Flood as a natural disaster follows certain erratic patterns which was made confounding factor. Flood risk is variable and complex that depends on very phenomena such as rainfall, runoff concentration and high exposure of the flooding downstream areas.

This are changes over time and from regions due to natural conditions, human activities, and damage culture of the community at risk. Occurrence of chaos at flood risk changes the trend of predictable processes. In the other words, although flood is a disaster, the occurred irregularities in its patterns can reveal its complicated nature. Flood pattern irregularities are the incident evidence of chaos in the system which can be studied by fractal geometry. The occurred events in spatial variability of floods in the last 50 years show they can be occur as unusual urban flood in Tehran.

Tehran city may experiences the difference life and property damages because the high varieties in the socio-economic and the life quality level in regions, also structural varieties in the city fabric??. Ignoring the natural factors in spatial planning, overrun and destruction of natural morphology as a result of urban activities and subsequently disturbing urban drainage system lead to unpredictable and destructive floods in Tehran.

The Tehran precipitation layer was prepared based on 27 weather stations data in the period of 10 years (1998-2009) and Kriging model with a Gaussian function. The runoff is calculated by Soil Conservation Service Curve Number (SCS-CN) and precipitation layer. The flood hazard potential map has been created by 8 variables and Analytic Hierarchy Process (AHP). This map as an index to define the said complexity was prepared in 5 categories of risk by combination of Tehran metropolis flood hazard and vulnerability maps. Then it was divided into hydrological basins and 12 basins were selected randomly. The Perimeter-Area Fractal and Number-Area Model were used to study the chaos and turbulence in the Tehran’s flood pattern.

Explanation of locational changes of risk between the basins needs to calculate the weighted average risk and the independent variables in 12 basins that obtained by zonal statistics. Based on these average values the factor analysis used to determine the Varifactors or main components of the variability in flood risk between the basins. Finally, fractal geometry models (perimeter-area and cumulative number-area) were used to demonstrate the chaos of the flood risk value in 5 categories of risk.

In this research the Tehran flood zoning map was calculated at 5 hazard categories. The fractal of sample basins had increased by increasing in the level of hazard map. Generally, the higher DAP values from 1 represented increasing in the chaos or irregularities of Tehran floodhazard. The obtained DAP from very low to very high risk levels are 1.206, 1.216, 1.23, 1.263 and 1.293 respectively. The increasing of DA indicated that turbulence hazard increases based on Perimeter-Area fractal model, thus, with the increase in hazard the DAP and DP values were greater. Also, the results of Number-Area Model showed turbulence floods in the five classes of hazard. The area cumulative number of risk levels are 0.74, 0.79, 0.85, 0.86 and 0.88 respectively; this trend showed the less size of flood risk polygons from very low to very high risk levels. In the other words, by increasing the risk level the polygons gets smaller and indicates the increase the flood risk chaos.

The occurrence pattern of natural phenomena and even natural hazards have a regularity type in normally condition; if this regularity disrupts for any reason, irregularities or chaos happens. In present study, the results of fractal analysis in sample basins presented the chaos pattern in Tehran floods. Also the heavy rainfall can be predicted in Tehran but the prediction of the flooding distribution was not provided. According to the recorded floods in Tehran the flooding begins always in the northern valleys of Tehran, like Darband, Kan or Golabdareh basins, are not similar to damage pattern. As a result, despite several studies and projects which have been implemented about flood phenomenon in Tehran, this is unpredictable and uncontrollable in the city.