Discrete time representation of continuous time ARMA processes

This paper derives exact discrete time representations for data generated by a continuous time autoregressive moving average (ARMA) system with mixed stock and flow data. The representations for systems comprised entirely of stocks or of flows are also given. In each case the discrete time representations are shown to be of ARMA form, the orders depending on those of the continuous time system. Three examples and applications are also provided, two of which concern the stationary ARMA(2, 1) model with stock variables (with applications to sunspot data and a short-term interest rate) and one concerning the nonstationary ARMA(2, 1) model with a flow variable (with an application to U.S. nondurable consumers’ expenditure). In all three examples the presence of an MA(1) component in the continuous time system has a dramatic impact on eradicating unaccounted-for serial correlation that is present in the discrete time version of the ARMA(2, 0) specification, even though the form of the discrete time model is ARMA(2, 1) for both models.

Discrete demand side control performance under dynamic building simulation: a heat pump application

This study presents the findings of applying a Discrete Demand Side Control (DDSC) approach to the space heating of two case study buildings. High and low tolerance scenarios are implemented on the space heating controller to assess the impact of DDSC upon buildings with different thermal capacitances, light-weight and heavy-weight construction. Space heating is provided by an electric heat pump powered from a wind turbine, with a back-up electrical network connection in the event of insufficient wind being available when a demand occurs. Findings highlight that thermal comfort is maintained within an acceptable range while the DDSC controller maintains the demand/supply balance. Whilst it is noted that energy demand increases slightly, as this is mostly supplied from the wind turbine, this is of little significance and hence a reduction in operating costs and carbon emissions is still attained.

Assessing bee species richness in two Mediterranean communities: importance of habitat type and sampling techniques

The decline of bees has raised concerns regarding their conservation and the maintenance of ecosystem services they provide to bee-pollinated wild flowers and crops. Although the Mediterranean region is a hotspot for bee species richness, their status remains poorly studied. There is an urgent need for cost-effective, reliable, and unbiased sampling methods that give good bee species richness estimates. This study aims: (a) to assess bee species richness in two common Mediterranean habitat types: semi-natural scrub (phrygana) and managed olive groves; (b) to compare species richness in those systems to that of other biogeographic regions, and (c) to assess whether six different sampling methods (pan traps, variable and standardized transect walks, observation plots and trap nests), previously tested in other European biogeographic regions, are suitable in Mediterranean communities. Eight study sites, four per habitat type, were selected on the island of Lesvos, Greece. The species richness observed was high compared to other habitat types worldwide for which comparable data exist. Pan traps collected the highest proportion of the total bee species richness across all methods at the scale of a study site. Variable and standardized transect walks detected the highest total richness over all eight study sites. Trap nests and observation plots detected only a limited fraction of the bee species richness. To assess the total bee species richness in bee diversity hotspots, such as the studied habitats, we suggest a combination of transect walks conducted by trained bee collectors and pan trap sampling

Relevance of sampling schemes in light of Ruelle's linear response theory

We reconsider the theory of the linear response of non-equilibrium steady states to perturbations. We �rst show that by using a general functional decomposition for space-time dependent forcings, we can de�ne elementary susceptibilities that allow to construct the response of the system to general perturbations. Starting from the de�nition of SRB measure, we then study the consequence of taking di�erent sampling schemes for analysing the response of the system. We show that only a speci�c choice of the time horizon for evaluating the response of the system to a general time-dependent perturbation allows to obtain the formula �rst presented by Ruelle. We also discuss the special case of periodic perturbations, showing that when they are taken into consideration the sampling can be �ne-tuned to make the de�nition of the correct time horizon immaterial. Finally, we discuss the implications of our results in terms of strategies for analyzing the outputs of numerical experiments by providing a critical review of a formula proposed by Reick.

Gaussian quadrature 4D-VAR

A new incremental four-dimensional variational (4D-Var) data assimilation algorithm is introduced. The algorithm does not require the computationally expensive integrations with the nonlinear model in the outer loops. Nonlinearity is accounted for by modifying the linearization trajectory of the observation operator based on integrations with the tangent linear (TL) model. This allows us to update the linearization trajectory of the observation operator in the inner loops at negligible computational cost. As a result the distinction between inner and outer loops is no longer necessary. The key idea on which the proposed 4D-Var method is based is that by using Gaussian quadrature it is possible to get an exact correspondence between the nonlinear time evolution of perturbations and the time evolution in the TL model. It is shown that J-point Gaussian quadrature can be used to derive the exact adjoint-based observation impact equations and furthermore that it is straightforward to account for the effect of multiple outer loops in these equations if the proposed 4D-Var method is used. The method is illustrated using a three-level quasi-geostrophic model and the Lorenz (1996) model.

Measures of observation impact in non-Gaussian data assimilation

ABSTRACT Non-Gaussian/non-linear data assimilation is becoming an increasingly important area of research in the Geosciences as the resolution and non-linearity of models are increased and more and more non-linear observation operators are being used. In this study, we look at the effect of relaxing the assumption of a Gaussian prior on the impact of observations within the data assimilation system. Three different measures of observation impact are studied: the sensitivity of the posterior mean to the observations, mutual information and relative entropy. The sensitivity of the posterior mean is derived analytically when the prior is modelled by a simplified Gaussian mixture and the observation errors are Gaussian. It is found that the sensitivity is a strong function of the value of the observation and proportional to the posterior variance. Similarly, relative entropy is found to be a strong function of the value of the observation. However, the errors in estimating these two measures using a Gaussian approximation to the prior can differ significantly. This hampers conclusions about the effect of the non-Gaussian prior on observation impact. Mutual information does not depend on the value of the observation and is seen to be close to its Gaussian approximation. These findings are illustrated with the particle filter applied to the Lorenz ’63 system. This article is concluded with a discussion of the appropriateness of these measures of observation impact for different situations.

A study on orthogonality sampling.

The goal of this paper is to study and further develop the orthogonality sampling or stationary waves algorithm for the detection of the location and shape of objects from the far field pattern of scattered waves in electromagnetics or acoustics. Orthogonality sampling can be seen as a special beam forming algorithm with some links to the point source method and to the linear sampling method. The basic idea of orthogonality sampling is to sample the space under consideration by calculating scalar products of the measured far field pattern , with a test function for all y in a subset Q of the space , m = 2, 3. The way in which this is carried out is important to extract the information which the scattered fields contain. The theoretical foundation of orthogonality sampling is only partly resolved, and the goal of this work is to initiate further research by numerical demonstration of the high potential of the approach. We implement the method for a two-dimensional setting for the Helmholtz equation, which represents electromagnetic scattering when the setup is independent of the third coordinate. We show reconstructions of the location and shape of objects from measurements of the scattered field for one or several directions of incidence and one or many frequencies or wave numbers, respectively. In particular, we visualize the indicator function both with the Dirichlet and Neumann boundary condition and for complicated inhomogeneous media.

A Gaussian-mixture ensemble transform filter

We generalize the popular ensemble Kalman filter to an ensemble transform filter, in which the prior distribution can take the form of a Gaussian mixture or a Gaussian kernel density estimator. The design of the filter is based on a continuous formulation of the Bayesian filter analysis step. We call the new filter algorithm the ensemble Gaussian-mixture filter (EGMF). The EGMF is implemented for three simple test problems (Brownian dynamics in one dimension, Langevin dynamics in two dimensions and the three-dimensional Lorenz-63 model). It is demonstrated that the EGMF is capable of tracking systems with non-Gaussian uni- and multimodal ensemble distributions. Copyright © 2011 Royal Meteorological Society

A nonparametric ensemble transform method for Bayesian inference

Many applications, such as intermittent data assimilation, lead to a recursive application of Bayesian inference within a Monte Carlo context. Popular data assimilation algorithms include sequential Monte Carlo methods and ensemble Kalman filters (EnKFs). These methods differ in the way Bayesian inference is implemented. Sequential Monte Carlo methods rely on importance sampling combined with a resampling step, while EnKFs utilize a linear transformation of Monte Carlo samples based on the classic Kalman filter. While EnKFs have proven to be quite robust even for small ensemble sizes, they are not consistent since their derivation relies on a linear regression ansatz. In this paper, we propose another transform method, which does not rely on any a priori assumptions on the underlying prior and posterior distributions. The new method is based on solving an optimal transportation problem for discrete random variables. © 2013, Society for Industrial and Applied Mathematics

A refined sampling strategy for intra-tooth stable isotope analysis of mammalian enamel

Serial sampling and stable isotope analysis performed along the growth axis of vertebrate tooth enamel records differences attributed to seasonal variation in diet, climate or animal movement. Because several months are required to obtain mature enamel in large mammals, modifications in the isotopic composition of environmental parameters are not instantaneously recorded, and stable isotope analysis of tooth enamel returns a time-averaged signal attenuated in its amplitude relative to the input signal. For convenience, stable isotope profiles are usually determined on the side of the tooth where enamel is thickest. Here we investigate the possibility of improving the time resolution by targeting the side of the tooth where enamel is thinnest. Observation of developing third molars (M3) in sheep shows that the tooth growth rate is not constant but decreases exponentially, while the angle between the first layer of enamel deposited and the enamel–dentine junction increases as a tooth approaches its maximal length. We also noted differences in thickness and geometry of enamel growth between the mesial side (i.e., the side facing the M2) and the buccal side (i.e., the side facing the cheek) of the M3. Carbon and oxygen isotope variations were measured along the M3 teeth from eight sheep raised under controlled conditions. Intra-tooth variability was systematically larger along the mesial side and the difference in amplitude between the two sides was proportional to the time of exposure to the input signal. Although attenuated, the mesial side records variations in the environmental signal more faithfully than the buccal side. This approach can be adapted to other mammals whose teeth show lateral variation in enamel thickness and could potentially be used as an internal check for diagenesis.

Rheology of discrete failure regimes of anisotropic sea ice

A rheological model of sea ice is presented that incorporates the orientational distribution of ice thickness in leads embedded in isotropic floe ice. Sea ice internal stress is determined by coulombic, ridging and tensile failure at orientations where corresponding failure criteria are satisfied at minimum stresses. Because sea ice traction increases in thinner leads and cohesion is finite, such failure line angles are determined by the orientational distribution of sea ice thickness relative to the imposed stresses. In contrast to the isotropic case, sea ice thickness anisotropy results in these failure lines becoming dependent on the stress magnitude. Although generally a given failure criteria type can be satisfied at many directions, only two at most are considered. The strain rate is determined by shearing along slip lines accompanied by dilatancy and closing or opening across orientations affected by ridging or tensile failure. The rheology is illustrated by a yield curve determined by combining coulombic and ridging failure for the case of two pairs of isotropically formed leads of different thicknesses rotated with regard to each other, which models two events of coulombic failure followed by dilatancy and refreezing. The yield curve consists of linear segments describing coulombic and ridging yield as failure switches from one lead to another as the stress grows. Because sliding along slip lines is accompanied by dilatancy, at typical Arctic sea ice deformation rates a one-day-long deformation event produces enough open water that these freshly formed slip lines are preferential places of ridging failure.

Using attribute importance rankings within discrete choice experiments: an application to valuing bread attributes

We present a new Bayesian econometric specification for a hypothetical Discrete Choice Experiment (DCE) incorporating respondent ranking information about attribute importance. Our results indicate that a DCE debriefing question that asks respondents to rank the importance of attributes helps to explain the resulting choices. We also examine how mode of survey delivery (online and mail) impacts model performance, finding that results are not substantively a§ected by the mode of survey delivery. We conclude that the ranking data is a complementary source of information about respondent utility functions within hypothetical DCEs

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.