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Geoscientific Model Development An interactive open-access journal of the European Geosciences Union
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© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.

Submitted as: model description paper 18 Mar 2020

Submitted as: model description paper | 18 Mar 2020

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A revised version of this preprint is currently under review for the journal GMD.

A Spatiotemporal Weighted Regression Model (STWRv1.0) for Analyzing Local Non-stationarity in Space and Time

Xiang Que1,2, Xiaogang Ma2, Chao Ma2, and Qiyu Chen3 Xiang Que et al.
  • 1Computer and Information College, FujianAgriculture and Forestry University,Fuzhou, Fujian, China
  • 2Department of Computer Science, University of Idaho, 875 Perimeter Drive MS 1010, Moscow, ID 83844-1010, USA
  • 3School of Computer Science, China University of Geosciences (Wuhan), 388 Lumo Road, Wuhan 430074, China

Abstract. Local spatiotemporal non-stationarity occurs in various natural and socioeconomic processes. Many studies have attempted to introduce time as a new dimension into the geographically weighted regression model (GWR), but the actual results are sometimes not satisfied or even worse than the original GWR model. The core issue here is a mechanism for weighting effects of both temporal variation and spatial variation. In many geographical and temporal weighted regression models (GTWR), the concept of time distance has been inappropriately treated as time interval. Consequently, the combined effect of temporal and spatial variation is often inaccurate in the resulting spatiotemporal kernel function. This limitation restricts the configuration and performance of spatiotemporal weights in many existing GTWR models. To address this issue, we propose a new spatiotemporal weighted regression (STWR) model and the calibration method for it. A highlight of STWR is a new temporal kernel function, in which the method for temporal weighting is based on the degree of impact from each observed point to a regression point. The degree of impact, in turn, is based on the rate of value variation of the nearby observed point during the time interval. The updated spatiotemporal kernel function is based on a weighted combination of the temporal kernel with a commonly used spatial kernel (Gaussian or bi-square) by specifying a linear function of spatial bandwidth versus time. Three simulated datasets of spatiotemporal processes were used to test the performance of GWR, GTWR and STWR. Results show that STWR significantly improves the quality of fit and accuracy. Similar results were obtained by using real-world data for the precipitation hydrogen isotopes (δ2H) in Northeastern United States. The Leave-one-out cross-validation (LOOCV) test demonstrates that, comparing with GWR, the total prediction error of STWR is reduced by using recent observed points. Prediction surfaces of models in this case study show that STWR is more localized than GWR. Our research validates the ability of STWR to take full advantage of all the value variation of past observed points. We hope STWR can bring fresh ideas and new capabilities for analyzing and interpreting local spatiotemporal non-stationarity in many disciplines.

Xiang Que et al.

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Status: final response (author comments only)
Status: final response (author comments only)
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Xiang Que et al.

Model code and software

Spatiotemporal Weighted 1 Regression Model (STWR v1.0) X. Que, X. Ma, C. Ma, and Q. Chen

Xiang Que et al.


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Latest update: 23 Sep 2020
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Short summary
This paper presents a spatiotemporal weighted regression (STWR) model for exploring non-stationary spatio-temporal processes in nature and socioeconomics. Value change rate is introduced in the temporal kernel which presents significant model fitting and accuracy in both simulated and real world data. STWR fully incorporates the observed data in past time, and outperforms the geographic temporal weighted regression (GTWR) and geographic weighted regression (GWR) models in several experiments.
This paper presents a spatiotemporal weighted regression (STWR) model for exploring...