In this study, the risk 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. To analyze the risk varieties, the hydrological catchments of Tehran were extracted by Arc Hydro model and 12 catchments were selected. Using land use, roads network, and the percentage of residential floor area, bridges, altitude, slope and drainage density variables, the flood hazard map was calculated. Dilapidated urban blocks, population density, land use, bridges, slope and drainage density layers were used as variables which affecting the flood vulnerability. Covariance index was applied for matched variables and considering the locational coherence between the values of them. Based on the new raster layers, flood risk variability in Tehran metropolis as well as in each of the catchments were analyzed using stepwise regression model. Explanation of locational changes of risk between the catchments needs to calculate the weighted average risk and the independent variables in 12 catchments 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 catchments. 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. According to the flood hazard zoning map of Tehran metropolitan area, the extent of high hazard zone is 129.6 square kilometers. High risk zone covers 28.6% of Tehranchr('39')s area, indicating that most of the citychr('39')s extents (174.4 square kilometers) are located in the high flood risk zone. After that, the moderate hazard zone is 28.5% of the city area. Very low zones with 3.53% of the total area are the smallest zones in the city, which are only 21.5 square kilometers. Overall, 78.3 percent of the total area of the city is located in the moderate to very high zones of flood hazard, reflecting Tehranchr('39')s challenge to flooding. The vulnerability map defines that 138 km2 of the Tehran city area is located in high and very high zones of the flood vulnerability. According to Tehran metropolitan flood risk zoning map, 163.1 km2 of Tehran city area is located in high risk zone which has the highest rate among flood risk categories in Tehran metropolis (26.9%).
