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Using ANFIS and Fuzzy Clustering to Predict

Extreme Climate in Indonesian regions

The Houw Liong

2)

and Plato M.Siregar

1)

ICICI 2007 proceedingsJl. Ganesha 10

Bandung, 40132 INA1) Faculty of Earth Science and Mineral Technology, ITB2) Faculty of Mathematics and Natural Sciences, ITB

Abstract

Extreme climate in Indonesia is influenced by four

main quasi periodic cycles: Solar Activity Cycle (Sunspot

Numbers Cycle), Galactic Cosmic Ray Cycle, El Nino

Southern Oscillation (ENSO) Cycle, and Indian Ocean Dipole

Mode (IOD) Cycle. It can be shown that solar activity cycle

can be considered as primary cycle that influence other cycles.

In practice eastern Indonesian region is dominantly

influenced by ENSO. When the heat pools moves to eastern

Indonesian region, then rainfall in this region will be above

normal. On the other hand when the heat pool leaves eastern

Indonesian region and moves to Pacific Ocean then the rainfall

in this region will be below normal.

During a typical Indian Ocean Dipole Mode (IOD)event the weakening and reversal of winds in the central

equatorial Indian Ocean lead to the development of unusually

warm sea surface temperatures in the western Indian Ocean.

IOD negative means wet condition or the rainfall will be above

normal along the western Indonesian region.

Precipitation in Pontianak region which represent

middle Indonesian region correlated strongly with sunspotnumbers cycle (solar activity cycle).

Using ANFIS (Adaptive Neuro Fuzzy Inference System)

we are able to predict sunspot numbers cycles so that extreme

weather in Indonesian regions can be predicted.

Fuzzy c-means is used to classify regions that are

influenced strongly by sunspot numbers (solar activity), IOD,and ENSO cycles. This method is based on fuzzy set as fuzzyc-partition of three cycles above and as clustercenter. Fuzzy c-

partition matrix for grouping a collection of n data set into c

classes.

This study explores the physical of climate predictions

and classifications of Indonesian regions and its physical

interpretations.

Keywords: ANFIS, fuzzy clustering, climate, solar activity

I. INTRODUCTION

The relative positions of the sun in the sky during the

seasons, as well as the cycles of solar activity influence the

weather and climate throughout the Indonesian archipelago.

Solar irradiance and ultraviolet intensity increases with higher

solar activity. This in turn will be followed by coronal mass

ejection (CME) that increases the charged particles emitted by

the sun which could alter the interplanetary magnetic field, and

hence the intensity of galactic cosmic rays reaching the earth.

The galactic cosmic ray intensity reaching the earth decreases

with higher solar activity. Thus the solar activity is often

considered as the dominant factor that determines the dynamics

of climate [1, 2]. The dynamics of earth's atmosphere and

oceans, evaporation, clouds formation and rainfall, are

influenced by the solar energy entering the earth. Several

studies indicate that strong correlations exist between the cloud

cover and the intensity of galactic cosmic ray reaching the

earth [3].

During 1645 1715 exceptionally low solar activity

(also known as the Maunder minimum) which means high

intensity of galactic cosmic ray reached the earth increased

cloud cover that led to low temperatures causing what is known

as the little ice age.

The present study shows that there is a strong correlation

between rainfall in the Indonesian archipelago and solar

activity or sunspot numbers.

II. THE RELATION BETWEEN SOLAR ACTIVITY

AND CLIMATEThe galactic cosmic rays collide with air molecules in

the upper atmosphere and produce secondary particles.

Generally the charged particles so produced cannot penetrate to

lower layers of the atmosphere, except gamma ray, neutrons

and the muons. When gamma ray, neutrons and muons interact

with the air molecules or water molecules, they become

charged and together with aerosols particles act as

condensation nuclei for the formation of clouds. The cosmic

ray becomes the source of ions in the air besides radiation

coming from earth originated by the radio isotope radon.


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During the sunspot minimum, the intensity of the

galactic cosmic ray that penetrates earth atmosphere becomes

maximum which in turn increases the coverage of clouds. This

implies that solar irradiation reaching the earth will be

minimized. Conversely, during solar activity maximum or

sunspot maximum, the intensity of galactic cosmic ray

reaching lower levels of the atmosphere decreases, less cloud

condensation nuclei are produced, hence the cloud cover

decreases, furthermore extra energy received from flares during

prominent eruptions, maximizes the amount of solar energy

reaches the earth.

Although global cloud cover produces a warming effect

or the greenhouse effect, but a cooling effect due to reflections

against direct solar irradiation is more dominant factor [1, 3].

Furthermore during solar activity maximum, the

intensity of ultraviolet that penetrates the earth increases. Solar

activity maximum usually is followed by increasing coronal

mass ejection. Both effects caused greater amount of energy

penetrates the earth and this will influence the climate through

the dynamics of the atmosphere and oceans.

III. Adaptive Neuro-Fuzzy Inference System (ANFIS)

and Fuzzy Clustering

Adaptive network-based fuzzy inference system used a

feed forward network to search for fuzzy decision rules that

perform well on a given task. Using a given input-output data

set ANFIS creates a fuzzy inference system whose

membership function parameters are adjusted using a

backpropagation algorithm alone or combination between abackpropagation algorithm with a least squares method. This

allows the fuzzy systems to learn from the data being modeled.

ANFIS provide a method for the fuzzy modeling procedure to

learn information from the data set, followed by creating the

membership function parameters that best performing the given

task. Consider a first order Takagi-Sugeno fuzzy model with a

two input, one output system having two membership functions

for each input.[6]

The functioning of ANFIS is a five layered feed forward neural

structure and the functionality of the nodes in these layers can

be summarized as follows:Layer 1: Every node i in this layer is an adaptive node with a

node output defined by:

(1)

wherex(ory) is the input to the node; Ai (orBi-2) is a fuzzy set

associated with this node, characterized by the shape of the

membership function in this node and can be any appropriate

functions that are continuous and piecewise differentiable such

as Gaussian , generalized bell shaped, trapezoidal shaped and

triangular shaped functions. Assuming a bell shaped function

as the membership function,Ai can be computed as,

(2)

ai and ci are the parameter set. Parameters in this layer are

referred to as premise (antecedent) parameters.

Layer 2: Every node in this layer is a fixed node labeled ,

which multiplies the incoming signals and outputs the product.

For instance,

(3)

Each node output represents the firing strength of a rule.

Layer 3: Every node in this layer is a circle node labeledN. The

ith node calculates the ratio of the ith rule's firing strength to

the sum of all rule's firing strengths. Output of this layer will be

called normalized firing strengths.

(4)

Layer 4: Node i in this layer compute the contribution of the ith

rule towards the model output, with the following node

functions:

(5)

Layer 5: The single node in this layer is a fixed node labeled

that computes the overall output as the summation of all

incoming signals.

Overall output =

(6)

Using ANFIS and data from Royal Observatory of Belgium

and Sunspot Index Data Centerhttp://www.astro.oma.be/SIDC

we can get prediction of sunspot numbers time series as in

Figure 1.

b2

i

i

A

a

cx1

1

)x( +

=

2,1i)y()x(wO ii BA1i,2 ===

2,1i,ww

wwO

21

iii,3 =

+

==

)ryqxp(wfwO iiiiiii,4 ++==

,4,3ifor),

y(O

or,2,1i

for),x(O

2i

i

Bi,1

Ai,1

==

==

==

i

i

i

i

ii

ii5w

fw

fwO
http://www.astro.oma.be/SIDChttp://www.astro.oma.be/SIDChttp://www.astro.oma.be/SIDC


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We use rainfall data in Indonesia from NCEP

Reanalysis at

http://www.cdc.noaa.gov/cdc/data.ncep.reanalysis

and fuzzy c-means method with three seeding regions

for initial matrix fuzzy c-partition of three cluster centers i.e. :

ANFIS PREDICTION

0

50

100

150

200

1948

1952

1956

1960

1964

1968

1972

1976

1980

1984

1988

1992

1996

2000

2004

2008

2012

Years

NumbersSunspo

ANFIS Prediction Obs. Sunsspot

Figure 1. ANFIS prediction of sunspot numbertime series.

Bukittingi region for western Indonesia,, Jayapura

region for eastern Indonesia and Pontianak region for middle

Indonesia. This method is based on fuzzy set as partition

matrix for grouping a collection of n data set in to c classes, we

define object function for fuzzy as Euclidian distance. The

result of the clustering is shown in Figure 2. It is shown that

Jakarta region (Jabodetabek) is similar (0.6) to middle region

which is dominated by solar cycle, is similar (0.5) to western

region which is dominated by IOD cycle, and is similar (0.5) to

eastern region which is dominated by ENSO cycle. The result

of climate clustering in Indonesia is using the following

algorithm.

Fuzzy c-means Algorithm

1. Fix c (2c n) and select a value for parameter m,initialize the partition matrix U(0), each step in this

algorithm will labeled r, where r=0,1,2,..

2. Calculate the c centers {v i(r)} for each step.

3. Update the partition matrix forrth step, U (r) as follow:

=

=

=+

kIfor

m

c

j drjk

drikr

ik

1)1'/(2

1 )(

)()1(

(7)

4. If + )()1( rr UU ,stop; otherwise set r=r+1 and

return to step 2

5. Calculate the similarities of the c center :

=

== n

k

mik

n

k kjxm

ik

ijv

1

'

1

.'

(8)

Figure 2. Climate regions in Indonesia based on fuzzy clustering

IV.The Correlation of Sunspot Number to Rainfall in

Indonesia

With the equator crossing Indonesia, the sensible heat

flux plays an important role in global circulations. The latent

heat which originates mainly from the release of latent heat

when water vapor condenses into clouds droplets(a number of

large clouds form through convections in the Inter Tropical

Convergence Zone (ITCZ) which is above Indonesia). The cold

monsoon season in northern hemisphere (Asian monsoon) andin the southern hemisphere (Australian monsoon) are

influenced by the heat source distribution or the release of

latent heat above Asia and in the neighborhood regions. At

present it seems that the Indonesian zone holds the key to

southern oscillation system which determines the forcing of

Jaya Pura

0

100

200

300

400

Years

0

50

100

150

200

Avg precip sspot

Figure 3 Yearly precipitations in Jayapura region vs.

sunspot numbers.
http://www.cdc.noaa.gov/cdc/data.ncep.reanalysishttp://www.cdc.noaa.gov/cdc/data.ncep.reanalysis


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Pontianak Region

Corre lation Sunspot vs Precip =0.88

0

100

200

Years

Sunspot/Pre

cip

-200

0

200

ave-sunspot ave-precip

Figure 4. Correlation between sunspot numbers and

yearly precipitation in Pontianak region.

El Nino Southern Oscillation (ENSO). Therefore,

Indonesia, through which the equator crosses, has the

maximum sensible heat flux, high rainfall, and monsoon

circulations. Consequently, it is one of the most primal zones

for convection processes, an equatorial-tropical zone where

Coriolis effects are practically nullified, where atmosphericcirculations are very different compared to the extra-tropical

zones.The observations and studies on Indonesian climate are

limited, and the mathematical formulations of tropical

dynamics are far more complex relative to those in the extra-

tropical zones. The distinct daily convection variability induced

by land-sea wind circulations over some islands in Indonesia

characterizes the aspect of rainfall throughout the Indonesian

Archipelago which are very different from other regions on the

earth. The studies mentioned above, show that rainfall is an

important quantity in the Indonesian Archipelago and sunspot

is believed to be the major predictor.

Using rainfall data in Indonesia from NCEP Reanalysis

http://www.cdc.noaa.gov/cdc/data.ncep.reanalysis

We can get links between sunspot numbers and rainfall,

although the correlations which existed in general are weak. In

other words, these signify that the dynamics of the atmosphere

is being viewed as the cause of the small correlations.

However, in the case of static model atmosphere, determination

of correlations based on data averaging of sunspot numbers on

yearly basis against the yearly rainfall for various regions in

Indonesia, one comes to time series as shown in Figures 3, 4

and 5 .

From Figure 3 we can conclude that eastern Indonesia

(Jayapura region) which represented Eastern Indonesian

Maritime Continent is strongly influenced by ENSO.

Jabodetabek

0

200

400

Years

mm/month

0

100

200

Avg Precip Avg-sspot

Figure 5. Maximum precipitation in Jabodetabek in

1968, 1981, 1992, 2002 correspond to sunspot number

maximum. Precipitation maximum in 1976, 1986, 1996,

and (2007) correspond to sunspot number minimum or

galactic cosmic ray maximum.

After 1976 sunspot numbers maximum SMax and

sunspot numbers minimum SMin correspond to precipitations

above normal also to La Nina and maximum eruptions ME or

CME corresponding to precipitations below normal and also toEl Nino.[4, 5] In Pontianak region which represent middle

Indonesian Maritime Continent, the yearly precipitation is

mainly determined by sunspot cycles (Figure 4). Precipitations

above normal occur at sunspot maximum SMax, and

precipitations below normal at sunspot minimum SMin.

Precipitations in east Indonesia which represent North

Australia Indonesian Monsoon are influenced by ENSO similar

to those observed in Jayapura region. (Figure 3) Precipitations

in Jakarta region or Jabodetabek are weakly influenced by

ENSO. The peaks of yearly precipitations correspond to the

peaks of sunspot numbers, but at the sunspot numbers

minimum which correspond to galactic comic ray maximum,

the yearly precipitations also maximum.(Figure 5).

The west Indonesian region is mainly influenced by IOD

that also correlated to solar cycle. [5]

The fuzzy c-means clustering shows that the western

Indonesian region is influenced mainly by IOD, the eastern

Indonesian region is influenced mainly by ENSO and the

middle region is mainly influenced by solar activity.

So, by knowing sunspot number time series as predicted

by ANFIS and fuzzy clustering of climate regions we can

predict the coming extreme weather for each regions in

Indonesia

REFERENCES[1] H. Svensmark, Cosmoclimatology : a new theory emerges. Astronomy &

Geophysics,Vol. 48, pp 1.18-1.24, 2007[2] T. Landscheidt, Solar Activity: A Dominant Factor in Climate Dynamics,

Schroeter Institute for Research in Cycles of Solar Activity,http://www.johndaly.com/solar/solar.htm, 1988.

[3] K.S. Carlslaw, R.G. Harrison, J. Kirkby, Cosmic Rays, Clouds, and

Climate, Sciences Compass, Vol. 298, 2002.

[4] T. Landscheidt, New ENSO Forecast Based on Solar Model, SchroeterInstitute for Research in Cycles of Solar Activity, 2003.

[5] The H. L., P. M. Siregar,Using System Dynamics of Ciliwung River to

Predict Floods, Workshop on Nonlinearity 2k6, IPB, Bogor, 2006.

[6] J.S.R.Jang, C.T. Sun, E. Mizutani, Neuro-Fuzzy and Soft Computing,Prentice Hall, Inc., 1997.
http://www.cdc.noaa.gov/cdc/data.ncep.reanalysishttp://www.cdc.noaa.gov/cdc/data.ncep.reanalysis


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