Résumé: The vertical organisation of karst conduit networks has been the focus of speleogenetic studies for more than a century. The four state model of Ford and Ewers (1978), which still is considered as the most general, relates the geometry of caves to the frequency of permeable fissures. The model suggests that the water table caves are common in areas with high fissure frequency, which is often the case in natural settings. However, in Alpine karst systems, water table caves are more the exception than the rule. Alpine speleogenesis is influenced by high uplift, valley incision rates and irregular recharge. To study the potential role of these processes for speleogenesis in the dimensions of length and depth, we apply a simple mathematical model based on coupling of flow, dissolution and transport. We assume a master conduit draining the water to the spring at a base level. Incision of the valley triggers evolution of deeper flow pathways, which are initially in a proto-conduit state. The master conduit evolves into a canyon following the valley incision, while the deep pathways evolve towards maturity and tend to capture the water from the master conduits. Two outcomes are possible: a) deep pathways evolve fast enough to capture all the recharge, leaving the master conduit dry; or b) the canyon reaches the level of deep pathways before these evolve to maturity. We introduce the Loop-to-Canyon Ratio (LCR), which predicts which of the two outcomes is more likely to occur in certain settings. Our model is extended to account for transient flow conditions. In the case of an undulating master conduit, floodwater is stored in troughs after the flood retreat. This water seeps through sub-vertical fractures (soutirages) connecting the master conduit with the deep pathways. Therefore, the loops evolve also during the dry season, and the LCR is considerably increased. Although the model is based on several approximations, it leads to some important conclusions for vertical organisation of karst conduit networks and stresses the importance of base-level changes and transient recharge conditions. It therefore gives an explanation of speleogenesis that relies much more on the dynamic nature of water flow than on the static fracture density

Résumé: During the chemically based recession flow phase of karstic springs the carbonate (dissolved limestone) concentration can be expressed as negative power of the flow rate. The empirically determined Conc/Q relationship allows two parameters (a and A) to be defined, of which one (a ) depends on the geometric dimensions of the saturated (submerged) karstic network. In this paper we present a deterministic model which simulates the concentration of carbonate at the outlet of a network of circular rectilinear conduits as a function of flow rate. This model, based on hydraulic principles and the calcite dissolution kinetics, allows the sensitivity of the a and A parameters to be studied under different chemical, physical and geometric scenarios. Simulation results show that A is a function of the calcite saturation concentration, whereas a depends on the spatial dimensions of the karstic network (void length and aperture). The deterministic model results were applied to real karstic systems to evaluate the geometric dimensions of submerged karstic networks. q 2002 Elsevier Science B.V. All rights reserved.

Résumé: A pragmatic and simple approach for estimating the groundwater recharge of karst aquifers in mountainous regions by extrapolation of the hydrological regimes of gauged and well-documented systems is presented. Specific discharge rates are derived using annual precipitation and spring measurements by taking into account catchment size and elevation which are assumed to be the dominant factors. Reference sites with high data reliability are used for calibration and regional extrapolation. This is performed with normalized values employing spatial precipitation deviations and correlation with the elevation of the catchment areas. A tiered step procedure provides minimum and maximum normalized gradients for the relationship between recharge quantity and elevation for karst regions. The normalized recharge can therefore be obtained and extrapolated for any location using the spatial precipitation variability to provide an estimate of annual groundwater recharge. The approach was applied to Switzerland (approx. 7,500 km2 of karst terrain situated between 200 and over 4,000 m a.s.l.) using annual precipitation data from meteorological stations for the years 2000 to 2011. Results show that the average recharge rates of different Swiss karst domains range from 20 to 46 L/km2s, which corresponds to an infiltration ratio between 0.6 and 0.9 of total precipitation. Despite uncertainties inherent in the approach, these results provide a benchmark for renewable karst groundwater resources in Switzerland of about 8.4 km3 per year. The approach can be applied to any other mountainous karst region, i.e. where a clear relationship between elevation, precipitation and recharge can be assumed. This article is protected by copyright. All rights reserved.