Spatial and Temporal Low-Dimensional Models for Fluid Flow

A document discusses work that obtains a low-dimensional model that captures both temporal and spatial flow by constructing spatial and temporal four-mode models for two classic flow problems. The models are based on the proper orthogonal decomposition at two reference Reynolds numbers. Model predictions are made at an intermediate Reynolds number and compared with direct numerical simulation results at the new Reynolds number

Algorithm for Stabilizing a POD-Based Dynamical System

This algorithm provides a new way to improve the accuracy and asymptotic behavior of a low-dimensional system based on the proper orthogonal decomposition (POD). Given a data set representing the evolution of a system of partial differential equations (PDEs), such as the Navier-Stokes equations for incompressible flow, one may obtain a low-dimensional model in the form of ordinary differential equations (ODEs) that should model the dynamics of the flow. Temporal sampling of the direct numerical simulation of the PDEs produces a spatial time series. The POD extracts the temporal and spatial eigenfunctions of this data set. Truncated to retain only the most energetic modes followed by Galerkin projection of these modes onto the PDEs obtains a dynamical system of ordinary differential equations for the time-dependent behavior of the flow. In practice, the steps leading to this system of ODEs entail numerically computing first-order derivatives of the mean data field and the eigenfunctions, and the computation of many inner products. This is far from a perfect process, and often results in the lack of long-term stability of the system and incorrect asymptotic behavior of the model. This algorithm describes a new stabilization method that utilizes the temporal eigenfunctions to derive correction terms for the coefficients of the dynamical system to significantly reduce these errors

Parameterizing Coefficients of a POD-Based Dynamical System

A method of parameterizing the coefficients of a dynamical system based of a proper orthogonal decomposition (POD) representing the flow dynamics of a viscous fluid has been introduced. (A brief description of POD is presented in the immediately preceding article.) The present parameterization method is intended to enable construction of the dynamical system to accurately represent the temporal evolution of the flow dynamics over a range of Reynolds numbers. The need for this or a similar method arises as follows: A procedure that includes direct numerical simulation followed by POD, followed by Galerkin projection to a dynamical system has been proven to enable representation of flow dynamics by a low-dimensional model at the Reynolds number of the simulation. However, a more difficult task is to obtain models that are valid over a range of Reynolds numbers. Extrapolation of low-dimensional models by use of straightforward Reynolds-number-based parameter continuation has proven to be inadequate for successful prediction of flows. A key part of the problem of constructing a dynamical system to accurately represent the temporal evolution of the flow dynamics over a range of Reynolds numbers is the problem of understanding and providing for the variation of the coefficients of the dynamical system with the Reynolds number. Prior methods do not enable capture of temporal dynamics over ranges of Reynolds numbers in low-dimensional models, and are not even satisfactory when large numbers of modes are used. The basic idea of the present method is to solve the problem through a suitable parameterization of the coefficients of the dynamical system. The parameterization computations involve utilization of the transfer of kinetic energy between modes as a function of Reynolds number. The thus-parameterized dynamical system accurately predicts the flow dynamics and is applicable to a range of flow problems in the dynamical regime around the Hopf bifurcation. Parameter-continuation software can be used on the parameterized dynamical system to derive a bifurcation diagram that accurately predicts the temporal flow behavior

Flow Solver for Incompressible 2-D Drive Cavity

This software solves the Navier-Stokes equations for the incompressible driven cavity flow problem. The code uses second-order finite differencing on a staggered grid using the Chorin projection method. The resulting intermediate Poisson equation is efficiently solved using the fast Fourier transform. Time stepping is done using fourth-order Runge-Kutta for stability at high Reynolds numbers. Features include check-pointing, periodic field snapshots, ongoing reporting of kinetic energy and changes between time steps, time histories at selected points, and optional streakline generation

Low-dimensional models for fluid flow

Despite the temporal and spatial complexity of fluid flow, model dimensionality can often be greatly reduced while both capturing and illuminating the nonlinear dynamics of the flow. This dissertation follows the methodology of direct numerical simulation (DNS) followed by Proper Orthogonal Decomposition of temporally sampled DNS data to derive temporal and spatial eigenfunctions. The DNS calculations use Chorin's projection scheme; 2-d validation and results are presented for driven cavity and square cylinder wake flows. The flow velocity is expressed as a linear combination of the spatial eigenfunctions with time-dependent coefficients. Galerkin projection of these modes onto the Navier-Stokes equations obtains a dynamical system with quadratic nonlinearity and explicit Reynolds number (Re) dependence. Truncated to retain only the most energetic modes produces a low-dimensional model for the flow at the decomposition Re. This dissertation demonstrates that these low-dimensional models reproduce the flow dynamics, but with small errors in amplitude, phase, and particularly long term dynamics. A new stabilization algorithm is presented that projects the error onto the derived temporal eigenfunctions, then modifies the dynamical system coefficients to significantly reduce these errors. Its effectiveness is demonstrated with low-dimensional dynamical systems for driven cavity flow in the periodic regime, quasi-periodic flow at Re 10000, and the wake flow. This dissertation also addresses the task of obtaining more useful models that are valid over a range of Reynolds numbers. Straightforward Re-based parameter continuation applied to extrapolate the model proves inadequate for successful flow prediction. A new concept of parameterizing the dynamical system coefficients is introduced that utilizes the kinetic energy transfer between modes as a function of Re to predict the flow dynamics correctly. Results for the driven cavity flow include a minimal four-mode dynamical system that captures the flow dynamics for Re up to 10000. A four-mode dynamical system for the square cylinder wake flow demonstrates accurate amplitude predictions for Re up to 100. The most robust low-dimensional models are obtained by further including a model for the frequency variation with Re. Low-dimensional models that incorporate spatial mode changes with Re are developed and quantitatively assessed for both test flows

MODIS Technical Report Series. Volume 4: MODIS data access user's guide: Scan cube format

The software described in this document provides I/O functions to be used with Moderate Resolution Spectroradiometer (MODIS) level 1 and 2 data, and could be easily extended to other data sources. This data is in a scan cube data format: a 3-dimensional ragged array containing multiple bands which have resolutions ranging from 250 to 1000 meters. The complexity of the data structure is handled internally by the library. The I/O calls allow the user to access any pixel in any band through 'C' structure syntax. The high MODIS data volume (approaching half a terabyte per day) has been a driving factor in the library design. To avoid recopying data for user access, all I/O is performed through dynamic 'C' pointer manipulation. This manual contains background material on MODIS, several coding examples of library usage, in-depth discussions of each function, reference 'man' type pages, and several appendices with details of the included files used to customize a user's data product for use with the library

NASA's Black Marble Product Suite: Validation Strategy

NASA's Black Marble nighttime lights product suite (VNP46) is available at 500m resolution since January 2012 with data fro the Visible Infrared Imaging Radiometer Suite (VIIRS) Day/Night Band (DNB) onboard the Suomi National Polar-orbiting Platform (SNPP). The retrieval algorithm, developed and implemented for routine global processing at NASA's Land Science Investigator-led Processing System (SIPS), utilizes all high-quality, cloud-free, atmospheric-terrain, vegetation, snow, lunar and stray light corrected radiances to estimate daily nighttime lights (NTL) and other intrinsic surface optical properties. Extensive benchmark tests at representative spatial and temporal scales were conducted on the VNP46 time series record to characterize the uncertainties stemming from upstream data sources. Current and planned validation activities under the Group on Earth Observations (GEO) Human Planet Initiative are aimed at evaluating the products at difference geographic locations and time periods representing the full range of retrieval conditions

PolyQ Repeat Expansions in ATXN2 Associated with ALS Are CAA Interrupted Repeats

Amyotrophic lateral sclerosis (ALS) is a devastating, rapidly progressive disease leading to paralysis and death. Recently, intermediate length polyglutamine (polyQ) repeats of 27–33 in ATAXIN-2 (ATXN2), encoding the ATXN2 protein, were found to increase risk for ALS. In ATXN2, polyQ expansions of ≥34, which are pure CAG repeat expansions, cause spinocerebellar ataxia type 2. However, similar length expansions that are interrupted with other codons, can present atypically with parkinsonism, suggesting that configuration of the repeat sequence plays an important role in disease manifestation in ATXN2 polyQ expansion diseases. Here we determined whether the expansions in ATXN2 associated with ALS were pure or interrupted CAG repeats, and defined single nucleotide polymorphisms (SNPs) rs695871 and rs695872 in exon 1 of the gene, to assess haplotype association. We found that the expanded repeat alleles of 40 ALS patients and 9 long-repeat length controls were all interrupted, bearing 1–3 CAA codons within the CAG repeat. 21/21 expanded ALS chromosomes with 3CAA interruptions arose from one haplotype (GT), while 18/19 expanded ALS chromosomes with <3CAA interruptions arose from a different haplotype (CC). Moreover, age of disease onset was significantly earlier in patients bearing 3 interruptions vs fewer, and was distinct between haplotypes. These results indicate that CAG repeat expansions in ATXN2 associated with ALS are uniformly interrupted repeats and that the nature of the repeat sequence and haplotype, as well as length of polyQ repeat, may play a role in the neurological effect conferred by expansions in ATXN2

Aurora Detection From Nighttime Lights for Earth and Space Science Applications

Abstract This research leverages data from the Day/Night Band (DNB) of the Visible Infrared Imaging Radiometer (VIIRS) instrument onboard the Suomi National Polar‐orbiting Partnership (S‐NPP) satellite. We demonstrate the value of mining the VIIRS DNB for aurora and describe our use of unsupervised machine learning to create a binary mask for aurora occurrence. This mask can be used to flag aurora‐contaminated observations for NASA's nighttime lights products for Earth science applications. The identification of auroral regions can also be used for Space Weather applications, for example, for comparison with aurora forecast model and with other satellite‐ or ground‐based aurora observations. The DNB is a broadband channel that is sensitive to wavelengths from 500 to 900 nm, which covers most of the visible light spectrum, and as the name implies, captures light even at night with a sensitivity at the nanowatt level. This band is suitable for aurora observations since the light emitted by the aurora tends to be dominated by emissions from atomic oxygen, resulting in a greenish glow at a wavelength of 557.7 nm, especially at an altitude of 110 km. This study compares the global nighttime derived aurora regions for 17 and 18 March with the NOAA Space Weather Prediction Center's (SWPC) probability product for the St. Patrick's Day geomagnetic storm in 2015. VIIRS sensors are slated to be added to the next generation of polar‐orbiting operational satellites. Our novel automated approach to aurora identification opens up an efficient way to leverage this unique data source

Potentially underestimated gas flaring activities—a new approach to detect combustion using machine learning and NASA’s Black Marble product suite

Monitoring changes in greenhouse gas (GHG) emission is critical for assessing climate mitigation efforts towards the Paris Agreement goal. A crucial aspect of science-based GHG monitoring is to provide objective information for quality assurance and uncertainty assessment of the reported emissions. Emission estimates from combustion events (gas flaring and biomass burning) are often calculated based on activity data (AD) from satellite observations, such as those detected from the visible infrared imaging radiometer suite (VIIRS) onboard the Suomi-NPP and NOAA-20 satellites. These estimates are often incorporated into carbon models for calculating emissions and removals. Consequently, errors and uncertainties associated with AD propagate into these models and impact emission estimates. Deriving uncertainty of AD is therefore crucial for transparency of emission estimates but remains a challenge due to the lack of evaluation data or alternate estimates. This work proposes a new approach using machine learning (ML) for combustion detection from NASA’s Black Marble product suite and explores the assessment of potential uncertainties through comparison with existing detections. We jointly characterize combustion using thermal and light emission signals, with the latter improving detection of probable weaker combustion with less distinct thermal signatures. Being methodologically independent, the differences in ML-derived estimates with existing approaches can indicate the potential uncertainties in detection. The approach was applied to detect gas flares over the Eagle Ford Shale, Texas. We analyzed the spatio-temporal variations in detections and found that approximately 79.04% and 72.14% of the light emission-based detections are missed by ML-derived detections from VIIRS thermal bands and existing datasets, respectively. This improvement in combustion detection and scope for uncertainty assessment is essential for comprehensive monitoring of resulting emissions and we discuss the steps for extending this globally