Land Use-Land Cover Dynamics at the Metropolitan Fringe

Abstract

Diverse pressures for change operate at the outer metropolitan fringe. This paper examines the spatial and temporal dynamics of change in this area. We set up a simple model that incorporates spatial and temporal dynamics of functional (land use) and structural (land cover) interactions. We posit that land use (development) changes the ecosystem functions at the edge of urban areas expressed in change in land cover. Additionally, the characteristics of land cover (forest, agriculture, bare soil, neighboring cover etc.) mutually influence the land use. We estimate a model where land values and land use are jointly determined while land use and land cover interact recursively. We use historical data, probability estimation and land use simulation to generate panel data of future patterns of land value, land use and land cover at the outer edge of the Tel Aviv metropolitan area for the period 1995–2023. The modeling system combines panel 2SLS (2-stage least squares) estimation to investigate land value-land use interactions. Land use-land cover dynamics are estimated using panel MNL (multi-nomial logit) estimation. Results of simple simulations of the probability of land cover change are presented. When coupled with an appropriate biodiversity model, this system could potentially be extended to forecasting other aspects of the environmental stress of metropolitan expansion, for example impacts on vegetation or ecological dynamics.

Appendices

Appendix 1

Writing Eqs. 5 and 6 in matrix form:

$$ {U}_t={\mathrm{AA}}_N{U}_{t-1}+\lambda W{U}_{t-1}+\delta {V}_t+K{\mathrm{XX}}_t+{v}_t $$

$$ {C}_t={\Gamma}_M{C}_{t-1}+\alpha {U}_{t-1}+\lambda {U}^{*}+K{\mathrm{XX}}_t+{u}_t $$

where: A _N, Γ _M are probability transition matrices for LU and LC.

Using the time series lag operator (L) which operates on an element, in order to produce the previous element, we solve for U_t and U_t−1:

$$ \left(I-\boldsymbol{\varGamma} L\right){C}_t=B{U}_{t-1}+{u}_t $$

(9)

$$ \left(I-\boldsymbol{A}L\right){U}_t={v}_t $$

(10)

$$ {U}_t={\left(I-\boldsymbol{A}L\right)}^{-1}{v}_t $$

(11)

$$ \begin{array}{l}{\left(I-\boldsymbol{A}L\right)}^{-1}=I+\boldsymbol{A}L+{\boldsymbol{A}}^2{L}^2+\dots \\ {}{A}^n\to 0\ n\to \infty \end{array} $$

(12)

$$ {U}_{t-1}={v}_{t-1}\boldsymbol{A}{v}_{t-2}+{\boldsymbol{A}}^2{v}_{t-3}+\dots $$

(13)

Substituting for U _t−1 in Eq. 9 and re-arranging:

$$ {C}_t={\left(I-\boldsymbol{\varGamma} L\right)}^{-1}B\left(\ {v}_{t-1}\boldsymbol{A}{v}_{t-2}+{\boldsymbol{A}}^2{v}_{t-3}+\dots.\right) $$

The inverse of the polynomial is:

$$ {\left(I-\boldsymbol{\varGamma} L\right)}^{-1}=I+\boldsymbol{\varGamma} L+{\boldsymbol{\varGamma}}^2{L}^2+{\boldsymbol{\varGamma}}^3{L}^3+\dots $$

Appendix 2: Probability Estimation of Land Cover Data

We use MNL regression for historic (2002) data to create log odds of land cover (LC) e change (from bare soil, forests, orchards, fields to built areas). Independent variables are: LC for 1995 (lc95), the most frequent LC in the neighboring cells in 19955 (neigh95), distance from 2 digit highways (2dgt), distance from 1 digit highways (1dgt), distance from metropolitan CBD (core), parks area (prk), 1995 residential land value (lv95), 1995 commercial square feet (comm95), 1995 industrial square feet (ind95), 1995 governmental square feet (gov95), 1995 number of residential units (res95). Non –significant variables are excluded and the regression re-estimated with 0.2445 misclassification rate which is equal to 51.1 % accuracy. Coefficient values are as follows:

Log odds for	Intercept	2dgt	1dgt	core	prk	Lc95[2]
2/6	1.06300627	0.02128593	−0.0212716	−0.0000239	−0.000018435	1.39784825
3/6	1.6741873	0.0547843	−0.0546622	−0.000070779	−0.0001232	0.00525623
4/6	0.01532415	0.01373619	−0.0138219	−0.0000009686	−0.0001346	−0.8704572
5/6	0.11464507	0.02095321	−0.021061	−0.0000082171	−0.000061941	−0.0847443

Log odds for	Lc95[3]	Lc95[4]	Lc95[5]	neigh95[2]	neigh95[3]
2/6	1.3162059	−0.5565036	−0.9872424	0.81029937	0.24571899
3/6	2.21462143	0.91567457	−0.8596639	−0.1341568	1.35462331
4/6	−0.6881597	3.05639013	−0.1230151	−0.2588099	−1.0215386
5/6	−1.5210677	0.23063331	2.64963015	−0.0652665	−1.1603799

Log odds for	neigh95[4]	neigh95[5]	lv95	res95
2/6	−0.0369579	−0.4688555	−0.0000000056334	−0.0053964
3/6	0.33465383	−0.9959705	−0.0000038221	−0.0217897
4/6	1.39302637	0.11419243	−0.0000018486	−0.0196984
5/6	0.19326558	1.08702141	−0.0000033074	−0.016155

These parameters are then tested by using the 2002 LC data and 2002 land use model outputs as independent variables. The predictions of this regression generate 53.48 % accuracy when compared with actual 2009 LC data. After each round, the outputs of the previous round become the t-1 values for a new round, i.e. LC value calculated in round t becomes LC data for round t + 1. This is repeated for each time period with time lags of t = 7.