Estimation des ressources en eau superficielle aux pas de temps mensuel et annuel, application à un pays semi-aride Monthly water resources assessment, application to a semi-arid country

Résumé

On connait l'extrême variabilité des ressources en eau superficielle et les problèmes que cela pose en aménagement du territoire. En conséquence, générer de longues séries de débits annuels (ou mensuels) est une nécessité pour l'étude de la disponibilité des ressources en eau (BURGES et LETTENMAIER, 1977).

Cette génération de longues séries peut se faire à partir de la connaissance des pluies si l'on dispose d'un modèle fiable de transformation pluie-débit. Un premier modèle linéaire visant à l'estimation du seul débit annuel, déjà utile pour un premier dégrossissage de la ressource, est bâti à partir de la pluie annuelle et de sa répartition entre les mois. Il constitue un outil de base que l'on a jugé néanmoins un peu trop rudimentaire. La recherche d'un modèle conceptuel simple nous a semblé une voie plus prometteuse. Exploitant une recherche déjà entreprise sur ce type de modèle au pas de temps journalier, on a construit un modèle mensuel à trois paramètres dont l'élaboration a été justifiée point par point par une meilleure efficacité des résultats fournis sur une soixantaine de bassins versants appartenant à la partie septentrionale de l'Algérie. Nous avons analysé les paramètres du modèle et obtenu une estimation approchée de la matrice des variances-covariances de ces paramètres afin de disposer d'un outil similaire à celui existant pour le modèle linéaire général.

Mots-clés:

• Ressources en eau,
• modèle conceptuel,
• pas de temps mensuel et annuel,
• sensibilité des paramètres

Abstract

Availability of long series of annual or monthly streamflows appears to be a necessity in water resources studies. In regions where such data do not exist we may resort to rainfall data to obtain the required long series of streamflows. In this case we need a reliable rainfall-runoff model. Such a model is often called a water balance model although this designation ignores the dynamics involved in the model. A first attempt was to establish a linear model connecting an annual streamflow to the concurrent rainfall and its allocation within the year.

This model was calibrated on 63 catchments throughout northern Algeria, an area of about 200,000 km² where mean annual streamflows range from 5 to 350 mm.

The standard error of the model, expressed as a percentage of the mean annual streamflow was about 41 %. This relatively poor result led us to explore the capabilities of lumped conceptual models. Hydrologic models may be of the following three types :

- the linear black box model,

- the lumped conceptual model,

- the physically based model.

The linear black box model may benefit from huge mathematical developments but is very poor from a hydrologic point of view. The physically based model is a permanent search to comply more and more to the whole catchment and all processes which are supposed to take place in it. It is tantamount to sheer utopia since the required fine description of the catchment will be definitely out of reach for economical reasons. The only workable solution lies in the design of a lumped conceptual model. But we have to bear in mind that such models cannot rely on a comprehensive physical basis and thus, all specifications have to be justified by the outputs of the model.

We benefited from a recent research upon a daily conceptual model that served as a starting sketch for the monthly model. After having tested numerous alternatives we worked out a simple model with only three parameters to be calibrated. The standard error of this model was about 27 % of the mean annual flow. According to recent analyses about the sensitivity of model parameters, we calculated the matrix of covariances of the parameters.

This was necessary because, due to the lack of a long series of data, we could not achieve an actual validation of the model against a streamflow sequence not used in the calibration process. However, the extreme parcimony of the model may alleviate the need of such a validation and the model compared favourably with well-known water balance models. As a conclusion, we may hope that the tool we have devised will be of valuable help in water resources management.

Keywords:

• Water resources,
• monthly lumped models,
• parameter uncertainty