[1] The transport experiment at the MADE site (a highly heterogeneous aquifer) was investigated extensively in the last 25 years. The longitudinal mass distribution m(x,t) of the observed solute plume differed from the Gaussian shape and displayed strong asymmetry. This is in variance with the prediction of stochastic models of flow and transport in weakly heterogeneous aquifers. In the last decade, we have forwarded a model coined as MIM (multi-indicator), in which the heterogeneous structure consists of blocks of different of different and independent random lognormal K. Thus, the structure is completely characterized by K G (the geometric mean), 2 Y (the logconducitvity variance) and the integral scale I. Flow (uniform in the mean) and advective transport were solved by the semianalytical SCA (self-consistent approximation). The SCA models the travel time of a solute parcel from an injection to a control plane as a sequence of independent time steps, each resulting from the simple solution for isolated blocks surrounded by a uniform matrix. The aim of the article is to determine whether the model could predict the observed mass distribution of MADE ( 2 Y ' 7 based on the most recent direct-push injection logger data), by using the recently collected detailed K data and the observed mean head gradient. It was found that the agreement with the measured plume is quite satisfactory, differences related to incomplete mass recovery, injection condition and ergodicity notwithstanding. It is concluded that the physical mechanism of advection, modeled by the local ADE, and the heterogeneity of K, are able to explain the MADE plume behavior and the stochastic model could predict it.Citation: Fiori, A., G. Dagan, I. Jankovic, and A. Zarlenga (2013), The plume spreading in the MADE transport experiment: Could it be predicted by stochastic models? Water Resour.

Fiori et al. (2015) examine the predictive capabilities of (among others) two ''proxy'' non-Fickian transport models, MRMT (Multi-Rate Mass Transfer) and CTRW (Continuous-Time Random Walk). In particular, they compare proxy model predictions of mean breakthrough curves (BTCs) at a sequence of control planes with near-ergodic BTCs generated through two-and three-dimensional simulations of nonreactive, mean-uniform advective transport in single realizations of stationary, randomly heterogeneous porous media. The authors find fitted proxy model parameters to be nonunique and devoid of clear physical meaning. This notwithstanding, they conclude optimistically that ''i. Fitting the proxy models to match the BTC at [one control plane] automatically ensures prediction at downstream control planes [and thus] ii. . . . the measured BTC can be used directly for prediction, with no need to use models underlain by fitting.'' I show that (a) the authors' findings follow directly from (and thus confirm) theoretical considerations discussed earlier by Neuman and Tartakovsky (2009), which (b) additionally demonstrate that proxy models will lack similar predictive capabilities under more realistic, non-Markovian flow and transport conditions that prevail under flow through nonstationary (e.g., multiscale) media in the presence of boundaries and/or nonuniformly distributed sources, and/or when flow/transport are conditioned on measurements.

No abstract

No abstract

Abstract. We present HYPERstream, an innovative streamflow routing scheme based on the width function instantaneous unit hydrograph (WFIUH) theory, which is specifically designed to facilitate coupling with weather forecasting and climate models. The proposed routing scheme preserves geomorphological dispersion of the river network when dealing with horizontal hydrological fluxes, irrespective of the computational grid size inherited from the overlaying climate model providing the meteorological forcing. This is achieved by simulating routing within the river network through suitable transfer functions obtained by applying the WFIUH theory to the desired level of detail. The underlying principle is similar to the block-effective dispersion employed in groundwater hydrology, with the transfer functions used to represent the effect on streamflow of morphological heterogeneity at scales smaller than the computational grid. Transfer functions are constructed for each grid cell with respect to the nodes of the network where streamflow is simulated, by taking advantage of the detailed morphological information contained in the digital elevation model (DEM) of the zone of interest. These characteristics make HYPERstream well suited for multi-scale applications, ranging from catchment up to continental scale, and to investigate extreme events (e.g., floods) that require an accurate description of routing through the river network. The routing scheme enjoys parsimony in the adopted parametrization and computational efficiency, leading to a dramatic reduction of the computational effort with respect to full-gridded models at comparable level of accuracy. HYPERstream is designed with a simple and flexible modular structure that allows for the selection of any rainfall-runoff model to be coupled with the routing scheme and the choice of different hillslope processes to be represented, and it makes the framework particularly suitable to massive parallelization, customization according to the specific user needs and preferences, and continuous development and improvements.