Boundary value problems for third-order linear PDEs in time-dependent domains

We present the extension of a methodology to solve moving boundary value problems from the second-order case to the case of the third-order linear evolution PDE qt + qxxx = 0. This extension is the crucial step needed to generalize this methodology to PDEs of arbitrary order. The methodology is based on the derivation of inversion formulae for a class of integral transforms that generalize the Fourier transform and on the analysis of the global relation associated with the PDE. The study of this relation and its inversion using the appropriate generalized transform are the main elements of the proof of our results.

Fine sediment delivery and transfer in lowland catchments: modelling suspended sediment concentrations in response to hydrological forcing

Fine sediment delivery to and storage in stream channel reaches can disrupt aquatic habitats, impact river hydromorphology, and transfer adsorbed nutrients and pollutants from catchment slopes to the fluvial system. This paper presents a modelling toot for simulating the time-dependent response of the fine sediment system in catchments, using an integrated approach that incorporates both land phase and in-stream processes of sediment generation, storage and transfer. The performance of the model is demonstrated by applying it to simulate in-stream suspended sediment concentrations in two lowland catchments in southern England, the Enborne and the Lambourn, which exhibit contrasting hydrological and sediment responses due to differences in substrate permeability. The sediment model performs well in the Enborne catchment, where direct runoff events are frequent and peak suspended sediment concentrations can exceed 600 mg l(-1). The general trends in the in-stream concentrations in the Lambourn catchment are also reproduced by the model, although the observed concentrations are low (rarely exceeding 50 mg l(-1)) and the background variability in the concentrations is not fully characterized by the model. Direct runoff events are rare in this highly permeable catchment, resulting in a weak coupling between the sediment delivery system and the catchment hydrology. The generic performance of the model is also assessed using a generalized sensitivity analysis based on the parameter bounds identified in the catchment applications. Results indicate that the hydrological parameters contributing to the sediment response include those controlling (1) the partitioning of runoff between surface and soil zone flows and (2) the fractional loss of direct runoff volume prior to channel delivery. The principal sediment processes controlling model behaviour in the simulations are the transport capacity of direct runoff and the in-stream generation, storage and release of the fine sediment fraction. The in-stream processes appear to be important in maintaining the suspended sediment concentrations during low flows in the River Enborne and throughout much of the year in the River Lambourn. Copyright (c) 2007 John Wiley & Sons, Ltd.

Morphology, biomass and nutrient status of fine roots of Scots pine (Pinus sylvestris) as influenced by seasonal fluctuations in soil moisture and soil solution chemistry

A field monitoring study was carried out to follow the changes of fine root morphology, biomass and nutrient status in relation to seasonal changes in soil solution chemistry and moisture regime in a mature Scots pine stand on acid soil. Seasonal and yearly fluctuations in soil moisture and soil solution chemistry have been observed. Changes in soil moisture accounted for some of the changes in the soil solution chemistry. The results showed that when natural acidification in the soil occurs with low pH (3.5-4.2) and high aluminium concentration in the soil solution (> 3-10 mg l(-1)), fine root longevity and distribution could be affected. However, fine root growth of Scots pine may not be negatively influenced by adverse soil chemical conditions if soil moisture is not a limiting factor for root growth. In contrast, dry soil conditions increase Scots pine susceptibility to soil acidification and this could significantly reduce fine root growth and increase root mortality. It is therefore important to study seasonal fluctuations of the environmental variables when investigating and modelling cause-effect relationships.

Short-term effects of manipulated increase in acid deposition on soil, soil solution chemistry and fine roots in Scots pine (Pinus sylvestris) stand on a podzol

A manipulated increase in acid deposition (15 kg S ha(-1)), carried out for three months in a mature Scots pine (Pinus sylvestris) stand on a podzol, acidified the soil and raised dissolved Al at concentrations above the critical level of 5 mg l(-1) previously determined in a controlled experiment with Scots pine seedlings. The induced soil acidification reduced tree fine root density and biomass significantly in the top 15 cm of soil in the field. The results suggested that the reduction in fine root growth was a response not simply to high Al in solution but to the depletion of exchangeable Ca and Mg in the organic layer, K deficiency, the increase in NH4:NO3 ratio in solution and the high proton input to the soil by the acid manipulation. The results from this study could not justify the hypothesis of Al-induced root damage under field conditions, at least not in the short term. However, the study suggests that a short exposure to soil acidity may affect the fine root growth of mature Scots pine.

Coupled simulations of the Indian monsoon intraseasonal oscillation using a fine-resolution mixed-layer ocean model

The intraseasonal variability (ISV) of the Indian summer monsoon is dominated by a 30–50 day oscillation between “active” and “break” events of enhanced and reduced rainfall over the subcontinent, respectively. These organized convective events form in the equatorial Indian Ocean and propagate north to India. Atmosphere–ocean coupled processes are thought to play a key role the intensity and propagation of these events. A high-resolution, coupled atmosphere–mixed-layer-oceanmodel is assembled: HadKPP. HadKPP comprises the Hadley Centre Atmospheric Model (HadAM3) and the K Profile Parameterization (KPP) mixed-layer ocean model. Following studies that upper-ocean vertical resolution and sub-diurnal coupling frequencies improve the simulation of ISV in SSTs, KPP is run at 1 m vertical resolution near the surface; the atmosphere and ocean are coupled every three hours. HadKPP accurately simulates the 30–50 day ISV in rainfall and SSTs over India and the Bay of Bengal, respectively, but suffers from low ISV on the equator. This is due to the HadAM3 convection scheme producing limited ISV in surface fluxes. HadKPP demonstrates little of the observed northward propagation of intraseasonal events, producing instead a standing oscillation. The lack of equatorial ISV in convection in HadAM3 constrains the ability of KPP to produce equatorial SST anomalies, which further weakens the ISV of convection. It is concluded that while atmosphere–ocean interactions are undoubtedly essential to an accurate simulation of ISV, they are not a panacea for model deficiencies. In regions where the atmospheric forcing is adequate, such as the Bay of Bengal, KPP produces SST anomalies that are comparable to the Tropical Rainfall Measuring Mission Microwave Imager (TMI) SST analyses in both their magnitude and their timing with respect to rainfall anomalies over India. HadKPP also displays a much-improved phase relationship between rainfall and SSTs over a HadAM3 ensemble forced by observed SSTs, when both are compared to observations. Coupling to mixed-layer models such as KPP has the potential to improve operational predictions of ISV, particularly when the persistence time of SST anomalies is shorter than the forecast lead time.

A contour-advective semi-lagrangian numerical algorithm for simulating fine-scale conservative dynamical fields

This paper describes a novel numerical algorithm for simulating the evolution of fine-scale conservative fields in layer-wise two-dimensional flows, the most important examples of which are the earth's atmosphere and oceans. the algorithm combines two radically different algorithms, one Lagrangian and the other Eulerian, to achieve an unexpected gain in computational efficiency. The algorithm is demonstrated for multi-layer quasi-geostrophic flow, and results are presented for a simulation of a tilted stratospheric polar vortex and of nearly-inviscid quasi-geostrophic turbulence. the turbulence results contradict previous arguments and simulation results that have suggested an ultimate two-dimensional, vertically-coherent character of the flow. Ongoing extensions of the algorithm to the generally ageostrophic flows characteristic of planetary fluid dynamics are outlined.

Fine wire resistance thermometer amplifier for atmospheric measurements

An improved amplifier for atmospheric fine wire resistance thermometry is described. The amplifier uses a low excitation current (50 mu A). This is shown to ensure negligible self-heating of the low mass fine wire resistance sensor, compared with measured nocturnal surface air temperature fluctuations. The system provides sufficient amplification for a +/- 50 degrees C span using a +/- 5 V dynamic range analog-to-digital converter, with a noise level of less than 0.01 degrees C. A Kelvin four-wire connection cancels the effect of long lead resistances: a 50 m length of screened cable connecting the Reading design of fine wire thermometer to the amplifier produced no measurable temperature change at 12 bit resolution.

Integrable evolution equations in time-dependent domains

We discuss the implementation of a method of solving initial boundary value problems in the case of integrable evolution equations in a time-dependent domain. This method is applied to a dispersive linear evolution equation with spatial derivatives of arbitrary order and to the defocusing nonlinear Schrödinger equation, in the domain l(t)