introductory spatial statistics workshop part 1: interpolation with geostatistical analyst · ·...

Introductory Spatial Statistics Workshop

Part 1: Interpolation with Geostatistical

Analyst

Jeff W. Hollister

St. Lawrence University

6 December 2002

Spatial Statistics Workshop: Geostatistical Analyst Slide 2 of 26

Introduction

What is interpolation?

• Spatial prediction

• Tobler’s Law

Types of interpolation

• Deterministic• Exact or inexact (smoothed)

• Geostatistical


Introduction:Deterministic

Interpolators

Inverse Distance Weighting (IDW)

• Description

• Exact, Deterministic Interpolator

• Requires little input

• Predicted values weighted by

distance

• No assumptions required



Interpolators


• Power function

Distance

Re

lative

We

igh

t p = 0

p = 1

p = 2



• Search Neighborhood• Limit number of samples in calculations

• Total number of neighbors

• Search radius


Interpolators



Interpolators

Radial Basis Functions (RBFs)

• Description

• Exact, Deterministic Interpolator

• Requires slightly more input than IDW

• Like fitting a rubber sheet to the data

points

• Used for calculating gently varying

surfaces




Interpolators

Radial Basis Functions(RBFs)

• How they work• An RBF is created for each point

• Essentially a cone shaped function

• Provides weight based on distance

IDW RBF



Interpolators

Radial Basis Functions(RBFs)

• Many algorithms• Completely regularizd spline

• Spline with tension

• Multiquadratic RBFs

• Inverse multiquadratic RBFs

• Thin plate spline

• Parameter• Controls the “smoothness” of the surface

• Higher values = more smoothing



InterpolatorsPolynomial Functions

• Description

• Inexact, deterministic interpolators

• Global and Local

• Global

• Coarse scale patterns

• Slowly varying surface

• Long-range or global trends

• Local

• Fine scale patterns

• Sensitive to neighborhood definition




InterpolatorsPolynomial Functions

• Global• Fits a polynomial function to all data

• Local• Fits a polynomial function to neighborhood

1st order 2nd order


Introduction:Geostatistical

InterpolatorsKriging

• Description

• Exact or inexact, geostatistical

interpolator

• Requires considerable input

• Several different types

• Ordinary, Simple, Universal

• Co-kriging




• Description(cont.)

• Requires several assumptions

• Stationarity

• Some methods assume normality

• Isotropy

• Fits a theoretical statistical model to

empirical data

• Allows for estimate of prediction error




• The semivariogram

Lag Distance

Nugget

Range

(si,sj)

Partial Sill Sill


Refrences

• Johnston, K., Ver Hoef, J. M., Krivoruchko, K.,

Lucas, N. 2001. Using ArcGIS Geostatistical

Analyst. ESRI, Redlands, CA.• also available in ArcGIS online help


Demo:

Geostatistical Analyst

Introductory Spatial Statistics Workshop

Part 2: Landscape Metrics with Fragstats

Jeff W. Hollister


6 December 2002


Introduction

What are landscape metrics?

• Composition

• Configuration

Why are these important?

• Basic concept of Landscape Ecology

• Ecological processes are linked to ecological patterns

• Comparison

• Prediction


Data Types

What types of data can be used?

• Aerial photographs

• Satellite imagery

• Published data

• Field data

How is this data used?

• Thematic GIS data

• e.g. Land Use/Land Cover in an Anderson Level I classification


Data Types

Thematic Mapper (TM) Classification Process Landscape Metrics

Landscape

Class

Patch


Metric Types

Landscape

• Metrics that quantify characteristics

of the total area

• Examples • Total number of patches

• Mean shape index

• Diversity


Metric Types

Class


of individual classes

• Examples• Percentage

• Class fractal dimension

• Total number of patches

per class


Metric Types

Patch


of each individual patch

• Examples• Patch area

• Perimeter/area ratio

• Nearest neighbor distance


Metric Types

Metrics describe various aspects

of landscape structure

• Area/Density/Edge

• Shape

• Core Area

• Isolation/Proximity

• Contrast

• Contagion/Interspersion

• Connectivity

• Diversity


Caveats

Think before you leap!!!

• Clear purpose

• Classification scheme

• Scale

• Patch

• Correlation

• Ecological vs. statistical significance

• Edge Effects


References

Turner, M.G., Gardner, R.H.,O’Neill, R.V. 2001. Chapter 5. Landscape Ecology in Theory and Practice:Pattern and Process. Springer-Verlag, New York.

McGarigal, K. 2001. Fragstats Manuals. Available On-line at http://www.umass.edu/landeco/research/fragstats/fragstats.html or through the software help pages

Gustafson, E. J. 1998. Quantifying landscape spatial pattern: What is the state of the art. Ecosystems:143-156.


Demo:

Fragstats Version 3.3

Introduction to remote sensing

Jeff W. Hollister


5 December 2002

What is remote sensing?

Remote Sensing is the observation of

the Earth from distant vantage points,

usually by/from satellites or aircraft.

Sensors mounted on these platforms

capture detailed images of the Earth that

reveal features not apparent to the

naked eye.

The images captured are passed on to

analysts who interpret the data, extract

information, and use it to answer

questions.

History of remote sensing

1600’s

1900’s

Today

Observation of the earth’s surfaces by means of reflected or emitted electromagnetic energy

(Campbell 1996)

Basics of remote sensing

graphic from http://www.landsat.gsfc.nasa.gov

Two sources of energy•Active•Passive

Basics of remote sensing:active remote sensing

Definition

• remote sensing platform provides the energy source

Examples

• RAdio Detection And Ranging (RADAR)

• LIght Detection And Ranging (LIDAR)

graphics from http://www.soonet.ca/eliris/remotesensing/ and http://www.nature.nps.gov/im/units/nw10/slides/CBN-Milstead%20Denver%20Aug2002_files/frame.htm

Basics of remote sensing:passive remote sensing

Definition

• remote sensing platform sense energy provided by

another source, usually the sun.

Examples

• Landsat Enhanced Thematic Mapper + (ETM+)

• Advanced Very High Resolution Radiometer (AVHRR)

graphic from http://www.soonet.ca/eliris/remotesensing/

Basics of remote sensing: electromagnetic radiation

Visible Light

EMR reflected off the Earth allows a researcher to determine

the spectral response, or spectral signature, of a feature on the

ground.

graphic from http://www.astro.cornell.edu

Basics of remote sensing: spectral signatures

Spectral signatures are used to ‘train’ a classification algorithm, the output of which is land cover information.

graphic from http://www.iupui.edu

Basics of remote sensing: resolution

Definition

• Spectral and spatial structure of satellite images

Spectral resolution

• Describes the number of bands and range of wavelengths

represented by the satellite (i.e., Systeme Pour

l'Observation de la Terre (SPOT-XS) 4 bands, and

500 – 1750 nm)

• High spectral resolution = many bands and wide range

of wavelengths

Spatial resolution

• Describes the size of the smallest unit of area,

represented by a picture element or pixel, in a satellite

image (i.e., SPOT-XS 20m pixels)

• High spatial resolution = small pixel size

5 0 5 10 Kilometers

N

one mile buffer zonecity limit

Providence,

Rhode Island

Providence, RI

orthophotography

Comparing spatial resolutions

Orthophotography0.8 m (2.5 ft ) resolution

Landsat ETM+30 m resolution

ATLAS7.5 m resolution

of

20

SeaWiFS

Spatial Resolution• 1.1 km

Spectral Resolution• 8 Bands

• 402 – 885 nm

ETM +Spatial Resolution

• 15,30 and

60 km

Spectral Resolution• 8 Bands

• 450 – 2350 nm

•Thermal

•Panchromatic

IkonosSpatial Resolution

• 1 and 4 m

Spectral Resolution• 4 bands

• 450 – 850 nm

•Panchromatic

Biological and ecological uses

Developed

Agriculture

Rangeland

Forest

Water

Wetlands

Barren

Land cover mapping

Fire monitoring and modeling

http://www.fs.fed.us/land/wfas/exp_fp_4.gif

Wetland change

Pollution monitoring and modeling

Habitat modeling

http://www.epa.gov/airnow/ozone.html

http://www.esd.ornl.gov/

http://www.nrcs.usda.gov/technical/land/meta/m3631.html

Acknowledgements

Thanks to Greg Bonynge and Y.Q. Wang for

letting me steal many of their slides

introductory spatial statistics workshop part 1: interpolation with geostatistical analyst · ·...

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