Comparison of several methods for the solution of the Helmholtz equation

Summary A series of Helmholtz equations has to be solved in short-range weather forecast models which use a splitting scheme of integration. For these purposes the successive overrelaxation, the Gauss-Seidel relaxation, the conjugate gradient method, the steepest descent method, the full-multigrid method and the direct method based on the minimum degree algorithm were used and their efficiencies were compared. It was found that the full-multigrid method was the most efficient among the iterative methods in terms of computational time, and that the effect rapidly increased with the grid size. The direct method may be an appropriate approach if the solution is repeated for various right-hand sides, but it requires large auxiliary computer memory. The selection of the optimum method depends on the concrete problem being solved and on the computer memory available.     

A radar-based verification of precipitation forecast for local convective storms

Local flash flood storms with a rapid hydrological response are a real challenge for quantitative precipitation forecasting (QPF). It is relevant to assess space domains, to which the QPF approaches are applicable. In this paper an attempt is made to evaluate the forecasting capability of a high-resolution numerical weather prediction (NWP) model by means of area-related QPF verification. The results presented concern two local convective events, which occurred in the Czech Republic (CR) on 13 and 15 July 2002 and caused local flash floods. We used the LM COSMO model (Lokall Model of the COSMO consortium) adapted to the horizontal resolution of 2.8 km over a model domain covering the CR. The 18 h forecast of convective precipitation was verified by using radar rainfall totals adjusted to the measured rain gauge data. The grid point-related root mean square error (RMSE) value was calculated over a square around the grid point under the assumption that rainfall values were randomly distributed within the square. The forecast accuracy was characterized by the mean RMSE over the whole verification domain. We attempt to show a dependence of both the RMSE field and the mean RMSE on the square size. The importance of a suitable merger between the radar and rain gauge datasets is demonstrated by a comparison between the verification results obtained with and without the gauge adjustment. The application of verification procedure demonstrates uncertainties in the precipitation forecasts. The model was integrated with initial conditions shifted by 0.5° distances. The four verifications, corresponding to the shifts in the four directions, show differences in the resulting QPF, which depend on the size of verification area and on the direction of the shift.     

Visualization of the solar magnetic field using coefficients of harmonic expansion in the potential approximation

A method for visualization of the solar magnetic field is suggested and implemented. The harmonic expansion coefficients obtained in the potential approximation from magnetic-field observations at the photospheric level are used as an input. Three-dimensional equations for field lines are numerically integrated, and the results are presented in the form of projections onto the picture plane. The density of the line number is assumed to be proportional to the magnetic flux density. The lines of different topological connectedness are differently colored and show areas with open and closed configurations, thus mapping the information about the field direction and magnitude. This method is useful for research and applied studies related to investigation and forecasting of space weather.     

On the visible shape of the cold plasma jets in the solar chromosphere

Lines of equal optical thickness are calculated for cold plasma jets propagating in the simplest magnetic configuration. The paraxial approximation is used in the case of jets directed along the axis of a magnetic dipole. The results explain the apparently convergent as well as divergent shapes of the jets in a divergent magnetic configuration.     

On interplanetary electric and magnetic fields

A kinematic model of the stationary electromagnetic fields in interplanetary space with finite conductivity is considered. The electrodynamic problem is solved for a medium with uniform conductivity and radial plasma outflow from a spherical source. Simple analytical formulae are obtained for electric and magnetic fields, currents and charges in the case of a uniformly-magnetized rotating sphere.     

Radiation conditions of a mission to Jupiter and Europa

Radiation conditions in Jupiter’s environment and the plasma environment in interplanetary space during a Jupiter-Europa mission are estimated. The numerical modeling results can be used when planning the mission.     

Statistical distributions and classification of X-ray flares according to their duration on the sun

The results of the statistical analysis of the GOES data related to the length of the period, during which the X-ray emission of solar flares increases, provide reliable grounds for the objective distinction of different types, sometimes referred to in the literature as typical and nontypical for bimodal classification. The events may be also partitioned into three (“impulsive”, “typical”, and “long duration”) or more “types”. These “types” should be separated from statistical fluctuations in the case of rare events. When the number of analyzed events increases, these fluctuations are gradually smoothed and become less significant, and the distribution of flares according to the duration of their growth is, on the whole, well described by the single lognormal law.     

Geodynamic Regimes of Carbonatite Formation According to the Paleo-Reconstruction Method

Doklady Earth Sciences - Three models of geodynamic regimes of carbonatite formation are now actively being developed because of the high trace metal potential of this rock type: carbonatite melt...     

Hydrodynamic Classification of Solar Wind Flows

At the present time, there is no generally accepted classification of the solar wind flows. There are various approaches to this problem depending on the goal of the study. In our paper, we propose the binary classification of the solar wind types by the main hydrodynamic parameters (velocity, temperature, and density) based on the statistical analysis of the solar wind. The analysis of the OMNIWeb one-minute data is performed for the period from 1996 to 2017, which encompasses solar cycle 23 and current solar cycle 24. Eight types of the solar wind are distinguished: fast-hot-dense, fast-hot-rarefied, fast-cold-dense, fast-cold-rarefied, slow-hot-dense, slow-hot-rarefied, slow-cold-dense, slow-cold-rarefied. These types occur with different frequency and are the consequences of different manifestations of solar activity. Of particular interest are the solar wind flows, the parameters of which deviate from the averages most significantly.