The raster data model is widely used in applications ranging far beyond geographic information systems (GIS). Most likely, you are already very familiar with this data model if you have any experience with digital photographs. The ubiquitous JPEG, BMP, and TIFF file formats (among others) are based on the raster data model. Take a moment to view your favorite digital image. If you zoom deeply into the image, you will notice that it is composed of an array of tiny square pixels (or picture elements). Each of these uniquely colored pixels, when viewed as a whole, combines to form a coherent image.
Furthermore, all liquid crystal display (LCD) computer monitors are based on raster technology as they are composed of a set number of rows and columns of pixels. Notably, the foundation of this technology predates computers and digital cameras by nearly a century. The neo-impressionist artist, Georges Seurat, developed a painting technique referred to as “pointillism” in the 1880s, which similarly relies on the amassing of small, monochromatic “dots” of ink that combine to form a larger image. If you are as generous as the author, you may indeed think of your raster dataset creations as sublime works of art.
The raster data model consists of rows and columns of equally sized pixels interconnected to form a planar surface. These pixels are used as building blocks for creating points, lines, areas, networks, and surfaces. Although pixels may be triangles, hexagons, or even octagons, square pixels represent the simplest geometric form with which to work. Accordingly, the vast majority of available raster GIS data are built on the square pixel. These squares are typically reformed into rectangles of various dimensions if the data model is transformed from one projection to another (e.g., from State Plane coordinates to UTM [Universal Transverse Mercator] coordinates).
Because of the reliance on a uniform series of square pixels, the raster data model is referred to as a grid-based system. Typically, a single data value will be assigned to each grid locale. Each cell in a raster carries a single value, which represents the characteristic of the spatial phenomenon at a location denoted by its row and column. The data type for that cell value can be either integer or floating-point. Alternatively, the raster graphic can reference a database management system wherein open-ended attribute tables can be used to associate multiple data values to each pixel. The advance of computer technology has made this second methodology increasingly feasible as computer storage issues no longer constrain large datasets as they were previously.
The raster model will average all values within a given pixel to yield a single value. Therefore, the more area covered per pixel, the less accurate the associated data values. The area covered by each pixel determines the spatial resolution of the raster model from which it is derived. Specifically, resolution is determined by measuring one side of the square pixel. A raster model with pixels representing 10×10 meters (or 100 square meters) in the real world has a spatial resolution of 10 meters. A raster model with pixels measuring 1×1 kilometer (1 square kilometer) in the real world would be said to have a spatial resolution of 1 kilometer. Care must be taken when determining the resolution of a raster because using an overly coarse pixel resolution will cause a loss of information, whereas using overly fine pixel resolution will result in significant increases in file size and computer processing requirements during display and/or analysis. An effective pixel resolution will take both the map scale and the minimum mapping unit of the other GIS data into consideration. In the case of raster graphics with coarse spatial resolution, the data values associated with specific locations are not necessarily explicit in the raster data model. For example, if the location of telephone poles was mapped on a coarse raster graphic, it would be clear that the pole would not fill the entire cell. Instead, the pole would be assumed to be located somewhere within that cell (typically at the center).
Imagery employing the raster data model must exhibit several properties. First, each pixel must hold at least one value, even if that data value is zero. Furthermore, if no data are present for a given pixel, a data value placeholder must be assigned to this grid cell. Often, an arbitrary, readily identifiable value (e.g., −9999) will be assigned to pixels for which there is no data value. Second, a cell can hold any alphanumeric index that represents an attribute. In the case of quantitative datasets, attribute assignation is relatively straightforward. For example, if a raster image denotes elevation, the data values for each pixel would be some indication of elevation, usually in feet or meters. In the case of qualitative datasets, data values are indices that necessarily refer to some predetermined translational rule. In the case of a land-use/land-cover raster graphic, the following rule may be applied: 1 = grassland, 2 = agricultural, 3 = disturbed, and so forth (Figure 4.4 “Land-Use/Land-Cover Raster Image”). The third property of the raster data model is that points and lines “move” to the center of the cell. As one might expect, if a 1 km resolution raster image contains a river or stream, the location of the actual waterway within the “river” pixel will be unclear. Therefore, there is a general assumption that all zero-dimensional (point) and one-dimensional (line) features will be located toward the center of the cell. As a corollary, the minimum width for any line feature must necessarily be one cell regardless of the actual width of the feature. If it is not, the feature will not be represented in the image and will, therefore, be assumed to be absent.
Several methods exist for encoding raster data from scratch. Three of these models are as follows:
- Cell-by-cell raster encoding. This minimally intensive method encodes a raster by creating records for each cell value by row and column. This method could be thought of as a large spreadsheet wherein each cell of the spreadsheet represents a pixel in the raster image. This method is also referred to as “exhaustive enumeration.”
- Run-length raster encoding. This method encodes cell values in runs of similarly valued pixels and can result in a highly compressed image file. The run-length encoding method is useful in situations where large groups of neighboring pixels have similar values (e.g., discrete datasets such as land use/land cover or habitat suitability) and is less useful where neighboring pixel values vary widely (e.g., continuous datasets such as elevation or sea-surface temperatures).
- Quad-tree raster encoding. This method divides a raster into a hierarchy of quadrants that are subdivided based on similarly valued pixels. The division of the raster stops when a quadrant is made entirely from cells of the same value. A quadrant that cannot be subdivided is called a “leaf node.”
Basic Geoprocessing with Rasters
Like the geoprocessing tools available for use on vector datasets, 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 geoprocessing techniques covered here include both single layer and multiple-layer operations.
Reclassifying, or recoding, a dataset is commonly one of the first steps undertaken during raster analysis. Reclassification is the single layer process of assigning a new class or range value to all pixels in the dataset based on their original values (Figure 8.1 “Raster Reclassification.” For example, an elevation grid commonly contains a different value for nearly every cell within its extent. These values could be simplified by aggregating each pixel value in a few discrete classes (i.e., 0–100 = “1,” 101–200 = “2,” 201–300 = “3,” etc.). This simplification allows for fewer unique values and cheaper storage requirements. Besides, these reclassified layers are often used as inputs in secondary analyses, such as those discussed later in this section.
Buffering is the process of creating an output dataset that contains a zone (or zones) of a specified width around an input feature. In the case of raster datasets, these input features are given as a grid cell or a group of grid cells containing a uniform value (e.g., buffer all cells whose value = 1). Buffers are particularly suited for determining the area of influence around features of interest. Whereas buffering vector data results in a precise area of influence at a specified distance from the target feature, raster buffers tend to be approximations representing those cells that are within the specified distance range of the target. Most geographic information systems calculate raster buffers by creating a grid of distance values from the center of the target cell(s) to the center of the neighboring cells and then reclassifying those distances such that a “1” represents those cells composing the original target, a “2” represents those cells within the user-defined buffer area, and a “0” 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 “3,” “4,” “5,” and so forth, to represent concentric distances around the target cell(s).
A raster dataset can also be clipped similar to a vector dataset (Figure 8.3 “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.
Raster overlays are relatively simple compared to their vector counterparts and require much less computational power. Despite their simplicity, it is vital to ensure that all overlain rasters are coregistered (i.e., spatially aligned), cover identical areas, and maintain equal resolution (i.e., cell size). If these assumptions are violated, the analysis will either fail, or the resulting output layer will be flawed. With this in mind, there are several different methodologies for performing a raster overlay.
The mathematical raster overlay is the most common overlay method. The numbers within the aligned cells of the input grids can undergo any user-specified mathematical transformation. Following the calculation, an output raster is produced that contains a new value for each cell (Figure 8.4 “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 risk/reward.
The Boolean raster overlay method represents a second powerful technique. The Boolean connectors AND, OR, and XOR can be employed to combine the information of two overlying input raster datasets into a single output raster. Similarly, the relational raster overlay method utilizes relational operators (<, <=, =, <>, >, and =>) to evaluate conditions of the input raster datasets. In both the Boolean and relational overlay methods, cells that meet the evaluation criteria are typically coded in the output raster layer with a 1. At the same time, those evaluated as false receive a value of 0.
The simplicity of this methodology, however, can also lead to easily overlooked errors in interpretation if the overlay is not appropriately designed. Assume that a natural resource manager has two input raster datasets she plans to overlay; one showing the location of trees (“0” = no tree; “1” = tree) and one showing the location of urban areas (“0” = not urban; “1” = urban). If she hopes to find the location of trees in urban areas, a simple mathematical sum of these datasets will yield a “2” in all pixels containing a tree in an urban area similarly. If she hopes to find the location of all treeless (or “non-tree,” nonurban areas), she can examine the summed output raster for all “0” entries. Finally, if she hopes to locate urban, treeless areas, she will look for all cells containing a “1.” Unfortunately, the cell value “1” 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.
Scale of Analysis
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 is presented here in this section.
Local operations can be performed on single or multiple rasters. When used on a single raster, a local operation usually takes the form of applying some mathematical transformation to each 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 * 0.3048 = new elevation in meters) of each cell value can be performed locally to accomplish this task.
When applied to multiple rasters, it becomes possible to perform such analyses as changes over time. Given two rasters 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 8.5 “Local Operation on a Raster Dataset”). These local analyses can become somewhat more complicated; however, as the number of input rasters increases. For example, the Universal Soil Loss Equation (USLE) applies a local mathematical formula to several overlying rasters, including rainfall intensity, erodibility of the soil, slope, cultivation type, and vegetation type to determine the average soil loss (in tons) in a grid cell.
Tobler’s first law of geography states that “everything is related to everything else, but near things are more related than distant things.” 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 datasets as well as on raster datasets. In the case of vector datasets, neighborhood analysis is most frequently used to perform basic searches. For example, given a point dataset containing the location of convenience stores, a GIS could be employed to determine the number of stores within 5 miles of a linear feature (i.e., Interstate 10 in California).
Neighborhood analyses are often more sophisticated when used with raster datasets. Raster analyses employ moving windows, also called filters or kernels, to calculate new cell values for every location throughout the raster layer’s 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, 3-by-3 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 8.6 “Common Neighborhood Types around Target Cell “x”: (a) 3 by 3, (b) Circle, (c) Annulus, (d) Wedge”). The target cell is that cell found in the center of the 3-by-3 moving window. The moving window passes over every cell in the raster. As it passes each central target cell, the nine values in the 3-by-3 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 influence around the target cells, the moving window could be expanded to 5 by 5, 7 by 7. Additionally, the moving window need not be a simple rectangle. Other shapes used to calculate neighborhood statistics include the annulus, wedge, and circle (Figure 8.6 “Common Neighborhood Types around Target Cell “x”: (a) 3 by 3, (b) Circle, (c) Annulus, (d) Wedge”).
Neighborhood operations are commonly used for data simplification on raster datasets. An analysis that averages neighborhood values would result in a smoothed output raster with dampened highs and lows as the influence of the outlying data values are reduced by the averaging process. Alternatively, neighborhood analyses can be used to exaggerate differences in a dataset. Edge enhancement is a type of neighborhood analysis that examines the range of values in the moving window. A significant range value would indicate that an edge occurs within the extent of the window, while a small range indicates the lack of an edge.
A zonal operation is employed on groups of cells of similar value or like features, not surprisingly called zones (e.g., land parcels, political/municipal units, water bodies, soil/vegetation types). These zones could be conceptualized as raster versions of polygons. Zonal rasters are often created by reclassifying an input raster into just a few categories (see Section 8.2.2 “Neighborhood Operations”). Zonal operations may be applied to a single raster or two overlaying rasters. 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 rasters 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 8.7 “Zonal Operation on a Raster Dataset”).
Zonal operations and analyses are valuable in fields of study such as landscape ecology where the geometry and spatial arrangement of habitat patches can significantly affect the type and number of species that can reside in them. Similarly, zonal analyses can effectively quantify the narrow habitat corridors that are important for the regional movement of flightless, migratory animal species moving through otherwise densely urbanized areas.
Global operations are similar to zonal operations, whereby the entire raster dataset’s extent represents a single zone. Typical global operations include determining fundamental statistical values for the raster as a whole. For example, the minimum, maximum, average, range 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 8.8 “Global Operation on a Raster Dataset”).
Surface Analysis: Spatial Interpolation
A surface is a vector or raster dataset that contains an attribute value for every locale throughout its extent. In a sense, all raster datasets are surfaces, but not all vector datasets 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 datasets or Triangular Irregular Networks (TINs), but isolines 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 Tobler’s first law of geography, which states that “everything is related to everything else, but near things are more related than distant things.” Indeed, this basic tenet of positive spatial autocorrelation forms the backbone of many spatial analyses (Figure 8.9 “Positive and Negative Spatial Autocorrelation”).
The ability to create a surface is a valuable tool in 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 Thiessen (or Voronoi) polygons. Thiessen polygons are mathematically generated areas that define the sphere of influence around each point in the dataset relative to all other points (Figure 8.10 “A Vector Surface Created Using Thiessen Polygons”). Specifically, polygon boundaries are calculated as the perpendicular bisectors of the lines between each pair of neighboring points. The derived Thiessen polygons can then be used as crude vector surfaces that provide attribute information across the entire area of interest. A typical example of Thiessen polygons is the creation of a rainfall surface from an array of rain gauge point locations. Employing some basic reclassification techniques, these Thiessen polygons can be easily converted to equivalent raster representations.
While the creation of Thiessen polygons 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 primary methods used to create interpolated surfaces are spline, inverse distance weighting (IDW), and trend surface. The spline interpolation method forces a smoothed curve through the set of known input points to estimate the unknown, intervening values. IDW 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’s value. Finally, trend surface interpolation is the most sophisticated 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 sophisticated interpolation methods exist, such as kriging. Kriging is a complex geostatistical technique, similar to IDW, that employs semivariograms to interpolate the values of an input point layer and is more akin to regression analysis.
Inversely, raster data can also be used to create vector surfaces. For instance, isoline maps are made up of continuous, nonoverlapping lines that connect points of equal value. Isolines have specific markers depending on the type of information they model (e.g., elevation = contour lines, temperature = isotherms, barometric pressure = isobars, wind speed = isotachs). As the elevation values of this digital elevation model (DEM) range from 450 to 950 feet, the contour lines are placed at 500, 600, 700, 800, and 900 feet elevations throughout the extent of the image. In this example, the contour interval, defined as the vertical distance between each contour line, is 100 feet. The user determines the contour interval during the creating of the surface.
Surface Analysis: Terrain Mapping
Surface analysis is often referred to as terrain (elevation) analysis when information related to slope, aspect, viewshed, hydrology, volume are calculated on raster surfaces such as DEMs (digital elevation models. In addition, surface analysis techniques can also be applied to more esoteric mapping efforts such as the probability of tornados or concentration of infant mortalities in a given region. In this section, we discuss a few methods for creating surfaces and common surface analysis techniques related to terrain datasets.
Several common raster-based neighborhood analyses provide valuable insights into the surface properties of the terrain. Slope maps (part (a) of Figure 8.12 “(a) Slope, (b) Aspect, and (c and d) Hillshade Maps”) are excellent for analyzing and visualizing landform characteristics. They are frequently used in conjunction with aspect maps (defined later) to assess watershed units, inventory forest resources, determine habitat suitability, estimate slope erosion potential. They are typically created by fitting a planar surface to a 3-by-3 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 definition, be oriented in a known direction. This orientation is referred to as an aspect. Aspect maps (part (b) of Figure 8.12 “(a) Slope, (b) Aspect, and (c and d) Hillshade 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 1° (nearly due north) to 360° (back to due north). Flat surfaces have no aspect and are given a value of −1. To calculate aspect, a 3-by-3 moving window is used to find the highest and lowest elevations around the target cell. If the highest cell value is located at the top-left of the window (“top” being due north) and the lowest value is at the bottom-right, 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 north-facing and south-facing slopes. Indeed, the various light and moisture regimes resulting from aspect changes encourage vegetative and edaphic differences.
A hillside map (part (c) of Figure 8.12 “(a) Slope, (b) Aspect, and (c and d) Hillshade Maps”) represents the illumination of a surface from some hypothetical, user-defined 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 hillshade process codes each cell in the output raster with an 8-bit value (0–255) increasing from black to white. As you can see in part (c) of Figure 8.12 “(a) Slope, (b) Aspect, and (c and d) Hillshade Maps,” hillshade representations are an effective way to visualize the three-dimensional nature of land elevations on a two-dimensional monitor or paper map. Hillshade maps can also be used effectively as a baseline map when overlaid with a semitransparent layer, such as a false-color digital elevation model (DEM; part (d) of Figure 8.12 “(a) Slope, (b) Aspect, and (c and d) Hillshade Maps”).
Viewshed 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 specific location(s) (part (a) of Figure 8.13 “(a) Viewshed and (b) Watershed Maps”). The viewing location can be either a point or line layer and can be placed at any desired elevation. The output of the viewshed analysis is a binary raster that classifies cells as either 1 (visible) or 0 (not visible). In the case of two viewing locations, the output raster values would be 2 (visible from both points), 1 (visible from one point), or 0 (not visible from either point).
Additional parameters influencing the resultant viewshed map are the viewing azimuth (horizontal and/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 360°. The user may want to change this value to 90° if, for example, the desired viewshed included only the area that could be seen from an office window. Similarly, vertical viewing angle can be set from 0° to 180°. Finally, the viewing radius determines the distance from the viewing location that is to be included in the output. This parameter is typically set to infinity (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 km broadcast range of a radio station.
/’/Similarly, watershed analyses are a series of surface analysis techniques that define the topographic divides that drain surface water for stream networks (part (b) of Figure 8.13 “(a) Viewshed and (b) Watershed Maps”). In geographic information systems (GISs), a watershed analysis is based on the input of a “filled” DEM. A filled DEM is one that contains no internal depressions (such as would be seen in a pothole, sink wetland, or quarry). From these inputs, a flow direction raster is created to model the direction of water movement across the surface. From the flow direction information, a flow accumulation raster calculates the number of cells that contribute flow to each cell. Generally speaking, cells with a high value of flow accumulation represent stream channels, while cells with low flow accumulation represent uplands. With this in mind, a network of rasterized stream segments is created. These stream networks are based on some user-defined minimum threshold of flow 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 topologically connected to stream intersections (nodes). Finally, the flow direction and stream link raster datasets are combined to determine the output watershed raster, as seen in part (b) of Figure 8.13 “(a) Viewshed and (b) Watershed Maps.” Such analyses are invaluable for watershed management and hydrologic modeling.
Advantages and Disadvantages of the Raster Model
The use of a raster data model confers many advantages. First, the technology required to create raster graphics is inexpensive and ubiquitous. Nearly everyone currently owns some sort of raster image generator, namely a digital camera, and few cellular phones are sold today that do not include such functionality. Similarly, a plethora of satellites are continually beaming up-to-the-minute raster graphics to scientific facilities across the globe. These graphics are often posted online for private and/or public use, occasionally at no cost to the user.
Additional advantages of raster graphics are the relative simplicity of the underlying data structure. Each grid location represented in the raster image correlates to a single value (or series of values if attributes tables are included). This simple data structure may also help explain why it is relatively easy to perform overlay analyses on raster data. This simplicity also lends itself to straightforward interpretation and maintenance of the graphics, relative to its vector counterpart.
Despite the advantages, there are also several disadvantages to using the raster data model. The first disadvantage is that raster files are typically very large. Particularly in the case of raster images built from the cell-by-cell encoding methodology, the sheer number of values stored for a given dataset result in potentially large files. Any raster file that covers a large area and has somewhat finely resolved pixels will quickly reach hundreds of megabytes in size or more. These large files are only getting more significant as the quantity and quality of raster datasets continue to keep pace with the quantity and quality of computer resources and raster data collectors (e.g., digital cameras, satellites).
A second disadvantage of the raster model is that the output images are less “pretty” than their vector counterparts. This is particularly noticeable when the raster images are enlarged or zoomed (refer to Figure 4.1 “Digital Picture with Zoomed Inset Showing Pixilation of Raster Image”). Depending on how far one zooms into a raster image, the details and coherence of that image will quickly be lost amid a pixilated sea of seemingly randomly colored grid cells.
The geometric transformations that arise during map reprojection efforts can cause problems for raster graphics and represent a third disadvantage to using the raster data model. Changing map projections will alter the size and shape of the original input layer and frequently result in the loss or addition of pixels. These alterations will result in the perfect square pixels of the input layer, taking on some alternate rhomboidal dimensions. However, the problem is more significant than a simple reformation of the square pixel. Indeed, the reprojection of a raster image dataset from one projection to another brings change to pixel values that may, in turn, significantly alter the output information.
The final disadvantage of using the raster data model is that it is not suitable for some types of spatial analyses. For example, difficulties arise when attempting to overlay and analyze multiple raster graphics produced at differing scales and pixel resolutions. Combining information from a raster image with a 10 m spatial resolution with a raster image with a 1 km spatial resolution will most likely produce nonsensical output information as the scales of analysis are far too disparate to result in meaningful and/or interpretable conclusions. Also, some network and spatial analyses (i.e., determining directionality or geocoding) can be problematic to perform on raster data.