An analysis technique used to estimate the integrated liquid water content (LWC) from the measured solar irradiance is described. The cloud transmittance is computed by dividing the irradiance measured at some time by a clear sky value obtained at the same time on a cloudless day. From the transmittance and the zenith angle, the cloud LWC is computed using the radiative transfer parameterizations of Stephens et al., (1984). The results are compared with 17 days of mm-wave (20.6 and 31.65 GHz) radiometer measurements made during the First ISCCP Regional Experiment (FIRE) Intensive Field Observation (IFO) in July of 1987

Fairall, C. W.

Rabadi, Raja El-Salem

Snider, Jack B.

Breton 

NASA Technical Reports Server

E s t i m a t i n g  I n t e g r a t e d  Cloud Liquid  Water from 
E x t e n d e d  Time Obse rva t ions  of S o l a r  I r r a d i a n c e  
C.W. F a i r a l l  and Raja  El-Salem Rabadi 
Department of Meteorology 
Pennsy lvan ia  S t a t e  U n i v e r s i t y  
U n i v e r s i t y  Park ,  PA 16802 
---- 
and 
J .  Sn ider  
NOfiA/EfiL/WPL 
325 Broadwav 
Boulder ,  CO 80303 
I Y T RG I i U C  T I ci t4 
Extended t ime o b s e r v a t i o n s  ! E T D )  were made a t  San Nico la s  I s l a n d  !SNI)  
from March t o  Oc tobe r ,  1987. A small  ground s t a t i o n  was i n s t a l l e d  a t  t h e  NRi. 
t r a i l e r -  ( S i t e  B i .  Hourly a v e i a g e s  of  a i r  t e m p e r a t u r e ,  r e l a t i v e  humid i ty ,  w i n d  
speed  and d i r e c t i o n ,  s o l a r  i r r a d i a n c e ,  and downward lonawave i r r a d i a n c e  were 
r eco rded .  The r a d i a t i o n  s e n s o r s  were s t anda rd  Eppley pyranometers  ( s h o r t w a v e )  
and pyrgeometers  ( longwave) .  D a t a  r e c o r d s  of SNI rawinsonde l aunches  t o r  t h i s  
p e r i o d  have been r e q u e s t e d  from t h e  P a c i f i c  M i s s i l e  Tes t  Center  ( P M T C ) .  
the  s t r a t o c u m u l u s  covered  n a r i n e  boundary l a y e r  (MBL) .  From t h e  t e m p e r a t u r e  
and humidi ty  t h e  l i f t i n g  condensa t ion  l e v e l ,  which i s  at e s t i m a t e  o f  t h e  
h e i g h t  of t h e  c loud  b o t t o m ,  can be computed. Combinat ions o f  shor twave  and 
lonqwa*/e i r r a d i a n c e  s t a t i s t i c s  can b e  used t o  e s t i m a t e  f r a c t i o n a l  c loud  cover  
pa rame te r s .  
i n t e g r a t e d  l i q u i d  water  c o n t e n t  ( W !  froin the measured s o l a r  i r r a d i a n c e .  The 
c loud  tt-ansmi t t a n c e  is c o m p u t e d  b y  d i v i d i n g  t h e  i r r a d i a n c e  measured a t  some 
t ime  b y  a c l e a r  s k y  v a l u e  ob ta ined  a t  t h e  same time o n  a c l o u d l e s s  day.  From 
t h e  t r a n s m i t t a n c e  a n d  t h e  z e n i t h  a n g l e ,  t h e  cloud LlJC is computed us ing  t h e  
r a d i a t i v e  t r a n s f e r  pa rame te r i : a t ions  o f  Stephens  e t  a l .  ( 1 9 8 4 ) .  T h e  r e s u l t s  
a r e  c3mpared wi th  1 7  days  o f  mm-wave !20.6 a n d  31 .65  GH:) r ad iomete r  
measurements made d u r i n g  t h e  F f R E  I F 0  i n  J u l y  o f  1'587. 
T h i s  d a t a  w i l l  he p rocessed  i n  a v a r i e t y  o f  was t o  deduce p r o p e r t i e s  o f  
This  paper  d e s c r i b e s  an a n a l y s i s  t echn ique  u s e d  t o  e s t i m a t e  t h e  
C L O U D  R D I D I U T I V E  TRANSFER COMPUTATIONS 
S tephens  (1978)  h a s  developed a s imple  p a r a m e t e r i z a t i o n  of  c loud  a l b e d c  
(He),  t r a n s m i t t a n c e  ( T r ) ,  and a b s o r p t i o n  ( f i b )  i n  terms, o f  t h e  c loud  o p t i c a l  
t h i c k n e s s  ( T I  and t h e  z e n i t h  a n g l e  (9). T h e  p a r a m e t e r i z a t i o n  i s  based o n  t h e  
two-stream approximat ion  of Coakley and Chylek ( 1 9 7 5 ) .  A l o o k - u p  t a b l e  o f  
v a l u e s  f o r  s i n g l e  s c a t t e r i n g  a lbedo  ( o )  and b a c k s c a t t e r  f r a c t i o n  ( e )  is g iven  
a s  a f u n c t i o n  o f  T and y=cos!9!. The v a l u e s  a r e  based on r e s u l t s  o f  
sop h i s t i c a t  e d 1 Q - 1 a yer , 15- b and r ad  i a t  i ve t r an s f e r  c o mp u t a t  i o n  5 .  The r ev i s ed  
look-up t a b l e  ( S t e p h e n s  e t  a l . ,  1984) was used f o r  t h e  work p r e s e n t e d  h e r e .  
Non abso rb ing  ( X ( 0 . 7  y m )  and abso rb ing  ( A  i 0 . 7  y m )  wa./elength r e g i o n s  a r e  
c o n s i d e r e d .  The two-stream model i c ,  a s  fo l lows :  
f i )  Non a b s o r b i n g ,  o = l  
307 
https://ntrs.nasa.gov/search.jsp?R=19910001197 2020-03-19T20:30:12+00:00Z
Tr = 1 - Re ( l b )  
( i i )  A bsorbing, w < l  
Tr = 4u/R 12b) 
Ab = 1 - Re - Tr (2c 1 
w h e r e  
R = ( u  + e x p i T r f )  - ( u  - 1 ) ”  exp(-Tef) (3c) 
T h e  optical t h i c k n e s s  is calculated from t h e  cloud W using a parameterization 
obtained from a number of measured cluud properties. 
S i n c e  t h e  S t e p h e n s  parameterization w a s  developed t o  apply t o  s o m e  15 
cloud types, w e  decided tu c o m p a r e  it t o  a model with microphysics specific t o  
t h e  m a r i n e  stratocumulus, which W E  shall refer t o  a s  t h e  DFBS (Davidson et‘ 
al., 1984, model. TTte DFBS model is a 15-band, delta-Eddington r a d i a t i v e  
transfer model that assumes a linear liquid Hater p r o f i l e  in t h e  cloud with a 
log-radius gaussian cloud droplet distribution w h e r e  t h e  m o d e  r a d i u s  1 5  
determined from t h e  liquid water assuming a constant number of cloud droplets 
( l O O / c c ) .  F i g u r e  1 s h o w s  a comparison of transmittances for t h e  t w o  models at 
t h r e e  different zenith a n g l e s  for a generic California s t r a t o c u m u l u s  with 
cloudtop at 600  m and total water (liquid plus vapor) mixing r a t i o  of 8 g/kg. 
Optical thickness was varied by varying t h e  cloud t h i c k n e s s  from 50 m t o  450 
m .  T h e  comparison is very  good but t h e  Stephens paraaeteri:ations (Eqs. 4) 
appear t o  underestimate t h e  optical thickness at low v a l u e s  of W ,  which a r e  at 
t h e  lower limit o f  h i s  fit. Since marine stratocumulus often h a v e  low ./slues 
of W ,  w e  used t h e  parameterization given below f o r  W(100 g / m ” 2  (see  Fig. 2 ) .  
which is obtained from t h e  DFbS model: 
Using t h i s  slightly modified form of t h e  Stephens model, a noaogram c a n  b e  
constructed in t e r m s  of c o n t o u r s  of transmittance v e r s u s  zenith a n g l e  and 
intEgrated liquid water path (Fig. .3). 
RESULTS 
Using t h e  c l e a r  skv irrsdiance, t h e  cloud t r a n s m i t t a n c e  w a s  computed f o r  
each day from July 1 t o  July 16 for t h e  times l b i l 0  t o  0100 GHT. Low incidence 
a n g l e s  ( y C . 4 )  w e r e  not used because of t h e  potential for large errors. F Q r  
t h e  Sarie r e a s o n ,  transmittances greater than 0.9 we r e  not considered. For a 
308 
g i v e n  v a l u e  o f  T r  and p ,  t h e  v a l u e  o f  W was i t e r a t e d  u n t i l  t h e  Stephens a o d e l  
gave t h e  measured t r a n s m i t t a n c e .  T h i s  computed v a l u e  o f  W i s  compared w i t h  
t h e  v a l u e s  f r o m  t h e  NOAA r a d i o m e t e r  ( F i g .  4 ) .  
t h e  v a l u e s  e s t i m a t e d  f r o m  t h e  t r a n s m i t t a n c e .  The rms s c a t t e r  is about  35%. 
The NOAA r a d i o m e t e r  i s  b e l i e v e d  t o  be a c c u r a t e  t o  20%, b u t  a 50% f r a c t i o n a l  
b i a s  i s  n o t  o u t  o f  t h e  q u e s t i o n .  Some o f  t h e  rms s c a t t e r  i s  due t o  
d i f f e r e n c e s  i n  s a m p l i n g  geometry ,  s i n c e  t h e  py ranomete r  has  a h e m i s p h e r i c a l  
f i e l d  o f  v i e w  and t h e  r a d i o m e t e r  has a na r row f i e l d  o f  v iew .  These 
d i f f e r e n c e s  i n  f i e l d  o f  v i e w  a r e  somewhat moderated b y  a v e r a g i n g  f o r  one hour .  
Ano the r  s o u r c e  o f  e r r o r  i s  t h e  use o f  a s i n g l e  c l e a r  sky  i r r a d i a n c e  f o r  t h e  
e n t i r e  17 day p e r i o d ,  u h i c h  i g n o r e s  v a r i a b i l i t y  i n  t h e  m e t e o r o l o g i c a l  
c o n d i t i o n s  above t h e  m i x e d - l a y e r .  Once t h e s e  i s s u e s  a r e  s o r t e d  o u t ,  He e x p e c t  
t o  use  t h i s  method t o  a n a l y z e  t h e  e n t i r e  d a t a  base. 
The mm-wave r a d i o m e t e r  v a l u e s  o f  W a r e  on ave rage  abou t  5 0 %  g r e a t e r  t h a n  
REFERENCES 
Cgakley,  J.R. and P. Chy lek ,  1975: The two s t r e a m  a p p r o x i m a t i o n  i n  r a d i a t i v e  
t r a n s f e r :  I n c l u d i n g  t h e  a n g l e  o f  t h e  i n c i d e n t  r a d i a t i o n .  3_. Atmos. 
S c i . ,  -- 3 2 ,  409-418. 
Davidcon,  K.L., C.W. F a i r a l l ,  P. Jones B o y l e  and G.E. Schacher ,  1984: 
V e r i f i c a t i o n  o f  an a tmospher i c  m i x e d - l a y e r  model f o r  a c o a s t a l  
r e g i o n .  &. C A E .  Aiel_. bt., 2 3 ,  617-636. 
Stephens, G.L., 1978: R a d i a t i o n  p r o f i l e s  i n  ex tended  n a t e r  c l o u d s .  11: 
P a r a m e t e r i z a t i o n  schemes. J. Atmos. G., 35, 2 1 2 3 ~ 2 1 3 2 .  
Stephens,.G.L., S. Ackerman, and E.A Smi th ,  1984: CI s h o r t w a v e  p a r a m e t e r i - a t i o n  
r e v i s e d  t o  improve  c l o u d  a b s o r p t i o n .  J-. Atmos. S 2 ,  4 1 ,  687-690. 
AcknoHledgewents . T h i s  w o r k  i s  s u p p o r t e d  by NASCI g r a n t  NAG 1-652.  
P a r t  o f  t h i s  w o r k  was pe r fo rmed  w h i l e  CWF Has a v i s i t i n g  s c i e n t i s t  a t  t h e  
Nava l  E n v i r o n m e n t a l  P r e d i c t i o n  and R e s e a r c h ’ F a c i l i t y .  The a u t h o r s  w ish  t o  
e x p r e s s  s p e c i a l  t h a n k s  t o  R i c h a r d  D i x o n  and C a r l  O t t e n  o f  PMTC f o r  a i d i n g  and 
a b e t t i n g  t h e  i n s t a l l a t i o n  and m a i n t a i n e n c e  o f  t h e  ET0 sys tem a t  S N I  and t o  
D i c k  Thompson o f  t h e  Department o f  N e t e o r o l o g y ,  PSU, who p u t  t h e  system 
t o g e t h e r  and k e p t  t h e  d a t a  f l o w i n g .  
309 
F i g .  1 C o m p a r i s o n  o f  t r a n s m i t t a n c e  v e r s u s  i n t e g r a t e d  c l o u d  LUC a t  z e n i t h  
a n g l e s  o f  0 ,  60, a n d  80 d e g r e e s  f o r  t h e  S t e p h e n s  ( c i r c l e s )  a n d  DFBS ( l i n e 1  
m o d e l s .  
F i g .  2 O p t i c a l  t h i c k n e s s  v e r s u s  
p a r a m e t e r i z a t i o n  o f  Eq. 4 a  ( S o l i d  
Eq. 5 ( d o t t e d  l i n e ) .  
F i g .  3 C o n t o u r s  o f  t r a n s a i t t a n c e  
n t e g r a t e d  c l o u d  LWC f o r  t h e  S t e p h e n s  
l i n e ) ,  t h e  DFBS c a l c u l a t i o n s  ( c i r c l e s ) ,  a n d  
a s  a f u n c t i o n  o f  s o l a r  z e n i t h  a n g l e  a n d  
i n t e g r a t e d  c l o u d  LWC f r o m  t h e  m o d i f i e d  S t e p h e n s  p a r a r e t e r i z a t i o n .  
F i g .  4 I n t e g r a t e d  c l o u d  LWC: t h e  v e r t i c a l  a x i s  i s  c o m p u t e d  f r o m  s o l a r  
i r r a d i a n c e  v e r s u s  W f r o m  t h e  NOAA r a d i o m e t e r  m e a s u r e a e n t s .  
31 0 
1 
.9 
.8 
- 7  
.6 
.5 
. 4  
. 3  
. 2  
. I  
Q 
Fig. 1 Comparison o f  transmittance versus integrated cloud LWC it zenith 
0, b o ,  and EO degrees for the Stephens (circles) and DFbS (line) angles o f  
models. 
c 
t- 
It) 
i,'c 
u) 
c 
0 
I 
I- 
* 
2 
.C 
- 
IO 
0 
e 
0 
(ZJ 
.- 
Fig. 2 Optical thickness versus integrated cloud LWC for the Stephens 
parameteri:ation of Eq. 4 1  (solid liner, the DFBS calculations Lcircles), anc 
Eq. 5 (dotted line). 
31 1 
1 18 180 
L i yci i d  Inlater P a t h  (g,f'm*2 1 
F i g .  3 Contours of t r a n s a i t t a n c e  as a f u n c t i o n  of s o l a r  z e n i t h  a n g l e  a n d  
i n t e g r a t e d  c loud LWC from the rpodified Stephens  p a r a a e t e r i z a t i o n .  
+ 
+ 
/' 
F i g .  4 Integrated c loud LWC: t h e  v e r t i c a l  a x i s  i s  computed from s o l a r  
i r r a d i a n c e  v e r s u s  W from the N O A A  r a d i o n e t e r  a e a s u r e s e n t s .  
31 2 


Estimating integrated cloud liquid water from extended time observations of solar irradiance

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