r600,p = r980,p ⋅0.95e600×1⋅10−4

INTRODUTION

A raining simulation model for the volcanic tropical island

1 Department of Geophysical sciences and Geophysics of the University of French Polynesia, Papeete, Tahiti, French Polynesia;

2 Department of Hydrogeology of the University of Rennes 1, Rennes, France;

3 Vai-Natura, Eau, Sol et Environnement Conseil et ingénérie, BP.83 98735, Raiatea, French Polynesia.

M. AUREAU1

, A. CHRETIEN2

, J.P BARRIOT1

, R. HAVERKAMP1,3

The main objective of this study is to create a rainfall prediction model for Tahiti or more generally for volcanic tropical islands. This model should be simple, user-friendly and easy to transport; moreover, it should use the existing network of rain measurement stations and should be able describing rainfalls on small scale time period (daily, weekly, monthly).

Here we present our results for two independent geographic areas, the West coast of Tahiti (Punaruu/Marau/Vaiami) subject to West seasonal depressions and the East coast of Tahiti (Hitiaa/Papehia) subject to the East trade wind.

We show that the altitude is the predominant input variable to describe rainfall in these specific areas.

To validate the model we compare results from the model with measurements of a rain gauge that has not been used to build the model.

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1. BERTRAND-KRAJEWSKI J.-L. 2007. URGC Hydrologie Urbaine, INSA Lyon.2. BRIAT P. 1994. Analyse Statistique des Pluies, Cours L552 de forma-tion approfondie en assainissement - Lyonnaise de Eaux, Bordeaux.3. FERRY L. 1988. Contribution à l’étude des régimes hydrologiques de l’ile de Tahiti - Université de Paris XI.4. FETTER C.W. 2001. Applied Hydrogeology - Fourth Edition - Pearson Education International.5. WOTLING G. 1998 . Etude de l’Aléa Pluviométrique à Tahiti - ORS-TOM Centre de Tahiti.6. WOTLING G. 1998. Etude Hydrologique à Tahiti de petites bassins versants - ORTSOM Centre de Tahiti

We show that the altitude has definitely an important influence on the rain distribu-tion if we work in geographic and topographic situation homogeneous.

The model gives very good results predicting the dynamics of rain events correctly. The results are increasingly precise with bigger time scales (e.g., monthly scale). With the daily scale, the model has difficulties to simulate some local storms.

The model allows for drawing isohyetal lines for each uniform area; For example, weekly maps can easily be generated to express the rainfall evolution on Tahiti Island.

Tahiti island is the largest island of French Polynesia, lo-cated in the archipelago of the Society island in the sou-thern Pacific Ocean (coordinates: 17°40’S ; 149°25’W). It is a volcanic island with high mountains marking deep valleys with a total land area of 1,045 sq. km. There are four peaks on the island, the tallest of which is Mount Orohena that stands at 7,618 feet above sea level. It has a tropical climate characterized by eastern winds and strong localized rainfalls and two seasons: a wet season from November to April, and a dry season between May and September. Rainfalls are often violent and unequally spread over the island. Circular geography of the island allows for locating the valleys with respect to the prevai-ling winds and the recurring meteorological events.

The network density of rain gauge stations does not allow describing rainfalls in a deep tropical valley. As reported by Wotling (1998) the rainfall pattern on Ta-hiti is heterogeneous making the use of traditional sta-tistical methods inappropriate. The rainfall pattern is mainly conditioned by the orientation and direction of slopes, ridges and valleys, much more than the altitude. Hence, when choosing a homogeneous study area (i.e., watersheds that are in same direction relative to prevai-ling winds and ridges less than 1500 meters between two watersheds), a correct rainfall prediction model can be designed using the altitude as the dominant input va-riable.

Mean  Error 39%Sd  Error 25% Total  Error 12%

Mean  Error 20%Sd  Error 16.60% Total  Error 12%

MODel valIDaTION - WesT aRea

Mean  Error 5.40%Sd  Error 4.30% Total  Error 9%

Mean  Error 16%Sd  Error 30% Total  Error 24%

Station 1Altitude A1

Rain

Station 2Altitude A2

Rain

Station nAltitude An

Rain

... Station AAltitude ARain

Mean Station

Altitude

Rain

Altitude  (m) 15 380 1000Coef. 0.77 0.96 1.63

Study of correlations between the Mean Station and the «Real» Stations

Rainfall equation depending on altitude

The precipitation values can then be computed for a virtual rain gauge.

r700,p = r465,p ⋅0.77e700×8⋅10−4 r700,p = r465,p ⋅0.66e

700×8⋅10−4

r600,p = r980,p ⋅0.762e600×3⋅10−4

MODel valIDaTION - easT aRea

rA,p

Validation

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r̂A,p = rAm ,p ⋅αeβA rA,p

p : time scale (day, week, month, ...)

: parameters depending on network and

areas specificities

α,β

Additionally, the Tahiti Rain Model works with just three rain gauges in one area. With a denser network, the model gives better results.

In the coming future the model will be tested on the other volcanic islands in French Polynesia. Moreover, it will be interesting to work with specific seasons such as the wet season.