2UP

The 2Up model is a spatially explicit global urbanisation and population growth model.

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

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