Fast identification algorithms for Gaussian process model

A class identification algorithms is introduced for Gaussian process(GP)models.The fundamental approach is to propose a new kernel function which leads to a covariance matrix with low rank,a property that is consequently exploited for computational efficiency for both model parameter estimation and model predictions.The objective of either maximizing the marginal likelihood or the Kullback–Leibler (K–L) divergence between the estimated output probability density function(pdf)and the true pdf has been used as respective cost functions.For each cost function,an efficient coordinate descent algorithm is proposed to estimate the kernel parameters using a one dimensional derivative free search, and noise variance using a fast gradient descent algorithm. Numerical examples are included to demonstrate the effectiveness of the new identification approaches.

On the spectra and pseudospectra of a class of non-self-adjoint random matrices and operators

In this paper we develop and apply methods for the spectral analysis of non-selfadjoint tridiagonal infinite and finite random matrices, and for the spectral analysis of analogous deterministic matrices which are pseudo-ergodic in the sense of E. B. Davies (Commun. Math. Phys. 216 (2001), 687–704). As a major application to illustrate our methods we focus on the “hopping sign model” introduced by J. Feinberg and A. Zee (Phys. Rev. E 59 (1999), 6433–6443), in which the main objects of study are random tridiagonal matrices which have zeros on the main diagonal and random ±1’s as the other entries. We explore the relationship between spectral sets in the finite and infinite matrix cases, and between the semi-infinite and bi-infinite matrix cases, for example showing that the numerical range and p-norm ε - pseudospectra (ε > 0, p ∈ [1,∞] ) of the random finite matrices converge almost surely to their infinite matrix counterparts, and that the finite matrix spectra are contained in the infinite matrix spectrum Σ. We also propose a sequence of inclusion sets for Σ which we show is convergent to Σ, with the nth element of the sequence computable by calculating smallest singular values of (large numbers of) n×n matrices. We propose similar convergent approximations for the 2-norm ε -pseudospectra of the infinite random matrices, these approximations sandwiching the infinite matrix pseudospectra from above and below.

Key conclusions of the first international urban land surface model comparison project

he first international urban land surface model comparison was designed to identify three aspects of the urban surface-atmosphere interactions: (1) the dominant physical processes, (2) the level of complexity required to model these, and 3) the parameter requirements for such a model. Offline simulations from 32 land surface schemes, with varying complexity, contributed to the comparison. Model results were analysed within a framework of physical classifications and over four stages. The results show that the following are important urban processes; (i) multiple reflections of shortwave radiation within street canyons, (ii) reduction in the amount of visible sky from within the canyon, which impacts on the net long-wave radiation, iii) the contrast in surface temperatures between building roofs and street canyons, and (iv) evaporation from vegetation. Models that use an appropriate bulk albedo based on multiple solar reflections, represent building roof surfaces separately from street canyons and include a representation of vegetation demonstrate more skill, but require parameter information on the albedo, height of the buildings relative to the width of the streets (height to width ratio), the fraction of building roofs compared to street canyons from a plan view (plan area fraction) and the fraction of the surface that is vegetated. These results, whilst based on a single site and less than 18 months of data, have implications for the future design of urban land surface models, the data that need to be measured in urban observational campaigns, and what needs to be included in initiatives for regional and global parameter databases.

Using an individual-based model to select among alternative foraging strategies of woodpigeons: data support a memory-based model with a flocking mechanism

Population modelling is increasingly recognised as a useful tool for pesticide risk assessment. For vertebrates that may ingest pesticides with their food, such as woodpigeon (Columba palumbus), population models that simulate foraging behaviour explicitly can help predicting both exposure and population-level impact. Optimal foraging theory is often assumed to explain the individual-level decisions driving distributions of individuals in the field, but it may not adequately predict spatial and temporal characteristics of woodpigeon foraging because of the woodpigeons’ excellent memory, ability to fly long distances, and distinctive flocking behaviour. Here we present an individual-based model (IBM) of the woodpigeon. We used the model to predict distributions of foraging woodpigeons that use one of six alternative foraging strategies: optimal foraging, memory-based foraging and random foraging, each with or without flocking mechanisms. We used pattern-oriented modelling to determine which of the foraging strategies is best able to reproduce observed data patterns. Data used for model evaluation were gathered during a long-term woodpigeon study conducted between 1961 and 2004 and a radiotracking study conducted in 2003 and 2004, both in the UK, and are summarised here as three complex patterns: the distributions of foraging birds between vegetation types during the year, the number of fields visited daily by individuals, and the proportion of fields revisited by them on subsequent days. The model with a memory-based foraging strategy and a flocking mechanism was the only one to reproduce these three data patterns, and the optimal foraging model produced poor matches to all of them. The random foraging strategy reproduced two of the three patterns but was not able to guarantee population persistence. We conclude that with the memory-based foraging strategy including a flocking mechanism our model is realistic enough to estimate the potential exposure of woodpigeons to pesticides. We discuss how exposure can be linked to our model, and how the model could be used for risk assessment of pesticides, for example predicting exposure and effects in heterogeneous landscapes planted seasonally with a variety of crops, while accounting for differences in land use between landscapes.

An energy budget agent-based model of earthworm populations and its application to study the effects of pesticides

Earthworms are important organisms in soil communities and so are used as model organisms in environmental risk assessments of chemicals. However current risk assessments of soil invertebrates are based on short-term laboratory studies, of limited ecological relevance, supplemented if necessary by site-specific field trials, which sometimes are challenging to apply across the whole agricultural landscape. Here, we investigate whether population responses to environmental stressors and pesticide exposure can be accurately predicted by combining energy budget and agent-based models (ABMs), based on knowledge of how individuals respond to their local circumstances. A simple energy budget model was implemented within each earthworm Eisenia fetida in the ABM, based on a priori parameter estimates. From broadly accepted physiological principles, simple algorithms specify how energy acquisition and expenditure drive life cycle processes. Each individual allocates energy between maintenance, growth and/or reproduction under varying conditions of food density, soil temperature and soil moisture. When simulating published experiments, good model fits were obtained to experimental data on individual growth, reproduction and starvation. Using the energy budget model as a platform we developed methods to identify which of the physiological parameters in the energy budget model (rates of ingestion, maintenance, growth or reproduction) are primarily affected by pesticide applications, producing four hypotheses about how toxicity acts. We tested these hypotheses by comparing model outputs with published toxicity data on the effects of copper oxychloride and chlorpyrifos on E. fetida. Both growth and reproduction were directly affected in experiments in which sufficient food was provided, whilst maintenance was targeted under food limitation. Although we only incorporate toxic effects at the individual level we show how ABMs can readily extrapolate to larger scales by providing good model fits to field population data. The ability of the presented model to fit the available field and laboratory data for E. fetida demonstrates the promise of the agent-based approach in ecology, by showing how biological knowledge can be used to make ecological inferences. Further work is required to extend the approach to populations of more ecologically relevant species studied at the field scale. Such a model could help extrapolate from laboratory to field conditions and from one set of field conditions to another or from species to species.

How the magnetopause transition parameter works

The transition parameter is based on the electron characteristics close to the Earth's dayside magnetopause, but reveals systematic ordering of other, independent, data such as the ion flow, density and temperature and the rientation and strength of the magnetic field. Potentially, therefore, it is a very useful tool for resolving ambiguities in a sequence of satellite data caused by the effects of structure and motion of the boundary; however, its application has been limited because there has been no clear understanding of how it works. We present an analysis of data from the AMPTE-UKS satellite which shows that the transition parameter orders magnetopause data because magnetic reconnection generates newly-opened field lines which coat the boundary: a direct relationship is found with the time elapsed since the boundary-layer field line was opened. A simple model is used to reproduce this behaviour.

Unrestricted Skyrme-tensor time-dependent Hartree-Fock model and its application to the nuclear response from spherical to triaxial nuclei

The nuclear time-dependent Hartree-Fock model formulated in three-dimensional space, based on the full standard Skyrme energy density functional complemented with the tensor force, is presented. Full self-consistency is achieved by the model. The application to the isovector giant dipole resonance is discussed in the linear limit, ranging from spherical nuclei (16O and 120Sn) to systems displaying axial or triaxial deformation (24Mg, 28Si, 178Os, 190W and 238U). Particular attention is paid to the spin-dependent terms from the central sector of the functional, recently included together with the tensor. They turn out to be capable of producing a qualitative change on the strength distribution in this channel. The effect on the deformation properties is also discussed. The quantitative effects on the linear response are small and, overall, the giant dipole energy remains unaffected. Calculations are compared to predictions from the (quasi)-particle random-phase approximation and experimental data where available, finding good agreement

A simple method for integrating a complex model into an ensemble data assimilation system using MPI

This paper details a strategy for modifying the source code of a complex model so that the model may be used in a data assimilation context, {and gives the standards for implementing a data assimilation code to use such a model}. The strategy relies on keeping the model separate from any data assimilation code, and coupling the two through the use of Message Passing Interface (MPI) {functionality}. This strategy limits the changes necessary to the model and as such is rapid to program, at the expense of ultimate performance. The implementation technique is applied in different models with state dimension up to $2.7 \times 10^8$. The overheads added by using this implementation strategy in a coupled ocean-atmosphere climate model are shown to be an order of magnitude smaller than the addition of correlated stochastic random errors necessary for some nonlinear data assimilation techniques.

Sensitivity of a coupled climate model to canopy interception capacity

The canopy interception capacity is a small but key part of the surface hydrology, which affects the amount of water intercepted by vegetation and therefore the partitioning of evaporation and transpiration. However, little research with climate models has been done to understand the effects of a range of possible canopy interception capacity parameter values. This is in part due to the assumption that it does not significantly affect climate. Near global evapotranspiration products now make evaluation of canopy interception capacity parameterisations possible. We use a range of canopy water interception capacity values from the literature to investigate the effect on climate within the climate model HadCM3. We find that the global mean temperature is affected by up to -0.64 K globally and -1.9 K regionally. These temperature impacts are predominantly due to changes in the evaporative fraction and top of atmosphere albedo. In the tropics, the variations in evapotranspiration affect precipitation, significantly enhancing rainfall. Comparing the model output to measurements, we find that the default canopy interception capacity parameterisation overestimates canopy interception loss (i.e. canopy evaporation) and underestimates transpiration. Overall, decreasing canopy interception capacity improves the evapotranspiration partitioning in HadCM3, though the measurement literature more strongly supports an increase. The high sensitivity of climate to the parameterisation of canopy interception capacity is partially due to the high number of light rain-days in the climate model that means that interception is overestimated. This work highlights the hitherto underestimated importance of canopy interception capacity in climate model hydroclimatology and the need to acknowledge the role of precipitation representation limitations in determining parameterisations.

Estimation of Gaussian process regression model using probability distance measures

A new class of parameter estimation algorithms is introduced for Gaussian process regression (GPR) models. It is shown that the integration of the GPR model with probability distance measures of (i) the integrated square error and (ii) Kullback–Leibler (K–L) divergence are analytically tractable. An efficient coordinate descent algorithm is proposed to iteratively estimate the kernel width using golden section search which includes a fast gradient descent algorithm as an inner loop to estimate the noise variance. Numerical examples are included to demonstrate the effectiveness of the new identification approaches.

Tensor regression based on linked multiway parameter analysis

Classical regression methods take vectors as covariates and estimate the corresponding vectors of regression parameters. When addressing regression problems on covariates of more complex form such as multi-dimensional arrays (i.e. tensors), traditional computational models can be severely compromised by ultrahigh dimensionality as well as complex structure. By exploiting the special structure of tensor covariates, the tensor regression model provides a promising solution to reduce the model’s dimensionality to a manageable level, thus leading to efficient estimation. Most of the existing tensor-based methods independently estimate each individual regression problem based on tensor decomposition which allows the simultaneous projections of an input tensor to more than one direction along each mode. As a matter of fact, multi-dimensional data are collected under the same or very similar conditions, so that data share some common latent components but can also have their own independent parameters for each regression task. Therefore, it is beneficial to analyse regression parameters among all the regressions in a linked way. In this paper, we propose a tensor regression model based on Tucker Decomposition, which identifies not only the common components of parameters across all the regression tasks, but also independent factors contributing to each particular regression task simultaneously. Under this paradigm, the number of independent parameters along each mode is constrained by a sparsity-preserving regulariser. Linked multiway parameter analysis and sparsity modeling further reduce the total number of parameters, with lower memory cost than their tensor-based counterparts. The effectiveness of the new method is demonstrated on real data sets.

A model analysis of climate and CO2 controls on tree growth in a semi-arid woodland

We used a light-use efficiency model of photosynthesis coupled with a dynamic carbon allocation and tree-growth model to simulate annual growth of the gymnosperm Callitris columellaris in the semi-arid Great Western Woodlands, Western Australia, over the past 100 years. Parameter values were derived from independent observations except for sapwood specific respiration rate, fine-root turnover time, fine-root specific respiration rate and the ratio of fine-root mass to foliage area, which were estimated by Bayesian optimization. The model reproduced the general pattern of interannual variability in radial growth (tree-ring width), including the response to the shift in precipitation regimes that occurred in the 1960s. Simulated and observed responses to climate were consistent. Both showed a significant positive response of tree-ring width to total photosynthetically active radiation received and to the ratio of modeled actual to equilibrium evapotranspiration, and a significant negative response to vapour pressure deficit. However, the simulations showed an enhancement of radial growth in response to increasing atmospheric CO2 concentration (ppm) ([CO2]) during recent decades that is not present in the observations. The discrepancy disappeared when the model was recalibrated on successive 30-year windows. Then the ratio of fine-root mass to foliage area increases by 14% (from 0.127 to 0.144 kg C m-2) as [CO2] increased while the other three estimated parameters remained constant. The absence of a signal of increasing [CO2] has been noted in many tree-ring records, despite the enhancement of photosynthetic rates and water-use efficiency resulting from increasing [CO2]. Our simulations suggest that this behaviour could be explained as a consequence of a shift towards below-ground carbon allocation.

The potential of flood forecasting using a variable-resolution global Digital Terrain Model and flood extents from Synthetic Aperture Radar images

A basic data requirement of a river flood inundation model is a Digital Terrain Model (DTM) of the reach being studied. The scale at which modeling is required determines the accuracy required of the DTM. For modeling floods in urban areas, a high resolution DTM such as that produced by airborne LiDAR (Light Detection And Ranging) is most useful, and large parts of many developed countries have now been mapped using LiDAR. In remoter areas, it is possible to model flooding on a larger scale using a lower resolution DTM, and in the near future the DTM of choice is likely to be that derived from the TanDEM-X Digital Elevation Model (DEM). A variable-resolution global DTM obtained by combining existing high and low resolution data sets would be useful for modeling flood water dynamics globally, at high resolution wherever possible and at lower resolution over larger rivers in remote areas. A further important data resource used in flood modeling is the flood extent, commonly derived from Synthetic Aperture Radar (SAR) images. Flood extents become more useful if they are intersected with the DTM, when water level observations (WLOs) at the flood boundary can be estimated at various points along the river reach. To illustrate the utility of such a global DTM, two examples of recent research involving WLOs at opposite ends of the spatial scale are discussed. The first requires high resolution spatial data, and involves the assimilation of WLOs from a real sequence of high resolution SAR images into a flood model to update the model state with observations over time, and to estimate river discharge and model parameters, including river bathymetry and friction. The results indicate the feasibility of such an Earth Observation-based flood forecasting system. The second example is at a larger scale, and uses SAR-derived WLOs to improve the lower-resolution TanDEM-X DEM in the area covered by the flood extents. The resulting reduction in random height error is significant.

The inconstancy of the transient climate response parameter under increasing CO₂

In the Coupled Model Intercomparison Project Phase 5 (CMIP5), the model-mean increase in global mean surface air temperature T under the 1pctCO2 scenario (atmospheric CO2 increasing at 1% yr−1) during the second doubling of CO2 is 40% larger than the transient climate response (TCR), i.e. the increase in T during the first doubling. We identify four possible contributory effects. First, the surface climate system loses heat less readily into the ocean beneath as the latter warms. The model spread in the thermal coupling between the upper and deep ocean largely explains the model spread in ocean heat uptake efficiency. Second, CO2 radiative forcing may rise more rapidly than logarithmically with CO2 concentration. Third, the climate feedback parameter may decline as the CO2 concentration rises. With CMIP5 data, we cannot distinguish the second and third possibilities. Fourth, the climate feedback parameter declines as time passes or T rises; in 1pctCO2, this effect is less important than the others. We find that T projected for the end of the twenty-first century correlates more highly with T at the time of quadrupled CO2 in 1pctCO2 than with the TCR, and we suggest that the TCR may be underestimated from observed climate change.

Collusion in a Bertrand duopoly model with decreasing returns and product differentiation

We study cartel stability in a differentiated price-setting duopoly with returns to scale. We show that a cartel may be equally stable in the presence of lower differentiation, provided that the decreasing returns parameter is high. In addition we demonstrate that for a given factor of discount, there are technologies that can have decreasing returns to scale where the cartel always is stable independent of the differentiation degree.