spatial statistic

8/8/2019 Spatial Statistic

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SPATIAL STATISTICFianal report

Presented by: Do Thi Kim Anh

Date: June 23, 2010


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SPATIAL STATISTICFianal report

Table content

1. Source data and Exploratory Data Analysis

2. Spatial structure analysis

3. Result estimate and uncertainty

4. Discussion and conclusion


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Source data and Exploratory Data Analysis

- Data file: data2.prn

- Obtained from 95 rainfallstations in Australia

- Includes two attributes, lowest

rainfall and highest rainfall.

http://www.bom.gov.au/climate/cdo/about/sitedata.shtml

Distribution of lowest rainfall Distribution of highest rainfall

Lack of

measurement

-Irregular configuration

-Have no outliers

-High value areas focuson boundary


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Exploratory Data AnalysisA histogram is a useful device for exploring the shape of the distribution of the

values of a variable. Histograms are used for screening of outliers, checking

normality, or suggesting another parametric shape for the distribution

Figure.3.Histogram of lowest rainfall Figure.3.Histogram of highest rainfall

Skew right

Fairly

symmetric


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Exploratory Data Analysis

Q-Qplot for equal weight

Q-Q plot for declusted

Scatterplot of lowest rainfalland highest rainfall

-to know relationship between two variables we use

scatterplot

-The pattern can be seen in a scatterplot is uncorrelate

-spatial clustering which create redundancy

- Use declus program to determine

declustering weights

-The table show the equal-weighted mean and

median are higher declusted weight

-However, Q-Q plots of equal weigh anddeclusted are the same

Data is impacted by clustered

configuration very little. Use

equal weighted to continute

spatial structure ananylis


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Spatial structure analysis

1. Experimental semivariogram

Experimental omnidirectional semivariogram

of Lowest rainfall

The experimental variogram is calculated by averaging onehalf the difference

squared of the z-values over all pairs of observations with the specified separationdistance and direction

- Considers all azimuths simultaneously.- Contains more sample pairs per lag than

any directional variogram, and therefore is

more likely to show structure.

-is the average of all directional variograms.

-The Nugget Effect is more easily determined

from the omni-directional variogram.

- Data configuration has not obviously

anisotropy Use omnidirectional

semivariogram


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Spatial structure analysis1. Fitting semivariogramEmpirical semivariogram only computed overall variance for each speicfic lag

distance h and due to variation in the estimation it is not ensured that it is a valid

variogram, However Kriging need valid semivariograms p Need to semivariogram

model

Fitting

semivari

ogram

forlowest

rainfall

Fittingsemivari

ogram

for

highest

rainfall


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Spatial structure analysis

1. Fitting cross-semivariogram

2. Validation of permissibility

All principal minor determinants of order 2 are non-negative

The linear model of coregionalization (1) is positive semi definite.

Satisfy permissibility condition

(1)


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Estimation and uncertainty

Estimation for primary attribute: lowest rainfall by ordinary kriging

Estimation lowest rainfall by OK

- OK allow accounting for all data in search neighborhood, even if they are no correlatedwith the point being estimated

- OK is one such estimation approach that minimize uncertainty

- OK requires neither knowledge nor stationary of the mean over the entire area.

-The proportions of high and low values

in the estimate field do not reflect those

in the sample


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Estimation for primary attribute with second information:

Estimation lowest rainfall by OCK

- Second information: highest rainfall distribution as the same locations with primary

attribute, lowest rainfall non exhaustive secondary information

- Use ordinary cokriging approach that explicitly accounts for spatial cross correlation

between primary and secondary variables

-Estimation map is similar with OK

estimation map

Estimation lowest rainfall by OK


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Conclusion and Discussion


- Kriging integrates the knowledge gained fromanalyzing the spatial structure: the variogram

- Kriging provides an indication of the estimation error

In areas of poor samplingp error map will show largevalues

In areas of dense samplingp error map will show lowvalues.

- Cokriging approach has smaller uncertainty thankriging.

- Ordinary kriging variance assumption: The first-orderstationarity and Lagrange optimization estimation

map exhibit a smoothing effect


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THANK YOU FOR YOUR

ATTENTION

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