University of California Los Angeles Department of Statistics Introduction to GRASS R spatial data analysis What is Geographic Information Systems GIS A geographic information system GIS integrates hardware software and data for capturing managing analyzing and displaying all forms of geographically referenced information ESRI http www gis com GIS are tools that allow for the processing of spatial data into information and used to make decisions about some portion of the earth Fundamentals of Geographic Information Systems DeMers M Third Edition 2005 GIS is often described as integration of data hardware and software designed for management processing analysis and visualization of georeferenced data OPEN SOURCE GIS A GRASS GIS APPROACH Neteler M Mitasova H Third Edition 2008 Why GIS Needed for map analysis operations in areas such as Forestry Fire Departments Police Departments EMS Traffic Water resources Real estate Military Business Mining geology Hydrology Wildlife management Epidemiology Agriculture Election results Etc Useful tool for statisticians that work with spatial data Geographical Data Four main components Input Administration Analysis Presentation 1 With GIS we can study Land Elevation Forests Population densities Energy consumption Mineral resources etc A GIS map has layers Each layer represents geographic objects that are similar For example cities can be one layer rivers another one roads lakes etc With a click of a button we can include all these layers on our GIS map or simply have as many layers as we want GIS can help us understood our geographic data easily 3D visualization and animation see snapshot below from GRASS 2 Spatial data Geostatistics Why spatial statistics Noel Cressie in his textbook Statistics for Spatial Data writes why how when are not enough to describe our data We need to add where where did they occur First demonstration of spatial data appear in the form of maps Halley 1686 Spatial models appeared much later Student 1907 R A Fisher 1935 Fairfield 1938 Whittle 1954 Matheron 1960s etc Today spatial statistics models appear in areas such as mining geology hydrology ecology environmental science medicine image processing crop science epidemiology forestry atmospheric science etc Need to develop models that deal with data collected at different spatial locations The basic components are the spatial locations s1 s2 sn and the data observed at these locations denoted as Z s1 Z s2 Z sn The distance between the observations is important in analyzing spatial data With distance we mostly mean Euclidean distance However there are other forms of distances e g road miles travel time etc The latter is modeled through multidimensional scaling Here we will consider mostly if not always Euclidean distances Geostatistics was developed for geology and mining but in general it means statistics applied to problems in the earth geo earth in Greek sciences A very popular method for analyzing spatial data is kriging which was developed by Georges Matheron 1960s and 1970s He coined the term kriging in honor of a South African mining engineer Danie Krige Terminology in kriging Variogram nugget range sill correlogram stationarity variance covariance matrix spherical variogram exponential variogram ordinary kriging universal kriging block kriging isotropic and anisotropic variogram spatial prediction Other methods of spatial prediction and interpolation 42 42 Raster map of the predicted values 5 0 06 38 40 0 08 5 5 34 0 075 0 0 8 0 0 36 0 07 0 05 38 0 05 0 07 y 36 40 0 08 0 07 0 06 0 07 32 South to North 34 6 32 0 0 124 122 120 118 116 114 West to East 124 122 120 118 x 3 116 114 General GIS principles It is important to understand the basic terminology and functionality of GIS certain principles are common to all systems Some widely used GIS softwares commercial or open source can be found at http en wikipedia org wiki List of GIS software http www freegis org Georeferenced data include spatial component and attribute component Spatial component Two basic models Field representation raster data model Things such as temperature elevation air pollution vegetation rain fall wind speed do not have shapes Instead they have measurable values for any particular location on the surface of earth The most common surface is a raster It is a matrix of equally sized square cells pixels where each cell represents a unit of surface area for example 1 square meter A raster map that represents elevation may cover an area of 100 square kilometers If there were 100 cells in this raster each cell would represent one square kilometer of equal width and height that is 1km 1km Each cell contains a measured or estimated value for that location Here are two examples Elevation Snow level Another type of raster maps are the so called thematic maps Each cell gets a categorical value for example if we analyze vegetation data 1 2 3 4 5 may represent different categories of vegetation Here is one example 4 The resolution of the raster map controls the level of spatial detail The smaller the cell size the smoother the raster will be however it takes longer to process it and requires larger storage space On the other hand if the cell size is too large information may be lost Geometrical objects representation vector data model Geographic features are represented by lines e g roads rivers points e g cities data points polygons e g county or state boundaries This representation is given by the coordinates The vector data model is based on arc node representation where an arc is a series of points given by x y coordinates The two endpoints of an arc are called nodes while points along a line are called vertices Two consecutive points define an arc segment Here is one example Can you guess what this vector map represents Attributes Attributes are descriptive data that provide information associated with raster or vector data 5 Introduction to Geographical Resources Analysis Support System GRASS General information GRASS Website http grass fbk eu GRASS logo GRASS Team http grass ibiblio org community team php GRASS Wiki site http grass osgeo org wiki GRASS manual http grass ibiblio org gdp html grass64 GRASS was originally developed for the U S Army Construction Engineering Research Laboratories 1982 1995 as a tool for land managing GRASS is a free software used for data management image processing graphics production spatial modelling and visualization of many types of data It is currently used in