Dealing with spatial heterogeneity in pointwise-to-gridded- data comparisons

Most studies on validation of satellite trace gas retrievals or atmospheric chemical transport models assume that pointwise measurements, which roughly represent the element of space, should compare well with satellite (model) pixels (grid box). This assumption implies that the field of interest must possess a high degree of spatial homogeneity within the pixels (grid box), which may not hold true for species with short atmospheric lifetimes or in the proximity of plumes. Results of this assumption often lead to a perception of a nonphysical discrepancy between data, resulting from different spatial scales, potentially making the comparisons prone to overinterpretation. Semivariogram is a mathematical expression of spatial variability in discrete data. Modeling the semivariogram behavior permits carrying out spatial optimal linear prediction of a random process field using kriging. Kriging can extract the spatial information (variance) pertaining to a specific scale, which in turn translates pointwise data to a gridded space with quantified uncertainty such that a grid-to-grid comparison can be made. Here, using both theoretical and real-world experiments, we demonstrate that this classical geostatistical approach can be well adapted to solving problems in evaluating model-predicted or satellite-derived atmospheric trace gases. This study suggests that satellite validation procedures using the present method must take kriging variance and satellite spatial response functions into account. We present the comparison of Ozone Monitoring Instrument (OMI) tropospheric NO2 columns against 11 Pandora spectrometer instrument (PSI) systems during the DISCOVER-AQ campaign over Houston. The least-squares fit to the paired data shows a low slope (OMI=0.76×PSI+1.18×1015 molecules cm−2, r2=0.66), which is indicative of varying biases in OMI. This perceived slope, induced by the problem of spatial scale, disappears in the comparison of the convolved kriged PSI and OMI (0.96×PSI+0.66×1015 molecules cm−2, r2=0.72), illustrating that OMI possibly has a constant systematic bias over the area. To avoid gross errors in comparisons made between gridded data vs. pointwise measurements, we argue that the concept of semivariogram (or spatial autocorrelation) should be taken into consideration, particularly if the field exhibits a strong degree of spatial heterogeneity at the scale of satellite and/or model footprints.

Molecular Dynamics Studies of Entropic Elasticity of Condensed Lattice Networks Connected with Uniform Functionality f = 4

To study the linear region of entropic elasticity, we considered the simplest physical model possible and extracted the linear entropic regime by using the least squares fit and the minimum...

Spatially Highly Resolved Solar-wind-induced Magnetic Field on Venus

The current work investigates the Venusian solar-wind-induced magnetosphere at a high spatial resolution using all Venus Express (VEX) magnetic observations through an unbiased statistical method. We first evaluate the predictability of the interplanetary magnetic field (IMF) during VEX’s Venusian magnetospheric transits and then map the induced field in a cylindrical coordinate system under different IMF conditions. Our mapping resolves structures on various scales, ranging from the ionopause to the classical IMF draping. We also resolve two recently reported structures, a low-ionosphere magnetization over the terminator, and a global “looping” structure in the near magnetotail. In contrast to the reported IMF-independent cylindrical magnetic field of both structures, our results illustrate their IMF dependence. In both structures, the cylindrical magnetic component is more intense in the hemisphere with an upward solar wind electric field (E SW) than in the opposite hemisphere. Under downward E SW, the looping structure even breaks, which is attributable to an additional draped magnetic field structure wrapping toward −E SW. In addition, our results suggest that these two structures are spatially separate. The low-ionosphere magnetization occurs in a very narrow region, at about 88°–95° solar zenith angle and 185–210 km altitude. A least-squares fit reveals that this structure is attributable to an antisunward line current with 191.1 A intensity at 179 ± 10 km altitude, developed potentially in a Cowling channel.

Bathymetry Determination Based on Abundant Wavenumbers Estimated from the Local Phase Gradient of X-Band Radar Images

A phase gradient (PG)-based algorithm is proposed in this study to determine coastal bathymetry from X-band radar images. Although local wavenumbers with the same spatial resolution of the wave field can be obtained from the wave field using the PG method, only a single wavenumber result can be extracted from each location theoretically. Due to the influence of unavoidable noise on the wave field image, single wavenumber estimation often shows high uncertainty. This study combines a bandpass filter and directional pass filter to produce different nearly monocomponent wave fields from X-band radar images and then estimates more wavenumbers from these wave fields using the PG method. However, the distributions of wavenumbers in higher-frequency bins still show high variance because the strength of wave signals is weak. We confirmed that the uncertain wavenumber–frequency pairs can be improved using the Kalman filter and are more consistent with the dispersion relation curve. To decrease the influence of inaccurate wavenumbers, we also use the strength of the wave signals as the weights for the least-squares fit. Although the depth errors from shallow-water areas are still unavoidable, we can remove the inaccurate depth estimation from shallow-water areas according to the coefficients of determination of the fitting. In summary, the algorithm proposed in this study can obtain a bathymetry map with high spatial resolution. In contrast to the depth result estimated using a single wavenumber of each frequency bin, we confirm that more wavenumbers from each of the frequency bins are helpful in fitting the dispersion relation curve and obtaining a more reliable depth result.

Dealing with Spatial Heterogeneity in Pointwise to Gridded Data Comparisons

Atmospheric modelers and the trace gas retrieval community typically presuppose that pointwise measurements, which roughly represent the element of space, should compare well with satellite (model) pixels (grids). This assumption implies that the field of interest must possess a high degree of spatial homogeneity within the pixels (grids), which may not hold true for species with short atmospheric lifetimes or in the proximity of plumes. Results of this assumption often lead to a perception of a nonphysical discrepancy between data, resulting from different spatial scales, potentially making the comparisons prone to overinterpretation. Semivariogram is a mathematical expression of spatial variability in discrete data. Modeling the semivariogram behavior permits carrying out spatial optimal linear prediction of a random process field using kriging. Kriging can extract the spatial information (variance) pertaining to a specific scale, which in turn translating pointwise data to a grid space with quantified uncertainty such that a grid-to-grid comparison can be made. Here, using both theoretical and real-world experiments, we demonstrate that this classical geostatistical approach can be well adapted to solving problems in evaluating model-predicted or satellite-derived atmospheric trace gases. This study demonstrates that satellite validation procedures must take kriging variance and satellite spatial response functions into account. We present the comparison of Ozone Monitoring Instrument (OMI) tropospheric NO2 columns against 11 Pandora Spectrometer Instrument (PSI) systems during the DISCOVER-AQ campaign over Houston. The least-squares fit to the paired data shows a low slope (OMI=0.76×PSI+1.18×1015 molecules cm−2, r2=0.67) which is indicative of varying biases in OMI. This perceived slope, induced by the problem of spatial scale, disappears in the comparison of the convolved kriged PSI and OMI (0.96×PSI+0.66×1015 molecules cm−2, r2=0.72) illustrating that OMI possibly has a constant systematic bias over the area. To avoid gross errors in comparisons made between gridded data versus pointwise measurements, we argue that the concept of semivariogram (or spatial auto-correlation) should be taken into consideration, particularly if the field exhibits a strong degree of spatial heterogeneity at the scale of satellite and/or model footprints.

FRACTURE ANALYSIS OF RUBBER TOUGHENED ADDITIVELY MANUFACTURED THERMOSETS

This study explores the role of rubber toughening on the dynamic fracture behavior of additively manufactured (AM) high-performance thermosetting polymers formed through digital light processing (DLP). Using DLP to create these polymers allows for rapid, agile manufacturing of prototypes meeting the lightweight and building speed requirements of relevance to military mission applications. This method also provides flexibility in part complexity while maintaining relatively high isotropy compared to traditional AM techniques. Previous work has demonstrated a dependence of these DLP specimens on print layer orientation and loading rate, prompting further investigation into other manufacturing parameters to improve toughness [1]. This study examines the role of rubber toughening on the quasi-static and dynamic fracture behavior of bis-GMA thermosets. Current literature largely reports on quasi-static behavior of DLP specimens, although dynamic conditions are more applicable to many realistic loading scenarios and extreme environments often seen in defense applications. Dynamic experiments leverage a unique long bar striker device that impacts a specimen opposite a pre-crack, sending a stress-wave driven load to initiate a dynamic Mode-I (opening) fracture event. Full-field displacement data ahead of the propagating crack is obtained using ultra high-speed imaging combined with 2D digital image correlation (DIC). An elastodynamic solution following the principles of dynamic fracture mechanics extracts the stress intensity factor (SIF) using a least squares fit at crack initiation and a Newton-Raphson scheme for crack propagation. The rubber toughened thermosets in this study exhibited a rate dependence in fracture toughness with the quasi-static SIF being 1.20 MPa and the dynamic SIF being 0.41 MPa .

Model misspecification and bias in the least-squares algorithm: Implications for linearized isotropic AVO

When inversions use incorrectly specified models, the estimated least-squares model parameters are biased. Their expected values are not the true underlying quantitative parameters being estimated. This means the least-squares model parameters cannot be compared to the equivalent values from forward modeling. In addition, the bias propagates into other quantities, such as elastic reflectivities in amplitude variation with offset (AVO) analysis. I give an outline of the framework to analyze bias, provided by the theory of omitted variable bias (OVB). I use OVB to calculate exactly the bias due to model misspecification in linearized isotropic two-term AVO. The resulting equations can be used to forward model unbiased AVO quantities, using the least-squares fit results, the weights given by OVB analysis, and the omitted variables. I show how uncertainty due to bias propagates into derived quantities, such as the χ-angle and elastic reflectivity expressions. The result can be used to build tables of unique relative rock property relationships for any AVO model, which replace the unbiased, forward-model results.

Parameter inference from event ensembles and the top-quark mass

One of the key tasks of any particle collider is measurement. In practice, this is often done by fitting data to a simulation, which depends on many parameters. Sometimes, when the effects of varying different parameters are highly correlated, a large ensemble of data may be needed to resolve parameter-space degeneracies. An important example is measuring the top-quark mass, where other physical and unphysical parameters in the simulation must be profiled when fitting the top-quark mass parameter. We compare four different methodologies for top-quark mass measurement: a classical histogram fit similar to one commonly used in experiment augmented by soft-drop jet grooming; a 2D profile likelihood fit with a nuisance parameter; a machine-learning method called DCTR; and a linear regression approach, either using a least-squares fit or with a dense linearly-activated neural network. Despite the fact that individual events are totally uncorrelated, we find that the linear regression methods work most effectively when we input an ensemble of events sorted by mass, rather than training them on individual events. Although all methods provide robust extraction of the top-quark mass parameter, the linear network does marginally best and is remarkably simple. For the top study, we conclude that the Monte-Carlo-based uncertainty on current extractions of the top-quark mass from LHC data can be reduced significantly (by perhaps a factor of 2) using networks trained on sorted event ensembles. More generally, machine learning from ensembles for parameter estimation has broad potential for collider physics measurements.

Development and Deployment of the Surface Current Imaging Nowcast System

This paper describes the development and installation of an ocean surface current monitoring device called SCINS: Surface Current Imaging Nowcast System. We describe the process of designing and building the prototype system, installation on an offshore platform, implementation of real-time reporting, and results from one year of operations. SCINS utilizes passive long-wave infrared imaging of the ocean to derive surface currents. This is done using a time-series of images to observe the phase-speed of the ocean waves. Then, the Doppler shift of the observed waves due to the surface current is determined using a non-linear least squares fit. The primary components of SCINS are a long-wave infrared camera and a data acquisition computer. The camera is mounted several 10s of m above the water surface. The system collects imagery at 2 Hz for 5 minutes every 15 minutes, day and night, and calculates surface currents in real-time. In this paper, we describe the results from deploying SCINS on an offshore platform, Chevron's Big Foot TLP, in the Gulf of Mexico for one year of continuous data collections, including several tropical storm and hurricane events. Results are compared to environmental data to describe system performance as a function of wind, wave, and sea conditions. We describe the engineering challenges and lessons learned from designing and installing this new type of passive imaging system for offshore use. We conclude that SCINS is an effective method for measuring surface currents in the vicinity of offshore platforms, requiring very little maintenance and without the need to put any instrumentation in the water.

Estimating Real-Time qPCR Amplification Efficiency from Single-Reaction Data

Methods for estimating the qPCR amplification efficiency E from data for single reactions are tested on six multireplicate datasets, with emphasis on their performance as a function of the range of cycles n1–n2 included in the analysis. The two-parameter exponential growth (EG) model that has been relied upon almost exclusively does not allow for the decline of E(n) with increasing cycle number n through the growth region and accordingly gives low-biased estimates. Further, the standard procedure of “baselining”—separately estimating and subtracting a baseline before analysis—leads to reduced precision. The three-parameter logistic model (LRE) does allow for such decline and includes a parameter E0 that represents E through the baseline region. Several four-parameter extensions of this model that accommodate some asymmetry in the growth profiles but still retain the significance of E0 are tested against the LRE and EG models. The recursion method of Carr and Moore also describes a declining E(n) but tacitly assumes E0 = 2 in the baseline region. Two modifications that permit varying E0 are tested, as well as a recursion method that directly fits E(n) to a sigmoidal function. All but the last of these can give E0 estimates that agree fairly well with calibration-based estimates but perform best when the calculations are extended to only about one cycle below the first-derivative maximum (FDM). The LRE model performs as well as any of the four-parameter forms and is easier to use. Its proper implementation requires fitting to it plus a suitable baseline function, which typically requires four–six adjustable parameters in a nonlinear least-squares fit.