Modeling with Rasters III: Weighted Overlay

Data Transformation Approaches: Categories Approach

• define a scale for suitability

• Often scale from 1-9 is used

• Reclassified to give relative suitability

• use the same scale for all layers in a model

Data Transformation Approaches: Range of Values Approach- reclassify

Uses quantile: which will put the same number of pixels in each of the categories

• If there are ties it will mean slight variation

Same data with equal interval

• Will make a different

• Lots of variability through amounts in each category

• These may mean the 9 is completely eliminated in the final comparison

• Can be exclusionary

Data Transformation Approaches: Mathematical Functions Approach - rescale by function

With distance variables we can use rescale by function

Large values more preferable than small ones max distance is just over 6000

Any thing greater than the midpoint has increasing preference

• So greater than the 1000 is preferable

in image green is 8s and 9s: what it would look like if large values are prefered

What is a Decision Rule?

• a method or logic used to combine multiple criteria

• set constraints, combines, handle tradeoffs, rank alternatives

Weighted Sum Decision Rule

• Certain layers will be more significant than others and are weighted(weight x layer) before they are combined

• can apply weighted as a multiplier or as a percentage

  • multiplier- the scales of the suitability surface will provide. higher contrast between the scores of the most suitable locations

  • percentages- by applying weights as a percentage, the user defined suitability scale is maintained

    • Apply as a multipliers(most suitably location will be quite different in values than those that are not); if percentage is used(the original values will stay the same?)

    • To do this you can use..

      • The weighted sum tool and; or weighted overlay tool

Weighted Overlay Tool

Uses only integer data

• So you may have to reclass rescaled data into integer rasters

1. Set scales

2. Add rasters

   1. If they are already on their 1-9 scale you won't have to reorganize them

3. Then add the weight and run

Pros of Weighted Sum

• handles continuous and integer

• no need to rescales inputs

• higher precision(floating point)

• simple linear combination

Pros of Weighted Overlay

• Standardizes different scales automatically

• works will with categorical data

• Scaled result: easy interpretation

Cons of Weighted Sum

• no automatic rescaling

• no built in handling of categorical data

• hard to interpret results of scales mismatched

• the decision rule:

  • highly sensitive to weights(though arbitrary and subjective)

  • weighted sum assumed linearity, not all relationships are linear

  • heavily dependent on the data transformation approach

Weighted Overlay

• only supports integer data

• less control over how rescaling works

• can introduce bias if rescaling is poorly calibrated

Locating Regions

• creation of candidate sites:

  • finding contiguous areas that meet the model goal

  • need to considers shape, size and other characteristics

    • size can specify:

      • total area you are interested in

      • minimum area

      • maximum area

Approaches to Weighting?

Either Ranking or Rating Methods

Ranking Methods

• simplest method of all weighting techniques

• every criterion under consideration is ranked in preference order

  • either straight rank(1 is most important) or inverse rank (1 is least important)

• Once rank is established, several procedures are available for generating numerical weights from rank order informations

  • Types:

    • Ranks Sum

    • Ranks reciprocal

    • rank exponent

Advantages of Ranking Methods

• simple(non complex calculations)

• intuitive appeal(focus on relative importance rather than specific numeric values)

• efficiency(useful where there is limited time, resources or data availability)

• Low data requirements (rely on qualitative informations rather than extensive datasets or technical expertise)

Disadvantages of Rankling Methods

• subjectivity- different decision makers may rank differently

• loss of information -= only consider ordinal position of criteria

• limited discriminations - limited to a small number of criterion

  • larger the number the harder to derive reliable ranking

• Difficulty in handling ties - may require additional subjective judgment or arbitrary tie breaking rules

Rating Methods: Point Allocation

• decision marker estimates weights on predetermined scale

• each criteria would be allocated points with the total of all points = 100

• the greater the points, the greater the relative strength of the criterion

• Individual criterion$ can be normalized using: IMAGE

• best one

Rating Methods: Ration Estimation Approach

• Assign 100 to the more important criteria

• Assign proportionally lower weights to criterion of less importance(in order of ranked positions)

• Take ratio of each criterion to the least important criterion

• Ratio expresses relative desirability of a change from the worst level to the best level

• Weights are more normalized at the end by dividing each weight by the total of all weights

Advantages of Rating Methods

• simplicity, intuitive appeal(like ranking approaches)

• efficiency and low data requirements (like ranking approaches)

• ease of aggregation of ratings from different decision makers that is another disadvantage of ranking methods

Disadvantages of Rating Methods

• subjectivity- leads to inconsistency and variabilities in weights

• difficulty in comparing dissimilar criteria

• practically limited to small number or criteria

  • same issues arises in ranking too

• Lack of consistency - without clear guidelines of how to assign points, decision makers struggle to maintain consistency

Whi is Better Ranking or Rating Methods?

• both flawed, subjective, and lack mathematical rigor, but…

• Rating is stronger theoretically

  • have quantification instead of ordinal ranking

  • mathematical transformations- can turn points to weights

  • statistical analysis- can be used to asses reliability