1973).
-------
551
Interpretation of Doppler shifted signals has, with few exceptions,
been based on the work published by Clifford and Brown (1970), Beran and
Clifford (1972), Brown (1972), Brown and Clifford (1973) and Georges and
Clifford (1972). In the above papers the nature of acoustic propagation
through a refracting and turbulent atmospheric medium to the scattering
volume was discussed. Thus, both changes in the magnitude of the Doppler
shift as a consequence of changes in the wave vector along the propagation
path and at the scatterer were assessed, and broadening of the Doppler
spectrum due to propagation through a turbulent atmosphere has been eval-
uated. One result of the modeling work discussed in this paper is an
analysis of the Doppler shift and spectrum produced by many discrete scat-
terers distributed and moving in space.
When one is attempting to quantitatively analyze the relative impor-
tance of both system and atmospheric parameters upon the nature of the
received signal, it is useful to be able to conduct experiments using a
"controlled" rather than the real, and somewhat capricious, atmosphere.
Thus, we've chosen, initially, to numerically model or "simulate" using
several different techniques, the time-dependent, phase and amplitude
fluctuations of a complex acdar signal. The modeling results will be
directly compared with acdar Doppler measurements (; nd airborne meteo-
rological measurements) once the phase-coherent sounder presently under
construction at Penn State is completed.
-------
552
II. Phase Space Geometry and Signal Doppler Shifts
The Doppler frequency shift of a received acoustic signal may be
associated with the translation of a "scatterer" through equiphase surfaces,
the family of surfaces of constant path length, defined by the transmitter-
receiver system operating at a wave length X. The Doppler shift, f may
be written as the rate of change of phase, ,
-*£--**•"• U>
where L is the ray path length from the transmitter to the receiver which
_*
passes through the scatterer moving at velocity V. An equivalent expres-
sion in terms of the wave vectors K of the transmitted wave and K of the
o s
scattered wave is
f d = ^ <*s - *o> ' ? (2)
Both expressions illustrate the dependence of the Doppler frequency shift
on the motion of a scatterer relative to the surfaces of equal phase.
The simplest equiphase surface geometry is associated with a mono-
static sounder operating in a non-turbulent, isothermal atmosphere with no
horizontal or vertical motions. For this case the equiphase surfaces are
spherical shells separated by 2lT radians in phase or Ar = X in space.
Because the Doppler frequency is proportional to the rate at which a moving
scatterer "cuts" through the equiphase surfaces, radial velocities such as
vertical at the zenith or horizontal in the up and downwind directions at
the horizon will produce the maximum observed Doppler frequencies. Clearly,
the phase space geometry is independent of the antennas which serve only
as illumination "weighting" functions. In fact, for the above case, the
-------
553
acdar geometry is analogous to Doppler radar and may be analyzed using the
same principles. (See e.g. Lhermitte, 1966; Browning and Atlas, 1966; and
Browning and Wexler, 1968).
Consider the trajectory of a single scatterer moving horizontally
with the mean wind and passing above an acdar. The relationship between
accumulated signal phase and distance may be written
A = 6 - d> , = 2TT : Ar = r - r - = A (3)
n n-1 n n-1
where r and r are adjacent equiphase surfaces (figure 1). The hori-
zontal distance required for a moving scatterer at height z to create a
phase path length change of 2lT is:
. , 2 2.1/2 lt ,%2 2Nl/2 ,.,
Ax = (r - z ) - ((r - A) - z ) (A)
The Doppler frequency at any given displacement and height is minus the
local derivative of the plotted d(f>/dx curve (figure 2) times the scatterer
velocity:
d dt dx dt dx H
The phase space geometry of a bistatic acdar is somewhat more com-
plicated because separation of the transmitter and receiver creates a
position-dependent separation of the equiphase surfaces. In terms of an
x, y, z coordinate system in which the origin is located at the midpoint
of the chord (x axis) between the receiver and transmitter, which are sit
uated at -4-d and -d, respectively, and y and z are in the cross chord and
vertical directions,
-------
554
L - [(d + x)2 + y2 + z2]172 + [(d - x)2 + y2 + z2]1/2 . (6)
For a bistatic system operating in an isothermal, windless atmosphere,
0
the equiphase surfaces are, thus, ellipsoids of revolution. The transmitter-
receiver separation is D = 2d. The single scatterer Doppler frequency is
f£* r O Xf . O JC O X* -i
, = - Y [U 77— + V 7T- + W 7T-]
u A dx dy dz
where £ = L/2 and V = iu + jv + kw, or
f - 4 ux(l - 4d2/L2) + vy + w z ,,,.
d ~ ~ XL . nc 2 J2 (/)
1-16 x d
L4
In the midpath, x = 0, plane
4
f , = - YT (^ "*" wz) '8)
d Ali
In the case of a monostatic acdar, horizontal motions at the zenith
did not produce Doppler shifts. But for a bistatic system both vertical
and "crosspath" motions at midpath can produce Doppler shifts. Clearly,
the complete expression (7), which includes u, v and w components must be
used for analyzing Doppler data obtained with bistatic systems which include
one vertically pointing and one tilted antenna. Note, that the observed
Doppler shift not only depends upon the inverse of the wavelength but also
upon the transmitter-receiver separation and the position of the scatterer.
Equation 7 may be used to determine the family of d(j)/dx curves, as for
the monostatic case in figure 2, for any given bistatic acdar system. The
Doppler shift associated with a scatterer moving at any point in space is
then obtained by scaling by the appropriate velocity, V.
-------
555
Two orthogonal, say N-S and E-W oriented, bistatic systems simul-
taneously sounding the same region may be used to determine both the
horizontal and vertical velocity components. If eaih system has narrow
beam antennas which are pointed along its x axis, y = 0 and the observed
Doppler frequency, from (8), will be the result of ve/tical velocities only.
fd = " Ad Cw z)
If the antennas from the two systems are then synchrono isly pointed away
from their respective x axes, y > 0 and the observed Doppler shifts will
be proportional to the E-W and N-S wind components. The Doppler shift
from vertical motions is the same for both systems and may be extracted.
System N-S
fdNS = - & (VEW ^ + W Z)
System E-W (9)
A
f = — (v v + w z)
d^ Ad ^ NS y W ;
In the normal atmosphere vertical temperature and wind gradients
refractively distort the "ideal" equiphase surfaces. Temperatures decreasing
(increasing) with height tend to flatten (peak) the equiphase surfaces.
The vector wind changing with height creates significant asymmetries in
the phase space which locally alter d/dx, d/dy and d4>/dz. The extent to
which observations must be corrected for refractive effects depends upon
the particular atmospheric conditions at the time of the experiments
(Georges and Clifford, 1972). In our numerical simulation studies, ray
-------
556
tracing has been used to compute the actual phase space geometry for each
specified situation.
-------
557
III. System and Atmospheric Weighting Functions
A primary objective of many acdar research programs is to quantify
the relationships of the acoustic extinction and volume backscatter coef-
2 2
ficients, a(r) and 3(r), with the meteorological variables CT , GV , and
the state parameters and winds. In this section we show that quantitative
estimates of a(r) and 3(r) require, especially for bistatic systems, care-
ful analysis of the "system" function.
A received acdar signal is not a "point-target" echo but rather the
resultant signal from many scatterers of varying phase and amplitude dis-
tributed throughout the volume defined by the antennas and the pulse length
in space. In order to evaluate the received power as a function of range
we write the "acdar" equation:
fScat. rRec.
A A - a(r)dr - a(r)dr
P(r) = PQ 7^ • -| L • e 'Trans. • 3(6,r) • e 'Scat. (10)
T R V
where P = peak transmitted power
A = area common to transmitter and receiver beams
A,^ = area of transmit antenna
A = area of receiver antenna
R = range from scatterer to receiver
r = range along L
L = length of scattering volume in space
a(r) = extinction coefficient
3(6,r) a scattering angle dependent volume scatter coefficient
All parameters other than a(r) and 3(r) are dependent upon the system.
Hence, we designate
-------
558
A A
-f L (ID
R V
the system function.
For monostatic systems the system function is easily evaluated since
2
AC = AT . Thus S(r) is simply proportional to A /R • L . However, for
the bistatic geometry in which the transmitter and receiver are separated
and one beam is tilted with respect to the other, determination of the
scattering volume as a function of range can be a difficult analytical
problem. The volume defined by the transmitter and receiver antennas and
the pulse length in space is V(r) = A (t, or r) • L (figure 3). But the
scattered wave front returned to the receiver at time t is tilted $/2 with
respect to both the transmitter and receiver axes. Because the equitime
wave front is tilted at /2, the length of the scattering volume L changes
from v T/2, as for the monostatic case, to v T/2 cos.
s s
Since the value of A varies continuously as a function of range, and
varies significantly even along the length of the scattering volume LV,
V(r) can best be evaluated as
V(r)
r + L
o v
A (r) dr (12)
c
r
o
For the bistatic case A is the area common to two ellipses (figure 4), each
c
the resultant of cutting an antenna (transmit and receive) cone at an angle
of /2. The ellipses have major axes
"Tlote that the equitime surfaces are coincident, as expected, with the equi-
phase surfaces.
-------
559
~ R sin g
b = / .'/0—;—;5T- , transmit
cos(/2 + 3)
and . (13)
, R' sin a • ,
b = TTT^ r •> receive
cos(/2 - a) '
where R and R are as indicated in figure A. Each can be geometrically
related to r. With b and b defined, the value of A is determined to be
c
X V
AC = ab cos'1 (~) + ab cos'1 (-^) - |yi S| (14)
where x^, y are the intersections of the ellipses shown in figure 4, a,
a are the semi-major axes, and £ is the distance between the centers of
the ellipses. All are known functions, albeit quite complicated, of a, B,
(f>, D and r. Equation 14 may be numerically integrated to yield V(r) to
any required accuracy.
Figure 5 illustrates the results of performing the integration to
evaluate the common volume as a function of range. As a pulse of width v 1
traverses the common volume the resulting signal from V(r) typically varies
as shown in figure 5. Between points x.. and x7 (figure 3) the volume (and,
subsequently, signal level) increases rapidly through 3 orders of magnitude
in a matter of 200 msec. Between points x? and x_, when the sensed volume
is completely within both beams V(r) increases much less rapidly. In fact,
2
for ~ 500 msec it increases simply as r . Finally, from x_ -»• x, the volume
falls off rapidly, though not so rapidly (= 500 msec) as it rose between
x, and x_. The lengths of these segments is a strong function of , a, 3
and D, but are easily evaluated geometrically. The shape of these curves
is independent of T (unless v T » x~ - x,), even though the volume sensed
is, of course, directly related. Also, if a = 8» i.e. the transmitter and
-------
560
receiver are of equal beamwidth, then for most cases x_ - x« and the
middle portion of the curves disappears.
A
y»
Including the rest ofethe system function (—=—) results in curves
r Aj
such as figure 6. These curves indicate the variation of the signal
strength, assuming uniform scattering throughout, as a pulse traverses the
common volume. There is a strong dependence on a, g, <{>, D and the strength
varies considerably as the volume is traversed. There is a rapid rise from
x, to x9 followed by a decrease (« —r-) from x0 to x0, because -=r -^- •> -\ .
*• *• / / J 2 A A
r r r r
and then from x, to x, it falls off very rapidly.
The implications of this are readily seen. Assume, for example, a thin
layer of scatterers of thickness much less than x, - x.. In this case the
2 2
value of Cv and/or C determined can vary by a large amount depending upon
the location of the layer within the common volume. On the other hand, if
the layer is thick and encompasses a large portion of the common volume,
then even with a constant scatter coefficient the signal will vary consid-
erably as a function of range. In the section from x - x , one might be
1 2
able to compensate for the —z- drop-off by analog multiplication by r .
r
Unfortunately, this is not possible in the lower and uppermost regions of
the common volume. Proper compensation can, however, be readily handled
digitally, just by specifying a, 3> <|> and D.
The Doppler spectrum which results from the many scatterers that con-
tribute to the resultant received signal depends upon not only system but
also atmospheric parameters. We write the Doppler spectrum S(f) as
S(f) df = G(a,<|>) W() da (15)
-------
561
where G(a,) is related to the distribution of energy within the antenna
beams and the antenna pointing angle, and W(4>) is the scattering angle
dependent volume scatter coefficient, B(6,r), expressed in terms of the
antenna pointing angle. For an individual scatterer, f and the antenna
pointing angle may be related using (7). However, in order to determine
the average Doppler shift of a "many scatterer" signal, the Doppler spectrum
must be evaluated. One technique is that employed by Bello (1965) in which
the average frequency is given by
f " ff S(f) df/ |S(f) df (16)
Application and numerical evaluation of this integral (Section V) clearly
demonstrates the dependence of the derived Doppler frequency upon both the
system parameters and the ambient atmospheric conditions.
-------
562
IV. Models for Signal Simulation
We are using several different modeling techniques to simulate signal
phase and amplitude fluctuations from scatterers distributed in space. The
first, designated DS, is a "distributed scatterer" model in which the signal
as a function of time is derived from artificial scatterers moving in a specified
(temperature and wind profile) atmosphere and illuminated by the transmit-
receive antennas. In a second "RP" model, the individual signal contributions
are simply simulated using a set of phasors of random phase, amplitude and
angular velocity. The distribution of phasor amplitudes and angular velocities
is proscribed as the basis of system and atmospheric parameters. However, no
assumptions are made regarding the actual atmospheric conditions and the
actual acoustic signal scattering.
In the DS model, which is two-dimensional, all significant signal
scattering is forced to occur within a layer of limited vertical extent.
The scatterers are assumed to represent small regions (or "eddies") of en-
hanced scatter or "partial-reflection". In a 3-dimensional geometry, the
scatterers would be flat "platelets" with no vertical dimension, in the two-
dimensional model they are short lines parallel to the surface.
The existance and horizontal position of each scatterer is determined
using a "flip of a coin" technique. Thus, in the horizontal the scatterers
are uniformly, randomly distributed. In order to generate a layer of finite
vertical thickness, the uniform random numbers generated to produce the
horizontal distribution are transformed, two at a time, into any array of
normally distributed random numbers using:
1/2
N - (- 2 In BN1) ' cos(2lTRNi)
1/2
(- 2 In RN±) ' sin(2irRN )
-------
563
where
N, , N . =•• normally distributed random numbers
and
RN
, RN. . = uniformly distributed random numbers.
The normally distributed random numbers have a zero mean and unity variance
and in this form are not suitable for use as spatial coordinates. Thus,
they are modified using:
z. = 0"N. + ~z
with z. and z. .. representing the vertical coordinates of scatterer i and
i+1. The total thickness in meters of the scattering layer, situated at
mean height "z, is approximately 2a.
Using a ray tracing technique, the horizontal coordinate and angle of
rays propagated from the transmitter are determined at a level 2a below ~z.
Thus, in the DS model refractive temperature effects are included although,
at least to date, asymmetric distortion of the phase space by wind has not.
From the base of the layer individual rays are then propagated into it. In
order to ensure that scatterers which exist within the layer are intersected,
the mean spacing between rays is constrained to be less than the mean hori-
zontal scatterer dimension. When a ray intersects a scatterer, its phase
angle and amplitude are stored in an array from which the resultant signal
phase and amplitude are calculated.
-------
564
For the results presented in this paper, the signal amplitude
[G(a,) • W(<|>)] associated with a single scatterer was assumed to be a
function of the position of the scatterer in the antenna beam and the angle
of incidence of the ray upon the "flat" scatterer. The energy in the trans-
mitter beam G(a,) , was assumed to be Gaussian distributed about the beam
axis and the atmospheric scattering "angular dependence", W($) to be depen-
dent on the cosine of the incidence angle. Figure 7 illustrates several
combined amplitude weighting functions for different antenna angles. Maxi-
mum signal is clearly associated with scatterers located at the zenith in the
boresight of vertically pointing antennas. A major objective of planned
field experiments at Penn State is evaluation of W(
-------
565
determine the direction of rotation of the resultant phasor and to remove
the "2TT ambiguity." In the DS model, this was accomplished by computing the
average phase change for the entire scatterer array — assuming that the
average phase change could be associated with motion of the centroid of
intercepted scatterers. The direction of rotation of the resultant phasor
was thus defined in terms of the change in path length to the centroid. It
was found that by allowing scatterer shifts of the order of one-half the
scatterer size, that average phasor rotations of no more than 2i\ radians
between adjacent time steps occurred.
The "RP" model uses as its basis any number of phasors. Although each
phasor represents an individual scatterer, no assumptions are made regarding
the nature or structure of the scatterers which the phasors represent. Each
phasor rotates at a different rate, has a different initial phase angle and,
finally, a different amplitude. The rotation rate corresponds to the scatterer's
Doppler frequency. Initially, phase angles are randomly distributed. At
later times they are determined by the movement of the scatterers relative to
the phase space. Thus, here the basic information is -r^- from each scatterer,
whereas in the DS model it is §.
The received signal, however, consists only of the time-varying ampli-
tude and phase of the resultant phasor. As in the DS model the resultant
is the vector sum of all the individual phasor contributions, i.e.,
7 91/7
A (t) = ((£ A Cos(u.t + $.))+ (I A. Sin (to t + 4>.)) )
i .1 XI ,1 11
Z A Sin(u) t + <(> )
= Tan""1 Tr-r^
-------
566
where
j(w (t)t + 4 (t))
Sr(t) = Ar(t)e r
A^, ^ Ai Cos(co.t +<{>.), is the in-phase and A , Z A. Sin(co t + .) ,
the quadrature phase component of the received signal. By measuring j~
as a function of time one obtains both the Doppler frequency and the ampli-
tude as a function of time. The resultant Doppler spectrum can, thus, be
obtained.
The input spectrum is a function of the system parameters and atmos-
pheric conditions. The amplitude spectrum is determined by the antenna
weighting functions, the distance to the scatterers and the specified
scattering angle dependence. The frequency spectrum is determined by the
phase space geometry and the wind velocity components.
For any model such as this, which requires finite difference tech-
niques, it must be assumed that the scatterer exists for a length of time
long compared to the time step of the model. Furthermore, it is necessary
to assume an effective scatterer "center" in order to determine the phase.
In actuality, scatterers probably occupy some finite volume.
-------
567
V. Characteristics of Simulated Signals
The DS model was first tested by performing a "beam-filling" experi-
ment. Consider a vertically pointing monostatic "CW" acdar operating in
an isothermal, windless (except at the scattering layer) atmosphere. Assume,
initially, its beam to be devoid of scatterers. If a patch of randomly dis-
tributed scatterers (as described in the previous section) moves into the
beam, initially only up-Doppler scatterers on the upwind edge of the beam
will be illuminated. Thus, although the instantaneous Doppler frequency may
significantly depart from the mean, the tendency will be for the path length
to continuously decrease (figure 8) and for the average received frequency
to exceed the transmitted. After the antenna bean is filled to the zenith
point, both up and down Doppler scatterers will contribute to the received
signal, and after the entire beam is filled, the average phase path length
change will be zero. At any given time the instantaneous slope of the phase
versus time plot may correspond to any one of the many Doppler frequencies
present in the spectrum of the received signal.
Next the DS model was used to examine the differences between Doppler
frequency shifts predicted on the basis of single scatter theory and those
produced by distributed scatterers in a layer contained within the antenna
beam (or in the case of a bistatic system, within the common volume).
A tabulation of the average Doppler frequency, A/At as a function of
antenna pointing angle, 4>, for a single scatterer on the beam axis and a
many scatterer layer a two heights, 123 and 246 m, is presented and plotted
in Table 1 and figure 9, respectively. In order to approximate a "worst"
case condition of beam spreading in a highly turbulent mixing layer, the
simulation was based on a super-adiabatic temperature gradient of - 2°C/100 m
and a very large beamwidth of 18°.
-------
568
Note the decrease in average Doppler frequency which results from the
combined weighting function acting on the distributed scatterers. Due to
the heavier weighting of scatterers positioned closer to the zenith, the
peak of the Doppler spectrum is shifted to a lower frequency. Note also that
two scattering layers moving at the same velocity, but at different heights
will produce different Doppler frequencies. In terms of the phase space
geometry, the result is simply the consequence of a scatterer (at the same
horizontal displacement from the zenith) at a lower level intercepting more
phase surfaces per unit time than one at a higher level. The results sug-
gest that a properly analyzed Doppler spread may provide a measure of
vertical wind shear.
Figures 10 and 11 illustrate typical signal phase and amplitude fluc-
tuations obtained using the DS model. The dependence of the average Doppler
frequency and the signal amplitude fading upon the antenna pointing angle is
evident.
The above results regarding the differences between single and arrays
of scatterers have also been noted in the analysis of phase-coherent tropo-
scatter radio signals (Birkemeier et al. (1968); Atlas et al. (1969); and
Birkemeier and Thomson (1968)). Changes in the Doppler spectrum are, clearly,
most significant when systems with large antenna beamwidths are used to probe
layers with highly directional scattering or "reflecting" characteristics.
If the acoustic scattering only weakly depends upon the scattering angle and
an acdar system has narrow antenna beams, a simple model, equations (1) or
(2), may be used to satisfactorily derive wind velocities from the calculated
Doppler spectrum.
-------
569
Examples of the random phasor "RP" model output are shown in figures 12,
13 and 14. Rather than the accumulated phase, its time derivative is directly
computed. With this model as opposed to the DS model, it is not necessary to
make assumptions regarding changes in position of the scattering centroid or to
average phase data from several time steps to derive the "instantaneous"
Doppler shift.
For the example shown, the amplitudes of individual phasors were speci-
fied to be Gaussian distributed about the mean. That is
A± = AO exp [- (u>± - w)2/2aj
Such a distribution could be associated with the signal received from a
thermal rising within the beam of a vertically pointing acdar. In the model
0)At = const. = 0.07. Thus, if w = 5 Hz, a single time step corresponds to
14 msec.
The illustrated output was produced using only 15 phasors. As shown
by Slack (1946), the probability density of n phasors is not Rayleigh dis-
tributed when n is less than about 10. Prior to using the RP model for
predicting signal phase behavior, the statistical properties of signal ampli-
tude fluctuations computed for varying numbers of phasors were compared with
and verified against Slack's results. The purpose was to be able to adequately
simulate the signa1 properties using as few independent phasors (scatterers)
as possible.
Figure 12 is representative of simulated signal amplitude fluctuations.
As expected, minimum amplitudes tend to occur when the Doppler frequencies
(figure 13) are eitner a minimum or a maximum. In other words, when the
-------
570
relatively large amplitude phasors which control the "average" Doppler shift
interfere to "0," the smaller phasors associated with scatterers at the edge
of the antenna beam, will tend to control the signal phase fluctuations.
Figure 14 illustrates both the input spectrum (inset) of the 15 phasors
and the resultant power spectrum of dc|>/dt. Because the resultant phase of
a number of rotating phasors may "instantaneously" shift by mr (n >. 1) radi-
ans, the resultant spectrum will normally be wider than the input. When
the resultant Doppler frequencies are numerically simulated, the maximum and
minimum frequencies are TT/At and - TT/At, respectively. This effect is also
easily seen on figure 13.
The simple RP model results shown here have not included variable
rotation rates and phase angles for each phasor at each time step. Thus,
the sicnal -f« r*>npMi-i.ve at t = 2ir/Af where Af is the smallest frequency
difference between any two phasors. When variable rotation rates and phase
angles are included, which does more correctly simulate the motion of
scatterers within the phase space, apparent periodicities in the signal
phase and amplitude fluctuations disappear. However, the basic shape of
the Doppler spectrum is not altered.
The primary advantage of the RP model is that few (> 15) phasors are
required to numerically simulate the received signal and derive a suitable
estimate of its Doppler spectrum. Our computational costs for running the
"small n" RP model were a small fraction of those of runs of the "several
hundred n" DS model. If, however, a measured acdar signal is clearly non-
Rayleigh, an RP model may be used to relate the signal amplitude and phase
fluctuations to observed structural features.
-------
571
ACKNOWLEDGEMENTS
The formative stages of this research were completed while the lead
author was a visiting scientist at the Universitat Hamburg, Hamburg,
Germany, supported by the Deutscher Akademischer Austauschdienst. Research
support has since been provided by the Meteorology Laboratory of the U. S.
Environmental Protection Agency (Grant R-800397), The Pennsylvania State
University (PSU) and the PSU Center for Air Environment Studies. We wish
to acknowledge the programming and computations for the DS model completed
by R. Przywarty as a part of his meteorology M.S. studies and L. Cook's
assistance in preparation of the final manuscript.
-------
572
VI. References
Atlas, D., R. C. Srivastava, R. E. Carbone and 1). H. Sargeant, Doppler
Crosswlnd Relations in Radio Troposcatter Beam Swinging for a Thin
Scatter Layer, J. Atmos. Sci., 26, No. 5 (part 2), 1104-1117, 1969.
Bean, B. R., A. S. Frisch, L. G. McAllister and J. R. Pollard, Planetary
Boundary-Layer Turbulence Studies from Acoustic Sounder and In-situ
Measurements, Boundary Layer Meteorol.. 4^ 449-474, 1973.
Bello, P. A., Some Techniques for the Instantaneous Real-Tiine Measurement
of Multipath and Doppler Spread, IEEE Trans on Comm. Tech, 13, No. 3,
285-292, 1965.
Beran, D. W. and S. F. Clifford, Acoustic Doppler Measurements of the Total
Wind Vector, Second Symp. on Meteorol. Obs. and Inst., 100-109, Aner.
Meteorol. Soc., San Diego, Cal., 27-30 March 1972.
Beran, D. W., W. H. Hooke and S. F. Clifford, Acoustic Echo-Sounding Tech-
niques and Theor Application to Gravity Wave, Turbulence, and Stability
Studies, Boundary-Layer Meteorol., 4_, 133-153, 1973.
Beran, D. W., C. G. Little and B. C. Willmarth, Acoustic Doppler Measurements
of Vertical Velocities in the Atmosphere, Nature, 230, No. 5290, 160-
162, 1971.
Beran, D. W. and B. C. Willmarth, Doppler Winds from a Bistatic Acoustic
Sounder, Proc. Seventh Inter. Symp. Remote Sens. Environ., _3_, 1699-
1714, Univ. of Mich., Ann Arbor, 17-21 May 1971.
Birkemeier, W. P., H. S. Merrill, Jr., D. H. Sargeant, D. W. Thomson, C. M.
Beamer and G. T. Bergemann, Observation of Wind-Produced Doppler Shifts
in Tropospheric Scatter Propagation, Radio Sci., ^ (New Series), No. 4,
309-317, 1968.
-------
573
Birkemeier, W. P. and D. W. Thomson, Observations of Atmospheric Structure
with Phase-Coherent Measurements of Troposcatter Multipath and Doppler
Shift, Conf. on Tropospheric Wave Prop., 85-92, IEE, London, 30 Sept. -
2 Oct. 1968.
Brown, E. H., Acoustic-Doppler-Radar Scattering Equation and General Solution,
.J. Ac oust. Soc. Am., 52_, No. 5 (part 2), 1391-1396, 1972.
Brown, E. H. and S. F. Clifford, Spectral Broadening of an Acoustic Pulse
Propagating Through Turbulence, J_. Acoust. Soc. Am., 54, No. 1, 36-39, 1973.
Browning, K. A. and D. Atlas, Velocity Characteristics of Some Clear-Air
Dot Angels, J_. Atmos. Sci. , 23, 592-604, 1966.
Browning, K. A. and R. Wexler, The Determination of Kinematic Properties
of a Wind Field Using Doppler Radar, J_. Applied Meteorol., 7_, 105-113,
1968.
Clifford, S. F. and E. H. Brown, Propagation of Sound in a Turbulent
Atmosphere, J_. Acoust. Soc. Am. , 48, No. 5 (part 2), 1123-1127, 1970.
Georges, T. M. and S. F. Clifford, Acoustic Sounding in a Refracting
Atmosphere, J_. Acoust. Soc. Am. , 52, No. 5 (part 2), 1397-1405, 1972.
Hooke, W. H., F. F. Hall, Jr. and E. E. Gossard, Observed Generation of
an Atmospheric Gravity Wave by Shear Instability in the Mean Flow
of the Planetary Boundary Layer, Boundary-Layer Meteorol., _5_, 29-41,
1973.
Lhermitte, R. M., Probing Air Motion by Doppler Analysis of Radar Clear
Air Returns, £. Atmos. Sci. , 2,3, No. 5, 575-591, 1966.
Mahoney, A. R., L. G. McAllister and J. R. Pollard, The Remote Sensing of
Wind Velocity in the Lower Troposphere Using an Acoustic Sounder,
Boundary-Layer Meteorol., 4., No. 4, 155-167, 1973.
-------
574
Slack, M., The Probability Distributions of Sinusoidal Oscillations Com-
bined in Random Phase, _J. Inst. Elec. Engrs., £3 (part 3), 76-86,
1946.
-------
575
Table I Doppler Frequency (rad/sec) as a Function of Antenna
Pointing Angle and Layer Height.
Pointing Angle, 4> (°)
Elevation 0.0 U.5 9-0 13-5 18.0 22.5
Single Scatter
z = 123 0.00 1.26 2.68 U.28 6.31 9-11
z = 123 0.00 3.07 5-16 T-99
z = 2U6 0.00 O.U3 1.19 3.86
-------
576
FIGURE LEGEND
Figure 1. Two-dimensional equiphase surfaces In an isothermal, windless
atmosphere.
Figure 2. Accumulated signal phase versus scatterer displacement for a
single scatterer moving horizontally through the beam of a
vertically pointing sounder.
Figure 3. Cross section of bistatic link antenna and pulse geometry.
Figure 4. Intersection of transmit and receive antenna beams on a surface
of equitime or equiphase.
Figure 5. Common volume as a function of range for pulse lengths of
40, 80, 120 and 240 ms. a = 1°, 3 - 2°, D = 100 m, $ - 10°.
Figure 6. System function as a function of ra.ige and transmitter-receiver
separation. Pulse lengths are 40 and 100 ms, a = 1°, 8 = 2°,
and - 20°.
Figure 7. Combined amplitude weighting functions for antenna pointing
angles range from 0 to 9° from zenith and cosine dependent
scattering angle dependence. Antenna beamwidth = 9°.
Figure 8. Accumulated total phase from scatterers moving into a vertically
pointing beam, f, = A/At.
Figure 9. Comparison of mean Doppler frequencies computed for multiply
scattering layers of 246 and 123 m, and for a single scatterer
at 123 m and varying distances from the zenith.
Figure 10. Example of accumulated phase versus time output of DS model.
-------
577
Fi.gure 11. Example of signal amplitude versus time output of DS model.
Figure 12. Amplitude returns from "RP" model versus time, with t sub-
divisions every 4At, where At is determined from toAt = .07.
Figure 13. Doppler frequencies returns from "RP" model versus time.
d
Figure 14. Received power spectrum of -r— and input power spectrum. Units
•
of j the same as for to..
at i
-------
578
H
O
(-4
fa
= x
-------
579
-400
-80
-40 0 40
SCATTERER DISPLACEMENT (m)
FIGURE 2
-------
580
-------
581
g
-------
582
I04
10° -
UJ
I io2
10!
10'
i 1 1 1 1 r
= 240
i i i i i i i
400 500
600 700
RANGE (m)
800
FIGURE 5
-------
10
10
D=100
r-40
SYS
FUNG.
10
-6
D = 200
10
-7
_L
100 200 300 400
RANGE(m)
FIGURE 6
500
600
7OO
800
-------
584
I04r
103
CD
•o
§
•
e
O 102
101
-.20 -.10 0 .10 .20 .30 .40
RAY-SCATTERER INCIDENCE ANGLE (radians)
FIGURE 7
-------
585
in
OJ
o
OJ
LJ
§
in
O
in
ro
O
in
CVJ
o
m
O
10
O
m
i
3SVHd dOSVHd
-------
586
18.0
22.5
FIGURE 9
-------
587
650
550
450
(A
C
g
1 350
UJ
CO
250
cc
o
CO
150
50
0=18'
-50
30
60
TIME (sec)
90
120
FIGURE 10
-------
588
o
C\J
o
o
O "
CD L-J
O
ro
O
10
i
O
o
(GP)
o
o
CVJ
I
-------
N
O
G
f <*t
589
4
O
00
CO
o
5J-
CM
t * f^ f f
'
*»•••••
*f +
r
^M*^*
>
%ff f
O
+ *
O
i
O
CVJ
i
o
ro
i
O
O
CVJ
LL
O
CO
CVJ
o
CO
og
-------
590
G
. I--
* *
o
-l-o
CJ
**+ t
*HV°
&
t
t » t 1 1 I
(:
cvj
ffffffT
-------
591
0>
CO
in
ro
CM
(SP)
indNi
g
O)
CD
CD
in
CVJ
w
u
O
ro
O
CO
o
(8P) U3MOd
O
I
-------
592
V AIRBORNE MEASUREMENT SYSTEMS
Part 2
-------
593
1.0 AIRBORNE MEASUREMENT SYSTEMS
D. W. Thomson
1.1 Introductory Remarks
Research in the airborne measurements task group may be conveniently
divided into two general areas. In "systems development" we have during
the past year, firstly, substantially altered and improved the isokinetic
probe for airborne air sampling. Secondly, we have designed, fabricated
and tested an airborne radiometer package which includes eight up and
down looking hemispherical radiometers with varying wavelength response
for use in urban and regional scale energy budget studies. The second
general area of research is analysis of a variety of airborne measure-
ments. Turbulence and aerosol observations obtained during the 1973
and 1974 St. Louis RAPS programs and data obtained during the extensive
in-house regional measurement program in October, 1973, are serving
as the basic data set.
It is important to note that each of the six graduate students
participating in the group has not only been assisting in data analysis,
but also has through direct participation in the field programs obtained
invaluable field measurements experience. Without the combined scientific,
engineering and technical expertise contributed by various members of the
group, the unique measurements (which for the most part are still being
analyzed) discussed in the following sections would not have been pos-
sible.
-------
594
2.0 PSU ISOKINETIC INTAKE FOR AIRBORNE AIR SAMPLING
J. Pena, J. M. Norman and D. W. Thomson
Air pollution studies often require simultaneous measurements of
many different parameters. Furthermore, the sampling condition re-
quirements are, in general, different for each sampling instrument.
The PSU aircraft is equipped with six different simultaneously operated
instruments including particle and condensation nucleus analyzers and
an integrating nephelometer. Although it would be preferable to have
individual intakes for each of the different instruments, in a medium
size aircraft tne cost of designing and mounting many parts in
the limited available space is prohibitive. Air for each of the instru-
ments could also be sampled from a common chamber where environmental
air circulated. However, interpretation of the spatial variation of
the air parameters with respect to meteorological variables would then
be exceedingly difficult.
For aerosol measurements, especially those concerned with analysis
of particle size and distribution, it is very important to sample in
isokinetic conditions, that is that air speed at the sampler intake is
the same as the air speed across an equal area in the free stream. In
order to simplify the adjustment for isokinetic conditions for a particu-
lar instrument, it is convenient to have a low air speed (relative to
typical aircraft speeds) in the sampling chamber.
A general description of a suitable sampler is as follows: Air
enters the sampler through a circular intake and, then, the air speed is
-------
595
reduced as the cross section increases along a conical section. When the
air reaches a cylindrical chamber, its speed is at its minimum value.
Behind the sampling chamber, the air (remaining) is again accelerated
along a conical section to an end exhaust port.
On board an aircraft truly isokinetic flow can probably not be
achieved. A well designed sampler can, however, provide nearly isokinetic
conditions. Because of the energy losses at the air intake, along the
conical expansion, and at the exhaust, we can expect that the air velocity
at the intake will be somewhat lower than the air speed in the free stream.
On the other hand, according to Goodale et al (1), the pumping action of
the external air stream in passing the exhaust can be enough to compensate
the losses and, thus, help to achieve isokinetic conditions.
Another problem with this type of sampler is that when the various
sampling instruments are operating, the applied suction can change the
operating conditions of the sampler. One way to minimize this effect is
to make the primary air flow through the sampler much larger than the
combined total flow required by the instruments. Thus, any change in
the number of operating instruments will have little influence on the
operation of the sampler.
2.1 Design of the PSU Model II Probe
A cross-sectional view of the sampler is shown in Figure 1. In the
sampler air is taken through a circular intake of 2.03 cm diameter and
its velocity in a conical expander reduced by a factor of 16.6 times
before it reaches the sampling chamber.
The flow through the probe is 10 times the flow of the six instru-
ments sampling from it.
-------
LJ
m
o
cr
a.
o
z
_i
Q.
2
<
V)
cr
O
y eo
I- z
So!
K 5
«*• <
CO
I-
o
LJ
(O
CO
CO
o
cr
o
UJ
cr
o
-------
597
(a) Air Intake
The air intake profile was designed according to formulas given by
Kuchemann and Weber (2) for circular intakes. With the notation of
Figure 2 the outer shape is given by
R R R 0 1/2
r-r*«-r> a-a-i= r>2>
m m m m
and the inner shape by
R R R R 1/2
— = — (— — (\ - (\ - — —1s!
RD ^T> ' D * ^ T D ' '
K. J\. JtV Li.tV.
m m i m i i
The inner and outer thickness and the lengths of the inner and outer
A±
curved portions are given in terms of the area ratio — and the four
m
constants
R R A. 1/2
_P- • —P. - IT (. ^\
R. ' R " Kl (A }
i m m
R A. R
- - - 1 •
3 A ' L " K. (K. -
m i 4 i
being the values of the constants:
^ - 1.15 K2 = 0.2
K— 19"^ If — 1 ^
«~"J-^«-> Jx.~J-.-J
-------
598
T'
OUTER
THICKNESS
R, 7»
J I
I —»K
FIGURE 2 ' CROSS-SECTION OF SAMPLER AIR INTAKE.
1.0
g 0.8
K
UJ
(O
X
Ul
0.6
0.4
U0/U
FIGURE 3 • EXHAUST AREA RATIO AS A FUNCTION OF
FREE STREAM AND SAMPLER INTAKE
VELOCITIES.
-------
599
For our intake we have taken
A
R. = 0.89 cm and -^ = 0.25
± A
m
(b) Conical Diffuser
The diffuser has an angle of 7° which minimizes both losses
and flow separation. The cone was constructed on a model using polyester
resin and fiberglass. The previous model (see 1973 Annual Report) with
a cone of 19° exhibited a wind velocity profile within the sampling
chamber which indicated a substantial amount of flow separation. The
change of cone angle from 19° to 7° reduced the level of turbulence
u
( r-m-s") from 0.32 to 0.05.
u
(c) Sampling Chamber
The sampling chamber is cylindrical in shape with an I.D. of
8.28 cm and a total length of 10 cm. The tubes leading to the individual
instruments are located in the area limited by the distances 7.5 cm and
12.5 cm from the entrance to the chamber. There are five 0.635 cm I.D.
stainless steel and one 2.54 cm I.D. p.v.c. tubes. Each of these tubes may
be individually adapted for isokinetic sampling by using the appropriate
size nozzle to match the local air speed in the sampling chamber.
(d) Sampler Exhaust
According to Goodale et al (1) the pumping action of the air
stream in passing the exhaust can be used to compensate the losses inside
the sampler. They used a value that enabled them to modify the exhaust
area.
-------
600
In wind tunnel tests, we measured the behavior of the sampler as
u
a function of exhaust port diameter. Figure 3 shows a plot of — vs
d 2 u
the exhaust area ratio (-7-) where
dt
u = air velocity in free stream
u = mean air velocity at the sampler intake
dt = reference exhaust diameter. It is the diameter for which %
u
we obtained the lowest test values of —.
u
d = exhaust diameter
2.2 Sampler Performance
The performance of the sampler is characterized by the value of
u
u /u. For — = 1 the sampling will be approximately isokinetic. From
u
Figure 3 it can be seen that isokinetic conditions can be obtained with
the proper choice of d. The final size is chosen, of course, by measuring
the velocity profile within the sampler during test, flights.
The value of u was determined from the velocity profile in the
sampling chamber as measured with a hot wire anemometer. It is given by
A ff
eft /,\
u = v e —— (3)
m A
where
v is the mean velocity in the sampling chamber and it is obtained
m
from the measured velocity profiles
e is air expansion rate inside the sampler
-------
601
R 9
t sx 2.
<) (4)
being R is the radius of the sampling chamber and R. that of
S -L
the intake
A is the area of the geometrical cross section of the sampling
chamber
A = TTRg2 (5)
and
Aeff = U (Rs -
is the effective area.
*
The displacement thickness o is given by (3)
6* = 1.74 /& [cm] -(y)
being
2 -1
V = kinetic viscosity for V = 0.17 cm sec
X = distance from the entrance to the chamber % = 10 cm
v = air velocity at the center line of the chamber in cm/sec
Taking into account (3), (4), (5), and (6), we obtain
u u R.2
O 01
^ (8)
u v (R - 6 )
m x s '
-------
602
u
From (8) It can be seen — depends mainly on v .
— m
u
There are two circumstances we have carefully checked:
(1) How v changes when u changes
m o
(2) How vm changes when the sampler is tilted from the horizontal
position
(a) Influence of u on v
o m
The sampler was thoroughly wind tunnel tested at a wind speed
of 46 m/sec. (the tunnel's maximum). Although the aircraft speed when
sampling is 62m/sec, this difference in wind speed is not important
because the performance of the intake (u /u) is not affected by a change
in the Reynolds number once it exceeds about 3000.
u
Thus, we expect that — will remain constant.
m
Measurements of v = f(u ) were made with the sampler installed in
mo
the aircraft for u in the range 40 to 81 m/sec. Measurements in the
o
wind tunnel at 42 m/sec fit well with those obtained in the aircraft.
(b) Dependence on tilting of the sampler
The value of v was measured in the wind tunnel with the
m
sampler in the horizontal position and tilted 8° (the maximum expected
attack angle variation) from the horizontal. The results indicated
negligible sensitivity to angle of attack.
2.3 Conclusions
Although a few final airborne tests for the sampler are planned, it
has been installed in the aircraft and was successfully used during the
August, 1974, St. Louis measurements.
-------
603
According to the wind tunnel tests
u
^•= 1.18
u
Although this value is certainly very close to being correct, we do want to
better determine in normal flight conditions how exhaust size affects
the sampler efficiency.
-------
604
3.0 INSTRUMENTATION FOR MULTIWAVELENGTH AIRBORNE
PRECISION SPECTRAL RADIOMETER MEASUREMENTS
J. M. Norman, D. W. Thomson, W. Benson, J. P. Breon
At the request of the EPA Meteorology Laboratory, a capability
of measuring hemispherical radiation in four wavelength bands, from
0.295 ym to 60 ym, has been added to the existing Pennsylvania State
University aircraft instrumentation system. Eight Eppley radiometers
(to monitor both upward and downward radiation streams) have been
mounted on the aircraft. The radiometers are interfaced to the
existing data logging system through individual especially constructed
preamplifiers so that signals from all eight may be sampled at up to
twice per second.
3.1 The Radiometers
Six Eppley, Model 2, precision spectral radiometers (PSR), sensitive
in three wavelength bands of the solar spectrum, have been obtained
from the EPA expressly for mounting on the aircraft, and two Eppley
precision infrared radiometers (PIR) have been purchased to facilitate
measurements in the wavelength band from 4 to 60 ym. Thus the wavelength
band from 0.295 to 60 ym is partitioned into 4 regions: (1) 0.295 - 3ym,
(2) 0.395 - 3 ym, (3) 0.695 - 3 ym and (4) 4 to 60 ym. Three PSR's and one
PIR are mounted facing upwards to measure the downward directed irradiance
and a similar complement is mounted facing downwards to sense the upward
radiation stream. Figure 1 shows the spectral transmittances for the
-------
605
IOO
80
UJ
z1 60
h-
X
z
I 40
H
Z
III
UJ
u
IT
Ul
O.
20
0
-
-
-
-
-
2
f
r*
i
GG 395
i i
YG 295
^~~*i=i:*^
RG 695
i i i i i i i i i i i i
0.8 1.4 2.0 2.6
WAVELENGTH (m)
FIGURE I •• SPECTRAL RESPONSE OF EPPLEY MODEL 2 DOMES
-------
606
domes of the various pyronometers as published by the Eppley Corporation.
The spectral response of the pyrgeometer is described as follows:
"The composite envelope transmission exhibits a sharp transition
between about 3 and 4 ym, from complete opaqu€>ness to maximum
transparency, and (apart from the normal waviriess associated with
such interference patterns) a general transmittance of about 0.50
decreasing, with increasing wavelength, to 0.30-0.40 around 50 ym."
The calibration factors provided by Eppley were checked with a Link-
Fuessner pyrheliometer recently acquired by the Meteorology Department.
On a clear day the Link-Fuessner is used to determine the solar beam flux
density (in a plane perpendicular to the direction of the sun) and at the
same time a PSR is shaded with a paddle that is designed to obscure the
same solid angle as the Link-Fuessner views. After accounting for the
sun incidence angle, which is calculated from true solar time (as well as
measured with the Link-Fuessner), the difference between the total output
(unshaded) and the diffuse only output (shaded) should correspond to the
flux density indicated by the Link-Fuessner. Zero drifts on all radiometers
must be carefully monitored if 1% accuracy is to be obtained. The pyranometer
with the RG695 is subject to particularly large zero shifts fcften greater
than 4%) under high radiation conditions with light winds due to heating of
the outer dome by the absorbed visible radiation. This is likely to be
completely negligible during operation on the aircraft. Since only a
RG695 filter (calibrated) was available with the Link-Fuessner, it was not
possible to check the PSR with the GG395 dome by this technique. However,
each of the pyronometers was checked by a second method that involved
comparison with a reference pyronometer (serial no. 12699F3)• The WG295
-------
607
TABLE I : RESULTS OF EPPLEY MODEL 2 CALIBRATIONS THAT WERE
CONDUCTED AT THE PENNSYLVANIA STATE UNIVERSITY IN 1974.
RADIOMETER
SERIAL NO.
I2699F3
1 2698 F3
12708 F3
12709 F3
12623 F3
12624 F3
FILTER
DOME
WG 295
WG 295
RG 695
RG 695
GG 395
GG 395
CALIBRATION FROM
EPPLEY CORP.
mv ~min
Ly
6.79
6.92
6.97
7.15
5.97
5.69
RATIO TO
#I2699F3
1.000
1.019
1.027
1.053
0.879
0.838
CALIBRATION WITH
LINK JUNE 9
mv ~ min
Ly
6.74
~~
7.08
7.20
-
RATIO TO
IH2699F3
1.000
^
1.050
1.068
-
CALIBRATION WITH
WG 295 ON
EACH RADIOMETER
JUNE 10- RATIO
TO * I2699F3
1.000
1.017
1.025
1.053
0.880
0.835
-------
608
TABLE g: SPECIFICATIONS FOR EPPLEY PRECISION SPECTRAL RADIOMETER
(PSR) AND PRECISION INFRARED RADIOMETER (PIR).
SPECIFICATION
IMPEDANCE
TEMPERATURE COEFFICIENT
TIME CONSTANT
PSR
300 OHM
PIR
400 OHM
10.5% 10.5%
- 20°C TO+40°C -20°CTO+40°C
I SEC.
2 SEC.
COSINE RESPONSE
LINEARITY
ORIENTATION
MECHANICAL VIBRATION
±1% 10°-90° <5%
< I % TO 4 Ly/min 1 I % TO I Ly/min
NO EFFECT ON INSTRUMENT
PERFORMANCE
WITHSTAND UP TO 20 g's
-------
609
AEROSOL
SAMPLER
N x-V\ \
VENTURI },
. \ U,l
FIGURE 2- HEMISPHERICAL VIEW OF (A) UPWARD FACING AND (B)
DOWNWARD FACING RADIOMETERS WHEN MOUNTED ON THE AIRCRAFT.
-------
610
dome from pyranometer number 12698F3 was installed on each radiometer, and
one at a time the output of each PSR was compared to the reference PSR.
All of the calibration results are contained in Table. 1. The PIR's
are more difficult to calibrate and Eppley's calibrations were not
checked except to insure that they gave reasonable readings in a cavity
of known temperatures. At the present time, a calibration cavity is
being designed so that more precise calibration can be obtained.
The angular response of the radiometer is sufficiently close to an
*
ideal cosine response so that negligible errors occur in hemispherical
readings because of improper angular response. However, on some occasions,
it may be desirable to restrict the view of the downward facing radiometers
to something less than a full hemisphere. To faciliate this, blackened
cylinders have been fabricated to restrict the radiometer view to
within +_ 30° of a perpendicular through the center of the thermopile sur-
face. These cylinders also have tops and, thus, otherwise, serve as
protective covers for the radiometer domes. The top of the PIR cylinder
also has provision for a dessicant to prolong the life of the KRS-5 dome.
A brief summary of the specifications of the PSR and PIR is contained
in Table 2.
3.2 Radiometer Mounting
The eight radiometers were mounted on the aircraft with four facing
upwards (fuselage mount) and four facing downwards (starboard wing mount).
Both the upward and downward mounts are designed so that the plane of the
thermopile is level when the aircraft is in its normal flying altitude,
which is - 5° nose-up. This requires a carefully designed "double-angle"
shim for the wing mourtts.
-------
611
When mounting radiometers, it is most desirable not to have any
unwanted structures in the radiometer view. Unfortunately, this is
not possible on the Aerocommander so we have dealt with it in a way
that allows us to correct for existing blockage. The upward facing
radiometers view the top of the wings and forward fuselage, propellers,
tail, aerosol sampler, venturi and the other radiometers. The fuselage
and wing, which are painted white, constitute the greatest potential
source of error so a blackened shadow band has been added to each
radiometer to black the radiometer view within 6.5° of horizontal,
Fig. 2a. This also blackens most of the venturi as well as the other
radiometers. The aerosol sampler and venturi are painted black and the
extremely small area of view occuped by propellers and tail is corrected
for. Furthermore, it is highly unlikely that the sun could glare from
one of these surfaces (those that protrude above the shading band) and
the view lost by blackening out these structures is simply not worth the
effort which would be required. Glare that finds its way to the thermo-
pile by reflection from the dome also is likely to be negligible.
The downward facing radiometers are mounted below the wing instead
of on the lower fuselage for several reasons: (1) It is not necessary
to develop elaborate shielding to protect the radiometers during take
off and landing. (2) The radiometer domes will be very much easier to
keep clean since no oil spray exists as under the fuselage. (3) Suitable
mounting points already existed on the starboard wing. The only dis-
advantage to the wing location is that a substantial fraction (about 13%)
of the radiometer view is occupied by the fuselage. Thus, a special
blackened mask has been designed to blacken the aircraft structure from
the view of the radiometer, Fig. 2b.
-------
612
This was accomplished by mounting a camera in the precise position
of the radiometers, and then photographing their effective view through
a hemispherical lens.
Since downward facing pyranometers sense only reflected radiation,
which is much smaller than the downward incident radiation, it is very
important that no glare from the sun strike the domes or thermopiles.
With the shade of the wing and the fuselage blocked by the blackened mask,
there is no chance of this happening except at extremely low (few degree)
sun angles.
3.3 Radiometer Signal Conditioning
Expected radiation values will usually produce full scale pyranometer
output voltages ranging from 30 microvolts to 12 millivolts. With the
low irradiance values, particularly in the infrared, it is also desirable
to maximize the readout resolution of the records. Normally, to satisfy
such requirements, a commerically available, low drift, high gain amplifier
system could be used for each pyranometer.
Because the pyranometers had to be physically installed far enough
from the aircraft's surfaces to prevent blockage which would have jeopardized
the accuracy of the radiation values obtained, the downward looking radiometers
were mounted out on the wing approximately 20 feet from the main instrumen-
tation and data acquisition console, and the upward units on the main
fuselage about 10 feet from the acquisition console.
-------
613
This installation posed several major problems in signal conditioning
since some of the pyranometers were expected to have very low radiation
values. These values had to be transmitted back noise free to the main
data console for further conditioning and recording. Furthermore, for
the low radiation values, an extended readout resolution or span was
necessary to prevent any system sensitivity involvement in the recording
process. The final span chosen for each radiometer yields the maximum
possible number of counts and accuracy for data reduction.
The low level radiation values required that the amplifier circuits be
located near the radiometers to prevent noise generation and signal losses
which can be caused in transferring low signal levels over long lines.
For the wing installation, airflow considerations had to be made to account
for possible influence of temperature variations during flight on the
electronic circuits. Space was another prime consideration because of the
aircraft wing and inspection plate (which provides wing access) size.
Finally, cabling was a major concern. It is always desirable to keep
the number of wires to a minimum in such installations to prevent ground
loops, excessive weight, and signal interference from other operational
systems.
Consultations were made with other research groups and companies that
had been involved in the construction and use of analogous instruments.
Most groups recommended that improvements to their systems or changes
could be made to obtain a more reliable and stable system. This prompted
our group to investigate several possible novel circuits.
-------
614
A study was made of each of the various analog operational amplifier
circuits which could be used to provide the gain and stability required
in the air flight environment. The list included chopper stabilized,
FET, and instrumentation operational amplifiers. A test procedure
which included short circuit, open circuit and constant voltage settings
over the expected range of operation was established to compare all these
circuits. The units were all simultaneously evaluated in a laboratory
temperature controlled chamber. With some further studies, an additional
circuit was included for evaluation. It consisted of a two wire trans-
mitter circuit as shown in Fig. 3.
The amplifier is a linear integrated circuit designed to convert the
voltage obtained from the sensor into a current, and send it through to a
receiver, utilizing the same simple twisted pair as the power supply.
Use of the power supply leads as signal transmission leads eliminates two
or three extra wires for each amplifer. Furthermore, current output
minimizes susceptability to voltage noise spikes and also eliminates line
drop problems.
Fig. 4 is a plot of the test results of the amplifiers compared.
Observe that the two wire transmitter provided the best stability in the
desired range of operation (under the test conditions instituted). This
unit was also the simplest to construct and required the least space.
Most importantly, it only needed 2 wires to transmit both the power and
the radiation signal value to the data console, and thus, it was not
necessary to install additional cables in the aircraft wing.
-------
615
tr.
UJ
\-
(O
<
a:
UJ
a:
a:
ID
O
UJ
a:
o
h-H-
DO O
fO
UJ
CC
c
>"
-------
616
CE
LU
Q |~
LU t
^ 2
_| CO
— z
00 <
co
o:
LU
CL
a.
o
X
o
t-
z
LU
or
cr
Z3
O
r
O
oo
o
N
O
CO
C\J
CO
(O
to
CVI
o
ro
OJ
LU
o:
or
LU
Q.
5
LU
U 2
O
CO I-
LU (J>
LU Z
IT 3
O LL
LU
Q <
CO
CD
CO
(£
LU
O.
<
LU
-------
617
The total error for a 2 wire transmitter is:
AIs
=-^— = AV - + AV + ARg
I ref os 6
span
where:
1 = open loop supply current
O
I = change in output current from 0% to 100%
span
V - = reference voltage regulation
V = input offset voltage
OS
Rg = current setting resistor
Typical values for our conditions were approximately 0.45%. To assist
in constant evaluation of this error an auto ground reference system was in-
corporated into the installation. It provides checks for temperatures and
zero drift which can then be corrected in data reduction. The two wire
transmitter has an operating voltage range from 10 to 50 volts DC which
allowed use of the aircraft supply voltage. This prevented further drain
on other instrumentation power supplies or the installation of new supplies.
Lastly, the transmitter unit is capable of gains up to 1500 with the same
stability factor — an important feature in this type of operation.
The output of the two wire transmitter is fed to the extender circuit
shown in Fig. 5. This circuit has an operational amplifier that has a
voltage divider and adjustable input compensation network. The circuit,
with all its possible gain and output adjustments enabled full range coverage
-------
618
r
o
oc
o
V)
o
o_
a:
LJ
o
1
X
LJ
m
Lul
tr
o
u_
-------
619
from all of the radiometer output signals to cover a full +_ 1 volt
input range for data recording. A complete calibration procedure has
been developed for the two wire transmitter. It is reasonably easy and
can be accomplished with available standards for signals of this level
and type.
3.4 Correction of Radiometer Outputs
The task of correcting the output of a radiometer due to obscured
portions of its view requires that the radiant intensity in the portion
of view in question be known. For this reason a blackened mask (using 3M
velvet black paint) is used to obscure the view so that negligible amounts
of pyranometer signal arise from this region and so that the thermal
emissivity of this region is known for correction of the PIR. The total
flux density received by a cosine-compensated sensor can be written
l rTT/2 f2TT
E = - 1(9, ) sin 9 cos 9d 9d
0 0
where 0 is the angle from the normal to the sensing surface and is
its orthogonal counterpart for spherical coordinates, I(9,(j)) is the
radiant intensity and E the flux density. The sensor output arising from
the incident energy is cE where c is the calibration factor (mv/Ly/min).
If the illuminated hemisphere is assumed isotropic, which certainly is
reasonable since the view corrections are small anyway, the fraction of
the sensor view arising from any region of the hemisphere is
-------
620
1 f°2 f*2
f « - sin 6 cos 6d 8d<()
91 *1
2
[sin 62 - sin 6;L]
If the output, which arises only from diffuse radiation, from a partially
obscured pyranometer is V and f is the fraction of the hemispherical
view blocked, then the corrected voltage is given by V = V./(l-f).
Correction of the PIR output is more difficult because the temperature
of the obscured region must be known. The output of the PIR thus has
contributions from two sources; the surface of interest and the shield.
Again assuming isotropy of the diffuse angular distribution, the true
flux density arising from the underlying surface and corrected for the
effect of the shield becomes
V V ,
~=[-~- foT84]/(l-f)
where T is the shield temperature (probably very near the measured air
5
temperature), a is the Stephan-Baltzman constant and V is the actual
voltage recorded from the partially obscured radiometer. For the upward
facing radiometers f = 0.022 and for the downward facing f = 0.136.
•
A precise view factor correction for the upward facing pyranometers
requires separation of beam and diffuse components of the irradiance;
however, the total correction is so small that values accurate to 1% can
-------
621
be obtained by using f = 0.01 for all conditions. Using f = 0.01 may
also be most reasonable under overcast conditions since it is well
known that an overcast sky is brighter near the zenith than near the
horizon. Under hazy conditions when direct beam and diffuse components
may be comparable, using f = 0.01 is likely to be most suitable.
3.5 Data Analysis
When direct beam radiation from the sun is the major contributor
to downward irradiance, for instantaneous readings it may be necessary
to correct the radiometer outputs for changes in aircraft altitude.
In the PSU aircraft altitude angles are available from gyroscopes,
however, corrections should not be necessary if averages over substantial
periods are desired.
When the aircraft passes over discontinuities in terrain, the
radiometers will lag behind the actual irradiance change because of their
time constants. Some of this information can be recovered by reconstruction
the time series using the known time constant of the instrument (see Button,
1962, and Bauer and Button,1962). Although the radiometer system has
already been used for urban energy budget studies in RAPS, several tests
do remain to be conducted. They include zero shifts under rapidly
changing air temperature conditions and calibration runs over relatively
homogeneous surfaces such as a large lake.
-------
622
REFERENCES
Bauer, K. G. and J. A. Dutton, 1962: Albedo Variations Measured from an
Airplane Over Several Types of Surfaces, J_. Geophys. Res., 67, No. 6.
pp. 2367-2376.
Dutton, J. A., 1962: Space and Time Response of Airborne Radiation Sensors
for the Measurement of Found Variables, J^. Geophys. Res., 67, No. 1,
pp. 195-205.
-------
623
4.0 AIRBORNE MEASUREMENTS OF TURBULENCE
IN THE PLANETARY BOUNDARY LAYER
T. G. Redford, M.S. Thesis Research in Progress
During the past two years, a comprehensive series of aircraft
flights to measure the statistical properties of turbulence in the
planetary boundary layer have been conducted under a variety of conditions,
They have been flown during all four seasons, day and night, over urban
and rural areas, and over mountainous and flat terrain. Most of the
flights have been in neutral or unstable weather conditions, clear of
clouds and precipitation, during the day and over or near the city of
St. Louis, Missouri. Many of the flights were coordinated with other
research efforts underway in the EPA RAPS program. Altitudes for the
observations ranged from 1000 feet above the surface to 9,500 feet, but
measurements below 5,000 were emphasized. We quickly established that
there was little point in attempting to measure turbulence at night or
in stable low wind conditions. The aircraft turbulence system lacked
sufficient sensitivity to resolve the low levels of turbulence existing
under those conditions.
The properties of boundary layer turbulence are affected by the
inter-relation of many factors including wind speed, stability, topography
and altitude. Therefore, our efforts to analyze the turbulence have been
made by statistical analysis of each related independent and dependent
parameters. As the measure of turbulence, the vertical wind speed is used
because we expect the scale of the vertical gusts to be on the same order
-------
624
of magnitude as that of air motion usually referred to as turbulence.
In order to compute the vertical gust velocities, we combine outputs
from the following sensors:
P = static pressure
T = temperature
IAS = indicated air speed
•
W = vertical acceleration
ac
0 = pitch angle
AP * pressure difference between upward and downward oriented
impact pressure probes
Additional information such as Doppler winds was recorded for navigation
purposes and to allow for future analysis of more subtly related factors.
The output from each respective transducer, converted to an electrical
signal, is fed into a multichannel Analog-to-Digital Converter. All
signals are scanned twice per second, converted to a digital format and
recorded on computer compatible magnetic tape.
The vertical wind velocity is calculated for each half second interval
using the following basic routines:
W = W - W
ac meas
Vertical wind equals vertical aircraft velocity minus aircraft
velocity relative to the air.
-------
625
W = W dt with linear trend removed
ac ac
W - TAS (0 - a)
meas
a = where 11 is the wind tunnel determined empirical
constant for the PSU gust probe
Pstd (IAS)2
q = ±-—
TAS » / ~*— where p is the air density
PSTD
_
P ~ RT* Pstd
Making all the necessary subsitutions
w . MS ( _ +
(IAS) ac
where temperatures are specified in degrees Kelvin, pressures in millibars,
velocities in meters per second, and angles in radians, respectively.
After the vertical velocities are computed, they are spectrally
analyzed using the PSU SAFFT (Spectral Analysis Fast Fourier Transform)
program. Figure 1 is an example of a ten minute run on a flight over
St. Louis on August 17, 1973. It clearly shows that the wavelength
(approximately scaled for the mean aircraft velocity) with the largest
amount of energy is = 105 meters. A large number of such analyses allows
-------
626
@
w
Pn
Phugoid Frequency
66000
i i - 1 - 1 — i — i — i i i 1 1
6600 3300 1650 660
330 165 110 66
SPATIAL WAVE LENGTH (METERS)
Figure 1. Spectrum of vertical velocity fluctuations recorded on
12 min run at =1300 AGL, 0830 CAT, 17 August 1973 over
St. Louis, Mo.
-------
20001
1500
1000
_i
<
627
+ 4-
500
+ + 4 -H-
•++4
+ -H-
+ -H-
_L
FIGURE 2
100 200
WAVE LENGTH (M)
300
400
CALCULATED WAVELENGTHS AS A FUNCTION OF
ALTITUDE.
-------
628
8
o
o
in
Q 6
ID O
D 100 200 300 400
WAVE LENGTH (M)
TURBULENCE ANALYSIS FIGURE 3= ARITHMETIC AVERAGE
WAVELENGTH AS A FUNCTION OF ALTITUDE.
BARS DENOTE STANDARD DEVIATION.
-------
629
us to plot the wavelengths or frequencies containing maximum energy
against other factors such as altitude, surface roughness, or stability.
Figure 2 is a scatter diagram of calculated wavelength versus altitude
for 47 runs, all flown in August, 1973 on six different flights. Fig. 3
presents the arithmetic average wavelength as a function of altitude.
Standard deviations of the means are also shown.
It should be noted that some observed data has been edited from
our scatter diagrams. One occasional source of error is, for example,
the aircraft's natural"phugoidal" period of oscillation, which is
directly proportional to the air speed. It often appears in the spectral
analysis during conditions with very Light or essentially no turbulence.
In these situations the phugoid will often have the largest amplitude
on the spectral graph, but it obviously must be disregarded. Sometimes
the dominant wavelengths in the analysis are larger than the altitude
above the ground. In the turbulent planetary bounary layer, we assume
that vertical wavelengths should be about the same as the horizontal and
that the vertical should not normally exceed the altitudes at which they
are measured. To date, these cases have not been included in the analysis,
Although processing of the individual turbulence runs is largely
complete, analysis of the set of reduced data has only recently begun.
The distribution of turbulent wavelengths as measured by the aircraft
does seem to be in general agreement with the theory proposed by Blackadar
in an unpublished NASA report . The mixing length is given by
Panofsky, H. A., 1972: Tower Micrometeorology. AMS Workshop on
Micrometeorology.
-------
630
1000
900 h
800 h
700 h
600 h
UJ
§ 500
_j
<
400 h
300 h
200 h
100 h
30
60 90
MIXING LENGTH (M)
120
FIGURE 4 • MIXING LENGTH VS. ALTITUDE AS PREDICTED BY
BLACKADAR MODEL .
-------
631
0.0063 U,
f
kzf
, C0.0063 u.
''o ( *c
( kzf
e0.0063 UA
- kzf
c 0.0063u^Q
|£'kzf
e 0.0063U,
u. - (V + 15 fz)k
*Q 2 C
fz _ - fz
0.0063 u. 0.0063u.
in ( —= ^ 5 i£)
fz -fz '
o o
e
0.0063u. 0.0063u.
*o *o
where £ = mixing length (m)
Uj. = surface friction velocity (m/s)
*o
f = Coriolis parameter = 9 x 10 (sec~ ) at latitude 38 °N
k = von Karman constant * 0.4
z = altitude (mO
V = wind velocity (m/s)
z = roughness length = .5 (m) over the city
Neutral conditions and homogeneous terrain are assumed.
Figure 4 shows the relationship of mixing length to altitude for
5 different wind speeds. The curves were calculated and plotted using a
programmable desk calculator. Since the aircraft data were gathered during a
variety of stability conditions and over non-homogeneous terrain, it is
not surprising that there is not better quantitative agreement with the
-------
632
model. In particular, the slightly unstable average conditions combined
with the large roughness length of the city compared to its surroundings
have probably increased the depth of the planetary boundary layer to
several times the predicted depth. Nevertheless, there is agreement
to within an order of magnitude between predicted mixing lengths and
observed turbulent wavelengths and, further, in the. shape of the curves
in that the larger values are observed in the middle altitudes. (Compare
Figures 3 and 4.) Additional study is now underway to better establish
the relationships between theory and the observations.
-------
633
5.0 AIRBORNE MEASUREMENTS OF
AEROSOL IN THE ST. LOUIS URBAN AREA
K. L. Schere
M. S. Thesis Research in Progress
Aerosol concentrations and the size spectrum of aerosols are
expected to vary both as a function of distance from an urban
complex and upon meteorological parameters. This research study
consists of analysis of airborne aerosol measurements taken in and
around the metropolitan St. Louis area during August, 1973, and
July-August, 1974.
The instrument package on board the PSU Meteorology} twin-engine
Aerocommander provides comprehensive meteorological, aerosol, turbulence
and radiation measurements. The aerosol sampling instruments include
a Royco particle counter #225, an M.R.I. Integrating Nephalometer, an
Environment One-Model Rich 100 condensation nucleus counter, and a Thermo-
Systems 3200A Mass Monitor. The Royco instrument has the capability of
sampling small particles within discrete size ranges and can, thus, be
used to measure in situ size distributions of aerosol particles within a
range of about .5y diameter to approximately 8y diameter. The Integrating
Nephalometer and the Mass Monitor provide indications of the total mass
loading of small particles within the air. Although the two instruments
utilize different physical principles in their operation, taken together
they provide an adequate picture of the total particulate loading. The
-------
634
Rich 100 instrument provides a count of the total number of condensation
nuclei in the air, but the instrument cannot sample within discrete size
ranges. Thus, in this study, the data^from the Royco almost exclusively
are used, while the data collected from the other aerosol sensors, although
they provide perfectly good data sets by themselves, are being used only
as reference or backup data. The isokinetic sampling probe, which is
located on the top of the plane's fuselage so as to be adequately re-
moved from the engine exhausts and skin venting, has been windtunnel
tested to verify that isokinetic flow exists at an air speed of 140 mph.
This speed is maintained on all aerosol sampling flights in the Aero-
commander .
Flight patterns used for measurements were of two types: (1)
a vertical sampling pattern, and (2) a horizontal sampling pattern. The
St. Louis area is assumed to be a 50 km diameter circle centered in
northwest St. Louis city. The circle, thus, includes most of the major
industries and the bulk of the population for the area. On any given
flight day, the mean wind is then aligned through the center of this
circle. For the vertical sampling pattern, four points are chosen on this
line, over which samples are taken at altitudes ranging from 1500 feet msl
(- 1000 ft msl) to approximately 2000 feet above the height of the observed
haze layer in steps of 1000 feet. The points are picked so that they are
far upwind, near upwind, near downwind, and far downwind of the city. For
the horizontal sampling pattern, six legs of varying length are flown
normal to the mean wind line so that the entire. St. Louis area is covered.
The pattern extends 75 km downwind of center city and 50 km upwind. It is
flown at one level within the haze layer and one level above it during the
-------
635
afternoon hours. The vertical sampling pattern is flown three times
during the same 24-hour period: Once in the morning hours around sunrise
when the air is most stratified, once in the afternoon when the mixing
is strongest, and once in the late evening when the inversion is just
starting to form.
The data analyzed to date was collected during flights conducted
in August, 1973. It appears that many non-source factors are influencing
the distribution of particulates present in the air; including mean wind
direction and speed, relative humidity, type of prevailing air mass, and
time of day. From a previous study done in the St. Louis area, it
was found that the mean mixing-depth for this time of year was about 1500 m.
However, it was noted that afternoon mixing depths are often much higher
than this. In order to more clearly see the vertical variation of total
particulates (> .5y dia.) plots were made from the data. It is found that
during stable conditions, such as are prevalent at night, the atmosphere
becomes stratified as a surface inversion frequently develops. When this
happens, the total number of particulates gradually drops off with altitude
until reaching a fairly constant background level. Figure 1 is such an
illustration. This is the vertical profile of total particulates on
August 11, 1973 between 2100-2200. The air mass over the St. Louis region
at this time was a quite clean one as evidenced from the low particle counts.
Figure 2 is a similar plot. Here the vertical profile is shown on
August 18, 1973, at 1000 (solid line) and 1100 (dashed line). This plot
illustrates two principles. First, during the daylight hours when the
-------
636
t
CJ
c
FIGURE I: VERTICAL PROFILE
(ALL PARTICLES >,5u DIA.)
I I AUG. 1973
2100 MRS.
. . I . . i . I . . . . I . . . . I
I 2
ALTITUDE
[Km.)
100.
u
d
c
1.0
FIGURE 2: VERTICAL PROFILE
(ALL PARTICLES >.5u DIA.)
18 AUG. 1973
• • 1000 MRS.
a-— x I 100 MRS.
ALTITUDE (Km.)
-------
637
mixing layer has been stirred well by convective currents, the homogeneity
is very marked. There is a sharp drop-off of particle concentration above
the mixed layer. Secondly, it is seen that the depth of the mixing layer
increases as the convective heating from the earth increases. This is
manifest by the displacement of the vertical profile to the right from 1000
to 1100 hours.
The size distribution of particles in the atmosphere was also
estimated. The results are plotted using the same form as that used by
Junge in his earlier work on this subject; that is dN/d(log r) vs. log r.
This scheme was chosen because the area under a plot of this type
represents the number of particles. Junge found that for tropospheric
aerosols the size distribution of particles greater than .1 ydia. could
_3
be approximated by a power law of the form dN/d(log r) ~ r . In computing
size distributions from the Royco particle counter data, a least-squares-
fit technique was applied to the five points in each distribution. Since this
is plotted on log-log axes a power-law results from each. It was found that
in the mixed layer a typical plot was such as that shown in Fig. 3. A total
of 19 particle size spectra were computed from the 1973 data, 18 of which
were within the mixed-layer and only one of which was taken from data in
the relatively clean air above the mixed layer. This distribution is
shown in Figure 4. Note that the magnitude of the slope is less here and
that the whole plot is displaced to a position beneath the one in Figure 3.
This reflects the fact that the total particle loading is much smaller above
the mixed layer and furthermore, that the decrease in number of the smaller
-------
to.
E
u
o
638
100. c-
10.0
1.0
XI
>x
Z
FIGURE 3 : PARTICLE SIZE SPECTRUM
18 AUG. 1979
1000 HRS.
ALTITUDE = .56 KM.
dN/d(log r) = 1.79 r
-3.23
.01
.001
Dl
100.
10.0
10.
u
>%
6 1.0
i ''m| L_._!_-' * ^JJ I —i.-.--Iriii J 4 1 M Mi.
.1 1.0 10.
RADIUS (u)
FIGURE 4 : PARTICLE SIZE SPECTRUM
15 AUG. 1973
2000 HRS.
ALTITUDE * 2.65 KM.
dN/d (log r) " 0.227 r
-2.57
.01
.001
1.0 10.
RADIUS (u)
-------
639
particles is possibly more accentuated than the decrease of the larger
particles here. Of course, more size distributions taken above the mixed
layer are needed to establish this and thus, a special effort was made
during the 1974 project to obtain these.
As this report was being written, preliminary analysis of the 1974
RAPS flight data was already underway. Figure 5, prepared by Y. Mamane,
is an example of our most recent observations. Changes in the aerosol
number concentration between the upwind (north) and downwind (south) sides
of the city as well as the apparent structure of the planetary boundary
layer are evident. These observations were extracted from the observer's
1°8- Final "calibrated" results will not be available until the high
resolution digitally-logged data is processed.
-------
640
cc
Ul
o
UJ
_i
o
u.
o
~O
O
UJ
-1(0
JJrO
O o
or _i
o.
o:
UJ
in
ui
UJ
UJ
UJ
CD
o:
UJ
U-
o
cc
<
Q.
CC
UJ
OD
8
g
8
SS
o
o
in
in
O
o
m
8 8
1C
m
CM
aaniinv
-------
641
6.0 SURFACE MEASUREMENTS OF AEROSOL IN A RURAL
AREA USING DIFFERENT METHODS
Y. Mamane, Thesis Research in Progress
6.1 Introduction
The purposes of this project are to study in detail the characteristics
of the suspended particulates in a rural area and to evaluate and inter-
compare different instruments, especially their indications of mass con-
centration, visibility and size distribution.
This report describes briefly one experiment, and summarizes and
presents a preliminary analysis of selected data. Most of the data,
recorded on magnetic tape, is to be processed during fall, 1974.
6.2 Instrumentation
In order to compare several "in situ" instruments, one must have a
sampling system which causes negligible changes in the concentration and
size distribution of the aerosol that is sampled. Furthermore, it must
enable the instruments insofar as possible to simultaneously sense nearly
the same sample of air. The sampling line shown in Figure 1 was designed
and used for this study.
The sampling line has the following features. It:
(a) is short,
(b) has short horizontal sections,
-------
642
o,
o
UJ
Ez
< —
•UN
UJ
a.
LJ
Q.
O
> M
O CM
ac.
I Q
o 5
(T ~
Z
_J
a.
5
<
V)
UJ
I
o
I-
UJ
•XL
V)
UJ
(£
3
CD
O I
UJ t-
UJ
« w IE
-------
643
(c) is "smooth" with no change in cross section, and
(d) is made of a large (diameter) pipe.
The instruments used continuously in this study were:
(1) Integrating Nephelometer - MRI
(2) Royco 225 Particle Analyzer
(3) Mass Monitor, Thermo Systems 3200A
(4) Rich 100 Condensation Nucleus Counter
Some other instruments such as a high volume sampler and cascade
impactor were also occasionally used. Table I summarizes the characteristics
of each instrument.
Instrument failures in the primitive field station and adverse
weather conditions during the winter of 1973/74 made it difficult to obtain
several days of continuous measurements from all the instruments.
The instruments were located in a cabin far from local sources of
air pollution. At first, the instruments were run continuously, and the
data was recorded on a strip chart (all the channels on the same chart).
Beginning in summer (1974), the data was recorded on magnetic tape during
the day and on a strip chart at night. This is described in Figure 2. The
magnetic tape data has not yet been processed.
6.3 Summary of a Selected Data
Figure 3 summarizes data collected on March 5-6, 1974 by the
Nephelometer and the Mass Monitor. There is fair correlation between the
light scattering parameter and the mass concentration measured by the mass
monitor. The factor which converts the light scattering to mass concentration,
-------
644
tn
vt
H
UJ
2
UJ
(E
CO
^
UJ
5
UJ
u
-
1-
Q
Z
<
>-
(£
<
5
2
^
CO
1
CM
UJ
tr
o
o
u.
U o
< 8
5 CM
— CM
c m
0 o ^
*~ O —
~" N_ 1 1
^ f- V
Is ~
w y o
3i x g a
5 5 o 1 t Q ~L
^ 2 2 I % S
3: cj cr — uj uj
. , Z H~ ^* 1 1 1 ^ «
UJ O CO 0 < W
5 « 5 5 ' ' '
*i <0 n, ^ 0
0 CO m •y
S < N Z - ,
-Q 5 CO 0 * §
••
O
UJ
o:
CO
i g|
CD
co oL
a:
UJ
l-
UI
S
<
tr
< •>-
°- <
o
ttl
$
*~ ol
t oL
Y/
%
4
A
$v
\N
1
3%
5O<
2^
i
i
YX
^^^
y,
//
/
8 S
CM 7
3|
CO
CO
<
2
-r'
Q ±
O uj
CO 2
$
£
i 1
o
0
z
0 O
S"
O 0 O
to uj ir
o cc
" I1
z
8 ^
8 i
o
(£
X
H
U.
8
CM
1
UJ
a.
t-
o
i-
UJ
y
o
4
Z
X
UJ
a.
Z
<
o
z
DAY RECORDII
i
_)
<
^^
CO
>-
a:
o
o
z
CLEANI
i
in
MAINTENANCI
1
_ f_
E o
H tr
S 2
CD (K
5£
0 Q
o uj
a: N
S «
o
1 z
CHECKI
OBTAIN
i i
-------
645
o
LU
t i
d o
JC.
i 12
T 5
E
Q.
Q
a:
V)
LU
cc
o
o
LU
X
a:
LJ
LJ
5
O
LU
X
a.
LU
LU
X
2
LU
LU
ui
CD
Z
o
a.
o
o
LU
cc
ca
-------
646
Table 1
Instrumentation (aerosol)
Function
Particle
Diameter
Mass
Monitor
Concentration
0.01 -
(probab]
20u
Ly not
Nephelometer
Scattering
Coefficient
No limit
Rich 100
Condensation
Nuclei
>0.0025y
(probably not
Royco
Size
Distribution
0.5 - 0.7
0.7 - 1.4
larger than
5-lOu)
Maintenance 1) Cleaning
Crystals
Warm-up
Response
Time
Sampling
Air Speed
Power
Input
30 min.
Order of Isec
~70 cm/sec
larger than 1.4 - 3.0
5-10U)
Flow Rate
Signal
Output
1 £pm
0-7.5 vde
-800 £pm
0 - 5 vde
3.0 - 5.0
> 5.0
or 0.5--10U
3 &pm 0.27 - 2.7 £pm
0 - 10 mv dc 0 - 0.1 v dc
Calibration By Manufacturer Freon-12
By Manufc.
1) Electronic 1) Adding
Calibration Distilled
Water
30 min.
- 1 sec
30 min.
~2 sec
By Manufc.
1) Electronic
Calibration
Few min.
- 1 sec
-900 cm/sec -200 cm/sec -200 cm/sec
70 W
80 W
65 W
-------
647
suggested by MRI, yields numbers which are more than five times higher than
the results indicated by the mass monitor. A typical size distribution for
that day is shown in Figure 4. This distribution is well represented by
the model suggested by Junge:
dN -3
3— = ar
dr
for this special case;
dN 1 — -3.02
— = 1.87 r
dr
Figures 5 and 6 show the highly correlated outputs of the Integrating
Nephelometer and the Royco (for one class of sizes).
A meaningful comparison between the High Volume Sampler and the Mass
Monitor is not yet available. Some data indicates that the mass monitor
is underestimating total mass.
-------
HGURE 4 = TYPICAL SIZE DISTRIBUTION ON MARCH 5,1974
10 ~
10
dN_
"dI r
TIMBER
O.I
0.01
ACTUAL DATA
I
I
0.3 0.6 1.1 2.0
PARTICLE RADIUS - urn
-------
o
^-
8
649
s
o
o
g
cc
ui
a.
ui
Z
o
s
O £
d
in
vn
o
in
OJ
o
m
•s-
evj
o
o
*
PJ
O
O>
to
111
cc
111
UI
o
UI
X
a.
ui
z
o
o
o
tr
cc
t-
o
\-
X
o
TE
to
5
X
-
"e
o
\
t/5
UI
O
CC
2
10
N.
6
CM
CM
~E
^-
'0
—
X
O
n
0
CL
d
op
6
Z
UJ
U-
lll
o
o
UJ
cc
cc
o
o
\ \
15
O
II
rf Q
IT
O
X
v>
cc
a
o
111
X
o
z
cc
UJ
1
X
a.
UJ
z
ui
o
in
1
5
cc
>
UI
IR
CVJ
o
E
d
m
HI
cc
ts
CJ
o
-------
P
co
UJ
(T
UI
1-
UJ
§
— 1
UJ
X
a.
UI
z
o
u
5
cc
7E
'0
X
(0
00
o
-Si
H
cc
a.
ao
s
UJ
a:
UI
to
(0
rO
to
(0
z
2
(-
Q
?E
*0
x
CO
0^
0
u
• •
CC
a
d
z
o
Q i-
o >
6
o>
h-"
UJ
z
d
UJ
u.
u.
UI
o
o
z
o
UI
tr
O
ui a:
x ui
i- a.
UJ
a:
-------
651
7.0 TECHNIQUES FOR THE "MESOSCALE"
INTERPRETATION OF AIRCRAFT MEASUREMENTS
T. Chin, M.S. Thesis Research in Progress
Aircraft data can be used to precisely determine the state of the
atmosphere on many scales as long as the time and space limits in which
it was obtained are recognized. Clearly, the limits of validity also
depend upon the method of data collection and the eventual use for which
the data is required. The limitations, in both time and space, result
from the basic nature of aircraft data. That is, it is asynchronous
because a single aircraft flying at a finite speed can only sample a
small atmospheric volume.
The aircraft data collected in conjunction with the SRG program
consists, basically of two sets taken on an urban scale (2.5-25 km) and one
on a mesoscale (25-250 km). The urban scale data was taken in the St. Louis
area during the summers of 1973 and 1974. Each "urban" sampling run was
on the order of ten minutes (36 km) long. The mesoscale data taken during
October 16 and 17, 1974, within the boundaries defined by the SRG mesoscale
model, consists of six flights of about 3-1/2 hours each, taken over the
two day experiment period.
The ultimate utilization of each data set dictates the techniques
which must be used in its reduction. Processing of the St. Louis data
is, essentially, a problem of a categorizing and tabulating nature. The
state of the atmosphere is measured and tabulated for various flight paths
-------
652
at various times and altitudes over the St. Louis area. The time
intervals of the sampling runs are short compared to the time scale of
the large scale phenomena under study, such as changes in stability and
changes in the concentration and distribution of aerosol. In this case,
then, the problem of asynchronous data is relatively unimportant. Each
sampling run may be treated as if all the data points were obtained simul-
taneously.
Because the SRG group had accumulated experience in processing
turbulence data, its processing presented no serious problems. However,
corresponding aerosol measurements were plotted and found to have a
much larger high frequency content than anticipated. To aid in visual
inspection of the data, we decided to digitially filter it and, thus,
remove most of the high frequency flutuations. Initially, a seven point
"Martin-Graham" filter with a cutoff frequency of 0.1 hz and termination
frequency of 0.6 hz was tried. (The aircraft sampling frequency
was 2.0 hz.) Due to the nature of the filter, it did not adequately attenuate
the high frequency components. This is because the response function of
such a filter is not zero beyond the termination frequency, but in fact,
increases in the negative direction until it becomes - 0.2 at 1.0 hz. A
second disadvantage of a filter with such a response function (with changing
signs) is that there will be phase shifts in any Fourier analyzed data.
To eliminate these undesirable features, the data was filtered by a seven
point binomial filter, whose response function is always positive and
effectively zero beyond 0.7 Hz. Figure 1 compares the response functions of the
two filters. It appears that although the Martin-Graham type digital filters
-------
653
I
CO
o
z
u. cr
LU
CO
O
Q.
CO
UJ
a:
o o
o
z
m
x
~ C5
9 W
I a*0* afar !
I I
00
Ifl
i
cr
i
z
i-
cr
CO
+• S w
CO —
z u-
o
. Il
to
m
^ 2
CO <
UJ
cc
tr
-------
654
can be designed with extremely sharp cutoff characteristics, for most
urban-scale aircraft data interpretation problems, the binomial filter
has better properties.
The mesoscale data is being used, in conjunction with other data
sources such as radiosondes and surface observations, for initialization
and verification at the mesoscale model. In this experiment, an entire
sampling run took two days to complete. Each day's data collection
consisted of flying over the same ground tract in a series of three flights
(see Fig. 2). Each flight leg required a flight of about 3-1/2 hours
duration. Refueling stops were made between legs. Thus, the time
scale of the phenomena under study, evaluation of the mesoscale features
of the atmospheric flow, was of the same order as the total sampling interval,
The asynchronous nature of the data must, thus, be taken into account.
Firstly, to facilitate the use of this data for initialization and/or
verification purposes, a pressure normalization program was written. Given
a representative sounding, i.e., the distribution of temperature, dew point
temperature, wind speed, and wind direction with pressure, the same variables
as measured by the aircraft are reduced or normalized to any desired
pressure level. As the program is now used, the atmosphere is assumed to be
in a steady state condition and the gradients of the above variables to be
horizontally homogeneous. These conditions are imposed because to date only
one sounding has been utilized for normalizing the data collected during an
-------
655
h-
O
*
&
(O
O
Nl
O
CO
ro
N-
O)
O
O
h-
O
CO
o
n 22
to —
«C\J
-
h-
C5
I-
UJ
5
Uj CL.
3S
LU
IT
O
C3
-------
656
- 12 hour period. The main purpose of this program is to, of course,
provide a means for generating values for the temperature field, the
moisture field, and the wind fields at any pressure level in the domain
covered by the aircraft. Since the aircraft flies the ground track at
various altitudes, it is normally difficult to separate vertical from
horizontal variations. Analysis to date indicates that the normalized
data does reflect much more clearly the horizontal gradients in temperature
moisture and wind speed and direction.
Figure 3 illustrates the effects of pressure normalization on flight
pressure and temperature traces,, respectively.
The straight forward pressure normalization program described above
represents, clearly, only a first step at best, and it does stretch the
limits of validity of the data. Nevertheless, it is, even in its present
form, still useful. For the conditions on October 16 and 17, the mesoscale
model predicted a warm surface low in the southeasternmost region of the
model domain. The warm region was barely discernable in the unnormalized
plots of the temperature field, but clearly evident in the normalized plots.
A two dimensional plotting program has also been written. It divides
the region of aircraft coverage into a grid in which the grid lengths are
4 to 5 times smaller than the grid lengths of the mesoscale model. Using
the normalized data and calculating the position of the aircraft ground
track with respect to this new grid, all data occurring inside a single grid
interval are simply averaged. In this way an averaged, spatial picture is
obtained for the pressure level to which the data was normalized. Fitting
-------
657
UJ
§
UJ
Q.
5 _
UJ o
t- o
J
g
j
I
E
3
F
£
5
UJ
CO
UJ
IT
Q.
a
in
N
s
-------
658
and interpolation schemes are being added to this program to fill in
neighboring grid points through which the aircraft did not fly. By
combining this program with the pressure normalization program for
various pressure levels, a three dimensional description of the various
parameter fields can be obtained. Once the three dimensional array is
generated, it is a simple matter to generate any vertical cross section
of the region or to generate any surfaces (at levels appropriate in the
model) of the fields under study.
Modifications are underway to include a scheme for updating the sounding
information used in the pressure normalization program. This will remove
the present steady state restriction. The desirability of removing the
horizontal homogeneity restriction in the gradients of the fields is
low at this time. A numerical model should be initialized and verified
against observed not computed data.
The asynchronous nature of the data can be dealt with, especially
when the data is used for verification. The times at which the aircraft
passes over the grid points in the mesoscale model are known. The model is
simply instructed to output its predicted values for the fields at the
times the aircraft flies over a grid point. The predicted value at that
grid point is then compared to the averaged pressure normalized aircraft
values, at any pressure level. In a similar fashion, this data can be used
in the initialization made by first starting the model with balanced large
scale data and then updating the appropriate grid points at the correct times.
-------
659
VI OTHER CONTRIBUTIONS
Part 1
A GENERAL APPROACH TO DIFFUSION FROM CONTINUOUS SOURCES
R. Draxler
H. Panofsky
-------
660
1.0 A GENERAL APPROACH TO DIFFUSION FROM CONTINUOUS SOURCES
R. Draxler and H. Panofaky, Research in Progress
1.1 Theory
There exist many methods for estimating dispersion from continous
point sources. In this project, an effort is made to bring together
experimental data from many field studies in order to formulate a useful
generalized treatment.
We begin with Taylor's diffusion theorem in Pasquill's form
for lateral and vertical dispersion respectively:
a
_y_
a t
v
and
^ - / f Fw
J
dn (2)
w
Here a and a are the standard deviation of the mass distribution in
Y z
the lateral and vertical directions, a and a the standard deviations
v w
of the lateral and vertical wind components. The diffusion time is t and is
approximated by x, the travel distance, divided by mean wind speed. Hence
Y(t) and Z(t) can alternatively be defined by
-------
661
a
-^Z O)
In these expressions, x is mean downstream distance, F(n) denotes
normalized Lagrangian operator of velocity components shown by the subscript
and n is Lagrangian frequency; a. and O are standard derivations of
A. Hi
azimuth and elevation angle.
The quantities Y(t) = Y(x/V) and Z(t) = Z(x/V) are often expressed
by power laws. However, in contradiction to power laws, both these
quantities approach unitjr for small x. We have attempted to remove this
incons is tency.
In order to evaluate the behavior of Y(t) and Z(t), we assume that,
as for Eulerian spectra, we may write:
nFv(n) = $y (f)
v
and (4)
nFw(n) = *w (°
w
where
-------
662
For practical diffusion estimates, T and T have to be estimated
v w
first; then, eq. (1) gives Y(t) and Z(t) from which a and a can be
y z
calculated given a and a .
A £j
The method is most likely to be useful for estimates of a , because
y
the assumption underlying Taylor's diffusion law are best satisifed in the
lateral direction.
1.2 Analysis
In practice, lateral and vertical dispersion from ground and elevated
sources are analyzed separately, giving a total of 4 categories. There is
some hope that lateral dispersion from ground and elevation sources behave
in about the same manner except in very stable conditions.
At the time of writing of this report, only lateral dispersion from
ground sources has been analyzed completely.
Figures (1) and (2) show the quantities Y plotted as function of T/T
for 5 field experiments with ground releases for day and night. The same
function appears to fit both figures about equally well. An approximate
fit is provided by:
1 + 1.022 (|-)0'595
o
(5)
except that the; actual decrease at large a/T- is somewhat slower than that
indicated by the equations.
-------
663
MM
aid
Sui
n
B
iL'EL LJ
o:u!> y
trvirir
ILD6 in
I
H
Z
_ w
•^ «
Hi
OJ 4-1
a. c
rH CO
CO 3
zed
liz
ali
1
a
1
N
o
n
n
m -H
. °^
"§^
0) -^ iH
(-1 4J
3 0 >•
00 C C
fe LM B
-------
664
trn:
h
I
44-
+, *
4 +* *4 *
• + 4
•» + . ++
t *******
+ 4 Oj.t 4
04t
T +4
* *+ * 1
4 1 *4
t n* *
*
44
"2 s
o3 "H
(U 4-1
a c
0} O
i-i
i-l (0
« 3
0) N
N -H
§C1
a
!Z O
o o
id
-------
665
The Lagrangian scale T depends upon the Richardson number but only weakly,
in the sense that T is largest in unstable air. Unfortunately, the
results from Hanford (Greenglow) give systematically larger T 's than
expected from elsewhere. The reason for this discrepancy is not yet known to
the authors. However, if we disregard this anomaly, we can obtain T from
Ri; hence, equation (5) gives Y, which yields a if a is known.
y A
A similar analysis for vertical spreading from ground sources is
in progress and appears less successful. There are only a few usable
experiments and, so far they have yielded inconsistent results. One
difficulty may be that this category least obeys the assumptions (such as
homogeneity) underlying Taylor's theory.
Elevated sources look promising, but analysis is just beginning
-------
666
VI OTHER CONTRIBUTIONS
Part 2
THE NIGHT-TIME MIXING DEPTH AT PHILADELPHIA
R. Hall
H. Panofsky
-------
667
2.0 THE NIGHT-TIME MIXING DEPTH AT PHILADELPHIA
R. Hall and H. Panofsky, Research In Progress
2.1 Introduction
In cities, night-time pollution concentrations are commonly higher
than day-time concentrations; in part due to the low wind speed, and,
in part due to the small mixing depth. Both must be estimated from
relatively limited information.
It has become customary to estimate night-time depth using a rural
sounding by adding a 3°C increment to the surface temperature and drawing
an adiabat to the sounding. Clearly, such mixing depths are unsatisfactory,
for they imply that the "heat-island" effect of the city is always 3°C.
We know from many models of the heat island that the temperature increment
is quite variable depending on heat input, wind speed and the initial lapse
rate. We have attempted to compare actual mixing depths with 3°C mixing
depth (denoted here by h,o).
Ideally, two soundings are needed for such a test; an upwind
rural sounding, and a sounding just downwind of the city. Lacking such data,
observations were obtained from Philadelphia where one sounding is
made every morning near sunrise to the south of the city. With north
winds, the city's heat island should be evident; even with south winds,
there ought to be a heat island (perhaps smaller) due to an industrial
complex situated to the south of the radiosonde launch site.
-------
668
2.2 Analysis of observations
Winds and temperature sounds were selected according to the following
criteria: wind direction between 315° and 45°, or between 135° and 225°;
unstable or near-neutral large rates in the lower levels; mixing depth
less than 400 m; low-cloud cover less than 3/10 and/or high clouds less
than 7/10 at 10,000 ft or above. Also h . was recorded as estimated by
National Weather Service personnel.
The observed mixing depths were subjected to various types of re-
gression analysis, guided by Summer's formula which states
2H
h = 7 X (1)
u ape
where H is the heat flux, u the mean wind speed, x the fetch over the
city, a the difference between rural and city lapse rates, p the
density and c the specific heat at constant pressure. The rural lapse
rate was assumed to be the lapse rate above the mixed layer.
2.3 Results
The winter mixing depths for north winds were generally high in
accordance with the fact that pollution problems rarely arise under
such conditions. This is probably because the lower atmosphere is
-------
669
well-mixed before it reaches the city, due to heating from below.
The additional heating by the city sometimes shows up as a slightly
more unstable lapse rate in the lowest few hundred meters.
This "incremental" heat island effect was small and not significantly
related to any of the available predictions. It is probably of little
operational importance, as the mixing depth is already high before the
air reaches the city.
Summer mixing depths are consistently lower than in winter. They
were analyzed in terms of wind speed and direction. In contrast to the
predictions of eq. (1), the mixing depth appears to increase slightly
with increasing wind, suggesting that the heat flux may be greater on
windy than on calm nights. The effect of wind on lapse rate did not
explain the result.
The best relation appeared between measured mixing depth and h_,
(Fig. 1) where
h = 0.6 h+3
suggesting that h _ overestimates the mixing depth significantly and
underestimates the pollution potential severely. Of course, this
result is valid for Philadelphia only, and analogous studies should be
made elsewhere.
-------
670
IK
UJ
V)
o
o
O
O
o
o
to
•H-
ro
+
f
O
O
CO
10
CO
UJ
tr
O
O
o
o
in
o
o
o
o
CVJ
o
o
sqot
-------
VI OTHER CONTRIBUTIONS
Part 3
S02 CONCENTRATIONS AT KEYSTONE, PA.
R. Boomer
H. Panofsky
671
-------
672
3.0 S02 CONCENTRATIONS AT KEYSTONE, PA.
R. Boomer and H. Panofsky, Research in Progress
3.1 The Purpose of the Project
For several years, SO from the high stacks at the Keystone power
plant near Indiana, Pennsylvania, was monitored along with the meteorological
conditions.
The SO concentrations were measured by helicopter through plume
cross sections at various distances downstream of the plant and
surface concentrations obtained from bubblers. This study primarily
concerns the bubbler data.
Since dispersion and plume rise are controlled by wind and stability
conditions, surface concentrations should be statistically related to
the wind and temperature structure. In practice, wind at one level,
and insolation, which are often available, could be used as surrogate
predictors for the more complex wind and temperature information required.
It was therefore decided to statistically analyze the relation
between surface concentration of S02, wind at one level, and insolation.
Next, a simple technique was developed for estimating maximum ground
concentration for a day for which wind and insolation could be obtained.
3.2 Analysis
The first step was to analyze the distribution of bubbler data for
various dates. Isopleths of ground concentrations were constructed as
function of time and distance from the stacks. Maximum concentrations
generally occurred at 11 a.m. on sunny days.
-------
673
Based on that information, the maximum concentration was determined
separately for each day. These were plotted as functions of insolation
and wind speed at the top of the stack. Fig. (1) shows the resulting
isopleths. The greatest concentrations occurred on days when medium
wind (~ 4 m/sec) and medium insolation. Presumably, on days with
light winds, the effective stack height was too great for severe ground
pollution; and for strong winds, the concentrations aloft were too small.
An attempt was made to account for the observed ground concentrations.
First, vertical average concentrations were determined by summing the
concentrations measured by helicopter in the center of the plume. It
was expected that the vertically averaged concentrations would be an
upper limit to the ground concentrations, which would exist right after
fumigation. But there were many examples where the maximum ground con-
centrations exceeded the vertically averaged concentrations in the center
of the plume.
This apparent discrepancy was probably caused by an inconsistency
in time. The helicopter soundings were made early in the morning (~ 8 a.m.)
but the maximum surface concentrations occurred, as mentioned, about 11 a.m.
At 8 a.m. wind direction turned significantly with height, a factor that
contributes to lateral spread. As Fig. (2) shows, the turning with
height decreases to almost nothing at noon due to the decreased hydro-
static stability. Hence the width of the plume at 11 a.m. would be
le«» than at 8 a.m. and central concentrations larger. Unfortunately,
no helicopter soundings were made near 11 a.m.
-------
e
CT> ^
O ^
X
UL.
O
CD
6 g
h-
H-
o
5
^ O
O X
to
O
o
<
-------
675
Ul
o
z
u.
<
v>
DC
til
o
u
(T
(M
UJ
X.
o
O O O
" 338930) 8V3HS QNIM
-------
676
A more direct attempt at accounting for the 11 a.m. concentration
was based on estimates of o~, (lateral standard deviation of mass) by
Pasquill's method. Then, two alternate formulae were tried to estimate
the concentration, one based on the assumption of vertically uniform
distribution
/27T U Ha
y
(i)
(where H is the height of the top of the plume) and the other on a
completely Gaussian model
Xo - IT u a a (2)
y z
where a was also found by Pasquill's method, U was the mean speed below
Z
H. In practice, Eq. (1) was almost never exceeded, and (2) was usually
exceeded. Hence, we conclude that we cannot predict actual ground maximum
concentrations, but only prescribe probable upper and lower limits.
-------
m
D
O
o
Tt
n
S *
? ?
•Z 15
:; 2
W —
a -f 3>
S 0"i
&§?!
__< « r m
I a
•>?-
:|?S
!li3
«j 2 n
' -• ,. H
O
-<
m
33
DO
o
o
On
O
N
fD
dJ CD
CL -
Q. _
^ -.
fD
•J, <
oo O
c:
£ o
fD -H
;i
n
zr
r>
0-D
O
85 O
81
(S
< C
m
n
I? t
O
2
n
------- |