A perturbation approach to coherent propagation of energetic charged particles in random magnetic fields

The Fokker-Planck equation describing the propagation of charged particles in magnetic fields that consist of a dominant constant guiding field and superposed random fluctuations is solved by applying the perturbation method of dividing the total particle density into an averaged isotropic and a small anisotropic component. A particle transport equation is derived which describes the 'coherent' propagation of a particle pulse whose center moves at half the constant total particle velocity in either the positive or negative direction. The range of validity of the coherent solution is examined, and the general formulas for coherent propagation are applied to the slab, isotropic, and Alfven-wave models of magnetic-field fluctuations. Ranges of magnetic-fluctuation spectral indices are identified over which diffusive and coherent particle-transport modes can exist in the three models considered

Linear response separation of a solid into atomic constituents: Li, Al, and their evolution under pressure

We present the first realization of the generalized pseudoatom concept introduced by Ball, and adopt the name enatom to minimize confusion. This enatom, which consists of a unique decomposition of the total charge density (or potential) of any solid into a sum of overlapping atomiclike contributions that move rigidly with the nuclei to first order, is calculated using (numerical) linear response methods, and is analyzed for both fcc Li and Al at pressures of 0, 35, and 50 GPa. These two simple fcc metals (Li is fcc and a good superconductor in the 20-40 GPa range) show different physical behaviors under pressure, which reflects the increasing covalency in Li and the lack of it in Al. The nonrigid (deformation) parts of the enatom charge and potential have opposite signs in Li and Al; they become larger under pressure only in Li. These results establish a method of construction of the enatom, whose potential can be used to obtain a real-space understanding of the vibrational properties and electron-phonon interaction in solids.Comment: 13 pages, 9 figures, 1 table, V2: fixed problem with Fig. 7, V3: minor correction

Copula-based assimilation of radar and gauge information to derive bias corrected precipitation fields

This study addresses the problem of combining radar information and gauge measurements. Gauge measurements are the best available source of absolute rainfall intensity albeit their spatial availability is limited. Precipitation information obtained by radar mimics well the spatial patterns but is biased for their absolute values. <br><br> In this study copula models are used to describe the dependence structure between gauge observations and rainfall derived from radar reflectivity at the corresponding grid cells. After appropriate time series transformation to generate "iid" variates, only the positive pairs (radar >0, gauge >0) of the residuals are considered. As not each grid cell can be assigned to one gauge, the integration of point information, i.e. gauge rainfall intensities, is achieved by considering the structure and the strength of dependence between the radar pixels and all the gauges within the radar image. Two different approaches, namely <i>Maximum Theta</i> and <i>Multiple Theta</i>, are presented. They finally allow for generating precipitation fields that mimic the spatial patterns of the radar fields and correct them for biases in their absolute rainfall intensities. The performance of the approach, which can be seen as a bias-correction for radar fields, is demonstrated for the Bavarian Alps. The bias-corrected rainfall fields are compared to a field of interpolated gauge values (ordinary kriging) and are validated with available gauge measurements. The simulated precipitation fields are compared to an operationally corrected radar precipitation field (RADOLAN). The copula-based approach performs similarly well as indicated by different validation measures and successfully corrects for errors in the radar precipitation

Exploring the potential of the cost-efficient tahmo observation data for hydro-meteorological applications in sub-saharan africa

The Trans-African Hydro-Meteorological Observatory (TAHMO) is a promising initiative aiming to install 20,000 stations in sub-Saharan Africa counteracting the decreasing trend of available measuring stations. To achieve this goal, it is particularly important that the installed weather stations are cost-efficient, appropriate for African conditions, and reliably measure the most important variables for hydro-meteorological applications. Since there exist no performance studies of TAHMO stations while operating in Africa, it is necessary to investigate their performance under different climate conditions. This study provides a first analysis of the performance of 10 selected TAHMO stations across Burkina Faso (BF). More specifically, the analysis consists of missing value statistics, plausibility tests of temperature (minimum, maximum) and precipitation, spatial dependencies (correlograms) by comparison with daily observations from synoptical stations of the BF meteorological service as well as cross-comparison between the TAHMO stations. Based on the results of this study for BF for the period from May 2017 to December 2020, it is concluded that TAHMO potentially offers a reliable and cost-efficient solution for applications in hydro-meteorology. The usage of wind speed measurements cannot be recommended without reservation, at least not without bias correcting of the data. The limited measurement period of TAHMO still prevents its usability in climate (impact) research. It is also stressed that TAHMO cannot replace existing observation networks operated by the local meteorological services, but it can be a complement and has great potential for detailed spatial analyses. Since restricted to BF in this analysis, more evaluation studies of TAHMO are needed considering different environmental and climate conditions across SSA

Local well-posedness for the nonlinear Schr\"odinger equation in the intersection of modulation spaces Mp,qs(Rd)∩M∞,1(Rd)M_{p, q}^s(\mathbb{R}^d) \cap M_{\infty, 1}(\mathbb{R}^d)

We introduce a Littlewood-Paley characterization of modulation spaces and use it to give an alternative proof of the algebra property, somehow implicitly contained in Sugimoto (2011), of the intersection $M^s_{p,q}(\mathbb{R}^d) \cap M_{\infty, 1}(\mathbb{R}^d)$ for $d \in \mathbb{N}$, $p, q \in [1, \infty]$ and $s \geq 0$. We employ this algebra property to show the local well-posedness of the Cauchy problem for the cubic nonlinear Schr\"odinger equation in the above intersection. This improves Theorem 1.1 by B\'enyi and Okoudjou (2009), where only the case $q = 1$ is considered, and closes a gap in the literature. If $q > 1$ and $s > d \left(1 - \frac{1}{q}\right)$ or if $q = 1$ and $s \geq 0$ then $M^s_{p,q}(\mathbb{R}^d) \hookrightarrow M_{\infty, 1}(\mathbb{R}^d)$ and the above intersection is superfluous. For this case we also reobtain a H\"older-type inequality for modulation spaces.Comment: 14 page

Simultaneous multicopter-based air sampling and sensing of meteorological variables

The state and composition of the lowest part of the planetary boundary layer (PBL), i.e., the atmospheric surface layer (SL), reflects the interactions of external forcing, land surface, vegetation, human influence and the atmosphere. Vertical profiles of atmospheric variables in the SL at high spatial and temporal resolution increase our understanding of these interactions, but are still challenging to measure appropriately. Traditional ground-based observations include towers that often cover only few measurement heights on a fixed location. At the same time, remote sensing techniques and aircraft measurements are challenged to achieve sufficient detail close to the ground. Vertical and horizontal sounding of the PBL can be complemented by unmanned aerial vehicles (UAV). Our aim in this case study is to assess the use of a multicopter-type UAV to simultaneously support the spatial sampling of air and the sensing of meteorological variables for the study of the surface exchange processes. To this end, a UAV was equipped with onboard air temperature and humidity sensors, while wind conditions were determined from the UAV’s flight control sensors. Further, the UAV was used to systematically change the location of a sample inlet connected to a sample tube, allowing the observation of methane abundance using a ground-based analyzer. Vertical methane gradients were found during stable atmospheric conditions with a gradient of about 300 ppb. Our results showed that both methane and meteorological conditions were in agreement with other observations at the site during the ScaleX-2015 campaign. The multicopter-type UAV was capable of simultaneous in situ sensing of meteorological state variables and sampling of air up to 50 m above the surface, which extended the vertical profile height of existing tower-based infrastructure by a factor of five