Ensemble clustering in deterministic ensemble Kalman filters

Ensemble clustering (EC) can arise in data assimilation with ensemble square root filters (EnSRFs) using non-linear models: an M-member ensemble splits into a single outlier and a cluster of M−1 members. The stochastic Ensemble Kalman Filter does not present this problem. Modifications to the EnSRFs by a periodic resampling of the ensemble through random rotations have been proposed to address it. We introduce a metric to quantify the presence of EC and present evidence to dispel the notion that EC leads to filter failure. Starting from a univariate model, we show that EC is not a permanent but transient phenomenon; it occurs intermittently in non-linear models. We perform a series of data assimilation experiments using a standard EnSRF and a modified EnSRF by a resampling though random rotations. The modified EnSRF thus alleviates issues associated with EC at the cost of traceability of individual ensemble trajectories and cannot use some of algorithms that enhance performance of standard EnSRF. In the non-linear regimes of low-dimensional models, the analysis root mean square error of the standard EnSRF slowly grows with ensemble size if the size is larger than the dimension of the model state. However, we do not observe this problem in a more complex model that uses an ensemble size much smaller than the dimension of the model state, along with inflation and localisation. Overall, we find that transient EC does not handicap the performance of the standard EnSRF.

Wind observations above an urban river using a new lidar technique, scintillometry and anemometry

Flow along rivers, an integral part of many cities, might provide a key mechanism for ventilation – which is important for air quality and heat stress. Since the flow varies in space and time around rivers, there is limited utility in point measurements. Ground-based remote sensing offers the opportunity to study 3D flow in locations which are hard to observe. For three months in the winter and spring of 2011, the atmospheric flow above the River Thames in central London was observed using a scanning Doppler lidar, a dual-beam scintillometer and sonic anemometry. First, an inter-comparison showed that lidar-derived mean wind-speed estimates compare almost as well to sonic anemometers (root-mean-square error (rmse) 0.65–0.68 m s–1) as comparisons between sonic anemometers (0.35–0.73 m s–1). Second, the lidar duo-beam scanning strategy provided horizontal transects of wind vectors comparison with scintillometer rmse 1.12–1.63 m s–1) which revealed mean and turbulent flow across the river and surrounds; in particular: chanelling flow along the river and turbulence changes consistent with the roughness changes between built to river environments. The results have important consequences for air quality and dispersion around urban rivers, especially given that many cities have high traffic rates on bankside roads.

The kinetics of the gas-phase reactions of selected monoterpenes and cyclo-alkenes with ozone and the NO3 radical

The relative rate method has been used to measure the room-temperature rate constants for the gasphase reactions of ozone and NO3 with selected monoterpenes and cyclo-alkenes with structural similarities to monoterpenes. Measurements were carried out at 298 ! 2 K and 760 ! 10 Torr. The following rate constants (in units of 10"18 cm3 molecule"1 s"1) were obtained for the reaction with ozone: methyl cyclohexene (132 ! 17), terpinolene (1290 ! 360), ethylidene cyclohexane (223 ! 57), norbornene (860 ! 240), t-butyl isopropylidene cyclohexane (1500 ! 460), cyclopentene (543 ! 94), cyclohexene (81 ! 18), cyclooctene (451 ! 66), dicyclopentadiene (1460 ! 170) and a-pinene (107 ! 13). For the reaction with NO3 the rate constants obtained (in units of 10"12 cm3 molecule"1 s"1) were: methyl cyclohexene (7.92 ! 0.95), terpinolene (47.9 ! 4.0), ethylidene cyclohexane (4.30 ! 0.24), norbornene (0.266 ! 0.029), cyclohexene (0.540 ! 0.017), cyclooctene (0.513 ! 0.029), dicyclopentadiene (1.20 ! 0.10) and a-pinene (5.17 ! 0.62). Errors are quoted as the root mean square of the statistical error (95% con!dence) and the quoted error in the rate constant for the reference compound. Combining these results with previous studies, new recommendations for the rate constants are presented. Molecular orbital energies were calculated for each alkene and the kinetic data are discussed in terms of the deviation from the structureeactivity relationship obtained from the rate constants for a series of simple alkenes. Lifetimes with respect to key initiators of atmospheric oxidation have been calculated suggesting that the studied reactions play dominant roles in the night-time removal of these compounds from the atmosphere.

Cyclic prefixed OQAM-OFDM and its application to single-carrier FDMA

Single-carrier frequency division multiple access (SC-FDMA) has appeared to be a promising technique for high data rate uplink communications. Aimed at SC-FDMA applications, a cyclic prefixed version of the offset quadrature amplitude modulation based OFDM (OQAM-OFDM) is first proposed in this paper. We show that cyclic prefixed OQAMOFDM CP-OQAM-OFDM) can be realized within the framework of the standard OFDM system, and perfect recovery condition in the ideal channel is derived. We then apply CP-OQAMOFDM to SC-FDMA transmission in frequency selective fading channels. Signal model and joint widely linear minimum mean square error (WLMMSE) equalization using a prior information with low complexity are developed. Compared with the existing DFTS-OFDM based SC-FDMA, the proposed SC-FDMA can significantly reduce envelope fluctuation (EF) of the transmitted signal while maintaining the bandwidth efficiency. The inherent structure of CP-OQAM-OFDM enables low-complexity joint equalization in the frequency domain to combat both the multiple access interference and the intersymbol interference. The joint WLMMSE equalization using a prior information guarantees optimal MMSE performance and supports Turbo receiver for improved bit error rate (BER) performance. Simulation resultsconfirm the effectiveness of the proposed SC-FDMA in termsof EF (including peak-to-average power ratio, instantaneous-toaverage power ratio and cubic metric) and BER performances.

Chaotic mixing and transport in Rossby-wave critical layers

A simple, dynamically consistent model of mixing and transport in Rossby-wave critical layers is obtained from the well-known Stewartson–Warn–Warn (SWW) solution of Rossby-wave critical-layer theory. The SWW solution is thought to be a useful conceptual model of Rossby-wave breaking in the stratosphere. Chaotic advection in the model is a consequence of the interaction between a stationary and a transient Rossby wave. Mixing and transport are characterized separately with a number of quantitative diagnostics (e.g. mean-square dispersion, lobe dynamics, and spectral moments), and with particular emphasis on the dynamics of the tracer field itself. The parameter dependences of the diagnostics are examined: transport tends to increase monotonically with increasing perturbation amplitude whereas mixing does not. The robustness of the results is investigated by stochastically perturbing the transient-wave phase speed. The two-wave chaotic advection model is contrasted with a stochastic single-wave model. It is shown that the effects of chaotic advection cannot be captured by stochasticity alone.

Toward vicarious calibration of microwave remote-sensing satellites in arid environments

The Soil Moisture and Ocean Salinity (SMOS) satellite marks the commencement of dedicated global surface soil moisture missions, and the first mission to make passive microwave observations at L-band. On-orbit calibration is an essential part of the instrument calibration strategy, but on-board beam-filling targets are not practical for such large apertures. Therefore, areas to serve as vicarious calibration targets need to be identified. Such sites can only be identified through field experiments including both in situ and airborne measurements. For this purpose, two field experiments were performed in central Australia. Three areas are studied as follows: 1) Lake Eyre, a typically dry salt lake; 2) Wirrangula Hill, with sparse vegetation and a dense cover of surface rock; and 3) Simpson Desert, characterized by dry sand dunes. Of those sites, only Wirrangula Hill and the Simpson Desert are found to be potentially suitable targets, as they have a spatial variation in brightness temperatures of <4 K under normal conditions. However, some limitations are observed for the Simpson Desert, where a bias of 15 K in vertical and 20 K in horizontal polarization exists between model predictions and observations, suggesting a lack of understanding of the underlying physics in this environment. Subsequent comparison with model predictions indicates a SMOS bias of 5 K in vertical and 11 K in horizontal polarization, and an unbiased root mean square difference of 10 K in both polarizations for Wirrangula Hill. Most importantly, the SMOS observations show that the brightness temperature evolution is dominated by regular seasonal patterns and that precipitation events have only little impact.

Estimation of sea surface temperature from the Spinning Enhanced Visible and Infra Red Imager, improved using numerical weather prediction

Most of the operational Sea Surface Temperature (SST) products derived from satellite infrared radiometry use multi-spectral algorithms. They show, in general, reasonable performances with root mean square (RMS) residuals around 0.5 K when validated against buoy measurements, but have limitations, particularly a component of the retrieval error that relates to such algorithms' limited ability to cope with the full variability of atmospheric absorption and emission. We propose to use forecast atmospheric profiles and a radiative transfer model to simulate the algorithmic errors of multi-spectral algorithms. In the practical case of SST derived from the Spinning Enhanced Visible and Infrared Imager (SEVIRI) onboard Meteosat Second Generation (MSG), we demonstrate that simulated algorithmic errors do explain a significant component of the actual errors observed for the non linear (NL) split window algorithm in operational use at the Centre de Météorologie Spatiale (CMS). The simulated errors, used as correction terms, reduce significantly the regional biases of the NL algorithm as well as the standard deviation of the differences with drifting buoy measurements. The availability of atmospheric profiles associated with observed satellite-buoy differences allows us to analyze the origins of the main algorithmic errors observed in the SEVIRI field of view: a negative bias in the inter-tropical zone, and a mid-latitude positive bias. We demonstrate how these errors are explained by the sensitivity of observed brightness temperatures to the vertical distribution of water vapour, propagated through the SST retrieval algorithm.

CP-OQAM-OFDM based SC-FDMA: adjustable user bandwidth and space-time coding

The discrete Fourier transmission spread OFDM DFTS-OFDM) based single-carrier frequency division multiple access (SC-FDMA) has been widely adopted due to its lower peak-to-average power ratio (PAPR) of transmit signals compared with OFDM. However, the offset modulation, which has lower PAPR than general modulation, cannot be directly applied into the existing SC-FDMA. When pulse-shaping filters are employed to further reduce the envelope fluctuation of transmit signals of SC-FDMA, the spectral efficiency degrades as well. In order to overcome such limitations of conventional SC-FDMA, this paper for the first time investigated cyclic prefixed OQAMOFDM (CP-OQAM-OFDM) based SC-FDMA transmission with adjustable user bandwidth and space-time coding. Firstly, we propose CP-OQAM-OFDM transmission with unequally-spaced subbands. We then apply it to SC-FDMA transmission and propose a SC-FDMA scheme with the following features: a) the transmit signal of each user is offset modulated single-carrier with frequency-domain pulse-shaping; b) the bandwidth of each user is adjustable; c) the spectral efficiency does not decrease with increasing roll-off factors. To combat both inter-symbolinterference and multiple access interference in frequencyselective fading channels, a joint linear minimum mean square error frequency domain equalization using a prior information with low complexity is developed. Subsequently, we construct space-time codes for the proposed SC-FDMA. Simulation results confirm the powerfulness of the proposed CP-OQAM-OFDM scheme (i.e., effective yet with low complexity).

Forecasting with difference and trend stationary models

Although difference-stationary (DS) and trend-stationary (TS) processes have been subject to considerable analysis, there are no direct comparisons for each being the data-generation process (DGP). We examine incorrect choice between these models for forecasting for both known and estimated parameters. Three sets of Monte Carlo simulations illustrate the analysis, to evaluate the biases in conventional standard errors when each model is mis-specified, compute the relative mean-square forecast errors of the two models for both DGPs, and investigate autocorrelated errors, so both models can better approximate the converse DGP. The outcomes are surprisingly different from established results.

Real-time forecasting of inflation and output growth with autoregressive models in the presence of data revisions

We examine how the accuracy of real-time forecasts from models that include autoregressive terms can be improved by estimating the models on ‘lightly revised’ data instead of using data from the latest-available vintage. The benefits of estimating autoregressive models on lightly revised data are related to the nature of the data revision process and the underlying process for the true values. Empirically, we find improvements in root mean square forecasting error of 2–4% when forecasting output growth and inflation with univariate models, and of 8% with multivariate models. We show that multiple-vintage models, which explicitly model data revisions, require large estimation samples to deliver competitive forecasts. Copyright © 2012 John Wiley & Sons, Ltd.

Systematic model forecast error in Rossby wave structure

Diabatic processes can alter Rossby wave structure; consequently errors arising from model processes propagate downstream. However, the chaotic spread of forecasts from initial condition uncertainty renders it difficult to trace back from root mean square forecast errors to model errors. Here diagnostics unaffected by phase errors are used, enabling investigation of systematic errors in Rossby waves in winter-season forecasts from three operational centers. Tropopause sharpness adjacent to ridges decreases with forecast lead time. It depends strongly on model resolution, even though models are examined on a common grid. Rossby wave amplitude reduces with lead time up to about five days, consistent with under-representation of diabatic modification and transport of air from the lower troposphere into upper-tropospheric ridges, and with too weak humidity gradients across the tropopause. However, amplitude also decreases when resolution is decreased. Further work is necessary to isolate the contribution from errors in the representation of diabatic processes.

Elastic net orthogonal forward regression

An efficient two-level model identification method aiming at maximising a model׳s generalisation capability is proposed for a large class of linear-in-the-parameters models from the observational data. A new elastic net orthogonal forward regression (ENOFR) algorithm is employed at the lower level to carry out simultaneous model selection and elastic net parameter estimation. The two regularisation parameters in the elastic net are optimised using a particle swarm optimisation (PSO) algorithm at the upper level by minimising the leave one out (LOO) mean square error (LOOMSE). There are two elements of original contributions. Firstly an elastic net cost function is defined and applied based on orthogonal decomposition, which facilitates the automatic model structure selection process with no need of using a predetermined error tolerance to terminate the forward selection process. Secondly it is shown that the LOOMSE based on the resultant ENOFR models can be analytically computed without actually splitting the data set, and the associate computation cost is small due to the ENOFR procedure. Consequently a fully automated procedure is achieved without resort to any other validation data set for iterative model evaluation. Illustrative examples are included to demonstrate the effectiveness of the new approaches.

Temperature-dependent orientational ordering on a spherical surface modeled with a lattice spin model

We study the orientational ordering on the surface of a sphere using Monte Carlo and Brownian dynamics simulations of rods interacting with an anisotropic potential. We restrict the orientations to the local tangent plane of the spherical surface and fix the position of each rod to be at a discrete point on the spherical surface. On the surface of a sphere, orientational ordering cannot be perfectly nematic due to the inevitable presence of defects. We find that the ground state of four +1/2 point defects is stable across a broad range of temperatures. We investigate the transition from disordered to ordered phase by decreasing the temperature and find a very smooth transition. We use fluctuations of the local directors to estimate the Frank elastic constant on the surface of a sphere and compare it to the planar case. We observe subdiffusive behavior in the mean square displacement of the defect cores and estimate their diffusion constants.

Can dynamically downscaled windstorm footprints be improved by observations through a probabilistic approach?

Windstorms are a main feature of the European climate and exert strong socioeconomic impacts. Large effort has been made in developing and enhancing models to simulate the intensification of windstorms, resulting footprints, and associated impacts. Simulated wind or gust speeds usually differ from observations, as regional climate models have biases and cannot capture all local effects. An approach to adjust regional climate model (RCM) simulations of wind and wind gust toward observations is introduced. For this purpose, 100 windstorms are selected and observations of 173 (111) test sites of the German Weather Service are considered for wind (gust) speed. Theoretical Weibull distributions are fitted to observed and simulated wind and gust speeds, and the distribution parameters of the observations are interpolated onto the RCM computational grid. A probability mapping approach is applied to relate the distributions and to correct the modeled footprints. The results are not only achieved for single test sites but for an area-wide regular grid. The approach is validated using root-mean-square errors on event and site basis, documenting that the method is generally able to adjust the RCM output toward observations. For gust speeds, an improvement on 88 of 100 events and at about 64% of the test sites is reached. For wind, 99 of 100 improved events and ~84% improved sites can be obtained. This gives confidence on the potential of the introduced approach for many applications, in particular those considering wind data.

Boundary condition effects in the simulation study of equilibrium properties of magnetic dipolar fluids

In this paper we investigate the equilibrium properties of magnetic dipolar (ferro-) fluids and discuss finite-size effects originating from the use of different boundary conditions in computer simulations. Both periodic boundary conditions and a finite spherical box are studied. We demonstrate that periodic boundary conditions and subsequent use of Ewald sum to account for the long-range dipolar interactions lead to a much faster convergence (in terms of the number of investigated dipolar particles) of the magnetization curve and the initial susceptibility to their thermodynamic limits. Another unwanted effect of the simulations in a finite spherical box geometry is a considerable sensitivity to the container size. We further investigate the influence of the surface term in the Ewald sum-that is, due to the surrounding continuum with magnetic permeability mu(BC)-on the convergence properties of our observables and on the final results. The two different ways of evaluating the initial susceptibility, i.e., (1) by the magnetization response of the system to an applied field and (2) by the zero-field fluctuation of the mean-square dipole moment of the system, are compared in terms of speed and accuracy.