Allocation

Allocation is the process of assigning land to its various uses. In land use modelling, claims at the regional or national level are usually allocated to grid cells based on suitability scores. Every allocation method needs a suitability for each alternative: for each land use type, a map that gives a suitability to each land unit. A model can also set restrictions per land use type on the total amount of allocated land.

Continuous and discrete allocation

The two main methods differ in what a land unit can hold.

• The allocation is continuous when each land unit can have any non-negative amount of each land use type, up to a fixed total.
• The allocation is discrete when each land unit goes to one land use type out of a limited set.

Table 1. The two methods compared.

	Continuous allocation	Discrete allocation
A land unit gets	A share of every land use type	One land use type
The model finds the result by	Iterating until two sets of balancing factors fit the land and the claims	Maximising total suitability under the claims
Suits	Larger land units with mixed use	Small land units with one use
Weak point	Small amounts of many types can end up in one cell, and a map of the dominant type misrepresents the amounts	Each cell shows one use, even where uses mix
In GeoDMS	The loop or for_each operator	The discrete alloc function

When both start from the same point, they produce comparable results (Loonen & Koomen, 2009).

If the intensity of land use varies by location, or if land use types do not exclude each other, one needs quantitative allocation, in which a land unit can hold more than one use or a varying amount of it.

Nested allocation

When a model has many land use types and a hierarchy of types makes sense, allocation can be nested, which is comparable to nested discrete choice modelling. The model first allocates the main types and then divides each of them among its subtypes. If the subtypes have no claims of their own, this can often be done afterwards as a simple classification. If they do have claims, it takes another round of allocation within the space of the main type.

Nesting deals with types that are close substitutes, the problem known as the independence of irrelevant alternatives. Any nested result can also be generated without nesting, by altering the suitability maps. But if some factors strongly influence the choice within a main type and hardly influence the choice of the main type itself, a nested model is more elegant than correcting the suitability of the main type with the term $\log \sum \exp(\text{subtype suitabilities})$. And if a change in claims and shadow prices should mainly affect other subtypes of the same main type, this correction has to depend on the shadow prices, and one ends up with a nested logit model anyway.

Step-by-step allocation

Continuous and discrete allocation consider all land use types together. Other approaches work in a fixed order of land use types or priorities, or give the highest values first, without taking alternatives and their opportunity costs into account. RSLight2021 and RSopen allocate sector by sector, with competition within a sector.

In GeoDMS

The allocation functions page of the GeoDMS wiki describes the available functions.