**1. Introduction**

Monte Carlo simulation, or probability simulation, is a technique used to understand the impact of risk and uncertainty in natural occurrences, project management, cost and other forecasting models [1]. You must make certain assumptions—for any model that plans ahead for the future—when you develop a forecasting model. In this research, there might be assumptions about the future shape of river curvatures which is called as river meanders. These are projections into the future, and the best you can do is to estimate the expected value. What the actual value will be you cannot know with certainty, but based on historical data, or expertise in the field, or past experience, you can draw an estimate value. It contains some inherent uncertainty and risk, because it is an estimate of an unknown value.

The Monte Carlo simulation performs random sampling and conducts a large number of experiments on computer, which is different from a physical experiment, At the first step, experimental statistical properties (model values) are given, and results for the model outputs are calculated with a computer program. According to the calculation procedure, the input random variables are distributed randomly. The output Y variables are given as a function of x in formula Y = g (x), where this function is called as performance function. After collecting the necessary input values from each experiment carried out in this manner, a set of samples of output variable Y are available for the statistical analysis, which estimates the characteristics of the output variable Y. In **Figure 1,** the flowing

computer chart is given as an example where the three steps are required in the simulation process:

Step 1: Sampling on random input variables X.

Step 2: Evaluating model output Y.

Step 3: Performing statistical analysis on the model output.

The discussion about the choosing of independent random variables will be given. But, the Monte Carlo simulation is applicable for dependent variables where it is needed to follow the three steps [2].

Monte Carlo methods generally follow the following steps:

1.Determining the statistical properties of possible inputs.

2.Generating many sets of possible inputs that follow the above properties.

3.Performing a deterministic calculation with these sets.

4.Analysing statistically the results.

The error on the results typically decreases as 1/√N [3].
