FR :

L'analyse de l'origine et de la dynamique des écoulements souterrains dans l'aquifère du milieu alluvial de la plaine d'Aoste (Italie) a été menée en étudiant les teneurs isotopiques (¹⁸O et ³H) des eaux sur l'ensemble du système hydrologique. La démarche a consisté en un suivi isotopique des précipitations pluvio-neigeuses, des sources de versants, du réseau de surface et de l'aquifère alluvial, complété par des analyses ponctuelles concernant l'horizon superficiel des glaciers et les sous-écoulements glaciaires. Le signal d'entrée en ¹⁸O porté par les précipitations présente une grande variabilité liée au contexte orographique (effet d'écran) et climatique (pluie ou neige). Celle-ci est mise en évidence par les changements saisonniers du gradient ¹⁸O/altitude. En moyenne annuelle (1994), ce gradient établi en Vallée d'Aoste à partir de mesures sur les précipitations récoltées entre 300 et 3500 m d'altitude (sur huit stations) est de - 0.18 ± 0.02 ‰ pour 100 m, avec un écart-type (s) des valeurs de ± 4,8 ‰. L'ensemble des résultats en 18O montre au cours du cycle hydrologique, un amortissement à la fois important et progressif du signal d'entrée fourni par les précipitations. Cet amortissement, de l'ordre de 30 fois dans l'aquifère alluvial (sigma=± 0.15 ‰), est particulièrement sensible au niveau de la glace et des sous-écoulements glaciaires. En ce qui concerne les résultats en 3H, les teneurs mesurées dans les précipitations se révèlent être étroitement liées avec l'origine et la trajectoire des masses d'air humide. Par ailleurs, on note une bonne concordance entre les temps de séjour des eaux dans l'aquifère alluvial calculés à partir des valeurs en 18O et ceux fournis par le 3H.

EN :

The hydrogeological study of the alluvial aquifer of the Aosta plain (Italy) is chosen as one of the most appropriate examples representative of the Italian-French-Swiss Alps. This study has been carried out using two environmental isotopes (¹⁸O and ³H) for groundwater samples taken from this aquifer in order to shed light on the origin of water and the hydrodynamic characteristics of the aquifer.

The surface area of this aquifer is 70 km_ and mean elevation ranges between 400 and 700 m (asl). This surface area constitutes a part of the watershed area that amounts 2400 km_ with a mean elevation of 2200 m (asl). The watershed possesses several mountain peaks, Mt. Blanc, Mt. Cervin, Mt. Grand Paradis, the elevation of which rise to over 4000 m.

The input signal, quantitative and qualitative as well, provided by the precipitation shows a wide variability linked to both orographic (screen effect) and climatic (rain or snow) influences. This variability is marked by differences in the ¹⁸O/altitude gradient, which is seasonally dependent. A unique and linear relation is observed during spring and summer ; in autumn and winter results show an important gradient up to 2000 m but a less important one for higher altitudes.

The mean annual (1994) gradient of - 0.18 ± 0.02 ‰ for 100 m is determined in Aosta valley for altitudes between 300 and 3500 m, and the standard deviation (sigma) of the mean volume-weighted value for precipitation is ± 4.8 ‰. Furthermore, the ¹⁸O values measured in the alluvial aquifer have shown a very low dispersion (sigma=± 0.15 ‰), which corresponds to a buffering effect of a factor 30. These results evidenced, thus, an homogenization process within the different water bodies.

To analyze this homogenization process, the different components of the hydrologic system have been studied, i.e. the monitoring of the springs and runoff waters, with complementary local measurements of the upper part of ice cores and the glacier underflows. Using standard deviations (sigma) as criteria for the homogenization process, one can see a large and progressive decrease along the hydrological cycle, with a special amplitude in ice cores and glacier underflows : precipitation (± 4.8 ‰), ice core (± 0.8 ‰), glacier underflow (± 0.10 ‰), spring (± 0.15 ‰), surface runoff network (± 0.3 ‰), alluvial aquifer (± 0.15 ‰).

In ice cores, the different process : freezing and thawing, compression, and vapor / liquid / solid exchanges have caused the ¹⁸O homogenization. Dealing with the springs on the slopes of the valley, the preferential flow paths linked to the fracturation lead to a mixing of waters and hence to a very buffered outflow signal. The combined effect of all these explains the stability and the uniformity of the data found in the alluvial water body.

As far as the ³H concentrations are concerned, the values measured are tightly linked with the origin and the transport of humid air masses. For closely spaced stations, a significant difference in the input signal has been correlated to various climatic influences. Using ³H data from the Thonon-les-Bains station (included in the WMO-IAEA observation network) as input, the calculated transit times of 2.5 to 7.5 years are very close to those calculated with ¹⁸O, i.e. 4 to 7 years.

FR :

En Bretagne, le bocage est un paysage typique constitué d'un réseau de haies planté sur un talus de terre entourant les parcelles. La première partie résume les connaissances actuelles sur le rôle hydrologique du bocage.

L'article porte sur le rôle du bocage sur les écoulements de surface (écoulement hortonien). Il s'agit d'une première étape pour intégrer le rôle des haies dans la modélisation hydrologique distribuée. On s'attache à la description de la modification du réseau de drainage par les haies.

Ce travail a nécessité la mise au pont d'un logiciel en C qui permet de créer le réseau de drainage sous contrainte topographique à partir d'un modèle numérique de terrain, puis de le modifier en intégrant la présence des haies. Cinq situations représentant une grande diversité bocagère (de 39 m/ha jusqu'à 200 m/ha) ont été étudiées.

On constate une profonde modification du réseau de drainage, puisque jusqu'à 90% des mailles voient leur place changer dans le réseau de drainage. Cependant, l'effet le plus important est la déconnexion de certaines branches du réseau de drainage, qui était précédemment continu jusqu'à l'exutoire. En effet, certaines haies jouent le rôle de puits, où l'eau ne peut que s'infiltrer (haies parallèles aux courbes de niveau). Ces puits contrôlent ainsi des zones du bassin versant, qui peuvent atteindre jusqu'à 40 % de la surface totale. Des modifications sont également observées sur la longueur de ruissellement réduite en moyenne, mais dans des proportions faibles (10 à 20 %). Enfin, les pentes des mailles dont la direction a été modifiée par la présence d'une haie à leur endroit sont également diminuées d'environ 50 %.

La densité de haies, qui est pourtant souvent le seul facteur disponible pour qualifier le bocage dans les opérations d'aménagement, apparaît insuffisante pour caractériser le rôle " tampon " du bocage sur le plan hydrologique. En conclusion, on attire l'attention sur la nécessité de prendre en compte la structure du bocage pour intégrer son rôle hydrologique dans les opérations d'aménagement.

EN :

In Brittany, the bocage is the typical landscape, a network of hedgerows planted on an earthen bank. It could play a hydrological role by modifying the water pathways. This was studied by analysing the modification of the drainage network at the catchment scale, for 5 densities of the hedgerow network. The drainage network, basically controlled by the topography, was modified taking into account the hedges, which cannot be crossed by the water pathway. The digital elevation model and a vector map of hedges were the data used.

The impact of hedgerows on different parameters influencing surface runoff was tested. The main modification is that a part of the catchment, up to 40% of the total area, is disconnected from the river course due to the presence of hedges acting as sinks. A reduction of the surface runoff length and a decrease of the slope of the pixel-hedges in the drainage direction are also measured. But none of these factors is dependent of the hedgerow density, which appears as a poor descriptor of the hydrological buffer capacity of the bocage landscape. We draw attention to the need to take into account the hedgerow structure for hydrological purposes, in order to improve the new policy of re-building a bocage landscape that is currently being implemented.

FR :

Une étude des espèces chironomidiennes du lac de l'Abbaye a été effectuée au cours de l'année 1993. Le répertoire spécifique a été établi à partir de l'étude des peuplements imaginaux, nymphals et larvaires échantillonnés selon 5 méthodes: récolte des imagos au filet entomologique, récolte des exuvies nymphales, mise en élevage de stades pré-imaginaux, prélèvements de larves dans les sédiments et mise en place de substrats artificiels. Le peuplement chironomidien obtenu est constitué de 69 espèces. Une comparaison de la composition des peuplements obtenus par les différents modes d'échantillonnage permet de mettre en évidence les particularités de chaque méthode. La récolte des exuvies nymphales semble être la méthode la plus appropriée pour l'établissement d'un répertoire spécifique. Deux espèces dominantes du lac Chironomus anthracinus et Psilotanypus rufovittatus témoignent du caractère polyhumique et désoxygéné du lac. Cependant, la présence simultanée en forte proportion de Tanytarsus niger, Cladotanytarsus iucundus et C. atridorsum témoignent de la faible production pélagique et de la température froide du lac susceptible de minimiser les effets de la désoxygénation sur la communauté chironomidienne.

EN :

A study of chironomid species was undertaken in Lake Abbaye during the year 1993. Lake Abbaye is located 910 m a.s.l., in a karstic area in the east of France near Switzerland (Figure 1). It covers 80 ha with a maximum depth of 19 m and a mean depth of 7.2 m. Profundal sediment has a high level of organic matter (30.2% dry weight) of mainly terrestrial origin. The accumulation of the organic matter resulted in hypoxic conditions at depth during the summer stratification. The lake is rather cold (maximum surface temperature: 23°C), holodimictic, and is ice-covered from late November to early April.

The list of chironomid species obtained resulted from the use of 5 different sampling methods: (i) adults caught with an entomological net; (ii) pupal exuviae sampling at the sites where they were accumulated; (iii) rearing of larvae; (iv) sediment sampling and (v) sampling of larvae using artificial substrates. The sampling site locations are indicated in Figure 1. The present paper gives results and discussions about i) the taxonomic richness and composition of the total chironomid community, ii) the composition of the different communities collected and the characteristics of the five sampling methods, iii) a characterization of Lake Abbaye according to the dominating species.

1. Total chironomid community

The chironomid community of Lake Abbaye consisted of 69 species (Table 1). Compared to other European lakes, this community showed a rather high richness. In some great lakes, however, the number of chironomid species amounted to 140 or 168 species (Lake Innaren, Lake Constance). These particularly high richnesses probably resulted from the great number of substrata according to the great surface of the littoral zone of these lakes. The chironomid community of Lake Abbaye is specific to a mountain area as shown by the high proportion of species collected (82% of the total richness) found by SERRA-TOSIO and LAVILLE (1991) at altitudes exceeding 500 m. According to REISS and FITTKAU (1971), the presence of two particular species (Tanytarsus niger and T. miriforceps) reflects the glacial origin of the lake.

2. Composition of the different chironomid communities

Sampling the pupal exuviae allowed us to collect more than 90% of the species with less than 5000 individuals whereas by catching adults this percentage did not exceed 79% with more than 28000 individuals collected and identified. By rearing larvae both the number of species (46 species, 66% of the total richness) and the number of emerging adults (1386 individuals) were low. The least efficient method appeared to be the sediment sampling, which allowed the identification of only 19 taxa (genera and species) compared to the 31 taxa collected by artificial substrates. This study clearly showed that pupal exuviae sampling was the most appropriate method to establish a list of species yielding the greatest ratio between species richness and the effectives.

A comparison of the major contributed species among the different communities led to the conclusion that the sampling method strongly affects community composition. Whereas in adult population (Figure 2) the dominating species (relative density=10%) were Tanytarsus niger, Ablabesmyia monilis, A. longistyla and Polypedilum nubeculosum, the community of pupal exuviae (Figure 2) was dominated by Cladotanytarsus iucundus and that obtained by larvae rearing (Figure 2) showed two other (genera and species) dominating species (Psilotanypus rufovittatus and Einfeldia dissidens).

The study of the chironomid community by catching adults presented two major difficulties. The first resulted from the sampling of adults that did not emerge from the lake itself. The second problem involved a better sampling of the bigger and/or the more accessible swarms. This method led to an overestimate of the species richness of the lake and modified the species proportions in the community. For example, the great proportion of two species, Ablabesmyia monilis and A. longistyla, in the adult community was observed in none of the other communities (Figure 2).

In both larval populations (Figure 3), the genera Chironomus, Tanytarsus, Cladotanytarsus and Procladius dominated. The use of artificial substrates induced, however, a lot of modifications in some genera contributions. For example, the genus Einfeldia was collected at higher relative density in artificial substrates than in the sediment samples. Moreover, a lot of taxa (Glyptotendipes, Microtendipes, Paratendipes, Polypedilum, Cricotopus, Parakiefferiella) were exclusively collected, in larval communities, with the artificial substrates. Despite the well-known differences between the benthic communities collected in-situ and those sampled by artificial substrates (ROSENBERG et RESH, 1982), we think such a technique allows a correct study of the taxonomic richness. The use of identical substrates in different lakes should allow one to define a potential community also related solely to the water quality.

3. Characterization of the Lake Abbaye

The study of the taxonomic composition of five different chironomid communities stresses the difficulty in characterizing the lake according to the dominating species. However, comparison between larval community (Figure 3) and imagos or exuviae populations (Figure 2) led to the conclusion that Lake Abbaye could be classified in the category of lakes with Tanytarsus (specially T. niger) and Cladotanytarsus (C. iucundus and C. atridorsum). The particularity of Lake Abbaye is that two groups of species dominated the community. The first, constituted by the aforementioned three species, is dominating in oligotrophic lakes (BRUNDIN, 1949). The second group, represented by Chironomus anthracinus and Psilotanypus rufovittatus, reflected the polyhumic and hypoxic characteristics of the lake. These results indicate that Lake Abbaye has low phytoplanktonic biomass but high organic matter content in its sediment, which originates from terrestrial or littoral inputs (VERNEAUX et al., 1987). The quite low temperature of the water probably minimizes both the degradation of the organic matter and the impact of hypoxic conditions on the chironomid community.

4. Conclusion

The present paper clearly demonstrates the importance of the sampling method used to study chironomid communities. Sampling the pupal exuviae in the accumulation zones is the most appropriate method to study chironomids. In order to contribute to a better understanding of the relations between the chironomid species and the environmental conditions, our further research will concentrate on a study of the bathymetric distribution of these species. For this purpose, pupal exuviae will be sampled at different isobaths simultaneously with chemical and physical analyses of the water and sediments. The drift phenomenon of exuviae that could affect the bathymetric pattern of species seemed to be avoided when a criterion of minimum occurrence was taken into account (VERNEAUX, 1996).

FR :

Un modèle décrivant la température d'équilibre des lagunes a été développé, tenant compte des différents flux de chaleur que celles-ci échangent avec l'air et le sol environnant. Six composantes différentes ont été inclues dans le calcul de ce bilan thermique: radiation solaire, évaporation, convection, rayonnement atmosphérique, rayonnement de la surface du plan d'eau, échange via les parois en contact avec le sol.

Le modèle ainsi obtenu a été testé avec efficacité sur deux lagunes aérées et une lagune naturelle situées sous climat tempéré ; sa précision sur l'estimation des températures d'équilibre étant de l'ordre de 0.7 °C. Des simulations en continu ont également pu être effectuées au moyen d'une variante dynamique, tenant compte de l'inertie thermique qu'entraîne le volume des bassins.

Quelle que soit la saison envisagée, la principale forme d'apport de chaleur est représentée par la radiation solaire tandis que la dissipation d'énergie se partage entre les flux d'évaporation et la balance des deux flux de rayonnement. Les bassins échangeraient en moyenne plus de 250 W/m² ; le maximum de transfert de chaleur correspondant au printemps et à la période estivale.

Enfin, l'analyse de sensibilité du modèle nous a permis de mettre en évidence la contribution de chacun des termes intervenant dans le calcul de ce bilan thermique et de révéler sa dépendance vis-à-vis principalement de la température d'entrée, du rayonnement solaire et de la température de l'air.

EN :

Very few studies have ever focused on the thermal balance of a wastewater treatment process, despite its major impact on various aspects of sanitary engineering, such as biological growth, oxygen transfer and, most importantly, purification kinetics. This lack of knowledge is particularly worrying for the design of aerated lagoons and waste stabilization ponds, since these two extensive treatment technologies are extremely dependent on climatic conditions and subject to high thermal variations. In temperate regions, a pond annual temperature range can even exceed 20 °C, while a 10 °C variation will induce a more than 60% drop or increase in its removal yield. Our paper intends to present a comprehensive temperature prediction model which accounts for the main heat loss and gain terms exchanged through the pond surface and walls.

Our approach includes six different energy inputs and outputs, namely: solar radiation, air-water surface convection, atmospheric radiation, back surface radiation, evaporation and ground-water-walls convection. Each of these components was described extensively by means of a literature review of all previous efforts made to predict equilibrium temperature in lakes, rivers, salt-gradient solar ponds, cooling tanks, even outdoor pools. The best aspects of each prediction model were then incorporated into a new computer model developed as two different but complementary variants: one for steady-state conditions and the other for continuous and therefore also transient simulations. The main difference between these two approaches is that the first one neglects enthalpy variation while the second one takes the form of a differential equation, with basin temperatures being estimated by an iterative calculation procedure and a numerical integration method, respectively.

Two hypotheses were necessary to develop this model. The first one posits that pond hydrodynamics correspond to completely mixed conditions. Such hydraulic behavior is extremely frequent in aerated lagoons and waste stabilization ponds in temperate climates, but less so in tropical or Mediterranean regions, where thermal balances appear much more complex since stabilization ponds are often thermally stratified. The second hypothesis is that all radiation fluxes received by the ponds are completely absorbed by the pond's contents and are never reflected, even partially, by their bottoms or walls.

This model, which is in fact the thermal balance of the basins, relies mainly on meteorological factors and pond characteristics. Only two out of the six estimated fluxes - evaporation rates and solar radiation - are measured directly in situ. It seemed too difficult to estimate them, since predictive equations found in literature constantly gave unsatisfactory results.

To establish the validity of this model, experimental data were collected at a wastewater treatment plant located in the southern part of Belgium. This plant consists of a series of two aerated lagoons and four waste stabilization ponds, designed for a nominal capacity of 7,500 inhabitant-equivalents. Five rounds of measurements, each lasting from five to twenty days, were conducted at different periods of the year. Meteorological factors were continuously monitored by a data acquisition unit while the pond water temperatures and hydraulic flows were measured hourly. Evaporation rates were determined daily with several floating evaporation pans set at the pond surfaces. Vertical temperature and illumination profiles were also measured in order to verify the strict applicability of the two previous hypotheses.

Ninety-three experimental data sets were collected on this particular facility. Predicted temperatures were compared with measured temperatures as well as with the results of three other models previously developed for waste stabilization ponds. Our new model systematically proved more reliable and accurate than previous approaches, since equilibrium temperatures were predicted with a mean absolute error of only 0.7 °C. More than 52% of the deviations between calculated and observed temperatures were even below 0.5 °C, which indicates their relatively low dispersion.

Continuous simulations were also conducted during a one-day period to demonstrate the importance of the ponds' large thermal capacities. The steady-state approach, which does not account for this latter phenomenon, failed to give consistent results, unlike our dynamic heat balance approach, which yielded extremely good fits with experimental data.

A sensitivity analysis allowed us to show the influence of the various meteorological factors on the basins' equilibrium temperatures. In decreasing order, the fits seemed particularly sensitive to inlet temperature, solar radiation, air temperature and evaporation. Surprisingly, wind speed made only a small contribution to the total heat balance. However, this must be seen as a direct consequence of the fact that in our model this latter parameter is no longer used to calculate the predominant evaporation rates but only to estimate the much smaller convection term.

Whatever the season considered, more than 90% of the ponds' energy inputs come from solar radiation while the dominating loss mechanisms are represented by the balance of the two infrared radiation fluxes (46%) and evaporation (42%). The sign of the air-water convection term varies according to the period of the year but never accounts for more than 10% of the total heat balance. Heat losses or gains from basin walls always remain insignificant and could therefore easily be neglected in order to simplify our approach to basin equilibrium temperatures.

FR :

La modélisation de synthèse en débit-durée-fréquence des régimes d'étiage observés s'inspire de travaux développés ces dernières années sur les modèles continus (multidurée et multifréquence) de prédétermination des crues (GALEA et PRUDHOMME, 1996). La variabilité des régimes d'étiage du bassin hydrographique de la Loire (S=117 000 km²) est étudiée à partir de deux variables hydrologiques, définies sur une durée (d) continue (1≤d≤90j), traduisant deux notions de régime complémentaires : la notion de débit-volume (moyen) minimal (VCNd) annuel et de débit-seuil minimal (QCNd) annuel non dépassé. L'étude statistique multidurée des événements annuels observés en 57 sites sélectionnés, selon la loi log-normale à deux paramètres (écart-type et moyenne), permet de répartir les différents bassins en 4 familles typologiquement homogènes. Pour chacune de ces familles est choisi un bassin versant de référence dont les courbes débit-durée-fréquence normées en débit et durée gagnent alors en représentativité régionale. L'utilisation de ces courbes adimensionnelles est rendue plus aisée, grâce à un formalisme mathématique. La norme de débit retenue est le débit journalier minimal annuel de période moyenne de retour 2 ans. La norme de durée quant à elle est déduite des courbes de tarissement observées et décrites selon l'équation de MAILLET. Ces deux normes (ou encore descripteurs de régime) constituent les seuls paramètres d'entrée des 4 modèles adimensionnels QdF d'étiage. Ces modèles et leur typologie associée, appliqués au bassin hydrographique de la Loire, ont permis de montrer la cohérence des quantiles observés et modélisés en chacun des 57 sites retenus. Une première validation de la méthodologie QdF d'étiage, établie sur le bassin de la Loire, a concerné 12 bassins versants du Crisu-Alb (S=3000 km²) en Roumanie. Cela n'a pas nécessité de nouveaux modèles de référence autres que ceux élaborés pour la Loire. Autrement dit, pour chacun des sites étudiés, la valeur de l'écart-type de la loi ajustée sur les VCNd=1j a permis de choisir la famille hydrologique d'appartenance et donc le modèle QdF d'étiage qui lui est associé. La qualité des modélisations effectuées confirment par ailleurs que les deux descripteurs locaux de régime retenus sont de bons intégrateurs des processus d'écoulement liés aux étiages. D'une manière générale, la démarche a permis d'éprouver la fiabilité de la méthodologie QdF développée en étiage et ces premiers résultats sont encourageants pour l'avenir. Notamment, l'usage opérationnel des modèles QdF d'étiage sur des sites non observés nécessite de poursuivre l'effort de recherche vers une explicitation du critère de choix ainsi que des deux descripteurs locaux du régime de basses eaux.

EN :

The French Department of the Environment entrusted to the CEMAGREF the realization of a study relating to an ecosystemic approach to the management of the Loire watershed. Over the long term, this approach is designed to establish orientations for the protection and management of the natural aquatic environments of the Loire. To this end, a good knowledge of the variability of the hydrological regimes is necessary. The method presented relates primarily to low flow discharges. In spite of the great heterogeneity in space and time of low flows, a regionalization study of watershed low flow regimes of Loire (S=117 000 km²) has been attempted on the basis of the same QdF (discharge-duration-frequency) concept developed for floods (GALEA and PRUDHOMME, 1996). To allow an objective evaluation of developed methodology, we present here the details of the conceptual approach used to model and synthesize the low flow regimes observed, and present the results obtained.

The methodology relates primarily to relatively undisturbed basins with perennial flow. The variability of low flow regimes takes into account two hydrologic variables expressing two notions of complementary regimes: the notion of annual minimal average flow (VCNd), and the annual minimal threshold discharge (QCNd) below which the flow does not decrease for a continuous duration (d) which varies from one day to 90 days. The statistical study of annual events demonstrates that the Log-Normal law (two parameters) is generally adequate for a given duration d. From the low flow typology observed on 57 selected sites, the statistical study of annual events revealed four homogeneous groups of hydrological low flow regimes. In each of the 4 groups a reference basin is chosen. Its flow-duration-frequency curves normalized to discharge and duration show a regional representativity and the mathematical formalism yields easy-to-use dimensionless curves. The normative discharge VCN(2,1) is the minimum annual daily flow for a two year return period. The normative duration of flow (De) of a basin results from the recession curves described by MAILLET's equation. In each group, a large diversity of low flow regimes exists, as indicated by the two local descriptors (De and VCN(2,1)), which are the only input parameters for the low flow QdF models. Concerning the Loire watershed, these 4 models and their associated typology characterize the large diversity in space and time of low flows observed for the 57 studied cases.

A first validation of the low flow QdF methodology concerned 12 basins of Crisu-Alb watershed, in Romania. It was not necessary to establish new reference models for the regionalization of low flows for these 12 studied cases in the Crisu-Alb watershed. The quality of the transposed models confirms, on another hand, that the two local descriptors of the low flow regime are good integrators of flow processes in relation with low flows. The initial results from the synthetic low flow models are promising. Use of these models on ungauged basins will require additional research to explain the model's choice criterion and the two local descriptors of the low flow regime.

FR :

La deuxième partie de cette synthèse bibliographique sur la genèse des débits montre comment les connaissances acquises sur le fonctionnement des petits bassins ruraux (cf. Partie 1) peuvent être utilisées pour les modéliser. Elle présente les différents types de modèles hydrologiques (empiriques globaux de type "boîte noire", conceptuels globaux ou semi-spatialisés, physiques spatialisés, physico-conceptuels semi-spatialisés) disponibles pour générer des chroniques événementielles ou continues, et déduit de l'analyse de leurs avantages et limites respectifs certaines recommandations pour leur choix et leur usage. Elle indique ensuite différents problèmes rencontrés dans toute modélisation, et quelques pistes possibles pour les résoudre: incorporation des flux couplés à l'eau dans les modèles hydrologiques, erreurs liées à la structure du modèle (limites et simplifications théoriques, approximations numériques, discrétisations temporelle et spatiale), problèmes métrologiques et méthodologiques limitant la disponibilité des données, hétérogénéités à toutes les échelles limitant l'adéquation des données pour paramétrer les modèles, calage du modèle limitant son aptitude à simuler des scénarios de changement. Elle souligne la nécessité d'une validation multicritère des modèles et d'une estimation de l'incertitude sur les simulations générée par ces diverses sources d'erreurs, ainsi que le besoin d'une meilleure interaction entre expérimentation de terrain et modélisation.

EN :

The second part of this review on streamflow generation analyses how the knowledge available from field studies (see Part 1) has been used since the 1960s or could be used to improve catchment modelling. After a presentation of the main model types, the various problems encountered during the modelling process are discussed.

The large variety of hydrologic models available for event or continuous simulation can be reduced to a few main types according to the ways the functional, spatial and temporal aspects of the catchment behaviour are represented. Lumped "blackbox" models are useful for many engineering problems but can not be used in "extrapolation" and give no information on the internal catchment dynamics. Lumped conceptual models, which consider a catchment as a system of interconnected reservoirs and simulate the main global fluxes, use empirical lumped relationships and parameters that often have no great physical meaning and are not measurable. Semi-distributed conceptual models use the same reservoir description, but at the scale of "homogeneous" units derived from a space discretisation, which allows one to take catchment structure explicitly into account. Physically-based distributed models, which use theoretical equations and measurable parameters, provide a dynamic explanation of catchment behaviour but require too much information and are too complex to be easily used at the catchment scale. Physico-conceptual semi-distributed models try to overcome the limits of the previous types, while keeping their advantages, by simplifying the dynamic approach and discretization using new concepts.

Physically-based or conceptual models, which describe or explain the water cycle at the catchment scale, are very useful for research, but their use in practical applications comes up against several problems. It is still difficult to incorporate into catchment models the water-coupled fluxes (energy, sediments, solutes, biomass) because of the poorly-known complexity of their interactions. Even sophisticated models are based on many approximations of the reality: lack of suitable theory for some processes, simplification of the theories available, numerical approximation, space and time discretisation all generate simulation errors related to the chosen model structure. Data availability is limited by measurement problems (differences in measurement scale, lack of appropriate measurement techniques), and methodological problems (sampling and interpolation procedures, ...), even though remote sensing is expected to help solve some of them. Data suitability is limited by space and time heterogeneity at all scales, which reduces the representativity of any measurement and complicates the parameterization and upscaling needed. Model calibration (either manual, automatic, or stochastic), which leads to the numerical equifinality of both model parameterization and structure, limits the validity domain of the model, its transposability to other conditions and catchments, and its ability to simulate change scenarios. The effects of these limitations on model quality could be reduced by using multivariable and multiscale validation procedures and should be quantified using stochastic estimation of the simulation uncertainties associated with model and data uncertainties. In order to further progress in catchment modelling, as needed by a large range of environmental issues, field hydrologists and modelers should reinforce their co-operation, especially through interdisciplinary studies on long-term research catchments and carefully designed field experiments.

FR :

De nombreuses méthodes régionales ont été développées pour améliorer l'estimation de la distribution des débits de crues en des sites où l'on dispose de peu d'information ou même d'aucune information. Cet article présente une synthèse de modèles hydrologiques utilisés en France et au Québec (Canada), à l'occasion d'un séminaire relatif aux " méthodes d'estimation régionale en hydrologie " tenu à Lyon en mai 1997. Les modèles français sont fortement liés à une technique d'extrapolation de la distribution des crues, la méthode du Gradex, qui repose sur l'exploitation probabiliste conjointe des séries hydrométriques et pluviométriques. Ceci explique les deux principaux volets d'études régionales pratiquées en France : les travaux liés à la régionalisation des pluies et ceux liés à la régionalisation des débits. Les modèles québecois comprennent généralement deux étapes : la définition et la détermination de régions hydrologiquement homogènes, puis l'estimation régionale, par le transfert à l'intérieur d'une même région de l'information des sites jaugés à un site non-jaugé ou partiellement jaugé pour lequel on ne dispose pas d'information suffisante. Après avoir donné un aperçu des méthodes pratiquées dans les deux pays, une discussion dégage les caractéristiques principales et les complémentarités des différentes approches et met en évidence l'intérêt de développer une collaboration plus étroite pour mieux tenir compte des particularités et des complémentarités des méthodes développées de part et d'autre. Une des pistes évoquées consiste à combiner l'information régionale pluviométrique (approche française) et hydrométrique (approche québécoise).

EN :

Design flood estimates at ungauged sites or at gauged sites with short records can be obtained through regionalization techniques. Various methods have been employed in different parts of the world for the regional analysis of extreme hydrological events. These regionalization approaches make different assumptions and hypotheses concerning the hydrological phenomena being modeled, rely on various types of continuous and non-continuous data, and often fall under completely different theories. A research seminar dealing with " regional estimation methods in hydrology " took place in Lyon during the month of May 1997, and brought together various researchers and practitioners mainly from France and the Province of Quebec (Canada). The present paper is based on the conferences and discussions that took place during this seminar and aims to review, classify, comparatively evaluate, and potentially propose improvements to the most prominent regionalization techniques utilized in France and Quebec.

The specific objectives of this paper are :

· to review the main regional hydrologic models that have been proposed and commonly used during the last three decades ;

· to classify the literature into different groups according to the origin of the method, its specific objective, and the technique it adopts ;

· to present a comprehensive evaluation of the characteristics of the methods, and to point out the hypotheses, data requirements, strengths and weaknesses of each particular one ; and

· to investigate and identify potential improvements to the reviewed methods, by combining and extending the various approaches and integrating their particular strengths.

Regionalization approaches adopted in France include the Gradex method which represents a simplified rainfall-runoff model which provides estimates of flood magnitudes of given probabilities and is based on rainfall data which often cover longer periods and are more reliable than flow data (Guillot and Duband, 1967 ; CFGB, 1994). It is based on the hypotheses that beyond a given rainfall threshold (known as the pivot point), all water is transformed into runoff, and that a rainfall event of a given duration generates runoff for the same length of time. These hypotheses are equivalent to assuming that, beyond the pivot point, the rainfall-runoff relationship is linear and that the precipitation and runoff probability curves are parallel on a Gumbel plot.

In Quebec (and generally in North America), regional flood frequency analysis involves usually two steps : delineation of homogeneous regions, and regional estimation. In the first step, the focus is on identifying and regrouping sites which seem sufficiently homogeneous or sufficiently similar to the target ungauged site to provide a basis for information transfer. The second step of the analysis consists in inferring flood information (such as quantiles) at the target site using data from the stations identified in the first step of the analysis. Two types of " homogeneous " regions can be proposed : fixed set regions (geographically contiguous or non-contiguous) and neighborhood type of regions. The second type includes the methods of canonical correlation analysis and of the regions of influence. Regional estimation can be accomplished using one of two main approaches : index flood or quantile regression methods.

The results of this work indicate that the philosophies of regionalization and the methods utilized in France and Quebec are complementary to each other and are based on different needs and outlooks. While the approaches followed in France are characterized by strong conceptual and geographic aspects with an emphasis on the utilization of information related to other phenomena (such as precipitations), the approaches adopted in Quebec rely on the strength of their statistical and stochastic components and usually condense the spatial and temporal information to a realistic functional form. This dissimilarity in the approaches being followed on either side may be originated by the distinct topographic and climatic characteristics of each region (France and Quebec) and by the differences in basin sizes and hydrometeorologic network densities. The conclusions of the seminar point to the large potential of improvements in regional estimation methods, which may result from an enhanced exchange between scientists from both sides : indeed, there is much to gain from learning about the dissimilarities between the various approaches, comparing their performances, and devising new methods that combine their individual strengths. Hence, the Gradex method for example could benefit from an increased utilization of regional flood information, while flood regionalization methods utilized in Quebec could gain much from the formalization of the use of rainfall information and from the integration of an improved modeling of physical hydrologic phenomena. This should result in the enhancement of the efficiency of regional estimation methods and their ability to handle various practical conditions.

It is hoped that this research will contribute towards closing the gap between French and Quebec literature, and more generally between the European and the North American hydrological schools of thought, by narrowing the large literature that is available, by providing the necessary cross-evaluation of regional flood analysis models, and by providing comprehensive propositions for improved approaches for regional hydrologic modeling.

FR :

L'influence de l'ENSO (El Niño/Southern Oscillation) sur les précipitations a fait l'objet de nombreuses études dans différentes régions de la planète et de l'Amérique du Sud en particulier. L'Equateur, situé entre le Pérou et la Colombie, est particulièrement touché par ce phénomène, mais les limites précises de son influence sont encore mal connues. L'homogénéisation des séries pluviométriques de 210 stations réparties entre les régions côtières, la cordillère des Andes et le versant amazonien de l'Equateur nous a permis de la préciser.

Cette critique a été réalisée à l'aide de la méthode du vecteur régional et a été complétée par une régionalisation de la pluviométrie annuelle qui a permis de définir 18 zones homogènes à l'intérieur desquelles les variations inter-annuelles de la pluie sont représentées par un indice pluviométrique qui a pu être déterminé sur la période 1964-93. Les événements ENSO de cette période sont identifiés à partir de la série de température superficielle de la mer (TSM) du bloc Niño 1+2 grâce à une méthode numérique simple.

Nous avons analysé et quantifié l'influence de l'El Niño sur les précipitations à l'aide de deux méthodes simples et de deux tests statistiques qui permettent de mettre en évidence le lien entre les précipitations annuelles et l'El Niño ou la TSM du Pacifique oriental. Nous avons examiné dans un premier temps la coïncidence entre les années Niño et les années de pluviométrie excédentaires. Puis, nous avons déterminé les différences entre les moyennes des totaux pluviométriques annuels des années Niño et normales des dix-huit zones. Une classification hiérarchique ascendante des indices pluviométriques et de la TSM du bloc Niño 1+2 permet ensuite de regrouper les zones pluviométriques en fonction de la similarité entre leurs variations inter-annuelles et de déterminer lesquelles sont les plus proches des variations de la TSM du Pacifique oriental et donc liées à l'El Niño. Nous terminons par une analyse en composantes principales des indices pluviométriques annuels qui a également pour objectif de regrouper les indices en fonction de la similitude de leur variabilité inter-annuelle et de leur sensibilité à l'ENSO. La comparaison et la synthèse des résultats de ces analyses nous a permis de diviser l'Equateur en trois grandes régions, la première est caractérisée par une forte influence de l'ENSO sur les totaux pluviométriques annuels, à l'inverse de la troisième où l'influence n'est pas significative, la deuxième région est intermédiaire entre les deux autres.

EN :

The influence of ENSO (El Niño/Southern Oscillation) on rainfall has been studied in numerous regions of the world and especially in South America. Ecuador, located between Peru and Colombia, is one of the regions most affected by this phenomenon. This country has been little studied and this part of the world remains undefined in global studies due to lack of data. We propose to fill this gap by homogenization of rainfall series from 210 stations spread between the coastal regions, the Andes and the Amazonian slope of Ecuador. This study was carried out with the regional vector method of Brunet-Moret (1979), based on the hypothesis of pseudo-proportionality between the total rainfall of the stations located in a homogeneous area. This method also allowed us to regionalize the annual rainfall and thus to define 18 homogeneous areas in which the inter-annual variations are represented by a rainfall index. This zoning differs from previous ones (Pourrut, 1994) in that the parameter determining the regionalization is the chronological evolution of total rainfall and not the mean rainfall values. This approach is the most appropriate for the analysis of annual rainfall evolution. The available data permit the calculation of these indices in a continuous way for the 30-year period between 1964 and 1993, the annual cycle considered being the hydrological year that begins in September and finishes in August of the following year.

We propose a simple numeric method to identify the various El Niño events considered as the regional consequence in South America of the global ENSO phenomenon. We consider that an El Niño event corresponds to a sequence of at least three consecutive months during which the monthly sea surface temperature (SST) of a Niño 1+2 block is superior to 23°C and presents a positive anomaly of more than 1°C (Rossel, 1997). In the period 1964-93, the years 1965, 1969, 1972, 1973, 1976, 1983, 1987 and 1992 correspond to this definition. The observed rainfalls during the El Niño of 1983 are exceptional, and taking them into account would mask the influence of the other events. We thus studied the year 1983 separately and removed it from the global analysis.

We analyzed and quantified the influence of El Niño on rainfall using two simple methods and two statistical tests that allowed us to demonstrate the link between the annual rainfalls and El Niño or the SST of the eastern Pacific. For this, we first examined the coincidence between the Niño years and years with rainfall surpluses. Then we determined the differences between the average annual rainfall totals of the Niño and normal years within the 18 zones. This difference, expressed in millimeters, affords an appreciation of the quantity of rainfall associated on average with El Niño. Expressed in percentage, it yields an estimate of the importance of the event compared to the normal rainfall. Using an ascending classification of the rainfall indices and of the SST of the Niño 1+2 block, we grouped the rainfall zones according to the similarities between their inter-annual variation and determined which zones were best related to the SST variation of eastern Pacific and thus linked to El Niño. We finished by a principal component analysis of the annual rainfall indices in order to group the indices with respect to the similarity between their inter-annual variability and their sensitivity to ENSO. The comparison and synthesis of these analyses allowed us to divide Ecuador into three regions. ENSO has a strong influence on the annual rainfalls in the majority of the Ecuador coastal zone included between Esmeraldas in the north (1°N) and Peru in the south. On the other hand, there is no direct link between ENSO and total rainfall in the inter-Andean and Amazonian slope regions. Finally, the western slopes of the Andes, the northern coastal regions and the eastern slope of the coastal range represent a transition area influenced by ENSO, but to a lesser extent than the rest of the coastal regions.

FR :

Quel est le nombre d'échantillons à prélever pour analyse bactériologique dans un réseau de distribution d'eau potable afin réaliser un autocontrôle optimal du point de vue économique (coûts analytiques et coût des actions curatives), tout en limitant les risques de dégradation de la qualité ? Pour répondre à cette question, nous proposons un modèle probabiliste qui simule le choix de la décision curative lorsque les analyses indiquent des résultats insatisfaisants ainsi que l'effet de cette décision sur la qualité de l'eau du réseau. Les différentes actions curatives et leur efficacité ont été déterminées empiriquement à partir de l'expertise du gestionnaire du réseau de la Banlieue de Paris et des données collectées de 1992 à 1996. Le modèle s'appuie sur un schéma Markovien d'évolution du couple (Qualité de l'eau, Action curative). Par programmation dynamique, on calcule le coût moyen de la politique décisionnelle de la Banlieue de Paris et le risque généré par cette politique en terme de qualité de l'eau (fréquence des états dégradés), pour différents niveaux d'autocontrôle (nombre d'analyses d'autocontrôle). Le risque d'avoir un état dégradé diminue avec le nombre d'analyses jusqu'au seuil de 140 analyses (autocontrôle et contrôle réglementaire) puis reste quasiment constant, tandis que les coûts continuent d'augmenter.

EN :

Drinking water quality is monitored regularly by state officers (DDASS), and also by the water distributor at a level of his own choice. A model has been constructed to simulate decision making after observations of one or more bacteriological-positive samples from the drinking water distribution system of suburban Paris (four million inhabitants in 144 boroughs). In cases of non-conformity, a curative action is taken (rinsing, chlorinating...) that tends to increase the level of water quality for the ensuing weeks. The model compares the trade-offs between the global cost of the policy and the risk of quality failure, based on various sampling plans of different intensity which the quality manager may design to get information from the distribution system. The more weekly analyses he makes, the more money he spends in control, but at the same time, the more valuable is the information that he receives with which to assess the appropriateness of curative actions to increase quality within the system.

The state of quality in the distribution system is supposed to be homogeneous, with each sampling station representative of the overall water quality. Three discrete classes of quality (acceptable, poor, unsatisfactory) have been defined, corresponding respectively to an average frequency of 5%, 10% and 15% of coliform-positive samples from the control design. The set of alternatives is composed of eight curative actions presently in use in the distribution system when a defect sample is registered: (1) complementary checking of measurements of the quality parameters, such as chlorine and temperature; (2) additional analyses of bacteriological counts; (3) rinses (water is released during a few hours from certain pipes directly into the sewage system, to allow its replacement by fresh water supposedly of better quality); (4) purges (same as rinses, but for a longer period in larger zones); (5) disinfection (the defective zone is isolated and a specialized truck introduces a large amount of chlorine into the distribution pipes); (6) deep cleaning (a yearly cleaning of 3% of the distribution system); (7) chlorinating (the level of free chlorine injection is increased in the water treatment plant); (8) a change in the treatment plant mode of operation (the complete process is checked to prevent the possible transfer of bacteria from the river to the distribution system). It also includes the standard decision of "doing nothing," i.e., let the system evolve on its own. The cost of each decision has been evaluated according to the economic data available from the distribution company, taking mainly into account controllers' work hours and travel expenses. Water quality dynamics in the distribution system are modeled as a Markov chain controlled by the possible decisions at each stage. For each curative action a (3*3) transition matrix is empirically elicited, using both available data and expertise from the team of quality managers. The present control strategy of the distribution company is embedded in the model, by respecting the observed constraints in the sequence of decisions: for instance, if a previous rinse has not been followed by a decrease in the number of coliform-positive samples in the following week, a stronger action such as a purge or disinfection is enforced, rather than repeating the rinse. The strategy also mimics the empirical rules of the quality manager's behavior in facing bacteriological incidents: for example, a single occurrence of coliforms with no specific curative action taken in a previous week will generally dictate a rinse (84% of time), sometimes demand a purge (12%), and occasionally require a disinfection (1%). The Markov model is run in a simulation mode for the spring-summer period: for a given value of the sample size, the average cost of the quality monitoring policy and a failure index (average frequency in the two lowest quality states) can be evaluated by backward induction. Although the assessment of the parameters has been made empirically, the model exhibits realistic performances with regard to side criteria used as discrepancy measures for model rejection checking: the relative use of each curative action and the average time necessary to escape from a non-acceptable state (resiliency) are of the same order of magnitude as the corresponding real indices. A sensitivity analysis reveals that the results are fairly robust to small changes in the probabilities of transition, but do depend on the way the range of water qualities is divided into discrete classes. With the data chosen, the model showed a satisfactory cost/risk balance at 110-140 analyses per week, for the homogeneous subsystem under study. In the case of more data availability, this model could become a valuable decision tool. Provided that a criterion of joint global utility between risk and cost can be defined, it could be used to design a control policy with a weekly varying sample.

FR :

Cette étude en laboratoire traite de l'accumulation et de l'élimination du Cd réalisées par deux mousses aquatiques indigènes du Québec, Fontinalis dalecarlica et Platyhypnidium riparioides. Les expositions au Cd étaient de 0 (témoin), 0,8, 2 et 10 µg·L^-1, concentrations retrouvées en milieu naturel (non contaminé) et contaminé. Les expériences ont été réalisées à trois niveaux de dureté de l'eau (10 à 15, 40 à 50, 80 à 100 mg·L^-1 de CaCO3), à alcalinité constante (80 à 100 mg·L-1 de CaCO³) et à pH stable (7,30) durant une période de 28 jours. Les facteurs d'augmentation des concentrations (FAC) ont démontré une diminution de l'accumulation totale de Cd dans les mousses dans 75% des cas lorsque la dureté de l'eau passe de très douce à dure. Les facteurs de contamination résiduelle (FCR) démontrent la lenteur de l'élimination du Cd par les mousses, et ce, indépendamment de la dureté de l'eau ou de la contamination préalablement subie. Deux équations de régression multiple par étape (Stepwise) ont été établies pour expliquer les facteurs influençant l'accumulation et l'élimination de Cd réalisées par les mousses. Les variables indépendantes incluses dans les équations linéaires de prédiction pour l'accumulation et l'élimination étaient la concentration de Cd dans l'eau, le temps d'exposition, la dureté de l'eau, l'espèce de mousses utilisée et/ou les interactions de ces variables. Les équations linéaires de prédiction pour l'accumulation et l'élimination ont permis d'expliquer respectivement 92% et 71% de la variance observée. Cette identification des principaux facteurs influençant l'accumulation et l'élimination du Cd dans les mousses est d'une grande importance pour la compréhension des processus complexes dirigeant l'absortion des métaux lourds par des organismes vivants. Les équations permettent également de mieux expliquer les interactions engendrées par la variation de divers paramètres sur l'accumulation et l'élimination du Cd par les mousses aquatiques.

EN :

Aquatic mosses have played a large part in the assessment of toxic elements in water. The advantage of mosses over direct water sampling is that the use of the former lessens spatial and temporal variations, enhances the level of contaminant identification by concentrating toxic elements, and provides information relative to the bioavailable portion. However, the concentration of metals that can be measured in mosses is not a reliable indicator of the concentration of toxic elements in the water, which is why we need to model the bioaccumulation phenomenon.

The present laboratory study deals with the accumulation and elimination of Cd by two indigenous Quebec aquatic mosses: Fontinalis dalecarlica and Platyhypnidium riparioides. The previously acclimatized mosses were treated with different concentrations of Cd, three different levels of water hardness, a constant alkalinity and constant pH level for a period of 28 days, in order to establish their bioaccumulative capacity. Cd exposure concentrations were 0 (control), 0.8, 2 and 10 mg·L^-1, with a replication at 10 mg·L^-1. The experiments were carried out at three levels of water hardness (10 to 15, 40 to 50, 80 to 100 mg·L^-1 of CaCO₃), with a constant degree of alkalinity (80 to 100 mg·L^-1 of CaCO₃) and stable pH (7.30). The mosses subsequently went through an elimination period (Cd-free water) of 28 days. The triplicate moss samples were mineralized using nitric acid and all Cd measurements were made by atomic absorption spectrophotometry.

The results indicate that the water chemistry conditions remained stable and were properly controlled. The aquatic mosses demonstrated a considerable ability to absorb and adsorb Cd: the measured Cd water concentrations were less than the nominal concentrations. Nonetheless, moss uptake of Cd improves with an increase in Cd contamination and the concentration factors (CF) range from 6 to 122. For the same exposure concentration, the CF drops in some 63% of those instances where water hardness rises from very soft, through soft, to hard. In 75% of the cases there is a drop in CF when water hardness increases directly from very soft to hard. With a stable concentration (e.g. 2 mg·L^-1), F. dalecarlica has respective CFs of 26.3, 22.2 and 18, which demonstrates the negative gradation of Cd accumulation as water hardness increases. The residual contamination factors (RCF) bear witness to the slow rate of Cd elimination by the mosses, irrespective of the level of water hardness or of any previous contamination. The elimination factor for RCF is never greater than 2. Mosses take up metals faster than they can eliminate them and have a memory of past contaminations, which is an advantage when it comes to studying ad hoc and/or sporadic contamination phenomena.

Two stepwise multiple regression equations have been set up to explain the factors that impact on accumulation and elimination of Cd by mosses. The variables included in the equations were: level of Cd concentration in the water; exposure time; water hardness; the moss species involved, and/or the interactions between these variables. The predictive linear equations for the accumulation and elimination provided explanations for 92% and 71% respectively of the observed variances. The predictive linear equation for accumulation establishes that the length of exposure is the principal parameter responsible for the uptake of Cd by the aquatic mosses. It shows that the accumulation of Cd by the mosses is initially influenced by the level of Cd concentration in the water, but also depends on the length of time over which the bryophytes are exposed to this concentration. Thus, the higher the Cd concentration, the shorter the exposure time for the moss contamination, and vice versa. The second variable is the effect of water hardness taken together with the exposure time. This is a negative variable: the greater the increase in water hardness, the greater the exposure time required to obtain the same degree of moss contamination. This is indicative of the impact of Ca⁺⁺ and Mg⁺⁺ on moss uptake. The impact of water hardness is probably the consequence of the availability of or preference of plant-binding sites for Ca⁺⁺ and Mg⁺⁺ ions, thus reducing the number of available locations for Cd accumulation. Water hardness and Cd concentration levels are the third variable in this equation and are probably linked to the effect of water hardness on the bioavailability of Cd for the mosses. This variable may also explain why the increase in Cd concentration levels in the water lessens the impact of water hardness on the total accumulation of Cd in the mosses. Finally, the equation identifies a greater level of accumulation in the P. riparoides.

Release linear regression shows that the absence of Cd in the water is the major parameter in the elimination of Cd by aquatic mosses. We should remember that the bryophytes are seeking to achieve a steady state condition with their environment, since the Cd is an element that is neither regulated or essential. Its elimination has little to do with water hardness, but is caused by the inversion of a diffusion gradient when the environment is no longer Cd contaminated. During the elimination process, the Ca⁺⁺ and Mg⁺⁺ ions have no real impact on the release of Cd by the mosses. The length of prior exposure does affect elimination: the greater it is, the longer the release period required for moss decontamination. Exposure time is less important during elimination than during accumulation. Elimination is a very slow process, and a longer study would probably have shown that this is a major factor in the elimination of moss-accumulated Cd.

The present identification of the major factors impacting on the accumulation and elimination of Cd in mosses is extremely important if we are to understand the complex processes that determine the absorption of heavy metals by living organisms. The equations also allow us to better explain the interactions caused by variations in the different parameters with respect to the accumulation and elimination of Cd by aquatic mosses.