Statistical Evaluation of Spatial Interpolation Methods for Small-Sampled Region. A Case Study of...

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