J ouma/ rifG/aci%gy, TIoI. 43, No. 143, 1997
Response of the longwave radiation over tnelting snow and ice
to attnospheric wartning
A NTOO:--r M EESTER S, I MrCHl E L VAN DEN BROEKE
2
IFaculty rif Earth Sciences, Vr!je Unive1"siteit, J081 HVAmsterdam, The Netherlands
'llnstituteJor M arine and AtmosJ;/zeric R esearch, Utrec/Zt University, 3508 TA Utrecht, T he Netherlands
ABSTRACT. Pa ra meteri zing th e inco ming lo ngwave radi ati on L 1 in terms of th c
fourth power of th e absolute temperature at the rcfer ence height is used in gl aciology for
severa l purposes. In this paper, the validity of this kind o fp aramete ri zatio n is investigatcd
for the Gree nla nd ice sheet, both b y obser vati ons a nd by numerical si mulation with a
m eso-scale model. It is found that such a parameteri zation severely underestim ates th e
increase of L 1 in response to la rge-sca le warming in a n area where surface melting is
importa nt. Thi s is expla ined by the systematic inDuence that is exerted o n th e shape o f
the temperature profil es by surface melting.
1. INTRODUCTION
Thi s paper conce rn s the parameteri zation of the incoming
longwave radi ati on L 1 above a la rge ice sheet under condition s with surface m elting. Such a p a ra mete ri za ti o n is r equir e d fo r m o d e ls to inv es ti ga t e t he res pon se of th e
Gree nl and ice sheet to global wa rming. In principle, L 1 can
be determin ed fai rl y accurately from profiles of tempe ra ture
(T ), water-vapo ur density (Pv) and liquid or solid water density. H oweve r, it is often ass umed that L 1 ca n be expressed in
term s of para meters at the reference height (h), as
(1)
in whi ch Tb is th e a bso lute temp e r a ture at th e r e fe rence
height, (J is th e Ste fa n- Boltzma nn co nstant and f e ff is th e
effecti ve emitta nce. Empirically, f e fl" is found to be a fun ctio n of cloudin ess (N ), water-vap o ur densit y a t th e reference height (Pvh) a nd a lso of the geog ra phi ca l locati on .
Th e dependence on location is caused by systema ti c differences between t he profil es a nd cloud properties, as well as
by differences in sur face elevation.
Th e parameteri zation (Equ a tio n (I)) is used in glaciology for several purpo es. It has often been applied to evalua te L 1 for field campaigns in which N, 11, and Pvh have bee n
obser ved but L 1 h as not. Recently, Equ ati on (I ) has a lso
b ee n used in m o d el studies rela ted to th e respon se of th e
Gree nla nd ice sh eet to clim ate cha nge. In those studi es, L 1
is d etermin ed from a presc rib ed , id ealized temp e r a ture
seri es. Greuell a nd K onzel ma nn (1994) appli ed thi s p a ram eteri zati on to estim ate the yea rly energy balance fo r one
site (ETH Camp, so uthwest Gr('enl a nd ), with f eff as d etermin ed by K on zelm a nn a nd oth er s (1994) from m eas urem ents at the sam e site. Va n de vVa l a nd O erl em a ns (1994)
use d it to perfo rm yea rl y energy-ba la nce calc ula ti o n s for
the whole Gree nl a nd ice shee t. M o re resea rch a lo n g this
line is expected in thc near future.
Though th e validity of Equ a tio n (1) has been ra th er well
confirmed for typica l cases such as ordin a ry la nd surface.
during the d ay tim e, it has no t bee n so for glac ier s where
m elting occ urs. There is a pa rtic ul a r difficult y with such
66
surfaces. As the a ir te mperatures ri se, the glacier surface
rem a ins a t th e melting point a nd hence the tempera ture
rise cann ot be unifo rm with height. It sho uld be expec ted
th en that the rise in 11, is smaller than th e ri se in th e tempera tures abO\·e. Sin ce th e latter a lso yield a contributi o n
to L L L 1 rises fas ter tha n n ~, so tha t fen is a ri sing functi on of 11,.
Actua lly, it is well known th at large errors wo uld occ ur
for melting mOllntain gl ac ie rs, for whi ch the T profiles a r e
obviou sly perturbed b y a d vecti on of a i r from the ice-free
surroundings. For such g laciers, it is obvi o us th at Equ ati on
(1) cannot be appli ed with a 11, measured above the glacier.
Gre uell a nd O erl emans (1989) ca lcul a ted L 1 from a 711
measured a t a site b eyo nd the th erm a l inDu ence of th e
glacier, whereas Kuhn (1989) used a weig hted ave rage of
n~ beyo nd the inDu e nce of the glacier a nd above it. Fo r
la rge ice sheets witho ut a d vection from ice-free surroundings, the m atter is differe nt. The use of Equati on (1) for t ha t
case is based on th e a ss umpti on th at th e a tmos ph ere will
adapt to the surface conditi ons up to a sufficient height, so
tha t T h is "representa tive" (Greuell, 1992).
In ea rli er papers, a ttempts have bee n m ade to eva lua te
th e validity of Equ ation (1) from data th a t we re acquired o n
th e Greenl and ice shee t. Greuell (1992) investigated th e d ependence of Eeff on 11, fo r the ETH Ca mp (see above ) a nd
found that it could no t be determin ed whether f pff was d ependent on or independent of l1l , due to the la rge scatter of
f eff . H e r ecalled a n interesting result fro m Ohmura (1981 ),
who found from a long sequence of da ta, ta ken on Axel H eiberg Isla nd (this concern s a smaller ice cap), th at f eff is a n
increasing functi on of 71,. K onzelma nn a nd oth ers (1994)
a lso fou nd a large scatte r in f eff . Ano th er problem is tha t
Equ a ti o n (1) has no t b ee n tes ted fo r the a bl a ti on zo n e,
wh ere th e highest air temperatures above the ice shee t a r e
found.
A theo retical test h as a lso been tried . K onzelm ann a nd
oth ers (1994) calcula ted L 1 with a na rrow-band model fr0111
profiles of T and p,.. Sta nd a rd profil es were chose n, based o n
in sp ec tio n of ra di o so undings, a nd th e n py a nd T we r e
va rie d by amounts th a t did not dep e nd on height. Thi s
,Ifeestas and Van den Broeke: R esponse cif longwaue mdiation to atmospheTic warming
yielded g oo d acco rd w ith Equati on (I). H o w ever, a crucia l
fl aw in this num erica l expe riment is that th e bounda ry condition for a m elting g lacie r was not incorpo rated, so th a t
there is a systematic differ e nce between th e ideal ized profiles of the experim ent (vvhi ch differ mutu a ll y by a n additive co nsta nt) a nd th e real profil cs (whic h differ the more,
th e greate r th e height b ecomes), once meltin g occurs.
In the prese nt pa per, th e usefuln ess of Equa ti on (I) fo r
the lowe r p a rt of th e Greenl a nd ice sheet is evalua ted. Thi s
is do ne in two ways. Fi rs t, the rela tio n b e twee n obser ved
va lues for 11,4 and L1 is il1\"Csti gated for a lo cati on on a
melting surface where a la rge ra nge of po sitive
valu es
occ urs. It is noted here tha t such meas ure m e nts have ra rely
been done, which is to be a ttributed prim a ril y to the experimenta l diffi c ulties in volved in perfo rming m eas urements
O\'er a n ice surface with a hi g h melting ra te (O erl ema ns
a nd Vug ts, 1993). Seco ndl y, a case stud y with a numerieal
meso-sca le m odel is a nalysed , in which th e c h a nge of th e T
profil e is calcul ated fr om th e cha nges in air flow a nd turbulence, whi c h in th eir turn d e pend on th e te mpe rature difference b e twee n air a nd a tm os phere (M ees te rs, 1994). If th e
differe nce with Equ ation (I) is la rge, it sho u ld be co ncluded
th at pa ra m e te ri zing L 1 al o ng this lin e is in a ppropri ate in a
model ro stud y the reac tio n of a la rge ice s h eet to clim a te
ch ange.
n
2. OBSERVATIONS
the east-so utheas t wind (Va n d en Broeke a nd o the rs, 199+).
The glacier surface at thi s location is ve ry rou g h: the regula rl y spaced ice hill s (form ed by mecha nica l d e form a tion
a nd differential melting) have ty pical dimensio ns of several
metres ve rticall y a nd hori zo nta ll y. This a nd lh e high seasonal melt ra te (3.1m water equi vale nt; Van de \\'al a nd others,
1995) prevents th e operation of ta ll m as ts and se nsitive equipment. Instead , we used a 6 m m a t tha t rested fr ee ly on th e ice
with its fo ur legs a nd melted d o wn with the surface in the
course of the a bl a ti on seaso n.
Al 1.5 m a b o \'e th e surface, shortwa\'e ra di a ti o n was
measured with Kipp C IVI 14· p y ranom eters a nd tota l radiati on with Aa nde raa 2811 pyrra d iometers. A s th ese se nsors
we re not ve ntil a ted , the meas urem ents were p e rturbed by
heating of th e se nsor housing clu e to in sola tio n. After t he
ex perim ent, a ll th e radiation se nsors were reca libra ted a nd
several co rrec ti o ns were applied befo re the d a ta could be
a na lysed. Si n ce lo ngwave radia ti o n was no t m easured directly, it was ca lcul ated by subtrac ting the glo ba l from th e
tota l radi a ti o n . Thi s procedure, toge ther with the ty pi cal
measuring acc urac y of the se n so rs, yields a n estim a ted acc ura cy of th e m eas ured daily m ean inco ming lo ng wa ve radiation L 1 of 10 \V m 2
1c mp e ra ture a nd humidit y we re meas ure d a t three
levels. I n thi s p a pe r, onl y tempe ra ture a nd humidity measurements a t h = 2 m a re used.
2.2. Results and comparison with theory
2.1. Site and set-up of the observations
A ge nera l d esc ripti on of th e Gree nl a nd Ice 1\ [a rg in EXperime nt (GIlV[EX ) ca n b e fo und in O erlem a n s and Vu g ts
(1993). A m o re detailed desc ription of th e c lim a te of the a blati o n z on e ca n be fo und in Va n de n Broe ke a nd o th e r
(1994). Se\'e ra l papers o n GIMEX have bee n publi shed in a
spec ial iss ue of Global and Pla llet{lI), Change (No. 9, 1994-).
During GI1\IEX- 91, r a dia tion da ta we re coll ec ted during 52 d, 10 Jun e-31Jul y 199 1. In this stud y, we will use da ta
collec ted a t "s it e 4-" o n Ru sse ll Gl ac ie r, 2.5 km fr om th e
bo undary b e twee n g lac ie r a nd tundra a t a n elevation of
340 m a.s.1. (Fi g. I). Th ese m easurements w e r e p erform ed
by th e In stitute for 1\Ia rin e a nd Atm os ph e ric R esea rch,
U ni ve rsit y o f Utrec ht. Ad vec ti o n o f wa rm a ir fr om th e
tundra pl ays no role a t thi s site, at leas t a t th e lower heights,
as is shown by the ve ry hig h di rec ti onal co nstancy (0.97) of
Onl y diurn a l m ea ns have b ee n used for compa ri son with
th eory to minimi ze th e influe nce of errors in th e m easured
r a di a ti o n a nd in t he obse rve d clo ud in ess . Th e cl i u rn al
co urse of th e te mp e ra ture a t th e refe re nce heig ht, 71" is
sma ll so lh a t th e a verage of th e fo urth power o f 11, ca n be
estimated as th e fo urth power o f th e ave rage ofTl, .
A pro b le m is th a t th e in co min g radi a ti o n d e p e nd s
strongly o n l h e c lo udin ess N, even if N is sm a ll. In Fi g ure
2 the obse rved fdf is shown as a fun ction of N o nl y. A linear
d ependence is see n. Thi s beh ay io ur differs stro n g ly from
0.95
:t:
...
••
,la
w
J""III• •~
observed
Konzelmann and others (1994)
Konig-Langlo and Augstein (1994)
o
0.9
CD
!I1
0.85
ISlINGUATA SERMIA
0.8
0.75
o
0.2
0.4
0.6
Cloud cover (N)
0.8
N
i
Fig. 1. L ocation cif the site (,'s ile 4") fro m which observalions
were used.
Fig. 2. Observed almoslJheric emiltance dependellt on cloudilIess,Jor ''site -1': J une Jll£V 1991. Also shown aTe two jJaTa meteri::.atiol7s, based 011 measurements al other IJo/aT siles
(equ ilibrium Line oJ so ulhwest Greenlan d in tlte case oJ
J."oll;:.elmal1ll and others (1994) and Koldewe)1(SuaLbard)
and Geolg VO Il Neu111a)'fI" ( Anlarctica) i ll the case qf KonigLanglo and Augslein (1994)).
67
Journal rifGlaciology
oth er results fo r pol a r regions (Koni g-Langlo a nd Augstein,
1994; K onzelm a nn and others, 1994), which a re also shown
in Fig ure 2. Acco rding to those res u lts, the cloud contribution is a bout proporti o nal to the thi rd power o[ N . Konzelm a nn a nd others (1994) explain ed thi s by rema rking tha t, in
th e case ofl ow N, on ly high cirri a re prese nt, which ha ve a
small in fl uence on L L wh ereas hig h N is related to cloud s
with a low b ase. This ru le appa rently does not hold [o r the
C I MEX site 4. For a clea r sky, h o w ever, there is a g o o d
ag ree ment betwee n th e observa tio ns [or site 4 a nd the two
p a ra me teri zations.
A straightforward way to account [or th e infl u e nce of
the cl o ud s, sta rting from th e ass um ed prop ortion a lity o[
L l to 71,4, is to ass um e tha t the [ollo wing approx im a tion
ca n be used:
(2)
The best va lues [o r a a nd {3 have b een dete rm i ned from
L lObS' N and Th by a leas t- squ a r es ca lcul a tion. It was
fo und th a t a = 0.78 ± 0.01 a nd {3 = 0.14 ± 0.01, with a
hi g h correla ti o n o[ T oJ =- 0. 8. I n Fi g ure 3, L 1 as d e te rmin ed by Eq ua tion (2) is co mpa r ed to th e obser ve d L 1.
The correlati on b etween the observed a nd ex plained L 1 is
ra th e r high, T.ry = 0.88, sugges ting th a t th e model is good.
However, t hings becom e different i[ o ne looks at th e p rediction s for depende nce o n
for fix ed N . To do so, th e data
poi nts have b ee n class ifi ed acc ordin g to N bein g " low "
( N::; 0.3), " m o d e r a t e" (0.3 < N::; 0.7) a n d " hig h "
(N) 0.7). I n Fig ure 3, th e d a ta p o ints have bee n m a rked
accord ingly. The least-sq ua res linear fit for each cl ass is also
shown. The slo pes of these fit s a ppea r to be 0.50 ± O.ll for
low N, 0.39 ± 0.10 [or moderate N a nd 0.24 ± 0.26 [o r high
N. A ll slopes a re sig nificantl y sm all er than I. This indicates
that L lobs rises considerably fas ter th a n n ~ [or fix ed N, so
that Equation (2) and hence Equ ation (1) a re refuted [or t hi s
casc. \ Ve have no t tried to obta in a b etter relation, sin ce it
would be impossible to genera li ze it to cove r a larger area
as th e observa ti ons have been done a t a rather special locati o n. It is emphasized tha t the noted di screpa ncy cannot be
expla in ed, as [or sm a ll glac iers, b y a d vecti on o[ wa rm a ir
from the snow-fr ee surro undings, since the surface wind was
a lways from the ice shee t as noted in section 2.1. I n the [0 1-
n
320
"'E
~
~
...J
"0
300
3. NUMERICAL CALCULATIONS
3.1. Set-up of the numerical calculations
A two-d i m ensional meteo rological meso -scale model has
bee n u se d ; thi s was d e v e lop ed to stud y th e r elation b etween the a tm ospheric ci rc ulation a nd the surface-energy
bala nce [o r the western m a rgin of the Gree n la nd ice shee t.
Th e model has bee n described a nd va l id a ted by Mees te rs
(1994) a nd M eesters and o th ers (1994). On ly those features
that a re most importa n t for the present pa p er a re briefl y reviewed.
Figure 4 indi ca tes t h e topog ra ph y i n t h e mod el. A
terrain-fo llowing stagge red g rid is used . There a re 13 level s
fo r th e te mp e rat ure ab ove th e surface, w it h t he lowes t
height s a t lO, 20, 40, 80, 120 m a nd th e h igh es t leve l at
5000 m. N o clouds a re a ss umed to be prese nt. L 1 is para m eteri zed at th e surface a ltitude Zsur according to
(3)
in which E( ZSlIr, s) is a fun ct ion of the wa te r-vap our content
between ZRUl" a nd s, para m e teri zed according to the suggestion or Sav ij a rvi (1990).
o L-_seo
_ _L-L-......L._ _--II:...-_--L.._ _...L._ _..L..._--'
- 300
-200
-100
0
100
0
400
x (km )
Fig. 4. Topography usedfor the two -dimensional mesa -scale
model.
330
310
low ing sec tion it will be sh own th at thi s discrepa ncy is likely to occ ur for the whole a r ea where melting is importa nt.
lt
0.0 s N s 0.3
o : 0.3 < N " 0.7
• : 0.7 < N s 1.0
3.2. Results of the numerical calculations
lt
x :
Two ru n s (A a nd B) w ith t h e model wi ll b e co nsidered here .
They correspond to run s A a nd C disc ussed by M ees te l-s
0
290
(1994). R un A is a stand a rd run with a clear sky, no large-
8
280
u
270
representing a day inJ u ly. R un B differs from run A only in
260
th a t the in iti a l air te mpe ra ture is inc reased by 5 K a t a ll
levels. This causes la rge differences in the w ind field a nd in
:;
'"
<0
u
::;40<:/~O
sca le w i nd a nd temper a ture, moisture a nd ice cond itio n s
270
280
290
300
310
320
observed L.1 (W m" )
Fig. 3. Observed vs calculated incoming longwave ra diation
Jo r ''site 4'; Th ree classesJor cloudiness (N) have been discerned. Th e solid lines are the best linearjils jor the three
classes.
68
330
t he turbu le nt exchange, as has been di sc ussed by M eester s
(1994). Both runs sta rted a t midnight and las ted for 48 h. In
this sec tion, averages for the latter o[ th e 2 d are considered .
Fig ure 5 shows th e diurnall y averaged temperatures, a t
the surfa ce and at the r efe re nce height (lO m ), [or both ru ns.
It is seen that th e differe nce b etween b o th runs is small [or
sm a ll x a nd increases with increasing a ltitude. Yet, [or the
highest a ltitude (x = 400 km ), the increase is still conside r-
jllees/as and Van den B roeke: R esjJonse qf longwave radia/ion/o atmosjJheric warming
th e ice sheet, th e increase of L 1 fo r clear-sky con diti ons is
underestim ated by a facto r of up to 3 if one ap plies Equation
(I).
6
4
..........~~.
2
Q
0
0..
e
~
::
.........................
10
9
.-~~........------...........
8
-2
7
~
;::
.,
e
-4
-6
~
u
-8
0
50
100
150
200
250
300
350
400
x (km)
450
\
'"" 300
H
H
L
L)
01)
] 200
150
100
I
50
910
------/"',.
-5
0
4
3
T'h
x (km)
500r----.~----._~._--~.-_.--~._--~
.i:: 250
5
%~--5~0~~10~0~~17
50n--=20~0~~2~5~0~3~0~0--~3~5~0--4~00
ably sm a ller th a n the imp osed rise of the fr ee-atmosphere
temperature, .1 K.
These features have the following backgro und. Close to
th e ice margin, the average a ir temperatures a re high due to
the low a ltitude. Surface m elting inhibits large diITerences
between ru ns A a nd B. \ Vith i ncreas ing a l ti tude, temperatures generall y become lower. At th e highest a ltitude, melting occ urs onl y during a sm a ll part of the d ay fo r run A but
during a cons iderabl e p art of th e day for run B (Meesters,
1994). H e nce, th e difference betwee n th e mean te mp eratun's for runs A a nd B a t hi g h a ltitude is, a lt hough much
higher th a n for low a ltitudes, co nsiderably sm a ll er than th e
difference of 5 K imposed on the free-atm os ph ere tem perature.
Figure 6 shows the diurn a l a\'erages for the temperature
profil es fo r both runs, for three loca ti ons. L ocati ons "L" a nd
"H " are a t the foot a nd a t the top (surface elevati on 2.5 km ) of
the slope, respectively, and locati on "M " is at x =90 km, for
which the surface elevation is 1.2 km. Thi s fi gure illustrates
that suppression of th e temperature rise, w hi ch occ urs for
th e "warm" part of the ice sheet, is restricted to a sha llow
layer. Fi g ure 7 shows th e relati ve increase, from run A to run
B, of L 1 as well as 7114 It is seen that for the "warm" part of
5
q
2
Fig. 5. SU1jace (Ts) andreference height (Ttt) temjJeratw-efor
nms A (solid) and B (dashed). Daily averaged values, as a
function qf/he distance to the ice margin.
400
350
.5
6
5
10
temp (C)
Fig. 6. Tempemture jmifilesJor sites with a low ( L ), middle
( JIJ ) and high ( H ) altitude, Jor TUns A (sofid) alld B
( dashed). Dail.J; averaged values.
15
Fig. 1 Increment qf the incoming longwave radiation ( L 1)
and qf the jOllrth fJo wer qf Ihe temjJerature at reference height
( 711 4). Daily averaged values as ajunctioll qflhe distance 10
the ice ma/gin.
Th e difTere nce ca nn ot be ex pl a in ed from th e ch a nge in
water-vapour conte nt P vh . In sp ec tion shows that P vh increases by o nl y 5% from run A to r un B, averaged over the
zone 0::::: x ::::: 160 km. But s i nee (for clea r s ky a nd with
cha nges in the sh apes o[ the profiles neglected ) Ecff shou ld
be proportional to a low power of P vh (power accordi ng
to K o nze lm a nn a nd o th ers (1994·)), thi s ca n ex pl a in a
cha nge of less th an 1% in Edl'. H ence, the no ted change in
L 1 has to be a ttributed for the g reater part to the systematic change in the sh apes of the profiles.
The appare nt sha ll owness of the layer that is a d a pted to
th e surface ca nnot be a co nsequence of the li mited simu lation time (2 d ). A katabatic w ind flows over Greenland with
a typical le ngt h scalc of 500 km a nd a speed (coastwa rd
component ) of 5 m s I, yielding a time-scale of only 103 s or
abo ut 1d.
k
4. DISCUSSION
The assum pt io n th a t th e i Ilco mi ng (clear-sky ) longwave
radiation L1 sho uld be rough ly proportiona l to the fourt h
power of the te mp erature a t the refe rence heig ht 711-1 has
been tested for the Green la nd ice sheet. It has been found ,
both from observations and from simul at io ns, tha t in response to a la rge-sca le warming a rise in L1 occ urs which
is much larger th a n the rise in 71,4 for th ose sites where melting occurs during a large pan o f th e day. This is expl a in ed
from th e facL th a t Th is kep t low by the me lting surface,
whereas L1 ri ses more strongly sin ce th e temperatures at
hi g her leve ls a lso contribute to L 1. The ex iste nce of this
eITect was known beforehand but it has usua ll y been considered as negli g ibl e. Th e present stud y has show n that this is in
ge neral not the case.
It is emph asized th at even relatively small e rrors in the
calc ulation of L 1 lead to la rge erro rs in the net radi ation if
the latte r is small. Thi s is the case fo r the Greenland ice sheet
during the m elting seaso n, when t he net longwave radi ati on
a nd net sho rtwave radi ati o n tend to cance l because of th e
69
Journal qfGlaciology
high a lbedo of the iee (e.g. Va n de \Va l and Oerlemans, 1994).
H e nce, study ing the respon se of th e ice sheet to cl imate
change requires an accurate parameterization of L 1.
Equation (1) has rarely bee n applied to cases with h igh
air temperatures over melting glaciers. However, Van de ' Va l
a nd Oerlemans (1994) used Equ at ion (1) in a model for th e
res ponse of the Greenland ice sheet to climate change. They
stipu lated the effect of climate change by increasing the ai r
temperature Tb by 1 K everywhere. Since the effect of surface melting on 11, has not bee n taken into account, it is
likely that the calcu lated increase in L 1 would be relatively
well in accord with the stipu lated climate change, whereas
t he presc rib ed increase in 1\, its elf wou ld not be. So, th e
effects of a wrong 11] and a wrong rela tion between Th and
L 1 cancel (whereas, on the other hand, the turbulent f1uxes
is wrong but
wi ll be calculated wrongly to the extent that
this problem is beyond the scope of the present study ).
It is concluded that the use of Equation (1) in models to
simulate the response of ice sheets to large-scale warm ing
lead s, as far as the equation is taken li terall y, to a st rong
underestimation of the change in the incoming longwave
a nd net radiation once surfacf' mdting occurs. For this reason, th e u e of models with severa l T levels within the atmosphere is strongly recommended.
n
ACKNOWLEDGEMENTS
"Ve thank the members of th e GI MEX-9l team for th eir
participation by undertaking the measurements at site 4.
P. G. Duynkerke, ' V. Greuell , J. Oerl emans a nd R . S. ' V. van
d e \ Val (I nstitute or Marine and Atmospheric Scie nces,
Utrecht ) are thanked for helpfu l disc ussions. Financial support was obtained from the Dutch National Resea rch Program on Globa l Air Pollution and Climate Change
(contract 276/91-NOP ), from th e Commission of the European Communit ies (contract EPOC-CT90-00 J5) and
frol11 the Netherlands Organisation for Scientific Research
(Werkgemeenschap CO 2 -Problematiek ).
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i\ IS received 27 October 1995 and accepted 22 July 1996
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