Transcript Week 12
Spatial analysis Measurements - Points: centroid, clustering, density – Lines: Length, sinuosity – Polygons: Length, perimeter, area, shape The Centroid of point data The centroid is the spatial mean. The ‘average’ location of all points. The centroid can also be thought of as the balance point of a set of points. Centroid The spatial mean is called the centroid. For a set of (x,y) coordinates, the mean center (x,y) is computed using: i=n i=n S xi x= i=1 n S yi y= i=1 n Point Pattern Analysis There are many ways to quantify the dispersion of points in region. Clustered Regular Random Applications of Point pattern analysis 1. whether the geographical incidence of disease shows any tendency towards clustering in geographical space? 2. Do cases of disease tend to occur in proximity to other cases? 3. Rural-urban migrants’ spatial clustering in the urban setting Solutions: Spatial Statistics such as Moran's I, Monte carlo simulation Nang Rong Bangkok 22 source villages and 1085 rural-urban migrants Results: spatial clustering of migrants at village level Point density Point Density calculates the density of point features around each output raster cell. Kernel Function Example The result of applying a 150km-wide kernel to points distributed over California A typical kernel function (Gatrell et al., 1996) Kernel Size •The smoothness of the resulting field depends on the width of the kernel •Wide kernels produce smooth surfaces •Narrow kernels produce bumpy surfaces Kernel Size Kernel width is 16 km instead of 150 km. This shows the S. California part of the database. Kernel Density in Nicaraguan Health Facilities Objective: assess health accessibility Data Facilities' staffing information GPS receivers to collect latitude and longitude coordinates for every facility Population data from the Nicaragua Census Bureau (the location and population of all communities ) Local peaks for migrant’s locations (intensity surface) Measuring Linear Objects 1D: Length Vector Distance measurements affected by elevation changes – Easily calculated with computer A A B B Measuring Linear Objects Raster Add up # grid cells, multiply by resolution But what about diagonal or highly sinuous lines? Length possibly underrepresented Take home: Vector best for length calculations! Measuring Shape: Sinuosity Relating objects to their environment – Sinuosity • Closer to 1, less sinuous • Sometimes want to know about curvature http://forest.mtu.edu/staff/mdhyslop/gis/sinuosity.html Measuring Polygons 2D: Length, width – More dimensionality, more measurements! Orientation, elongation, perimeter, area, shape Measuring Polygons: Length Vector Calculate lengths of all opposing polygon vertices Compare to see which is longest Ratio of major to minor axes elongation Measuring Polygons: Perimeter Vector Calculate & sum the distance of each line segment making up polygon Raster Identify perimeter cells, sum & multiply by cell resolution – Less accurate for complex polygons Take home: Vector best for perimeter calculations! Measuring Polygons: Areas Vector Simple polygons (e.g., rectangle, triangle, circle)easy calculation Complex polygonsdivide polygon into shapes easily measured with available formulas Often calculated during the digitizing process Perimeter/area ratio: Measure of polygon complexity Measuring Polygons: Areas Raster Regions – Assign a unique value to each region (recode/reclassify), then count the number of cells for each region & multiply by area Tabulate data to find # grid cells for each attribute – Provides measure of proportion of different attribute types Measuring polygon: Shape Major axis • Along longest part of polygon • Must divide polygon in two equal parts Minor axis Major axis Minor axis 2.5 2.5 R=1 3.5 1.5 R = 2.33 • Along shortest part of polygon • Must divide the polygon in two equal parts Major axis / Minor axis ratio • Values > 1 denote elongated polygon • Value = 1 denotes uniform polygon Graphic: Dr. Jean-Paul Rodrigue, Dept. of Economics & Geography, Hofstra University Measuring polygon: Shape Perimeter = 7 miles Area = 25 sqr miles Shape Perimeter to Area Ratio CI = 7 / 25 = 0.28 – perimeter/area – Expression of the geographical complexity of a polygon CI = 15 / 25 = 0.60 • High ratio complex • Low ratio simple Area = 25 sqr miles Perimeter = 15 miles Graphic: Dr. Jean-Paul Rodrigue, Dept. of Economics & Geography, Hofstra University Final Project Introduction Why you wanted to do the project What’s the need, what purpose might the data serve? What features are you planning to map? Materials & Methods Datasets – Source: Where did you obtain it from – Scale – Projection – Use the metadata! Materials & Methods Notes on Metadata Check the Data Quality Section to determine the data set's fitness-for-use as far as scale and resolution – Attribute Accuracy & Horizontal Positional Accuracy can describe the scale/resolution of the data set (either directly or indirectly). Check the Lineage subsection – For each contributing source to the data set pertinent information must be included such as the source's title, media (paper, digital), and source scale. Check the Process Steps in the Data Quality section. – In well-documented metadata, the Process Steps will describe not only how the data set was created (e.g. from paper maps), but also provide information or links to other documents containing information on how the contributing sources were created, as well. Materials & Methods Describe your analyses – Did you have to query data out of a larger dataset? – How did you use that query to generate a separate shapefile for your analysis? Results & Discussion Present whatever maps and tables you create Discuss their meaning Conclusions What did you learn from your analysis?