Nonlinear error dynamics for cycled data assimilation methods

We investigate the error dynamics for cycled data assimilation systems, such that the inverse problem of state determination is solved at tk, k = 1, 2, 3, ..., with a first guess given by the state propagated via a dynamical system model from time tk − 1 to time tk. In particular, for nonlinear dynamical systems that are Lipschitz continuous with respect to their initial states, we provide deterministic estimates for the development of the error ||ek|| := ||x(a)k − x(t)k|| between the estimated state x(a) and the true state x(t) over time. Clearly, observation error of size δ > 0 leads to an estimation error in every assimilation step. These errors can accumulate, if they are not (a) controlled in the reconstruction and (b) damped by the dynamical system under consideration. A data assimilation method is called stable, if the error in the estimate is bounded in time by some constant C. The key task of this work is to provide estimates for the error ||ek||, depending on the size δ of the observation error, the reconstruction operator Rα, the observation operator H and the Lipschitz constants K(1) and K(2) on the lower and higher modes of controlling the damping behaviour of the dynamics. We show that systems can be stabilized by choosing α sufficiently small, but the bound C will then depend on the data error δ in the form c||Rα||δ with some constant c. Since ||Rα|| → ∞ for α → 0, the constant might be large. Numerical examples for this behaviour in the nonlinear case are provided using a (low-dimensional) Lorenz '63 system.

Sparse shape representation using the Laplace-Beltrami eigenfunctions and its application to modeling subcortical structures

We present a new sparse shape modeling framework on the Laplace-Beltrami (LB) eigenfunctions. Traditionally, the LB-eigenfunctions are used as a basis for intrinsically representing surface shapes by forming a Fourier series expansion. To reduce high frequency noise, only the first few terms are used in the expansion and higher frequency terms are simply thrown away. However, some lower frequency terms may not necessarily contribute significantly in reconstructing the surfaces. Motivated by this idea, we propose to filter out only the significant eigenfunctions by imposing l1-penalty. The new sparse framework can further avoid additional surface-based smoothing often used in the field. The proposed approach is applied in investigating the influence of age (38-79 years) and gender on amygdala and hippocampus shapes in the normal population. In addition, we show how the emotional response is related to the anatomy of the subcortical structures.

Gut bacteria-host metabolic interplay during conventionalisation of the mouse germfree colon

The interplay between dietary nutrients, gut microbiota and mammalian host tissues of the gastrointestinal tract is recognised as highly relevant for host health. Combined transcriptome, metabonome and microbial profiling tools were employed to analyse the dynamic responses of germfree mouse colonic mucosa to colonisation by normal mouse microbiota (conventionalisation) at different time-points during 16 days. The colonising microbiota showed a shift from early (days 1 and 2) to later colonisers (days 8 and 16). The dynamic changes in the microbial community were rapidly reflected by the urine metabolic profiles (day 1) and at later stages (day 4 onward) by the colon mucosa transcriptome and metabolic profiles. Correlations of host transcriptomes, metabolite patterns and microbiota composition revealed associations between Bacilli and Proteobacteria, and differential expression of host genes involved in energy and anabolic metabolism. Differential gene expression correlated with scyllo- and myo-inositol, glutamine, glycine and alanine levels in colonic tissues during the time span of conventionalisation. Our combined time-resolved analyses may help to expand the understanding of host-microbe molecular interactions during the microbial establishment.

Decadal climate prediction: an update from the trenches

This paper provides an update on research in the relatively new and fast-moving field of decadal climate prediction, and addresses the use of decadal climate predictions not only for potential users of such information but also for improving our understanding of processes in the climate system. External forcing influences the predictions throughout, but their contributions to predictive skill become dominant after most of the improved skill from initialization with observations vanishes after about six to nine years. Recent multi-model results suggest that there is relatively more decadal predictive skill in the North Atlantic, western Pacific, and Indian Oceans than in other regions of the world oceans. Aspects of decadal variability of SSTs, like the mid-1970s shift in the Pacific, the mid-1990s shift in the northern North Atlantic and western Pacific, and the early-2000s hiatus, are better represented in initialized hindcasts compared to uninitialized simulations. There is evidence of higher skill in initialized multi-model ensemble decadal hindcasts than in single model results, with multi-model initialized predictions for near term climate showing somewhat less global warming than uninitialized simulations. Some decadal hindcasts have shown statistically reliable predictions of surface temperature over various land and ocean regions for lead times of up to 6-9 years, but this needs to be investigated in a wider set of models. As in the early days of El Niño-Southern Oscillation (ENSO) prediction, improvements to models will reduce the need for bias adjustment, and increase the reliability, and thus usefulness, of decadal climate predictions in the future.

Visualizing probabilistic flood forecast information: expert preferences and perceptions of best practice in uncertainty communication

The aim of this article is to improve the communication of the probabilistic flood forecasts generated by hydrological ensemble prediction systems (HEPS) by understanding perceptions of different methods of visualizing probabilistic forecast information. This study focuses on interexpert communication and accounts for differences in visualization requirements based on the information content necessary for individual users. The perceptions of the expert group addressed in this study are important because they are the designers and primary users of existing HEPS. Nevertheless, they have sometimes resisted the release of uncertainty information to the general public because of doubts about whether it can be successfully communicated in ways that would be readily understood to nonexperts. In this article, we explore the strengths and weaknesses of existing HEPS visualization methods and thereby formulate some wider recommendations about the best practice for HEPS visualization and communication. We suggest that specific training on probabilistic forecasting would foster use of probabilistic forecasts with a wider range of applications. The result of a case study exercise showed that there is no overarching agreement between experts on how to display probabilistic forecasts and what they consider the essential information that should accompany plots and diagrams. In this article, we propose a list of minimum properties that, if consistently displayed with probabilistic forecasts, would make the products more easily understandable. Copyright © 2012 John Wiley & Sons, Ltd.

WCCC 2013: the 20th World Computer Chess Championship

The 20th World Computer Chess Championship took place in Yokohama, Japan during August 2013. It was narrowly won by JUNIOR from JONNY with HIARCS, PANDIX, SHREDDER and MERLIN occupying the remaining positions. There are references to the detailed chess biographies of the engines and engine-authors in the Chessprogramming Wiki. The games, occasionally annotated, are available here.

WCSC 2013: the 3rd World Chess Software Championship

The 3rd World Chess Software Championship took place in Yokohama, Japan during August 2013. It pits chess engines against each other on a common hardware platform - in this instance, the Intel i7 2740 Ivy Bridge with 16GB RAM supporting a potential eight processing threads. It was narrowly won by HIARCS from JUNIOR and PANDIX with JONNY, SHREDDER and MERLIN taking the remaining places. Games, occasionally annotated, are available here.

Efficient fully nonlinear data assimilation for geophysical fluid dynamics

A potential problem with Ensemble Kalman Filter is the implicit Gaussian assumption at analysis times. Here we explore the performance of a recently proposed fully nonlinear particle filter on a high-dimensional but simplified ocean model, in which the Gaussian assumption is not made. The model simulates the evolution of the vorticity field in time, described by the barotropic vorticity equation, in a highly nonlinear flow regime. While common knowledge is that particle filters are inefficient and need large numbers of model runs to avoid degeneracy, the newly developed particle filter needs only of the order of 10-100 particles on large scale problems. The crucial new ingredient is that the proposal density cannot only be used to ensure all particles end up in high-probability regions of state space as defined by the observations, but also to ensure that most of the particles have similar weights. Using identical twin experiments we found that the ensemble mean follows the truth reliably, and the difference from the truth is captured by the ensemble spread. A rank histogram is used to show that the truth run is indistinguishable from any of the particles, showing statistical consistency of the method.

Botrytis species: relentless necrotrophic thugs or endophytes gone rogue?

Plant pathology has a long-standing tradition of classifying microbes as pathogens, endophytes or saprophytes. Lifestyles of pathogens are categorized as biotrophic, necrotrophic or hemibiotrophic. Botrytis species are considered by many to be archetypal examples of necrotrophic fungi, with B. cinerea being the most extensively studied species because of its broad host range and economic impact. In this review, we discuss recent work which illustrates that B. cinerea is capable of colonizing plants internally, presumably as an endophyte, without causing any disease or stress symptoms. The extent of the facultative endophytic behaviour of B. cinerea and its relevance in the ecology and disease epidemiology may be vastly underestimated. Moreover, we discuss the recent discovery of a novel Botrytis species, B. deweyae, which normally grows as an endophyte in ornamental daylilies (Hemerocallis), but displays facultative pathogenic behaviour, and is increasingly causing economic damage. We propose that the emergence of endophytes ‘gone rogue’ as novel diseases may be related to increased inbreeding of hybrid lines and reduced genetic diversity. These observations lead us to argue that the sometimes inflexible classification of pathogenic microbes by their lifestyles requires serious reconsideration. There is much more variety to the interactions of Botrytis with its hosts than the eye (or the plant pathologist) can see, and this may be true for other microbes interacting with plants.

Observation impact in data assimilation: the effect of non-Gaussian observation error.

Data assimilation methods which avoid the assumption of Gaussian error statistics are being developed for geoscience applications. We investigate how the relaxation of the Gaussian assumption affects the impact observations have within the assimilation process. The effect of non-Gaussian observation error (described by the likelihood) is compared to previously published work studying the effect of a non-Gaussian prior. The observation impact is measured in three ways: the sensitivity of the analysis to the observations, the mutual information, and the relative entropy. These three measures have all been studied in the case of Gaussian data assimilation and, in this case, have a known analytical form. It is shown that the analysis sensitivity can also be derived analytically when at least one of the prior or likelihood is Gaussian. This derivation shows an interesting asymmetry in the relationship between analysis sensitivity and analysis error covariance when the two different sources of non-Gaussian structure are considered (likelihood vs. prior). This is illustrated for a simple scalar case and used to infer the effect of the non-Gaussian structure on mutual information and relative entropy, which are more natural choices of metric in non-Gaussian data assimilation. It is concluded that approximating non-Gaussian error distributions as Gaussian can give significantly erroneous estimates of observation impact. The degree of the error depends not only on the nature of the non-Gaussian structure, but also on the metric used to measure the observation impact and the source of the non-Gaussian structure.

Adsorption of organic molecules at the TiO2(110) surface: the effect of van der Waals interactions

Understanding the interaction of organic molecules with TiO2 surfaces is important for a wide range of technological applications. While density functional theory (DFT) calculations can provide valuable insight about these interactions, traditional DFT approaches with local exchange-correlation functionals suffer from a poor description of non-bonding van der Waals (vdW) interactions. We examine here the contribution of vdW forces to the interaction of small organic molecules (methane, methanol, formic acid and glycine) with the TiO2 (110) surface, based on DFT calculations with the optB88-vdW functional. The adsorption geometries and energies at different configurations were also obtained in the standard generalized gradient approximation (GGA-PBE) for comparison. We find that the optB88-vdW consistently gives shorter surface adsorbate-to-surface distances and slightly stronger interactions than PBE for the weak (physisorbed) modes of adsorption. In the case of strongly adsorbed (chemisorbed) molecules both functionals give similar results for the adsorption geometries, and also similar values of the relative energies between different chemisorption modes for each molecule. In particular both functionals predict that dissociative adsorption is more favourable than molecular adsorption for methanol, formic acid and glycine, in general agreement with experiment. The dissociation energies obtained from both functionals are also very similar, indicating that vdW interactions do not affect the thermodynamics of surface deprotonation. However, the optB88-vdW always predicts stronger adsorption than PBE. The comparison of the methanol adsorption energies with values obtained from a Redhead analysis of temperature programmed desorption data suggests that optB88-vdW significantly overestimates the adsorption strength, although we warn about the uncertainties involved in such comparisons.

Representation errors and retrievals in linear and nonlinear data assimilation

This article shows how one can formulate the representation problem starting from Bayes’ theorem. The purpose of this article is to raise awareness of the formal solutions,so that approximations can be placed in a proper context. The representation errors appear in the likelihood, and the different possibilities for the representation of reality in model and observations are discussed, including nonlinear representation probability density functions. Specifically, the assumptions needed in the usual procedure to add a representation error covariance to the error covariance of the observations are discussed,and it is shown that, when several sub-grid observations are present, their mean still has a representation error ; socalled ‘superobbing’ does not resolve the issue. Connection is made to the off-line or on-line retrieval problem, providing a new simple proof of the equivalence of assimilating linear retrievals and original observations. Furthermore, it is shown how nonlinear retrievals can be assimilated without loss of information. Finally we discuss how errors in the observation operator model can be treated consistently in the Bayesian framework, connecting to previous work in this area.