From Recipes to Models

What's the difference between a recipe and a model? Both seem to mix a bunch of things together to create something else. Both result in a synergistic amalgamation that's more than the sum of the parts. Both start with basic ingredients and describe the processing steps required to produce the desired result-be it a chocolate cake or a landslide susceptibihty map.

In a GIS, the ingredients are base maps, and the processing steps are spatial handling opera- tions. For example, a simple recipe for locating landslide susceptibility involves ingredients such as terrain steepness, soil type and vegetation cover: areas that are steep, unstable and bare are the most susceptible.

Before computers, identifying areas of high susceptibility required tedious manual map analysis procedures. A transparency was taped over a contour map of elevation, and areas where contour lines were spaced closely (steep) were outlined and filled with a dark color. Similar transparent overlavs were interpreted for areas of unstable soils and sparse vegetation from soil and vegetation base maps. When the three transparencies were overlaid on a strong light source, the combination was deciphered easily--clear = not susceptible, and dark = susceptible. That basic recipe has been with us for a long time. Of course, the methods changed as modern drafting aids replaced the thin parchment, quill pens and stained glass windows of the 1800s, but the conceptual approach remains the same.

In a typical vector GIS, a logical combination is achieved by first generating a topological overlay of the three maps (SLOPE, SOILS, COVER- TYPE), then querying the resultant table (TSV-OVLI for susceptible areas. The Structured Query Language (SQL) query might look hke the following:

   Select columns: %slope, stability, vegtype
   from tables:   TSV -OVL
   where condition: %slope > 13 and stability =
                  "Unstable" AND vegtype =
                  "Bare"
   into table named: L-HAZARD

The flowchart in the accompanying figure depicts a typical raster-based binary model (only two states, either Yes or No), which mimics the manual map analysis process and achieves the same result as the overlay/SQL query. A slope map is created by calculating the change in elevation throughout the project area (first derivative of the elevation surface). A binary solution codes as 1 all of the susceptible areas on each of the factor maps (> 30 percent slope, unstable soils, bare vegeta- tive cover), whereas the nonsusceptible areas are coded as 0. The product of the three binarv maps (SL-binary, SO-bmary, CO-binary) creates a final map of landslide potential - 1 = susceptible, and 0 = not susceptible. Only locations susceptible on all three maps retain the "susceptible" classification (1 * 1 * 1 = 1). In the other instances, multiplying 0 times any number forces the product to 0 (not susceptible). The mapematical model corresponding to the flowchart in the figure might be expressed (in TMAP modeling language') as

   SLOPE ELEVANON FOR SLOPES
   RENUMBER SLOPE FOR SL binary
   ASSIGNING 0 TO 1 THRU 12
        ASSIGNING I TO 13
        THRU 1000            (> 13%, steep)
   RENUMBER SOILS FOR SO-binary
   ASSIGNING 0 TO 0 THRU 2
        ASSIGNING 1 TO 3
        THRU 4       (soils 3 and 4, unstable)
   RENUMBER R-OVERTYPE FOR CO-binary
   ASSIGNING 0 TO I
        ASSGNING 0 TO 3
        ASSIGNING 1 TO 2      (cover 2, bare)
   COMPUTE SL   -binary TIMES SO_binary
        TIMES CO-binary
        FOR L-HAZARD       (1'1 *1 = 1, hazard)

In the multiplicative case, the arithmetic combination of the maps yields the original two states dark or 1 = susceptible, and clear or 0 = not susceptible. It's analogous to the "AND" condition of the logical combination in the SQL query. But other combinations can be derived. For example, the visual analysis could be extended by interpreting the various shades of gray on the stack of transparent overlays: clear = not susceptible, light gray = low susceptibility, medium gray = moderate susceptibility and dark gray = high susceptibility. in an analogous mapematical approach, the computed sum of the three binary maps yields a similar ranking: 0 - not susceptible, 1 - low susceptibility, 2 - moderate susceptibility and 3 - high susceptibility ( 1 + 1 + 1 = 3). That approach is called a ranking model, because it develops an ordinal scale of increasing landslide potentials value of two is more susceptible than a value of 1, but not necessarily twice as susceptible.

A rating model is different, because it uses a consistent scale with more than two states to characterize the relative landslide potential for various conditions on each factor map. For example, a value of 1 is assigned to the least susceptible steepness condition (e.g., from 0 percent to 5 percent slope), while a value of 9 is assigned to the most susceptible condition (e.g., > 30 percent slope ). The intermediate conditions are assigned appropriate values between the landslide susceptibility extremes of 1 and 9. That calibration results in three maps with relative susceptibility ratings (SL-rate, SO-rate, CO-rate) based on the 1-9 scale.

Computing the simple average of the three rate maps determines an overall landslide potential based on the relative ratings for each factor at each map location. For example, a particular grid cell might be rated 9, because it's steep, 3 because its soil is fairly stable and 1 because it's forested. The average landslide susceptibility rating under these conditions is [(9+3+3)/3] = 5, indicating a moderate landslide potential.

A weighted average of the three maps expresses the relative importance of each factor to determine overall susceptibility. For example, steepness might be identified as five times more important than either soils or vegetative cover in estimating landslide potential. For the example grid cell described previously, the weighted average computes to [([9*5]+3+3)/7]= 7.28, which is closer to a high overall rating. The weighted average is influenced preferentially by the SL rate map's high rating, yielding a much higher overall rating than the simple average.

All that may be a bit confusing. The four different "recipes" for landslide potential produced strikingly different results for the example grid cell in figure 24. 1 -from not susceptible to highly susceptible. It's Like baking banana bread. Some folks follow the traditional recipe, some add chopped walnuts or a few cranberries. By the time diced dates and candied cherries are tossed in, you can't tell the difference between your banana bread and last year's fruitcake.

So back to the main point-what's the difference between a recipe and a model? Merely semantics? Simply marketing jargon? The real difference between a recipe and a model isn't in the ingredients, nor the processing steps themselves. It's in the conceptual fabric of the process. But more on that later.

GIS Worid Inc., 155 E. Boardwalk Drive. Suite 250, Fort Collins, CO 805256 USA DECEMBER 1995