Geographic Information Systems: Spatial Interpolation Techniques and Methods, Lab Reports of Agricultural engineering

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CSS 4200

Geographic Information Systems

Lecture 14: Spatial Interpolation (

Bolstad, Chap 12)

Lab07 preview (next Tuesday…)

Methods of Interpolation*

From: Burrough, P.A. and R.A. McDonnell. 1998. Principles of Geographical Information Systems. Oxford University Press. New York.

Summary of Methods

•^

Global v. Local– Global techniques use all points in dataset– Local techniques use a user-defined subset of points

-^

Deterministic v. Stochastic– Deterministic: based on measurement or formula– Stochastic: based on statistical models that include

trend, spatial autocorrelation, stochastic variation

• Can provide measure of accuracy or certainty

Sampling Issues

Classification

Trend Surface

•Fit a surface to set of points•Susceptible to outliers•Low-order polynomial will not fit points well•High order can result in values well outsidereasonable range

GDD50 = 12741 - 1.76 [Elev_m] - 0.00212 [UTMn]Predictor

Coef

Constant

Elev_m

-1.

UTMn

-0.

R-Sq(adj)

82.9%

Spatial Regression

Examples:

Local Deterministic

•^

Thiessen polygons

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Inverse Distance Weighting (IDW)

-^

Splines

-^

Interpolation (Pycnophylactic)

-^

Interpolation (Linear)

Inverse Distance Weighting (IDW)

•^

Each input point has local influence thatdiminishes with distance

-^

Output values are determined by points within auser-specified radius, or number of points

-^

Does not preserve local maxima

-^

Parameters control the significance ofsurrounding points– Higher power results in less influence by distant

points (“inverse weighting”)

Spline

•^

Fits a minimum-curvature surface to input points

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Mathematical function that uses a specifiednumber of nearest input points– Named after drafting tool used to draw smooth curves– Best for gently varying surfaces– Not appropriate for modeling abrupt changes in Z-axis

values

Kriging

•^

Based on the rate at which the variancebetween points changes over space

-^

Developed by G. Matheron and D. G. Krige asmethod for mining industry

-^

Function of trend, spatial autocorrelation, andstochastic variation

= 5.5 24 h

• Eq. 12.
  • n = 2, i =
    • h
  • = - h - = 2. - h^13 = - h^34 =2. = 8^23 h - =
• =12 = - =