Conceptual rainfall–runoff model with a two‐parameter,infinite characteristic time transfer function

A two‐parameter transfer function with an infinite characteristic time is proposed for conceptual rainfall–runoff models. The large time behaviour of the unit response is an inverse power function of time. The infinite characteristic time allows long‐term memory effects to be accounted for. Such effects are observed in mountainous and karst catchments. The governing equation of the model is a fractional differential equation in the limit of long times. Although linear, the proposed transfer function yields discharge signals that can usually be obtained only using non‐linear models. The model is applied successfully to two catchments, the Dud Koshi mountainous catchment in the Himalayas and the Durzon karst catchment in France. It compares favourably to the linear, non‐linear single reservoir models and to the GR4J model. With a single reservoir and a single transfer function, the model is capable of reproducing hysteretic behaviours identified as typical of long‐term memory effects. Computational efficiency is enhanced by approximating the infinite characteristic time transfer function with a sum of simpler, exponential transfer functions. This amounts to partitioning the reservoir into several linear sub‐reservoirs, the output discharges of which are easy to compute. An efficient partitioning strategy is presented to facilitate the practical implementation of the model. Copyright © 2015 John Wiley & Sons, Ltd.     

On the failure of a discrete axial chain using a continualized nonlocal Continuum Damage Mechanics approach

The failure of a discrete elastic‐damage axial system is investigated using both a discrete and an equivalent continuum approach. The Discrete Damage Mechanics approach is based on a microstructured model composed of a series of periodic elastic‐damage springs (axial Discrete Damage Mechanics lattice system). Such a discrete damage system can be associated with the finite difference formulation of a Continuum Damage Mechanics evolution problem. Several analytical and numerical results are presented for the tensile failure of this axial damage chain under its own weight. The nonlocal Continuum Damage Mechanics models examined in this paper are mainly built from a continualization procedure applied to centered or uncentered finite difference schemes. The asymptotic expansion of the first‐order upward difference equations leads to a first‐order nonlocal model, whereas the asymptotic expansion of the centered finite difference equations leads to a second‐order nonlocal Eringen's approach. To complete this study, a phenomenological nonlocal gradient approach is also examined and compared with the first continualization methods. A comparison of the discrete and the continuous problems for the chains shows the effectiveness of the new micromechanics‐based nonlocal Continuum Damage modeling, especially for capturing scale effects. For both continualized approaches, the length scale of the nonlocal models depends only on the cell size, while for the so‐called phenomenological approach, the length scale may depend on the loading parameter. This apparent load‐dependent length scale, already discussed in the literature with numerical arguments, is found to be sensitive to the postulated structure of the nonlocal model calibrated according to a lattice approach. Copyright © 2015 John Wiley & Sons, Ltd.     

Aquifer–peatland connectivity in southern Quebec (Canada)

In areas where peatlands are abundant, they are likely to play a significant role in the hydrological and hydrogeological dynamics of a watershed. Although individual case studies are reported in the literature, there is a large range of aquifer–peatland interactions and there is a need to understand the controls of these interactions. The objectives of this study were (1) to better understand aquifer–peatland connections and how these may be predicted by geology and geomorphic location and (2) to provide a variety of reference sites for glacial geological settings. Slope and depression peatlands were studied in the Abitibi‐Témiscamingue region and in the St. Lawrence Lowlands, two contrasting regions of southern Quebec. A total of 12 transects that span a shallow aquifer–peatland interface were instrumented with piezometers. Field investigations included peatland characterization, monthly water level monitoring, and continuous hydraulic head measurements with pressure transducers. The results indicate that 7 of the 12 transects receive groundwater from the surrounding shallow aquifer. At the peatland margin, four lateral flow patterns were identified and associated with slope peatlands (parallel inflow and divergent flow) and with depression peatlands (convergent flow and parallel outflow). Vertical hydraulic gradients suggest that water flows mainly downwards, i.e. from the peatland to the underlying mineral deposits. Vertical connectivity appears to decrease as the distance from the peatland margin increases. All of these exchanges are important components in the sustainability of peatland hydrogeological functions. The regional comparison of aquifer–peatland flow dynamics performed in this study provides a new set of referenced data for the assessment of aquifer–peatland connectivity. Copyright © 2014 John Wiley & Sons, Ltd.     

Estimating the uncertainty of video-based flow velocity and discharge measurements due to the conversion of field to image coordinates

Video-based hydrometry continues to develop for contactless discharge measurements, automated flood gauging stations and the use of crowd-sourced flood videos for discharge reconstruction. Irrespective of the velocimetry algorithm used (LSPIV, STIV, PTV…), orthorectification of the images is necessary beforehand, so that each pixel has the same known physical size. Most times, the orthorectification transformation is a plane-to-plane projection from the water surface to the camera sensor. Two approaches are typically used to compute the coefficients of this transformation: their calibration from ground reference points (GRPs) with known image and real-world coordinates (“implicit calibration”) or their calculation from the values of the intrinsic (focal length, sensor size) and extrinsic (position, angles) parameters of the camera (“explicit calibration”). In this paper, we develop a Bayesian method which makes it possible to combine the implicit and explicit approaches in a probabilistic framework. The Bayesian approach can be used from situations suitable for the implicit approach (plenty of GRPs) to situations propitious to the explicit approach (well-known camera parameters). The method is illustrated using synthetic views of a typical streamgauging scene with known true values of the parameters and GRP coordinates. We show that combining observational and prior information is generally beneficial to get precise estimates. Further tests carried out with a real scene of the Arc River at Randens, France, in flood conditions illustrate the impact of the number, uncertainty and spatial distribution of GRPs on the final uncertainty of flow velocity and discharge.     

Mesoscale analysis of failure in quasi‐brittle materials: comparison between lattice model and acoustic emission data

The purpose of this paper is to analyse the development and the evolution of the fracture process zone during fracture and damage in quasi‐brittle materials. A model taking into account the material details at the mesoscale is used to describe the failure process at the scale of the heterogeneities. This model is used to compute histograms of the relative distances between damaged points. These numerical results are compared with experimental data, where the damage evolution is monitored using acoustic emissions. Histograms of the relative distances between damage events in the numerical calculations and acoustic events in the experiments exhibit good agreement. It is shown that the mesoscale model provides relevant information from the point of view of both global responses and the local failure process. © 2015 The Authors. International Journal for Numerical and Analytical Methods in Geomechanics published by John Wiley & Sons Ltd.     

Remote sensing of soybean stress as an indicator of chemical concentration of biosolid amended surface soils

The accumulation of heavy metals in the biosolid amended soils and the risk of their uptake into different plant parts is a topic of great concern. This study examines the accumulation of several heavy metals and nutrients in soybeans grown on biosolid applied soils and the use of remote sensing to monitor the metal uptake and plant stress. Field and greenhouse studies were conducted with soybeans grown on soils applied with biosolids at varying rates. The plant growth was monitored using Landsat TM imagery and handheld spectroradiometer in field and greenhouse studies, respectively. Soil and plant samples were collected and then analyzed for several elemental concentrations. The chemical concentrations in soils and roots increased significantly with increase in applied biosolid concentrations. Copper (Cu) and Molybdenum (Mo) accumulated significantly in the shoots of the metal-treated plants. Our spectral and Landsat TM image analysis revealed that the Normalized Difference Vegetative Index (NDVI) can be used to distinguish the metal stressed plants. The NDVI showed significant negative correlation with increase in soil Cu concentrations followed by other elements. This study suggests the use of remote sensing to monitor soybean stress patterns and thus indirectly assess soil chemical characteristics.