Hysteresis‐based analysis of overland metal transport

Introducing a concept of equivalent mass depth of flow, this study describes the phenomenon of non‐point source pollutant (metal) transport for pavement (or overland) flow in analogy with wave propagation in wide open channels. Hysteretic and normal mass rating curves are developed for runoff rate and mass of 12 dissolved and particulate‐bound metal elements (pollutants) using the rainfall‐runoff and water quality data of the 15 × 20 m² instrumented pavement in Cincinnati, USA. Normal mass rating curves developed for easy computation of pollutant load are found to be of a form similar to Manning's, which is valid for open channel flows. Based on the hysteresis analysis, wave types for dissolution and mixing of particulate‐bound metals are identified. The analysis finds that the second‐order partial‐differential equation normally used for metal transport does not have the efficacy to describe fully the strong non‐linear phenomena such as is described for various metal elements by dynamic waves. In addition, the proportionality concept of the popular SCS‐CN concept is extended for determining the potential maximum metal mass M_p of all the 12 elements transported by a rain storm and related to the antecedent dry period (ADP). For the primary metal zinc element, M_p is found to increase with the ADP and vice versa. Copyright © 2003 John Wiley & Sons, Ltd.     

Modelling the effect of low soil temperatures on transpiration by Scots pine

For ecosystem modelling of the Boreal forest it is important to include processes associated with low soil temperature during spring‐early summer, as these affect the tree water uptake. The COUP model, a physically based SVAT model, was tested with 2 years of soil and snow physical measurements and sap flow measurements in a 70‐year‐old Scots pine stand in the boreal zone of northern Sweden. During the first year the extent and duration of soil frost was manipulated in the field. The model was successful in reproducing the timing of the soil warming after the snowmelt and frost thaw. A delayed soil warming, into the growing season, severely reduced the transpiration. We demonstrated the potential for considerable overestimation of transpiration by the model if the reduction of the trees' capacity to transpire due to low soil temperatures is not taken into account. We also demonstrated that the accumulated effect of aboveground conditions could be included when simulating the relationship between soil temperature and tree water uptake. This improved the estimated transpiration for the control plot and when soil warming was delayed into the growing season. The study illustrates the need of including antecedent conditions on root growth in the model in order to catch these effects on transpiration. The COUP model is a promising tool for predicting transpiration in high‐latitude stands. Copyright © 2006 John Wiley & Sons, Ltd.     

The influence of macrophyte growth,typical of eutrophic conditions,on river flow velocities and turbulence production

The influence of emergent and submerged macrophytes on flow velocity and turbulence production is demonstrated in a 140 m reach of the River Blackwater in Farnborough, Hampshire, UK. Macrophyte growth occurs in patches and is dominated by Sparganium erectum and Sparganium emersum. In May 2001, patches of S. erectum were already established and occupied 18% of the channel area. The flow adjusted to these (predominantly lateral) patches by being channelled through a narrower cross‐section. The measured velocity profiles showed a logarithmic form, with deviations attributable to topographic control. The channel bed was the main source of turbulence. In September 2001, in‐stream macrophytes occupied 27% of the channel, and overhanging bank vegetation affected 32% of the area. Overall flow resistance, described by Manning's n, showed a threefold increase that could be attributed to the growth of S. emersum in the middle of the channel. Velocity profiles showed different characteristic forms depending on their position relative to plant stems and leaves. The overall velocity field had a three‐dimensional structure. Turbulence intensities were generally higher and turbulence profiles tended to mirror the velocity profiles. Evidence for the generation of coherent eddies was provided by ratios of the root mean square velocities. Spectral analysis identified deviations from the Kolmogorov ?5/3 power law and provided statistical evidence for a spectral short‐cut, indicative of additional turbulence production. This was most marked for the submerged vegetation and, in some instances, the overhanging bank vegetation. The long strap‐like leaves of S. emersum being aligned approximately parallel to the flow and the highly variable velocity field created by the patch arrangement of macrophytes suggest that the dominant mechanism for turbulence production is vortex shedding along shear zones. Wake production around individual stems of S. emersum close to the bed may also be important locally. Copyright © 2006 John Wiley & Sons, Ltd.     

Functional responses for zooplankton feeding on multiple resources: a review of assumptions and biological dynamics

Modelers often need to quantify the rates at which zooplankton consume a variety of species, size classes and trophic types. Implicit in the equations used to describe the multiple resource functional response (i.e. how nutritional intake varies with resource densities) are assumptions that are not often stated, let alone tested. This is problematic because models are sensitive to the details of these formulations. Here, we enable modelers to make more informed decisions by providing them with a new framework for considering zooplankton feeding on multiple resources. We define a new classification of multiple resource responses that is based on preference, selection and switching, and we develop a set of mathematical diagnostics that elucidate model assumptions. We use these tools to evaluate the assumptions and biological dynamics inherent in published multiple resource responses. These models are shown to simulate different resource preferences, implied single resource responses, changes in intake with changing resource densities, nutritional benefits of generalism, and nutritional costs of selection. Certain formulations are further shown to exhibit anomalous dynamics such as negative switching and sub-optimal feeding. Such varied responses can have vastly different ecological consequences for both zooplankton and their resources; inappropriate choices may incorrectly quantify biologically-mediated fluxes and predict spurious dynamics. We discuss how our classes and diagnostics can help constrain parameters, interpret behaviors, and identify limitations to a formulation's applicability for both regional (e.g. High-Nitrate-Low-Chlorophyll regions comprising large areas of the Pacific) and large-scale applications (e.g. global biogeochemical or climate change models). Strategies for assessing uncertainty and for using the mathematics to guide future experimental investigations are also discussed.     

Numerical study of enhanced energy dissipation near a seamount

Using a two-dimensional primitive equation model, we examine nonlinear responses of a semidiurnal tidal flow impinging on a seamount with a background Garrett-Munk-like (GM-like) internal wavefield. It is found that horizontally elongated pancake-like structures of high vertical wavenumber near-inertial current shear are created both in the near-field (the region over the slope of the seamount) and far-field (the region over the flat bottom of the ocean). An important distinction is that the high vertical wavenumber near-inertial current shear is amplified only at mid-latitudes in the far-field (owing to a parametric subharmonic instability (PSI)), whereas it is amplified both at mid-and high-latitudes (above the latitude where PSI can occur) in the near-field. In order to clarify the generating mechanism for the strong shear in the near-field, additional numerical experiments are carried out with the GM-like background internal waves removed. The experiments show that the strong shear is also created, indicating that it is not caused by the interaction between the background GM-like internal waves and the semidiurnal internal tides. One possible explanation is proposed for the amplification of high vertical wavenumber near-inertial current shear in the near-field where tide residual flow resulting from tide-topography interaction plays an important role in transferring energy from high-mode internal tides to near-inertial internal waves.     

Fully nonlinear numerical wave tank (NWT) simulations and wave run-up prediction around 3-D structures

A finite-difference scheme and a modified marker-and-cell (MAC) algorithm have been developed to investigate the interactions of fully nonlinear waves with two- or three-dimensional structures of arbitrary shape. The Navier–Stokes (NS) and continuity equations are solved in the computational domain and the boundary values are updated at each time step by the finite-difference time-marching scheme in the framework of a rectangular coordinate system. The fully nonlinear kinematic free-surface condition is implemented by the marker-density function (MDF) technique developed for two fluid layers.To demonstrate the capability and accuracy of the present method, the numerical simulation of backstep flows with free-surface, and the numerical tests of the MDF technique with limit functions are conducted. The 3D program was then applied to nonlinear wave interactions with conical gravity platforms of circular and octagonal cross-sections. The numerical prediction of maximum wave run-up on arctic structures is compared with the prediction of the Shore Protection Manual (SPM) method and those of linear and second-order diffraction analyses based on potential theory and boundary element method (BEM). Through this comparison, the effects of non-linearity and viscosity on wave loading and run-up are discussed.