Numerical analyses of Runge–Kutta implicit–explicit schemes for horizontally explicit, vertically implicit solutions of atmospheric models

With the prospect of exascale computing, computational methods requiring only local data become especially attractive. Consequently, the typical domain decomposition of atmospheric models means horizontally-explicit vertically-implicit (HEVI) time-stepping schemes warrant further attention. In this analysis, Runge-Kutta implicit-explicit schemes from the literature are analysed for their stability and accuracy using a von Neumann stability analysis of two linear systems. Attention is paid to the numerical phase to indicate the behaviour of phase and group velocities. Where the analysis is tractable, analytically derived expressions are considered. For more complicated cases, amplification factors have been numerically generated and the associated amplitudes and phase diagnosed. Analysis of a system describing acoustic waves has necessitated attributing the three resultant eigenvalues to the three physical modes of the system. To do so, a series of algorithms has been devised to track the eigenvalues across the frequency space. The result enables analysis of whether the schemes exactly preserve the non-divergent mode; and whether there is evidence of spurious reversal in the direction of group velocities or asymmetry in the damping for the pair of acoustic modes. Frequency ranges that span next-generation high-resolution weather models to coarse-resolution climate models are considered; and a comparison is made of errors accumulated from multiple stability-constrained shorter time-steps from the HEVI scheme with a single integration from a fully implicit scheme over the same time interval. Two schemes, “Trap2(2,3,2)” and “UJ3(1,3,2)”, both already used in atmospheric models, are identified as offering consistently good stability and representation of phase across all the analyses. Furthermore, according to a simple measure of computational cost, “Trap2(2,3,2)” is the least expensive.

Extraction of tidal channel networks from aerial photographs alone and combined with laser altimetry

Tidal channel networks play an important role in the intertidal zone, exerting substantial control over the hydrodynamics and sediment transport of the region and hence over the evolution of the salt marshes and tidal flats. The study of the morphodynamics of tidal channels is currently an active area of research, and a number of theories have been proposed which require for their validation measurement of channels over extensive areas. Remotely sensed data provide a suitable means for such channel mapping. The paper describes a technique that may be adapted to extract tidal channels from either aerial photographs or LiDAR data separately, or from both types of data used together in a fusion approach. Application of the technique to channel extraction from LiDAR data has been described previously. However, aerial photographs of intertidal zones are much more commonly available than LiDAR data, and most LiDAR flights now involve acquisition of multispectral images to complement the LiDAR data. In view of this, the paper investigates the use of multispectral data for semiautomatic identification of tidal channels, firstly from only aerial photographs or linescanner data, and secondly from fused linescanner and LiDAR data sets. A multi-level, knowledge-based approach is employed. The algorithm based on aerial photography can achieve a useful channel extraction, though may fail to detect some of the smaller channels, partly because the spectral response of parts of the non-channel areas may be similar to that of the channels. The algorithm for channel extraction from fused LiDAR and spectral data gives an increased accuracy, though only slightly higher than that obtained using LiDAR data alone. The results illustrate the difficulty of developing a fully automated method, and justify the semi-automatic approach adopted.

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.

Curl free pressure gradients over orography in a solution of the fully compressible Euler equations with implicit treatment of acoustic and gravity waves

Steep orography can cause noisy solutions and instability in models of the atmosphere. A new technique for modelling flow over orography is introduced which guarantees curl free gradients on arbitrary grids, implying that the pressure gradient term is not a spurious source of vorticity. This mimetic property leads to better hydrostatic balance and better energy conservation on test cases using terrain following grids. Curl-free gradients are achieved by using the co-variant components of velocity over orography rather than the usual horizontal and vertical components. In addition, gravity and acoustic waves are treated implicitly without the need for mean and perturbation variables or a hydrostatic reference profile. This enables a straightforward description of the implicit treatment of gravity waves. Results are presented of a resting atmosphere over orography and the curl-free pressure gradient formulation is advantageous. Results of gravity waves over orography are insensitive to the placement of terrain-following layers. The model with implicit gravity waves is stable in strongly stratified conditions, with N∆t up to at least 10 (where N is the Brunt-V ̈ais ̈al ̈a frequency). A warm bubble rising over orography is simulated and the curl free pressure gradient formulation gives much more accurate results for this test case than a model without this mimetic property.

A general-method for tracking analysis and its application to meteorological data

Recent interest in the validation of general circulation models (GCMs) has been devoted to objective methods. A small number of authors have used the direct synoptic identification of phenomena together with a statistical analysis to perform the objective comparison between various datasets. This paper describes a general method for performing the synoptic identification of phenomena that can be used for an objective analysis of atmospheric, or oceanographic, datasets obtained from numerical models and remote sensing. Methods usually associated with image processing have been used to segment the scene and to identify suitable feature points to represent the phenomena of interest. This is performed for each time level. A technique from dynamic scene analysis is then used to link the feature points to form trajectories. The method is fully automatic and should be applicable to a wide range of geophysical fields. An example will be shown of results obtained from this method using data obtained from a run of the Universities Global Atmospheric Modelling Project GCM.

Testing symmetry and homogeneity in the almost ideal demand system with co-integrated data using fully modified estimation and the bootstrap

Conventional seemingly unrelated estimation of the almost ideal demand system is shown to lead to small sample bias and distortions in the size of a Wald test for symmetry and homogeneity when the data are co-integrated. A fully modified estimator is developed in an attempt to remedy these problems. It is shown that this estimator reduces the small sample bias but fails to eliminate the size distortion.. Bootstrapping is shown to be ineffective as a method of removing small sample bias in both the conventional and fully modified estimators. Bootstrapping is effective, however, as a method of removing. size distortion and performs equally well in this respect with both estimators.

Implicit memory and consumer choice: the mediating role of brand familiarity

Two experiments investigated the influence of implicit memory on consumer choice for brands with varying levels of familiarity. Priming was measured using a consideration-choice task, developed by Coates, Butler and Berry (2004). Experiment 1 employed a coupon-rating task at encoding that required participants to meaningfully process individual brand names, to assess whether priming could affect participants' final (preferred) choices for familiar brands. Experiment 2 used this same method to assess the impact of implicit memory on consideration and choice for unknown and leader brands, presented in conjunction with familiar competitors. Significant priming was obtained in both experiments, and was shown to directly influence final choice in the case of familiar and highly familiar leader brands. Moreover, it was shown that a single prior exposure could lead participants to consider buying an unknown, and indeed fictitious, brand. Copyright (c) 2006 John Wiley & Sons, Ltd.

A practical method for testing high-speed networking hardware architectures

This paper deals with the key issues encountered in testing during the development of high-speed networking hardware systems by documenting a practical method for "real-life like" testing. The proposed method is empowered by modern and commonly available Field Programmable Gate Array (FPGA) technology. Innovative application of standard FPGA blocks in combination with reconfigurability are used as a back-bone of the method. A detailed elaboration of the method is given so as to serve as a general reference. The method is fully characterised and compared to alternatives through a case study proving it to be the most efficient and effective one at a reasonable cost.

Error estimates for a fully discrete spectral scheme for a class of nonlinear, nonlocal dispersive wave equations

We analyze a fully discrete spectral method for the numerical solution of the initial- and periodic boundary-value problem for two nonlinear, nonlocal, dispersive wave equations, the Benjamin–Ono and the Intermediate Long Wave equations. The equations are discretized in space by the standard Fourier–Galerkin spectral method and in time by the explicit leap-frog scheme. For the resulting fully discrete, conditionally stable scheme we prove an L2-error bound of spectral accuracy in space and of second-order accuracy in time.

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.

Fully automated software solution for protein quantitation by global metabolic labeling with stable isotopes

Metabolic stable isotope labeling is increasingly employed for accurate protein (and metabolite) quantitation using mass spectrometry (MS). It provides sample-specific isotopologues that can be used to facilitate comparative analysis of two or more samples. Stable Isotope Labeling by Amino acids in Cell culture (SILAC) has been used for almost a decade in proteomic research and analytical software solutions have been established that provide an easy and integrated workflow for elucidating sample abundance ratios for most MS data formats. While SILAC is a discrete labeling method using specific amino acids, global metabolic stable isotope labeling using isotopes such as (15)N labels the entire element content of the sample, i.e. for (15)N the entire peptide backbone in addition to all nitrogen-containing side chains. Although global metabolic labeling can deliver advantages with regard to isotope incorporation and costs, the requirements for data analysis are more demanding because, for instance for polypeptides, the mass difference introduced by the label depends on the amino acid composition. Consequently, there has been less progress on the automation of the data processing and mining steps for this type of protein quantitation. Here, we present a new integrated software solution for the quantitative analysis of protein expression in differential samples and show the benefits of high-resolution MS data in quantitative proteomic analyses.

Improvement of the GenTHREADER method for genomic fold recognition

Motivation: In order to enhance genome annotation, the fully automatic fold recognition method GenTHREADER has been improved and benchmarked. The previous version of GenTHREADER consisted of a simple neural network which was trained to combine sequence alignment score, length information and energy potentials derived from threading into a single score representing the relationship between two proteins, as designated by CATH. The improved version incorporates PSI-BLAST searches, which have been jumpstarted with structural alignment profiles from FSSP, and now also makes use of PSIPRED predicted secondary structure and bi-directional scoring in order to calculate the final alignment score. Pairwise potentials and solvation potentials are calculated from the given sequence alignment which are then used as inputs to a multi-layer, feed-forward neural network, along with the alignment score, alignment length and sequence length. The neural network has also been expanded to accommodate the secondary structure element alignment (SSEA) score as an extra input and it is now trained to learn the FSSP Z-score as a measurement of similarity between two proteins. Results: The improvements made to GenTHREADER increase the number of remote homologues that can be detected with a low error rate, implying higher reliability of score, whilst also increasing the quality of the models produced. We find that up to five times as many true positives can be detected with low error rate per query. Total MaxSub score is doubled at low false positive rates using the improved method.

A data assimilation method for using low-resolution Earth observation data in heterogeneous ecosystems

We present an approach for dealing with coarse-resolution Earth observations (EO) in terrestrial ecosystem data assimilation schemes. The use of coarse-scale observations in ecological data assimilation schemes is complicated by spatial heterogeneity and nonlinear processes in natural ecosystems. If these complications are not appropriately dealt with, then the data assimilation will produce biased results. The “disaggregation” approach that we describe in this paper combines frequent coarse-resolution observations with temporally sparse fine-resolution measurements. We demonstrate the approach using a demonstration data set based on measurements of an Arctic ecosystem. In this example, normalized difference vegetation index observations are assimilated into a “zero-order” model of leaf area index and carbon uptake. The disaggregation approach conserves key ecosystem characteristics regardless of the observation resolution and estimates the carbon uptake to within 1% of the demonstration data set “truth.” Assimilating the same data in the normal manner, but without the disaggregation approach, results in carbon uptake being underestimated by 58% at an observation resolution of 250 m. The disaggregation method allows the combination of multiresolution EO and improves in spatial resolution if observations are located on a grid that shifts from one observation time to the next. Additionally, the approach is not tied to a particular data assimilation scheme, model, or EO product and can cope with complex observation distributions, as it makes no implicit assumptions of normality.

Entrepreneurial opportunities, implicit contracts and market making for complex consumer goods

This article extends the theory of entrepreneurial opportunity exploitation, outlining how under certain conditions, opportunity exploitation is dependent on market making innovations. Where adverse selection and moral hazard characterize markets, consumers are likely to withdraw regardless of product quality. In order to overcome consumer resistance, entrepreneurs must signal credible commitments. But because consumers purchase without fully specifying requirements, entrepreneurs' commitments take the partial form of implicit contracts, creating strong mutual commitments to repeated transactions. These commitments enable novel markets to function, but introduce additional costs. This article illustrates the theory with the historic case of Singer in sewing machines

A method for incorporating climate variability in climate change impact assessments: sensitivity of river flows in the Eden catchment to precipitation scenarios

Interest in the impacts of climate change is ever increasing. This is particularly true of the water sector where understanding potential changes in the occurrence of both floods and droughts is important for strategic planning. Climate variability has been shown to have a significant impact on UK climate and accounting for this in future climate cahgne projections is essential to fully anticipate potential future impacts. In this paper a new resampling methodology is developed which includes the variability of both baseline and future precipitation. The resampling methodology is applied to 13 CMIP3 climate models for the 2080s, resulting in an ensemble of monthly precipitation change factors. The change factors are applied to the Eden catchment in eastern Scotland with analysis undertaken for the sensitivity of future river flows to the changes in precipitation. Climate variability is shown to influence the magnitude and direction of change of both precipitation and in turn river flow, which are not apparent without the use of the resampling methodology. The transformation of precipitation changes to river flow changes display a degree of non-linearity due to the catchment's role in buffering the response. The resampling methodology developed in this paper provides a new technique for creating climate change scenarios which incorporate the important issue of climate variability.