A mosphe ic and Clima e Sciences, 2012, 2, 191-195
h p://dx.doi.o g/10.4236/acs.2012.22019 Published Online Ap il 2012 (h p://www.SciRP.o g/jou nal/acs) 191
Backg ound Sola I adiance and he Clima e o he Ea h
in he End o he 20 h Cen u y
Maxim Ogu so 1,2, Ma kus Lindholm3, Ris o Jalkanen3
1Io e Physico-Technical Ins i u e, Russian Academy o Sciences, S . Pe e sbu g, Russia
2Gene al As onomical Obse a o y a Pulko o, S . Pe e sbu g, Russia
3Me la, Ro aniemi, Finland
Email: maxim[email p o ec ed] e. u
Recei ed Janua y 13, 2012; e ised Feb ua y 26, 2012; accep ed Ma ch 9, 2012
ABSTRACT
The possible esponse o global clima e o he changes o backg ound adia ion de i ed om sa elli e measu emen
du ing 1983-2001 is analyzed. Es ima ion is made by means o one-dimensional ene gy-balance clima ic model. I is
shown ha he inc ease o he global su ace adia ion by 3 W × m–2 h ough 1983-2001 should esul in a co espond-
ing ise o empe a u e, which exceeds he ac ual obse ed alues by 0.6˚C - 2.0˚C. Possible causes o such disag ee-
men a e discussed.
Keywo ds: Clima e; Sola I adiance
1. In oduc ion
I is gene ally ag eed ha he global wa ming o ecen
decades is caused p ima ily by an h opogenic inc ease o
g eenhouse gases concen a ion [1,2]. Howe e , no only
human-made a ia ions o a mosphe ic composi ion in-
luence global clima e. Changes in he clima e o he
Ea h depend e iden ly on he backg ound sola i adi-
ance, i.e. on he amoun o sho wa e sola adia ion in-
coming in o he a mosphe e and he ac ion o his a-
dia ion, which is e lec ed back o he space. Recen e i-
dence show ha sola adia ion inciden a he Ea h’s
su ace has inc eased app eciably in he end o 20 h cen-
u y [3]. The phenomenon is o en called a global b igh-
ening. Es ima ions o he adia i e o cing (Figu e 1)
global pe u ba ion o he adia ion balance o he e es-
ial a mosphe e—a e based on he ollowing da a:
1) Sola adia ion a he Ea h’s su ace, a e aged o e
he globe, which was de i ed in he wo k [4] om he
da a on cloudiness ob ained in amewo k o he In e na-
ional Sa elli e Cloud Clima ology P ojec (ISCCP) du -
ing 1983-2001;
2) Globally-a e aged change in sola adia ion a he
Ea h’s su ace du ing 1984-2003, de i ed om he da a
on he Ea h’s e lec ance ob ained by Palle e al. [5]
using ISCCP da a and he da a on dayside ea hligh e-
lec ed om he Moon.
3) A e age o he 8 eco ds o anomalies in g ound-
based obse a ions o he sola adia ion inciden on he
Ea h’s su ace du ing 1993-2001 [6].
Change in backg ound sola adia ion h ough 1983-
2001 causes a posi i e adia i e o cing anging om 3
W × m–2 o 6 - 7 W × m–2 [3] (Figu e 1). I we ake a
alue o clima ic sensi i i y adop ed by IPCC (

с =
0.53˚C - 1.23˚C × m2/W) [2], we ob ain ha inc ease o
he global empe a u e by 1.5˚C - 3.6°C is a esul o he
adia i e o cing o 3 W × m–2. Thus, an inc ease o he
amoun o sola adia ion ha eaches Ea h’s su ace in
he end o he 20 h cen u y, de e mined in di e en ways,
should cause a jump o he global empe a u e, which,
howe e , has no been obse ed. O cou se, he o e sim-
pli ied es ima ion abo e is no su icien o any decisi e
conclusion. A mo e p ecise model assessmen is neces-
sa y. In he p esen wo k such an e alua ion is done by
means o he ene gy-balance clima e model.
2. Ene gy-Balance Model o Global Clima e
In amewo k o he ene gy balance app oach, changes in
he clima e sys em a e es ima ed om an analysis o he
change in he Ea h’s hea s o age. The basis o hese
models was in oduced by Budyko and Selle s [7,8]. In
i s simples o m, ene gy-balance model p o ides glob-
ally a e aged alues o he compu ed a iables. We use
he su ace-ene gy balance clima e model coupled wi h
deep ocean wi h ho izon ally uni o m e ical hea di u-
sion and a cons an upwelling:

   
d
d
sSW LW
inc ou oc c
T
qF F F F

C
opy igh © 2012 SciRes. ACS
M. OGURTSOV ET AL.
192
Figu e 1. Sho -wa e adia i e o cing assessed by means o :
(a) Sa elli e-de i ed su ace adia ion ( he da a we e elec-
onically scanned and digi ized om [4]); (b) Su ace a-
dia ion es ima ed using he da a on he Ea h’s albedo [5]
(solid line wi h squa es), su ace adia ion es ima ed using
he da a on g ound-based measu emen (dashed line wi h
he emp y ci cles). The da a we e elec onically scanned
and digi ized om [3,4].
  
2
2
,,
OO
z
Tz Tz
k
z



,
O
z
Tz
w
z




T

,Tz

SW
inc
(1)
whe e: s is he global-mean su ace empe a u e,
o is he global-mean empe a u e o he ocean a
he dep h z, q is he e ec i e plane a y hea capaci y,
F

LW
ou
is he abso bed sho -wa e sola adia ion,
F

is he ou going long-wa e e es ial adia ion,
oc
F
is he hea exchange be ween he su ace and he
deep laye s o he ocean,


c
F


oc
desc ibes he di e en
adia i e o cings, kz is he e ical hea di usion coe i-
cien , wz is an upwelling eloci y.
F
is exp essed
as:
  
0
,
z O
z
wTz
d,
1
d
O
oc z
Tz
F k
hz


  



(2)
whe e h is he dep h o he mixed ocean laye .
 
1
4
S
SW
inc
F



LW
ou
(3)
S( ) is he o al sola i adiance (TSI) o he sola con-
s an ,

is he e es ial albedo.
F
is exp essed as
a linea unc ion o TS:


00
LW
ou S
F
abT 
0.144 0.096qh
(4)
E ec i e global hea capaci y is de e mined by o -
mula, gene alizing he esul s o [9]:


NET
(5)
whe e q in W × y × m–2 × K–1, h in me e s.
3. Resul s
Clima e o cings used in calcula ions (Figu e 2) we e as
ollows. G eenhouse gases o cing and an h opogenic
( oposphe ic) ae osol o cing was aken om [10]. Vol-
canic (s a osphe ic) ae osol o cings we e aken om
[11]. We used h ee TSI econs uc ions ob ained in he
wo ks [12-14]. The o al (ne ) clima e o cing
F

calcula ed using TSI econs uc ion [14] is shown in Fig-
u e 2( ). The same o cing bu conside ing he amoun o
sola adia ion ha eaches he Ea h’s su ace de i ed
om sa elli e obse a ions
N
ET
F


0
T


00T

S is shown in Figu e
2(g). The model (1) was sol ed by he me hod o con-
secu i e app oxima ion. Ini ially we ob ained he em-
pe a u e in a ze o app oxima ion S by solu ion o
he i s equa ion o he model (1) wi h he ini ial condi-
ion S = 14.6˚C and wi hou he accoun o he
hea lux om he ocean, i.e.

oc
F




= 0. Then he sec-
ond equa ion o (1) is sol ed wi h he ini ial condi ion:
0
,0 0 exp
z
OpSp
z
zw
Tz T T T k

   





0
0,
OS
T T 
(6)
and he ollowing bounda y condi ions:
(7)


,,
O
z
Ozpz
zH
Tz
kTz wTw
z





(8)
The second bounda y condi ion [15] desc ibes balance
o he hea luxes—di usion and upwelling nea a bo -
om compensa e he powe ul sink o cold wa e o e he
a eas o he deep wa e o ma ion (G eenland, No we-
gian and Lab ado seas in No he n Hemisphe e, Wed-
dell and Ross seas in Sou he n Hemisphe e). The pola
sea empe a u e Tp was equal o 1.2˚C [15] and he dep h
o he ocean H was conside ed o be 5000 m. The solu-
ion o he second equa ion o (1) wi h condi ions (6-8)
b ings us


,Tz


0,Tz


0,Tz


1
T


2


3
T
O. A e his we sol e he i s equa ion
o (1) de e mining he O wi h o mula (2) by
using O. This esul s in he i s app oxima ion
o he su ace empe a u e S. Repea ing he p o-
cedu e b ings o he app oxima ions S
T , S
e c., bu he i s app oxima ion usually is enough. Cal-
cula ions a e pe o med by using he ollowing pa ame-
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M. OGURTSOV ET AL.
Copy igh © 2012 SciRes. ACS
193
Figu e 2. Clima e o cings (in W × m–2) used in calcula ions. (a) G eenhouse gases o cing [10]; (b) Human-made ae osol
o cing [10]; (c) To al sola i adiance econs uc ions a e Hoy and Scha en ([12], hick line), Lean e al. ([13], do ed line),
Mo d ino e al. ([14], hin line); (d) Volcanic ae osol o cing [11]; (e) Sa elli e-de i ed backg ound adia ion [4]; ( ) Ne o c-
ing wi hou he accoun o a sa elli e-measu ed adia ion; (g)-( ) Ne o cing wi h he accoun o a sa elli e-measu ed adia-
ion. Time esolu ion 0.5 yea .
e s o he model: kz = 3000 m2 × y –1, wz = 5 m × y –1, h
= 150 m, α = 0.3, q = 14.6 W × y × m–2 × K–1, a0 =
204.0 W × m–2, b0 = 2.05 W × m–2 × K–1. The ne o cing
N
ET
F
 and TSI econs uc ion [14] a e used in calcula-
ions (Figu e 3(a)). S anda d de ia ion be ween he
empe a u e calcula ed om he model and ins umen-
ally measu ed empe a u e h ough 1880-2009 is 0.15.
Da a on he global empe a u e we e aken om he si e
p:// p.ncdc.noaa.go /pub/da a/anomalies/mon hly.land
_ocean.90S.90N.d _1901-2000mean.da . The use o o he
TSI eco ds in calcula ions b ings simila esul s. The
model cu e ep oduces se e al impo an ea u es o he
global-mean su ace empe a u e (Figu e 3(a)). Howe e ,
i we use he o al o cing
N
ET
FS, which akes in o ac-
coun he global b igh ening, he di e gence be ween he
model and ac ual empe a u e eaches 2˚C, i.e. hi een
imes mo e han he modeling e o is (Figu e 3(b)).
Such disag eemen , in p inciple, could appea i he long-
wa e emission


LW
ou
F
du ing he las decades di e s
app eciably om he p e ious alues. The e o e i is use-
M. OGURTSOV ET AL.
194
Figu e 3. (a) Ins umen al global empe a u e
( p:// p.ncdc.noaa.go /pub/da a/anomalies/, hin line), global
empe a u e calcula ed om he model using ne o cing
ΔFNET ( hick line); (b) Ins umen al global empe a u e
( hin line), global empe a u e calcula ed om he model
using ne o cing ( hick line). Time esolu ion 0.5
yea .
NET
S
F
ul o es he model o e he ime in e al 1983-2001.
Fi ing o he model pa ame e s o e 1983-2001 showed
ha he bes ag eemen be ween he calcula ed and ac ual
empe a u e is eached when a0 = 205.0 W × m–2, b0 =
2.2 W × m–2 × K–1 (Figu e 4, mon hly da a we e used).
S anda d de ia ion be ween he calcula ed and ins u-
men ally measu ed empe a u e o e 1983-1999 is 0.13.
Howe e du ing 1999-2001 he wo cu es appa en ly
di e ge and he di e ence eaches 0.6˚C (almos 5 imes
mo e han he e o o e 1983-1999). As in he p e ious
case, calcula ion using he ene gy balance model, which
conside s he da a o he su ace adia ion measu emen ,
g ea ly o e es ima es he ac ual empe a u e.
4. Conclusions
An analysis o he possible clima e esponse o he
changes in sola adia ion a he Ea h’s su ace based on
sa elli e measu emen s [4] du ing 1983-2001, pe o med
by means o bo h quali a i e es ima ions and calcula ions
o he ene gy-balance model, sugges ha he obse ed
inc ease o he backg ound adia ion by 3 W × m–2 should
esul in a s ong ise o he global empe a u e, which
exceeds he ac ually measu ed alues by 0.6˚C - 2.0˚C. I
we use he o he expe imen al es ima ions o global
b igh ening, which p o ides 6 - 7 W × m–2 o cing h ough
1983-2001 [3], he disag eemen would be e en la ge .
I has been sugges ed ha he global b igh ening s a -
ing in 1990s was p eceded by p olonged global dimming
subs an ial dec ease in su ace sola adia ion du ing he
pe iod 1960-1990 [16-18]. Thus, sola b igh ening o
ecen decades only compensa es p e ious dec ease in
sola adia ion and does no app eciably change he
global empe a u e end, caused by g eenhouse e ec
[17,18]. I should be no ed, howe e , ha he spa ial
co e age o he su ace adia ion s a ions, which da a
we e used in he wo ks [16-18], is a he limi ed—all he
s a ion a e si ua ed o e he land and hey a e clus e ed a
he domains o high popula ion densi y—see Figu e 1 o
he wo k [18]. Mo eo e e idence has been ob ained ha
he dimming o 1950-1980 ac ually was no global bu had
local o egional na u e and was obse ed mainly o e
Figu e 4. Ins umen al global empe a u e ( p:// p.ncdc.noaa.go /pub/da a/anomalies/, hin line), global empe a u e calcu-
a ed om he model using ne o cing ( hick line). Time esolu ion 1 mon h.
NET
S
Fl
Copy igh © 2012 SciRes. ACS
M. OGURTSOV ET AL. 195
a eas o high indus ial ac i i y [19]. The e o e i is di -
icul o make a decisi e conclusion abou he global-
scale change in he su ace sola adia ion o e 1960-1990.
Thus, we conclude ha he expe imen al es ima ions o
sola adia ion ha eaches he Ea h’s su ace appa en ly
con adic wi h he ac ually measu ed global empe a-
u es a leas in he amewo k o he ene gy balance ap-
p oach. We belie e ha he disag eemen could be a e-
sul o he ollowing causes:
1) The o e simpli ied ene gy-balance app oach is no
enough o analysis o he p ocesses in a eal clima e
sys em.
2) The ise o empe a u e, caused by a global b igh -
ening du ing 1983-2001, has been compensa ed by a cu -
en ly unknown, ex a cooling ac o .
In any case, he eac ion o a global clima e sys em o
changes in backg ound adia ion in he end o he 20 h
cen u y needs u he p o ound in es iga ion using he
no el global ci cula ion models.
5. Acknowledgemen s
M. G. Ogu so exp esses his hanks o he exchange p o-
g am be ween he Russian and Finnish Academies (p ojec
No. 16), RFBR g an s No. 10-05-00129, 11-02- 00755 o
inancial suppo . R. Jalkanen and M. Lindholm hank he
Finnish Academy (SA138937) o esea ch suppo .
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