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+---
+title: "Modeling Movement in GRASS"
+author: "Michael Barton & Anna Petrasova"
+date: 2025-02-10
+date-modified: today
+format: 
+  html:
+    embed-resources: true
+    toc: true
+    code-tools: true
+    code-copy: true
+    code-fold: false
+page-layout: article
+categories: [intermediate, advanced, GUI, raster, cost surface, least cost path]
+description: Generating a cumulative cost surface and least cost path with *r.walk* and *r.path* to model movement by walking across a landscape.
+engine: jupyter
+execute: 
+  eval: false
+Jupyter: python3
+copyright: 
+  holder: Michael Barton & Anna Petrasova
+  year: 2025
+funding: "Creation of this tutorial was supported in part by US National Science Foundation grant FAIN 2303651."
+
+---
+
+GRASS has sophisticated tools to model movement across terrain, including [r.cost](https://grass.osgeo.org/grass-stable/manuals/r.cost.html), [r.walk](https://grass.osgeo.org/grass-stable/manuals/r.walk.html), [r.drain](https://grass.osgeo.org/grass-stable/manuals/r.drain.html), and [r.path](https://grass.osgeo.org/grass-stable/manuals/r.path.html). In this tutorial, we will use ***r.walk*** and ***r.path*** to determine the best walking path to reach a destination, like a hospital.
+
+::: {.callout-note title="Dataset"}
+This tutorial uses one of the standard GRASS demo data: flagstaff_arizona_usa. We will refer to place names in that data set, but it can be completed with any of the standard demo data sets for any region. We will use the *elevation* DEM, the *hospitals* vector points file (any other vector point file will serve), and the *landuse* raster map.
+
+This tutorial is designed so that you can complete it using the **GRASS GUI**, GRASS commands from the **console or terminal**, or using GRASS commands in a **Jupyter Notebook** environment.
+:::
+
+::: {.callout-note title="Don't know how to get started?"}
+If you are not sure how to get started with GRASS using its graphical user interface or using Python, checkout the tutorials [Get started with GRASS GIS GUI](../get_started/fast_track.qmd) and [Get started with GRASS & Python in Jupyter Notebooks](../get_started/fast_track_grass_and_python.qmd).
+:::
+
+## What is a cost surface?
+
+::::: grid
+::: g-col-6
+
+-   A **cost surface** is a raster in which each cell represents the “cost” or difficulty to move across landscape.
+
+-   A **cumulative cost surface** shows the total accumulated cost of moving from a starting point to a location. Cumulative cost surfaces are also used to find a **least cost path** between a location and the starting point.
+
+-   GRASS [r.walk](https://grass.osgeo.org/grass-stable/manuals/r.walk.html) tool generates a cumulative cost surface using Naismith's rule for walking times where each cell has the value in **seconds** of the time it takes to walk from the start point to that cell.
+:::
+
+::: g-col-6
+![cost surface](img_movement/GRASS_movement_0.webp){fig-align="right" width="100%"}
+:::
+:::::
+
+# Modeling movement with a cumulative cost surface
+
+## Overview
+
+::::: grid
+::: g-col-6
+
+1.  Start with a **DEM of elevation** for topography to determine movement costs.
+
+2.  Create a **friction map** with a value of 0 (or other values for additional movement costs).
+
+3.  Select **start point(s)**.
+
+4.  Create a **cost surface**.
+
+5.  A **least cost** path can then be calculated between any point on the cost surface and the start point.
+:::
+
+::: g-col-6
+![DEM](img_movement/GRASS_movement_1.webp)
+:::
+:::::
+
+## Friction map
+
+-   The GRASS [map calculator](https://grass.osgeo.org/grass-stable/manuals/r.mapcalc.html) lets you create a map, alter a map, or combine maps using **map algebra**. The map calculator can be used from the GUI or as a command.
+
+-   Before you make a friction map, make sure the [**computational region**](https://grass.osgeo.org/grass-stable/manuals/g.region.html) matches the elevation map.
+
+-   Create the *friction0* map with 0 in every cell.
+
+:::::: {.panel-tabset group="language"}
+
+#### GUI
+
+::::: grid
+::: g-col-6
+
+1.  Add the *elevation* raster to the Layer Manager.
+
+2.  Right click *elevation* in Layer Manager.
+
+3.  Select **Set computational region from selected map**.
+
+4.  Open the **Raster Map Calculator** from the top toolbar ("abacus" icon).
+
+5.  Fill in the output map name as *friction0* and enter 0 in the expression field.
+
+6.  Press Run.
+:::
+
+::: g-col-6
+![Raster map calculator](img_movement/GRASS_movement_2.webp)
+:::
+:::::
+
+#### Command line
+
+1.  Set the region to match the elevation map
+
+2.  Create a friction map with a value of 0 in all cells that matches the extent and resolution of the elevation map
+
+```{python}
+g.region raster=elevation
+r.mapcalc "friction0 = 0"
+```
+
+#### Python
+
+1.  Set the region to match the elevation map
+
+2.  Create a friction map with a value of 0 in all cells that matches the extent and resolution of the elevation map
+
+```{python}
+gs.run_command("g.region", raster="elevation")
+gs.mapcalc("friction0 = 0")
+```
+::::::
+
+## Choose a start point
+
+-   Now that we have a DEM map for terrain and a friction map, all we need for a cumulative cost surface is a start point: the point from which to calculate movement costs.
+
+-   A start point can be a vector point, a raster cell, or even a pair of coordinates.
+
+-   A cost surface in *r.walk* can have multiple start points.
+
+-   We’ll make a start point from the Flagstaff Medical Center, found in the *hospitals* vector points file.
+
+:::::: {.panel-tabset group="language"}
+
+#### GUI
+
+::::: grid
+::: g-col-6
+Use the **Attribute Table Manager** for *hospitals*:
+
+1.  Display *hospitals* map by adding it to the Layer Manager from Data Catalog.
+
+2.  Right click and open the Attribute Table Manager.
+
+3.  Select "Flagstaff Medical Center" record.
+
+4.  Right click and select **Extract selected features** from the context menu.
+
+5.  Name the new map *FMC*
+:::
+
+::: g-col-6
+![data table tool for hospitals vector points map](img_movement/GRASS_movement_3.webp)
+
+![table row context menu](img_movement/GRASS_movement_4.webp){width="60%"}
+:::
+:::::
+
+#### Command line
+
+Use the v.extract tool to create a vector point map named *FMC* from the *hospitals* map.
+
+```{python}
+v.extract input=hospitals type=point where="FACILITY_N = 'FLAGSTAFF MEDICAL CENTER'" output=FMC
+```
+
+#### Python
+
+Use the v.extract tool to create a vector point map named *FMC* from the *hospitals* map.
+
+```{python}
+gs.run_command("v.extract", input="hospitals", type="point", where="FACILITY_N = 'FLAGSTAFF MEDICAL CENTER'", output="FMC")
+```
+::::::
+
+-   Use the *d.vect* tool by double clicking FMC in the layer manager to display the point with a color and size to see it better
+
+![](img_movement/GRASS_movement_5.webp)
+
+## Generate the cumulative cost surface {#generate-cumulative-cost-surface}
+
+::::::::::::: {.panel-tabset group="language"}
+
+#### GUI
+
+-   Use the *r.walk* tool from the **Raster/Terrain Analysis** menu
+
+::::: grid
+::: g-col-6
+
+1.  Enter the **elevation map** ( *elevation* ), **friction map** ( *friction0* ), and **name of the cost surface** to create (FMC_cost_seconds)
+
+![](img_movement/GRASS_movement_6.webp){fig-align="left" width="100%"}
+:::
+
+::: g-col-6
+2.  Enter the name of a **directions map** ( *FMC_directions* ) to use for creating a least cost path.
+
+![](img_movement/GRASS_movement_7.webp){fig-align="left" width="100%"}
+:::
+:::::
+
+::::: grid
+::: g-col-6
+3.  Enter the **start point** ( *FMC* ).
+
+![](img_movement/GRASS_movement_8.webp){fig-align="left" width="100%"}
+:::
+
+::: g-col-6
+4.  Optional: control the **spatial extent** of cost surface.
+
+![](img_movement/GRASS_movement_9.webp)
+:::
+:::::
+
+::::: grid
+::: g-col-6
+5.  Optional: adjust **Movement parameter** settings.
+
+![](img_movement/GRASS_movement_10.webp){fig-align="left" width="100%"}
+:::
+
+::: g-col-6
+6.  Recommended: select **knight's move** for calculating cost and direction.
+
+![](img_movement/GRASS_movement_11.webp){fig-align="left" width="100%"}
+:::
+:::::
+
+::: {.callout-note title="Tip"}
+Click the "copy" button to copy the GRASS command. You can save it in a text file for later reuse or to document your work.
+:::
+
+#### Command line
+
+-   Use the r.walk command to generate the cumulative cost surface.
+
+```{python}
+r.walk elevation=elevation friction=friction0 output=FMC_cost_seconds outdir=FMC_directions start_points=FMC -k
+```
+
+#### Python
+
+-   Use the r.walk command to generate the cumulative cost surface.
+
+```{python}
+gs.run_command("r.walk",
+               elevation="elevation",
+               friction="friction0",
+               output="FMC_cost_seconds",
+               outdir="FMC_directions",
+               start_points="FMC",
+               flags="k")
+```
+:::::::::::::
+
+## Cumulative cost surface map
+
+-   Each raster cell value in the cost surface is the time in seconds to walk from FMC to that cell over the terrain of the Flagstaff DEM
+
+![](img_movement/GRASS_movement_12.webp)
+
+::: {.callout-note title="Tip"}
+Tip: You can display the cumulative cost surface over a shaded relief map in the **layer manager** using the [d.shade](https://grass.osgeo.org/grass-stable/manuals/d.shade.html) tool and a relief map of *elevation* made with [r.relief](https://grass.osgeo.org/grass-stable/manuals/d.shade.html).
+:::
+
+## Movement across a cumulative cost surface {#movement-across-cost-surface}
+
+-   You can transform the walking time in seconds to hours by dividing the map by 3600 using the map calculator
+
+:::::: {.panel-tabset group="language"}
+
+#### GUI
+
+::::: grid
+::: g-col-6
+
+1.  Open the map calculator.
+
+2.  Enter the name of the new map of walking time in hours: *FMC_cost_hours*.
+
+3.  Enter FMC_cost_seconds / 3600 into the expressions field
+
+4.  Press Run.
+:::
+
+::: g-col-6
+![](img_movement/GRASS_movement_13.webp){fig-align="left" width="100%"}
+:::
+:::::
+
+#### Command line
+
+```{python}
+r.mapcalc "FMC_cost_hours = FMC_cost_seconds / 3600"
+```
+
+#### Python
+
+```{python}
+gs.mapcalc("FMC_cost_hours = FMC_cost_seconds / 3600")
+```
+::::::
+
+------------------------------------------------------------------------
+
+::::: grid
+::: g-col-6
+
+-   We can query or filter this hourly cumulative cost surface to areas of equivalent walking time.
+
+-   For example, in the **layer manager** we can used the *d.rast* tool to show the area within a 2 hour walk of FMC and then set the opacity of the cost surface to 50% to see the underlying terrain\
+:::
+
+::: g-col-6
+![](img_movement/GRASS_movement_15.webp)
+:::
+:::::
+
+![Shaded area represents terrain reached within a 2 hour walk from FMC](img_movement/GRASS_movement_14.webp)
+
+# Least cost paths {#least-cost-path}
+
+## Overview
+
+-   We can also plot a **least cost path** (LCP), which is the least costly (shortest time) route between any point on the cumulative cost surface and FMC.
+
+-   Imagine a stranded hiker NE of Flagstaff who has to walk to FMC.
+
+-   What path would take the least time?
+
+![](img_movement/GRASS_movement_16.webp)
+
+## Generating a least cost path
+
+To create a LCP in GRASS, we will use [r.path](https://grass.osgeo.org/grass-stable/manuals/r.path.html) (also under the Raster/Terrain analysis menu).
+
+:::::::: {.panel-tabset group="language"}
+
+#### GUI
+
+::::: grid
+::: g-col-6
+
+1.  Input the **directions map** (*FMC_directions*) we also made when we created the cumulative cost surface.\
+    ![](img_movement/GRASS_movement_17.webp)
+:::
+
+::: g-col-6
+2.  Input the **coordinates of the hiker** as the starting point for the LCP. (We could also use a pre-defined vector point).
+
+![](img_movement/GRASS_movement_18.webp)
+:::
+:::::
+
+:::: grid
+::: g-col-6
+3.  Specify the **name of the output vector path map** (*LCP_cumulative*).
+
+![](img_movement/GRASS_movement_19.webp)
+:::
+::::
+
+#### Command line
+
+```{python}
+r.path input=FMC_directions format=auto vector_path=LCP_cumulative start_coordinates=477476,13914951
+```
+
+#### Python
+
+```{python}
+gs.run_command("r.path",
+               input="FMC_directions",
+               format="auto",
+               vector_path="LCP_cumulative",
+               start_coordinates=[477476, 13914951])
+```
+::::::::
+
+## Least cost path generated
+
+-   Here is the LCP result.
+
+![](img_movement/GRASS_movement_20.webp)
+
+# Adding a friction map to movement costs
+
+## Overview
+
+-   A **friction map** can be used to incorporate other factors than just terrain into creating a cumulative cost surface and modeling movement
+
+-   The value of each cell in a friction map raster is the amount of walking time, in seconds/meter, *in addition to* the time needed because of terrain
+
+-   We can **reclassify** the *landuse* map to create a friction map of the amount of extra time it would take to walk through different kinds of land cover
+
+![Reclassification of *landuse* to show major land cover types](img_movement/GRASS_movement_21.webp)
+
+## Reclassifying *landuse* to create a friction map
+
+A standard walking speed across flat terrain is about 5 km/hr = 0.72 sec/m.
+
+We might then estimate that it would take an additional
+
+-   3 sec/m to walk through dense pinyon-juniper woodland
+
+-   1 sec/m to cross conifer forest
+
+-   2 sec/m to wander through urban Flagstaff
+
+-   5 sec/m to clamber over lava fields
+
+-   10 sec/m to try and cross water
+
+We can create this friction map by reclassifying the *landuse* map using [*r.reclass*](https://grass.osgeo.org/grass-stable/manuals/r.reclass.html) to assign new friction values to the existing land cover categories.  
+
+:::::: {.panel-tabset group="language"}
+
+## GUI
+
+The [r.reclass](https://grass.osgeo.org/grass-stable/manuals/r.reclass.html) tool is found under the Raster/Change category… menu.
+
+::::: grid
+::: g-col-6
+
+1.  Enter *landuse* for the raster to be reclassified
+
+2.  Enter *friction_reclassified* for the output reclassified map
+
+3.  Enter the reclass rules directly in the text box or from a saved text file. Use and \* symbol to represent everything not covered by the specific reclass rules
+
+  > 11 90 95 = 10 water  
+  > 21 thru 24 = 2 urban  
+  > 31 = 5 lava  
+  > 41 thru 43 = 1 conifer forest  
+  > 52 = 3 pinyon juniper woodland  
+  > \* = 0 no friction  
+  
+:::
+
+::: g-col-6
+
+-   This creates a new friction map named *friction_landcover*
+
+![](img_movement/GRASS_movement_22.webp)
+:::
+:::::
+
+## Command line
+
+```{python}
+r.reclass input=landuse output=friction_landcover rules=- << EOF
+11 90 95 = 10 water
+21 thru 24 = 2 urban
+31 = 5 lava
+41 thru 43 = 1 conifer forest
+52 = 3 pinyon juniper woodland
+* = 0 no friction
+EOF
+```
+
+## Python
+
+```{python}
+rules = """\
+11 90 95 = 10 water
+21 thru 24 = 2 urban
+31 = 5 lava
+41 thru 43 = 1 conifer forest
+52 = 3 pinyon juniper woodland
+* = 0 no friction
+"""
+gs.write_command("r.reclass",
+                 input="landuse",
+                 output="friction_landcover",
+                 rules="-",
+                 stdin=rules)
+```
+::::::
+
+![The reclassified friction map (*friction_landcover*)](img_movement/GRASS_movement_23.webp)
+
+## Modifying a cumulative cost surface with a friction map
+
+We can now create a new cumulative cost surface using this new friction map and convert it from seconds to hours, as we did before:
+
+::: {.panel-tabset group="language"}
+
+#### GUI
+
+1. Follow the procedures in the [Generate the cumulative cost surface
+section](#generate-cumulative-cost-surface) and substitute the new *friction_landcover* map for the *friction0* map used previously.
+
+2. Convert the cumulative cost surface to hours instead of seconds following the procedures in the [Movement across a cumulative cost surface section]({#movement-across-cost-surface})
+
+#### Command line
+
+```{python}
+r.walk elevation=elevation friction=friction_landcover output=FMC_vegcost_seconds outdir=FMC_vegcost_directions start_points=FMC -k
+r.mapcalc "FMC_vegcost_hours = FMC_vegcost_seconds / 3600"
+```
+
+#### Python
+
+```{python}
+gs.run_command("r.walk",
+               elevation="elevation",
+               friction="friction_landcover",
+               output="FMC_vegcost_seconds",
+               outdir="FMC_vegcost_directions",
+               start_points="FMC",
+               flags="k")
+gs.mapcalc("FMC_vegcost_hours = FMC_vegcost_seconds / 3600")
+```
+:::
+
+![cumulative cost surface with additional friction from land cover](img_movement/GRASS_movement_24.webp)
+
+## Least cost paths and friction
+
+-   We can create a new LCP from the stranded hiker to FMC over terrain where land cover also affects the cost of movement
+
+::: {.panel-tabset group="language"}
+
+#### GUI
+
+1. Follow the procedures in the [Least cost path section](#least-cost-path), substituting the new direction map made along with the cumulative cost surface with land cover friction map.
+
+2. Give this new LCP the name *LCP_vegcost* to distinguish from the previous LCP.
+
+#### Command line
+
+```{python}
+r.path input=FMC_vegcost_directions format=auto vector_path=LCP_vegcost start_coordinates=477476,13914951
+```
+
+#### Python
+
+```{python}
+gs.run_command("r.path",
+               input="FMC_vegcost_directions",
+               format="auto",
+               vector_path="LCP_vegcost",
+               start_coordinates=[477476, 13914951])
+```
+:::
+
+-   It takes more time to reach FMC if the hiker has to navigate dense vegetation as well as terrain.
+
+-   In the map below, terrain colored by land cover, the original LCP with terrain only is shown by the blue line. The LCP with a land cover friction map is shown by the heavier yellow line
+
+![comparing LCP with terrain only and with land cover friction](img_movement/GRASS_movement_25.webp)
+
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