Statistical Evaluation of Spatial Interpolation Methods for Small- Sampled Region. A Case Study of Temperature Change Phenomenon in Bangladesh

Transcription

1 Statistical Evaluation of Spatial Interpolation Methods for Small- Sampled Region. A Case Study of Temperature Change Phenomenon in Bangladesh Presented by: Avit Kumar Bhowmik

2 Outline Description of the Problem Trend Analysis Interpolation Statistical Evaluation. Aim. Study Area Bangladesh. Objectives Average Maximum Minimum Temp.. Spline. IDW. Ordinary Kriging Univariate Statistics Willmott (1984) Statistics Results & Major Findings

3 Description of the Problem. Aim. Study Area Bangladesh. Objectives

4 Aim Identify most appropriate interpolation method.

5 Study Area - Bangladesh Total Area : 1,47,570 sq.km. Mean annual temperature has increased during the period of at c and the annual mean maximum temperature will increase to c and c by the year of 2050 and 2100 respectively. Small Sample Size 34 Meteorological Stations.

6 Objectives Describe overall and station specific Average, Maximum and Minimum temperature trend. Interpolate trend values obtained from trend analysis using Spline, IDW and Ordinary Kriging. Evaluate interpolation results using Univariate and Willmott Statistical method.thus identifying the most appropriate interpolation method.

7 Trend Analysis. Average. Maximum. Minimum Temp.

8 Trend Analysis y= a + bx Trend Value, Goodness to fit or Co-efficient of Significance,

9 Trend Analysis - Results Average Temperature Maximum Temperature Minimum Temperature

10 Trend Analysis - Results Phenomenon Maximum Trend Corresponding Station Goodness to Fit Minimum Trend Corresponding Station Goodness to Fit Average Temperature 3.27 Kutubdia Rangamati 0.09 Maximum Temperature 5.8 Sitakunda Rangpur 0.19 Minimum Temperature 4.04 Bogra Tangail 0.07

11 Interpolation. Spline. IDW. Ordinary Kriging

12 Variograms Lag Number = 10 Lag size = 3 Average Temperature Range = 8 Maximum Temperature Range = 7 Minimum Temperature Range = 3

13 Interpolation-Average Temperature Change

14 Interpolation-Maximum Temperature Change

15 Interpolation-Minimum Temperature Change

16 Statistical Evaluation. Univariate Statistics. Willmott (1984) Statistics

17 Univariate Statistical Analysis Mean Bias Error (MBE) Standard Deviation of Observed (SD o ) Standard Deviation of Estimated (SD e )

18 Univariate Statistical Analysis - Results Summary Univariate Measures for Average Temperature Change Method Obar Pbar MBE SDo SDe RMSE N SPLINE IDW Kriging

19 Univariate Statistical Analysis - Results Summary Univariate Measures for Maximum Temperature Change Method Obar Pbar MBE SDo SDe RMSE N SPLINE IDW Kriging

20 Univariate Statistical Analysis - Results Summary Univariate Measures for Minimum Temperature Change Method Obar Pbar MBE SDo SDe RMSE N SPLINE IDW Kriging

21 Estimated Temperature Change Evaluation of Univariate Statistical Analysis Observed Temperature Change Average Temperature

22 Estimated Temperature Change Evaluation of Univariate Statistical Analysis Observed Temperature Change Maximum Temperature

23 Estimated Temperature Change Evaluation of Univariate Statistical Analysis Observed Temperature Change Minimum Temperature

24 Willmott (1984) Statistical Analysis

25 Willmott (1984) Statistical Analysis - Results Simple Linear OLS coefficients Average Temperature Change Difference Measures Method n a b MAE RMSE RMSEs RMSEu d SPLINE IDW Kriging

26 Willmott (1984) Statistical Analysis - Results Maximum Temperature Change Simple Linear OLS Difference Measures coefficients Method n a b MAE RMSE RMSEs RMSEu d SPLINE IDW Kriging

27 Willmott (1984) Statistical Analysis - Results Minimum Temperature Change Simple Linear Difference Measures OLS coefficients Method n a b MAE RMSE RMSEs RMSEu d SPLINE IDW Kriging

28 Results & Major Findings

29 Results Temperature Change Phenomenon Best Spatial Interpolation Method Average Temperature Maximum Temperature Minimum Temperature Inverse Distance Weighting Ordinary Kriging Inverse Distance Weighting

30 Major Findings Not only Mean Bias Error, but Root Mean Square Error has significant Influence in determining the best Spatial Interpolation Method. The best approach is to look for Error in the Errors.

31 Standard Errors Discussion Measured Values

32 Thanks for your Attention Questions or Comments