Apparent statistical correlation between Arctic heat budget and zonal circulatio

Fletcher, J. O.

Huschke, R. E.

Rapp, R. R.

English

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MEMORANDUM 
RM-5234-NASA 
JANUARY 1967 
I 
\ - '  * I  
NA§r-21-(07! 
AN APPARENT STATISTICAL RELATIONSHIP 
BETWEEN POLAR HEAT BUDGET AND 
ZONAL CIRCULATION 
R. E. Huschke, J. 0. Fletcher and R. R. Rapp 
(THRUI 
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January 1967 RB-5234 
RM-5234-NASA, An Apparent S t a t i s t i ca l  Relat ionship Between Polar 
Heat Budget and Zonal C i rcu la t ion ,  J. 0. F l e t c h e r ,  R. E .  Huschke, 
and R. R. Rapp, RAND Memorandum, January 1967, 14 pp. 
PURPOSE: To r e p o r t  q u a n t i t a t i v e  evidence t h a t  v a r i a t i o n s  i n  atmospheric c i r c u l a t i o n  
a r e  d i r e c t l y  r e l a t a b l e  t o  v a r i a t i o n s  i n  n e t  atmospheric h e a t  l o s s  i n  the  p o l a r  
r e g i o n s ,  and t o  suggest t h a t  t h e  meteorological s a t e l l i t e  i s  an i d e a l  device f o r  
providing d a t a  needed i n  the  fo recas t ing  of atmospheric c i r c u l a t i o n .  
RELATED TO: RAND'S work i n  A r c t i c  meteorology f o r  A i r  Force P ro jec t  RAND and i n  
s a t e l l i t e  meteorology f o r  NASA. The f i g u r e s  on ne t  l o s s  of heat  from t h e  A r c t i c  
atmosphere used he re  were drawn from RAND Report R-444-PR, The Heat Budget of 
t h e  Arctic Basin and I ts  Relat ion t o  Climate,  October 1965, and are a l s o  found 
i n  RM-5233-NSF, Proceedings of t h e  Symposium on t h e  A r c t i c  Heat Budget and Atmo- 
s p h e r i c  Circulat ion:  January 31-February 4 ,  1966. 
METHODOLOGY: I n  a t tempting t o  determine t h e  d i f f e r e n c e  between the r a d i a t i o n  balance 
of t he  earth-atmosphere system and the h e a t  suppl ied t o  the  atmosphere from t h e  
underlying su r face ,  t he  g r e a t e s t  u n c e r t a i n t i e s  l i e  i n  t h e  r o l e  of atmospheric 
abso rp t ion  and emission of shortwave and longwave r a d i a t i o n .  Lacking the  precise 
d a t a  of  s a t e l l i t e  measurements, ca l cu la t ed  values  were used i n  t h i s  f i r s t  a t tempt  
t o  quan t i fy  t h e  r e l a t i o n s h i p  of atmospheric c i r c u l a t i o n  t o  t h e  n e t  atmospheric 
h e a t  loss i n  t h e  A r c t i c  region. 
sumes a c loud les s  A r c t i c  atmosphere, devoid of longwave absorpt ion by l i q u i d  
water o r  ice  p a r t i c l e s .  The o t h e r ,  which may b e  more r e a l i s t i c ,  assumes a prev- 
a l e n t  dense i c e - c r y s t a l  haze. 
during the  yea r s  1941 t o  1961 were compared with a mean monthly index of t he  
c i r c u l a t i o n  i n  the  s u b a r c t i c  zone, the zonal c i r c u l a t i o n  index being t h e  d i f f e r -  
ence i n  t h e  average height  of t h e  500-millibar su r face  a t  60 and a t  70 degrees 
North i n  the  s e c t o r  from 40 degrees West t o  30 degrees East. For each of  t h e  
two methods, h e a t  l o s s  was lag-correlated with the  mean monthly index of sub- 
a r c t i c  zonal c i r c u l a t i o n  f o r  periods of  one month ahead t o  t h r e e  months behind. 
Arctic h e a t  loss w a s  es t imated by two d i f f e r e n t  methods. One estimate as- 
Mean monthly va lues  of t h e  n e t  Arctic h e a t  loss 
FINDINGS: The r e s u l t s  of t he  c a l c u l a t i o n s  show t h a t  t h e  two methods are remarkably 
similar i n  t h e i r  c o r r e l a t i o n s  with atmospheric c i r c u l a t i o n .  
cyc le s  of Arctic atmospheric h e a t  l o s s  y i e l d  c o r r e l a t i o n  c o e f f i c i e n t s  of  about 
0.95 (0.956 and 0.945) with the  zonal index lagged one month. 
Both of  t h e  der ived 
SUGGESTIONS FOR FURTHER WORK: The r e l a t i o n s h i p  between va lues  of A r c t i c  atmospheric 
h e a t  l o s s  and a zonal index should b e  t e s t e d  f o r  s p e c i f i c  months. Also,  p l ans  
f o r  t h e  r e g u l a r  c o l l e c t i o n  of po la r  d a t a  should b e  developed and implemented. 
S a t e l l i t e  measurements should include: d a t a  on the  t o t a l  outgoing f luxes  of  
shortwave and longwave r a d i a t i o n ;  data on the  su r face  albedo and i t s  d i s t r i b u t i o n ;  
d a t a  on su r face  temperatures;  and any d a t a  from which t h e  abso rp t ion  and emission 
c h a r a c t e r i s t i c s  of  the atmosphere and a e r o s o l s  can be i n f e r r e d .  
MEMORANDUM 
3 RM-5234-NASA I i' ' 
' \  JANUARY 1967 \ '  i '4 
4 
AN APPARENT STATISTICAL RELATIONSHIP 
BETWEEN POLAR HEAT BUDGET AND 
ZONAL CIRCULATION '.- 
, R. E. Huschke, J. 0. Fletcher and R. R. Rapp '\ 
This research is supporte by the National Aeronautics and Space Administration under 
National Aeronautics and Space Administration. 
A 7 ', Contract No. NASr-21. P This report does not necessarily represent the views of the 
I 7 0 0  M A I N  ST.:. $ A N T A  M O N I C A  * C A l I F O R N I A  *.;*pdQ* ________( 
PREFACE 
This Memorandum relates a potentia function of meteorologica 
satellites to the possible fulfillment of a gross need in forecasting. 
Several approaches are suggested for investigating the feasibility of 
relating the polar heat budgets to atmospheric circulation. The sug- 
gestion expressed here grew out of RAND'S work in satellite meteorology 
for the National Aeronautics and Space Administration, and our related 
interest and activity in the field of Arctic meteorology. 
On t h e  b a s i s  of t he  b e s t  ava i l ab le  da t a  and s e v e r a l  reasonable 
assumptions, i t  i s  poss ib l e  t o  show a 0.95 c o r r e l a t i o n  between the  
annual cyc le  of t h e  atmospheric heat loss i n  t he  Arc t i c  and t h e  cyc le  
of t h e  genera l  c i r c u l a t i o n  of t he  atmosphere wi th  a l a g  of one month. 
The ch ief  u n c e r t a i n t i e s  i n  t h i s  p o t e n t i a l l y  va luable  c o r r e l a t i o n  could 
be removed e n t i r e l y  or  diminished s i g n i f i c a n t l y  i f  s a t e l l i t e s  were used 
t o  c o l l e c t  p e r t i n e n t  d a t a  on the  Arctic h e a t  budget. 
L 
JWCEDING PAGE BLAWK NOT FILMED. 
-vii- 
CONTENTS 
PREFACE ....................................................... iii 
SIiMMARY ....................................................... v 
I. INTRODUCTION ............................................ 1 
11. DISCUSSION .............................................. 2 
111. IMPLICATIONS ............................................ 5 
REFERENCES .................................................... 7 
-1- 
I. INTRODUCTION 
I n  a previous paper, F l e t che r  (1965) sys t ema t i ca l ly  examined t h e  
a v a i l a b l e  empir ica l  da t a  and the  hypotheses needed t o  deduce a l l  t he  
terms of t he  equat ions desc r ib ing  the hea t  budget of t he  Arc t i c .  H i s  
purpose was t o  de r ive  the  ind iv idua l  annual cyc les  of t he  major com- 
ponents of t he  hea t  budget. Therefore,  t he  da t a  were used, and the  
r e s u l t s  couched, i n  the  form of long-period monthly means. 
I n  the  course of t h a t  work and i n  a subsequent search  f o r  Ant- 
a r c t i c  heat-budget d a t a ,  i t  became c l e a r  t h a t ,  f o r  po lar  observa t ions ,  
advantage was not  being taken of s a t e l l i t e s  t o  the  degree warranted 
by t h e  p o t e n t i a l  value of t he  da ta .  
A heat-budget component of p a r t i c u l a r  i n t e r e s t  i s  the  n e t  loss of 
h e a t  from t h e  Arc t i c  atmosphere. A t  p r e sen t ,  t h i s  n e t  loss can be 
es t imated  only by making assumptions (1) a s  t o  t o t a l  r a d i a t i o n  escaping 
t o  space ,  and (2)  a s  t o  the  q u a n t i t i e s  of r a d i a t i o n  absorbed and emit- 
t e d  wi th in  the  atmosphere. The s a t e l l i t e  is  the  i d e a l  device f o r  
measuring the  t o t a l  r ad ian t  loss t o  space and can provide da t a  t h a t  
would g r e a t l y  enhance t h e  q u a n t i f i c a t i o n  of atmospheric absorp t ion  
and emission. 
t he  polar  atmosphere, i n  conjunction with the  ne t  warming of t he  atmo- 
sphere a t  low l a t i t u d e s ,  provides t h e  bas i c  fo rce  to d r i v e  t h e  atmo- 
s p h e r i c  genera l  c i r c u l a t i o n .  
constant  throughout t he  yea r ,  t h e  amount of atmospheric cool ing  a t  t he  
poles  shows a l a r g e  seasonal  va r i a t ion .  
atmospheric c i r c u l a t i o n  should, t he re fo re ,  be q u i t e  d i r e c t l y  r e l a t a b l e  
t o  v a r i a t i o n s  i n  ne t  atmospheric hea t  loss i n  t he  po la r  regions.  
The thermal gradient  e s t a b l i s h e d  by t h e  n e t  cool ing  of 
While t r o p i c a l  hea t ing  remains r e l a t i v e l y  
The r e s u l t i n g  v a r i a t i o n s  i n  
Lacking s a t e l l i t e  d a t a ,  f o r  a f i r s t  s t e p  i n  a t tempting t o  quan t i fy  
t h i s  r e l a t i o n s h i p ,  w e  have taken F l e t c h e r ' s  mean monthly values  of 
Arc t i c  atmospheric hea t  l o s s  and have lag-cor re la ted  them wi th  a mean 
monthly index of sub-Arctic zona) c i r c u l a t i o n .  Of f i v e  l-month-interval 
l ag -co r re l a t ions  examined, t he  h ighes t  ( r  = 0.95) i s  found when the  c i r -  
c u l a t i o n  ind ices  a r e  lagged one month behind t h e  hea t - lo s s  d a t a .  
course ,  no p r a c t i c a l  prognost ic  in ferences  can o r  should be drawn from 
t h i s  pre l iminary  r e s u l t .  
Of 
-2 - I ,. 
11. DISCUSSION 
The mean monthly values of Arctic atmospheric heat loss derived 
by Fletcher are discussed in three papers (Fletcher, 1965; Fletcher, 
Keller, and Olenicoff, 1966; Fletcher (ea.), 1966). This quantity 
is determined simply as the difference between the radiation balance 
of the earth--atmosphere system and the heat supplied to the atmosphere 
from the underlying surface. Of all the variables involved in this com- 
putation, the greatest uncertainties center on the role of atmospheric 
absorption and emission of shortwave and longwave radiation. In deriv- 
ing his first estimate of atmospheric heat loss, Fletcher followed the 
assumptions of Marshunova, principally that an Arctic atmosphere with 
no reported clouds is a truly "cloudless" atmosphere, that is, devoid 
of longwave absorption by liquid water or ice particles. Alternatively, 
Fletcher has re-estimated the annual cycle of atmospheric heat loss 
assuming a prevalent dense, ice-crystal haze high in the Arctic tropo- 
sphere. The results of these two calculations are shown as bars in 
Fig. 1. The reason for employing both sets of results in this Memorandum 
lies not in the implications of their differences; on the contrary, it 
lies in the remarkable similarity of their correlations with atmospheric 
circulation. 
An index of the sub-Arctic, zonal, atmospheric circulation that 
was available for comparison with the Arctic heat-budget data was the 
zonal index published by Putnins (1963). This index is the average 
difference between the height of the 500-millihar surface at 60% and 
its height at 7OoN in the sector from 4OoW to 30°E. The mean monthly 
values of this zonal index (computed for the period 1949 to 1961) are 
shown as dots, also in Fig. 1. 
It is obvious from the figure that the correlation between heat 
loss and zonal index one month later is a strong one. Indeed, the cor- 
relation coefficients corroborate this emphatically. Both of the derived 
cycles of Arctic atmospheric heat loss yield correlation coefficients 
of about 0.95 (0.956 and 0.945) with the zonal index lagged one month. A 
complete set of correlation coefficients with the zonal index lagged 
from -1, to +3 months is plotted in Fig. 2 .  
. 
cy 
E, 
1 
0 
0 
Y 
c 
0 al 
I 
0 .- 
t 
5+ 
2 
I 
0 
E 
-3 - 
Heat loss without Arctic haze 
Heat loss with dense Arctic haze 0 
* a * * *  500-rnb height difference between 60" N 
and 70" N in  the sector 40°W to 30"E [I 
X 
Q, 
U 
C 
120 *; 
0 .- 
c 
60 
Fig. 1-Comparison of the calculated monthly atmospheric heat losses 
(bars 1 in the Arctic with a sub-Arctic zonal circulation index (dots 1 
1 .o 
0.8 
c 
C 
0) 
0 
0 
0 
0 
.- .- 
Z 0.6 
0' 
- 0.4 2 
0' 
V 
.- 
c 
0 
0.2 
0 
0 
El 
-4 - 
I 
8 
I I 
0 
0 Heat loss without Arctic haze 
El Heat loss with dense Arctic haze 
0 
-1  0 1 2 3 
Lag of zonal index behind atmospheric heat loss (months) 
Fig.2-Lag correlation of mean monthly Arctic atmospheric 
heat loss with mean monthly zonal index 
, 
. 
w 
-5 - 
111. IMPLICATIONS 
The f a c t  t h a t  w e  have used long-period monthly means as parameters 
i n  t h i s  c o r r e l a t i o n  makes i t  impossible f o r  us  t o  conclude even t h a t  w e  
have i d e n t i f i e d  a phys ica l  r e l a t i o n s h i p ,  much l e s s  a p red ic t ab le  cause 
and e f f e c t .  On the  o the r  hand, what is now being learned  about genera l  
atmospheric dynamics leads  u s  t o  be considerably more op t imis t i c .  I n  
t h e  Mintz--Arakawa genera l  c i r c u l a t i o n  model, f o r  example, it takes  
about 20 t o  30 days f o r  t he  atmosphere t o  reach dynamic equi l ibr ium 
fo l lowing  the  establ ishment  of a meridional hea t ing  g rad ien t  ( tu rn ing-  
on t h e  sun) ,  which makes an i n t e r e s t i n g  comparison wi th  t h e  h ighes t  
c o r r e l a t i o n  c o e f f i c i e n t  shown i n  Fig.  2 .  
Of t h e  s e v e r a l  courses which t h i s  s tudy  could next t ake ,  probably 
the  m o s t  informative would be t o  t e s t ,  f o r  i nd iv idua l  months, the r e -  
l a t i o n s h i p  between va lues  of Arc t i c  atmospheric hea t  l o s s  and a zonal  
index.  I f  it should appear from t h i s  i nqu i ry  t h a t  monthly depar tures  
from the  mean hea t - lo s s  d a t a  a r e  r e f l e c t e d  i n  corresponding depar tures  
i n  t h e  sub-Arctic c i r c u l a t i o n ,  a number of f u r t h e r  measures a r e  immedi- 
a t e l y  ind ica t ed .  
F i r s t ,  p lans  f o r  the  r egu la r  a c q u i s i t i o n  of p e r t i n e n t  po la r  r a d i -  
A number of s a t e l l i t e  a t i o n  da ta  should be developed and implemented. 
measurements a r e  d e f i n i t e l y  id ica ted  : t he  t o t a l  outgoing f luxes  of 
shortwave and longwave r a d i a t i o n ;  the  su r face  albedo,  e s p e c i a l l y  the  
d i s t r i b u t i o n  of t h e  albedo of t he  snow and i c e ;  s u r f a c e  temperatures;  
and any da ta  from which the  absorpt ion and emission c h a r a c t e r i s t i c s  of 
t h e  atmosphere and aerosols  can be i n f e r r e d .  
Concurrent ly ,  t h e  fol lowing approaches w i l l  deserve a t t e n t i o n :  
1. Extension of s t u d i e s  t o  inc lude  a v a i l a b l e  h i s t o r i c a l  
d a t a  i n  the  Southern Hemisphere and An ta rc t i ca .  
2. Attempts t o  de r ive  es t imates  of t r o p i c a l  atmospheric 
h e a t  ga in  t h a t  a r e  compatible with the  polar  hea t - loss  
da t a .  
3. Extension and refinement of t he  s t a t i s t i c a l  d e f i n i t i o n  
of atmospheric response,  through c o r r e l a t i o n  with o t h e r  
parameter iza t ions  of t he  c i r c u l a t i o n .  
-6 - 
4 .  Investigation of the physical details of the assumed 
cause and effect; for example, by ad hoc testing in a 
numerical general-circulation model. 
L 
-7 - 
REFERENCES 
F l e t c h e r ,  J. O . ,  The Heat Budget of t h e  A r c t i c  Basin and I t s  Re la t ion  
t o  Climate,  The RAND Corporation, R-444-PR, October 1965. 
F l e t c h e r ,  J .  O . ,  B .  Keller,  and S.  M. Olenicoff ( eds . ) ,  Soviet  Data on 
t h e  A r c t i c  Heat Budpet and I t s  Climatic In f luence ,  The RAND Corporation, 
RM-5003-PR, May 1966. 
F l e t c h e r ,  J. 0. ( ed . ) ,  Proceedings of t h e  Symposium on t h e  Arctic Heat 
Budget and Atmospheric C i r c u l a t i o n ,  The RAND Corporation, i n  process.  


An apparent statistical relationship between polar heat budget and zonal circulation

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