Climate Model

Weather/Climate Model in Indonesia and Terrestrial Effects of Solar Activity Plato M. Siregar 1) Deni Septiadi 2) The Houw Liong 3) 1)

Science Atmosphere Division, Faculty of Earth Science and Mineral Technology, ITB Climatology Station of Siantan Pontianak, Meteorologycal and Geophysical Agency, BMG 3) Physics of Complex System Division, Faculty of Mathematics and Natural Sciences, ITB 2)

ABSTRACT Weather/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 sunspot numbers 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 fuzzy c-partition of three cycles above and as cluster center. 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 1. Introduction Weather/climate model always being interest topic to explored, even no one can give high accuracy and stable that applicable for different of time and space. This model especially for predicting necessary, needs involving complex parameters of weather/climate. Although that condition, weather/climate prediction technique indicated significant progress. The pattern not only limit by statistics approach but dispersion as mathematics through computation technique. Quantitative Forecast of Precipitation (QPF) could make by subjective prediction technique, statistics prediction technique, and dynamic prediction technique. Subjective prediction technique making by experience, expertise and forecaster comprehension. Statistics prediction technique making by statistics prosedure, mean while, dynamic prediction technique make based on equations solution of simplified atmosphere processes [Rainbird, 1970]. Weather/Climate model can be constructed by using the law of physics for the atmosphere i.e.: The Navier-Stokes equation, the conservation of mass, the conservation of energy, the equations of states, including schemes for cloud formations, carbon and sulfur cycle, interactions between atmosphere and land surface, oceans, cryosphere, and biosphere, furthermore we have to include forcing by volcanic eruptions, the solar activity and galactic cosmic rays.

Researchers from LAPAN using GCM and DARLAM have reported some results of climate prediction for Indonesian regions [Ratag, 2002]. Under a scenario that CO 2 concentration doubled in 100 years then the temperature in Indonesian regions will increase on the average about 0.03 degrees Celsius per year. This research showed that the result of prediction of rainfall in these regions is still poor (the correlations on the average are below 0.5) and need some modification on cloud formation scheme. 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 [Svensmark, 2007; Landscheidt, 1988]. 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 [Carlslaw, 2002]. 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 middle Indonesian region and solar activity and the relation of solar activity and rainfall of other regions. Using this fact we can predict the climate in Indonesian regions by predicting the sunspot numbers (solar activity). It can be shown that to get a good accuracy of predicting a quasi periodic time series as sunspot numbers is possible. The possibility of reducing the negative effect of climate using weather modification methods is also considered. 2. Data Used This research using monthly rainfall data (mm) collected by 5 raingauges in West Kalimantan (BMKG) with 46 years length of data (1961-2006). Additionally data are monthly sunspot and cosmic rays data (1961-2006) of Royal Observatory of Belgium and Sunspot Index Data Center at http://www.astro.oma.be/SIDC.

3. 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 a backpropagation 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: O

1 ,i

= µ

A

i

O

1 ,i

= µ

B

i − 2

(x ) ( y, ) ,

fo rfo r

i = 1, 2 , o i = 3,4 , r

(1)

where x(or y) is the input to the node; Ai (or Bi-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,

1

µA ( x ) =

2b

x −c i 1+ ai

(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 Π , which multiplies the incoming signals and outputs the product. For instance, (3)

O 2,i = w 1 = µ Ai (x ) µ Bi ( y) i = 1,2

Each node output represents the firing strength of a rule. Layer 3: Every node in this layer is a circle node labeled N. 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.

wi , i = 1,2 w1 + w 2

O 3, i = w i =

(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)

O 4,i = w i f i = w i (p i x + q i y + ri )

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 = O

5

=

∑

w

i

f

i

∑ ∑

=

w

i

f

i

i

w

i

(6)

i

i

Fuzzy c-means Algorithm 1. Fix c (2≤c≤ 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 {vi(r)} for each step. 3. Update the partition matrix for rth step, U (r) as follow: −1  2 /(m'−1)       (r )   c d  (7)  µ (r +1) =  ∑  ik  for I = Φ k ik  j =1 (r )    d jk      



( r +1) − U ( r ) ≤ ε ,stop; otherwise set r=r+1 and return to step 2 4. If U n m' .x ∑ µik kj k = 1 vij = n m' ∑ µik k = 1 Calculate the similarities of the c center :

(8)

4. Discussion and Conclussion Fuzzy c-means method with three seeding regions for initial matrix fuzzy c-partition of three cluster centers i.e. : 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 1. 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.

Figure 1. Climate regions in Indonesia based on fuzzy clustering To get the connection between rainfall area and sun activity, need to divide the rainfall area until independent climatic area are reached. Using Thiessen Polygon :

Then, Catchment area = total (Rainfall x Area)/total (Area)

Station 1 2 3 4 5

Rainfall (mm) 261.42 242.42 258.83 277.12 236

Area (Scale) 27.5306 17.667 143.7368 17.474 76.474

Rainfall x Area 7197 4283 37203 21192 18035

Table 1. Thiessen tabulation sample

Figure 2. Five Independent climatic area resulted by Thiessen model

Figure 3. Yearly Rainfall in Kalimantan Barat area vs. Sunspot number

Figure 4. Correlation between sunspot numbers and yearly precipitation in Pontianak region 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) and in 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 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 atmospheric circulations are very different compared to the extra-tropical zones.

Figure 5. Lanina and Elnino Years during Sunspot Periods 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. From Figure 7 we can conclude that eastern Indonesia (Jayapura region) which represented Eastern Indonesian Maritime Continent is strongly influenced by ENSO.

Figure 6.

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.

Figure 7. Yearly precipitations in Jayapura region vs. sunspot numbers.

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 to El Nino.[4, 5] In West Kalimantan and Pontianak region which represent middle Indonesian Maritime Continent, the yearly precipitation is mainly determined by sunspot cycles (Figure 3 and 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 7).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 6). 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. ANFIS PREDICTION Numbers Sunspot

200 150 100 50 0 2012

2008

2004

2000

1996

1992

1988

1984

1980

1976

1972

1968

1964

1960

1956

1952

1948

Years ANFIS Prediction

Obs. Sunsspot

Figure 8. ANFIS prediction of sunspot number time series. Using ANFIS prediction we need to aware about characteristic weather/climate that could be happen in 2012. In which that year, sunspot indicate the maximum of number. Even needs more exploration, at least from the evidence of connection between sunspot and weather/climate once again we need to consider. 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, Science’s Compass, Vol. 298, 2002. [4] T. Landscheidt, New ENSO Forecast Based on Solar Model, Schroeter Institute 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. [7] Rainbird, A. F. (1970), Factors influencing rainfall formation and distribution. WMO Proceeding Forecasting of Heavy Rains and Floods, WMO, Genewa.