Calculations in WGS 84 are inaccurate about climate

[Nowosad]

Is not there a 3rd choice - just to use a better approximation of the distances? If I understand the underlining code, it uses the Euclidean distance -

climate/R/nearest_stations_imgw.R

Line 72 in 1c23d1f

distance_points = stats::dist(distmatrix, method = "euclidean")[1:dim(result)[1]]

.
However, we could use https://pl.wikibooks.org/wiki/Astronomiczne_podstawy_geografii/Odleg%C5%82o%C5%9Bci - it would require implementing a new dist function.

[bczernecki]

Thanks Krzysztof for the valuable comment!
I was considering to use GIS standards in the package, but since sf and sp are based on quite heavy system dependencies (which are causing sometimes lot of problems with installation) it was decided to use as simple approach as possible for the price of lower accurracy.
Please also note that we have nearest_stations_* family of functions where EPSG 2180 might be not the best choice.
To sum it up I think it might be worthy adding following items:

• extra argument for nearest_stations* (e.g. use_sf = TRUE) to calculate distances based on CRS projections if sf package is available;
• if there's no sf packages - use the default computing engine, but provide warning message about possible inaccuracies

[kadyb]

Here I implemented formulae to calculate the distance between points on a sphere. The simple formula is the first formula from the source from Jakub. Two more (haversine and Vincenty) come from here. I haven't done any accuracy and speed benchmarks, but referring to Wikipedia, the Vincenty formula is slower, but more accurate.

spherical_dist = function(p1, p2, formula = NULL) {

  if (is.null(formula))
    stop("formula should be: 'simple', 'haversine' or 'Vincenty'")

  if (p1[1] > 180 || p2[1] > 180) stop("x should be longitude")
  if (p1[2] > 90 || p2[2] > 90) stop("y should be latitude")

  r = 6371009 # mean earth radius in meters
  deg2rad = function(deg) {deg * pi / 180}

  vec = c(p1, p2)
  vec = sapply(vec, FUN = deg2rad)
  diff_long = vec[3] - vec[1]
  diff_lat = vec[4] - vec[2]

  if (formula == "simple") {
    d = sqrt(diff_lat^2 + (cos((vec[2] + vec[4]) / 2) * diff_long)^2)
  }

  if (formula == "haversine") {
    d = (sin(diff_lat / 2))^2 + (1 - (sin(diff_lat / 2))^2 - (sin((vec[2] + vec[4]) / 2))^2) * (sin(diff_long / 2))^2
    d = 2 * asin(sqrt(d))
  }

  if (formula == "Vincenty") {
    num = (cos(vec[4]) * sin(diff_long))^2 + (cos(vec[2]) * sin(vec[4]) - sin(vec[2]) * cos(vec[4]) * cos(diff_long))^2
    denom = sin(vec[2]) * sin(vec[4]) + cos(vec[2]) * cos(vec[4]) * cos(diff_long)
    d = atan(sqrt(num) / denom)
  }

  d = d * r
  return(d/1000) # output in km

}


# correct: 105.4737 km
p1 = c(18.633333, 54.366667) # Gdańsk
p2 = c(17.016667, 54.466667) # Słupsk
spherical_dist(p1, p2, formula = "simple") #> 105.1923
spherical_dist(p1, p2, formula = "haversine") #> 105.19
spherical_dist(p1, p2, formula = "Vincenty") #> 105.19

# correct: 21.01992 km
p1 = c(17.16716, 54.64006) # GARDNA WIELKA
p2 = c(16.85410, 54.58831) # USTKA
spherical_dist(p1, p2, formula = "simple") #> 20.96341
spherical_dist(p1, p2, formula = "haversine") #> 20.96339
spherical_dist(p1, p2, formula = "Vincenty") #> 20.96339

Correct distances in comments are calculated in the planar coordinate system (EPSG 2180), but there are also some distortions.