Essentials of Geographic Information Systems Chapter 8 Geospatial Analysis II Raster Data

Chapter Analysis Raster Data Following our discussion of attribute and vector data analysis , raster data analysis presents the powerful data mining tool available to . Raster data are particularly suited to certain types of analyses , such as basic ( Section Basic with ) surface analysis ( Section Scale of Analysis ) and terrain mapping ( Section Surface Analysis Spatial Interpolation ) While not always true , raster data can simplify many types of spatial analyses that would otherwise be overly cumbersome to perform on vector . Some of the most common of these techniques are presented in this chapter . URL books 186

Basic with LEARNING OBJECTIVE . The objective of this section is to become familiar with basic single and multiple raster techniques . Like the tools available for use on vector ( Section Basic with ) raster data can undergo similar spatial operations . Although the actual computation of these operations is significantly different from their vector counterparts , their conceptual underpinning is similar . The techniques covered here include both single layer ( Section Single Layer Analysis ) and multiple layer ( Section Multiple Layer Analysis ) operations . Single Layer Analysis Reclassifying , or , a is commonly one of the first steps undertaken during raster analysis . Reclassification is basically the single layer process of assigning a new class or range value to all pixels in the based on their original values ( Figure Raster . For example , an elevation grid commonly contains a different value for nearly every cell within its extent . These values could be simplified by each pixel value in a few discrete classes ( 300 , This allows for fewer unique values and cheaper storage requirements . In addition , these layers are often used as inputs in secondary analyses , such as those discussed later in this section . URL books 187

Figure ( I ( Input Raster 456 416 364 326 243 448 364 315 276 218 359 325 268 234 164 306 296 201 133 44 274 231 184 65 , Reclass Raster As described in Analysis Vector Opera ions , buffering is the process of creating an output that contains a zone ( or zones ) of a width around an input feature . In the case URL books 188

of raster , these input features are given as a grid cell or a group of grid cells containing a uniform value ( buffer all cells whose value ) Buffers are particularly suited for determining the area of around features of interest . Whereas buffering vector data results in a precise area of at a specified distance from the target feature , raster buffers tend to be representing those cells that are within the specified distance range of the target ( Figure Raster Buffer around a Target Cell ( Most geographic information system ( GIS ) programs calculate raster buffers by creating a grid of distance values from the center of the target cell ( to the center of the neighboring cells and then reclassifying those distances such that a represents those cells composing the original target , a represents those cells within the buffer area , and a represents those cells outside of the target and buffer areas . These cells could also be further classified to represent multiple ring buffers by including values of , and so forth , to represent concentric distances around the target cell ( Figure i ' Multiple Layer Analysis URL books 189

A raster can also be clipped similar to a vector ( Figure Clipping a Raster to a Vector Polygon Layer ) Here , the input raster is overlain by a vector polygon clip layer . The raster clip process results in a single raster that is identical to the input raster but shares the extent of the polygon clip layer . Figure Clipping ( fU ( ol ( Input Raster Clip Vector Output Raster Raster overlays are relatively simple compared to their vector counterparts and require much less computational power ( 1983 ) Despite their simplicity , it is important to ensure that all overlain are ( spatially aligned ) cover identical areas , and maintain equal URL books 190

resolution ( cell size ) If these assumptions are violated , the analysis will either fail or the resulting output layer will be . With this in mind , there are several different for performing a raster overlay ( 2002 ) The mathematical raster overlay is the most common overlay method . The numbers within the aligned cells of the input grids can undergo any mathematical transformation . Following the calculation , an output raster is produced that contains a new value for each cell ( Figure Mathematical Raster Overlay ) As you can imagine , there are many uses for such functionality . In particular , raster overlay is often used in risk assessment studies where various layers are combined to produce an outcome map showing areas of high . Figure ' I Two input raster layers are overlain to produce an output raster with summed cell values . URL books 191

The raster overlay method represents a second powerful technique . As discussed in Chapter Data Characteristics and Visualization , the connectors AND , OR , and can be employed to combine the information of two overlying input raster into a single output raster . Similarly , the relational raster overlay method utilizes relational operators ( and ) to evaluate conditions of the input raster . In both the and relational overlay methods , cells that meet the evaluation criteria are typically coded in the output raster layer with a , while those evaluated as false receive a value of . The simplicity of this methodology , however , can also lead to easily overlooked errors in interpretation if the overlay is not designed properly . Assume that a natural resource manager has two input raster she plans to overlay one showing the location of trees ( no tree tree ) and one showing the location of urban areas ( not urban urban ) If she hopes to the location of trees in urban areas , a simple mathematical sum of these will yield a in all pixels containing a tree in an urban area . Similarly , if she hopes to find the location of all treeless ( or , nonurban areas , she can examine the summed output raster for all entries . Finally , if she hopes to locate urban , treeless areas , she will look for all cells containing a Unfortunately , the cell value also is coded into each pixel for nonurban , tree cells . Indeed , the choice of input pixel values and overlay equation in this example will yield confounding results due to the poorly devised overlay scheme . KEY TAKEAWAYS Overlay processes place two or more thematic maps on top of one another to form a new map . Overlay operations available for use with vector data include the , or models . Union , intersection , symmetrical difference , and identity are common operations used to combine information from various overlain . Raster overlay operations can employ powerful mathematical , or relational operators to create new output . EXERCISES . From your own field of study , describe three theoretical data layers that could be overlain to create a new output map that answers a complex spatial question such as , Where is the best place to put a mall ?

URL books 192 . Go online and find vector or raster related to the question you just posed . 1983 . Geographical Information Natural Resources Assessment . New York Oxford University Press . 2002 . Exploring Geographic Information Systems . ed . New York John Wiley and Sons . Scale of Analysis LEARNING OBJECTIVE . The objective of this section is to understand how local , neighborhood , zonal , and global analyses can be applied to raster . Raster analyses can be undertaken on four different scales of operation local , neighborhood , zonal , and global . Each of these presents unique options to the GIS analyst and are presented here in this section . Local Operations Local operations can be performed on single or multiple . When used on a single raster , a local operation usually takes the form of applying some mathematical transformation to each individual cell in the grid . For example , a researcher may obtain a digital elevation model ( DEM ) with each cell value representing elevation in feet . If it is preferred to represent those elevations in meters , a simple , arithmetic transformation ( original elevation in feet new elevation in meters ) of each cell value can be performed locally to accomplish this task . When applied to multiple , it becomes possible to perform such analyses as changes over time . Given two containing information on groundwater depth on a parcel of land at Year 2000 and Year 2010 , it is simple to subtract these values and place the difference in an output raster that will note the change in groundwater between those two times ( Figure Local Operation on a Raster ) These local analyses can become somewhat more complicated however , as the number of input increase . For example , the Universal Soil Loss Equation ( applies a local mathematical formula to URL books 193

several overlying including rainfall intensity , of the soil , slope , cultivation type , and vegetation type to determine the average soil loss ( in tons ) in a grid cell . URL books 194 Figure ( 11 ( Ifi ( on ( ut ( Input Raster 456 416 364 326 243 448 364 315 276 218 359 325 268 234 164 306 296 201 133 44 274 231 184 65 Output Raster ( 4560 4160 3640 3260 2430 4480 3640 3150 2760 2180 3590 3250 2680 2340 1640 3060 2960 201 1330 440 2740 2310 1840 650 50 Neighborhood Operations URL books 195

law of geography states that everything is related to everything else , but near things are more related than distant Neighborhood operations represent a group of frequently used spatial analysis techniques that rely heavily on this concept . Neighborhood functions examine the relationship of an object with similar surrounding objects . They can be performed on point , line , or polygon vector as well as on raster . In the case of vector , neighborhood analysis is most frequently used to perform basic searches . For example , given a point containing the location of convenience stores , a GIS could be employed to determine the number of stores within miles of a linear feature ( Interstate 10 in California ) Neighborhood analyses are often more sophisticated when used with raster . Raster analyses employ moving windows , also called filters or kernels , to calculate new cell values for every location throughout the raster layer extent . These moving windows can take many different forms depending on the type of output desired and the phenomena being examined . For example , a rectangular , moving window is commonly used to calculate the mean , standard deviation , sum , minimum , maximum , or range of values immediately surrounding a given target cell ( Figure Common Neighborhood Types around Target Cell ( a ) by , Circle , Annulus , Wedge ) cell is that cell found in the center of the moving window . The moving window passes over every cell in the raster . As it passes each central target cell , the nine values in the window are used to calculate a new value for that target cell . This new value is placed in the identical location in the output raster . If one wanted to examine a larger sphere of around the target cells , the moving window could be expanded to by , by , and so forth . Additionally , the moving window need not be a simple rectangle . Other shapes used to calculate neighborhood statistics include the annulus , wedge , and circle ( Figure Common Neighborhood Types around Target Cell ( a ) by , Circle , Annulus , Wedge ) URL books 195

Figure ( Neighborhood operations are commonly used for data simplification on raster . An analysis that averages neighborhood values would result in a smoothed output raster with dampened highs and lows as the of the outlying data values are reduced by the averaging process . Alternatively , neighborhood analyses can be used to exaggerate differences in a . Edge enhancement is a type of neighborhood analysis that examines the range of values in the moving window . A large range value would indicate that an edge occurs within the extent of the window , while a small range indicates the lack of an edge . Zonal Operations URL books 197

A zonal operation is employed on groups of cells of similar value or like features , not surprisingly called zones ( land parcels , units , types ) These zones could be as raster versions of . Zonal are often created by reclassifying an input raster into just a few categories ( see Section Neighborhood Operations ) Zonal operations may be applied to a single raster or two overlaying . Given a single input raster , zonal operations measure the geometry of each zone in the raster , such as area , perimeter , thickness , and centroid . Given two in a zonal operation , one input raster and one zonal raster , a zonal operation produces an output raster , which summarizes the cell values in the input raster for each zone in the zonal raster ( Figure Zonal Operation on a Raster ) Figure on ( Raster Input Raster Zonal Raster , Output Raster of Zonal Means Zonal operations and analyses are valuable in of study such as landscape ecology where the geometry and spatial arrangement of habitat patches can affect the type and number of URL books ) a 198

species that can reside in them . Similarly , zonal analyses can effectively quantify the narrow habitat corridors that are important for regional movement of , migratory animal species moving through otherwise densely areas . Global Operations Global operations are similar to zonal operations whereby the entire raster extent represents a single zone . Typical global operations include determining basic statistical values for the raster as a whole . For example , the minimum , maximum , average , range , and so forth can be quickly calculated over the entire extent of the input raster and subsequently be output to a raster in which every cell contains that calculated value ( Figure Global Operation on a Raster ) Figure Global ( on ( Raster Input Raster 456 41 364 326 243 448 364 276 21 359 325 268 234 I 64 306 296 201 33 44 274 231 84 65 , Output Raster of Global Mean URL books ?

199 KEY TAKEAWAYS Local raster operations examine only a single target cell during analysis . Neighborhood raster operations examine the relationship of a target cell proximal surrounding cells . Zonal raster operations examine groups of cells that occur within a uniform feature type . Global raster operations examine the entire areal extent of the . I . What are the four neighborhood shapes described in this chapter ?

Although not discussed here , can you think of specific situations for which each of these shapes could be used ?

URL books zoo Surface Analysis Spatial Interpolation LEARNING OBJECTIVE . The objective of this section is to become familiar with concepts and terms related to GIS surfaces , how to create them , and how they are used to answer specific spatial questions . A surface is a vector or raster that contains an attribute value for every locale throughout its extent . In a sense , all raster are surfaces , but not all vector are surfaces . Surfaces are commonly used in a geographic information system ( GIS ) to Visualize phenomena such as elevation , temperature , slope , aspect , rainfall , and more . In a GIS , surface analyses are usually carried out on either raster or TINs ( Triangular Irregular Network Chapter Data Management , Section Vector File Formats ) but or point arrays can also be used . Interpolation is used to estimate the value of a variable at an unsampled location from measurements made at nearby or neighboring locales . Spatial interpolation methods draw on the theoretical creed of law of geography , which states that everything is related to everything else , but near things are more related than distant Indeed , this basic tenet of positive spatial forms the backbone of many spatial analyses ( Figure Positive and Negative Spatial ) Figure Positive and Negative POSITIVE Pattern of Similarity NEGATIVE Pattern of Dissimilarity URL books 39 ?

201 Creating Surfaces The ability to create a surface is a valuable tool in a GIS . The creation of raster surfaces , however , often starts with the creation of a vector surface . One common method to create such a vector surface from point data is via the generation of ( or ) are mathematically generated areas that define the sphere of around each point in the relative to all other points ( Figure A Vector Surface Created Using ) Specifically , polygon boundaries are calculated as the perpendicular of the lines between each pair of neighboring points . The derived can then be used as crude vector surfaces that provide attribute information across the entire area of interest . A common example of is the creation of a rainfall surface from an array of rain gauge point locations . Employing some basic reclassification techniques , these can be easily converted to equivalent raster representations . Figure ( re ( Using While the creation of results in a polygon layer whereby each polygon , or raster zone , maintains a single value , interpolation is a potentially complex statistical technique that estimates the value of all unknown points between the known points . The three basic methods used to create surfaces are spline , inverse distance weighting ( and trend surface . The spline URL books 202

interpolation method forces a smoothed curve through the set of known input points to estimate the unknown , intervening values . interpolation estimates the values of unknown locations using the distance to proximal , known values . The weight placed on the value of each proximal value is in inverse proportion to its spatial distance from the target locale . Therefore , the farther the proximal point , the less weight it carries in defining the target point value . Finally , trend surface interpolation is the most complex method as it fits a multivariate statistical regression model to the known points , assigning a value to each unknown location based on that model . Other highly complex interpolation methods exist such as . is a complex technique , similar to , that employs to interpolate the values of an input point layer and is more akin to a regression analysis ( 1951 ) The specifics of the methodology will not be covered here as this is beyond the scope of this text . For more information on , consult review texts such as Stein ( 1999 ) Inversely , raster data can also be used to create vector surfaces . For instance , maps are made up of continuous , nonoverlapping lines that connect points of equal value . have specific depending on the type of information they model ( elevation contour lines , temperature , barometric pressure , wind speed ) Figure Contour Lines Derived from a DEM shows an elevation map . As the elevation values of this digital elevation model ( DEM ) range from 450 to 950 feet , the contour lines are placed at , 700 , and 900 feet elevations throughout the extent of the image . In this example , the contour interval , as the vertical distance between each contour line , is feet . The contour interval is determined by the user during the creating of the surface . URL books 203

Figure ) DEM KEY TAKEAWAYS Spatial interpolation is used to estimate those unknown values found between known data points . Spatial is positive when mapped features are clustered and is negative when mapped features are uniformly distributed . are a valuable tool for converting point arrays into polygon surfaces . EXERCISES . Give an example of five phenomena in the real world that exhibit positive spatial . Give an example of five phenomena in the real world that exhibit negative spatial . 1951 . A Statistical Approach to Some Mine Valuations Problems at the . Master thesis . University of . Stein , 1999 . Statistical Interpolation of Data Some Theories for . New York Springer . URL books 204

Surface Analysis Terrain Mapping LEARNING OBJECTIVE . The objective of this section is to learn to apply basic raster surface analyses to terrain mapping applications . Surface analysis is often referred to as terrain ( elevation ) analysis when information related to slope , aspect , hydrology , volume , and so forth are calculated on raster surfaces such as DEMs ( digital elevation models Chapter Data Management , Section Vector File Formats ) In addition , surface analysis techniques can also be applied to more esoteric mapping efforts such as probability of tornados or concentration of infant in a given region . In this section we discuss a few methods for creating surfaces and common surface analysis techniques related to terrain . Several common neighborhood analyses provide valuable insights into the surface properties of terrain . Slope maps ( part ( a ) of Figure ( a ) Slope , Aspect , and ( and ) Maps ) are excellent for analyzing and visualizing characteristics and are frequently used in conjunction with aspect maps ( later ) to assess watershed units , inventory forest resources , determine habitat suitability , estimate slope erosion potential , and so forth . They are typically created by a planar surface to a moving window around each target cell . When dividing the horizontal distance across the moving window ( which is determined via the spatial resolution of the raster image ) by the vertical distance within the window ( measure as the difference between the largest cell value and the central cell value ) the slope is relatively easily obtained . The output raster of slope values can be calculated as either percent slope or degree of slope . Any cell that exhibits a slope must , by , be oriented in a known direction . This orientation is referred to as aspect . Aspect maps ( part ( a ) Slope , Aspect , and ( and ) Maps ) use slope information to produce output raster images whereby the value of each cell denotes the direction it faces . This is usually coded as either one of the eight ordinal directions ( north , south , east , west , northwest , northeast , southwest , southeast ) or in degrees from ( nearly URL books 205

due north ) to ( back to due north ) Flat surfaces have no aspect and are given a value of . To calculate aspect , a moving window is used to the highest and lowest elevations around the target cell . If the highest cell value is located at the of the window ( top being due north ) and the lowest value is at the , it can be assumed that the aspect is southeast . The combination of slope and aspect information is of great value to researchers such as botanists and soil scientists because sunlight availability varies widely between and slopes . Indeed , the various light and moisture regimes resulting from aspect changes encourage vegetative and edaphic differences . A map ( part ( of Figure ( a ) Slope , Aspect , and ( and ) Maps ) represents the illumination of a surface from some hypothetical , light source ( presumably , the sun ) Indeed , the slope of a hill is relatively brightly lit when facing the sun and dark when facing away . Using the surface slope , aspect , angle of incoming light , and solar altitude as inputs , the process codes each cell in the output raster with an value ( increasing from black to white . As you can see in part ( of Figure ( a ) Slope , Aspect , and ( and ) Maps , representations are an effective way to visualize the dimensional nature of land elevations on a monitor or paper map . maps can also be used effectively as a baseline map when overlain with a semitransparent layer , such as a digital elevation model ( DEM part ( of Figure ( a ) Slope , Aspect , and ( and ) Maps ) URL books 205

Figure ( Slope . and ( Source Data available from US . Geological Survey , Earth Resources Observation and Science ( EROS ) Center , Sioux Falls , analysis is a valuable visualization technique that uses the elevation value of cells in a DEM or TIN ( Triangulated Irregular Network ) to determine those areas that can be seen from one or more location ( part ( a ) of Figure ( a ) and ( Watershed Maps ) The viewing URL books 207

location can be either a point or line layer and can be placed at any desired elevation . The output of the analysis is a binary raster that cells as either ( visible ) or ( not visible ) In the case of two viewing locations , the output raster values would be ( visible from both points ) visible from one point ) or ( not visible from either point ) Additional parameters the resultant map are the viewing azimuth ( horizontal or vertical ) and viewing radius . The horizontal viewing azimuth is the horizontal angle of the view area and is set to a default value of . The user may want to change this value to if , for example , the desired included only the area that could be seen from an window . Similarly , vertical viewing angle can be set from to . Finally , the viewing radius determines the distance from the viewing location that is to be included in the output This parameter is normally set to ( functionally , this includes all areas within the DEM or TIN under examination ) It may be decreased if , for instance , you only wanted to include the area within the 100 broadcast range of a radio station . Similarly , watershed analyses are a series of surface analysis techniques that the topographic divides that drain surface water for stream networks ( part ( of Figure ( a ) and ( Watershed Maps ) In geographic information systems ( a watershed analysis is based on input of a filled DEM . A DEM is one that contains no internal depressions ( such as would be seen in a pothole , sink wetland , or quarry ) From these inputs , a direction raster is created to model the direction of water movement across the surface . From the direction information , a accumulation raster calculates the number of cells that contribute to each cell . Generally speaking , cells with a high value of accumulation represent stream channels , while cells with low accumulation represent uplands . With this in mind , a network of stream segments is created . These stream networks are based on some minimum threshold of accumulation . For example , it may be decided that a cell needs at least one thousand contributing cells to be considered a stream segment . Altering this threshold value will change the density of the stream network . Following the creation of the stream network , a stream link raster is calculated whereby each stream segment ( line ) is connected to stream intersections ( nodes ) Finally , the direction and stream link raster are combined to determine the URL books 208

output watershed raster as seen in part ( of Figure ( a ) and ( Watershed Maps ( Chang 2008 ) Such analyses are invaluable for watershed management and hydrologic modeling . Figure ( a ) and ( Maps . Source Data available from Geological Survey , Earth Resources Observation and Science ( EROS ) Center , Sioux Falls , KEY TAKEAWAY Nearest neighborhood functions are frequently used to on raster surfaces to create slope , aspect , and watershed maps . How are slope and aspect maps utilized in the creation of a map ?

If you were going to build a new home , how might you use a map to assist your effort ?

Chang , 2008 . Introduction to Geographic Information Systems . New York . URL books ) a 209