An iterative contractive framework for probe methods: LASSO

We present a new iterative approach called Line Adaptation for the Singular Sources Objective (LASSO) to object or shape reconstruction based on the singular sources method (or probe method) for the reconstruction of scatterers from the far-field pattern of scattered acoustic or electromagnetic waves. The scheme is based on the construction of an indicator function given by the scattered field for incident point sources in its source point from the given far-field patterns for plane waves. The indicator function is then used to drive the contraction of a surface which surrounds the unknown scatterers. A stopping criterion for those parts of the surfaces that touch the unknown scatterers is formulated. A splitting approach for the contracting surfaces is formulated, such that scatterers consisting of several separate components can be reconstructed. Convergence of the scheme is shown, and its feasibility is demonstrated using a numerical study with several examples.

Rank histograms of stratified Monte-Carlo ensembles

The application of forecast ensembles to probabilistic weather prediction has spurred considerable interest in their evaluation. Such ensembles are commonly interpreted as Monte Carlo ensembles meaning that the ensemble members are perceived as random draws from a distribution. Under this interpretation, a reasonable property to ask for is statistical consistency, which demands that the ensemble members and the verification behave like draws from the same distribution. A widely used technique to assess statistical consistency of a historical dataset is the rank histogram, which uses as a criterion the number of times that the verification falls between pairs of members of the ordered ensemble. Ensemble evaluation is rendered more specific by stratification, which means that ensembles that satisfy a certain condition (e.g., a certain meteorological regime) are evaluated separately. Fundamental relationships between Monte Carlo ensembles, their rank histograms, and random sampling from the probability simplex according to the Dirichlet distribution are pointed out. Furthermore, the possible benefits and complications of ensemble stratification are discussed. The main conclusion is that a stratified Monte Carlo ensemble might appear inconsistent with the verification even though the original (unstratified) ensemble is consistent. The apparent inconsistency is merely a result of stratification. Stratified rank histograms are thus not necessarily flat. This result is demonstrated by perfect ensemble simulations and supplemented by mathematical arguments. Possible methods to avoid or remove artifacts that stratification induces in the rank histogram are suggested.

Challenges in communicating and using ensembles in operational flood forecasting.

Following trends in operational weather forecasting, where ensemble prediction systems (EPS) are now increasingly the norm, flood forecasters are beginning to experiment with using similar ensemble methods. Most of the effort to date has focused on the substantial technical challenges of developing coupled rainfall-runoff systems to represent the full cascade of uncertainties involved in predicting future flooding. As a consequence much less attention has been given to the communication and eventual use of EPS flood forecasts. Drawing on interviews and other research with operational flood forecasters from across Europe, this paper highlights a number of challenges to communicating and using ensemble flood forecasts operationally. It is shown that operational flood forecasters understand the skill, operational limitations, and informational value of EPS products in a variety of different and sometimes contradictory ways. Despite the efforts of forecasting agencies to design effective ways to communicate EPS forecasts to non-experts, operational flood forecasters were often skeptical about the ability of forecast recipients to understand or use them appropriately. It is argued that better training and closer contacts between operational flood forecasters and EPS system designers can help ensure the uncertainty represented by EPS forecasts is represented in ways that are most appropriate and meaningful for their intended consumers, but some fundamental political and institutional challenges to using ensembles, such as differing attitudes to false alarms and to responsibility for management of blame in the event of poor or mistaken forecasts are also highlighted. Copyright © 2010 Royal Meteorological Society.

Predictability of the western North Pacific summer climate associated with different ENSO phases by ENSEMBLES multi-model seasonal forecasts

Predictability of the western North Pacific (WNP) summer climate associated with different El Niño–Southern Oscillation (ENSO) phases is investigated in this study based on the 1-month lead retrospective forecasts of five state-of-the-art coupled models from ENSEMBLES. During the period from 1960 to 2005, the models well capture the WNP summer climate anomalies during most of years in different ENSO phases except the La Niña decaying summers. In the El Niño developing, El Niño decaying and La Niña developing summers, the prediction skills are high for the WNP summer monsoon index (WNPMI), with the prediction correlation larger than 0.7. The high prediction skills of the lower-tropospheric circulation during these phases are found mainly over the tropical western Pacific Ocean, South China Sea and subtropical WNP. These good predictions correspond well to their close teleconnection with ENSO and the high prediction skills of tropical SSTs. By contrast, for the La Niña decaying summers, the prediction skills are considerably low with the prediction correlation for the WNPMI near to zero and low prediction skills around the Philippines and subtropical WNP. These poor predictions relate to the weak summer anomalies of the WNPMI during the La Niña decaying years and no significant connections between the WNP lower-tropospheric circulation anomalies and the SSTs over the tropical central and eastern Pacific Ocean in observations. However, the models tend to predict an apparent anomalous cyclone over the WNP during the La Niña decaying years, indicating a linearity of the circulation response over WNP in the models prediction in comparison with that during the El Niño decaying years which differs from observations. In addition, the models show considerable capability in describing the WNP summer anomalies during the ENSO neutral summers. These anomalies are related to the positive feedback between the WNP lower-tropospheric circulation and the local SSTs. The models can capture this positive feedback but with some uncertainties from different ensemble members during the ENSO neutral summers.

A spatial view of ensemble spread in convection permitting ensembles

With movement toward kilometer-scale ensembles, new techniques are needed for their characterization. A new methodology is presented for detailed spatial ensemble characterization using the fractions skill score (FSS). To evaluate spatial forecast differences, the average and standard deviation are taken of the FSS calculated over all ensemble member–member pairs at different scales and lead times. These methods were found to give important information about the ensemble behavior allowing the identification of useful spatial scales, spinup times for the model, and upscale growth of errors and forecast differences. The ensemble spread was found to be highly dependent on the spatial scales considered and the threshold applied to the field. High thresholds picked out localized and intense values that gave large temporal variability in ensemble spread: local processes and undersampling dominate for these thresholds. For lower thresholds the ensemble spread increases with time as differences between the ensemble members upscale. Two convective cases were investigated based on the Met Office United Model run at 2.2-km resolution. Different ensemble types were considered: ensembles produced using the Met Office Global and Regional Ensemble Prediction System (MOGREPS) and an ensemble produced using different model physics configurations. Comparison of the MOGREPS and multiphysics ensembles demonstrated the utility of spatial ensemble evaluation techniques for assessing the impact of different perturbation strategies and the need for assessing spread at different, believable, spatial scales.

Method for exploratory cluster analysis and visualisation of single-trial ERP ensembles

Background: The validity of ensemble averaging on event-related potential (ERP) data has been questioned, due to its assumption that the ERP is identical across trials. Thus, there is a need for preliminary testing for cluster structure in the data. New method: We propose a complete pipeline for the cluster analysis of ERP data. To increase the signalto-noise (SNR) ratio of the raw single-trials, we used a denoising method based on Empirical Mode Decomposition (EMD). Next, we used a bootstrap-based method to determine the number of clusters, through a measure called the Stability Index (SI). We then used a clustering algorithm based on a Genetic Algorithm (GA)to define initial cluster centroids for subsequent k-means clustering. Finally, we visualised the clustering results through a scheme based on Principal Component Analysis (PCA). Results: After validating the pipeline on simulated data, we tested it on data from two experiments – a P300 speller paradigm on a single subject and a language processing study on 25 subjects. Results revealed evidence for the existence of 6 clusters in one experimental condition from the language processing study. Further, a two-way chi-square test revealed an influence of subject on cluster membership.

The utility of convection-permitting ensembles for the prediction of stationary convective bands

This study examines convection-permitting numerical simulations of four cases of terrain-locked quasi-stationary convective bands over the UK. For each case, a 2.2-km grid-length 12-member ensemble and 1.5-km grid-length deterministic forecast are analyzed, each with two different initialization times. Object-based verification is applied to determine whether the simulations capture the structure, location, timing, intensity and duration of the observed precipitation. These verification diagnostics reveal that the forecast skill varies greatly between the four cases. Although the deterministic and ensemble simulations captured some aspects of the precipitation correctly in each case, they never simultaneously captured all of them satisfactorily. In general, the models predicted banded precipitation accumulations at approximately the correct time and location, but the precipitating structures were more cellular and less persistent than the coherent quasi-stationary bands that were observed. Ensemble simulations from the two different initialization times were not significantly different, which suggests a potential benefit of time-lagging subsequent ensembles to increase ensemble size. The predictive skill of the upstream larger-scale flow conditions and the simulated precipitation on the convection-permitting grids were strongly correlated, which suggests that more accurate forecasts from the parent ensemble should improve the performance of the convection-permitting ensemble nested within it.

A new method for the characterisation and verification of local spatial predictability for convective scale ensembles

The use of kilometre-scale ensembles in operational forecasting provides new challenges for forecast interpretation and evaluation to account for uncertainty on the convective scale. A new neighbourhood based method is presented for evaluating and characterising the local predictability variations from convective scale ensembles. Spatial scales over which ensemble forecasts agree (agreement scales, S^A) are calculated at each grid point ij, providing a map of the spatial agreement between forecasts. By comparing the average agreement scale obtained from ensemble member pairs (S^A(mm)_ij), with that between members and radar observations (S^A(mo)_ij), this approach allows the location-dependent spatial spread-skill relationship of the ensemble to be assessed. The properties of the agreement scales are demonstrated using an idealised experiment. To demonstrate the methods in an operational context the S^A(mm)_ij and S^A(mo)_ij are calculated for six convective cases run with the Met Office UK Ensemble Prediction System. The S^A(mm)_ij highlight predictability differences between cases, which can be linked to physical processes. Maps of S^A(mm)_ij are found to summarise the spatial predictability in a compact and physically meaningful manner that is useful for forecasting and for model interpretation. Comparison of S^A(mm)_ij and S^A(mo)_ij demonstrates the case-by-case and temporal variability of the spatial spread-skill, which can again be linked to physical processes.

Iterative strong coupling of dimensionally heterogeneous models

In this article we address decomposition strategies especially tailored to perform strong coupling of dimensionally heterogeneous models, under the hypothesis that one wants to solve each submodel separately and implement the interaction between subdomains by boundary conditions alone. The novel methodology takes full advantage of the small number of interface unknowns in this kind of problems. Existing algorithms can be viewed as variants of the `natural` staggered algorithm in which each domain transfers function values to the other, and receives fluxes (or forces), and vice versa. This natural algorithm is known as Dirichlet-to-Neumann in the Domain Decomposition literature. Essentially, we propose a framework in which this algorithm is equivalent to applying Gauss-Seidel iterations to a suitably defined (linear or nonlinear) system of equations. It is then immediate to switch to other iterative solvers such as GMRES or other Krylov-based method. which we assess through numerical experiments showing the significant gain that can be achieved. indeed. the benefit is that an extremely flexible, automatic coupling strategy can be developed, which in addition leads to iterative procedures that are parameter-free and rapidly converging. Further, in linear problems they have the finite termination property. Copyright (C) 2009 John Wiley & Sons, Ltd.

Conformal deformation of equilibrium measures in normal random ensembles

We investigate the eigenvalue statistics of ensembles of normal random matrices when their order N tends to infinite. In the model, the eigenvalues have uniform density within a region determined by a simple analytic polynomial curve. We study the conformal deformations of equilibrium measures of normal random ensembles to the real line and give sufficient conditions for it to weakly converge to a Wigner measure.

Conservative ensembles for nonequilibrium lattice-gas systems

We show how to set up a constant particle ensemble for the steady state of nonequilibrium lattice-gas systems which originally are defined on a constant rate ensemble. We focus on nonequilibrium systems in which particles are created and annihilated on the sites of a lattice and described by a master equation. We consider also the case in which a quantity other than the number of particle is conserved. The conservative ensembles can be useful in the study of phase transitions and critical phenomena particularly discontinuous phase transitions.

A novel MAP-MRF approach for multispectral image contextual classification using combination of suboptimal iterative algorithms

In this paper we present a novel approach for multispectral image contextual classification by combining iterative combinatorial optimization algorithms. The pixel-wise decision rule is defined using a Bayesian approach to combine two MRF models: a Gaussian Markov Random Field (GMRF) for the observations (likelihood) and a Potts model for the a priori knowledge, to regularize the solution in the presence of noisy data. Hence, the classification problem is stated according to a Maximum a Posteriori (MAP) framework. In order to approximate the MAP solution we apply several combinatorial optimization methods using multiple simultaneous initializations, making the solution less sensitive to the initial conditions and reducing both computational cost and time in comparison to Simulated Annealing, often unfeasible in many real image processing applications. Markov Random Field model parameters are estimated by Maximum Pseudo-Likelihood (MPL) approach, avoiding manual adjustments in the choice of the regularization parameters. Asymptotic evaluations assess the accuracy of the proposed parameter estimation procedure. To test and evaluate the proposed classification method, we adopt metrics for quantitative performance assessment (Cohen`s Kappa coefficient), allowing a robust and accurate statistical analysis. The obtained results clearly show that combining sub-optimal contextual algorithms significantly improves the classification performance, indicating the effectiveness of the proposed methodology. (C) 2010 Elsevier B.V. All rights reserved.