Applied Geostatistics Geostatistical techniques are designed to evaluate the spatial structure of a...
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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