A weak formulation of Roe's approximate Riemann Solver applied to 'Barotropic' flows

A weak formulation of Roe's approximate Riemann solver is applied to the equations of ‘barotropic’ flow, including the shallow water equations, and it is shown that this leads to an approximate Riemann solver recently presented for such flows.

Wavelet filtered modelling applied to measurements of a waveguide's THz time domain response

A quasi-optical de-embedding technique for characterizing waveguides is demonstrated using wideband time-resolved terahertz spectroscopy. A transfer function representation is adopted for the description of the signal in the input and output port of the waveguides. The time domain responses were discretised and the waveguide transfer function was obtained through a parametric approach in the z-domain after describing the system with an ARX as well as with a state space model. Prior to the identification procedure, filtering was performed in the wavelet domain to minimize signal distortion and the noise propagating in the ARX and subspace models. The model identification procedure requires isolation of the phase delay in the structure and therefore the time-domain signatures must be firstly aligned with respect to each other before they are compared. An initial estimate of the number of propagating modes was provided by comparing the measured phase delay in the structure with theoretical calculations that take into account the physical dimensions of the waveguide. Models derived from measurements of THz transients in a precision WR-8 waveguide adjustable short will be presented.

Linear-wavelet models for non-linear identification applied to a pressure plant

A nonlinear regression structure comprising a wavelet network and a linear term is proposed for system identification. The theoretical foundation of the approach is laid by proving that radial wavelets are orthogonal to linear functions. A constructive procedure for building such models is described and the approach is tested with experimental data.

Linear-wavelet models applied to the identification of a two-link manipulator

This paper shows that a wavelet network and a linear term can be advantageously combined for the purpose of non linear system identification. The theoretical foundation of this approach is laid by proving that radial wavelets are orthogonal to linear functions. A constructive procedure for building such nonlinear regression structures, termed linear-wavelet models, is described. For illustration, sim ulation data are used to identify a model for a two-link robotic manipulator. The results show that the introduction of wavelets does improve the prediction ability of a linear model.

A critical review of methodologies for measuring rental depreciation applied to UK commercial real estate

Real estate depreciation continues to be a critical issue for investors and the appraisal profession in the UK in the 1990s. Depreciation-sensitive cash flow models have been developed, but there is a real need to develop further empirical methodologies to determine rental depreciation rates for input into these models. Although building quality has been found to be an important explanatory variable in depreciation it is very difficult to incorporate it into such models or to analyse it retrospectively. It is essential to examine previous depreciation research from real estate and economics in the USA and UK to understand the issues in constructing a valid and pragmatic way of calculating rental depreciation. Distinguishing between 'depreciation' and 'obsolescence' is important, and the pattern of depreciation in any study can be influenced by such factors as the type (longitudinal or crosssectional) and timing of the study, and the market state. Longitudinal studies can analyse change more directly than cross-sectional studies. Any methodology for calculating rental depreciation rate should be formulated in the context of such issues as 'censored sample bias', 'lemons' and 'filtering', which have been highlighted in key US literature from the field of economic depreciation. Property depreciation studies in the UK have tended to overlook this literature, however. Although data limitations and constraints reduce the ability of empirical property depreciation work in the UK to consider these issues fully, 'averaging' techniques and ordinary least squares (OLS) regression can both provide a consistent way of calculating rental depreciation rates within a 'cohort' framework.

Mathematics applied to the climate system: outstanding challenges and recent progress

The societal need for reliable climate predictions and a proper assessment of their uncertainties is pressing. Uncertainties arise not only from initial conditions and forcing scenarios, but also from model formulation. Here, we identify and document three broad classes of problems, each representing what we regard to be an outstanding challenge in the area of mathematics applied to the climate system. First, there is the problem of the development and evaluation of simple physically based models of the global climate. Second, there is the problem of the development and evaluation of the components of complex models such as general circulation models. Third, there is the problem of the development and evaluation of appropriate statistical frameworks. We discuss these problems in turn, emphasizing the recent progress made by the papers presented in this Theme Issue. Many pressing challenges in climate science require closer collaboration between climate scientists, mathematicians and statisticians. We hope the papers contained in this Theme Issue will act as inspiration for such collaborations and for setting future research directions.

Climate change scenarios applied to viticultural zoning in Europe

Climate is one of the main factors controlling winegrape production. Bioclimatic indices describing the suitability of a particular region for wine production are a widely used zoning tool. Seven suitable bioclimatic indices characterize regions in Europe with different viticultural suitability, and their possible geographical shifts under future climate conditions are addressed using regional climate model simulations. The indices are calculated from climatic variables (daily values of temperature and precipitation) obtained from transient ensemble simulations with the regional model COSMO-CLM. Index maps for recent decades (1960–2000) and for the 21st century (following the IPCC-SRES B1 and A1B scenarios) are compared. Results show that climate change is projected to have a significant effect on European viticultural geography. Detrimental impacts on winegrowing are predicted in southern Europe, mainly due to increased dryness and cumulative thermal effects during the growing season. These changes represent an important constraint to grapevine growth and development, making adaptation strategies crucial, such as changing varieties or introducing water supply by irrigation. Conversely, in western and central Europe, projected future changes will benefit not only wine quality, but might also demarcate new potential areas for viticulture, despite some likely threats associated with diseases. Regardless of the inherent uncertainties, this approach provides valuable information for implementing proper and diverse adaptation measures in different European regions.

Late Quaternary highstands at Lake Chilwa, Malawi: frequency, timing and possible forcing mechanisms in the last 44ka

The extensive shoreline deposits of Lake Chilwa, southern Malawi, a shallow water body today covering 600 km2 of a basin of 7500 km2, are investigated for their record of late Quaternary highstands. OSL dating, applied to 36 samples from five sediment cores from the northern and western marginal sand ridges, reveal a highstand record spanning 44 ka. Using two different grouping methods, highstand phases are identified at 43.7–33.3 ka, 26.2–21.0 ka and 17.9–12.0 ka (total error method) or 38.4–35.5 ka, 24.3–22.3 ka, 16.2–15.1 ka and 13.5–12.7 ka (Finite Mixture Model age components) with two further discrete events recorded at 11.01 ± 0.76 ka and 8.52 ± 0.56 ka. Highstands are comparable to the timing of wet phases from other basins in East and southern Africa, demonstrating wet conditions in the region before the LGM, which was dry, and a wet Lateglacial, which commenced earlier in the southern compared to northern hemisphere in East Africa. We find no evidence that wet phases are insolation driven, but analysis of the dataset and GCM modelling experiments suggest that Heinrich events may be associated with enhanced monsoon activity in East Africa in both timing and as a possible causal mechanism.

New age estimates for the Palaeolithic assemblages and Pleistocene succession of Casablanca, Morocco

Marine and aeolian Quaternary sediments from Casablanca, Morocco were dated using the optically stimulated luminescence (OSL) signal of quartz grains. These sediments form part of an extensive succession spanning the Pleistocene, and contain a rich faunal and archaeological record, including an Acheulian lithic assemblage from before the Brunhes–Matayama boundary, and a Homo erectus jaw from younger cave deposits. Sediment samples from the sites of Reddad Ben Ali, Oulad J’mel, Sidi Abderhamane and Thomas Quarries have been dated, in order to assess the upper limits of OSL. The revision of previously measured mammalian tooth enamel electron spin resonance (ESR) dates from the Grotte des Rhinocéros, Oulad Hamida Quarry 1, incorporating updated environmental dose rate measurements and attenuation calculations, also provide chronological constraint for the archaeological material preserved at Thomas Quarries. Several OSL age estimates extend back to around 500,000 years, with a single sample providing an OSL age close to 1 Ma in magnetically reversed sediments. These luminescence dates are some of the oldest determined, and their reliability is assessed using both internal criteria based on stratigraphic consistency, and external lithostratigraphic, morphostratigraphic and independent chronological constraints. For most samples, good internal agreement is observed using single aliquot regenerative-dose OSL measurements, while multiple aliquot additive-dose measurements generally have poorer resolution and consistency. Novel slow-component and component-resolved OSL approaches applied to four samples provide significantly enhanced dating precision, and an examination of the degree of signal zeroing at deposition. A comparison of the OSL age estimates with the updated ESR dates and one U-series date demonstrate that this method has great potential for providing reliable age estimates for sediments of this antiquity. We consider the cause of some slight age inversion observed at Thomas Quarries, and provide recommendations for further luminescence dating within this succession.

The WFDEI meteorological forcing data set: WATCH Forcing Data methodology applied to ERA-Interim reanalysis data

The WFDEI meteorological forcing data set has been generated using the same methodology as the widely used WATCH Forcing Data (WFD) by making use of the ERA-Interim reanalysis data. We discuss the specifics of how changes in the reanalysis and processing have led to improvement over the WFD. We attribute improvements in precipitation and wind speed to the latest reanalysis basis data and improved downward shortwave fluxes to the changes in the aerosol corrections. Covering 1979–2012, the WFDEI will allow more thorough comparisons of hydrological and Earth System model outputs with hydrologically and phenologically relevant satellite products than using the WFD.