Workshop on urban growth modeling with FUTURES

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Workshop introduction

r.futures.* is an implementation of the FUTure Urban-Regional Environment Simulation (FUTURES)[1] 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).

[1] 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


There are a number of software requirements to run FUTURES that will need to be download and installed. Required software includes:


We use the R statistical software for our calculation of site suitability (i.e. development potential) in FUTURES. R is a free software environment for statistical computing and graphics. If you don't have R, or you have older an version, please download and install the software from install R and be sure to additionally add these required packages:

install.packages(c("MuMIn", "lme4", "optparse", "rgrass7"))

MS Windows

We will be using GRASS GIS 7.0.3 that can be found here in the OSGeo4W package manager. Please install the latest stable GRASS GIS 7 version and the SciPy Python package using the Advanced install option. A guide with step by step screen shot instructions is available here.

In order for GRASS to be able to find R executables, GRASS must be on the PATH variable. Follow this [solution] to make R accessible from GRASS permanently. A simple but temporary solution is to open GRASS GIS and paste this in the black terminal:

set PATH=%PATH%;C:\Program Files\R\R-3.0.2\bin

This has to be repeated after restarting GRASS session.

Ubuntu Linux

Install GRASS GIS from packages:

sudo add-apt-repository ppa:ubuntugis/ubuntugis-unstable
sudo apt-get update
sudo apt-get install grass

Workshop data

The data that we will be using for the workshop can be download here: sample dataset. Please place these layers in your local GRASS directory:

  • digital elevation model (NED)
  • NLCD 2001, 2006, 2011
  • NLCD 1992/2001 Retrofit Land Cover Change Product
  • transportation network (TIGER)
  • county boundaries (TIGER)
  • protected areas (Secured Lands)
  • cities as points (USGS)

In addition, download population information as text files:

  • county population past estimates and future projections (NC OSBM) per county (nonspatial)

GRASS GIS introduction

Here we provide an overview of the GRASS GIS project: that might be helpful to review if you are a first time user. For this exercise it's not necessary to have a full understanding of how to use GRASS GIS. However, you will need to know how to place your data in the correct GRASS GIS database directory, as well as some basic GRASS functionality. Here we introduce main concepts necessary for running the tutorial:

Setting up GRASS for the tutorial

GRASS uses unique database terminology and structure (GRASS database) that are important to understand for the set up of this tutorial, as you will need to place the required data (e.g. Location) in a specific GRASS database. In the following we review important terminology and give step by step directions on how to download and place you data in the correct location.

Important GRASS directory terminology

  • A GRASS database consists of directory with specific Locations (projects) where data layer are stored
  • Location is a directory with data related to one geographic location or a project. All data within one Location has the same coordinate reference system.
  • Mapset is a collection of maps within Location, containing data related to a specific task, user or a smaller project

Creating a GRASS database for the tutorial

You need to create a GRASS database with the Mapset that we will use for the tutorial before we can run the FUTURES model. Please Download the workshop location, noting where the files are located on your local directory. Now, create (unless you already have it) a directory named grassdata (GRASS database) in your home folder (or Documents), unzip the downloaded data into this directory. You should now have a Location futures_ncspm in grassdata.

Launching and exploring data in GRASS

Now that we have the data in the correct GRASS database, we can launch the Graphical User Interface (GUI). The GUI interface allows you to display raster, vector data as well as navigate through zooming in and out. Advanced exploration and visualization, like many popular GIS software, is also possible in GRASS (e.g. queries, adding legend). The print screens below depicts how you can add different map layers (left) and display the metadata of your data layers.

GRASS functionality

One of the advantages of GRASS is the diversity and number of modules that let you analyze all manner of spatial and temporal. GRASS GIS has over 500 different modules in the core distribution and over 230 addon modules that can be used to prepare and analyze data layers.

Prefix Function Example
r.* raster processing r.mapcalc: map algebra
v.* vector processing v.clean: topological cleaning
i.* imagery processing i.segment: object recognition
db.* database management select values from table
r3.* 3D raster processing r3.stats: 3D raster statistics
t.* temporal data processing t.rast.aggregate: temporal aggregation
g.* general data management g.rename: renames map
d.* display d.rast: display raster map

Command line vs. GUI interface

GRASS modules can be executed either through a GUI or command line interface. The GUI offers a user-friendly approach to executing modules where the user can navigate to data layers that they would like to analyze and modify processing options with simple check boxes. The GUI also offers an easily accessible manual on how to execute a model. The command line interface allows users to execute a module using command prompts specific to that module. This is handy when you are running similar analyses with minor modification or are familiar with the module commands for quick efficient processing. In this workshop we provide module prompts that can be copy and pasted into the command line for our workflow, but you can use both GUI and command line depending on personal preference. Look how GUI and command line interface represent the same tool.
Task: compute aspect (orientation) from provided digital elevation model using module r.slope.aspect using both module dialog and command line.

  • How to find modules? Modules are organized by their functionality in wxGUI menu, or we can search for them in Search modules tab. If we already know which module to use, we can just type it in the wxGUI command console.
  • Modules can be found in wxGUI menu

  • You can search modules by name, description or keywords in Search modules tab

  • By typing prefix r. we make a list of modules starting with that prefix to show up.

Computational region

Computational region - is an important raster concept in GRASS GIS. In GRASS a computational region can be set, subsetting larger extent data for quicker testing of analysis or analysis of specific regions based on administrative units. We provide a few points to keep in mind when using the computational region function:

  • defined by region extent and raster resolution
  • applies to all raster operations
  • persists between GRASS sessions, can be different for different mapsets
  • advantages: keeps your results consistent, avoid clipping, for computationally demanding tasks set region to smaller extent, check your result is good and then set the computational region to the entire study area and rerun analysis
  • run g.region -p or in menu Settings - Region - Display region to see current region settings
Simple ways to set computational region from GUI. On the left, set region to match raster map. On the right, select the highlighted option and then set region by drawing rectangle.

GRASS 3D view

We can explore our study area in 3D view.

  1. Add elevation_30m and uncheck or remove any other layers.
  2. Zoom to an area around Asheville and in Map Display select Various zoom options - Set computational region extent from display. Switch to 3D view (in the right corner on Map Display).
  3. Adjust the view (perspective, height, vertical exaggeration)
  4. In Data tab, set Fine mode resolution to 1 and set landuse_2011 as the color of the surface.
  5. When finished, switch back to 2D view.
Land cover 2011 draped over elevation

Modeling with FUTURES

Initial steps and data preparation

First we will set the computational region of our analyses to an extent covering our study area that aligns with our base landuse rasters. Like explained in the instructions above, you simply need copy and paste these commands into the command prompt of GRASS or open dialog.html g.region dialog.

g.region raster=landuse_2011 -p

The FUTURES model uses the locations of development and new development to predict when and where new urban growth will occur. This requires longitudinal data on urban land use. We will derive urbanized areas from NLCD dataset for year 1992, 2001, 2006 and 2011 by extracting categories category 21 - 24 into a new binary map where developed is 1, undeveloped 0 and NULL (no data). The NULL area is important in simulating urban growth as it precludes these are from becoming development. For this exercise we assume that water, wetlands and protected areas can not be developed, setting them to NULL.

First we will convert protected areas from vector to raster. We set NULLs to zeros (for simpler raster algebra expression in the next step) using r.null: input=protected_areas output=protected_areas use=val
r.null map=protected_areas null=0

And then create rasters of developed/undeveloped areas using raster algebra:

r.mapcalc "urban_1992 = if(landuse_1992 >= 21 && landuse_1992 <= 24, 1, if(landuse_1992 == 11 || landuse_1992 >= 90 || protected_areas, null(), 0))"
r.mapcalc "urban_2001 = if(landuse_2001 >= 21 && landuse_2001 <= 24, 1, if(landuse_2001 == 11 || landuse_2001 >= 90 || protected_areas, null(), 0))"
r.mapcalc "urban_2006 = if(landuse_2006 >= 21 && landuse_2006 <= 24, 1, if(landuse_2006 == 11 || landuse_2006 >= 90 || protected_areas, null(), 0))"
r.mapcalc "urban_2011 = if(landuse_2011 >= 21 && landuse_2011 <= 24, 1, if(landuse_2011 == 11 || landuse_2011 >= 90 || protected_areas, null(), 0))"

FUTURES is a multi-level modelling framework meaning that we model population projections for subregions and assume that these subregions are influenced differently by the factors that influence where development happens. This requires defining subregions for model implementation. For this exercise we use the county level, which is the finest scale of population data that is available to us. We therefore need to convert vectors of counties to a raster with the values of the FIPS attribute which links to population file: input=counties type=area use=attr attribute_column=FIPS output=counties

Before further steps, we will set our working directory so that the input population files and text files we are going to create are saved in one directory and easily accessible. You can do that from menu SettingsGRASS working environmentChange working directory. Select (or create) a directory and move there the downloaded files population_projection.csv and population_trend.csv.

Potential submodel

Module r.futures.potential implements the POTENTIAL submodel as a part of FUTURES land change model. POTENTIAL is implemented using a set of coefficients that relate a selection of site suitability factors to the probability of a place becoming developed. This is implemented using the parameter table in combination with maps of those site suitability factors (mapped predictors). The coefficients are obtained by conducting multilevel logistic regression in R with package lme4 where the coefficients may vary by county. The best model is selected automatically using dredge function from package MuMIn.

First, we will derive possible predictors of urban growth using GRASS modules.



Slope possibly influences urban growth as steep areas are difficult to build on. We will derive slope in degrees from digital elevation model using r.slope.aspect module:

r.slope.aspect elevation=elevation_30m slope=slope

Distance from lakes/rivers

Distance to lakes or rivers may contribute to an amenity draw where people would like to build a house in a location where they can view water. First we will extract category Open Water from 2011 NLCD dataset:

r.mapcalc "water = if(landuse_2011 == 11, 1, null())"

Then we compute the distance to water with module r.grow.distance and set color table to shades of blue:

r.grow.distance input=water distance=dist_to_water
r.colors -n map=dist_to_water color=blues

Distance from protected areas

Like water protected areas can attract urban growth as people enjoy living near scenic areas. We will use raster protected of protected areas we already created, but we will set NULL values to zero. We compute the distance to protected areas with module r.grow.distance and set color table from green to red:

r.null map=protected_areas setnull=0
r.grow.distance input=protected_areas distance=dist_to_protected
r.colors map=dist_to_protected color=gyr


Forest may influence urban growth in different ways. On the one hand it might be costly for developments as tree will need to be removed. On the other hand, people may want to live near forests. We calculate the percentage forest for a 1 km pixel to test forest influence, see NLCD category Open Water:

r.mapcalc "forest = if(landuse_2011 >= 41 && landuse_2011 <= 43, 1, 0)"
r.neighbors -c input=forest output=forest_smooth size=15 method=average
r.colors map=forest_smooth color=ndvi

Travel time to cities

Travel time to urban centers can often play a role in development with access to centers where employment is concentrated. Here we will compute travel time to cities (with population > 5000) as cumulative cost distance where cost is defined as travel time on roads. First we specify the speed on different types of roads. We copy the roads raster into our mapset so that we can change it by adding a new attribute field speed. Then we assign speed values (km/h) based on the type of road:

g.copy vector=roads,myroads
v.db.addcolumn map=myroads columns="speed double precision"
v.db.update map=myroads column=speed value=50 where="MTFCC = 'S1400'"
v.db.update map=myroads column=speed value=100 where="MTFCC IN ('S1100', 'S1200')"

Now we rasterize the selected road types using the speed values from the attribute table as raster values. input=myroads type=line where="MTFCC IN ('S1100', 'S1200', 'S1400')" output=roads_speed use=attr attribute_column=speed

We set the rest of the area to low speed and recompute the speed as time to travel through a 30m cell in minutes:

r.null map=roads_speed null=5
r.mapcalc "roads_travel_time = 1.8 / roads_speed"

Finally we compute the travel time to larger cities using r.cost:

r.cost input=roads_travel_time output=travel_time_cities start_points=cities
r.colors map=travel_time_cities color=byr

Road density

Dense road construction often occurs in suburban areas where much much development occurs in U.S. cities. To capture this influence we can calculate road density based on the road network. We rasterize roads and use a moving window analysis (r.neighbors) to compute road density for a 1 km area: input=roads output=roads use=val type=line
r.null map=roads null=0
r.neighbors -c input=roads output=road_dens size=25 method=average

Distance to interchanges

In the U.S. urban development often is clustered around interchanges as this provides easy access on transportation networks. To calculate this influence we will use the TIGER road database of type Ramp as interchanges, rasterize them and compute euclidean distance to them: input=roads type=line where="MTFCC = 'S1630'" output=interchanges use=val
r.grow.distance -m input=interchanges distance=dist_interchanges

Development pressure

Development pressure is an important variable in the FUTURES model that is always include as a dynamic variable reinforcing the pressure of past development. We assume that urban development in one location will increase the chance of development in near proximity. New simulated development is incorporated into calculating this development pressure every time step that FUTURES simulates urban growth. To estimate the influence that this local development pressure has, we include the development pressure r.futures.devpressure in our initial model estimates. Development pressure is based on number of neighboring developed cells within a specified search distance, weighted by distance. Its special role in the model allows for path dependent feedback between predicted change and change in subsequent steps.

r.futures.devpressure -n input=urban_2011 output=devpressure_2 method=gravity size=7 gamma=2 scaling_factor=10
r.futures.devpressure -n input=urban_2011 output=devpressure_1 method=gravity size=10 gamma=1 scaling_factor=1
r.futures.devpressure -n input=urban_2011 output=devpressure_0_5 method=gravity size=30 gamma=0.5 scaling_factor=0.1

When gamma increases, development influence decreases more rapidly with distance. Size is half the size of the moving window. When gamma is low, local development influences more distant places. We will derive 3 layers with different gamma and size parameters for the potential statistical model.

Rescaling variables

First we will look at the ranges of our predictor variables by running a short Python code snippet in Python shell:

for name in ['slope', 'dist_to_water', 'dist_to_protected', 'forest_smooth', 'travel_time_cities', 'road_dens', 'dist_interchanges', 'devpressure_0_5', 'devpressure_1']:
    minmax = grass.raster_info(name)
    print name, minmax['min'], minmax['max']

We will rescale some of our input variables:

r.mapcalc "dist_to_water_km = dist_to_water / 1000"
r.mapcalc "dist_to_protected_km = dist_to_protected / 1000"
r.mapcalc "dist_interchanges_km = dist_interchanges / 1000"
r.mapcalc "road_dens_perc = road_dens * 100"
r.mapcalc "forest_smooth_perc = forest_smooth * 100"


To sample only in the analyzed counties, we will clip development layer:

r.mapcalc "urban_change_01_11 = if(urban_2011 == 1, if(urban_2001 == 0, 1, null()), 0)"
r.mapcalc "urban_change_clip = if(counties, urban_change_01_11)"

To estimate the number of sampling points, we can use to report number of developed/undeveloped cells and their ratio. map=urban_change_clip units=h,c,p

We will sample the predictors and the response variable with 5000 random points in undeveloped areas and 1000 points in developed area:

r.sample.category input=urban_change_clip output=sampling sampled=counties,devpressure_0_5,devpressure_1,devpressure_2,slope,road_dens_perc,forest_smooth_perc,dist_to_water_km,dist_to_protected_km,dist_interchanges_km,travel_time_cities npoints=5000,1000

The attribute table can be exported as CSV file (not necessary step): map=sampling columns=urban_change_clip,counties,devpressure_0_5,devpressure_1,slope,road_dens_perc,forest_smooth_perc,dist_to_water_km,dist_to_protected_km,dist_interchanges_km,travel_time_cities separator=comma file=samples.csv

Development potential

Now we find best model for predicting urbanization using r.futures.potential which wraps an R script.

We can run R dredge function to find "best" model. We can specify minimum and maximum number of predictors the final model should use.

r.futures.potential -d input=sampling output=potential.csv columns=devpressure_1,slope,road_dens_perc,forest_smooth_perc,dist_to_water_km,dist_to_protected_km,dist_interchanges_km,travel_time_cities developed_column=urban_change_clip subregions_column=counties min_variables=4

Also, we can play with different combinations of predictors, for example:

r.futures.potential input=sampling output=potential.csv columns=devpressure_2,road_dens_perc,slope,dist_interchanges_km,dist_to_water_km developed_column=urban_change_clip subregions_column=counties --o
r.futures.potential input=sampling output=potential.csv columns=devpressure_1,road_dens_perc,slope,dist_interchanges_km,dist_to_water_km developed_column=urban_change_clip subregions_column=counties --o

You can then open the output file potential.csv, which is a CSV file with tabs as separators.

For this tutorial, the final potential is created with:

r.futures.potential input=sampling output=potential.csv columns=devpressure_2,road_dens_perc,slope,dist_interchanges_km,dist_to_water_km developed_column=urban_change_clip subregions_column=counties --o

We can now visualize the suitability surface using module r.futures.potsurface. It creates initial development potential (suitability) raster from predictors and model coefficients and serves only for evaluating development potential model. The values of the resulting raster range from 0 to 1.

r.futures.potsurface input=potential.csv subregions=counties output=suitability
r.colors map=suitability color=byr

Demand submodel

First we will mask out roads so that they don't influence into per capita land demand relation. input=roads type=line output=roads_mask use=val
r.mask roads_mask -i

We will use r.futures.demand which derives the population vs. development relation. The relation can be linear/logarithmic/logarithmic2/exponential/exponential approach. Look for examples of the different relations in the manual.

  • linear: y = A + Bx
  • logarithmic: y = A + Bln(x)
  • logarithmic2: y = A + B * ln(x - C)        (requires SciPy)
  • exponential: y = Ae^(BX)
  • exp_approach: y = (1 - e^(-A(x - B))) + C        (requires SciPy)

The format of the input population CSV files is described in the manual. It is important to have synchronized categories of subregions and the column headers of the CSV files (in our case FIPS number). How to simply generate the list of years (for which demand is computed) is described in r.futures.demand manual, for example run this in Python console:

','.join([str(i) for i in range(2011, 2036)])

Then we can create the DEMAND file:

r.futures.demand development=urban_1992,urban_2001,urban_2011 subregions=counties observed_population=population_trend.csv projected_population=population_projection.csv simulation_times=2011,2012,2013,2014,2015,2016,2017,2018,2019,2020,2021,2022,2023,2024,2025,2026,2027,2028,2029,2030,2031,2032,2033,2034,2035 plot=plot_demand.pdf demand=demand.csv separator=comma

In your current working directory, you should find files plot_demand.png and demand.csv.

If you have SciPy installed, you can experiment with other methods for fitting the functions:

r.futures.demand ... method=logarithmic2
r.futures.demand ... method=exp_approach

If necessary, you can create a set of demand files produced by fitting each method separately and then pick for each county the method which seems best and manually create a new demand file.

When you are finished, remove the mask as it is not needed for the next steps.

r.mask -r

Patch calibration

Patch calibration can be a very time consuming computation. Therefore we select only one county (Buncombe): input=counties type=area where="FIPS == 37021" use=attr attribute_column=FIPS output=calib_county
g.region raster=calib_county zoom=calib_county

to derive patches of new development by comparing historical and latest development. We can keep only patches with minimum size 2 cells (1800 = 2 x 30 x 30 m).

r.futures.calib development_start=urban_1992 development_end=urban_2011 subregions=counties patch_sizes=patches.txt patch_threshold=1800  -l

We obtained a file patches.txt (used later in the PGA) - a patch size distribution file - containing sizes of all found patches.

We can look at the distribution of the patch sizes:

from matplotlib import pyplot as plt
with open('patches.txt') as f:
    patches = [int(patch) for patch in f.readlines()]
plt.hist(patches, 2000)

At this point, we start the calibration to get best parameters of patch shape (for this tutorial, this step can be skipped and the suggested parameters are used).

r.futures.calib development_start=urban_1992 development_end=urban_2011 subregions=calib_county patch_sizes=patches.txt calibration_results=calib.csv patch_threshold=1800 repeat=5 compactness_mean=0.1,0.3,0.5,0.7,0.9 compactness_range=0.05 discount_factor=0.1,0.3,0.5,0.7,0.9 predictors=road_dens_perc,forest_smooth_perc,dist_to_protected_km demand=demand.csv devpot_params=potential.csv num_neighbors=4 seed_search=2 development_pressure=devpressure_0_5 development_pressure_approach=gravity n_dev_neighbourhood=30 gamma=0.5 scaling_factor=0.1

FUTURES simulation

We will switch back to our previous region:

g.region raster=landuse_2011 -p

Now we have all the inputs necessary for running r.futures.pga:

The entire command is here:

r.futures.pga subregions=counties developed=urban_2011 predictors=slope,forest_smooth_perc,dist_interchanges_km,travel_time_cities devpot_params=potential.csv development_pressure=devpressure_1 n_dev_neighbourhood=10 development_pressure_approach=gravity gamma=1 scaling_factor=1 demand=demand.csv discount_factor=0.3 compactness_mean=0.2 compactness_range=0.1 patch_sizes=patches.txt num_neighbors=4 seed_search=2 random_seed=1 output=final output_series=final

Quick description

The command parameters and their values:

  • raster map of counties with their categories

... subregions=counties ...

  • raster of developed (1), undeveloped (0) and NULLs for undevelopable areas

... developed=urban_2011 ...

  • predictors selected with r.futures.potential and their coefficients in a potential.csv file. The order of predictors must match the order in the file and the categories of the counties must match raster counties.

... predictors=slope,forest_smooth_perc,dist_interchanges_km,travel_time_cities devpot_params=potential.csv ...

  • initial development pressure computed by r.futures.devpressure, it's important to set here the same parameters

... development_pressure=devpressure_1 n_dev_neighbourhood=10 development_pressure_approach=gravity gamma=1 scaling_factor=1 ...

  • per capita land demand computed by r.futures.demand, the categories of the counties must match raster counties.

... demand=demand.csv ...

  • patch parameters from the calibration step

... discount_factor=0.3 compactness_mean=0.4 compactness_range=0.08 patch_sizes=patches.txt ...

  • recommended parameters for patch growing algorithm

... num_neighbors=4 seed_search=2 ...

  • set random seed for repeatable results or set flag -s to generate seed automatically

... random_seed=1 ...

  • specify final output map and optionally basename for intermediate raster maps

output=final output_series=final


Scenarios involving policies that encourage infill versus sprawl can be explored using the incentive_power parameter of r.futures.pga, which uses a power function to transform the evenness of the probability gradient in POTENTIAL. You can change the power to a number between 0.25 and 4 to test urban sprawl/infill scenarios. Higher power leads to infill behavior, lower power to urban sprawl.


Follow a tutorial how to make an animation from the results.