Novel Probabilistic Cellular Automata Based Approach for Prediction of Hot Mudflow Disaster area and volume
Novel probabilistic cellular automata based approach for prediction of hot mudflow disaster is proposed. Hot mudflow is spreading like a fluid dynamic with velocity, viscosity and thermal flow parameters. Therefore, a prediction model based on fluid dynamic is proposed. We use cellular automata approach because that is relatively simple and have a good enough performance for visualization of fluid dynamics. We use much simpler approach based on discrete cellular automata model for simulation of hot mudflow with adding some probabilistic parameters based on Gaussian function. We add some new rules to represent hot mudflow movement such as moving rule, precipitation rule, obstacle-changing rule and absorption rule.
The prediction results show a highly accurate elevation changes at the predicted points and its surrounding areas. We compare these predicted results to the digital elevation map derived from ASTER/DEM. We use some period of maps to evaluate the prediction accuracy of the proposed method.
hot mudflow, prediction model, cellular automata, Gaussian function, fluid dynamics.
Sidoarjo hot mudflow disaster is one of the biggest unstopped disasters that occurred on May 29th 2006 suddenly caused by a gas exploration. For last three years, the disaster destroyed some villages, thousand of houses and buildings, framings, schools, markets and factories. Over 21,000 peoples had lost their homes and their works. The weight of the mud on the ground is reported already and is corresponding to the weight for pressing down a large area of Sidoarjo land by approximately one meter. Nowadays mud blows around 150,000m³ per day . It is also reported that the plumed mud contains 70% of water. It implies that 687,000-barrel water is spread out every day. How big impacts of disaster are in environment, economic and human resource in the future if this disaster cannot be stopped .
One of the possible solutions for reducing disaster may be a spillway the mudflow to the near by Porong river. It is not promising and is not guaranteed for a long time. Also it insists the peoples who are living in the suffered areas to move safe areas. In other word, the current problem is how to reduce the impacts, so that prediction of mudflow areas and inundated areas in time and space domains. If inundated area can be defined before the mudflow comes, government and the peoples may reduce its impact.
Assuming that mudflow is similar to fluid flow, a fluid flow model creates the prediction model of mudflow movement. The simple fluid flow model proposed by Argentini  is used for the cellular automata that are proposed here. This model is useful for visualization of fluid flow phenomena with some parameters such as volume, velocity and obstacle avoidance. This model cannot be used for mudflow simulation because it does not handle viscosity and thermal parameter. The other model is lava flow model proposed by Vicari  that is based on a cellular automata approach. This model is better model for representation of hot mudflow because it can treat the parameters, volume, velocity, viscosity and thermal situations. The cellular automata approach can visualize hot mudflow disaster in free-space area. It, however, is necessary to add some additional approaches for visualization of the actual conditions those are not only natural conditions but also human factor parameters such as dike, building and road. Thus a combination of Argentini's and Vicari's models is proposed. It should be a better prediction model of hot mudflow spreading with a consideration of the human factors. Due to the fact that the Argentini's model uses limited integer state and Vicari's model uses floating point state, the proposed model uses a discrete model with floating points.
The proposed model uses cellular automata with stochastic lattice Boltzmann, neighbor weight-moment to determine direction of mudflow movement and Navier Stroke approach to calculate volume of mudflow movement. On precursor model, we can visualize mudflow movement like a combination between fluid flow and lava flow models. Although the model has a good visualization capability of mudflow movement, we have to add some properties, map data and rules to make it better to show the actual condition that have some obstacles like dikes and building. The proposed prediction model is to inform of where some inundated locations are. It will be used to restrain geological impact of hot mudflow disaster. We use some basic parameters of dynamic system to simulate prediction model. That is an approximation model to describe actual model for representation of actual situations. We use ASTER (Advanced Spaceborne Thermal Emission and Reflection)/DEM (Digital Elevation Model) data for landscape map of the disaster area and its surroundings on some periods in order to show how the prediction results and the actual situations differ. Also prediction accuracy of the proposed method is compared to the some other fluid flow model with the reference to the ASTER/DEM derived elevation as a true landscape map.
2. Theoretical Background
2.1. Cellular Automata
Cellular automata (CA) are a set of array of automata called cell. They interact one to another cells. Array model of CA is expressed with one-dimensional shape, two-dimensional (2D) model grids, or three-dimensional (3D) solids as are shown in 3. Almost all the cells are aligned at the simple lattice points, but are aligned in a complicated form like honeycomb in other rules. Finally, CA is a simple model to describe the complex system of life.
As simple model, CA only has three fundamental properties, state, neighborhood and program. The state is a given variable for defining each cell. It can be shown in numbers or properties. In simple way, each cell is written as sub-landscape; therefore state is sum of individual location or type of growing area. The neighborhood is a set of cells. That interact each other in the physical grid, and two fundamental neighborhood models are Von Nuemann Neighborhood and Moore Neighborhood as are shown in 1. The program is a set of defined rules to change state as response in a time depending on its neighborhood. In CA model approach, we can develop some new rules based on state condition and neighborhood.
(a) The Von Neumann Neighborhood (b) The Moore Neighborhood
Mathematical point of view of cellular automata, the state at position (x,y) at time t that is written st(x,y) will change into st+1(x,y) at time t+1 with rule that can be written:
where , are position of its neighbors.
Formally cellular automata have three basic components  such as:
· A regular lattice of cells covering a portion of n-dimensional space
· A set of of Boolean variables attached to site (x,y) of the lattice and giving a local state of each cell at time t=1,2,3,….
· A rule which specific function of state that is written:
Where is given neighbor.
2.2. Fluid Dynamic Cellular Automata
CA model can be used to describe fluid dynamic phenomena such as fluid flow, lava flow and gases dynamic. There are four types of update state changing model in fluid dynamic CA as is shown in 2, such as growth model , Icing-Like dynamic model , moving model  and majority model . These models have different state types and update state rules. Many fluid dynamic models use growth model and moving model such as Argentini's model and sea-wave simulation. The other models - Icing-Like model and majority model – usually use to append the properties of fluid dynamic such as viscosity as shown as lava flow model and mudflow model.
The main focus in fluid dynamic is update rules, and the main processes in this rule are collision between cells, and cell moving. The example common rules in fluid dynamic, introduced by Albertini  as shown in 3(a), is the rule of cell moving, because this rule can be ran if the state have fluid particle or st(i,j)=1. This rule uses Moore neighborhood, and the direction of cell moving depends on neighbor position because it related on force of particle interaction. This rule also is basic simple rule of fluid dynamic for simulate flood hazard . The result of this rule is shown on 3(b)
Another model for fluid flow model, developed by Avolio , is Cellular Automata model for simulation of 1992 Tessina Landslide. This model is mudflow model, and uses Von-Neumann neighborhood. It is quite different with Argentini models, because this model uses floating point states and the example rules on this model as shown in 4. This model is simple and useful, and has good performance for landside caused by mudflow. But on high volume mud blows, this model has a problem to identify how much mud will move to other area, because there is no eliminated cell on center of mud blows. Combination of basic rule on Albertini's model, Vicari's model and this model makes a new cellular automata approach to simulate hot mud flow that has a good performance to predict where mud will flow in future.
2.2. Minimization Rules
4 show the CA rules that is used on some fluid flow simulations. This rules was called as Minimization Rules. The minimization rules describes how the material will flow from a cell to its neighbors. D'Ambrosio show the description of minimization rule for soil erosion by water that shown in 5. In this rules we have two values E(i) as number of solid material and H(i) as number of fluid material:
a. E(1)>H(0), E(2)>H(0) à cell 1 and 3 eliminated
b. Er=31/3=10.3, E(4)<Er à cell 4 eliminated
c. Er=20/2=10, no cell eliminated
d. Reconfiguration △H=Er-min(E)=(10-6)=4 à E(0)=7; E(2)=10
Although this rules show the material transport, but it can not show how much materials will move and how much materials will stay on a cell because it will change from fluid to soil.
3. Proposed Model
Hot mudflow model is similar to fluid dynamic flow model. We, however, need to combine all basic updating state models of CA to make it look like real condition because the state properties in each algorithm is binary state except growth model, otherwise mudflow model is floating point model. In this research, we combine fluid dynamic flow model from Argentini and lava flow model. Our model uses Argentini's model as primary model because the Argentini's model is very simple model based on growth model to describe fluid dynamic flow with discrete state. The Argentini's model, however, is not enough to describe mudflow because there are how to move and growth fluid particles but also viscosity, erosion and deposition.
As many fluid dynamic cellular automata models, our model uses 2D cellular automata with Moore neighborhood (8 neighbor nodes). But we use floating-point states for describe current states of mudflow map, it is different with Albertini's model, because floating-point state is more easy to define map data similar with real data. The state S is float between 0 and 1. In this research, we define three-type variables: mud st(x,y), ground ht(x,y) and dike (use same variable with ground because the dike have same characteristics with ground), as shown in 6.
We define s(x,y) as number of mud particles on node (x,y), T(x,y) is temperature on node (x,y) and elementary rules in update state:
(1) The mud blow in center point (cx,cy) with mud volume vol as shown in 7, that is written by:
Where: is a neighbor points
is Gaussian based function of mud blow.
T0 is initial temperature on center area of mud blow.
We use uniform temperature on center area.
(2) The mud is situated at the every lattice point. The mudflows from a higher position to lower neighborhood with probability Pv as the function of height different, volume and velocity as is shown in 8(a). The number of moving mud which is based on this rule can be expressed by the following equation:
is total of ground height and mud height in time t.
= Probability to move
d(m,e) is function of heat transfer.
(3) The mud is changed its material to solid particles by pvis of the probability as the function of viscosity as is shown in 8(b). The number of moving mud which is based on this rule can be represented with the following equation:
K is constants, and Tt(x,y) is temperature on node (x,y) at time t.
(4) When the neighbor is dike that have higher position that mud with probability absorption Pa the mud throughout into dike and will appear in the next of dike position as shown in 9.
is total of ground height and mud height in time t.
is node around the neighbor
= Probability of absorption
Based on minimization rules, the rules for hot mudflow using the material transport in moving rule and material changing in viscosity rules is defined as following rules, as shown in 10:
a. E(1)>H(0), E(2)>H(0) à cell 1 and 3 eliminated
b. Er=31/3=10.3, E(4)<Er à cell 4 eliminated
c. Er=20/2=10, no cell eliminated
d. Reconfiguration △H=0.5*(1+e)*(Er-min(E))=3.5 à E(0)=7.5; E(2)=9.5.
Where e is material transport based on the moving rule and viscosity rule.
11 shows the simple rule in our model to simulate mudflow movement with constant velocity and viscosity. This rule finds the lowest neighborhood. Also the rule arranges its height at the center and surrounding areas to have a smooth slope. In the left picture, the center point shows the maximum difference of 5 with its neighborhoods. When the maximum difference is greater than α (tolerance value to make pile shape), the particle is moved to a lower point with probability, G(δ). The right picture shows all points have small differences each other.
3.3. Data Specifications
We use SPOT-5 of HRV (Satellite Pour l'Observation de la Terre-5/High Resolution Visible) image as a base map as is shown in 12(a). HRV size is 447×487 pixels which is corresponding to 3.7km×4km area, it means 1 pixel have area 8.27m×8.21m. We also use ASTER/DEM data for determination the landscape of intensive study area. The spatial resolution of ASTER/DEM is 30m×30m. SPOT-5/HRV image have good enough spatial resolution for relief the intensive study area. It, however, does not have not well information of landscape so that ASTER/DEM data is used for creation of landscape. Re-quatization and interpolation between ASTER/DEM and some height of dike derived from SPOT-5/HRV are required. The resultant images are shown in 12(b).
Sidoarjo hot mudflow disaster is one of big disaster because mud blows around 150.000m3 per day, and mud volumes come out. The mud consists 70% of water and its surface temperature is around 90oC. When we use resolution nx×ny pixels, it implies:
4. Simulation Result
In order to find inundated area in the future, CA parameters such as spatial resolution and volume scaling have to be optimized for making the prediction much better. We use SPOT-5/HRV data in order to show the disaster area clearly. 13(a) and 13(b) show the actual disaster area map in February 2008 and August 2008 while 13(c) shows its simulation result. The simulation begins with the actual disaster area map in February 2008 as is shown in 13(a).
14 shows the comparison between the actual disaster area maps colored in blue area while the simulation result colored in red area, respectively. The magenta colored area shows the intersection between the actual disaster area map and the simulation result. In this , although there is some different areas between the actual disaster area map and the simulation result, the direction of mudflow and inundated area are quite similar between both. Although the simulation result that is shown in the is derived from CA, it is possible to create a new model of mudflow with some other adding parameters such as dike and mud parameters.
On this simulation, we find the same inundated location on the outside of dike. The inundated location in our simulation result is on the east and south that same with the real condition of hot mudflow disaster. The overlay of the new inundated area between real map and simulation result is 36.44%.
The simulation runs with the parameters, the lattice size of 400×400 pixels, the minimum mud volume of around 104 m3 per day and the mud contains 70% fluid particles (mostly water) and 30% solid particles. The mud volume is generated by a normal distribution of random number with the mean of around 104 m3, as well as velocity and viscosity is constant. Since the simulation size, 1 pixel is corresponding to 9.25m×10m area, this resolution is appropriate enough to show the mudflow characteristic.
CA approach is a microscopic-level of approach so that it needs a high resolution of simulation data. In the experiment, the relations between the resolution (simulation lattice size) and prediction accuracy is intended to clarify. 15 shows the simulation results with some different resolutions.
16 shows the simulation results that are based on the map resolution. In the simulation, we use the resolution of 5.71m-20m for a pixel. The simulation result of the intersection area shows that prediction accuracy is increasing in accordance with increasing resolution as is shown in 15. It implies that the CA approach needs a high-resolution map to improve the accuracy.
Another simulation result of elevation changes at hot mudflow erupted areas is shown in 17. This result shows that mud elevation is changed depending upon the initial and the final conditions. 17 also shows the one-dimensional profile of the mud elevation changes. The red line shows the mud elevation at the initial state that we take the landscape data of February 2008. The green line shows the mud elevation at the final state, three months later from the initial state. The average elevation difference between the initial and the final states is 1.01meter. It implies that the mud elevation changes about 0.3meter per-month.
5. Discussion and Conclusion
Cellular Automata approach is a model-based approach that depends on some parameters such as resolution, neighborhood, and rules. This model is accurate when the resolution is appropriate for representation of particles or cells. Meanwhile the proposed model makes a relaxant on the required resolution. Even for the minimum resolution of 100×100pixels, the proposed method makes an enough simulation result (the maximum resolution is 2000×2000 pixels). The minimum resolution is corresponding to 37m×40m a pixel that is also corresponding to the lower resolution of ASTER/DEM data with 30m×30m so that the proposed method is justified and evaluated with ASTER/DEM data. The maximum resolution (800×800 pixels) of simulation results is shown here. This resolution corresponds to 4.625m×5m a pixel. It is concluded that the proposed method is valid for detection and prediction of hot mudflow spreading direction and volume as well as appropriate inundated areas that are situated surrounding areas.
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