The University of Texas at Dallas Implementation of Neural network Interpolation in ArcGIS and Case Study for Spatial-Temporal Interpolation of Temperature Master Project POEC 6389 Xiaogang Yang GIS Program The University of Texas at Dallas Instructor Dr. Fang Qiu July, 2005

Outline Introduction. Objectives. Theory of neural network interpolation. Software design and implementation. Case study: spatial-temporal interpolation of temperature Conclusion.

Introduction The concept interpolation Example: temperature, rainfall, Ozone, Housing price. Most common used interpolation techniques: IDW, Spline, Kriging, Tin. Spatial interpolation: 2D, 3D. Spatial-temporal interpolation. Major vendor’s application of interpolation: ESRI: IDW, Spline, Kring, Polynomial Mapinfo: IDW, TIN. Most interpolation application is 2D based, few of them are 3D interpolation. No application involving spatial-temporal interpolation.

Theory of neural network interpolation Potential algorithm for spatial-temporal interpolation: Neural network Neural network algorithm and back-Propagation (BP) model Network Training: Forwards and Backwards

Software design and implementation Integrated with ESRI ArcGIS: “Neural Network Extension” Programming language: .NET platform, VB.net, ArcObject Released Dynamic Linked Library (DLL). Friendly user interface. Standard data input and output: ESRI data format: Shape file, geodatabase, raster Easy to use.

Software interface Neural Network Extension

Software interface

Software interface

Software interface

Software interface

Software interface

Case study: spatial-temporal interpolation of temperature: Data Source Study area: southern California, 26 stations. Temperature data: daily temperature records of year (1997, 1998 and 1999). Elevation Data: -40 ~3443 feet. Station Group: train group and verification group

Case study: spatial-temporal interpolation of temperature Multi dimensional interpolation Spatial interpolation: 2D, 3D Spatial-Temporal interpolation: 2D-temporal and 3D-temporal Analysis and comparison.

Case study: spatial-temporal interpolation of temperature: 2D Interpolation by ESRI tools IDW power 2 (Jan,1,1997) IDW power 4 (Jan,1,1997) Spline Regulation (Jan,1,1997) Spline Tension (Jan,1,1997) Global polynomial (Jan,1,1997) Local polynomial (Jan,1,1997) The R2 value of IDW and Sprine is high but very low for polynomial

Temperature vs. Elevation Day1

Case study: spatial-temporal interpolation of temperature: Neural network 2D Interpolation NN 2D: Day 1,1997 R2 = 0.3686 NN 2D: Day 50,1997 R2 = 0.1055 NN 2D: Day 100,1997 R2 = 0.7271 NN 2D: Day 150,1997 R2 = 0.3898 NN 2D: Day 200,1997 R2 = 0.5891 NN 2D: Day 250,1997 R2 = 0.5891 The distribute pattern switch a lot, and it is too general to provide the detail info. Not good at all.

Neural network interpolation 2D Day1 Temperature distribution change raptly along with train loop 30000 loops R2 = 0.3686 150000 loops R2 = 0.9675

Case study: spatial-temporal interpolation of temperature: Neural network 3D Interpolation NN 3D: Day 1,1997 R2 = 0.4964 NN 3D: Day 50,1997 R2 = 0.6842 NN 3D: Day 100,1997 R2 = 0.7355 NN 3D: Day 150,1997 R2 = 0.72041 NN 3D: Day 200,1997 R2 = 0.3207 NN 3D: Day 250,1997 R2 = 0.6118

Neural network interpolation 3D Day1

Neural network interpolation 3D Day50

Neural network interpolation 3D Day100

Neural network interpolation 3D Day150

Neural network interpolation 3D Day200

Neural network interpolation 3D Day250

Case study: spatial-temporal interpolation of temperature: Neural network 2D-temporal Interpolation NN 2D-T: Day 50,1997 R2 = 0.3447 NN 2D-T: Day 100,1997 R2 = 0.7299 NN 2D-T: Day 1,1997 R2 = 0.4921 NN 2D-T: Day 200,1997 R2 = 0.6259 NN 2D-T: Day 250,1997 R2 = 0.7146 NN 2D-T: Day 150,1997 R2 = 0.7788

Case study: spatial-temporal interpolation of temperature: Neural network 3D- temporal Interpolation NN 3D-T: Day 100,1997 R2 = 0.7011 NN 3D-T: Day 1,1997 R2 = 0.4592 NN 3D-T: Day 50,1997 R2 = 0.3422 NN 3D-T: Day 150,1997 R2 = 0.7613 NN 3D-T: Day 200,1997 R2 = 0.6915 NN 3D-T: Day 250,1997 R2 = 0.6976

Neural network interpolation 3D-temporal Day1

Neural network interpolation 3D-temporal Day50

Neural network interpolation 3D-temporal Day100

Neural network interpolation 3D-temporal Day150

Neural network interpolation 3D-temporal Day200

Neural network interpolation 3D-temporal Day250

Comparison The interpolation result of 2D is unrealistic Elevation play major effect on the temperature distribution. 3D interpolation generate better result Temperature varies with time, The spatial-temporal (2D and 3D) interpolation takes time as an independent parameter, it can capture the trend of temperature overall. For each specific time, 3D give the best result.

Project Conclusion Neural network can be used to interpolation GIS data on multi-dimensional based interpolation for GIS dataset, 2D, 3D, spatial-temporal, even higher dimensions The neural network interpolation application provide a very useful interpolation tool for GIS user. The case study of spatial-temporal interpolation give very interesting result. Spatial-temporal interpolation could be used to interpolate the irregular GIS dataset, such at housing sale price.

Thanks!