Aspects of particle filtering in high-dimensional spaces

Nonlinear data assimilation is high on the agenda in all fields of the geosciences as with ever increasing model resolution and inclusion of more physical (biological etc.) processes, and more complex observation operators the data-assimilation problem becomes more and more nonlinear. The suitability of particle filters to solve the nonlinear data assimilation problem in high-dimensional geophysical problems will be discussed. Several existing and new schemes will be presented and it is shown that at least one of them, the Equivalent-Weights Particle Filter, does indeed beat the curse of dimensionality and provides a way forward to solve the problem of nonlinear data assimilation in high-dimensional systems.

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.

Bioclimatic envelope model of climate change impacts on blanket peatland distribution in Great Britain

Blanket peatlands are rain-fed mires that cover the landscape almost regardless of topography. The geographical extent of this type of peatland is highly sensitive to climate. We applied a global process-based bioclimatic envelope model, PeatStash, to predict the distribution of British blanket peatlands. The model captures the present areal extent (Kappa = 0.77) and is highly sensitive to both temperature and precipitation changes. When the model is run using the UKCIP02 climate projections for the time periods 2011–2040, 2041–2070 and 2071–2100, the geographical distribution of blanket peatlands gradually retreats towards the north and the west. In the UKCIP02 high emissions scenario for 2071–2100, the blanket peatland bioclimatic space is ~84% smaller than contemporary conditions (1961–1990); only parts of the west of Scotland remain inside this space. Increasing summer temperature is the main driver of the projected changes in areal extent. Simulations using 7 climate model outputs resulted in generally similar patterns of declining aereal extent of the bioclimatic space, although differing in degree. The results presented in this study should be viewed as a first step towards understanding the trends likely to affect the blanket peatland distribution in Great Britain. The eventual fate of existing blanket peatlands left outside their bioclimatic space remains uncertain.

Problems in four-dimensional data assimilation

With the introduction of new observing systems based on asynoptic observations, the analysis problem has changed in character. In the near future we may expect that a considerable part of meteorological observations will be unevenly distributed in four dimensions, i.e. three dimensions in space and one in time. The term analysis, or objective analysis in meteorology, means the process of interpolating observed meteorological observations from unevenly distributed locations to a network of regularly spaced grid points. Necessitated by the requirement of numerical weather prediction models to solve the governing finite difference equations on such a grid lattice, the objective analysis is a three-dimensional (or mostly two-dimensional) interpolation technique. As a consequence of the structure of the conventional synoptic network with separated data-sparse and data-dense areas, four-dimensional analysis has in fact been intensively used for many years. Weather services have thus based their analysis not only on synoptic data at the time of the analysis and climatology, but also on the fields predicted from the previous observation hour and valid at the time of the analysis. The inclusion of the time dimension in objective analysis will be called four-dimensional data assimilation. From one point of view it seems possible to apply the conventional technique on the new data sources by simply reducing the time interval in the analysis-forecasting cycle. This could in fact be justified also for the conventional observations. We have a fairly good coverage of surface observations 8 times a day and several upper air stations are making radiosonde and radiowind observations 4 times a day. If we have a 3-hour step in the analysis-forecasting cycle instead of 12 hours, which is applied most often, we may without any difficulties treat all observations as synoptic. No observation would thus be more than 90 minutes off time and the observations even during strong transient motion would fall within a horizontal mesh of 500 km * 500 km.

Flight periodicity and the vertical distribution of high-altitude moth migration over southern Britain

The continuous operation of insect-monitoring radars in the UK has permitted, for the first time, the characterization of various phenomena associated with high-altitude migration of large insects over this part of northern Europe. Previous studies have taken a case-study approach, concentrating on a small number of nights of particular interest. Here, combining data from two radars, and from an extensive suction- and light-trapping network, we have undertaken a more systematic, longer-term study of diel flight periodicity and vertical distribution of macro-insects in the atmosphere. Firstly, we identify general features of insect abundance and stratification, occurring during the 24-hour cycle, which emerge from four years’ aggregated radar data for the summer months in southern Britain. These features include mass emigrations at dusk and to a lesser extent at dawn, and daytime concentrations associated with thermal convection. We then focus our attention on the well-defined layers of large nocturnal migrants that form in the early evening, usually at heights of 200–500 m above ground. We present evidence from both radar and trap data that these nocturnal layers are composed mainly of noctuid moths, with species such as Noctua pronuba, Autographa gamma, Agrotis exclamationis, A. segetum, Xestia c-nigrum and Phlogophora meticulosa predominating.

Molecular tools to investigate Rhizoctonia solani distribution in soil

Real-time PCR protocols were developed to detect and discriminate 11 anastomosis groups (AGs) of Rhizoctonia solani using ribosomal internal transcribed spacer (ITS) regions (AG-1-IA, AG-1-IC, AG-2-1, AG-2-2, AG-4HGI+II, AG-4HGIII, AG-8) or beta-tubulin (AG-3, AG-4HGII, AG-5 and AG-9) sequences. All real-time assays were target group specific, except AG-2-2, which showed a weak cross-reaction with AG-2tabac. In addition, methods were developed for the high throughput extraction of DNA from soil and compost samples. The DNA extraction method was used with the AG-2-1 assay and shown to be quantitative with a detection threshold of 10-7 g of R. solani per g of soil. A similar DNA extraction efficiency was observed for samples from three contrasting soil types. The developed methods were then used to investigate the spatial distribution of R. solani AG-2-1 in field soils. Soil from shallow depths of a field planted with Brassica oleracea tested positive for R. solani AG-2-1 more frequently than soil collected from greater depths. Quantification of R. solani inoculum in field samples proved challenging due to low levels of inoculum in naturally occurring soils. The potential uses of real-time PCR and DNA extraction protocols to investigate the epidemiology of R. solani are discussed.

Microblock ionomers: a new concept in high temperature, swelling-resistant membranes for PEM fuel cells

A novel series of polyaromatic ionomers with similar equivalent weights but very different sulphonic acid distributions along the ionomer backbone has been designed and prepared. By synthetically organising the sequence-distribution so that it consists of fully defined ionic segments (containing singlets, doublets or quadruplets of sulphonic acid groups) alternating strictly with equally well-defined nonionic spacer segments, a new class of polymers which may be described as microblock ionomers has been developed. These materials exhibit very different properties and morphologies from analogous randomly substituted systems. Progressively extending the nonionic spacer length in the repeat unit (maintaining a constant equivalent weight by increasing the degree of sulphonation. of the ionic segment) leads to an increasing degree of nanophase separation between hydrophilic and hydrophobic domains in these materials. Membranes cast from ionomers with the more highly phase-separated morphologies show significantly higher onset temperatures for uncontrolled swelling in water. This new type of ionomer design has enabled the fabrication of swelling-resistant hydrocarbon membranes, suitable for fuel cell operation, with very much higher ion exchange capacities (>2 meq g(-1)) than those previously reported in the literature. When tested in a fuel cell at high temperature (120 degrees C) and low relative humidity (35% RH), the best microblock membrane matched the performance of Nafion 112. Moreover, comparative low load cycle testing of membrane -electrode assemblies suggests that the durability of the new membranes under conditions of high temperature and low relative humidity is superior to that of conventional perfluorinated materials.

Space partitioning for scalable K-means

K-Means is a popular clustering algorithm which adopts an iterative refinement procedure to determine data partitions and to compute their associated centres of mass, called centroids. The straightforward implementation of the algorithm is often referred to as `brute force' since it computes a proximity measure from each data point to each centroid at every iteration of the K-Means process. Efficient implementations of the K-Means algorithm have been predominantly based on multi-dimensional binary search trees (KD-Trees). A combination of an efficient data structure and geometrical constraints allow to reduce the number of distance computations required at each iteration. In this work we present a general space partitioning approach for improving the efficiency and the scalability of the K-Means algorithm. We propose to adopt approximate hierarchical clustering methods to generate binary space partitioning trees in contrast to KD-Trees. In the experimental analysis, we have tested the performance of the proposed Binary Space Partitioning K-Means (BSP-KM) when a divisive clustering algorithm is used. We have carried out extensive experimental tests to compare the proposed approach to the one based on KD-Trees (KD-KM) in a wide range of the parameters space. BSP-KM is more scalable than KDKM, while keeping the deterministic nature of the `brute force' algorithm. In particular, the proposed space partitioning approach has shown to overcome the well-known limitation of KD-Trees in high-dimensional spaces and can also be adopted to improve the efficiency of other algorithms in which KD-Trees have been used.

A method for merging flow-dependent forecast error statistics from an ensemble with static statistics for use in high resolution variational data assimilation

The background error covariance matrix, B, is often used in variational data assimilation for numerical weather prediction as a static and hence poor approximation to the fully dynamic forecast error covariance matrix, Pf. In this paper the concept of an Ensemble Reduced Rank Kalman Filter (EnRRKF) is outlined. In the EnRRKF the forecast error statistics in a subspace defined by an ensemble of states forecast by the dynamic model are found. These statistics are merged in a formal way with the static statistics, which apply in the remainder of the space. The combined statistics may then be used in a variational data assimilation setting. It is hoped that the nonlinear error growth of small-scale weather systems will be accurately captured by the EnRRKF, to produce accurate analyses and ultimately improved forecasts of extreme events.

Stirring and mixing in two-dimensional divergent flow

While stirring and mixing properties in the stratosphere are reasonably well understood in the context of balanced (slow) dynamics, as is evidenced in numerous studies of chaotic advection, the strongly enhanced presence of high-frequency gravity waves in the mesosphere gives rise to a significant unbalanced (fast) component to the flow. The present investigation analyses result from two idealized shallow-water numerical simulations representative of stratospheric and mesospheric dynamics on a quasi-horizontal isentropic surface. A generalization of the Hua–Klein Eulerian diagnostic to divergent flow reveals that velocity gradients are strongly influenced by the unbalanced component of the flow. The Lagrangian diagnostic of patchiness nevertheless demonstrates the persistence of coherent features in the zonal component of the flow, in contrast to the destruction of coherent features in the meridional component. Single-particle statistics demonstrate t2 scaling for both the stratospheric and mesospheric regimes in the case of zonal dispersion, and distinctive scaling laws for the two regimes in the case of meridional dispersion. This is in contrast to two-particle statistics, which in the mesospheric (unbalanced) regime demonstrate a more rapid approach to Richardson’s t3 law in the case of zonal dispersion and is evidence of enhanced meridional dispersion.

Spectral nonlocality, absolute equilibria and Kraichnan-Leith-Batchelor phenomenology in two-dimensional turbulent energy cascades

We study the degree to which Kraichnan–Leith–Batchelor (KLB) phenomenology describes two-dimensional energy cascades in α turbulence, governed by ∂θ/∂t+J(ψ,θ)=ν∇2θ+f, where θ=(−Δ)α/2ψ is generalized vorticity, and ψ^(k)=k−αθ^(k) in Fourier space. These models differ in spectral non-locality, and include surface quasigeostrophic flow (α=1), regular two-dimensional flow (α=2) and rotating shallow flow (α=3), which is the isotropic limit of a mantle convection model. We re-examine arguments for dual inverse energy and direct enstrophy cascades, including Fjørtoft analysis, which we extend to general α, and point out their limitations. Using an α-dependent eddy-damped quasinormal Markovian (EDQNM) closure, we seek self-similar inertial range solutions and study their characteristics. Our present focus is not on coherent structures, which the EDQNM filters out, but on any self-similar and approximately Gaussian turbulent component that may exist in the flow and be described by KLB phenomenology. For this, the EDQNM is an appropriate tool. Non-local triads contribute increasingly to the energy flux as α increases. More importantly, the energy cascade is downscale in the self-similar inertial range for 2.5<α<10. At α=2.5 and α=10, the KLB spectra correspond, respectively, to enstrophy and energy equipartition, and the triad energy transfers and flux vanish identically. Eddy turnover time and strain rate arguments suggest the inverse energy cascade should obey KLB phenomenology and be self-similar for α<4. However, downscale energy flux in the EDQNM self-similar inertial range for α>2.5 leads us to predict that any inverse cascade for α≥2.5 will not exhibit KLB phenomenology, and specifically the KLB energy spectrum. Numerical simulations confirm this: the inverse cascade energy spectrum for α≥2.5 is significantly steeper than the KLB prediction, while for α<2.5 we obtain the KLB spectrum.

Spatial patterns of gluten protein and polymer distribution in wheat grain

The starchy endosperm is the major storage tissue in the mature wheat grain and exhibits quantitative and qualitative gradients in composition, with the outermost cell layers being rich in protein, mainly gliadins, and the inner cells being low in protein but enriched in high-molecular-weight (HMW) subunits of glutenin. We have used sequential pearling to produce flour fractions enriched in particular cell layers to determine the protein gradients in four different cultivars grown at two nitrogen levels. The results show that the steepness of the protein gradient is determined by both genetic and nutritional factors, with three high-protein breadmaking cultivars being more responsive to the N treatment than a low-protein cultivar suitable for livestock feed. Nitrogen also affected the relative abundances of the three main classes of wheat prolamins: the sulfur-poor ω-gliadins showed the greatest response to nitrogen and increased evenly across the grain; the HMW subunits also increased in response to nitrogen but proportionally more in the outer layers of the starchy endosperm than near the core, while the sulfur-rich prolamins showed the opposite trend.

High-resolution (space, time) anthropogenic heat emissions: London 1970-2025

The anthropogenic heat emissions generated by human activities in London are analysed in detail for 2005–2008 and considered in context of long-term past and future trends (1970–2025). Emissions from buildings, road traffic and human metabolism are finely resolved in space (30 min) and time (200 × 200 m2). Software to compute and visualize the results is provided. The annual mean anthropogenic heat flux for Greater London is 10.9 W m−2 for 2005–2008, with the highest peaks in the central activities zone (CAZ) associated with extensive service industry activities. Towards the outskirts of the city, emissions from the domestic sector and road traffic dominate. Anthropogenic heat is mostly emitted as sensible heat, with a latent heat fraction of 7.3% and a heat-to-wastewater fraction of 12%; the implications related to the use of evaporative cooling towers are briefly addressed. Projections indicate a further increase of heat emissions within the CAZ in the next two decades related to further intensification of activities within this area.