Many spatial analysis methods suffer from the scaling issue identified as part of the Modifiable Areal Unit Problem (MAUP). This article introduces the Pyramid Model (PM), a hierarchical data framework integrating space and spatial scale in a 3D environment to support multi-scale analysis. The utility of the PM is tested in examining quadrat density and kernel density, which are commonly used measures of point patterns. The two metrics computed from a simulated point set with varying scaling parameters (i.e. quadrats and bandwidths) are represented in the PM. The PM permits examination of the variation of the density metrics computed at all different scales. 3D visualization techniques (e.g. volume display, isosurfaces, and slicing) allow users to observe nested relations between spatial patterns at different scales and understand the scaling issue and MAUP in spatial analysis. A tool with interactive controls is developed to support visual exploration of the internal patterns in the PM. In addition to the point pattern measures, the PM has potential in analyzing other spatial indices, such as spatial autocorrelation indicators, coefficients of regression analysis and accuracy measures of spatial models. The implementation of the PM further advances the development of a multi-scale framework for spatio-temporal analysis.
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A spatiotemporal weighted regression model (STWR v1.0) for analyzing local nonstationarity in space and time
Abstract. Local spatiotemporal nonstationarity occurs in various naturaland socioeconomic processes. Many studies have attempted to introduce timeas a new dimension into a geographically weighted regression (GWR) model,but the actual results are sometimes not satisfying or even worse than theoriginal GWR model. The core issue here is a mechanism for weighting the effectsof both temporal variation and spatial variation. In many geographical andtemporal weighted regression (GTWR) models, the concept of time distance hasbeen inappropriately treated as a time interval. Consequently, the combinedeffect of temporal and spatial variation is often inaccurate in theresulting spatiotemporal kernel function. This limitation restricts theconfiguration and performance of spatiotemporal weights in many existingGTWR models. To address this issue, we propose a new spatiotemporal weightedregression (STWR) model and the calibration method for it. A highlight ofSTWR is a new temporal kernel function, wherein the method for temporalweighting is based on the degree of impact from each observed point to aregression point. The degree of impact, in turn, is based on the rate ofvalue variation of the nearby observed point during the time interval. Theupdated spatiotemporal kernel function is based on a weighted combination ofthe temporal kernel with a commonly used spatial kernel (Gaussian orbi-square) by specifying a linear function of spatial bandwidth versus time.Three simulated datasets of spatiotemporal processes were used to test theperformance of GWR, GTWR, and STWR. Results show that STWR significantlyimproves the quality of fit and accuracy. Similar results were obtained byusing real-world data for precipitation hydrogen isotopes (δ2H) in the northeastern United States. The leave-one-out cross-validation(LOOCV) test demonstrates that, compared with GWR, the total predictionerror of STWR is reduced by using recent observed points. Predictionsurfaces of models in this case study show that STWR is more localized thanGWR. Our research validates the ability of STWR to take full advantage ofall the value variation of past observed points. We hope STWR can bringfresh ideas and new capabilities for analyzing and interpreting localspatiotemporal nonstationarity in many disciplines.
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- Award ID(s):
- 2019609
- NSF-PAR ID:
- 10231457
- Date Published:
- Journal Name:
- Geoscientific Model Development
- Volume:
- 13
- Issue:
- 12
- ISSN:
- 1991-9603
- Page Range / eLocation ID:
- 6149 to 6164
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.5194/gmd-13-6149-2020
