A high-order arbitrarily unstructured finite-volume model of the global atmosphere: tests solving the shallow-water equations

Simulations of the global atmosphere for weather and climate forecasting require fast and accurate solutions and so operational models use high-order finite differences on regular structured grids. This precludes the use of local refinement; techniques allowing local refinement are either expensive (eg. high-order finite element techniques) or have reduced accuracy at changes in resolution (eg. unstructured finite-volume with linear differencing). We present solutions of the shallow-water equations for westerly flow over a mid-latitude mountain from a finite-volume model written using OpenFOAM. A second/third-order accurate differencing scheme is applied on arbitrarily unstructured meshes made up of various shapes and refinement patterns. The results are as accurate as equivalent resolution spectral methods. Using lower order differencing reduces accuracy at a refinement pattern which allows errors from refinement of the mountain to accumulate and reduces the global accuracy over a 15 day simulation. We have therefore introduced a scheme which fits a 2D cubic polynomial approximately on a stencil around each cell. Using this scheme means that refinement of the mountain improves the accuracy after a 15 day simulation. This is a more severe test of local mesh refinement for global simulations than has been presented but a realistic test if these techniques are to be used operationally. These efficient, high-order schemes may make it possible for local mesh refinement to be used by weather and climate forecast models.

Second order accurate upwind difference schemes for scalar conservation laws with source terms

A second order accurate, characteristic-based, finite difference scheme is developed for scalar conservation laws with source terms. The scheme is an extension of well-known second order scalar schemes for homogeneous conservation laws. Such schemes have proved immensely powerful when applied to homogeneous systems of conservation laws using flux-difference splitting. Many application areas, however, involve inhomogeneous systems of conservation laws with source terms, and the scheme presented here is applied to such systems in a subsequent paper.

Adaptive B-spline neural network based nonlinear equalization for high-order QAM systems with nonlinear transmit high power amplifier

High bandwidth-efficiency quadrature amplitude modulation (QAM) signaling widely adopted in high-rate communication systems suffers from a drawback of high peak-toaverage power ratio, which may cause the nonlinear saturation of the high power amplifier (HPA) at transmitter. Thus, practical high-throughput QAM communication systems exhibit nonlinear and dispersive channel characteristics that must be modeled as a Hammerstein channel. Standard linear equalization becomes inadequate for such Hammerstein communication systems. In this paper, we advocate an adaptive B-Spline neural network based nonlinear equalizer. Specifically, during the training phase, an efficient alternating least squares (LS) scheme is employed to estimate the parameters of the Hammerstein channel, including both the channel impulse response (CIR) coefficients and the parameters of the B-spline neural network that models the HPA’s nonlinearity. In addition, another B-spline neural network is used to model the inversion of the nonlinear HPA, and the parameters of this inverting B-spline model can easily be estimated using the standard LS algorithm based on the pseudo training data obtained as a natural byproduct of the Hammerstein channel identification. Nonlinear equalisation of the Hammerstein channel is then accomplished by the linear equalization based on the estimated CIR as well as the inverse B-spline neural network model. Furthermore, during the data communication phase, the decision-directed LS channel estimation is adopted to track the time-varying CIR. Extensive simulation results demonstrate the effectiveness of our proposed B-Spline neural network based nonlinear equalization scheme.

A priori error analysis of space–time Trefftz discontinuous Galerkin methods for wave problems

We present and analyse a space–time discontinuous Galerkin method for wave propagation problems. The special feature of the scheme is that it is a Trefftz method, namely that trial and test functions are solution of the partial differential equation to be discretised in each element of the (space–time) mesh. The method considered is a modification of the discontinuous Galerkin schemes of Kretzschmar et al. (2014) and of Monk & Richter (2005). For Maxwell’s equations in one space dimension, we prove stability of the method, quasi-optimality, best approximation estimates for polynomial Trefftz spaces and (fully explicit) error bounds with high order in the meshwidth and in the polynomial degree. The analysis framework also applies to scalar wave problems and Maxwell’s equations in higher space dimensions. Some numerical experiments demonstrate the theoretical results proved and the faster convergence compared to the non-Trefftz version of the scheme.

Methane cross-validation between three Fourier Transform Spectrometers: SCISAT ACE-FTS, GOSAT TANSO-FTS, and ground-based FTS measurements in the Canadian high Arctic

We present cross-validation of remote sensing measurements of methane profiles in the Canadian high Arctic. Accurate and precise measurements of methane are essential to understand quantitatively its role in the climate system and in global change. Here, we show a cross-validation between three datasets: two from spaceborne instruments and one from a ground-based instrument. All are Fourier Transform Spectrometers (FTSs). We consider the Canadian SCISAT Atmospheric Chemistry Experiment (ACE)-FTS, a solar occultation infrared spectrometer operating since 2004, and the thermal infrared band of the Japanese Greenhouse Gases Observing Satellite (GOSAT) Thermal And Near infrared Sensor for carbon Observation (TANSO)-FTS, a nadir/off-nadir scanning FTS instrument operating at solar and terrestrial infrared wavelengths, since 2009. The ground-based instrument is a Bruker 125HR Fourier Transform Infrared (FTIR) spectrometer, measuring mid-infrared solar absorption spectra at the Polar Environment Atmospheric Research Laboratory (PEARL) Ridge Lab at Eureka, Nunavut (80° N, 86° W) since 2006. For each pair of instruments, measurements are collocated within 500 km and 24 h. An additional criterion based on potential vorticity values was found not to significantly affect differences between measurements. Profiles are regridded to a common vertical grid for each comparison set. To account for differing vertical resolutions, ACE-FTS measurements are smoothed to the resolution of either PEARL-FTS or TANSO-FTS, and PEARL-FTS measurements are smoothed to the TANSO-FTS resolution. Differences for each pair are examined in terms of profile and partial columns. During the period considered, the number of collocations for each pair is large enough to obtain a good sample size (from several hundred to tens of thousands depending on pair and configuration). Considering full profiles, the degrees of freedom for signal (DOFS) are between 0.2 and 0.7 for TANSO-FTS and between 1.5 and 3 for PEARL-FTS, while ACE-FTS has considerably more information (roughly 1° of freedom per altitude level). We take partial columns between roughly 5 and 30 km for the ACE-FTS–PEARL-FTS comparison, and between 5 and 10 km for the other pairs. The DOFS for the partial columns are between 1.2 and 2 for PEARL-FTS collocated with ACE-FTS, between 0.1 and 0.5 for PEARL-FTS collocated with TANSO-FTS or for TANSO-FTS collocated with either other instrument, while ACE-FTS has much higher information content. For all pairs, the partial column differences are within ± 3 × 1022 molecules cm−2. Expressed as median ± median absolute deviation (expressed in absolute or relative terms), these differences are 0.11 ± 9.60 × 10^20 molecules cm−2 (0.012 ± 1.018 %) for TANSO-FTS–PEARL-FTS, −2.6 ± 2.6 × 10^21 molecules cm−2 (−1.6 ± 1.6 %) for ACE-FTS–PEARL-FTS, and 7.4 ± 6.0 × 10^20 molecules cm−2 (0.78 ± 0.64 %) for TANSO-FTS–ACE-FTS. The differences for ACE-FTS–PEARL-FTS and TANSO-FTS–PEARL-FTS partial columns decrease significantly as a function of PEARL partial columns, whereas the range of partial column values for TANSO-FTS–ACE-FTS collocations is too small to draw any conclusion on its dependence on ACE-FTS partial columns.

Annual textural banding in Holocene estuarine silts, Severn Estuary Levels (SW Britain): patterns, cause and implications

A high-resolution textural study has been made of laminated and banded estuarine silts exposed intertidally at representative localities and horizons in the Holocene deposits of the Severn Estuary Levels. The laminae, on a submillimetre to millimetre scale, are sharp-based, graded couplets formed of a lower silty part overlain by a finer-textured clayey element. The centimetre- to decimetre-scale banding is formed of laminae in alternating, gradually intergrading sets of relatively coarse and relative fine-grained examples. At outcrop in the field, the banding is recognizable because the coarse sets prove to be recessive to varying degrees under the influence of weathering and current action. Independent evidence at two localities points toward an annual origin for the banding; at a third it arose during part of what appears to have been a relatively short period. Quantified physical arguments suggest that the textural banding is a response of suspended fine sediment to marked seasonal changes in sea temperature and windiness. The banded silts occur in four distinct stratigraphical contexts and record high deposition rates (order 0.01-0.1 m/yr). Because physical factors determine their textures, the silts potentially afford insights in all contexts into aspects of changing Holocene climatic conditions. In one context, the thickness of the bands points to high (order 0.01-0.1 m/yr) but comparatively short-lived (order 10s-100s yrs) rates of relative water-level rise. In the others, however, the banding has no implications for sea-level behaviour, and simply records gross environmental disequilibrium, for example, the recovery of mudflats/marshes after an erosional episode. Similarly, because on account of their rapid accumulation the banded silts preserve animal and human tracks and trackways especially well, they provide an archive of animal and human behaviour in the area during the Holocene.

Generation of attosecond pulses in molecular nitrogen

We have generated attosecond pulse trains in an ensemble of randomly aligned nitrogen molecules. Measurements of the high-order harmonic relative phases and amplitudes allow us to reconstruct the temporal profile of the attosecond pulses. We show that in the considered spectral range, the latter is very similar to the pulse train generated in argon under the same conditions. We discuss the possible influence of the molecular structure in the generation process, and how it can induce subtle differences on the relative phases.

Perturbations in the infrared spectrum of monofluoroacetylene, and their relationship to intramolecular vibrational energy redistribution

Several high-order vibration-rotation perturbations in the high-resolution infrared spectrum of monofluoroacetylene, HCCF, are assigned and analyzed in detail. They result in avoided crossings in the rotational structure of several bands, and precise values for the effective high-order terms in the Hamiltonian have been determined. The significance of these results for intramolecular vibrational redistribution is discussed.

Transient teleconnection event at the onset of a planet-encircling dust storm on Mars

We use proper orthogonal decomposition (POD) to study a transient teleconnection event at the onset of the 2001 planet-encircling dust storm on Mars, in terms of empirical orthogonal functions (EOFs). There are several differences between this and previous studies of atmospheric events using EOFs. First, instead of using a single variable such as surface pressure or geopotential height on a given pressure surface, we use a dataset describing the evolution in time of global and fully three-dimensional atmospheric fields such as horizontal velocity and temperature. These fields are produced by assimilating Thermal Emission Spectrometer observations from NASA's Mars Global Surveyor spacecraft into a Mars general circulation model. We use total atmospheric energy (TE) as a physically meaningful quantity which weights the state variables. Second, instead of adopting the EOFs to define teleconnection patterns as planetary-scale correlations that explain a large portion of long time-scale variability, we use EOFs to understand transient processes due to localised heating perturbations that have implications for the atmospheric circulation over distant regions. The localised perturbation is given by anomalous heating due to the enhanced presence of dust around the northern edge of the Hellas Planitia basin on Mars. We show that the localised disturbance is seemingly restricted to a small number (a few tens) of EOFs. These can be classified as low-order, transitional, or high-order EOFs according to the TE amount they explain throughout the event. Despite the global character of the EOFs, they show the capability of accounting for the localised effects of the perturbation via the presence of specific centres of action. We finally discuss possible applications for the study of terrestrial phenomena with similar characteristics.

Aqueous gels of mixtures of ionic surfactant SDS with pluronic copolymers P123 or F127

Gel diagrams based on tube inversion and oscillatory rheometry are reported for Pluronic copolymers F127 (E98P67E98) and P123 (E21P67E21) in mixtures with anionic surfactant sodium dodecyl sulfate (SDS). Total concentrations (e, SDS+copolymer) were as high as 50 wt% with mole ratios SDS/copolymer (mr) in the ranges 1-5 (F127) a lid 1-7 (PI 23). Temperatures were its high as 90 degrees C. Determination of the temperature dependences of the dynamic moduli served to confirm the gel boundaries from tube inversion and to reveal the high elastic moduli of the gels, e.g., compared at corn parable positions in the gel phase, a 50 wt% SDS/P123 wit h mr = 7 had G' three times that of a corresponding gel of P123 alone. Sin all-angle X-ray scattering (SAX S) was used to show that the structures of all the SDS/F127 gels were bee and that the structures of the SDS/P123 gels with mr = I were either fcc(c = 30 wt%) or hex (c = 40 wt%). Assignment of structures to SDS/P123 gels with values of mr in the range 3-7 was more difficult, as high-order scattering peaks Could be very weak, and at the higher values of c and mr, the SAXS peaks included multiple reflections.

GSHMC: an efficient method for molecular simulation

The hybrid Monte Carlo (HMC) method is a popular and rigorous method for sampling from a canonical ensemble. The HMC method is based on classical molecular dynamics simulations combined with a Metropolis acceptance criterion and a momentum resampling step. While the HMC method completely resamples the momentum after each Monte Carlo step, the generalized hybrid Monte Carlo (GHMC) method can be implemented with a partial momentum refreshment step. This property seems desirable for keeping some of the dynamic information throughout the sampling process similar to stochastic Langevin and Brownian dynamics simulations. It is, however, ultimate to the success of the GHMC method that the rejection rate in the molecular dynamics part is kept at a minimum. Otherwise an undesirable Zitterbewegung in the Monte Carlo samples is observed. In this paper, we describe a method to achieve very low rejection rates by using a modified energy, which is preserved to high-order along molecular dynamics trajectories. The modified energy is based on backward error results for symplectic time-stepping methods. The proposed generalized shadow hybrid Monte Carlo (GSHMC) method is applicable to NVT as well as NPT ensemble simulations.

The RELQUAL scale: a measure of relationship quality in export market ventures

In this article, the authors develop a new measurement scale (the RELQUAL scale) to assess the degree of relationship quality between the exporting firm and the importer. Relationship quality is presented as a high-order concept. Findings reveal that a better quality of the relationship results in a greater (1) amount of information sharing, (2) communication quality, (3) long-term orientation, as well as (4) satisfaction with the relationship. The four multi-item scales show strong evidence of reliability as well as convergent, discriminant and nomological validity in a sample of British exporters. Findings also reveal that relationship quality is positively and significantly associated with export performance. Suggestions for applying the measure in future research are presented.

Achieving accurate FTIR measurements on high performance bandpass filters

The sources of ordinate error in FTIR spectrometers are reviewed with reference to measuring small out-of-band features in the spectra of bandpass filters. Procedures for identifying instrumental artefacts are described. It is shown that features well below 0.01%T can be measured reliably.

A calibrated, non-invasive method for measuring the internal interface height field at high resolution in the rotating, two-layer annulus

We describe a remote sensing method for measuring the internal interface height field in a rotating, two-layer annulus laboratory experiment. The method is non-invasive, avoiding the possibility of an interaction between the flow and the measurement device. The height fields retrieved are accurate and highly resolved in both space and time. The technique is based on a flow visualization method developed by previous workers, and relies upon the optical rotation properties of the working liquids. The previous methods returned only qualitative interface maps, however. In the present study, a technique is developed for deriving quantitative maps by calibrating height against the colour fields registered by a camera which views the flow from above. We use a layer-wise torque balance analysis to determine the equilibrium interface height field analytically, in order to derive the calibration curves. With the current system, viewing an annulus of outer radius 125 mm and depth 250 mm from a distance of 2 m, the inferred height fields have horizontal, vertical and temporal resolutions of up to 0.2 mm, 1 mm and 0.04 s, respectively.

A fast radiative transfer model for the assimilation of water vapor radiances from the Kalpana very high resolution radiometer

A fast radiative transfer model (RTM) to compute emitted infrared radiances for a very high resolution radiometer (VHRR), onboard the operational Indian geostationary satellite Kalpana has been developed and verified. This work is a step towards the assimilation of Kalpana water vapor (WV) radiances into numerical weather prediction models. The fast RTM uses a regression‐based approach to parameterize channel‐specific convolved level to space transmittances. A comparison between the fast RTM and the line‐by‐line RTM demonstrated that the fast RTM can simulate line‐by‐line radiances for the Kalpana WV channel to an accuracy better than the instrument noise, while offering more rapid radiance calculations. A comparison of clear sky radiances of the Kalpana WV channel with the ECMWF model first guess radiances is also presented, aiming to demonstrate the fast RTM performance with the real observations. In order to assimilate the radiances from Kalpana, a simple scheme for bias correction has been suggested.