Bernhard H. Schmid

On the transient storage equations for longitudinal solute transport in open channels: temporal moments accounting for the effects of first-order decay

Solute concentrations in streams due to instantaneous slug releases are frequently influenced both by decay and by exchange with dead zones, among others. Based on the transient storage equations with first-order decay terms, explicit relationships are given for the computation of the zeroth to third temporal moments. The equations presented were applied within the framework of moment-based similarity functions which yield approximate temporal distributions of concentration. Results thus obtained were subsequently compared to finite difference solutions of the transient storage equations, in order to investigate the relationship between these approaches. Within the previously established ranges of applicability of the two similarity functions employed the comparisons indicated fairly good agreement.

Temporal moments routing in streams and rivers with transient storage

Abstract Closed-form expressions for the temporal moments of concentration–time distributions in streams and rivers with transient storage (TS) have been derived. In addition to the mathematical relationships known already for the case of an instantaneous slug release, further and more general results were obtained for stream reaches with arbitrary inflow pollutographs. Thus, the temporal moments of the concentration-versus-time distribution at the lower end of a reach can be linked to the respective moments at the upper end and the transport and mixing parameters of the so-called TS or Dead Zone Model. Therefore, starting from the site of a release (or some arbitrary cross-section within the zone of validity of the TS model), the first to fourth temporal moments of concentration–time distributions can be routed in flow direction along a cascade of stream reaches. The moment-routing equations presented are expected to be useful in the interpretation of measured field data (including estimation of the transport and mixing parameters) as well as for simulation purposes and as an easily used tool to check the accuracy of numerical codes.

On overland flow modelling: can rainfall excess be treated as independent of flow depth?

Abstract Simulation runs, with and without accounting for the effect of flow depth, indicate that in most cases of storm runoff computations the usual procedure of neglecting this influence on rainfall excess will lead to errors of less than 10%. Compared to the uncertainty introduced by inaccurate soil data this figure may still be regarded as sufficiently small.

Sediment Retention in Constructed Wetland Ponds—A Laboratory Study

Abstract Laboratory experiments on sediment removal and particle settlement were conducted in a hydraulic laboratory model scaled 1:1 to study processes and mechanisms governing sediment transport under well defined and reproducible conditions. Parameters governing particle settling were varied and their effect studied ceteris paribus. These governing parameters were flow velocity, TSS input concentration, presence of plants, vegetation density, and the presence of wind. Changes in sediment removal due to different parameters were analyzed by means of deposition curves in main flow direction. We found that particle settling is enhanced by increased inflow concentrations of suspended solids in the absence of plant stems (substance used: kaolin), whereas deposition is reduced by wind shear. The presence of plant stems strengthens vertical mixing and, consequently, does not generally result in enhanced deposition of suspended solids. Higher plant densities tend to be associated with lower settling rates. The effect of flow velocity on particle settling is small for the present experimental set-up.

On kinematic cascades : derivation of a generalized shock formation criterion

Shock formation may present problems in the course of kinematic cascade modelling. With regard to the choice of an adequate algorithm of solution it is therefore important to know beforehand, if discontinuities are to be expected or not. A generalized criterion including cases of time-dependent rates of rainfall excess is derived. For constant lateral inflow it can be shown to correspond to the previously derived Kibler- Woolhiser criterion.

Derivation of an explicit equation for infiltration on the basis of the Mein-Larson model

Proceeding from the well-known infiltration model by Mein & Larson (1973) and several extensions, explicit equations for time-dependent infiltration rate and cumulative infiltration are proposed in this paper. Although the time-range of validity is limited due to the chosen mode of derivation, the formulae seem well suited for application in the course of storm runoff modelling for small catchments. Major advantages of the proposed equations are constituted by the comparatively simple structure and by a high degree of versatility allowing a considerable number of effects to be explicitly accounted for. The parameters involved can be identified from measurements. Rules of thumb regarding the range of applicability are given.

Critical rainfall duration for overland flow from an infiltrating plane surface

Abstract Design flows from infiltrating micro-catchments are investigated using a kinematic model of overland flow and a physics-based representation of the infiltration process. Critical storm duration is shown to be governed by two relationships, one equivalent to the traditional approach of setting concentration time equal to rainfall duration and the other yielding a potentially critical duration independent of plane length. In case of two competing results, the valid one is recognized as giving the shorter of the two durations calculated. Derivation of the governing equations has been carried out preserving as much generality as possible. In addition to the equations mentioned, a “rainfall window” describing all overland flow producing storms in accordance with a given intensity-duration-frequency (IDF) relationship is identified and mathematical expressions for its evaluation are given. Practical application is demonstrated by a number of sample computations.

Convective oxygen transport in a constructed wetland pond : Mechanism, measurements and modelling by multilayer perceptrons

Abstract The study presented here found evidence for the presence and importance of convective flows and associated oxygen transport in a constructed wetland pond in southern Finland. These flows are triggered by nightly cooling of the water at the surface, which may then become denser than the water lower down in the pond. The resulting layering (heavier water overlying less dense one) is hydromechanically unstable and—almost immediately—starts driving convective motion. This flow takes oxygen enriched water from the surface to the bottom of the wetland, where a distinct rise in oxygen saturation is recorded after some time lag. The process described can be modelled successfully by means of so-called Multilayer Perceptrons (MLPs), a class of Artificial Neural Networks. As explored in this study, these models are well suited to “learn” the mechanism of convective transport, which results in their ability to forecast oxygen saturation near the wetland bottom at a satisfactory level of accuracy.

The matched diffusivity technique applied to kinematic cascades. I. Model description and validation.

Abstract Three models based on the matched diffusivity approach are described and tested against experimental data. Results are evaluated and the most suitable model for application to kinematic cascades is selected. Further analysis of model performance with the aid of semianalytical solutions is the subject of Part II of this paper.

The matched diffusivity technique applied to kinematic cascades. II. Analysis of model performance

Abstract Performance of the Muskingum-Cunge (MC) method is investigated by comparing numerical results with semianalytical solutions. Special attention is paid to cases involving discontinuous solutions. The adequacy of the MC approach is demonstrated for turbulent kinematic flows with and without the influence of reasonably strong shocks. The matched diffusivity technique also yields satisfactory results for laminar flows without shocks, whereas application of this method to shock-affected laminar flow cannot be advised.