An Exponentially Convergent Nonpolynomial Finite Element Method for Time-Harmonic Scattering from Polygons

In recent years nonpolynomial finite element methods have received increasing attention for the efficient solution of wave problems. As with their close cousin the method of particular solutions, high efficiency comes from using solutions to the Helmholtz equation as basis functions. We present and analyze such a method for the scattering of two-dimensional scalar waves from a polygonal domain that achieves exponential convergence purely by increasing the number of basis functions in each element. Key ingredients are the use of basis functions that capture the singularities at corners and the representation of the scattered field towards infinity by a combination of fundamental solutions. The solution is obtained by minimizing a least-squares functional, which we discretize in such a way that a matrix least-squares problem is obtained. We give computable exponential bounds on the rate of convergence of the least-squares functional that are in very good agreement with the observed numerical convergence. Challenging numerical examples, including a nonconvex polygon with several corner singularities, and a cavity domain, are solved to around 10 digits of accuracy with a few seconds of CPU time. The examples are implemented concisely with MPSpack, a MATLAB toolbox for wave computations with nonpolynomial basis functions, developed by the authors. A code example is included.

Managing threatened species – the ecological toolbox, evolutionary theory and the declining-population paradigm

1. The management of threatened species is an important practical way in which conservationists can intervene in the extinction process and reduce the loss of biodiversity. Understanding the causes of population declines (past, present and future) is pivotal to designing effective practical management. This is the declining-population paradigm identified by Caughley. 2. There are three broad classes of ecological tool used by conservationists to guide management decisions for threatened species: statistical models of habitat use, demographic models and behaviour-based models. Each of these is described here, illustrated with a case study and evaluated critically in terms of its practical application. 3. These tools are fundamentally different. Statistical models of habitat use and demographic models both use descriptions of patterns in abundance and demography, in relation to a range of factors, to inform management decisions. In contrast, behaviourbased models describe the evolutionary processes underlying these patterns, and derive such patterns from the strategies employed by individuals when competing for resources under a specific set of environmental conditions. 4. Statistical models of habitat use and demographic models have been used successfully to make management recommendations for declining populations. To do this, assumptions are made about population growth or vital rates that will apply when environmental conditions are restored, based on either past data collected under favourable environmental conditions or estimates of these parameters when the agent of decline is removed. As a result, they can only be used to make reliable quantitative predictions about future environments when a comparable environment has been experienced by the population of interest in the past. 5. Many future changes in the environment driven by management will not have been experienced by a population in the past. Under these circumstances, vital rates and their relationship with population density will change in the future in a way that is not predictable from past patterns. Reliable quantitative predictions about population-level responses then need to be based on an explicit consideration of the evolutionary processes operating at the individual level. 6. Synthesis and applications. It is argued that evolutionary theory underpins Caughley’s declining-population paradigm, and that it needs to become much more widely used within mainstream conservation biology. This will help conservationists examine critically the reliability of the tools they have traditionally used to aid management decision-making. It will also give them access to alternative tools, particularly when predictions are required for changes in the environment that have not been experienced by a population in the past.

Managing threatened species: the ecological toolbox, evolutionary theory and declining-population paradigm

1. The management of threatened species is an important practical way in which conservationists can intervene in the extinction process and reduce the loss of biodiversity. Understanding the causes of population declines (past, present and future) is pivotal to designing effective practical management. This is the declining-population paradigm identified by Caughley. 2. There are three broad classes of ecological tool used by conservationists to guide management decisions for threatened species: statistical models of habitat use, demographic models and behaviour-based models. Each of these is described here, illustrated with a case study and evaluated critically in terms of its practical application. 3. These tools are fundamentally different. Statistical models of habitat use and demographic models both use descriptions of patterns in abundance and demography, in relation to a range of factors, to inform management decisions. In contrast, behaviour-based models describe the evolutionary processes underlying these patterns, and derive such patterns from the strategies employed by individuals when competing for resources under a specific set of environmental conditions. 4. Statistical models of habitat use and demographic models have been used successfully to make management recommendations for declining populations. To do this, assumptions are made about population growth or vital rates that will apply when environmental conditions are restored, based on either past data collected under favourable environmental conditions or estimates of these parameters when the agent of decline is removed. As a result, they can only be used to make reliable quantitative predictions about future environments when a comparable environment has been experienced by the population of interest in the past. 5. Many future changes in the environment driven by management will not have been experienced by a population in the past. Under these circumstances, vital rates and their relationship with population density will change in the future in a way that is not predictable from past patterns. Reliable quantitative predictions about population-level responses then need to be based on an explicit consideration of the evolutionary processes operating at the individual level. 6. Synthesis and applications. It is argued that evolutionary theory underpins Caughley's declining-population paradigm, and that it needs to become much more widely used within mainstream conservation biology. This will help conservationists examine critically the reliability of the tools they have traditionally used to aid management decision-making. It will also give them access to alternative tools, particularly when predictions are required for changes in the environment that have not been experienced by a population in the past.

Improved MATLAB GUIs for learning frequency response methods

The author developed two GUIs for asymptotic Bode plots and identification from such plots aimed at improving the learning of frequency response methods: these were presented at UKACC Control 2012. Student feedback and reflection by the author suggested various improvements to these GUIs, which have now been implemented. This paper reviews the earlier work, describes the improvements, and includes positive feedback from the students on the GUIs and how they have helped their understanding of the methods.

A MATLAB GUI for learning controller design in the frequency domain

A MATLAB GUI is presented which is used to help students learn to design controllers in the frequency domain. It complements the author’s two previous GUIs for plotting and identification of systems in the frequency domain. It also incorporates the concept used in the “electronic calculator that makes students think” to assist learning. Positive student feedback affirms that the GUI has helped their understanding.

An aggregated wind power generation model based on MERRA reanalysis data: MATLAB model and example data for the April 2014 wind farm distribution of Great Britain.

The MATLAB model is contained within the compressed folders (versions are available as .zip and .tgz). This model uses MERRA reanalysis data (>34 years available) to estimate the hourly aggregated wind power generation for a predefined (fixed) distribution of wind farms. A ready made example is included for the wind farm distribution of Great Britain, April 2014 ("CF.dat"). This consists of an hourly time series of GB-total capacity factor spanning the period 1980-2013 inclusive. Given the global nature of reanalysis data, the model can be applied to any specified distribution of wind farms in any region of the world. Users are, however, strongly advised to bear in mind the limitations of reanalysis data when using this model/data. This is discussed in our paper: Cannon, Brayshaw, Methven, Coker, Lenaghan. "Using reanalysis data to quantify extreme wind power generation statistics: a 33 year case study in Great Britain". Submitted to Renewable Energy in March, 2014. Additional information about the model is contained in the model code itself, in the accompanying ReadMe file, and on our website: http://www.met.reading.ac.uk/~energymet/data/Cannon2014/

An integrated model of soil-canopy spectral radiances, photosynthesis, fluorescence, temperature and energy balance

This paper presents the model SCOPE (Soil Canopy Observation, Photochemistry and Energy fluxes), which is a vertical (1-D) integrated radiative transfer and energy balance model. The model links visible to thermal infrared radiance spectra (0.4 to 50 μm) as observed above the canopy to the fluxes of water, heat and carbon dioxide, as a function of vegetation structure, and the vertical profiles of temperature. Output of the model is the spectrum of outgoing radiation in the viewing direction and the turbulent heat fluxes, photosynthesis and chlorophyll fluorescence. A special routine is dedicated to the calculation of photosynthesis rate and chlorophyll fluorescence at the leaf level as a function of net radiation and leaf temperature. The fluorescence contributions from individual leaves are integrated over the canopy layer to calculate top-of-canopy fluorescence. The calculation of radiative transfer and the energy balance is fully integrated, allowing for feedback between leaf temperatures, leaf chlorophyll fluorescence and radiative fluxes. Leaf temperatures are calculated on the basis of energy balance closure. Model simulations were evaluated against observations reported in the literature and against data collected during field campaigns. These evaluations showed that SCOPE is able to reproduce realistic radiance spectra, directional radiance and energy balance fluxes. The model may be applied for the design of algorithms for the retrieval of evapotranspiration from optical and thermal earth observation data, for validation of existing methods to monitor vegetation functioning, to help interpret canopy fluorescence measurements, and to study the relationships between synoptic observations with diurnally integrated quantities. The model has been implemented in Matlab and has a modular design, thus allowing for great flexibility and scalability.

Calibration and sensitivity analysis of a river water quality model under unsteady flow conditions

Water quality models generally require a relatively large number of parameters to define their functional relationships, and since prior information on parameter values is limited, these are commonly defined by fitting the model to observed data. In this paper, the identifiability of water quality parameters and the associated uncertainty in model simulations are investigated. A modification to the water quality model `Quality Simulation Along River Systems' is presented in which an improved flow component is used within the existing water quality model framework. The performance of the model is evaluated in an application to the Bedford Ouse river, UK, using a Monte-Carlo analysis toolbox. The essential framework of the model proved to be sound, and calibration and validation performance was generally good. However some supposedly important water quality parameters associated with algal activity were found to be completely insensitive, and hence non-identifiable, within the model structure, while others (nitrification and sedimentation) had optimum values at or close to zero, indicating that those processes were not detectable from the data set examined. (C) 2003 Elsevier Science B.V. All rights reserved.