2UP

The 2UP model is a spatially explicit global urbanisation and population growth model (Koomen et al., 2023). It derives a regional demand for urban land per country and allocates it with a form of discrete allocation.

2UP is maintained by PBL Netherlands Environmental Assessment Agency, and little development takes place on it now. For new global projections it has been superseded by CRISP, a model by Object Vision and the Joint Research Centre of the European Commission that projects built-up land and population on a global grid of 1 km.

Indices

• i: Land Unit, a 30" x 30" lat long part.
• c: Country
• t: Time step: {2010, 2020, 2030, 2040, 2050, 2060, 2070, 2080}

Urban allocation

Static variables

• I_cⁱ: Incidence matrix; for each i: $\sum\limits_c I^i_c = 1$
• A_i: Area of land unit i

Dynamic variables

• $\sideset{^t}{_i}S$: Suitability, a function or combination of spatially explicit suitability factors
• $\sideset{^t}{^c}P$: Projected population, source: SSP database - Institute of Applied Systems Analysis (IIASA) - 1
• $\sideset{^t}{^c}D$: Hyde population density index, source: History Database of the Global Environment - Klein Goldewijk, Dr. ir. C.G.M. (Utrecht University) (2017): Anthropogenic land-use estimates for the Holocene; HYDE 3.2. DANS. 2
• $\sideset{^t}{^c}C$: Urban Claim

Urban Claim

• $\sideset{^t}{^c}U := \sideset{^{2010}}{^c}U \cdot {\sideset{^t}{^c}P \over \sideset{^{2010}}{^c}P} \cdot {\sideset{^{2010}}{^c}D \over \sideset{^t}{^c}D}$
• $\sideset{^t}{^c}C := \min(\sideset{^t}{^c}U, \sum\limits_i{A_i \cdot I^i_c})$ Claim is U, but no more than the available land

Urban Spatial Allocation

• X_i ∈ {0, 1} such that ∑S_i ⋅ X_i is maximal and that for each c: $\sum\limits_i X_i \cdot A_i \cdot I^i_c = C^c$ where X_i = 1 represents projected urban land use.

This allocation is done by taking the $C^c \over \sum\limits_i A_i \cdot I^i_c$ th percentile of the land units of c, descendingly ordered by S_i and weighted by A_i.

Population projection

Projected population growth $\sideset{^t}{^c}{EP} := \sideset{^t}{^c}P - \sideset{^{t-1}}{^c}P$ is spatially allocated according to the same suitability $\sideset{^t}{_i}S$, taking into account a spatially explicit maximum population density $\sideset{^t}{_i}{MD}$.

• $\sideset{^t}{_i}{MD} := \max\left(\sqrt{\sum\limits_{j \in W(i)} \left( \sideset{^{t-1}}{_i}P \over A_i \right)^2 \cdot \sideset{^t}{_i}X \cdot {dd}_{ij} \over \sum\limits_{j \in W(i)} \sideset{^t}{_i}X \cdot {dd}_{ij}}, \sum\limits_c { I^i_c \cdot {\sum\limits_i \sideset{^{t-1}}{_i}P \cdot \sideset{^t}{_i}X \cdot I^i_c \over \sum\limits_i A_i \cdot \sideset{^t}{_i}X \cdot I^i_c} } \right)$
• dd_ij: distance decay function.
• W(i): A window around land unit i such that dd_ij ≠ 0 ⟹ j ∈ W(i).

If $\sideset{^t}{^c}{EP} > 0$

• $\sideset{^t}{_i}\Delta := \sum\limits_c I^i_c \cdot \sideset{^t}{^c}{EP} \cdot { \sideset{^t}{_i}S \cdot A_i \cdot \sideset{^t}{_i}X \cdot (\sideset{^{t-1}}{_i}P < \sideset{^{t-1}}{_i}{MD} * A_i ) \over \sum\limits_i I^i_c \cdot \sideset{^t}{_i}S \cdot A_i \cdot \sideset{^t}{_i}X \cdot (\sideset{^{t-1}}{_i}P < \sideset{^{t-1}}{_i}{MD} * A_i ) }$