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Can Simple Metrics Identify the Process(es) Driving Extreme Precipitation?
This work seeks an automatic algorithm to determine the primary meteorological cause(s) of individual extreme precipitation events. Such determinations have been made before, but required a by-hand analysis of each separate event. This is very time-consuming and the field would benefit from an automatic process. This is especially relevant when comparing different datasets to determine which ones most closely hew towards reality. This paper tests three simple metrics over the continental United States using the European Center for Medium-Range Weather Forecasting’s (ECMWF) atmospheric reanalysis (ERA5). The metrics tested measure and compare the strength of three meteorological processes associated with extreme precipitation: fronts, convection, and cyclones. A multivariate statistical technique as well as individual case studies show evidence that the three meteorological processes of interest cannot be isolated from one another using these simple physical metrics. This shows the difficulty in finding “pure” cases of these precipitation-generating processes and suggests approaching these processes with an eye toward mixed-type events.
Accounting for 3D Radiative Effects in MODIS Aerosol Retrievals near Clouds using CALIPSO Observations
Retrievals of aerosol properties near clouds from passive remote sensing is challenging. Sunlight scattered by clouds into nearby clear regions can effectively enhance the clear area reflectance. These cloud 3D radiative effects may lead to large biases in aerosol retrievals if uncorrected, risking an incorrect interpretation of satellite observations for aerosol-cloud interaction in cloudy atmosphere. In earlier studies, we developed a simple two-layer model (2LM) to estimate the cloud-induced clear-sky radiance enhancements in cloud fields. In this study, we take advantage of CALIPSO lidar observations, which should not be affected by the 3D radiative effect, to study passive aerosol retrievals in cloud fields in the Amazon region, specifically those produced by the operational Dark Target algorithm applied to Aqua-MODIS. From two-years’ worth of co-located CALIPSO/MODIS aerosol retrievals, we find a larger increase in operationally retrieved MODIS AOD from clear to cloudy regions (~0.075 or ~40%) than for the CALIPSO AOD (~0.021 or ~20%). The much larger increase in MODIS AOD is mainly due to the 3D radiative effects. After using the 2LM model to account for cloud 3D radiative effects, the clear to cloudy increase in MODIS AOD was reduced to ~0.043 (~23%), much closer to CALIPSO observations. The 3D corrected average MODIS AOD for cloudy scenes is significantly larger than AOD for clear conditions, even for cloud fraction (CF) less than 0.1, suggesting aerosols in cloudy scenes are characteristically different from aerosols in clear conditions. Furthermore, the 3D correction of AOD (i.e., τ_1D-τ_3D) increases linearly with CF for a large range of CF. We have also examined the impact of the 3D effect on aerosol Ångström Exponent (AE) and fine model fraction (FMF) of AOD. We found that the uncorrected average AE and FMF depend strongly on CF, ~25% increase in AE (decrease in particle size) and ~60% increase in FMF as CF increases from 0.05 to 0.45. The 3D correction leads to smaller average AE (bigger particle size) and FMF that are almost independent of CF. Thus, the 3D corrected aerosol properties are expected to provide more accurate information for better understanding aerosol-cloud interactions.
Use of Digital Real-Time Simulation and Optimization to Identify Maximum Real Power Injection on Banshee Distribution Network
This study investigates the hosting capacity of the Banshee Distribution Network by optimizing the real power injection at carefully selected Distributed Energy Resource (DER) locations. The analysis is conducted within the framework of power system operational constraints, including bus voltage ranges, thermal line ratings, and transformer loading limits. A Python-based Genetic Algorithm (GA), implemented using the PyGAD library, is employed to iteratively identify the optimal power injection configuration that maximizes network utilization while preserving system reliability. The methodology integrates a real-time simulation environment using the Real-Time Digital Simulator (RTDS), allowing high-fidelity evaluation of power flow and voltage behavior under each proposed injection scenario. By coupling the optimization algorithm with real-time simulation feedback, this approach ensures that both static and dynamic constraints are enforced during the evaluation process. The GA leverages evolutionary operators such as selection, crossover, and mutation to navigate the nonlinear search space efficiently. The results of the study delineate the feasible hosting capacity at three targeted buses, reflecting maximum real power levels that can be injected without causing voltage violations, transformer overloading, or line congestion. These findings provide a decision- support tool for distribution planners and utilities aiming to integrate higher penetrations of DERs in existing infrastructure. Additionally, the work lays the foundation for extending such optimization techniques to multi-objective formulations, including economic dispatch and reactive power coordination, in future studies.
Use of Digital Real-Time Simulation and Optimization to Identify Maximum Real Power Injection on the Banshee Distribution Network: Preprint
This study investigates the hosting capacity of the Banshee Distribution Network by optimizing the real power injection at carefully selected Distributed Energy Resource (DER) locations. The analysis is conducted within the framework of power system operational constraints, including bus voltage ranges, thermal line ratings, and transformer loading limits. A Python-based Genetic Algorithm (GA), implemented using the PyGAD library, is employed to iteratively identify the optimal power injection configuration that maximizes network utilization while preserving system reliability. The methodology integrates a real-time simulation environment using the Real-Time Digital Simulator (RTDS), allowing high-fidelity evaluation of power flow and voltage behavior under each proposed injection scenario. By coupling the optimization algorithm with real-time simulation feedback, this approach ensures that both static and dynamic constraints are enforced during the evaluation process. The GA leverages evolutionary operators such as selection, crossover, and mutation to navigate the nonlinear search space efficiently. The results of the study delineate the feasible hosting capacity at three targeted buses, reflecting maximum real power levels that can be injected without causing voltage violations, transformer overloading, or line congestion. These findings provide a decision- support tool for distribution planners and utilities aiming to integrate higher penetrations of DERs in existing infrastructure. Additionally, the work lays the foundation for extending such optimization techniques to multi-objective formulations, including economic dispatch and reactive power coordination, in future studies.
Deep Learning Scene Classification Experiments in Automatic Detection of Slums on Planetscope Imagery
Population growth is increasingly happening in slum settlements of the large urban centers in the Global South. The term "slum" encompasses a wide range of communities, located mostly in underserved areas, and often exhibiting distinct structural and functional informalities with a relatively high concentration of marginalized populations. To address the issues confronting slums for effective planning and development, including the realistic estimation of the resident population, identifying them accurately is fundamental. Given the disagreements over a universal definition, diverse characteristic features, and socio-political limitations, global detection of slums is a veritable challenge. In this paper, we present experiments in slum detection using a scene classification algorithm and 3-meter spatial resolution satellite imagery. We train and evaluate the model for slum detection in Mumbai, India for the year 2023 and test the temporal generalization of the trained model on Mumbai in 2020 and 2018. In addition, we explore the pathways toward geographic generalization to Kolkata and Delhi (India). We discuss several limitations in the workflow and model, situate our findings in the existing literature, and suggest improvements and alternatives. With this, we establish baseline methods and experiments as a first step towards developing an image-based global slum detection framework and algorithm. This work adds to the community discussion on methods, data challenges, and open questions related to the detection of slums globally. With this research, we hope to improve our understanding of human settlements, especially in critical areas, improve population estimates, and help measure progress towards the sustainable development goals.
Integration of the Radiation Belt Environment Model Into the Space Weather Modeling Framework
We have integrated the Fok radiation belt environment (RBE) model into the space weather modeling framework (SWMF). RBE is coupled to the global magnetohydrodynamics component (represented by the Block-Adaptive-Tree Solar-wind Roe-type Upwind Scheme, BATS-R-US, code) and the Ionosphere Electrodynamics component of the SWMF, following initial results using the Weimer empirical model for the ionospheric potential. The radiation belt (RB) model solves the convection-diffusion equation of the plasma in the energy range of 10 keV to a few MeV. In stand-alone mode RBE uses Tsyganenko's empirical models for the magnetic field, and Weimer's empirical model for the ionospheric potential. In the SWMF the BATS-R-US model provides the time dependent magnetic field by efficiently tracing the closed magnetic field-lines and passing the geometrical and field strength information to RBE at a regular cadence. The ionosphere electrodynamics component uses a two-dimensional vertical potential solver to provide new potential maps to the RBE model at regular intervals. We discuss the coupling algorithm and show some preliminary results with the coupled code. We run our newly coupled model for periods of steady solar wind conditions and compare our results to the RB model using an empirical magnetic field and potential model. We also simulate the RB for an active time period and find that there are substantial differences in the RB model results when changing either the magnetic field or the electric field, including the creation of an outer belt enhancement via rapid inward transport on the time scale of tens of minutes.
An Overview of the Tropospheric Aerosol Radiative Forcing Observational Experiment
Aerosol effects on atmospheric radiation are a leading source of uncertainty in predicting future climate. As a result, the International Global Atmospheric Chemistry Program has established a Focus on Atmospheric Aerosols (IGAC/FAA) and endorsed a series of aerosol field campaigns. TARFOX, the second in the IGAC/FAA series, was designed to reduce this uncertainty by measuring aerosol properties and effects in the US eastern seaboard, where one of the world's major plumes of industrial haze moves from the continent over the Atlantic Ocean. TARFOX's objectives are to: 1. Make simultaneous measurements of: (a) aerosol effects on radiation fields, and (b) the chemical, physical, and optical properties of the aerosols causing those effects. 2. Perform a variety of closure studies by using overdetermined data sets to test the mutual consistency of measurements and calculations of a wide range of aerosol properties and effects. 3. Use the results of the closure studies to assess and reduce uncertainties in estimates of aerosol radiative forcing, as well as to guide future field programs. An important subset of the closure studies is tests and improvements of algorithms used to derive aerosol properties and radiative effects from satellite measurements. The TARFOX Intensive Field Period (IFP) was conducted July 10-31, 1996. It included coordinated measurements from four satellites (GOES-8, NOAA-14, ERS-2, LANDSAT), four aircraft (ER-2, C-130, C-131, and a modified Cessna), land sites, and ships. A variety of aerosol conditions was sampled, ranging from relatively clean behind frontal passages to moderately polluted with aerosol optical depths exceeding 0.5 at mid-visible wavelengths. The latter conditions included separate incidents of enhancements caused primarily by anthropogenic sources and another incident of enhancement apparently influenced by recent fog processing. Spatial gradients of aerosol optical thickness were sampled to aid in isolating aerosol effects from other radiative effects and to more tightly constrain closure tests, including those of satellite retrievals. This talk gives an overview of TARFOX goals, rationale, methods, and initial key findings.
Classical Benchmarks for Variational Quantum Eigensolver Simulations of the Hubbard Model
Simulating the Hubbard model is of great interest to a wide range of applications within condensed matter physics, however its solution on classical computers remains challenging in dimensions larger than one. The relative simplicity of this model, embodied by the sparseness of the Hamiltonian matrix, allows for its efficient implementation on quantum computers, and for its approximate solution using variational algorithms such as the variational quantum eigensolver. While these algorithms have been shown to reproduce the qualitative features of the Hubbard model, their quantitative accuracy in terms of producing true ground state energies and other properties, and the dependence of this accuracy on the system size and interaction strength, the choice of variational ansatz, and the degree of spatial inhomogeneity in the model, remains unknown. Here we present a rigorous classical benchmarking study, demonstrating the potential impact of these factors on the accuracy of the variational solution of the Hubbard model on quantum hardware, for systems with up to 32 qubits. We find that even when using the most accurate wavefunction ansätze for the Hubbard model, the error in its ground state energy and wavefunction plateaus for larger lattices, while stronger electronic correlations magnify this issue. Concurrently, spatially inhomogeneous parameters and the presence of off-site Coulomb interactions only have a small effect on the accuracy of the computed ground state energies. Our study highlights the capabilities and limitations of current approaches for solving the Hubbard model on quantum hardware, and we discuss potential future avenues of research.
Enhancing the Range and Reliability of the Spacer Layer Imaging Method
The spacer layer imaging method (SLIM) is widely used to measure the thickness of additive and lubricant films, in lubricant development and evaluation, and for fundamental research into elastohydrodynamic lubrication and tribofilm formation mechanisms. The film thickness measurement, as implemented on several popular tribometers, provides powerful, non-destructive in-situ mapping of film topography with nanometre-scale height sensitivity. However, the results can be highly sensitive to experimental procedure, machine condition, and image analysis, in some cases reporting unphysical film thickness trends. The prevailing image analysis techniques make it challenging to interrogate these errors, often hiding their multivariate nonlinear behaviour from the user by spatial averaging. Herein, several common ‘silent errors’ in the SLIM measurement, including colour matching to incorrect fringe orders, and colour drift due to the optical properties of the system or film itself, are discussed, with examples. A robust suite of novel a priori and a posteriori methods to address these issues, and to improve the accuracy and reliability of the measurement, are also presented, including a novel, computationally inexpensive circle-finding algorithm for automated image processing. In combination, these methods allow reliable mapping of films up to at least 800 nm in thickness, representing a significant milestone for the utility of SLIM applied to elastohydrodynamic contact.
Validation of the EDGES Low-band Antenna Beam Model
The response of the antenna is a source of uncertainty in measurements with the Experiment to Detect the Global Epoch of Reionization Signature (EDGES). We aim to validate the electromagnetic beam model of the low-band (50–100 MHz) dipole antenna with comparisons between models and against data. We find that simulations of a simplified model of the antenna over an infinite perfectly conducting ground plane are, with one exception, robust to changes in the numerical electromagnetic solver code or algorithm. For simulations of the antenna with the actual finite ground plane and realistic soil properties, we find that two out of three numerical solvers agree well. Applying our analysis pipeline to a simulated drift-scan observation from an early EDGES low-band instrument that had a 10 m × 10 m ground plane, we find residual levels after fitting and removing a five-term foreground model from the simulated data binned in local sidereal time (LST) average about 250 mK with ±40 mK variation between numerical solvers. A similar analysis of the primary 30 m × 30 m sawtooth ground plane reduced the LST-averaged residuals to about 90 mK with ±10 mK between the two viable solvers. More broadly we show that larger ground planes generally perform better than smaller ground planes. Simulated data have a power that is within 4% of real observations, a limitation of net accuracy of the sky and beam models. We observe that residual spectral structures after foreground model fits match qualitatively between simulated data and observations, suggesting that the frequency dependence of the beam is reasonably represented by the models. We find that a soil conductivity of 0.02 S m{sup -1} and relative permittivity of 3.5 yield good agreement between simulated spectra and observations. This is consistent with the soil properties reported by Sutinjo et al. for the Murchison Radio-astronomy Observatory, where EDGES is located.
Generative adversarial networks (GAN) based efficient sampling of chemical composition space for inverse design of inorganic materials
A major challenge in materials design is how to efficiently search the vast chemical design space to find the materials with desired properties. One effective strategy is to develop sampling algorithms that can exploit both explicit chemical knowledge and implicit composition rules embodied in the large materials database. Here, we propose a generative machine learning model (MatGAN) based on a generative adversarial network (GAN) for efficient generation of new hypothetical inorganic materials. Trained with materials from the ICSD database, our GAN model can generate hypothetical materials not existing in the training dataset, reaching a novelty of 92.53% when generating 2 million samples. The percentage of chemically valid (charge-neutral and electronegativity-balanced) samples out of all generated ones reaches 84.5% when generated by our GAN trained with such samples screened from ICSD, even though no such chemical rules are explicitly enforced in our GAN model, indicating its capability to learn implicit chemical composition rules to form compounds. Our algorithm is expected to be used to greatly expand the range of the design space for inverse design and large-scale computational screening of inorganic materials.
Web-Based Tools for Data-Informed Remedy Optimization: Software Theory and User Guide
This report documents the development and application of two web-based decision-support tools for pump-and-treat (P&T) groundwater remediation systems: PTOLEMY (Pump-and-Treat Optimized Location Evaluation to Maximize Yields) and OPTIMA (Optimization for Pump-and-Treat Implementation, Management, & Assessment). These tools enhance remedy design and management by leveraging advanced computational methods – specifically deep learning and multi-objective optimization – within a user-friendly platform. By integrating data-driven models with established hydrogeological knowledge, PTOLEMY and OPTIMA enable more efficient evaluation of well placement and operational strategies, helping site managers balance multiple remediation objectives under complex conditions. Both tools are implemented as modules within the SOCRATES (Suite Of Comprehensive Rapid Analysis Tools for Environmental Sites) web platform, which provides data access, visualization, and analytics to support remedy optimization across sites in the U.S. Department of Energy Office of Environmental Management complex. PTOLEMY is a rapid screening module designed to identify promising locations for new extraction wells. It employs a multi-channel three-dimensional convolutional neural network (MC3D-CNN) trained on high-fidelity simulation data to predict the relative performance (in terms of contaminant mass recovery) of potential well sites. Through an interactive web interface, PTOLEMY visualizes the probability of high performance across a site, highlighting areas where an extraction well is likely to yield above-threshold contaminant removal over a multi-year period. PTOLEMY’s map-based displays and exportable results support transparent communication of screening analyses. By focusing attention on the most favorable candidate locations, the tool augments traditional engineering judgment and physics-based modeling, providing a data informed basis for subsequent detailed evaluations. OPTIMA is a multi objective optimization module designed to find wellfield layouts and operating schedules that meet various cleanup goals. It quickly evaluates thousands of candidate setups – combinations of well locations, timing, and rates – and returns a small set of best trade-off options for comparison. At its core, OPTIMA uses a U-Net-based surrogate model – a deep-learning emulator of a groundwater flow and transport simulator – to dramatically accelerate scenario evaluations. Coupling this fast surrogate with the NSGA-II (Non-dominated Sorting Genetic Algorithm II) evolutionary algorithm, OPTIMA explores a wide decision space of well locations and schedules to identify Pareto-optimal solutions that trade off key objectives (e.g., minimizing cleanup time, maximizing contaminant mass removal, and minimizing plume extent). The tool outputs a family of optimal configurations and visualizes their trade-offs (Pareto frontiers of cleanup metrics and maps of optimized well placements). Site managers can use these results to understand the range of viable strategies and to select candidate designs for more detailed verification. OPTIMA is currently under active development and not yet fully released; this guide provides early documentation to support planning and gather user feedback.
Characteristics of the 2012 Geminids
The parent of the Geminids, 3200 Phaethon, is a unique body in that it is classified as an asteroid, however is responsible for one of the most prolific meteor showers of the year and has shown comet-like behavior in its past (Jewitt and Li 2010). The Geminid meteor shower is also anomalous as its rates have been increasing since it was first detected. Understanding the composition and properties of meteoroids that belong to this meteor shower is an important area of study and of interest to both theoreticians and experimentalists. Using the light curve and decelerations of ten double-station Geminids as seen in the Meteoroid Environment Office's widefield meteor cameras, densities were able to be approximated using a model of meteoroid ablation by Campbell-Brown et al (2013) which employs thermal disruption to model the release of grains during ablation. Bulk densities of Geminids give unique insight into the composition of Phaethon that would only be derived by going to the asteroid itself. The bulk densities of these ten Geminids were found to be between 2.6 and 3.0 g/cm(3), supporting results from Babadzhanov (2009) and Borovicka et al (2010) which prove Phaethon has a much lower porosity than most other meteor shower parents. NASA's Meteoroid Environment Office established these two wide-field meteor cameras to observe meteors in the milligram-mass-range. Each camera consists of a 17 mm focal length Schneider lens (f/0.95) on a Watec 902U2 Ultimate CCD video camera, producing a 21.7x15.5 degree field-of-view. This configuration sees meteors down to a magnitude of +6. Data from these cameras are currently being used to calculate daily automated meteor fluxes. On the first night of operation, December 13-14, 2012, 18 double-station and 53 unique single-station Geminids were detected. The Geminid flux results from this system will be presented as well as ZHR's over the peak of the Geminids. The average flux density over the night was 0.058, 0.052, and 0.062 meteors/km(2)/hour down to a limiting magnitude of +6.5, for the double-station results and each single-station's results. This equates to ZHR's of 113, 102, and 122 respectively. Included in the flux algorithm is a process to find the collecting area per height and a method to find the limiting meteor magnitude per 10 minute time period.
Operational Implementation of a Pc Uncertainty Construct for Conjunction Assessment Risk Analysis
Earlier this year the NASA Conjunction Assessment and Risk Analysis (CARA) project presented the theoretical and algorithmic aspects of a method to include the uncertainties in the calculation inputs when computing the probability of collision (Pc) between two space objects, principally uncertainties in the covariances and the hard-body radius. The output of this calculation approach is to produce rather than a single Pc value an entire probability density function that will represent the range of possible Pc values given the uncertainties in the inputs and bring CA risk analysis methodologies more in line with modern risk management theory. The present study provides results from the exercise of this method against an extended dataset of satellite conjunctions in order to determine the effect of its use on the evaluation of conjunction assessment (CA) event risk posture. The effects are found to be considerable: a good number of events are downgraded from or upgraded to a serious risk designation on the basis of consideration of the Pc uncertainty. The findings counsel the integration of the developed methods into NASA CA operations.
ICESat-2 Photon Classification: Finding Signal Photons in the ATL03 Geolocated Photon Data Product
ICESat-2 carries NASA's next-generation laser altimeter, ATLAS, (Advanced Topographic Laser Altimeter System), designed to measure changes in ice sheet height, sea ice freeboard, and vegetation canopy height. ATLAS contains a photon-counting lidar which transmits green (532-nm) pulses at 10kHz. Each pulse is split into 3 pairs of beams (one strong and one weak). Approximately 1014 photons per pulse travel from ATLAS through the atmosphere to reflect off the Earth's surface. Some return back into the ATLAS telescope where they are recorded. Photons from sunlight and instrument noise at the same wavelength are also recorded. The flight software time tags all photons within a 500m to 6 km range window and generates histograms. Using the histograms, it selects a telemetry window which varies from 20m over flat surfaces to hundreds of meters over rougher terrain. ATL03 contains the time, height (relative to the WGS-84 ellipsoid), latitude and longitude of every photon within the telemetry window. The basic challenge is to determine which of these photons were reflected off the surface. We have developed an algorithm that identifies these signal photons and assigns a confidence level (low, medium, or high) to each signal photon based on the signal to noise ratio. We present an overview of the signal identification algorithm and show the results on actual ICESat-2 data over ice sheet, sea ice, vegetated, and water surfaces. Higher level ATLAS products work with aggregations of the photons in order to determine the ellipsoidal height of the Earth, canopy height and structure, and other quantities of geophysical interest.
Adaptive Bio-Inspired Wireless Network Routing for Planetary Surface Exploration
Wireless mobile networks suffer connectivity loss when used in a terrain that has hills, and valleys when line of sight is interrupted or range is exceeded. To resolve this problem and achieve acceptable network performance, we have designed an adaptive, configurable, hybrid system to automatically route network packets along the best path between multiple geographically dispersed modules. This is very useful in planetary surface exploration, especially for ad-hoc mobile networks, where computational devices take an active part in creating a network infrastructure, and can actually be used to route data dynamically and even store data for later transmission between networks. Using inspiration from biological systems, this research proposes to use ant trail algorithms with multi-layered information maps (topographic maps, RF coverage maps) to determine the best route through ad-hoc network at real time. The determination of best route is a complex one, and requires research into the appropriate metrics, best method to identify the best path, optimizing traffic capacity, network performance, reliability, processing capabilities and cost. Real ants are capable of finding the shortest path from their nest to a food source without visual sensing through the use of pheromones. They are also able to adapt to changes in the environment using subtle clues. To use ant trail algorithms, we need to define the probability function. The artificial ant is, in this case, a software agent that moves from node to node on a network graph. The function to calculate the fitness (evaluate the better path) includes: length of the network edge, the coverage index, topology graph index, and pheromone trail left behind by other ant agents. Each agent modifies the environment in two different ways: 1) Local trail updating: As the ant moves between nodes it updates the amount of pheromone on the edge; and 2) Global trail updating: When all ants have completed a tour the ant that found the shortest route updates the edges in its path.
Introduction to Vector Field Visualization
Vector field visualization techniques are essential to help us understand the complex dynamics of flow fields. These can be found in a wide range of applications such as study of flows around an aircraft, the blood flow in our heart chambers, ocean circulation models, and severe weather predictions. The vector fields from these various applications can be visually depicted using a number of techniques such as particle traces and advecting textures. In this tutorial, we present several fundamental algorithms in flow visualization including particle integration, particle tracking in time-dependent flows, and seeding strategies. For flows near surfaces, a wide variety of synthetic texture-based algorithms have been developed to depict near-body flow features. The most common approach is based on the Line Integral Convolution (LIC) algorithm. There also exist extensions of LIC to support more flexible texture generations for 3D flow data. This tutorial reviews these algorithms. Tensor fields are found in several real-world applications and also require the aid of visualization to help users understand their data sets. Examples where one can find tensor fields include mechanics to see how material respond to external forces, civil engineering and geomechanics of roads and bridges, and the study of neural pathway via diffusion tensor imaging. This tutorial will provide an overview of the different tensor field visualization techniques, discuss basic tensor decompositions, and go into detail on glyph based methods, deformation based methods, and streamline based methods. Practical examples will be used when presenting the methods; and applications from some case studies will be used as part of the motivation.