Attractiveness & Distance

Attractiveness & Distance

Applying the First Law of Geography…

First Law of Geography• "Everything is related to everything else, but near things are more

related than distant things." [Tobler, 1970, p.236]

• This observation is embedded in the gravity model of trip distribution. It is also related to the law of demand, in that interactions between places are inversely proportional to the cost of travel between them, which is much like the probability of purchasing a good is inversely proportional to the cost.

• It is also related to the ideas of Isaac Newton's Law of universal gravitation and is essentially synonymous with the concept of spatial dependence that forms the foundation of geostatistics.

• TOBLER, W. R. (1970). "A computer model simulation of urban growth in the Detroit region". Economic Geography, 46(2): 234-240.

Source: Wikipedia, 2007

Relating Attractiveness and Distance

• Simple Bifurcation Model– You want to be as close as possible to

“Amenities”• Parks, Restaurants, Streams, etc.

– You want to be as far as possible from “Disamenities”

• Landfills, diesel 18 wheel truck routes, etc.

– With no further elaboration, can create a simple multifactor GIS attractiveness model

Example Attractiveness Model 1

• Want to be near the university and near shops (two amenities)

• Calculate (for now) Straight-line distance to Amenities

• Add the distance maps

• Lowest values = best sites

Implementation of Model 1

• Setup Spatial Analyst– Extent = urban_*– Cell Size = 5 meters

• Use a selected polygon near the university center as “univerisity”

• Use “Urban_commercial” Land use as proxy for “shops”

• Use straight line distance with 1600 meter cut-off as measure of fall-off in amenity

Factor Map Cartography

• Goals– Map should be

freestanding and self-explanatory

– Cartographic quality sufficient for final presentation/report

– Maps in a series should have exactly the same extent

Cartographic Methods 1

• Pay attention to Layer Names– Simply edit in layer TOC

as needed– Rename layers

descriptively, use subheads for units

• Format Legend Labels– For number ranges, in

Properties->Symbology, right mouse and “format labels” to appropriate rounding

Cartographic Methods 2

• Set number format rounding to 0 significant decimal places where appropriate (usually!)

• Show thousands separators

Cartographic Methods 3

• Add titles, subtitles and brief descriptive text as needed

• Add scale bar

• (North Arrow / data sources optional)

Attractiveness Mapping Revisited

• What’s wrong with Model 1?

Common Attractiveness Model Critiques

• You missed an important factor…– Amenities or dis-amenities

• Fall-off with distance more complicated than simple distance– Ignores actual travel routes

• Need travel times across pedestrian network

– Many amenities have short-range disamenity• Example: Living next to park is good – except for

busy public recreation areas

Attractiveness Model 2

• Land Cost (a proxy of market rent) added as a factor

• Note– Land cost is a dis-amenity (from the student’s

perspective anyway)– Can no longer simply add maps– Must “normalize” attractiveness factors

Normalizing Attractiveness Factors Step 1: Establishing Common Evaluation Scale

• Manually adjust symbolization category breaks

• With layer selected, choose Spatial Analyst->Reclassify

• Defaults to visual symbology breaks

• May need to adjust new values to scale 1..9

Normalizing Attractiveness Factors Step 2: Inverting Factor Scales

– Want to end up with logically consistent factor scale• 1 = best, 9 = worst• (or vice versa as long as consistent)

– In some cases, numeric values ok by default– short distance to amenity is better: small numbers = good

– higher rent is worse: small numbers = good again

– In other cases, numeric values must be inverted• Most commonly, need to invert scale of distance to dis-

amenity– Distance to industry: small numbers would be bad (flip needed)

Inverting Factor Scales

• Simplest Method– Use reclass operation– Invert output values

Implementing Attractiveness Model 2

• Use Reclassify for both– Distance to Commercial– Distance to University– In both cases, Low Values = Most Attractive

• Use Reclassify to scale land value– In this case, Low Values also = Most Attractive

• For equal-weighted model, simply add all three factors again– Lowest values will be best across all three measures– High values worst…

Assignment for Thursday

• Develop an attractiveness model for a target customer type– Model should have approximately 3 factors– All factors should be individually mapped with

careful scaling– Summary should be equally-weighted sum of

individual factors