Well-posed boundary value problems for integrable evolution equations on a finite interval

We consider boundary value problems posed on an interval [0,L] for an arbitrary linear evolution equation in one space dimension with spatial derivatives of order n. We characterize a class of such problems that admit a unique solution and are well posed in this sense. Such well-posed boundary value problems are obtained by prescribing N conditions at x=0 and n–N conditions at x=L, where N depends on n and on the sign of the highest-degree coefficient n in the dispersion relation of the equation. For the problems in this class, we give a spectrally decomposed integral representation of the solution; moreover, we show that these are the only problems that admit such a representation. These results can be used to establish the well-posedness, at least locally in time, of some physically relevant nonlinear evolution equations in one space dimension.

Nonlinear channel equalizer design using directional evolutionary multi-objective optimization

In this paper, a new equalizer learning scheme is introduced based on the algorithm of the directional evolutionary multi-objective optimization (EMOO). Whilst nonlinear channel equalizers such as the radial basis function (RBF) equalizers have been widely studied to combat the linear and nonlinear distortions in the modern communication systems, most of them do not take into account the equalizers' generalization capabilities. In this paper, equalizers are designed aiming at improving their generalization capabilities. It is proposed that this objective can be achieved by treating the equalizer design problem as a multi-objective optimization (MOO) problem, with each objective based on one of several training sets, followed by deriving equalizers with good capabilities of recovering the signals for all the training sets. Conventional EMOO which is widely applied in the MOO problems suffers from disadvantages such as slow convergence speed. Directional EMOO improves the computational efficiency of the conventional EMOO by explicitly making use of the directional information. The new equalizer learning scheme based on the directional EMOO is applied to the RBF equalizer design. Computer simulation demonstrates that the new scheme can be used to derive RBF equalizers with good generalization capabilities, i.e., good performance on predicting the unseen samples.

Adaptive general predictive controller for nonlinear systems

A nonlinear general predictive controller (NLGPC) is described which is based on the use of a Hammerstein model within a recursive control algorithm. A key contribution of the paper is the use of a novel, one-step simple root solving procedure for the Hammerstein model, this being a fundamental part of the overall tuning algorithm. A comparison is made between NLGPC and nonlinear deadbeat control (NLDBC) using the same one-step nonlinear components, in order to investigate NLGPC advantages and disadvantages.

The signature of ENSO in the Northern Hemisphere midlatitude seasonal mean flow and high-frequency intraseasonal variability

The impact of pronounced positive and negative sea surface temperature (STT) anomalies in the tropical Pacific associated with the El Niño/Southern Oscillation (ENSO) phenomenon on the atmospheric circulation in the Northern Hemisphere extratropics during the boreal winter season is investigated. This includes both the impact on the seasonal mean flow and on the intraseasonal variability on synoptic time scales. Moreover, the interaction between the transient fluctuations on these times scales and the mean circulation is examined. Both data from an ensemble of five simulations with the ECHAM3 atmospheric general circulation model at a horizontal resolution of T42 each covering the period from 1979 through 1992 and operational analyses from ECMWF for the corresponding period are examined. In each of the simulations observed SSTs for the period of investigation are given as lower boundary forcing, but different atmospheric initial conditions are prescribed. The simulations with ECHAM3 reveal a distinct impact of the pronounced SST-anomalies in the tropical Pacific on the atmospheric circulation in the Northern Hemisphere extratropics during El Niño as well as during La Niña events. These changes in the atmospheric circulation, which are found to be highly significant in the Pacific/North American as well as in the Atlantic/European region, are consistent with the essential results obtained from the analyses. The pronounced SST-anomalies in the tropical Pacific lead to changes in the mean circulation, which are characterized by typical circulation patterns. These changes in the mean circulation are accompanied by marked variations of the activity of the transient fluctuations on synoptic time scales, that are changes in both the kinetic energy on these time scales and the atmospheric transports of momentum and heat accomplished by the short baroclinic waves. The synoptic disturbances, on the other hand, play also an important role in controlling the changes in the mean circulation associated with the ENSO phenomenon. They maintain these typical circulation patterns via barotropic, but counteract them via baroclinic processes. The hypothesis of an impact of the ENSO phenomenon in the Atlantic/European region can be supported. As the determining factor the intensification (reduction) of the Aleutian low and the simultaneous reduction (intensification) of the Icelandic low during El Niño and during La Niña events respectively, is identified. The changes in the intensity of the Aleutian low during the ENSO-events are accompanied by an alteration of the transport of momentum caused by the short baroclinic waves over the North American continent in such a way that the changes in the intensity of the Icelandic low during El Niño as well as during La Niña events are maintained.

Numerical modelling of the energy and water cycle of the Baltic Sea

This paper will introduce the Baltex research programme and summarize associated numerical modelling work which has been undertaken during the last five years. The research has broadly managed to clarify the main mechanisms determining the water and energy cycle in the Baltic region, such as the strong dependence upon the large scale atmospheric circulation. It has further been shown that the Baltic Sea has a positive water balance, albeit with large interannual variations. The focus on the modelling studies has been the use of limited area models at ultra-high resolution driven by boundary conditions from global models or from reanalysis data sets. The programme has further initiated a comprehensive integration of atmospheric, land surface and hydrological modelling incorporating snow, sea ice and special lake models. Other aspects of the programme include process studies such as the role of deep convection, air sea interaction and the handling of land surface moisture. Studies have also been undertaken to investigate synoptic and sub-synoptic events over the Baltic region, thus exploring the role of transient weather systems for the hydrological cycle. A special aspect has been the strong interests and commitments of the meteorological and hydrological services because of the potentially large societal interests of operational applications of the research. As a result of this interests special attention has been put on data-assimilation aspects and the use of new types of data such as SSM/I, GPS-measurements and digital radar. A series of high resolution data sets are being produced. One of those, a 1/6 degree daily precipitation climatology for the years 1996–1999, is such a unique contribution. The specific research achievements to be presented in this volume of Meteorology and Atmospheric Physics is the result of a cooperative venture between 11 European research groups supported under the EU-Framework programmes.

Heat and moisture budgets from airborne measurements and high-resolution model simulations

High-resolution simulations with a mesoscale model are performed to estimate heat and moisture budgets of a well-mixed boundary layer. The model budgets are validated against energy budgets obtained from airborne measurements over heterogeneous terrain in Western Germany. Time rate of change, vertical divergence, and horizontal advection for an atmospheric column of air are estimated. Results show that the time trend of specific humidity exhibits some deficiencies, while the potential temperature trend is matched accurately. Furthermore, the simulated turbulent surface fluxes of sensible and latent heat are comparable to the measured fluxes, leading to similar values of the vertical divergence. The analysis of different horizontal model resolutions exhibits improved surface fluxes with increased resolution, a fact attributed to a reduced aggregation effect. Scale-interaction effects could be identified: while time trends and advection are strongly influenced by mesoscale forcing, the turbulent surface fluxes are mainly controlled by microscale processes.

Wave-activity conservation laws and stability theorems for semi-geostrophic dynamics: part 1. pseudomomentum-based theory

There exists a well-developed body of theory based on quasi-geostrophic (QG) dynamics that is central to our present understanding of large-scale atmospheric and oceanic dynamics. An important question is the extent to which this body of theory may generalize to more accurate dynamical models. As a first step in this process, we here generalize a set of theoretical results, concerning the evolution of disturbances to prescribed basic states, to semi-geostrophic (SG) dynamics. SG dynamics, like QG dynamics, is a Hamiltonian balanced model whose evolution is described by the material conservation of potential vorticity, together with an invertibility principle relating the potential vorticity to the advecting fields. SG dynamics has features that make it a good prototype for balanced models that are more accurate than QG dynamics. In the first part of this two-part study, we derive a pseudomomentum invariant for the SG equations, and use it to obtain: (i) linear and nonlinear generalized Charney–Stern theorems for disturbances to parallel flows; (ii) a finite-amplitude local conservation law for the invariant, obeying the group-velocity property in the WKB limit; and (iii) a wave-mean-flow interaction theorem consisting of generalized Eliassen–Palm flux diagnostics, an elliptic equation for the stream-function tendency, and a non-acceleration theorem. All these results are analogous to their QG forms. The pseudomomentum invariant – a conserved second-order disturbance quantity that is associated with zonal symmetry – is constructed using a variational principle in a similar manner to the QG calculations. Such an approach is possible when the equations of motion under the geostrophic momentum approximation are transformed to isentropic and geostrophic coordinates, in which the ageostrophic advection terms are no longer explicit. Symmetry-related wave-activity invariants such as the pseudomomentum then arise naturally from the Hamiltonian structure of the SG equations. We avoid use of the so-called ‘massless layer’ approach to the modelling of isentropic gradients at the lower boundary, preferring instead to incorporate explicitly those boundary contributions into the wave-activity and stability results. This makes the analogy with QG dynamics most transparent. This paper treats the f-plane Boussinesq form of SG dynamics, and its recent extension to β-plane, compressible flow by Magnusdottir & Schubert. In the limit of small Rossby number, the results reduce to their respective QG forms. Novel features particular to SG dynamics include apparently unnoticed lateral boundary stability criteria in (i), and the necessity of including additional zonal-mean eddy correlation terms besides the zonal-mean potential vorticity fluxes in the wave-mean-flow balance in (iii). In the companion paper, wave-activity conservation laws and stability theorems based on the SG form of the pseudoenergy are presented.

Urban surface energy balance models: model characteristics and methodology for a comparison study

Many urban surface energy balance models now exist. These vary in complexity from simple schemes that represent the city as a concrete slab, to those which incorporate detailed representations of momentum and energy fluxes distributed within the atmospheric boundary layer. While many of these schemes have been evaluated against observations, with some models even compared with the same data sets, such evaluations have not been undertaken in a controlled manner to enable direct comparison. For other types of climate model, for instance the Project for Intercomparison of Land-Surface Parameterization Schemes (PILPS) experiments (Henderson-Sellers et al., 1993), such controlled comparisons have been shown to provide important insights into both the mechanics of the models and the physics of the real world. This paper describes the progress that has been made to date on a systematic and controlled comparison of urban surface schemes. The models to be considered, and their key attributes, are described, along with the methodology to be used for the evaluation.

Cross-correlations and cross-bicorrelations in Sterling exchange rates

This paper proposes two new tests for linear and nonlinear lead/lag relationships between time series based on the concepts of cross-correlations and cross-bicorrelations, respectively. The tests are then applied to a set of Sterling-denominated exchange rates. Our analysis indicates that there existed periods during the post-Bretton Woods era where the temporal relationship between different exchange rates was strong, although these periods have become less frequent over the past 20 years. In particular, our results demonstrate the episodic nature of the nonlinearity, and have implications for the speed of flow of information between financial series. The method generalises recently proposed tests for nonlinearity to the multivariate context.

The science case for an orbital mission to Uranus: Exploring the origins and evolution of ice giant planets

Giant planets helped to shape the conditions we see in the Solar System today and they account for more than 99% of the mass of the Sun’s planetary system. They can be subdivided into the Ice Giants (Uranus and Neptune) and the Gas Giants (Jupiter and Saturn), which differ from each other in a number of fundamental ways. Uranus, in particular is the most challenging to our understanding of planetary formation and evolution, with its large obliquity, low self-luminosity, highly asymmetrical internal field, and puzzling internal structure. Uranus also has a rich planetary system consisting of a system of inner natural satellites and complex ring system, five major natural icy satellites, a system of irregular moons with varied dynamical histories, and a highly asymmetrical magnetosphere. Voyager 2 is the only spacecraft to have explored Uranus, with a flyby in 1986, and no mission is currently planned to this enigmatic system. However, a mission to the uranian system would open a new window on the origin and evolution of the Solar System and would provide crucial information on a wide variety of physicochemical processes in our Solar System. These have clear implications for understanding exoplanetary systems. In this paper we describe the science case for an orbital mission to Uranus with an atmospheric entry probe to sample the composition and atmospheric physics in Uranus’ atmosphere. The characteristics of such an orbiter and a strawman scientific payload are described and we discuss the technical challenges for such a mission. This paper is based on a white paper submitted to the European Space Agency’s call for science themes for its large-class mission programme in 2013.

EISCAT observations of ion composition and temperature anisotropy in the high-latitude F-region

The papers by Winser et al. [(1990) J. atmos. terr. Phys.52, 501] and Häggström and Collis [(1990) J. atmos. terr. Phys.52, 519] used plasma flows and ion temperatures, as measured by the EISCAT tristatic incoherent scatter radar, to investigate changes in the ion composition of the ionospheric F-layer at high latitudes, in response to increases in the speed of plasma convection. These studies reported that the ion composition rapidly changed from mainly O+ to almost completely (>90%) molecular ions, following rapid increases in ion drift speed by >1 km s−1. These changes appeared inconsisent with theoretical considerations of the ion chemistry, which could not account for the large fractions of molecular ions inferred from the obsevations. In this paper, we discuss two causes of this discrepancy. First, we reevaluate the theoretical calculations for chemical equilibrium and show that, if we correct the derived temperatures for the effect of the molecular ions, and if we employ more realistic dependences of the reaction rates on the ion temperature, the composition changes derived for the faster convection speeds can be explained. For the Winser et al. observations with the radar beam at an aspect angle of ϕ = 54.7° to the geomagnetic field, we now compute a change to 89% molecular ions in < 2 min, in response to the 3 km s−1 drift. This is broadly consistent with the observations. But for the two cases considered by Häggström and Collis, looking along the field line (ϕ = 0°), we compute the proportion of molecular ions to be only 4 and 16% for the observed plasma drifts of 1.2 and 1.6 km s−1, respectively. These computed proportions are much smaller than those derived experimentally (70 and 90%). We attribute the differences to the effects of non-Maxwellian, anisotropic ion velocity distribution functions. We also discuss the effect of ion composition changes on the various radar observations that report anisotropies of ion temperature.

Sondrestrom and EISCAT radar observations of poleward-moving auroral forms

During many magnetospheric substorms, the auroral oval near midnight is observed to expand poleward in association with strong negative perturbations measured by local ground magnetometers. We show Sondrestrom and EISCAT incoherent scatter radar measurements during three such events. In each of the events, enhanced ionization produced by the precipitation moved northward by several degrees of latitude within 10–20 min. The electric fields measured during the three events were significantly different. In one event the electric field was southward everywhere within the precipitation region. In the other two events a reversal in the meridional component of the field was observed. In one case the reversal occurred within the precipitation region, while in the other case the reversal was at the poleward boundary of the precipitation. The westward electrojet that produces the negative H-perturbation in the ground magnetic field has Hall and Pedersen components to varying degrees. In one case the Hall component was eastward and the Pedersen component was westward, but the net magnetic H-deflection on the ground was negative. Simultaneous EISCAT measurements made near the dawn meridian during one of the events show that the polar cap boundary moved northward at the same time as the aurora expanded northward at Sondrestrom. Most of the differences in the electrodynamic configuration in the three events can be accounted for in terms of the location at which the measurements were made relative to the center of the auroral bulge.

Measuring ion temperatures and studying the ion energy balance in the high-latitude ionosphere

Data are presented for a nighttime ion heating event observed by the EISCAT radar on 16 December 1988. In the experiment, the aspect angle between the radar beam and the geomagnetic field was fixed at 54.7°, which avoids any ambiguity in derived ion temperature caused by anisotropy in the ion velocity distribution function. The data were analyzed with an algorithm which takes account of the non-Maxwellian line-of-sight ion velocity distribution. During the heating event, the derived spectral distortion parameter (D∗) indicated that the distribution function was highly distorted from a Maxwellian form when the ion drift increased to 4 km s−1. The true three-dimensional ion temperature was used in the simplified ion balance equation to compute the ion mass during the heating event. The ion composition was found to change from predominantly O4 to mainly molecular ions. A theoretical analysis of the ion composition, using the MSIS86 model and published values of the chemical rate coefficients, accounts for the order-of-magnitude increase in the atomic/molecular ion ratio during the event, but does not successfully explain the very high proportion of molecular ions that was observed.