# Preparation of input data: geomorphological analysis with whitebox

#### Alban de Lavenne & Antoine Casquin

#### 2025-03-20

The hydrological modelling of the `transfR` package is based on a geomorphological analysis of the studied catchments. In this vignette, we give some guidance on how to perform this geomorphological analysis. More specifically, we extract the catchment delineation and hydraulic length maps from a digital elevation model (DEM). This analysis is one of the two inputs needed (together with the time series of flow observations) to build a `transfR` object and start using the `transfR` package (see the Get started with transfR vignette).

Hydraulic length is defined as the distance within the river network along an identified flow path to the outlet. It can be extracted from a DEM in many different ways, such as with the GRASS toolkits (Jasiewicz and Metz 2011), Whitebox GAT (see J. B. Lindsay (2016) or WhiteboxTools), TauDEM (D. Tarboton, Utah State University) or online services (Squividant et al. (2015) for catchment delineation only). This vignette presents one possible workflow by making use of two main R packages:

- `elevatr` that provides elevation data worldwide from Various APIs.
- `whitebox`, an R frontend for the ‘WhiteboxTools’ library, which is an advanced geospatial data analysis platform.

Functions of the `whitebox` package generally do not work with objects in R memory, but with files written on the disk storage. It is therefore advised to define the working directory where these files will be written.

    wbt_wd <- tempdir(check = TRUE)

## 1. Retrieve elevation data with `elevatr`

The `elevatr` package allows retrieving grids (rasters) of elevation data worldwide for various zoom levels and data sources. It uses the Open Topography Global Datasets API for accessing Shuttle Radar Topography Mission (SRTM) data.

It is necessary to assign a geographic projection for the catchment delineation and hydraulic length maps with the `whitebox` package. We chose to use the Lambert93 projection, the official projection for maps of metropolitan France, for which the EPSG code is 2154.

    library(elevatr)
    library(progress) # Needed by elevatr

    # Set up a projection (French Lambert-93 projection)
    EPSG <- 2154

    # Define a bbox that will encompass the catchments of the study area
    blavet_bbox <- st_bbox(c(xmin = -3.3, xmax = -2.7, ymax = 48.11, ymin = 47.77),
                               crs = st_crs(4326))
    blavet_loc <- st_as_sfc(blavet_bbox) |> st_sf()

    # Retrieve elevation data as raster
    dem_raw <- elevatr::get_elev_raster(blavet_loc, z = 10) # ~76m resolution

    # Project and define spatial resolution:
    dem_100m  <- st_warp(st_as_stars(dem_raw), cellsize = 100, crs = st_crs(EPSG))
    names(dem_100m) <- "warp"

    # Set negative values (ocean) to NA
    dem_100m[dem_100m < 0] <- NA

    # Write to file
    write_stars(dem_100m["warp"], file.path(wbt_wd,"dem_100m.tif"))

## 2. Retrieve a known river network and burn it into DEM (optional)

The hydrological modelling distinguish the hillslope from the river network. Both will have very different transfer dynamics, and the `transfR` package aims to describe the transfer function of the river network only. Defining where this river network begins and the flow path it takes is a key, and non-trivial, issue for hydrogeomorphologists. The easiest way to draw a drainage network from a DEM is usually to define a minimum drainage area threshold at which the drainage network is assumed to start. However, defining this threshold can be difficult as it may vary spatially, especially with the geology of the region. It may therefore be better to use a known river network and force the flow paths to follow it. Here we will use the French TOPAGE river network as a reference (see the description of the `Blavet` dataset to download it from the Web Feature Service (WFS) “Sandre - Eau France”). We will implement a stream burning technique into the DEM using the function `whitebox::wbt_burn_streams_at_roads()` and following John B. Lindsay (2016).

    library(transfR)
    library(whitebox)

    # Get the French Topage river network from the Blavet dataset
    data(Blavet)
    CoursEau_Topage2019 <- Blavet$network

    # Change projection and write files
    network_topage <- st_transform(CoursEau_Topage2019, EPSG)
    st_write(network_topage, file.path(wbt_wd, "network_topage.shp"),
                 delete_layer = TRUE, quiet = TRUE)
    whitebox::wbt_rasterize_streams("network_topage.shp",
                                    base = "dem_100m.tif",
                                    output = "network_topage.tif",
                                    nodata = 0,
                                    wd = wbt_wd)

    # Burn this river network on the DEM
    # We will neglect the effect of the road embankments at this DEM resolution of 100m
    # by creating an empty shapefile for roads
    st_write(st_sfc(st_multilinestring(),crs = EPSG), file.path(wbt_wd,"roads.shp"),
                 delete_layer = TRUE, quiet = TRUE)
    whitebox::wbt_burn_streams_at_roads(dem = "dem_100m.tif",
                            streams = "network_topage.shp",
                            roads = "roads.shp",
                            output = "dem_100m_burn.tif",
                            wd = wbt_wd)

## 3. Delineate catchments from their outlets coordinates

The `whitebox` package provides all the tools to perform a usual catchment delineation workflow from a DEM and outlet’s coordinates. It can be done in 6 different steps:

- Fill the depressions,
- Compute flow direction using D8 algorithm,
- Compute flow accumulation according to flow direction,
- Extract a river network using a threshold in flow accumulation,
- Snap the outlets to this river network,
- Delimit the catchments.

    # Remove the depressions on the DEM
    whitebox::wbt_fill_depressions(dem = "dem_100m_burn.tif",
                                   output = "dem_fill.tif",
                                   wd = wbt_wd)

    # Flow direction raster
    whitebox::wbt_d8_pointer(dem = "dem_fill.tif",
                             output = "d8.tif",
                             wd = wbt_wd)

    # Compute flow accumulation
    whitebox::wbt_d8_flow_accumulation(input = "d8.tif",
                                       pntr = TRUE,
                                       output ="facc.tif",
                                       wd = wbt_wd)

    # Extract a stream network (threshold = 1 km2) consistent with flow direction
    whitebox::wbt_extract_streams(flow_accum =  "facc.tif",
                                  threshold = 100, # 100 cells for 1 km2
                                  output = "network_1km2.tif",
                                  zero_background = TRUE,
                                  wd = wbt_wd)
    whitebox::wbt_remove_short_streams(d8_pntr = "d8.tif",
                                       streams = "network_1km2.tif",
                                       output = "network_d8.tif",
                                       min_length= 200,
                                       wd = wbt_wd)

Coordinates of the outlets are retrieved from hydro.eaufrance.fr and snapped to the pixel of the river network that is consistent with the previously defined flow directions.

    # Localize the outlets of the studied catchments (with manual adjustments to help snapping)
    outlets_coordinates <- data.frame(id = names(Blavet$hl),
                                 X = c(254010.612,255940-100,255903,237201,273672,265550),
                                 Y = c(6772515.474,6776418-200,6776495,6774304-200,6762681,6783313))
    outlets <- st_as_sf(outlets_coordinates, coords = c("X", "Y"), crs=2154)
    st_write(outlets, dsn = file.path(wbt_wd, "outlets.shp"),
                 delete_layer = TRUE, quiet = TRUE)

    # Snap the outlets on the stream raster
    whitebox::wbt_jenson_snap_pour_points(pour_pts = "outlets.shp",
                                          streams = "network_d8.tif",
                                          output = "outlets_snapped.shp",
                                          snap_dist = 200,
                                          wd = wbt_wd)
    outlets_snapped <- st_read(file.path(wbt_wd, "outlets_snapped.shp"), quiet = TRUE)

    # Delineate catchments
    catchments <- st_sfc(crs = EPSG)
    for(id in outlets_snapped$id){
      st_write(outlets_snapped[outlets_snapped$id==id,],
                   file.path(wbt_wd, paste0(id, "_outlet.shp")), delete_layer = TRUE, quiet = TRUE)
      whitebox::wbt_watershed(d8_pntr = "d8.tif",
                              pour_pts = paste0(id, "_outlet.shp"),
                              output = paste0(id, "_catchment.tif"),
                              wd = wbt_wd)
      # Vectorize catchments
      drainage <- read_stars(file.path(wbt_wd, paste0(id, "_catchment.tif")))
      contours <- st_contour(drainage, breaks = 1) |> st_geometry() |> st_cast("POLYGON")
      contours <- contours[which.max(st_area(contours))]
      catchments <- rbind(catchments, st_sf(data.frame(id, geom = contours)))
    }

Resulting catchments delineation can be plotted and checked.

    # Compare drainage areas to the dataset provided with transfR
    compare_areas <- data.frame(
      name = names(Blavet$hl),
      expected_area =  st_area(st_geometry(Blavet$obs)) |> units::set_units("km^2") |> round(1),
      computed_area = st_area(catchments) |> units::set_units("km^2") |> round(1)
    )

    print(compare_areas)
    #>            name expected_area computed_area
    #> 1      J5613010  314.8 [km^2]  314.8 [km^2]
    #> 2      J5618310   15.5 [km^2]   15.6 [km^2]
    #> 3      J5618320    6.8 [km^2]    6.7 [km^2]
    #> 4      J5704810   45.3 [km^2]   45.8 [km^2]
    #> 5      J8433020  134.5 [km^2]  134.7 [km^2]
    #> 6 AgrHys_Naizin    4.9 [km^2]    5.2 [km^2]

    # Plot catchment delineation
    par(oma = c(0, 0, 0, 6))
    plot(catchments[,"id"], main = "Catchments delineation", key.pos = 4, reset = FALSE)
    plot(st_geometry(st_intersection(network_topage,catchments)),
         col = "white", lwd = 1.5, add = TRUE)
    plot(outlets_snapped, col = "black", pch = 16, add = TRUE)

## 4. Compute flow path length and hydraulic length for each catchments

The `whitebox` package does not provide a function to compute hydraulic length directly. However, it can compute the total downslope flow path length to the outlet using `whitebox::wbt_downslope_flowpath_length()` function and the downslope distance to the stream using `whitebox::wbt_downslope_distance_to_stream()` function. The hydraulic length does not take into account the length of the flow path over the hillslopes, so it can be calculated simply by the difference of these two flow distances.

Flow path lengths are computed once for all the study area. For each catchment, this raster is then trimmed (i.e. removing NA values outside the bounding box of the catchment) and the values of flow path lengths are corrected such as the minimum flow path length is equal to half a pixel width/height. The hydraulic lengths are finally gathered in a list as expected by the `as_transfr()` function.

    # Compute hydraulic length
    whitebox::wbt_downslope_flowpath_length(d8_pntr = "d8.tif",
                                            output = "fpl.tif",
                                            wd = wbt_wd)
    whitebox::wbt_downslope_distance_to_stream(dem = "dem_fill.tif",
                                               streams = "network_topage.tif",
                                               output = "d2s.tif",
                                               wd = wbt_wd)
    fpl <- read_stars(file.path(wbt_wd, "fpl.tif"))
    d2s <- read_stars(file.path(wbt_wd, "d2s.tif"))
    hl_region <- fpl-d2s
    names(hl_region) <- "hl"

    # Crop hydraulic length for each catchment
    hl <- list()
    for(id in catchments$id){
      crop <- st_crop(hl_region, catchments[catchments$id==id,])
      crop <- crop-min(crop$hl, na.rm = TRUE)
      crop$hl <- units::set_units(crop$hl, "m")
      hl[[id]] <- crop
    }

Resulting maps of hydraulic length can be plotted and checked.

    i <- 1
    network <- st_geometry(st_intersection(network_topage,catchments[i,]))
    plot(hl[[i]], main = paste("Hydraulic length of catchment", i,"[m]"),
         col = hcl.colors(20, palette = "Teal"), key.pos = 1, reset = FALSE)
    plot(network, col = "white", lwd = 1.5, add = TRUE)

## 5. Creating a transfR object and running a simulation

Catchment delineations can be used as the spatial dimension of `stars` objects to georeference the observed flow time series of gauged catchments and locate ungauged catchments (see vignette Preparation of input data: creation of a stars object for details). Here we will create a `stars` object using the observed discharge of the `Blavet` dataset and the delineations that we just computed with `whitebox`.

    obs_st <- st_as_stars(list(Qobs = Blavet$obs$Qobs),
                                dimensions = st_dimensions(
                                  time = st_get_dimension_values(Blavet$obs,1),
                                  space = st_geometry(catchments)))

The maps of hydraulic length can finally be used to create an object of class `transfR` by using the function `as_transfr()` (argument `hl`) and perform simulations.

    obs <- as_transfr(st = obs_st, hl = hl)

A transfer of hydrograph from the gauged catchments to the ungauged catchments can then quickly be implemented using the `quick_transfr()` function.

    obs <- quick_transfr(obs, velocity = "brittany2013", parallel = TRUE, cores = 2, cv = TRUE)

The simulated time series will be available in its stars object as new attributes.

    obs$st

## References

Jasiewicz, JarosŁaw, and Markus Metz. 2011. “A New GRASS GIS Toolkit for Hortonian Analysis of Drainage Networks.” Computers & Geosciences 37 (8): 1162–73. https://doi.org/10.1016/j.cageo.2011.03.003.
Lindsay, J. B. 2016. “Whitebox GAT: A Case Study in Geomorphometric Analysis.” Computers & Geosciences 95 (October): 75–84. https://doi.org/10.1016/j.cageo.2016.07.003.
Lindsay, John B. 2016. “The Practice of DEM Stream Burning Revisited.” Earth Surface Processes and Landforms 41 (5): 658–68. https://doi.org/10.1002/esp.3888.
Squividant, H., R. Bera, P. Aurousseau, and C. Cudennec. 2015. “Online Watershed Boundary Delineation: Sharing Models Through Spatial Data Infrastructures.” Proceedings of the International Association of Hydrological Sciences 368: 144–49. https://doi.org/10.5194/piahs-368-144-2015.