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NASA NTRS1990

Flow field analysis for a class of waverider configurations

A package of computer codes for analysis of flow fields for waverider configurations is described. The package consists of a surface/volume grid generator and a finite-volume flow solver. The grid generator defines body geometries and computational grids by an algebraic homotopy procedure. The algebraic procedure is versatile in its application and can readily generate configurations in the class of blended wing-body geometries. This code has the ability to produce a wide variety of geometries in the given class with varying geometrical attributes. The flow solver employs a finite-volume formation and solves the explicit, Runge-Kutta integration technique. The method or flow simulation incorporates several techniques for acceleration of the convergence of the interaction process and an entropy corrected enthalpy damping procedure for efficient computation of high Mach number flows.

Moitra, Anutosh↗

NASA NTRS2008

Computer-implemented system and method for automated and highly accurate plaque analysis, reporting, and visualization

A computer-implemented system and method of intra-oral analysis for measuring plaque removal is disclosed. The system includes hardware for real-time image acquisition and software to store the acquired images on a patient-by-patient basis. The system implements algorithms to segment teeth of interest from surrounding gum, and uses a real-time image-based morphing procedure to automatically overlay a grid onto each segmented tooth. Pattern recognition methods are used to classify plaque from surrounding gum and enamel, while ignoring glare effects due to the reflection of camera light and ambient light from enamel regions. The system integrates these components into a single software suite with an easy-to-use graphical user interface (GUI) that allows users to do an end-to-end run of a patient record, including tooth segmentation of all teeth, grid morphing of each segmented tooth, and plaque classification of each tooth image.

Kemp, James Herbert↗

NASA NTRS2006

New Software for Predicting Charging of Spacecraft

Charging System Analyzer Program (Nascap-2K) is a comprehensive update, revision, and extension of several NASA and Air Force codes for predicting electrical charging of spacecraft. Nascap-2K integrates the capabilities and models included in four independent programs: NASCAP/LEO for low-Earth orbits, NASCAP/GEO for geosynchronous orbits, POLAR for auroral charging in polar orbits, and DynaPAC (Dynamic Plasma Analysis Code) for time-dependent plasma interactions. While each of the earlier codes works well for the range of problems for which it was designed, by today s standards these codes are difficult to learn, cumbersome to use, and overly restrictive in their geometric modeling capabilities. Nascap-2K incorporates these models into a single software package that includes spacecraft surface modeling, spatial gridding, environmental specifications, calculating scripting, and post-processing analysis and visualization. The provided material properties database includes values from earlier programs as well as values from recent measurements. Development of Nascap-2K continues with future capabilities to include interactions with dense plasma such as those produced by electric propulsion.

Mandell, Myron↗

NASA NTRS2014

Global Top-Down Smoke-Aerosol Emissions Estimation Using Satellite Fire Radiative Power Measurements

Fire emissions estimates have long been based on bottom-up approaches that are not only complex, but also fraught with compounding uncertainties. We present the development of a global gridded (1 deg ×1 deg) emission coefficients (Ce) product for smoke total particulate matter (TPM) based on a top-down approach using coincident measurements of fire radiative power (FRP) and aerosol optical thickness (AOT) from the Moderate-resolution Imaging Spectroradiometer (MODIS) sensors aboard the Terra and Aqua satellites. This new Fire Energetics and Emissions Research version 1.0 (FEER.v1) Ce product has now been released to the community and can be obtained from http://feer.gsfc. nasa.gov/, along with the corresponding 1-to-1 mapping of their quality assurance (QA) flags that will enable the Ce values to be filtered by quality for use in various applications. The regional averages of Ce values for different ecosystem types were found to be in the ranges of 16-21/gMJ−1 for savanna and grasslands, 15-32/gMJ−1 for tropical forest, 9-12/gMJ−1 for North American boreal forest, and 18- 26/MJ−1 for Russian boreal forest, croplands and natural vegetation. The FEER.v1 Ce product was multiplied by time-integrated FRP data to calculate regional smoke TPM emissions, which were compared with equivalent emissions products from three existing inventories. FEER.v1 showed higher and more reasonable smoke TPM estimates than two other emissions inventories that are based on bottom-up approaches and already reported in the literature to be too low, but portrayed an overall reasonable agreement with another top-down approach. This suggests that top-down approaches may hold better promise and need to be further developed to accelerate the reduction of uncertainty associated with fire emissions estimation in air-quality and climate research and applications. Results of the analysis of FEER.v1 data for 2004-2011 show that 65-85 Tg yr−1 of TPM is emitted globally from open biomass burning, with a generally decreasing trend over this short time period. The FEER.v1 Ce product is the first global gridded product in the family of "emission factors", that is based essentially on satellite measurements, and requires only direct satellite FRP measurements of an actively burning fire anywhere to evaluate its emission rate in near-real time, which is essential for operational activities, such as the monitoring and forecasting of smoke emission impacts on air quality.

biomass burning↗

NASA NTRS1991

Developing and utilizing an Euler computational method for predicting the airframe/propulsion effects for an aft-mounted turboprop transport. Volume 1: Theory document

An Euler flow solver was developed for predicting the airframe/propulsion integration effects for an aft-mounted turboprop transport. This solver employs a highly efficient multigrid scheme, with a successive mesh-refinement procedure to accelerate the convergence of the solution. A new dissipation model was also implemented to render solutions that are grid insensitive. The propeller power effects are simulated by the actuator disk concept. An embedded flow solution method was developed for predicting the detailed flow characteristics in the local vicinity of an aft-mounted propfan engine in the presence of a flow field induced by a complete aircraft. Results from test case analysis are presented. A user's guide for execution of computer programs, including format of various input files, sample job decks, and sample input files, is provided in an accompanying volume.

Chen, H. C.↗

NASA NTRS1990

Time scales and variability of area-averaged tropical oceanic rainfall

A statistical analysis of time series of area-averaged rainfall over the oceans has been conducted around the diurnal time scale. The results of this analysis can be applied directly to the problem of establishing the magnitude of expected errors to be incurred in the estimation of monthly area-averaged rain rate from low orbiting satellites. Such statistics as the mean, standard deviation, integral time scale of background red noise, and spectral analyses were performed on time series of the GOES precipitation index taken at 3-hour intervals during the period spanning December 19, 1987 to March 31, 1988 over the central and eastern tropical Pacific. The analyses have been conducted on 2.5 x 2.5 deg and 5 x 5 deg grid boxes, separately. The study shows that rainfall measurements by a sun-synchronous satellite visiting a spot twice per day will include a bias due to the existence of the semidiurnal cycle in the SPCZ ranging from 5 to 10 percentage points. The bias in the ITCZ may be of the order of 5 percentage points.

Shin, Kyung-Sup↗

NASA NTRS2000

Towards Flange-to-Flange Turbopump Simulations for Liquid Rocket Engines

The primary objective of this research is to support the design of liquid rocket systems for the Advanced Space Transportation System. Since the space launch systems in the near future are likely to rely on liquid rocket engines, increasing the efficiency and reliability of the engine components is an important task. One of the major problems in the liquid rocket engine is to understand fluid dynamics of fuel and oxidizer flows from the fuel tank to plume. Understanding the flow through the entire turbopump geometry through numerical simulation will be of significant value toward design. This will help to improve safety of future space missions. One of the milestones of this effort is to develop, apply and demonstrate the capability and accuracy of 3D CFD methods as efficient design analysis tools on high performance computer platforms. The development of the MPI and MLP versions of the INS3D code is currently underway. The serial version of INS3D code is a multidimensional incompressible Navier-Stokes solver based on overset grid technology. INS3D-MPI is based on the explicit massage-passing interface across processors and is primarily suited for distributed memory systems. INS3D-MLP is based on multi-level parallel method and is suitable for distributed-shared memory systems. For the entire turbopump simulations, moving boundary capability and an efficient time-accurate integration methods are build in the flow solver. To handle the geometric complexity and moving boundary problems, overset grid scheme is incorporated with the solver that new connectivity data will be obtained at each time step. The Chimera overlapped grid scheme allows subdomains move relative to each other, and provides a great flexibility when the boundary movement creates large displacements. The performance of the two time integration schemes for time-accurate computations is investigated. For an unsteady flow which requires small physical time step, the pressure projection method was found to be computationally efficient since it does not require any subiterations procedure. It was observed that the artificial compressibility method requires a fast convergence scheme at each physical time step in order to satisfy incompressibility condition. This was obtained by using a GMRES-ILU(0) solver in our computations. When a line-relaxation scheme was used, the time accuracy was degraded and time-accurate computations became very expensive. The current geometry for the LOX boost turbopump has various rotating and stationary components, such as inducer, stators, kicker, hydrolic turbine, where the flow is extremely unsteady. Figure 1 shows the geometry and computed surface pressure of the inducer. The inducer and the hydrolic turbine rotate in different rotational speed.

Kiris, Cetin↗

NASA NTRS1996

EUVS Sounding Rocket Payload

During the first half of this year (CY 1996), the EUVS project began preparations of the EUVS payload for the upcoming NASA sounding rocket flight 36.148CL, slated for launch on July 26, 1996 to observe and record a high-resolution (approx. 2 A FWHM) EUV spectrum of the planet Venus. These preparations were designed to improve the spectral resolution and sensitivity performance of the EUVS payload as well as prepare the payload for this upcoming mission. The following is a list of the EUVS project activities that have taken place since the beginning of this CY: (1) Applied a fresh, new SiC optical coating to our existing 2400 groove/mm grating to boost its reflectivity; (2) modified the Ranicon science detector to boost its detective quantum efficiency with the addition of a repeller grid; (3) constructed a new entrance slit plane to achieve 2 A FWHM spectral resolution; (4) prepared and held the Payload Initiation Conference (PIC) with the assigned NASA support team from Wallops Island for the upcoming 36.148CL flight (PIC held on March 8, 1996; see Attachment A); (5) began wavelength calibration activities of EUVS in the laboratory; (6) made arrangements for travel to WSMR to begin integration activities in preparation for the July 1996 launch; (7) paper detailing our previous EUVS Venus mission (NASA flight 36.117CL) published in Icarus (see Attachment B); and (8) continued data analysis of the previous EUVS mission 36.137CL (Spica occultation flight).

Stern, Alan S.↗

NASA NTRS1982

Evaluation of an improved finite-element thermal stress calculation technique

A procedure for generating accurate thermal stresses with coarse finite element grids (Ojalvo's method) is described. The procedure is based on the observation that for linear thermoelastic problems, the thermal stresses may be envisioned as being composed of two contributions; the first due to the strains in the structure which depend on the integral of the temperature distribution over the finite element and the second due to the local variation of the temperature in the element. The first contribution can be accurately predicted with a coarse finite-element mesh. The resulting strain distribution can then be combined via the constitutive relations with detailed temperatures from a separate thermal analysis. The result is accurate thermal stresses from coarse finite element structural models even where the temperature distributions have sharp variations. The range of applicability of the method for various classes of thermostructural problems such as in-plane or bending type problems and the effect of the nature of the temperature distribution and edge constraints are addressed. Ojalvo's method is used in conjunction with the SPAR finite element program. Results are obtained for rods, membranes, a box beam and a stiffened panel.

Camarda, C. J.↗

NASA NTRS1999

Integrated Computational System for Aerodynamic Steering and Visualization

In February of 1994, an effort from the Fluid Dynamics and Information Sciences Divisions at NASA Ames Research Center with McDonnel Douglas Aerospace Company and Stanford University was initiated to develop, demonstrate, validate and disseminate automated software for numerical aerodynamic simulation. The goal of the initiative was to develop a tri-discipline approach encompassing CFD, Intelligent Systems, and Automated Flow Feature Recognition to improve the utility of CFD in the design cycle. This approach would then be represented through an intelligent computational system which could accept an engineer's definition of a problem and construct an optimal and reliable CFD solution. Stanford University's role focused on developing technologies that advance visualization capabilities for analysis of CFD data, extract specific flow features useful for the design process, and compare CFD data with experimental data. During the years 1995-1997, Stanford University focused on developing techniques in the area of tensor visualization and flow feature extraction. Software libraries were created enabling feature extraction and exploration of tensor fields. As a proof of concept, a prototype system called the Integrated Computational System (ICS) was developed to demonstrate CFD design cycle. The current research effort focuses on finding a quantitative comparison of general vector fields based on topological features. Since the method relies on topological information, grid matching and vector alignment is not needed in the comparison. This is often a problem with many data comparison techniques. In addition, since only topology based information is stored and compared for each field, there is a significant compression of information that enables large databases to be quickly searched. This report will (1) briefly review the technologies developed during 1995-1997 (2) describe current technologies in the area of comparison techniques, (4) describe the theory of our new method researched during the grant year (5) summarize a few of the results and finally (6) discuss work within the last 6 months that are direct extensions from the grant.

Hesselink, Lambertus↗

NASA NTRS1995

Interaction of the terrestrial and atmospheric hydrological cycles in the context of the North American southwest summer monsoon

Work under this grant has used information on precipitation and water vapor fluxes in the area of the Mexican Monsoon to analyze the regional precipitation climatology, to understand the nature of water vapor transport during the monsoon using model and observational data, and to analyze the ability of the TRMM remote sensing algorithm to characterize precipitation. An algorithm for estimating daily surface rain volumes from hourly GOES infrared images was developed and compared to radar data. Estimates were usually within a factor of two, but different linear relations between satellite reflectances and rainfall rate were obtained for each day, storm type and storm development stage. This result suggests that using TRMM sensors to calibrate other satellite IR will need to be a complex process taking into account all three of the above factors. Another study, this one of the space-time variability of the Mexican Monsoon, indicate that TRMM will have a difficult time, over the course of its expected three year lifetime, identifying the diurnal cycle of precipitation over monsoon region. Even when considering monthly rainfalls, projected satellite estimates of August rainfall show a root mean square error of 38 percent. A related examination of spatial variability of mean monthly rainfall using a novel method for removing the effects of elevation from gridded gauge data, show wide variation from a satellite-based rainfall estimates for the same time and space resolution. One issue addressed by our research, relating to the basic character of the monsoon circulation, is the determination of the source region for moisture. The monthly maps produced from our study of monsoon variability show the presence of two rainfall maxima in the analysis normalized to sea level, one in south-central Arizona associated with the Mexican monsoon maximum and one in southeastern New Mexico associated with the Gulf of Mexico. From the point of view of vertically-integrated fluxes and flux divergence of water vapor from ECMWF data, most moisture at upper levels arrives from the Gulf of Mexico, while low level moisture comes from the northern Gulf of California. Composites of ECMWF analyses for wet and dry periods (classified by rain gauge data) show that both regimes show low level moisture arriving from northern and central Gulf of California. Above 700 MB, moisture comes from both source regions and the Sierra Madre Occidental. During wet periods a longer fetch through the moist air mass above western Mexico results in a greater moisture flux into the Sonoran Desert region, while there is less moisture from the Gulf of Mexico both above and below 700 mb. Work on the grant subcontract at the University of Colorado concentrated on the development of a technique useful to TRMM combining visible, infrared and passive microwave data for measuring precipitation. Two established techniques using either visible or infrared data applied over the US Southwest correlated with gauges at the 0.58 to 0.70 level. The application of some established passive microwave techniques were less successful for a variety of reason, including problems in both the gauge and satellite data quality, sampling problems and weaknesses inherent in the algorithms themselves. A more promising solution for accurate rainfall estimation was explored using visible and infrared data to perform a cloud classification, which when combined with information about the background (e.g. Iand/ocean), was used to select the most appropriate microwave algorithm from a suite of possibilities.

Dickinson, Robert E.↗

NASA NTRS1988

Fully-coupled analysis of jet mixing problems. Three-dimensional PNS model, SCIP3D

Numerical procedures formulated for the analysis of 3D jet mixing problems, as incorporated in the computer model, SCIP3D, are described. The overall methodology closely parallels that developed in the earlier 2D axisymmetric jet mixing model, SCIPVIS. SCIP3D integrates the 3D parabolized Navier-Stokes (PNS) jet mixing equations, cast in mapped cartesian or cylindrical coordinates, employing the explicit MacCormack Algorithm. A pressure split variant of this algorithm is employed in subsonic regions with a sublayer approximation utilized for treating the streamwise pressure component. SCIP3D contains both the ks and kW turbulence models, and employs a two component mixture approach to treat jet exhausts of arbitrary composition. Specialized grid procedures are used to adjust the grid growth in accordance with the growth of the jet, including a hybrid cartesian/cylindrical grid procedure for rectangular jets which moves the hybrid coordinate origin towards the flow origin as the jet transitions from a rectangular to circular shape. Numerous calculations are presented for rectangular mixing problems, as well as for a variety of basic unit problems exhibiting overall capabilities of SCIP3D.

Wolf, D. E.↗

NASA NTRS2019

Geometry Modeling for Unstructured Mesh Adaptation

The quantification and control of discretization error is critical to obtaining reliable simulation results. Adaptive mesh techniques have the potential to automate discretization error control, but have made limited impact on production analysis workflow. Recent progress has matured a number of independent implementations of flow solvers, error estimation methods, and anisotropic mesh adaptation mechanics. However, the poor integration of initial mesh generation and adaptive mesh mechanics to typical sources of geometry has hindered adoption of adaptive mesh techniques, where these geometries are often created in Mechanical Computer- Aided Design (MCAD) systems. The difficulty of this coupling is compounded by two factors: the inherent complexity of the model (e.g., large range of scales, bodies in proximity, details not required for analysis) and unintended geometry construction artifacts (e.g., translation, uneven parameterization, degeneracy, self-intersection, sliver faces, gaps, large tolerances be- tween topological elements, local high curvature to enforce continuity). Manual preparation of geometry is commonly employed to enable fixed-grid and adaptive-grid workflows by reducing the severity and negative impacts of these construction artifacts, but manual process interaction inhibits workflow automation. Techniques to permit the use of complex geometry models and reduce the impact of geometry construction artifacts on unstructured grid workflows are models from the AIAA Sonic Boom and High Lift Prediction are shown to demonstrate the utility of the current approach.

Park, Michael A.↗

NASA NTRS2010

Effects of Lightning and Other Meteorological Factors on Fire Activity in the North American Boreal Forest: Implications for Fire Weather Forecasting

The effects of lightning and other meteorological factors on wildfire activity in the North American boreal forest are statistically analyzed during the fire seasons of 2000-2006 through an integration of the following data sets: the MODerate Resolution Imaging Spectroradiometer (MODIS) level 2 fire products, the 3-hourly 32-kin gridded meteorological data from North American Regional Reanalysis (NARR), and the lightning data collected by the Canadian Lightning Detection Network (CLDN) and the Alaska Lightning Detection Network (ALDN). Positive anomalies of the 500 hPa geopotential height field, convective available potential energy (CAPE), number of cloud-to-ground lightning strikes, and the number of consecutive dry days are found to be statistically important to the seasonal variation of MODIS fire counts in a large portion of Canada and the entirety of Alaska. Analysis of fire occurrence patterns in the eastern and western boreal forest regions shows that dry (in the absence of precipitation) lightning strikes account for only 20% of the total lightning strikes, but are associated with (and likely cause) 40% of the MODIS observed fire counts in these regions. The chance for ignition increases when a threshold of at least 10 dry strikes per NARR grid box and at least 10 consecutive dry days is reached. Due to the orientation of the large-scale pattern, complex differences in fire and lightning occurrence and variability were also found between the eastern and western sub-regions. Locations with a high percentage of dry strikes commonly experience an increased number of fire counts, but the mean number of fire counts per dry strike is more than 50% higher in western boreal forest sub-region, suggesting a geographic and possible topographic influence. While wet lightning events are found to occur with a large range of CAPE values, a high probability for dry lightning occurs only when 500 hPa geopotential heights are above 5700m and CAPE values are near the maximum observed level, underscoring the importance of low-level instability to boreal fire weather forecasts-

Peterson, D.↗

NASA NTRS2023

PCLAM: a Python Module for Computing Surface Lineloads and Moments

Lineloads serve a unique and important role in aerodynamic database development as well as configuration design and analysis. A new software suite was constructed which can compute lineloads rapidly enough that the calculations can run in tandem with high-fidelity fluid flow solvers. This enables the calculation of iteration- or time-dependent lineloads, which have thus far been too computationally costly to create for complicated systems like launch vehicles. The suite is organized into a standalone Python module named PCLAM (PCLAM Computes Lineloads And Moments) which can be imported into other software with minimal restructuring by the user or developer. The computed lineloads are integrated with a $C^0$ numerical quality and exhibit the expected sensitivity to underlying grid resolution. Even at low grid and lineload resolutions, the computed lineloads were found to be in strong agreement with several analytical test cases.

sectional loads↗

NASA NTRS2000

Supercomputing Aspects for Simulating Incompressible Flow

The primary objective of this research is to support the design of liquid rocket systems for the Advanced Space Transportation System. Since the space launch systems in the near future are likely to rely on liquid rocket engines, increasing the efficiency and reliability of the engine components is an important task. One of the major problems in the liquid rocket engine is to understand fluid dynamics of fuel and oxidizer flows from the fuel tank to plume. Understanding the flow through the entire turbo-pump geometry through numerical simulation will be of significant value toward design. One of the milestones of this effort is to develop, apply and demonstrate the capability and accuracy of 3D CFD methods as efficient design analysis tools on high performance computer platforms. The development of the Message Passage Interface (MPI) and Multi Level Parallel (MLP) versions of the INS3D code is currently underway. The serial version of INS3D code is a multidimensional incompressible Navier-Stokes solver based on overset grid technology, INS3D-MPI is based on the explicit massage-passing interface across processors and is primarily suited for distributed memory systems. INS3D-MLP is based on multi-level parallel method and is suitable for distributed-shared memory systems. For the entire turbo-pump simulations, moving boundary capability and efficient time-accurate integration methods are built in the flow solver, To handle the geometric complexity and moving boundary problems, an overset grid scheme is incorporated with the solver so that new connectivity data will be obtained at each time step. The Chimera overlapped grid scheme allows subdomains move relative to each other, and provides a great flexibility when the boundary movement creates large displacements. Two numerical procedures, one based on artificial compressibility method and the other pressure projection method, are outlined for obtaining time-accurate solutions of the incompressible Navier-Stokes equations. The performance of the two methods is compared by obtaining unsteady solutions for the evolution of twin vortices behind a flat plate. Calculated results are compared with experimental and other numerical results. For an unsteady flow, which requires small physical time step, the pressure projection method was found to be computationally efficient since it does not require any subiteration procedure. It was observed that the artificial compressibility method requires a fast convergence scheme at each physical time step in order to satisfy the incompressibility condition. This was obtained by using a GMRES-ILU(0) solver in present computations. When a line-relaxation scheme was used, the time accuracy was degraded and time-accurate computations became very expensive.

Kwak, Dochan↗

NASA NTRS2017

Weather from 250 Miles Up: Visualizing Precipitation Satellite Data (and Other Weather Applications) Using CesiumJS

Geospatial weather visualization remains predominately a two-dimensional endeavor. Even popular advanced tools like the Nullschool Earth display 2-dimensional fields on a 3-dimensional globe. Yet much of the observational data and model output contains detailed three-dimensional fields. In 2014, NASA and JAXA (Japanese Space Agency) launched the Global Precipitation Measurement (GPM) satellite. Its two instruments, the Dual-frequency Precipitation Radar (DPR) and GPM Microwave Imager (GMI) observe much of the Earth's atmosphere between 65 degrees North Latitude and 65 degrees South Latitude. As part of the analysis and visualization tools developed by the Precipitation Processing System (PPS) Group at NASA Goddard, a series of CesiumJS [Using Cesium Markup Language (CZML), JavaScript (JS) and JavaScript Object Notation (JSON)] -based globe viewers have been developed to improve data acquisition decision making and to enhance scientific investigation of the satellite data. Other demos have also been built to illustrate the capabilities of CesiumJS in presenting atmospheric data, including model forecasts of hurricanes, observed surface radar data, and gridded analyses of global precipitation. This talk will present these websites and the various workflows used to convert binary satellite and model data into a form easily integrated with CesiumJS.

web applications↗

NASA NTRS1985

Geologic analysis of averaged magnetic satellite anomalies

To investigate relative advantages and limitations for quantitative geologic analysis of magnetic satellite scalar anomalies derived from arithmetic averaging of orbital profiles within equal-angle or equal-area parallelograms, the anomaly averaging process was simulated by orbital profiles computed from spherical-earth crustal magnetic anomaly modeling experiments using Gauss-Legendre quadrature integration. The results indicate that averaging can provide reasonable values at satellite elevations, where contributing error factors within a given parallelogram include the elevation distribution of the data, and orbital noise and geomagnetic field attributes. Various inversion schemes including the use of equivalent point dipoles are also investigated as an alternative to arithmetic averaging. Although inversion can provide improved spherical grid anomaly estimates, these procedures are problematic in practice where computer scaling difficulties frequently arise due to a combination of factors including large source-to-observation distances ( 400 km), high geographic latitudes, and low geomagnetic field inclinations.

Goyal, H. K.↗