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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Modeling Streamflow and Sediment Transport Under Current and Future Climates at the West Valley Site - 20231

Performance Assessment models often require inputs representing specific hydrologic processes such as streamflow and sediment flux. This paper details the development of a process-level hydrologic model and its use in a Probabilistic Performance Assessment (PPA) system-level model for the West Valley Site in western New York. For this PPA model, a watershed model was developed using SWAT (Soil and Water Assessment Tool) and used to evaluate water and sediment fluxes in nearby streams draining the Site. A particular challenge of probabilistic modeling over long periods of time is scaling parameters appropriately so that outcomes are not grossly over- or underestimated. This challenge is especially important when the spatial and temporal scales of process and system level models differ. In this instance, the SWAT watershed model and GoldSim PPA model have similar spatial scales of stream reaches and sub-catchments within a single watershed (approximately hundreds to tens of thousands of square meters, but the temporal scales differ considerably. The SWAT model calculates streamflow and sediment transport rates at the daily scale, while the PPA model requires long-term average values that are applied over hundreds to thousands of year-long periods. As such, distributions of daily climatic parameters such as average precipitation rate, temperature, wind speed, and relative humidity were developed to force a transient SWAT model that captures the dynamic behavior of the watershed in response to daily changes in the weather. Output from the model, which includes stream flow (m{sup 3}/y) and sediment transport rate (Mg/y) is then averaged over a 100-year period as an approximation for the long-term average values which can be applied in GoldSim. A single SWAT model was run 5000 times with varying climatic inputs and deterministic soil, land use, and elevation data, and the range of outputs were compiled into a distribution which can be implemented stochastically into the PPA Model. Additionally, this paper includes a high-level discussion of how changes in future climate affect weather input distributions, and a summary of how those changes in weather affect the outcomes from the SWAT model and the inputs into the PPA model. In this analysis, future climate distributions were developed based on climate research documenting the expected changes to precipitation and temperature in western New York. The 5,000 SWAT simulations were then repeated with these future climate distributions, and the resulting output was implemented into the PPA Model as hydrologic conditions under a future climate. In the current version of the PPA Model, hydrologic parameters change linearly from the 'current climate' conditions to the 'future climate' conditions over a period of 100 years, after which they remain constant. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2020

Patchy particle model of hydrated amorphous silica

Glasses corroded in static aqueous conditions typically reach a slow, residual rate of dissolution as a result of the complex interplay between multiple processes. While intrinsically suited to address this problem, Monte Carlo (MC) models developed to date have relied on lattices to describe the amorphous structure of glass and are thus unable to reproduce the residual rate of glass corrosion. A recently developed MC approach based on amorphous structures derived from molecular dynamics simulations offers a solution [Kerisit and Du J. Non-Cryst. Solids 522 (2019) 119601], but it requires a simple model that can rapidly relax the glass-water interface upon each dissolution/condensation event to retain the ability of MC simulations to reach large spatial and temporal scales. To this end, a patchy particle model of hydrated amorphous silica was developed and evaluated against atomistic simulations in this work. Models of water and amorphous silica were first developed separately, and cross terms were then defined to enable simulations of hydrated amorphous silica structures with varying water content. While the nature of its interaction potential prevents the patchy particle model from reproducing simultaneously the structure and dynamics of the systems of interest with a single set of parameters, it described well the connectivity of hydrated amorphous silica structures and the local coordination geometry of individual species. Therefore, this model opens the door to MC simulations of the residual rate of glass corrosion and offers an alternative to atomistic models to investigate the evolution of silica gels over large spatial and temporal scales.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2026

Data for A Hybrid Biophysical-Machine Learning Framework for Diurnal Surface Energy Flux Estimation Using Proximal Sensing

Thermal infrared-based remote sensing of surface energy fluxes has traditionally relied on high spatial resolution satellite data with revisit frequencies on the order of weeks. In this study, we evaluate a biophysics-based analytical surface energy balance model for predicting latent energy (LE) and sensible heat (H) fluxes using proximal sensing observations. The Surface Temperature Initiated Closure (STIC1.2) model has been extensively validated across a wide range of spatial and temporal scales using various satellite-derived thermal infrared data sets. Here we extend this validation by applying STIC at sub-hourly temporal resolution over multiple growing seasons for four distinct agricultural systems. We further develop and evaluate novel STIC variants that incorporate machine learning (ML) techniques to eliminate the need for surface energy balance observations, specifically net radiation and soil heat flux, thereby enhancing model applicability in data-sparse settings. The integration of a ML component to estimate surface available energy is shown to have strong predictive performance for both LE (R2 = 0.81–0.94) and H (R2 = 0.46–0.72) across all agricultural systems examined here, demonstrating the potential of hybrid biophysical-machine learning approaches for surface energy balance modeling with minimal data requirements. This study concludes with a novel application of explainable machine learning (exML) to diagnose sources of model error. This exML framework attributes residual prediction errors to both model input variables and environmental drivers not explicitly included in the simulation experiments. This approach provides a new pathway for improving model design and integrating previously overlooked yet influential variables into future model iterations.

AI/ML↗
NASA NTRS1999

Is It Possible to Distinguish Between Dust and Salt Aerosol Over Waters with Unknown Chlorophyll Concentrations Using Spectral Remote Sensing?

Atmospheric aerosol has uncertain impacts on the global climate system, as well as on atmospheric and bio-geo-chemical processes of regional and local scales. EOS-MODIS is one example of a satellite sensor designed to improve understanding of the aerosols' type, size and distribution at all temporal and spatial scales. Ocean scientists also plan to use data from EOS-MODIS to assess the temporal and spatial coverage of in-water chlorophyll. MODIS is the first sensor planned to observe the combined ocean-atmosphere system with a wide spectral range (from 410 to 2200 nm). Dust aerosol and salt aerosol have similar spectral signals for wavelengths longer than 550 nm, but because dust selectively absorbs blue light, they have divergent signals in the blue wavelength regions (412 to 490 nm). Chlorophyll also selectively absorbs blue radiation, so that varying chlorophyll concentrations produces a highly varying signal in the blue regions, but less variability in the green, and almost no signal in the red to mid-infrared regions. Thus, theoretically, it may be difficult to differentiate dust and salt in the presence of unknown chlorophyll in the ocean. This study attempts to address the cases in which aerosol and chlorophyll signals can and cannot be separated. For the aerosol spectra, we use the aerosol lookup table from the operational MODIS aerosol-over-ocean algorithm, and for chlorophyll spectra, we use the SeaBAM data set (created for SeaWiFS). We compare the signals using Principal Component Analysis and attempt to retrieve both chlorophyll and aerosol properties using a variant of the operational MODIS aerosol-over-ocean algorithm. Results show that for small optical depths, less than 0.5, it is not possible to differentiate between dust and salt and to determine the chlorophyll concentration at the same time. For larger aerosol optical depths, the chlorophyll signals are comparatively insignificant, and we can hope to distinguish between dust and salt.

Levy, R. C.↗
DOE OSTI2022

Quantifying albedo susceptibility biases in shallow clouds

The evaluation of radiative forcing associated with aerosol–cloud interactions remains a significant source of uncertainty in future climate projections. The problem is confounded by the fact that aerosol particles influence clouds locally and that averaging to larger spatial and/or temporal scales carries biases that depend on the heterogeneity and spatial correlation of the interacting fields and the nonlinearity of the responses. Mimicking commonly applied satellite data analyses for calculation of albedo susceptibility S o , we quantify S o aggregation biases using an ensemble of 127 large eddy simulations of marine stratocumulus. We explore the cloud field properties that control this spatial aggregation bias and quantify the bias for a large range of shallow stratocumulus cloud conditions manifesting a variety of morphologies and ranges of cloud fractions. We show that S o spatial aggregation biases can be on the order of hundreds of percent, depending on the methodology. Key uncertainties emanate from the typically applied adiabatic drop concentration N d retrieval, the correlation between aerosol and cloud fields, and the extent to which averaging reduces the variance in cloud albedo A c and N d . So biases are more often positive than negative and are highly correlated with biases in the liquid water path adjustment. Temporal aggregation biases are shown to offset spatial aggregation biases. Both spatial and temporal biases have significant implications for observationally based assessments of aerosol indirect effects and our inferences of underlying aerosol–cloud–radiation effects.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2019

Redefining Temperate Forest Responses to Climate and Disturbance in the Eastern United States: New Insights at the Mesoscale

Climate and disturbance alter forest dynamics, from individual trees to biomes and from years to millennia, leaving legacies that vary with local, meso and macroscales. Motivated by recent insights in temperate forests, we argue that temporal and spatial extents equivalent to that of the underlying drivers are necessary to characterize forest dynamics across scales. We focus specifically on characterizing mesoscale forest dynamics because they bridge fine‐scale (local) processes and the continental scale (macrosystems) in ways that are highly relevant for climate change science and ecosystem management. We revisit ecological concepts related to spatial and temporal scales and discuss approaches to gain a better understanding of climate–forest dynamics across scales.

climate↗
NASA NTRS2001

Fractal Characterization of Multitemporal Remote Sensing Data

Scale is an 'innate' concept in geographical information systems (GIS). It is recognized as something that is intrinsic to the capture, storage, manipulation, analysis, modelling, and output of space and time data within a GIS purview, yet the relative meaning and ramifications of scaling spatial and temporal data from this perspective remain enigmatic. As GIS becomes more sophisticated as a product of more robust software and more powerful computer systems, there is an urgent need to examine the issue of scale, and its relationship to the whole body of spatiotemporal data, as imparted in GIS. Scale is fundamental to the characterization of geo-spatial data as represented in GIS, but we have relatively little insight on how to measure the effects of scale in representing data that are acquired in different formats and exist in varying spatial, temporal and radiometric configurations. Moreover, the complexities associated with the integration of multi-scaled data sets in a multitude of formats are exacerbated by the confusion of what the term 'scale' means from a multidisciplinary perspective. 'Scale' takes on significantly different meanings depending upon one's disciplinary background and spatial perspective, which can lead to substantial confusion in the input, manipulation, analysis, and output operations. Hence, we must begin to look at the universality of scale and begin to develop the theory, methods and techniques necessary to advance knowledge on the 'Science of scale' across all disciplines that use GIS.

Quattrochi, Dale A.↗
NASA NTRS2019

Diurnal and Seasonal Variations in Chlorophyll Fluorescence Associated with Photosynthesis at Leaf and Canopy Scales

There is a critical need for sensitive remote sensing approaches to monitor the parameters governing photosynthesis, at the temporal scales relevant to their natural dynamics. The photochemical reflectance index (PRI) and chlorophyll fluorescence (F) offer a strong potential for monitoring photosynthesis at local, regional, and global scales, however the relationships between photosynthesis and solar induced F (SIF) on diurnal and seasonal scales are not fully understood. This study examines how the fine spatial and temporal scale SIF observations relate to leaf level chlorophyll fluorescence metrics (i.e., PSII yield, YII and electron transport rate, ETR), canopy gross primary productivity (GPP), and PRI. The results contribute to enhancing the understanding of how SIF can be used to monitor canopy photosynthesis. This effort captured the seasonal and diurnal variation in GPP, reflectance, F, and SIF in the O2A (SIFA) and O2B (SIFB) atmospheric bands for corn (Zea mays L.) at a study site in Greenbelt, MD. Positive linear relationships of SIF to canopy GPP and to leaf ETR were documented, corroborating published reports. Our findings demonstrate that canopy SIF metrics are able to capture the dynamics in photosynthesis at both leaf and canopy levels, and show that the relationship between GPP and SIF metrics differs depending on the light conditions (i.e., above or below saturation level for photosynthesis). The sum of SIFA and SIFB (SIFA+B), as well as the SIFA+B yield, captured the dynamics in GPP and light use efficiency, suggesting the importance of including SIFB in monitoring photosynthetic function. Further efforts are required to determine if these findings will scale successfully to airborne and satellite levels, and to document the effects of data uncertainties on the scaling.

Campbell, Petya K.↗
NASA NTRS2022

Investigation of Microphysics and Precipitation for Atlantic Coast Threatening Snowstorms (IMPACTS): the 2022 Deployment

The Investigation of Microphysics and Precipitation for Atlantic Coast Threatening Snowstorms (IMPACTS) is a NASA-supported field campaign to study snowstorms particularly over the northeastern United States. Snowfall within these winter storms is often organized in banded structures that can vary on multiple scales. The goals of IMPACTS are to characterize the spatial and temporal scale of snowbands, understand the processes controlling the structure and evolution of the bands and apply this knowledge to improving remote sensing and numerical modeling. IMPACTS takes place over three winter seasons, 2020, 2022 and 2023. IMPACTS flies two aircraft: the ER-2 equipped with satellite-simulating remote sensing instruments; and the P-3 equipped with in situ microphysics probes and environmental instrumentation. Stationary and mobile radar facilities and mobile sounding teams round out the observational assets. The preliminary results from the 2022 deployment are highlighted here.

Lynn A McMurdie↗
DOE OSTI2026

A low-latitude, high-elevation 10Be production-rate calibration from the Rwenzori Mountains, Uganda

Cosmogenic nuclide surface-exposure dating has become a key tool in geomorphology. Robust application of the technique relies on determination of local nuclide production rates using independently dated calibration sites. However, there are few existing calibration sites in certain regions, particularly in low-latitude, high-elevation regions where cosmogenic nuclide production is theoretically more sensitive to changes in Earth's magnetic field and atmospheric conditions. We present a new cosmogenic beryllium-10 (10Be) production-rate calibration from the equatorial Rwenzori Mountains in Uganda. The calibration is based on radiocarbon dating of basal lake sediments (∼21.3 kyr BP) from Lake Mahoma (2900 m asl) and measured 10Be concentrations from boulders on the crest of a moraine which dams the lake. Our results indicate a time-integrated 10Be production rate of 15.83 ± 0.81 at/g/yr at Lake Mahoma. We then use these calibration data and two public online calculators to calculate ages for moraines in a separate Rwenzori valley for which there exists a minimum-limiting radiocarbon age constraint (∼12 kyr BP) on surficial glacial sediments. This enables us to assess the performance of different parameters used to scale production rates spatially and temporally (e.g., scaling frameworks, geomagnetic field reconstructions, atmospheric models) for surface-exposure age calculation in the region. Our results highlight the sensitivity of low-latitude cosmogenic nuclide surface-exposure ages to discrete calculation parameters, such as scaling framework or reconstructions of Earth's magnetic field, and the utility of determining production rates at sites where limiting age data exists for other nearby landforms.

Anderson, N [Dartmouth College]↗
DOE OSTI2024

Intermittent Criticality Multi‐Scale Processes Leading to Large Slip Events on Rough Laboratory Faults

Abstract We discuss data of three laboratory stick‐slip experiments on Westerly Granite samples performed at elevated confining pressure and constant displacement rate on rough fracture surfaces. The experiments produced complex slip patterns including fast and slow ruptures with large and small fault slips, as well as failure events on the fault surface producing acoustic emission bursts without externally‐detectable stress drop. Preparatory processes leading to large slips were tracked with an ensemble of ten seismo‐mechanical and statistical parameters characterizing local and global damage and stress evolution, localization and clustering processes, as well as event interactions. We decompose complex spatio‐temporal trends in the lab‐quake characteristics and identify persistent effects of evolving fault roughness and damage at different length scales, and local stress evolution approaching large events. The observed trends highlight labquake localization processes on different spatial and temporal scales. The preparatory process of large slip events includes smaller events marked by confined bursts of acoustic emission activity that collectively prepare the fault surface for a system‐wide failure by conditioning the large‐scale stress field. Our results are consistent overall with an evolving process of intermittent criticality leading to large failure events, and may contribute to improved forecasting of large natural earthquakes.

Geochemistry & Geophysics↗
NASA NTRS1996

Paleobiology, community ecology, and scales of ecological pattern

The fossil record provides a wealth of data on the role of regional processes and historical events in shaping biological communities over a variety of time scales. The Quaternary record with its evidence of repeated climatic change shows that both terrestrial and marine species shifted independently rather than as cohesive assemblages over scales of thousands of years. Larger scale patterns also show a strong individualistic component to taxon dynamics; assemblage stability, when it occurs, is difficult to separate from shared responses to low rates of environmental change. Nevertheless, the fossil record does suggest that some biotic interactions influence large-scale ecological and evolutionary patterns, albeit in more diffuse and protracted fashions than those generally studied by community ecologists. These include: (1) the resistance by incumbents to the establishment of new or invading taxa, with episodes of explosive diversification often appearing contingent on the removal of incumbents at extinction events; (2) steady states of within-habitat and global diversity at longer time scales (10(7)-l0(8) yr), despite enormous turnover of taxa; and (3) morphological and biogeographic responses to increased intensities of predation and substratum disturbance over similarly long time scales. The behavior of species and communities over the array of temporal and spatial scales in the fossil record takes on additional significance for framing conservation strategies, and for understanding recovery of species, lineages, and communities from environmental changes.

NASA Discipline Exobiology↗
NASA NTRS2019

Solar Activity Modeling: From Subgranular Dynamical Scales to the Solar Cycles

Dynamical effects of solar magnetoconvection span a wide range spatial and temporal scales that extends from the interior to the corona and from fast turbulent motions to the global-Sun magnetic activity. To study the solar activity on short temporal scales (from minutes to hours), we use 3D radiative MHD simulations that allow us to investigate complex turbulent interactions that drive various phenomena, such as plasma eruptions, spontaneous formation of magnetic structures, funnel-like structures and magnetic loops in the corona, and others. In particular, we focus on multi-scale processes of energy exchange across the different layers, which contribute to the corona heating and eruptive dynamics, as well as interlinks between different layers of the solar interior and atmosphere. For modeling the global-scale activity we use the data assimilation approach that has demonstrated great potential for building reliable long-term forecasts of solar activity. In particular, it has been shown that the Ensemble Kalman Filter (EnKF) method applied to the Parker-Kleeorin-Ruzmakin dynamo model is capable of predicting solar activity up to one sunspot cycle ahead in time, as well as estimating the properties of the next cycle a few years before it begins. In this presentation, using the available magnetogram data, we discuss development of the methodology and forecast quality criteria (including forecast uncertainties and sources of errors). We demonstrate the influence of observational limitation on the prediction accuracy. We present the EnKF predictions of the upcoming Solar Cycle 25 based on both the sunspot number series and observed magnetic fields, and discuss the uncertainties and potential of the data assimilation approach for modeling and forecasting the solar activity.

Kitiashvili, I. N.↗
NASA NTRS2015

Higher-Order Methods for Compressible Turbulent Flows Using Entropy Variables

Turbulent flows have a large range of spatial and temporal scales which need to be resolved in order to obtain accurate predictions. Higher-order methods can provide greater efficiency for simulations requiring high spatial and temporal resolution, allowing for solutions with fewer degrees of freedom and lower computational cost than traditional second-order computational fluid dynamics (CFD) methods.1 Higher-order methods have been widely used for turbulent flows. However, the reduced numerical stabilization present in higher-order schemes implies that special care needs to be taken in the development of numerical methods to suppress nonlinear instabilities.2–6 In this work we present the development of a higher-order space-time discontinuous Galerkin method with a focus on the aspects of our numerical scheme required for ensuring nonlinear stability for turbulent simulations at high Reynolds numbers.

Diosady, Laslo T.↗
NASA NTRS2000

Fractal Characterization of Multitemporal Remote Sensing Data

Scale is an "innate" concept in geographic information systems. It is recognized as something that is intrinsic to the capture, storage, manipulation, analysis, modeling, and output of space and time data within a GIS purview, yet the relative meaning and ramifications of scaling spatial and temporal data from this perspective remain enigmatic. As GISs become more sophisticated as a product of more robust software and more powerful computer systems, there is an urgent need to examine the issue of scale, and its relationship to the whole body of spatiotemporal data, as imparted in GISs. Scale is fundamental to the characterization of geo-spatial data as represented in GISs, but we have relatively little insight on how to measure the effects of scale in representing data that are acquired in different formats and exist in varying spatial, temporal and radiometric configurations. Moreover, the complexities associated with the integration of multiscaled data sets in a multitude of formats are exacerbated by the confusion of what the term "scale" is from a multidisciplinary perspective. "Scale" takes on significantly different meanings depending upon one's disciplinary background and spatial perspective which lead to substantial confusion in the input, manipulation, analysis, and output operations. Hence, we must begin to look at the universality of scale and begin to develop the theory, methods, and techniques necessary to advance knowledge on the "Science of Scale' across all disciplines that use GISs.

Quattrochi, Dale A.↗
NASA NTRS2019

Solar Activity Modeling: From Subgranular Dynamical Scales to the Solar Cycles

The dynamical effects of solar magnetoconvection span a wide range spatial and temporal scales that extend from the interior to the corona and from fast turbulent motions to global magnetic activity. To study the solar activity on short temporal scales (from minutes to hours), we use 3D radiative MHD simulations that allow us to investigate complex turbulent interactions that drive various phenomena, such as plasma eruptions, spontaneous formation of magnetic structures, funnel-like structures and magnetic loops in the corona, and others. In particular, we focus on multi-scale processes of energy exchange across layers of the solar interior and atmosphere, which contribute to coronal heating and eruptive dynamics. For modeling global-scale activity, we use a data assimilation approach that has demonstrated great potential for building reliable long-term forecasts of solar activity. In particular, it has been shown that the Ensemble Kalman Filter (EnKF) method applied to the Parker-Kleeorin-Ruzmakin dynamo model is capable of predicting solar activity up to one sunspot cycle ahead in time, as well as estimating the properties of the next cycle a few years before it begins. In this presentation, using the available magnetogram data, we discuss development of the methodology and forecast quality criteria (including forecast uncertainties and sources of errors). We demonstrate the influence of observational limitations on prediction accuracy, and we present the EnKF predictions of the upcoming Solar Cycle (25) based on both the sunspot number series and observed magnetic fields and discuss the uncertainties and potential of the data assimilation approach for modeling and forecasting solar activity.

Kitiashvili, I. N.↗
NASA NTRS2009

The Structure of Coronal Loops

It is widely believed that the simple coronal loops observed by XUV imagers, such as EIT, TRACE, or XRT, actually have a complex internal structure consisting of many (perhaps hundreds) of unresolved, interwoven "strands". According to the nanoflare model, photospheric motions tangle the strands, causing them to reconnect and release the energy required to produce the observed loop plasma. Although the strands, themselves, are unresolved by present-generation imagers, there is compelling evidence for their existence and for the nanoflare model from analysis of loop intensities and temporal evolution. A problem with this scenario is that, although reconnection can eliminate some of the strand tangles, it cannot destroy helicity, which should eventually build up to observable scales. we consider, therefore, the injection and evolution of helicity by the nanoflare process and its implications for the observed structure of loops and the large-scale corona. we argue that helicity does survive and build up to observable levels, but on spatial and temporal scales larger than those of coronal loops. we discuss the implications of these results for coronal loops and the corona, in general .

Antiochos, Spiro K.↗
NASA NTRS1998

Fractal Characterization of Multitemporal Scaled Remote Sensing Data

Scale is an "innate" concept in geographic information systems. It is recognized as something that is intrinsic to the ingestion, storage, manipulation, analysis, modeling, and output of space and time data within a GIS purview, yet the relative meaning and ramifications of scaling spatial and temporal data from this perspective remain enigmatic. As GISs become more sophisticated as a product of more robust software and more powerful computer systems, there is an urgent need to examine the issue of scale, and its relationship to the whole body of spatiotemporal data, as imparted in GISS. Scale is fundamental to the characterization of geo-spatial data as represented in GISS, but we have relatively little insight on the effects of, or how to measure the effects of, scale in representing multiscaled data; i.e., data that are acquired in different formats (e.g., map, digital) and exist in varying spatial, temporal, and in the case of remote sensing data, radiometric, configurations. This is particularly true in the emerging era of Integrated GISs (IGIS), wherein spatial data in a variety of formats (e.g., raster, vector) are combined with multiscaled remote sensing data, capable of performing highly sophisticated space-time data analyses and modeling. Moreover, the complexities associated with the integration of multiscaled data sets in a multitude of formats are exacerbated by the confusion of what the term "scale" is from a multidisciplinary perspective; i.e., "scale" takes on significantly different meanings depending upon one's disciplinary background and spatial perspective which can lead to substantive confusion in the input, manipulation, analyses, and output of IGISs (Quattrochi, 1993). Hence, we must begin to look at the universality of scale and begin to develop the theory, methods, and techniques necessary to advance knowledge on the "Science of Scale" across a wide number of spatial disciplines that use GISs.

Quattrochi, Dale A.↗