Lecture 8. Spatial Estimation

Transcription

1 Lecture 8 Spatial Estimation

2 Lecture Outline Spatial Estimation Spatial Interpolation Spatial Prediction Sampling Spatial Interpolation Methods Spatial Prediction Methods Interpolating Raster Surfaces with ArcGIS Spatial Analyst:

3 Spatial Estimation/Prediction Spatial Prediction: Estimate values at unsampled locations. Why do we need to do this? Resource limitations (time and money). You can t measure every single location. Access or safety constraints. Missing or unsuitable samples. Estimates required when changing to a smaller raster cell size.

4 Spatial Interpolation The prediction of variables at unmeasured locations based on the sampling of the same variables at known locations. Usually used to estimate air and water temperature, soil moisture, elevation, population density, etc.

5 Spatial Prediction The estimation of variables at unsampled locations, based partially on other variables. Ex. Use elevation to measure temperature. Combine elevation and temperature layers to better predict temperature at unknown locations.

6 Translating Spatial Prediction From lower to higher spatial dimensions. i.e. generate points or lines from point data. From higher to lower spatial dimension. i.e. estimate point values from areas or lines. MAUP: The Modifiable Areal Unit Problem A potential source of error that can affect spatial studies which utilize aggregate data sources.

7 Sampling Two characteristics of sampling: Location of samples Number of samples Sometimes we can t control sampling. i.e. You may be limited to occurrences of an event.

8 Common Sampling Patterns a) Systematic Sampling: Simple, uniform intervals Random Sampling: Randomly placed samples. a) Cluster Sampling: Groups samples Adaptive Sampling: Higher sampling densities where feature of interest is more variable.

9 Spatial Interpolation Methods No one interpolation method is superior for all datasets. Method choice depends on: Characteristics of the variable to be measured Cost of sampling Available resources Accuracy requirements of the users Methods differ in the mathematical functions used to weight each observation, and the number of observations used. Methods: Nearest Neighbor IDW Fixed Distance Spline

10 Spatial Interpolation Methods Nearest Neighbor Nearest Neighbor* (Thiessen Polygon) Assigns a value to an unsampled location that is equal to the value found at the nearest sample location. Exact interpolator: Value at each sample point is preserved. *Referred to as Natural Neighbor/Voronoi Polygons in lab exercise.

11 Spatial Interpolation Methods IDW (Inverse Distance Weighted) Uses distance and values to nearby known points. Reduces the contribution of distant points. Weight of each sample point is an inverse proportion to the distance. Further points = less weight Closer points = more weight The solid line represents more power and the dashed line represents less power. The higher the power, the more localized an affect a sample point's value has on the resulting surface.

12 Spatial Interpolation Methods Fixed Radius and Spline Fixed Radius: Cell values estimated based on average of nearby samples. Depends on search radius. Spline: Used to interpolate along a smooth curve. Force a smooth line to pass through a set of points.

13 Spatial Prediction Methods Often generated via a statistical process. Type of predictive modeling. Primary Methods: Spatial Autocorrelation Spatial Regression Kriging

14 Spatial Prediction Methods Autocorrelation Tendency of nearby objects to vary together. Everything in the universe is related to everything else, but closer things are more related. Tobler s First Law of Geography

15 Spatial Prediction Methods Spatial Regression Establishes relationships between numerous input variables and presents the relationships in a succinct manner. A regression analysis has two parts: The dependent variable, which is the phenomenon whose level or presence you are trying to predict or explain for each location in a study site. The independent variables, which are the known attributes of the locations that influence the level or presence of the dependent variable.

16 Spatial Prediction Methods Kriging Weights the surrounding measured values to derive a prediction for each location. However, the weights are based not only on the distance between the measured points and the prediction location but also on the overall spatial arrangement among the measured points. 3 Components: 1. Spatial Trend: increase or decrease in variable depending on direction. Ex. Temp to NW 2. Spatial Autocorrelation: Tendency for points near each other to have similar values. 3. Random variation of measured points.

17 Spatial Estimation in ArcGIS Analysis performed using Spatial Analyst Tools Interpolation Toolbox.