applied geostatistics geostatistical techniques are designed to evaluate the spatial structure of a...

Applied GeostatisticsApplied GeostatisticsGeostatistical techniques are designed to evaluate the spatial

structure of a variable, or the relationship between a value measured at a point in one place, versus a value from another point measured a certain distance away

Ho in Spatial Statistics states that:

•events, •highs, •lows, •differences between

•evenly distributed•Randomly arranged•Illustrated on directional trend

Features

are

We assume either:

Randomization - the observed pattern is one of many possible arrangements of the population; or

Normalization – the observations is a sample of a larger population and it was obtained randomly

We consider:

Global statistics – pattern across the whole of the study area

Local statistics – individual’s relationship with nearby features

Spatial Mean:

•The average x-coordinate and average y-coordinate for all features in the study area (or select set).

•Comparing changes in spatial distributions

Central Feature:

• The feature having the shortest total distance to all other features in the study area (or select set)

• Describes the most accessible feature

Center

Mean

Standard Distance, Standard Deviational Ellipse

• The extent to which the distances between the mean center and the features vary from the average distance.

• The standard deviation of the features from the mean center separately for the X and Y coordinates

Linear Directional Mean

• The angle of the line that represents the mean direction (or orientation )

A B C D E F G H I J

First Order Neighbors TopologyBinary Connectivity Matrix

Distance ClassConnectivity Matrix

1

1 1

1 0 1

1 0 0 1

0 0 0 1 1

0 0 1 1 0 1

0 0 0 0 0 1 1

0 1 1 0 0 0 1 1

0 1 0 0 0 0 0 1 1

A

B

C

D

E

F

G

H

I

J

A B C D E F G H I J

1

1 2

1 2 1

1 2 2 1

2 3 2 1 1

2 2 1 1 2 1

3 2 2 2 2 1 1

2 1 1 2 3 2 1 1

2 1 2 3 3 2 2 1 1

A

B

C

D

E

F

G

H

I

J

J I H

B G C F D A E

1= connected, 0=not connected

Join Count

•Categorical (nominal) data•Are values clustered or dispersed•Easy to construct

Moran’s I …Geary’s C

• Continuous data• Similarity of nearby features• Single statistics summarizing pattern• Doesn’t indicate clustering of “highs” or “lows”

General-G

• Continuous data• Concentration of “high/low”• Not “so good” if both highs and lows are clustered

Nearest Neighbor

• Average distance between features• Results may be biased by edge• Evaluated with Z-score

K-function, Ripley’s-K

• Count of features within defined distances• Concentration at a range of scale• Edge plays an important role• Evaluation through simulations for random distribution envelope