Monte Carlo simulation (5)

Example of uncertainty analysis on river Jadar


River Jadar runs through west of Serbia and Montenegro state. Since the landuse is highly variable and not the same over years, due to urbanisation and diferent agrycultural plans, it is required to analyse risk of flooding under influence of uncertain Manning coeficient in the main channel and in flood plains. Representation of uncertain parameters is choosen to be represented as statistical distribution.


Grafical representation of mathematical model of river Jadar

River Jadar is modeled from the bridge in Osecina to cross section 1650 m upstream. It was divided in 15 crossections. As flow is subcritical, critical depth in the most dounstream cross section is assumed as boundary condition. The discharge was Q=147 m3/s.

The riverhead in control section was analyzed due to uncertainty of input Manning roughness values of main channel and inundation areas. Due to pictures from the field, the roughness coefficients were estimated as an uncertain values. Since in the main channel we have gravel on the river bed, normal distribution with parameters N(0.04,0.0052), and for the inundations, covered with crops and locally the bushes and trees, normal distribution with parameters N(0.08,0.0052) was chosen.


Schematic representation of main channel and inundation areas


The Monte Carlo simulation had 100 simulations, after which the statistical parameters of output value (water head) stabilized.


Monte Carlo simulation on a diagram
Statistical distribution of water head in control cross section

Statistical parameters of a statistical distribution of water depth in the cross section of interest are mean=3.49 m std=0.053 m.

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