Estimate grid cell area from satelite data using a Stereographic polar projection - r

Question

I am trying to work with satelite data from polar regions. They can be download as .nc (netcdf, see below).
They are in polar stereographic projection in a regular grid (https://nsidc.org/data/polar-stereo/ps_grids.html).
I would like to estimate each cell area to calculate the area of ice cover by multiplying the fraction of ice cover in each cell with the area of the cell.
I am able to extract cell area using "area" from {raster} only when the uniform grid is in geographical coordinates (lat-lon). However I could not find any R function to do this when the grid is uniform in stereographic coordinates.
I am very new to spatial data and projections and perhaps I am missing something important.
Below some relevant information and a piece of code with two trials.
RELEVANT DATA AND INFORMATION SOURCES
Polar Watch
https://polarwatch.noaa.gov/erddap/
Sea Ice concentration data
url to downoald data
https://polarwatch.noaa.gov/erddap/griddap/nsidcCDRiceSQnhmday.nc?seaice_conc_monthly_cdr[(2019-12-16T00:00:00Z):1:(2019-12-16T00:00:00Z)][(5837500.0):1:(-5337500.0)][(-3837500.0):1:(3737500.0)]
Can be download in R using
url1<- "https://polarwatch.noaa.gov/erddap/griddap/nsidcCDRiceSQnhmday.nc?seaice_conc_monthly_cdr[(2019-12-16T00:00:00Z):1:(2019-12-16T00:00:00Z)][(5837500.0):1:(-5337500.0)][(-3837500.0):1:(3737500.0)]"
download.file(url1, destfile='nsidcCDRiceSQnhmday_935c_47bd_a147.nc')
Data for the grid
Sea Ice Concentration Lat-Lon Grid, NOAA/NSIDC Climate Data Record V3,
Antarctic, 25km
Dataset ID: nsidcCDRice_sh_grid
url
https://polarwatch.noaa.gov/erddap/griddap/nsidcCDRice_sh_grid.nc?latitude[(4337500.0):1:(-3937500.0)][(-3937500.0):1:(3937500.0)],longitude[(4337500.0):1:(-3937500.0)][(-3937500.0):1:(3937500.0)]
url2<- "https://polarwatch.noaa.gov/erddap/griddap/nsidcCDRice_sh_grid.nc?latitude[(4337500.0):1:(-3937500.0)][(-3937500.0):1:(3937500.0)],longitude[(4337500.0):1:(-3937500.0)][(-3937500.0):1:(3937500.0)]"
download.file(url2, destfile="nsidcCDRice_sh_grid_c513_9d75_76c1.nc")
https://nsidc.org/data/polar-stereo/ps_grids.html
Table 4. Southern Hemisphere Projection Based on WGS 1984
Latitude of True Origin -70
SOME R TRIALS
require(raster)
require(ncdf4)
br<-brick("nsidcCDRiceSQnhmday_935c_47bd_a147.nc")
projection(br)<- CRS("+init=epsg:3976 +proj=stere +lat_0=-90 +lat_ts=-70 +lon_0=0 +k=1 +x_0=0 +y_0=0 +datum=WGS84 +units=m +no_defs") #https://polarwatch.noaa.gov/tools-training/code-gallery/
br
res(br)
area(br)
which gives
Warning message:
In .local(x, ...) :
This function is only useful for Raster* objects with a longitude/latitude coordinates
Using the grid provided in the data sources
IceFgrid<-nc_open("nsidcCDRice_sh_grid_c513_9d75_76c1.nc")
ygridLatLon <- ncvar_get(IceFgrid, varid="ygrid")
xgridLatLon <- ncvar_get(IceFgrid, varid="xgrid")
longitude <- ncvar_get(IceFgrid, varid="longitude")
latitude <- ncvar_get(IceFgrid, varid="latitude")
nc_close(IceFgrid)
dim(longitude) # Matrix with Longitude of each grid point.
length(xgridLatLon)
length(ygridLatLon)
## Try to convert to data frame and the to raster.
dims <- dim(longitude)
icemap.df <- data.frame(Longitude=array(longitude,dims[1]*dims[2]),
Latitude=array(latitude,dims[1]*dims[2]))
icemap.df$Seaice <- array(1,dims[1]*dims[2])# Here I use 1 for ice cover just
rast<-rasterFromXYZ(icemap.df, crs="+proj=stere +lat_0=-90 +lat_ts=-70 +lon_0=0 +k=1 +x_0=0 +y_0=0 +a=6378273 +b=6356889.449 +units=m +no_defs")
But gives
Error in rasterFromXYZ(icemap.df, crs = "+proj=stere +lat_0=-90 +lat_ts=-70 +lon_0=0 +k=1 +x_0=0 +y_0=0 +a=6378273 +b=6356889.449 +units=m +no_defs") :
x cell sizes are not regular
Any help will be appreciated.
Thanks in advance
Angel

Answer 1

Here I use terra the replacement for raster
url1 <- "https://polarwatch.noaa.gov/erddap/griddap/nsidcCDRiceSQnhmday.nc?seaice_conc_monthly_cdr[(2019-12-16T00:00:00Z):1:(2019-12-16T00:00:00Z)][(5837500.0):1:(-5337500.0)][(-3837500.0):1:(3737500.0)]"
f <- 'nsidcCDRiceSQnhmday_935c_47bd_a147.nc'
download.file(url1, destfile='nsidcCDRiceSQnhmday_935c_47bd_a147.nc', mode="wb")
library(terra)
#terra version 1.3.4
r <- rast(f)
crs(r) <- "epsg:3976"
r
class : SpatRaster
dimensions : 448, 304, 1 (nrow, ncol, nlyr)
resolution : 25000, 25000 (x, y)
extent : -3850000, 3750000, -5350000, 5850000 (xmin, xmax, ymin, ymax)
coord. ref. : +proj=stere +lat_0=-90 +lat_ts=-70 +lon_0=0 +x_0=0 +y_0=0 +datum=WGS84 +units=m +no_defs
source : nsidcCDRiceSQnhmday_935c_47bd_a147.nc
varname : seaice_conc_monthly_cdr (NOAA/NSIDC Climate Data Record of Passive Microwave Monthly Northern Hemisphere Sea Ice Concentration)
name : seaice_conc_monthly_cdr
unit : 1
time : 2019-12-16
As you can see, the nominal cell resolution is 25000 x 25000
res(r)
[1] 25000 25000
Because it is constant, raster does not want to compute it for you. But terra will give you either the naïve area (based on the constant the nominal resolution):
na <- cellSize(r, transform=FALSE)
minmax(na)
# area
#[1,] 6.25e+08
#[2,] 6.25e+08
Or the the true area. That is, accounting for distortion:
a <- cellSize(r, mask=F, unit="m", transform=TRUE)
a <- mask(a, r)
a
#class : SpatRaster
#dimensions : 448, 304, 1 (nrow, ncol, nlyr)
#resolution : 25000, 25000 (x, y)
#extent : -3850000, 3750000, -5350000, 5850000 (xmin, xmax, ymin, ymax)
#coord. ref. : +proj=stere +lat_0=-90 +lat_ts=-70 +lon_0=0 +x_0=0 +y_0=0 +datum=WGS84 +units=m +no_defs
#source : memory
#name : area
#min value : 385538624
#max value : 664449196
#time : 2019-12-16
plot(a)
To get the sea-ice area in km2
x <- r * a / 1000000
global(x, "sum", na.rm=TRUE)
# sum
#_conc_monthly_cdr 11312232
The naïve estimate yields
n <- r * prod(res(r)) / 1000000
global(n, "sum", na.rm=TRUE)
# sum
#seaice_conc_monthly_cdr 11134025
That is about 1.5% lower
round(11134025 / 11312232, 3)
#[1] 0.984
This is not that different, because there is no ice at the edges, in the areas of severe distortion. And there is also some compensation in the central area (both smaller and larger areas) than 25*25 km2