The equivalent-weights particle filter in a high-dimensional system

In general, particle filters need large numbers of model runs in order to avoid filter degeneracy in high-dimensional systems. The recently proposed, fully nonlinear equivalent-weights particle filter overcomes this requirement by replacing the standard model transition density with two different proposal transition densities. The first proposal density is used to relax all particles towards the high-probability regions of state space as defined by the observations. The crucial second proposal density is then used to ensure that the majority of particles have equivalent weights at observation time. Here, the performance of the scheme in a high, 65 500 dimensional, simplified ocean model is explored. The success of the equivalent-weights particle filter in matching the true model state is shown using the mean of just 32 particles in twin experiments. It is of particular significance that this remains true even as the number and spatial variability of the observations are changed. The results from rank histograms are less easy to interpret and can be influenced considerably by the parameter values used. This article also explores the sensitivity of the performance of the scheme to the chosen parameter values and the effect of using different model error parameters in the truth compared with the ensemble model runs.

The effect of the equivalent-weights particle filter on dynamical balance in a primitive equation model

The disadvantage of the majority of data assimilation schemes is the assumption that the conditional probability density function of the state of the system given the observations [posterior probability density function (PDF)] is distributed either locally or globally as a Gaussian. The advantage, however, is that through various different mechanisms they ensure initial conditions that are predominantly in linear balance and therefore spurious gravity wave generation is suppressed. The equivalent-weights particle filter is a data assimilation scheme that allows for a representation of a potentially multimodal posterior PDF. It does this via proposal densities that lead to extra terms being added to the model equations and means the advantage of the traditional data assimilation schemes, in generating predominantly balanced initial conditions, is no longer guaranteed. This paper looks in detail at the impact the equivalent-weights particle filter has on dynamical balance and gravity wave generation in a primitive equation model. The primary conclusions are that (i) provided the model error covariance matrix imposes geostrophic balance, then each additional term required by the equivalent-weights particle filter is also geostrophically balanced; (ii) the relaxation term required to ensure the particles are in the locality of the observations has little effect on gravity waves and actually induces a reduction in gravity wave energy if sufficiently large; and (iii) the equivalent-weights term, which leads to the particles having equivalent significance in the posterior PDF, produces a change in gravity wave energy comparable to the stochastic model error. Thus, the scheme does not produce significant spurious gravity wave energy and so has potential for application in real high-dimensional geophysical applications.

Twin experiments with the equivalent weights particle filter and HadCM3

This paper investigates the use of a particle filter for data assimilation with a full scale coupled ocean–atmosphere general circulation model. Synthetic twin experiments are performed to assess the performance of the equivalent weights filter in such a high-dimensional system. Artificial 2-dimensional sea surface temperature fields are used as observational data every day. Results are presented for different values of the free parameters in the method. Measures of the performance of the filter are root mean square errors, trajectories of individual variables in the model and rank histograms. Filter degeneracy is not observed and the performance of the filter is shown to depend on the ability to keep maximum spread in the ensemble.

Compositional control of the electrical transport properties in the new series of thiospinels Ga1-xGexV4S8-delta (0 <=x<=1)

A new series of non-stoichiometric sulfides Ga1−xGexV4S8−δ (0≤x≤1; δ≤0.23) has been synthesized at high temperatures by heating stoichiometric mixtures of the elements in sealed quartz tubes. The samples have been characterized by powder X-ray diffraction, SQUID magnetometry and electrical transport-property measurements. Structural analysis reveals that a solid solution is formed throughout this composition range, whilst thermogravimetric data reveal sulfur deficiency of up to 2.9% in the quaternary phases. Magnetic measurements suggest that the ferromagnetic behavior of the end-member phase GaV4S8 is retained at x≤0.7; samples in this composition range showing a marked increase in magnetization at low temperatures. By contrast Ga0.25Ge0.75V4S8−δ appears to undergo antiferromagnetic ordering at ca. 15 K. All materials with x≠1 are n-type semiconductors whose resistivity falls by almost six orders of magnitude with decreasing Ga content, whilst the end-member phase GeV4S8−δ is a p-type semiconductor. The results demonstrate that the physical properties are determined principally by the degree of electron filling of narrow-band states arising from intracluster V–V interactions.

Structure and electrical transport properties of the ordered skutterudites MGe1.5S1.5 (M = Co, Rh, Ir)

High-resolution powder neutron diffraction data collected for the skutterudites MGe1.5S1.5 (M=Co, Rh, Ir) reveal that these materials adopt an ordered skutterudite structure (space group R3¯), in which the anions are ordered in layers perpendicular to the [111] direction. In this ordered structure, the anions form two-crystallographically distinct four-membered rings, with stoichiometry Ge2S2, in which the Ge and S atoms are trans to each other. The transport properties of these materials, which are p-type semiconductors, are discussed in the light of the structural results. The effect of iron substitution in CoGe1.5S1.5 has been investigated. While doping of CoGe1.5S1.5 has a marked effect on both the electrical resistivity and the Seebeck coefficient, these ternary skutterudites exhibit significantly higher electrical resistivities than their binary counterparts.

Time-lapse geophysical investigations over known archaeological features using electrical resistivity imaging and earth resistance

Electrical methods of geophysical survey are known to produce results that are hard to predict at different times of the year, and under differing weather conditions. This is a problem which can lead to misinterpretation of archaeological features under investigation. The dynamic relationship between a ‘natural’ soil matrix and an archaeological feature is a complex one, which greatly affects the success of the feature’s detection when using active electrical methods of geophysical survey. This study has monitored the gradual variation of measured resistivity over a selection of study areas. By targeting difficult to find, and often ‘missing’ electrical anomalies of known archaeological features, this study has increased the understanding of both the detection and interpretation capabilities of such geophysical surveys. A 16 month time-lapse study over 4 archaeological features has taken place to investigate the aforementioned detection problem across different soils and environments. In addition to the commonly used Twin-Probe earth resistance survey, electrical resistivity imaging (ERI) and quadrature electro-magnetic induction (EMI) were also utilised to explore the problem. Statistical analyses have provided a novel interpretation, which has yielded new insights into how the detection of archaeological features is influenced by the relationship between the target feature and the surrounding ‘natural’ soils. The study has highlighted both the complexity and previous misconceptions around the predictability of the electrical methods. The analysis has confirmed that each site provides an individual and nuanced situation, the variation clearly relating to the composition of the soils (particularly pore size) and the local weather history. The wide range of reasons behind survey success at each specific study site has been revealed. The outcomes have shown that a simplistic model of seasonality is not universally applicable to the electrical detection of archaeological features. This has led to the development of a method for quantifying survey success, enabling a deeper understanding of the unique way in which each site is affected by the interaction of local environmental and geological conditions.