A GLUE‐based uncertainty assessment framework for tritium‐inferred transit time estimations under baseflow conditions

The last decade has seen major technical and scientific improvements in the study of water transfer time through catchments. Nevertheless, it has been argued that most of these developments used conservative tracers that may disregard the oldest component of water transfer, which often has transit times greater than 5 years. Indeed, although the analytical reproducibility of tracers limits the detection of the older flow components associated with the most dampened seasonal fluctuations, this is very rarely taken into account in modelling applications. Tritium is the only environmental tracer at hand to investigate transfer times in the 5‐ to 50‐year range in surface waters, as dissolved gases are not suitable due to the degassing process. Water dating with tritium has often been difficult because of the complex history of its atmospheric concentration, but its current stabilization together with recent analytical improvements open promising perspectives. In this context, the innovative contribution of this study lies in the development of a generalized likelihood uncertainty estimation‐based approach for analysing the uncertainties associated with the modelling of transit time due to both parameter identification and tracer analytical precision issues. A coupled resampling procedure allows assessment of the statistical significance of the transfer time differences found in diverse waters. This approach was developed for tritium and the exponential‐piston model but can be implemented for virtually any tracer and model. Stream baseflow, spring and shallow aquifer waters from the Vallcebre research catchments, analysed for tritium in different years with different analytical precisions, were investigated by using this approach and taking into account other sources of uncertainty. The results showed three groups of waters of different mean transit times, with all the stream baseflow and spring waters older than the 5‐year threshold needing tritium. Low sensitivity of the results to the model structure was also demonstrated. Dual solutions were found for the waters sampled in 2013, but these results may be disambiguated when additional analyses will be made in a few years. Copyright © 2016 John Wiley & Sons, Ltd.     

Towards more systematic perceptual model development: a case study using 3 Luxembourgish catchments

The synthesis of experimental understanding of catchment behaviour and its translation into qualitative perceptual models is an important objective of hydrological sciences. We explore this challenge by examining the cumulative understanding of the hydrology of three experimental catchments and how it evolves through the application of different investigation techniques. The case study considers the Huewelerbach, Weierbach and Wollefsbach headwater catchments of the Attert basin in Luxembourg. Subsurface investigations including bore holes and pits, analysis of soil samples and Electrical Resistivity Tomography measurements are presented and discussed. Streamflow and tracer data are used to gain further insights into the streamflow dynamics of the catchments, using end‐member mixing analysis and hydrograph separation based on dissolved silica and electrical conductivity. We show that the streamflow generating processes in all three catchments are controlled primarily by the subsolum and underlying bedrock. In the Huewelerbach, the permeable sandstone formation supports a stable groundwater component with little seasonality, which reaches the stream through a series of sources at the contact zone with the impermeable marls formation. In the Weierbach, the schist formation is relatively impermeable and supports a ‘fill and spill’‐type of flow mechanism; during wet conditions, it produces a delayed response dominated by pre‐event water. In the Wollefsbach, the impermeable marls formation is responsible for a saturation‐excess runoff generating process, producing a fast and highly seasonal response dominated by event water. The distinct streamflow generating processes of the three catchments are represented qualitatively using perceptual models. The perceptual models are in turn translated into quantitative conceptual models, which simulate the hydrological processes using networks of connected reservoirs and transfer functions. More generally, the paper illustrates the evolution of perceptual models based on experimental fieldwork data, the translation of perceptual models into conceptual models and the value of different types of data for processes understanding and model representation. Copyright © 2014 John Wiley & Sons, Ltd.     

P–T–t–d evolution of orogenic middle crust of the Roc de Frausa Massif (Eastern Pyrenees): a result of horizontal crustal flow and Carboniferous doming?

Structural, petrological and textural studies are combined with phase equilibria modelling of metapelites from different structural levels of the Roc de Frausa Massif in the Eastern Pyrenees. The pre‐Variscan lithological succession is divided into the Upper, Intermediate and Lower series by two orthogneiss sheets and intruded by Variscan igneous rocks. Structural analysis reveals two phases of Variscan deformation. D1 is marked by tight to isoclinal small‐scale folds and an associated flat‐lying foliation (S1) that affects the whole crustal section. D2 structures are characterized by tight upright folds facing to the NW with steep NE–SW axial planes. D2 heterogeneously reworks the D1 fabrics, leading to an almost complete transposition into a sub‐vertical foliation (S2) in the high‐grade metamorphic domain. All structures are affected by late open to tight, steeply inclined south‐verging NW–SE folds (F3) compatible with steep greenschist facies dextral shear zones of probable Alpine age. In the micaschists of the Upper series, andalusite and sillimanite grew during the formation of the S1 foliation indicating heating from 580 to 640 °C associated with an increase in pressure. Subsequent static growth of cordierite points to post‐D1 decompression. In the Intermediate series, a sillimanite–biotite–muscovite‐bearing assemblage that is parallel to the S1 fabric is statically overgrown by cordierite and K‐feldspar. This sequence points to ~1 kbar of post‐D1 decompression at 630–650 °C. The Intermediate series is intruded by a gabbro–diorite stock that has an aureole marked by widespread migmatization. In the aureole, the migmatitic S1 foliation is defined by the assemblage biotite–sillimanite–K‐feldspar–garnet. The microstructural relationships and garnet zoning are compatible with the D1 pressure peak at ~7.5 kbar and ~750 °C. Late‐ to post‐S2 cordierite growth implies that F2 folds and the associated S2 axial planar leucosomes developed during nearly isothermal decompression to <5 kbar. The Lower series migmatites form a composite S1–S2 fabric; the garnet‐bearing assemblage suggests peak P–T conditions of >5 kbar at suprasolidus conditions. Almost complete consumption of garnet and late cordierite growth points to post‐D2 equilibration at <4 kbar and <750 °C. The early metamorphic history associated with the S1 fabric is interpreted as a result of horizontal middle crustal flow associated with progressive heating and possible burial. The upright F2 folding and S2 foliation are associated with a pressure decrease coeval with the intrusion of mafic magma at mid‐crustal levels. The D2 tectono‐metamorphic evolution may be explained by a crustal‐scale doming associated with emplacement of mafic magmas into the core of the dome.     

A probabilistic approach for computing water retention of particulate systems from statistics of grain size and tessellated pore network

The paper offers an analytical determination of the hydraulic properties of an unsaturated soil with reference to its retention curve, which describes the relationship between the volumetric water content and capillarity through matric suction. The analysis combines a particulate approach focused on the physics at the pore scale, including microstructural aspects, with a probabilistic approach where the void space and grain size are considered as random variables. In the end, the soil water characteristic curve of an unsaturated granular medium along a drying path can be derived analytically based on the sole information of particle size distribution. The analysis hinges on the tessellation of a wet granular system into an assemblage of tetrahedral unit cells revealing a pore network upon which capillary physics are computed with respect to pore throat invasion by a non-wetting fluid with evolving pendular capillary bridges. The crux of the paper is to pass from particle size probability distribution to a matching void space distribution to eventually reveal key information such as void cell and solid volume statistics. Making reasonable statistically based assumptions to render calculations tractable, the water retention curve can be readily constructed. Model predictions compare quite favourably with experimental data available for actual soils, especially in the high saturation range. Having a sound scientific basis, the model can be made amenable to address a variety of soils with a wider range of particle sizes.     

Slab–mantle flow interaction: influence on subduction dynamics and duration

We investigate the influence of mantle flow relative to the lithosphere on subduction dynamics. We use 2D thermo‐mechanical models assuming incompressible non‐Newtonian fluid rheology. Different mantle flow velocities consistent with absolute plate motion models are tested, as well as both directions of flow, either sustaining or opposing slab dip. The effects of different inflow/outflow velocity profiles, slab strengths and upper–lower mantle viscosity contrasts are also evaluated. Slab dip deviations between models with opposite mantle flow directions range from 37° for relatively strong slabs (η_max = 10²⁵ Pa s) to 50° for weaker slabs (η_max = 10²⁴ Pa s), accounting for a significant amount of natural slab dip variability. For imposed mantle flow supporting the slab, the initial stage of slab steepening is followed by a stage of continuous slab dip decrease. This slab shallowing eventually leads to mantle wedge closure, subduction cessation and slab break‐off, possibly driving subduction flips.