Modélisation statistique des apports de MES associés au régime des crues d’un sous- bassin du Timis-Béga (Roumanie) Statistical modelling of the wash load associated with the flood regime in a sub-basin of the Timis-Bega Rivers (Romania)

Résumé

Dans cette thématique concernant le transport solide des cours d’eau, il nous semble opportun de résumer le cadre général et d’y situer notre approche. Les formules classiques du transport solide évaluent le débit en matériaux du lit (charriage et suspension) à partir de ses déformations. Elles ne permettent pas d’estimer le débit des matériaux provenant directement du lessivage des versants et qui transite sans interaction avec le lit. Dans cet article, nous considérons uniquement la phase en suspension "MES" mesurée sans distinction à priori de l’origine des grains qui la constitue : provenance directe du bassin versant (phase directe) et (ou) reprise des stocks disponibles dans le lit (phase différée). Le bassin hydrographique du Timis-Béga (Roumanie) est particulièrement bien équipé pour le suivi des débits de 28 sous bassins et le contrôle des flux de MES de douze d’entre eux. De plus, son contexte physiographique nous permet de penser que la phase directe est prépondérante. Le protocole de mesure des flux de MES prévoit, entre autres, une densification variable des observations selon l’intensité des crues liquides. Ces considérations précédentes nous permettent d’envisager une modélisation statistique des apports solides en MES des sous-bassins du Timis-Béga. Celle-ci est directement inspirée des connaissances acquises sur la modélisation statistique "QdF" des régimes hydrologiques des bassins versants. Sur l’exemple du sous-bassin du Béga à Balint, qui draine une superficie de 1064 km², nous retiendrons deux principaux résultats issus de la transposition du concept QdF aux débits solides QMESdF : Les analyses statistiques des régimes liquide et solide montrent que les débits solides de MES ne sont pas simplement proportionnels aux débits liquides mais croissent plus rapidement. Les deux lois de distributions privilégiées, Pareto généralisée pour les MES et exponentielle pour les débits, permettent de le justifier. Le temps de montée des hydrogrammes de projet liquide ou solide est quasiment identique, autrement dit nous vérifions la quasi concomitance de leurs débits de pointe. Ce résultat n’est possible que si le débit solide de MES provient essentiellement du lessivage des versants, ce qui était supposé à priori.

Mots-clés:

• QdF,
• débit de crue,
• débit solide MES,
• Timis-Béga,
• Roumanie

Abstract

With respect to sediment transport, we detailed the general framework and how our approach contributes to these developments. Starting from the single traditional relation for the bed material load, specialists in river hydraulics cannot assess sediment yield of basins, when it involves the auto-suspension of fine sediments coming mainly from slope erosion (wash load). This latter estimate is needed for simulating the transfer of sediments and possible deposition in certain areas, particularly when a strong slowing down occurs. The Timis-Bega drainage basin (Romania) is fairly well equipped for the monitoring of discharge and suspended materials (sediment discharge). The hydrometric network includes 28 stations, of which 12 allow a monitoring of wash load. Moreover, its physiographic characteristics led us to think that the wash load dominates. Thus we assumed that sediment discharge was correlated with the physiographic features of the catchment area. The protocol for the measurement of the suspended sediment load was intensified during the floods. Thus, statistical modelling of the sub-basin sediment yields could be performed.

The current study was directly inspired by the knowledge obtained in the domain of statistical modelling that describes hydrological regimes. The approach adopted was based on the flood-duration-frequency (QdF) analysis that takes into account the temporal variability of floods. The QdF approach analyses maximum average flows (Vd) over various durations (d), equivalent to intensity-duration-frequency (IdF) curves commonly used for rainfall analysis. The proposed model allows QdF curves V(d, T) for a given basin to be estimated using a minimum number of parameters. When the statistical law is the exponential law, this model contains only three parameters, due to observed scale invariance properties. The ∆ parameter that informs about the shape of the flood hydrograph is consequently the flood characteristic duration of the studied basin. The two parameters of the exponential maximum flood distribution for d=0 (a₀ and x₀) and ∆ were fitted to sample discharges (Vd). This model is called a converging QdF model because of the observed convergence of distributions towards small return periods. This model is also useful for the determination of threshold discharges (Qd). The analytical formulation of the V(d,T) model can be derived according to d, in order to obtain a Q(d,T) model. This model then permits the calculation of the hydrograph for any return period (T) and any duration (d).

The regionalization of the sediment yield was achieved within the framework of the Riverlife European project, in collaboration with NIHWM (National Institute of Hydrology and Water Management of Romania). Initially, local models were built. As an example, starting from the Bega sub-basin at Balint, with a surface of 1,064 km², our intent was to present the transposition of the discharge-duration-frequency analysis concept (or QdF) to the wash load Q_MES dF. The latter relates to the measurement procedure, the statistical processing of the observed data Q_MES (t), and to the building of the discharge hydrographs of the associated projects.

The main results were:

- The statistical analyses of floods and sediment discharges show that the wash loads were not simply proportional to the discharge, but rather they increased more rapidly. The selection of the appropriate distribution laws (Pareto generalised for the Q_MESdF model (four parameters) and exponential for the QdF model) reinforced this result.

- The lag-time was the same for both hydrographs with respect to flood and sediment discharge. This result can be achieved if the sediment transport comes primarily from the scrubbing of the slopes (wash load), which was hypothesised a priori. However, falling limb of the sediment hydrograph decreases more quickly than for the discharge hydrograph (∆_MES is lower than ∆).

The Bega sub-basin example at Balint was a first test towards the regional modelling of the contributions to sediment discharge in the catchment area of Timis-Béga. This flood and sediment discharge regionalization is necessary for the study of the protection of the town of Timisoara against flooding.

Keywords:

• QdF curves,
• flood discharge,
• sediment discharge,
• wash load,
• Timis-Béga,
• Romania