Modeling Space/Time Variability with BMEGUI

1. Modeling Space/Time Variability with BMEGUI Prahlad Jat(1) and Marc Serre(1) (1) University of North Carolina at Chapel Hill

2. Agenda • Introduction • Mean Trend Analysis • Space/Time Covariance Analysis

3. Introduction

4. Temporal GIS analysis process Read Data File Data Field Screen Check Data Distribution Data Distribution Screen Exploratory Data Analysis Screen Exploratory Data Analysis Mean Trend Analysis Screen Mean Trend Analysis Space/Time Covariance Analysis Screen Covariance Analysis BME Analysis BME Estimation Screen

5. Mean Trend Analysis Screen • Display temporal mean trend • Display spatial mean trend (Raw & Smooth) • Model Parameter (Exponential Smoothing)

6. Space/Time Covariance Analysis Screen • Display spatial & temporal covariance • Plot covariance models

7. Mean Trend Analysis

8. Mean Trend Calculation • Assume a separable additive space/time mean trend model • Input Parameter • Spatial Radius/Spatial Range • Temporal Radius/Temporal Range • Averaging the measurement at each MS (or at each time point) • Find measurements within “Radius”, then apply exponential filter

9. Tradius Sradius Smoothed Mean Trend

10. Remove Mean Trend • Removing the mean trend from data Z - (SSM+STM-mean(STM)) Z: Value SSM: Smoothed Spatial Mean Trend STM: Smoothed Temporal Mean Trend

11. Calculate Mean Trend • Click “Model mean trend and remove it from data” • BMEGUI automatically calculate mean trend using the default parameters

12. Temporal Mean Trend • Raw Temporal Mean Trend is shown in dotted line • Smoothed Temporal Mean Trend in shown in solid line • Zoom in/out

13. Spatial Mean Trend • Two tabs – Spatial Mean Trend (Raw) Spatial Mean Trend (Smoothed) • Zoom in/out • Point Layer File

14. Recalculate Mean Trend • Input parameters and click “Recalculate Mean Trend” button • Spatial Radius/Spatial Range • Temporal Radius/Temporal Range Spatial Range Spatial Radius Click Button Temporal Radius Temporal Range

15. Space/Time Covariance Analysis

16. Space/Time Covariance Analysis • Experimental Covariance (Red dots) • Fit experimental covariance with covariance model (Solid Line)

17. Spatial/Temporal Components • Two tabs • Spatial Component • Temporal Component Temporal Component Tab Spatial Component Tab

18. Experimental Covariance • BMEGUI automatically calculate experimental covariance using the default lag setting • User can modify the lag setting • Change the number of lags • Input user-defined lag and lag tolerance

19. Change number of lags • Input the number of lags, then click “Recalculate Spatial/Temporal Covariance” button Recalculate Spatial Cov. Number of lags for Spatial Cov. Recalculate Temporal Cov. Number of lags for Temporal Cov.

20. Modify lag and lag tolerance • Click “Edit Spatial/Temporal Lags…” • Input lag and tolerance in dialog box, then click “OK” (Use “,” to separate the values)

21. Covariance Model • BMEGUI supports • homogeneous/stationary Space/Time random field • Space/Time separable model • Maximum four model structures • Following covariance model • exponential • gaussian • spherical • holecos • holesin

22. Set the number of model structures • Set the number of model structures • Input the number into text box (1-4) • The number of tabs will change

23. Select covariance model • Select model from the combo box • Input sill and range, then click “Plot Model”

24. Clear covariance model • Plot “Clear Plot” button • Covariance model will be erased from the figures