Alain Mangin

RAINFALL–RUNOFF RELATIONS FOR KARSTIC SPRINGS. PART II: CONTINUOUS WAVELET AND DISCRETE ORTHOGONAL MULTIRESOLUTION ANALYSES

Abstract Karstic watersheds appear as highly non-linear and non-stationary systems. The main focus of this paper is a heuristic study of this non-stationarity using a time-scale localisation method called the wavelet transform. First, a mathematical overview of these analysis methods is given. The wavelet transform methods used here can be divided into two main parts: the continuous Morlet wavelet transform and the multiresolution orthogonal analysis. A statistical interpretation of the wavelet coefficients is also presented, introducing wavelet spectrum analyses (univariate and cross-wavelet analyses). These wavelet methods are applied to rainfall rates and runoffs measured at different sampling rates, from daily to half-hourly sampling rate. The karstic springs under study are located in the Pyrenees Mountains (Ariege, France) and in the Causses of Larzac (Aveyron, France). They are first applied to a pumping and a naturally intermittent runoff process, allowing the separation of different sub-processes. Wavelet analyses of rainfall rates and runoffs and wavelet rainfall–runoff cross-analyses also give meaningful information on the temporal variability of the rainfall–runoff relationship. In particular, this kind of analysis provides a simple interpretation of the distribution of energy between the different scales. Finally, it is demonstrated that wavelet transforms make possible a physical explanation of the temporal structure of the basin response to rainfall allowing discrimination between a rapid response and recharge due to the karst drainage system and a slower one corresponding to infiltration response.

Contribution of correlation and spectral analyses to the regional study of a large karst aquifer (Charente, France)

The purpose of the study is to demonstrate that correlation and spectral analyses can contribute to the regional study of a large karst aquifer. An example is presented for the La Rochefoucauld karst aquifer (Charente, France). Different types of spatially distributed time series provide valuable spatio-temporal information for the karst aquifer. The available time series consist of the spring flow rates, the flow rates at different locations in sinking streams, the piezometric levels, the electrical conductivity and temperature of the water, the atmospheric pressure and the precipitation. The analysis of the flow rates at the springs shows that the aquifer empties very slowly and has a large storage capacity. Hydrodynamic links were established between three of the four rivers flowing on the aquifer and the springs. The results also demonstrate the important spatial heterogeneity of the aquifer and indicate that the most rapid flow occurs in the northern part of the aquifer. Hourly piezometric and electrical conductivity time series indicate that the transmissivity of the aquifer varies when some conductive channels become desaturated during the low water period. The delays between the distributed recharge and the piezometric level, between the localized river input and the flow rates at the springs and between the electrical conductivities in rivers and the main spring provide information on the travel times in the aquifer. The observation of earth tides and barometric effects indicate that this apparently unconfined aquifer has a confined behaviour.

Pour une meilleure connaissance des systèmes hydrologiques à partir des analyses corrélatoire et spectrale

Abstract Using the correlogram and variance spectral density, the time series of rainfall and discharge of a hydrological system are analysed in a descriptive way differing from the traditional method. From a methodological viewpoint some computational working choices are made. Applied to three karstic systems in the Pyrenean Mountains (France-Spain), these analyses permitted a comparison and a study of the different reactions of these three systems. They showed the presence of memory effects which modulated the input rainfall for short, medium and long term. These modulations characterize each system. They reflect the storages and the manner in which these fill and empty, thus indicating the karstification of the aquifer. The examples discussed indicate that these analyses provide an excellent method for the investigation of a hydrological system.

Rainfall-runoff relations for karstic springs. Part I : convolution and spectral analyses

Karstic basins contain large reserves of subsurface water. In this paper, three karstic systems located in the Pyrenees Mountains (Ariege, France) are studied. Long records of rainfall and discharge rates for these karstic springs are available, sampled at different rates: daily, hourly and half-hourly. This study aims at illustrating and assessing the capabilities and limitations of linear black-box methods for analysing rainfall–runoff type relationships and reconstructing runoffs from rainfall rate data using such systems. In this study, precipitation and discharge rates are considered as two autocorrelated and cross-correlated stochastic processes. A linear and stationary rainfall–runoff model is adopted, which is used for identification and simulation purposes. Different versions are analysed, including a model based on a convolution integral between the precipitation rate P(τ) and a transfer function h(t−τ) which can be thought of as the unit impulse response of the system. It is shown that this linear stochastic model (i.e. the statistical version), although accurate in some respects, does not represent the hydraulic behaviour of the system very well during low flow episodes and floods. It is also shown that the use of Fourier analysis, alone, does not lead to a satisfactory reconstitution of observed runoff sequences. For these reasons, the use of non-linear random process input–output models based on Volterra integral series is proposed and discussed.

Rainfall–runoff relations for karstic springs: multifractal analyses

Karstic watersheds appear as highly as non-linear and non-stationary systems. The behaviour of karstic springs has been previously studied using non-linear simulation methods (Volterra expansion) and non-stationary analyses methods based on wavelet transforms. The main issue of karstic spring behaviour consists of the presence and the identification of characteristic time-scales. In order to highlight more precisely the scale-properties of the rainfall–runoff relations for karstic springs, the multifractal analysis is introduced. These methods are applied daily and half-hourly rainfall rates and runoffs measured on a three French karstic springs located in the Pyrenees Mountains (Ariege, France): Aliou, Baget and Fontestorbes. They are characterised by a variable development of the drainage systems. We have at our disposal long and uninterrupted series of data over period of several years, which constitute a high quality bank data. Multifractal analyses of both daily and half-hourly rainfall rates and runoffs give evident a scale-dependant behaviour. Effectively, it highlights the presence of different multifractal processes at each sampling rate. Using a universal class of multifractal models based on cascade multiplicative processes, the identified multifractal sub-processes are characterised by the classical parameters α and C1. All these results should lead to several improvements in karstic springflow simulation models.

Apports du traçage isotopique naturel a la connaissance du fonctionnement d'un systeme karstique - teneurs en oxygene-18 de trois systemes des Pyrenees, France

Abstract Three karstic systems in the Pyrenees (France) have been subjected to a monthly systematic sampling in view of isotopic analysis of oxygen-18. In addition, a higher frequency sampling in overflow conditions has been made in one of the systems which is also continuously studied as regards hydrodynamics, geochemistry and biology. After analysing the sample representativity, an attempt has been made to find out the meaning of the variations of the contents in oxygen-18 in function of time. In the case of these systems of the Pyrenees, a relation between the altitude of the catchment area and the contents in oxygen-18 of their risings has been established which does not agree with Dansgaards relation. The variations of the isotopic contents in function of the hydrogeologic events confirm the heterogeneity of the submerged zone and the importance of the part played by the percolation, chiefly by considering the connection with the surface saturated zone, named “epikarstic aquifer”. These results, obtained with those of hydrodynamic, geochemical and biological studies of the karst, are not likely to be interpreted without the help of these disciplines.

Turbidity mechanism of water from a karstic spring: example of the Ain Asserdoune spring (Beni Mellal Atlas, Morocco)

To understand the turbidity phenomenon that occurs during floodwater periods in the water of some karstic aquifers, a study was carried out on the Ain Asserdoune spring in the Beni Mellal Atlas. The application of correlation and spectral analyses to turbidity, rainfall and discharge rate with a daily sampling for three hydrological cycles showed that the Ain Asserdoune turbidity corresponded to the beginning of the unclogging of the karstic conduits affecting the saturated area. The appearance of turbidity during the increased flow rate was due to instability in the chaotic regime that was represented by suspended matter, which was evacuated independent of the discharge rate. This phenomenon only appears in polyphase karst, which is frequently found, and thus must be taken into account when karstic water is used for drinking as it could become unfit for human consumption.

Comment on “Carbon uptake by karsts in the Houzhai Basin, southwest China” by Junhua Yan et al.

[1] In a recent paper Yan et al. [2011] estimate the carbon uptake in the Houzhai Basin due to dissolution of carbonate by rainwater using dissolved carbon measurements on this basin. Since both the surface and the underground river networks are known to converge toward a single outlet, this could be achieved with one hydrological station, monitoring water discharge and providing water for chemical analyses. From a nearly monthly record over the 1986–2007 period, they were able to monitor the seasonal variations of dissolved carbon uptake and to compute a mean yearly uptake of 20.7 g C m 2 yr 1 for the Houzhai Basin, which is further extended to estimate the total carbon uptake by karst in south China. Since several karstic basins are located in China, the study by Yan et al. is of great interest for the scientific community. Our concern is that it neglects the gaseous component of the carbon budget. However, it is known that karstic voids contain a few percent volume of CO2, and we will present below evidence that this CO2 is drained downward with rainwater from organic soils, collected by karstic voids and finally advected toward the Earth’s atmosphere, which can significantly alter the carbon budget computed by Yan et al. As the conclusions presented by Yan et al. are designed to constrain global atmospheric models, we suggest that the gaseous CO2 should also be considered in the estimates of the budget of carbon flowing through the Houzhai Basin. [2] Our team has accumulated more than 20 years’ research experience on this topic. Our studies were mainly motivated by the conservation of caves, including prehistoric painted caves, which requires the stability of the inner atmosphere. It is well known that the CO2 concentration can reach a few percent volume in the cave atmosphere [James, 1977], and we monitored its concentration in a large set of French caves [Bourges et al., 2001, 2006]. We have strong indications that this CO2 is mainly biogenic and produced in soils. This inference is supported by numerous dC measurements in the Villard Cave (SW France) with a mean dC of CO2 = 22.7‰ (50 samples from 2005 to 2010), where its variation has been correlated with the CO2 air concentration [Genty, 2008], and in the Chauvet Cave (SE France) with a mean dC of CO2 = 22.7‰ (20 samples from 2000 to 2010). There is also growing evidence that CO2 is transported downward both as dissolved species and in biphasic flow with water seeping toward the phreatic zone [Atkinson, 1977; Bourges et al., 2006;Mudry et al., 2008;Milanolo and Gabrovšek, 2009]. One of our most original results is that the cave atmosphere is not at rest but is continuously flowing toward the Earth’s atmosphere through large openings [Bourges et al., 2001]. Our interpretation is that soil air enriched with CO2 is dragged downward both in biphasic flow and as dissolved species during infiltration of rainwater and collected as gaseous CO2 by the network of macroscopic voids including fissures and caves. Our results indicate that a significant part of this CO2 is directly drained to the outside atmosphere through open fissures and large cave openings. This interpretation is now widely accepted by scientists working on caves [Baldini et al., 2006; Serrano-Ortiz et al., 2010]. After reviewing CO2 data gathered by the flux tower community and showing an anomalously high CO2 rate escaping from karst terrains toward the atmosphere, SerranoOrtiz et al. [2010] proposed an explanation similar to ours, involving a downward infiltration of CO2 with rainwater followed by an outflow of gaseous CO2 toward the terrestrial atmosphere. In some instances, winds flowing on permeable soils can further enhance the exchanges of CO2 between the cave atmosphere and the Earth’s atmosphere [SanchezCañete et al., 2011; Cuezva et al., 2011]. [3] We were able to observe the outward flow of CO2 on several occasions and to estimate the annual flow of gaseous CO2 at one French cave: the Aven d’Orgnac network (Figure 1). In winter, the outside air is colder and denser than the cave atmosphere, and the cave is therefore ventilated by downward flow of the outside air; then, in most parts of the cave the CO2 content is similar to that of the terrestrial atmosphere [Bourges et al., 2006; Kowalski and SanchezCañete, 2010]. This was shown with temperature, CO2 concentration and Rn concentration profiling along the cave system. Due to this thermo-compositional venting, the CO2 derived from soils and conveyed to the cave would be efficiently transferred to the Earth’s atmosphere. However, direct measurements of CO2 flux were impossible in winter, GEConseil, St.-Girons, Ariège, France. IRD/HSM, University of Montpellier II, Montpellier, France. LSCE, UMR CEA/CNRS/UVSQ 1572, L’Orme des Merisiers CEA Saclay, Gif-sur-Yvette, France. EcoEx-Moulis, Moulis, Ariège, France.

La conservation des grottes ornées: un problème de stabilité d'un système naturel (l'exemple de la grotte préhistorique de Gargas, Pyrénées françaises)

Painted caves are karstic cavities here considered as stable physical systems in a state of dynamic equilibrium. From the example of the Gargas cave, we show that introduction of excess energy (visitors, lighting) causes a loss of stability and introduces a risk of degradation in the cavity. From different approaches, we identify the periods and the causes of instability and we determine the maximum level of introduced energy which would preserve the conservative properties of the cavity. These results allow cave equipment and visitor capacity compatible with satisfactory conservation conditions to be defined.

Analyse en ondelettes en hydrologie karstique. 2e partie : analyse en ondelettes croisée pluie-débit

Abstract A method of cross-analysis of rainfall-runoff time series based on wavelet transforms (continuous Morlet wavelet transform and orthogonal multiresolution analysis), is presented and applied to rainfall rates and spring outflow rates measured on karstic Pyrenean watersheds. Results are compared to classical cross-correlation and Fourier cross-spectral analyses. The multiscale wavelet method appears as powerful in the study of the joint temporal variability and non-stationarity of the rainfall-runoff relationship, and it yields more precise results than Fourier cross-spectral analysis.