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International Workshop ADVANCES IN STATISTICAL HYDROLOGY

May 23-25, 2010 Taormina, Italy

Bergaoui, Analysis of maximum daily rainfalls 1

ANALYSIS OF MAXIMUM DAILY RAINFALLS. SAIDA

MANOUBIA STATION, TUNIS.by

Bergaoui Mohamed(1)

)[email protected]( Address. IRESA 30 Rue Alain Savary 1002 Tunis(1)

ABSTRACT

The purpose of this study is to determine" rain project" used for the sizing networks of storm drainage.

Thus, our approach is based on the analysis and study of rainfall data in terms of normality and stationarity.

We first checked distribution normality of precipitation series using Kolmogorov-Smirnov test and a

graphical way. Then the frequency analysis of maximum daily rainfall is made while the quantiles of scarce

spectrum are determined. Finally, the study of stationary series and the development of rain project aredeveloped. Based on a series of long observation period, we have highlighted the non stationarity of the

series. Several breaks in studied series are detected. According to Hubert and al.(1989), this segmentation

procedure can be considered as a test on the stationarity of the series . Such a method is appropriate for

changes research of the mean. We found out that general trend of series is downward. However, the daily

rainfall maxima picks are observed in recent decades, reflecting a change in climate. Maxima daily rainfalls

are due to intense storms and short durations. In Tunis, we recorded 193 mm of rain in 90 minutes in 2003.

This rain has a return period of 500 years. These exceptional rains are then processed in order to define the

rain project. A "rain project" is a rain fictitious defined by a synthetic hyetograph and statistically

representative of real rain. Results of this study are interesting: they help to diagnostic the behavior of the

network of storm drainage (size and emptying time) and reduce the impact of these events during flooding

periods.

Key words: rain, frequency analysis, stationarity, design storm

1 INTRODUCTION

Frequency Analysis is a statistical method of prediction. It consists of studying past events,

process characteristics (rain, flow) to define the probabilities of future occurrence. This predictionis based on fitting the act of probability to the empirical frequencies of past observation. On

18/09/2003 Tunis has witnessed an extreme exceptional event.. Heavy rain fell over the wholecatchment area of Tunis main ly the municipalities of Ariana and Mannouba and caused flooding.These exceptional rains are of great intensity. It is a rain of 193 mm in one day, which had

caused a lot of damage. The rain of 28/09/2003, even with a lower intensity, led to new

flooding with regard to the fact that soil saturation. Frequency analysis of rain helps to predictthe characteristics in terms of quantiles, return period, and response time of the watershed. Theanalysis is used to quantify the extent of flooding and to take decisions necessary for stormwater drainage (size of network storm, emptying time) to mitigate the impact of these events generally

on the urban map. To develop this study, we used the rainfall observations at Mannouba Saidastation.

2 DATA AND METHOD

The method adopted in this study is based on the predetermination of extreme rainfalls, frequency

analysis, and development of design storm in hydrologic modeling.

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3 DATA SAIDA MANNOUBIA STATION

The used series is based on daily maximum rainfall "Pjmax" that is observed over 132 years,from 1872 to 2003. The Characteristics of the concerned series are summarized in Table No. 1below. We have noticed: the minimum recorded is of 17.40 mm (1919) while the maximum is of

193mm (September 2003). The gap between the two extreme values is of 175.6 mm . The rain of September 2003 is three times more than the daily average rain.

Table 1. Series characteristics.

Available sample(years)e 132

Minimum(mm) 17.40

Maximum(mm) 193.00

mean (mm) 54.76

Median(mm) 47.30

Standard deviation(mm) 29.97Cœfficient of. Variation 0.55

Skewness coefficient 1.69

Kurtosis coefficient 7.08

The Skewness coefficient is equal to 1.69 which is a positive asymmetry. The coefficient of variation is equal to 0.55. We can say that the distribution is spread right. Also the kurtosis

coefficient (( γ = 2.87> 0) is strong. If the kurtosis is clearly different zero, than them the

distribution is either flatter or more peaked than normal.

Figure 1 of Histogram of maximum daily rainfall shows a significant variability in rainfall withvery two high peaks.

Figure n 1.Histogram of maximum daily rainfall.

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Frequency analysis. The adjustment to empirical frequencies of the observed rainfall shows

two laws can adequately describe the variation of the observations. Which are the Gumbel

distribution and Log Normal. In fact, the graphs 2 mentioned below, at an interval confidence of 99%, show that the laws adopted comfortably fit on the scatter plot. The log-normal parameters µand σ admits the probability density function.

for x> 0. µ and σ are the mean and standard deviation of the logarithm of the variable.

The Gumbel distribution is widely used in hydrology to estimate the extreme values of studied

phenomena. We say that X follows the Gumbel distribution with parameters a and b if itsdistribution function is:

Then X has a first-order moment and a variance.

Figure 2: Fitting of the Gumbel distribution with confidence interval 99 ℅.

In addition to this descriptive analysis of the package, we determined the quantiles of different

return periods, table 2.

Table 2: Quantiles of different return periods.

Return period

(years)

Quantile

(mm)

Probability

10 90.74 0.9000

20 108.49 0.9500

50 132.66 0.9800

100 151.69 0.9900

200 171.49 0.9950

500 198.98 0.9980

1000 220.85 0.9990

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The maximum value represents an exceptional rainfall with the return period of 440 years.

4 SEGMENTATION OF HUBERT

The maximum daily rainfall series presents breaks of different medium, Table No.3. It turns outthat the average of the first sequence (1872-1899) is greater than the second (1900-2020). The

procedure produced an acceptable segmentation order greater than 2. According to Hubert et al.(1989), this segmentation procedure can be interpreted as a test of stationarity. In our case the null

hypothesis is rejected and therefore the series is not stationniare.

Tableau n°3 Segmentation d'Hubert.

Initiation end average(mm) standard deviation(mm)1872 1899 71.68 33.4

1900 2002 48.46 22.06

2000 2003 193 0,0

4 DAILY MAXIMUM RAINFALL ANALYSIS, SAIDA MANNOUBIA

(1872-2003)

Having determined the frequency of rares quantiles, we propose a detailed analysis of the heavyrain for different time based on the observed rainfall hyetograph. Indeed, the heavy rain causesthe damage in terms of flooding. However, design storm is characterized by

• The duration of rainfall and associated intensity.

• The heavy rain period

• The form of rain.

It involves setting up a synthetic hyetograph containing basic information provided by real

hyetographs. To simulate the behavior of hydrological catchments during a major flood, thequestion that is always asked and had never answered, are we able to say that the return periodfor a rainfall project remains the same for the flow generated at the outlet of the watershed. It

should be noted that the development of a design storm must be on a series of observations,relatively long. Several types of projects rains have been the subject of research work, Chicago

rain, triangular rain and doubly triangular rain (Desbordes M., P. Raous 1980). A design stormassigned a return period which is one or more of its components (Hemain AD 1983 ). Thetransformation from hyetograph project rain of runoff hydrograph is used in forecasting model.Often it is assumed that the return period peak flow is equal to that obtained from the rain project

that gave birth. The development of the design storm is based on statistical analysis of theelements that characterize the rain events. We mainly include the duration of the rain (DP),maximum heights precipitated on different time intervals, the position of the intense period, the

duration of this period. The total duration of the rain duration project can be a mean value on allevents. Possibly according to the concentration. The preferred field in use of rain project is the

design of networks. For a given return period T, the sizing of the network requires the

determination of peak flow in the same period. The flow is calculate according to the intensity of rainfall observed in the concentration time. The rational formula and / or model Caquot are the

most used methods to calculate the maximum flows. In the Mediterranean basin (Montpellier);design storms (BERGAOUI 1984, Desbordes 1982) are characterized by a total height 110 mmfor a return period of 30 years, and a time step of two hours , as maximum height of 90 mm,within two hours.

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5 CHARACTERISTICS OF DESIGN STORM, SAIDA MANOUBIA.

Manoubia Saida Basin has an area of 7 km ². It is a small catchment. The time of concentration is125mn. The estimated shift parameter "K" proposed by Desbordes, which represents thedifference between the center of gravity of the hydrograph and hyetograph correspondent, gave

the same order of magnitude, 120 min. Thus, the design storm selected for the Saida Manoubiabasin is characterized by: A total of two hours duration with an intense duration (DM) of one

hour, Saidi A2008. Often, the design storm is considered less than or equal time or Tc. Generally,the average duration of rain events observed can also be selected as the duration of the designstorm.

The intensity of rain on the duration of DM is 98 mm / h. Finally, it is given that the design formsstorms are generally triangular and / or double triangular, figure 3. By hypothesis, we propose thetriangular shape. This intensity of 98 mm in one hour is taken into account dealing with floodingand drainage systems sizing storm water in Greater Tunis, with a return period of 440 years. It

would also be useful to determine the maximum flood flow for the same return period.

Figure n.3. Design storm, model Desbordes Type.

6 CONCLUSIONS

This study has provided a better understanding of the genesis of floods and flooding. Estimating

quantiles with rare and exceptional frequencies based on the behavior of the frequencydistributions to extremes which will analyze the risks associated with hydrological extreme

events. Regarding the floods themselves, their main causes are the high rainfall intensities for short durations. Design storm is an indispensable tool for the sizing network of drainage of stormwater and hydrological models to forecast extremes.

7 REFERENCESDesbordes M. Raous P. 1980. Fondements de l’élaboration d’une pluie de projet Urbaine,la Métrologie , -(20-21),

pp.317-326.LHM. USTL. Montpellier France.

Bergaoui Med. 1984. Evaluation de l'influence des apports des zones perméables sur les débits et volumes ruisselés

des bassins versants urbanisés. DEA , LHM USTL. Montpellier. France 1984.

Hemain J.C 1983. Guide de Construction et d'utilisation des pluies de projet. Rapport LHM. USTL. Octoblre 1983.Montpellier. France.

tp

DM

t

DP

HM

IM

I(t)

0τ

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HUBERT P., CARBONNEL J. P., CHAOUCHE A., 1989. Segmentation des séries hydrométéorologiques.

Application à des séries de précipitations et de débits de l'Afrique de l'Ouest. Journal of Hydrology, vol. 110, pp

349-367.

SAIDI A. 2008. Etude de la pluie de Projet: Détermination et XCaractérisation cas du bassin Versantettadhamen.2008. Mastère. ESIER

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