Dynamics between clear, cloudy and all-sky conditions: Cloud forcing effects

Abstract

The author has analyzed the dynamics of atmospheric changes between all-sky, clear and cloudy sky conditions. The basis of analyses is the calculation of flux values at the balance states. The analyses depend essentially on the time constants of basic processes, which can be analyzed separately. Two time constants are based on the former research results, and three time constants have been developed and estimated in this study. The basic processes in dynamic analyses have been the very rapid changes in cloudiness and cloud temperatures, the rapid change in upward atmospheric longwave radiation caused by solar insolation change, the slow change in temperature of the land and sea, and the transient change in the atmosphere temperature. This transient atmospheric process has an essential role in explaining why the surface temperature increases when at the same time the cloud forcing decreases. The dynamic simulations reveal that in all cases, two rapid changes in the atmosphere can bring the outgoing longwave radiation at the top of the atmosphere almost exactly (a difference of 0% to 0.3%) to the observed pseudo-balance values of clear and cloudy skies. Pseudo-balance values for clear and cloudy skies are not very time-sensitive because the values stay within ±1 W/m2 from one day to 13 days. According to the true energy balance values, the slightly nonlinear cloud forcing would be -0.56 Wm-2 per 1% increase in cloudiness and -0.1 °C per 1% increase in cloudiness over the normal cloudiness range variation from 60% to 70%. According to this study, the commonly used cloud forcing in the units of W/m2 yields effects that are about 40% too low for the long-term cloudiness changes. Cloudiness changes could alone explain the global warming.

Full text

November 2013 – January 2014, Vol. 4, No. 1; 557-575. E- ISSN: 2249 –1929
Journal of Chemical, Biological and Physical Sciences
An International Peer Review E-3 Journal of Sciences
Available online at
www.jcbsc.org
Section C: Physical Sciences
CODEN (USA): JCBPAT
Research Article
557
J. Chem. Bio. Phy. Sci. Sec. C; Nov. 2013-Jan .2014; Vol.4, No.1; 557-575.
Dynamics between Clear, Cloudy and All-Sky Conditions:
Cloud Forcing Effects
Antero Ollila
Department of Civil and Environmental Engineering, School of Engineering, Aalto University,
Espoo, Finland,
Received: 19 December 2013; Revised: 06 January 2014; Accepted: 14 January 2014
Abstract: The author has analyzed the dynamics of atmospheric changes between all-
sky, clear and cloudy sky conditions. The basis of analyses is the calculation of flux
values at the balance states. The analyses depend essentially on the time constants of
basic processes, which can be analyzed separately. Two time constants are based on
the former research results, and three time constants have been developed and
estimated in this study. The basic processes in dynamic analyses have been the very
rapid changes in cloudiness and cloud temperatures, the rapid change in upward
atmospheric long wave radiation caused by solar insolation change, the slow change
in temperature of the land and sea, and the transient change in the atmosphere
temperature. This transient atmospheric process has an essential role in explaining
why the surface temperature increases when at the same time the cloud forcing
decreases. The dynamic simulations reveal that in all cases, two rapid changes in the
atmosphere can bring the outgoing long wave radiation at the top of the atmosphere
almost exactly (a difference of 0% to 0.3%) to the observed pseudo-balance values of
clear and cloudy skies. Pseudo-balance values for clear and cloudy skies are not very
time-sensitive because the values stay within ±1 W/m
2
from one day to 13 days.
According to the true energy balance values, the slightly nonlinear cloud forcing
would be -0.56 Wm
-2
per 1% increase in cloudiness and -0.1 °C per 1% increase in
cloudiness over the normal cloudiness range variation from 60% to 70%. According to

Dynamics... Antero Ollila.
558 J. Chem. Bio. Phy. Sci. Sec. C; Nov. 2013-Jan .2014; Vol.4, No.1; 557-575.
this study, the commonly used cloud forcing in the units of W/m
2
yields effects that
are about 40% too low for the long-term cloudiness changes. Cloudiness changes
could alone explain the global warming.
Keywords:
Dynamics of atmosphere, energy balance of atmosphere, time constants of
climate, cloud forcing
INTRODUCTION AND OBJECTIVES
The objectives of this paper are to find the time dependent behaviors of outgoing long wave radiation
(OLR) flux changes caused by the incoming shortwave radiation flux changes due to the cloudiness
and albedo changes between all-sky, cloudy and clear sky conditions, and to analyze the time-
dependent behavior of the pseudo-balance radiation fluxes of cloudy and clear skies for identifying the
dominant time delays. One objective is also to show that the cloud forcing values for the long-term
cloudiness changes are bigger than the forcing values based on the values of pseudo-balance skies.
The response times of the Earth’s climate system have been studied from various perspectives, and
therefore the values vary on a broad scale. The shortest value is from Douglass
et al.
1
, which is a 3-
month response time for solar irradiation.
Time constants based on the solar cycle analyses are in the range of 0.4 to 12 years (Scafetta
2
) and 5 ±
1 year (Schwartz
3
). The longest estimates are from Hansen
et al
.
4
, which are from 10 to 100 years, and
the perspective has been from the long-time changes due to the forcing factors of the climate. Stine
et
al
.
5
have analyzed the annual cycles of the surface temperature, and the result is a mean time lag of 56
± 11 days for oceans and 29 ± 6 days for land.
Besides the relatively long time constants, there are also short time diurnal changes in surface
temperatures and in outgoing long wave radiation fluxes. One study of surface temperature changes in
the solar irradiation diurnal changes show time constants that are only 5 to 10 minutes (Esala
6
).
There are some factors that may explain this large variation. One factor is a question of the feedback
mechanisms of the climate system elements. It seems that when including these mechanisms in the
calculation models, the time constants become longer.
Another factor is the mixing of ocean layers and how deep this mixing actually happens. The time
domain perspective in this study is relatively quick changes from one sky condition to another – a
matter of days. Also the true balance changes have been analyzed and then the time perspective has
been in years.
Finally cloud forcing values have been calculated on two theoretical basis and the impacts of the
forcing values of long-term cloudiness changes have been compared based on the values of pseudo-
balance skies and the true balance skies.
ENERGY BALANCES FOR CLEAR, CLOUDY AND ALL-SKIES
In this text clear sky is indicated by the subscript
b
, cloudy atmosphere by the subscript
o
, and all-sky
atmosphere by the subscript
a
. The energy balance values of different skies in pseudo-balance and true
balance conditions are presented in
Table 2
.

Dynamics... Antero Ollila.
559 J. Chem. Bio. Phy. Sci. Sec. C; Nov. 2013-Jan .2014; Vol.4, No.1; 557-575.
The values of Table 2 are based on the research paper of Ollila
7
but the all-sky OLR flux value is
updated to be 237.8 W/m
2
(the original value was 236.5 W/m
2
). The value 237.8 W/m
2
is closer the
most recent research papers and it satisfies the equation used by Ollila
7
in combining the flux values
between different skies.
The new OLR
a
value changes slightly some other flux values, which have been calculated using the
same methods as described by Ollila
7
. The budget calculations are based mainly on the published SW
and LW flux data of Zhang et al.
8
, Bodas-Salcedo et al.
9
, Raschke et al.
10
, and Loeb et al.
11
but other
methods have also been applied in quantifying non-measurable fluxes.
The fluxes in Table 1 and Table 2 are in W/m
2
, and the fluxes are always stated as such in this paper.
The true balance calculations
7
show that the clear sky surface temperature is 24.5 °C, and the cloud
sky surface temperature is 13.2 °C.
Table- 1: Shortwave radiation flux values
7
in W/m
2
.
Shortwave radiation budget Abbr. Clear Cloudy
All
-
sky
Uncertainty
Incident solar radiation flux at TOA
SWin
342.0
342.0
342.0
4
–
6
3
Total reflected SW radiat. flux into space
Rt
53.0
120.0
104.2
5
-
10
1
SW flux reflected by clouds
Rc
0.0
85.40
64.1
7
-
15
3
SW flux reflected by air
Rp
23.2
14.4
17.4
7
-
15
3
Incoming SW flux (Sx = SWin
-
Rc
-
Rp)
Sx
318.8
242.4
260.5
5
-
10
1
Incoming SW
flux absorbed by clear air
Sb
69.0
52.4
56.1
5
–
10
3
Incoming SW flux absorbed by clouds
Sc
0.0
18.0
13.6
5
-
10
3
Total incoming SW absorp. flux by the atm.
Si
69.0
70.4
69.7
5
-
10
3
SW flux of Rs flux absorbed by cloudy sky
Sr
0.0
1.6
1.3
0.3
–
0.9
3
Total SW flux absorbed in the atmosphere
Sa
69.0
72.0
71.0
5
-
10
3
Incoming SW flux reaching the surface
Sd
248.9
171.8
190.8
10
-
15
1
SW flux reflected by the surface
Rs
29.8
21.8
24.0
5
-
10
2
Reflected Rs flux into space. Ra = Rs
-
Sr
Ra
29.8
20.2
22.7
5
-
10
2
SW flux absorbed by the surface
Ss
220.0
150.0
166.8
10
-
15
1
Net incoming SW flux (NSR = SWin
–
Rt)
NSR
289.0
222.0
237.8
5
-
10
1
SW flux absorbed by the atm. and surface
ASR
289.0
222.0
237.8
5
-
10
1

Dynamics... Antero Ollila.
560 J. Chem. Bio. Phy. Sci. Sec. C; Nov. 2013-Jan .2014; Vol.4, No.1; 557-575.
Table- 2: The summary of Earth’s energy budgets for clears, cloudy and all-skies (Ollila
7, 12
). The
values are in W/m
2
.
Pseudo-balance True balance
Uncertain
ty
Surface in
Abbr.
Clear
Cloudy
All
-
Sky
Clear
Cloudy
SW flux absorbed by surface
Ss
190.0
154.8
166.8
220
150
5
–
10
1
Downward LW
flux emitted by the atm.
Ed
318.0
359.0
344.7
378
302
10
–
15
3
SFC
-
balance
Bs
508.0
513.8
511.5
598
452
11
–
22
3
Surface out
Thermals
T
26.4
27.3
24.9
33
15
5
–
10
2
Latent heat flux
L
87.5
90.3
91.0
120
56
5
–
15
2
LW surface flux
transmitted to space
Eu
83.2
0.0
28.3
67
0
3
–
7
3
LW surface flux absorbed by clouds
Ac
0.0
84.0
55.4
0
79
3
–
7
3
LW surface flux absorbed by GH gases
Ag
310.9
312.2
311.9
378
302
3
–
7
3
SFC
-
balance
Bs
508.0
513.8
511.5
598
452
11
–
22
3
Atmosphere in
Incoming SW flux absorbed by clear air
Sb
69.0
52.4
56.1
69
53
5
–
10
3
Total SW flux absorbed by clouds
Sc+Sr
0.0
19.6
14.9
0
19
5
–
10
3
Thermals
T
26.4
27.3
24.9
33
15
5
–
10
2
Latent heat flux
L
87.5
90.3
91.0
120
56
5
–
15
2
LW surface
flux absorbed by clouds
Ac
0.0
84.0
55.4
0
79
3
–
7
3
LW surface flux absorbed by GH gases
Ag
310.9
312.2
311.9
378
302
3
–
7
3
ATM
-
balance
Ba
493.8
585.8
554.2
600
524
11
–
23
3
Atmosphere out
Upward LW flux emitted by the atm.
Eg
175.8
166.7
169.8
222
163
7
–
15
3
Upward LW flux emitted by clouds
Ec
0.0
60.1
39.7
0
59
5
–
10
3
Downward LW flux emitted by the atm.
Ed
318.0
359.0
344.7
378
302
10
–
15
3
ATM
-
balance
Ba
493.8
585.8
554.2
600
524
11
–
23
3
TOA
Upward LW flux emitted
by the atm.
Eg
175.8
166.7
169.8
222
163
7
–
15
3
LW surface flux transmitted to space
Eu
83.2
0.0
28.3
67
0
3
–
7
3
Upward LW flux emitted by clouds Ec 0.0 60.1 39.7 0 59 5 – 103
OLR OLR 259.0 226.8 237.8 289 222 5 – 101
DYNAMICS OF ATMOSPHERIC CHANGES
Dynamic Model of the Atmosphere: The term “pseudo-balance” is needed for the clear and cloudy
sky conditions. Theoretically the outgoing longwave flux (OLR) at the top of atmosphere (TOA)
should be the same as the net incoming SW flux (NSR=ASR), if the Earth is thermodynamically in
balance. Only in all-sky conditions this is true but the balance value for OLR cannot be reached in
clear and cloudy sky climate conditions. The actual measured values show that for clear and cloudy
sky conditions: NSR
b
= ASR
b
= 289 W/m
2
versus OLR
b
= 259 W/m
2
and NSR
o
= ASR
o
= 222 W/m
2
versus OLR
b
= 226.8 W/m
2
. The basic reason is in the dynamics of the atmosphere, because the clear

Dynamics... Antero Ollila.
561 J. Chem. Bio. Phy. Sci. Sec. C; Nov. 2013-Jan .2014; Vol.4, No.1; 557-575.
and cloudy sky conditions cannot prevail on the global scale for periods of adequate length. In pseudo-
balance energy balance calculations Ollila
7
has used an Ss
b
value of 190 W/m
2
, because it produces the
correct balance value at TOA: Ss
b
+ Sb
b
= 190 + 69 = 259 = OLR
b
. The value of Ss
o
can be calculated
in the same way: Ss
o
= 226.8 – 72.0 = 154.8.
In many research papers the clear and cloudy sky OLR values (259 W/m
2
and 226.8 W/m
2
in this
study) have been applied as if they were true balance values and therefore applicable for short-term
and long-term climate changes. One of the objectives of this study is to show that the pseudo-balance
values are applicable for short term climate changes only and the true balance values should be applied
for long-term (longer than one year) climate change calculations. The schematic process diagram of
the energy fluxes are depicted in Figure 1.
Figure 1: Schematic flow diagram of Earth’s energy flux processes in dynamical analysis.
There are three process steps that dominate the atmospheric changes; these are the warming or cooling
of the land and sea and the warming or cooling of the atmosphere. The seas cover 71% of the globe,
and therefore the global surface temperature is mainly depending on the sea surface temperature. The
floating ice decreases slightly the sea cover to 70%. This means that the percentage shares of the
surface’s radioactive emissions are: sea 70% and land 30%.The first-order dynamic model can be used
to estimate the time-domain behavior of even very complex processes, as shown by Ollila
13
. The step
change for the first-order process without amplification applied to this process is
F
out
(t) = (1- e
-t/Ƭ
) * F
in
(t), 1
Where F
out
(t) is the outgoing LW radiation flux (=process output), F
in
(t) is the incoming radiation flux
(= process input, which can be SW or LW radiation flux), t is time, and Ƭ is the time constant of the
process. As shown in Figure 1,OLR(t) is the sum of the three LW radiation fluxes Eg, Eu and Ec

Dynamics... Antero Ollila.
562 J. Chem. Bio. Phy. Sci. Sec. C; Nov. 2013-Jan .2014; Vol.4, No.1; 557-575.
originating from different sources. The time domain behavior of each of these fluxes can be
approximated by Equation (1) if there is a stepwise change from one sky condition to another. The
typical feature of the first order process is that the output value is 63% from the step input change at
the point of the time constant Ƭ, and at the point of 4*Ƭ, the output is about 98 % of the input value.
Time constants of the main processes: The dynamic analysis of this study means the calculation of
the outgoing LW flux (OLR) as a function of time in respect to the step SW insolation change from
one sky condition to another. The dynamic processes that dominate the change from one sky condition
to another are the very rapid change of cloudiness, the rapid rate of the temperature change of clouds,
the rapid change of atmosphere temperature caused by SW insolation flux change, the slow
temperature change of the land and sea, and the transient change of the atmosphere temperature. As
shown in Figure 2, the warming/cooling processes of land and sea must proceed through the
atmosphere before they have impact on the outgoing LW flux Eg. Therefore, in dynamic analyses, the
change of Eg travels through two sequential dynamic processes with different time constants and all
changes start with the cloudiness change process.
The transient change of the atmosphere temperature can be realized from the surface temperatures and
from the downward LW fluxes (Ed) of the different skies in a pseudo-balance situation. For example,
as the sky turns from all-sky to cloudy, the Ed
a
flux of 344.7 grows to Ed
o
flux 359 and the surface
temperature increases from 15.9 °C to 16.0 °C, even though the step input change of the driving force
SW insolation has decreased from 237.8 to 222. Finally, the Ed
a
would decrease to 302 W/m
2
if the
cloudy conditions could prevail long enough. When there is a step change like this, the temperature of
the atmosphere moves in the opposite direction (higher temperature) before the very slow change of
land and sea temperatures finally decrease the upward LW radiation flux Es
o
and thus also decrease the
temperature of the atmosphere. The author calls this phenomenon the transient change of atmosphere
because it can be analyzed as a separate dynamic process. The dynamics of this process is governed by
the time constant of the atmosphere, which has been marked by the acronym Ƭ
atm
.
The transient change in the atmosphere has a small effect on the OLR flux. The magnitude of this
change is very small and it is difficult to calculate. Therefore in this study the transient change has
been utilized only in the surface temperature change calculations, where it is directly measureable and
can be quantified.
Stine et al.
5
have found that the mean time lags between the annual irradiation and temperature cycles
are 29±6 days over the land and 56±11 days over the ocean. Kauppinen et al.
14
have analyzed different
studies of time delays, and they have used these values as a basis for calculating the time constants of
the land and the ocean. Their final results were Ƭ
land
= 1.04 months and Ƭ
sea
= 2.74 months, utilizing
the dynamic analysis of the sinusoidal input. The author has also used these time constants in this
study. The time constant of the atmosphere is not available, and therefore the author has used the heat
capacity difference of the ocean, which is 30 times the heat capacity of the atmosphere (Kauppinen et
al.
14
), resulting in the time constant Ƭ
atm
= 0.091 months = 2.74 days. There are three processes that
have very short time constants: the temperature change of clouds, the absorption of SW radiation in the
atmosphere and the change in cloudiness, which causes a rapid change of the upward LW flux Eu
transmitting into space as well as the rapid change of the upward flux Ec emitted by clouds. Long
15
has
estimated the clear sky upwelling fluxes and he has utilized the Atmospheric Radiation Measurement
(ARM) Program data of diurnal variations. The author has utilized the same data (ARM
16
) and
prepared Figure 2, naming the fluxes according to the acronyms used in this paper.

Dynamics...
563
J. Chem. Bio. Phy. Sci. Sec. C; Nov. 2013
Figure 2:
Fluxes at the Atmospheric Radiation Measurement (ARM) SGP site in January 2004
(ARM
16
). The thin vertical blue lines ind
This graphical presentation shows that the cloudiness change (starting at 21:00 on January 19 and
ending at about 3:00 on January 20) produces the Ec i
analysis reveals
that the time delay is about 15 minutes, corresponding to the time constant
minutes. Theoretically
also the temperature of clouds changes, when the cloudy sky stays a long period
over
the same place. This change can be estimated to be so small that it has no practical effect in
dynamic analysis. The top layer of clouds absorbs the same amount of solar insolation in all climate
conditions all the time and therefore the temperature is al
upwards remains almost constant. The total amount of water in the atmosphere is 13.2*10
only 0.01 % is in liquid form (clouds). The total mass of the atmosphere is 5.3*10
constant of the clouds (Ƭ
cloud
)
can be estimated to be only 0.1 minutes calculated from the atmosphere’s
time constant.
In the clear day, the LW flux at TOA reacts rapidly to the increasing SW insolation. In
this situation, OLR flux is the sum of the transmitted flux
warming of the atmosphere caused by SW absorption of the clear air. It is impossible to separate these
two radiation fluxes from each other during the clear atmosphere. The peak of OLR during daytime on
January 20 is c
aused mainly by the absorption of SW in the atmosphere, because the LW flux Eu is
totally absorbed by clouds. The SW absorption process time lag can be estimated with reasonable
accuracy. The digital data analysis shows that the time delay is about 30 minu
constant Ƭ
air
= 8 minutes. It
should be noticed that
results of different absorption processes. SW insolation absorption by the atmosphere starts from the
upper layers of the atmosphere
atmosphere is much smaller than the lower part. The upward LW radiation is slowed down by the heat
capacity of the atmosphere before any changes occur in the outgoing LW flux Eg at TOA.
of downward LW flux Ed as shown in
temperature. Ohmura
17
has analyzed the behavior of Ed; the main results are that 67
from the first 10 m, 89% from the first 1
the results of Ollila
12
that LW absorption caused by greenhouse gases takes place 95% during the first
2 km. Because the warming of almost the whole atmospheric mass is needed before the outg
Dynamics...
J. Chem. Bio. Phy. Sci. Sec. C; Nov. 2013
-
Jan .2014; Vol.4, No.1; 557
Fluxes at the Atmospheric Radiation Measurement (ARM) SGP site in January 2004
). The thin vertical blue lines ind
icate the times of the SW flux changes.
This graphical presentation shows that the cloudiness change (starting at 21:00 on January 19 and
ending at about 3:00 on January 20) produces the Ec i
ncrease almost
instantaneously.
that the time delay is about 15 minutes, corresponding to the time constant
also the temperature of clouds changes, when the cloudy sky stays a long period
the same place. This change can be estimated to be so small that it has no practical effect in
dynamic analysis. The top layer of clouds absorbs the same amount of solar insolation in all climate
conditions all the time and therefore the temperature is al
most constant and therefore emitted radiation
upwards remains almost constant. The total amount of water in the atmosphere is 13.2*10
only 0.01 % is in liquid form (clouds). The total mass of the atmosphere is 5.3*10
can be estimated to be only 0.1 minutes calculated from the atmosphere’s
In the clear day, the LW flux at TOA reacts rapidly to the increasing SW insolation. In
this situation, OLR flux is the sum of the transmitted flux
Eu caused by the warming of land and
warming of the atmosphere caused by SW absorption of the clear air. It is impossible to separate these
two radiation fluxes from each other during the clear atmosphere. The peak of OLR during daytime on
aused mainly by the absorption of SW in the atmosphere, because the LW flux Eu is
totally absorbed by clouds. The SW absorption process time lag can be estimated with reasonable
accuracy. The digital data analysis shows that the time delay is about 30 minu
should be noticed that
Ƭ
air
and Ƭ
atm
are different because they are the
results of different absorption processes. SW insolation absorption by the atmosphere starts from the
upper layers of the atmosphere
and it proceeds downwards. The heat capacity of the upper parts of the
atmosphere is much smaller than the lower part. The upward LW radiation is slowed down by the heat
capacity of the atmosphere before any changes occur in the outgoing LW flux Eg at TOA.
of downward LW flux Ed as shown in
Figure 1
reveals that it reacts slowly with the increasing surface
has analyzed the behavior of Ed; the main results are that 67
from the first 10 m, 89% from the first 1
km, and 95% from the first 2 km. This is perfectly in line with
that LW absorption caused by greenhouse gases takes place 95% during the first
2 km. Because the warming of almost the whole atmospheric mass is needed before the outg
Dynamics...
Antero Ollila.
Jan .2014; Vol.4, No.1; 557
-575.
Fluxes at the Atmospheric Radiation Measurement (ARM) SGP site in January 2004
icate the times of the SW flux changes.
This graphical presentation shows that the cloudiness change (starting at 21:00 on January 19 and
instantaneously.
The digital data
that the time delay is about 15 minutes, corresponding to the time constant
Ƭ
clch
= 4
also the temperature of clouds changes, when the cloudy sky stays a long period
the same place. This change can be estimated to be so small that it has no practical effect in
dynamic analysis. The top layer of clouds absorbs the same amount of solar insolation in all climate
most constant and therefore emitted radiation
upwards remains almost constant. The total amount of water in the atmosphere is 13.2*10
12
tons and
only 0.01 % is in liquid form (clouds). The total mass of the atmosphere is 5.3*10
15
tons. The time
can be estimated to be only 0.1 minutes calculated from the atmosphere’s
In the clear day, the LW flux at TOA reacts rapidly to the increasing SW insolation. In
Eu caused by the warming of land and
warming of the atmosphere caused by SW absorption of the clear air. It is impossible to separate these
two radiation fluxes from each other during the clear atmosphere. The peak of OLR during daytime on
aused mainly by the absorption of SW in the atmosphere, because the LW flux Eu is
totally absorbed by clouds. The SW absorption process time lag can be estimated with reasonable
accuracy. The digital data analysis shows that the time delay is about 30 minu
tes, giving the time
are different because they are the
results of different absorption processes. SW insolation absorption by the atmosphere starts from the
and it proceeds downwards. The heat capacity of the upper parts of the
atmosphere is much smaller than the lower part. The upward LW radiation is slowed down by the heat
capacity of the atmosphere before any changes occur in the outgoing LW flux Eg at TOA.
The analysis
reveals that it reacts slowly with the increasing surface
has analyzed the behavior of Ed; the main results are that 67
-73% originates
km, and 95% from the first 2 km. This is perfectly in line with
that LW absorption caused by greenhouse gases takes place 95% during the first
2 km. Because the warming of almost the whole atmospheric mass is needed before the outg
oing Eg

Dynamics... Antero Ollila.
564 J. Chem. Bio. Phy. Sci. Sec. C; Nov. 2013-Jan .2014; Vol.4, No.1; 557-575.
radiation reaches the equilibrium value, the time constant of 2.74 days is reasonable. Locally, the
winds can change this ideal situation very quickly.
DYNAMIC ANALYSES
Change from all-sky to clear sky conditions: Using the information of the division between sea and
land processes, the step input change 51.2 W/m
2
from 237.8 W/m
2
to 289 W/m
2
can be divided into
three parts. Ec
a
disappears very quickly (Ƭ
clch
4 min.), which means that Eu
b
is the same as the Eu
a
+Ac
a
in the beginning of the change. The magnitude of this change is Ac
a
- Ec
a
= +15.7 W/m
2
. The rapid
change of Eg flux (Ƭ
air
8 min.) caused by clear air absorption is Eg
air
= Eg
b
– Eg
a
= 175.8 – 169.8 = 6.0
W/m
2
. The rest of the change happens through the warming processes of sea and land. The total size of
this change is 289 – 237.8 – 15.7 – 6.0 = 29.5 W/m
2
. This change happens through the changes of Eu
b
and Eg
b
. The true balance value of Eu
b
is 67, and therefore this change (dynamic delay Ƭ
land
) is 67 –
(55.4 + 28.3) = -16.7 W/m
2
. The Eg
b
changes from the pseudo-balance value of 175.8 to the true
balance value of 222 through two processes (Ƭ
land
and Ƭ
atm
), and the size is +46.2 W/m
2
. Both changes
must be divided between land and sea. These changes have been depicted in Figure 3, where the time
scale is a combination of two scales. The first part is linear from 0 to 0.1 day and the end part of the
scale is logarithmic from 0.1 to 600 days. This arrangement illustrates more accurately the changes
around the pseudo-balance states. This time scale presentation has been applied also in other figures.
Figure 3: Dynamic response of the OLR
b
to the stepwise change from all-sky ASR 237.8 W/m
2
to
clear sky ASR
b
289 W/m
2
. The pseudo-balance of clear sky is the observed OLR
b
259 W/m
2
.
The stepwise change of the solar radiation from all-sky 237.8 W/m
2
to clear sky 289 W/m
2
first causes
OLR
b
= 259 W/m
2
as observed by Zhang et al.
8
at TOA, which can be called a pseudo-balance value.
This value corresponds to a 41.4 % change from 237.8 W/m
2
and on the time scale it happens at the
point of 0.02 days. The OLR values between 258 and 260 could be measured during the time span of

Dynamics... Antero Ollila.
565 J. Chem. Bio. Phy. Sci. Sec. C; Nov. 2013-Jan .2014; Vol.4, No.1; 557-575.
0.01 to 3.0 days. The pseudo-balance value is not sensitive for the measurement moment, because it
has been caused by two rapid process changes, which shoot Eg
b
0.2 % over the pseudo-balance value.
Change from all-sky to cloudy sky conditions: Also the stepwise change from all-sky conditions to
totally cloudy conditions cannot reach the final steady-state value, which would be the SW input ASR
o
= 222 W/m
2
. The measured (Zhang et al.
8
) OLR
o
is 226.8 W/m
2
, which means that the change (226.8
– 237.8 = -11.0 W/m
2
) has reached 69.6% of the total input step (222 – 237.8 = -15.8 W/m
2
).
In the change from all-sky to cloudy sky, the three radiation fluxes Eg, Eu and Ec forming the OLR
o
behave in different ways. Transmitted radiation into space Eu
a
28.3 W/m
2
disappears totally as soon as
the sky turns cloudy. The Ec
o
value is 60.1 W/m
2
and the change 60.1 - (28.3+39.7) = -7.9 W/m
2
follows the increase rate of the amount of clouds (time delay Ƭ
clch
4 min. and Ƭ
cloud
0.1 min). The rapid
change of Eg flux caused by clear air absorption (time delay Ƭ
air
8 min.) is Eg
o
- Eg
a
= 166.7 -169.8 = -
3.1 W/m
2
.
The rest of the change happens through the cooling processes of sea and land. The total size of this
change is 222 – 237.8 + 7.9 + 3.1 = -4.8 W/m
2
. This change happens through the changes of Ec
o
and
Eg
o
. The true balance value of Ec
o
is 59, and therefore this change is 59.0 - 60.1 = -1.1 W/m
2
. Eg
o
changes from the value of 166.7 to the true balance value of 163, and the size is -3.7 W/m
2
. Both
changes must be divided between land and sea. The results are depicted in Figure 4.
Figure 4: Dynamic response of the OLR
o
to the stepwise change from all-sky ASR
237.8 W/m
2
to the cloudy sky ASR
o
222 W/m
2
. The pseudo-balance of the cloudy sky
OLR
o
is the observed 226.8 W/m
2
.
In this case, the exact observed OLR
o
value of 226.8 can be measured immediately. The OLR values
between 227.8 – 225.8 could be measured during the time span of 0 to 13.0 days. The observed value
of OLR
o
226.8 W/m
2
can be explained by the fact that the rapid process changes in the atmosphere

Dynamics... Antero Ollila.
566 J. Chem. Bio. Phy. Sci. Sec. C; Nov. 2013-Jan .2014; Vol.4, No.1; 557-575.
cause 100% of the change. Because the pseudo-balance value is close to the real balance value, the
small errors in measurements and data can easily change the time scale behavior.
Change from cloudy sky to clear sky conditions: The initial state in this analysis is cloudy sky in the
pseudo-balance state. In this change Ec
o
disappears very quickly (Ƭ
clch
4 min) and it is replaced by Ac
o
.
The magnitude of this change is Ac
o
– Ec
o
= 84 – 60.1 = +23.9 W/m
2
. The rapid change of Eg flux
(Ƭ
air
8 min) caused by clear air absorption is Eg
b
– Eg
o
= 175.8 – 166.7 = 9.1 W/m
2
.
The rest of the change happens through the warming processes of sea and land. The total size of this
change is 289 – 226.8 – 23.9 – 9.1 = 29.2 W/m
2
. This change happens through the changes of Eu
b
and
Ac
b
. The true balance value of Eu
b
is 67, and therefore this change is 67 – 84 = -17.0 W/m
2
. Eg
b
changes from the pseudo-balance value of 175.8 to the true balance value of 222, and the size is +46.2
W/m
2
. Both changes must be divided between land and sea. The results of this change are depicted in
Figure 5.
Figure 5: Dynamic response of the OLR
b
to the stepwise change from cloudy sky ASR 226.8 W/m
2
to
clear sky ASR
b
289 W/m
2
. The pseudo-balance of clear sky is the observed OLR
b
259 W/m
2
.
The stepwise change of the solar radiation from the cloudy sky 226.8 W/m
2
to clear sky 289 W/m
2
first causes the observed OLR
b
259 W/m
2
at TOA. This value corresponds to a 54% change from
226.8 W/m
2
, and on the time scale it happens immediately. The OLR values from 258 to 260 could be
measured during the time span of 0 to 2.0 days. Also in this case, the pseudo-balance value is not
sensitive for the measurement moment because it has been caused by two rapid process changes,
which shoot Eg
b
0.3 % over the pseudo-balance value, and the rest of the change is very slow.

Dynamics... Antero Ollila.
567 J. Chem. Bio. Phy. Sci. Sec. C; Nov. 2013-Jan .2014; Vol.4, No.1; 557-575.
Temperature trends between different skies: In this analysis the transient change impact has been
utilized. The step changes to cloudy and clear skies start from the all-sky conditions. As shown in the
earlier step changes, the pseudo-balance conditions will be reached very quickly – even in hours. The
measured Es fluxes emitted by surface in pseudo-balance reveal that the phenomenon “the transient
change” exists. Es values of the different skies reported by Zhang et al.
8
are: Es
b
= 394.1, Es
o
= 396.3,
and Es
a
= 395.6. These values correspond to the following black surface temperatures: 15.6°C, 16.0°C,
and 15.9°C. The clear sky value of 15.6°C is the lowest values but if the clear sky conditions could
prevail long enough – and locally it can happen – the surface temperature would be the highest of all.
The reason for this seemingly illogical situation is that clouds prevent cooling of the surface during the
night time and this effect exceeds the slow warming of the surface caused by increased SW solar
radiation during day time even for several days. The dynamic analysis will reveal, how long time this
situation can prevail. The transient time of this phenomenon is the time required that the temperature
of the atmosphere corresponds to the new flux emitted by the surface. This time depends on mainly the
time constant Ƭ
atm
(2.74 days) of the atmosphere. The size of the transient change is 0.1°C for the
cloudy sky change and 0.3°C for the clear sky change.
Figure 6.Dynamic responses of the surface temperatures to the stepwise changes from all-sky
conditions to the clear and cloudy sky conditions. The pseudo-balance values are the observed values.
The temperatures have been calculated from the LW upward fluxes emitted by the surface. The all-sky
surface temperature is 15.9 °C. The surface temperature is related to the upward LW flux Es
(=Ag+Ac+Eu) emitted by the surface. The total change from Es
a
395.6 to Es
b
445 (= the true balance
value) is 49.4 W/m
2
and the change from Es
a
395.6 to Es
o
381.0 (= the true balance value) is -14.6
W/m
2
. The temperature change can be calculated as described above dividing the flux changes
between land and sea and using the corresponding time constants. Finally the surface temperature can
be calculated based on the Es values. This relationship needs radiation emission and absorption
calculations applying the average global atmosphere as described by Ollila
7
. The temperature graphs

Dynamics... Antero Ollila.
568 J. Chem. Bio. Phy. Sci. Sec. C; Nov. 2013-Jan .2014; Vol.4, No.1; 557-575.
are depicted in Figure 6. The all-sky surface temperature is 15.9 °C, the clear sky true balance value is
24.5° C and the cloudy sky true balance temperature is 13.2° C (Ollila
7
).The pseudo-balance
temperatures can be reached and explained only by the fact the atmosphere temperature moves in the
beginning to the opposite direction as the final change.
CLOUD FORCING
Traditional Calculation Method: The differences between sky conditions are due to the degrees of
cloudiness in different skies. This effect is generally called cloud forcing. Normally the cloud forcing
has been calculated at TOA as the difference between clear sky and all-sky in pseudo-balance
conditions. The albedo change is the difference between Rt
b
and Rt
a
, which is -51.2 W/m
2
(using the
values of this study). The outgoing LW radiation decrease is the difference between OLR
b
and OLR
a
,
which is 21.2 W/m
2
. According to the most common definition, the cloud forcing (CF) is the sum of
these two fluxes, which in this case is -30.0 W/m
2
, a cooling effect. This value is close to the values
used in other studies (Ohring and Clapp
18
, Harrison et al.
19
, Ardany et al.
20
, Zhang et al.
8
, Raschke et
al.
10
, Loeb et al.
11
, Stephens et al.
21
), which vary between -17.0 and -28 W/m
2
average being -23.4
W/m
2
. Using the CF value of -30 Wm
-2
and the cloudiness change 66% between clear and all-sky, the
CS (Cloudiness Sensitivity) would be -0.46 Wm
-2
/CL-%. It should be noticed that the calculation of
CF with the traditional method is sensitive for small errors in SW and LW flux values. Spencer and
Braswell
22
have created a more complicated calculation method for cloud forcing by separating causes
and effect of the clouds. Their final conclusion is that clouds have a negative impact on the surface
temperature. Dressler
23
has analyzed the TOA radiation budget in response to short-term climate
variations from the years 2000 to 2010, and his results showed positive feedback of the clouds. So the
issue of cloud forcing still remains unclear without common acceptance and understanding. The
author’s approach is to use the results of the energy balance calculations and the analyses of the
dynamic behavior of the climate system. On the global scale, the climate is in the all-sky condition.
Locally the sky can be clear or cloudy for shorter or longer periods. Actually the global values of the
clear and cloudy skies have been calculated by combining locally measured flux values because on the
global scale the real clear and cloudy skies do not exist.
Cloudiness and albedo effects on the surface temperature: The simplest possible way to analyze
the cloudiness and albedo effects on the surface temperature is through the total energy balance of the
Earth equalizing the absorbed and emitted radiation fluxes according to the following equation
SC * (1-α) * (¶r
2
) = sT
4
* (4¶r
2
), 2
Where SC is solar constant (1368 W/m
2
), α is the total albedo of the Earth, s is Stefan-Bolzmann
constant (5.6704*10
-8
), and T is the temperature (K). The temperature T
a
can be calculated from this
equation:
T
a
= (SC * (1 – α) / (4s))
0.25
3
Where T
a
is the temperature of the atmosphere corresponding the emitted LW flux. The average albedo
according to this study values (Ollila
7
) is 104.2/342 = 0.30468. Using this albedo value, the
temperature T
a
would be -18.7 °C according to equation (3). Using this temperature and the Planck’s
equation, the emitted LW radiation flux of the Earth would be 237.8 W/m
2
, which is the measured
value of OLR
a
and the same as used in this study. The temperature T
a
calculated according to Equation
(3) is not the actual surface temperature of the Earth but the temperature at a certain level in the

Dynamics... Antero Ollila.
569 J. Chem. Bio. Phy. Sci. Sec. C; Nov. 2013-Jan .2014; Vol.4, No.1; 557-575.
atmosphere corresponding to the LW radiation flux emitted by the Earth’s atmosphere into the space.
The most common global surface temperature of the Earth calculated as the average value of the
surface measurements is 15 °C which means that the greenhouse effect would be 33.7 °C. Because
Equation (3) does not include the GH effect, the surface temperature T
s
has been taken into account by
adding 33.7 K into T
a
T
s
= T
a
+33.7 4
The Earth’s albedo depends mainly on the cloudiness. Ollila
7
has used the following values of
cloudiness and albedos for clear, all-sky and cloudy sky conditions: (0%, 53/342), (66%, 104.2/342),
and (100%, 120/342). The second-order polynomial can be fitted through these points and the result is
α = 0.15497 + 0.0028623 * CL – 0.000009 * CL
2
5
Where CL is cloudiness-%.The surface temperatures T
s
can be now calculated according to equations
(3) and (4) by using the different cloudiness (CL) and the albedo values of equation (5). The minimum
and maximum values of the Earth are 10.6 °C and 27.7 °C, which gives the average CS of 0.171
°C/CL-%. The graphical presentation of the surface temperature as the function of cloudiness and
albedo is depicted in Figure 8.
Cloud forcing according to true balance values: Figure 7presents a graph of the cloudiness trend
copied from the website of ISCCP
24
(International Satellite Cloud Climatology Project).In this
illustration we can see that the long-term changes in cloudiness level may take years. Utilizing the true
balance values of the different skies
7,8
(222 W/m
2
, 237.8 W/m
2
and 289 W/m
2
), a graph can be
prepared where the differences of the net incoming SW flux (NSR) are functions of the cloudiness
percentage. The surface temperatures follow the same relationship for the three different skies
7
(13.2
°C, 15.9 °C and 24.5 °C).
Using these three points of the different skies, a mathematical fitting can be made showing a slight
nonlinear dependency. Proper fittings are second-order curves, which are the following polynomials:
CF
F
= -0.98105* CL + 0.0031105 * CL
2
6
CF
T
= 24.5 – 0.16389 * CL + 0.0005089 * CL
2
7
Where CF
F
is the cloud forcing in W/m
2
, CF
T
is the cloud forcing in °C, and CL is the cloudiness
percentage. The surface temperature according to Equation (7) is also depicted in Figure 8. The
differences between the surface temperatures of the two curves in Figure 8 are due to the different
calculation bases. In Equation (4) the surface temperature is based on the global temperature
measurements. The temperature of Equation (7) is based on the measured LW flux values emitted by
the Earth’s surface. The difference is 15.9 °C – 15.0 °C = 0.9 °C when the cloudiness is 66%. The
explanation for this difference is in the accuracies and methods applied in calculating the average
global values.

Dynamics...
570
J. Chem. Bio. Phy. Sci. Sec. C; Nov. 2013
Figure 7.
The average global cloudiness (%) graph as monthly means from 1983 to 2010, presented as
anomalies of
Figure 8:
The surface temperatures as the functions of the cloudiness percentage and albedos based on
the energy balance calculations and radiation flux analyses.
The cloudiness forcing can be calculated over
values would be 0.67 Wm
-2
/CL
cloudiness can be estimated to vary in the range from 60% to 70%, as can be seen from the behavior of
the cloudiness during the last 30 years.
range. The angle coefficients of these fittings are
values are the CF values for the cloudiness changes,
Dynamics...
J. Chem. Bio. Phy. Sci. Sec. C; Nov. 2013
-
Jan .2014; Vol.4, No.1; 557
The average global cloudiness (%) graph as monthly means from 1983 to 2010, presented as
anomalies of
the global monthly mean of 66.32% (ISCCP
24
The surface temperatures as the functions of the cloudiness percentage and albedos based on
the energy balance calculations and radiation flux analyses.
The cloudiness forcing can be calculated over
the whole range from 0% to 100% and the cloud forcing
/CL
-% or 0.113 °C/CL-% (24.5 °C –
13.2 °C). In reality the average global
cloudiness can be estimated to vary in the range from 60% to 70%, as can be seen from the behavior of
the cloudiness during the last 30 years.
That is why a linear fitting is a good estimate in this limited
range. The angle coefficients of these fittings are
-0.564 W/m
2
per CL-% and
-
values are the CF values for the cloudiness changes,
assuming that the change has settled to another
Dynamics...
Antero Ollila.
Jan .2014; Vol.4, No.1; 557
-575.
The average global cloudiness (%) graph as monthly means from 1983 to 2010, presented as
24
).
The surface temperatures as the functions of the cloudiness percentage and albedos based on
the energy balance calculations and radiation flux analyses.
the whole range from 0% to 100% and the cloud forcing
13.2 °C). In reality the average global
cloudiness can be estimated to vary in the range from 60% to 70%, as can be seen from the behavior of
That is why a linear fitting is a good estimate in this limited
-
0.096 °C/CL-%. These
assuming that the change has settled to another

Dynamics... Antero Ollila.
571 J. Chem. Bio. Phy. Sci. Sec. C; Nov. 2013-Jan .2014; Vol.4, No.1; 557-575.
level during the longer time period. This time span is about one year, based on the time constants of
land and sea as previously analyzed.
Analysis of different cloud forcing values: In Table 3 is a summary of different cloud forcing values
calculated by different methods.
Table-3: The summary of cloud forcing values. The asterisk (*) values have been calculated by using
the climate sensitivity parameterλ. According to IPCC
25
a typical λ value is 0.5* but according to the
AR5
26,
the value of λ is only 0.85 K / 2.34 Wm
-2
= 0.363** K/(Wm
-2
) .
Method
Cloud forcing, Wm
-
2/CL
-
%
Cloud forcing, °C/CL
-
%
Traditional, average value (
-
23.4 Wm
-
2)
-
0.36
-
0.18*,
-
0.13**
Traditional, this study
(
-
30.0 Wm
-
2)
-
0.46
-
0.23*,
-
0.17**
Radiation balance equations (eq. 2
-
4)
-
0.471**
-
0.171
Total energy balance, cloud. range 0
-
100%
-
0.67
-
0.11
Total energy balance, linearized 60%
-
70%
-
0.564
-
0.096
The difference between 0.363 W/m
2
and 0.46 W/m
2
calculated in the traditional way is due to the
different SW and LW flux values measured at TOA. These flux values are measured in clear and all-
sky conditions. The final result is that clouds should have a negative impact on the surface
temperature. At the same time the measured LW fluxes emitted by the surface show that the all-sky
LW flux upward
8
is 395.6 W/m
2
corresponding to a temperature
7
of 15.9 °C and the clear sky values
7,8
are 394.1 W/m
2
and 15.6 °C. If we compare the cloud impacts and the real surface temperatures, there
is a most profound contradiction: the cooling effect of CF has caused the increased surface
temperature!
The explanation is in the dynamical delays of the climate system. The pseudo-balance values as
depicted in Table 2 show that the real measured values of the upward LW radiation fluxes from the
surface (and the surface temperatures) move in the beginning toward the opposite direction when
compared to the final change. As previously analyzed, this behavior is due to the warming effects of
clouds at night and the heat capacity of the atmosphere. This state is temporary and will vanish in
about one week. This dynamic behavior may lead to the wrong conclusion that an increase in
cloudiness has a positive impact on the surface temperature, which is not possible in the long run.
A theoretical problem in calculating the CF in the traditional way is the OLR
b
value of the clear sky
(259 W/m
2
), which is actually a pseudo-balance value caused by the cloudiness change from 66% to
0%. The real CF is same as the net SW radiation change, which is 289 - 237.8 = 51.2 W/m
2
in the
cloudiness range 0-66% and 289 - 222 = 67 W/m
2
in the cloudiness range 0-100%. As shown above,
the change needs time, because the surface temperature has increased at the same time as the CF has
caused a cooling effect. Using the pseudo-balance OLR
b
value of the clear sky is simply not the right
choice in calculating cloud forcing, because this OLR
b
flux is not a direct forcing but it is a result of
the real forcing caused by SW radiation change.

Dynamics... Antero Ollila.
572 J. Chem. Bio. Phy. Sci. Sec. C; Nov. 2013-Jan .2014; Vol.4, No.1; 557-575.
The author’s choice is to calculate the CF value by applying the total SW radiation change caused by
cloudiness change, to use true balance values, and to calculate the CF for cloudiness percentage in the
cloudiness range from 60% to 70%, which is the normal range of cloudiness variation. The value of the
climate sensitivity parameter λ seems to vary in IPCC’s reports and which means that the right value
of λ is still unclear.
There is a difference, if compared 0.171 °C/CL-% to the value of 0.11 °C/CL-%. The latter value is
based on the GH effect calculations in the atmosphere but the radiation balance equations (2-5) does
not take GH effect into account and in this respect the CS value of 0.171 °C/CL-% can be assessed to
be more theoretical. The CF value of 0.67 Wm
-2
/CL-% is 45.6% bigger than the 0.46 Wm
-2
/CL-%
calculated on the traditional way. This difference is same as is the difference between pseudo-balance
and true balance values of radiation fluxes at TOA.
A short analysis can also be carried out to find out whether a cloudiness change could have a role in
global warming. According to IPCC
27
, the historical warming till 2005 has been 0.76 °C. Applying the
cloud forcing value 0.096°C/CL-% of this study, the 7.9 cloudiness-% decrease is needed for the same
increase if no other impacts have been included. This kind of change may be possible if compared to
the trend graph of Figure 7.
DISCUSSION AND CONCLUSIONS
In this study, dynamic analyses have been carried out for the changes between different sky conditions.
The time constant of the land process has been 1.04 months and for sea process 2.74 months. The
author has analyzed the real time data (ARM
16
) and found that the time constant for the cloudiness
change process is 4 minutes, cloud heating/cooling 0.1 minutes, and for absorption/emission of SW
radiation the time constant is 8 minutes. The accuracies of these time constants are not critical. The
time constant of the atmosphere warming/cooling as a response to the LW upward radiation has been
estimated to be 2.74 days. The accuracy of the time constants of land and sea processes has a dominant
effect on the time domain behavior of the true balance value. The true balance values of radiation
fluxes are quite theoretical and cannot be achieved on the global scale if applied to the clear and
cloudy sky conditions. On the other hand the cloudiness changes having surface temperature effects
may reach new true balance states, because the changes can take years.
The simulations of dynamic changes using the achieved time constants reveal that in all changes, two
rapid changes in the atmosphere can bring the outgoing LW radiation at TOA almost exactly
(difference from 0% to 0.3%) to the observed pseudo-balance values of clear and cloudy skies (259
W/m
2
and 226.8 W/m
2)
. Actually so small differences mean that the pseudo-balance values have been
reached after the atmospheric flux changes. These rapid processes are the cloudiness change process
and the SW insolation absorption process in the atmosphere. Because the time constants of these
processes are only 4 minutes and 8 minutes, the pseudo-balance values can be measured as quickly as
diurnal variations have been included in the data. Because the main change depends on the very slow
change of the temperature of land and sea, according to dynamic analyses, the pseudo-balance values
stay within ±1 W/m
2
from 1 to 13 days depending on the change type. This means that the
measurement time of pseudo-balance values for clear and cloudy skies is not very time-sensitive.
The analysis of pseudo-balance radiation fluxes reveal why the surface temperature moves in the
beginning of the change to the opposite direction as the final change. For example, the change from

Dynamics... Antero Ollila.
573 J. Chem. Bio. Phy. Sci. Sec. C; Nov. 2013-Jan .2014; Vol.4, No.1; 557-575.
all-sky to cloudy sky increases the LW upward and downward fluxes in the beginning so much that at
pseudo-balance, the surface temperature has increased from 15.9 °C to 16.0 °C, but finally the true
balance value of the cloudy sky surface temperature would be 13.2 °C. The reason for this
phenomenon is the temporary warming of the lower atmosphere because of clouds. In cloudy
conditions the night time cooling, according to Sfefan-Bolzmann’s law, is so much smaller than the
corresponding cooling under a clear sky that the average temperature will increase slightly even
though the daytime insolation is higher. There is a good illustration of this phenomenon in Figure 2
based on the real data. The author has called this process the transient change of atmosphere. The time
constant of this process has been assumed to be the same as warming and cooling of the atmosphere
due to the LW radiation change, which is estimated to be 2.74 days.
The only explanation for the small changes in opposite directions in the beginning of the change is this
transient process of the atmosphere. The measured emitted flux values by surface in the pseudo-
balance skies could be a reason that some researchers have concluded that the clouds have a positive
impact on the surface temperature. When the climate effects and changes are addressed, the time scale
should be at least one year and preferably 10 years.
The calculated results mean that the cloudiness increase from 0% to 66% decreases the balance
temperature of the earth from 24.5 °C to 15.9 °C and the further increase to 100% would decrease the
surface temperature to 13.2 °C. The cloud effect would be -0.65 W/m
2
per 1 CL-% and -0.113 °C/CL-
% over the whole cloudiness range. Kauppinen and his research team (their research paper is in a
review process - private communications) have calculated this sensitivity based on a dynamic physical
analysis, with the value being -0.11 °C/CL-%, which is the same value as calculated on the basis of the
total energy balance.
It should also be noticed that the common used cloud forcing values of 21-28 W/m
2
(cooling) is
applicable only for short term impact calculations because this value is based on the pseudo-balance
values of the clear sky. The cloudiness change based on the long-term changes originating, for
example, from the sun and cosmic radiation changes, happens over a span of years, and it means that a
new balance state can be reached. Scientists report different results on the impact of clouds. The
majority of researchers have found that clouds have cooling effects on the climate. Some researchers,
e.g. Dressler
23
and Lacis et al.
28
, have reported warming effects of clouds in the GH phenomena. In
this sense, the results of this study are very clear: long term cloudiness changes have a negative impact
on surface temperatures as well as on the OLR fluxes, which is already a known fact.
According to the IPCC
26
, the radiation forcing value of 1.6 W/m
2
of 99 ppm CO
2
increase has caused
the temperature increase of 0.76 °C from 1750 to 2005 assuming that the warming effect has totally
reached the new balance value. Utilizing the linearized cloud forcing values 0.564 Wm
-2
/CL-% and
0.096 °C/CL-% calculated according to the true balance method, 3% cloudiness change would cause
1.6 W/m
2
climate forcing corresponding to only 0.29 °C increase and 7.9% cloudiness decrease is
needed for 0.76 °C increase. Ollila
12
has calculated the warming value of 0.2 °C for the 99 ppm CO
2
increase utilizing spectral calculation methods.
Two potential reasons could explain the results of IPCC. One explanation is that the water feedback,
which doubles the CO
2
impact, has been used in the calculations referred by IPCC and/or the water
content of the atmosphere has been smaller than in the real global average atmosphere, which increases
the warming effect of CO
2
. IPCC has omitted the cloud forcing effects in its warming analyses even

Dynamics... Antero Ollila.
574 J. Chem. Bio. Phy. Sci. Sec. C; Nov. 2013-Jan .2014; Vol.4, No.1; 557-575.
though 6% cloudiness change and the conservative climate sensitivity value of 0.3 Wm
2
/CL-% would
cause 1.8 Wm
-2
forcing having the same effect as CO
2
.
The primary energy comes always from the sun and the LW radiation fluxes depend on this energy
source in the long run. The real cloud forcing starts therefore from the SW radiation flux changes,
which force the climate finally to another balance state. The forcing process goes through the different
atmospheric processes including the changes of LW radiation fluxes caused by clouds. The cloud
forcing issue can be also simplified by calculating the long-term (min. 1 year) surface temperature
changes caused by the global cloudiness changes. The increased cloudiness always decreases the
surface temperature in the long run.
ACKNOWLEDGEMENTS
Data for the SGP site were obtained from the Atmospheric Radiation Measurement (ARM) Program
sponsored by the U.S. Department of Energy, Office of Science, Office of Biological and
Environmental Research, Climate and Environmental Sciences Division.:
The ISCCP D2 cloudiness image was obtained on December 2012 from the International Satellite
Cloud Climatology Project website http://isccp.giss.nasa.gov/climanal1.html, maintained by the
ISCCP research group at the NASA Goddard Institute for Space Studies, New York, NY.
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Corresponding author: Antero Ollila,
Department of Civil and Environmental Engineering, School of Engineering,
Aalto University, Espoo, Finland,