Which objective function to calibrate rainfall–runoff models for low-flow index simulations?

Much has been written on the subject of objective functions to calibrate rainfall–runoff models. Many studies focus on the best choice for low-flow simulations or different multi-objective purposes. Only a few studies, however, investigate objective functions to optimize the simulations of low-flow indices that are important for water management. Here, we test different objective functions, from single objective functions with different discharge transformations or using low-flow indices, to combinations of single objective functions, and we evaluate their robustness and sensitivity to the rainfall–runoff model. We find that the Kling and Gupta efficiency (KGE) applied to a transformation of discharge is inadequate to fulfil all assessment criteria, whereas the mean of the KGE applied to the discharge and the KGE applied to the inverse of the discharge is sufficient. The robustness depends on the climate variability rather than the objective function and the results are insensitive to the model.

EDITOR A. Castellarin; ASSOCIATE EDITOR C. Perrin     

One‐dimensional analysis of a poroelastic medium during freezing

A solution to the problem of freezing of a poroelastic material is derived and analysed in the case of one‐dimensional deformation. The solution is sought within the framework of thermo‐poroelasticity, with specific account of the behaviour of freezing materials. The governing equations of the problem can be combined into a pair of coupled partial differential equations for the temperature and the fluid pressure, with particular forms in the freezing and the unfrozen regions. In the freezing region, the equations are highly non‐linear, partly due to the dependence of thermal and hydraulic properties on water saturation, which varies with temperature. Consequently, the solution is obtained through numerical methods, with special attention to the propagation of the freezing front boundary. The response to one‐dimensional freezing is illustrated for the case of cement paste. Finally, the influence on the solution of varying selected parameters is analysed, such as the temperature boundary conditions, the parameters characterizing the geometry of the porous system, the ratio of fluid and thermal diffusivities, and the rate of cooling applied at the freezing end. Copyright © 2008 John Wiley & Sons, Ltd.     

Behaviour of lithium and its isotopes during weathering in the Mackenzie Basin, Canada

We report Li isotopic compositions, for river waters and suspended sediments, of about 40 rivers sampled within the Mackenzie River Basin in northwestern Canada. The aim of this study is to characterize the behaviour of Li and its isotopes during weathering at the scale of a large mixed lithology basin. The Mackenzie River waters display systematically heavier Li isotopic compositions relative to source rocks and suspended sediments. The range in δ⁷Li is larger in dissolved load (from +9.3‰ to +29.0‰) compared to suspended sediments (from −1.7‰ to +3.2‰), which are not significantly different from δ⁷Li values in bedrocks. Our study shows that dissolved Li is essentially derived from the weathering of silicates and that its isotopic composition in the dissolved load is inversely correlated with its relative mobility when compared to Na. The highest enrichment of ⁷Li in the dissolved load is reported when Li is not or poorly incorporated in secondary phases after its release into solution by mineral dissolution. This counterintuitive observation is interpreted by the mixing of water types derived from two different weathering regimes producing different Li isotopic compositions within the Mackenzie River Basin. The incipient weathering regime characterizing the Rocky Mountains and the Shield areas produces ⁷Li enrichment in the fluid phase that is most simply explained by the precipitation of oxyhydroxide phases fractionating Li isotopes. The second weathering regime is found in the lowland area and produces the lower δ⁷Li waters (but still enriched in ⁷Li compared to bedrocks) and the most Li-depleted waters (compared to Na). Fractionation factors suggest that the incorporation of Li in clay minerals is the mechanism that explains the isotopic composition of the lowland rivers. The correlation of boron and lithium concentrations found in the dissolved load of the Mackenzie Rivers suggests that precipitation of clay minerals is favoured by the relatively high residence time of water in groundwater. In the Shield and Rocky Mountains, Li isotopes suggest that clay minerals are not forming and that secondary minerals with stronger affinity for ⁷Li appear.Although the weathering mechanisms operating in the Mackenzie Basin need to be characterized more precisely, the Li isotope data reported here clearly show the control of Li isotopes by the weathering intensity. The spatial diversity of weathering regimes, resulting from a complex combination of factors such as topography, geology, climate and hydrology explains, in fine, the spatial distribution of Li isotopic ratios in the large drainage basin of the Mackenzie River. There is no simple relationship between Li isotopic composition and chemical denudation fluxes in the Mackenzie River Basin.