Week 2 - TASK

Simulation of 300 years return period event and 
comparison with 1994 event (flood extent and water elevation)

In order to achieve this task, we first had to :
- get good quality data
- statistical analysis 
- hydrographs for 300 year return period 
- hydraulic modelling


To obtain hydrograph for 300 year return period rainfall, statistical method have been used. There are different statistical analysis to analyse flood frequency.
Probability distributions can be Normal (Normal, Lognormal, Lognormal-III), General Extreme Value (Gumbel, GEV, Weibull) or Exponential/Pearson type (Exponential, Pearson type III, Log-Pearson typeIII).

In this case study, peaks over threshold’s (POT) for quick flow periods for rainfall and discharge were extracted from historical datasets using WETSPRO software (Willems, 2004) and the distribution type was analysed using ECQ software, in order to find the proper method that is fitted to this particular case study (Willems, 2004). Historical rainfall and discharge data from the Var river catchment were analysed using ECQ to check slopes, MSE and Q-Q plots. Results of analysis showed a generalized extreme value type of POT distribution. The Gumbel method was chosen to get peaks for 300 years return period. 

In this study, the Gumbel method was applied for flood frequency analysis. The Gumbel method was chosen because peak flow data is homogeneous and independent, hence lacks long-term trends. Additionally, the river is less regulated, and hence is not significantly affected by reservoir operations, diversions or urbanization. 
Finally, flow data covers a relatively long record (more than 10 years) and is of good quality.

So, there's a direct statistical analysis of flow database.

The Gumbel distribution with location parameter alpha and scale parameter beta is implemented in the Wolfram Language as Gumbel Distribution (alpha, beta). It has probability density function and distribution function, the mean, variance, skewness, and kurtosis. In this case study, the flow data base of the Var river consists of measurements taken at Napoleon III bridge, it contains 16 years of daily flow data (1985-2000). In order to estimate alpha and beta parameters (population parameters) and generating Gumbel variables,

Method of Moments was used.  At the beginning, annual maxima was extracted from data base, after sorting and assigning ranges, probability and non-probability of exceedance were measured.

Parameters calculated are in this table below :

Expected discharge with the corresponding IDF and CDF curve is presented as follow :

So this is the statistical analysis of daily database :

After calculation of peak flow for 300years return period a hydrograph was designed by linear interpolation of each time step according to difference of peak flows in 1994 and 300 years return period event (rescaling).

To allow for rescaling, in order to achieve a more accurate result, the following steps were performed:

1. Rescaling the 1994 hydrograph by the rescaling factor of (300 yr return period peak/maximum daily flow of 1994 event)
2. Extracting hourly flow data from Eaufrance
3. Calculation the annual maxima for each year
4. Performing Gumbel distribution analysis
5. Rescaling the 1994 hydrograph by the rescaling factor of (300yr return period peak/maximum hourly flow of 1994 event)

Result of Gumbel distribution of hourly data is displayed in this table below :


For hydraulic modelling, we used IBER software to obtain floodmaps of 1994 and 300 year return period event.

Results & Comparison with 1994 flood event