In this exercise we will explore the Spatial Decision Modeler (SDM) modeling environment. Spatial Decision Modeler is a graphical decision support tool that provides a graphical interface for developing decision models that can resolve complex resource allocation decisions. For this exercise we will develop a planning map for the metro west area of Massachusetts with the goal of allocating 3600 ha for additional protection and 3600 ha for residential development. Fundamentally, the development of a planning map is a multi-objective/multi-criteria decision problem. In this case, we would like to allocate land for two objectives. Each of these objectives requires a number of criteria. For example, to calculate the suitability for the protected area objective may require such factors as proximity to primary roads, proximity to urban areas, proximity to residential areas, etc.
The Spatial Decision Modeler uses the language and the logic developed around the TerrSet decision support tools, including the
development of factors and constraints with tools such as FUZZY and RECLASS, the combination of factors to produce suitability maps with the MCE tool (multi-criterion evaluation), and the combination of multiple objectives with the MOLA tool (multi-objective land allocation).
The SDM graphical interface is modeled after Macro Modeler. It will be useful to review the help and tutorial on Macro Modeler and decision support before modeling with SDM.
We have identified many data layers to address the competing objectives of protection and residential development.
The variables which influence the suitability for protected areas include:
1) Distance from Primary Roads 2) Distance from Secondary Roads 3) Distance from Tertiary Roads 4) Proximity to Protected Areas 5) Distance from Urban Areas 6) Distance from Residential Areas
The variables which influence the suitability for residential areas include:
1) Cost distance from Urban Area 2) Distance from Primary Roads
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3) Distance from Secondary Roads 4) Percent open water in view
5) Slopes
Notice that some variables can apply to both objectives. There is as well a Boolean constraint map, CONSTRAINT, with will constrain the result from existing urban areas, residential areas and water bodies.
Protected Area Objective
Our first step is to build the protected area model by adding all the variable files and the constraint file to the SDM workspace.
A
From the SDM menu or the toolbar, click Decision Variables and then Add variable. From the pick list, add the first variable, distance from primary roads, DIST_PRIMARY. Do this for the remaining 5 variables, DIST_SECONDARY, DIST_TERTIARY, DIST_URBAN, DIST_RESID, and PROX_PROTECTED.B
Next, add the constraint from the Decision Variable menu by selecting Add constraint. Add the file CONSTRAINT.Now that we have all the protected area input variables on the workspace, our next step is to convert these variables to factor maps using the FUZZY decision operator. The use of the FUZZY operator not only converts each variable to be on the same scale, but also allows the user to define what is suitable for a given variable. For example, we have a distance from primary roads variable. Should 10 km from a road be given the same preference during the aggregation process as 500 meters from the same road? The FUZZY operator allows us to define these variable preferences, or in the language of the FUZZY operator, its membership function. We will use the FUZZY module to convert the value in each variable map to a specific range with a specific membership so that they can be combined to create a suitability map using the MCE
procedure.
C
Insert a FUZZY operation into the modeling area, either from the Decision Operations menu or its associated icon on the toolbar.Since each variable has to be converted through a fuzzy operation, the number of FUZZY operators inserted has to equal to the number of variables. Not including the constraint variable, insert six FUZZY operators onto the workspace and place each next to a variable. Then link each variable with a FUZZY operator using the Connect link icon on the toolbar. The output of FUZZY operators will be factors, shown with default output filenames in the blue rectangle.
D
Finally, for each FUZZY output, change the output filename. Right-click on each output filename and replace the initial characters with the characters “fprot”, denoting the fuzzy result for protected land variables. The new names should be: FPROT_PRIMARY, FPROT_SECONDARY, FPROT_TERTIARY, FPROT_URBAN, FPROT_RESID, and FPROT_PROTECTED.E
Next we need to enter the fuzzy parameters for each variable in order to transform them into factors. Right-click on each FUZZY operator and set each according to the table below.Variable name Function shape Function type Control points
EXERCISE 2-13 SPATIAL DECISION MODLER (SDM) 167
FPROT_PRIMARY Monotonically Increasing Sigmoidal a: 500; b:5000 FPROT_SECONDARY Monotonically Increasing Sigmoidal a: 100; b:2000 FPROT_TERTIARY Monotonically Increasing Sigmoidal a: 0; b:1000 FPROT_PROTECTED Monotonically Decreasing Sigmoidal c: 0; d:1000 FPROT_URBAN Monotonically Increasing Sigmoidal a: 500; b:5000 FPROT_RESID Monotonically Increasing Sigmoidal a: 0; b:1000
After defining the fuzzy parameters for each protected area variable, the next step is the MCE aggregation that will combine all the factors to create a protected area suitability map, our first objective. We will link each factor to one MCE operator to accomplish this task.
F
Add an MCE operation from the Decision Operations menu. Then, using the Connect option, link each factor to the MCE operation. Also link the constraint file, CONSTRAINT, to the MCE operation.G
Right-click on the MCE output filename and rename the output to OBJ_PROT.H
Since MCE is a weighted linear combination, we next need to set the weights that will be applied to each factor during the MCE aggregation operation. Right-click the MCE operator and set the aggregation operation as medium decision risk / no tradeoff.Then, for each factor set the weight listed below.
Factor name Weights
DIST_PRIMARY 0.4085
DIST_SECONDARY 0.1158
DIST_TERTIARY 0.0610
PROX_PROTECTED 0.0243
DIST_URBAN 0.2550
DIST_RESID 0.1355
I
Save the model, use the name TUTOR_SDM. If you want, you can run the model at this point to check if all the parameters are set correctly. Click the Run menu item or the Run icon on the toolbar.Residential Objective
We have now completed the first half of the analysis, deriving the protected area objective. Since our problem is a multi-objetive problem with competing objectives, the next phase is to add the residential land allocation portion of the model to our SDM workspace.
EXERCISE 2-13 SPATIAL DECISION MODLER (SDM) 168
J
From the SDM menu or the toolbar, click Decision Variables and then Add variable. From the pick list, add the first variable, cost distance from urban areas, COSTDIST_URBAN. Add the remaining 4 variables: DIST_PRIMARY, DIST_SECONDARY, OPEN_WATER_VIEW, and SLOPE.K
Next, add the constraint from the Decision Variable menu by selecting Add constraint. Add the file CONSTRAINT. This step is optional; you could use the existing constraint file already on the workspace.As we did previously, we need to develop factor maps (suitability maps) based on each variable using the FUZZY module.
L
Insert a FUZZY operation next to each of the five residential variables. Then link each variable with a FUZZY operator using the Connect link icon on the toolbar. The output of FUZZY operators will be factors, shown as a blue rectangle.M
Next, change the output name for each fuzzy output. Replace the initial characters and precede each with “fres”, denoting fuzzy for the residential land evaluation. The new names should be: FRES_PRIMARY, FRES_SECONDARY, FRES_URBAN,FRES_OPEN_WATER, and FRES_SLOPE.
N
Then, enter the fuzzy parameters for each variable in order to transform them into factors. Right-click each FUZZY operator and set each according to the table below.Variable name Function shape Function type Control points DIST_PRIMARY Monotonically Increasing Sigmoidal a: 0; b:1000 DIST_SECONDARY Monotonically Increasing Sigmoidal a: 0; b:500
COSTDIST_URBAN Symmetric Sigmoidal a: 2; b:5; c:10; d:20 OPEN_WATER_VIEW Monotonically Increasing Linear a:0; b:0.08
SLOPE Monotonically Decreasing Sigmoidal c:0; d:25
We can now link all the outputs from FUZZY to a new MCE operation that will calculate the residential objective.
O
Add an MCE operation into the workspace. Link each of the five residential factors to this new MCE operation. And also link the constraint file, CONSTRAINT, to the MCE operation.P
Rename the MCE operator output file for residential land allocation to be OBJ_RES.Q
Next, set the weights for each factor to be applied during the MCE operation. Right-click the MCE operator for residential land allocation and set the aggregation operation as medium decision risk / no tradeoff. Then, for each factor set the weight as listed below.Factor name Weights
FRES_URBAN 0.0811
EXERCISE 2-13 SPATIAL DECISION MODLER (SDM) 169
FRES_PRIMARY 0.2900
FRES_SECONDARY 0.1628
FRES_SLOPE 0.4340
FRES_OPEN_WATER 0.0321
Multi-objective Land Allocation - Competing Objectives
Now that we have defined our two objectives as defined by the two suitability images created by MCE, protected areas and residential lands, we will use the MOLA operation to allocate land for these two competing objectives.
R
Add the MOLA operation into the SDM workspace from the Decision Operations menu. Then link the two result images from the MCE operations to the MOLA operator. Also, link the constraint file, CONSTRAINT, to the MOLA operator. Although the constraint map was taken into account during the MCE operations, it can be included in the MOLA step to speed up the allocation calculation.S
Right-click the MOLA operator to set its parameters. Select to use area requirement. The grid should show two records, our two objectives. Leave the objective weight for each at 1 (equal weight). Then set the area requirement for both objectives at 40000.(40,000 is in the number of cells, which given the 30 meter resolution of the data, is equivalent to 3600 ha.) Deselect both of the force options for contiguity and compactness for now.
T
Right-click on the output filename for MOLA, enter MOLA as the new filename.U
Save the model and click Run from the menu.V
When the model finishes MOLA image will be autodisplayed. Also display the two MCE output images, OBJ_PROT and OBJ_RES.1
Viewing the two MCE results, for each, which factors seem to dominate in the determination of the suitabilities?2
Viewing the MOLA output, notice how the allocation of pixels are scattered throughout the study area. What do you suppose accounts for the residential allocation to be less contiguous than the protected area allocation?Suppose one would like to use the allocation for residential area to start a housing construction project. A final allocation that has one or several contiguous areas would be more ideal. We will now take into account contiguity.
W
Right-click on the MOLA operator and select the force contiguous allocation option. Close the parameter dialog by clicking OK, then rename the MOLA output to MOLA_CONTIG. Run the model again.EXERCISE 2-13 SPATIAL DECISION MODLER (SDM) 170
This time the results are two contiguous regions, one for residential and for protected area.
Now suppose we want to find the best three parcels for residential development. We can do this as a single objective problem by running MOLA with just one objective.
X
Disconnect the link between "OBJ_PROT" and MOLA operator. You can do this by selecting the link. Once it is highlighted you can select delete. This leaves only the residential objective.Y
Now right-click the MOLA operator so set parameters. Notice how the parameters dialog is very different now that we have only one objective. Select to force contiguous allocations and set the number of clusters to 3. Next, select areal requirement and enter a value of 40000. Then close the parameters dialog.Z
Rename the MOLA output to MOLA_CLUSTER. Run the model again.Multi-objective Land Allocation - Complementary Objectives
The case above is an example where you have two objectives that conflict with each other, which means one pixel can only be allocated to meet one single objective. What if you have two complementary objectives? For example one may want to allocate land for protected areas, but also want to maximize the total water maintained by those parcels. One pixel can serve both objectives at the same time. The following example demonstrates such a case.
EXERCISE 2-13 SPATIAL DECISION MODLER (SDM) 171
AA
Using the same model in the previous example, we will delete everything related to the residential land allocation, including all the FUZZY, MCE and MOLA operators and their inputs and outputs. What remains are the FUZZY operators for creating factors related to protected land allocation and the MCE operator for creating the corresponding suitability map.BB
Add another variable, WATER_YIELD and connect this new variable to a new FUZZY operator. Change the output name to FWATER_YIELD. Right-click the FUZZY operator and set the water yield parameters below:Variable name Function shape Function type Control points WATER_YIELD Monotonically Increasing Sigmoidal a: 0; b:1000