AFCRL-68-0337

THE TURBULENCE CLIMATOLOGY OF THE UNITED STATES

BETWEEN 20,000 AND 45,000 FEETESTIMATED FROM AIRCRAFT REPORTS

AND METEOROLOGICAL DATA

By

ROY M. ENDLICH ROBERT L. MANCUSO

CONTRACT AF 19(628)-5173PROJECT NO. 8624

TASK NO. 862402WORK UNIT NO. 36240201

Final Report

Period Covered: 10 May 1965 through 9 Jule 1968

June 1968

Contract Monitor: NORMAN SISSENWINEA•.rjspace instrumentation Laboratory

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AFCRL-68-0337

THE TURBULENCE CLIMATOLOGY OF THE UNITED STATESBETWEEN 20,000 AND 45,000 FEET

ESTIMATED FROM AIRCRAFT REPORTSAND METEOROLOGICAL DATA

By

ROY M. ENDLICH ROBERT L. MANCUSO

SRI Project 5521

CONTRACT AF 19(628)-5173PROJECT NO. 8624TASK NO. 862402

WORK UNIT NO. 86240201

Final Report

Period Covered: 10 May 1965 through 9 June 1968

June 1968

Contract Monitor: NORMAN SISSENWINEAerospace Instrumentation Laboratory

Distribution of this document is unlimtisd. It may be released to theClearinghouse, Department of Commerce, for sale to the general public.

Prepared for

AIR FORCE CAMBRIDGE RESEARCH LABORATORIESOFFICE OF AEROSPACE RESEARCH

UNITED STATES AIR FORCEBEDFORD, MASSACHUSETTS 01730

Approved: R. T. H. COLLIS, MANAGERAerophysics Laboratory

D. R. SCHEUCH, VICE PRESIDENTEngnIering

F

ABSTRACT

The climtyology of clear-air turbulence is defined herein as the

likelihood that an aircraft or missile will encounter turbulent air at

a given locality, altitude, and time of year. Turbulence data of three

types were used in this study, these include obervations by instrumented

research aircraft, balloon tracks measured by FPS-16 radar, and turbu-

lence reports made by pilots. The measurements that have been made by

research aircraft show good relationships between turbulence and certain

aspects of mesoscale atmospheric structure, but the data are too limited

in number to permit broad generalizations. The FPS-16 tracks of rising

Jimsphere and Rose balloons were obtained during studies of detailed

wind profiles. We investigated their potential value in identifying

turbulent layers. In general, the existing data are too noisy to serve

this purpose; however, further special trials are recommended. The sub-

jective turbulence reports from pilots collected during special five-day

reporting periods comprise by far the largest volume of data available.

Meteorological conditions for these periods were analyzed by computer

from standard rawinsonde data and were correlated with the turbulence

reports. The correlations show that the vertical vector wind ihear

corresponds most closely to turbulence frequency determined from the

pilot reports. Little additional reduction of variance in the turbulence

frequencies is achieved by including other meteorological factors. Op-

timum multiple regression equations between turbulence frequency and the

mean and standard deviation of the vertical vector wind shear were ob-

tained. In summer a different regression equation was found than in

other seasons.

These turbulence observations taken in toto are too few to permit

a direct computation of turbulence frequency; therefore an indirect

method was used to obtain the turbulence climatology. This involved

iii •

________ _ __ ____ ___

applying the regression e4uations to existing statistics of wind shear

over the United States. These wind-shear compilations, prepared almost

ten years ago, appear to "- -:f e'uestionable reliability in the upper

troposphere and stratosphere due to a large propovtion of missing wind

observations under conditions of high wind speeds aloft. Due to uncer-

tainties in the regression equations and shear statistics, the deduced

turbulence climatology (given by seasons for levels between approxi-

mately 20,000 and 45,000 feet) must be considered a first estimate.

Recommendations are made that an up-to-date wind-shear climatology

be computed for the United States, and that consideration be given to

developing a balloon-borne turbulence sensor to augment data from

research aircraft and airline pilots.

iv

CONTENTS

ABSTRACT ..................... ... .......................... iii

LIST OF ILLUSTRATIONS .......... .................... vii

LIST OF TABLES ............... ........................ ix

I INTRODUCTION ............. ...................... I

If DATA SOURCES....................... 3

III TURBULENCE IDENTIFICATION FROM PATHS OF

RISING BALLOONS .......... ..................... . .

IV REGRESSION EQUATIONS RELATING TURBULENCEFREQUENCY TO METEOROLOGICAL CONDITIONS ........... .. 17

A. Winter, Spring, and Fall .... .............. ... 17

1B. Regression Equations for Summer .. .......... .. 21

C. Mountain Effects ...... .................. ... 22

D. Application to Other Areas and Altitudes ...... 24

V AN ESTIMATED TURBULENCE CLIMLATOLOGY FOR

THE UNITED STATES .......... ................... 27

VI DISCUSSION AND RECOMMENDATIONS ....... ............. 43

APPENDIX: SELECTED CLIMATOLOGICAL DATA FOR

THE UNITED STATES ....... ................. .. 45

ACKNOWLEDGEMENTS ............. ....................... 63

REFERENCES ................. .......................... 65

D)) Form 1473

V÷

ILLUSTRATIONS

Fig. 1 Graphs of Range Deviations Measured by Two FPS-16

Radars Tracking a Rising Rose Balloon ImmediatelyAfter Launch ........... .................. ... 13

Fig. 2 Graphs of Range Deviations Measured by Two FPS-16Radars Tracking a Rising Rose Balloon in the UpperTroposphere ............ ............... .. ... 13

Fig. 3 Map of Principal Mountain-Wave Areas of the UnitedStates ........... ....................... ... 23

Fig, 4 Curves of Average Turbulence Frequency vs. Heightfor the United StatesY Decermined from Figs. 5Through 8 . . . . . . . . . . . . . . . . . . . . 27

Fig. 5 Estimated Probabilities of Encountering Turbulencein l00-Miie Sectors over the United States inWinter, at 425, 375, 325, 225, 187 and 162 mb . . 30

Fig. 6 Estimated Probabilities of Encountering Turbulencein 100-Mile Sectors over the United States in

Spring, at 425, 375, 325, 225, 187, and 162 mb . . . 33

Fig. 7 Estimated Probabilities of Encountering Turbulencein 100-Mile Sectors over the United States inSummer, at 425, 375Y 325, 225, 187, and 162 mb . . . 36

Fig. 8 Estimated Probabilities of Encountering Turbulencein 100-Mile Sectors over the United States in Fall,at 425, 375, 325, 225, 187, and 162 mb ....... ... 39

Fig. A-1 Statistics on the Vertical Wind Shtlr Vector inWinter, Based on Schamach's Data for Station•s

Indicated by Small Circles, .nd Wind Speedsfrom U.S. Air Force Manual SACM 105-2 ...... ....... 17

Fig. A-2 Statistics on the Vertical Wind Shear Vector

in Spring, Based on Schamach's Data for Stations

Indi'cated by Small Circles .... ............. 1

Fig. A-3 Sta:.stics on the Vertical Wind Shear Vector inSummer, Based on Schamach's Data for StationsIndicated by Small Circles, and Wind Speeds

from U.S. Air Force Manual SACM 105-2 . . .... 54

Fig. A-4 Statistics on the Vertical Wind Shear Vector

in Fall, Bsed on Schamach's Data fcr StationsIndicated by Small Circles .... ............. ... 59

vii

A.

TABLES

Table I Correlations Between the Average PercentageFrequencies of Moderate or Severe Turbulenceand. Meteorelccglcal Factors .. .. ....................... 7

Table II Correlations Between Meteorological FactorsBased on Objective Analyses for SpecialTurbulence Reporting Periods in December 1964and March 1965. .. .. ..............................20

Table III Correlations Between Percentage Frequency ofModerate or Severe Turbulence (from PilotReports) and Climuatological Factors, forJune 9-14, 1965 .. .. .................................22

lxI

U - " a. % a'~ -~.* .... !! -|

I INTRODUCTION

The purpose of this study was to develop methods for estimating the

probability that an aircraft will encounter turbulent air at a given

locality, altitude, and time of year. The discussion pertains to clear-

air turbulence, which is perhaps more accurately described as non-storm

t.irbuler.,.e--i.e., turbulence directly associated with convective or

precipitating clouds is excluded. Since direct turbulence observations

are not made routinely, oe cannot now refer to an archive to obtain

data for making a climatological study. Instead, an alternate method

must be formulated that uses various types of fragmentary infor'nation.

The general plan is as follows. On a limited number of occasions in-

strumented airciaft have measured turbulencc as well as the associated

meteorological conditions, and thus provide basic i:-forma.tion concerning

atmospheric conditions that are associated with turbuletrte. Next, tur-

bulence frequencies on certain days were computed from reports .)f tur-

bulent or smooth flight collect.ed from. airline pilots. These frequeicies

were correlated with concurrent meteorological -:onditions determined as

well as possible from standard upper-air data, Qnd :egdssion equations

were found. The final step was to apply the regression equations between

turbulence and meteorological factors to existing climatological recoros

of meteorological conditions, in ord,ýr to obtain the estimated turbulence

climatology.

Numerous difficulties, some Anticipated arid othtrs not foreseen,

are inherent in this indirect approach. These will be discussed ir,

detail later. Conceptuallh, the simnplest way to oha,•i a tbibulence

climatol.1gy would be to equip enough aircraft to directly dorterminle the

turbulence frequency at a variety of places, altitudes, and t~ees

however, costs would be prohibitive. Anot'-er approAch. which we have

advocatea but which is still untried, would be to develop atall,.n-

txbrne ,urbuience sensor to fly as part of the standard radiosonde ".i-

strument. or sej-ratel%. If an inexpensite sensor proved feasible.

the turbulenrc e imatolt.x up t,1 the alt itude l 1 ,t c'f ball,,n flih

*

(approxiiately 100,000 feet) could be found, and correlations could be

made with meteorological factors at the same times and places. A

similar idea is involved in the use of rising uninstrumented balloons

tracked by high-precision radar to reveal erratic portions of the se-

qu'ence of flight coordinates that would indicate turbulent layers.

This subject is discussed in Sec. III. Other possible methods exist

for remotely sensing turbulence using elactromagnetic radiation, but

their practicality is not established. Such methods are not considered

in this report.

Among designers of aircraft and missiles, a strong interest in

turbulence hn,; existed for years (e.g., Loving, 1966; Houbolt, 1967).

The aeronautical profession has perfected complex aircraft instrumenta-

tion that gives information on turbulence spectra, probabilities of

gusts greater than certain threshold values, etc. Using this approach

to deteriaine the turbulence environment at new altitude leviels, such as

the stratosphere, requires that an aircraft of some sort be used as the

initial probe. Generally, the number of flights made is far too low to

indicate viriations in the percentage of turbulent air to be expected

under different weather conditions, places, altitudes and seasons. It

is this climatological distribution of turbulence that is of primary

interest in the present investigation.

This report does not summarize or review the voluminous literature

on turbulence in the free atmosphere; however, references to pertinent

papers are given at appropriate points. In Sec. II, the different data

sources that we used are described, and 'heir limitations are given.

Section III is entirely devoted to a description of our attempt to

identify turbulent layers from paths of Rose balloons tracked by FPS-16

radar. Section IV contains the regression equations used to obtain the

e3timated turbulence frequencies of Sec. V. (Examples of the climatolo-

gical meteorological data used are given in the Appendix.) Recommenda-

tions aje given in Sec. VI. A scientific report concerning the first

year's work was issued under this project tn May 1966.

)A

2

i

II DATA SOURCES

As discussed in Scientific Report 1, data obtained by the AFCRL

B-47 research aircraft (which measured turbulence intensity objectively,

and also recorded concurrent winds and temperature) were carefully re-

viewed. In recent years data of this type have been analyzed by a

number of writers including Briggs and Roach (1963), Endlich (1964),

Endlich and McLean (1965), McLean (1965), and Kao and Woods (1966).

From such information, it is usually possible to identify detailed

"mesoscale" features of atmospheric structure that accompany turbulence.

We found that the turbulent gust intensity recorded by the B-47 corre-

lated best with vertical vector wind shear, with large directional wind

shear, and with deformation in the horizontal plane. Correlations be-

tween turbulent gust intensity and these quantities were in the range

from 0.5 to 0.8. The vertical and horizontal structure of the tempera-

ture field appeared to be less important. However, the mesoscale me-

teorological patterns that produce or accompany turbulence are not

adequately depicted by standard upper-air soandings. Therefore, rela-

tionships between turbulence and meteorological factors are invariably

more obscure when only standard meteorological observations are available

for analysis. The correlations of this report, which relate standard

meteorological data and subjective pilot reports, are much lower than

the correlations mentioned above.

Instrumented gliders and aircraft have also documented the severe

turbulence that occurs in certain portions of well developed mountain

waves (Kuettner, 1958; Jones and Atnip, 1964). Quite recently, instru-

mented U-2 aircraft have explored stratospheric turbulence (Penn and

Pisinski, 1967; Crooks, et al., 1967). These data apparently show

that relationships exist between turbulence and mesoscale wind features

similar to those found earlier in the troposphere.

Since the variability of mesoscale features is very broad while

the amount of high-quality, detailed aircraft data that describe them

is small, it is difficult to generalize from the aircraft data.

3)

Another possible source of information comes from balloons tracked by

FPS-16 radar. Flight tracks of Jimsphere balloons had been obtained by

NASA at Cape Kennedy, Florida (Scoggins, 1965), and 3f Rose balloons by

the Air Force at Vandenberg AFB, California, for use in measuring accu-

rate winds and vertical wind shears over small increments of height.

It was thought that if these data yielded information on turbulence,

they would augment other turbulence measurements, particularly in the

stratosphere. From the analysis of ten Jimsphere flights, the approach

appeared feasible, as reported by Endlich and Davies (1967). As a re-

sult, a major effort was made to use the Rose series of flights from

Vandenberg for turbulence studies. For the stratospheric layers of

interest, this was not successful for reasons discussed further in

Sec. III. However, the basic concept of detecting turbulence from

erratic portions of the balloon path is still believed to be useful,

and might be implemented by procedural changes described in Sec. III.

The main source of data used in this investigation is that from

&irline pilots, who have reported turbulence severity encountered during

j commercial flights under programs organized by Colson (1963, 1965, 1966)

in association with the International Civil Aviation Organization. Each

j program was five days in length. Reporting periods were held in February

1963, December 1964, and March, June, and September 1965. These data

have the major advantage that they are numerous, and give a reasonably

good depiction of turbulence within the airspace over the United States

during these periods. For example, in the March 1965 data, there were

approximately 20,000 reports, each pertaining to a 100-mile flight seg-

ment. Turbulence of moderate intensity occurred in approximately six

percent of these, while severe turbulence occurred only in 0.3 percent

of the cases. The average wind patterns during this five-day period

were by no means typical of average conditions in March, as can be seen

from upper-air charts for this interval given by Endlich and Mancuso

(1967). The same is true of other five-day periods. Therefore, one

would not expect the pilot reports of turbulence for such brief periods

to be representative of seasonal conditions--i.e., they do not give an

approximate turbulence climatology. But by matching the turbulence

4

reports to concurrent meteorological conditions, we wished to obtain

reliable statistical relationships to use in estimating a turbulence

climatology.

The principal disadvantage of the pilot reports is their subjec-

tivity in regard to the severity of turbulence. Another difficulty is

that in summer considerable turbulence included in the clear-air category

is located in the vicinity of convective storms or downstream; these

cases are probably an indirect result of the convective storms. There-

fore, the June turbulence has different relationships to meteorological

factors than found in other seasons.

Colson divided the airspace into volume elements approximately

4000 feet deep and bounded by 2-1/2 degree latitude-longitude lines,

and determined the number of flights during twelve-hour periods that

encountered smooth flight and turbulence in the categories light,

moderate, or severe. From such tabulations furnished to us by Colson

for the first two periods, and by the Federal Aviation Administration

for the latter three periods, we computed the frequency of turbulence in

each time period for each volume element. The concurrent meteorological

conditions (i.e., wind speed and direction, vertical v~ctor shear, tem-

perature, lapse rate, horizontal wind shear, deformation, vorticity,

divergence, and twelve-hour vector change in wind) in each volume were

analyzed by computer from standard rawinsonde data at synoptic hours, as

described by Endlich and Mancuso (1967). Thus a complete "turbulence

report" consists of the turbulence frequency in a volume element, plus

the associated wind speed, shear, etc. As the typical flight distance

through a volume elempnt is approximately lu nautical miles, the tur-

bulence frequencies should be interpreted as the likelihood of encoun-

tering turbulence within that distance. (This distance can be converted

to an equivalent flight time by dividing it by the appropriate aircraft

groundspeed .) The center of each volume element is represented by a

grid point. Statistics on the length of turbulent patches are not given

by these data, but sources such as Steiner ( 1965) and Coy (1967) indicate

that in approximately 50 percent of the cases the length is less than

ten miles.

5

To use the pilot reports in obtaining regression equations for the

frequency of turbulence, a "climatology" of wind speeds, shears, etc.

at each grid point was constructed from ten values of each factor during

each five-day pnriod. Then a multiple-regression computer program de-

veloped by M. Gorfinkel of SRI was used to relate the frequency (in per-

cent) of moderate or severe turbulence to the wind speed, vertical shear,

deformation, lapse rate, etc., during the period. Correlations between

turbulence frequency and individual meteorological factors in December

and March are given in Table I. Further details are given in Sec. IV.

The next step was to apply the regression equations to existing

climatological records of pertinent meteorological factors in order to

estimate the turbulence climatology over the United States. It was

assumed at the beginning of this study that such climatological data

would be available; determination of new climatological descriptions of

the upper atmospheric structure was not contemplated. Climatological

data concerning wind shear over the United States were given by Ratner

(1958) in the altitude range 700 to 50 mb (10,000 to 67,000 feet) for

the period 1951-1956, and relied upon subjective interpolation to com-

pensate for missing wind observations. The amount of missing data was

not presented, but as indicated below, must have been large. Further

unpublished wind shear statistics mentioned by Crutcher (1963) had been

compiled by S. Schamach of the National Weather Records Center for a

ten-year period. These were generously made available to us by Dr.

Crutcher. They are for levels between 450 and 150 mb for the period

July 1948 through June 1958. The statistics are comprehensive, and

obviously excellently computed and organized. The number of observations

used is also given; no subjective interpolation was performed. In this

compilation, there are approximately 900 possible observations at each

station for each season (once a day for three months for ten years).

The actual number of obse:-vations shows a drastic decrease with

altitude, particularly during the winter se.i~on. For example, at

Washington, D.C. (one of the better stations), 532 wind observations in

summer reached the 200-mb level. In winter at 200 mb, the corresponding

number is down to 300. At Ely, Nevada, the numbers of wind observations

6

I

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at 200 mb in summer and winter are 256 and 115, respectively, again out

of 900 possible. Thus the samples of measured winds and shears are

quite small. This in itself is not of overpowering importance; the

remaining samples might be representative. But from the nature of the

observational method, we know that wind data are lost most frequently

during conditions of high winds when elevation angles become too low

to permit accurate tracking. Thus the remaining wind sample is biased

towards low speeds, low shears, etc. In portraying the geographical

and latitudinal variation in these statistics over the United States,

the differing numbers of observations at radiosonde stations enter

into the picture. Although we have looked briefly into the possibility

of standardizing the statistics on the basis of the numbpr of observa-

tions that went into each, no simple correcting procedure appears

possible. In retrospect, one recalls that the present GMD-l type of

wind finding equipment was introduced at some stations in 1954, and at

most others in 1960. Thierefore, the number of observations obtained at

each station evidently depends in part on the date of installation of

this equipment.

This discussion of the observations that go into available statis-

tics of .pper winds and shears has been rather lengthy because of the

importance of this matter to the present problem. The reliability of

the averages and standard deviations of vertical vector shear (used

later in the regression equations) is difficult to judge, and may be

somewha* questionable for the present purpose. Typical patterns of

the magnitude of the average vertical wind shear and the standard

vector deviation of shear, as read at grid points from data at twenty-

five stations given by Schamach, are shown in the Appendix. A future

remedy appears to be the recomputation of such statistics using recent

data, although even today a significant number of winds are missed in

the critically important jet stream cases. A further important step

that can be taken to obtain more accurate winds and shears from present

equipment is a computer computation using all the data points measured

by the GMD-l (instead of certain points one or two minutes apart), as

discussed iy Danielsen and Duquet (1987).

An alternative type of climatological information might describe

the number of times certain subsynoptic features that favor turbalerice

(ruch as jet streams passing through sharp troughs and ridges, jet

lronts or tropopauses with strong wind shear, mountain waves, etc.)

occur as a function of geographical location and time. One would also

need to know the probabilitN of turbulence associated with each meteoro-

logical feature. But such statistics are not available, and dnyway.

these phenomena should be reflected indirectly in means and standard

dv.viations of winds, vertical shears and temperature lapse rates.

The wind shear data of Schamach are over 50-mb intervals tLjlowI 2X0) mb, and then are from 200 to 175 mb, and 175 to 150 mb. Thus their

average thicknesses are variable, and we wished to normalize the 3hear

data to a -t000-foot thickness as used in analyzing the aircraft data.

A well known teature of wind shears is that average values and standard

L-.viations computed for thin I.-,ers tend to be larger than values coin-

putId over greater distance intervals (Dvoskin and Sissenwtne, 1958).

FaCtO,., zI-.lat ing shears over various intervals hl've been given by

Essenwanger (1963) and Arendariz and Rider (1966). From the latter

paper, we estimated correction factors of 0.5, 0.67, 1.0, and 1.3 for

layers 1000, 2000, 4000, and 6000 feet in thickness, respectively, and

interpolated for other thickness values. For example, an average shear

compoted over 1000 feet must be multiplied by 0.5 to normalize it to

tht. desired 4000-toot shear.

4I

_ _ _ _ _ _ -- -- - -- ~ -

III TURBULENCE IDENTIFICATION FROM PATHS OF RISING BALLOONS

As mentioned in the Introduction, quantitative measure..... Its of

turbulence intensity and as~sociated winds and shear are scarce. There-

fore, we investigated the applicability of data from Jimsphere and Rose

balloons tracked by the highly accurate FPS-16 radar. The basic concept

is simply that the balloon path will be relatively erratic in turbulent

layers as compared to laminar portions of the atrmosphere (Endlich and

Davies, 1S67). A preliminary study was made of ten Jimsph-re flights

from Cape Kennedy, and these appeared to indicate the existence of

several turbulent layers under seemingly favorable conditions. With

this encouragement, the technique was applied to Rose balloons tracked

by FPS-16 radar at Vandenberg Air Force Base, California,

As discussed in the referer-ed paper, data processing can be done

in terms of range (R), elevation angle (E), and azimuth (A), or after

converting these basic measorements to coordinates towards east, north,

and up (x, v, z). We choose to use the former three coordinates. Since

the variations in R, E, A expected due to turbulence are a small, high-

frequency component superimposed on large overall trends, for turbulence

to be detected it is necessary that errors due to radar tracking and to

self-induced balloon motions be relatively small. A number of Rose

balloon flights had been made using two radirs located side by !kide to

obtain independent measurements of the balloon's coor.dinates versus

time. If radar tracking errors were small, plots f.-om the dual tracks

should be essentially identical, arýi should unequivocably identify tur--

bulent layers.

Computer programs ,t-re writtet, "v, utilize ;i%? fPS-16 Rose data.

These programs are as fo) lows:

(1) The first program converts units -,f R, E, A to meters and

radians, and averages fi'-e 0,1--second puints T-0 give poi;-.ts

at 0.5-- 'con•tl int rvr:.A1 . ( •T, . (lens iv of -nformit ion is

more than adequate for tne prer-ent purp,)sc, as the bail ooz

-irises at• a rat•e •,f oniv4- to 5 .i sec . ) The *.i.e se-que-•ce

Ii

of points is then examined to isolate occasional spurious

points. The relevant computation is made between adjacent

points; for example, if IR. - R. I > L (where L is

approximately 50 m, the upper limit of differences in

range that would be produced by a 100 m sec wind

in 0.5 seconds), R. is replaced with an interpolated

point. Elevation and azimuth are treated similarly.

(2) The next program smooths the R, E: and A (separately)

over one-minute intervals using a triangular-shaped

weighting function. Mean wind speed and direction,

height, and balloon ascent rate over one-minute inter-

vals are computed from the smoothed values (Rs, Es) As

Then deviations (R - R ), (E - E ), and (A - A ) areS' S S m

computed at each 0.5 second, and a plot tape is written

to graph the deviations as a function of time using a

California Computer Company plotter.

(3) Initially it was also planned to use an existing computer

program to compute autocorrelations and spectra of the

deviations, but this was not done for reasons given below.

Plotted v'ilues oi (R - R ) from the dual tracked flights wereS

graphed as sho%:. in Fig. I. A minute in time corresponds approxi[.,ately

to 1000 fcet in a'ltitude. In the low levels, the plots from the two

radars generally agreed well, and indicate self-induced balloon motions,

and occasional turbulence in the boundary layer of the atmosphere.

Such turbulence is shown in Fig. I for the interval from two to three

m'nutes after launch. uust speeds indicated by the slope of the graphs

arte 1 to 2 m sec" , signifying light turbulence. Other similar cases

appart. tlv verify the basic concept. But at longer ranges and low

elevat-:on angles, the curves of thc. two radars did not Keneratlly agret-

in their sm.iAll-scale fe.Aturtes. More than fift" Rose flights were

plc-es.sett, involvn ing i fairlv sireable teffort in manpvwer and computer

ct,. ts. In this sample-, tri clear-cut cases of turbuience in 'he upper

tropAYsphere o: lower stratosphere could be iden:tif ied from the duil

plots, although or-, radar -r the other 4om.etimes had an erratic path

12

- - -- - T T - - - -- -

10 METER DEVIATION

Ajý -

RADAR I

1.0 2.0 3.0 4.0 5.0 6.0 7.0

MINUTES AFTER LAUNCH

-vF10 METER DEVIATION

ADRAA2

38.3 39.0 40.0 41.0 420 430 41.0

WN~UES "<OM L.-AUNClH

FIG. 1 GRAPHS OF RANGE DEVIATIONS MEASURED BY TWO FPS-16RADARS TRACKING A RISING ROSE BALLOON IMMEDIATELYAFTER LAUNCH. Taken from Test 6408 at Vandenberg AFB, Caiifornio,

• ,on 7 September 1966.7.0 8.0

T-- T r -----

FiG. 2 GRAPýS 4F RANGE DE',,AT:ONS MEASURED BY T*O FPS- 16RADARS TRAC'.NO A R.S+NG ROSE BALLOON ýN THE UPPERTROFGSPERE T:-. • T. Test 64_08 : zndenb4rg AFB, Calfo,,"o

44-0 45.0

suggesting turbulence. Close agreement was not found. A typical plot

(from a portion of the same flight in the upper troposphere) is shown

in Fig. 2. The duplication of the two curves is obviously less than

in Fig. 1.--

It is our opinion that the difficulties are due to tracking uncer- i

tainties that increased with time, particularly at long ranges where

signal strength was low. These uncertainties could not be removed by

the editing procedure of the first computer program mentioned above.

Also, operational modes of the two radars may not have been optimum or

identical. Thirily, the balloon motion may be partly aerodynamic in

its detailed behavior. Differences between the motions of Rose and

[ Jimsphere bo1 1oons have been noted by Scoggins (1967).

Unforbunately, the present study of rising Rose balloons tracked

by two FPS-16 radars was not successful in isolating turbulent layers.

Still we do not consider the concept discredited since the Vandenberg

flights were not specifically designed to obtain measurements of tur-

bulence. We suggest a trial based on very carefully controlled measure-

ments where a balloon is released upstream so as to pass over the two

radars at a favorable (> 20 degree) elevation angle and a relatively

close range, The assistance of a search radar would probably be needed

to aid the FPS-16's in locating the approaching balloon. At Vandenberg

AFB, where the ocean is in the upstream direction, it might be possible

to release a balloon from a helicopter. In spite of these problems,

further experiments with FPS-16 tracking of rising balloons are recom-

mended in Sec. VI.

15

K _

IV REGRESSION EQUATIONS RELATING TURBULENCE FREQUENCY

TO METEOROLOGICAL CONDITIONS

A. Winter, Spring, and Fall

As mentioned earlier, by far the most numerous turbulence reports

available are those made by commercial and military pilots during

special five-day reporting periods discussed in Sec. II. For these

periods we had computed turbulence frequencies in volume elements

covering the U. S. airspace between approximately 24,000 and 40,000 feet

at each synoptic hour (00 and 12 GMT). Also, at the same times a number

of meteorological quantities were computed from objective onalyses of

standard upper-air observations (see Endlich and Mancuso, 1967). The

selection of quantities to be computed was made on the basis of previous

experience with data frcm many sources, and on our estimate of what can

reasonably be determined from standard rawinsondes. [Opinions on this

matter differ; for example, Moore and Krishnamurti (1966) advocate

somewhat different quantities than ours.] The quantities computed for

each volume element included zonal and meridional wind components (or

wind speed and direction), vertical vector shear and its square, vertical

speed shear, temperature, lapse rate, and height. From the winds, vorti-

city, divergence, deformation, and horizontal shear along the flow and

across the flow were computed. The values of all these quantitics are,

of course, subject to various errors inherent in upper-air data. Fur-

ther derivatives of these fields (e.g., the Laplacian and Jacobian)

were not used since we believe such terms contain an unacceptable level

of uncertainty.

For a given five-day period, a "climatology" was constructed for

each of the approximately 500 volume elements over the United States.

This climatology was computed from the ten values of turbulence fre-

quency and ten values of each meteorological quantity. For example,

the mean vertical vector shear and standard vector deviation of shear

were computed in each element. Usually about 50 volume elements had

less than twenty flights during the period; these were discarded. Indi-

vidual correlations of turbulence frequency with each meteorological

17

•.

quantity were determined for each period from approximately 450 values

of each variable. Thus the sample sizes are large. Also, a multiple

regression program (Gorfinkel, 1S67) was used to calculate the correla-

tion of variables with each other, the multiple correlation, and the

coefficients of linear regression equations. This program also gives

the standard errors in the estimate of each coefficient in a regression

equation. When the individual correlations are all relatively low

(less than 0.5), as in these data, the standard errors in coefficients

are appreciable. If the data are separated into sub-groups, for example,

on the basis of altitude, the standard errors of the coefficients

enable one to judge whether differences in the coefficients are most

like2v real or random. It was found that most differences among sub-

samples (based on season and altitude) were random, except for major

differences between the data for June as compared to the other periods.

In general, the turbulence frequencies (for a certain period at

particular points) were related most closely to vertical vector shear,

and somewhat less to the vertical speed shear. The probability density

function of vertical vector shear is not known precisely, but presumably

approximates a circular normal distribution. If so, its properties are

well described by the vector mean and standard deviations, Also, itfollows that the mean and standard deviation of the speed snear could

be determined from the vectoz mean and standard deviation using methods

given by Brooks and Carruthers (1954). Both types of statistics (for

vector shear and speed shear) are given in the compilation of Schamach.

Correlations between frequencies of moderate or severe turbulence

and the best climatological indicators were given in Table I. If light

turbulence is included with moderate and severe, the correlations of

Table I increase by amounts of approximately 0.1. Thus all correlations

obtained from these data are considerably lower than those obtained

using data from special researzh aircraft, as described in Scientific

Report 1. Undoubtedly, the difficulties discussed earlier have ad-

versely affected the correlations. Numerous trials were made using

different combinations of the meteorological quantities, and a simple

18

linear equation based on the mean and standard deviation of vector shear

gave a multiple correlation as high as when additional terms were used.

The relevant empirical equation for p(M), the percentage frequency of

moderate or severe turbulence is

Magnitude of 1 Standard 1p(M) = C(s) + 2.0 X raverage vertical - 0.5 l deviation of (1)

vector shear J Lvector shea:J-3 -l

where the units of vertical vector shear ir the brackets are 10 sec

and C(s) is a constant depe ,ing on season, taken as 6 in winter, and

5 in spring and fall. (These values are in accord with the average

turbulence frequencies for samples of data for different seasons.) This

equation has bejn applied to the climatological dota of the Appendix to

obtain estimated turbulence frequencies discussed in the next section

of this report. On the dependent data, the multiple correlation is

0.36. The standard errors in the coefficients in this equation (as

given by the program) are approximately one-fifth of the values given.

No systematic differences among these coefficients were found when the

turbulence data were sub-divided into altitude groups. Also, no diurnal

differences in turbulence frequency were found.

Since climatological wind shear data are available only for the

United States and perhaps a few other industrialized countries, Eq. (1)

cannot be applied in other geographical areas. However, smoothed maps

of mean winds and the standard vector deviation of winds are given in

various sources (such as Air Force Manual SACM 105-2) for the entire

northern hemisphere. In Table I we saw that turbulen- frequency is

related, although weakly, to these two quantities. Table II shows them

to be highly correlated with each other, so that wind speed alone will

specify turbulence about as well as a combination oi the two. The pat-

terns of strong winds over the United States given in SACM 105-2 compare

in broad features to the turbulence frequency estimated from Eq. (1) as

one would expect from the well known general association of turbulence

and jet streams. The rough correspondence of turbulence frequency and

average wind speed carn be seen by comparing Fig. 5(c) (see Sec. V) with

Fig. A-l(c), and Fig. 5(d) with Fig. A-l(f). Actually, the regions

19

Table II

CORRELATIONS BETWEEN METEOROLOGICAL FACTORS BASED ON

OBJECTIVE ANALYSES FOR SPECIAL TURBULENCE REPORTING

PERIODS IN DECEMBER 1964 AND MARCH 1965*

Factor Factor Factor Factor Factor FactorMeteorological Factor 1 2 3 4 5 6

1. Average verticalspeed shear 1.0 0.73 - - 0.54 0.59

2. Standard deviationof vertical speedshear 0.73 1.0 - -

3. Magnitude of averagevertical vector wind

shear - - 1.0 0.17 0.40 0.43

4. Standard deviationof vector windshear - - 0.17 1.0 0,24 0.26

5. Wind speed 0.54 - 0.40 0.24 1.0 0.88

6. Standard deviationof "I 0.59 - 0.43 0.26 0.88 1.0

*Each correlation is based on approximately 900 pairs.

estimated to have the highest frequency of turbulence lie on the south

side of the centers of the average isotachs, Nevertheless, preliminary

estimates of turbulence from average wind speeds as given in U.S. Air

Force Manual SACM 105-2 may be useful for certain purposes. Linear

regression equations between turbulence frequency and average wind

speed varied considerably among subsamples of our data. Overall, the

regression equation that relates turbulence frequency to avtrage wind-l

speed in m sec and that appears to give reasonable results over the

United States is

p(M) = C(a) + 0.12 x [Average wind speed) (2)

where C(a) depends on altitude and is taken as 5 percent at 400 mb,

4 percent at 300 mb, and 3 percent at 200 mb. It would be interesting

to test this equation in other geographical areas, particularly Japan,

20 4.

where the jet stream reaches maxihmum speeds. Howe./er, the use of wind

speeds to estimate turbulence frequency is less .,.liable than the use

of shear statistics, as stated previously.

B. Regression Equations for Summer

Compared to pilot reports for several wint-r periods that are dis-cussed above, reports from only a single five-day period (June 9-14,

S 1965) were available to represent summer conditions. It would be desir-

able to verify the present results with other summer data. As mentioned

previously, associations of tirbulence with meteorological quantities

* over tile United States in June are considerably different than in

winter. The mean position of maximum winds in summer is over the

Great Lakes, north of the main flight routes. The vertical wind shear

is generally much weaker than in winter. W a large degree the weather

disturbances over the United States are convective in nature. Much of

the convection occurs in areas where vertical shear in the upper tropo-

sphere is small. Even the turbulericte outside convective clouds and re-

ported by pilots as clear-air turbulence may have been indirectly of

convE tive origin. Probably in and north of the average jet stream 'n

summer, turbulent frequencies depend primarily on wind shear, as in the

other seasons over the United States. However, the June data show nega-

tive correlations of turbulence frequencies with average vertical shear,

average wind speed, and the standard vector deviation of wind. Of the

quantities computed, only re-lative vorticity has a small positive corrv-

lalton, as shown in Table I11.

Table Ill

CORRELATIONS BETWEEN PERCENTAGE FREQUENCY OF MODERATE OR

SEVERE TURBULENCE (FROM PILOT REPORTS) AND CLIMATOLOGICAL

FACTORS, FOR JUNE 9-]-I, 1965*

Magnitude Standard Standardof Average Vect'_ r Average Vector

Vertical Vector Deviation of Wind Deviation RelativeWind Shear -Wind Shear Speed of Wind j Vorticitv

-0.20 -0.15 -0,29 -0.21 0.13

Each correlation is based on approximatelv 400 pairs.

The best regression equation fonnd, ha% 'ng a multiple correlation of

0.38, is

21

-------------- i

r rJ

agnitude of average 0 Standard devitionp(M) 8.0 + 1.7 X Lvertical vector shearJ 1.0 X of vector shear J-3t1--3 -1units 10 sec units 10 sec

Fstandard deviation1

-0.5 X [Wind Speed] + 0.1 x f wind vecto r

units m sec-1 -1units m sec

+ 0.03 (Relative vorticity]-6 -I

units 10 bec (3)

Thic equation is used to obtain the estimated turbulence frequencies

for summer given in Sec. V. The values of mean wina speed ind direction

in summer, and the standard deviation of wind were taken from Air Force

Manual SACM-105-2. Vorticity was computed from the mean winds. Typical

examples of these fields are shown in the App;ndix, in Fig. A-3. In

these summer data a diurnal effect was found, such that computed turbu-

lence frequencies at 00 GMT (evening) should be increased by 15 percent,

while at 12 GMT (morning) the probabilities should be decreased by the

same amounts.

C. Mountain Effects

In these regression equations, no separation was made between

mountainous and non-mountainous terrain. The flight frequency is such

that the majority of data pertain to non-mouz'.ainous areas. To isolate

terrAln effects, grid points were separated into mountainous and non-

mountainous categories. Then under similar meteorological conditions,

differences in turbulence probability between the two categories were

found. These show that turbulence frequencies are generally higher in

mountainous regions than would be indicated by a regression equation

based only on synoptic parameters. This effect can be Adequately rep-

resented by increasing the turbulence frequencies in mountainous areas

by an appropriate amount. The mountainous regions of the United States

(generally having elevations greater than 1'OO m) are shown by light

shading in Fig. 3. Within these ar*as, the turbulence frequencies

given in Sec. V should be multiplied by a factor k2 , taken as 1.3 in

22

I- t

120"* 1,0" too. so*" so. Oe

14

00

00

-* 0 0 0,

00

FIG. 3 MAP OF PRiNCIPAL MOUNTAIN-WAVE AREAS OF THE UNITED STATES.

Within th akrsaig ublnefroquencoo. o subsequent figures should bot multipliedbyk oaccount for average mvountain-wave effects. in areas of lighter shading

temultiplication factor is k2 Values of Iadk 2 r given in Sec. IV-C.

23

winter and 1.15 in spring and fall. In summer, no such correction is

needed. It is known that the largest corrections should be made on the

lee side of major steep-sided mountain ranges that produce prominent

mountain waves. Such areas, shown in Fig. 3 by dark shading, were sub-

jectively estimated from topographic maps of the United States, and in-

clude mountain wave regions identified by Harrison and Sowa (1966) and

Foltz (1967). To account for wave activity in these areas, turbulence

frequencies, of Sec. V. should be multiplied by k,, taken as 1.6 in

winter and as 1.3 in spring and fall.

D. Application to Other Areas and Altitudes

If relevant wind shear statistics were available for continental

areas cf the aid-latitudes other than the United States, it would be

reasonahle, in our opinion, to apply the same r3gression equations in

order to obtain a first estimate of turbulence frequency. Over the

oceans of mid-lmtitudes where terrain disturbances are lacking, the

regression equations probably give turbulence frequencies that are too

large. According to Clodman, Morgan, and Ball (1960), turbulence over

oceans is an order of magnitude less frequent than over land. However,

recent data analy~ed by Colson (1968) indicate that moderate or severe

turbulence over oceans is about 0.7 times as frequent as over land, and

that the same sort of meteorological conditions (jet streams, troughs,

and ridges) are important for both. Thus, a simple correction of this

magnitude might be used in applying Eq. (1) to the oceans of mid-

latitudes. In polar regions, one might expect that the wintertime

procedure should be applied in all seasons. Perhaps the summer regres-

sion equation could be applied in the tropics, but this also is specula-

tive since we have no experience with aircraft turbulence data for ti.ese

regions.

it must be borne in mind also that the most comprehensive turbulence

data (from pilots) have been obtained in ar. altitude range restricted to

approximately 20,000 to 40,000 feet. At lower altitudes, the regression

equations might be applicable to the United States except for changes In

the constant values to accommcdate greater turbulence amounts due to the

influences of low-level conve:tlon and terrain. In estimating turbulence

24

____ ___ ____ _________________.1--

frequency in the stratosphere, one is faced with the drastic reduction

in available information, as noted by Mitchell (1966). However, the

descriptions of U-2 measurements of turbulence in and above jet streams

given by Penn and Pisinski (1967) indicate that the wind field is of

predominant importance, with a possible tendency for turbulence to be

associated with intermediate values of lapse rate. (The contention

that stratospheric turbulence is more closely related to temperature

inversions than to the wind field appears dubious to us.) Due to the

apparent similarity to conditions lower down, it appears reasonable to

apply the regression equations for turbulence to the lower stratosphere.

We have done so in the next section, subject to the limitation of de-

creasing reliability of standard climatological data in the stratosphere.

But (or altitudes above 30,000 feet a new range of problems enters, iii

that future aircraft ,perating at these levels will be supersonic, and

will be affected by turbulent eddies of longer wavelengths than are sLJ-

sonic crait. Spectrumn c:urvvs of turbulence show that longer wavelengths

have higher energy; therefore under identical atmospheric conditions

supersonic planes may encounter more turbulence than would conventional

aircraft. A fairly large amount of turbulence encountered in a small

number of flights made by the XB-70 aircraft (Ehrenberger, 196b) ap-

parently supports this expectation. For this reason the present re-

g "e.ssion equations, it applied to the straLSphere, might underestimate

turbulence probabilities for supersonic aircraft. This problem deserves

further invest igat ion.

"q

2-i

V AN• ESTIMATED TURBULENCE CLIMATOLOGY FOR THE UNITED STATES

The method of determining the turbulence frequtncies presented in

this section was described in Sec. IV. An explanation of the interpre-

tation and use of the fr quencies is as follows: The perceniage fre-

quencies p(.M) given in subsequent figures perti.in to the likelihood

that turbulence of moderate or severe intensity (as evaluatec by pilots)

will be encountered during a 100-mile segment of a flight made at a

;;cirticuiar location and altitude. The average value of p(M) over the

United Stat~s is shown versus altitude in Fig. 4. If light turbulence

is combined with moderate and severe tt give p(T), the overall turbulence

45

WINTER

40 SPRING

o •FALL

- -l

2-

35

2 3 4 5 6 , I 9 10P[UC[NT TU bLEN" I'LIGHT

FIG. 4 CURVES OF AVERAGE TUR1JULENCE FREQUENCY,s. HE!GHT FOR THE JNITED STATES,

DETERMINED FROM FiGS. S THROUGH 8

27

Zrequency (light, moderate, or severe) within 100-mile sectors, the

pilot reports show that p(T) = 3.Sp(M) in winter and spring, and

p(T) = 4.5p(M) in summer and fall. As discussed oy Endlich and Mancuso

(1967), the frequency of encountering the same intensity of turbulence

in a flight segment shorter than 100 miles decreases proportionately

with the smaller length. Data from Steiner (1965) and Endlich (1965)

indicate that the frequency of encountering moderate or severe turbulence

at a giren instant is less than two percent. This amount is about one-

fifth of the frequency of encountering the same degree of turbulence in

soiae portion (or possibly all) of a 100-mile segment. Thus, divid:Lng

the frequencies p(M) by five will give p(m), an estimate of the instanta-

neuus frequency of encountering moderate or severe turbulence. Similarly,

dividing p(T) by five will give p(t), the instantaneous likelihood of

encountering light or greater turbulence.

in summary, the turbulence frequencies that follow may be inter-

preted in the following ways:

(1) The frequencies p(M) of this section pertain to the

likelihood of encountering moderate or se-ere clear-air

turbulence within a 100-mile flight segment.

(2) To obtain p(T), the frequencies of encountering light or

greater turbulence within 100-mile flight segments, multiply

p(M) by 3.5 in winter and spring, and by 4°5 in sunmer

and fall.

(3) To obtain p(m), the likelihood of encountering moderate or

severe turbulence at a given instant, divide p(M) by 5.

(4) Similarly, to obtain p(t), the instantaneous risk of

encountering light o, greater turbulence, divide p(T)

by 5.

The turbulence frequencies were computed at 5-degree latitude-

longitude interrections based on climatological data at the twenty-five

stations whose locations are indicatfd by circles in Fig. 5. Frequencies

are given at the midpoint of those altitude layers having wind-shear

data--i.e., at 425, 375, 325, 225, 187, and 162 mb. These levels

correspond to heights of approximately 22,000, 25,000, 28,000, 36,000, j28iI

40,000 and 43,000 feet respectively. No shear data were available at

the 275-mb (32,000-foot) level. Charts for winter are given in Figs.

5(a) through 5(f), for spring in Figs. 6(a) through 6(f), for 3ummer

in Figs. 7(a) through 7(f), and for fall in Figs. 8(a) through 8(f).

The terrain corrections indicated by Fig. 3 have not been made in

Figs. 5-8; this must be done by the reader for a particular locality.

Similarly, a diurnal correction (Sec. IV-B) should be made to interpret

Fig. 7 to a particular time of day.

These turbulence frequencies are believed to apply t9 problems

where turbulence frequency is needed by season, altitude, and place.

They provide a rough basis for estimating the overall turbulence expo-

sure associated with different mission profiles. Operational planning

to avoid turbulence--for example, for air refuel4,ng missions--should

obtain some guidance. Also, turbulence-seeking pi-1grams may be directed

to areas of maximum probable exposure. Other applic'ions of this sort

will probably be found.

29

*W "&"__

t

1201w 110o. 190, W. 70wI0W I 0 I00 I0 I0 I0w:

501 - 6 6. 4 6.7? 67 6.6 6_..7 Lit. 6 6.5 6.6 6.e8 7 .1-5o.N

6. 5 5.9 5.4 06.1 6.6 7.1 ?.3 7.43" .0o s 66. 5 5s . 8 ,, . .6.1\ 7.7 07.2 7'. 2 7.3 • ; 7 L o

i ~6.,6 6.5 . % •]"':--.o_6.o9. . . 8700

6,8 6.8 . 7.1 7.5 . 7.7 7. 7.

I I I I I

120*W 1 00" 90* 0 70*W

FIG. 5(a) ESTIMATED PROBABILITIES (percent) OF ENCOUNTERING TURBULENCE IN100-MILE SECTORS OVER THE UNITED STATES IN WNTER, AT 425 mb

(approx. 22,000 feet). Average percent turbulence = 7.0. See Sec. V for an interpretation

of these frequencies.

120*W II0e I00I 90* s0* '0eW

50 9- 7.4 6 .7 (. 0 5 . 2 5. 3 400N--

5.9, 6.2 6.1 6 0- 6 0 6.4 . 6. . . . -

8

4 0 1 - 5. 6 .6 6.9 6 .4 6 .4 7 . 7.1 7 .6 7.1 8 .5 8 .1 7 8 .I - 4 0

08I- 05.N A 6 .6 • 6.8 ?- . .D 7.-- , . 81 81 3 -

66.4 6 7.3 7.9. 8.5 8.9 8.8 8.7

. I 7.40 7.7- 7.7 7.8 7.7 7.5 _30 -

4.1• 4.20 .7 6".1 . . . 64 . . .

1 II 1 1I 1 0 o 60 0 * 9 0 * s o , 7 0 * W

FIG. 5(b) ESTIMATED PROBABILITIES (percent) OF ENCOUNTERING TURBULENCE IN

100-MILE SECTORS OVER THE UNITED STATES IN WINTER, AT 375 mb

(approx. 25,000 feet). Average percent turbulence = 6.6.

30

.4.

120 "w I 10o 100 ° 90 " so, 70.w51 6 i';-- I 6I 6 I ;' -

5 ' 6 0'ý 6 65N- 4.2 5.1 6.1 6.4 6.2 " .6. 6.0 .•6.1 6.1 . 1 5. 9 50N

5 0 0 °65. 5.5 .3 6.9 6.7 6.7 67 6.7 7. .2-- 6.7.

6 0

4, 6 5.6 5.4 6.6 7.0 1.2 7.3 6.9 7. 7 74 7. $84)0 0 V _

0 06.6 6.4 6.3 6.4 6.5 7.0 t.6 7.8 7.7 7.7 768 7.6

00

8.1 5.5 /4.9 748 53 . 66.3 73 7.2 6.9

i ~ i i C w1201W 1i0* I00" 90, Boo 7'0o W

FIG. 5(c) ESTIMATED PROBABILITIES (percent) OF ENCOUNTERING TURBULENCE !N100-MILE SECTORS OVER THE UNITED STATES IN WINTER, AT 325 mb(approx. 28,000 feet). Average percent turbulance = 6.6.

120% 1 0 lOo00' 90° Boo 7 0Ow

3 3 3

2.0 2.1 2.5 2.9-3.5 3.1 2.8 2.8 3.1 3.1

4 3. 4.7 .7 5.9 5 4.5 3.5 2.7 2. .2 3. 1.?

5.2 6.3 7. 8.2 8. 4.7 4.2 4.7 3.7 2.55 0 09 '3

(0 0 34 5.3 7.0 9.1 9.2 90 8.1 5 .4 4.0 425

30"N- 3. 5.0 7.6 8.0 8.5 8.70 8.9 7.4 6.6o

4.6. 7.2 . 7.9 7.5

4 5 6 7 8It 5 I I120*W 110O 1001 90* Boo 70o W

FIG. 5(d) ESTIMATED PROBABILITIES (percent) OF ENCOUNTERING TURBULENCE IN100-MILE SECTORS OVER THE UNITED STATES IN WINTER, AT 225 mb(approx. 36,000 feet). Average percent turbulence 5.5.

31

"J120*W 10° t00* 90 90 g. ?7O1w

4 3 3

4.9 4.2 .7 .7 32 3.7 3.8 365 .7 11 37 3.4 3. 1-501

50

5.j 4.3 57- 5. 4.4 4.4 3.8 3 4 1 3

04

4.3 4.7 5.5 U 5.4 5.7 2, 4 . . 3.40 . 0

3 2.,. . 5 3.3 3.5 4./. 7 . . .

2 -

0 2.1 1.9 2. 3.3 3.7 4.6 5.90 5. 3.6 24 I. 1.6-30-N -2

32.3 2.3 2.5 6 .10 43 5.1 5.1I 4 . 6 3.4 3.5S3 4 5 51 1 1 1 1 1

120*W 110. 100* 90 80e 70 w

FIG. 5(e) ESTIMATED PROBABILITIES (percent) OF ENCOUNTERING TURBULENCE IN100-MILE SECTORS OVER THE UNITED STATES IN WINTER, AT 187 mb(approx. 40,000 feet). Average percent turbulence = 3.8.

120*'* 1 O0 100. 90* s0o 70wII ¶\ I I4 II!

4 1 3.115 _. 4., 4.1 4.1 4.5 3.6 3.1 3.4 3.1 3.1 3.5 3.7 3.5 - oN4

3 31 34 40 4.6 4.4 4.1 3.8 2.5 3. .0 3. 6

4 28 38 5.5 58 R.7 2.8 2. .4 4.1 1 -40-40"--~ , 5/5, .4 2. -0

2.7 3.3 4.0 4.4 4.5 4.4 4.2 4.6 4.9 3.0 1.3 1.2

30*N - I.? 2.7 3 .6 4.4 1- 4. 4.0 2.4 .,6 1.7 3I

L 2 - 2.- 2. 1 2.2 _ 2.4 3.2 3. h 4 . 4. 1 ) 1; .6 2.2 2.2\-• 3 4 4 3

I 20*w 110110 90, 80*10

FIG. 5(f) ESTIMATED PROBABILITIES (percent) OF ENCOUNTERING TURBULENCE IN100-MILE SECTORS OVER THE UNITED STATES IN WINTER, AT 162 mb(upprox. 43,000 feet). Average percent turbulence 3.5.

32

1200* 1 t.00 too so. 70,WI I I• / I1

5WI*N 5.9 4.7 4.5 4.9 4.2 4 . 5 5.0 5.4 5.6 5.6 5.4 5. 0 -WON

4. 4.3 3.5 3.8 4.4 .2 5.7 6.,T-,, . -. 0., 605o.- 5.6 4.8 4.5 4.6 4.6 .4 6. 6 .4 0 6.2 6 6.7_,0.

.0 6

6 0 0 6 O6.1 6.1 6.1 6.4 5.6 6.0 6.3 6.2 5.9 6.3 6.7 6.7

Wc.N- 6.5 7. 0 7. 6.7 6.2 6.3 6.70 6.9-- 6.7 ,6.5 6.5 6"2- 0

I7 ! 7 7 I711 2 0 " W 1 1 0 tO O O " 9 0 , s o ,? "

I SI

FIG. 6(a) ESTIMATED PROBABILITIES (percent) OF ENCOUNTERING TURBULENCE IN100-MILE SECTORS OVER THE UN!TED STATES IN SPRING AT 425 mb(approx. 22,000 feet). Average percent turbulence = 5.9. See Sec. V for an interpretation

of these frequencies.

120V to. I00" 90" s0" '0wI I lI ' I I I

.- 5.446 4.5 5.0 4.6 4 . 6 4. 5 4.7 5 1 5.0 5.3 5.9

51 4.0 4.1)4.4 .3 5.6 l5 7 5 .0 54 1.3

5 1I, ýF-.1 1 '41

0f 6 .0 6, ~o0 .. 9 4.4, 4. 5 ,, . 7 ,, . 4 '.5 5 .9 6 .3 6 .6' 7.0 ,.-o7

&9 5.2 5. 6.8 6.? 6.0 61 61 62 62 59 5.5

j ~05 - - ,-

30'N 4.7 4.7 5. 6 .2 6.3 -6.5 6.80 680- 6.4 .8 8 4.2-_

3.9 4.0 4.6 ý5.4 6.1 6.4 66 .6 64 .0 5

\4 5 6 '5I I

In- 100* 90*so

FIG. 6(b) ESTIMATED PROBABILITIES (percent) OF ENCOUNTERING TURBULENCE IN100-MILE SECTORS OVER THE UNITED STATES IN SPRING, AT 375 mb(approx. 25,000 feet). Average percent turbulence = 5.5.

33

.. , .:,.,,.w• -__"'-' ... -- ' -: • _ • .__ -- - _ I L '•&

I4rJ120 1w 110 lO. so0. 40 0 YW'

'o•- • 5.9 5.3 5.0 4.8 4.1 4.8 5.6 5.4 5.0 5.8 5

50 \. 4.6 4. .2 4.7 X 5.8 6. 6-.-

-0i 62 . . 6.63 6. . .4 \. 9 6 6

005 .4. 3 4 2 5. 9 . 6.5 i 5. . .4 67 - o

FIG. 6(c) ESTIMATED PROBA3ILITIES (percent) OF ENCOUNTERING TURBULENCE IN

100-MILE SECTORS OVER THE UNITED STATES IN SPRING, AT 325 mb

(approx. 28,000 feet). Average percent turbulence =5.8.

120 ,0 100 80 7

'X' - 2.5) '.,.8 1.4 I.jT i 2.3 2.4u 2.1 2.0 2.3 '.4 2.3 2.! - ON

00

5 . 5 . 6 . - - . 5 . 5 . 5 .2 5 .I L ., 6.. . 1 6.6_ 7 . 7.- _ 36 0

6.2 4 .5 G 6.3 .6. 555. . ... 4.9 2.5 2.7

3.7 46 57 72 85.9 7.0 70 7 2' 7..6 6.0 5.) ý .2-6.4-

S.97. 7 .9 o "•

4 7.o77- 8 8~4 7.3 4

3.6. .8>6.3 43 6.6

4 5 67 7 (6

2 00w to o , 9 0 " so , C,

FIG. 6(d) ESTIMATED PROBABILITIES (percent) OF ENCOUNTERING T URBULENCE IN

100-MILE SECTORS OVER THE UNITED STATES IN SPRING, AT 225 mb

(approx. 36,000 feet). Average percent turbulence 4.8.

34I0

IZO*e 110. 100. so* go. 7 WC

I I I I I O5 4 2ý 4 4

,o-- 5.6 4.7 3.4 3.7 3.3 3. 3.4 4.3 4.2 \ .0 2.7 2.9 WON

0 0 4 - 5

4.1 2.6 3.0 4.5 3. 2. 2.7 .6 5. .7 32 5.2

0 5

40-- 2.8 2.5 .1 .3 4.0 .2 2.4 4.2 5.3 4.1 2. 4.--40.

3.0 2.6 3.2 4.4 5.1 4.1 3.6 3.7 3.8 3. 4.1 5.2 5

4

2.2 1.4 I.9 3.7 3 ,4.0 3.00 2.3- 2. 3.8 3.4 3 . 3-,0N.

44~ 3

2 "• 25+ 16 1

1.4 1. 2 1A .2 2.5 2.9- 2-2 1. 1.7 2.3 2.2

2?SI I I I

.20*W 1 1O^ O0 "* 90o so, 70 "*

FIG. 6(e) ESTIMATED PROBABILITIES (percent, OF ENCOUNTERING TURBULENCE IN

100-MILE SECTORS OVER THE UNITED STATES IN SPRING, AT 187 mb

(approx. 40,000 feet). Average percent turbulence = 3.4.

i20* 110, ' 90* Go. ?7WI 1 4( ; '

3•' 4

y -- 4.0 3.ý 3.4 3.9 3.9 3.3 3.2 3.3 3.6 4.3 4.3 4.O-5o •1-4-• " -- --- - - "- - -0, -5

0/3, 3.2 3.1 2.6 2.0 2.7 29 3.4

0r

4 2 3

4G/- & 3.9 4.4 4. .7 .9 2.1 2.4 3.6 3 7 2.7 2.7-40-

-0 0 /- 0/ I/ 3

S2.9 1.9 I. 3. 35.6D~ 2.9- 2.0 1.8 2.3 3 0-0 .,,-.~*1o, 1, \ ý.

2 1. 1.4 1.4 1.5 1.2 1.0 1.4 1.5 I2 2.5

201 so. 7.0.FIG. 6(f) ESTIMATED PROBABILITIES (percent) OF ENCOUNicriNG TURBULENCE IN

100-MILE SECTORS OVER THE UNITED STATES IN SPRING, AT 162 mb

(approx. 43,000 feet). Average percent turbulence 3.0.

35

1200W 110. o o 00. TO-*070

4.0 5.6 5.0 5.1 5.4 5.6ý 5.1 1..4 455 4.6 5.61

5 /

f0- 4.5 4.9 5. .0 5.7 5.4 5 .4o 5.1 5.1 .5. 5.0- 5.6,.

4. .6 4. 6.7 63. 5.2 5.7 46.70 4.6 4.5 5.5 ý5.2 5.?

(apox 2.00 feet). A1er1 pe0en tblee 5.. so.Se. V o ?n neprtto

of theso frequencies.

I I I 15 4 4\' 4 3

~o- 5.7 5.6 '14.6 3.5 3.9 .41 4. 1 4.3 4.3 3. 7 2.9 .- N

30 o 4

400 4.6 5.3 5.7 5.6 5.7 %.5 5.4 5.8 5.6 5.3 5.054_ .

0 6 o

55.4 5.4 6.0 6.7 5.9 5.1 5.3 5.4 4.V .6 47 .

-5.0 4.9 4. .4 5.2 (4.5 4. a 5.L~- 5.2 ,4.6 4.? 4.6_

4A 4.6 C.7 .1 5.1 49 .1 -5 5.2 '~2 5.4 5.4

FIG. 7(b) ESTIMATED PROBABILITIES (percent) OF ENCOUNTERING TURBULENCE IN100MILE SECTORS OVER THE UNITED STATES IN SUMMER, AT 375 mb(approxw. 25,000 feet). Average percent turbulence 5.0.

36

Ito,* 0o to* W. ~ oW

55

6 0

00

_ ._ 4.3 .. 5. 2 4.3 4.9 4.4 46 4. 43

S 4.9 5.3 5.• 5.0 5. 0 4-- _- 47

5.2 5.3 5.2 &. 5.2 2 4.9 4.9 5 5. 3 .4 5.4

65 I

FIG. 7(c) ESTIMATED PROBABILITIES (percent) OF ENCCJNTER'NG TURBULENCE IN

100-MILE SECTORS OVER THE UNITED STATES IN SUMMER, AT 325 mb

(approx. 2t3,0(O feet). Average ptrcent turbulence 3 .. 1.

20OW ,'O ,0'00" 90" S0"O

2 t I 2y 2 !

__ 22 . . ..16 17 1010 0. 0.

0. 5.9 $. . . 1 49 51 4 4 4 .8 4.9 2.

2.7- 3. 0 3. 3.o 2.6 2. .7 o••. ,3

00

3,,4.0 4.3 5. 3 49 ,. 39.0 37 . 3. .4. 4.0-0

54 . . 5.2~ 5. 50 4. C9 54 . 5. 54

FIG. 7i() ESTIMATED PROBABILITIES (percent) OF ENCOJN T ER'NG TURBULENCE IN

'00-MILE SECTCRS OVER THE UNITED STATES IN SUMMER, AT 225 mb

(approx. 28,000 feet). Aver,-ag perc.nt turbu I oece 3.3.

37

*

Z3 '.4 2.2 2. 5 . .0 .4 2.9 1. 3 I 2.24.5. 2.6

.I _. 3.- !2. 2.4 2.? 1. t.0 '? 1 v?0? L 0.6 0..0...4O2.

0 e

00

2.)ý3 0" 3. . 235 21 1.4 I.?

-ý1 3.4 3.0 3.1 4 0 4,2 4.5 40ý .6-3. 3.0 2.5 2. o

39 .9 3.4 5.6 4.0 4'2j 4.1 3.7 3.7 3. 33

4 4

FfG. 7We ESTIMATED PRO8ABIL!TIES (percen~t) Of (ENCOUNTER ING TURBULENCE IN

100-MILE SECTORS OVER THE UNITED SIATES IN SUMMER, AT 187 mb(iappox. 40,000 feet). Averaq* pwcont turbulencea 2.6.

.2010 1' c' -'.9C w."

2 i II.7 2.41 2 0. .? C ' - 2 I3 c.,..~.

2.6 2.1 IF l ~ 4 0.4 0A6 ý . 7 . - -

1 1 14 18 1 5 14 1.5 . - - "

2,9.,

3 5.36 - 2,-' 2 3 - 9 1.2247-

3i 343 4. 41 40 3' 30 13

4 4 2

clG. 74 ESTIMATfD- P9C-A8'L'TES Owe F ENCOiJNTEWNIG T UlRBU LE NC E N.

10C-PAILE S ECTOR5i OdcR T'-'E UNi TEDý, ST ATfS 7N SUMMER, AT 362' mb

A43 000 ft . Awr t.2

38

in-if to. 1)0 ow so. ?0Yw

., 5.1 S. I 5.2 5O . 0 5.2 IS 8.4 5.1 SI.

,.5.2 4 3 46 4 4 49 5$2 5 3 *57 1 •• _--v

536 5 5O \ 4576 -55 57 4 ' 555255

5-5 Ij 5.5

0 . 0 C g0 '

FIG. 8(c) ESTiMATED PROBABILITIES (percent) OF ENCOUNTERING TURBULENCE IN100.MILE SECTORS OVER THE UNITED STATES IN FALL, AT 425 mb (approx.22,000 feet). Average percent turbulence = 5.3. See Sec. V for an nterpretation ofthe se frequencies.

~~00 so*" , -4

5o, 5Q S49 5 %Z " C'- 5.| 5l 4, 5.- 3 • 5 5 4 49 58 4 3 .

55

, I\,-!-

48 5 gn 4 Gi 63, 64-- 6 . 3 65 93 C..

FCG. 8;b! ESTIMATED PROBABLITIES pece-t) OF ENCOUNTERING TURBULENCE IN

100IMILE SECTORS OVER THE UNITED STATES :N FALL, AT "75 lb•, 2S•,00 Ce'.t) ever ge pe ece = .i*ee S-e .5.1

I39

•p•,o.0 2•00••. . A --, . -.e• " -• • - -. -.

2o.,W 1,o. loo. so* cc. 701W

6m

5.8 5.7 5.4 5.4 5.3 5.0-4.9'..1 5.7 5.6 5.9 5.8 SO.N

0

00•4.• 4.2 4.7 4.8 4.5 g. 5.2• 4.6 x , .5 5 1•- .

4

4__ 4. 4.3 4.70 .2 5.4 %-4 5.5 5 5 5.5 6.0 6. 7.3.....

0 0

51 50 5.6 6. 6.3 6.4 6.4 6.2 6.0 6.2 6.60 7.1

30'N 56 56 0 Is. . 6.4 6.70 6.4- 6.1 .7 5.6 .QON~

5,2 5.2 5.1 5.6 56.0 - 0- 5.8 5 .1 5.1 5.1

i 201W l O O0" 90, •"1* 7O W

FIG. 8(c) EST!,,ATHD PROBABILITIES (percent) OF ENCOUNTERING TURBULENCE IN100-MILE SECTORS OVE'R THE UNITED STATES IN FALL, AT 325 mb(a;-piox, 26,(d0 feet). Average psrcent tuP!)L;!enct. = 5.6.

I 1," * O"00. 90 ° d0o ?0 "WSI i r2 2 2 3 4 3..

-19 2.4 2.4 3 4 / 3 I : 2.s 2.8

/0. .4'2 .2 35 a

' ' • ' " / 1O" 3C"• 0 I ":0

4o--4 ro/ . 5.6( fe 3 4.5 % 5 3.0 4? 4.6 4.2 3. 3 40

4.7 Nd.S 5 6 68 elA\ 5.1 5.2 62 6. 5.7 5 5 5.6

4

S3 2 .1 4. 52 5.7 4.54805.a 5.. 45.55 5.4 5300N3

2 3 23 31 6 3.9 3.8 3.6 9 .2 4. 3.9

110. 100, go. so. oW

F'iG. b~d) ESTIMATED PROBABILITIES (percent) OF ENCOUNT1ERING TURBULENCE IN-GO MILE SECTORS OVER THE U1NITED STATES IN FALL, AT 22-3 mb(3pprox. 36,000 feei). Average percent turbulen~ce -~4.1.

40

1H01% 110* 100. 900 ?s* 70.w

3

32 2.2 1.8 2.1 3.8 317 3.8 3.5 3.2 s

4 -4. 3.8 3.7 -3.3 31 2.4 1. 2.2 2 3.2 3. f- 2

4 -4 4.0 4.3 4 9 2.6 2.3 1.9 - 1.62000

3.2.3 2.4 .3 3.8 1 2.8 2.7 2.2 0 1.6 1.9 2 5 3.5

002

2

30*N 1 2.1 2.4 2.4 2. 1 _ 2.1 2.20 2.5ý- 2.6 3. 34 3530* -

2-2.0 2.3 2.4 2.7 2.6 2.5 2.3 2.3 .3 2.3

'' 20.W ',10. 00, 9O* 8 0" 0 *

FIG. 8(e) ESTIMATED PROBABILITIES (pecent) OF ENCOUNTERING TURBULENCE IN100-MILE SECTORS OVER THE UNITED STATES IN FALL, AT 187 mb(approx. 40,000 feem). Average percent turbulence = 2.8.

120*W I 10* I00° 90" 60" ?OW

22 2 2 2

50"- 2- 23 1. 14 1- -- 0o-- 2 2.7.o•.••1 2.1 -50-N

23.0 1.9 2.1 2.7 2.1 2.3 3. .0 3 1.9

1 ~4 ,4uo- 2.4 3,5 4.4 3.7 ý.8 2.2 2.2 2.8 2.8 3. 4.7 -40'

C. 0 0

02.6 2.8 3.1 4.0 3.4 3.2 2.8 2.4 2.3 2,7 3.1 3.1/"oI 6 Z.3 2.3 2.7 2.9o 2.3 :. 1 2.2 2.

20 20 2_2 2. 22 5 25 20 1.8 .6 1.7 1.6

I I I I I20'• 10' '00' 90' 50' s70.

FIG. 8(f) ESTIMATED PROBABILITIES (percent) OF ENCOUNTERING TURBULENCE INI00-MILE SECTORS OVER THE UNITED STATES IN FALL, AT 162 mb(approx. 43,000 feet). Average percent turbulence - 2.5.

41

WN1

_____ ____ __ I

VI DISCUSSION AND RECOMMENDATIONS

At this point we briefly recapitulate our view of efforts to

estimate the turbulence climatology of the globe.

Flights by instrumented research aircraft provide very valuable

basic knowledge about turbulence as well as statistical information

for design purposes, but often cannot answer important questions such

as the following:

(1) What is the three-dimensional extent of a turbulent volume?

(2) What are the special conditions in the generating region

of the turtalence?

(3) How long does the turbulent area last, and how far does

it travel in association with synoptic meteorological

features?

(4) If thV mesoscale meteorological conditions were slightly

different, would the turbulence still have been present?

Lack of answers makes generalization from limited flights quite

difficult. Future flight programs should attempt to obtain inforr-cion

concerning these matters insofar as possible.

Pilot reports have been of major importance in describing turbu-

lence frequencies at altitudes below 40,000 feet. Since equivalent

information is not available in the stratosphere, knowledge of strato-

spheric turbulence will tend to remain incomplete until a new generation

of aircraft has been built and flown. At that point, design decisions

will have already been made. Mistakes in design due to poor knowledge

of turbulence may be costly.

Many people have recognized these problems, and have suggested

that remote sensors on the ground, in aircraft, or satellites might be

able to detect turbulence or associated mesopbenomena (for example,

see Reiter, 1967). Probably the stratosphere will present special

difficulties if viewed from belc-'. Efforts to develop remote sensors

are being carried forward, as they should be. However, the fact that

approximately 150 weather balloons rise through the atmosphere to the

43

< .

In

100,000-foot level in the United States every day has been ignored in

regard to the possibility of their carrying direct turbulence sensors

aloft. The sole exception in the United States is the very interesting

work reported by Anderson (1957) using the gustsonde; since that time

technology has improved greatly. Certainly on low-level towers, direct

measurements of turbulence predominate over indirect sensing, and this

might be taken as a partial guide for the stratosphere. Instrumental

problems related to balloon-borne sensors are unknown, but might be

much simpler to solve than the similarly uncertain problems of remote

sensors. Development of a balloon-borne turbulence sensor should be

undertaken immediately as a possible means of augmenting other types

of data. Also, such a sensor might be useful prior tc flights oi in-

str-umented aircraft in locating favorable atmospheric layers to be

probed for turbulence.

As discussed in Sec. III, special trials are recommended to deter-

mine whether the FPS-16 Rose system can detect turbulence in the strato-

sphere. Of course, this can only be done at those few sites having

FPS-16 radars.

Since the presently available statistics of wind shear over the

United States are based on data obtained prior to 1960 that are unrep-

resentative of jet-stream conditions, it -would be desirable to recompute

them. This is a fairly large but straightforward task that could be

done from recent highi-altitude wind measurements made by GMD-l (or

equivalent) equipment. Appreciable differences between the new wind-

shear climatology and earlier values would dictate that the estimated

turbulence frequencies of Sec. V be redetermined.

44

4

APPENDIX

SELECTED CLIMATOLOGICAL DATA

FOR THE UNITED STATES

45

45

I-

120W 0 to- I00. 90" S00 701W

I 1.5 I.,5 \ I

eN i 0. 1.2 I.5 1.7 .5 1, I.4)I , I1.5-- 1.5 1.4 1.4-50-N

0 0

0 . 1 •.Z 1.5 1.d 1. 9 1.7 1.8 2.0 .2.1 2, -2.0-2

1.5- 2. 1. 5 C ,) 1 o 2 % 2.4 2--...5 . .4 26 23-,

0 2.52.2 1.9 1.9 2.0 2.0 2.2 (2 .6 2.8 2.7 2.7 2.7 2.7

2.3 20 '*= P22.530*N- 23 2.0 1 . . .? "1 6 .5-30-N

9 19 1.4 .3 1.5 1.7 1.9 2.0 2.1 2.0 1.9

2 /i1 '5 1 1.5 I i i ;

120*W I IO* t00° so, 80* 7o.

(a) Magnitude of the mean shear vector at 325 mb in winter, units 10-3 sec-1

120"W I tO* tO0' 90' 80" 7 O7 WI I 6 t•II I

50N 7.0 6,4 6.0 6.1 5.8 54 5.8 5 9 5.8 5.6 5.4 5. 6 -50-N

6

7. .9 6.3 5.- 5.7 5.8 6.5 6.9 .4 5 9 .0-- 6.60 7

40-- 7.1 6.2 5.3 5.7 6.1 6.3 7.0 .I 6.9 6.8 7.3 7. 7-40o

7.0 6.7 6.9 -7 7.0 6. 7.1 7.5 7.2 7.3 7.4 7.4

0 1~'7

30"Nm 7., 7.6 8.0 8.6 6.1 7.2 6.9o 6.7- 6 6.4 6.4 6

.4

- 30-,N

67.5 7.5 7.7 .7 7.3 6.7 6.2,,,,5.9 5.7 .7 5.7 5.7

7 6

i20tW I O' 0OO' 90, s0' 70.

(b) Standard deviation of the shear vector at 325 mb in winter, units 10-3 soc-1

FIG. A-1 STATISTICS ON THE VERT;CAL WIND SHEAR VECTOR (normalized to a4000-foot thickness) IN WINTER, BASED ON SCHAMACH'S DATA

FOR STATIONS INDICATED BY SMALL CIRCLES, AND WIND SPEEDS FROM

U.S. AIR FORCE MANUAL SACM 105-2

47

120** 10 100' too* go. ?.W

I I I I~- 2~ 22 23 23 24 26 27 26 30 31 32 32 -WIN

yS 0 0

24~ 24 25 26 26 29 30 33 6 -36

25- 3401- 2 26 29 3 31 33 5 37 39 39

0 0 0 0

25 0 30

24 24 25 26 28 30 32 33 34 33 31 29

301- 21 22 23 24 26 _.27 2 o 268 2 '26 2 5 -30*N

2020

le is 19 22 23 22 20 Is 17 17 17

1201W 110. 00o 90* 80. 70,W

(c) Mean wind speed at 325 mb in, winter, units m sec-

12O*w 1 i0. too. 90* go. ? CVW

I I I110.5-0. 05

WI 4 02 0. . "'D.4) 0.3 0.2 0.1 0.1 0.1 0. 1-50',N

13 1.6 1.6 1.5 1.2 0. 6 4 3 0.

40-- 1.9 2. 1 2. 1 2.6 3.1 ~.? 1.5 1.2 1. 0.9 0.? .- 0

0

30*04- 1.1 1.6 2.1 2.6 . 0 3 3o 3.6- 3 '2.9 2.5 2.5- 3-

2 1 1

FIG. A-i (Continued)

48

A

1201W 110. 10o 900 so, 70.w

II I I,o'- 9.5 61.6 6.3 6.4 7.2 6.9 7 7.2 .9 6.3 6.3 /7.1 850-N

9. 7.9 6.6 7.4 7.6 6.0 6.3 6.1 .5 63 6 9.2

0

70

40-- 9. .7 6.3 6.2 7.4 6.6 6.6 8.6 7.6 . 0 0

0 0o 1

7. 98.6 8.3 7.6 6.4 7.5 7.7 6.1 6.5 8.7 9.4 1 9.7

1' 9*30*%- 8.4 8.4 6. 7.4 73 7.1 7.9 e.4- 6.7 L8.9 6.9 8.9.O.

.. 88

97.1 7.11 6.6 .6 6.6 6.6 7.1l 7.77 7.19 .9 . 7.9

1201w 110. too 90 so, o

(e) Standard deviation of the shear vector at 225 mb in winter, units 16-3 s.c-1

25

03

0 3

27) 26 26 27 26 30 31 33 'A4 3

0 030 40

32 33 33 34 35 36 37 38 03ý1-.-40 39 36

30111 29 30 31 3 2 13,-4 34 34 31-, -.33 32 30 -7- 30,

25 .-- 25

22 2 26 2,6 2 8 28 /27 26 25 4 24 4

25 2 0

()Moan wind speed at 225 mb in winter, units m see -

FIG. A-i (Continued'

49

120" 110. tOo* W0* 00 1W

I 0.5 I I

•Ot_ ,.5 1.0 \0o3 0.4 0.3 0.2 0.3 0.3 0.2 0.2 0.2 0.2 -5o.N

1.9 1.1 0.9 1.4 1.3 0.7 0.9 0.7 0.4 6,.. 0.7

051 1. 5 ID 1.3 o.3 . .30 0 005.-., 0• , 1

0.2 0.2 1.0 k2 03 07 1.3 1.9 '1.3 0.7 0.4-.4-050 /2

3.40.2 0.2 0. 01.2 2.O I.6 .0 '0.5 0.4 0.4__o3.0

0.2 0.2 0.2 1.0 1.5 1. 4 . . 1.1

0.5 1 i' 0 " 9 0 " s0o

(g) Magnitude of the mean shear vector at 187 mb in winter, units 10- 3 sec-I

,20** t1. 'O0O 90, so. I O*W

8 87 6 6

8.. . ~. 96../ 19 .S 5.6 a 5.9 5.6 5.3 5.)S 6.5 - o

8.4 7.3 .. 9 6.7 ,, 7.7 9

01

-- 7.4 7.2 7.1 6. 5. 7.0 1. 7.5 6.4 7 I. 1.1 --.0

"7 .2 a. 7.9 .5 6.5 7.6 6.5 7.9 7.3 I9.1 0.? 10.7

, 7.2 6.9 7.5 .1 6. 641 0. 10.2 10.5

6.2 S.1 717 T.5 7.5 76 7S 6.3 .0 4.5 9.5 9.3

(k'l) Stmadard deiation of -.he sieer victor at 187 mb in winter, uni t s 10-3 sec-1

FIG. A-1 tCwnclud.d)

50

I

lzo* 1.°w,0" 100° 90, so. 'CO'l

115.. , 1,7 1.5 1. 2 1.5 I.7 1.5 1.2 5

I2",.• .3. " .s•",' •_ o _., 'i-/J

'. . 9 1.2 . 1.5 1.? 1.6 . 1.72 I 2 12.5 2.7

2.5

"•4"- 1.7 t 1.3 1.0 0 1.0# 16 0•. 2.? 2. 1 .0 2. 1 2.• 12.7_40. -

I.8 1.7 1.9I 1.9 1,8 f'? 1. 2.l 2.3 25 2.7

2.2 2.3 2.4 \2.4 Z.2 2. i.7, I.L-- 2.'0 2.2 2.3 2.3 30,,

22.4 2.4 2.5 2.5 2.4 2.5 2.2 1.19 -9 '.9 1 9

2

7" " 90. C

(a) Magnitude of the mean shear vector at 325 mb in spring, units 10 sec

2* 0. C.

5.3 55 54 '' 5. 5

5c. 5-2 5.2 5.5ý 5.2 5.6 5. \4 5 .

6 - 6

6.1i 6.2 6.1 6.7 6.4 6.0 5.6 5.9 5.6 5.3 5 6'16.6

. 6.2 5.9 5.5 5.-, 6.3 9.3 .6 6.2 6.2 2 .0 6. 7.3

5.6 5.6 5.4 5.3 5.9 5.9 5.9 6.4 62.2 '. 2 6.2

3014- 6.5 6.5 6.4 6.5 6 3 .9 5 2- 3 & .2

65.g 5.9 5-9 5.0\ 5.7 5.0~S 57 578 2 4/

(b) Standnrd deviation of the shear vector at 325 nib ,n sprtg, un,fs IC sec

FIG A-2 STATIzTICS ON THE VERTICAL WIND SHEAR VECTOR noriolzod o- aJ000-foot thicknes.s IN SPRING BASED 04 SC&,MAACH'S DATA

FOR STATiONS INDICATED BY SMA.LL C0RULES

51

O.1 IK 4 0.2 0.4 03 . i 0.1 0.2 0.3 0.3 0.2 0.3-50..

i0

14 1.. . 0.3 0.6 00

N 04Q .~2 1. 2.6 2.6 z.i3-Ito 1.5 1.* 1.? 0.6 0.

00 0

3$ 22"1 . N 2.6 3.1 34 35 33-- 3 .6 3..

09 °4 .• C IC IC *"\J

'2 4 *S .0\ 7.. 2-1 2.2 2.4 2. 3.4 3ý.0 2.7

(c) Man~tudeofINC.

(c) Mani lnude of th e taloe ."aor vec Tr at ' 225 m6 in spring, wnits 03 Sc-1

8, 7• 6 \6

-G i V. 3 G.7 6.6 63 4 66.

"--, \ 0 I ,.-/62 62 65 6. 6.63. . 7 64 a C

6. C Z -- - . 65 '. 6 . - 0

7.0 21 -. 6- 6 63 .r0 7.3 7.2 "It.6 / 6 3 6I

NY.

16 ~5~ 3 73 '3 7 0Q~ 7 6 7-4

-.-. N ,,.-Zs

dlStierdo~ ide.oter. of , shieer vecwo at 225 mb tm sj'ng vf-10 10- -.cI FiG A-i Cce-,,'n.,#

$ 52

IS

to*t

!4- 09 4/ o 1.0 0.7 05\ 0 t I 1 0 1 0 51. 9/ 1 4i -4

0.) T2. .3 0 1.7 2

LI 0.5i ?05 * 0 '

0.0 .( 1.4 ! 1 /01 1.9 0. /2.2- .

0.9 0 7 0 .6 12 1. . 1 5 1.>

,1) \,1 2'\•~ r" 1 ° ,-L! .. \ ,1"

0 .5 0. . . , ,

,0. 5 0.6 0.4 04 4 0 . 0 0a 0 7

it) Magnitude of the meon $hear vector ot 187 -b in spring, unit 10- sec

6 4 64 6.3 6.5 6.1 5.8 5,7 5.8e 15 5.s :2 5O--5O%

" 65 66 6.5 62 65 6a 6.9 ," .I - 66 7

. - . /, -'\:i, 65 5, 2 5 . 2t 627 I e ,>-9 • -4C

• --- __ , • ,,. / i < • - . _ .." ,3 a . 6 0 T ,?

6 4 11 ' 0 . 1 DO- a 8 0 1

SStendord 6iov?,or of ?)4 we. vcfcr v 18, - F so g. n.,s -

C3

120W 110 o 1000 too So. ?O#W1. 4 1 '(• 2 I I I1.5 2

5O t - 1.0 1.2 1.5 1.6 1.g 2.1' 2. O0N•" ",, .9 1. $ 1.7 1.6 1.7 - W ON

1.1 1.2 1.4 1.7 .1 2.3 2.3 2.2 1.9 1.7 1 og

409- 1.5 1.6 1.6 1.6 1.7 .- . 1.5---T.4\ 1.6 I. 40•~ o oý 0.• lv /.

00 g

1 .2 1.3 I. 50.5 0.6 080 (N0.5

3o.__ 0 . 8 0 6 0 \ ,•O.9 0 V 5 0.2 0 04.- 0.5 •0.4 0.3 0.3 30.

0.5

0.5 0.5 0.k N 0.7 0.7 0.7 0.6 0.7 0.7

0 o5S I I I I I

(a) Magnitude of the mean shear vector at 325 mb in summer, units 10-3 sec-1

120oW 10* I00 90* 60* ?0w

5 5.6 5.654 59 5

4 5.0 5.2 5.6 5.65"------------------------------------------- .ThI• ~~55 0 5.O58 7 5952 4

0

401- 5.0 5.0 " 4.9 4.7 4. 7 .9 4.9 4.9 5.0 5.2 5.5 5.7 -40"0 0 0

05

4.7 4.5 4.3 3.9 4.2 4.2 4.1 4.4 4.0 4.8 4.8 4.9

4.5 4.3 4. 3.8 3.9 3.9 4.2o 4.2- 4. '4.1 4.0-4.0•30*N-

4.2 4.1 3.9 .9 3.9 3.9 3.9 3.9 3.9 3.8 3.6 3.8

SI I I I1201W 10 100. 90 o 0o* 70 W

(b) Standard deviation of the shear vector at 325 mb in summer, units 10-3 sec- 1

FIG. A-3 STATISTICS ON THE VERTICAL WIND SHEAR VECTOR (normaDized to A4000-foot thickness) IN SUMMER, BASED ON SCHAMACH'S DATA taFOR STATIONS INDICATED BY SMALL CIRCLES, AND WIND SPEEDSFROM U.S. AIR FORCE MANUAL SACM 105-2

5I.

1209W 90 too00. 90 ' go. OOW

0I o

5TN- 1 15 16 97 is8 2 2 23 25 25 25 24-o,

0' 520 2220

II0

0 -0

_5 3'- ,5-

30'h__ 5 4 "4 . 4 40 • < 4 -3O*N"

0 15

2 31 4 -" 6 -5 5 42 2

i'0' 1O 00' 90" 80* 1O.*

(c) Mean wind speed at 325 mb in summer, units m sec-

120*W no '0"e'0 90' 80' 70OW

0 .

0-- 20 19 19 1 1 8 1 18 18 14 18 18 118--o

4o. 1 17 I5 PT 16 i 16 16 5

10 0

0

14 04 14 4 4 4 43 13 2 3 3 I4 9-1'2

30"t __ 12 12 l0 20- 80, II

110' IO lOCI" 90' O O

-I(d) Standard deviation of the wind vector at 325 mb in summer, units m sec-1

FIG. A-3 (Continued)

5s s

VkJ

1201* 110. 100. 90* S0* 7O1W

I 1 6 i7 1 20 I

Is0" is 1 15 16 16 17 1• 6 19/ 23 25 27 27-50-N

,o. 2 2 -2' -3 -5 -6 -7 -8 -6 -6 -6" -•-.

0 0

0 20 -

F o -)-I -II -II-- I -l -II -14 -16 -16 -15 -t5 -14 -II

30N* -3 3 -13 -16 18 12 9 "9 -30.N

-3 -3 -10\ 11I -13 -1 6 -!a -15 -14 2 -9 -3

-10-10I I I I I - oIi 20*W 110* 100 90, 80s ?0. W

(e) Relative vorticity computed from mean winds at 325 mb in summer, units 10-6 sec-

120*W 1;01 I00. 90, 80s 70*W

I 0 1 1.5 11 1 1.5I I

=0.2 0.4 0.6 .7. 1.4 .9 0.4 0. 3 -50.N

0 ol .. .8 0.ll

4. 1.1.5- .6 0. 1.4 1.1 0. -8 ~ii40. . I .. 2 1..4 ,.8 O.a

.o 9700

0 .8 0.8 01.8 0.9 0.1.5 0. 8 6 0.8 0.,9. 0.9 1 .1 1 -4.4

0 0

-. - -. . _ ' "

0.2 0.2 0.4 0.9 0.9 0.5 0.6 0.3 0 0. 1.1 1.4

00.5

'20-W I110 00, 90" 80s 7,0. W

(f) Magnitude of the mean sheor vector at 225 mb in summer, units 10-3 sec-1

FIG. A-3 (Continued)

561.

120°W 110, 1000 90, 100 70.W1 7 1 1• ý I 1 ISW 50"N-- 6.3 6.0• 7.3 7.6 7.5 ". 7.7 7.6 7.6 1 7.1 7.1 7. ON

S0, o .. .. .. .....6.4 6.6 6.6 6.5 6.6 6.9 6.9 6.6 6.7 6.5 6 .5?!e. 5

0

40,.- 6.0-. 5.9 5.3 5.4 5.6.0 60 6.4 6.3 6.340

0- 0 5.0 5..05N 6.00 6.0 ,

54 5.3 5.0 5.4 5..

3N 5.1 .9 4. 9 4.8 4.5 4.5 5.1 54.4- 5.4 5.4 55 5.5__

5.Z24 5, 5 5 5.

4.9 4.8 4.7 4.5 4.4 4.5 5.0 5.0

I201W ,0* I00* 90* s0o 70. W

(g) Standard deviation of the shear vector at 225 mb in summer, units 10-3 sec-1

120"W 110. I00* 90* go0 7O1W

i .5 ' , I I I1. 41 I• . 1.5 . 16'5

50*N 0.9 0.8 0.9 1.4 ý\\ý17 I7.1 4 I7' 1 '*15 3.6S._ o• o° o, . . --,.• , ,,-.• . - ''

0

So~o~o o O o 4, g

0 .3 0.3 0.4" 0.3" 0.1 0.3 0.30 0.3 /,0,60 05 0.2 0.2 3.0

0.7 0.6 0.7Y. 2 003 0 0 ý3 0. ./.

30 0 .0 N-

50

0.1 0.1 2 0.3 0.4 0.6 0.7 0.7 0.7\ 0.3 0.3

Q5 0.5'0.W C'001 90, so, 70*W

(h) Magnitude of the mean shear vector at 187 mb in summer, units 10- ze-

FIG. A-3 (Continued)

57

II

1201WIO'."* 90* sO. 70*W

SOON 6.3 6.6 6.8 7.2 7.5 7 .5 7.3 7.0 6.9 6.8 6.8 6."--sO*N

6.6 7.4 7.4 69 s, r.5 .5.-- 6.5

X6.1 5. 9 7.40-0 6.1 5.9 5.9 6.0 6.3 %.6 6.7 6.9 6.9 6.9 400

5.4 5.2 5.2 5.3 5.2 5.2 5. 6.2 6.6 6 6.7 0F 6.7

i530'N 4.9 4.9 4. 5.0 4.8 4.8 5.3o 5. 6. 6.3 6.2 6.1 30N

48 4.8 5.0 5.0 4.8 4.8 15.1 5.3 5.4 5.5 5.6 5.5i I 5 5 I 5III

120*W 110" 100. goo s0o 70 W

0 (i) Standard deviation of the shear vector at 187 mb in summer, units 10-3 sec-1.

FIG. A-3 (Concluded)

58

jI.

IV

10. w i o* too* ,o* go. 70.w

WIN .9 . 1. 1.9 .9 9.ý I' .7 1.9 1.9 1.9 9.9 S*

•' .1 .5-.-4 1 • .

0

40- 1.1 1.02

,. /9 '1ý 9.0 . .

1.9.3 16 1.7 1.9 2.1 2.2 2.2 2.2 2.2 2. 27

1.5 ___- 2.5

.7•N . - . 3 . 2.71 .1. 2.2-.- 2.9 1.9 .9 2.'1..ZI0 . N

1.,5

5 1.711.I I I I I1201W 1 100* 90, 80s 70. w

(a) Magnitude of the mean shear vector at 325 mb in fall, units 10-3 sec-1

120 "% 110 1001 90, go 70-W

3 6 6

~ 6.2 6.2 6.5 9 6.9 6.4 6.4 6.2 5.0 5.8 5

6. , 5.' 7 6.0 6.3 6.4 6.. 5.6 5.9 5.2 5.6 0

4T- 5.7 5.4 5.4• 5.6 5.6 %.5 5.6 5.6 56 56 60

0 0 7

5.3 5.2 4.9 4.9 5.1 5.5 5.6 6.2 067 66 6.6 6.9

0

3*- 5. 5.0 4. 4 51 5.5 5.6w 6.0.- 691 0 . -93-

4.7 4.6 4.6 47 4.8 ..~59 52 5 2 5 0

5\

I I0 " 90 " 80 70

(b) Standard deviation of the shear vector at 325 mb in fall, units n-3 sec-1.

FIG. A-4 STATISTICS ON THE VERTICAL WIND SHEAR VECTOR (normalized to a4000-foot thickness) IN FALL, BASED ON SCHAMACH'S DATA

FOR STATIONS INDICATED BY SMALL CIRCLES

59

'2OV• Ho' 100 * 60w' 7Ow <

0.O. . . . . 0.9 .6 0.3 0.4 0.? 0.6-5O.,

S! !I I I

61.3 1.9 .9 0.7 1.3 1.2 0.9 0 .6 0.04 6.-3

00

N 2

, I .. 0. "

0.8 0.8 . 1.6 .6 1.7.- 1.9 '•.0 1.

0. 0.30. 0.8

cc. 90, s5**

(c) Magnitude of the mean $hear vector at 225 mb in fall, units 10-3 sec-ý

6. 6

~Q~~8.0 7.7 7. 5 8.0 7.5 6.6 5. 5.6 6.0 5.9 6.0 C6 7.6

7.6 .8 -,l 7.2 7.5 / 6.9 6.8 6.9 6 . - 8.0

(,6 L.2 1

40" 6.5 6.0 ý5.A 6 6.2 6.6 1.5 6.2 6.9 6.9 6.8 7.8e S.4_.

08

6.7 6.5 5.9 5.5 6.0 6.7 6.9 7.0 7.0 7.5 7.8 7.8

/ 7

30"'- 6.9 6.9 68 6.3 6.1 6.6 6.9c 6.9- 6.9 .6.9 6.9 6.9.03c...

6.8 6.0 6.6 6.4 5 9 6.0.6 6C 6.2 6.5 6.5 6.4

2010 0. Oc" •9c" SO" "

(d) Standard deviation of the sheor vector at 225 mb in fall, units 10-3 sec 1

FIG. A-A (Continued)

60

IL

1201W I ." 000. 903 go0 701W

' % I I I

0o.5 0.5 1 1

I,.) 0.4a0td of / h m s .e vcor 18. , u.nit 0 .8 o.-0.0

I'. 1o .0 1.0 0. 0 4. 0.3 0.4 o.0 o 0 9 .

- 7.5 7 7.2 07 5 0 6.50"o 00

o.1 . .3 ý .1,3 0.7 8.6 0.360.7 6..1 \0..2 7.. 6.. ,74

\00

0 . ..5 7.0 7.2 0.7 6.8 6. .6 6. .305 69 . 1 .930a

3,N - 0 1 0203 0 1 02 ., 05- . . . ._.I.--0.

0.1 0.2 0.2.6 0.3 0." 6.3 1'Q- .3 7 .4 0.4 0.4

6 2,.. 5. 60 I 6. . 7.-. .

I.• ,• OC* 90* so, 70O°W

(e) Magnitude of the mean shear vector at 187 mb in fall, units 10-3 sec-1.1201W " '0 . 100. 90C so. To.*

., 7.5 7 2 7.2 7 .5 7.3 7\ 6. 6.5 61.9 6.7 61. 1 6.0 613 so. N

6.%, 6.7 •6.6 \ 7.2• 7.2 6. 7.4 T. 6. 61 67 79

64 60 65 7.0 7.2 1 -6.8 6.6 6.5 69 8.• " .9-40.

6.2 6 1 6. S. " 6.4 6.9 C '7B 8. 82 8.2

6 .6 6.6 6.3 " 6- 6 3 6.C 6.9 , 7.G..-- 7.2 .7.4 ,-'6 7".5-- 0" 4

6 .6

•)Standard deviation of the sheu, vector at 187 mb irn fall, units 10 3 sec

i ~FIG. A-4 Concluded,•

61

ACKNOWLEDGMENTS

It is a pleasure to acknowledge the aid and advice given by

Mr. Norman Sissenwine of AFCRL during this study; however, all opinions

expressed are those of the writers. We are indebted to our coworker

Mr. William Viezee for reviewing and criticizing the manuscript.

I 1

I

REF EREINCES

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Armendariz, M. and L. J. Rider, 1966: Wind shear for small thickness

layers. Amer. Inst. Aeron. and Astron., Paper 66-352, AIAA, New

York, N. Y., 11 pp.

Briggs, J. and W. T. Roach, 1963: Aircraft observations near jet

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Brooks. C. E. P. and H. Carruthers, 1953: Handbouk of Statistical

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Clodpnan, J., G. M. Morgan, and J. T. Ball, 1961: High level turbulence,

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1962. MonWea. Re.iew, 91, pp. 73-82.

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Conference, March 1968, London, Committee on Aeronautical

Meteorology, World Meteorological organization. Techniques

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Coy, R. G., 1967: Atmospheric" turuulence spectra from B-52 flight

loAds data. Tech. Rerort U 'DL-TR-67-13, University of Dayton

Research Institute, Dayton, Ohio, '0 pp.

Crooks, W. M. , F. M. Hob!it, I). T. P .,;p et-, et al 1967: Pro, ec.

Hicat, an investigazion of htgh z!titude clear air turbulence.

AFFDL-TR-67-123, Vol. 1, Cctrdct &Y' 33(657}-11143, Lckheed

California Co., Burbank, Cilif.. 255 pp.

Crutcher. H. L.. 1963: Clima•ology of the upper asr as related Io the

design and operation cf s'pers.nc aircraft. C. S. Weather

Bureau. ESSA, 72 pp.

6 5

Danielsen, E. F. and R. T. Duquet, 1967: A comparison of FPS-16 and

GMD-l measurements and methods for processing wind data, J.=_pl.

Meteor., 6, pp. 824-836.

Dvoskin, N. and N. Sissenwine, 1958: Evaluation of AN/GMD-2 wind shear

data for development of missile design criteria. Air Force Surveys

in Geephysics No. 99, AFCRL, Bedford, Mass., 72 pp.

Ehrenberger, L. J., 1968: Atmospheric conditions associated with

turbulence encountered by the XB-70 airplane above 40,000 feet

altitude. Proceedings of the Third National Conference on

Aerospace Meteorology, American Meteorological Society, Boston,

Mass., pp. 461-474.

Endlich, R. M., 1964: The mesoscale structure of some regions o!

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66

Harrison, H. T., and D. F. Sowa, 1966: Mountain wave exposure on jet

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67

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Possible future developments. Astronautics and Aeronautics,

August 19S7, pp. 56-58.

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turbulence. J. Appl. Meteor, 3, pp. 247-260.

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University, Ft. Collins, Colorado, 43 pp.

Schacich. S., 1960: Preliminary report on vertical wind shear parameter*

for 25 U.S. Stattons, Unpublished report, Nationnl Weather Records

Center, ESSA, 61 pp.

* Scoggins, J. R., 1964: Aerodynamics of spherical balloon wind sensors

J. Geophys. Res. 69, pp. 591-599.

Scoggins, J. R., 1967: A comparison of Rose and Jimsphere balloon

motions. blemo, R-AERO-Y-196-67, George C. Marshal Spact Flight

Center, NASA, Huntsville, Alabama, 23 pp,

Steiner, R. 1965: A review of NASA high altituae clear air turbulence

sampling programs. Amer. Inst. Aeron. and Astron. Paper No. 65-13,

AIAA, New York, N. Y., 12 pp.

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isogon-isotach charts. SACM 105-2, Vol. II, Hdqs., Strategic Air

Command, Offutt Air Force Base, Nebraska.

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Offutt Air Force Base, Nebraska.

68

'7

S.t

IU

I[NCLASS I F I El)DSecurity Classification

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%lcrtlJo Pa rk, (iI I llfo rin ia p-4025 N11 /GOU

I REPORT TITLE

15000 FEET, ESTIMATED) FRO.1 AIRCRAFT REPORTS AND) METEOROLOGICAL IDATA

T4. DESCRPTIV NOTESE (TTypE of00 reotad nlsvedls

Robert L. Mancuiso

REPORT DATE 7C81A O.O AE 4 O rRF

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C;ontra~ct AF 19(628)-5173 SRI Project 5521b.PROJECT, TASK, WORK UNIT NOS.

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IT. SUPPLEMENTARY NOTES 12. SONSORING MILITARY ACTIVITY

Tlie cininatolg ii i of i lear-air tirhitilerice is defiilsd herein as the likelIihooid hiat an ai rcraft or

iri]s.Si Ic will ericiiiiter tiirliilertt air alt a givell local it,N ,al t ititde, arid t irw (if scar. Turaiule!,ce dataifthree types were uised iii till, sit dv7 Ithese inrlridie (lmrvat lors lIv instromierited research aircraft,I llooi tracks treasiured 1,\ FIN- It) radar, arid t urhri lerice r,'jurts mnade Irs- pilots. Thle mleasurecuepnts tiat

hiave lien nade i.\ research aircrFaft show goodl re lat itilrr.i'.p betwoeri turbulence arid certain aspects oifriiwoscia I atmnospierii strirct ire, bItjt tile data are, too im ited in tiunilier to permit, liroad general iza-

urins. Tie FI'- lii tracks 1f' ri sing linus piere arid Riseo laIlh,lws were obt atined during stiudres of de-tille lis im prohl I.- Vo invýtise t I~te tictr lolentit al vsIncij In idertit fstig Itirlilernt tavers . In

genetra I thle exjiitinf data are to niurot ss to serve ti 5 o 1 iehiiwever, ftrither spca tri nalI, arerecotrneiiln ed . TIP s i t r stie nit rbili eice repori t s f rile 1t i. ir lnleIit ed iirt iring speciralI five -dav rep0- ti trigpertiods imnuprtsev Iv fat the largest %oiilitiun o~f data avai labnle . \eiiriiliigica I conirlt ioins for these

wjiotr \f ereý aia lszed i l (xiiknnitter from standard rawirisitrde data. anii kere corre lated w ith the tiili-it-cricv repnirt ., '14 nrre hrtionn qhnw Likat. ilte vertical %cclor 9,mrd hliar c orrespxitds miost c lose Is to

tuirluiler-ice rrvqijicins let erminied from tilie pitlint report., L~itti ha dditionatl redictiotiii of %ariance inihie tiiti-ilerice frequient- os is achieved 1Av oIc lidtini othter ntii*vriiloigria I' ftor1s. qit (IimiarnTill I t 11 pe

regresslir Ioneit iriotns [let %eer tnr~nleince: frenpicuit , at~id tile nueati antd stanidard deviat otr if thle vert ica Ini-i Aor ar shear w ir- ibta tined. I ii situter a dlifferenit regress run eqitat tori was fiu,.rd than I innoter

flus, tiririlirie lisersat tion, taken ini tot(. are t~i few~ tI, lernut a dtirect rotiiinitat oli (if torbn '-riceIr'e(ijueric\ thereflore II tndid rect n'tediiui %as used tot obtla in the ttirblrletuce c I iartnaoliig. l1ii tsinviilved

tills hug the, regrresslilti eqitulttiltis tiiexistinrig statist its of wind shear over the britted states. Thesefiio-.ier ifislutitIS iris. preprenl almosit ten sears agoi, iJpiear to 1,e (if quiesti luirihle relrahilhits tin

the 111,10'r rp nreantI stirat.,slaliere dunv toi a large uroitoiit ti if its ing * ind ol)servitliots ottder,olldl iri h igh gli wni spee-ds a loft . I~ie to iricertarint is lin rte regressio Nii qal Ions arid shear

,toi.tI,,, the, dedniwed ttitholItrce I iliato tloig% (giseri 11N seasoins for levelIs luetwrenr afuproiutntate!\t, uuat-l l~h~tt feet ) nfltist lie cout~isdered a ftrst est imtune.

W(a u'I ioql~ii s ale rukde r liar atii ui-tt-date wind-smear i-I ittatinlog\ -% lig)-itnitted for the Iniredýand> trilIhat t orts utrat titr lie given to develtjnlng a alul vuri-Ibirruc t ir iii entue senisoir to aoritelit

-itraira reeati( hi aircraft atid ttlltiie 1,ults.

DO '01%N6 1473

Security Classification

-. ~ '~-- -.. ....

UNCLASS IFEDSecuarity Cassaification

14. Ke ODILINK A L106K U LINK C

__________________________________ OLE OFT ROLE I UT ROLE_ IT

Turbulence, clear-airWind shear

Jet stream

Mountain waves

Pilot reports

Turbulent gustsRose balloons

Turbulence sensors

INSTRUCTIONS

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Security c~laasillics~fe.

sum