Dasymetric Mapping [PDF]

relative magnitudes across the surface of the map. In contrast, the dasymetric method highlights areas of homogeneity an

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Dasymetric Mapping Some geographical distributions are best mapped as ‘volumes’ that represent surfaces characterized by plateaus of relative uniformity separated from one another by relatively steep slopes or escarpments where there is a marked change in statistical value. There are two techniques for defining this stepped surface, the choroplethic and the dasymetric. The choroplethic technique requires only grouping of similar values, and detail is constrained by the boundaries of enumeration units which rarely have to do with the variable being mapped. In choroplethic mapping, emphasis in the graphic statement is placed upon comparing relative magnitudes across the surface of the map. In contrast, the dasymetric method highlights areas of homogeneity and areas of sudden change and is produced by refining the values estimated by the choroplethic technique. Your task is to produce a dasymetric map of cropland in south central Ohio counties, using four variables to refine the enumerated data. Prepare this map and all related maps using ArcView GIS. It might be a good idea to keep a journal log while you are working through this exercise, annotated with hardcopy maps if you prefer, personal notes describing in your own words what the commands you performed in ArcView do, for later reference. Data for the initial distribution is given on the base map on page 4. Initial files for the assignment are in the Handouts folder in the usual Csiss folder on \\ubar\labs\. Copy the folder labeled dasy_ohio from the Handouts directory to your personal directory (for example to E:). Open the file dasy.apr in your directory with ArcView. When opening the project file you might be asked where certain missing files are. If so, select the files in your directory that have the same name as the missing ones, and click each time OK to continue. Once all the data is reassigned you should see an open view, labeled Cropland in Ohio 1959 with the five themes described below. Go to FILE: SET WORKING DIRECTORY... type in: your_local_directory:/your_personal _directory/dasy_ohio/ to set your working directory to your home directory and the lab folder you copied over. ArcView will produce a bunch of files and you want to make sure that are all stored in the lab directory. Make sure that any folder or file associated with this lab in your directory does not have any spacing in the label, nor Uppercase. Please Note: You might not be able to finish this lab in one sitting. So, don’t worry if you don’t. You can find the result maps at the end of this handout just in case.

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For much of the exercise, the following classes will be used: 0 10 30 50 70 90

– 9% coverage of cropland – 29% – 49% – 69% – 89% – 100%

On any maps you print out, include the following information: • an appropriate title • a legend • a scale • your name • data source and year Use partial spectral progressions to indicate the classes of your map and for all worksheet maps except for economic activity which should be mapped using a full spectral progression. We have briefly touched on this concept in lectures. Part spectral progressions are generated as linear transects across or through the color wheel; full spectral progressions are generated as arcs of full or partial circumference. Think about the layer you are mapping (e.g. coverage by woodland, coverage by urban areas, terrain configuration, and coverage by cropland) and apply a meaningful progression. The following materials are provided to help you complete this exercise. The files are scanned or digitized from 1:100,000 scale copies of 1:24,000 maps. The stated resolution (.60 km per cell) is meaningful, and should guide your decisions about how much detail to include or simplify. This handout A discussion of the dasymetric technique and the methods to employ, including step-by-step procedures for preparing a dasymetric map. Maps • choropleth % crop A base map displaying the percentage of total area classed as cropland for each county. The single figure for each county includes several classes of cropland: cropland harvested, cropland used only for pasture, cropland not harvested and not pastured, areas in grasses and legumes for soil improvement, and idle cropland (fallow) and crop failure. For each county, these values have been summed and the total divided by total county acreage to give the percentage. The remaining area in each county consists of urban and rural non-agricultural landuses, woodland (pastured and non pastured), and non urban built-up land (e.g. farmsteads). Data are derived from the 1959 Census of Agriculture. The county names are included in the theme’s attribute table. In addition, there is a theme with county labels called county names. • towns A map of urban and rural non-agricultural land use areas. The areas outlined are occupied by residential, commercial, industrial, transportation, mining and similar land uses. Areas of many sizes have been shown, from the completely built-up city and metropolitan areas to crossroads settlements, hamlets, and galaxies of strip mines which dot the Ohio countryside. The

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areas are shown as close to scale as possible, but crude reproduction techniques do involve some exaggeration. These data are derived from 1:24,000 topographic sheets. Maps from the 1960 Census were used to outline the urban areas. • woodland A map showing the amount of woodland cover throughout the area in six classes. It was derived from the same topographic sheets and reflects a series of estimates based on USGS 7.5 minute quadrangles. • terrain A ‘surface configuration’ map shows in four classes the nature of the terrain. This map was generalized using the work of Guy-Harold Smith, “The Relative Relief of Ohio”, Geographical Review vol.25, p. 272-284, 1935. • economy A map of ‘economic regions’ outlines areas by agricultural economic type. This is based on work by Alfred J. Wright, “Types of Farming Areas”, Economic Geography of Ohio Columbus Division of the Geological Survey of Ohio, Bulletin #50, 1953, Figure 13. It is important to realize that the concern in this exercise is with the dasymetric procedure and not with cropland in Ohio. Since this exercise marks the first time that you are presented with this particular mapping technique (map overlay) the methods are set down in considerable detail. After gaining understanding of the nature of the technique from the following section, the simplest way to proceed is simply to follow the steps in the order of presentation. Once accomplished here, map overlay techniques as used in conventional geographical information systems or for spatial modeling should be more readily understood.

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The Dasymetric technique The dasymetric technique provides one solution to the problem of mapping data gathered on the basis of enumeration areas whose boundaries bear no direct relation to the variable being mapped. It is based on certain assumptions. Assumption 1 the variable being mapped occurs non-uniformly over the statistical unit area (in this case, counties). Assumption 2 even though wide overall variations exist for the distribution, it basically consists of areas of relative uniformity separated by sudden changes in value. Assumption 3 other variables may be collected in association with the variable in question whose relation to the variable may be determined and expressed as a set of rules. These variables will enable the cartographer to adjust and refine the given data to form homogeneous regions whose boundaries are independent of the enumeration unit boundaries. The variable in question for this exercise is cropland (density). The four other variables are urban and non agricultural land use, woodland area, terrain, and economic activity. These variables may be characterized as being either “limiting variables” or “related variables”. We will tackle the limiting variables first. The limiting variables In some degree limiting variables restrict the possible occurrence of cropland. That is, a certain percentage of a limiting variable occurring in an area will set an absolute upper limit on the percentage of the mapped variable (cropland) that can occur in the same area. Two limiting variables are being employed in this exercise – urban landuse and woodland. An area devoted to urban landuse precludes the occurrence of cropland. In a categorical fashion, this may be expressed by the following rule: if urban landuses are present, then there can be no cropland. If there are no urban landuses, then cropland can exist (see Figure 1). In terms of the six categories of cropland, note that the presence of urban land use restricts an area to cropland category 1, namely, 0% cropland. All six classes are possible where no urban land use occurs. 1 urban land use 0-9

cropland classes (%) 2 3 4 5 10-29 30-49 50-69 70-89

6 90-100

present not present cropland not possible Figure 1: the limiting variable urban landuse It is also possible to compute a precise adjusted percentage for the cropland density, using a formula first published by J.K. Wright. It is called the computation of fractional parts of densities. In the formula below, D stands for Density, A stands for Area: Dn =

Do − Dm Am 52 − (0 ∗ 0.1) 52 = = = 57.7 1 − Am 1 − 0.1 0.9

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Thus, for a county with 52% cropland, 10% of the county covered by urban landuse, the percentage of cropland in the remaining county area must be approximately 58%. TASK 1 Revise estimates of county cropland density using this formula and the layer of urbanized areas. The first step is to generalize this layer, and the second is to do the computations. Tools You will be working with ArcView’s Spatial Analyst, a raster-based GIS module. Open the view called Map Calculations by making the dasy.apr window active, selecting the view icon and double clicking on the label Map Calculations. We will store all the following calculations in this view. Step 1 – Generalizing the urbanized layer Look at the towns theme in the Cropland in Ohio 1959 view. Notice there are many regions that are only a pixel or a couple of pixels in size, at this level of resolution. To include these will generate an overly complex visual display, partially obscuring the dasymetric patterns. So before we begin to compute the fractional densities, you need to eliminate the smallest regions from this map, creating a new, generalized towns map. Here’s how to eliminate the regions. • • • • •

Select towns layer Go to Analysis: Neighborhood Statistics... Statistics: Sum Neighborhood: Rectangle 3x3 Cells

The result map has classes in somewhat concentric bands. You can generalize your towns map by deciding on which of the bands to keep and which ones to get rid of by setting them to No Data. Do this first graphically. Double click the theme’s legend and set the first couple of classes to white, and the remaining to any identical shade. Look at the generalization effect. Once you have decided how much to generalize create a new layer with the new classification. • • • • •

Go to Reclassify... Click into New Values Make the two classes Keep the No Data class and reassign No Data to the classes you want to get rid of Assign 1 to the remaining classes.

To rename the towns layer go to THEME: PROPERTIES and label the new towns layer new towns. Cut the theme from the Cropland in Ohio view and paste it into the Map Calculations view (in the EDIT menu, CUT & PASTE). You just created a map layer whose cells contain frequency counts of the number of non-“No Data” cells around each pixel. A 3x3 cell selection is the diagonal size (in pixels) of the square moving search window. Compare new towns to towns and you’ll see how much simplification you have effected. Write down in your journal log the exact parameter values you use.

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Step 2 – Computing fractional parts of densities. In any GIS, numerical analysis can be somewhat convoluted – ArcView is no different. The following steps will build up the various parts of J. K. Wright’s original formula given above. Spatial Analyst operators will be used to apply it as a whole to the choropleth map, and the result will be a new map layer of revised cropland density values. Here’s the tricky part – ArcView wants everything in integers (no percentages) to retain access to the attribute tables of raster layers (in ArcView lingo called GRIDS). We need to transform J. K. Wright’s original formula algebraically, to express it in terms GIS raster layers.

revised crop density =

revised crop density =

revised crop density =

original crop density - (0 ∗ urban area [%]) 1 - urban area [%] original crop density county area in pixels urban area in pixels − county area in pixels urban area in pixels original crop density ∗ county area in pixels nonurban area in pixels

First, you will compute a frequency count of how many cells are contained in each zone of your choropleth map (‘county areas in pixels’ in above revised formula). Make the Cropland in Ohio view active. Go to ANALYSIS: MAP CALCULATOR. To see the complete variable names in the left list, make the Map Calculator Window bigger by dragging its lower right corner towards the lower right. Double click on the [choropleth crop.Count] layer in the Layers List. Click on the evaluate button to compute a new layer. Rename the new theme called “Map Calculation 1” to county areas and cut/paste this map into the Map Calculations view. You just computed the variable ‘county areas in pixels’ from above formula). Before we can calculate the area devoted to urban landuse within each county we need to combine the urban layer with the county layer. Copy the choropleth % crop into the Map Calculations view. Select new towns and go to ANALYSIS: RECLASSIFY. The category with value No Data has to be reassigned to value 1 (one). The category with 1 is reassigned 0 (zero). Make both this reclassified towns map and choropleth % crop active by shift clicking on their names in the legend. Go to DASYMETRIC: COMBINE. This command is a script that I wrote in Avenue (ArcView’s programming language) that generates unique values for all existing combinations of values in the two input themes. The result is a new theme called “Combined X w/ Y”, where X and Y are the input theme names. Label the new theme choropleth w/urban. You can explore all the scripts used for this lab by making the ohio.apr window active, selecting the script icon from the list and double clicking on any of the labels. Next, we need the denominator of above formula, the nonurban area. We will compute this in several steps. First, we computes a frequency count of urban landuse pixels within each county of the “choropleth % crop” map. So, go to ANALYSIS: MAP CALCULATOR again, and double click on the [choropleth w/urban.Count] layer in the Layers List. Click on the evaluate button to compute a new layer. Rename the new theme called “Map Calculation 1” to area of choro w/urban and cut/paste this map into the Map Calculations view. Ok, now we need to cookie

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cut the urban areas out of this map to get the remaining area that is not devoted to urban landuse. The new towns theme is our cookie cutter mask. To do this we need to reclassify the towns layer first. Select new towns and go to ANALYSIS: RECLASSIFY. The category with value 1 (urban) needs to be reclassified to No Data, and category No Data is reassigned value 1 (one). Next, make the reclassed of new towns (cookie cutter) and the area of choro w/urban themes active (shift click) and go to DASYMETRIC: COVER. Rename the result theme nonurban area. Inspecting again above formula you have now computed the denominator of J.K. Wright’s formula, sort of (e.g. ‘nonurban area in pixels’). This map contains the number of pixels within each county that that IS NOT devoted to urban uses. Meaning, the theme nonurban area gives you the area of each county that could be devoted to cropland. So, now we have got all those things we need for above formula, the original crop density (choropleth % crop), the county areas, and the nonurban areas. The original choropleth map takes a bit of manual reclassifying, modify the choropleth % crop theme in the Map Calculations view and change each class value to correspond with the actual cropland density value. Since only integers are acceptable, you can multiply by 10, thus class 1 becomes 111. Class 2 becomes 124. Put a note into the journal – you will have to reclassify other map layers accordingly. You can round the values if you wish. Make the choropleth % crop theme in the Map Calculations view active, go to ANALYSIS: RECLASSIFY and reclassify each class accordingly. Okay (phew!), now we can compute the fractional parts of densities. Compute below formula with the Map Calculator: ([Reclass of choropleth % crop] * [county area]) / [nonurban area]) Label the new theme choropleth w/urban limits, put a hardcopy into the journal. Remember, the values that you see in this map have to be divided by 10 or 100 to reflect the reclassification you performed earlier. Therefore a value of 921 is 92,1 percent (if a reclassification factor of 10 was used). Now compare this map to the original choropleth % crop. Which counties have drastically revised cropland values? Why do you think it is so, for each drastically changed county? Include a hard copy of this map in the journal file, annotate the changed counties and write a note on the map telling why (presence of big city, presence of lots of mines, etc.). To summarize the previous steps: we have taken an initial pass at revising the choropleth estimates with a first limiting variable ‘urban areas’. The choropleth w/urban limits theme is the map layer to use for all remaining tasks involving crop density overlays. TASK 2 – second limiting variable woodland The second limiting variable we will introduce into our dasymetric model is percentage area in woodland. Adding its six categories (0-9%, 10-29%, etc.) to the above classification system expands the number of potential categories from 12 to 72, as shown in Figure 2. 1 urban land use woodland 0-9 1 0-9 2 10-29 3 30-49 present 4 50-69

cropland classes (%) 2 3 4 5 10-29 30-49 50-69 70-89

6 90-100

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not present

5 6 1 2 3 4 5 6

70-89 90-100 0-9 10-29 30-49 50-69 70-89 90-100

cropland not possible Figure 2: the limiting variable woodland But where urban types are used, we are restricted to class 1 (from Figure 1, this follows directly). Thus 30 of the 72 categories are immediately eliminated (shown by the gray shading in the diagram). The addition of woodland will eliminate more, according to the following rule. Given a certain percentage of woodland in an area, only the balance of the area may be in cropland. Thus if 35% of an area is in woodland, then the highest possible value of cropland which can exist anywhere else in the county is 65%. Notice that some portions could have as much as 95% cropland, if these were offset by other portions of lesser percentage cropland, to the extent that the sum of all cropland percentages in the county as a whole average out to the enumerated total. So as shown in Figure 2, if an area is 90% woodland, then only 10% of that area may be in cropland. If it is 70 -89%, then only classes (1) or (2) are possible, etc. Through this direct process of limiting variables, we can eliminate 15 more categories for the map. This could be accomplished using J.K. Wright’s formula, above, and repeating the process in turn for each of the six woodland classes, subsequently covering each class with the others. This would in the end provide 28 revised values for each county’s cropland density. However, let’s be realistic about time and do it in classed fashion. This way we will get a prediction in six classes, and then approximate the unclassed solution by map overlay. Make a duplicate of the woodland theme in the Cropland in Ohio 1959 view and paste it into the Map Calculations view. Reclassify this theme. If you multiplied earlier by 10, your new class labels should be 99, 299, 499, etc. Next, click on the legend text to invert ranges from woodland to cropland, as follows: class 36 is assigned class class 35 is assigned class class 34 is assigned class class 33 is assigned class class 32 is assigned class class 31 is assigned class

99 299 499 699 899 999

new new new new new new

legend legend legend legend legend legend

text text text text text text

should should should should should should

read: read: read: read: read: read:

0 - 9 % crop 10 - 29 % crop 30 - 49 % crop 50 - 69 % crop 70 - 89 % crop 90 -100 % crop

Rename this theme Reclass of woodland % crop and change the legend text in this theme to match the above classes. Use the Legend Editor and fill in the label field accordingly. Now overlay to produce the limiting variables map, and then overlay that on the unclassed choropleth to make your first refined estimate of cropland densities. The second formula approximates what Wright’s density formula would have produced by taking the minimum value cell-by-cell throughout the map matrices. Here is how: Use the Map Calculator and type in

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([Reclass of new towns] * [Reclass of woodland % crop]) Rename the result limiting variables. Now select both, limiting variables and choropleth w/urban limits in your Map Calculations view by shift clicking on the theme names. Go to ANALYSIS: CELL STATISTICS… and choose MINIMUM from the drop down list. Rename the result choropleth w/ limits. Clean up the legend and color scheme. Put hardcopies into the journal file, annotating with notes about what patterns you see. Put a statement in the journal file comparing choropleth w/ limits with choropleth w/urban limits, and with choropleth % crop (original choropleth map). TASK 3 – Related variables Related variables may be associated with the variable being mapped in complex ways. In this case the related variables are the terrain and the economy map layers. Figure 4 shows the cropland classes (99, 299, 499, etc.) associated with each combination of the related variables’ classes. terrain 21 steep 44 hilly 43 rolling 42 level 44

22

23

economy 24 25 26

27

28

29

cropland classes 699 99 299 899 499 999 21 22 23 24 25

Truck Farming (w/ dairy & poultry) Truck Farming (w/ mixed or cash grain farming) Cash-grain Farming (w/ some livestock) Mixed Farming (primarily cash crops) Mixed Farming

26 27 28 29

Dairy Farming (w/ large areas in crops) General Farming Dairy Farming (w/ little cropland) Livestock Ranching

Figure 3: cropland classes for related variables Accomplishing this step is quite similar to the woodland task. There are two ways to do it. The first is to overlay the two layers with the COMBINE command and then manually reclassifying a bunch of classes. This is pretty inefficient, will take a long time and probably result in numerous mistakes. The easier way is to use the CROSS command in the DASYMETRIC menu. CROSS is a script that combines two map layers (terrain & economy) and automatically reclassifies the output theme based on conditions shown in Figure 4. Make the Cropland Ohio view active. Select CROSS and a new theme will be added to the view called related variables. Put a hardcopy in your journal. Cut/Paste this theme into the Map Calculations view. Compare this with the choropleth w/ limits in your journal notes. Notice that neither the limiting variables nor the related variables map should display county boundaries – this is because neither have been derived from county-based enumeration, and therefore including the boundaries might mislead the map reader about data sources. As you combine these maps with the original choropleth data (e.g., with choropleth w/urban limits), the boundaries will be

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incorporated automatically. Think about why that distinction might be important for decision making, in your journal. Step 2 – Dasymetric model With the related variables and the limiting variables layers you have made so far, you can predict what the dasymetric map should look like, in the absence of any choropleth data. The procedure assumes that the related variables map layer is a good basic estimator of variations in cropland density that actually existed in 1959. The cartographer feels confident that if surface topography and economic activity were the only data available, then the “related variables” map would by itself yield a pretty good approximation of the spatial distribution of cropland. The purpose served by the limiting variables is to limit the estimates at any place. The general rule is that the related variables estimate is valid except where the limiting variables (i.e., maximum possible cropland) are lower than the estimate. Figure 5 illustrates the principle. If the predicted class in the related variables map layer is category 5 (that is, 70 - 89% cropland) but there is an upper limit of category 2 (that is, 10 - 29% cropland) for this area, then this area is limited to class 2. However, if the limited variables map layer shows an upper limit of category 6, as in the right half of the limits map in the Figure, then the predicted cropland class (class 4) is accepted as valid for the area. 5

2

6

limiting

+

4

related

5

=

2

4

dasymetric

Figure 4: dasymetric overlay principle Statistically speaking, your dasymetric solution displays the more conservative of the two estimates for percentage cropland. This is the estimate of cropland based solely on limiting and related variables. Select both, limiting variables and related variables in your Map Calculations view by shift clicking on the theme names. Go to ANALYSIS: CELL STATISTICS… and select MINIMUM from the drop down list. Rename the result dasymetric model. Color code, label legend appropriately, and put a hardcopy into the journal file. Dasymetric map It is also possible to refine the original choropleth data, to see the dasymetric pattern. This is the estimate of cropland based on related and limiting variables, AND incorporating the original choropleth data. Repeat the MINIMUM function, this time by selecting related variables and choropleth w/ limits in your Map Calculations view. Rename the new map dasymetric map. Color code, label legend appropriately, and put a hardcopy into the journal file. Once you have the symbology in comparable visual form, compare the dasymetric model and the dasymetric map with each other, and with the original choropleth map (choropleth % crop). What differences do you see – where are the high and low regions, where is the pattern uniform, non-

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uniform, etc.? To compare your result maps with the ‘correct’ ones, you can have a peek at the maps attached at the end of this handout. Things to consider when looking at the result maps... How would you appropriately color your maps? Did your final displays turn out as you intended? Think about this – the “choropleth % crop” and the “dasymetric model” are both predictive models of cropland density in Ohio in 1959. What is the difference between the two types of classification procedures (generalization), and the two resulting maps? Next, consider the “dasymetric map” which is a refinement of the original cropland density estimate. What do you gain by combining the original choropleth estimate with the dasymetric model? Now think in terms of the geography, what WAS the pattern of cropland in Ohio in 1959? How much of this pattern appears to be associated (or even determined by) the limiting and related variables? Is it uniform across the study area? Where does it vary, and why? Try to think about it as a geographer – elevate your mind. © Original by Dr. B.P. Buttenfield, ported to ArcView and modified by sara fabrikant, 2001.

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