In ITSLeeds/slopes: Calculate Slopes of Roads, Rivers and Trajectories

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)

Introduction

This article aims to provide external verification of the results provided by the package. So far only one verification dataset has been used, but we hope to find others. If you know of verification datasets, please let us know --- initially we planned to use a dataset from a paper on river slopes [@cohen_global_2018], but we could find no way of extracting the underlying data to do the calculation.

For this article we primarily used the following packages, although others are loaded in subsequent code chunks.

library(slopes)
library(sf)

The results are reproducible (requires downloading input data manually and installing additional packages). To keep package build times low, only the results are presented below.

Comparison with results from ArcMap 3D Analyst

Three-dimensional traces of roads dataset

An input dataset, comprising a 3D linestring recorded using a dual frequency GNSS receiver (a Leica 1200) with a vertical accuracy of 20 mm [@ariza-lopez_dataset_2019] was downloaded from the figshare website as a .zip file and unzipped and inflated in the working directory as follows (not evaluated to reduce package build times):

download.file("https://ndownloader.figshare.com/files/14331185", "3DGRT_AXIS_EPSG25830_v2.zip")
unzip("3DGRT_AXIS_EPSG25830_v2.zip")
trace = sf::read_sf("3DGRT_AXIS_EPSG25830_v2.shp")
plot(trace)
nrow(trace)
#> 11304
summary(trace$X3DGRT_h)
#>  Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
#>   642.9   690.3   751.4   759.9   834.3   884.9

# original trace dataset
traces = sf::read_sf("vignettes/3DGRT_TRACES_EPSG25830_v2.shp")
traces = sf::read_sf("3DGRT_TRACES_EPSG25830_v2.shp")
nrow(traces)
#> [1] 111113

To verify our estimates of hilliness, we generated slope estimates for each segment and compared them with Table 7 in @ariza-lopez_dataset_2019. The absolute gradient measure published in that paper were:

res_gps = c(0.00, 4.58, 1136.36, 6.97)
res_final = c(0.00, 4.96, 40.70, 3.41)
res = data.frame(cbind(
  c("GPS", "Dual frequency GNSS receiver"),
  rbind(res_gps, res_final)
))
names(res) = c("Source", "min", " mean", " max", " stdev")
knitr::kable(res, row.names = FALSE)

# mapview::mapview(trace) # check extent: it's above 6km in height
# remotes::install_github("hypertidy/ceramic")
loc = colMeans(sf::st_coordinates(sf::st_transform(trace, 4326)))
e = ceramic::cc_elevation(loc = loc[1:2], buffer = 3000)
trace_projected = sf::st_transform(trace, 3857)
plot(e)
plot(trace_projected$geometry, add = TRUE)

# aim: get max distance from centrepoint
bb = sf::st_bbox(sf::st_transform(trace, 4326))
geosphere::distHaversine(c(bb[1], bb[2]), c(bb[3], bb[2]))
geosphere::distHaversine(c(bb[1], bb[2]), c(bb[1], bb[4]))
# max of those 2 and divide by 2

knitr::include_graphics("https://user-images.githubusercontent.com/1825120/81125221-75c06780-8f2f-11ea-8cea-ad6322ef99e7.png")

The slopes were estimated as follows:

# source: https://www.robinlovelace.net/presentations/munster.html#31
points2line_trajectory = function(p) {
  c = st_coordinates(p)
  i = seq(nrow(p) - 2)
  l = purrr::map(i, ~ sf::st_linestring(c[.x:(.x + 1), ]))
  lfc = sf::st_sfc(l)
  a = seq(length(lfc)) + 1 # sequence to subset
  p_data = cbind(sf::st_set_geometry(p[a, ], NULL))
  sf::st_sf(p_data, geometry = lfc)
}
r = points2line_trajectory(trace_projected)
# summary(st_length(r)) # mean distance is 1m! Doesn't make sense, need to create segments
s = slope_raster(r, e = e)
slope_summary = data.frame(min = min(s), mean = mean(s), max = max(s), stdev = sd(s))
slope_summary = slope_summary * 100
knitr::kable(slope_summary, digits = 1)

| min| mean| max| stdev| |---:|----:|----:|-----:| | 0| 6.2| 48.2| 5.6|

Combined with the previous table from @ariza-lopez_dataset_2019, these results can be compared with those obtained from mainstream GPS, and an accurate GNSS receiver:

|Source |min | mean | max | stdev | |:----------------------------|:---|:-----|:-------|:------| |GPS |0 |4.58 |1136.36 |6.97 | |Dual frequency GNSS receiver |0 |4.96 |40.7 |3.41 | |Slopes R package |0 |6.2 |48.2 |5.6 |

It is notable that the package substantially overestimates the gradient, perhaps due to the low resolution of the underlying elevation raster. However, the slopes package seems to provide less noisy slope estimates than the GPS approach, with lower maximum values and low standard deviation.

References

# failed tests
raster::extract(e, trace_projected)
raster::writeRaster(e, "e.tif")
e_terra = terra::rast("e.tif")
terra::crs(e_terra)
v = terra::vect("vignettes/3DGRT_TRACES_EPSG25830_v2.shp")
e_wgs = terra::project(e_terra, v)
e_stars = stars::st_as_stars(e)
e_wgs = sf::st_transform(e_stars, 4326)
stars::write_stars(e_wgs, "e_wgs.tif")
e2 = raster::raster("e_wgs.tif")
raster::plot(e)
plot(trace$geometry, add = TRUE)

# discarded way:
remotes::install_github("jhollist/elevatr")
sp_bbox = sp::bbox(sf::as_Spatial(sf::st_transform(trace, 4326)))
e = elevatr::get_aws_terrain(locations = sp_bbox, prj = "+init:4326")