A fast convergence fourth-order Vlasov model for Hall thruster ionization oscillation analyses

A 1D1V hybrid Vlasov-fluid model was developed for this study to elucidate ionization oscillations of Hall thrusters (HTs). The Vlasov equation for ions velocity distribution function (IVDF) with ionization source term is solved using a constrained interpolation profile conservative semi-Lagrangian (CIP-CSL) method. The fourth-order weighted essentially non-oscillatory (4th WENO) limiter is applied to the first derivative term to minimize numerical oscillation in the discharge oscillation analyses. The fourth-order spatial accuracy is verified through a 1D scalar test case. Nonoscillatory and high-resolution features of the Vlasov model are confirmed by simulating the test cases of the Vlasov–Poisson (VP) system and by comparing the results with a particle-in-cell (PIC) method. A 1D1V Hall thruster simulation is performed through the hybrid Vlasov-fluid model. The ionization oscillation is analysed. The macroscopic plasma properties are compared with those obtained from a hybrid PIC method. The comparison indicates that the hybrid Vlasov-fluid model yields noiseless results and that the steady-state waveform is calculable in a short time period.

Spatio-temporal soil moisture retrieval at the catchment scale using a dense network of cosmic-ray neutron sensors

Cosmic-ray neutron sensing (CRNS) is a powerful technique for retrieving representative estimates of soil water content at a horizontal scale of hectometres (the “field scale”) and depths of tens of centimetres (“the root zone”). This study demonstrates the potential of the CRNS technique to obtain spatio-temporal patterns of soil moisture beyond the integrated volume from isolated CRNS footprints. We use data from an observational campaign carried out between May and July 2019 that featured a dense network of more than 20 neutron detectors with partly overlapping footprints in an area that exhibits pronounced soil moisture gradients within one square kilometre. The present study is the first to combine these observations in order to represent the heterogeneity of soil water content at the sub-footprint scale as well as between the CRNS stations. First, we apply a state-of-the-art procedure to correct the observed neutron count rates for static effects (heterogeneity in space, e.g. soil organic matter) and dynamic effects (heterogeneity in time, e.g. barometric pressure). Based on the homogenized neutron data, we investigate the robustness of a calibration approach that uses a single calibration parameter across all CRNS stations. Finally, we benchmark two different interpolation techniques for obtaining spatio-temporal representations of soil moisture: first, ordinary Kriging with a fixed range; second, spatial interpolation complemented by geophysical inversion (“constrained interpolation”). To that end, we optimize the parameters of a geostatistical interpolation model so that the error in the forward-simulated neutron count rates is minimized, and suggest a heuristic forward operator to make the optimization problem computationally feasible. Comparison with independent measurements from a cluster of soil moisture sensors (SoilNet) shows that the constrained interpolation approach is superior for representing horizontal soil moisture gradients at the hectometre scale. The study demonstrates how a CRNS network can be used to generate coherent, consistent, and continuous soil moisture patterns that could be used to validate hydrological models or remote sensing products.

A New Approach of Constrained Interpolation Based on Cubic Hermite Splines

Suppose we have a constrained set of data and wish to approximate it using a suitable function. It is natural to require the approximant to preserve the constraints. In this work, we state the problem in an interpolating setting and propose a parameter-based method and use the well-known cubic Hermite splines to interpolate the data with a constrained spline to provide with a C 1 interpolant. Then, more smoothing constraints are added to obtain C 2 continuity. Additionally, a minimization criterion is presented as a theoretical support to the proposed study; this is performed using linear programming. The proposed methods are demonstrated with illustrious examples.

Implementation of higher-order advection schemes in a numerical ice-sheet model for ice-core studies

<p>Computation of temperature and age fields by numerical ice-sheet models is an important issue for ice-core related studies.  Generally the evolution of temperature and/or age in an ice-sheet model is formulated using an advection equation.  There are many variation of the formulation, which differ in numerical aspects such as stability, accuracy, numerical diffusivity, conservation and/or computational costs.  Saito et al (2020, GMD) implement Rational Constrained Interpolation Profile (RCIP) scheme on vertical 1-d age computation of ice sheet, and demonstrate its efficiency, in particular, to preserve surface mass balance properties recorded at the deposit in terms of annual layer thickness.  Successively, we have been extending the development using RCIP or similar higher-order advection schemes on 3-d age or temperature computation.  In this study, we demonstrate 1-d temperature computation by various numerical schemes including classical upwind schemes and compare the accuracy of those schemes.</p>

Application of Dynamically Constrained Interpolation Methodology in Simulating National-Scale Spatial Distribution of PM2.5 Concentrations in China

Numerous studies have revealed that the sparse spatiotemporal distributions of ground-level PM2.5 measurements affect the accuracy of PM2.5 simulation, especially in large geographical regions. However, the high precision and stability of ground-level PM2.5 measurements make their role irreplaceable in PM2.5 simulations. This article applies a dynamically constrained interpolation methodology (DCIM) to evaluate sparse PM2.5 measurements captured at scattered monitoring sites for national-scale PM2.5 simulations and spatial distributions. The DCIM takes a PM2.5 transport model as a dynamic constraint and provides the characteristics of the spatiotemporal variations of key model parameters using the adjoint method to improve the accuracy of PM2.5 simulations. From the perspective of interpolation accuracy and effect, kriging interpolation and orthogonal polynomial fitting using Chebyshev basis functions (COPF), which have been proved to have high PM2.5 simulation accuracy, were adopted to make a comparative assessment of DCIM performance and accuracy. Results of the cross validation confirm the feasibility of the DCIM. A comparison between the final interpolated values and observations show that the DCIM is better for national-scale simulations than kriging or COPF. Furthermore, the DCIM presents smoother spatially interpolated distributions of the PM2.5 simulations with smaller simulation errors than the other two methods. Admittedly, the sparse PM2.5 measurements in a highly polluted region have a certain degree of influence on the interpolated distribution accuracy and rationality. To some extent, adding the right amount of observations can improve the effectiveness of the DCIM around existing monitoring sites. Compared with the kriging interpolation and COPF, the results show that the DCIM used in this study would be more helpful for providing reasonable information for monitoring PM2.5 pollution in China.

Spatio-temporal soil moisture retrieval at the catchment-scale using a dense network of cosmic-ray neutron sensors

The method of Cosmic-Ray Neutron Sensing (CRNS) is a powerful technique to retrieve representative estimates of soil water content at a horizontal scale of hectometers (the field scale) and depths of tens of centimeters (the root zone). This study demonstrates the potential of the CRNS technique to obtain spatio-temporal patterns of soil moisture beyond the integrated volume from isolated CRNS footprints. We use data from an observational campaign between May and July 2019 which featured a network of more than 20 neutron detectors with partly overlapping footprints in an area that exhibits pronounced soil moisture gradients within 1 km2. The present study is the first to combine these observations in order to represent the heterogeneity of soil water content at the sub-footprint scale as well as between the CRNS stations. First, we apply a state-of-the-art procedure to correct the observed neutron count rates for static effects such as sensor sensitivity, vegetation biomass, soil organic carbon and lattice water, as well as for the influence of the temporally dynamic factors barometric pressure, air humidity, and incoming flux of neutrons. Based on the homogenised neutron data, we investigate the robustness of a uniform calibration approach using one calibration parameter value across all CRNS stations. Finally, we benchmark two different interpolation techniques in order to obtain space-time representations of soil moisture: first, Ordinary Kriging with a fixed range; second, a heuristic approach that complements the concept of spatial interpolation by the idea of a geophysical inversion (constrained interpolation). For the latter, we define a geostatistical model of the spatial soil moisture variation in the study area, and then optimize the parameters of that model so that the error of the forward-simulated neutron count rates is minimized. In order to make the optimization problem computationally feasible, we use a heuristic forward operator that is based on the physics of horizontal sensitivity of the neutron detector. The comparison with independent measurements from a cluster of soil moisture sensors (SoilNet) shows that the constrained interpolation approach outperforms Ordinary Kriging by putting a stronger emphasis on horizontal soil moisture gradients at the hectometer scale. The study demonstrates how a CRNS network can be used to generate consistent interpolated soil moisture patterns that could be used to validate hydrological models or remote sensing products.