Labs Labs 5 & 6 are on the website. Lab 5 is due Tuesday (Oct. 31st). Lab 6 is due Thursday (Nov. 2nd). No class Tuesday. Lecture 12B

Project Progress Report Due: Nov. 9th Description of what you have accomplished to date and your data dictionary. The data dictionary and data sources will be included as appendices to your final project report. Lecture 12B

The Table Inventory BIOLOGICAL INVENTORY Comprehensive Inventory Program for Birds at Six Pennsylvania National Parks, 1999-2001 BirdEvents Events Locations LocCanopy LocGroundCover LocHerbVegHeight LocOverstory LocUnderstory&Shrub OwlSurvey PointCountSurvey RaptorSurvey RiparianBirdSurvey RoadSurvey ShrikeSurvey LinkObservers BirdSpecies ParkName Lecture 12B

BirdEvents Table Field Name Type Width Field Description EventID Text 50 Sampling Event ID such as EISE_BIRDS_SHRIKE_2000-May-15_00:01 where EISE=park code, BIRDS=general survey type, SHRIKE=specific survey type, 2000-May-15=date, 00:01=time where applicable or 00:00 where the last digit(s) are the survey point Temp Double 8 Temperature in degrees Fahrenheit Wind Wind speed in miles per hour Clouds Percentage of cloud cover Precip Indication of precipitation: 0 = none and 1 = light snow during winter or mist to light drizzle during spring, breed, or fall. Snow Long 4 Snow depth in centimeters Lecture 12B

Appendices to Final Report Appendix A Data used in project and its source. Appendix B Table Inventory Appendix C Data Dictionary Lecture 12B

Spatial Estimation Chapter 12 – Part 2 Lecture 12B

The Farm Lecture 12B

Fixed-Radius – Local Averaging INTERPOLATION Fixed-Radius – Local Averaging Lecture 12B

Fixed Radius Radius 0.17 Radius 0.34 Radius 0.68 Lecture 12B

INTERPOLATION Inverse Distance Weighted (IDW) Zi is value of known point Dij is distance to known point Zj is the unknown point n is a user selected exponent Lecture 12B

IDW Power 1 Power 2 Power 4 Lecture 12B

Global Mathematical Functions Polynomial Trend Surface Lecture 12B

Polynomial Trend Function Order 1 Order 2 Order 4 Order 8 Lecture 12B

Kriging Kriging (weighted average technique) Measures distances between all possible pairs of sample points - Lags Models the spatial autocorrelation for the surface Tailors its calculations to the surface Analyzing all the data points to find out how much autocorrelation they exhibit Factors that information into the weighted average estimation Incorporates trends as expressed through the data's variogram Lecture 12B

Kriging - Quantifying Spatial Autocorrelation Lecture 12B

Kriging Kriging (weighted average technique) The variogram model Mathematically specifies the spatial variability Mathematically specifies the resulting grid Geostatistics assume that adjoining points are spatially related Variogram models the correlation between spatial variables Modeling the variogram Allows quantification of the correlation between any two values separated by a distance (lag) Uses this to apply the most appropriate interpolation procedure Lecture 12B

Kriging Interpolating a surface using Kriging Spatial autocorrelation is determined for the sample point set Best-fit model is automatically applied to the data Unknown values are predicted Lecture 12B

Kriging - Semivariogram Model (h) Nugget Partial Sill Range Lecture 12B

Kriging - Fitting a Semivariogram Model Lecture 12B

Kriging Typically the initial kriged surface is considered a first draft Surface against which future iterations can be compared Kriging methods Ordinary Kriging Assumes there is no trend in the data Highly reliable and is recommended for most data sets Universal Kriging Assumes that there is an overriding trend in the data Lecture 12B

Kriging A surface created with Kriging can exceed the value range of the sample points but will not pass through the points. Lecture 12B

Kriging Simple Kriging Ordinary Kriging Universal Kriging Lecture 12B

Core Area Mapping Mean Center and Mean Circle Convex Hulls Kernel Mapping Time-Geographic Density Mapping https://sandbox.idre.ucla.edu/sandbox/wp-content/uploads/2014/01/hotspot.png Lecture 12B

Mean Center and Mean Circle The mean center is the average of the X and Y coordinates of the sample points. Mean circles are defined by a radius measured from the mean center. Farthest distance Average distance of sample points Or some other statistical measure Lecture 12B

Mean Center and Mean Circle Advantages: Simplicity Ease of contruction Disadvantage They assume a uniformly circular shape for the core area. Lecture 12B

Convex Hulls (Minimum Convex Polygon) The simplest way to identify core areas with an irregular shape. The smallest polygon created by edges that completely enclose a set of points and for which all exterior angles are greater than or equal to 180o. Concave – some angles less than 180o. Convex. Lecture 12B

Kernel Mapping Uses a set of sample locations to estimate a continuous density surface. Based on a density distribution for each sample. Lecture 12B

Results of Kernel Mapping Depends on Method Lecture 12B

Kernel Mapping Polynomial Order 0 Polynomial Order 1

Problems in Interpolation When performing any of the methods of interpolation Four factors need to be considered: The number of control points The location of control points The problem of saddle points The area containing data points Lecture 12B

Problems in Interpolation The number / location of control points Generally it is safe to say that the more sample points… More accurate the interpolation will be More like the surface will be our model Eventually reach a point of diminishing returns Increases in computation time Too much data will tend to produce unusual results Data clusters may create an unevenly generalized surface Having more data points does not always improve accuracy The more complex the surface, the more data points you need Sure of capturing the necessary detail Lecture 12B

Problems in Interpolation  The saddle-point problem Both members of one pair of diagonally opposite Z values are located below and both members of the second pair lie above the value the interpolation algorithm is attempting to solve This generally occurs only in linear interpolation Any distance weighting will likely solve the problem Software is presented with two probable solutions Average the interpolated values produced Place this average value at the center of the diagonal Lecture 12B

Problems in Interpolation The area containing data points Interpolation data must have control points on all sides Need to interpolate points near the margins of the study area The map border precludes any data points beyond the margin  In the absence of these surrounding data points Algorithm will use whatever is available  The interpolation is performed…it will tend to underestimate Solution…extend the borders of the elevation coverage Margins of the study area can be used to shave the edges Extending the margins 10% will guarantee good results Lecture 12B

Assignment Read Chapter 12 Lecture 12B