Reminder Data Dictionary is due Thursday (Nov. 9th) Lecture 13B

Spatial Models & Modeling Ch. 13 Part 2 Lecture 13B

Types of Spatial Models Cartographic Models (Automated Mapping Analysis & Processing) Often applied to ranking areas in support of decision making. Nominal or ordinal output Uses processes such as overlay, buffers, reclassification etc. Simple Spatial Models –focus on applying mathematical relationships Subject of SIE 512 Output is often interval or ratio Spatio-Temporal Models (Process Models) Lecture 13B

An Example of a Simple Cartographic Model Lecture 13B

Multicriteria Evaluation Rankings – The assignment of relative values within a layer. Weighting – the assignment of different values to each layer. Lecture 13B

Weighted Overlay Boolean operators are appropriate when each factor is equally important. We can take relative importance into account by using weights. wi*pik where w is the weight assigned to each layer and p is 0 or 1 depending upon whether the factor was present or absent at a given location k. The weights should sum to 1. Lecture 13B

Weighted Overlay If each layer in the overlay operation itself consists of various types within the layer, then each type may have a different score according to its perceived importance within the layer. Score each type on a score of 0 to 9 for suitability, and assign a weight to each score. Lecture 13B

Assignment of Weights The weights may reflect the preferences of the decision maker. These may be based on some cost; money, time, etc. Another approach – Saaty’s Analytical Hierarchy Process (AHP) which builds a matrix of pairwise comparisons between the factors. Lecture 13B

The Analytical Hierarchy Process https://en.wikipedia.org/wiki/Analytic_hierarchy_process Lecture 13B

Suitability Analysis Using Spatial Analyst Lecture 13B

The Problem The Wildcat Boat Company is planning to construct a small testing facility and office building to evaluate new designs. They’ve narrowed the proposed site to a farming area near a large lake, and several small towns. The company now needs to select a specific site that meets the following requirements: The site should not have trees to reduce the cost of clearing the land. The town does not allow the conversion of farmland, and other land used (urban, barren and wetlands are also out. That leave brush land. The building must reside on soil suitable for construction. A local ordinance designed to prevent rampant development allows new construction only within 300 meters of existing sewer lines. Water quality legislation requires that no construction occur within 20 meters of streams. The site must be at least 4,000 sq. m in size to provide space for building and grounds. Lecture 13B

The original data are all vectors, but we can convert from vector to raster. Lecture 13B

Since we are working with rasters, we need the Spatial Analyst Extnsion. Lecture 13B

The Raster Environment The raster is a rectangle, and when you combine rasters, you want them to represent the same area, so we will set the output extent to and projection to one of the features. I’ll use the soils feature and round the values to the nearest tenth of a meter. They must also be the same cell size. Lecture 13B

Set the Cell Size to 10.0 Lecture 13B

Setting the General and Raster Environment Set the environment and scratch variables as usual, then set the Processing extent. Lecture 13B

Converting Features to Rasters SUIT is suitability: 0,1, 2 or 3. Where 0 indicates “no data”. NOTE: This is NOT stored in the Geodatabase. Lecture 13B

Geometry Lecture 13B

Attribute Tables Feature Class Raster Lecture 13B

Create another soils grid with a 5 m resolution. NOTE: The change in resolution produces a change in precision. Lecture 13B

Since this is a small dataset, we are going to increase the resolution to 2 m. The resolution has gone from 10 m to 2 m (5 fold), thus increasing storage 52, or 25 fold. Lecture 13B

Lecture 13B

Landcover Code Lecture 13B

Lecture 13B

Lecture 13B

Lecture 13B

The process was repeated with streams, using stream code as the field. Lecture 13B

And with roads, using road_code. Lecture 13B

It is difficult to create a good buffer with Spatial Analyst It is difficult to create a good buffer with Spatial Analyst. We will buffer the vector files and convert to rasters. Lecture 13B

Sewer_Buff as a raster Lecture 13B

The same was done with a 20 m buffer around the streams. Lecture 13B

Reclassifying the Data Lecture 13B

Change all values to 0 except 300 (brush). Lecture 13B

Soils: 0 & 1 are unsuitable, change to 0, 2 and 3 change to 1. Lecture 13B

Sewer_Buff becomes 1. Lecture 13B

Stream_Buff: Replace value with no data, and nodata becomes 1. Lecture 13B

Overlay using the Raster Calculator Lecture 13B

Results Lecture 13B

Adding Weights and Ranks to the Problem We could have decided that the 300 meter sewer restriction could be avoided by constructing a septic system, which would be more costly. We could favor the 300 m buffer by the cost factor, but the rest of the area would be acceptable. Instead of simply adding the layers in the raster calculator would could have weighed the layers differently: Sewer2+Stream2+(2*Landcover2)+(2.5*Soils2) Lecture 13B

Modeling Human Processes It is difficult to model humans spatial behavior. How do people move through space when constrained by roads, buildings, fences, etc.? How do people choose where to live, shop, vacation? Lecture 13B

Spatial Interaction Models An abstract, idealized, representation of any and all kinds of spatial interaction phenomenon. It is the flow of products, people, services, or information among places, in response to localized supply and demand. These models describe the flows between a set of origin and destination zones on a map. These are commercial models outside of most GIS packages. Lecture 13B

Three interdependent conditions are necessary for a spatial interaction to occur: Complementarity. There must be a supply and a demand between the interacting locations; e.g., a store and its customers. Intervening opportunity. There must not be another location that may offer a better alternative as a point of origin or as a point of destination. For instance, in order to have an interaction of a customer to a store, there must not be a closer store that offers a similar array of goods. Transferability. Freight, persons or information being transferred must be supported by transport infrastructures, implying that the origin and the destination must be linked. Three interdependent conditions are necessary for a spatial interaction to occur: Complementarity. There must be a supply and a demand between the interacting locations. A residential zone is complementary to an industrial zone because the first is supplying workers while the second is supplying jobs. The same can be said concerning the complementarity between a store and its customers and between an industry and its suppliers (movements of freight). Intervening opportunity. There must not be another location that may offer a better alternative as a point of origin or as a point of destination. For instance, in order to have an interaction of a customer to a store, there must not be a closer store that offers a similar array of goods. Transferability. Freight, persons or information being transferred must be supported by transport infrastructures, implying that the origin and the destination must be linked. Costs to overcome distance must not be higher than the benefits of related interaction, even if there is complementarity and no alternative opportunity. Lecture 13B

Lecture 13B

Inputs and Outputs Beta Deterrence Parameter Destination Totals Origin Totals Interzonal Costs Spatial Interaction Model (an equation) A common term for any parameter or parameter estimate used in an equation for predicting Y from X Supply and demand are important concepts for the spatial interaction model Distance between the supply and the demand operates as a friction – the greater the distance, the more effort required to get there. But it also depends on the type of activity. Predicted Trips Lecture 13B 44

Origin/Destination Matrix In the O/D matrix the sum of a row (Ti) represents the total outputs of a location (flows originating from), while the sum of a column (Tj) represents the total inputs (flows bound to) of a location. The summation of inputs is always equals to the summation of outputs. Otherwise, there are movements that are coming from or going to outside the considered system. The sum of inputs or outputs gives the total flows taking place within the system (T). It is also possible to have O/D matrices according to the age group, income, gender, etc. Under such circumstances they are labeled sub-matrices since they account for only a share of the total flows. Lecture 13B

The Relationship between Distance and Interaction The above figure portrays a classic non-linear relationship between distance and the level of interactions of location A with other locations (B, C and D). It assumes that each location has the same complementarity level and that no intervening opportunities are present. The closest location, B, has the highest level of interaction with location A, while locations C and D have lower levels of interaction since they are located further away. Lecture 13B

Three Basic Interaction Models The top part of the figure presents the general formulation of the spatial interaction model where Tij is the interaction between location i (origin) and location j (destination), Vi are the attributes of the location of origin i, Wj are the attributes of the location of destination j, and Sij are the attributes of separation between the location of origin i and the location of destination j. From this formulation, three basic types of interaction models can be elaborated: Lecture 13B

Three Basic Interaction Models 1. Gravity model. The level of interaction between two locations is measured by multiplying their attributes, which is then pondered by their level of separation. Separation is often squared to reflect the growing friction of distance. On the above figure, two locations (i and j) have a respective "weight" (importance) of 35 and 20 and are at a distance (degree of separation) of 8. The resulting interaction is 10.9, which is reciprocal. Lecture 13B

Three Basic Interaction Models 2. Potential model. The level of interaction between one location and all the others is measured by the summation of the attributes of each other location pondered by their level of separation (again squared to reflect the friction of distance). On the above figure, the potential interaction of location i (Ti) is measured by adding the ratio "weight" / squared distance for each other locations (j, k and l). The potential interaction is 3.8, which is not reciprocal. Lecture 13B

Three Basic Interaction Models 3. Retail model. This model deals with boundaries, instead of interactions. It assumes that the market boundary between two locations is a function of their separation pondered by the ratio of their respective weights. If two locations have the same importance, their market boundary would be halfway between. On the above figure, the market boundary between locations i and j (Bij) is at a distance of 4.9 from i (and consequently at a distance of 2.1 from j). Lecture 13B

Conventional Models Are: Over 25 years old. Reflect a data poor era. Non-linear but only in a simple way. Designed to minimize computation. Possibly poor performer. Lecture 13B

Neural Networks Make use of AI. Uses data to learn (or discover) patterns and relationships instead of relying totally on people to specify them. It offers equation free modeling. It is highly automated modeling. It has universal modeling capabilities It is noisy data resistant. Lecture 13B 52

Modeling the Decision Making Process Outputs from models are the raw information required for making decisions. Map overlay is the traditional method for spatial decision making, however this can be problematic: Overlay can be difficult to understand if multiple factors are involved. Some GIS packages do not allow different weights for the variables. Threshold values, important for polygon overlay, may be based on opinion. Lecture 13B

The Solution Use Multi-Criteria Evaluation (MCE) Techniques. This allows map layers to be weighted, based on importance. This also has problems: Different algorithms produce slightly different results. The specification of weights is also based on opinion. Lecture 13B