GASP cloud-and particle-encounter statistics and their application to ...

NASA Technical Memorandum 8 5835

GASP Cloud- and Particle-Encounter Statistics, and Their Application to LFC Aircraft Studies Volzcme I: Analysi~a l ~ dConclusions

William H. Jasperson and Gregory D. Nastrom Control Data Corporation Minneapolis, Minnesota Richard E. Davis Langley Research Center Humpton, Virginia James D. Holdeman

Lewis Reseurcb Center Cleveland, Ohio

National Aeronautics and Space Administration Scientific and Technical Information Branch

CONTENTS VOLUME I

.......................................................................... ..................................................................... AND ........................................................ 2 ............................................................................. ......................................................... to Features ........................................ and ............................................. and ............................................. .................................................. in and ........................................ of to S t u d i e s ........................................................... ................ o v e r a l l ~ e s u l t s................................................................ With to ...................................... 17 With to From t h e .................. ................................. 20 ................................................................ .......................................................... ...................................................................... ....................................................................... 25 ........................................................................... ..........................................................................54

SUMMARY

1

INTRODUCTION

1

SYMBOLS

mBREVIATIONS

DATA

4

CLOUD-ENCOUNTER ANALYSIS Relation Global Circulation Cloudiness Relative Vorticity Cloudiness. Temperature. Ozone

8 9 10 12

PARTICLE-CONCENTRATION ANALYSIS Concentrations Clear Cloudy A i r Application GASP P a r t i c l e - C o n c e n t r a t i o n Aircraft

13 13

APPLICATION O F GASP CLOUD-ENCOUNTER

Data

LFC

14

DATA TO A I R L I N E ROUTE S T U D I E S

R e s u l t s Analyzed Respect Altitude Results Analyzed Respect Distance R e s u l t s D e r i v e d D i r e c t l y From R o u t e S t a t i s t i c s ~ m p i r i c a lM o d e l

Tropopause

16 16

19 20

EFFECT OF CLOUDS ON LFC

22

CONCLUSIONS

22

REFERENCES

29

TABLES

FIGURES

iii

VOLUME I1 SUMMARY

1

....................*.............*......*.**e.****......e.a.**.......

APPENDIX A

.GASP

APPENDIX B

.INDIVIDUAL

APPENDIX C

.INDEPENDENCE

............................ ........................................

3

..........................

142

CLOUD AND PARTICLE INSTRUMENTATION FLIGWT SUMMARIES

OF CLOUD OBSERVATION PERIODS

2

APPENDIX D .CLOUD-ENCOUNTER STATISTICS AS FUNCTIONS OF LATITUDE, LONGITUDE. NORTHERN HEMISPHERE SEASON. AND ALTITUDE

........................... 147

.CLCIUD-ENCOUNTER STATISTICS AS FUNCTIONS OF LATITUDE, LONGITUDE, NORTHERN HEMISPHERE SEASON, AND DISTANCE FROM THE NMC TROPOPAUSE

APPENDIX E

................................................................ 177

SUMMARY Summary s t a t i s t i c s , t a b u l a t i o n s , and v a r i a b i l i t y s t u d i e s a r e p r e s e n t e d f o r t h e e n t i r e c l o u d o b s e r v a t i o n a r c h i v e - n e a r l y 88 000 s a m p l e s - from the NASA G l o b a l Atmos p h e r i c S a m p l i n g Program (GASP), which was c o n d u c t e d from 1975 t o 1979 a b o a r d f o u r commercial a i r l i n e r s i n r e g u l a r s e r v i c e . Summary s t a t i s t i c s , t a b u l a t i o n s , and v a r i a b i l i t y s t u d i e s a r e a l s o p r e s e n t e d f o r GASP p a r t i c l e - c o n c e n t r a t i o n d a t a - n e a r l y 56 000 s a m p l e s - g a t h e r e d c o n c u r r e n t l y w i t h the c l o u d o b s e r v a t i o n s . Clouds w e r e e n c o u n t e r e d i n a b o u t 15 p e r c e n t of t h e d a t a s a m p l e s , b u t t h e p r o b a b i l i t y of c l o u d e n c o u n t e r i s shown t o v a r y s i g n i f i c a n t l y w i t h a l t i t u d e , l a t i t u d e , and d i s t a n c e f r o m t h e t r o p o p a u s e , and less s i g n i f i c a n t l y w i t h s e a s o n . Several meteorological circulat i o n f e a t u r e s , s u c h a s t h e I n t e r t r o p i c a l Convergence Zone, are a p p a r e n t i n t h e l a t i t u d i n a l d i s t r i b u t i o n of c l o u d c o v e r , The c l o u d - e n c o u n t e r s t a t i s t i c s are shown t o he c o n s i s t e n t w i t h the c l a s s i c a l m i d - l a t i t u d e c y c l o n e model, w i t h more c l o u d s encount e r e d i n t h e upper t r o p o s p h e r e i n h i g h s t h a n i n l o w s . O b s e r v a t i o n s of c l o u d s spaced more c l o s e l y than 90 m i n u t e s of f l i g h t t i m e a r e shown t o be s t a t i s t i c a l l y d e p e n d e n t . The number d e n s i t y of p a r t i c l e s w i t h a d i a m e t e r g r e a t e r t h a n 3 p a l s o v a r i e s w i t h * t i m e and l o c a t i o n . I t depends p r i m a r i l y on the h o r i z o n t a l e x t e n t of c l o u d i n e s s , Thus, t h a t is, t h e p o r t i o n of e a c h s a m p l i n g i n t e r v a l t h a t is s p e n t w i t h i n c l o u d s . t h e v a r i a b i l i t y of t i m e i n c l o u d s and the v a r i a b i l i t y of p a r t i c l e number d e n s i t y a r e closely related. The summary s t a t i s t i c s f o r c l o u d and p a r t i c l e e n c o u n t e r are u t i l i z e d t o e s t i m a t e t h e f r e q u e n c y of c l o u d e n c o u n t e r on l o n g - r a n g e commercial t r a n s p o r t r o u t e s a n d t o a s s e s s the p r o b a b i l i t y and e x t e n t of l a m i n a r f l o w (LF) l o s s due t o c l o u d o r p a r t i c l e e n c o u n t e r by a i r c r a f t u t i l i z i n g l a m i n a r f l o w c o n t r o l (LFC). The o b s e r v a t i o n s o f r o u t e - a v e r a g e d t i m e i n c l o u d s are found t o f i t a n e m p i r i c a l model b a s e d on a gamma p r o b a b i l i t y d e n s i t y f u n c t i o n ; t h i s model c a n be u s e d t o estimate t h e p r o b a b i l i t y o f extended cloud encounter along a r o u t e . The a n a l y s i s i n t h i s r e p o r t shows t h a t t h e p r o b a b i l i t y of LF l o s s i n c l e a r a i r is n e g l i g i b l e and t h a t t h e p r o b a b i l i t y of e x t e n d e d c l o u d e n c o u n t e r , and a s s o c i a t e d s i g n i f i c a n t loss of LF, i s t o o low, of i t s e l f , t o make LFC i m p r a c t i c a l , F o r u s e r c o n v e n i e n c e , t h i s r e p o r t i s p r e s e n t e d i n two volumes. Volume I cont a i n s t h e n a r r a t i v e , a n a l y s i s , and c o n c l u s i o n s . Volume I1 i s composed of f i v e a p p e n d i x e s , as f o l l o w s : A GASP Cloud and P a r t i c l e I n s t r u m e n t a t i o n ; B Individual I n d e p e n d e n c e of Cloud O b s e r v a t i o n P e r i o d s ; D - C l o u d - E n c o u n t e r F l i g h t Summaries; C S t a t i s t i c s a s F u n c t i o n s of L a t i t u d e , L o n g i t u d e , N o r t h e r n Hemisphere S e a s o n , and ~ l tt uid e ; and E Cloud-Encounter S t a t i s t i c s a s F u n c t i o n s of L a t i t u d e , L o n g i t u d e , N o r t h e r n Hemisphere S e a s o n , and D i s t a n c e From t h e N a t i o n a l M e t e o r o l o g i c a l C e n t e r (NMC)Tropopause.

-

-

-

-

INTRODUCTION The p u r p o s e of t h i s r e p o r t i s t o p r e s e n t summary r e s u l t s of t h e a n a l y s i s o f a l l c l o u d - and p a r t i c l e - e n c o u n t e r measurements taken i n t h e NASA G l o b a l A t m o s p h e r i c S a m p l i n g Program (GASP) ( r e f s . 1 t o 3 ) , which w a s c o n d u c t e d from 1975 t o 1 9 7 9 f r o m as many a s f o u r Boeing 747 a i r c r a f t o p e r a t i n g i n r e g u l a r commercial s e r v i c e w o r l d w i d e .

T h i s r e p o r t e x t e n d s and g e n e r a l i z e s the p r e l i m i n a r y r e s u l t s g i v e n e a r l i e r i n r e f e r e n c e s 4 , 5, and 6, which were b a s e d on t h e f r a c t i o n of G A S P d a t a from o n l y December 1975 t o December 1977. Those p r e l i m i n a r y a n a l y s e s were b a s e d on t h e f i r s t 5 2 000 c l o u d o b s e r v a t i o n p e r i o d s i n t h e s e t , whereas t h e a n a l y s e s i n t h i s r e p o r t a r e The p r i m a r y b a s e d on the t o t a l s e t , a p p r o x i m a t e l y 88 000 c l o u d o b s e r v a t i o n p e r i o d s . m o t i v a t i o n f o r t h i s s t u d y i s e v i d e n c e t h a t t h e low-drag c h a r a c t e r i s t i c s of l a m i n a r f l o w c o n t r o l ( L F C ) wings a r e l o s t ( a l b e i t t e m p o r a r i l y ) i n v i s i b l e c l o u d s a n d a r e a l s o occasionally l o s t i n c i r r u s hazes. These i n c r e a s e s i n d r a g i n f l u e n c e t h e e c o n o m i c f e a s i b i l i t y of LFC-winged a i r c r a f t ( r e f s . 7 t o 1 0 ) . he i n c r e a s e i n d r a g i s due t o t u r b u l e n t wakes b e h i n d p a r t i c l e s which p e n e t r a t e t h e b o u n d a r y l a y e r ( r e f . 1 0 ) . C l o u d ice p a r t i c l e s a l s o c a u s e aerodynamic p r o b l e m s for r e e n t r y v e h i c l e n o s e c o n e s p e n e t r a t i n g c i r r u s clouds ( r e f . 1 1 ). Therefore, using instrumentation d e s c r i b e d i n r e f e r e n c e s 1 2 t o 1 4 , the U . S . A i r F o r c e h a s a l s o b e e n p u r s u i n g a r e s e a r c h e f f o r t on c i r r u s particle d i s t r i b u t i o n s . T h e r e s e a r c h r e p o r t e d h e r e l i e s w i t h i n t h e f i r s t of a t w o - p a r t r e s e a r c h e f f o r t by NASA s 4 : a s s e s s t h e i m p a c t of c l o u d p a r t i c l e s on LFC p e r f o r m a n c e . In the f i r s t p a r t , a c l i m a t o l o g y of c l o u d and p a r t i c l e e n c o u n t e r s i s b e i n g d e v e l o p e d t o a d d r e s s t h e f u n d a m e n t a l q u e s t i o n s : What i s t h e p r o b a b i l i t y of c l o u d e n c o u n t e r on a i r l i n e r o u t e s , and what i s t h e v a r i a b i l i t y of c l o u d e n c o u n t e r w i t h a l t i t u d e , s e a s o n , and l o c a t i o n ? These c l i m a t o l o g i c a l . d a t a , t o g e t h e r w i t h t h e o r e t i c a l e s t i m a t e s of t h e e f f e c t of ice c r y s t a l s on LFC ( r e f . l o ) , and USAF p a r t i c l e measurements i n c i r r u s c l o u d s ( e .g., r e f s . 1 5 and 1 6 ) have a l r e a d y been u s e d i n making p r e l i m i n a r y estimates o f t h e p o r t i o n of t i m e t h a t LFC would be l o s t i n c l o u d s and c l e a r air ( r e f . 1 7 ) . I n t h e s e c o n d p a r t of t h e r e s e a r c h e f f o r t , t o be implemented d u r i n g 1984, NASA w i l l make p r e c i s e i n s i t u measurements of the c l o u d and p a r t i c l e e n v i r o n m e n t on f l i g h t s of a n LFC-winged r e s e a r c h a i r c r a f t i n a n a t t e m p t t o q u a n t i f y b e t t e r t h e e f f e c t s of c l o u d s on LFC ( r e f s . 1 8 and 1 9 ) .

The l o c a t i o n of c l o u d s and t h e i r e x t e n t are a l s o of i n t e r e s t f o r s e v e r a l meteor o l o g i c a l r e a s o n s , s u c h a s t h e E a r t h ' s r a d i a t i o n b a l a n c e Ir e f . 201, and l o n g - t e r m ( c l i m a t i c ) v a r i a t i o n s of global. t e m p e r a t u r e ( r e f s . 21 and 2 2 ) ; t h u s , b o t h the meteor o l o g i c a l and t h e LFC a p p l i c a t i o n s of c l o u d - e n c o u n t e r r e s u l t s a r e d i s c u s s e d h e r e . his r e p o r t b e g i n s by d e s c r i b i n g t h e c l o u d - e n c o u n t e r and p a r t i c l e - c o n c e n t r a t i o n data sets u s e d i n t h i s s t u d y . Then, c l o u d - e n c o u n t e r d a t a a r e a n a l y z e d i n t e r m s of a l t i t u d e , l a t i t u d e , s e a s o n , and d i s t a n c e from the t r o p o p a u s e ; t h e s e d a t a are a l s o i n t e r p r e t e d i n terms of g l o b a l m e t e o r o l o g i c a l c i r c u l a t i o n f e a t u r e s and r e l a t i v e v o r t i c i t y . The p a r t i c l e - c o n c e n t r a t i o n d a t a a r e then a n a l y z e d . The r e p o r t t h e n s h i f t s i t s ernphasis t o t h e a p p l i c a t i o n s of both c l o u d and p a r t i c l e d a t a t o t h e e s t i m a t i o n of l a m i n a r f l o w l o s s f o r LFC a i r c r a f t and c o n c l u d e s w i t h the p r e s e n t a t i o n of a n e m p i r i c a l model f o r t h e p r o b a b i l i t y of c l o u d c o v e r a l o n g a i r l i n e r o u t e s . The f i v e a p p e n d i x e s c i t e d i n t h i s volume a l l a p p e a r i n Volume 11. A much s h o r t e n e d v e r s i o n of t h i s r e p o r t , w i t h o u t a p p e n d i x e s and w i t h p r i m a r y emphasis on t h e m e t e o r o l o g i c a l c o n c l u s i o n s , a p p e a r s i n r e f e r e n c e 23.

SYMBOLS AND ABBREVIATIONS ABV

above

ANOVA

a n a l y s i s of v a r i a n c e

A1

p r e s s u r e a l t i t u d e band from 28.5 t o 33.5 kft

A2

p r e s s u r e a l t i t u d e band from 33.5 t o 38.5 k f t

A3

p r e s s u r e a l t i t u d e band from 38.5 t o 43.5 k f t

BLO o r BLW

below

B747

~ o e i n g747 a i r c r a f t

CIV

"clouds i n v i c i n i t y "

CLAYR

number of c l o u d p a t c h e s e n c o u n t e r e d d u r i n g a 256-second

D

d i a m e t e r of p a r t i c l e ,

EMD

e q u i v a l e n t melted d i a m e t e r of p a r t i c l e , pm (cf

GASP

G l o b a l ~ t m o s p h e r i cSampling Program (NASA)

ICAO

I n t e r n a t i o n a l C i v i l Aviation Organization

ITCZ

i n t e r t r o p i c a l convergence zone

LF

l a m i n a r flow

LFC

laminar flow c o n t r o l

N

number of o b s e r v a t i o n s , d i m e n s i o n l e s s

NH

N o r t h e r n Hemisphere

NMC

N a t i o n a l M e t e o r o l o g i c a l C e n t e r (NOAA)

NOAA

N a t i o n a l Oceanic and Atmospheric A d m i n i s t r a t i o n

P

probability, percent

P ( TIC>O

[i.e.,

c l o u d s a l o n g t h e f l i g h t path) cloud observation

pm

p r o b a b i l i t y of c l o u d e n c o u n t e r , p e r c e n t , PCE (q.~.)

. ref.

15)

numerically e q u i v a l e n t t o

PCE

p r o b a b i l i t y of c l o u d e n c o u n t e r , p e r c e n t ( s e e fig. 1 )

PD5

t o t a l p a r t i c l e c o n c e n t r a t i o n o r number d e n s i t y f o r p a r t i c l e s l a r g e r t h a n 3 pm i n d i a m e t e r , p r t i c l e s / m 3

PP~V

p a r t s p e r b i l l i o n by volume ( a s i n ozone c o n c e n t r a t i o n )

TIC

t i m e i n clouds ( t o t a l i n d i c a t e d t i m e i n clouds during an observation p e r i o d d i v i d e d by p e r i o d o b s e r v a t i o n t i m e ), p e r c e n t ( s e e f i g . 1 )

TICF

a v e r a g e time i n c l o u d s p e r o b s e r v a t i o n p e r i o d for a g i v e n f l i g h t ( p e r c e n t T I C i n appendix B listings (Vol. I1 ) ) a v e r a g e t i m e i n c l o u d per o b s e r v a t i o n p e r i o d f o r a l l t h e f l i g h t s on a g i v e n r o u t e , o b t a i n e d from t h e a v e r a g e of TIC^ v a l u e s ; a l s o termed " r o u t e a v e r a g e d time i n c l o u d s "

time i n c l o u d s w i t h c l o u d s a l o n g the f l i g h t p a t h (as i n TIC, b u t d e f i n e d o n l y f o r a s e t of non-zero T I C o b s e r v a t i o n s , i.e., o b s e r v a t i o n s w i t h T I C > 01, p e r c e n t ( s e e f i g . 1 )

TICIV

t r o p o p a u s e s e p a r a t i o n band l o c a t e d 10 t o 15 k f t below t h e t r o p o p a u s e

T2

t r o p o p a u s e s e p a r a t i o n band l o c a t e d 5 t o 10 k f t below t h e t r o p o p a u s e t r o p o p a u s e s e p a r a t i o n band l o c a t e d 0 t o 5 k f t below t h e t r o p o p a u s e t r o p o p a u s e s e p a r a t i o n band l o c a t e d 0 t o 5 kf t above the t r o p o p a u s e

VLXXXX

d e s i g n a t o r f o r GASP a r c h i v e t a p e number XXXX

t:

r e l a t i v e v o r t i c i t y , set-I ( l e s s t h a n 0 f o r a n t i c y c l o n i c flow; g r e a t e r t h a n 0 f o r cyclonic flow) p a r a m e t e r i n gamma p r o b a b i l i t y d e n s i t y f u n c t i o n model f o r TICF, e q u a l t o 0.7 standard deviation

CJ A

b a r o v e r a symbol o r a b b r e v i a t i o n d e n o t e s the mean v a l u e .

~ d d i t i o n a lSymbols i n T a b l e s and Appendixes ( V o l . 11) SIGMA(X)

s t a n d a r d d e v i a t i o n of q u a n t i t y

x, p e r c e n t

number of o b s e r v a t i o n s

N

-

T CLEAR

a v e r a g e t e m p e r a t u r e i n c l e a r a i r , OC

T

average temperature i n clouds,

-

CLOUD

-

"cLEm

-

AzcLouo

O C

d i s t a n c e from t r o p o p a u s e d u r i n g f l i g h t i n c l e a r a i r , k f t d i s t a n c e from t r o p o p a u s e d u r i n g f l i g h t i n c l o u d s , kft

DATA The c l o u d - e n c o u n t e r and p a r t i c l e - c o n c e n t r a t i o n (particle-number-density) d a t a used i n t h i s s t u d y were measured i n the G l o b a l Atmospheric Sampling Program (GASP) from December 1975 t o J u l y 1979. These d a t a are from GASP t a p e s ~ L 0 0 0 4t o VL0031 , which have been a r c h i v e d a t the NOAA N a t i o n a l C l i m a t i c C e n t e r , A s h e v i l l e , North C a r o l i n a . The c o n t e n t s and f o r m a t s of t h e s e t a p e s a r e d e s c r i b e d i n r e f e r e n c e s 24 t o 32. B r i e f l y , the d a t a a c q u i s i t i o n phase of GASP began i n March 1975; o p e r a t i o n a l measurements began i n December 1975 and c o n t i n u e d t o J u l y 1979. M e t e o r o l o g i c a l and t r a c e c o n s t i t u e n t d a t a were o b t a i n e d w i t h i n s t r u m e n t s p l a c e d a b o a r d a s many as f o u r Boeing 747 a i r l i n e r s i n r o u t i n e commercial s e r v i c e . Data c o l l e c t e d on t h e s e f l i g h t s s h o u l d t h u s be r e p r e s e n t a t i v e of c o n d i t i o n s e n c o u n t e r e d by commercial a i r l i n e r s , even though t h e o b s e r v a t i o n s do n o t c o n s t i t u t e a t r u l y random sample of a l l p o s s i b l e atmos p h e r i c c o n d i t i o n s from a s t a t i s t i c a l p o i n t of view. O b s e r v a t i o n s were r e c o r d e d a t nominal 5- o r 10-minute i n t e r v a l s a t a l l a l t i t u d e s above a b o u t 20 k f t .

The p r e s e n c e of c l o u d s a t c r u i s e a l t i t u d e was d e t e r m i n e d w i t h a l i g h t - s c a t t e r i n g p a r t i c l e c o u n t e r ( r e f s . 24 t o 3 4 ) , h e r e i n a f t e r r e f e r r e d t o a s t h e " c l o u d d e t e c t o r , " The GASP c l o u d and p a r t i c l e i n s t r u m e n t a t i o n i s d e s c r i b e d f u r t h e r i n a p p e n d i x A (Vol. 11). A c l o u d - d e t e c t i o n t h r e s h o l d l e v e l f o r p a r t i c l e s l a r g e r t h a n 3 pm i n diame t e r was s e t e m p i r i c a l l y , based on v i s u a l o b s e r v a t i o n of a l i g h t h a z e o u t s i d e t h e a i r c r a f t . The same t h r e s h o l d l e v e l was used f o r a l l GASP c l o u d d e t e c t o r s and r e s u l t e d i n an " i n c l o u d s " r e g i s t r a t i o n whenever the l o c a l p a r t i c l e c o n c e n t r a t i o n , o r number d e n s i t y PD5 ( o f p a r t i c l e s w i t h d i a m e t e r D > 3 p),w a s g r e a t e r t h a n The sampling t i m e f o r t h e c l o u d d e t e c t o r was 256 s e c ( 4 m i n u t e s 16 sec66 000/m3. o n d s ) , c o r r e s p o n d i n g a p p r o x i m a t e l y t o a h o r i z o n t a l d i s t a n c e of 36 n.mi. a t a g r o u n d s p e e d of 500 k n o t s . A t t h e end of each sampling c y c l e f o r the GASP s y s t e m , t h e t i m e ( o u t of t h e l a s t 256 s e c ) which r e g i s t e r e d a s " i n c l o u d s " was r e c o r d e d . Also, t h e number of c l o u d p a t c h e s e n c o u n t e r e d d u r i n g the sampling p e r i o d was r e c o r d e d ; a new p a t c h was r e g i s t e r e d i f , h a v i n g once e n t e r e d a c l o u d ( P D ~ > 66 000/rn3) and s u b s e q u e n t l y l e f t it ( P D ~< 8250/rn3), the c l o u d d e t e c t o r a g a i n r e a c h e d t h e c l o u d detection threshold. (See d i s c u s s i o n of CLAYR i n r e f s . 24 t o 32.) During the f i r s t minute of each sampling p e r i o d , t h e numbers of particles i n s e l e c t e d s i z e r a n g e s were c o u n t e d . Although GASP c l o u d d a t a were f i r s t r e p o r t e d i n December 1975 ( r e f . 2 4 ) , p a r t i c l e c o u n t d a t a were n o t r e p o r t e d u n t i l J a n u a r y 1977 because of a r a t h e r l a r g e u n c e r t a i n t y i n t h e t o t a l p a r t i c l e c o u n t r e s u l t i n g from nonuniform i l l u m i n a t i o n of t h e sample chamber and h i g h n o i s e - t o - s i g n a l r a t i o on chann e l s measuring p a r t i c l e s s m a l l e r t h a n 1 . 4 pn i n d i a m e t e r ( r e f s . 2 8 t o 3 2 ) . While t h r e e c h a n n e l s were r e p o r t e d f o r t h e p a r t i c l e c o u n t e r , o n l y the l a r g e s t p a r t i c l e c h a n n e l ( f o r D > 3 ym) h a s been used h e r e i n because o n l y t h e l a r g e s t p a r t i c l e s a r e b e l i e v e d t o be s i g n i f i c a n t f o r l a m i n a r f l o w (LF) d e g r a d a t i o n . The GASP d a t a w e r e r e c o r d e d a t nominal 5- o r 10-minute i n t e r v a l s d u r i n g f l i g h t I n a d d i t i o n t o t h e b a s i c GASP measurements, the t r o p o p a u s e p r e s s u r e a t above 2 0 k f t . e a c h GASP d a t a l o c a t i o n h a s been time and s p a c e i n t e r p o l a t e d from t h e NOAA N a t i o n a l M e t e o r o l o g i c a l C e n t e r (NMC) g r i d s , when a v a i l a b l e , and added t o the a r c h i v e d t a p e s , A u x i l i a r y m e t e o r o l o g i c a l d a t a used herein, such a s v o r t i c i t y , have been computed f r o m t h e NMC i s o b a r i c h e i g h t f i e l d s f o r each GASP d a t a l o c a t i o n ( r e f . 3 5 ) . B e f o r e p r o c e e d i n g , it i s n e c e s s a r y t o e s t a b l i s h t h r e e q u a n t i t i e s of c l o u d TIC, e n c o u n t e r nomenclature which w i l l be used r e p e a t e d l y i n t h e a n a l y s e s t o f o l l o w : PCE, and TICIV. F i r s t , GASP o b s e r v a t i o n p e r i o d s a r e s e p a r a t e d a c c o r d i n g t o w h e t h e r o r n o t c l o u d s a r e e n c o u n t e r e d d u r i n g each 256-sec p e r i o d . Figure 1 i l l u s t r a t e s f o u r s u c c e s s i v e o b s e r v a t i o n p e r i o d s , one w i t h no c l o u d e n c o u n t e r and t h r e e with one o r more c l o u d p a t c h e s e n c o u n t e r e d . The t i m e w i t h i n each c l o u d p a t c h i s i n d i c a t e d ( e. g . , d e n o t e s t h e t i m e , i n s e c o n d s , w i t h i n t h e f i r s t cloud patch d u r i n g t h e second TZ1 o b s e r v a t i o n p e r i o d ) . The p o r t i o n of time i n c l o u d s (TIC), e x p r e s s e d as a p e r c e n t a g e , o r t h e four observation p e r i o d s i n f i g u r e 1 is c a l c u l a t e d a s follows:

TIC, =

*I 1

+ 256

T x 100

T

TIC

3

=

31

+ T 33

+ T

32 256

x 100

The a v e r a g e p o r t i o n of time i n c l o u d s f o r t h e s e f o u r o b s e r v a t i o n p e r i o d s i s

TIC TIC =

1

+

TIC

2

+

TIC

3

+

TIC

4

4

A n o b s e r v a t i o n p e r i o d w i t h TIC = 0 i s a p p r o p r i a t e l y termed " i n c l e a r a i r " because a t no t i m e d u r i n g t h a t o b s e r v a t i o n p e r i o d d i d t h e p a r t i c l e c o n c e n t r a t i o n Those o b s e r v a t i o n periods d u r i n g exceed 66 000/m3, the t h r e s h o l d c o n c e n t r a t i o n (TC ) which t h e p a r t i c l e c o n c e n t r a t i o n s exceeded t h e n: f o r some p o r t i o n of t h e p e r i o d i l, 0 < TIC C 100 p e r c e n t ) had c l o u d s a l o n g t h e f l i g h t p a t h , o r a r e s a i d t o have had " c l o u d s i n t h e v i c i n i t y ' ' (CIV). A low T I C , f o r example, 10 t o 40 p e r c e n t , would T I C = 50 t o 90 p e r c e n t would i n d i c a t e a broken i n d i c a t e a s c a t t e r e d cloud l a y e r ; c l o u d l a y e r ; and TIC = 90 t o 100 p e r c e n t would i n d i c a t e a n o v e r c a s t deck of c l o u d s .

.

The p r o b a b i l i t y of c l o u d e n c o u n t e r (PCE) d u r i n g an o b s e r v a t i o n p e r i o d i s o b t a i n e d by d i v i d i n g t h e number of o b s e r v a t i o n p e r i o d s w i t h C I V ( i.em, TIC > 0 ) For t h e example i n f i g u r e 1 , by t h e t o t a l number of o b s e r v a t i o n p e r i o d s .

PCE =

3 observations with CIV = 0.75 4 observations total.

Note that PCE i s e q u i v a l e n t t o the t e r m P(T1C > 0 ) i n r e f e r e n c e s 4 , 5, 6 , and 17 and i n appendixes D and E (Vol. 11) of t h e p r e s e n t r e p o r t . Now c o n s i d e r o n l y t h o s e o b s e r v a t i o n p e r i o d s w i t h some c l o u d p r e s e n c e , t h a t i s , w i t h TIC > 0 . The a v e r a g e p o r t i o n of t i m e i n c l o u d s d u r i n g an o b s e r v a t i o n p e r i o d w i t h c l o u d s i n the v i c i n i t y (TICIV) i s

1

TICIV =

+

T*C2 + *IC3 3

These t h r e e c l o u d - e n c o u n t e r q u a n t i t i e s a r e r e l a t e d by

TIC =

PCE x TICIV

E q u a t i o n (1 ) is d e m o n s t r a t e d f o r the example i n f i g u r e 1 as f o l l o w s : TIC

1

+

For c o n v e n i e n c e ,

TIC

2 4

+

TIC

TIC, PCE,

3

+

TIC

4

+

TIC = 0.75

1

+

TIC 2

3

+

TIC

3

TIC 4

and TICIV a r e a l l e x p r e s s e d a s p e r c e n t a g e s .

From December 1975 t o J u l y 1979, 1748 GASP f l i g h t s g a t h e r e d c l o u d d e t e c t i o n d a t a ( n o t n e c e s s a r i l y c l o u d e n c o u n t e r s ) . A summary of t h e s e f l i g h t s , by month and cont r i b u t i n g a i r c r a f t , i s g i v e n i n t a b l e I and a monthly and s e a s o n a l summary of a l l t h e f l i g h t r o u t e s is p r e s e n t e d i n t a b l e 11. Note t h a t p a r t i c l e c o u n t (PD5) was n o t r e p o r t e d u n t i l J a n u a r y 1977 ( i t i s a v a i l a b l e f o r 1341 f l i g h t s ) . I n d i v i d u a l f l i g h t summaries and averaged d a t a a r e l i s t e d i n appendix B (Vol. 11). The r o u t e s a r e l i s t e d a l p h a b e t i c a l l y by a i r p o r t p a i r and i n d i v i d u a l f l i g h t s a r e o r d e r e d by d a t e . Cloud e n c o u n t e r and p a r t i c l e d a t a a r e r e p o r t e d w i t h r e s p e c t t o two d i f f e r e n t h e i g h t r e f e r e n c e s i n t h i s r e p o r t . The f i r s t i s t h e p r e s s u r e a l t i t u d e , w i t h which a l l pilots are familiar. Each p r e s s u r e a l t i t u d e c o r r e s p o n d s t o a g i v e n v a l u e of atmos p h e r i c p r e s s u r e a c c o r d i n g t o t h e ICAO S t a n d a r d Atmosphere ( r e f . 3 6 ) . The second h e i g h t r e f e r e n c e is t h e d i s t a n c e from t h e N a t i o n a l M e t e o r o l o g i c a l C e n t e r (NMC) t r o p o pause. The t r o p o p a u s e s e p a r a t e s t h e w e a t h e r - a c t i v e t r o p o s p h e r e from t h e t h e r m a l l y s t a b l e and g e n e r a l l y c l o u d - f r e e s t r a t o s p h e r e . The a c t u a l t r o p o p a u s e h e i g h t v a r i e s p r i m a r i l y with l a t i t u d e and s e a s o n w i t h day-to-day changes superimposed a s l a r g e s c a l e storms d e v e l o p and decay. F i g u r e 2 p r e s e n t s t h e a v e r a g e t r o p o p a u s e h e i g h t o v e r t h e world f o r each s e a s o n ( r e f . 37 ) For s i m p l i c i t y , t h e term " a l t i t u d e " w i l l d e n o t e " p r e s s u r e a l t i t u d e " and t h e term " t r o p o p a u s e " w i l l d e n o t e t h e "NMC t r o p o p a u s e . "

.

The complete GASP d a t a s e t c o n s i s t s of 87 9 2 2 c l o u d o b s e r v a t i o n p e r i o d s , 256 s e c each, f o r a t o t a l of a p p r o x i m a t e l y 6250 hours i n a l l . A s shown i n f i g u r e 3 , t h e s e o b s e r v a t i o n s t e n d t o be more numerous i n t h e Northern Hemisphere ( N H ) midl a t i t u d e s b u t a r e f a i r l y u n i f o r m l y d i s t r i b u t e d by Northern Hemisphere s e a s o n s . About 58 p e r c e n t of t h e o b s e r v a t i o n s were made i n w i n t e r and s p r i n g and a b o u t 4 2 p e r c e n t were made i n summer and autumn. The shaded a r e a s i n f i g u r e 3 (and s u b s e q u e n t s i m i l a r f i g u r e s ) denote o b s e r v a t i o n p e r i o d s having c l o u d s i n t h e v i c i n i t y , t h a t i s , w i t h TIC > 0. The numbers above t h e b a r s i n d i c a t e t h e p e r c e n t a g e of o b s e r v a t i o n p e r i o d s i n each b a r having c l o u d s i n t h e v i c i n i t y e . , t h e p e r c e n t a g e i s e q u a l t o t h e shaded a r e a of t h e b a r d i v i d e d by t h e t o t a l . a r e a f o r each b a r and m u l t i p l i e d by 1 0 0 ) . O f t h e t o t a l 87 922 c l o u d o b s e r v a t i o n p e r i o d s , 1 3 206 ( 1 5 . 2 5 p e r c e n t ) were i n t h e v i c i n i t y of c l o u d s . The d i s t r i b u t i o n of c l o u d o b s e r v a t i o n p e r i o d s as a f u n c t i o n of a l t i t u d e i s shown i n f i g u r e 4 ( a ) . Over 96 p e r c e n t of t h e o b s e r v a t i o n p e r i o d s f a l l between t h e n o r m a l F i g u r e 4 ( b ) shows t h a t t h e disa i r l i n e c r u i s e a l t i t u d e s of 28.5 kft and 43.5 k f t . t r i b u t i o n of c l o u d o b s e r v a t i o n p e r i o d s as a f u n c t i o n of d i s t a n c e from t h e NMC t r o p o pause i s much more uniform. Because t h e NMC t r o p o p a u s e d a t a were o c c a s i o n a l l y n o t a v a i l a b l e , o n l y 70 340 o b s e r v a t i o n p e r i o d s a r e r e p r e s e n t e d i n f i g u r e 4 ( b ) , T h i s p a n e l c l e a r l y i l l u s t r a t e s t h a t v e r y few c l o u d s a r e e n c o u n t e r e d i n the s t r a t o s p h e r e ( 3 p e r c e n t i n t h e 5000 f e e t above t h e t r o p o p a u s e v e r s u s 19 p e r c e n t i n t h e 5000 f e e t I n f a c t , the f r e q u e n c y of c l o u d s i n the s t r a t o s p h e r e may be below t h e t r o p o p a u s e ) . even s m a l l e r t h a n i n d i c a t e d because t h e GASP data a r e l o c a l measurements, whereas t h e t r o p o p a u s e p r e s s u r e s a r e i n t e r p o l a t e d from l a r g e - s c a l e g r i d s (2.5O l a t i t u d e by 2.5O l o n g i t u d e by 12 h o u r s ) , s o t h a t t h e s m a l l - s c a l e u n d u l a t i o n s of t h e t r o p o p a u s e may be missed by the NMC g r i d . The g r a p h i c a l r e s u l t s of f i g u r e s 3(b) and 4 a r e summarized n u m e r i c a l l y i n t a b l e 111, Cloud-encounter d a t a a r e used h e r e i n a s r e p o r t e d , w i t h a l l o b s e r v a t i o n p e r i o d s g i v e n e q u a l w e i g h t . However, because c l o u d i n e s s ( o r t h e l a c k t h e r e o f ) i s a s s o c i a t e d A w i t h l a r g e - s c a l e weather systems, n o t a l l o b s e r v a t i o n _periods a r e i n d e p e n d e n t . s t u d y of t h e o b s e r v a t i o n p e r i o d independence i s p r e s e n t e d i n appendix C (Vol. 11). The r e s u l t s of t h i s s t u d y i n d i c a t e t h a t t o be c o n s i d e r e d s t a t i s t i c a l l y i n d e p e n d e n t , o b s e r v a t i o n s of cloud o r no c l o u d c o n d i t i o n must be s e p a r a t e d by 90 t o 120 m i n u t e s of f l i g h t time. T h i s s t u d y a l s o a n a l y z e d the independence of T I C v a l u e s w i t h i n a c l o u d .

I t was found that f o r T I C v a l u e s of l e s s t h a n SO p e r c e n t , o b s e r v a t i o n s s e p a r a t e d by 1 0 t o 20 m i n u t e s could be c o n s i d e r e d i n d e p e n d e n t . For T I C v a l u e s l a r g e r t h a n 50 p e r c e n t , t h e sample-to-sample o b s e r v a t i o n s a r e h i g h l y c o r r e l a t e d , and t h e t i m e between i n d e p e n d e n t o b s e r v a t i o n s c a n n o t be r e l i a b l y e s t i m a t e d . I t can be assumed, however, t o l i e between 2 0 and 120 m i n u t e s .

P a r t i c l e - c o n c e n t r a t i o n ( P D ~ )d a t a p e r i o d s a r e shown i n f i g u r e 5 t o have n e a r l y t h e same d i s t r i b u t i o n s w i t h ( a ) l a t i t u d e and ( b ) s e a s o n a s t h e c l o u d - d e t e c t o r d a t a ( f i g . 3) I n t o t a l , t h e r e were 7 0 304 p a r t i c l e - c o n c e n t r a t i o n o b s e r v a t i o n p e r i o d s , of which 55 718 were c o i n c i d e n t w i t h c l o u d o b s e r v a t i o n p e r i o d s , a b o u t 6 3 p e r c e n t o f t h e t o t a l number of c l o u d o b s e r v a t i o n p e r i o d s (87 9 2 2 ) . About 1 3 p e r c e n t of t h e p a r t i c l e d a t a were g a t h e r e d i n c l o u d s o r i n t h e v i c i n i t y of c l o u d s ; t h i s compares w i t h 15.25 p e r c e n t f o r c l o u d o b s e r v a t i o n p e r i o d s . The d i s t r i b u t i o n s of p a r t i c l e c o n c e n t r a t i o n o b s e r v a t i o n p e r i o d s p r e s e n t e d i n f i g u r e 6 a s a f u n c t i o n of ( a ) a l t i t u d e and (b) d i s t a n c e from t h e NMC t r o p o p a u s e a r e a l s o v e r y s i m i l a r t o t h e d i s t r i b u t i o n s There a r e 51 676 p a r t i c l e - c o n c e n t r a t i o n of c l o u d o b s e r v a t i o n p e r i o d s ( f i g . 5 ) o b s e r v a t i o n p e r i o d s a t times when t h e NMC t r o p o p a u s e d a t a w e r e a v a i l a b l e .

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CLOUD-ENCOUNTER ANALYSIS Complete t a b u l a t i o n s of the c l o u d - e n c o u n t e r s t a t i s t i c s a s f u n c t i o n s of l a t i t u d e , l o n g i t u d e , and s e a s o n ( N o r t h e r n Hemisphere) a r e g i v e n i n a p p e n d i x D ( V o l . 11) as f u n c t i o n s of a l t i t u d e and i n appendix E (Vol. 11) a s f u n c t i o n s of d i s t a n c e from t h e A map t o p r o v i d e g e o g r a p h i c a l o r i e n t a t i o n f o r t h e l a t i t u d e - l o n g i t u d e tropopause c e l l s is g i v e n a t t h e f r o n t of appendix D, and t h e d a t a e n t r i e s a r e e x p l a i n e d a t t h e b e g i n n i n g of appendixes D and E m I n t h e right column f o r each s e a s o n and a l t i t u d e band, t h e r e s u l t s from a l l d a t a i n each l a t i t u d e band a r e g i v e n under the h e a d i n g " z o n a l mean." For convenience, t h e s e z o n a l means of each v a r i a b l e a r e summarized i n t a b l e s I V and V as f u n c t i o n s of l a t i t u d e and s e a s o n . T a b l e IV g i v e s the r e s u l t s i n t e r m s of a l t i t u d e and t a b l e V g i v e s them i n terms of d i s t a n c e from t h e t r o p o p a u s e While t h e t a b u l a t i o n s and summaries h e r e i n were f o r m a t t e d f o r optimum u s e f u l n e s s t o t h e LFC a i r c r a f t s t u d i e s , it i s a n t i c i p a t e d t h a t t h e r e s u l t s w i l l be of i n t e r e s t t o a b r o a d e r segment of t h e s c i e n t i f i c community. T h e r e f o r e , t h e r e s u l t s of t h e a n a l y s i s of c l o u d - e n c o u n t e r v a r i a b i l i t y and t h e r e l a t i o n of t h e s e d a t a t o o t h e r m e t e o r o l o g i c a l v a r i a b l e s a r e d i s c u s s e d i n the s u b s e q u e n t p a r a g r a p h s .

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The p r o b a b i l i t y of c l o u d e n c o u n t e r (PCE) and t h e mean t i m e i n c l o u d s (TIC)b o t h d e c r e a s e r a p i d l y above t h e t r o p o p a u s e , a s shown i n f i g u r e 7. F i g u r e 8 shows the c u m u l a t i v e f r e q u e n c y d i s t r i b u t i o n s c o r r e s p o n d i n g t o t h e d a t a shown i n f i g u r e 7. These c u r v e s g i v e t h e p e r c e n t a g e of o b s e r v a t i o n s (on t h e o r d i n a t e ) i n which TIC e q u a l e d o r exceeded any g i v e n p e r c e n t a g e ( o n t h e a b s c i s s a ) . I f t h e s e curves may b e assumed t o be r e p r e s e n t a t i v e of p o p u l a t i o n - b a s e d p r o b a b i l i t y v a l u e s , t h e n they may be c o n s i d e r e d c u m u l a t i v e p r o b a b i l i t y d i s t r i b u t i o n s a l s o and t h e o r d i n a t e l a b e l P ( > TIC) is appropriate. c o r r e s p o n d i n g t o f i g u r e s 7 and 8, b u t a s f u n c t i o n s of a l t i t u d e i n s t e a d of d i s The d e c r e a s e i n t a n c e from t h e t r o p o p a u s e , a r e f i g u r e s 9 ( a ) and 9 ( b ) , r e s p e c t i v e l y . c l o u d i n e s s w i t h a l t i t u d e i n f i g u r e 9 ( a ) is p r i m a r i l y due t o t h e i n c r e a s e d l i k e l i h o o d of b e i n g i n t h e s t r a t o s p h e r e i n t h e upper a l t i t u d e s . Although a l l a v a i l a b l e d a t a were used i n p r e p a r i n g f i g u r e s 7 t o 9, we do n o t i n t e n d t o imply t h a t t h e s e a r e u n i v e r s a l c u r v e s . I n fact, c l o u d i n e s s v a r i e s s i g n i f i c a n t l y w i t h b o t h l a t i t u d e and s e a s o n . These v a r i a t i o n s may be s e e n i n t a b l e s I V and V as w e l l as i n t h e f i g u r e s p r e s e n t e d w i t h t h e f o l l o w i n g d i s c u s s i o n .

V a r i a t i o n s w i t h l a t i t u d e and s e a s o n of t h e a v e r a g e p e r c e n t a g e of t i m e i n c l o u d s a r e p r e s e n t e d i n f i g u r e 10 f o r t h e t h r e e primary a l t i t u d e r a n g e s . Some of t h e v a r i a b i l i t y i n f i g u r e s 1 0 ( a ) , 1 0 ( b ) , and 1 0 ( d ) can be e x p l a i n e d by s e a s o n a l v a r i a t i o n s of t h e mean h e i g h t of t h e t r o p o p a u s e . Other f e a t u r e s may be r e l a t e d t o t h e g l o b a l c i r c u l a t i o n o r semipermanent c i r c u l a t i o n f e a t u r e s i l , h i g h s and lows ) , as d i s c u s s e d below. (TIC)

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R e l a t i o n t o Global C i r c u l a t i o n F e a t u r e s The g e n e r a l s e a s o n a l d i f f e r e n c e s i n maxima and minima i n c l o u d i n e s s a r e e x p l a i n e d by t h e s e a s o n a l m i g r a t i o n of t h e I n t e r t r o p i c a l Convergence Zone ( I T C Z ) and o t h e r g e n e r a l c i r c u l a t i o n f e a t u r e s . The r e g i o n of maximum c l o u d i n e s s r a n g e s between a p p r o x i m a t e l y 18ON i n NH summer and 18's i n NH w i n t e r . The Hadley c e l l c i r c u l a t i o n t o t h e n o r t h and s o u t h of t h e ITCZ s h i f t s w i t h t h e Zone r e s u l t i n g , f o r t h e N o r t h e r n Hemisphere, i n maximum descending motions (minimum c l o u d i n e s s ) n e a r 3S0N i n summer and lS0N i n w i n t e r . Thus, d u r i n g w i n t e r ( f i g . 1 0 ( a )), t h e d e p r e s s e d v a l u e s of c l o u d e n c o u n t e r f r e q u e n c y i n t h e 10°N t o 20°N i n t e r v a l and enhanced v a l u e s s o u t h of 10°N a r e c o n s i s t e n t w i t h t h e z o n a l mean Hadley c i r c u l a t i o n , which h a s i t s a x i s n e a r 10°N w i t h descending motions t o t h e n o r t h and a s c e n d i n g motions t o the s o u t h of the a x i s ( r e f . 38 ) Meteorologists w i l l recognize t h a t t h e following a d d i t i o n a l s p e c i f i c f e a t u r e s a r e c o n s i s t e n t w i t h the mean g l o b a l c i r c u l a t i o n :

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1 . The peak i n mean c l o u d i n e s s g e n e r a l l y o c c u r s n e a r t h e s u b s o l a r l a t i t u d e ( s u n overhead a t noon), l a g g i n g it by a few d e g r e e s . In the NH w i n t e r , t h e peak o c c u r s n e a r 15OS, i n s p r i n g and autumn n e a r the Equator, and i n summer n e a r 1 SON. Some e v i dence of s e a s o n a l symmetry between hemispheres is shown i n f i g u r e 11 ; t h i s i s n o t unexpected.

2 . A secondary maximum, l o c a t e d between 40°N and 60°N, i s n o t e d i n a l l t h e c u r v e s of f i g u r e 10. This i s t h e r e s u l t of t h e i n c r e a s e d f r e q u e n c y of c y c l o n e e n c o u n t e r a l o n g t h e Northern Hemisphere p o l a r f r o n t . The e f f e c t i s l a r g e s t i n wint e r , a s would be e x p e c t e d because the maximum i n t e n s i t y of t h e m i d - l a t i t u d e baroc l i n i c storm systems o c c u r s t h e n . Indeed, f o r the w i n t e r s e a s o n s of b o t h hemis p h e r e s , t h e secondary and primary maxima a r e of n e a r l y t h e same magnitude. Because of t h e l a c k of a i r l i n e r o u t e s a t h i g h l a t i t u d e s i n t h e Southern Hemisphere, no comp a r a b l e r e l a t i v e maximum a p p e a r s i n t h e f i g u r e s ; n e v e r t h e l e s s , one r e l a t e d t o the Southern Hemisphere p o l a r f r o n t might be expected from symmetry c o n s i d e r a t i o n s and i s h i n t e d a t i n f i g u r e 11

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3 . When the minima of cloud e n c o u n t e r are s t u d i e d , we s e e t h a t a l a t i t u d i n a l d i s p l a c e m e n t a l s o o c c u r s d u r i n g t h e y e a r , w i t h t h e l a t i t u d e of t h e minimum p o i n t In winter, p r e c e d i n g t h e poleward o r equatorward movement of the s u b p o l a r p o i n t . this f e a t u r e i s f a r t h e s t s o u t h , a t a b o u t 15ON. I n s p r i n g , t h e p o i n t moves t o 30°N; i n summer, it r e a c h e s 35ON; t h e n i n autumn, i t r e t r e a t s t o 25ON a g a i n . The d a t a f o r t h e Southern Hemisphere, a l t h o u g h l i m i t e d i n l a t i t u d i n a l e x t e n t , s u g g e s t a r e l a t i v e minimum n e a r 3S0S i n w i n t e r (Southern Hemisphere summer) and a minimum n e a r 15OS t o 25OS f o r t h e o t h e r s e a s o n s . The minima f o r each hemisphere, s e a s o n and h e i g h t combination a l l have v a l u e s i n a narrow range from 1 t o 5 p e r c e n t .

F i g u r e 12 p r e s e n t s t h e a v e r a g e p e r c e n t a g e of t i m e i n c l o u d s ( T I C ) as a f u n c t i o n of l a t i t u d e and d i s t a n c e from the tropopause f o r each s e a s o n . The f o l l o w i n g c o n c l u s i o n s can be made:

1 . The p r i m a r y maximum of T I C i s l o c a t e d n e a r t h e E q u a t o r , 10 t o 15 k f t below t h e tropopause. T h i s peak c o r r e s p o n d s t o a T I C of a b o u t 20 p e r c e n t e x c e p t i n w i n t e r when it r e a c h e s n e a r l y 50 p e r c e n t . There a r e v e r y few d a t a from a l t i t u d e s above t h i s d i s t a n c e i n t e r v a l b e c a u s e t h e t r o p i c a l t r o p o p a u s e u s u a l l y e x c e e d s 50 k f t i n a l t i t u d e .

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2 . In g e n e r a l , TIC d e c r e a s e s as t h e d i s t a n c e t o t h e t r o p o p a u s e d e c r e a s e s . The p r i m a r y e x c e p t i o n s t o t h i s p a t t e r n o c c u r i n s p r i n g and autumn when, i n m i d - l a t i t u d e s , c l o u d i n e s s t e n d s t o peak i n t h e 5 t o 10 k f t i n t e r v a l below t h e t r o p o p a u s e .

The p r e c e d i n g r e s u l t s a r e c o n s i s t e n t w i t h t h e o b s e r v a t i o n s of P r o j e c t J e t Stream and o t h e r s ( r e f s . 39 t o 441, which showed a maximum o c c u r r e n c e of c i r r u s c l o u d s from 3.3 t o 6.6 k f t below t h e t r o p o p a u s e a t t e m p e r a t e l a t i t u d e s . For t r o p i c a l r e g i o n s , it was r e p o r t e d i n r e f e r e n c e 45 t h a t c i r r u s c l o u d s a r e c o n s i s t e n t l y 5 k m ( a b o u t 16 k f t ) or more below t h e t r o p o p a u s e , b u t t h a t c l o u d s o c c a s i o n a l l y a r e found above the t r o p o pause i n v e r y h i g h l a t i t u d e s . v a r i a t i o n s w i t h s e a s o n of the v e r t i c a l p r o f i l e of c l o u d - e n c o u n t e r p r o b a b i l i t y and t h e a v e r a g e t i m e i n c l o u d s f o r data from 40°N t o SOON a r e shown i n f i g u r e 1.3. The p r o b a b i l i t y of c l o u d e n c o u n t e r ( P C E ) d e c r e a s e s w i t h a l t i t u d e i n w i n t e r , s p r i n g , and autumn, b u t i n summer t h e r e is a peak between 3 3 . 5 and 38.5 k f t . This l a t t e r f e a t u r e may r e s u l t from c i r r u s c l o u d s blown o f f t h e t o p s of summer t h u n d e r s t o r m s n e a r the tropopause. The v a l u e s of TICIV r a n g e from 25 t o 40 p e r c e n t f o r s p r i n g , summer, I n t h e w i n t e r and s p r i n g , TICIV i n c r e a s e s w i t h a l t i t u d e w h i l e TIC and autumn. d e c r e a s e s , which s u g g e s t s l e s s h a z e o r s u b v i s i b l e c i r r u s w i t h i n c r e a s i n g a l t i t u d e . The w i n t e r TICIV v a r i e s from 48 p e r c e n t a t low a l t i t u d e s t o 66 p e r c e n t a t t h e h i g h e s t a l t i t u d e . These l a r g e v a l u e s may r e f l e c t t h e d e n s e c i r r o s t r a t u s s h i e l d s of l a r g e b a r o c l i n i c systems most p e r s i s t e n t d u r i n g w i n t e r , f o r example, t h e s e m i s t a t i o n a r y I c e l a n d i c and A l e u t i a n low-pressure s y s t e m s .

C l o u d i n e s s and R e l a t i v e V o r t i c i t y A s n o t e d p r e v i o u s l y i n c o n n e c t i o n w i t h t h e p e r s i s t e n c e of c l o u d i n e s s , c l o u d i n e s s i s o f t e n r e l a t e d t o l a r g e - s c a l e storm systems ( a g e n e r a l model i s p r e s e n t e d An o b j e c t i v e v a r i a b l e o f t e n used f o r s e p a r a t i n g t h e two f u n d a m e n t a l i n r e f . 46 dynamic r e g i m e s , c y c l o n e s and a n t i c y c l o n e s , i s the r e l a t i v e v o r t i c i t y 1: ( r e f . 36 ) F i g u r e 14 shows t h e c u m u l a t i v e f r e q u e n c y d i s t r i b u t i o n f o r all data o b t a i n e d a t 0 t o 10 k f t below t h e t r o p o p a u s e s e p a r a t e d o n l y by t h e a l g e b r a i c s i g n of t h e r e l a t i v e v o r t i c i t y ( c y c l o n i c flow is p o s i t i v e ; a n t i c y c l o n i c flow is n e g a t i v e ) The d i f f e r e n c e between t h e s e c u r v e s i s s i m i l a r t o t h e d i f f e r e n c e between t h e c u r v e s f o r t h e h i g h e s t and l o w e s t a l t i t u d e bands i n f i g u r e 9 ( b ) and is l a r g e r t h a n t h e d i f f e r e n c e between e tropopause ( f i g . 8 ) . Therefore t h i s d i f f e r e n c e t h e c u r v e s f o r the l a y e r s below t h i s i m p o r t a n t . F i g u r e 15 p r e s e n t s TIC a s a f u n c t i o n of d i s t a n c e from t h e t r o p o p a u s e and s i g n of t h e r e l a t i v e v o r t i c i t y f o r each NH s e a s o n f o r the l a t i t u d e r e g i o n from 3 0 ° N t o 70°N. Indeed, t h e d i f f e r e n c e i n c l o u d i n e s s between c y c l o n i c and a n t i c y c l o n i c c o n d i t i o n s w i t h r e s p e c t t o d i s t a n c e from the t r o p o p a u s e i s v e r y a p p a r e n t on t h i s f i g u r e and i s c o n s i s t e n t w i t h t h e ozone d i s t r i b u t i o n s i n c y c l o n e s and a n t i c y c l o n e s r e p o r t e d i n r e f e r e n c e s 4 and 47 and t h e known n e g a t i v e c o r r e l a t i o n a t t h e s e h e i g h t s between ozone and w a t e r v a p o r . (See r e f . 47. ) For t h e LFC a p p l i c a t i o n , t h i s r e s u l t i n d i c a t e s t h a t c o n d i t i o n s s i g n i f i c a n t l y d i f f e r e n t from t h e a v e r a g e of a l l d a t a can be e x p e c t e d i f s p e c i f i c f l i g h t r o u t e s a r e l i k e l y t o e n c o u n t e r more c y c l o n i c than a n t i c y c l o n i c c i r c u l a t i o n systems, o r v i c e versa.

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From f i g u r e 1 5 , t h e f o l l o w i n g c o n c l u s i o n s can he drawn:

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1 For w i n t e r , TIC i s s u b s t a n t i a l l y l a r g e r f o r n e g a t i v e v o r t i c i t y t h a n f o r p o s i t i v e v o r t i c i t y , p a r t i c u l a r l y n e a r t h e tropopause. The maximum o c c u r s i n t h e l a y e r immediately below t h e t r o p o p a u s e These r e s u l t s appear t o c o n t r a d i c t m e t e o r o l o g i c a l t e a c h i n g s , because nos t m e t e o r o l o g i s t s are accustomed t o a s s o c i a t i n g p o s i t i v e relat i v e v o r t i c i t y w i t h c l o u d s , which i s c e r t a i n l y t h e c a s e a t the E a r t h ' s s u r f a c e . Howe v e r , because of the v e r t i c a l s t r u c t u r e of t h e atmosphere and t h e t i l t i n g of the p r e s s u r e systems w i t h r e s p e c t t o a l t i t u d e , t h e o p p o s i t e t e n d s t o be t r u e a t a i r c r a f t flight altitudes.

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2 . ~ u r i n gsummer, TIC i s n e a r l y c o n s t a n t a t 5 p e r c e n t , i n d e p e n d e n t of t h e vort i c i t y and d i s t a n c e from t h e tropopause. This i s c o n s i s t e n t w i t h t h e s e a s o n a l d i f f e r e n c e s of fewer and weaker c y c l o n e s i n summer w i t h more c l o u d s , r e l a t i v e l y , stemming from c o n v e c t i v e s t o r m s , a s d i s c u s s e d i n t h e p r e v i o u s s e c t i o n .

3 . The behavior d u r i n g s p r i n g and autumn i s a p p r o p r i a t e f o r t r a n s i t i o n p e r i o d s between w i n t e r and summer.

F i g u r e 16 p r e s e n t s PCE a s a f u n c t i o n of s i g n of the r e l a t i v e v o r t i c i t y , d i s t a n c e from t h e tropopause, l a t i t u d e , and season ( w i n t e r and summer). The f o l l o w i n g c h a r a c t e r i s t i c s a r e observed i n t h i s f i g u r e : 1 . The v a l u e s of PCE f o r p o s i t i v e and n e g a t i v e r e l a t i v e v o r t i c i t y d i f f e r most i n A s mentioned b e f o r e , p o s i t i v e v o r t h e w i n t e r and a t a l t i t u d e s n e a r t h e tropopause. t i c i t y and clouds are c o r r e l a t e d i n t h e lower atmosphere and t h i s i s c o n s i s t e n t w i t h t h e c r o s s o v e r of t h e c u r v e s a t 10 t o 15 k f t below t h e t r o p o p a u s e i n w i n t e r .

2. For n e g a t i v e v o r t i c i t y (heavy c u r v e ) , w i n t e r v a l u e s of PCE a r e much l a r g e r than summer v a l u e s .

3 . I n w i n t e r , t h e maximum i n PCE is a t 0 t o 5 k f t below t h e t r o p o p a u s e when t h e r e l a t i v e v o r t i c i t y i s n e g a t i v e and a t 10 t o 15 k f t below t h e t r o p o p a u s e when the r e l a t i v e v o r t i c i t y is positive. 4 . For both s e a s o n s and b o t h s i g n s of r e l a t i v e v o r t i c i t y , PCE t e n d s t o be s m a l l e r f o r l a t i t u d e s from 3 0 ° N t o 40°N than f o r h i g h e r l a t i t u d e s .

F i g u r e 17 p r e s e n t s T I C I V a s a f u n c t i o n of s i g n of r e l a t i v e v o r t i c i t y , d i s t a n c e from t h e tropopause, l a t i t u d e , and season ( w i n t e r and summer ) The f o l l o w i n g c h a r a c t e r i s t i c s a r e observed i n t h i s f i g u r e :

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1 I n w i n t e r , TICIV i s c o n s i s t e n t l y l a r g e r a t a l l a l t i t u d e s when t h e r e l a t i v e v o r t i c i t y i s n e g a t i v e . This i s c o n s i s t e n t w i t h e a r l i e r d i s c u s s i o n s .

2.

I n w i n t e r , the maximum i n T I C I V o c c u r s 0 t o 5 k f t below t h e t r o p o p a u s e .

3 . For both s i g n s of r e l a t i v e v o r t i c i t y , T I C I V d e c r e a s e s s h a r p l y f o r a l t i t u d e s more than 10 k f t below t h e t r o p o p a u s e .

4 . There i s no d i s t i n g u i s h a b l e p a t t e r n between TICIV and d i s t a n c e from the tropopause i n summer, a l t h o u g h t h e magnitude of TICIV t e n d s t o be l a r g e r f o r p o s i t i v e v o r t i c i t y than f o r n e g a t i v e v o r t i c i t y

.

C l o u d i n e s s , Temperature, and Ozone Other t r a c e c o n s t i t u e n t s and m e t e o r o l o g i c a l v a r i a b l e s measured by G A S P a i r c r a f t d u r i n g t h e time of t h e d a t a analyzed h e r e i n ( n o t a l l c o n s t i t u e n t s were measured a t a l l t i m e s ) were water vapor, ozone, carbon monoxide, and wind. An i n - d e p t h s y n o p t i c and s t a t i s t i c a l a n a l y s i s of t h e i n t e r r e l a t i o n s h i p between c l o u d s and t h e s e v a r i a b l e s i s beyond t h e scope of t h i s s t u d y , b u t c o n s i d e r a b l e i n s i g h t i s a v a i l a b l e from t h e d i s t r i b u t i o n of mean v a l u e s of some of t h e s e parameters w i t h r e s p e c t t o t h e t r opopause

.

F i g u r e 1 8 p r e s e n t s t h e mean a i r t e m p e r a t u r e and ozone c o n c e n t r a t i o n , i n and o u t of c l o u d s , w i t h r e s p e c t t o t h e d i s t a n c e from t h e tropopause. The mean a i r temperat u r e i n t h e v i c i n i t y of clouds i s c o n s i s t e n t l y c o o l e r t h a n i n c l e a r a i r , p e r h a p s s u g g e s t i n g t h a t c l o u d s a r e more l i k e l y t o form i n c o o l a i r b e c a u s e l e s s water vapor is required for saturation. However, a s w a s shown i n f i g u r e 1 5 , c l o u d s tend t o o c c u r i n a r e a s of a n t i c y c l o n i c v o r t i c i t y ( i.e., i n r i d g e s 1, where t h e r e i s a p a t t e r n of upward v e r t i c a l motions and where the tropopause is g e n e r a l l y h i g h e r and c o l d e r t h a n i n t r o u g h s . Thus, c i r r u s c l o u d s form more r e a d i l y i n r i d g e s , n o t o n l y because it i s c o l d e r t h e r e b u t a l s o because t h e p a t t e r n of v e r t i c a l motions around t h e u n d e r l y i n g c y c l o n e s t e n d s t o produce upward motions of s u f f i c i e n t l y m o i s t a i r from below. I t is a l s o a p p a r e n t from f i g u r e 18 t h a t c o n c e n t r a t i o n s of ozone a r e c o n s i s t e n t l y Perhaps t h e s i m p l e s t e x p l a n a s m a l l e r i n t h e v i c i n i t y of c l o u d s t h a n i n c l e a r a i r . ' t i o n f o r t h e s t r o n g a n t i c o r r e l a t i o n between c i r r u s c l o u d s and ozone a t commercial a i r c r a f t c r u i s e a l t i t u d e s i s t h a t c i r r u s c l o u d s a r e a s s o c i a t e d w i t h m o i s t upwardmoving a i r coming from t h e ozone-poor t r o p o s p h e r e , and c l e a r a r e a s are a s s o c i a t e d This explanaw i t h d r y downward-moving a i r coming from t h e ozone-rich s t r a t o s p h e r e t i o n i s c o n s i s t e n t with t h e v e r t i c a l motions a t t h e t r o p o p a u s e l e v e l e x p e c t e d i n b a r o c l i n i c storms ( r e f . 46) and w i t h t h e p r e v i o u s o b s e r v a t i o n t h a t t h e r e i s less c l o u d i n e s s i n t h e upper atmosphere and more ozone i n a cyclone t h a n i n an a n t i cyclone. (See figs. 14 and 15 and r e f s . 4 and 47.)

.

Even though the p r e c e d i n g e x p l a n a t i o n is s t r a i g h t f o r w a r d , a t l e a s t three o t h e r f a c t o r s may i n f l u e n c e t h e observed l e v e l of c o r r e l a t i o n between c i r r u s c l o u d s and ozone : 1 . Sampling - The cloud and ozone d a t a a r e from i n s i t u GASP o b s e r v a t i o n s , b u t t h e tropopause d a t a have been i n t e r p o l a t e d i n t i m e and space from NMC g r i d maps (2.5O l a t i t u d e by 2.5O l o n g i t u d e ) which a r e a v a i l a b l e o n l y a t 12-hour i n t e r v a l s . see r e f . 48) Thus, some of t h e high-frequency u n d u l a t i o n s of t h e tropopause ( e .g a r e p r o b a b l y missed by t h e s e maps. T h i s l e a d s t o e r r o r s i n t h e c a l c u l a t e d h e i g h t of the tropopause

.,

.

2 . Chemistry - Enhanced chemical and photochemical d e s t r u c t i o n of ozone may occur i n t h e p r e s e n c e of h i g h r e l a t i v e humidity. A s reviewed i n r e f e r e n c e 49, ozone p h o t o c h e m i s t r y i s an a r e a of v e r y a c t i v e r e s e a r c h , and we l e a v e a s s e s s m e n t of t h i s p o s s i b i l i t y t o modelers working i n t h e f i e l d .

' I t was r e p o r t e d i n r e f e r e n c e 5 t h a t t h e c o n c e n t r a t i o n of ozone i n c l e a r a i r i s s i g n i f i c a n t l y d i f f e r e n t ( h i g h e r ) from t h a t i n cloudy a i r , a t t h e 99.9 p e r c e n t confidence level.

3. ~ e c h a n i c a ld e s t r u c t i o n - Ozone i s a r e l a t i v e l y u n s t a b l e g a s and i s known t o d i s s o c i a t e on c o n t a c t w i t h a h a r d s u r f a c e . The i c e c r y s t a l s and p a r t i c l e s i n a c l o u d p r o v i d e a r e l a t i v e l y l a r g e s u r f a c e a r e a f o r ozone d e s t r u c t i o n .

PARTICLE-CONCENTRATION ANALYSIS AS s t a t e d i n the s e c t i o n e n t i t l e d "Data, " GASP cloud-encounter d a t a a r e a v a i l a b l e beginning i n December '1975, b u t p a r t i c l e - n u m b e r - d e n s i t y d a t a (PD5) do n o t b e g i n u n t i l J a n u a r y 1 9 7 7 . Approximately 63 p e r c e n t of t h e c l o u d o b s e r v a t i o n p e r i o d s have c o r r e s p o n d i n g p a r t i c l e - c o n c e n t r a t i o n d a t a . F i g u r e 19 p r e s e n t s t h e c l o u d i n e s s v a r i a b l e s f o r o n l y t h o s e o b s e r v a t i o n p e r i o d s having p a r t i c l e - c o n c e n t r a t i o n measurements. The s i m i l a r i t y between t h i s f i g u r e and f i g u r e 13, t h e c o r r e s p o n d i n g f i g u r e f o r a l l cloud-encounter d a t a , and t h e marked s i m i l a r i t i e s of f i g u r e s 5 and 6 t o f i g u r e s 3 and 4, a l l p r o v i d e e v i d e n c e t h a t t h e p a r t i c l e - c o n c e n t r a t i o n d a t a s u b s e t is s t a t i s t i cally s i m i l a r t o the e n t i r e data s e t .

C o n c e n t r a t i o n s i n C l e a r and Cloudy A i r F i g u r e 20 shows t h a t t h e p a r t i c l e d e n s i t y PDS(D > 3 pm) is a b o u t t h r e e o r d e r s of magnitude g r e a t e r i n cloudy a i r ( T I C > 0 ) t h a n i n c l e a r a i r (TIC = 0). F i g u r e 21 shows t h e c u m u l a t i v e frequency d i s t r i b u t i o n s of all a v a i l a b l e PDS d a t a f o r s e v e r a l TIC values. Among o b s e r v a t i o n s i n t h e v i c i n i t y of c l o u d s ( 0 < TIC < 1 0 0 ) , t h e probab i l i t y of e n c o u n t e r i n g any g i v e n p a r t i c l e d e n s i t y i n c r e a s e s a s T I C i n c r e a s e s . Howe v e r , t h i s d i f f e r e n c e i s s m a l l compared w i t h the d i f f e r e n c e between c l e a r and c l o u d y a i r shown by t h e TIC = 0 and t h e T I C > 0 c u r v e s . F i g u r e 2 2 p r e s e n t s t h e cumulative frequency d i s t r i b u t i o n s of p a r t i c l e number d e n s i t y f o r c l e a r and cloudy a i r w i t h r e s p e c t t o (a) a l t i t u d e and (b) d i s t a n c e from t h e tropopause. The d i f f e r e n c e s i n t h e s e d i s t r i b u t i o n s f o r T I C > 0 and T I C > 75 w i t h r e s p e c t t o a l t i t u d e a r e very s m a l l , whereas more p a r t i c l e s t e n d t o be p r e s e n t i n t h e 0 t o 5 k f t i n t e r v a l below the tropopause. F i g u r e 23 p r e s e n t s s i m i l a r cumulative frequency d i s t r i b u t i o n s w i t h r e s p e c t t o ( a ) l a t i t u d e and ( b ) NH s e a s o n . I n the c l e a r a i r , more p a r t i c l e s a r e p r e s e n t between O 0 and 60°N t h a n o u t s i d e t h e s e l a t i t u d e s , and more p a r t i c l e s a r e p r e s e n t i n s p r i n g and summer t h a n i n w i n t e r and autumn. These same r e l a t i o n s h i p s a l s o t e n d t o h o l d f o r cloudy a i r , a t l e a s t f o r p a r t i c l e c o n c e n t r a t i o n s smaller t h a n a b o u t 1 o4 mm3. A s mentioned i n t h e s e c t i o n e n t i t l e d " I n t r o d u c t i o n , " t h e g o a l of t h i s r e s e a r c h i s t h e d e r i v a t i o n of t h e c l i m a t o l o g y i the s t a t i s t i c a l behavior w i t h l o c a t i o n , s e a s o n , a l t i t u d e , e t c . 1 of t h e p a r t i c l e number d e n s i t y to be e n c o u n t e r e d on a i r l i n e r o u t e s worldwide, from which t h e economic f e a s i b i l i t y of employing laminar-f lowc o n t r o l (LFC) wings may be, a s s e s s e d . I n t h i s r e g a r d , t h e PD5 d a t a i n t h e c u r r e n t i n v e s t i g a t i o n a r e most v a l u a b l e when t h e y p e r t a i n t o f l i g h t c o n d i t i o n s t h a t are e i t h e r t o t a l l y i n c l e a r a i r o r t o t a l l y w i t h i n c l o u d s . I t i s c r u c i a l t o know w h e t h e r t h e p a r t i c l e number d e n s i t y i n c l e a r a i r is, on t h e a v e r a g e , s u f f i c i e n t l y high t o make LFC i m p r a c t i c a l as a low-drag method. I f such i s the c a s e , t h e n the LF l o s s w i t h i n c l o u d s i s a l m o s t c e r t a i n t o be p r o h i b i t i v e . I f , however, t h e l o s s i n clear a i r is n o t c r i t i c a l , then cloud e n c o u n t e r i s t h e l i m i t i n g f a c t o r . T h e r e f o r e , it i s i m p o r t a n t t o e s t i m a t e t h e p o r t i o n of t h e t i m e t h a t c l o u d s w i l l be e n c o u n t e r e d , as w a s examined i n t h e s e c t i o n e n t i t l e d " C l o u d - ~ n c o u n t e r A n a l y s i s . " Most e s t i m a t e s t o d a t e assume t h a t a l l c l o u d s always cause LF l o s s and that LF l o s s i n c l e a r a i r d o e s n o t

.

o c c u r , b u t one p u r p o s e of t h e p r e s e n t r e s e a r c h was t o a s c e r t a i n what s u b s e t , i f any, of c l o u d e n c o u n t e r s would n o t c a u s e LF l o s s and what p o r t i o n of t h e t i m e LF would b e 10st i n c l e a r a i r . I n t h i s s t u d y , t h e P D 5 d a t a were examined t o d e r i v e s t a t i s t i c s on p a r t i c l e The r e s u l t s are summac o n c e n t r a t i o n s t o be e n c o u n t e r e d i n c l e a r a i r and cloudy a i r . r i z e d i n t a b l e VI, which p r e s e n t s a composite of t h e o v e r a l l p a r t i c l e - e n c o u n t e r exper i e n c e a s a f u n c t i o n of TIC. T h i s t a b l e , from which f i g u r e 21 was p l o t t e d , i n c l u d e s a l l c o n d i t i o n s from t o t a l l y c l o u d - f r e e t o t o t a l l y i n c l o u d s .

A p p l i c a t i o n of GASP P a r t i c l e - C o n c e n t r a t i o n LFC A i r c r a f t S t u d i e s

Data t o

The m o t i v a t i o n f o r a n a l y z i n g t h e GASP d a t a f o r c l o u d - e n c o u n t e r s t a t i s t i c s i n t h e format p r e v i o u s l y discussed is t h e requirement f o r o b t a i n i n g p a r t i c l e - c o n c e n t r a t i o n c l i m a t o l o g i c a l d a t a t o be u t i l i z e d i n f e a s i b i l i t y s t u d i e s f o r new l o n g - r a n g e a i r c r a f t designs. Such a i r c r a f t would u s e laminar-f l o w - c o n t r o l ( L F C ) w i n g s , o f f e r i n g promise of up t o a 30-percent d r a g r e d u c t i o n from t h a t of c u r r e n t wing d e s i g n s ( r e f . 7 ) . The p a r t i c u l a r need of cloud-encounter e s t i m a t e s for t h i s c l a s s of a i r c r a f t s t e m s from t h e f a c t t h a t LF i s t h o u g h t t o be l o s t , a l b e i t t e m p o r a r i l y , whenever t h e a i r c r a f t i s w i t h i n c l o u d s or i c e - c r y s t a l c o n c e n t r a t i o n s c o n t a i n i n g a s u f f i c i e n t l y l a r g e number d e n s i t y of hydrometeors l a r g e r t h a n a b o u t 30 pm i n e q u i v a l e n t m e l t e d d i a m e t e r (EMD) ( S e e r e f . 15 f o r d e f i n i t i o n of EMD.) E x p e r i e n c e w i t h the USAF X-21, an e a r l y LFCwinged r e s e a r c h a i r c r a f t , seemed t o show ( r e f s . 8 and 1 0 ) t h a t LF was a l w a y s l o s t i n v i s i b l e c l o u d s and sometimes w i t h i n c i r r u s h a z e s . M o t i v a t e d by the X-21 e x p e r i e n c e , H a l l ( r e f . 1 0 ) d e r i v e d , from aerodynamic c o n s i d e r a t i o n s , t h e r a n g e of i c e - p a r t i c l e f l u x e s which s h o u l d c a u s e s i g n i f i c a n t l o s s of LF. F i g u r e 24 i s a d a p t e d from the H a l l a n a l y s i s and is p r e s e n t e d a s a n example of t h e e s t i m a t e d LF d e g r a d a t i o n . Particle c o n c e n t r a t i o n ( 1 7 t - ~ ) i s p l o t t e d on t h e o r d i n a t e , a g a i n s t t h e e q u i v a l e n t m e l t e d diameter of t h e p a r t i c l e s . From t h i s f i g u r e , t h e f o l l o w i n g o b s e r v a t i o n s may be made:

.

1 . No l o s s of LF i s e x p e c t e d t o r e s u l t from p a r t i c l e s w i t h EMD s m a l l e r t h a n 33 pm, r e g a r d l e s s of t h e i r c o n c e n t r a t i o n , o r from t o t a l p a r t i c l e c o n c e n t r a t i o n s s m a l l e r t h a n 3.5 x 102 /rn 3 , r e g a r d l e s s of p a r t i c l e s i z e . 2 . T o t a l l o s s of LF i s e x p e c t e d i f t h e c o n c e n t r a t i o n of p a r t i c l e s w i t h EMD e q u a l t o o r l a r g e r t h a n 3 3 pm i s g r e a t e r t h a n o r e q u a l t o 1 .9 x 105 p a r t i c l e s / m 3 ( o r , e . g o , i f the c o n c e n t r a t i o n of particles l a r g e r than 60 pm is g r e a t e r t h a n o r e q u a l t o S i m i l a r c o n c l u s i o n s can be r e a c h e d i n t h i s manner f o r o t h e r p a r t i c l e 1 .3 x 1 05/m3 ) sizes.

.

i f the 3. Between no l o s s and t o t a l l o s s of LF, p a r t i a l l o s s i s e x p e c t e d e . . , number d e n s i t y of p a r t i c l e s w i t h EMD e u a l t o o r l a r g e r t h a n 33 pm i s g r e a t e r t h a n The t h r e s h o l d of LF l o s s was 10 p e r c e n t i n 8.0 x lo2/m3 b u t l e s s t h a n 1 .4 x 105 /m t h e H a l l a n a l y s i s . T h i s t h r e s h o l d i s r e p r e s e n t e d by the lower boundary of t h e r e g i o n l a b e l e d " P a r t i a l l o s s of LF" i n f i g u r e 24.

9.

The task a t hand, t h e n , i s t o u t i l i z e GASP d a t a f o r d e r i v i n g or e s t i m a t i n g the p r o b a b i l i t y that p a r t i c l e number d e n s i t i e s s u f f i c i e n t t o c a u s e LF l o s s w i l l be To e s t i m a t e t h e p r o b a b i l i t y and s e v e r i t y of LF e n c o u n t e r e d i n day-to-day o p e r a t i o n s . l o s s i n t h e p r e s e n c e of p a r t i c l e s , n o t o n l y t h e p r o b a b i l i t y of c l o u d e n c o u n t e r must

be known, b u t a l s o the p r t i c l e number d i s t r i b u t i o n w i t h i n c l o u d s and i n c l e a r a i r . ~ l th l e e l e m e n t s of t h e problem a r e r e p r e s e n t e d i n t h e f o l l o w i n g e q u a t i o n :

P(LFC l o s s )

= [P(LFC

+

1 Cloudy ] [P ( ~ l i ~ ihn tc l o u d s ) ] ] light i n c l e a r a i r ) ] loss) 1 Clear

loss)

[P(LFC

From t h e GASP c l o u d - e n c o u n t e r d a t a p r e s e n t e d e a r l i e r , t h e p r o b a b i l i t y of f l i g h t b o t h i n and o u t of c l o u d s can be e s t i m a t e d . The p r o b a b i l i t i e s of LF d e g r a d a t i o n i n and o u t of c l o u d s a x e , however, n o t d i r e c t l y a c c e s s i b l e from t h e GASP d a t a a n a l y z e d h e r e i n , s i n c e t h e s e p r o v i d e only t h e t o t a l number d e n s i t y of p a r t i c l e s w i t h EMDS l a r g e r t h a n 3 ym. However, e m p i r i c a l p a r t i c l e - d i s t r i b u t i o n d a t a a r e a v a i l a b l e f r o m m i s s i o n s c a r r y i n g Knollenberg-probe-type i n s t r u m e n t a t i o n . The i n v e s t i g a t i o n s of the U . S . A i r F o r c e Geophysics L a b o r a t o r y (AFGL) a r e p a r t i c u l a r l y v a l u a b l e s o u r c e s of t h e s e d a t a ( r e f s 15, 16, and 50 t o 5 6 ) . These AFGL d a t a were s t u d i e d t o d e t e r m i n e t h e v a r i a b i l i t y of t h e r a t i o of t h e number of p a r t i c l e s l a r g e r t h a n 3 p n t o t h e numb e r of p a r t i c l e s l a r g e r t h a n 33 p.m. T h i s r a t i o i s b e s t v i s u a l i z e d as t h e r a t i o of t h e two h a t c h e d a r e a s shown on f i g u r e 25, p r e s e n t e d t o show t h e c o n c e p t . This r a t i o depends on t h e t y p e of c l o u d e n c o u n t e r e d and r a n g e s from a b o u t 10 f o r t h i c k c l o u d s t o a b o u t 100 o r more f o r v e r y t h i n c i r r u s c l o u d s (numerous v e r y s m a l l c r y s t a l s ) and h a s a modal v a l u e of around 30. I n p r a c t i c a l u s a g e , t h e n , t h e number of p a r t i c l e s l a r g e r c o u l d be e s t i m a t e d by d i v i d i n g t h e number t h a n t h e L F C - c r i t i c a l s i z e (EMD of 33 m To p r o v i d e a o f p a r t i c l e s i n a GASP PD5 o b s e r v a t i o n by t h e a p p r o p r i a t e r a t i o . c o n s e r v a t i v e e s t i m a t e of LF l o s s , a w o r s t c a s e r a t i o i n c l o u d s i s t a k e n t o b e 10 a n d a w o r s t c a s e r a t i o i n c l e a r a i r i s t a k e n t o be 100. H e r e " w o r s t c a s e " s i g n i f i e s t h e g r e a t e s t upper bound f o r t h e c o n c e n t r a t i o n of L F C - c r i t i c a l p a r t i c l e s i z e s - h e n c e , t h e g r e a t e s t p r o b a b i l i t y of LF l o s s .

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With t h e s e a s s u m p t i o n s , the H a l l c r i t e r i a i n f i g u r e 2 4 and the PD5 a n a l y s e s i n t h e s e c t i o n e n t i t l e d " P a r t i c l e - C o n c e n t r a t i o n A n a l y s i s " can be r e l a t e d t o e s t i m a t e t h e d e g r e e of LF l o s s t o be e x p e c t e d , i n both t o t a l l y c l e a r air and t o t a l l y c l o u d y a i r . F i r s t , we r e c a l l from f i g u r e 24 t h a t t h e L F C - c r i t i c a l d e n s i t y of p a r t i c l e s l a r g e r M u l t i p l y i n g t h i s d e n s i t y by t h e clear a i r t h a n 33 pm i n d i a m e t e r i s 8.0 x 102 /m 3 r a t i o of 100, the c r i t i c a l d e n s i t y of p a r t i c l e s l a r g e r t h a n 3 pm i n d i a m e t e r would be From f i g u r e 21 and t a b l e V I , w e f i n d t h a t t h i s p a r t i c l e d e n s i t y w a s 8 x I 04/m3. never e n c o u n t e r e d i n c l e a r a here fore, the assumption t h a t no LF l o s s o c c u r s i n t r u l y c l e a r a i r seems a p p r o p r i a t e .

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The assumption of no LF l o s s i n c l e a r a i r d o e s n o t t o t a l l y a g r e e w i t h d a t a t a k e n d u r i n g t h e X-21 program, i n which some LF l o s s e v i d e n t l y o c c u r r e d i n v e r y l i g h t h a z e ( r e f s . 8 and 1 0 ) . However, no p a r t i c l e - c o n c e n t r a t i o n measurements w e r e t a k e n i n c o n j u n c t i o n w i t h t h e X-21 m i s s i o n s , s o t h e p a r t i c l e c o n c e n t r a t i o n s i n t h e h a z e w e r e unknown, and u n f o r t u n a t e l y c a n n o t be used t o r e f i n e t h e assumption of no l o s s i n clear air. I t i s r e p o r t e d i n r e f e r e n c e s 57 and 58 t h a t l o c a l c o n c e n t r a t i o n s of l a r g e p a r t i c l e s , r e s u l t i n g from p a r t i c l e f a l l o u t i n t o the c l e a r a i r , may be e n c o u n t e r e d b e n e a t h c i r r u s c l o u d decks d u r i n g f l i g h t i n o t h e r w i s e c l e a r a i r . The o b s e r v a t i o n s i n r e f e r e n c e 57, and c a l c u l a t i o n s i n r e f e r e n c e 58, show t h a t t h e s e p a r t i c l e s c a n s u r v i v e f a l l s of s e v e r a l k i l o m e t e r s . However, we b e l i e v e t h a t t h e c o n c e n t r a t i o n s of t h e s e p a r t i c l e s w i l l g e n e r a l l y be t o o low t o d e g r a d e LF, a l t h o u g h t h e p a r t i c l e s are large enough t o c a u s e a problem, i f e n c o u n t e r e d i n s u f f i c i e n t c o n c e n t r a t i o n .

I n c l o u d s , t h e c r i t i c a l number d e n s i t i e s of p a r t i c l e s w i t h EMD > 3 p a r e o b t a i n e d by m u l t i p l y i n g the w o r s t c a s e r a t i o ( 1 0 ) by the c r i t i c a l d e n s i t i e s of p a r t i cLes w i t h EMD > 3 3 ym: f o r 1 0 - p e r c e n t LF l o s s , ( 8 x 102 /m 2 ) ( 1 0 ) ; f o r t o t a l l o s s , ( 1 .9 x 105 /m 2 ) ( 10 ) The c u r v e s f o r T I C 3 75 i n f i g u r e 21 s u g g e s t t h a t t h e c r i t i c a l number d e n s i t y f o r a 1 0 - p e r c e n t L F l o s s , 8 x 10 3 /m 3 , would be exceeded 100 p e r c e n t of t h e t i m e , T o t a l l o s s of L F ( P D ~= 1 .9 x 106 /m 3 ) would be e x p e c t e d a p p r o x i m a t e l y 5 p e r c e n t of the time. Thus, a s i g n i f i c a n t degree of LF l o s s w i t h i n c l o u d s i s obvio u s l y p r e d i c t e d , and t h e p r e v i o u s l y s t a t e d assumption t h a t e n c o u n t e r s w i t h v i s i b l e c l o u d s always r e s u l t i n a l o s s of LF seems v a l i d u n t i l f u r t h e r o b s e r v a t i o n s a r e o b t a i n e d of LF d e g r a d a t i o n i n c l o u d s , w i t h modern c l o u d - p a r t i c l e - s a m p l i n g i n s t r u mentation. Such o b s e r v a t i o n s a r e planned f o r the near f u t u r e i n a NASA e x p e r i m e n t In t h a t ( r e f . 1 9 ) , i n which t h e H a l l c r i t e r i a can be v a l i d a t e d f o r t h e f i r s t t i m e . e x p e r i m e n t , a Knollenberg probe p a r t i c l e sampler ( r e f , 5 9 ) w i l l be flown aboard a NASA J e t S t a r a i r c r a f t modified with LFC w i n g s e c t i o n s , t o measure t h e p a r t i c l e e n v i ronment s i m u l t a n e o u s l y w i t h t h e a s s e s s m e n t of LFC system performance. The r e s u l t s of t h e experiment should a l l o w v a l i d a t i o n of t h e assumption of no LF l o s s i n c l e a r a i r and a new d e t e r m i n a t i o n of the l e v e l of LF d e g r a d a t i o n i n a v a r i e t y of c l o u d conditions. pending t h e s e r e v i s e d e s t i m a t e s of LF l o s s , no l o s s of LF i n c l e a r a i r and t o t a l l o s s of LF i n a l l c l o u d s a r e assumed; t h u s , the a n a l y s i s i n t h e n e x t s e c t i o n w i l l be c e n t e r e d around t h e GASP cloud-encounter d a t a .

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APPLICATION OF GASP CLOUD-ENCOUNTER DATA TO AIRLINE ROUTE STUDIES I n t h i s s e c t i o n , t h e GASP cloud-encounter d a t a a r e a p p l i e d t o t h e e s t i m a t i o n of cloud-encounter s t a t i s t i c s f o r a i r l i n e a p p l i c a t i o n , F i r s t , the o v e r a l l cloude n c o u n t e r v a r i a b i l i t y i s summarized i n t a b l e s and d i s c u s s e d from t h e v i e w p o i n t of s t a t i s t i c a l s i g n i f i c a n c e . Then, an e m p i r i c a l s t a t i s t i c a l model f o r the r o u t e averaged time i n c l o u d s i s developed. T h i s model is a p p l i e d t o s e v e n h i g h - d e n s i t y a i r l i n e r o u t e s , and t h e i m p l i c a t i o n s f o r t h e economic f e a s i b i l i t y of LFC t r a n s p o r t s a r e discussed.

Overall Results Tables V I I , V I I I , and I X p r e s e n t s t a t i s t i c s d e r i v e d from c l o u d o b s e r v a t i o n periods. R e c a l l t h a t each c l o u d o b s e r v a t i o n p e r i o d l a s t s o n l y 256 s e c , o r a p p r o x i I t is i m p o r t a n t t o r e a l i z e t h a t such m a t e l y 36 n,mi. a t a ground speed of 500 k n o t s , s t a t i s t i c s a r e d e r i v e d from t h e s e 256-sec i n t e r v a l s and a r e o n l y e s t i m a t e s of t h e c l o u d - d e t e c t i o n p r o b a b i l i t y o v e r o t h e r time i n t e r v a l s o r d i s t a n c e s . I t is shown i n appendix C ( v o l e 11) t h a t s u c c e s s i v e o b s e r v a t i o n s a r e n o t r e a l l y s t a t i s t i c a l l y i n d e pendent u n t i l a b o u t 20 i n t e r v e n i n g o b s e r v a t i o n s have e l a p s e d . With t h e s e c o n s i d e r a t i o n s f i r m l y i n mind, t a b l e s V I I , V I I I , and IX a r e s t i l l u s e f u l i n s t u d y i n g the r e l a t i v e p r o b a b i l i t y of c l o u d e n c o u n t e r a s a f u n c t i o n of a l t i t u d e , NH s e a s o n , and g e o g r a p h i c l o c a t i o n ; t h i s p r o b a b i l i t y is of use i n d e t e r m i n i n g t h e f e a s i b i l i t y of LFC flight. T a b l e V I I p r e s e n t s a composite of T I C s t a t i s t i c s a s a f u n c t i o n of a l t i t u d e f o r t h e g l o b a l d a t a s e t i . . , a l l s e a s o n s and l a t i t u d e s ) and r e p r e s e n t s a n e l a b o r a t i o n of t h e d a t a p l o t t e d i n f i g u r e 9 (h The b e n e f i t s of h i g h e r c r u i s e a l t i t u d e f o r c l o u d a v o i d a n c e a r e r e a d i l y a p p a r e n t from t h e t a b l e . For example, an a i r c r a f t c r u i s i n g a t 28.5 t o 33.5 k f t would be e x p e c t e d t o f l y through a 256-second time i n t e r v a l t o t a l l y c l e a r of c l o u d s 78.8 p e r c e n t of t h e time and t o e n c o u n t e r c l o u d s d u r i n g t h a t i n t e r v a l ( T I C > 0 ) 21 .2 p e r c e n t of t h e t i m e . There i s a 16-percent p r o b a b i l i t y of b e i n g i n

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c l o u d s f o r more t h a n 10 p e r c e n t of t h e i n t e r v a l (25.6 s e c ) and an 8 - p e r c e n t probaThere i s o n l y a b i l i t y of b e i n g i n c l o u d s h a l f o r more of t h e i n t e r v a l ( 128 s e c 1 .6-percent p r o b a b i l i t y t h a t more t h a n 90 p e r c e n t of t h e i n t e r v a l would be c l o u d y . By c r u i s i n g a t a h i g h e r a l t i t u d e , 33.5 t o 38.5 k f t , however, t h e p r o b a b i l i t y of In e n c o u n t e r i n g c l o u d s i n any 256-sec i n t e r v a l i s reduced from 21.2 t o 15.8 p e r c e n t . t h e c r u i s e a l t i t u d e r a n g e from 38.5 t o 43.5 k f t , r e p r e s e n t i n g t h e upper r a n g e of c u r r e n t t r a n s p o r t a i r c r a f t , t h e p r o b a b i l i t y of c l o u d e n c o u n t e r i n e a c h 256-sec i n t e r v a l is reduced s t i l l f u r t h e r t o 8.5 p e r c e n t . Above 43.5 k f t , t h e r e i s v i r t u a l l y no p r o b a b i l i t y of e n c o u n t e r i n g c l o u d s .

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R e s u l t s Analyzed With Respect t o A l t i t u d e The v a l u e s j u s t p r e s e n t e d i n t a b l e V I I a r e u s e f u l f o r e s t i m a t i n g t h e r e l a t i v e cloud-encounter f r e q u e n c y on a worldwide b a s i s , b u t f o r t h e o p e r a t i o n s of most a i r l i n e s , s t a t i s t i c s f o r more l i m i t e d g e o g r a p h i c r e g i o n s a r e of more p r a c t i c a l i n t e r e s t . For t h i s r e a s o n , t h e d a t a of t a b l e V I I I were e xt r a c t e d from appendix D (Vol. 11). For t a b l e V I I I , o n l y t h e a v e r a g e v a l u e of TIC (TIC) t h e p r o b a b i l i t y of c l o u d e n c o u n t e r (PCE, n u m e r i c a l l y e q u a l t o P(T1C > 0 ) i n appendix D), and t h e number of i n d e p e n d e n t o b s e r v a t i o n p e r i o d s making up t h e sample i n each c e l l of t h e l a t i t u d e season-altitude g r i d a r e presented. These p a r a m e t e r s were chosen from a l l t h o s e i n appendix D because t h e y a r e of most d i r e c t u s e f u l n e s s i n a s s e s s i n g t h e r e l a t i v e magn i t u d e s of cloud-encounter f r e q u e n c i e s . The d a t a i n t a b l e V I I I a r e p r e s e n t e d f o r 10' l a t i t u d e zones between 40°S and 80°N, and f o r t h e t h r e e primary a l t i t u d e bands a n a l y z e d i n t h i s r e p o r t , d e n o t e d f o r convenience a s f o l l o w s : Band Al:

28.5 t o 33.5 k f t

Rand A2:

33.5 t o 38.5 k f t

Band A3:

38.5 t o 43.5 k f t

The d a t a a r e f u r t h e r s u b d i v i d e d by NH s e a s o n . I t is immediately a p p a r e n t t h a t most For c o m p l e t e n e s s , d a t a a r e p r e d a t a were o b t a i n e d between 30°N and 60°N l a t i t u d e . s e n t e d f o r e v e r y l a t i t u d e zone having o b s e r v a t i o n s ; b l a n k s i n d i c a t e t h a t no d a t a were t a k e n i n a zone. The r e a d e r i s s t r o n g l y c a u t i o n e d t h a t t h e s t a t i s t i c s w i t h i n z o n e s h a v i n g fewer t h a n 30 i n d e p e n d e n t samples may n o t be r e p r e s e n t a t i v e of p o p u l a t i o n values. L a t i t u d e zone from 30°N t o 60°N.- Most c o n f i d e n c e may be p l a c e d i n t h e v a r i a b i l i t y of d a t a i n t a b l e V I I I o c c u r r i n g w i t h i n t h e 30°N t o 60°N l a t i t u d e band. This v a r i a b i l i t y was f u r t h e r t e s t e d f o r s t a t i s t i c a l s i g n i f i c a n c e , u s i n g t h e a n a l y s i s of v a r i a n c e (ANOVA) t e c h n i q u e ( r e f . 6 0 ) a s implemented through a w e l l - p r o v e n s o f t w a r e The f o l l o w i n g g e n e r a l c o n c l u s i o n s were reached f o r t h e 30°N t o package ( r e f . 61 1. 60 O N l a t i t u d e r e g i o n : 1 . The a v e r a g e v a l u e of TIC r a n g e s from 0 p e r c e n t , f o r a l t i t u d e band A3, t o 13.7 p e r c e n t , f o r band Al. The r e s p e c t i v e p r o b a b i l i t y of c l o u d e n c o u n t e r , PCE, r a n g e s from 0 t o 32.4 p e r c e n t .

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2. I n comparing t h e TICs t a t i s t i c s from d i f f e r e n t a l t i t u d e bands by t h e ANOVA t e c h n i q u e , we n o t e t h a t t h e TIC v a l u e i n band A3 ( h i g h e s t a l t i t u d e b a n d ) i s s i g n i f i c a n t l y lower ( t h u s a f f o r d i n g a s m a l l e r chance of l o s i n g LF) t h a n t h e v a l u e s i n

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bands A1 and A2, and t h a t t h e TIC v a l u e i n band A2 i s p r o b a b l y s i g n i f i c a n t l y lower t h a n t h a t i n band Al. Thus, i n t h i s l a t i t u d e r e g i o n , an i n c r e a s e i n a l t i t u d e prov i d e s a s i g n i f i c a n t l y lower p r o b a b i l i t y of c l o u d e n c o u n t e r . (1n t h i s r e p o r t , an e v e n t is termed " s i g n i f i c a n t " i f it could have o c c u r r e d by random chance 1 p e r c e n t o r I t i s termed " p r o b a b l y s i g n i f i c a n t " i f it c o u l d have o c c u r r e d no l e s s of t h e t i m e . more t h a n 5 p e r c e n t of t h e t i m e by chance. Events o c c u r r i n g more t h a n 5 p e r c e n t of t h e time by random chance were c o n s i d e r e d n o t s t a t i s t i c a l l y s i g n i f i c a n t . ) 3. With a l l s e a s o n s and a l t i t u d e s c o n s i d e r e d t o g e t h e r , t h e a v e r a g e t i m e i n c l o u d s ( T I C ) v a r i e s s i g n i f i c a n t l y w i t h a l t i t u d e , s e a s o n , and l a t i t u d e , and t h e probab i l i t y of c l o u d e n c o u n t e r (PCE) v a r i e s s i g n i f i c a n t l y w i t h a l t i t u d e and l a t i t u d e , b u t n o t with season.

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4 . When o n l y s p r i n g and summer a r e compared, TIC v a r i a b i l i t y w i t h a l t i t u d e and l a t i t u d e is p r o b a b l y s i g n i f i c a n t , b u t v a r i a b i l i t y w i t h s e a s o n i s n o t s i g n i f i c a n t . For PCE, o n l y a l t i t u d e is probably s i g n i f i c a n t , b u t l a t i t u d e and s e a s o n a r e n o t significant.

-

5 . When autumn and w i n t e r a r e compared, TIC v a r i a b i l i t y w i t h s e a s o n and a l t i t u d e i s s i g n i f i c a n t and v a r i a b i l i t y w i t h l a t i t u d e i s p r o b a b l y s i g n i f i c a n t . For PCE, s e a s o n is s t i l l n o t s i g n i f i c a n t , b u t a l t i t u d e i s s i g n i f i c a n t , and l a t i t u d e i s probably s i g n i f i c a n t . 6. From i t e m s 4 and 5 above, w e conclude t h a t t h e g r e a t e s t v a r i a b i l i t y o c c u r s i n winter. T h i s i s c o n s i s t e n t w i t h m e t e o r o l o g i c a l e x p e r i e n c e , which t e l l s us t h a t t h e r e i s both more l a t i t u d i n a l and a l t i t u d i n a l v a r i a b i l i t y i n t h e w i n t e r t h a n i n the o t h e r seasons.

7 . Comparing a l t i t u d e bands A1 and A2, over a l l s e a s o n s , w e n o t e s i g n i f i c a n t v a r i a b i l it y w i t h s e a s o n and l a t i t u d e , and p r o b a b l y s i g n i f i c a n t v a r i a b i l i t y w i t h a l t i t u d e f o r TIC. For PCE, o n l y the v a r i a b i l i t y w i t h a l t i t u d e is s i g n i f i c a n t , a t the 95 p e r c e n t l e v e l . 8. Comparing a l t i t u d e bands A2 and A 3 o v e r a l l s e a s o n s , we n o t e s i g n i f i c a n t v a r i a b i l i t y w i t h l a t i t u d e and a l t i t u d e , b u t no s i g n i f i c a n t seasonal. d i f f e r e n c e . For PCE, season i s n o t s i g n i f i c a n t , b u t a l t i t u d e and l a t i t u d e a r e s i g n i f i c a n t .

-

9. TO summarize i t e m s 1 t o 8 above, a l t i t u d e i s always i m p o r t a n t , l a t i t u d e is of less importance, and s e a s o n of l e a s t importance t o the v a r i a b i l i t y of T I C and PCE.

Other l a t i t u d e zones.- With t h e c a u t i o n s imposed by s m a l l sample s i z e f i r m l y i n mind, we conclude t h a t t h e f o l l o w i n g t r e n d s seem t o be p r e s e n t i n t a b l e V I I I f o r t h e o t h e r l a t i t u d e bands : 1 . For r e g i o n s poleward of 20° l a t i t u d e i n b o t h t h e N o r t h e r n and S o u t h e r n H e m i s p h e r e s , t h e s u p e r i o r i t y of a l t i t u d e band A 3 f o r c l o u d a v o i d a n c e becomes more e v i d e n t t h e more poleward one goes.

2. For t h e t r o p i c a l r e g i o n , 20°N t o 20°S, a l t i t u d e band A3 i s no l o n g e r obvio u s l y b e t t e r f o r c l o u d a v o i d a n c e t h a n bands A1 and A2; i n f a c t , band A2 i s p r o b a b l y t h e b e s t , o v e r a l l . Values f o r TIC of 10 p e r c e n t and PCE of 30 p e r c e n t a r e good repr e s e n t a t i v e v a l u e s f o r this r e g i o n and band. The t r o p o p a u s e i s a t i t s h i g h e s t i n t h e t r o p i c s , a t 50 t o 55 k f t , s o t h a t even band A 3 i s s t i l l w e l l below t h e t r o p o p a u s e and w i t h i n t h e c o n v e c t i v e r e g i o n of t h e atmosphere; it i s t h u s s u b j e c t t o c l o u d

-

o c c u r r e n c e and v e r t i c a l development. The f a c t t h a t t h e h i g h e s t v a l u e s of and PCE i n the t r o p i c a l r e g i o n b o t h o c c u r i n band A3 i s c o n s i s t e n t w i t h the r e s u l t s of o t h e r r e s e a r c h ( r e f . 45) showing c i r r u s c o n s i s t e n t l y o c c u r r i n g 5 km o r more b e n e a t h t h e t r o p i c a l t r o p o p a u s e - e x a c t l y w i t h i n band A3. Thus, f o r the t r o p i c a l r e g i o n , no s t r o n g ly f a v o r e d a l t i t u d e band f o r minimum c l o u d e n c o u n t e r e x i s t s , and w e recommend t h a t a TIC of a t l e a s t t 0 p e r c e n t and a PCE of 30 p e r c e n t be assumed f o r p l a n n i n g purposes.

R e s u l t s Analyzed With R e s p e c t t o D i s t a n c e From the Tropopause A companion a n a l y s i s t o t h a t f o r t a b l e V I I I was performed, i n which t h e d a t a w e r e a n a l y z e d w i t h r e s p e c t t o d i s t a n c e from the t r o p o p a u s e r a t h e r t h a n a l t i t u d e . For convenience, t h e f o u r t r o p o p a u s e s e p a r a t i o n bands are d e n o t e d as f o l l o w s :

Rand TI :

1 0 t o 15 k f t below the t r o p o p a u s e

Band T2:

5 t o 10 k f t below t h e t r o p o p a u s e

Band T3:

0 t o 5 k f t helow the t r o p o p a u s e

Band T4:

0 t o 5 k f t above t h e t r o p o p a u s e

A s before,

t h e d a t a were a n a l y z e d by 10' l a t i t u d e zones and by NH s e a s o n , and t h e p a r a m e t e r s p r e s e n t e d a r e a g a i n TIC, PCE, and t h e number of i n d e p e n d e n t o b s e r v a t i o n s . These d a t a were e x t r a c t e d from a p p e n d i x E The r e s u l t s a r e p r e s e n t e d i n t a b l e I X , ( ~ o l .11). However, much of t h e v a r i a n c e t h a t o c c u r s w i t h r e s p e c t t o s e a s o n and Therel a t i t u d e is c o n t a i n e d i n t h e s i n g l e v a r i a b l e " d i s t a n c e from t h e t r o p o p a u s e . " f o r e , t h e ANOVA t e c h n i q u e used i n the p r e v i o u s s e c t i o n c o u l d n o t be u s e d t o p r o v i d e An m e a n i n g f u l r e s u l t s f o r t h e d a t a s t r a t i f i e d by s e p a r a t i o n from t h e t r o p o p a u s e . ANOVA of t h e s e d a t a would g i v e s t a t i s t i c a l l y con£ounded r e s u l t s , N e v e r t h e l e s s , from an i n s p e c t i o n of t a b l e I X , t h e f o l l o w i n g c o n c l u s i o n s a p p e a r r e a s o n a b l e w i t h o u t f u r t h e r s t a t i s t i c a l con£ i r m a t i o n : L a t i t u d e zone from 30°N t o 6 0 ° N , made f o r l a t i t u d e s from 3 0 O ~t o BOON:

The f o l l o w i n g t e n t a t i v e c o n c l u s i o n s c a n be

-

1 , Band T4 ( t h e uppermost) seems t o have markedly lower v a l u e s of T I C and PCE t h a n t h e o t h e r bands. The t e x t b o o k maxim t h a t c l o u d s do n o t o f t e n e x i s t a t a l t i t u d e s

above t h e t r o p o p a u s e i s a g a i n proven h e r e ,

2 . The v a l u e s i n the two l o w e s t bands, TI and T2, do n o t a p p e a r markedly different. But c l o u d e n c o u n t e r a p p e a r s less p r o b a b l e f o r band T3 t h a n f o r bands TI and T2.

.-

O t h e r l a t i t u d e zones For t h e t h r e e l a t i t u d e zones from 20°N to 30°N, from 20°S t o 40°S, and from 60°N t o 8 0 ° ~ , t h e r e a r e g e n e r a l l y t o o few o b s e r v a t i o n s t o make r e l i a b l e c o n c l u s i o n s , b u t c o n c l u s i o n s '1 and 2 above seem t o be b o r n e o u t , For t h e t r o p i c a l r e g i o n 20°N t o 20'5, a11 data, as n o t e d p r e v i o u s l y f o r t h e a l t i t u d e d a t a , were o b t a i n e d w e l l below the t r o p i c a l t r o p o p a u s e ; i n most cases, band TI was t h e only one h a v i n g d a t a . T h e r e f o r e , no comparisons were p o s s i b l e ; a n y comparison i n t h i s l a t i t u d e zone must be made on a l t i t u d e d a t a ( t a b l e V I I I )

.

R e s u l t s Derived D i r e c t l y From Route S t a t i s t i c s ~ l t h o u g ht h e d a t a i n t a b l e s VIII and I X a r e h e l p f u l i n e s t i m a t i n g t h e c l o u d e n c o u n t e r v a r i a b i l i t y with a l t i t u d e , s e a s o n , and l a t i t u d e zone, f u r t h e r l o n g i t u d i n a l d e t a i l , imposed by g e o g r a p h i c and s e a s o n a l c l i m a t o l o g i c a l d i f f e r e n c e s , is needed t o derive the v a r i a b i l i t y pertinent t o various c i t y or regional p a i r s . Examples of i m p l i c i t c l i m a t o l o g i c a l e f f e c t s would i n c l u d e j e t streams with t h e i r a s s o c i a t e d c l o u d p a t t e r n s , the p r e s e n c e of semipermanent s y n o p t i c f e a t u r e s such as t h e A l e u t i a n and I c e l a n d i c lows, and monsoon c l o u d p a t t e r n s i n c o n n e c t i o n w i t h t h e I n d i a n s u b c o n t i n e n t . NO a t t e m p t was made t o model t h e e f f e c t of t h e s e f e a t u r e s d i r e c t l y , b u t t h e y and o t h e r s undoubtedly i n f l u e n c e t h e s t a t i s t i c s f o r t h e v a r i o u s c i t y p a i r s i n ways t h a t a r e n o t a p p a r e n t i n t h e z o n a l mean v a l u e s . Also i t i s i m p o r t a n t t o r e a l i z e that t h e s t a t i s t i c s u s e d i n t h e s e t a b l e s p e r t a i n t o t h e ensemble b e h a v i o r of 256-sec o b s e r v a t i o n p e r i o d s w i t h i n e a c h c e l l i n a latitude-longitude-season-altitude g r i d . I n e a r l i e r r e p o r t s , t h e g r i d d e d d a t a were used d i r e c t l y i n a first a t t e m p t t o p r o v i d e a n e s t i m a t e of c l o u d - e n c o u n t e r s t a t i s t i c s a l o n g s e v e r a l r o u t e s and a l t i t u d e s (refs 5, 6, and 17 ) However, because w e a t h e r s y s terns have a p p r e c i a b l e h o r i z o n t a l e x t e n t , a h i g h o r low p r e s s u r e system can c o v e r s e v e r a l c e l l s , s o , as d i s c u s s e d i n appendix C, t h e d a t a from a d j a c e n t c e l l s a r e n o t i n d e p e n d e n t . Thus, t h e r e a r e problems i n u s i n g c e l l s t a t i s t i c s t o e s t i m a t e t h e p r o b a b i l i t y of e n c o u n t e r i n g a g i v e n a v e r a g e amount of c l o u d i n e s s a l o n g an a i r l i n e r o u t e t h a t t r a v e r s e s one or more c e l l s - t h e e s t i m a t e t h a t i s needed i n a s s e s s i n g t h e f e a s i b i l i t y of employing LFC on a i r l i n e r o u t e s , For a l l t h e s e reasons, a n o t h e r approach was s o u g h t ,

.

.

E m p i r i c a l Model A more d i r e c t approach i s t o compute t h e c l o u d - e n c o u n t e r s t a t i s t i c s f o r r o u t e s of i n t e r e s t by s t u d y i n g the f r e q u e n c y d i s t r i b u t i o n of r o u t e - a v e r a g e d time-in-cloud v a l u e s f o r a l l f l i g h t s on a g i v e n r o u t e , A model based on t h i s a p p r o a c h was d e v e l oped as f o l l o w s :

.

1 The ensemble of f l i g h t s between each c i t y p a i r ( e . g o , JFK-LHR) was e x t r a c t e d from appendix B and each f l i g h t p l a c e d i n t o one of t h r e e p r i m a r y a l t i t u d e bands ( 2 8 . 5 t o 33.5 k f t , 33.5 t o 38.5 k f t , and 38.5 t o 43.5 k f t ) a c c o r d i n g t o the a v e r a g e a l t i t u d e d u r i n g t h e e n t i r e flight. 2. For each f l i g h t , t h e v a l u e of %TIC w a s o b t a i n e d from a p p e n d i x B. This value w i l l be d e n o t e d TIC^ and is t h e a v e r a g e p e r c e n t a g e of t i m e i n c l o u d s a l o n g the r o u t e f o r t h a t flight.

3 , Frequency d i s t r i b u t i o n s of TICF w e r e p r e p a r e d f o r each r o u t e and a l t i t u d e A n a v e r a g e v a l u e of TICF f o r t h e r o u t e , TICR, was t h e n computed by a v e r a g i n g band. a l l t h e v a l u e s of TICF from a l l f l i g h t s a l o n g the r o u t e .

.

4. For each r o u t e where a r e l a t i v e l y l a r g e number of f l i g h t s i l , more t h a n 30) were i n t h e sample, the f r e q u e n c y d i s t r i b u t i o n of TICF w a s p l o t t e d and its c h a r a c t e r s t u d i e d . T h i s s t u d y d i s c l o s e d t h a t f o r all r o u t e s t h e most f r e q u e n t TIC v a l u e F was 0 ( i , f l i g h t i n c l e a r a i r a t t h e s e a l t i t u d e s i s t h e most f r e q u e n t experience) , t h a t a TIC^ v a l u e of 100 p e r c e n t was never o b t a i n e d , and t h a t the f r e q u e n c y of TICF v a l u e s u s u a l l y d e c r e a s e d m o n o t o n i c a l l y as TICF i n c r e a s e d . T h i s b e h a v i o r s u g g e s t e d

.

t h a t t h e o b s e r v a t i o n s f o r each r o u t e c o u l d p e r h a p s be modeled by e i t h e r a n e g a t i v e exponential probability density function,

-

where t = TICF/TIC = TICF/TICR, TICR F gamma p r o b a b i l i t y d e n s i t y f u n c t i o n ,

>

0 percent,

and

TICF


5 k f t above

Total.

7 12 4 6 29

2720 3445 1510 2547 10222 13461 19235 13225 14161 60082

Observations i n vicinity o f clouds

W i nter Spring Summer Autumn Total

274 549 295 369 1487

593 569 437 51 1 21 10

88 1 960 348 843 3032

861 11 18 354 740 3073

104 237 72 78 491

Observations i n clear air

Wi n t e r

1323 1848 1779 1717 6667

1631 1966 2423 1869 7894

2022 2731 1928 2303 8984

2874 4592 1840 3500 12806

3555 5350 2909 3493 15307-------

2056 2748 2341 1279 8424

10004

12016

15879

15798

8453

Total

S p r i ng Summer Autumn Total

.,.............

81 54

.---

70304 I

TABLE IV.

-

SUMMARY OF ZONAL MEAN CLOUD-ENCOUNTER STATISTICS BY SEASON AS FUNCTIONS OF LATITUDE AND ALTITUDE [Data from appendix D ( V o l .

11) 1

WINTER L A T I TUDE :

75N

65N

55N

45N

35N

25N

15N

5N

5s

15s

25s

355

.9

0,O 6.8 10.0

4.6 9.1 13.7

3.1 7.8 10,2

.8 7.8 7.8

3.0 2.9 4.5

10.4 14.4 8.6

19.2 12.6 17.1

22.4 11.6 6.1

3.3 4 . 9 7 . 3

.8 3.5 7.6

2.7 14.6

0.0 21.7 24.7

18.6 24.4 28.4

14.7 21.1 23.8

7.1 2 0 3 21 3

10.5 72.3 18.0

23.5 26.8 20.2

30.0 25.0 27.4

31.0 25.7 17.1

13.1 17.6 20.8

7,2 15,3 21.3

54.7 43.1 42.2

0.0 54.8 46.8

65.8 50.2 48.5

50.8 39.7 42.4

31.2 37.6 43,9

20.6 32.0 58.4

40.2 41.6 35.2

47.2 37.5 36.4

41.3 45.7 29.4

26.5 40.2 42.6

36.4 41.7 39.8

14.3 0.0 27.8

0.0 34.2 33.7

30.9 34,5 34.1

34.3 31.6 31 . 7

30.4 29.5 31 . 3

20.2 26.9 32.5

30.4 30.8 2 . 1

29.9 30.6 29.9

31.4 32.3 26.8

27,7 33.6 31 . 9

34.2 34.0 33. 1

ALT. (KFT

-

TIC, %

38.5-43.5 33.5-38.5 28.5-33.5

.2

0.0

3.8

SIGMA,% 7.1

38.5-43.5 33.5-38.5 28.5-33.5

0.0

TI CIV, X 38.5-43. 5 33.5-38.5 28.5-33.5

0,O

SIGMA, X 38.5-43.5 33.5-38.5 28.5-33.5

0.0

38.5-43.5 33.5-38.5 28.5-33.5

T ( CLEAR I -51.8 -53.1 -56.3 -55.0

- CLOUDS T

38.5-43.5 33.5-38.5 28.5-33.5

(

-69.5 0.0 -65.0 -60.9

TABLE IV

SPR 1 NG

L A T I TlJDE :

75N

65N

ALT. (KFTI

-

TIC, %

38.5-43.5 33.5-38.5 28.5-33.5

0,O

. I

. O

0.0

16.9

SIGMA, %

38.5-43.5 33.5-38.5 28.5-33.5

0.0 .3 0.0 TI CIV,

38.5-43.5 33.5-38.5 28.5-33.5

. I 32.8

X

1.6 0.0

0.0 .5 63.0

-T ( CLEAR) 38.5-43.5 33.5-38.5 28.5-33.5

-50.4 -55.6 -50.2 -56.0 -56,7

P

A Z ( CLOUDS 1 3 8 , 5 - 4 3 .5

0.0

.- C o n t i n u e d

TABLE IV

SUMMER

L A T I TUDE : ALT .

(

75N

65N

55N

45N

KFT)

SIGMA- %

38.5-43.5 33.5-38.5 28.5-33.5

38.5-43.5 33,5-38.5 28.5-33.5

38.5-43.5 33.5-38.5 28.5-33.5

0.0 .1

1 9 4.3

1 , 8 1 1 .9 9.0 20.6 12.2 18.6

SIGMA, X 0 . 0 19.8 13.2 0 . 0 23.1 21.6 18.7

P(TIC>50%1 0.0 .1

0.0

.2

T CLEAR I

0.0 .9 2.0

27 1 28.9 29.4

2.3 7.5 5.8

(

38.5-43.5 33.5-38.5 28.5-33.5

-42.2 -47.4 -50.8 -55.6 -43.2 -49.3 -50.7 - 5 0 . 2 -48.1 -42.1

T CLOUDS) (

38.5-43.5 33,5-38.5 20.5-33.5

0 . 0 - 6 1 . 5 -60.2 - 6 1 . 0 -45.0 -55.7 -55.4 -52.3 -49.2 -42.0

Z Z (C L E A R )

38.5-43.5 33.5-38.5 28.5-33.5

7.5

6.0

5.1

2.5

38.5-43.5 33.5-38.5 28.5-33.5

0.0

nzc cLeuos 4.7

4.8 - 1 , 5 1 .I -6.8 -3.5 -1 1.0

)

-.6 -.7

1.6 -5.8 - 2 . 3 -8.1 - 3 . 6 -10.4

.- Continued

TABLE 1V.- Concluded

AUTUMN LAT 1 TUDE :

75N

65N

55N

.7 11.6 30. 9

3.9 77.5 21 .O

ALT. L KFT)

38.5-43,5 33,5-38.5 28.5-33.5

SIGMA, X 0.0

.I 0.0

38.5-43.5 33.5-38.5 28,s-33.5

T ( CLEAR 1 -51 . 5 - 5 0 . 1 - 5 7 . 3 -53 6 - 5 9 . 0 -50 6

T ( CLOUDS 38.5-43.5 33.5-38.5 28.5-33.5

0 . 0 -59.0 -62.0 -59.2 0 . 0 -52.4

TABLE V.

-

SUMMARY OF ZONAL MEAN CLOUD-ENCOUNTER STATISTICS BY SEASON AS FUNCTIONS OF LATITUDE AfJD DISTANCE FROM NMC TROPOPAUSE

[Data from appendix E ( V o l .

W l NTER LAT ITUDE : 75N TRBP OIST( KFT) 0- 5 0- 5 5-10 10-15

ABV BLW BLW BLW

0- 5 0- 5 5-10 10-15

ABV BLW BLW BLW

0- 5 0- 5 5-10 10-15

ABV BLW BLW BLW

0- 5 0- 5 5-10 10-15

ABV BLW BLW BLW

0- 5 0- 5 5-10 10-15

ABV BLW BLW BLW

0- 5 0- 5 5-10 10-15

ABV BLW BLW BLW

0- 5 0- 5 5-10 10-15

ABV BLW BLW BLW

0- 5 0- 5 5-10 10-15

AB\/ BLW BLW BLW

0- 5 0- 5 5-1 0 10-15

ABV BLW BLW BLW

0- 5 0- 5 5-10 10-15

ABV BLW BLW BLW

0- 5 0- 5 5-10 10-15

ABV BLW BLW BLW

0- 5 0- 5 5-10 10-15

ABV BLW BLW BLW

0- 5 0- 5 5-10 10-15

ABV BLW BLW BLW

65N

55N

45N

-

TIC, % 0.0

.8 11.3

-T CLOUDS (

)

0 . 0 -61.9 -60.5 -62.0 -60.5 -55.3 -45.3

A ZCCLEAR) 2.7

2.6 -1.3

-62.8 -59 6 -52.7 -47.3

2.8 2.3 -2.2 -2.2 -6.9 -7. 1 -11.6 -11.9

nz ( c ~ e u o 1s 0.0

.9 -1.2

.8 1.4 -2.6 -2.8 -6.8 -7.2 -12.0 -12.0

1111

TABLE V ,- C o n t i n u e d

SPR 1 NG LAT ITUOE : 75N TRBP D I ST ( K F T

65N

N 0- 5 0- 5 5-10 10-15

ABV BLW BLW BLW

0- 5 0- 5 5-10 10-15

ABV BLW BLW BLW

0- 5 0- 5 5-10 10-15

ABV BLW BLW BLW

0- 5 0- 5 5-10 10-15

ABV BLW BLW BLW

0- 5 0- 5 5-10 10-15

ABV BLW BLW BLW

0- 5 0- 5 5-10 10-15

ABV BLW BLW BLW

0- 5 0- 5 5-10 10-15

ABV BLW

289

12 11 0 0

42 0 0

TIC, %

0.0 .1

.O 16.5

SIGMA, X 0.0

1

.5

32.5

TIClV,% 0,O .6 1. 6 69.2

SIGMA, % 0.0 .4 0.0 28.0

P ( T 1C>O%; 0.0 9.1

2,4 23 8

P(TIC>lO%) 0.0 0.0 0 . 0 21.4

BLW BLW

0- 5 0- 5 5-10 10-15

ABV BLW

0- 5 0- 5 5-10 10-15

ABV BLW BLW BLW

P(TIC>25%) 0.0 0,0 0 0 21.4

BLW BLW P[TIC>5O%) 0.0 0.0 19.0 0.0

-T CLEAR I (

0- 5ABV 0 - 5 BLW 5 - 1 0 BLW 1 0 - 1 5 BLW

-59.1 - 5 2 4 -57 8 -57.1

- CLBUDS T(

0 - 5 ABV 0-5BLW 5 - 1 0 BLW 1 0 - 1 5 BLW

0 - 5 ABV 0-5BLW 5 - 1 0 BLW 1 0 - 1 5 BLW

0.0 -55.9 -59.0-57.0

-

~ ~ ( C L E A R ) 1.6 3.0 -1.3 -2.1

-

/ J Z ( CLBUDS 1

0- 5 0- 5 5-10 10-15

ABV BLW BLW BLW

0.0

-,7

2.8 -3.0

TABLE V,-

SUMMER L A T I TUDE : 75N TRBP D I S T ( K F T 1

65N

55N

45N

750 110

1341 391 102 12

1103 854 653

N 0- 5 0- 5 5-1 0 10-15

ABV BLW BLW BLW

11 0 0 0

0

0

699

TIC, %

0- 5 0- 5 5-10 10-15

ABV BLW BLW BLW

0- 5 0- 5 5-10 10-15

ABV BLW BLW BLW

0- 5 0- S 5-10 10-15

ABV BLW BLW BLW

0- 5 0- 5 5-10 10-15

ABV BLW BLW BLW

0- 5 0- 5 5-10 10-15

ABV BLW BLW BLW

0- 5 0- 5 5-10 10-!5

ABV BLW BLW BLW

0- 5 0- 5 5-10 10-15

ABV BLW BLW BLW

0- 5 0- 5 5-10 10-15

ABV BLW BLW BLW

0- 5 0- 5 5-10 10-15

ABV BLW BLW BLW

0- 5 0- 5 5-10 10-15

ABV BtW BLW BLW

0- 5 0- 5 5-10 10-15

ABV BLW BLW BLW

0- 5 0- 5 5-10 10-15

ABV BLW BLW BLW

.o 2.3

. O

- 3 3.8 5.9

8.0 10.1

.1 10.6

3.3 12.5 19.2 19.7

7.7 16.8 19.7 23.0

2.0 15.C

136 18.4 26.5 71 . 4

22.9 32.0 31 .O 34.4

8.0 SIGMA, % .1

T I CIV, % .4

SIGMA, X 0.0

1.2

5.7

1 . 3 16.7 2 3 . 3 21 . 9 26.8 0.0

25.6 27.3 28.1 31 . 2

-T CLEAR 1 (

-44.7 -50.8 -51.9 -57.6 -54.4 -49.1 -33.9

-T CLBUDS 1

-53.9 -54.4 -52.6 -48.8

(

-45.0 -57.0 -59.3 -59.1 -54.9 -45.5 -31 0

A

ZCCLEAR) 4.7 3.2 -1.9

-59.2 -56,6 -54.2 -49.7

2.8 2.0 -1.9 -2.5 -6.8 -7.6 -12.2 -12.5

6z c cLeuos) 4.7

1,9 -1.4

1.2 1 3 -2.3 -2.7 -7.1 -7.4 -10.9 -12.3

Continued

TABLE V

AUTUMN LAT I TUDE : 75N TROP D I S T ( K F T )

65N

N 0- 5 0- 5 5-10 10-15

ABV BLW BLW BLW

0- 5 0- 5 5-10 10-15

ABV BLW BLW BLU

0- 5 0- 5 5-10 10-15

ABV BLW BLW BLW

0- 5 0- 5 5-10 10-15

ABV BLW BLW BLW

0- 5 0- 5 5-10 10-15

ABV BLW BtW BLW

0- 5 0- 5 5-10 10-15

ABV BLW BLW BLW

0- 5 0- 5 5-1 0 10-15

ABV BLW BLW

0- 5 0- 5 5-10 10-15

ABV BLW BLW BLW

0- 5 0- 5 5-10 10-15

ABV BLW BLW BLW

39 0 0 0

538 203 45 0

TIC, %

.O

SIGMA,

.9 16.5 55.6

X

.1

6.9

29.9 38.6 TICIV,% . 4 31.7

49.3 67.6 SIGMA, % 0 . 0 24.6

32.3

31 .6 PtTIC>O%; 2.6 3.0 33.5 82.2

P(TIC>IO%) 0.0 2.2 29.1 75.6

BLW P ( T I C>25% 0.0 1.7

23.2 71. 1

P ( TIC>5O%) 0.0

.6

16.3 55.6 A

0- 5 0- 5 5-10 10-15

ABV BLW BLW BLW

T ( CLEAR I - 5 7 . 7 -53 0 -53.9 -52.9

-T CLOUDS) (

0 - 5 ABV

-62.0

0 - 5 BLW 5 - 1 0 BLW 1 0 - 1 5 BLW

hz

0- 5 0- 5 5-10 10-15

ABV BLW

0- 5 0- 5 5-10 10-15

ABV BLW BLW BLW

(

-57.7 -54.8 -50.1

CLEAR 1

3.2

2.8 -1 , 5 -6.2

BLW BLW

0 Z C CLOUDS 1 .6

1.0 -2.5

-6.6

.- Concluded

.-

TABLE VI CUMULATIVE FREQUENCY DISTRIBUTION OF MEAN PARTICLE CONCENTRATIONS~ AS A FUNCTION OF THE AVERAGE TIME IN CLOUDS (TIC) DURING AN OBSERVATION PERIOD (ALL GASP OBSERVATIONS INCLUDED) *

r

-

Percentage of observation periods w i t h PD5 (m-3)

,

TIC = 0% >O > 1o2 >3 x lo2 >lo3 >3 lo3 >lo4 >3 lo4 >5 lo4 >7 lo4 >lo5 >3 lo5 >7 lo5 >1o6 > 3 x lo6

-

PD5 a(PD5) N

31 .5 18.1 9.8 4.8 2.4 .7 .1 0 .O 0 .O 0 .O 0 .O 0 .O

449 16 403 47 374

TIC > 0% 9 0 .O 87.1 84.1 80.2 76 .O 68.9 57.6 49.9 43 -5 36.6 15.2 4.3 2.4 .3 164 722 359 583 8 302

TIC 2 10% 9 4 .O 92.0 90 -4 8 8 .I 85.2 80.1 71 .6 64.4 57.1 48.9 20.6 5.8 3.3 .4 218 194 407 224 5 989

TIC 2 25% 96.9 95.8 94.7 93 -0 91 .1 87.3 80.7 74.4 67.4 58.3 25.6 7.2 4.2 .6 265 206 451 673 4 429

TIC

>

50%

99 .O 98.5 98.1 97.1 96.3 94 .O 90.8 86.9 81 .O 71.6 33 .O 9 .I 5.3 .7 325 829 478 388 2 884

TIC

>

75%

TIC

>

90%

TIC

>

100%

100 .O 99.9 99.9 99.9 99.8 99.5 98.8 97.5 93.8 86.1 41 .5 10.1 5 -5 .6

100 .O 100 .O 100 .O 100 .O 100 .O 100.0 100 .O 100 .O 98.9 92.7 32.6 3.2 1 .1

100 .O 100 - 0 100 .O 100 .O 100 .O 100 .O 100 .O 100 .O 100 .O 100.0 7 .I

379 870 483 474 1 592

281 870 197 044 565

211 736 64 922

a ~ lpla r t i c l e s with diameters > 3 pm. b~xample: I n clear a i r (TIC = 0 % ) . there are > 3 x l o 3 particles/m3 i n 2.4% of cases. For TIC > O%, t h i s concentration is exceeded i n 76% of cases. For TIC > 50%, t h i s concentration i s exceeded i n 96.3% of cases.

TABLE V I I . -

CUMULATIVE PROBABILITY D I S T R I B U T I O N O F T I C AS A FUNCTION OF ALTITUDE WITH ALL SEASONS AND LATITUDES INCLUDH)

r P e r c e n t a g e of o b s e r v a t i o n p e r i o d s with Altitude, kft

T I C = 0%T I C

>

0% T I C

-

> 10% T I C > 20% T I C > 30% TIC > 40% T I C > 50% T I C > 60% T I C > 70% TIC

18.5 t o 23.5 k f t

68.4

31 .6

29 .O

27.2

27.2

25.4

22.8

21.9

23.5 t o 28 -5 k f t

80.0

20.0

14.5

13.2

1 1 .6

11 .O

9.8

8.6

28.5

t o 33.5 k f t

78.8

21 -2

16.0

13.2

11.2

9.4

8 .O

33.5 t o 38.5 k f t

84.2

15.8

11.3

9 .I

7.7

6.4

38.5 t o 43.5 k f t

91 .5

8.5

6.1

5 .O

4.2

43.5 t o 4 8 . 5 k f t

100.0

0.0

0 .O

0 .O

85.2

14.8

10.8

8.8

Total

20.2

Z 80% T I C

> 90%

18.4

18.3

7 -4

6 .O

2 .I

6.7

5.3

3.9

1.6

5.3

4.3

3.4

2.4

1 .O

3.5

3.0

2.5

1.9

1.4

.6

0 .O

0 -0

0 -0

0 .O

0 .O

0 .O

0 .O

7.4

6.3

5.3

4.3

3 -4

2.5

1 .O

I

TABLE V I I I

.- ZONAL

MEAN VALUES OF

-

Winter

O N

Summer

A l t i t u d e , kft

kft

Altitude,

8 0 ON-70

THREE ALTITUDE BANDS

Spring

L a ti t u d e

28.5-33.5

AND PCE , !?OR

No. of i n d e p e n d e n t o b s e r v a t i o n s

TIC, % PCE, %

Code:

TIC

33 -5-38.5

0.0 0 .O

2

.2 .4

25

38.5-43.5

38.5-43.5

28.5-33 a5 33.5-38.5

0.0 0.0

1

-1 .3

4

1316.9 26.8

5

0.0 2.2

35

0.0 0 .O

29

28.5-33.5

-

A U tumn

Altitude, k f t

Altitude, k i t

33.5-38.5

28.5-33.5

38.5-43.5

0.0 7.1

2

0.4 2.7

39

33.5-38.5

0.0 0.0

1

0.1 0.6

13916.1 28.3

0.0 0 .O

15

38.5-43.5

0.0

1

0.0 1 .9

6

32

2.2 6.1

36

0.0 0.3

31

0 .O

3.8 8.9

20

60°N-SOON

10.0 21.4

83

6.8 12.5

108

0.0 0 .O

50

5.2 20 .O

64

4.8 73.2

171

0.0 0.5

729

4.2 31 .O

38

2.0 10.3

99

0.1 1.1

148

8.1 22.0

152

5.1 13.1

213

0.4 2.4

106

50°N-40°N

13.7 28.3

206

9.1 18.2

211

4.6 6.9

92 11.6 32.4

203

6.8 1 8 .O

320

3.6 8.9

234

6.7 22 .O

99

8.5 25.8

185

2.7 9.9

16010.8 23.4

199

6.3 17.2

238

2.1 8.2

143

40°N-30°N

10.2 23.9

248

7.8 19.7

291

3.1 6 ,O

133

5.0 20.1

207

4.6 14.4

381

4.3 9.8

195

2.2 6.7

158

3.1 9.6

244

2.7 10.2

91

4.9 12.1

132

6.4 17.9

145

2.5 6.3

74

30°N-20

7.8 17.8

182

7.8 20.7

199

0.8 2.7

48

4.7 18.7

130

5.6 18.0

198

1.5 6.9

69

5.9 15.8

98

1.8 6 -5

126

1.1 9.1

12

5.8 1 5 .O

43

3.1 11.4

68

2.7 11.3

20

4.5 7.7

73

2.9

84

3.0 14.3

26

6.8 19.2

41

6.0 20 .O

78

8.3 21.2

33 22.5 50.5

2220 2 51 .9

19

5.7 17.9

3

5.8

30

5.9

8

15.3

6.7 17.5

27

9 .I

9 10.0 23.3

2 8 12.3 30.7

34 14.7 44.4

10

9.0 28.9

1 5 10.3 28 .O

22

4.7 9.4

12

1 10.8 33.7

16 14.9 40.4

28

4.3 19.0

7.7

20 1 3 . 5 35.4

41

70°N-60°N

.9

1 .6

A

O N

20°N-1 O O N

1 .4 12.9

10°N-O0

8.6 24.5

41 14.4 34.6

6 3 10.4 26 .O

33

0°-1 OOS

17.1 46.8

33 1 2 . 6 33.6

51 19.2 40.7

24 11 .1 30 .O

10°S-20°S

6.1 20.8

62 11 .6 25.4

67 22.4 54.3

33

20's-30's

7.3 17.2

63

4.9 12.2

62

3.3 12.5

12

30°S-40°S

7.6 19.0

89

3.5 8.5

78

0.8 2 .1

7.9 25.8

1 4 26.3 50 "0

8

20 10.1 27.3

1 6 37.9 73.4

6 11.2 43.6

1 .1 4.4

19

0.4 2 ,O

14

9.8 26.8

4

21.3

5

7.3 16.3

16

2.4 6.8

10

2.8 7.5

16

8.6 22.5

20

8.1 16.9

8

4.0 13.7

18

0.3 4.5

7

3.0 8.3

9

0.1 3.9

9

0.5 4.2

18

0.5 3.6

22

0.1 2.7

3 13.3 24.8

12

5.7 9.1

12

0.0 2.7

4

33 14.9 26.7

11

0.4 6.3

5

2.8 4.9

18

4.1 14.7

27

0.1 0.7

33

0.0 2.2

8

25

5.7 12.8

14

0.0 1 .9

10

27.5

5.8 9.2

TABLE IX.-

ZONAL MEAN VALUES OF

,;I

Code:

---

TIC,

TIC

AND PCE FOR FOUR TROPOPAUSE SEPARATION BANDS

No. of independent observations

% %

--

Latitude

-

Winter

Spring

summer

Separation from tropopause, k f t

Separation from tropopause, k f t

Separation from tropopause, k f t

10-15 BLO 5-10

EL0

0-5

BLO 0-5

ABV 10-1 5 BLO 5-10

BLO

0-5 BLO 0-5 ABV 10-15 BLO 5-10

0.0 0 -0

1

0.1 9.1

2 0.0 0 -0

3

11 .3 21 .6

12 0.8 2.5

38

16.5 23.8

60.0 2.4

37

40 15.4 30.8

5 8 2.0 3.8

98

80°N-70°N

70°N-60°N

60°N-50°N

24.6 47.7

16

25.8 53.4

50°N-40°N

20.6 41 - 4

77

28.5 48.3

40"N-3O0N

11.5 27.6

144

30°N-20°N

12.6 152 29 -7

7.2 21.9

111

6.0 22.5

1 .2 11.4

6

4.3 20.6

18

118 15.8 177 1.4 177 9 . 5 33.5 26.6 4.0

122

128

7.7 22.7

15

11.9 208 9 . 3 238 0.3 21 -7 28.0 1 .O

72.9 44.4

51

8.3 24.3

109 1.4 170 3 -9

BLO

Autumn

0-5 BLO 0-5 ABV 10-15 BLO 5-10

BLO

0-5

BLO 0-5

ABV

0.0 2.6

5

30 0.9 3.0

62

0.0 9 -1

3

2.3 15.5

11 0.0 0.4

84

3.8 20.7

90 0.3 2.4

145

7.5 26.6

58

110

9.3 22.6

165

12.5 29.5

232

7.5 1 4 3 21 .2

5.0 12.1

730

1.2 3.8

76 0.0 0 .O

27

5.3 17.9

42

3.9 11.3

21

0.9

60.0 0.0

2

4.2

6.7 19 . I

6

0.0 0 .O

2

22.5 4 8 -7

4

2.3

9

10

8.0 30.4

38

76.8 200 9 . 0 313 1.6 280 10.1 22.8 43 -5 4.7 29.2

117

8.0 25.8

149

5.7 164 1.2 17 -7 5.2

161

6.1 270 6.2 313 1.6 205 4.0 4 -3 17 -4 12.4 20 - 5

168

2.3 9.6

126

4.7 13.0

6.4 20.9

164

4.1 15.9

190

2.9 10.1

80

0.7 4.2

43

1.0 16.7

7.0 18.4

63

3.8 16 -6

12

1.4 11 .5

4

1.1 5.3

2

5.9 8 -3

Separation from tropopause, k f t

6 3 0.5 1 .7

20

55.6 82.2

11 16.5 33.5

1 4 . 3 113 8 . 0 20.2 37.2

188 0.6 1 7 3 1 .9

6.7 216 0.6 18.0 2.5

147

-I

20°N-10°N

23

5.2 14.2 0.0 0 -0

66 0.0 0.0

1

-p p p p -

4.3 16.2 0.0 0 .O

7 5 1.3 5.4

18

2

-

5

-

20.8 38 .O

12

0.0 0 .O

1

23.4 57 .I

2

18.7 58.8

1

29.3 69.2

12

13.1 36 -8

13

0.0

3

20"s-30°S

2.6 15.9

17

0.0 0 .O

6

0.0 0.0

4 0.0 0.0

1

0.2 4.2

8

0.0 0.0

3

0.0 0 .O

2 0.0 0 .O

1

0.1 2.2

17

0.8 4.6

13

0.0 0 .O

2 0.0 0.0

30's-40°S

4.6 13.7

59

5.1 12.3

40

2.3 10.1

25 0.0 0.0

11

3.8 4.3

12

2.5 16.7

11

0.0 0.0

8 0.0 0 .O

10

1.1 4.3

24

0.8 5.1

27

0.9 5.0

28 0 . 0 0.8

28.7 48.1

7

0°-1 OOS

47.5 100 .O

10's-20's

10°N-O0

0.0 0 .O

2

1 0 . 0 0.0

0 -0

0.0

1

7

0 .O

9.1

14

2.3 13.2

14

0.0 0 .O

8

0.0 0 -0

3 0.0 0 .O

2

1 5 11.4 17.6

16

8.0 13.3

18

1.2 3.8

16 0.0 5.3

8

TABLE X.PROBABILITY OF ENCOUNTERING VARIOUS LEVELS OF AVERAGE CLOUDINESS ON SEVEN LONG-RANGE A I R L I N E ROUTES, AS ESTIMATED FROM A GAMMA PROBABILITY D I S T R I B U T I O N

Code:

No.

of f l i g h t s

TIC^!

%

P(TIC~ P(TIC~

<


5 %),

%

P(TIC~

z 50 % I f

California Hawaii

-

-

East Coast West C o a s t (USA)

West C o a s t

-

Northwest Europe

East Coast Northwest Europe

Australia SE A s i a

-

-

West Coast Japan ( w e s t b o u n d

28 -5-33.5

22 9.4 17.3 47.6

52.4 32.5 8.9 1.2

3

33.5-38.5

177 5.5 24.7 62.8

%

37.2 17.4 2.1

38.5-43 - 5

2

=O

58 7.5 20.1 53.8

46.2 25.9 5.3 0.4

13 2.4 41 .3 8 6 .O

14.0 2.8 =0 =0

6 9.9 16.7 46.2

53.8 34 .O 9.9 1.4

26 2.7 38.6 83.1

16.9 4 .o 0.1 =0

26 2.8 37.7 82.2

17.8 4.4 0.1 =0

38 9.3 17.5 47.8

52.1 32.2 8.7 1 .1

99 7.9 19.5 52.3

47.7 27.4 6 .O 0.6

24 3.4 33.5 76.9

23 .1 7 .I 0.3 =0

16 8.4 18.7 50.6

49.4 29.2 7 .O 0.7

20 8.9 1 8 .O 49 .O

51 .O 30.9 7.9 0.9

30 3.8 31 .3 73.8

26.2 9.1 0.5 =O

14 2.2 43.5 87.9

=O =O

12 8.9 1 8 .O 49 .O

51 .O 30.9 7.9 0.9

29 3.6 32.3 75.3

24.7 8.1 0.3 =0

4

-

West C o a s t Japan ( e a s t b o u n d

2s % ) ,

kf t

Altitude, Route

%

No

data

No data

12.1 2.1

GASP

8747 FLIGHT PATH

Observation n o . 1

Observation no. 2

Observation no. 3

TICl

=

Percent o f time in clouds during observation

1 =

T1l + T12 256

TIC,

=

Percent o f time i n clouds during observation

2

=

T21

+

TIC

=

Percent o f time in clouds during observation

3

=

'31

+

3

TIC4 = Percent of tiine in clouds during observation

TIC

PC€

4 = 0/256

T22 256 '32 256 =

0

Average percent o f time in clouds during a l l observations

=

+

Observation no. 4

T23

' '33

x

100

x

100

TICl + TIC2 + TIC3 + TIC4

-

TICIV E

4

3 Observations with clouds i n v i c i n i t y 4 Observations t o t a l T I C l + TIC2 + T I C 3 Average percent o f nonzero time in clouds during an observation =

Probability of cloud encounter in an observation

INTERRELATION: TICl PROOF:

Figure 1

f

TIC

=

PCE

x

-

TICIV

TIC1 + T I C 2 + TIC3 + TIC4

T I C 2 + T I C , + TIC4 . 2

4

.- Example of

=

=

0.75

x

2 4

-

i n t e r r e l a t i o n of T I C , PCE and T I C I V f o r a s e t of four observation periods.

=

0.75

DEC - JAN - FEB

HEIGHT OF TROPOPAUSE

CHART 136

( a ) Winter,

~ i g u r e2.-

The average h e i g h t of t h e tropopause.

( ~ r o r nr e f . 3 7 . )

MAR - APR - MAY

HEIGHT OF TROPOPAUSE

(b) Spring. Figure 2. - -Continued.

CHART 146

JUN - JUL - A.UG

-

Mean Height (in wwa)of the Tropopoure.

HEIGHT OF TROPOPAUSE

11

(c) Summer.

Figure 2.-

Continued.

CHART 156

SEPT

- OCT - NOV

HEIGHT OF TROPOPAUSE

( d ) Autumn. F i g u r e 2.

-

Concluded.

CHART 166

ffl

u

."0 L OJ

a

( a ) By l a t i t u d e .

D

J Winter

F

M

A

M

Spring

J

J Summer

A

S

0

N

Autumn

( b ) By season. F i g u r e 3 . - ~ i s t r i b u t i o nof cloud o b s e r v a t i o n p e r i o d s by l a t i t u d e and season. Shading d e n o t e s observation periods with T I C > 0 . Numbers above bars a r e percentage PCE f o r each i n t e r v a l .

0

28.5

33.5

38.5

43.5

48.5

kft

( a ) By a l t i t u d e -

> 15 BLO

15

10

5

0

5

> 5 ABV

kft

( b ) By d i s t a n c e from tropopause.

.-

Figure 4 is t r i b u t i o n s of cloud observation periods by a l t i t u d e and d i s t a n c e from tropopause. Shading denotes observation periods with TIC > 0 . Numbers above bars are percentage PCE f o r each i n t e r v a l .

w

40

-

30

-

20

-

10

-

0

a

Cr

c

6,

0

L a, CL

0

TIC

I

,

30 B t O

25

20

15

10

5

0

5

Distance f r o m t r o p o p a u s e , k f t F i g u r e 7. - Variation of global a n n u a l mean v a l u e s of cloudiness parameters w i t h distance from t h e tropopause

.

10 ABV

D i stance f r o m tropopause ( k f t )

----

5 - 10 below

00-

5 below

5 above

TIC, percent

Figure 8.- Cumulative p r o b a b i l i t y d i s t r i b u t i o n s of the values of TIC for the g l o b a l annual data set. P l o t s are grouped s e p a r a t e l y f o r all data and f o r data with clouds i n the v i c i n i t y (CIV).

Pressure a1 t i tude, k f t ( a ) Cloudiness parameters.

Pressure a1 t i tude band, k f t

0

20

0 CI

28.5 - 33.5

A

38.5-43.5

33.5 - 38.5

40

60

80

100

TIC, percent ( b ) Cumulative p r o b a b i l i t y d i s t r i b u t i o n . Figure 9.

-

V a r i a t i o n of g l o b a l annual mean c l o u d i n e s s with p r e s s u r e a l t i t u d e .

30

P r e s s u r e a1 t i t u d e

r -----

28.5 - 33.5 k f t 33.5 38.5

20

-

10

-

0

-

38.5 k f t 43.5 k f t

< 200 o b s e r v a t i o n s

0 , 80N

60

40

20

0

20

40s

L a t i t u d e , deg

(a) Winter.

L a t i t u d e , deg

(b) Spring. ~ i g u r e10.- Variation of average time in clouds with latitude and height for Northern Hemisphere seasons. Symbols are plotted where there are fewer than 200 observations.

Latitude, deg

( c ) Summer.

L a t i t u d e , deg

( d ) Autumn. F i g u r e 10 . - Concluded.

/'\ ' \

: ;I

0

J a n . , Feb.

Dec.,

-----

June, J u l y , Aug.

\

/ /

\ \

I

I 80N

60

40

20

0

20

40

60

L a t i t u d e , deg

Mar.,

- - - - - Sept.,

A p r . , May O c t . , Nov.

Latitude, deg

Figure 1 1

.- S e a s o n a l

symmetry of a v e r a g e t i m e i n clouds w i t h l a t i t u d e . Altitude = 3 3 . 5 to 38.5 k f t .

80s

D i s t a n c e be1 ow tropopause, k f t

A

-

n .

1 0 - 15

.

5

- in

L a t i t u d e , deg

( a ) Winter.

L a t i t u d e , deg

( b ) Spring.

F i g u r e 12.- V a r i a t i o n of average time i n c l o u d s w i t h l a t i t u d e and d i s t a n c e from t h e NMC tropopause f o r Northern Hemisphere seasons. Symbols a r e p l o t t e d where t h e r e a r e fewer t h a n 100 o b s e r v a t i o n s .

Distance be1 ow tropopause, kft

Latitude, deg

(c) Summer.

L a t i t u d e , deg

( d ) Autumn. F i g u r e 12.-

Concluded.

0

Winter Spring

70

A

Summer Autumn

TICIV

PCE

TIC 5

Pressure a1 ti t u d e , k f t Figure 13.-

V a r i a t i o n of c l o u d i n e s s p a r a m e t e r s with p r e s s u r e a l t i t u d e and Northern Hemisphere seasons a t 40°N t o 50°N l a t i t u d e .

5 < 0 (anticyclone) - - - - - - ->- 0 (cyclone)

20

40

60

TIC, percent Figure 14.-

Cumulative p r o b a b i l i t y distribution of TIC a t 0 t o 10 kft below t h e tropopause in cyclones and a n t i c y c l o n e s .

-----

a

< 100 d a t a

-----

z