Climate Sensitivity Parameter in the Test of the Mount Pinatubo Eruption

Abstract

The author has developed a dynamic model (DM) to simulate the surface temperature change (∆T) caused by the eruption of Mount Pinatubo. The main objectives have been 1) to test the climate sensitivity parameter (λ) values of 0.27 K/(Wm-2) and 0.5 K/(Wm-2), 2) to test the time constants of a simple first-order dynamic model, and 3) to estimate and to test the downward longwave radiation anomaly (∆LWDN). The simulations show that the calculated ∆T of DM follows very accurately the real temperature change rate. This confirms that theoretically calculated time constants of earlier studies for the ocean (2.74 months) and for the land (1.04 months) are accurate and applicable in the dynamic analyses. The DM-predicted ∆T values are close to the measured value, if the λ-value of 0.27 K/(Wm-2) has been applied but the λ-value of 0.5 K/(Wm-2) gives ∆T values, which are about 100% too large. The main uncertainty in the Mount Pinatubo analyses is the ∆LWDN flux, because there are no direct measurements available during the eruption. The author has used the measured ERBS fluxes and has also estimated ∆LWDN flux using the apparent transmission measurements. This estimate gives the best and most consistent results in the simulation. A simple analysis shows that two earlier simulations utilising General Circulation Models (GCM) by two research groups are depending on the flux value choices as well as the measured ∆T choices. If the commonly used minimum value of-6 Wm-2 would have been used for the shortwave anomaly in the GCM Original Research Article Ollila; PSIJ, 9(4): 1-14, 2016; Article no.PSIJ.23242 2 simulations, instead of-4 Wm-2 , the ∆T values would differ from the measured ∆T values almost 100%. The main reason for this error seems be the λ-value of 0.5 K/(Wm-2).

Full text

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*Corresponding author: E-mail: aveollila@yahoo.com;
Physical Science International Journal
9(4): 1-14, 2016, Article no.PSIJ.23242
ISSN: 2348-0130
SCIENCEDOMAIN international
www.sciencedomain.org
Climate Sensitivity Parameter in the Test of the
Mount Pinatubo Eruption
Antero Ollila
1*
1
Department of Civil and Environmental Engineering (Emer.), School of Engineering, Aalto University,
Otakaari 1, Box 11000, 00076 AALTO, Espoo, Finland.
Author’s contribution
The sole author designed, analyzed and interpreted and prepared the manuscript.
Article Information
DOI: 10.9734/PSIJ/2016/23242
Editor(s):
(1)
Yichi Zhang, Key Laboratory of Water Cycle & Related Land Surface Processes, Institute of Geographic Sciences and
Natural Resources Research, Chinese Academy of Sciences, China.
(2)
Ismail Gultepe, Environment Canada, Cloud Physics and Severe Weather Res. Section, Canada.
(3)
Abbas Mohammed, Blekinge Institute of Technology, Sweden.
Reviewers:
(1)
Anonymous, University of St. Thomas, USA.
(2)
Mahmut Dogru, Bitlis Eren University, Turkey.
(3)
S. B. Ota, Institute of Physics, Bhubaneswar, India.
(4)
Bharat Raj Singh, Technical Campus, Lucknow, India.
Complete Peer review History:
http://sciencedomain.org/review-history/13553
Received 21
st
November 2015
Accepted 14
th
February 2016
Published 4
th
March 2016
ABSTRACT
The author has developed a dynamic model (DM) to simulate the surface temperature change (∆T)
caused by the eruption of Mount Pinatubo. The main objectives have been 1) to test the climate
sensitivity parameter (λ) values of 0.27 K/(Wm
-2
) and 0.5 K/(Wm
-2
), 2) to test the time constants of
a simple first-order dynamic model, and 3) to estimate and to test the downward longwave radiation
anomaly (∆LWDN). The simulations show that the calculated ∆T of DM follows very accurately the
real temperature change rate. This confirms that theoretically calculated time constants of earlier
studies for the ocean (2.74 months) and for the land (1.04 months) are accurate and applicable in
the dynamic analyses. The DM-predicted ∆T values are close to the measured value, if the λ-value
of 0.27 K/(Wm
-2
)
has been applied but the λ-value of 0.5 K/(Wm
-2
) gives ∆T values, which are about
100% too large. The main uncertainty in the Mount Pinatubo analyses is the ∆LWDN flux, because
there are no direct measurements available during the eruption. The author has used the measured
ERBS fluxes and has also estimated ∆LWDN flux using the apparent transmission measurements.
This estimate gives the best and most consistent results in the simulation. A simple analysis shows
that two earlier simulations utilising General Circulation Models (GCM) by two research groups are
depending on the flux value choices as well as the measured ∆T choices. If the commonly used
minimum value of -6 Wm
-2
would have been used for the shortwave anomaly in the GCM
Original Research Article

Ollila; PSIJ, 9(4): 1-14, 2016; Article no.PSIJ.23242
2
simulations, instead of -4 Wm
-
2
, the ∆T values would differ from the measured ∆T values almost
100%. The main reason for this error seems be the λ-value of 0.5 K/(Wm
-2
).
Keywords: Global warming; climate sensitivity parameter; climate response time; radiative forcing
response; downward radiative fluxes; Mount Pinatubo eruption.
1. INTRODUCTION
1.1 Objectives and Symbols
The Mount Pinatubo eruption in 1991 caused a
global cooling during the next five years as the
incoming shortwave radiation was reduced by 6
W/m
2
offering a unique opportunity to test and to
analyse the various phenomenon of the climate
system. Water vapour feedback has remained a
topic of debate since 1990 and the eruption can
be used to analyse this effect also. The first
objective of this paper is to test the two climate
sensitivity parameter values which have been
commonly used in the scientific studies. The
second objective is to test the climate system
time constants describing the dynamic behaviour
of the climate exposed to a relative big and
sudden change. The third objective is to estimate
and to test the downward longwave radiation
anomaly (∆LWDN). In the simulations a
theoretical feedback property of the climate
system has been also tested.
Table 1 includes all the symbols, abbreviations,
acronyms and definitions used repeatedly in this
paper.
1.2 The Mount Pinatubo Eruption
The main eruption of the Mount Pinatubo volcano
(15.1 °N, 120.3 °E) on the island of Luton in the
Philippines began on the 3
rd
of June, 1991 and
concluded on the next day. Four large explosions
generated eruption columns reaching the heights
of up to 24 km in the stratosphere. The estimate
of the stratospheric mass increase was 14–20 Mt
of SO
2,
which created 21-40 Mt of H
2
SO
4
–H
2
O
aerosols [1]. The eruption also injected vast
quantities of minerals and metals into the
troposphere and stratosphere in the form of ash
particles. The aerosols formed a global layer of
sulfuric acid haze over the globe and the global
temperatures dropped about 0.5°C in the years
1991 – 1993.
The sulphate aerosols caused scattering of the
visible light and therefore the incoming radiation
scattered more effectively back into space. Thus
the albedo of the Earth increased leading to a
cooling at the Earth’s surface. On the other hand
the plants utilized the climate conditions,
because they could photosynthesize more
effectively in the diffuse sunlight [2,3]. As a result
of the more intensive photosynthesis, there was
a negative anomaly of the global CO
2
concentration increase rate.
Table 1. List of symbols, abbreviations, and
acronyms
Acronym
Definition
DM One dimensional dynamic model
AT Apparent transmission
ENSO El Niño Southern Oscillation
ERBS NASA’s Earth Radiation Budget
Satellite
GCM General Circulation Model
ISCCP International Satellite Cloud
Climatology Project
LW Longwave
LWDN LW radiation flux downward
LWUP LW radiation flux upward
LWSRF LW radiation emitted by the
surface
OLR Outgoing longwave radiation
ONI Oceanic Niño Index
RF Radiative forcing change
SW Shortwave
SWATM SW radiation flux absorbed by
the atmosphere
SWIN SW radiation flux incoming at the
TOA
SWSRF SW radiation flux incoming at the
surface
TOA Top of the atmosphere
TPW Total precipitable water
T Surface temperature
Tm 1DM-predicted surface
temperature change
Tav Average surface temperature
change by four datasets
Tmsu Surface temperature change by
UAH MSU dataset
Tav-e Tav with ENSO correction
Tmsu-e Tmsu with ENSO correction
TCS Transient climate sensitivity
λ Climate sensitivity parameter
∆ Anomaly or change
Subscript
n
means step n in time domain.

Ollila; PSIJ, 9(4): 1-14, 2016; Article no.PSIJ.23242
3
Because the eruption happened at one point, it
took several weeks before the global effect was
fully developed. The volcanic aerosol cloud
encircled the Earth in 21 days driven by the
easterly winds in the tropical stratosphere. It
covered about 42% of the Earth in two weeks [4].
In Fig. 1 are depicted the global temperature [5]
and the apparent transmission measured at
Mauna Loa [6] (19.3°N, 155.4°W). It can be seen
that there is delay between the temperature
response and the apparent transmission (AT)
describing the reduction of the incoming
shortwave (SW) radiation.’
Fig. 1. The global satellite temperature and
the apparent transmission measured at
Mauna Loa, Hawaii
In Fig. 2 the apparent transmissions (AT) are
depicted at the various sites on the northern
hemisphere [7]. It can be seen that the absolute
values of the AT values are different depending
mainly on the local conditions. For example, the
low values of the Japanese sites describe the air
quality of the local conditions. The large value of
the Mauna Loa is due to the fact that it is at the
altitude of 3.4 km in the middle of the Pacific. An
important feature thinking the analysis methods
of this study is that the percentage decreases are
very close to each other in the range from 10.1%
to 13.2%.
The sites in Fig. 2 cover almost 85% of the
northern hemisphere. Thomas [8] has analyzed
the global apparent transmission measurements
after the eruption. The analysis shows that the
aerosol cloud was covering the latitudes from
60S to 60N after three months and practically
uniform over the hemispheres after six months.
This is also the moment of the maximum
temperature decrease. The main role in
spreading the cloud had planetary scale waves in
high latitudes, which transported the volcanic
aerosol from the tropics to high latitudes. The
reason why the decrease of apparent
transmission value was almost the same at the
high latitudes as in the tropics is probably due to
the zenith angle. Even though the sulphate cloud
would be thinner at the high latitudes, the
sunlight has a longer pathway through the
atmosphere. This phenomenon can compensate
the effects of possible thinner cloud conditions.
Two conclusions can be drawn from these
figures. The global delay called a dead time in
process dynamics, is estimated to be 1.6 months
between the incoming SW radiation change and
the global surface temperature response. This
value is used in the dynamical analyses of this
study.
Fig. 2. The apparent transmission values at
the various sites. The percentage values
show the maximum decreases of the
apparent transmissions after the eruption and
they are represented by light bars inside the
normal apparent values (total bar length)
Another conclusion is that after the fully
developed coverage of the sulphate cloud in the
stratosphere, the radiation effect changes can be
estimated to happen simultaneously over the
globe. Therefore it is justified to use the one
dimensional (1D) approach in developing a
dynamic model (called DM) for analysing the
temperature versus radiation flux relationships.
1.3 Literature Study
There have been numerous Pinatubo studies on
the three major fields. The first is on the aerosol
and chemical effects of the Pinatubo particles.
The second is focused on optical properties of
the aerosol particles and on the radiative forcing.
The third is on the responses to the forcing

Ollila; PSIJ, 9(4): 1-14, 2016; Article no.PSIJ.23242
4
affecting the temperature and the circulation
patterns.
This paper concentrates on the dynamic
behaviour of the surface temperature changes
caused by the radiative flux changes. Therefore
the survey of the earlier studies covers only the
subjects which are relevant for this study.
Even though the Pinatubo eruption is the best
documented major eruption so far, there was an
essential radiative flux, which was not directly
measured during the eruption. This was the LW
downward radiation flux (LWDN), which is
essential, because it compensates the major
portion of the cooling effects of the reduced SW
downward radiation flux (SWIN) decrease during
the early phases of the eruption [9].
The World Climate Research Programme
(WCRP) Radiative Fluxes Working Group
initiated a new Baseline Surface Radiation
Network (BSRN) to support the research
projects. Some years later the BSRN was
incorporated into the WCRP Global Energy and
Water Cycle Experiment (GEWEX). The BSRN
network stations started to operate in 1992 and
that is why these valuable measurements were
not available during the Pinatubo eruption.
There has been a special GEWEX project to
assess the surface radiation budget datasets [10]
based on the available data at the top of the
atmosphere (TOA). By studying the GEWEX
results, the author’s conclusion is that the LWDN
fluxes could not be estimated reliably in this
project based on the other existing flux data.
Therefore a major challenge in this study is to
estimate the ∆LWDN flux trend during the
Pinatubo eruption.
In Fig. 3 the main radiative fluxes of the Earth are
illustrated [11,12]. The climate forcing effect of a
volcano eruption can be analysed in the same
way as the cloud change forcing. Normally the
cloud forcing has been calculated as the sum of
changes in the downward SW flux change and
outgoing LW flux change between the clear and
all-sky conditions. Applying this same method,
the radiative forcing (RF) caused by the eruption,
is the sum of ∆SWIN and ∆LWUP and it is called
aerosol radiative forcing [13]. The change in the
flux values is calculated between the normal
conditions and during or after the eruption.
Because the outgoing LW flux is reduced during
the early phases of the eruption, it is a sign that
there is cooling happening on the surface.
The RF value calculated in this way is normally
called radiative or climate forcing (RF). Actually it
is only a measure of the real RF. There are two
fluxes which have the real forcing effect on the
Earth’s surface temperature (T) and they are
SWIN and LWDN. They are the only fluxes,
which form the radiation input on the surface. In
the change from the all-sky to the cloudy sky
conditions, the change of LWUP at the TOA is -
11 Wm
-2
and the change of LWDN at the surface
is +14.3 Wm
-2
[12]. These flux values show that if
the clear sky conditions do not prevail, the LWUP
change is not equal to the real warming/cooling
impact on the surface caused by the LWDN flux
change. This example also shows that the LWDN
flux change is greater than the LWUP flux
change. The major reason for this difference is
that the cloudy sky values are actually measured
in the dynamic situation and the LWUP flux is not
in the real equilibrium value.
Fig. 3. The main radiative fluxes of the Earth’s
energy balance
The small particle sizes less than 1 µm are more
effective in reflecting the SW solar radiation
SWIN than they are at reflecting the LW radiation
emitted by the surface. According to a
comprehensive study [1], the smallest particles
were sulphuric acid/water droplets and the
largest particles were ash fragments. The cooling
and warming effects of the aerosols and particles
depend on the particle sizes. The LWDN flux
increases especially during the early phases of
the eruption because there are larger aerosol
particles more in the atmosphere than in the later
phases. Therefore the warming effect of LWDN
is the most effective at the same time as the
cooling is in maximum [1,9]. The stratospheric
ash layer settled down just above the
troposphere staying there until March 1992. The
particle size measurements [1,4] showed that

Ollila; PSIJ, 9(4): 1-14, 2016; Article no.PSIJ.23242
5
there was a peak in both small and large particle
sizes after a few months after the eruption but by
1993 the high measurements values were
decaying back to pre-eruption values.
The ash cloud in the high altitudes of the
atmosphere absorbs and emits radiation. This
ash cloud had a measureable warming effect on
the northern hemisphere winter temperatures
[14,15]. The ash cloud has about the same effect
as the clouds have in the cold climate conditions,
it will prevent the cooling of the surface. In this
way it has a net warming effect.
The radiative forcing (RF) at TOA has a linear
relationship to the global mean surface
temperature change ∆T, if the equilibrium state is
assumed [16]:
∆T = λRF, (1)
where λ is the climate sensitivity parameter,
which is a nearly invariant parameter having a
value of 0.5 K/(Wm
-2
). IPCC uses still equation
(1) in its latest report AR5 but IPCC no longer
keeps the value of λ almost constant [17]. A
general experience and also a common practice
is to approximate the small changes around the
operating point to be linear by nature. The most
probable change of RF by the end of this century
is 6 Wm
-2
according to RCP6 (Representative
Concentration Pathways) [17]. This change is
only 2.5% about the average value of OLR
(outgoing longwave radiation) value of 239 Wm
-2
.
The author carried out a study about this issue
utilizing the MODTRAN code [18]. The
concentration of CO
2
varied from 357 ppm to 700
ppm and the sky conditions were clear and
cloudy, which were combined to calculate the all-
sky values. The average global atmosphere
profiles for GH gases, temperature and pressure
were applied. The results show that the
maximum nonlinearity between the OLR fluxes
was 0.01% and the maximum variation in λ
values was 2.5%, when the surface temperature
varied ±1°C. These results show that the
equation (1) is applicable for small RF and
temperature changes.
Ollila has analysed [19] the future warming
values based on the RF values of greenhouse
gases. This analysis showed that the warming
values of RCP2.5, RCP4.5, and RCP6 could be
calculated using the λ value of ~0.37 K/(Wm
-2
).
IPCC has calculated RCP warming values
applying GCMs but they do not inform the
possible λ values. On the other hand IPCC
reports in AR5 [17] that the transient climate
sensitivity (TCS) value is likely to lie in the range
1 to 2.5°C giving the average value 1.75°C. This
value is almost the same as calculated by
equation (1): ∆T = 0.5 K/(Wm-2) * 3.7 Wm
-2
=
1.85 K. The conclusion is that IPCC is very
inconsistent in using λ values and equation (1). If
λ is not “nearly invariant parameter”, IPCC
should have introduced something more credible
scientific evidence about the real nature of λ.
This inconsistency may be linked to the warming
values of the recent RF values. There should not
be any of IPCC’s own climate models, but in
reality there is such a model called “Radiative
Forcing by Emissions and Drivers” which has a
summary leading to the value of 2.34 Wm
-2
according to AR5 [17]. IPCC denies that there is
any IPCC’s model but the fact is that the IPCC
organization has selected a number of research
studies, which have been used in creating their
presentation. There are private researchers who
do not make the same selections and therefore
their models are different. If equation (1) is
applied in the same way as calculating the TCS
value above, the warming value of 2.34 Wm
-2
would be 1.17°C in 2011. IPCC does not show
this temperature increase in the AR5 [17], and
one reason might be that it is 38% greater than
the observed value of 0.85°C.
The possible water feedback is the only essential
feedback in TCS calculations. In the referred
GCM studies applied in the Pinatubo analyses,
there are no reported λ values. The lambda value
of 0.5 K/(Wm
-2
) means that there is a positive
water feedback included into a model. The
assumption that there is a positive water
feedback in the climate models means that
relative humidity (RH) should be constant despite
the moderate warming/cooling of the
atmosphere. This property of the positive water
feedback would double the warming effects of
GH gases according to AR4 [16]. IPCC reports in
AR5 that the positive water feedback can amplify
any forcing by a typical factor between two and
three [17]. This means that understanding of
water feedback magnitude is not becoming more
accurate but it has become more inaccurate.
The issue of a constant RH can be studied by
simply looking at the RH trends since 1948,
which are depicted in Fig. 4 [20]. It is clear that
RH has varied quite a lot. Even though the early
RH measurements may be unreliable, the
measurements since 1980 have better

Ollila; PSIJ, 9(4): 1-14, 2016; Article no.PSIJ.23242
6
technology and they are very accurate and
reliable.
The positive water feedback and high climate
sensitivity (CS) of climate models is a well-known
feature. Normally the equilibrium CS varies from
1.5°C to 4.5°C [21], which means that the
variation of TCS (Transient climate sensitivity) is
about half of this range. However there are
several studies, which have calculated the
climate sensitivity value to be about 1.0 – 1.2°C
[22-25] using the same radiative forcing value of
3.7 Wm
-2
for CO
2
as IPCC uses. It means a
lower λ value of about 0.27 - 0.3 K/(Wm
-2
). Some
researchers have calculated even lower values
like ~0.6°C for climate sensitivity [19,26] or 0.7°C
[27]. Ollila [19] has calculated the λ value using
three different methods and his results vary
between 0.245 and 0.331 the most reliable value
being 0.268 K/(Wm
-2
). In this study these two
most common values have been applied: 0.27
K/(Wm
-2
) and 0.5 K/(Wm
-2
).
Fig. 4. The global relative humidity trends
according to NOAA at different altitudes in
the troposhere
The forcing studies can be classified into two
categories namely forcing calculations utilising
General Circulation Models (GCM) 1) for
simulations of spatial flux and temperature
changes [8,28-31,2] other simulations resulting
the surface temperature change. In respect to
this study only the latter studies are relevant.
One of the earliest studies was that of Hansen et
al. [32]. They used the GISS global climate
model to assess the preliminary impacts of the
Pinatubo eruption. In their calculations they used
the peak value of -4 Wm
-2
for ∆SWIN and they
could show that the simulated ∆T was about -0.5
°C. The most common value of ∆SWIN has been
-6 Wm
-2
[8,13,14,29,33]. This value is also used
in this study.
In the later study Hansen et al. [34] applied the
same peak value of -4 Wm
-2
in the GCM
simulations by name SI94 and GRL92. Soden et
al. [35] applied a GCM and as input data they
used ERBS fluxes in calculating the RF values.
They also included the absolute atmospheric
water content as a variable. The peak value of –
4 Wm
-2
was used for ∆SWIN. Their major result
was the GCM simulations could calculate the
∆Tm values close to the measured value, if the
positive water feedback was included. The water
content was calculated using the NASA Water
Vapor Project (NVAP) values [36].
In Fig. 5 the NVAP dataset values as well the
NCEP/NCAR (National Center for Environmental
Prediction / National Center for Atmospheric
Research) values are depicted [37]. The NVAP
water content trends show great seasonal
changes of about 3 TPW mm. Soden et al. [35]
have reported that there has been ~0.75 TPW
mm peak reduction during the Pinatubo eruption.
The graphs show that the peak reduction
estimate [23] can be regarded a correct estimate.
This choice of using the peak values only can be
questioned, because the trend line of NVAP-M
values show increased rate of absolute water
content. A justified procedure would be to use
the monthly values but then the water feedback
effects would be huge. Because the seasonal
water content variations depend mainly on the
northern hemisphere seasonal changes, a better
method might be to combine zonal temperature
and water content values.
Fig. 5. The graphs of water contents
according to NVAP-M and NCEP/NCAR
datasets
In Fig. 5 it can be noticed that there are opposite
trends in these datasets during the Pinatubo
eruption. It is quite impossible to know, which of
these datasets is correct and therefore the
question of positive or negative water feedback

Ollila; PSIJ, 9(4): 1-14, 2016; Article no.PSIJ.23242
7
cannot be reliably tested utilising the Pinatubo
case and the global water content trends.
2. RADIATIVE FLUXES AND FORCING
ANOMALIES CAUSED BY THE
ERUPTION
The two SWIN flux datasets available during the
eruption are ISCCP [38] and ERBS [39]. They
are depicted in Fig. 6. Both datasets are unstable
and spiky. The SWIN flux anomaly can also be
estimated using the apparent transmission (AT)
signal or optical depth measurements. In this
case the AT signal of Mauna Loa has been used.
The ∆SWIN flux anomaly has been assumed to
follow exactly the trend of the AT-signal. The
time of the minimum value of the AT-signal has
been used to be also the time of the minimum
value of the SWIN flux value of -6 Wm
-2
. This
estimate of ∆SWIN flux is depicted in Fig. 6 and
it can be noticed that this flux is very stable and
its trend follows very well the average form of
ISCCP and ERBS fluxes. The smoothed ∆ERBS
SWIN flux signal follows the estimated AT
transformed ∆SWIN flux signal so well that they
could be used between each other.
Fig. 6. SW downward radiation flux anomalies
at TOA
Because there are no direct measurements of
LWDN flux, it has been estimated. As realized
before, the LWDN flux anomaly should follow the
amount of large aerosol particle amounts in the
atmosphere. Russell et al. [1] has a Fig. 6 in their
paper containing optical depth measurements of
the different particle size trends measured at
Mauna Loa during the eruption.
It has been assumed that the smaller particle
sizes from 0.382 to 0.500 µm are related to the
∆SWIN flux anomaly. The largest particle size is
1.020 µm and the graph of its aerosol optical
depth has been used to estimate the ∆LWDN
flux. The peak values relationship between the
1.020 µm and 0.382/0.500 µm is 0.6. Using this
relationship the peak value of estimated ∆LWDN
flux anomaly would be 0.6 * (-6 Wm
-2
) = -3.6 Wm
-
2
. The ∆LWDN is been estimated to follow the
aerosol optical depth signal of the particle size
1.020 µm at Mauna Loa and it is depicted in
Fig. 7.
Fig. 7. LW radiation flux anomalies at TOA
In Fig. 7 it can be noticed that the peak value of
estimated LWDN flux is greater than the ∆LWUP
values measured at TOA by ISCCP and by
ERBS. One explanation is that ∆LWUP fluxes
depend mainly on the surface temperature and
therefore there is a dynamic delay in comparison
to the ∆LWDN flux. The full effect of this delay is
about one year. In the dynamic situations like this
Pinatubo eruption anomaly, the maximum
temperature anomaly is about from 80% to 90%
from the full effect. This difference is analyzed
more deeply in the simulation section.
In the simulations the measured surface
temperature anomaly ∆T is a reference. There
are five dataset commonly available and four of
them are depicted in Fig. 8 [5,40-42]. There are
rather big differences in the trends. The
difference between the HadCRT4 and the UAH
MSU, which is a lower atmosphere temperature
measured by satellites, is even 0.4°C around the
beginning of the years 1992 and 1993. The UAH
MSU trend has the largest minimum value during
the eruption. Because of this situation, two
surface temperature trends have been used as
references namely Tmsu (UAH MSU dataset)
and Tav (average of all four datasets).
Hansen et al. [34] and Soden et al. [35] have
taken into account that the ENSO (El Niño
Southern Oscillation) phenomenon had the
maximum warming index in January 1992, when
the Pinatubo eruption had the strongest cooling

Ollila; PSIJ, 9(4): 1-14, 2016; Article no.PSIJ.23242
8
effects. The researchers elimated the ENSO
effect by calculating a modified surface
temperature of MSU UAH dataset. According to
the graphs of these two papers, the ENSO
corrected minimum peak of ∆T has been from -
0.7°C to -0.75°C. They refer to the study of
Santer et al. [43]. The author reads this same
paper that the maximum mean volcanically
induced cooling ∆T
max
at the surface is from-
0.35°C to -0.45°C and it is about double in the
troposphere. ENSO certainly has a warming
effect from 1991 to the end of 1992, and
therefore this result is not logical, because the
temperatures without ENSO corrections are
about the same. There is a graph [43], where the
temperature anomaly is about -0.75°C but it is for
the troposphere and not for the surface. Another
study of Thompson et al. [44] shows that the
maximum warming effect of ENSO is only
0.14°C.
Fig. 8. Surface temperature anomalies
according to four datasets
Because the quantified effects of ENSO are so
controversial, this study has used the results of
the own analyses. The elimination of ENSO is
based on the analysis of ONI values (Oceanic
Niño Index) [45] and the global ∆T values. The
ENSO effect creates fluctuations, which can be
identified as almost identical fluctuations of ∆T
values after 1-12 months delay. The four most
regular El Niño / La Niña cases were selected.
The relationship from peak to peak between
these fluctuations show that ∆T = 0.144 * ∆ONI
on average. This temperature effect formula has
been used in modifying the measured ∆T values
but there is no time delay applied, because the
peak values of ONI and ∆T values match. In
Fig. 9 is depicted the ENSO effect as a
temperature anomaly and its effect on the two
global ∆T trends. This approach gives the
maximum ENSO effect of ~0.23°C. The ENSO
during the Pinatubo eruption has a special
feature not having the negative La Niña
temperature peak at all.
Fig. 9. The ENSO signal removed from the
surface temperature measurement
The ENSO effect explains quite well why there is
a peak upward from January 1992 to July 1992,
when the surface temperature should be in
minimum because of forcing by ∆SWIN/∆LWDN
anomaly. After 1993 the ENSO effect is very
small, but it caused an upward tick at the end of
1995, when the Pinatubo event was practically
over. The ENSO modified surface temperatures
Tav-e and Tmsu-e have been used as
references in this study.
3. DYNAMIC MODEL SIMULATIONS
The Pinatubo eruption happened in such a way
that the forcing factors in the form of ∆SWIN and
∆LWDN flux anomalies changed all the time and
therefore the applied model must be dynamical.
A dynamical model is capable of simulating time
dependent variables and their impacts. In this
case a simple dynamical model DM has been
applied as described in Fig. 10.
Fig. 10. The dynamic simulation model of the
climate system
The output ∆FLIN of the disturbance process D(t)
is the difference of ∆SWIN and ∆LWDN created
by the Pinatubo eruption. ∆FLIN has been
delayed by 1.6 months called dead time in
process dynamics and it can be formulated as
follows:

Ollila; PSIJ, 9(4): 1-14, 2016; Article no.PSIJ.23242
9
∆FLIN = ∆SWIN(t-τ
D
) – ∆LWDN(t-τ
D
) (2)
where t is time and τ
D
is dead time. The input
variable ∆SWIN is a flux anomaly signal varying
according to the time as depicted in Fig. 6. Also
∆LWDN varies according to the time as depicted
in Fig. 7. The climate process C(t) includes two
elements: 1) the input signal ∆FLIN is
transformed into the surface temperature change
and 2) the dynamic behaviors of the climate
system delays according two parallel first order
transfer systems are included into ∆T effects:
∆T = λ * ∆FLIN * (K
sea
* exp(-t/Τ
sea
)
+ K
land
* exp(-t/Τ
land
)) (3)
where t is time (months), exp is exponent, K
sea
is
0.7, K
land
is 0.3, Τ
sea
is a time constant of 2.74
months and Τ
land
is a time constant of 1.04
months. These values are based on the earlier
studies [12,46,47]. The values of the K
parameters are the area portions of land and
ocean of the Earth. The climate process C(t) is a
combination of two parallel processes, because
the time delays of land and ocean are different.
Three different simulation cases have been
described and carried out: 1) ∆SWIN and
∆LWUP (the proxy of the LWDN) fluxes are from
ERBS datasets, 2) ∆SWIN and ∆LWDN are
estimated as described above based on the AT
measurements, 3) Feedback process experiment.
The ISCCP dataset turned out to be too swaying
and unreliable and therefore it has not been used.
In cases 1) and 2) the simulations have been
carried out by λ values of 0.27 K/(Wm
-2
) and 0.5
K/(Wm
-2
).
The dynamic processes according to eq. (2) are
first-order dynamic models, which can be
simulated in the discrete form enabling
continuously changing input variables:
Out(n)=(∆t/(T+∆t))((T/∆t)*(Out(n-1)+In(n)),(4)
where Out(n) is the output of the process in step
n, In(n) is the input of the process of step n, T is
the time constant, ∆t is the simulation step
interval (=0.2 months), and n-1 is the previous
step value.
The results of using ERBS flux values are
depicted in Fig. 11.
It can be noticed that the simulated temperature
values vary a lot because the fluxes ∆SWIN and
∆LWIN vary too much. Especially the λ value of
0.5 K/(Wm
-2
) gives ∆Tm peak values, which are
almost double as large as the ∆Tm values using
the λ value of 0.27 K/(Wm
-2
). A possible reason
for this is that the LWUP flux anomaly is not an
accurate enough estimate of the real ∆LWDN
flux anomaly and the flux measurements are too
inaccurate.
Fig. 11. The simulated surface temperature
according to the dynamic DM using ERBS
dataset ∆SWIN and ∆LWUP fluxes
Fig. 12. The simulated surface temperature
according to the dynamic model using
estimated SWIN and LWDN fluxes
In Fig. 12 the same graphs are depicted, when
the ∆SWIN and ∆LWDN are estimated according
to the AT and aerosol optical depth
measurements. The simulated ∆Tm signal is
stable and the dynamic changes follow very well
the real temperature changes ∆T. Also in
this case the λ value of 0.5 K/(Wm
-2
)
gives results, which do not follow the real
changes of the surface temperature changes but
gives about 100% too great ∆Tm during the
eruption.

Ollila; PSIJ, 9(4): 1-14, 2016; Article no.PSIJ.23242
10
The question of feedback has created the two
schools of thoughts. Some researchers think that
the climate system is like the other processes of
the nature, which are built on negative
feedbacks. A positive feedback system is
dangerous, because it drives any system out of
balance sooner or later. IPCC and some other
researchers think that the climate system for
example includes the positive water feedback as
well as positive albedo and cloud feedbacks [17].
It should be noticed that the positive water
feedback is included into the climate feedback
parameter λ, when its value is 0.5 K/(Wm
-2
) [16]
and should results in a constant RH trend in the
troposphere. The λ-value of 0.27 K/(Wm
-2
)
means a constant water content of the
atmosphere.
A theoretical feedback process is simulated
using the process model depicted in Fig. 13.
Fig. 13. A theoretical feedback process in the
case of Pinatubo eruption
The theoretical feedback process can be
constructed based on the assumption that the
∆SWIN flux anomaly is the only disturbance in a
very stable climate system, which tries to
eliminate this disturbance. The elimination
process is a theoretical PI-controller, which
detects a change in the surface temperature and
creates an eliminating phenomenon, which tries
to minimize the disturbance. In this case the
eliminating flux is the ∆LWDN flux. The climate
process C(s) has as an input only the ∆SWIN
anomaly. The PI-controller imitates the counter
effect of ∆LWDN flux but ∆LWDN flux values are
not needed to use in this simulation.
The mathematical form of the PI-controller
(Proportional-Integral) in time domain is
Out(t) = K
p
*e(t)
+ (1/T
i
)*∫e(t)dt (5)
Where K
p
is the gain of the controller, T
i
is the
integral time and e(t) is the error signal between
the set point and the measurement. The equation
(4) simulated in a discrete form in the time
domain is
Out(t) = K
p
* ∆e(t) + (K
p
/T
i
)Σe(t)∆t (6)
The PI-controller was tuned by trial and error
giving K
p
= 2 and T
i
= 500 months. The results of
the negative feedback process simulation are
depicted in Fig. 12. The output of the theoretical
feedback process follows the ∆Tm values of DM
surprisingly closely up to the end of 1993 as well
as the measured ∆T values.
One big difference between this study and the
three referred studies [32,35,36] is the use of
estimated ∆LWDN instead of measured ∆LWUP
fluxes. The basic reason is that these two fluxes
have different values. The measured ∆LWUP
fluxes are not stable, making the results very
unstable too. This problem can be eliminated to a
certain degree by heavy smoothing or even by
removing parts of a flux signal [35].
The actual ∆LWUP flux depends on the surface
temperature changes ∆T which is caused by the
RF change. The RF is the sum of
∆SWIN+∆LWDN flux changes. The ∆LWUP flux
can be calculated using the measured ∆T
changes. The author has used two calculation
methods. The first is MODTRAN radiation code
available through Internet [18]. By applying the
average global atmosphere profile, MODTRAN
can calculate the LWUP flux change at TOA. The
main parameters selected for these calculations
were: CO
2
357 ppm, fixed water vapor pressure,
cloudy sky with cumulus cloud base of 0.66 km
and top of 2.7 km. The 1°C change in the surface
temperature gives ∆LWUP change of 3.39 Wm
-2
for the clear sky and 3.08 Wm
-2
for the cloudy
sky at TOA.
By combining the two sky conditions, the all-sky
value of 3.18 can be calculated [10]. Ollila [10]
has calculated the same relationship using
another commercial spectral analysis tool
Spectral Calculator for the clear sky conditions.
The cloudy sky fluxes are estimated to be 25%
less than the clear sky fluxes [16]. This
calculation method gives the ∆LWUP change of
3.05 Wm
-2
for the 1 °C change. The results of
MODTRAN calculation have been used, which
gives a linear relationship
∆LWUP = 3.18 * ∆T. (7)
This linear relationship is applicable inside the
small temperature change of 1°C.
The surface temperature calculated ∆LWUP is
depicted in Fig. 14. It can be compared to the

Ollila; PSIJ, 9(4): 1-14, 2016; Article no.PSIJ.23242
11
measured ∆LWUP flux, which is in this case the
average of ISCCP and ERBS datasets. The flux
values are at about the same level except for the
first months of 1992. The SW+LW forcing flux is
about 1 Wm
-2
higher than the ISCCP & ERBE
flux during the period 3/1992 – 10/1992. This
could be due to the error of LWDN flux estimate.
The LWDN flux may reduce quicker than the
optical depth measurement indicates. This is also
a probable reason for the difference between the
Tm value of DM and the measurement based
temperature anomalies during the year 1992.
This is a very good result showing that ∆LWUP
depends on ∆SWIN +∆LWDN fluxes and their
dynamic effects on the ∆T at the Earth’s surface.
Therefore, ∆LWUP is not really the right choice
in calculating the surface temperature changes
caused by downward radiation flux anomalies of
SWIN and LWDN.
Fig. 14. The LW fluxes during the Pinatubo
eruption
4. RESULTS AND DISCUSSION
These results can be compared to the results
calculated by Hansen et al. [34] and Soden et al.
[35] who have used complicated GCMs in their
analyses. In these models the temperature
effects are based on the eruption aerosol
amounts and properties. When comparing the
dynamic behavior, the calculated Tm of GCMs
follows very accurately the real temperature
change as does the DM. The conclusion is that
the dynamical time delays in their GCMs must
come very close to the time constants applied in
this study.
The peak values of Tm of the GCM studies are -
0.6°C [34] and -0.7°C [35] and according to their
graphs, the model-predicted values are
practically same as the observed values. The
observed values of this study vary from -0.5°C to
-0.6°C based on the selected temperature
measurement. One explanation could be that in
the referred GCM studies the modified UAH MSU
dataset has been used having a greater ENSO
effect correction than in this study.
In the GCM calculations the researchers [34]-[35]
have used ERBS flux values. In both cases the
maximum value of SW anomaly ∆SWIN has
been about -4 Wm
-2
, which differs 33% from the
value of -6 Wm
-2
used in the majority of the other
GCM studies and also in this study. The
maximum LW anomaly ∆LWUP used in the GCM
studies has been about -2.3 Wm
-2
. Using
equation (1) for steady-state conditions, the
calculated peak Tm would be 0.5 * (-4 + 2.3)
= -0.85°C. This value is very close to the model-
predicted value of Soden et al. [35]. On the other
hand, if the commonly used value of -6 Wm
-2
would have been used, the calculated peak Tm
would be 0.5 *(-6+2.3) = -1.85°C. If the average
λ-value of 1.0 K/(Wm
-2
) commonly found in
GCMs is used, the Tm would be even larger. The
GCM simulations of Soden et al. [35] gave
results which are close to the measured ∆T
values. The major features of these two studies
are listed in Table 2.
The model calculated Tm values are for
equilibrium conditions and the values of the real
dynamic conditions are in brackets. The dynamic
simulations of this study show that in the
dynamic change condition the real equilibrium
Tm value cannot be reached but the real
temperature change is about +0.1°C smaller.
The values in Table 2 show that the results of
Soden et al. [35] can be generated using the λ
value of = 0.5 K/(Wm
-2
) and the flux values
applied by them.
This simple analysis shows that the model-
predicted Tm values are completely dependent
on the selected forcing fluxes, λ values and even
on the selected observed ∆T value. It appears
that in GCM simulations [34,35] the selected
∆SWIN flux cannot be regarded as the justifiable
choice. Actually the greatest uncertainty is about
the right ∆LWDN flux values, because there are
no direct measurements available. The
commonly used ∆LWUP flux at the TOA, is not
the same flux as ∆LWDN. ∆LWUP is mainly
dependent on the real RF fluxes (∆SWIN and
∆LWDN) and on the surface temperature.
Therefore the ∆LWUP flux contains the dynamic
delays of the land and ocean and the

Ollila; PSIJ, 9(4): 1-14, 2016; Article no.PSIJ.23242
12
Table 2. Comparison of the major differences between the study of Soden et al. [35] and this
study
Soden et al.
Ollila
Min. ∆SWIN, Wm
-
2
, min. -4.0 -6.0
Max. ∆LWDN, Wm
-
2
, max. +2.3 +3.6
Max. radiative forcing, Wm
-
2
-1.7 -2.4
Equil. Tm according to λ = 0.5 K/(Wm
-
2
), °C -0.85 (-0.75) -1.2 (-1.1)
Equil. Tm according to λ = 0.27 K/(Wm
-
2
), °C
-
0.46 (
-
0.36)
-
0.65 (
-
0.55)
warming/cooling effects of the forcing radiation
fluxes. In the dynamic simulations this is a
source of error. The real measured
∆LWUP fluxes are very spiky – especially ISCCP
fluxes.
5. CONCLUSION
The results show that a simple one dimensional
dynamic model DM gives results that are close to
the real surface temperature changes ∆T after
the Mount Pinatubo eruption using the climate
sensitivity parameter value of 0.27 K/(Wm
2
).
Timewise the changes follow very well the real
changes. It means that the applied time
constants for land (1.04 months) and for ocean
(2.74 months) are accurate and can be used in
any dynamic simulations. Especially the quick
and large ∆T during the early phase of the
eruption shows that the applied DM follows very
accurately the real change rate.
The maximum temperature decrease differs
+0.05° from the lowest dataset value (UAH MSU)
and -0.04°C from the highest dataset value
(T average) being actually in the middle of the
dataset changes. This is a very good accuracy.
The climate sensitivity parameter value of 0.5
K/(Wm
2
) gives the minimum peak value of -
1.02°C, which is almost double in comparison to
-0.55°C calculated by λ value of 0.27 K/(Wm
2
).
This means that the climate models are very
sensitive to the value of the climate sensitivity
parameter. The mean λ-value of 1.0 K/(Wm
-2
)
commonly used in GCMs would give 200% too
high values.
In this study ∆SWIN and ∆LWDN fluxes have
also been estimated utilizing the apparent
transmission measurements. The simulation
using these fluxes gives the best and consistent
results. The theoretical feedback simulation gives
values which are close to the DM model values
applying also the ∆LWDN flux values.
The correlation analysis between the model
calculated Tm and the measured Tav-e gave the
correlation r
2
= 0.6 and the standard error of Tm
= 0.066°C. When the standard error of Tm is
transformed into the standard error of λ,
the value is 0.036 K/(Wm
-2
). This means that the
uncertainty of λ is in the range from
0.234 K/(Wm
-2
) to 0.306 K/(Wm
-2
). The main
reason for the relatively poor correlation seems
to be the inaccurate surface temperature
measurements. The correlation r
2
between
Tmsu-e and Tav-s is 0.85 and the standard error
of the estimate 0.040°C. This error is 61% of the
standard error of the DM predicted temperature.
If the 7 months running mean is applied to Tm
and Tav-e like in the study of [35], r
2
= 0.76 and
the uncertainty range of λ improves from 0.245 to
0.295.
The theoretical simulation of negative feedback
of the climate system gives Tm results, which
follow well both the DM results and the real ∆T
measurements.
COMPETING INTERESTS
Author has declared that no competing interests
exist.
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Peer-review history:
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http://sciencedomain.org/review-history/13553