Interpolating global economic activity data
Preliminary results and methods
Input data
Using an enhanced DOSE data set, where a number of gaps have been filled with the World Development Indicator data on the national level.
Hierarchical indexed grids
H3
Developped by Uber
- original library in C
- open-source
- bindings to many other languages/systems
- hexagonal shapes
- hierarchical (see Figure 1)
- Theory:(Sahr 2014)
- edge indexation (useful to model flows for example), nearest neighbours
- node indexation
- the nature of the projection imposes that a constant number of 12 pentagons is present in the index at each level.
Example : Interpolation
Example : downscaling
In practice : simple example
A parent cell \(H_i^{(n)}\) with resolution \(n\) contains a set of children \(\{h^{(n+1)}_{ij}\}_{j=0...6}\) with resolution \(n+1\). A value \(W\) measured at \(H_i^{(n)}\), \(W(H)\) is downscaled into \(w(h)\).
Trivial rescaled case
For an extensive variable, if \(W(H^n_i)=21\), we can downscale into \[w(h_{ij})=\frac{W(H^n_i)}{N_c}=\frac{21}{7}=3\] for all j.
General rescaled case
If, we have a known underlying distribution at a finer scale, say \(g_W(h_{ij}) = 18/105\) for \(j=\{0,1,4,5,6\}\), and \(g_W(h_{i2})=1/21,g_W(h_{i3})=2/21\), we incorporate this data into the equation and get:
\[ w(h_{ij})=g_W(h_{ij})W(H_i) = \begin{cases} 3.6,& \text{for } j=0,1,4,5,6 \\ 1, & \text{for } j=2\\ 2, & \text{for } j=3\\ \end{cases} \] for each children cell.
In practice : GDP + Non-res buildings data
For a certain level (Admin0,Admin1), we know the GDP of an area (in USD$) for given sectors. We know the amount of non-residential infrastructure in the region at a fine resolution of 100x100m (GHSL data package 2023. 2023). We assume a typical value of gdp generated for a unit of infrastructure and rescale to obtain a density layer of infrastructure for the given area. Then combine it with the known economic output at a coarser scale to downscale it.
Further
In Practice 2: Agriculture yield + constraint layer
We have a raster grid with agricultural yields from MAPSPAM(“Spatially-Disaggregated Crop Production Statistics Data in Africa South of the Sahara for 2017,” n.d.). The raster grid cell size is \(10km\times 10km\). We can try to downscale this while taking into consideration the human settlements that are covered by the grid using the GHSL total built up ground surface. By removing the cells that are covered in infrastructure, we dowscale the agriculture layer by taking into consideration the constrain on where crops are more likely to be in fact cultivated.
Workflow
Literature
Tobler (1979)
pycnophylactic : mass preserving
Literature
Contemporary methods: DL
Gonzalez (2022)
python package: dl4ds
source : https://carlos-gg.github.io/dl4ds/dl4ds.html