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At least 559 records · Page 31

A data-driven global soil heterotrophic respiration dataset and the drivers of its inter-annual variability

Soil heterotrophic respiration (SHR), one of the primary carbon fluxes from terrestrial ecosystems to the atmosphere, is important for carbon-climate feedbacks because of its sensitivity to available litter and soil carbon, climatic conditions, and nutrient availability. However, until recently limited SHR data were available, and most published global SHR estimates have either a short time span, coarse spatial resolution, or reply on overly-simple model formulations. To better understand and quantify the global distribution of SHR and its sensitivity to climate variability, we produced a new global SHR dataset using Random Forest algorithms, up-scaling 455 point data from the Global Soil Respiration Database (SRDB 4.0) with gridded fields of climatic, edaphic and productivity as explanatory variables. We estimated a global total SHR of 46.8 Pg C yr-1 over 1985-2013 (95% confidence interval: 38.6-56.3 Pg C yr-1), with a significant increasing trend of 0.03 Pg C yr-2 during this period. We found that the choice of soil moisture datasets contributes more to the difference among these data-driven SHR members rather than that of productivity, temperature and precipitation data sources. We also analyzed the influence of climatic variables on the inter-annual variability (IAV) of our SHR product. Water availability was the dominant driver of IAV at global scales, although the inferred sensitivity depends on the choice of the soil moisture gridded dataset. At the ecosystem scale, temperature strongly controls the IAV of SHR in tropical forests, while water availability dominates in extra-tropical forest and semi-arid regions. Our machine-learning gridded SHR dataset and outputs from process-based land surface models (TRENDYv6) show agreement for a strong association between water variability and SHR IAV at the global scale, but the two approaches lead to different temporal trend globally and different controlling variables for IAV at the ecosystem scale. Our study provides evidence for the pervasive and important role of water availability in driving SHR, indicating both a direct effect limiting decomposition rates and an indirect effect through the amount of fresh organic matter made available to SHR from productivity. In consideration of potential limitations and uncertainties remaining in our data-driven SHR datasets, we call for a more scientifically designed observation network for SHR, more observation data compilation, and increased use of deep learning methods making maximum use of observation data in hand. This will benefit process-based models, and improve our understanding of SHR response to future anomalous environmental conditions.

Yao, Yitong↗

Machine learning of hidden variables in multiscale fluid simulation

Solving fluid dynamics equations often requires the use of closure relations that account for missing microphysics. For example, when solving equations related to fluid dynamics for systems with a large Reynolds number, sub-grid effects become important and a turbulence closure is required, and in systems with a large Knudsen number, kinetic effects become important and a kinetic closure is required. By adding an equation governing the growth and transport of the quantity requiring the closure relation, it becomes possible to capture microphysics through the introduction of ‘hidden variables’ that are non-local in space and time. The behavior of the ‘hidden variables’ in response to the fluid conditions can be learned from a higher fidelity or ab-initio model that contains all the microphysics. In our study, a partial differential equation simulator that is end-to-end differentiable is used to train judiciously placed neural networks against ground-truth simulations. We show that this method enables an Euler equation based approach to reproduce non-linear, large Knudsen number plasma physics that can otherwise only be modeled using Boltzmann-like equation simulators such as Vlasov or particle-in-cell modeling.

42 ENGINEERING↗

Hierarchical, Grid-Aware, and Economically Optimal Coordination of Distributed Energy Resources in Realistic Distribution Systems

Renewable portfolio standards are targeting high levels of variable solar photovoltaics (PV) in electric distribution systems, which makes reliability more challenging to maintain for distribution system operators (DSOs). Distributed energy resources (DERs), including smart, connected appliances and PV inverters, represent responsive grid resources that can provide flexibility to support the DSO in actively managing their networks to facilitate reliability under extreme levels of solar PV. This flexibility can also be used to optimize system operations with respect to economic signals from wholesale energy and ancillary service markets. Here, we present a novel hierarchical scheme that actively controls behind-the-meter DERs to reliably manage each unbalanced distribution feeder and exploits the available flexibility to ensure reliable operation and economically optimizes the entire distribution network. Each layer of the scheme employs advanced optimization methods at different timescales to ensure that the system operates within both grid and device limits. The hierarchy is validated in a large-scale realistic simulation based on data from the industry. Simulation results show that coordination of flexibility improves both system reliability and economics, and enables greater penetration of solar PV. Discussion is also provided on the practical viability of the required communications and controls to implement the presented scheme within a large DSO.

distribution network↗

Adjoint-Based Design of Rotors using the Navier-Stokes Equations in a Noninertial Reference Frame

Optimization of rotorcraft flowfields using an adjoint method generally requires a time-dependent implementation of the equations. The current study examines an intermediate approach in which a subset of rotor flowfields are cast as steady problems in a noninertial reference frame. This technique permits the use of an existing steady-state adjoint formulation with minor modifications to perform sensitivity analyses. The formulation is valid for isolated rigid rotors in hover or where the freestream velocity is aligned with the axis of rotation. Discrete consistency of the implementation is demonstrated using comparisons with a complex-variable technique, and a number of single- and multi-point optimizations for the rotorcraft figure of merit function are shown for varying blade collective angles. Design trends are shown to remain consistent as the grid is refined.

Nielsen, Eric J.↗

Embedding physics domain knowledge into a Bayesian network enables layer-by-layer process innovation for photovoltaics

Process optimization of photovoltaic devices is a time-intensive, trial-and-error endeavor, which lacks full transparency of the underlying physics and relies on user-imposed constraints that may or may not lead to a global optimum. Herein, we demonstrate that embedding physics domain knowledge into a Bayesian network enables an optimization approach for gallium arsenide (GaAs) solar cells that identifies the root cause(s) of underperformance with layer-by-layer resolution and reveals alternative optimal process windows beyond traditional black-box optimization. Our Bayesian network approach links a key GaAs process variable (growth temperature) to material descriptors (bulk and interface properties, e.g., bulk lifetime, doping, and surface recombination) and device performance parameters (e.g., cell efficiency). For this purpose, we combine a Bayesian inference framework with a neural network surrogate device-physics model that is 100× faster than numerical solvers. With the trained surrogate model and only a small number of experimental samples, our approach reduces significantly the time-consuming intervention and characterization required by the experimentalist. As a demonstration of our method, in only five metal organic chemical vapor depositions, we identify a superior growth temperature profile for the window, bulk, and back surface field layer of a GaAs solar cell, without any secondary measurements, and demonstrate a 6.5% relative AM1.5G efficiency improvement above traditional grid search methods.

14 SOLAR ENERGY↗

ARM shortwave spectrometers to study the clear-cloud transition zone and mixing processes

The proposed research is a collaborative effort between NASA/Goddard Space Flight Center and the Hebrew University of Jerusalem. While the NASA team focused on analyzing ground-based hyper-spectral radiance observations to understand cloud edge properties and their connection to mixing processes, the Hebrew University team tackled the problem through cloud modeling activities. By approximating the shortwave spectra in the cloud-clear transition zone as a linear combination of purely clear and purely cloudy spectra we can characterize the variations of cloud optical thickness and cloud droplet effective radius in the transition zone. When applying this method to the measurements of a ground-based shortwave spectroradiometer at the ARM’s SGP site, representing continental conditions, and MAGIC field campaign between Log Angeles, California and Honolulu, Hawaii, representing maritime scenarios, we found that cloud optical depth consistently decreases in both cases, but droplet size decreases much more substantially for the continental regime, suggesting different mixing processes for the continental and maritime conditions. The investigation and measurements of radiation clouds were coupled with a unique cloud modeling. A novel spectral bin microphysics was developed and implemented to the System of Atmospheric Modeling (SAM). In order to resolve cloud transition zones with high spatial gradients of microphysical variables a unique high resolution (10 m) was used in simulations. The model calculates droplet size distributions in each grid point. The model output was transferred to the NASA/GSFC team for utilization in radiative calculations and testing of both radiative algorithm and model representation.

54 ENVIRONMENTAL SCIENCES↗

COMPUTATIONAL MODELING OF IGNITION AND PREMIXED FLAME PROPAGATION INITIATED BY A PRE-CHAMBER TURBULENT JET

Addressing the pressing need for reduced carbon emissions, Turbulent Jet Ignition (TJI) emerges as a promising technology for ultra-lean combustion, offering enhanced thermal efficiencies and minimized cyclic variability in spark-ignited engines. To facilitate rapid testing and integration of this technology, a robust computational modeling framework is crucial. This study delves into the predictive capabilities of computational models for main-chamber ignition and premixed flame propagation using a single-cycle TJI rig measured by Biswas et al. (Applied Thermal Engineering, vol 106, 2016). Employing an open-source compressible flow simulation solver with Large Eddy Simulation (LES) for turbulence modeling, the investigation integrates the conventional Laminar Finite Rate Chemistry (LFRC) model alongside the transported Probability Density Method (PDF) for turbulence-chemistry interaction. A fully-consistent Eulerian Monte-Carlo Fields (EMCF) method is utilized to approximate the transported PDF, while Interaction by Exchange with Mean is employed to close micro-mixing terms in stochastic differential equations. A reduced chemical reaction mechanism with 21 species and 84 reactions (DRM-19) is used for solving chemical kinetics, and a double Gaussian energy deposition model is used to approximate the spark ignition in the pre-chamber. An unstructured O-grid mesh with 0.3 million cells in the prechamber and 1 million cells in the main chamber is employed. Results are divided into two phases: pre-chamber initialization and full TJI simulations. Validation of the predicted pre-chamber flame propagation and the lean ignition in the main-chamber is carried out by using available experimental data. Under quiescent conditions, both the LFRC and transported PDF methods largely underestimate the flame speed and subsequent pressure growth in the pre-chamber. A linear momentum forcing technique is applied to investigate the impact of initial turbulence in the pre-chamber, demonstrating a notable influence on flame propagation. Fine-tuning of the forcing coefficient reproduces the sudden pressure growth observed in the experiment. The experimentally validated pre-chamber simulation serves as the initial condition for the full TJI simulations. It is found that the LFRC model fails to predict lean-ignition in the main-chamber, resulting in a misfiring event. Incorporation of turbulence-chemistry interaction using the transported PDF method substantially improves the prediction of the ignition event in the main-chamber, achieving fair qualitative agreement and quantitative validation of combustion parameters within ±10% of the reported experimental data. The rich simulation results consisting of a full set of statistical description of the thermo-chemical states enable us to gain deep insights into the ignition mechanisms in the main chamber, which is limited when done experimentally. A novel dual ignition phenomenon is revealed in the TJI rig for the first time. Initially, a primary ignition kernel is formed at a downstream location which eventually detaches from the main jet. As the jet momentum decreases, a secondary ignition event follows, this time at a more upstream location which eventually combines with the primary ignition kernel to form a single connected flame front. Investigation of these ignition sequences in chemical composition space reveal distinct differences between the two. The primary ignition event in the main-chamber is followed by a large concentration of active radicals from the pre-chamber jet, accelerating the chain-branching steps, characterizing what has been referred to as flame ignition. In contrast, the secondary ignition occurs in the absence of active radicals in the pre-chamber jet, hence characterized as jet ignition. Further analysis of the effect of pre-chamber jet characteristics on lean ignition in the main-chamber is conducted by setting up cases with different initial pressure ratios (por) between the two chambers, a non-dimensional parameter, ranging from 1.2 to 3.2. As the initial pressure ratio increases, jet momentum increases, with dual ignition observed in cases above por= 2.2. Case with por= 3.2 lead to misfiring. The effect of ignition sequence on global combustion characteristics of TJI is analyzed. Dual ignition events lead to non-monotonicity in combustion characteristics such as global reaction progress variable, flame penetration, and global heat release rate. In dual ignition events, although the rate of fuel consumption and global heat release rate is initially lower, the secondary ignition leads to a sudden increase in flame surface area, resulting in a sudden jump and promoting the overall performance of the TJI system.

42 ENGINEERING↗

20-mN Variable Specific Impulse (Isp) Colloid Thruster

Busek Company, Inc., has designed and manufactured an electrospray emitter capable of generating 20 mN in a compact package (7x7x1.7 in). The thruster consists of nine porous-surface emitters operating in parallel from a common propellant supply. Each emitter is capable of supporting over 70,000 electrospray emission sites with the plume from each emitter being accelerated through a single aperture, eliminating the need for individual emission site alignment to an extraction grid. The total number of emission sites during operation is expected to approach 700,000. This Phase II project optimized and characterized the thruster fabricated during the Phase I effort. Additional porous emitters also were fabricated for full-scale testing. Propellant is supplied to the thruster via existing feed-system and microvalve technology previously developed by Busek, under the NASA Space Technology 7's Disturbance Reduction System (ST7-DRS) mission and via follow-on electric propulsion programs. This project investigated methods for extending thruster life beyond the previously demonstrated 450 hours. The life-extending capabilities will be demonstrated on a subscale version of the thruster.

Demmons, Nathaniel↗

The WRF-Solar Ensemble Prediction System: Development, Test, and Validation

Providing reliable probabilistic solar radiation information is needed to improve management of the uncertainty and variability of solar generation. Thus, guidance on how to develop skillful and accurate ensemble forecasts is essential and it will ultimately contribute to integration of high amounts of solar energy on the grid. A team from the National Renewable Energy Laboratory and the National Center for Atmospheric Research had been collaborating to develop the WRF-Solar ensemble prediction system (WRF-Solar EPS) in the past three years to produce probabilistic solar irradiance forecasts and better predict solar energy by quantifying forecast uncertainty. The WRF-Solar EPS basically generates ensemble members for solar irradiance based on stochastic perturbations to provide intraday and day-ahead probabilistic forecasts. This study will present main research steps in developing the WRF-Solar EPS including: (a) tangent linear analysis for identifying key input variables of six WRF-Solar modules significantly related to predicting of cloud and solar irradiance, (b) combining stochastic perturbation technique with the WRF-Solar model, and (c) ensemble calibration method to decrease error and uncertainty of ensemble-based solar forecasts. The capability of WRF-Solar EPS is now updated to the most recent version of standard WRF model. This presentation will summarize comprehensive results from the evaluation of forecasts against the National Solar Radiation Data Base as well as ground-measured observations. Moreover, we will introduce the user's guide for WRF-Solar EPS (e.g., parameters to configure stochastic perturbations) and future extension of this research.

day-ahead forecast↗

Land Surface Temperature Measurements from EOS MODIS Data

This report summarizes the accomplishments made by the MODIS LST (Land-Surface Temperature) group at University of California, Santa Barbara, under NASA Contract. Version 1 of the MODIS Land-Surface Temperature Algorithm Theoretical Basis Document (ATBD) was reviewed in June 1994, version 2 reviewed in November 1994, version 3.1 in August 1996, and version 3.3 updated in April 1999. Based on the ATBD, two LST algorithms were developed, one is the generalized split-window algorithm and another is the physics-based day/night LST algorithm. These two LST algorithms were implemented into the production generation executive code (PGE 16) for the daily standard MODIS LST products at level-2 (MODII-L2) and level-3 (MODIIA1 at 1 km resolution and MODIIB1 at 5km resolution). PGE codes for 8-day 1 km LST product (MODIIA2) and the daily, 8-day and monthly LST products at 0.05 degree latitude/longitude climate model grids (CMG) were also delivered. Four to six field campaigns were conducted each year since 2000 to validate the daily LST products generated by PGE16 and the calibration accuracies of the MODIS TIR bands used for the LST/emissivity retrieval from versions 2-4 of Terra MODIS data and versions 3-4 of Aqua MODIS data. Validation results from temperature-based and radiance-based methods indicate that the MODIS LST accuracy is better than 1 C in most clear-sky cases in the range from -10 to 58 C. One of the major lessons learn from multi- year temporal analysis of the consistent V4 daily Terra MODIS LST products in 2000-2003 over some selected target areas including lakes, snow/ice fields, and semi-arid sites is that there are variable numbers of cloud-contaminated LSTs in the MODIS LST products depending on surface elevation, land cover types, and atmospheric conditions. A cloud-screen scheme with constraints on spatial and temporal variations in LSTs was developed to remove cloud-contaminated LSTs. The 5km LST product was indirectly validated through comparisons to the 1 km LST product. Twenty three papers related to the LST research work were published in journals over the last decade.

Wan, Zheng-Ming↗

Application of FUN3D and CFL3D to the Third Workshop on CFD Uncertainty Analysis

Two Reynolds-averaged Navier-Stokes computer codes - one unstructured and one structured - are applied to two workshop cases (for the 3rd Workshop on CFD Uncertainty Analysis, held at Instituto Superior Tecnico, Lisbon, in October 2008) for the purpose of uncertainty analysis. The Spalart-Allmaras turbulence model is employed. The first case uses the method of manufactured solution and is intended as a verification case. In other words, the CFD solution is expected to approach the exact solution as the grid is refined. The second case is a validation case (comparison against experiment), for which modeling errors inherent in the turbulence model and errors/uncertainty in the experiment may prevent close agreement. The results from the two computer codes are also compared. This exercise verifies that the codes are consistent both with the exact manufactured solution and with each other. In terms of order property, both codes behave as expected for the manufactured solution. For the backward facing step, CFD uncertainty on the finest grid is computed and is generally very low for both codes (whose results are nearly identical). Agreement with experiment is good at some locations for particular variables, but there are also many areas where the CFD and experimental uncertainties do not overlap.

Rumsey, C. L.↗

Assessment of a parabolic analysis for axisymmetric internal flows in rocket and turbomachinery ducts

The flow paths in gas turbine passages encompass a wide range of flow properties such as Reynolds number and Mach number as well as many other variable flow conditions such as swirl, free-stream turbulence, and laminar/turbulent transition. An existing computer program, the Axisymmetric Diffuser Duct (ADD) code, which calculates compressible, turbulent, swirling flow through axisymmetric ducts has been modified to include the effects of free-stream turbulence and laminar/turbulent transition. The program has been evaluated on a matrix of test cases to determine its accuracy, robustness, and limits of applicability. This improved version of the ADD code calculates solutions which compare well with available data and can now be applied to a wider range of problems than previously possible. In addition a concept called local enhancement was developed and tested on a simple two-dimensional geometry in order to demonstrate a method to reduce computer time. In this concept the pressure distribution is calculated on a coarse grid using the ADD code and the viscous layer is locally enhanced using a boundary layer analysis. By applying this concept, an order of magnitude reduction in computer time was possible without any loss in accuracy.

Power, G. D.↗

In situ Detection of Plasma Induced Surface Interaction based on Deep Learning based Visual Diagnostics (Technical Report)

It is characteristic for many plasma devices to undergo plasma-material interaction leading to surface erosion. These processes, often not easily detectable, lead to changes in device performance and lifespan. State-of-the-art lifetime tests and wear experiments require over 1000s hours. A self-consistent model for accurately predicting the erosion's effects is not available. In situ detection of these processes is not a trivial task since the surface variations at the early stages have a micron scale. Such limitations not only restrict testing and prediction capabilities but also slow the development of new thrusters and limit mission duration. To address these challenges, an in-situ diagnostic for real-time erosion assessment has been developed, aiming to expedite lifetime testing and broaden experimental campaigns. Several works were dedicated to real-time and in situ monitoring of material erosion during plasma exposure using laser holography, microscopy, and with telemicroscopes. However, the applicability of these approaches is limited due to complexity, cost and less flexibility as they often require placing diagnostic equipment inside the vacuum chamber. In collaboration with Princeton Collaborative Research Facility (PCRF), Princeton Plasma Physics Laboratory (PPPL), a new diagnostic approach is developed, where geometry modifications to the ceramic channel walls were introduced that would result in accelerated channel erosion. We employed Long-distance microscope (LDM) imagery, combined with Deep-Learning based Shape from focus or depth from focus (DFF or SFF) approach, that provides an accessible and cost-effective solution. LDM employs focus variation techniques to continuously capture multiple images of the target object at distinct focal planes. DFF, an optical focus variation method, generates a 3D topographical surface depth map from a sequence of variably focused images. Combined with the developed diagnostic, this approach offers a controllable means to study erosion under accelerated conditions. In this work, we develop Neural Network-based DFF algorithm applicable for LDM data to quantitatively evaluate plasma induced surface modification from LDM data. Next, we develop Deep Learning-based super-resolution depth map image reconstruction technique to increase the resolution of depth maps obtained from DFF algorithm to improve the accuracy of erosion measurements. Thirdly, we develop several image processing techniques to remove noise and improve the quality of depth map image. Here we report the results of initial tests for this approach. An experimental setup designed and built in PPPL was employed that consists of a 3-cm gridded ion source that produces a neutralized argon beam with energies up to 600 eV. A hexagonal boron nitride (h-BN) ceramic target, designed based on computational predictions, was used. Tests were conducted to reconstruct the complex geometry of the target under the lighting conditions of the operated ion source.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

An investigation of the accuracy of finite difference methods in the solution of linear elasticity problems

The accuracy of the finite difference method in the solution of linear elasticity problems that involve either a stress discontinuity or a stress singularity is considered. Solutions to three elasticity problems are discussed in detail: a semi-infinite plane subjected to a uniform load over a portion of its boundary; a bimetallic plate under uniform tensile stress; and a long, midplane symmetric, fiber reinforced laminate subjected to uniform axial strain. Finite difference solutions to the three problems are compared with finite element solutions to corresponding problems. For the first problem a comparison with the exact solution is also made. The finite difference formulations for the three problems are based on second order finite difference formulas that provide for variable spacings in two perpendicular directions. Forward and backward difference formulas are used near boundaries where their use eliminates the need for fictitious grid points.

Bauld, N. R., Jr.↗

Validation Experiments of Incipient Turbulent Separation over an Axisymmetric Afterbody

Historically, the flow physics involved with most turbulent separated flows have presented fundamental challenges in validation between experimental and numerical approaches. As recognized by the CFD Vision 2030 study commissioned by NASA, validation of Reynolds-averaged Navier-Stokes (RANS) models and other scale-resolving methods for turbulent separated flow requires the support of advanced, high-fidelity experiments designed specifically for CFD implementation. In accordance with this effort, a new test platform, referred to as the NASA Axisymmetric Afterbody, was designed to obtain detailed information of the flow field over a smooth body, undergoing adverse pressure gradient induced separation for a fixed Reynolds number, Re = 180,000. The parametric body offers a range of flow states from fully attached,incipient separation, to fully separated flow based on variable afterbody geometries. In an initial effort to evaluate RANS turbulence model capabilities, the present configuration of the axisymmetric model features a mild adverse pressure gradient over the contoured boattail section, inducing incipient turbulent separation. Experiments include steady pressure measurements to serve as preliminary comparisons to simulation studies, which examine the effect of variable grid domains and RANS turbulence models, in an effort to understand and evaluate the critical variability between solutions for the present configuration. Results indicate potential discrepancies may be due to the effect of the square tunnel test section walls, relatively large blockage ratio, and inconsistent reference parameters. Ongoing work will focus on the experimental campaigns to obtain surface flow visualizations and high-resolution, off-body flow field measurements using Stereoscopic Particle Image Velocimetry (SPIV) and Laser Doppler Velocimetry (LDV) techniques to provide a detailed benchmark dataset to aid turbulence modelers.

axisymmetric afterbody↗

Myriad World Baseline: Global Geodemographic Estimates

The LandScan Myriad World Baseline (MWB) method produces global, residential (nighttime/home-location) gridded geodemographic estimates based on 5-year age/gender cohorts—at 30-arcsecond (≈1 km) resolution. MWB is designed to fill gaps where detailed, georeferenced survey data (e.g., Demographic and Health Surveys (DHS)) are missing or outdated, and to provide a baseline that can support human security analysis, including consequence assessment, “patterns of life” modeling, and scenario-based population futures. MWB’s workflow spatializes household-level age/gender characteristics from the GLOPOP-S dataset by conflating household and gridded expected relative wealth adapted from Global Gridded Relative Deprivation Index (GRDI), then adjusts them to a target year of interest. Age/gender estimates are then applied to harmonize lowest-administrative-level statistics with LandScan residential counts, yielding final geodemographic estimates. Two validation case studies are presented: Ghana (2021) and Tokyo/Kanagawa, Japan (2020), illustrating spatial variability in demographic cohorts and comparing MWB outputs to official gridded statistics. Results show close overall alignment relative to validation criteria including population pyramids and age-dependency ratios.

Tuccillo, Joe [ORNL] (ORCID:0000000259300943)↗

Motion detection in astronomical and ice floe images

Two approaches are presented for establishing correspondence between small areas in pairs of successive images for motion detection. The first one, based on local correlation, is used on a pair of successive Voyager images of the Jupiter which differ mainly in locally variable translations. This algorithm is implemented on a sequential machine (VAX 780) as well as the Massively Parallel Processor (MPP). In the case of the sequential algorithm, the pixel correspondence or match is computed on a sparse grid of points using nonoverlapping windows (typically 11 x 11) by local correlations over a predetermined search area. The displacement of the corresponding pixels in the two images is called the disparities to cubic surfaces. The disparities at points where the error between the computed values and the surface values exceeds a particular threshold are replaced by the surface values. A bilinear interpolation is then used to estimate disparities at all other pixels between the grid points. When this algorithm was applied at the red spot in the Jupiter image, the rotating velocity field of the storm was determined. The second method of motion detection is applicable to pairs of images in which corresponding areas can experience considerable translation as well as rotation.

Manohar, M.↗