Using non-predetermined spatial disaggregation

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Non-predetermined spatial disaggregation is a method for utilising spatial information in a very flexible way in a situation where predetermined grid structures cannot be used. This method makes it possible to start with a coarse spatial disaggregation, and refine disaggregation in locations where detailed data becomes available. The method is based on an information structure where aggregation or disaggregation of information is performed based on a separate

Scope

Let there be an area A, which is being examined in a collaborative assessment. Some parts of A are known with higher detail than others. The level of information available depends on the people that happen to collaborate. Therefore, it is not known beforehand, what data becomes available and what the best way to divide the area A is. Still, there should be an efficient way to divide A into sub-areas so that the information that occurs during the assessment can be effectively used. A further complication is that the disaggregation may change in time during the assessment, or it may have differential needs for different variables. How should the spatial disaggregation be performed in such a situation?

Definition

Input

The input data may be spatially distributed, or it may also be distributed along some other dimension. Different pieces of data may have very different spatial disaggregation.

Output

The output should be such that it can be seamlessly utilised in other, relevant variables in the assessment.

Rationale

The result is based on intuition and personal practical experience.

Result

Procedure

Area A is divided into n subareas A_i, i=1,2,...n. A_i must be exclusive and mutually exhaustive (i.e., they must not overlap, and together they must cover the whole area of A). A_i must be either

• spatially defined areas, or
• areas categorised based on another than spatial determinant. For example, A_i may be municipalities categorised into three groups based on the number of inhabitants: A₁: under 50000, A₂: 50000 - 250000, A₃: above 250000 inhabitants. Also in this case, A_i must have a spatial interpretation, but for the assessment, there is no need to specify it within A, given i.
  • In this case, the description of each A_i is divided into two parts: a) the description of the actual property per each unit (e.g., municipality), and b) the number of units (municipalities) in each A_i.

Any of A_i can be further divided in the same way as A. However, if the A_i is based on a non-spatial determinant, it can be further divided into non-spatial sub-areas but not into spatial sub-areas.

Management

Spatial disaggregation module

There is an Analytica module available for disaggregating and aggregating spatial information. The idea is that there are two pieces of information:

• the value of the property itself (here called result) in each area, and
• the disaggregation weight or aggregation function. The disaggregation weight means an array of relative values that can be used to allocate the result of A into A_i. The aggregation function contains information about which sub-areas belong to which area(s); the result of A is the sum of the results of A_i.

Analtytica functions disaggr and aggr (found in the module can be used for disaggregation and aggregation, respectively.

In an Analytica model, the spatial disaggregation is operationalised as a single index. The index has one row for each sub-area. Sub-areas may be from any level of disaggregation, as long as the combination of subareas in the index are exclusive and mutually exhaustive. Note that some sub-areas may be spatial and some non-spatial. For example, in a European model, municipalities in Germany may be spatially defined, but in Finland municipalities may be categorised into three groups based on population size. In this example, the spatial index would contain one row for each German municipality and three rows for all municipalities in Finland. In addition, there would be a need for frequency information for each row of the spatial index. Each German row would have 1, and the rows for Finland would reflect the number of municipalities of different sizes, summing up to the total amount of municipalities in Finland.

Transforming between spatial indices

It is possible to transform the data from one spatial disaggregation index to another index. Disggregation and aggregation can be used for any part to make this transformation. However, the rules of exclusiveness and mutual exhaustiveness must always be fulfilled.

Utilising data from different levels

Typically, the following formulas apply for Q(A), where Q is some quantitative property of A:

Q(A) = sum(Q(Ai))

(if there is more information about A_i than A)

Q(Ai) = Q(A)*fi,

where f_i are disaggregation weight factors (when there is more information about A than A_i).

There may also be cases where there is information about A and one of the A_i, say A₁. Then, it might be practical to calculate the results in the following way

Q(A1) = Q(A) - Q(A1)

and for other A_i than A₁

Q(Ai) = Q(A1)*fi,

where A¹ is A without A₁.