Localisation Radius Research Articles

Divergence of the Ensemble Transform Kalman Filter (LETKF) by Nonlocal Observations

Ensemble Kalman filters are powerful tools to merge model dynamics and observation data. For large system models, they are known to diverge due to subsampling errors at small ensemble size and thus possible spurious correlations in forecast error covariances. The Local Ensemble Transform Kalman filter (LETKF) remedies these disadvantages by localisation in observation space. However, its application to nonlocal observations is still under debate since it is still not clear how to optimally localize nonlocal observations. The present work studies intermittent divergence of filter innovations and shows that it increases forecast errors. Nonlocal observations enhance such innovation divergence under certain conditions, whereas similar localisation radius and sensitivity function width of nonlocal observations minimizes the divergence rate. The analysis of the LETKF reveals inconsistencies in the assimilation of observed and unobserved model grid points which may yield detrimental effects. These inconsistencies inter alia indicate that the localisation radius should be larger than the sensitivity function width if spatially synchronised system activity is expected. Moreover, the shift of observation power from observed to unobserved grid points hypothesised in the context of catastrophic filter divergence is supported for intermittent innovation divergence. Further possible mechanisms yielding such innovation divergence are ensemble member alignment and a novel covariation between background perturbations in location and observation space.

Localisation of intense sound produced by an optical pulsating discharge in the air

It is shown that the localisation radius and the spectrum of intense sound produced by an optical pulsating discharge in the air depend on the power and repetition rate of the repetitively pulsed laser radiation, which is associated with a manifestation of the wave merging mechanism and sound absorption in the air. The experiment makes use of a CO2 laser with a power of ∼1.5 kW and a repetition rate of microsecond pulses of ∼50 kHz.

Optimising assimilation of hydrographic profiles into isopycnal ocean models with ensemble data assimilation

Hydrographic profiles are crucial observational datasets for constraining ocean models and their vertical structure. In this study, we investigate a key implementation setup for optimising their assimilation into isopycnal ocean models. For this purpose, we use the Norwegian Climate Prediction Model (NorCPM), which is a fully-coupled climate prediction system based on the Norwegian Earth System Model and the ensemble Kalman filter. First, we revisit whether it is more accurate to assimilate observations in their original coordinate (z-level coordinate) or to transform them into isopycnal coordinates prior to assimilation. The analysis is performed with a single assimilation step using synthetic observations that mimic the characteristic properties of hydrographic profiles: varying vertical resolutions, profiles of only temperature and observations only in the top 1000 m. Assimilating profiles in their native coordinate (z-level coordinates) performs best because converting observations into isopycnal coordinates is strongly non-linear which reduces the efficiency of the assimilation. Secondly, we investigate how to set the horizontal localisation radius for our system. A radius that varies with latitude following a bimodal Gaussian function fits the system well. Thirdly, we estimate observation error, which consists of both instrumental error and representativeness error. In the proposed formulation only the instrumental error decreases with the number of observations during superobing, because the representativeness error is dominated by model limitation. Finally, we demonstrate the impact of assimilating hydrographic profiles from the observational EN4 dataset into NorCPM. An analysis of 10 years with monthly assimilation is performed with special focus on assessing the accuracy and the reliability of our analysis. The assimilation of hydrographic profiles into NorCPM is found to efficiently reduce the model bias and error, and the ensemble spread is found to be a reliable estimator for the forecast error in most regions.

Relaxation time distribution of distant‐pair recombination: Application to QFRS of PL in a‐Si:H

AbstractThe distribution function of relaxation time of distant‐pair (DP), or nongeminate recombination is derived in an analytic form from the existing theories of DP recombination to analyse the data of quadrature frequency resolved spectroscopy (QFRS) of photoluminescence (PL) in a‐Si:H with the competing recombination model. The distribution function has a single parameter of metastable carrier density n and yields too narrow QFRS spectrum to fit the experimental data. This is improved with introducing the fluctuation Δ of the electron localisation radius ae. The devised formula is demonstrated to predict the dependence of the DP recombination on the photogeneration rate and the defect density in the QFRS data of the high‐quality and defective a‐Si:H. (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Covariance localisation and balance in an Ensemble Kalman Filter

AbstractA major limitation of the Ensemble Kalman Filter (EnKF) is that the finite ensemble size introduces sampling error into the background covariances, with severe consequences for atmospheric and oceanographic applications. The negative effects of sampling error are customarily limited by covariance localisation, which earlier studies have suggested may introduce imbalance into the system. The deleterious effects of localisation upon balance are confirmed and detailed here, with localisation producing analyses with weaker geostrophic balance and stronger divergence than are obtained using the unlocalised covariances. These imbalances reduce as the localisation radius is increased, but are argued to be large for typical settings. An improved method for calculating local covariances from an ensemble is presented, in which the localisation is performed in streamfunction–velocity potential (ψ–χ), rather than wind component, space. Analyses using this method better preserve the balances contained within the unlocalised covariance model. This transformation further allows the option of intervariable localisation, in which the cross‐covariances involving χ, which are weak and therefore particularly subject to sampling error, are set to 0 instead of being calculated from the ensemble. The various localisations are compared in a series of identical‐twin experiments, with the new localisations producing analyses that are better balanced and significantly more accurate than the usual approach. The localisation with the χ cross‐covariances set to 0 is shown to be superior for the smaller ensemble sizes but not for the larger, implying that the larger ensembles are capable of resolving some of the true χ cross‐covariance in the test system. Copyright © 2009 Royal Meteorological Society

Water dynamics in lignite coal pores

The dynamics of water molecules in the pores of lignite coal have been studied by quasielastic neutron scattering (QENS) technique. Neutron incoherent quasielastic scattering data from the confined water are analysed following the procedure described by Volino and Dianoux (Mol. Phys. 41 (1980) 271). We have obtained the localisation radius, the translational diffusion coefficient and the residence time for translational diffusion at room temperature. It was found that the diffusion of water was significantly influenced due to the confinement effects.

Photoconductivity and photoluminescence processes in amorphous carbon

The photoconductivities of various sp 3 bonded amorphous carbons were studied to understand their recombination and photoluminescence processes. At temperatures >200 K, the photoconductivity of each type of carbon does not vary inversely with the paramagnetic defect density, indicating that paramagnetic defects are not the only recombination centres. This effect occurs because carrier demarcation levels lie in the band tails, so both defects and tail states act as recombination centres. The temperature regime <200 K is due to energy loss hopping. The localisation radius is not constant, so the capture radius cannot be treated as constant when describing luminescence efficiency in hydrogenated amorphous carbon (a-C:H) of different band gaps.

Dynamics of water contained in porous alumina

We report dynamics of water molecules contained in the pores of alumina gel as studied by neutron scattering technique. Neutron incoherent quasi-elastic scattering data from confined water are analysed. Radius of confinement (or the localisation radius), the translational diffusion coefficient and the residence time for translational diffusion at room temperature are obtained. It is found that the diffusion of water molecules contained in the pores of alumina gel differ from the bulk water diffusion phenomena.

Diffusion of water in porous alumina: Neutron scattering study

Dynamics of water molecules contained in the pores of alumina gel have been studied by the neutron scattering technique. Neutron incoherent quasi elastic scattering data from the confined water are analysed following the procedure described by Volino and Dianoux [15]. We have obtained the radius of confinement (or the localisation radius), the translational diffusion coefficient and the residence time for translational diffusion at room temperature. It was found that the bulk water diffusion phenomena are very much different from the diffusion of water molecules in a confined system.

Evidence for correlation effects in electronic hopping of CdF2:Y crystals

Current measurements in CDF2 crystals doped with 0.001-0.1 mol.% Y and with electron concentrations of order 1015 cm-3 are studied in the temperature range 10-60 K by applying electric fields up to 5*104 V cm-1. The current-voltage-temperature characteristics are examined according to the Apsley-Hughes model for hopping conduction. The value of the density of states at the Fermi level and of the localisation radius are obtained. Deviations from theoretical trend are observed at low applied fields, showing the existence of a conductivity drop that is attributed to the formation of collective ordered electronic structures, characteristics of compounds having low electronic density.

Conductivity in heavily doped and compensated epitaxial gallium arsenide layers

The dependence of conductivity on electric field and on temperature in heavily doped and strongly compensated liquid-phase epitaxial GaAs layers is investigated. From the dependences on temperature (in low electric fields) and electric field (in strong electric fields) determined experimentally, a localisation radius a and density of states at the Fermi level g(EF) are determined and the value of the degree of compensation K for 1-K<<1 is estimated. Good agreement between theory and experiment is obtained. At moderate electric fields qualitative agreement with the existing theoretical models is obtained.