Spatial Analysis and GIS Stephanie Watson Marine Mapping User Group (MMUG) Coordinator California Department of Fish and Game

Overview  Introduce scenario  Spatial data are unique  What is spatial analysis?  Example  Summary

Scenario

Spatial Data are Unique  Spatial data do not meet the assumptions for traditional statistics. Dependence exists between values Dependence exists between values Nearby things are more similar (Tobler’s First Law of Geography)Nearby things are more similar (Tobler’s First Law of Geography)

Spatial Datasets (Often) Include: First Order Effects  A global or large scale trend in the dataset  But, many spatial statistics require a normal distribution… often we must remove the trend

Spatial Datasets Include: Second Order Effects  The smaller scale spatial dependence between values in a dataset; Correlation in the deviations of the values from the mean  Second order effects = spatial dependence = spatial autocorrelation

First and Second Order Effects ©2002 Goddard Institute for Space Studies, NASA Larger scale trend; first order effects smaller scale, second order effects

Spatial Analysis:  Is a suite of statistical techniques developed to explicitly account for the uniqueness of spatial data  Involves a three-step methodology

Methodological Approach of Spatial Analysis 1. Visualize Show interesting patterns Show interesting patterns 2. Explore Quantify the patterns Quantify the patterns 3. Model Explain relationships Explain relationships

Scenario  Asked to create a GIS layer of bathymetry (continuous attribute) based on data sampled at discrete point locations  Make predictions of values at unsampled locations  Obtain standard error measures of the predicted values

Step One: Visualize the Data Does a trend exist?

Step Two: Explore the Data  First Order Effects – quantify and remove large scale trend from the dataset  Second Order Effects – quantify spatial dependence between values in the dataset Technique: semivariogram Technique: semivariogram

Step Two: Explore the Data What is involved in the semivariogram?  Examine all possible pairs of sample points.  Measure and plot the distance between two point locations (x axis)  Then plot the difference squared between the values at those locations (y axis) Result: a semiovariogram cloud Result: a semiovariogram cloud

Step Two: Explore the Data Semivariogram Y axis: squared difference between attribute values at the two locations in the pair X axis: distance between the locations of a pair of points

Step Two: Explore the Data Semivariogram: Sill: upper bound of the variance between the values of the two points Range: distance between points at which sill first occurs Nugget effect: measurement error

Step Two: Explore the Data Semivariogram

Step Three: Model the Data  Kriging – a spatial statistical method of interpolation that uses: the extent of spatial dependence found in the semivariogram and the extent of spatial dependence found in the semivariogram and the sample points the sample points to model predicted values at un- sampled locations and their error

Step Three: Model the Data  Kriging: Uses weights in the interpolation of values at unsampled locations Uses weights in the interpolation of values at unsampled locations Weights are based on Weights are based on distance between the measured points and the prediction locationdistance between the measured points and the prediction location and on the second order effects among the measured valuesand on the second order effects among the measured values

Example Summary  1: Visualized the data  2: Explored the data Quantified and removed the first order effects Quantified and removed the first order effects Quantified the second order effects (semivariogram) Quantified the second order effects (semivariogram)  3: Modeled the data Used the information from the semivariogram and the sampled points to do kriging Used the information from the semivariogram and the sampled points to do kriging Kriging produced a continuous layer of predicted values and standard errors Kriging produced a continuous layer of predicted values and standard errors

Summary Spatial Analysis Techniques:  explicitly account for the characteristics of spatial data  provide measures of confidence in your data  are inexpensive methods to achieve accurate information

Summary: Spatial Analysis Techniques  are available for all kinds of spatial data  involve a three-step approach: 1. visualize the data 2. explore first and second order effects 3. model predicted values

Closing  Thanks to Mira Park, CDFG  Additional information: Bailey, T.C. and Gatrell, A.C Interactive Spatial Data Analysis. Essex, England: Longman Group. 413 pp.