Vol. 3 No. 1 A D V A N C E S I N A T M O S P H E R I C S C I E N C E S February 1986

A THEORETICAL STUDY OF MULTI-WAVELENGTH

LIDAR EXPLORATION OF OPTICAL PROPERTIES OF

ATMOSPHERIC AEROSOLS

Yang Shu ( ~ '~];)

Graduate School, Academia Sinica, Bcijing

Zhou Xiuji ( ) t f g J ~ ) and Zhao Yanzeng ( ) ~ _ ~ )

Institute of Atmospheric Physics, Academia Sinica, Beijing

Received September 20, 1984

ABSTRACT

Feasibility is investigated of multi-wavelength lidar exploration of size distribution patterns (SDP) and complex refractive indices (CRI) of aerosols in different layers of a stratiiied atmosphere, and an improved observational scheme is worked out for the optical parameters (extinction coefficients, angular scattering coef- ficients and their ratios) of the substance in layers homogeneous horizontally in optical depth obtained by a bi-~latic lidar system. Variations arc examined of these parameters versus CRI (whose real part is 1.33 1.63 and imaginary 0.00 -0.1) and working wavelengths (0.3472, 0.53, 0.6943 and 1.06 #m) in such SDP as Jt|nge--3, 4 and 5. The Deirmendjian Haze M and I.. A method is thereupon developed for retrieval of aerosols' SDP aqd CRI from these parameters and tested by suitable numerical experiments.

I. INTRODUCTION

Aeroso ls are of much impor tance to such p rob lems as e a r t h - a t m o s p h e r e heat ba lance

and cl imatic condi t ions on the globe. Their content a long with the physical and chemical

changes in proper t ies undoub ted ly brings abou t f luctuat ion o f wor ld -wide average t e m p e r -

ature, whose rise and d rop depend in a large measure oil their S D P and C R I in the

visible and IR bands. Fu r the rmore , aerosols play an unusua l role in air pol lu t ion , e s -

pecially in acid rain format ion , f rom indust r ia l sources.

F o r this reason, the physical /chemical proper t ies and the t empora l / spa t i a l pa t t e rns are

receiving more and more a t tent ion , and deve loped for the fullest poss ible in format ion on

aerosols ' features are a variety o f measur ing means, pa r t i cu la r ly the remote sensing t e c h

nique, which, as highly valued by meteorologis ts , has s t r ik ing advan tages of a l lowing

extensive sounding, nearly con t inuous acquis i t ion o f r e a l - t i m e observa t ions and no direct

sampl ing to avoid affecting the natura l state of the detected substance.

The remote sensing technique is o f two types. One is k n o w n as the passive t e c h -

nique in which character is t ics o f aerosols over the dep th o f the whole a tmosphe re are o b t a i n -

ed with the aid o f solar rad ia t ion , and the o ther the active one where sounding is carr ied

out by virtue o f artificial r ad ia t ion sources. The main a p p a r a t u s o f the l a t t e r is a l idar

with a laser genera tor as the rad ia t ion source, which has s t r ik ing a d v a n t a g e over the fo rmer

( u s i n g o ther types o f rad ia t ion source) o f very high spat ia l reso lu t ion (of tens to several

24 A D V A N C E S IN ATMOSPHERIC SCIENCES Vol. 3

meters), thus giving vertical profiles of observed parameters.

A major problem of concern arising in recent years lies in how to retrieve SDP and

CRI from the observations through remote sensing. Reagan et al. (1980) t~l indicates

that, by separate use of radiometers and a bi-static lidar system, optical depth of the whole extent of the air, the polarization of an angular scattering coefficient (expressed as the ratio

of polarized scattering coefficients on mutually perpendicular planes) at a selected altitude

and K (known as the ratio of the back-scattering to the extinction coefficient) are obtained,

from which the SDP and the CRI are re-established. Qiu et al. (1981)Pa shows that by investigating sensitivity of scattering coefficients given at various angles throughout the

atmosphere to, and their correlation with, CRI, a method is developed both for retrieving RI from scattering coefficients acquired at angles ( 9 0 - 1 0 0 ~ 160--170 ~ most sensitive to

its real and imaginary part, respectively, and for getting SDP by coefficients in the vicinity

of forward-scattering angles less sensitive to CRI. But both studies lack investigation of change in aerosol properties with height. Theoretically, Zhou et al. (1984) Dl makes further contribution to variations of K in different SDP, indicating the possibility of re -

covering the CRI from K. It is on this basis that the feasibility is examined of the

exploration of SDP and CRI of the atmospheric aerosols at various layers by means of a multi-wavelength lidar in the present work.

II. APPLICATION OF A MULTI WAVEI.ENGTH I.IDAR IN FINDING THE EXTINCTION COEF- FICIENT WITtl ITS RATIO TO ANGULAR SCATTERING ONE

For the visible band, now widely-used types are YAG and ruby lidars, their t rans-

mission and frequency-doubling wavelengths being 1.06, 0.6943, 0.53 and 0.3472 #m, se-

parately. Here discussion is focused on the features and basic sounding procedures of the extinction coefficient ~, the angular scattering coefficient F (0) and the ratio I." (0)/~. Ac-

cording to Qiu and with consideration of operational feasibility of lidars, our discussion is

limited to the cases 0 = 1 8 0 ~ and 160 ~ .

1. Optical Parameters Describhlg Aerosol Properties at Four Wavelengths

For the visible band, as a rule, CRI varies slightly with wavelength and on the assum-

ption that CRI m:=m~--hn i does not change with wavelength, we employ Mie scattering

theory to calculate c~, F (180 ~ and F (160 ~ (for the expressions see Ref. [4].) from such

SDP's as Junge-3, 4 and 5, Deirmendjian Haze M and L (whose abbreviated forms J-3, J-4, J-5, D-M and D-L will be used hereafter), and the calculation results are briefly examined.

Here, a set of expressions for the optical parameters are introduced

=! �9 c~, Q~, (rn , r ,Z~) .n(r ) rcrZdr, ( l a )

f l , ~ F , ( 1 8 0 ~ 1 7 6 ( t b ) r ( ~ )

7 , = F ~ , ( 1 6 0 ~ 1 7 7 1 7 6 ( l e ) J

K,=f l , / c s , , ( l d )

R,-:v ,I~, , ( l e ) where Q,. t and Q~ . denote the extinction and scattering efficiency factors, respectively;

the integrated domain for particles with the radius r is between 0.01--10 # m ; the

No. 1 A LIDAR STUDY OF ATMOSPHERIC AEROSOLS 25 i

subscript 5_ represents the electric vector perpendicular to the scattering plane and i

wavelength. ~ has the following characteristics based on calculations:

(I) At a given wavelength cl increases with mr; v in the J patterns grows with m,.; c~ in the D patterns decreases slightly with m; and the change of ~ with CRI is found to be

related to SDP-- the more the big particles in the SDP, the smaller its relative change would

be. (2) At a fixed CRL the relative change of c~ with wavelength in different SDP reflects

their rough forms.

And fl and "r' are characterized by the following: (1) At a given wavelength, /3 and }, generally increase with mr and decrease with ml

and, as a rule, their relative change with mr or m; are much greater than that of c~, par t i -

cularly when the SDP is abundant in large particles. However, the exception is worth noting here that the relative change of ~, versus m r is sometimes smaller, approximating

that of corresponding c~. (2) At a constant CRI, /3 has a similar trend versus wavelength to that of c~. In addition, with both wavelength and CRI fixed, c~ and/3 are sensitive to variations

of SDP. It can be inferred, according to features of c~, /3 and ~,, that (I) at a given wavelength, K and R show weaker change with mr than/3 and 7,, respect-

ively, but on this occasion R in particular sometimes exhibits an opposite trend while K

and R are altered in general more strongly with m; as compared with /3 and },, separately. (2) at a constant CRI. K varies little with wavelength.

(3) K and R are independent of the overall concentration of aerosols.

Therefore, there arises feasibility of using the combination of c~, /3, ~ and or that of

K and R to produce SDP and CRI of aerosols in the atmosphere.

2. Lidar Exploration of ~, K attd R

M o n o and bi-static lidars constitute the sounding system for atmospheric aerosols.

Except the case of the samll scattering angle, the lidar equation has the general form

V ( r ) == C~ -J '~ ~ a~(r ' )dr ' . 7 ( r ~ , O ) . e - f ~ ' ~ ( r ' ) d r ' . . . . . - . . . . 0 ( 2 )

r~ s in: . . . . . 2

where V(r) is the voltage of echoes, CA the constant of the system, subscript 1 (2 ) r ep re - sents the transmission (reception) optical path, e. g. r, (r~) denotes the distance between

the transmitting (receiving) system and the scattering volume, and ~, is the scattering coef-

ficient of the volume. A mono-stat ic lidar has its emitting and receiving sets at the same site and both optical

paths well coincide in the sounded area with 0 = 180 ~ From Eq. (2), therefore, we obtain a

lidar equation for a single station

V ( r ) = CAri_. /3 ( r ) ' e -Z[ ~oa(r')dr' = - r -~--Ca . K ( r ) . c r ( r ) . e-2fo a(r')dr' , ( 3 )

where /3(r) /cr(r) :~K (r) is used in the operation. Obviously, K and cr can be determined by a mono-stat ic lidar but R only through

a bi-static system. Determination of g, K and R at the layer (Z2~Z, ) is dealt with below.

26 ADVANCES IN ATMOSPHERIC SCIENCES Vol. 3

( 1 ) Determination of o and K

In general, vertical profiles of (r and K obtained by use of a mon~-static lidar are de termined by angle--scanning measurements on the assumption that these parameters are

horizontally uniform. Zhao et al. (1984) L'l proposes methods of integration and ratio to

effectively eliminate the small-scale ttuctuation of the optical parameters of the atmosphere.

thus acquiring vertical profiles of cr and K with higher consistence and reliability, for exam- pie.

The aim of the present study is to explore c,, K and R at different layers through iidar

sensing and the integrated processes are included in the assumption to wipe out the fluctuation.

Therefore, the assumption of layers having horizontally homogeneous optical depth presented by Zhou et al. (1981)tq is employed, which states that for any aerosol stratified layer with

Z~.--ZA being deep enough (Z,, is the top altitude and Z , the bot tcm height of the layer),

i . r B _ Z BeSC a i the equation zB c s ( z ) d Z = s ina / ~Jt r ) d r holds, where a is an arbitrary eleva--

. Z A ~" r l--Z-- , l c s c a " .

tion angle. This assumption is also used in ti~c subsequent derivation of R. For the stratified layer with Z , - - Z , obtained from N elevation angles. Eq. (3) can be

rewritten as

V~(r)-'~ U, t r . r ~ K ~ ( r ) . ( ~ C r ) . e 2I[;cr'(r')dr' (.:[ h C A " , .

Integrating V,. over the range of Z o - - Z , . we have

!- . . . . " I r 2

! ~e~'~ g i ( r ) d r ~ K ! ~ ,e eJ'0~*,(r')dr' dr r t - = z l e s c ~ z I . r I

K :-~ �9 , . Z : ) ) , 3 ( 5 ,, L ( 7 " ( Z , ) ) . . . . . . ; - - ( 7 . . . . ~ . . . . . ,

T(ZD=:-e-J'~~ with n - - l , 2 and i - l, 2, ..., N. where transmittance

( 2 )

I f the angle-scanning method is used, K and T (Z,) can be specified, which leads to

1 l n ( 7 " ( Z , 3 / T ( Z o ) ) , / - . . . . . - �9

(~=- 2 v Z : - Z , ) " " -

B : : R ' ~ . ( 6 )

Determination of R through sounding

R is acquired with a bi--static lidar, as shown in Fig. I . A is lhe transmitting system,

V(r 2 ) dr~ . . . . . . sin a~0 . C' , s in ~ Oo

2

1 �9 R ( Z , O o ) ' e -tC . . . . , o+ . . . . 2o>f~(z ' )<lzq'crCZ)dZ, ( 7 ) Z 2

from which beams can be considered to be parallel, and B is the telescope-receiving system

having the viewing angle 2..Xa with elevation angles, transmitting and receiving, being a.0 and a,.0, respectively. The mean value of 0 is 00.

Following the bi--static formula (Eq. ( 2 ) ) and with " ? ( r 2 , 0 ) = R ( r 2 , 0 ) . ~ ( r ~ ) we have Eq. (7) based on the assumption of horizontal homogeneity of optical depth of the layer when Aa is small:

No. l A I . IDAR S T U D Y O F A T M O S P H E R I C A E R O S O L S 27

_ _ i

1

L L

Fig. 1. The disposi t ion o f bi-s ta t ic lidar.

- - - - - Z0

Z.'I

and, by se t t i ngp :=csca ,0+csca~0 and taking the approximation e-J'z~c~( z ' ) d z ' :=e-~z-z , ~ we have the following by performing partial integration

P " ~ i n 2 g') i r22:-z2 . . . . 20 f" e V(r2)/C'A.dr2 / , ! [ / , , , ~ v , [ 1

! ~2 2 , 7 7 " P ( Z , ) ? - " (1Z ' - - - - - " 2 - ' ~ z~ Z i- e-P'a(Z-Zl~" _: Zz

I r22 where all denominators can be found through ~ and ~5 and I/(r.,)dr2 is nothing more

than the integrated voltage value of scattered echoes in the angular range 00-:_, Aa within the layer Z.,--Z, detected by the telescope-receiving system. The scattered echoes outside the layer are not taken by it as planned and they are measured by photometers instead.

Taking the effect of atmospheric molecules from ~, ]s R and ~ obtained via sound-

ing gives their averages designated as csp,, K p , , t~p~ and flp~ in the layer Z,_--Z,, where i== l, 2, 3 and 4 denotes a variety of wavelengths. These averages are principal measurements for getting SDP and CR[ of the atmospheric aerosols.

III. R E T R I E V A L O F S DP A N D C R I

This section deals with the inversion of the SDP and CRI from basic measurements mentioned in II, in which equation system (1) can be referred to as that for remote sensing. For such recovery iterative performance is used based on analyses of these parameters made in the previous section. The steps are as follows:

(1) to assume the initial CRI ,n C~ and the SDP n c~ (r); (2) to restore the SDP, with nr ~ constant, by Eq. (la) or (lb), giving n ('~ (r) through

n(~ (3) to reinstate the CRI, with n ('~ (r) fixed, by means of Eqs. (ld) and (lc), thus

producing m (~ by mC~ (4) to repeat steps (2) and (3) N times until m (u~. and n!.w (r): satisfy necessary accuracy

211 ADVANCES IN ATMOSPHERIC SCIENCES Vol. 3

l rn ~N~--rnc~-'~[<e: and J" ~,n(N>(r) -n (U- '~ ( r ) l �9 d r < e , , respectively.

The retr ieval steps and analyses are detai led in the subsect ions.

I. The Retrieval Method o f S D P and Their Object Functions

King (1978) tT~ and many o ther studies demons t r a t e tha t the re ins ta tement can be a c c o m -

plished in terms o f opt ical dep th as measurements . Wi th the a id o f Eq. (6) and on the fact

that K varies slightly with wavelength as ment ioned in 1I it is found a p p r o p r i a t e that the

retr ieval o f SDP at a certain laycr is car red out by vir tue of cr or ft. On the o the r hand,

since the assumed m ~~ is to be used as the initial C R I in der iving n~'~(r), the sensit ivity

o f cr and /3 at four wavelengths (denoted as (cry} and { f l ; } ) to the C R I needs to be

�9 examined. Therefore , curves o f specif ic-values {cry/or,} and { /3 j /3~) (each has two lines tha t

oJo~ M#'

1.5

I.C

~-~'~ 1.5

�9 0.,~ " i . ~

1.0

J--3

0.5 t.O

, , /o, 3. ~ ~.0

[. t.0 0.5 1 .~ 0.5 1.0

01o4

I (7~04

0.5 1.0

0.5 1.0 2 ( l a x n ) '

10 /~,/B,

~ 7 4

] - - ,

0.~

0.5 Io0

D - M

...._--0.5--------- 1.0 ,l~lam)

Fig. 2. The curves of ratios {a,/o,~ and {flf/fl,~ for var;ous SDP.

No. I A LIDAR SI-UDY OF ATMOSPHERIC AEROSOLS 29

are farthest apart of all) are illustrated to show the conditions of {~J;} and (fl ;} in various S D P at the CRI (1.33--0.0i, 1.63--0.0i, 1.33--0.1iand 1.63--0.10. It is apparent from Fig. 2 that (1) { c~,/0, } curves in J types have diverse directions in curvature from those in D patterns

and (2) in the J-3 and D-M types with abundant big particles, { ~ / ~ , } curves are less sensi- tive to CRI and neither are ( f l J f l , } ones in J-5 with more smaller-sized particles. Both types o f curves in the J-4 pattern have similar features. As for the D - L type which is narrow-

shaped and deficient in large and small particules, its ( o , / a ( } and ( f l J f l , } curves change remarkably with CRI.

From the above it is appropriate to make use of { ~ ; / ~ ( } or {fl~/fl~} to get SDP. The object function with (Gp.} as measurements takes the form

t = 1 i = 1 \ CIPi / fJPI ,1 /

"where the CRI of ~Jpi is m* and {a~} comes from calculation with the assumed CRI to be rn c~ Likewise, the object function with {flo~) as measurements is in the from

- 4 - 4 . . . . . . . . . . . . . . .

(lO

in which denotations of {flp~},{fl~} and corresponding CRI are as given in the expression .of f;~. In conducting retrieval of SDP an object function less sensitive to CRI shouId be

picked out, depending on the features of ratio curves of ap and tip. In order to facilitate retrieval of both J types (n(r)=--Cr-") and D types (n(r)==:

C,..rC-'exp ( - -C3 x / - r ) ) , the SDP is given as

n(r lZ, ,Z~,Zs)-- -=Z,rZ2exp(- . Za ~ / r ). (11 )

The inversion is done through fitting all the parameters Z{ ( i = l, 2, 3). The procedure is as follows:

(I) The choice of J or D distribution is made to specify the initial state of SDP from the curvature of a t ratio curves and the initial distribution parameters arc denoted as .Z', ~ (i=~ 1, 2, 3).

(2) The size distribution parameters Z~ and Z , are put into fitting to minimize f;; or f~, while Z. and Z , in this situation are written as Zi '~ and Z~ '~.

(3) (crl ~} (or {fl~')}) is figured out from n(r;Z~% Z[ ~, Z~')), which leads to Z[~)=

Z}o~ . . . . 1 crpi/al ~) (or Z~')---Z~ ~ �9 1 . ,~,,'Tt'> Z~ ')) is 4 ,=, - i ~a,:. flt'i/fl~'>) Then n ( r ,Z~ '~,

denoted as n")(r ) . It is worth noting in particular that the retrieval fidelity by Z~ ') is dependent not only

upon that by Z, ~) and Z~ '~ but also on the difference between m ~~ and m*. Only when m* is quite close to its truth value does the specified Z[ u~ approach that of its own, Z*.

2. The Retrieval Method of CRI and the Object Function

Discussion of {K~} in II shows that {K~} plays a constraint role in finding out m, .and m~, implying that, given m, (m;), m; (m,) can be determined by {Is with greater precision. It should be noted that, in view of the fact that {K~} changes quite little versus wavelength,,~it seems impracticable to have m, and m~ concurrently through (K~}

.and, in this case, additional measurements are required. It is naturally of interest that, if CRI can be inverted from { cr~ } and { K ~ }, measurement

30 ADVANCES IN ATMOSPttERIC SCIENCES Vol. 3

can be performed with a mono-s t a t i c lidar. Unfor tunate ly , since n(:~(r) has to be employed

as a SDP to get m (n, the parameter Z} ~ is clearly affected by the initial m ~ as noted in III .

Besides, the sum of relative errors of four cr~ ( m = m C~ and corresponding crib.; ( re=m*) ,

has been minimized in evaluating Z~ n. Therefore, when CRI is obtained through the use

of n~'~(r) as a SDP, m ~~ approaching m* tends to increase the sum of these relative errors,.

thus leading to the growth of n-agnitude of the object function made up of{cry} and {K,-} .

If C R I is recovered from K and F (0)/or, its corresponding object function is no longer

affected by the size distribution parametcr Z, characterizing the overall concentra t ion o f

aerosols. The selection of scatter angles is examined below to find an optimal one for CRI

and sounding operation.

In Mie theory the relationship between scattcring cocfficients F (Z, O, m) and the CR1

m is rather complicated�9 It is therefore appropr ia te to nun=erically investigate the change

in sensitivity o f F (0) to CRI versus 0.

Suppose

d F ( O ) 1 OF(O) drn, _z_ 1 c3F(O) .drn~ =Szed~n~+S,drn~ (12)2, - V ( O ) = F--(O) . . . . o , n , ' I~ '~0) o r e ,

and, according to Ref. [2], Su and S [ arc referred to as sensitivity functions.

. i

. . . . . . . . . . . _ _ . . . . . . . . . . . . . . . . .

�9 i f l 0 ~

- - ' - - - ~ . . . . . i 4 ! i - - - - - - - - 1 8 0 " b '

! b '

Fig. 3. The variations in sensitivity of F(0) to CRI versus 0: (a) SR vs. 0, and (b) $1 vs. 0. Curves 1 for D--M; 2, D-L; 3, J 3; 4, J-4; 5, J-5. ).~0.6943 #'n and m:- l .51-0.0l i .

No. I A LIDAR STUDY O;.: ATMOSPHERIC AEROSOLS 31

Because polarized light transmitted by the lidar at work is normal to the scattering

plane, curves are shown delineating sensitivity of I:2. (0) (with 0 in the range of 106 to li:0 ~)

to CRI , as depicted in Fig. 3. It is apparent that

(1) in the case of 0, : 18@', Sa, and IS , '. are large enough to ensure that K is a stro;:2c:"

constraint between m~ and m . ;

(2) when 0 = 160 ~ , S,; becomes very ';mall but !S~ i even greater a~d in this situation.

like .Acr /Am~, .S'ze gets smaller with increasing the number o f big pa,'ticles; conside:i,<~

the variational trend of (7 and o? with CR! mentioned in IL we may cor_.clude that, at a fi,:ed

wavelength i t?~ : : ~ ' . increases in much less magnitude with m~ than it decreeses v. iJ~ ( O" i .J

nh and, when m~ is smaller, R~ diminishes as m, grey, s; obviously, {j?~} is sensitive t~.,

the imaginary and insensitive to the real part e l CRI , and

(3) if 0=. 120 ~ , S~e gets larger and iSz i smaller, but they have poorer sensitivity in this

case than when 0 160 ~ and the acconlplishmev.t o f observation is more difl]ctdt as vc!!.

Therefore, the retrieval o f CRI of aerosols caa be made by using { AT,~ ::qd {17~) as

mc.asumments. The object guncdon tJkc-: t~,c: f::r,., = i- -- J / Je, , , , . . . .

f " ' = 2 ~ i C r . ' " ~,),,~ _!J " ' . . . . )

wherc {/<p ~} and { 1~:. i ) ar,.." m,:asureme.~:;5 q:.d { :,( ~ j- and .{/< }- c~'ictilatcd ', ;.,its,:..,. To s:F, ced

down change of th~ o,'_'jccL i'[:i,'ctioi~, with X~ and rm/:c apprirel!t ![:" chan2.e ,aith { l ' ; . i } thc weJght;n 2, factor 14/-=0.5 ['5 i:.,troduced into this t:i:mti:.;,'L

Fig. 4 sho,vs isoplcths ,)r f , , in relation to C,:~ i~ vark,~;s Sl;:i >. l~ ;*; c],.:~:;' i;-~I{ vii

object Function,; are of higher cfl'ectiven..~ss except t.,~" the J 5 t-'pc. Also, the ;;;-,,.,~li: el'

m~, ~ will reduce the scnskivity of these functio~:,s.

Calculations and analyses indicate t;:at f,,, h~:s :~ cc:":air am,,u:: t ._T im;~:r;sith;ty to

Si)P, th~:s primarily ,.m:<:cing the iterative operatic: , [\>v ,-.y:rie'<~i.

Inv-wsion step:; el" CXt are described as ~..c ,.~,,,.,_, ....

(I) n(')(r) shoa.n in Ill is used as the SDP f<r ti'.. TM" r c i :b . a ! . ,.'~itla m (~ ::~ 11::: i,','~1:'._5

CRI.

(2) DL~ring rctricwfi o '?cmtion a s tep-by stc~ me!!;oJ is app[i~:d. The stc~ ;,::ngfl~ oi ,-:,'

is . \ m - a ~ . m ~ - i - i ~ , ' . . . :\n:~. \"alL'c- t:ti',C:! i7! i'A.r:l 2C; ~, 011',.] :"i a rc i i ) - !Jcqted in [i!C i'L'l](?\V!!~g

table. The work goes on tii; j ' , gc~s :-;~;i-'4a!.

S t c ? I 2 3 .I

~., i , !/2 o

dl 1 l 0 1/2

(3) The CR! just obtam.ed is dcn3ted ~':; ,,'-~ ' by which n<~(r) is derived.

3. Res:dts f r o m Nu.;mrica! s wit,': Ti:ch" Ana lyses

In the numerical experiment the trutl, value of C R I is designated as m* and to

32 ADVANCES 1;'.1 ATMOSPHEI?,IC SCIENCES Vol. 3

( cr ; (m*)} and {K, ( m * ) } is separatdy added 5% and, to { f l ; ( m * ) } , ~ 1 0 % , random error of Gauss distribution. In view of more assumptions and approximations introduced into the derivation of R, %1:)% stochastic error is put into {R~(rn*)}, which all come f rom the randomizer in computer. Subsequently, ( c r i ( m * ) }, { K~(m' : : ) } , ( / ; ' i (m*) } , and {/?~'m*)} with added errors arc used as measurements of their respective object functions.

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23".7 32.7

13".7 \ 30'.6

/ :,-<4 \ ~ 1.4.9 / \<_j 8.6 ~ l l . ~ 28',. 8

47.(} �9 29.3

66.2 33.7

67. I

63.2

60.5

i~8. !t

59.2

54.2

50.8

48.8 40

47.8 58.1

47.1 57.7

46.3 56.8

.5 55.0

51.6

30.8 39.4

(b) 0.02 ml 0.04

~.33!38.5

1 i tie

I t68 I , 225 I

:ei7

t95

2i9

1"63 t 3 i 4 0.0

aL,i'\ 5~. 3 7o. 1 \

2 9 : 8 ~ 52..3 65.2

2,1.6 ~, 4~'.2 61.6 \

:,.i. :.: \.,.:,,. !j 59.1 \

,A: ' : , 1 " 2 \,il.{~ 5 " / 1 [ \ \ ' , ,

! \ @ iL3 .2~ ~"9'tJ 5,:.0

. ,~g \

/~-J i i

~ .'"/:r,6' 5~.(~

;" 3 } . ~ \ 56.,;

4 8 : 2 ~ 3 6 . 5 ~ 2

67.7

76.4

72.7

69.8

67.8

66.2

(;4 .,~

63.2

61.2

58.~

5! .(:

36.3 41.3 �9 !'. ," {c? 0.02 0.04 m~

' k3~r I E ~ " " . i ~ ' " \ v9 x 43 U

31 i0 ~2;~. ] :I'i 7 ,I 7.8 �9 / \

41.9 "20.8 3:;.4 43.7

5r.<( 3i..7 Z x,

I \ \ ~ \ S,. "> I \ ,,\ :, L ~-'~ \20.0 ~,;.:~ \ \ ,'.' \ \ \ :~1.'3

5} 5 , 9.1.9 \I ;J .G\ '2,j o

p6., ,9.5,, 1 63~d1 . \ . \ �9 j , 39.9 14..3 14.3

.52. 8 ' ' '?

54 .7

5 i .0

47 .~

45.1

42.4

39. (;

3?.7

2g. 3

23.3 0.0 (d ) 0.02 m~ 0.04

No. 1 A L1DAR STUDY OF ATMOSPHERIC AEROSOLS 33

Fig. 4.

m, " 30".3

"1 16~3

=7.8

1.4~ 19~3

i 4 .6 1 19.0

5416

1.6316oi

5t .1

45 .4

40.1

35.3

30.7

26.4 20

62 .5 69".6

57.6

1 3 " . t / 4,.,'. 5

8.94 3 44".z

N' ,~o]z 5~0 z

\ / i22.2 36.2

20. I 6.06 2~. 1

65".4

61"2

sf.2

53.3

49,6

59,4

42.2

38.5

34.8

31.0 0.0 ( e ) 0 . 0 2 m, 0.04

Object functi,m fm in rclation to CRI in various SDP: (a) I ) -M, (b) D-L. (c) J--3, (d) J-4, and (c) J-5.

Results and analyses are given as follows:

(I) t77" -1 .51-0 .01 i and mr176 1.40--0.03i, 1.60 -0.0i and 1.60 -0.03i are

t:tkcn for retrieval at different SDP. Th~ results are summarized in Table 1, ~hzre Z*=: (Z*, Z*, Z,*) are the truth values of the distrib~:tion paraineters. The following is obvious.

1) The Iinal retrieval restllts of CRI are generally independent of" n. ~~ except the results

from the J-5 pattern. 2) The final results of the distribution paramet0rs show that Z~ ~) especially in the narrow-

slzancd type like the D-L one, differs significantly from its truth value, which, as indicated

in Ill, originates From the retrieval errors of Z~, Z:~ and CRI that exert influence upon Z,.

In addition, seeing that (cry} in the D-L type is more sensitive to CRi than that in others

but the J 5 pattern, the iterative pertbrmance has to be one step more.

3) Z ('1 obtained by use of the object function f~ in recovering the J-5 and J-4 typcs

have great discrepancy from their truth values, but since the object tklnction f,, used for

CRI has nothing to do with the overall concentration of aerosols, the difference in Z <t) ob-

tained has r.o influence on retricval of CRI, which has been confirmed by thc retrieval results

tYom J-5. (2) As far as D-M and J-4 are concerned, #n<~ 1.51- 0.01i and m* = 1.40--0.005i,

1.60 0.005i and 1.50 -0.05i are used for reinstatement. Rclative errors from superposition

t]?<,.m'.) = are ~ 5 , :~- I0 and ~ 10/o , respectively. Retrieval of (cri ' )n*) }, ~tzx. . . . . cm":" "~;~ and . . . . . ':'~ "/ results are summarized in Table 2, which indicates that, as the superposition error of (K~}

increases, CRI, particularly its real part, shows poorer precision, thus making the error of

Z[ 'v> even greater,

A D V A N C E S I N A T M O S P H E R I C S C I E N C E S V o t . 3 34

" l 'able 1. 'Yhc RcsLdt:~ o f N u m e r i c a l K x p c r i m e n t s f o r V a r i o u s S D P (1)

1. | : o r .I:_L};e 5 ( , 3 * = t 0 • ~ 5 . 0 , 0 . 0 ; m % = l . 5 1 - - 0 . 0 1 i )

: L a l V a l u e

2 . 0 ;.', .] 0 '~

� 84

0 . 0

,, 'o,(,')-~n(,~(r) . . . . [ . . . . . .

f~ i m{';

1 . 5 0 1 7

3.39~ - 0 . 0 0 9 6 6 i

1 �9 ,1987

3 . 2 2 2 - - 0 . 0 0 9 7 5 i

tnr J ) Z ( ! ) :

. . . . . . . . . . . i 1 .40 6 " 4 7 X 1 0 4 i

- - 0 . 0 3 i - -5 .075

0 .0 i

1 . 6 0 2 . 9 1 >~ 10 -~

- - 0 . 0 3 / - - 5 . 0 6 3

0 . 0 m

E

m ' .... m ( , ! n ( ' ) ( r ) -)n c'~(r)

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

f., Z '~) f{l r

3 . 6 . 1 / . . 10 TM i

5.222 ! -5 .o63 3 .572 0 . 0

3 . 5 8 X l 0 - ~ I

5 . ] 1 2 - -5 .063 3 .58 ~/g

0 .0

3 . 2 6 X 1 0 4 :

- 5 . 0 5 0 3 . 3 5 ~

0.0

4 .56 "< 10 -4

6 . 2 9 y~5 - - 5 . 0 5 3 3.5.1 ;-~o

0 .0

1 . 6 0 2 . 1 7 ; 1 0 '~ 1 . 5 4 1 8 :

-O.OOi - - 5 . 0 0 1.88~% -0.01161 ,1 .96~ f

0 .0

1 . 4 0 5 . C a 4 1 0 -~ 1..1511

--O.OOi - 5 .053 3 . 5 2 2 - 0 . 0 0 7 7 8 i

0 . 0

2. F o r J u n g e - 4 ( Z * = 3 . 0 x 1 0 - ' , - 4 . 0 , 0 . 0 ; m * : - l . 5 1 - 0 . 0 1 i )

( a ) r e t r i e v i n g n(r ) b y f~f

In i t i a l V a l u e n ( ~ , n ( : ) ( r ) m ( ) ) - , m (~)

Z(!:)

10 ;< 10 -z

- 2 . 0

0 . 0

ytl(C ) Z (I)

! .40 2 . 9 7 .< 10 -a

0 . 0 3 i - - 4 . 0 9 4 i

i 0 . 0

1 .60 2 .24> . :10 :~

- - 0 . 0 3 i .... t .075

0 . 0

1 .60 2 . 4 9 ; < 10 :~

- -O.OOi - 4 . 0 5 0

0 . 0

! . 1 0 3 . 6 5 x 1 0 :~

- - 0 . 0 0 i - .t ,025

0 . 0

f ',~ m ( ~ )

1.50.10

4 . 2 0 ~ - 0 . 0 0 9 1 9 i 5 . 2 3 ~

i ,5062

4 . 1 1 ~ - 0.00825i

I n ( , , ( , . ) , n ( 2 ) ( r )

f ,, Z (2) f;~

: 2 . 8 0 X 10 -a

4.056 i ,1 .09~

0 . 0 'I

; 2 . 7 7 " < 1 0 a

~ . 7 8 ~ -4 .062 4.10%

0 . 0

2 . 7 8 X.10 ~

5 . 0 9 2 : - - . i . 0 5 0 4 . 1 0 2

0 . 0

2 . 8 1 "< 10 -z

5 . 1 0 ~ ~ - 4 . 0 5 6 4 . 0 9 2

0 . 0

1 , 5 0 3 8

, 1 . 0 8 ~ - - 0 . 0 0 3 7 2 i

4.zz2

l , 5012

- - 0 . 0 0 8 8 1 i

N o . I A L I D A R S T [ q . ' : Y OT: A T M O S P t q E R 1 C A E R O S O L S 35

(b) r e t r i e v i n g n(r) b y f~ '

In i t ia l V a l u e

Z(c) 712(0)

J .40 1 , O : / I O :~ - - O . 0 3 /

J

"5.0 . . . .

1 . 6 0

i -- 0 . 0 3 / : 0 . 0

,7"X r) , n ' ' ( r )

8 . 1 [ : , tO

-- 4 . 0 8 7 5 �9 38 #,/,

0 . 0

2 . 6 9 >: 10 ~

.... 1.050 5. z3 %

0 . 0

In i t i a l V:Hue

/ ( c ) 7/1(u )

1 .60

1 ' 0 '< l0 '~ i O.OOf

- - 5 . 0 I . 40

0.0 -O.OO/

n(o,Cr) * n ( ' ~ ( r )

Z '~; f;i'

9 . 7 7 ; < 1 0 4 j

- - 3 . 8 9 7 a 2.05~d o.9 i

3 . 9 9 " < 1 0 3

- - 3 . 9 3 8 4 . 5 ! %

0 .0

3. F o r J u n g e 3 ( Z * = 0 . 0 1 , - 3 . 0 , 0 . 0 ; m * * : l . 5 1 - 0 . 0 1 i )

In i t ia l

Z (~)

1 .0.'< 10 3

4 . 0

n(O)(r) , n ( ,~ ( r )

Z~:, f ,;

I .020",," IO 2

�9 2 .90 1.12~ 0 . 0

l . '~8,'4

i V a l u e

rr /(0)

1 . 4 0

- - O . 0 3 f

1 .60 9 . 4 7 3 " : 1 0 a - - 2 . 9 5

0 . 0 3 / 0.0

1.60 9.,119.:.10 3 -- 2 .95

-O.O0i 0 . 0

1 . 4 0 1 . 0 1 8 " ' I 0 : 2 . 9 0

O.OO/ 0 . 0

o.o 1.53%

i 1 5 % . , /

t?l(:1) >1/2( :~

m ( ; ~ f , ,

t . 5 0 8 7 :~.51%

- - 0 . 0 0 9 6 6 i

1 .5086 3 . o ] . o ~

- - 0 . 0 0 9 8 4 f

1 . 5 0 9 1 3 . o 4 y/,

o .oo98 .1f

1 . 5 0 6 8 3 .74%

- 0 . 0 0 9 6 6 f

n : " ( r ) -,n<'-X r)

Z ( ~, f :

9 . 7 6 3 / 1 0 ~ - 2 . 9 2 8 1 . 0 9 % O.O

9. 175 y l0 '~ 2 . 9 2 8 I . 0 9 ~ O.O

9 . 7 6 1 : < J 0 3 2 . 9 2 8 1 .O9y/o 0 . 0

9 . 7 7 0 <10 "~ - 2 . 9 2 8 1 . 0 9 % 0 . 0

4. F o r l ) e i r m m ~ d j i a n H a z e M ( Z * - - 5 . 3 3 3 " - . 1 0 2 , 1.0, 8 . 9 4 4 3 : m * - l . 5 1 - - 0 . 0 1 i )

In i t ia l V a l u e

g ( ~ )

5 >4 I 0 3

2 . 0

12 .0

?11 (0)

i . 40

- O.03f i . . . . . . . .

1 .60

- 0 . 0 3 i

1 . 6 0

- O.OOi i

1 . 4 0 I L

- - 0 . 0 0 i i

. . ' ; ; (r) *n<'~(r)

Z") f~

1 . 5 2 2 • ~ i 1 .O 6 . 6 4 / ~ 7 , 6 2 5

8 . 426 • 102 i :0 i 6 . 9 8 % i 9 . 5 0 0 I i

9 . 2 0 5 X 1 0 : 1.0 6 . 4 5 ~ 9. 025

2 . 1 8 6 x 102 1.0 7.02% 8 .00

f l l (0) ~?n (1)

1 . 5 1 3 4

---O.OIO0i

L.5039

- - O . O l l l f

1 . 5 0 8 6

- - 0 . 0 0 8 7 2 i

1 . 5 1 3 4

- 0 . 0 0 9 9 4 i

f ~

i2 .9%

1 0 . 4 %

i !

lO.0%

J

io.7% I

nr

z , : , f:: .~.

4 . 9 3 x IO ~ 1.0 7 .28% 8.875

5.51 A 10 ~ 1 .0 7 . 2 3 y/o 9 . 0 0

5 . 5 0 x lO e 1 .0 7 , 3 3 ~ 9 .00

5 . 5 1 X I 0 : 1 .o 7 .28% 9 . 0 0

36 A D V A N C E S I N A T M O S P H E R I C S C I E N C E S Vol . 3

5. F o r l ) e i r m e n d j i a n Haze--l . (Z* . 4 . 9 7 • 2 .0 15.1186; m* 1 . 5 1 - - 0 . 0 1 0

i m( 1)-> re(z) In i t i a l Va lue

Z ( ! , ) r e ( o )

1.40

5 . 0 x 1 0 a

1.0

12.0

n(O)(r)-+nO)(r) m(a '~m (~) i

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

,7(I) f~ mr

2 . 3 1 7 • ~

2 .0

- 0 . 0 3 i 13.9,1

1.60 1.186"<104',

2 .0

- 0 . 0 3 i 16.50 t

1.60 1 .163•

i 2 .0

- - 0 . 0 0 i 16.50 _. ' . _ _

1 . 1 0 2.106;< 10 ~

2.0

--O.OOi 13.8,1 i

I

f ,,, i Z(~)

,1.71o~

: 1.5101

n ( ' ) ( r ) - . n ( = ) ( r )

Y :

i 6.166 X 10 ~

.~ 6 6 # 2 . 0 3 . 9 7 ~

- - 0 . 0 1 1 7 i 15..140

1.5072 6 . 0 8 3 • ~

4.19/~ ' 9 .70~

i - - 0 . 0 0 6 5 6 i '

1 .5059 !

~.13~

3 . 9 8 ~

i n(')(r).->n(3~(r)

- - 0 . 0 0 6 3 8 i

1.5078

- 0 . 0 1 1 1 i

i ! z,3, . . . . . ! . . . .

b

f~

a

1.5123 ' 6 . 6 0 7 • 10 4

2.0 3 .84%1 15.33~ 2.0 3.94% t I i

15.422 i-- 0 .00891 i [ 15.-t22 I

3

5.897."< 10 ~ 1.5117 6 . 1 3 9 X 104

, 9 .7 '1~ i 2 .0 i 3 . 8 5 ~ 5 .11~o 2 .0 ;3.92~ , I

15.375 ' I i -0 .00895i l 15.438

i i 6.016• i0 ~

6 .17ya 2 .0 3 . 9 6 ~

15. =103

T a b l e 2. The Resu l t s (,t" N u m e r i c a l l- .xDcrimcnts for V a r i o u s S O P ( l l )

1. Fo r J u n g e - 4 (Z* 3 .0 ,~10 % - 4 . 0 , 0 .0 ; tri ~,~ 1.51- 0 .01i)

In i t i a l Va lue

Z r i )

0.01

3

0 .0

, ~ ; ( r ) , n ~ " ( r )

Z c:) f;~

3 .368X 10 a 1.,1800

--3.950 g.63%

0.0 - 0 . 0 t a a i

2.364;< 10 '~ ! . 4 4 0 6

1.056 4 . 3 8 ~

0.0 - 0 . 0 0 7 4 7 i

i 2.999>r 10 "~ 1.6365 i

-4 .094 9.01~-g

0.0 - - 0 . 0 0 8 6 9 i

m ( I ) > i n ( ! )

m e : ) f,,,

6.71/~

6 . 5 2 ~

n ( , ~ ( r ) - > n r

Z~:', / ; i

3 . 2 4 7 •

- - 3 . 9 6 3 8.,16%

0 .0

4 , 9 2 1 • s

--1.056

0 .0

2 . 5 0 0 X 10 ~

- - 4 . 0 9 , 1

i 0 .0

T r u e V a i t l c

W/*

1.50 0 . 0 5 i

I

,1.92% 1 . , 1 0 - - 0 . 0 0 5 i

I

9 . 0 2 ~ 1 . 6 0 - - 0 . 0 0 5 i

N o . 1 A LIDAR STUDY OF ATMOSPHERIC AEROSOLS 37

2. For Deirmendj,an llaze--M (Z*--5.333y10-', 1.0, 8.9443; ~,,(o) 1.51 -0.01i)

l n i l i a l V a l u e

Z(o)

5 . 0 • ~

2 . 0

; r r i (9) , . t r l (~ ) n ( ~

f :,~ m ' , , ) f ,,, Z")

1 . 1 7 - 1 • ~

1 .0 .1.12~o /

9 . 8 7 5

I �9 783 :< 10 ~

1 . 0 4.105~g

] 0 . 4 6 9

2 . 2 1 5 :,": 10-'

1 . 0

8 . 2 5

1 2 . 0

1.5072

3. [9~o /

.... 0 -05 l,li

1,4275

0 , 0 0 3 5 3 /

i . . . . . . . . . . . . 1 . 5 9 7 t

5.59~o f

--0.00531 i

nr True Value

9 . 5 2 X 1 0 a 7

1 . 0 4 . 1 1 0 ~ 1 . 5 0 - - 0 . 0 5 i

9.59.1

8 . 9 9 "-'. 10:

16.7~ 1.0

9 . 5 9 4 i

. . . . . . . . . . [

4 . 9 6 • 102

8. t S ~ t .0

8 . 8 7 5

4 . t 5 ~ 1 . 4 0 - - 0 . 0 0 5 i

5 . a 6 ~ 1.60 -0 .005 i

IV . ( 7 O N C I _ U S I O N A N D D I S C U S S I O N

An improved scheme is presented for optical parameters within the layer Z..- 25. ush-g

a bi.-static tidar system. The combined cfl~ecl o1" gill types of" error caused by smal; :;caIc

fluctualion in the atmosphere, deviatio!-, of 0 and a:.. from 00 and cz:~0, respectively, back--

ground noise, etc. is put into consideration during operation and minimization of the effect is achieved through adjustment of the distance belween stations L, transmitting and rcceiving elevation angles a:0 and a~.~, and viewing angle of receiver 2 ka. The regulation of 2",.a in

particular provides possibility to get integrated values of these parameters over a section of the detected path to eliminate the effect due to the fluctuation, tlowever, there arises a

problem concerned wilh requirement of high precision opticaI pcrformal~ce of the ;eceivinl4 system, which is in turn followed by defect of decrease of the signal-noise ratio.

In general, Philips-Twomey method is employed to get SDP from {crp~} s~:~ meas-

urements. I lowever, in view of the facl that only four typcs of measurement of i t , j, ) are

applied in this study, an approach of fitting parameters of a given SDP has to be used for the purpose. Results from lmmerical experiments show that when relative errors of {crp,.}

are 5%, the other two distribution parameters differ very slightly in magnitude from lheir

truth values except Z, . But when rdative errors of (or,,.} produced through superposhion become considerable, a certain amount of confusion sometimes occurs between the D M

and D- L types. On the other hand, for a SDP with small particles in abundance .!fij,, }.

are used as measurements to get their SDP. The numerical retrieval results exclusive of tha! of Z, are found to be equally satisfactory.

The reason why { N j,,.} and { K p,.) are adopted for retrieving CRI consists main!y in that ; " ~A);: is less sensitive to the real but more sensitive to the imaginary part, that t ] ~ . ~ "

is of higher smlsitivity to both and that {Re} and { K ; } are independent o f the overall concentration of the aerosols detected. Numerical experiments give good resul t s for the

38 ADVANCES IN ATMOSPI-1ER.IC SCIENCi:.S Vol. 3

m o s t par t excep t when smal l par t ic les ave in a b u n d a n c e in the S D P o f the subs tance .

Besides, if the S D P takes a re la t ive ly n a r r o w shape , re t r ieva l i t e r a t i on is at t imes p e r -

f o r m e d i~ m o r e steps.

R Lf-"ER ENC~:'S

[ 1 ] }?.~agara J.A. et al., J. Ge,.~phys. Res., ,g5(1980), 1591--1599 [ 2 ] ~y:~,r:i~, r[~i~.?)~-;]~, 1984, 10:951--970 [ 3 ] Zho:~ Xiujl a~a'J Qiu Jinhuan, Adv. Atmas. Sci. , |(1984), 2: 179---187. [ 4 ] k)ci~-m.zndjian, ,_).. t:'!ectromag~eti,:" Sc~t ter i io :m .qph'~'ic, d Pot~,~!isp.'r.~i:ms, American

li~;hinz; Conai~any. lac. i9,59. [ 5 ] 2;i~a,:) Ya~xeng et al., Ad~'. Attacks. Sci., I ( 1 ~ ' ) , 1:53 51. [ 6 1 J , ' ; ] ; ~ ; , )<~-~:r']'-, 5(1981), 4, 444 -44?. [ "7 ] !r M.D. ct el., J . .4 t :nos . So!.: 35(1~)78), 11:2153 2157.

Elsevier P~b-