This vignette explains the data model of stars
objects, illustrated using artificial and real datasets.
stars
objects consist of
dimensions
with a dimensions
object carrying dimension metadatastars
A dimensions
object is a named list of dimension
elements, each describing the semantics a dimension of the data arrays (space, time, type etc). In addition to that, a dimensions
object has an attribute called raster
of class stars_raster
, which is a named list with three elements:
dimensions
length 2 character; the dimension names that constitute a spatial raster (or NA)affine
length 2 numeric; the two affine parameters of the geotransform (or NA)curvilinear
a boolean indicating whether a raster is a curvilinear raster (or NA)The affine
and curvilinear
values are only relevant in case of raster data, indicated by dimensions
to have non-NA values.
A dimension
object describes a single dimension; it is a list with named elements
from
: (numeric length 1): the start index of the arrayto
: (numeric length 1): the end index of the arrayoffset
: (numeric length 1): the start coordinate (or time) value of the first pixel (i.e., a pixel/cell boundary)delta
: (numeric length 1): the increment, or cell sizerefsys
: (character, or crs
): object describing the reference system; e.g. the PROJ string, or string POSIXct
or PCICt
(for 360 and 365 days/year calendars), or object of class crs
(containing both EPSG code and proj4string)point
: (logical length 1): boolean indicating whether cells/pixels refer to areas/periods, or to points/instances (may be NA)values
: one of
NULL
,POSIXct
, PCICt
, or sfc
),intervals
(a list with two vectors, start
and end
, with interval start- and end-values), orClearly, offset
and delta
only apply to regularly discretized dimensions, and are NA
if this is not the case. from
and to
will usually be 1 and the dimension size, but from
may be larger than 1 in case a regular sub-grid got cut out or was cropped. Rectilinear and curvilinear grids need grid values in values
; this can be irregularly spaced coordinate values, or coordinate intervals of irregular width, or spatial geometries encoded in an sfc
vector (“list-column”), or a matrix with grid cell centre values (longitude or latitude) for curvilinear grids.
With a very simple file created from a \(4 \times 5\) matrix
suppressPackageStartupMessages(library(stars)) m = matrix(1:20, nrow = 5, ncol = 4) dim(m) = c(x = 5, y = 4) # named dim (s = st_as_stars(m)) ## stars object with 2 dimensions and 1 attribute ## attribute(s): ## A1 ## Min. : 1.00 ## 1st Qu.: 5.75 ## Median :10.50 ## Mean :10.50 ## 3rd Qu.:15.25 ## Max. :20.00 ## dimension(s): ## from to offset delta refsys point values ## x 1 5 0 1 NA FALSE NULL [x] ## y 1 4 0 1 NA FALSE NULL [y]
we see that
from
and to
fields of each dimension define a range that corresponds to the array dimension:dim(s[[1]]) ## x y ## 5 4
When we plot this object, using the image
method for stars
objects,
image(s, text_values = TRUE, axes = TRUE)
we see that \((0,0)\) is the origin of the grid (grid corner), and \(1\) the coordinate value increase from one index (row, col) to the next. It means that consecutive matrix columns represent grid lines, going from south to north. Grids defined this way are regular: grid cell size is constant everywhere.
Many actual grid datasets have y coordinates (grid rows) going from North to South (top to bottom); this is realised with a negative value for delta
. We see that the grid origing \((0,0)\) did not change:
An example is the GeoTIFF carried in the package, which, as probably all data sources read through GDAL, has a negative delta
for the y
-coordinate:
tif = system.file("tif/L7_ETMs.tif", package = "stars") st_dimensions(read_stars(tif))["y"] ## from to offset delta refsys point values ## y 1 352 9120761 -28.5 PROJCS["UTM Zone 25, Sout... FALSE NULL
Dimension tables of stars
objects carry a raster
attribute:
str(attr(st_dimensions(s), "raster")) ## List of 3 ## $ affine : num [1:2] 0 0 ## $ dimensions : chr [1:2] "x" "y" ## $ curvilinear: logi FALSE ## - attr(*, "class")= chr "stars_raster"
which is a list that holds
dimensions
: character, the names of raster dimensions (if any), as opposed to e.g. spectral, temporal or other dimensionsaffine
: numeric, the affine parameterscurvilinear
: a logical indicating whether the raster is curvilinearThese fields are needed at this level, because they describe properties of the array at a higher level than individual dimensions do: a pair of dimensions forms a raster, both affine
and curvilinear
describe how x and y as a pair are derived from grid indexes (see below) when this cannot be done on a per-dimension basis.
With two affine parameters \(a_1\) and \(a_2\), \(x\) and \(y\) coordinates are derived from (1-based) grid indexes \(i\) and \(j\), grid offset values \(o_x\) and \(o_y\), and grid cell sizes \(d_x\) and \(d_y\) by
\[x = o_x + (i-1) d_x + (j-1) a_1\]
\[y = o_y + (i-1) a_2 + (j-1) d_y\] Clearly, when \(a_1=a_2=0\), \(x\) and \(y\) are entirely derived from their respective index, offset and cellsize.
Note that for integer indexes, the coordinates are that of the starting edge of a grid cell; to get the grid cell center of the top left grid cell (in case of a negative \(d_y\)), use \(i=1.5\) and \(j=1.5\).
We can rotate grids by setting \(a_1\) and \(a_2\) to a non-zero value:
attr(attr(s, "dimensions"), "raster")$affine = c(0.1, 0.1) plot(st_as_sf(s, as_points = FALSE), axes = TRUE, nbreaks = 20)
The rotation angle, in degrees, is
atan2(0.1, 1) * 180 / pi ## [1] 5.710593
Sheared grids are obtained when the two rotation coefficients, \(a_1\) and \(a_2\), are unequal:
attr(attr(s, "dimensions"), "raster")$affine = c(0.1, 0.2) plot(st_as_sf(s, as_points = FALSE), axes = TRUE, nbreaks = 20)
Now, the y-axis and x-axis have different rotation in degrees of respectively
Rectilinear grids have orthogonal axes, but do not have congruent (equally sized and shaped) cells: each axis has its own irregular subdivision.
We can define a rectilinear grid by specifying the cell boundaries, meaning for every dimension we specify one more value than the dimension size:
x = c(0, 0.5, 1, 2, 4, 5) # 6 numbers: boundaries! y = c(0.3, 0.5, 1, 2, 2.2) # 5 numbers: boundaries! (r = st_as_stars(list(m = m), dimensions = st_dimensions(x = x, y = y))) ## stars object with 2 dimensions and 1 attribute ## attribute(s): ## m ## Min. : 1.00 ## 1st Qu.: 5.75 ## Median :10.50 ## Mean :10.50 ## 3rd Qu.:15.25 ## Max. :20.00 ## dimension(s): ## from to offset delta refsys point values ## x 1 5 NA NA NA FALSE [0,0.5),...,[4,5) [x] ## y 1 4 NA NA NA FALSE [0.3,0.5),...,[2,2.2) [y] st_bbox(r) ## xmin ymin xmax ymax ## 0.0 0.3 5.0 2.2 image(r, axes = TRUE, col = grey((1:20)/20))
Would we leave out the last value, than stars
may come up with a different cell boundary for the last cell, as this is now derived from the width of the one-but-last cell:
x = c(0, 0.5, 1, 2, 4) # 5 numbers: offsets only! y = c(0.3, 0.5, 1, 2) # 4 numbers: offsets only! (r = st_as_stars(list(m = m), dimensions = st_dimensions(x = x, y = y))) ## stars object with 2 dimensions and 1 attribute ## attribute(s): ## m ## Min. : 1.00 ## 1st Qu.: 5.75 ## Median :10.50 ## Mean :10.50 ## 3rd Qu.:15.25 ## Max. :20.00 ## dimension(s): ## from to offset delta refsys point values ## x 1 5 NA NA NA FALSE [0,0.5),...,[4,6) [x] ## y 1 4 NA NA NA FALSE [0.3,0.5),...,[2,3) [y] st_bbox(r) ## xmin ymin xmax ymax ## 0.0 0.3 6.0 3.0
This is not problematic if cells have a constant width, in which case the boundaries are reduced to an offset
and delta
value, irrespective whether an upper boundary is given:
x = c(0, 1, 2, 3, 4) # 5 numbers: offsets only! y = c(0.5, 1, 1.5, 2) # 4 numbers: offsets only! (r = st_as_stars(list(m = m), dimensions = st_dimensions(x = x, y = y))) ## stars object with 2 dimensions and 1 attribute ## attribute(s): ## m ## Min. : 1.00 ## 1st Qu.: 5.75 ## Median :10.50 ## Mean :10.50 ## 3rd Qu.:15.25 ## Max. :20.00 ## dimension(s): ## from to offset delta refsys point values ## x 1 5 0 1 NA FALSE NULL [x] ## y 1 4 0.5 0.5 NA FALSE NULL [y] st_bbox(r) ## xmin ymin xmax ymax ## 0.0 0.5 5.0 2.5
Alternatively, one can also set the cell midpoints by specifying arguments cell_midpoints
to the st_dimensions
call:
x = st_as_stars(matrix(1:9, 3, 3), st_dimensions(x = c(1, 2, 3), y = c(2, 3, 10), cell_midpoints = TRUE))
When the dimension is regular, this results in offset
being shifted back with half a delta
, or else in intervals derived from the distances between cell centers. This should obviously not be done when cell boundaries are specified.
Curvilinear grids are grids whose grid lines are not straight. Rather than describing the curvature parametrically, the typical (HDF5 or NetCDF) files in which they are found have two raster layers, one with the latitudes and one with the longitudes for every grid cell. Using the GDAL interface, we need to compose a stars
object from the array and a long and lat matrix. The matrices with longitude and latitude values are stored in the values
field of their respective dimensions.
As an example, we will use a Sentinel 5P dataset available from package starsdata
; this package can be installed with
install.packages("starsdata", repos = "http://pebesma.staff.ifgi.de", type = "source")
The dataset is found here:
(s5p = system.file("sentinel5p/S5P_NRTI_L2__NO2____20180717T120113_20180717T120613_03932_01_010002_20180717T125231.nc", package = "starsdata")) ## [1] "/home/travis/R/Library/starsdata/sentinel5p/S5P_NRTI_L2__NO2____20180717T120113_20180717T120613_03932_01_010002_20180717T125231.nc"
We can construct the curvilinear stars
raster by calling st_as_stars
on three arrays, with data, longitude and latitudes:
nit.c = read_stars(s5p, sub = "//PRODUCT/SUPPORT_DATA/DETAILED_RESULTS/nitrogendioxide_summed_total_column", curvilinear = c("//PRODUCT/longitude", "//PRODUCT/latitude"), driver = NULL) ## //PRODUCT/longitude, ## //PRODUCT/latitude, ## //PRODUCT/SUPPORT_DATA/DETAILED_RESULTS/nitrogendioxide_summed_total_column, if (inherits(nit.c[[1]], "units")) { threshold = units::set_units(9e+36, mol/m^2) } else { threshold = 9e+36 } nit.c[[1]][nit.c[[1]] > threshold] = NA st_crs(nit.c) = 4326 nit.c ## stars object with 2 dimensions and 1 attribute ## attribute(s): ## nitrogendioxide_summed_total_column ## Min. :0e+00 ## 1st Qu.:1e-04 ## Median :1e-04 ## Mean :1e-04 ## 3rd Qu.:1e-04 ## Max. :5e-04 ## NA's :330 ## dimension(s): ## from to offset delta refsys point values ## x 1 450 NA NA EPSG:4326 NA [450x278] -5.81066,...,30.9468 [x] ## y 1 278 NA NA EPSG:4326 NA [450x278] 28.3605,...,51.4686 [y] ## curvilinear grid
plot(nit.c, breaks = "equal", reset = FALSE, axes = TRUE, as_points = TRUE, pch = 16, logz = TRUE, key.length = 1) maps::map('world', add = TRUE, col = 'red')
plot(nit.c, breaks = "equal", reset = FALSE, axes = TRUE, as_points = FALSE, border = NA, logz = TRUE, key.length = 1) maps::map('world', add = TRUE, col = 'red')
We can downsample the data by
(nit.c = stars:::st_downsample(nit.c, 8)) ## stars object with 2 dimensions and 1 attribute ## attribute(s): ## nitrogendioxide_summed_total_column ## Min. :0.00005 ## 1st Qu.:0.00007 ## Median :0.00008 ## Mean :0.00009 ## 3rd Qu.:0.00009 ## Max. :0.00023 ## NA's :36 ## dimension(s): ## from to offset delta refsys point values ## x 1 57 NA NA EPSG:4326 NA [57x35] -5.59621,...,30.8488 [x] ## y 1 35 NA NA EPSG:4326 NA [57x35] 28.3605,...,51.1544 [y] ## curvilinear grid plot(nit.c, breaks = "equal", reset = FALSE, axes = TRUE, as_points = TRUE, pch = 16, logz = TRUE, key.length = 1) maps::map('world', add = TRUE, col = 'red')
which doesn’t look nice, but plotting the cells as polygons looks better: