Range rules are applicable to environmental features with interval or ratio values (e.g. temperature, slope). The basic idea is when certain condition is satisfied, the optimality value is 1, as the value deviates from the optimality value, the optimality decreases. This idea is expressed as the following function
f(x): the optimality value
x: the environmental variable value in the location to be inferred
b: the environmental variable value at which the optimality for the soil type is the highest (the most ideal)
d: the difference between b and the environmental variable value at which the optimality value is 0.5 (soil is less typical of the specific soil type) .
From the function above, some concepts can be derived:
Low Unity and High Unity:
The highest optimality value (b) can be a single value or can be a range. Low unity is defined to be the "minimum b" while high unity is the "maximum b". So low unity and high unity being the same means b is a single point, otherwise, a range.
Low Cross and High Cross:
Low Cross and high cross are the environmental variable values when optimality value decreased to 0.5 . Low Cross is smaller than b while High Cross is greater than b.
We can derive three kinds of curves from the basic function
| • | bell-shape curve: For bell-shaped curve, optimality value decreases when environmental variable value is lower than low unity or higher than high unity. Low unity and high unity can be the same or different values. If they are equal, there is no flat top. If the difference between low unity and low cross and the difference between high cross and high unity is the same, the curve is symmetric. Otherwise, it is unsymmetrical. |
| • | S-shaped curve: S-shape curve can be created by setting the optimality value to 1 for x greater than b. It is a "the-higher-the-better" shape. The low unity and high unity is the same. High cross is not needed for S-shape curve. Optimality will be unity only if the environmental variable values are greater than low unity/high unity. For example, you may want a rule that indicates a particular soil is found at high elevations only. Elevations below low unity/high unity are sub-optimal, and elevations that are above low unity/high unity are optimal for the soil type. |
| • | Z-shaped curve: Z-shape curve can be created by setting the optimality value to 1 for x less than b. It is a "the-lower-the-better" shape. The low unity and high unity is the same. Low cross in not needed for Z-shape curve. Z-shape curve is entirely analogous to the s-shape, except that the values lower than low unity/high unity are optimal. |
To define a range rule, the curve type, the low unity, the high unity, the low cross and the high cross need to be specified by users.