statistical evaluation of spatial interpolation methods for small-sampled region. a case study of...
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Statistical Evaluation of Spatial Interpolation Methods for Small-Sampled Region. A Case Study of Temperature Change Phenomenon in BangladeshAvit Bhowmik, Pedro Cabral - Institute of Statistics and Information Management, New University of LisbonTRANSCRIPT
Statistical Evaluation of Spatial Interpolation
Methods for Small-Sampled Region.
A Case Study of Temperature Change
Phenomenon in Bangladesh Presented by: Avit Kumar Bhowmik
Outline
Description of the Problem
. Aim
. Study Area – Bangladesh
. Objectives
Trend Analysis
•Average
•Maximum
•Minimum Temp.
Interpolation
. Spline
. IDW
. Ordinary Kriging
Statistical Evaluation
•Univariate Statistics
•Willmott (1984) Statistics
Results & Major Findings
Description of the Problem
. Aim
. Study Area – Bangladesh
. Objectives
Aim
Identify most appropriate interpolation method.
Study Area - Bangladesh
Total Area : 1,47,570 sq.km. Mean annual temperature has increased during the
period of 1895-1980 at 0.310c and the annual mean maximum temperature will increase to 0.40c and 0.730c by the year of 2050 and 2100 respectively.
Small Sample Size – 34 Meteorological Stations.
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.
Trend Analysis
. Average
. Maximum
. Minimum Temp.
Trend Analysis
y= a + bx
Trend Value,
Goodness to fit or Co-efficient of Significance,
Trend Analysis - Results
Average Temperature
Maximum Temperature
Minimum Temperature
Trend Analysis - Results
Phenomenon
Maximum Trend
Corres-
ponding
Station
Goodness to Fit
Minimum
Trend
Corres-
ponding
Station
Goodness to Fit
Average Temperature 3.27
Kutubdia 0.41 -1.05 Rangam
ati 0.09
Maximum Temperature 5.8 Sitakun
da 0.66 -2.59 Rangpur 0.19
Minimum Temperatur
e4.04 Bogra 0.15 -2.34 Tangail 0.07
Interpolation
. Spline
. IDW
. Ordinary Kriging
Variograms
Average TemperatureRange = 8
Maximum TemperatureRange = 7
Minimum TemperatureRange = 3
Lag Number = 10 Lag size = 3
Interpolation-Average Temperature Change
Interpolation-Maximum Temperature Change
Interpolation-Minimum Temperature Change
Statistical Evaluation
. Univariate Statistics
. Willmott (1984) Statistics
Univariate Statistical Analysis
Mean Bias Error (MBE)
Standard Deviation of Observed (SDo)
Standard Deviation of Estimated (SDe)
Univariate Statistical Analysis - Results
Summary Univariate Measures for Average Temperature Change
Method Obar Pbar MBE SDo SDe RMSE N
SPLINE 1.17 1.32 0.15 1.11 1.11 1.7534
IDW 1.17 1.18 0.009 1.11 0.44 1.2634
Kriging 1.17 1.21 0.05 1.11 0.68 1.4134
Univariate Statistical Analysis - Results
Summary Univariate Measures for Maximum Temperature Change
Method
Obar Pbar MBE SDo SDe RMSE N
SPLINE 1.42 1.56 0.14 1.72 1.95 2.8134
IDW 1.42 1.57 0.15 1.72 1.05 1.92734
Kriging 1.42 1.46 0.03 1.72 0.98 1.77834
Univariate Statistical Analysis - Results
Summary Univariate Measures for Minimum Temperature Change
Method
Obar Pbar MBE SDo SDe RMSE N
SPLINE
0.95 1.03 0.09 1.67 1.37 2.1934
IDW 0.95 0.87 -0.08 1.67 0.66 1.6834
Kriging
0.95 0.96 0.02 1.67 0.99 1.9234
Evaluation of Univariate Statistical Analysis
Average Temperature
Observed Temperature Change
Est
imate
d T
em
pera
ture
C
hange
Evaluation of Univariate Statistical Analysis
Maximum Temperature
Observed Temperature Change
Est
imate
d T
em
pera
ture
C
hange
Minimum Temperature
Observed Temperature Change
Est
imate
d T
em
pera
ture
C
hange
Evaluation of Univariate Statistical Analysis
Willmott (1984) Statistical Analysis
Willmott (1984) Statistical Analysis - Results
Simple Linear OLS coefficients
Difference Measures
Method
n a b MAE RMSERMSE
sRMSE
ud
SPLINE
34 1.65 -0.03 1.40 1.75 1.41 1.05 0.25
IDW 34 1.29 -0.09 1.03 1.26 1.19 0.42 0.89
Kriging
34 1.41 -0.16 1.16 1.42 1.26 0.64 0.60
Average Temperature Change
Simple Linear OLS coefficients
Difference Measures
Method
n a b MAERMS
ERMSEs RMSEu d
SPLINE
34
1.89
-0.23
2.26 2.81 2.09 1.88 0.50
IDW34
1.51
0.04
1.44 1.93 1.63 1.03 0.62
Kriging
34
1.31
0.12
1.34 1.78 1.51 0.95 0.88
Maximum Temperature Change
Willmott (1984) Statistical Analysis - Results
Simple Linear OLS
coefficientsDifference Measures
Method
n a b MAE RMSE RMSEs RMSEu d
SPLINE
341.08
-0.05 1.78 2.19 1.73 1.35 0.13
IDW 340.81
0.06 1.40 1.68 1.55 0.64 0.78
Kriging
340.97
-0.00
71.57 1.92 1.66 0.98 0.43
Minimum Temperature Change
Willmott (1984) Statistical Analysis - Results
Results & Major Findings
Results
Temperature Change Phenomenon
Best Spatial Interpolation Method
Average Temperature Inverse Distance Weighting
Maximum Temperature Ordinary Kriging
Minimum Temperature Inverse Distance Weighting
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.
Measured Values
Stan
dard
Err
ors
Discussion
Thanks for your Attention
Questions or Comments