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DOE OSTI2024

Estimating scalar turbulent fluxes with slow-response sensors in the stable atmospheric boundary layer

Conventional and recently developed approaches for estimating turbulent scalar fluxes under stable atmospheric conditions are evaluated, with a focus on gases for which fast sensors are not readily available. First, the relaxed eddy accumulation (REA) classical approach and a recently proposed mixing length parameterization, labeled A22, are tested against eddy-covariance computations. Using high-frequency measurements collected from two contrasting sites (the frozen tundra near Utqiaġvik, Alaska, and a sparsely vegetated grassland in Wendell, Idaho, during winter), it is shown that the REA and A22 models outperform the conventional Monin–Obukhov similarity theory (MOST) utilized widely to infer fluxes from mean gradients. Second, scenarios where slow trace gas sensors are the only viable option in field measurements are investigated using digital filtering applied to fast-response sensors to simulate their slow-response counterparts. With a filtered scalar signal, the observed filtered eddy-covariance fluxes are referred to here as large-eddy-covariance (LEC) fluxes. A virtual eddy accumulation (VEA) approach, akin to the REA model but not requiring a mechanical apparatus to separate the gas flows, is also formulated and tested. A22 outperforms VEA and LEC in predicting the observed unfiltered (total) eddy-covariance (EC) fluxes; however, VEA can still capture the LEC fluxes well. This finding motivates the introduction of a sensor response time correction into the VEA formulation to offset the effect of sensor filtering on the underestimated net averaged fluxes. The only needed parameter for this correction is the mean velocity at the instrument height, a surrogate of the advective timescale. The VEA approach is very suitable and simple to use with gas sensors of intermediate speed (∼ 0.5 to 1 Hz) and with conventional open- or closed-path setups.

58 GEOSCIENCES↗

DOE OSTI2025

Uncovering multiscale structure-property correlations via active learning in scanning tunneling microscopy

Atomic arrangements and local sub-structures fundamentally influence emergent material functionalities. These structures are conventionally probed using spatially resolved studies and the property correlations are deciphered by a researcher based on sequential explorations, thereby limiting the efficiency and scope. Here we demonstrate a multi-scale Bayesian deep-learning based framework that automatically correlates material structure with its electronic properties using scanning tunneling microscopy (STM) measurements in real-time. Its predictions are used to autonomously direct exploration toward regions of the sample that optimize a given material property. This method is deployed on a low-temperature ultra-high vacuum STM to understand the structure-property relationship in a europium-based semimetal, EuZn 2 As 2 , a promising candidate relevant to magnetism-driven topological phenomena. The framework employs a sparse-sampling approach to efficiently construct the scalar-property space using minimal measurements, about 1–10% of the data required in standard hyperspectral methods. Moreover, we formulate the problem hierarchically across length scales, implementing autonomous workflow to locate mesoscopic and atomic structures that correspond to a target material property. This framework offers the choice to design scalar-property from the spectroscopic data to steer sample exploration. Our findings reveal correlations of the electronic properties unique to surface terminations, local defect density, and point defects.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2024

Refining HPCToolkit for application performance analysis at exascale

As part of the US Department of Energy’s Exascale Computing Project (ECP), Rice University has been refining its HPCToolkit performance tools to better support measurement and analysis of applications executing on exascale supercomputers. To efficiently collect performance measurements of GPU-accelerated applications, HPCToolkit employs novel non-blocking data structures to communicate performance measurements between tool threads and application threads. To attribute performance information in detail to source lines, loop nests, and inlined call chains, HPCToolkit performs parallel analysis of large CPU and GPU binaries involved in the execution of an exascale application to rapidly recover mappings between machine instructions and source code. To analyze terabytes of performance measurements gathered during executions at exascale, HPCToolkit employs distributed-memory parallelism, multithreading, sparse data structures, and out-of-core streaming analysis algorithms. To support interactive exploration of profiles up to terabytes in size, HPCToolkit’s hpcviewer graphical user interface uses out-of-core methods to visualize performance data. The result of these efforts is that HPCToolkit now supports collection, analysis, and presentation of profiles and traces of GPU-accelerated applications at exascale. These improvements have enabled HPCToolkit to efficiently measure, analyze and explore terabytes of performance data for executions using as many as 64K MPI ranks and 64K GPU tiles on ORNL’s Frontier supercomputer. HPCToolkit’s support for measurement and analysis of GPU-accelerated applications has been employed to study a collection of open-science applications developed as part of ECP. This paper reports on these experiences, which provided insight into opportunities for tuning applications, strengths and weaknesses of HPCToolkit itself, as well as unexpected behaviors in executions at exascale.

Adhianto, Laksono↗

DOE OSTI2025

powersqueeze

powersqueeze (psqz) is a truncated power iteration library intended for high-performance computing platforms. psqz efficiently produces low-dimensional, linear measurements of graph matrix spectra by combining classical power iteration with sparse Johnson-Lindenstrauss transforms. psqz is intended to produce high-quality, fast, data-oblivious low-dimensional representations of high-dimensional sparse data such as graphs and term-document matrices. psqz is intended to replace similar workflows that depend on directly approximating a truncated eigendecomposition (e.g., the first step of spectral clustering), which is a much more expensive operation.

Priest, BenjaminW [Lawrence Livermore National Lab↗

DOE OSTI2024

Aerosol size distribution properties associated with cold-air outbreaks in the Norwegian Arctic

The aerosol particles serving as cloud condensation and ice nuclei contribute to key cloud processes associated with cold-air outbreak (CAO) events but are poorly constrained in climate models due to sparse observations. Here we retrieve aerosol number size distribution modes from measurements at Andenes, Norway, during the Cold-Air Outbreaks in the Marine Boundary Layer Experiment (COMBLE) and at Zeppelin Observatory, approximately 1000 km upwind from Andenes at Svalbard. During CAO events at Andenes, the sea-spray-mode number concentration is correlated with strong over-ocean winds with a mean of 8±4 cm −3 that is 71 % higher than during non-CAO conditions. Additionally, during CAO events at Andenes, the mean Hoppel minimum diameter is 6 nm smaller than during non-CAO conditions, though the estimated supersaturation is lower, and the mean number concentration of particles that likely activated in-cloud is 109±61 cm −3 with no statistically significant difference from the non-CAO mean of 99±66 cm −3 . For CAO trajectories between Zeppelin Observatory and Andenes, the upwind-to-downwind change in number concentration is the largest for the accumulation mode with a mean decrease of 93±95 cm −3 , likely attributable primarily to precipitation scavenging. These characteristic properties of aerosol number size distributions during CAO events provide guidance for evaluating CAO aerosol–cloud interaction processes in models.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1984

Morphological study of near threshold fatigue crack growth in a coarse grain aluminum alloy

Fatigue crack propagation in the near-threshold region has been studied in coarse grain Al 7029 alloy. Over eighty percent of the crack surfaces are planar areas parallel to either 100-oriented or 111-oriented planes. The 100-plane crack surfaces show 'pine tree' morphological features formed by slip on two sets of intersecting planes. The 111-plane crack surfaces were planar and shiny. They were formed primarily by slip on a single dominant 111-oriented slip plane with sparse and very light secondary slip markings. Crack growth rates were measured and correlated with Delta-K.

Maurer, Gerhard↗

NASA NTRS2003

Polar Dunes Resolved by the Mars Orbiter Laser Altimeter Gridded Topography and Pulse Widths

The Mars Orbiter Laser Altimeter (MOLA) polar data have been refined to the extent that many features poorly imaged by Viking Orbiters are now resolved in densely gridded altimetry. Individual linear polar dunes with spacings of 0.5 km or more can be seen as well as sparsely distributed and partially mantled dunes. The refined altimetry will enable measurements of the extent and possibly volume of the north polar ergs. MOLA pulse widths have been recalibrated using inflight data, and a robust algorithm applied to solve for the surface optical impulse response. It shows the surface root-mean-square (RMS) roughness at the 75-m-diameter MOLA footprint scale, together with a geological map. While the roughness is of vital interest for landing site safety studies, a variety of geomorphological studies may also be performed. Pulse widths corrected for regional slope clearly delineate the extent of the polar dunes. The MOLA PEDR profile data have now been re-released in their entirety (Version L). The final Mission Experiment Gridded Data Records (MEGDR's) are now provided at up to 128 pixels per degree globally. Densities as high as 512 pixels per degree are available in a polar stereographic projection. A large computational effort has been expended in improving the accuracy of the MOLA altimetry themselves, both in improved orbital modeling and in after-the-fact adjustment of tracks to improve their registration at crossovers. The current release adopts the IAU2000 rotation model and cartographic frame recommended by the Mars Cartography Working Group. Adoption of the current standard will allow registration of images and profiles globally with an uncertainty of less than 100 m. The MOLA detector is still operational and is currently collecting radiometric data at 1064 nm. Seasonal images of the reflectivity of the polar caps can be generated with a resolution of about 300 m per pixel.

Gregory A Neumann↗

NASA NTRS2010

Transfer of Satellite Rainfall Uncertainty from Gauged to Ungauged Regions at Regional and Seasonal Timescales

Hydrologists and other users need to know the uncertainty of the satellite rainfall data sets across the range of time/space scales over the whole domain of the data set. Here, uncertainty' refers to the general concept of the deviation' of an estimate from the reference (or ground truth) where the deviation may be defined in multiple ways. This uncertainty information can provide insight to the user on the realistic limits of utility, such as hydrologic predictability, that can be achieved with these satellite rainfall data sets. However, satellite rainfall uncertainty estimation requires ground validation (GV) precipitation data. On the other hand, satellite data will be most useful over regions that lack GV data, for example developing countries. This paper addresses the open issues for developing an appropriate uncertainty transfer scheme that can routinely estimate various uncertainty metrics across the globe by leveraging a combination of spatially-dense GV data and temporally sparse surrogate (or proxy) GV data, such as the Tropical Rainfall Measuring Mission (TRMM) Precipitation Radar and the Global Precipitation Measurement (GPM) mission Dual-Frequency Precipitation Radar. The TRMM Multi-satellite Precipitation Analysis (TMPA) products over the US spanning a record of 6 years are used as a representative example of satellite rainfall. It is shown that there exists a quantifiable spatial structure in the uncertainty of satellite data for spatial interpolation. Probabilistic analysis of sampling offered by the existing constellation of passive microwave sensors indicate that transfer of uncertainty for hydrologic applications may be effective at daily time scales or higher during the GPM era. Finally, a commonly used spatial interpolation technique (kriging), that leverages the spatial correlation of estimation uncertainty, is assessed at climatologic, seasonal, monthly and weekly timescales. It is found that the effectiveness of kriging is sensitive to the type of uncertainty metric, time scale of transfer and the density of GV data within the transfer domain. Transfer accuracy is lowest at weekly timescales with the error doubling from monthly to weekly.However, at very low GV data density (<20% of the domain), the transfer accuracy is too low to show any distinction as a function of the timescale of transfer.

Tang, Ling↗

NASA NTRS2024

Aerosol Size Distribution Properties Associated With Cold-Air Outbreaks in the Norwegian Arctic

The aerosol particles serving as cloud condensation and ice nuclei contribute to key cloud processes associated with cold-air outbreak (CAO) events but are poorly constrained in climate models due to sparse observations. Here we retrieve aerosol number size distribution modes from measurements at Andenes, Norway, during the Cold-Air Outbreaks in the Marine Boundary Layer Experiment (COMBLE) and at Zeppelin Observatory, approximately 1000 km upwind from Andenes at Svalbard. During CAO events at Andenes, the sea-spray-mode number concentration is correlated with strong over-ocean winds with a mean of 8±4 cm−3 that is 71 % higher than during non-CAO conditions. Additionally, during CAO events at Andenes, the mean Hoppel minimum diameter is 6 nm smaller than during non-CAO conditions, though the estimated supersaturation is lower, and the mean number concentration of particles that likely activated in-cloud is 109±61 cm−3 with no statistically significant difference from the non-CAO mean of 99±66 cm−3. For CAO trajectories between Zeppelin Observatory and Andenes, the upwind-to-downwind change in number concentration is the largest for the accumulation mode with a mean decrease of 93±95 cm−3, likely attributable primarily to precipitation scavenging. These characteristic properties of aerosol number size distributions during CAO events provide guidance for evaluating CAO aerosol–cloud interaction processes in models.

accumulation mode particle scavenging↗

NASA NTRS2012

Monitoring Ocean CO2 Fluxes from Space: GOSAT and OCO-2

The ocean is a major component of the global carbon cycle, emitting over 330 billion tons of carbon dioxide (CO2) into the atmosphere each year, or about 10 times that emitted fossil fuel combustion and all other human activities [1, 2]. The ocean reabsorbs a comparable amount of CO2 each year, along with ~25% of the CO2 emitted by these human activities. The nature and geographic distribution of the processes controlling these ocean CO2 fluxes are still poorly constrained by observations. A better understanding of these processes is essential to predict how this important CO2 sink may evolve as the climate changes.While in situ measurements of ocean CO2 fluxes can be very precise, the sampling density is far too sparse to quantify ocean CO2 sources and sinks over much of the globe. One way to improve the spatial resolution, coverage, and sampling frequency is to make observations of the column averaged CO2 dry air mole fraction, XCO2, from space [4, 5, 6]. Such measurements could provide global coverage at high resolution (< 100 km) on monthly time scales. High precision (< 1 part per million, ppm) is essential to resolve the small, near-surface CO2 variations associated with ocean fluxes and to better constrain the CO2 transport over the ocean. The Japanese Greenhouse gases Observing Satellite (GOSAT) and the NASA Orbiting Carbon Observatory (OCO) were first two space based sensors designed specifically for this task. GOSAT was successfully launched on January 23, 2009, and has been returning measurements of XCO2 since April 2009. The OCO mission was lost in February 2009, when its launch vehicle malfunctioned and failed to reach orbit. In early 2010, NASA authorized a re-flight of OCO, called OCO-2, which is currently under development.

GOSAT↗

NASA NTRS1990

The theoretical relationship between foliage temperature and canopy resistance in sparse crops

One-dimensional, sparse-crop interaction theory is reformulated to allow calculation of the canopy resistance from measurements of foliage temperature. A submodel is introduced to describe eddy diffusion within the canopy which provides a simple, empirical simulation of the reported behavior obtained from a second-order closure model. The sensitivity of the calculated canopy resistance to the parameters and formulas assumed in the model is investigated. The calculation is shown to exhibit a significant but acceptable sensitivity to extreme changes in canopy aerodynamics, and to changes in the surface resistance of the substrate beneath the canopy at high and intermediate values of leaf area index. In very sparse crops changes in the surface resistance of the substrate are shown to contaminate the calculated canopy resistance, tending to amplify the apparent response to changes in water availability. The theory is developed to allow the use of a measurement of substrate temperature as an option to mitigate this contamination.

Shuttleworth, W. James↗

NASA NTRS2013

Classification of Dust Days by Satellite Remotely Sensed Aerosol Products

Considerable progress in satellite remote sensing (SRS) of dust particles has been seen in the last decade. From an environmental health perspective, such an event detection, after linking it to ground particulate matter (PM) concentrations, can proxy acute exposure to respirable particles of certain properties (i.e. size, composition, and toxicity). Being affected considerably by atmospheric dust, previous studies in the Eastern Mediterranean, and in Israel in particular, have focused on mechanistic and synoptic prediction, classification, and characterization of dust events. In particular, a scheme for identifying dust days (DD) in Israel based on ground PM10 (particulate matter of size smaller than 10 nm) measurements has been suggested, which has been validated by compositional analysis. This scheme requires information regarding ground PM10 levels, which is naturally limited in places with sparse ground-monitoring coverage. In such cases, SRS may be an efficient and cost-effective alternative to ground measurements. This work demonstrates a new model for identifying DD and non-DD (NDD) over Israel based on an integration of aerosol products from different satellite platforms (Moderate Resolution Imaging Spectroradiometer (MODIS) and Ozone Monitoring Instrument (OMI)). Analysis of ground-monitoring data from 2007 to 2008 in southern Israel revealed 67 DD, with more than 88 percent occurring during winter and spring. A Classification and Regression Tree (CART) model that was applied to a database containing ground monitoring (the dependent variable) and SRS aerosol product (the independent variables) records revealed an optimal set of binary variables for the identification of DD. These variables are combinations of the following primary variables: the calendar month, ground-level relative humidity (RH), the aerosol optical depth (AOD) from MODIS, and the aerosol absorbing index (AAI) from OMI. A logistic regression that uses these variables, coded as binary variables, demonstrated 93.2 percent correct classifications of DD and NDD. Evaluation of the combined CART-logistic regression scheme in an adjacent geographical region (Gush Dan) demonstrated good results. Using SRS aerosol products for DD and NDD, identification may enable us to distinguish between health, ecological, and environmental effects that result from exposure to these distinct particle populations.

satellite remote sensing↗

NASA NTRS2002

Bench top interferometric test bed for LISA

Adaptive optics systems with Shack-Hartmann wavefront sensors require reconstruction of the atmospheric phase error from slope measurements, with every sensor in the array being used in the computation of each actuator command. This fully populated reconstruction matrix can result in a significant computational burden for adaptive optics systems with large numbers of actuators. A method for generating sparse wavefront reconstruction matrices for adaptive optics is proposed. The method exploits the relevance of nearby slope measurements for control of an individual actuator, and relies upon the limited extent of the influence function for a zonal deformable mirror. Relying only on nearby sensor information can significantly reduce the calculation time for wavefront reconstruction. In addition, a hierarchic controller is proposed to recover some of the global wavefront information. The performance of these sparse wavefront reconstruction matrices was evaluated in simulation, and tested on the Palomar Adaptive Optics System. This paper will present some initial results from the simulations and experiments.

LISA↗

NASA NTRS2020

Recommendations for Using Noise Monitors to Estimate Noise Exposure During X-59 Community Tests

A low fidelity simulation approach is used to explore how to place and use noise monitors during X-59 QueSST community tests, where people’s annoyance to the noise produced by the X-59 aircraft will be gathered. Several recommendations are provided including: 1) the desired number of sparsely spaced noise monitor sites within the survey area, 2) whether to group and average measurements across multiple noise monitors located at a site, 3) what spacing should be used if grouped noise monitors are used, 4) an approach to mitigate ambient noise contamination at the measurement sites, 5) a method to combine empirical and predicted dose estimates to provide a single dose estimate for respondents, and 6) assessing how changes in turbulence intensity and array configuration affect dose uncertainty. To make these recommendations, the error that is expected when fitting contrived, smoothly varying sonic boom “reference exposure surfaces” is studied when a spatially sparse and scattered set of samples is used as responses for the fit. The reference exposure surfaces mimic the sonic boom exposure at ground level that might be expected in the X-59 survey area in the absence of atmospheric turbulence, ambient noise, and other localized effects. The spatial extent of these surfaces varies and is representative of the different survey area sizes that might be expected during future X-59 community overflight tests. These contrived reference surfaces are sampled, and those reference samples are then perturbed to mimic atmospheric turbulence, ambient noise and other localized effects that might affect noise monitor measurements within overflown communities. Two different surface fitting methods are investigated when fitting these perturbed samples to approximate the reference surface. The first method uses interpolation between the perturbed data at the scattered sites to compute the fit. The second method fits a polynomial surface model to the perturbed data using ordinary least squares regression analysis. For both fitting methods, the root mean square fit error is computed from the pointwise difference between the fit surface and the reference surface as the count and configuration of the sites is varied while also averaging the error across many different realizations of both the smooth variation of the reference exposure surface and the random, localized perturbations at the sample sites. Different site configurations are compared using this error statistic to make the recommendations noted above. Additionally, the two fitting approaches (interpolation vs linear regression) are compared based on the fit error observed in these simulations. These analyses, comparisons, and recommendations should inform future decisions on the noise monitor placement and the methods used to analyze the noise monitor data that is collected during X-59 community overflights.

sonic boom↗

NASA NTRS2020

Probing the Evolutionary History of Comets: an Investigation of the Hypervolatiles CO, CH4, and C2H6 in the Jupiter-Family Comet 21P/Giacobini–Zinner

Understanding the cosmogonic record encoded in the parent volatiles stored in cometary nuclei requires investigating whether evolution (thermal or otherwise) has modified the composition of short-period comets during successive perihelion passages. As the most volatile molecules systematically observed in comets, the abundances of CO, CH4, and C2H6 in short-period comets may serve to elucidate the interplay between natal conditions and post-formative evolution in setting present-day composition, yet secure measurements of CO and CH4 in Jupiter-family comets (JFCs) are especially sparse. The highly favorable 2018 apparition of JFC 21P/Giacobini–Zinner enabled a sensitive search for these "hypervolatiles" in a prototypical carbon-chain depleted comet. We observed 21P/Giacobini–Zinner with the iSHELL spectrograph at the NASA Infrared Telescope Facility on four pre-perihelion dates, two dates near-perihelion, and one post-perihelion date. We obtained detections of CO, CH4, and C2H6 simultaneously with H2O on multiple dates. We present rotational temperatures, production rates, and mixing ratios. Combined with previous work, our results may indicate that the hypervolatile coma composition of 21P/Giacobini–Zinner was variable across apparitions as well as within a particular perihelion passage, yet the spread in these measurements is a relatively small fraction of the variation in each molecule from comet to comet. We discuss the implications of our measured hypervolatile content of 21P/Giacobini–Zinner for the evolution of JFCs, and place our results in the context of findings from the Rosetta mission and ground-based studies of comets.

Roth, Nathan X.↗

NASA NTRS1989

Bidirectional reflectances of three soil surfaces and their characterization through model inversion

Spectral bidirectional reflectances were measured over three natural soil sites using a specially designed radiometer called the Parabola. Two of the sites were bare soils, and the third had a sparse cover of desert scrub. The reflectances were strongly non-Lambertian for all three surfaces, but with markedly different patterns. The measured data were fitted with a quasi-physical reflectance model in which the surface backscattering and forwardscattering are separately formulated. A soil reflectance characterization was obtained by assessing the contributions of the forward, backward, and Lambertian components. This three-parameter characterization produced a satisfactory fit to the measured reflectances and appears promising as a basis for soils categorization.

Deering, D. W.↗

DOE OSTI2025

Distributed Stochastic Optimization of a Neural Representation Network for Time-Space Tomography Reconstruction

4D time-space reconstruction of dynamic events or deforming objects using X-ray computed tomography (CT) is an important inverse problem in non-destructive evaluation. Conventional back-projection based reconstruction methods assume that the object remains static for the duration of several tens or hundreds of X-ray projection measurement images (reconstruction of consecutive limited-angle CT scans). However, this is an unrealistic assumption for many in-situ experiments that causes spurious artifacts and inaccurate morphological reconstructions of the object. To solve this problem, we propose to perform a 4D time-space reconstruction using a distributed implicit neural representation (DINR) network that is trained using a novel distributed stochastic training algorithm. Our DINR network learns to reconstruct the object at its output by iterative optimization of its network parameters such that the measured projection images best match the output of the CT forward measurement model. Here, we use a forward measurement model that is a function of the DINR outputs at a sparsely sampled set of continuous valued 4D object coordinates. Unlike previous neural representation architectures that forward and back propagate through dense voxel grids that sample the object's entire time-space coordinates, we only propagate through the DINR at a small subset of object coordinates in each iteration resulting in an order-of-magnitude reduction in memory and compute for training. DINR leverages distributed computation across several compute nodes and GPUs to produce high-fidelity 4D time-space reconstructions. We use both simulated parallel-beam and experimental cone-beam X-ray CT datasets to demonstrate the superior performance of our approach.

36 MATERIALS SCIENCE↗

NASA NTRS1999

Utilizing Multiple Datasets for Snow Cover Mapping

Snow-cover maps generated from surface data are based on direct measurements, however they are prone to interpolation errors where climate stations are sparsely distributed. Snow cover is clearly discernable using satellite-attained optical data because of the high albedo of snow, yet the surface is often obscured by cloud cover. Passive microwave (PM) data is unaffected by clouds, however, the snow-cover signature is significantly affected by melting snow and the microwaves may be transparent to thin snow (less than 3cm). Both optical and microwave sensors have problems discerning snow beneath forest canopies. This paper describes a method that combines ground and satellite data to produce a Multiple-Dataset Snow-Cover Product (MDSCP). Comparisons with current snow-cover products show that the MDSCP draws together the advantages of each of its component products while minimizing their potential errors. Improved estimates of the snow-covered area are derived through the addition of two snow-cover classes ("thin or patchy" and "high elevation" snow cover) and from the analysis of the climate station data within each class. The compatibility of this method for use with Moderate Resolution Imaging Spectroradiometer (MODIS) data, which will be available in 2000, is also discussed. With the assimilation of these data, the resolution of the MDSCP would be improved both spatially and temporally and the analysis would become completely automated.

Tait, Andrew B.↗