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Using the Belgian soil map for mapping groundwater vulnerability. Groundwater vulnerability mapping is a critical activity in the implementation of the water resources protection policy. The vulnerability of groundwater bodies is largely determined by the properties of the overlying soil. The soil map and associated data bases contain spatially distributed information, which can be easily introduced into the vulnerability mapping procedure. In this paper, soil information is used in the vulnerability mapping procedure through the "partial vulnerability from the soil" (VPS) concept. Three methods are presented for mapping the VPS: the first method uses the soil map only, while the second and third methods use data from the soil analytical data base. The three methods are applied to mapping the vulnerability of the Brusselean sands groundwater body, in the center of Belgium. The three approaches yield three different vulnerability maps, and explanations for these differences between approaches are given. Finally, a strategy is presented for validating the different approaches to mapping the partial vulnerability from the soil.

Making use of the Digital Soil Map of Wallonia and of an available soil analysis database for assessing the risk of pesticide leaching to groundwater. This study shows how the Digital Soil Map of Wallonia and the associated soil database Aardewerk can be combined with the MetaPEARL model to assess the sensitivity of agricultural soils to pesticide transfer into underground water tables in Wallonia (Southern Belgium). MetaPEARL is based on an analytical expression which describes the concentration of leached pesticides at the soil profile bottom depending on available data on soil characteristics, climate and pesticide properties. The results show an important soil sensitivity to pesticide transfer with a coefficient of retention on organic matter (Kom) very weak (about 10 dm3.kg-1) or with a relatively high half-life time (DT50 about 60 days). In this case, the pesticide is weakly retained by soil organic matter or slowly degraded and then stays available in the soil and can be quickly leached during rainfalls. In other respects, the pesticide sensitivity to leaching is strongly correlated with soil texture and its organic matter content. It is also observed that the concentration of leached pesticide is strongly depending of the rainfall surplus (water flux into the soil or hydrous balance). A sensitivity analysis has shown that the model is very sensitive to soil thickness, to organic matter content, to the bulk density of the mineral fraction by textural classes and of the organic matter. Therefore, these pedological variables have to be assessed with the highest precision to avoid adding further uncertainty to the predictions obtained. On the basis of the most sensitive soil variables, the analysis of "spatial" uncertainty related to the results delivered by MetaPEARL, due to the consideration of an unique representative value by soil type and by region (deterministic approach), shows that this approach tends to under-estimate the concentration of pesticide leached in the soil, compared to the use of a stochastic simulation (probabilistic approach) which takes into account the soil characteristic variability within a given soil type. This stochastic approach allows also the calculation of a more relevant threshold of risk probability (percentile) which can be compared to an imposed standard in view to enhance a sustainable management of natural resources.

The importance of spatial variability of antecedent soil moisture conditions on runoff response is widely acknowledged in hillslope hydrology. Using a distributed hydrologic model, this paper aims at investigating the effects of soil moisture spatial variability on runoff in various field conditions and at finding the structure of the soil moisture pattern that approaches the measured soil moisture pattern in terms of field scale runoff. High spatial resolution soil moisture was surveyed in ten different field campaigns using a proximal ground penetrating radar (GPR) mounted on a mobile platform. Based on these soil moisture measurements, seven scenarios of spatial structures of antecedent soil moisture were used and linked with a field scale distributed hydrological model to simulate field scale runoff. Accounting for spatial variability of soil moisture resulted in general in higher predicted field scale runoff as compared to the case where soil moisture was kept constant. The ranges of possible hydrographs were delineated by extreme scenarios where soil moisture was directly and inversely modelled according to the topographic wetness index (TWI). These behaviours could be explained by the sizes and locations of runoff contributing areas, knowing that runoff was generated by infiltration excess over a certain soil moisture threshold. The most efficient scenario for modelling the within field spatial structure of soil moisture appeared to be when soil moisture is directly arranged according to the TWI, especially when measured soil moisture and TWI were correlated. The novelty of this work is to benefit from a large set of high-resolution soil moisture measurements allowing to model effectively the within field distribution of soil moisture and its impact on the field scale hydrograph. These observations contributed to the current knowledge of the impact of antecedent soil moisture spatial variability on field scale runoff.

Solute transport in unsaturated soil is a scale- and flow rate-dependent process, and high quality experimental studies are needed to introduce scaling relationships in the governing flow and transport models. Within this paper, we present an experimental study to characterize the solute transport for an unsaturated and undisturbed subsoil monolith sampled in a sandy aquifer. Leaching experiments were performed at different flow rates, and solute breakthrough at different positions in the monolith was measured by time domain reflectometry (TDR) probes. At TDR probe scale, the transport is assessed as being a convective-dispersive process with mixing lengths 1 m. At the bottom of the monolith, the meso-scale dispersivity is at least two times larger than the local-scale dispersivity. In addition, this meso-scale dispersivity can be successfully predicted using a stream tube model in combination with a local scale convective-dispersive process. Important scale effects are also observed in the relationship between the square coefficient of variation of the local velocities and the dispersivity. In contrast to previous studies, we do not observe a significant difference in transport properties for different flow rates (from 1.05 to 54.16 cm [d.sup.-1). We attribute this insignificance either to a balance between the decrease of the tortuosity and the increase of the coefficient of variation of the velocity with the flow rate or a non-dependency of both terms on the flow rate.

A method is presented to mathematically characterize a wide range of solute transport processes in softs from time-domain-reflectometry (TDR)-based breakthrough curve (BTC) measurements. To do this, we combined the flexible generalized transfer function model (GTF) with the definition of the time normalized resident concentrations [C.sup.rt] *. The GTF is a four-parameter flexible transfer function able to describe both the convection-dispersive (CD) and the stochastic-convective (SC) process of dispersion in a soil. In addition, it allows other dispersion processes typical for heterogeneous soils to be modeled. To obtain robust estimations of the GTF model parameters, closed-form expressions of the GTF time normalized resident concentrations [C.sup.rt] * and temporal moments of [C.sup.rt] * were defined. These expressions allow the transport parameters to be estimated from TDR-based BTCs without relying on problematic probe calibrations and mass recovery assumptions. Since GTF is a four-parameter model, the robustness of the parameterization procedure was tested by fitting the [C.sup.rt] * of the GTF model to numerically generated, error-contaminated BTCs. Using the least-square optimization technique, robust estimates of the GTF parameters could be obtained from TDR observations at two different soil depths. Application of the proposed method was also tested for a real undisturbed sandy subsoil and compared with the convective lognormal transfer (CLT) and CD models. For this case, it was shown that the GTF model improved greatly the goodness of prediction of the BTCs. The proposed method offers a new powerful tool for analyzing transport processes of nonreactive solutes in soil.

This paper compares reservoir operating policies obtained from fuzzy and nonfuzzy explicit stochastic dynamic programming. The reservoir operation problem for the Mansour Eddahbi dam in Morocco can be formulated as either a classical stochastic dynamic programming (SDP) problem, where the objective function stresses energy maximization with particular volumes being released for irrigation, or a fuzzy stochastic dynamic programming (FSDP) problem, in which both hydropower generation and irrigation are considered as fuzzy constraints and aggregated by the weighting method. System performance is estimated from simulation based on continuous reoptimization models using either the cost-to-go function generated by the SDP algorithm, or the membership function generated by the FSDP algorithm. Despite major differences in the mathematical representation of operating objectives and/or constraints, we show that both formulations yield similar measures of system performance. DOI: 10.1061/(ASCE)0733-9496(2002)128:6(390) CE Database keywords: Reservoir operation; Decision making; Optimization; Fuzzy sets; Stochastic processes.

The lack of an adequate method for calibration of time domain reflectometry (TDR) measurement on bulk soil electrical conductivity is a limiting factor, especially for field-scale solute transport study. This study investigated an appropriate calibration method that can be applied to horizontally positioned TDR probes in situ. A nonlinear model (RM) has been proposed assuming a two-pathway conductance. Using the quadratic form, the RM equated electrical conductivity in the immobile phase of soil solution ([EC.sub.ws]) in a series-coupled pathway with electrical conductivity in the mobile phase of soil solution ([EC.sub.wc]) in a continuous pathway. We related bulk soil electrical conductivity ([EC.sub.a]) to electrical conductivity of soil water ([EC.sub.w]), assuming constant [EC.sub.ws] during breakthrough. This resulted in a linear relationship between [EC.sub.a] and [EC.sub.w]. The linear relation, termed here simple linear model (SLM), was tested using experimental data obtained from soil columns. Laboratory breakthrough experiments were performed on short and large columns by applying a pulse input of solute. At the end of breakthrough, separate calibration experiments were performed using a step input of solute. Both RM and SLM were compared with the step input calibration method (SIM) as a reference method. Results show that the SLM is better than RM in terms of mass recovery. In addition, parameters of the solute transport model were not affected within 20% of uncertainty in the slope coefficient of the SLM when compared with the reference method. Advantages of the SLM are that it has an identical equation form to the SIM but less effort is required, especially for soil columns showing preferential flow, and it can be readily applied to field conditions.

Prediction of solute transport in soils requires appropriate transport models and model parameters. The most suitable solute transport model and its parameters are likely to depend on both soil type and water flux. This dependency was investigated by means of transport experiments that were carried out in three different soils (Plaggept, Hapludalf, and Glossudalf) for two water application rates (0.5 and 1.0 cm [d.sup.-1]). Solute concentrations were measured during the transport experiment at six different depths in undisturbed soil monoliths (1.0-m length, 0.8-m i.d.) using time domain reflectomerry (TDR). For each depth, parameters of two solute transport models, (i) the convective lognormal transfer function (CLT) model assuming stochastic-convective solute transport or no solute mixing and (ii) the convective-dispersive (CDE) model assuming complete solute mixing, were derived. The transport in the Plaggept and Hapludalf soil was better modeled as a stochastic-convective process. Furthermore, solute transport in these two soils was very heterogeneous, resulting from considerable differences in local advection velocity. In the Glossudalf soil, solute transport was more homogeneous and characterized as a convective-dispersive process. The heterogeneity of solute transport in both Plaggept and Hapludalf soils increased with the applied water flux. This increase was more pronounced in the Hapludalf soil, as the higher water flux resulted in a larger contribution of macropores to flow and transport of solutes.

Time Domain Reflectometry (TDR) has become a popular method to obtain time series of resident concentrations in solute transport studies, so effective interpretation of TDR data is very useful. In this study, we evaluated three procedures to determine the parameters of the convective lognormal transfer function (CLT) model from such time series. In a first approach, the CLT model travel time probability density function (pdf) was related to time series of time-integral-normalized flux concentrations, [C.sup.f*](z,t). The normalization was based on mass balance calculations performed with time series of resident concentrations measured at several depths. The [C.sup.f*](z,t) data thus obtained were very erratic leading to a high parameter uncertainty. In a second approach, the CLT model travel depth pdf was related to time series of depth-integral- or mass-normalized resident concentrations, [C.sup.rm*](z,t). This approach suffered from uncertainty regarding calibration coefficients relating TDR measured impedance to resident concentrations and from uncertainty regarding the solute mass crossing the sampling volume of the TDR probe. The third approach used the relation between travel time and travel depth pdf for a stochastic-convective transport process to formulate a new expression relating time-integral-normalized resident concentrations, [C.sup.rt*](z,t), to the CLT model parameters. No information is needed about calibration coefficients while no a priori assumptions about the solute mass detected by the TDR probe are required. This approach yielded better CLT model fits to observed concentration data, and the variability of parameters fitted at different locations can be related to heterogeneity of solute and water flow after averaging across the TDR measurement window.

Time domain reflectometry (TDR) is rapidly becoming a popular method for measuring solute concentrations in the laboratory as well as in the field. Success or failure of TDR to represent solute resident concentrations depends on the accuracy of the invoked calibration. In this study, we compared three commonly used calibration methods that relate the impedance, [Z.sub.0] as measured with TDR, to the solute concentration such as the inlet concentration, [C.sub.0]. The comparison was carried out using solute transport data obtained from 1-m-long, 0.3-m-diam. undisturbed saturated soil columns. The first method comprised the application of a long enough solute pulse such that the concentration in a soil column became equal to the input concentration. The second method involved numerical integration of the observed response to a tracer pulse input function from which [Z.sub.0] could be obtained. The third method determined [Z.sub.0] using an independently measured relationship between the impedance and the solute concentration. The three calibration methods gave approximately the same results for the first observation depth at x = 0.05 m. However, the presence of heterogeneous transport processes involving solute diffusion from mobile to immobile water regions predicated the use of excessively long solute pulses in order to equilibrate the entire soil column to the input concentration. The first method hence was useful only for the shallower depths. The second method could be applied throughout the soil profile, provided impedance measurements were made for a reasonable time period, especially in the case of nonequilibrium transport. The procedure using an independently measured Z-C relationship underpredicted [Z.sub.0] in about 50% of the cases, presumably because of the use of repacked soil in the calibration.

Study by time domain reflectometry (TDR) gives detailed data quickly and nondestructively on transportation of an applied inert solute, during a quasi-steady-state flow, in an undisturbed, unsaturated, multilayered and sandy soil. An undisturbed multi-layered sandy lysimeter is used for the experiment. Results showed a constant value deeper in the lysimeter; dispersivity increased with depth.