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For analyzing distribution functions of relativistic plasma, we propose a mixture model composed of relativistic Maxwellian distributions. We first summarize the basic properties of the relativistic Maxwellian distribution, including the derivation of the normalization constant when there is a bulk velocity. We also examine the maximum likelihood estimation of the relativistic Maxwellian distribution. We then introduce a relativistic Maxwellian mixture model (R-MMM), which is a weighted sum of relativistic Maxwellian distributions. We develop an expectation–maximization algorithm for estimating the parameters of R-MMM, namely, the mixing proportion, the bulk velocity, and the temperature of each component. We apply a two-component R-MMM to a distribution function by a particle-in-cell (PIC) simulation of relativistic pair plasma and separate the simulated distribution function into two components. We find that one component has a large bulk velocity while the other is almost stagnant, and that the two components have almost the same temperatures, which is also consistent with the initial temperature of PIC simulation. [ABSTRACT FROM AUTHOR]

Non-Gaussian probability density functions (PDFs) in convection initiation (CI) and development were investigated using a particle filter with a storm-scale numerical prediction model and an adaptive observation error estimator (NHM-RPF). An observing system simulation experiment (OSSE) was conducted with a 90-min assimilation period and 1000 particles at a 2-km grid spacing. Pseudosurface observations of potential temperature (PT), winds, water vapor (QV), and pseudoradar observations of rainwater (QR) in the lower troposphere were created in a nature run that simulated a well-developed cumulonimbus. The results of the OSSE (PF) show a significant improvement in comparison to ensemble simulations without any observations. The Gaussianity of the PDFs for PF in the CI area was evaluated using the Bayesian information criterion to compare goodness-of-fit of Gaussian, two-Gaussian mixture, and histogram models. The PDFs are strongly non-Gaussian when NHM-RPF produces diverse particles over the CI period. The non-Gaussian PDF of the updraft is followed by the upper-bounded PDF of the relative humidity, which produces non- Gaussian PDFs of QV and PT. The PDFs of the cloud water and QR are strongly non-Gaussian throughout the experimental period. We conclude that the non-Gaussianity of the CI originated from the non- Gaussianity of the updraft. In addition, we show that the adaptive observation error estimator significantly contributes to the stability of PF and the robustness to many observations. [ABSTRACT FROM AUTHOR]

We develop a Bayesian technique for estimating the parameters in the observation-noise covariance matrix R t for ensemble data assimilation. We design a posterior distribution by using the ensemble-approximated likelihood and a Wishart prior distribution and present an iterative algorithm for parameter estimation. The temporal smoothness of R t can be controlled by an adequate choice of two parameters of the prior distribution, the covariance matrix S and the number of degrees of freedom ν. The ν parameter can be estimated by maximizing the marginal likelihood. The present formalism can handle cases in which the number of data points or data positions varies with time, the former of which is exemplified in the experiments. We present an application to a coupled atmosphere-ocean model under each of the following assumptions: R t is a scalar multiple of a fixed matrix ( R t= α t Σ, where α t is the scalar parameter and Σ is the fixed matrix), R t is diagonal, R t has fixed eigenvectors or R t has no specific structure. We verify that the proposed algorithm works well and that only a limited number of iterations are necessary. When R t has one of the structures mentioned above, by assuming S to be the previous estimate we obtain a Bayesian estimate of R t that varies smoothly in time compared with the maximum-likelihood estimate. When R t has no specific structure, we need to regularize S to maintain the positive-definiteness. Through twin experiments, we find that the best estimate of R t is, in general, obtained by a combination of structure-free R t and tapered S using decorrelation lengths of half the size of the model ocean basin. From experiments using real observations, we find that the estimates of the structured R t lead to overfitting of the data compared with the structure-free R t. [ABSTRACT FROM AUTHOR]

Abstract: We present an iterative algorithm for estimating the observation‐noise covariance matrix Rt for ensemble‐based data assimilation. The proposed algorithm enables us to estimate parameters in Rt, the number of which may become exceedingly large for data assimilation. The optimal Rt is estimated based on the maximum likelihood and the algorithm can be described as an expectation‐maximization (EM) algorithm. The key to constructing the algorithm is to obtain the optimality condition of Rt in a closed form. The proposed method estimates Rt, which is adaptive to the current observation yt. We present an application of the proposed method to a coupled atmosphere–ocean model and find that only a few iterations are necessary for convergence. We also find that Rt needs to have some kind of structure to obtain a reasonable covariance matrix using the proposed algorithm. [ABSTRACT FROM AUTHOR]

A local dispersion relation is derived for the lower-hybrid-drift instability including the effects of magnetic curvature associated with transverse electromagnetic perturbations. To account for the curvature drift, an alternative method proposed by Nakamura [Phys. Plasmas 4, 3765 (1997)] is applied to obtain the perturbed distribution function. It is found that the previous treatment, i.e., simulating the curvature drift by a virtual gravitational drift, is considerably inaccurate. When an ambient magnetic field has a curvature so that the curvature drift is directed opposite the ∇B drift, the maximum growth rate increases as long as the radius of curvature is larger than a certain value, while the rate decreases for a sharper magnetic field curvature. At the same time, the wave number giving the maximum growth decreases monotonically. The growth rate is increased by a curvature drift coincident with the ∇B drift. The effects of the magnetic curvature become larger in high-beta plasmas. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

EISCAT_3D is a project to build a multi-site phased-array incoherent scatter radar system in northern Fenno-Scandinavia. We demonstrate via numerical simulation how useful monochromatic images taken by a multi-point imager network are for auroral research in the EISCAT_3D project. We apply the generalized aurora computed tomography (G-ACT) method to modelled observational data from real instruments, such as the Auroral Large Imaging System (ALIS) and the EISCAT_3D radar. G-ACT is a method for reconstructing the three-dimensional (3D) distribution of auroral emissions and ionospheric electron density (corresponding to the horizontal two-dimensional (2D) distribution of energy spectra of precipitating electrons) from multi-instrument data. It is assumed that the EISCAT_3D radar scans an area of 0.8° in geographic latitude and 3° in longitude at an altitude of 130 km with 10 × 10 beams from the radar core site at Skibotn (69.35° N, 20.37° E). Two neighboring discrete arcs are assumed to appear in the observation region of the EISCAT_3D radar. The reconstruction results from G-ACT are compared with those from the normal ACT as well as the ionospheric electron density from the radar. It is found that G-ACT can interpolate the ionospheric electron density at a much higher spatial resolution than that observed by the EISCAT_3D radar. Furthermore, the multiple arcs reconstructed by G-ACT are more precise than those by ACT. In particular, underestimation of the ionospheric electron density and precipitating electrons' energy fluxes inside the arcs is significantly improved by G-ACT including the EISCAT_3D data. Even when the ACT reconstruction is difficult due to the unsuitable locations of the imager sites relative to the discrete arcs and/or a small number of available images, G-ACT allows us to obtain better reconstruction results. [ABSTRACT FROM AUTHOR]

We have developed a statistical downscaling method for generating probabilistic climate projections using multiple general circulation models (GCMs). A regression model was established so that the combination of coefficients of the GCMs reflects the characteristics of the variation of observations at each grid point. We adopted the elastic net penalty to estimate the regression model, considering model projection similarities. Using an observation system with a high spatial resolution, we conducted statistically downscaled probabilistic climate projections with 20-km horizontal grid spacing. Mean precipitation is generally projected to increase associated with higher temperatures and consequently increased atmospheric moisture content. Weakening of the winter monsoon may cause precipitation decreases in some areas. There is a high probability of a temperature increase in excess of 4 K in most areas of Japan by the end of the 21st century under the CMIP5 RCP8.5 scenario. The estimated probability of monthly precipitation exceeding 300 mm increases along the Pacific coast of Japan during the summer season and along the coast of the Japan Sea during the winter season. Our probabilistic climate projection using statistical methods is expected to provide useful information to stakeholders involved in impact studies and risk assessments. [ABSTRACT FROM AUTHOR]