Lab Exercise 7: Raster Spatial Analysis
Contents
1. 199 833 3282 228 C m 228 060 0001 258 E 258 533 3282 333 2 E 333 333 3439 430 C E 430 000 0001 477 2 Wi 477 200 3439 500 C Fig 8 hvalue_non0O Notice the no data cambordergd cells sticking out from under the new surface and notice that the interpolated values don t fall off close to the no data cells as rapidly as they did before e g near Harvard Square You ll also notice that the low value categories begin above 100 000 rather than at 0 the way they did before This surface is about as good an interpolation as we are going to get using the block group data Comment briefly on some of the characteristics of this interpolated surface of med_hvalue compares with the ones derived from the sales89 data Are the hot spots more concentrated or diffuse Does one or another approach lead to a broader range of spatial variability V Combining Grid Layers Using the Map Calculator Finally let us consider combining the interpolated housing value surfaces computed using the sales89 and med_hvalue methods ArcGIS provides a Raster calculator option that allows you to create a new grid layer based on a user specified combination of the values of two or more grid cell layers Let s compute the simple arithmetic average of the sale89_pw2 2 grid layer and the med_hvalue_non0 layer Select Spatial Analyst gt Raster Calculator and enter this formula hvalue_non0 sale89_pw2 2 2 and click Evaluate The result is a new gr2. Massachusetts Institute of Technology Department of Urban Studies and Planning 11 520 A Workshop on Geographic Information Systems 11 188 Urban Planning and Social Science Laboratory Lab Exercise 7 Raster Spatial Analysis Distributed Lab 7 Due Lab 8 Overview The purpose of this lab exercise is to introduce spatial analysis methods using raster models of geospatial phenomena Thus far we have represented spatial phenomena as discrete features modeled in the GIS as points lines or polygons i e so called vector models of geospatial features Sometimes it is useful to think of spatial phenomena as fields such as temperature wind velocity or elevation The spatial variation of these fields can be modeled in various ways including contour lines and raster grid cells In this lab exercise we shall focus on raster models and examine ArcGIS s Spatial Analyst extension We shall use raster models to create a housing value surface for Cambridge A housing value surface for Cambridge would show the high and low value neighborhoods much like an elevation map shows height To create the surface we will explore ArcGIS s tools for converting vector data sets into raster data sets in particular we will rasterize the 1989 housing sales data for Cambridge and the 1990 Census data for Cambridge block groups The block group census data and the sales data contain relevant information about housing values but the b
3. XTools gt Guides Effects Grid Geostatistical Analyst Data Frame Properties Dimensioning al Georeferencing Data Frame Tools Layout Utility Network Analyst Versioning Graphics Edit Cache Editor Customize View Source Fig 2 Add Spatial Analyst toolbar Once the Spatial Analyst tool bar loaded a new main menu heading called Spatial Analysis will be available whenever you launch the ArcGIS Setting Analysis Properties Before building and using raster data sets we should set the grid cell sizes the spatial extent of our grid and the no data regions that we wish to mask off Let s begin by specifying a grid cell size of 100 meters and an analysis extent covering all of Cambridge To do this click Spatial Analyst gt Option When the Options window pops up o In the General tab set your working directory select None for the Analysis mask We will set the mask later and select the first option for the Analysis Coordinate System o In the Extent tab select Same as Layer camborder polygon for the Analyst extent o In the Cell Size tab select As Specified Below then specify Cell size 100 Number of rows 57 Number of columns 79 Number of rows and Number of columns will be automatically computed Now that we ve set the analysis properties we are ready to cut up Cambridge into 100 meter raster grid cells Convert the camborder to a grid layer using these steps and parameter
4. ed on the parameters we set the cell value is an inverse distance weighted average of the 12 closest sales Since the power factor was set to the default 2 the weights are proportional to the square of the distance This interpolation heuristic seems reasonable but the surface extends far beyond the Cambridge borders all the way to the rectangular bounding box that covers Cambridge We can prevent the interpolation from computing values outside of the Cambridge boundary by masking off those cells that fall outside of Cambridge Do this by adding a mask to the Analysis Properties e Reopen the Spatial Analysis gt Options dialog box and set the Analysis Mask to be CAMBORDERGD the grid that we computed earlier from the camborder coverage With this analysis mask set interpolate the Realprice values in sales89 once again and save it as Sales89_pw2 2 The sales89_pw2 2 should look like this When using Quantile 9 classes E sale89_pw2 2 Yalue C 39 959 62891 166 C E 166 010 2501 193 E 193 918 4376 215 C m 215 079 7189 242 C E 242 092 3439 286 1 E 286 167 1876 349 5 Wl 349 513 1251 442 5 Wl 442 550 2189 569 7 WM 569 726 2501 1 33C Fig 4 Interpolation with mask All the values inside Cambridge are the same as before but the cells outside Cambridge are masked off To get some idea of how the interpolation method will affect the result redo the interpolation using the same mask with the po
5. er hvalue_point Click O K and you should get a shaded surface like this When using Quantile 9 classes E hvalue_point value C 17 44932175 94 140 E 94 140 96876 140 3 E 140 359 7657 180 6 E 180 612 5782 202 4 fi 202 420 9064 223 1 E 223 165 3439 257 7 Wl 257 731 5782 311 5 E 311 962 3126 403 7 E 403 745 8439 497 1 Fig 5 Interpolation with centroids of census block group polygons Next let s use the second approach using the polygon data to interpolate the housing value surface from the census block group data o Ifyou haven t already done so add the cambbgrp shp to your data frame o Select Spatial Analyst gt Convert gt Feature to Raster Features to Raster window will show up Choose cambbgrp for the Input features Choose MED_HVALUE for the Field Output cell size should be 100 Set the saving location your working directory and the name of the grid file cambbgrpgd and click OK As you can see from the below images except for the jagged edges the newly created grid layer looks just like a vector based thematic map of median housing value When using Quantile 9 classes Fig 6 Vector based thematic map vs Raster based thematic map Examine its attribute table It has 63 unique values except 0 one for each unique value of med_hvalue in the original cambbgrp coverage The attribute table for grid layers contains one row for each uniq
6. esponding cells on the map Find the cell containing the location of the highest price sales89 home in the northwest part of Cambridge What is the interpolated value of that cell using the two methods based on med_hvalue Many other variations on these interpolations are possible For example we know that med_hvalue is zero for several block groups presumably those around Harvard Square and MIT where campus and commercial industrial activities results in no households residing in the block group Perhaps we should exclude these cells from our interpolations not only to keep the zero value cells from being displayed but also to keep them from being included in the neighborhood statistics averages Copy and paste the cambbgrp shp layer and use the query tools in the Layer Properties gt Definition Query tab to exclude all block groups with med_hvalue 0 which means include all block groups with med_hvalue gt 0 Now recompute the polygon based interpolation including the neighborhood averaging and call this grid layer hvalue_non0 Select the same color scheme as before In the data window turn off all layers except the original cambordergd layer displayed in a non grayscale color like blue and the new hvalue_nonO layer that you just computed The resulting view window should look something like this When using Quantile 9 classes E hval_non0 Value C 110 700 149 844 42 E 149 844 4376 174 4 E 174 425 0001 199 E
7. id which is the average of the two estimates and looks something like this When using Quantile 9 classes E WM Calculation value C 129 593 164 737 81 E 164 737 8126 197 E 197 831 1251 220 4 E 220 489 9064 242 7 E 242 760 4064 290 C E 290 030 9689 363 E 263 584 4064 423 E 423 893 2189 513 2 W 513 335 0939 866 Fig 9 Raster Calculation The map calculator is a powerful and flexible tool For example if you felt the sales data was more important than the census data you could assign it a higher weight with a formula such as Med_hvalue 0 7 Sales_Price 1 3 2 The possibilities are endless and many of them won t be too meaningful Think about the reasons why one or another interpolation method might be misleading inaccurate or particularly appropriate For example you might want to compare the mean and standard deviation of the interpolated cell values for each method and make some normalization adjustments before combining the two estimates using a simple average For the lab assignment however all you need do at this point is determine the final interpolated value using the first map calculator formula for the cell containing the highest price sales89 house in the Northwest corner of Cambridge Write this value on the assignment sheet We have only scratched the surface of all the raster based interpolation and analysis tools that are available If you have extra ti
8. less weight to the neighbors and more to the expensive local sale compared with the case where the inverse distance weights are not squared power 1 Finally create a third interpolated surface this time with the interpolation based on all sales within 1000 meters and power 2 rather than the 12 closest neighbors To do this you have to set the Search radius type Fixed and Distance 1000 in the Inverse Distance Weighted dialog box Call this layer sales89 1000m and use the identify tool to find the interpolated value for the upper left cell with the highest priced sale Confirm that the display units are set to meters in View gt Data Frame Properties before interpolating the surface The distance units of the view determine what units are used for the distance that you enter in the dialog box What is this interpolated value and why is this estimate even higher than the power 1 estimate Note None of these interpolation methods is correct Each is plausible based on a heuristic algorithm that estimates the housing value at any particular point to be one or another function of nearby sales prices The general method of interpolating unobserved values based on location is called kriging and the field of spatial statistics studies how best to do the interpolation depending upon explicit underlying models of spatial variation See for example Spatial Stats User s Manual for Windows and Unix by Kaluzny Bega Cardoso and Shel
9. lock group data may be too coarse and the sales data may be too sparse One way to generate a smoother housing value surface is to interpolate the housing value at any particular location based on some combination of values observed for proximate housing sales or block groups To experiment with such methods we will use a so called raster data model and some of the ArcGIS Spatial Analyst s capabilities The computation needed to do such interpolations involve lots of proximity dependent calculations that are much easier using a so called raster data model instead of the vector model that we have been using Thus far we have represented spatial features such as Cambridge block group polygons by the sequence of boundary points that need to be connected to enclose the border of each spatial object for example the contiguous collection of city blocks that make up each Census block group A raster model would overlay a grid of fixed cell size over all of Cambridge and then assign a numeric value such as the block group median housing value to each grid cell depending upon say which block group contained the center of the grid cell Depending upon the grid cell size that is chosen such a raster model can be convenient but coarse grained with jagged boundaries or fine grained but overwhelming in the number of cells that must be encoded In this exercise we only have time for a few of the many types of spatial analyses that are possible using
10. ly MathSoft Inc 1998 ISBN 0 387 98226 4 for further discussion of kriging techniques using the Spatial Statistics add on of a high powered statistical package called S that is available on Athena IV Interpolating Housing Values Using CAMBBGRP Another strategy for interpolating a housing value surface would be to use the median housing value field med_hvalue for the census data available in cambbgrp There are several ways in which we could use the block group data to interpolate a housing value surface One approach would be exactly analogous to the sales89 method We could assume that the block group median was an appropriate value for some point in the center of each block group Then we could interpolate the surface as we did above if we assume that there was one house sale priced at the median for the block group at each block group s center point A second approach would be to treat each block group median as an average value that was appropriate across the entire block group We could then rasterize the block groups into grid cells and smooth the cell estimates by adjusting them up or down based on an average housing value of neighboring cells Let s begin with the first approach o Select Spatial Analyst gt Interpolate to Raster and choose Inverse Distance Weighted o Select cambbgrp_point as your input layer and med_hvalue as your Z Value Field Take the defaults for method neighbors and power Name this lay
11. me review the help files regarding the Spatial Analyst extension and work on those parts of the homework assignment that ask you to compute a population density surface for youths
12. rasterize data sets Remember that our immediate goal is to use the cmbbgrp and sales89 data to generate a housing value surface for the city of Cambridge We ll do this by rasterizing the block group and sales data and then taking advantage of the regular grid structure in the raster model so that we can easily do the computations that let us smooth out and interpolate the housing values I Setting Up Your Work Environment 1 Launch the ArcGIS and add five data layers listed below e M data cam_1u99 shp Cambridge land use in 1999 per MassGIS oii E ET EET E T Census 1990 block group centroids for Cambridge e M data cambbgrp shp Census 1990 block group polygons for Cambridge e M data cambtigr coverage U S Census 1990 TIGER file for Cambridge e M data sales89 Cambridge Housing Sales Data e M data camborder Cambridge polygon 2 Set Display unit meter In this exercise you will use Meter instead of using Mile II Spatial Analyst Setup ArcGIS s raster manipulation tools are bundled with its Spatial Analyst extension It s a big bundle so lets open ArcGIS s help system first to find out more about the tools Open the ArcGIS help page by clicking Help gt ArcGIS Desktop help from the menu bar Click the index tab and type Spatial analyst During the exercise you ll find these online help pages helpful in clarifying the choices and reasoning behind a number of the steps that we will explore Be sure at some point to
13. reported and only a sample of the population is asked to report The benefit of census data is that they are cheaply available and they cover the entire country We will use sales89 and cambbgrp to explore some of these ideas Let s begin with sales89 o Be sure your data frame contains at least these layers sales89 cambbgrp and cambordergd o Select Spatial Analyst gt Interpolate to Raster gt Inverse Distance Weighted Specify options when Inverse Distance Weighted window shows up Input points sales89 point Z value field REALPRICE Power 2 Search radius type Variable Number of points 12 Maximum distance leave it blank Uncheck the Use barrier polylines Output cell size 100 Output raster your working directory sale89_pw2 1 Click OK The grid layer that is created fills the entire bounding box for Cambridge and looks something like this When using Quantile 9 classes E W sale89_pw2 1 lt VALUE gt C 39 959 62891 150 E 150 888 3875 171 C E 171 057 2526 211 2 m 211 394 983 241 64 D 241 648 2807 307 1 E 207 197 0926 382 E 382 830 337 478 62 Wl 478 632 4465 589 B 589 561 205 1 330 Fig 3 Interpolation without mask The interpolated surface is shown thematically by shading each cell dark or light depending upon whether that cell is estimated to have a lower housing value darker shades or higher housing value lighter shades Bas
14. settings o Select Spatial Analyst gt Convert gt Feature to Raster Features to Raster window will show up Choose camborder polygon for the Input features Choose COUNTY for the Field We just want a single value entered into every grid cell at this point Using the County field will do this since it is the same across Cambridge Output cell size should be 100 Set the saving location your working directory and the name of the grid file cambordergd and click OK If successful the CAMBORDERGD layer will be added to the data frame window Turn it on and notice that the shading covers all the grid cells whose center point falls inside of the spatial extent of the camborder layer The cell value associated with the grid cells is 25017 the FIPS code number for the county Since we did not join feature attributes to the grid there is only one row in the attribute table for CAMBODERGER attribute tables for raster layers contain one row for each unique grid cell value hence there is only one row in this case At this point we don t need the old camborder coverage any longer We used it to set the spatial extent for our grid work but that setting is retained To reduce clutter you can delete the camborder layer III Interpolating Housing Values Using SALES89 This part of the lab will demonstrate some techniques for filling in missing values in your data using interpolation methods In this case we will explore differen
15. t ways to estimate housing values for Cambridge Keep in mind that there is no perfect way to determine the value of a property A city assessor s database of all properties in the city would generally be considered a good estimate of housing values because the data set is complete and maintained by an agency which has strong motivation to keep it accurate This database does have drawbacks though It is updated sporadically people lobby for the lowest assessment possible for their property and its values often lag behind market values by many years or even decades Recent sales are another way to get at the question On the one hand their numbers are believable because the price should reflect an informed negotiation between a buyer and a seller that results in the market value of the property being revealed if you are a believer in the economic market clearing model However the accuracy of such data sets are susceptible to short lived boom or bust trends not all sales are arms length sales that reflect market value and since individual houses and lots might be bigger or smaller than those typical of their neighborhood individual sale prices may or may not be representative of housing prices in their neighborhood Finally the census presents us with yet another estimate of housing value the median housing values aggregated to the block group level This data set is vulnerable to criticism from many angles The numbers are self
16. take a look at the Overview section The Spatial Analyst module is an extension so it must be loaded into ArcGIS separately To load the Spatial Analyst extension o Click the Tools menu o Click Extensions and check Spatial Analyst o Click Close Select the extensions you want to use Tools Window Help af Editor Toolbar O ArcPress Graphs O AreScan ie Spatial Analyst Reports StreetMap Europe OO StreetMap USA Geocoding Add XY Data 7 Add Route Events ra Route Events GeoProcessing Wizarc I Buffer Wizard F GeoProcessing Wizard EN ArcCatalog Macros Customize Extensions Options Fig O Survey Analyst O Tracking Analyst Description 3D Analyst 8 3 c ESRI 1998 2002 Provides tools for surface modeling and 3D visualization About Extensions 1 Add Extension Although you just activated the Spatial Analyst extension you have to add the Spatial Analyst tool bar on the menu manually to use the extension quite inconvenient To add Spatial Analyst tool bar go to View gt Tool bars from the menu bar and click Spatial Analyst View Insert Selection Tools Window Help amp Data View HAH melar eE A Layout View ja zoom Data b zoom Layout b Bookmarks gt 7 Man Menu El Table Of Contents v Standard v Status Bar v Tools Overflow Labels v Draw Identify Results a Scrollbars 3D Analyst Cs Rulers
17. ue value as long as the cell value is an integer and not a floating point number and a count column is included to indicate how many cells had that value Grid layer layers such as hvalue_points have floating point values for their cells and hence no attribute table is available You could reclassify the cells into integer value ranges if you wished to generate a histogram or chart the data Finally let s smooth this new grid layer using the Spatial Analyst gt Neighborhood Statistics option Let s recalculate each cell value to be the average of all the neighboring cells in this case we ll use the 9 cells a 3x3 matrix in and around each cell To do this choose the following settings they are the defaults Input data CAMBBGRPGD Field Value Statistic type Mean Neighborhood Rectangle Width 3 Height 3 Units cell Output cell size 100 Output raster your working space hvalue_poly 9 0 0 0O 0 0 0 070 Click OK and the hvalue_poly layer will be added on your data frame Change the classify method to Quantile You should get something like this When using Quantile 8 classes E hvalue_poly Yalue JO 141 900 E 141 900 0001 1 E 161 166 672 19 E 191 800 0001 2 E 228 060 0001 2 E 275 000 0001 Wl 420 822 5626 4 E 465 800 0001 5 Fig 7 Smoothing by neighborhood statistics function Note that selecting rows in the attribute table for hvalue_poly will highlight the corr
18. wer set to 1 instead of 2 Label this surface Sales89 pwl Use the identify tool to explore the differences between the values for the point data set sales89 and the two raster grids that you interpolated You will notice that the grid cell has slightly different values than the realprice in sales89 even if there is only one sale falling within a grid cell This is because the interpolation process looks at the city as a continuous value surface with the sale points being sample data that gives an insight into the local housing value The estimate assigned to any particular grid cell is a weighted average with distant sales counting less of the 12 closest sales including any within the grid cell In principle this might be a better estimate of typical values for that cell than an estimate based only on the few sales that might have occurred within the cell On your lab assignment sheet write down the original and interpolated values for the grid cell in the upper left that contains the most expensive Realprice value in the original sa1e89 data set Do you understand why the interpolated value using the power 1 model is considerably lower than the interpolated value using the power 2 model There was only one sale in this cell and it is the most expensive 1989 sale in Cambridge Averaging it with its 11 closest neighbors all costing less will yield a smaller number Weighting cases by the square of the inverse distance from cell power 2 gives
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