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.

Balitskiǐ-Fadin-Kuraev-Lipatov equation versus data from DESY HERA

The BFKL equation and the kT-factorization theorem are used to obtain predictions for F2 in the small Bjo/rken-x region over a wide range of Q2. The dependence on the parameters, especially on those concerning the infrared region, is discussed. After a background fit to recent experimental data obtained at DESY HERA and at Fermilab (E665 experiment) we find that the predicted, almost Q2 independent BFKL slope λ≳0.5 appears to be too steep at lower Q2 values. Thus there seems to be a chance that future HERA data can distinguish between pure BFKL and conventional field theoretic renormalization group approaches. © 1995 The American Physical Society.

On the stability and convergence of the finite section method for integral equation formulations of rough surface scattering

We consider the Dirichlet and Robin boundary value problems for the Helmholtz equation in a non-locally perturbed half-plane, modelling time harmonic acoustic scattering of an incident field by, respectively, sound-soft and impedance infinite rough surfaces.Recently proposed novel boundary integral equation formulations of these problems are discussed. It is usual in practical computations to truncate the infinite rough surface, solving a boundary integral equation on a finite section of the boundary, of length 2A, say. In the case of surfaces of small amplitude and slope we prove the stability and convergence as A→∞ of this approximation procedure. For surfaces of arbitrarily large amplitude and/or surface slope we prove stability and convergence of a modified finite section procedure in which the truncated boundary is ‘flattened’ in finite neighbourhoods of its two endpoints. Copyright © 2001 John Wiley & Sons, Ltd.

Noise propagation from a cutting of arbitrary cross-section and impedance

A boundary integral equation is described for the prediction of acoustic propagation from a monofrequency coherent line source in a cutting with impedance boundary conditions onto surrounding flat impedance ground. The problem is stated as a boundary value problem for the Helmholtz equation and is subsequently reformulated as a system of boundary integral equations via Green's theorem. It is shown that the integral equation formulation has a unique solution at all wavenumbers. The numerical solution of the coupled boundary integral equations by a simple boundary element method is then described. The convergence of the numerical scheme is demonstrated experimentally. Predictions of A-weighted excess attenuation for a traffic noise spectrum are made illustrating the effects of varying the depth of the cutting and the absorbency of the surrounding ground surface.

The impedance boundary value problem for the Helmholtz equation in a half-plane

We prove unique existence of solution for the impedance (or third) boundary value problem for the Helmholtz equation in a half-plane with arbitrary L∞ boundary data. This problem is of interest as a model of outdoor sound propagation over inhomogeneous flat terrain and as a model of rough surface scattering. To formulate the problem and prove uniqueness of solution we introduce a novel radiation condition, a generalization of that used in plane wave scattering by one-dimensional diffraction gratings. To prove existence of solution and a limiting absorption principle we first reformulate the problem as an equivalent second kind boundary integral equation to which we apply a form of Fredholm alternative, utilizing recent results on the solvability of integral equations on the real line in [5].

Scattering by rough surfaces: the Dirichlet problem for the Helmholtz equation in a non-locally perturbed half-plane

We consider the Dirichlet boundary value problem for the Helmholtz equation in a non-locally perturbed half-plane, this problem arising in electromagnetic scattering by one-dimensional rough, perfectly conducting surfaces. We propose a new boundary integral equation formulation for this problem, utilizing the Green's function for an impedance half-plane in place of the standard fundamental solution. We show, at least for surfaces not differing too much from the flat boundary, that the integral equation is uniquely solvable in the space of bounded and continuous functions, and hence that, for a variety of incident fields including an incident plane wave, the boundary value problem for the scattered field has a unique solution satisfying the limiting absorption principle. Finally, a result of continuous dependence of the solution on the boundary shape is obtained.

Infrared dynamics of decaying two-dimensional turbulence governed by the Charney-Hasegawa-Mima equation

The low wave number range of decaying turbulence governed by the Charney-Hasegawa-Mima (CHM) equation is examined theoretically and by direct numerical simulation. Here, the low wave number range is defined as values of the wave number k below the wave number kE corresponding to the peak of the energy spectrum, or alternatively the centroid wave number of the energy spectrum. The energy spectrum in the low wave number range in the infrared regime (k →0) is theoretically derived to be E(k) ∼k5, using a quasinormal Markovianized model of the CHM equation. This result is verified by direct numerical simulation of the CHM equation. The wave number triads (k,p,q) responsible for the formation of the low wave number spectrum are also examined. It is found that the energy flux Π(k) for k< kE can be entirely expressed by Π(-)(k), which is the total net input of energy to wave numbers k. Furthermore, the contribution of nonlocal triad interactions to the energy flux is found to be predominant in the range log (k/kE)<-0.5, where the nonlocal interactions are defined to be those triad interactions for which the ratio of the largest leg of the triad to the smallest leg is larger than four. ©2001 The Physical Society of Japan

The FunFOLD2 server for the prediction of protein-ligand interactions

The FunFOLD2 server is a new independent server that integrates our novel protein–ligand binding site and quality assessment protocols for the prediction of protein function (FN) from sequence via structure. Our guiding principles were, first, to provide a simple unified resource to make our function prediction software easily accessible to all via a simple web interface and, second, to produce integrated output for predictions that can be easily interpreted. The server provides a clean web interface so that results can be viewed on a single page and interpreted by non-experts at a glance. The output for the prediction is an image of the top predicted tertiary structure annotated to indicate putative ligand-binding site residues. The results page also includes a list of the most likely binding site residues and the types of predicted ligands and their frequencies in similar structures. The protein–ligand interactions can also be interactively visualized in 3D using the Jmol plug-in. The raw machine readable data are provided for developers, which comply with the Critical Assessment of Techniques for Protein Structure Prediction data standards for FN predictions. The FunFOLD2 webserver is freely available to all at the following web site: http://www.reading.ac.uk/bioinf/FunFOLD/FunFOLD_form_2_0.html.

Graph-based algorithms for comparison and prediction of household-level energy use profiles

We present an efficient graph-based algorithm for quantifying the similarity of household-level energy use profiles, using a notion of similarity that allows for small time–shifts when comparing profiles. Experimental results on a real smart meter data set demonstrate that in cases of practical interest our technique is far faster than the existing method for computing the same similarity measure. Having a fast algorithm for measuring profile similarity improves the efficiency of tasks such as clustering of customers and cross-validation of forecasting methods using historical data. Furthermore, we apply a generalisation of our algorithm to produce substantially better household-level energy use forecasts from historical smart meter data.