- GRASS GIS Reference Manual
is an implementation of FUTure Urban-Regional
Environment Simulation (FUTURES) which is a model for multilevel
simulations of emerging urban-rural landscape structure. FUTURES
produces regional projections of landscape patterns using coupled
submodels that integrate nonstationary drivers of land change: per
capita demand (DEMAND submodel), site suitability (POTENTIAL submodel),
and the spatial structure of conversion events (PGA submodel).
- DEMAND estimates the rate of per capita land consumption
specific to each subregion. Projections of land consumption are based
on extrapolations between historical changes in population
and land conversion based on scenarios of future population growth.
How to construct the per capita demand relationship for subregions depends
on user's preferences and data availability.
Land area conversion over time can be derived for the USA, e.g.
from National Land Cover Dataset.
A possible implementation of the DEMAND submodel is available as module
- The POTENTIAL submodel uses site suitability modeling approaches
to quantify spatial gradients of land development potential.
The model uses multilevel logistic regression to
account for hierarchical characteristics of the land use system
(variation among jurisdictional structures) and
account for divergent relationships between predictor and response variables.
To generate a binary, developed-undeveloped response variable
using a stratified-random sample,
see module r.sample.category.
The coefficients for the statistical model that are used to
calculate the value of development potential can be derived
with module r.futures.potential, which uses
multilevel logistic regression in R.
One of the predictor variables is development pressure (computed using
which is updated each step and thus creates positive feedback
resulting in new development attracting even more development.
- Patch-Growing Algorithm is a stochastic algorithm, which
simulates undeveloped to developed land change by iterative site selection
and a contextually aware region growing mechanism.
Simulations of change at each time step feed development pressure back
to the POTENTIAL submodel, influencing site suitability for the next step.
PGA is implemented in r.futures.pga.
Figure: FUTURES submodels and input data
We need to collect the following data:
- Study extent and resolution
- Specified with g.region command.
- FUTURES is designed to capture variation across specified subregions
within the full study extent. Subregions can be for example counties.
DEMAND and POTENTIAL can both be specified
according to subregions.
Subregion raster map contains the subregion index for each cell as integer starting from 1.
If you do not wish to model by subregion, all values in this map should be 1.
- Population data
- DEMAND submodel needs historical population data for each subregion
for reference period and population projections for the simulated period.
- Development change
- Based on the change in developed cells in the beginning and
end of the reference period, and the population data,
DEMAND computes how many cells to convert for each region at each time step.
Development change is also used for deriving the patch sizes and shape in calibration step
(see r.futures.calib) to be used in PGA submodel.
DEMAND and PGA require a raster map representing the starting state
of the landscape at the beginning of the simulation (developed = 1,
available for development = 0, excluded from development as NULLs).
- Development potential (POTENTIAL submodel) requires
a set of uncorrelated predictors (raster maps) driving the land change.
These can include distance to roads, distance to interchanges, slope, ...
- Development pressure
- The development pressure variable is one of the predictors,
but it is recalculated at each time step to allow for positive feedback
(new development attracts more development). For computing development pressure,
Figure: FUTURES simulation result
Simple example using nc_spm_08_grass7 dataset.
Please see tutorials on GRASS wiki
for more realistic examples.
Create rasters representing urbanization using NDVI, exclude lakes:
i.vi red=lsat7_2002_30@PERMANENT output=ndvi_2002 nir=lsat7_2002_40@PERMANENT
i.vi red=lsat5_1987_30@landsat output=ndvi_1987 nir=lsat5_1987_40@landsat
r.mapcalc expression="urban_1987 = if(ndvi_1987 <= 0.1 && isnull(lakes), 1, if(isnull(lakes), 0, null()))"
r.mapcalc expression="urban_2002 = if(ndvi_2002 <= 0.1 && isnull(lakes), 1, if(isnull(lakes), 0, null()))"
Create predictors - slope, distance from lakes in km, distance from roads in km, development pressure:
r.slope.aspect elevation=elevation slope=slope
r.grow.distance input=lakes distance=lakes_dist
r.mapcalc "lakes_dist_km = lakes_dist/1000."
v.to.rast input=streets_wake output=streets use=val
r.grow.distance input=streets distance=streets_dist
r.mapcalc "streets_dist_km = streets_dist/1000."
r.futures.devpressure input=urban_2002 output=devpressure method=gravity size=15 -n
Sample predictors and developed areas:
r.sample.category input=urban_2002 output=sampling sampled=slope,lakes_dist_km,streets_dist_km,devpressure,zipcodes npoints=300,100
Compute POTENTIAL regression coefficients, using zipcodes as subregion:
r.futures.potential input=sampling output=potential.csv columns=devpressure,slope,lakes_dist_km,streets_dist_km developed_column=urban_2002 subregions_column=zipcodes
Compute how many cells should be converted in each subregion:
r.futures.demand development=urban_1987,urban_2002 subregions=zipcodes observed_population=observed_population.csv projected_population=projected_population.csv \
simulation_times=2003,2004,2005,2006,2007,2008,2009,2010 method=linear,logarithmic,exponential demand=demand.csv
Create a list of patch sizes (here we skip calibration of patch sizes for simplicity):
r.futures.calib -l development_start=urban_1987 development_end=urban_2002 patch_threshold=0 patch_sizes=patches.txt subregions=zipcodes --o
Run patch growing to get final results:
r.futures.pga developed=urban_2002 subregions=zipcodes output=futures output_series=futures predictors=slope,lakes_dist_km,streets_dist_km devpot_params=potential.csv \
development_pressure=devpressure n_dev_neighbourhood=15 development_pressure_approach=gravity gamma=1.5 scaling_factor=1 demand=demand.csv discount_factor=0.1 \
compactness_mean=0.4 compactness_range=0.05 num_neighbors=4 seed_search=probability patch_sizes=patches.txt random_seed=1
Figure: One stochastic realization of FUTURES simulation, orange to yellow gradient represents new development
where yellow is the latest.
Meentemeyer, R. K., Tang, W., Dorning, M. A., Vogler, J. B., Cunniffe, N. J., & Shoemaker, D. A. (2013).
FUTURES: Multilevel Simulations of Emerging
Urban-Rural Landscape Structure Using a Stochastic Patch-Growing Algorithm.
Annals of the Association of American Geographers, 103(4), 785-807.
- Dorning, M. A., Koch, J., Shoemaker, D. A., & Meentemeyer, R. K. (2015).
Simulating urbanization scenarios reveals
tradeoffs between conservation planning strategies.
Landscape and Urban Planning, 136, 28-39.
- Petrasova, A., Petras, V., Van Berkel, D., Harmon, B. A., Mitasova, H., & Meentemeyer, R. K. (2016).
Open Source Approach to Urban Growth Simulation.
Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci., XLI-B7, 953-959.
Ross K. Meentemeyer, rkmeente ncsu edu,
Center for Geospatial Analytics, NCSU
Original standalone version:
Ross K. Meentemeyer *
Wenwu Tang *
Monica A. Dorning *
John B. Vogler *
Nik J. Cunniffe *
Douglas A. Shoemaker *
Jennifer A. Koch **
* Department of Geography and Earth Sciences, UNC Charlotte
** Center for Geospatial Analytics, NCSU
Port to GRASS GIS and GRASS-specific additions:
Vaclav Petras, NCSU GeoForAll
Development pressure, demand and calibration and preprocessing modules:
Anna Petrasova, NCSU GeoForAll
r.futures source code
Latest change: Monday Jan 30 19:52:26 2023 in commit: cac8d9d848299297977d1315b7e90cc3f7698730
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