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  dry periods Analysis for the dam management
in the North of Tunisia      Lebdi Fethi, Magid
Mathlouthi and Lamddalena.N INAT Tunisie 14 - 17
Février 2007 CIHEAM, Bari, Italy
WASAMED
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SUMMARY

• Identification of Dry Events
• Case survey of the Ghezala Dam in Tunisia

1. Use of chronological sets of dry events for Dams
   management

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Problematic To optimize a dam reservoir
management rules when occur dry extreme events

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Survey case Ghezala Dam in Tunisia
Station pluviométrique
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• The mean yearly rainfall recorded in the Ghézala
  dam pluviometer (1968 - 2004) is 680 mm 

• The mean monthly rainfall is 56,8 mm

• Among the 444 months that constitute the sample,
  53 months have a rainfall lower then 1 mm
  (roughly 13 of the sample).

• On the average the most humid month is December
  with 105,5 mms the driest month is July with 3
  mms of rain

• The humid season spreads from September to
  beginning May.

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1. Dry events identification

• A rainy event is defined according to a certain
  daily rain doorstep value

       
 
 
 

• A limit of 4 mm/j has been chosen, water quantity
  roughly corresponding to the middle daily
  evapotranspiration and indicating the lower
  physical limit thus considering rain that can
  produce a usable water surface resource

• the time between the end of a rain event and the
  beginning of the rain event according to is the
  event dry representative the number of days
  without rain between two consecutive events.

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• The dry event distribution is represented by the
  negative binomial law (Fig. 1)

où n 0, 1, .
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(No Transcript)
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Table 1. Dry events statistic
Obs. Period Data number Mean in days Ecart type in days Binom. negative distribution Parameters Binom. negative distribution Parameters Kolmogorov-Smirnov Statistic P- value associed
1968 / 2001 711 7.3 7.91 0.1007 0.7054 0.053 0.033

• 19 of the dry events lasted only one day. The
  
• average is of 7,3 days.

• Dry periods until 30 days and even more can
• to be recorded.

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• The length of rain events follows a geometric
  law
• (Fig. 2) 

n 1, 2, . . .
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CONCLUSIONS

• The dry event analysis permits to plan resources
  hydric on a different basis of the one of
  observations made in regular time intervals.

• The analysis by event permits to wedge functions
  of uncertain variable distribution.

• The analysis by event permits the generation of
  synthetic event by simulation for dams management
  more realistic.

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1. Use of the chronological sets of dry events for
   dams management

• A rainy event is a vector Ri,j

Où Di,j length of a rainy event j in a humid
season i
Zi,j length of a dry event j in a humid season
i
Hi,j total height of rain accumulated in Di,j
rainy days.
Where hk represents the daily total rain in mm.
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• The length of the rainy season Li is defined as
  the period between the beginning of the first and
  the end of the last rainy event of a given season

Where Ni rainy event number in a humid
season i.
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• Generation of rainy sets and dry events

Table 2. Maximal values of r2 determination
coefficients
Caractéristiques saisonnières Nbre de jours pluvieux/saison humide Nbre dévénements de pluie/saison humide Evénement sec maximum de la saison humide Longueur de lannée hydrologique
Hauteur de pluies (mm)/saison humide 0.69 0.49 0.50 0.02
Longueur de la saison humide (j) 0.007 0.33 0.21 0.62
Nombre de jours sans pluies pendant la saison humide 0.63 0.04 0.51 0.46
Longueur de lannée hydrologique 0.03 0.22 0.23 1
Caractéristiques entre événements Hauteur de pluies / événement (mm) Evénements pluvieux
Evénement pluvieux 0.64 1
Evénements secs 0.02 0.02
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• A middle report has been found between the length
  of the event Di,j and the height of rain Hi,j by
  event

• A non meaning interrelationship between Zi,j and
  the Di,j length and the height of Hi,j rain of
  events can be detected

• The number of events per season is practically
  independent of the other variables, exception of
  the total height, of rain that characterizes the
  rainy events of the humid season.

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Functions of probability distributions (fdp)
Number of events by humid season The
function of fish density describes the number of
events sufficiently per season.

• Hauteur de pluies par évènement
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• It exists a relation between the height of
  rain/event and the length, therefore it is
  necessary to distinguish between fdps of rain
  heights for different lengths of the event 1, 2,
  3, 45 and gt6 days.

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• For an event of length 1 day the negative
  binomial fdp
• provides a good adjustment (Fig.3).

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Length of the hydrologic year  
Table 3. Statistical features of the length of
the hydrologic year
Pluviomètre Durée des observations Moyenne arithmétique (j) Ecart type Coefficient de variation Coefficient dasymétrie (Pearson) Cp
Ghézala barrage 1968 / 2001 365.1 16.23 0.044 0.88

• The mathematical esperence confirms the yearly
  characteristic for this phenomenon.

• The weak variation coefficient gotten by the
  analysis indicates the stability of this value. 

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• Some synthetic event sequences were
• generated by simulation of probability laws
  (Bogardi and
• al., 1988).

Table 4. statistical Features of sets of rainy
events observed and generated (on a period of 50
years)
Nbre dannées observ. Nombre dévénements Nombre dévénements Nombre de jours de pluie Nombre de jours de pluie Longueur de lannée hydrologique (jours) Longueur de lannée hydrologique (jours) Longueur de la saison humide (jours) Longueur de la saison humide (jours) Temps dattente maximum (jours) Temps dattente maximum (jours) Hauteur totale de pluie / saison (mm) Hauteur totale de pluie / saison (mm)
Nbre dannées observ. Moy. Ecart type Moy Ecart type Moy. Ecart type Moy. Ecart type Moy. Ecart type Moy. Ecart type
34 22.5a 4.6 63.0 12.4 365.1 16.2 220.5 14.75 30.2 3.6 605.8 159.4
34 22.1b 4.16 61.9 13.9 364.96 18.4 218.0 43.5 29.2 3.5 583.2 153.5
a valeur observée b valeur générée
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CONCLUSIONS

• The case of survey, confirm the concept of the
  independence of the length of a rain event and
  the one of a dry event.

• The phenomenon of drought in the region of the
  Dam Ghezala seems to be described particularly
  well while adjusting the negative binomial law to
  the length of the dry event.

• The distribution of the rain height associated
  with different classes of length seems to adjust
  to the theoretical waitings.

• The association of the chronological sets of
  rainy évènements to a rain - out-flow model
  permits to get sets of contributions that one
  uses to studies of optimization of rules of dam
  management by events.

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FIN Merci