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meteoland
With the retirement
of rgdal
, rgeos
and maptools
R
packages, a complete update of meteoland
was necessary to
remove the hard dependency meteoland
has with
sp
and raster
R packages. Starting with
version 2.0.0 of meteoland
, any hard dependency on retired
packages as well as sp
and raster
has been
removed, and now sf
and stars
packages are
internally used for working with simple features and raster data.
By June 2023, sp
and raster
packages will
be completely removed from the dependency list.
As fundamental changes were required (meteoland
meteorology classes were based on sp
ones), a decision to
improve and make meteorological interpolation process simpler was taken.
In this vignette, we provide insights on the new ways of working with
meteoland
.
If you are interested in the equivalences between older and newer
functions of meteoland
, please see the appendix at the end of the vignette.
meteoland
now ships with new example objects, based on
the sf
and stars
packages. The following table
describes the new data examples:
Name | Description |
---|---|
meteoland_interpolator_example | A meteoland interpolator object, with daily
meteorological data in Catalonia (Spain) for April 2022. |
meteoland_meteo_example | Data from meteorological stations in Catalonia (Spain) for April 2022. |
meteoland_meteo_no_topo_example | Data from meteorological stations in Catalonia (Spain) for April 2022, without topographical information. |
meteoland_topo_example | Topographical information for meteorological stations in Catalonia (Spain). |
points_to_interpolate_example | Topographical information for 15 plots located in Catalonia (Spain). |
raster_to_interpolate_example | Topographical information for a 0.01 degree grid (10x10 cells) raster located in central Catalonia (Spain) |
The interpolation of meteorological information requires two kinds of information:
The topographical information of the target locations to interpolate. This includes elevation, aspect and slope. Elevation is the only mandatory topography variable, but interpolation results improve when also aspect and slope are provided in mountain areas.
The reference meteorological information that we will use to build the interpolator object. This information can come from meteorological stations in the area we are interested on or, alternatively, can be extracted from available rasters with meteorological variables.
In order to interpolate, we need our locations in a format that
meteoland
can understand. For point locations, this is a
sf
object including the elevation
(in
m.a.s.l.), slope
(in degrees) and aspect
(in
degrees) variables, such as:
points_to_interpolate_example
#> Simple feature collection with 15 features and 4 fields
#> Geometry type: POINT
#> Dimension: XY
#> Bounding box: xmin: 0.7578958 ymin: 41.31541 xmax: 2.98657 ymax: 42.6336
#> Geodetic CRS: WGS 84
#> # A tibble: 15 × 5
#> plot_id elevation slope aspect geometry
#> <chr> <dbl> <dbl> <dbl> <POINT [°]>
#> 1 P_05284 889. 25.2 313. (2.320167 42.24139)
#> 2 P_06572 680. 18.0 79.9 (2.552233 42.02596)
#> 3 P_07201 141. 4.17 52.9 (2.721874 41.88258)
#> 4 P_07512 254. 14.3 261. (2.98657 41.9006)
#> 5 P_08207 1860. 36.4 293. (2.209903 42.33968)
#> 6 P_08299 183. 4.12 92.9 (2.817143 42.24325)
#> 7 P_09341 819 23.4 128. (1.126766 42.42612)
#> 8 P_10272 860 34.8 347. (1.398528 42.26791)
#> 9 P_10861 706 22.4 22.6 (0.9314126 42.04226)
#> 10 P_11651 585 22.0 199. (0.7578958 41.8612)
#> 11 P_12150 674. 30.3 154. (1.481719 41.81838)
#> 12 P_12227 752. 6.04 27.7 (1.283161 41.591)
#> 13 P_12417 702 11.6 63.1 (0.8727224 41.35875)
#> 14 P_13007 972. 4.21 338. (1.120383 42.6336)
#> 15 P_14029 556. 14.1 41.4 (1.480716 41.31541)
For spatially-continuous data (i.e. a raster), we need a
stars
object including elevation
(in
m.a.s.l.), slope
(in degrees) and aspect
(in
degrees) as attributes, such as:
raster_to_interpolate_example
#> stars object with 2 dimensions and 3 attributes
#> attribute(s):
#> Min. 1st Qu. Median Mean 3rd Qu. Max.
#> elevation 240.000000 370.000000 447.00000 460.32231 525.00000 786.0000
#> slope 1.432096 5.720433 11.34812 13.07343 19.75851 31.0719
#> aspect 5.194427 74.744881 174.36932 181.67923 291.03751 360.0000
#> dimension(s):
#> from to offset delta refsys x/y
#> x 155 165 0.03648 0.01058 WGS 84 [x]
#> y 110 120 42.92 -0.01058 WGS 84 [y]
Both, sf
and stars
R packages have the
necessary functions to read most spatial formats, the only thing to
consider is ensuring that the topographical variables are included, have
the proper units and mandatory names (elevation
,
aspect
, slope
).
For interpolating the meteorological variables in our locations (see
above), we need a reference meteorological data. This is a
sf
object with the reference locations, and daily values of
the weather variables needed to perform the interpolation, for
example:
meteoland_meteo_example
#> Simple feature collection with 5652 features and 18 fields
#> Geometry type: POINT
#> Dimension: XY
#> Bounding box: xmin: 0.30565 ymin: 40.55786 xmax: 3.18165 ymax: 42.77011
#> Geodetic CRS: WGS 84
#> # A tibble: 5,652 × 19
#> dates service stationID station_name station_province elevation
#> * <dttm> <chr> <chr> <chr> <chr> <dbl>
#> 1 2022-04-01 00:00:00 meteoc… C6 Castellnou … Lleida 264
#> 2 2022-04-01 00:00:00 meteoc… C7 Tàrrega Lleida 427
#> 3 2022-04-01 00:00:00 meteoc… C8 Cervera Lleida 554
#> 4 2022-04-01 00:00:00 meteoc… C9 Mas de Barb… Tarragona 240
#> 5 2022-04-01 00:00:00 meteoc… CC Orís Barcelona 626
#> 6 2022-04-01 00:00:00 meteoc… CD la Seu d'Ur… Lleida 849
#> 7 2022-04-01 00:00:00 meteoc… CE els Hostale… Barcelona 316
#> 8 2022-04-01 00:00:00 meteoc… CG Molló - Fab… Girona 1405
#> 9 2022-04-01 00:00:00 meteoc… CI Sant Pau de… Girona 852
#> 10 2022-04-01 00:00:00 meteoc… CJ Organyà Lleida 566.
#> # ℹ 5,642 more rows
#> # ℹ 13 more variables: MeanTemperature <dbl>, MinTemperature <dbl>,
#> # MaxTemperature <dbl>, MeanRelativeHumidity <dbl>,
#> # MinRelativeHumidity <dbl>, MaxRelativeHumidity <dbl>, Precipitation <dbl>,
#> # WindDirection <dbl>, WindSpeed <dbl>, Radiation <dbl>, geom <POINT [°]>,
#> # aspect <dbl>, slope <dbl>
meteoland
expects variable names to be as indicated in
the example:
names(meteoland_meteo_example)
#> [1] "dates" "service" "stationID"
#> [4] "station_name" "station_province" "elevation"
#> [7] "MeanTemperature" "MinTemperature" "MaxTemperature"
#> [10] "MeanRelativeHumidity" "MinRelativeHumidity" "MaxRelativeHumidity"
#> [13] "Precipitation" "WindDirection" "WindSpeed"
#> [16] "Radiation" "geom" "aspect"
#> [19] "slope"
The only mandatory variables are MinTemperature
and
MaxTemperature
. Other variables
(Precipitation
, WindSpeed
…), when present,
allow for a more complete weather interpolation.
For more information on preparing meteorological data for
meteoland
, see
vignette("reshaping-meteo", package = "meteoland")
With the necessary data in the correct format we can perform the interpolation right away:
# creating the interpolator object
interpolator <- with_meteo(meteoland_meteo_example) |>
create_meteo_interpolator()
#> ℹ Checking meteorology object...
#> ✔ meteorology object ok
#> ℹ Creating interpolator...
#> Warning: No interpolation parameters provided, using defaults
#> ℹ Set the `params` argument to modify parameter default values
#> • Calculating smoothed variables...
#> • Updating intial_Rp parameter with the actual stations mean distance...
#> ✔ Interpolator created.
# performing the interpolation
points_interpolated <- points_to_interpolate_example |>
interpolate_data(interpolator)
#> ℹ Starting interpolation...
#> ℹ Temperature interpolation is needed also...
#> • Interpolating temperature...
#> ℹ Precipitation interpolation is needed also...
#> • Interpolating precipitation...
#> ℹ Relative humidity interpolation is needed also...
#> • Interpolating relative humidity...
#> ℹ Radiation calculation is needed also...
#> • Calculating radiation...
#> ℹ Wind interpolation is needed also...
#> • Interpolating wind...
#> • Calculating PET...
#> ✔ Interpolation done...
points_interpolated
#> Simple feature collection with 15 features and 5 fields
#> Geometry type: POINT
#> Dimension: XY
#> Bounding box: xmin: 0.7578958 ymin: 41.31541 xmax: 2.98657 ymax: 42.6336
#> Geodetic CRS: WGS 84
#> # A tibble: 15 × 6
#> plot_id elevation slope aspect geometry interpolated_data
#> <chr> <dbl> <dbl> <dbl> <POINT [°]> <list>
#> 1 P_05284 889. 25.2 313. (2.320167 42.24139) <tibble [30 × 13]>
#> 2 P_06572 680. 18.0 79.9 (2.552233 42.02596) <tibble [30 × 13]>
#> 3 P_07201 141. 4.17 52.9 (2.721874 41.88258) <tibble [30 × 13]>
#> 4 P_07512 254. 14.3 261. (2.98657 41.9006) <tibble [30 × 13]>
#> 5 P_08207 1860. 36.4 293. (2.209903 42.33968) <tibble [30 × 13]>
#> 6 P_08299 183. 4.12 92.9 (2.817143 42.24325) <tibble [30 × 13]>
#> 7 P_09341 819 23.4 128. (1.126766 42.42612) <tibble [30 × 13]>
#> 8 P_10272 860 34.8 347. (1.398528 42.26791) <tibble [30 × 13]>
#> 9 P_10861 706 22.4 22.6 (0.9314126 42.04226) <tibble [30 × 13]>
#> 10 P_11651 585 22.0 199. (0.7578958 41.8612) <tibble [30 × 13]>
#> 11 P_12150 674. 30.3 154. (1.481719 41.81838) <tibble [30 × 13]>
#> 12 P_12227 752. 6.04 27.7 (1.283161 41.591) <tibble [30 × 13]>
#> 13 P_12417 702 11.6 63.1 (0.8727224 41.35875) <tibble [30 × 13]>
#> 14 P_13007 972. 4.21 338. (1.120383 42.6336) <tibble [30 × 13]>
#> 15 P_14029 556. 14.1 41.4 (1.480716 41.31541) <tibble [30 × 13]>
Let’s see this step by step.
with_meteo(...)
ensures that the provided
meteorological information is in the correct format for using it with
meteoland
. It performs several checks and informs of any
error found. For example, if the meteorological information doesn’t have
the mandatory variables, an informative error is shown:meteo_without_temp <- meteoland_meteo_example
meteo_without_temp[["MinTemperature"]] <- NULL
meteo_without_temp[["MaxTemperature"]] <- NULL
with_meteo(meteo_without_temp)
#> ℹ Checking meteorology object...
#> Error: Names found in meteo don't comply with the required names:
#> meteo should have the following meteorology variables:
#> - MinTemperature ***
#> - MaxTemperature ***
#> - Precipitation
#> - RelativeHumidity
#> - Radiation
#> - WindSpeed
#> - WindDirection
#>
#> ***: mandatory variables
create_meteo_interpolator(...)
creates the interpolator
object from the meteorological information. This object stores not only
the meteorological information, but also the parameters that will be
used in the interpolation process. These parameters can be supplied as a
list in the params
argument from
create_meteo_interpolator()
function. If not supplied, a
default set of parameters is used. At any point, we can display the
interpolation parameters using
get_interpolation_params()
:# parameters
get_interpolation_params(interpolator)
#> $initial_Rp
#> [1] 1.136444
#>
#> $iterations
#> [1] 3
#>
#> $alpha_MinTemperature
#> [1] 3
#>
#> $alpha_MaxTemperature
#> [1] 3
#>
#> $alpha_DewTemperature
#> [1] 3
#>
#> $alpha_PrecipitationEvent
#> [1] 5
#>
#> $alpha_PrecipitationAmount
#> [1] 5
#>
#> $alpha_Wind
#> [1] 3
#>
#> $N_MinTemperature
#> [1] 30
#>
#> $N_MaxTemperature
#> [1] 30
#>
#> $N_DewTemperature
#> [1] 30
#>
#> $N_PrecipitationEvent
#> [1] 5
#>
#> $N_PrecipitationAmount
#> [1] 20
#>
#> $N_Wind
#> [1] 2
#>
#> $St_Precipitation
#> [1] 5
#>
#> $St_TemperatureRange
#> [1] 15
#>
#> $pop_crit
#> [1] 0.5
#>
#> $f_max
#> [1] 0.6
#>
#> $wind_height
#> [1] 10
#>
#> $wind_roughness_height
#> [1] 0.001
#>
#> $penman_albedo
#> [1] 0.25
#>
#> $penman_windfun
#> [1] "1956"
#>
#> $debug
#> [1] FALSE
interpolate_data(...)
performs the interpolation using
the topography provided and the interpolator object. If the
topographical information is in an sf
object, as in the
example above, interpolate_data
returns the same
sf
object with an additional column called
interpolated_data
:# interpolated meteo for the first location
points_interpolated[["interpolated_data"]][1]
#> [[1]]
#> # A tibble: 30 × 13
#> dates DOY MeanTemperature MinTemperature MaxTemperature
#> <dttm> <dbl> <dbl> <dbl> <dbl>
#> 1 2022-04-01 00:00:00 91 3.24 -2.53 6.99
#> 2 2022-04-02 00:00:00 92 2.99 -4.20 7.67
#> 3 2022-04-03 00:00:00 93 2.39 -5.61 7.59
#> 4 2022-04-04 00:00:00 94 4.02 -3.93 9.20
#> 5 2022-04-05 00:00:00 95 7.38 -3.29 14.3
#> 6 2022-04-06 00:00:00 96 8.78 1.31 13.6
#> 7 2022-04-07 00:00:00 97 12.1 2.44 18.4
#> 8 2022-04-08 00:00:00 98 12.9 3.32 19.1
#> 9 2022-04-09 00:00:00 99 10.0 3.83 14.1
#> 10 2022-04-10 00:00:00 100 11.4 4.85 15.6
#> # ℹ 20 more rows
#> # ℹ 8 more variables: Precipitation <dbl>, MeanRelativeHumidity <dbl>,
#> # MinRelativeHumidity <dbl>, MaxRelativeHumidity <dbl>, Radiation <dbl>,
#> # WindSpeed <dbl>, WindDirection <dbl>, PET <dbl>
We can “unnest” the results to get the data in a long format (each combination of location and date in a different row):
tidyr::unnest(points_interpolated, cols = "interpolated_data")
#> Simple feature collection with 450 features and 17 fields
#> Geometry type: POINT
#> Dimension: XY
#> Bounding box: xmin: 0.7578958 ymin: 41.31541 xmax: 2.98657 ymax: 42.6336
#> Geodetic CRS: WGS 84
#> # A tibble: 450 × 18
#> plot_id elevation slope aspect geometry dates
#> <chr> <dbl> <dbl> <dbl> <POINT [°]> <dttm>
#> 1 P_05284 889. 25.2 313. (2.320167 42.24139) 2022-04-01 00:00:00
#> 2 P_05284 889. 25.2 313. (2.320167 42.24139) 2022-04-02 00:00:00
#> 3 P_05284 889. 25.2 313. (2.320167 42.24139) 2022-04-03 00:00:00
#> 4 P_05284 889. 25.2 313. (2.320167 42.24139) 2022-04-04 00:00:00
#> 5 P_05284 889. 25.2 313. (2.320167 42.24139) 2022-04-05 00:00:00
#> 6 P_05284 889. 25.2 313. (2.320167 42.24139) 2022-04-06 00:00:00
#> 7 P_05284 889. 25.2 313. (2.320167 42.24139) 2022-04-07 00:00:00
#> 8 P_05284 889. 25.2 313. (2.320167 42.24139) 2022-04-08 00:00:00
#> 9 P_05284 889. 25.2 313. (2.320167 42.24139) 2022-04-09 00:00:00
#> 10 P_05284 889. 25.2 313. (2.320167 42.24139) 2022-04-10 00:00:00
#> # ℹ 440 more rows
#> # ℹ 12 more variables: DOY <dbl>, MeanTemperature <dbl>, MinTemperature <dbl>,
#> # MaxTemperature <dbl>, Precipitation <dbl>, MeanRelativeHumidity <dbl>,
#> # MinRelativeHumidity <dbl>, MaxRelativeHumidity <dbl>, Radiation <dbl>,
#> # WindSpeed <dbl>, WindDirection <dbl>, PET <dbl>
In older versions of meteoland, the interpolator object inherited the
MeteorologyInterpolationData
class (based on
sp
classes). Starting on meteoland v2.0.0
,
MeteorologyInterpolationData
class is deprecated, and the
interpolator object created by create_meteo_interpolator()
inherits directly from stars
class.
This object is a data cube, with reference weather locations and dates as dimensions, and meteorological and topographical variables as attributes.
interpolator
#> stars object with 2 dimensions and 13 attributes
#> attribute(s):
#> Min. 1st Qu. Median Mean 3rd Qu.
#> Temperature -14.200000 8.800000 12.60000 11.324991 14.80000
#> MinTemperature -15.900000 3.300000 6.90000 5.883189 9.40000
#> MaxTemperature -13.000000 13.900000 18.30000 17.364292 21.80000
#> RelativeHumidity 18.000000 57.000000 67.00000 67.720000 78.00000
#> Precipitation 0.000000 0.000000 0.00000 1.925434 0.10000
#> Radiation 7.707484 17.717235 22.04597 20.762628 23.61352
#> WindDirection 0.000000 116.000000 217.00000 196.861908 275.00000
#> WindSpeed 0.200000 0.900000 1.30000 1.603907 2.00000
#> elevation 0.000000 147.000000 317.00000 515.629630 668.00000
#> aspect 0.000000 0.000000 0.00000 0.000000 0.00000
#> slope 0.000000 0.000000 0.00000 0.000000 0.00000
#> SmoothedPrecipitation 0.100000 1.862500 5.55000 6.197496 9.07500
#> SmoothedTemperatureRange 4.695000 9.863542 11.66307 11.400932 13.26868
#> Max. NA's
#> Temperature 23.40000 148
#> MinTemperature 20.10000 138
#> MaxTemperature 29.90000 139
#> RelativeHumidity 100.00000 145
#> Precipitation 160.90000 79
#> Radiation 28.10878 139
#> WindDirection 359.00000 4171
#> WindSpeed 6.90000 4160
#> elevation 2535.00000 0
#> aspect 0.00000 0
#> slope 0.00000 0
#> SmoothedPrecipitation 65.10000 818
#> SmoothedTemperatureRange 17.72778 124
#> dimension(s):
#> from to offset delta refsys point
#> date 1 30 2022-04-01 UTC 1 days POSIXct FALSE
#> station 1 189 NA NA WGS 84 TRUE
#> values
#> date NULL
#> station POINT (0.95172 41.6566),...,POINT (1.89716 42.32211)
The object also contains the interpolation parameters as an
attribute, that can be accessed with
get_interpolation_params()
.
get_interpolation_params(interpolator)
#> $initial_Rp
#> [1] 1.136444
#>
#> $iterations
#> [1] 3
#>
#> $alpha_MinTemperature
#> [1] 3
#>
#> $alpha_MaxTemperature
#> [1] 3
#>
#> $alpha_DewTemperature
#> [1] 3
#>
#> $alpha_PrecipitationEvent
#> [1] 5
#>
#> $alpha_PrecipitationAmount
#> [1] 5
#>
#> $alpha_Wind
#> [1] 3
#>
#> $N_MinTemperature
#> [1] 30
#>
#> $N_MaxTemperature
#> [1] 30
#>
#> $N_DewTemperature
#> [1] 30
#>
#> $N_PrecipitationEvent
#> [1] 5
#>
#> $N_PrecipitationAmount
#> [1] 20
#>
#> $N_Wind
#> [1] 2
#>
#> $St_Precipitation
#> [1] 5
#>
#> $St_TemperatureRange
#> [1] 15
#>
#> $pop_crit
#> [1] 0.5
#>
#> $f_max
#> [1] 0.6
#>
#> $wind_height
#> [1] 10
#>
#> $wind_roughness_height
#> [1] 0.001
#>
#> $penman_albedo
#> [1] 0.25
#>
#> $penman_windfun
#> [1] "1956"
#>
#> $debug
#> [1] FALSE
Interpolation parameters can also be changed with
set_interpolation_params()
.
# wind_height parameter
get_interpolation_params(interpolator)$wind_height
#> [1] 10
# set a new wind_height parameter and check
interpolator <- set_interpolation_params(interpolator, params = list(wind_height = 5))
#> ℹ Some interpolation parameters are missing, using default values for those
get_interpolation_params(interpolator)$wind_height
#> [1] 5
Interpolator objects can be reused for different interpolations
exercises within the area covered by the interpolator. To allow
interpolator objects to be shared between sessions,
meteoland
offers functions to write and read these objects.
The interpolator is saved in NetCDF-CF format (https://cfconventions.org/cf-conventions/cf-conventions.html)
and can be also opened with any GIS software that supports
NetCDF-CF.
temporal_folder <- tempdir()
write_interpolator(interpolator, file.path(temporal_folder, "interpolator.nc"))
#> ℹ Creating nc file following the NetCDF-CF conventions <https://cfconventions.org/cf-conventions/cf-conventions.html>
#> ℹ Adding spatial info to nc file
#> ✔ Done
# file should exists now
file.exists(file.path(temporal_folder, "interpolator.nc"))
#> [1] TRUE
To load the interpolator in your session again, you can use the
read_interpolator()
function.
Interpolation parameters can be calibrated for individual variables
before performing the interpolation process. In fact, it’s
recommended to calibrate the interpolator object before using
it, as the default interpolation parameters can be not adequate for the
studied area. meteoland
offers a calibration process with
the interpolator_calibration()
function.
**Important!** Calibration process for one variable can take a long time to finish,
as it performs a *leave-one-out* interpolation for all stations present in the
interpolator and all combinations of N and alpha sequences provided. In this example
we reduce the N and alpha test values for the process to be faster, but is recommended
to explore a wider range of these values.
# min temperature N and alpha before calibration
get_interpolation_params(interpolator)$N_MinTemperature
#> [1] 30
get_interpolation_params(interpolator)$alpha_MinTemperature
#> [1] 3
# calibration
interpolator <- interpolator_calibration(
interpolator,
variable = "MinTemperature",
N_seq = c(5, 20),
alpha_seq = c(1, 10),
update_interpolation_params = TRUE
)
#> ℹ Total number of stations: 189
#> ℹ Number of stations with available data: 185
#> ℹ Number of stations used for MAE calculation: 185
#> ℹ Number of parameters combinations to test: 4
#> ℹ Starting evaluation of parameter combinations for "MinTemperature"...
#> • Evaluating N: 5, alpha: 1...
#> • Evaluating N: 5, alpha: 10...
#> • Evaluating N: 20, alpha: 1...
#> • Evaluating N: 20, alpha: 10...
#> ✔ Calibration done: Minimum MAE: 1.18956628899488; N: 20; alpha: 10
# parameters after calibration
get_interpolation_params(interpolator)$N_MinTemperature
#> [1] 20
get_interpolation_params(interpolator)$alpha_MinTemperature
#> [1] 10
One advantage of the new data flows in meteoland
is that
we can pipe the creation and the calibration of the
interpolator, as well as the writing:
interpolator <- with_meteo(meteoland_meteo_example) |>
create_meteo_interpolator() |>
interpolator_calibration(
variable = "MinTemperature",
N_seq = c(5, 20),
alpha_seq = c(1, 10),
update_interpolation_params = TRUE
) |>
interpolator_calibration(
variable = "MaxTemperature",
N_seq = c(5, 20),
alpha_seq = c(1, 10),
update_interpolation_params = TRUE
) |>
interpolator_calibration(
variable = "DewTemperature",
N_seq = c(5, 20),
alpha_seq = c(1, 10),
update_interpolation_params = TRUE
) |>
write_interpolator(
filename = file.path(temporal_folder, "interpolator.nc"),
.overwrite = TRUE
)
#> ℹ Checking meteorology object...
#> ✔ meteorology object ok
#> ℹ Creating interpolator...
#> Warning: No interpolation parameters provided, using defaults
#> ℹ Set the `params` argument to modify parameter default values
#> • Calculating smoothed variables...
#> • Updating intial_Rp parameter with the actual stations mean distance...
#> ✔ Interpolator created.
#> ℹ Total number of stations: 189
#> ℹ Number of stations with available data: 185
#> ℹ Number of stations used for MAE calculation: 185
#> ℹ Number of parameters combinations to test: 4
#> ℹ Starting evaluation of parameter combinations for "MinTemperature"...
#> • Evaluating N: 5, alpha: 1...
#> • Evaluating N: 5, alpha: 10...
#> • Evaluating N: 20, alpha: 1...
#> • Evaluating N: 20, alpha: 10...
#> ✔ Calibration done: Minimum MAE: 1.18956628899488; N: 20; alpha: 10
#> ℹ Total number of stations: 189
#> ℹ Number of stations with available data: 185
#> ℹ Number of stations used for MAE calculation: 185
#> ℹ Number of parameters combinations to test: 4
#> ℹ Starting evaluation of parameter combinations for "MaxTemperature"...
#> • Evaluating N: 5, alpha: 1...
#> • Evaluating N: 5, alpha: 10...
#> • Evaluating N: 20, alpha: 1...
#> • Evaluating N: 20, alpha: 10...
#> ✔ Calibration done: Minimum MAE: 0.849019890784243; N: 20; alpha: 10
#> ℹ Total number of stations: 189
#> ℹ Number of stations with available data: 185
#> ℹ Number of stations used for MAE calculation: 185
#> ℹ Number of parameters combinations to test: 4
#> ℹ Starting evaluation of parameter combinations for "DewTemperature"...
#> • Evaluating N: 5, alpha: 1...
#> • Evaluating N: 5, alpha: 10...
#> • Evaluating N: 20, alpha: 1...
#> • Evaluating N: 20, alpha: 10...
#> ✔ Calibration done: Minimum MAE: 1.37971537117584; N: 20; alpha: 10
#> ℹ Creating nc file following the NetCDF-CF conventions <https://cfconventions.org/cf-conventions/cf-conventions.html>
#> ℹ Adding spatial info to nc file
#> ✔ Done
This way we can create and calibrate the interpolator once, and using it in future sessions, avoiding the time consuming step of calibrating every time.
The interpolation process can be cross validated.
meteoland
offers the possibility with the
interpolation_cross_validation()
function. This function
takes an interpolator object and calculates different error
measures.
cross_validation <- interpolation_cross_validation(interpolator, verbose = FALSE)
cross_validation$errors
#> # A tibble: 5,670 × 21
#> dates station stationID MinTemperature_error
#> <dttm> <int> <chr> <dbl>
#> 1 2022-04-01 00:00:00 1 C6 0.125
#> 2 2022-04-02 00:00:00 1 C6 0.0598
#> 3 2022-04-03 00:00:00 1 C6 0.145
#> 4 2022-04-04 00:00:00 1 C6 -0.306
#> 5 2022-04-05 00:00:00 1 C6 -0.0977
#> 6 2022-04-06 00:00:00 1 C6 -0.248
#> 7 2022-04-07 00:00:00 1 C6 -0.457
#> 8 2022-04-08 00:00:00 1 C6 1.24
#> 9 2022-04-09 00:00:00 1 C6 -0.546
#> 10 2022-04-10 00:00:00 1 C6 0.601
#> # ℹ 5,660 more rows
#> # ℹ 17 more variables: MaxTemperature_error <dbl>,
#> # RangeTemperature_error <dbl>, RelativeHumidity_error <dbl>,
#> # Radiation_error <dbl>, Precipitation_error <dbl>,
#> # MinTemperature_predicted <dbl>, MaxTemperature_predicted <dbl>,
#> # RangeTemperature_predicted <dbl>, RelativeHumidity_predicted <dbl>,
#> # Radiation_predicted <dbl>, Precipitation_predicted <dbl>, …
cross_validation$station_stats
#> # A tibble: 189 × 20
#> station stationID MinTemperature_station_bias MaxTemperature_station_bias
#> <int> <chr> <dbl> <dbl>
#> 1 1 C6 -0.109 -0.606
#> 2 2 C7 -1.03 -0.582
#> 3 3 C8 0.0180 0.0356
#> 4 4 C9 -0.316 0.657
#> 5 5 CC -0.0373 -0.483
#> 6 6 CD 0.508 -1.03
#> 7 7 CE -1.62 -0.779
#> 8 8 CG -1.51 -0.379
#> 9 9 CI 0.888 0.509
#> 10 10 CJ 0.572 0.00525
#> # ℹ 179 more rows
#> # ℹ 16 more variables: RangeTemperature_station_bias <dbl>,
#> # RelativeHumidity_station_bias <dbl>, Radiation_station_bias <dbl>,
#> # MinTemperature_station_mae <dbl>, MaxTemperature_station_mae <dbl>,
#> # RangeTemperature_station_mae <dbl>, RelativeHumidity_station_mae <dbl>,
#> # Radiation_station_mae <dbl>, TotalPrecipitation_station_observed <dbl>,
#> # TotalPrecipitation_station_predicted <dbl>, …
cross_validation$dates_stats
#> # A tibble: 30 × 19
#> dates MinTemperature_date_bias MaxTemperature_date_bias
#> <dttm> <dbl> <dbl>
#> 1 2022-04-01 00:00:00 0.0125 0.0405
#> 2 2022-04-02 00:00:00 0.0329 0.0972
#> 3 2022-04-03 00:00:00 -0.116 0.0325
#> 4 2022-04-04 00:00:00 -0.142 0.0400
#> 5 2022-04-05 00:00:00 -0.185 0.0786
#> 6 2022-04-06 00:00:00 -0.0303 0.0688
#> 7 2022-04-07 00:00:00 -0.156 0.107
#> 8 2022-04-08 00:00:00 -0.0582 0.0600
#> 9 2022-04-09 00:00:00 0.0801 0.0474
#> 10 2022-04-10 00:00:00 -0.101 0.0761
#> # ℹ 20 more rows
#> # ℹ 16 more variables: RangeTemperature_date_bias <dbl>,
#> # RelativeHumidity_date_bias <dbl>, Radiation_date_bias <dbl>,
#> # MinTemperature_date_mae <dbl>, MaxTemperature_date_mae <dbl>,
#> # RangeTemperature_date_mae <dbl>, RelativeHumidity_date_mae <dbl>,
#> # Radiation_date_mae <dbl>, TotalPrecipitation_date_observed <dbl>,
#> # TotalPrecipitation_date_predicted <dbl>, …
cross_validation$r2
#> $MinTemperature
#> [1] 0.9388959
#>
#> $MaxTemperature
#> [1] 0.9788855
#>
#> $RangeTemperature
#> [1] 0.8835377
#>
#> $RelativeHumidity
#> [1] 0.8096727
#>
#> $Radiation
#> [1] 0.8911309
meteoland
also offers some utilities to work with the
interpolated data.
meteoland
works at the daily scale. But sometimes the
data needs to be aggregated into bigger temporal scales (monthly,
quarterly, yearly…). This can be done with the
summarise_interpolated_data()
function. This function takes
the result of interpolate_data
and creates summaries in the
desired frequency.
The function returns the same interpolated data given as input, but with
the weekly summary in an additional column.
summarise_interpolated_data(
points_interpolated,
fun = "mean",
frequency = "week"
)
#> Simple feature collection with 15 features and 6 fields
#> Geometry type: POINT
#> Dimension: XY
#> Bounding box: xmin: 0.7578958 ymin: 41.31541 xmax: 2.98657 ymax: 42.6336
#> Geodetic CRS: WGS 84
#> # A tibble: 15 × 7
#> plot_id elevation slope aspect geometry interpolated_data
#> * <chr> <dbl> <dbl> <dbl> <POINT [°]> <list>
#> 1 P_05284 889. 25.2 313. (2.320167 42.24139) <tibble [30 × 13]>
#> 2 P_06572 680. 18.0 79.9 (2.552233 42.02596) <tibble [30 × 13]>
#> 3 P_07201 141. 4.17 52.9 (2.721874 41.88258) <tibble [30 × 13]>
#> 4 P_07512 254. 14.3 261. (2.98657 41.9006) <tibble [30 × 13]>
#> 5 P_08207 1860. 36.4 293. (2.209903 42.33968) <tibble [30 × 13]>
#> 6 P_08299 183. 4.12 92.9 (2.817143 42.24325) <tibble [30 × 13]>
#> 7 P_09341 819 23.4 128. (1.126766 42.42612) <tibble [30 × 13]>
#> 8 P_10272 860 34.8 347. (1.398528 42.26791) <tibble [30 × 13]>
#> 9 P_10861 706 22.4 22.6 (0.9314126 42.04226) <tibble [30 × 13]>
#> 10 P_11651 585 22.0 199. (0.7578958 41.8612) <tibble [30 × 13]>
#> 11 P_12150 674. 30.3 154. (1.481719 41.81838) <tibble [30 × 13]>
#> 12 P_12227 752. 6.04 27.7 (1.283161 41.591) <tibble [30 × 13]>
#> 13 P_12417 702 11.6 63.1 (0.8727224 41.35875) <tibble [30 × 13]>
#> 14 P_13007 972. 4.21 338. (1.120383 42.6336) <tibble [30 × 13]>
#> 15 P_14029 556. 14.1 41.4 (1.480716 41.31541) <tibble [30 × 13]>
#> # ℹ 1 more variable: weekly_mean <list>
meteoland
also offers the possibility of calculating the
rainfall erosivity value, with the
precipitation_rainfall_erosivity()
function. This can be
used for individual locations:
precipitation_rainfall_erosivity(
points_interpolated$interpolated_data[[1]],
longitude = sf::st_coordinates(points_interpolated$geometry[[1]])[,1],
scale = 'month'
)
#> 4
#> 48.02896
But also for all locations in the results obtained from the call to
interpolate_data()
:
points_interpolated |>
mutate(erosivity = precipitation_rainfall_erosivity(
interpolated_data,
longitude = sf::st_coordinates(geometry)[,1],
scale = 'month'
))
#> Simple feature collection with 15 features and 6 fields
#> Geometry type: POINT
#> Dimension: XY
#> Bounding box: xmin: 0.7578958 ymin: 41.31541 xmax: 2.98657 ymax: 42.6336
#> Geodetic CRS: WGS 84
#> # A tibble: 15 × 7
#> plot_id elevation slope aspect geometry interpolated_data
#> * <chr> <dbl> <dbl> <dbl> <POINT [°]> <list>
#> 1 P_05284 889. 25.2 313. (2.320167 42.24139) <tibble [30 × 13]>
#> 2 P_06572 680. 18.0 79.9 (2.552233 42.02596) <tibble [30 × 13]>
#> 3 P_07201 141. 4.17 52.9 (2.721874 41.88258) <tibble [30 × 13]>
#> 4 P_07512 254. 14.3 261. (2.98657 41.9006) <tibble [30 × 13]>
#> 5 P_08207 1860. 36.4 293. (2.209903 42.33968) <tibble [30 × 13]>
#> 6 P_08299 183. 4.12 92.9 (2.817143 42.24325) <tibble [30 × 13]>
#> 7 P_09341 819 23.4 128. (1.126766 42.42612) <tibble [30 × 13]>
#> 8 P_10272 860 34.8 347. (1.398528 42.26791) <tibble [30 × 13]>
#> 9 P_10861 706 22.4 22.6 (0.9314126 42.04226) <tibble [30 × 13]>
#> 10 P_11651 585 22.0 199. (0.7578958 41.8612) <tibble [30 × 13]>
#> 11 P_12150 674. 30.3 154. (1.481719 41.81838) <tibble [30 × 13]>
#> 12 P_12227 752. 6.04 27.7 (1.283161 41.591) <tibble [30 × 13]>
#> 13 P_12417 702 11.6 63.1 (0.8727224 41.35875) <tibble [30 × 13]>
#> 14 P_13007 972. 4.21 338. (1.120383 42.6336) <tibble [30 × 13]>
#> 15 P_14029 556. 14.1 41.4 (1.480716 41.31541) <tibble [30 × 13]>
#> # ℹ 1 more variable: erosivity <list>
meteoland
new data flows also allows for piping all
processes:
points_interpolated <- points_to_interpolate_example |>
interpolate_data(interpolator) |>
summarise_interpolated_data(
fun = "mean",
frequency = "week"
) |>
summarise_interpolated_data(
fun = "max",
frequency = "month"
) |>
mutate(
monthly_erosivity = precipitation_rainfall_erosivity(
interpolated_data,
longitude = sf::st_coordinates(geometry)[,1],
scale = 'month'
)
)
#> ℹ Starting interpolation...
#> ℹ Temperature interpolation is needed also...
#> • Interpolating temperature...
#> ℹ Precipitation interpolation is needed also...
#> • Interpolating precipitation...
#> ℹ Relative humidity interpolation is needed also...
#> • Interpolating relative humidity...
#> ℹ Radiation calculation is needed also...
#> • Calculating radiation...
#> ℹ Wind interpolation is needed also...
#> • Interpolating wind...
#> • Calculating PET...
#> ✔ Interpolation done...
points_interpolated
#> Simple feature collection with 15 features and 8 fields
#> Geometry type: POINT
#> Dimension: XY
#> Bounding box: xmin: 0.7578958 ymin: 41.31541 xmax: 2.98657 ymax: 42.6336
#> Geodetic CRS: WGS 84
#> # A tibble: 15 × 9
#> plot_id elevation slope aspect geometry interpolated_data
#> * <chr> <dbl> <dbl> <dbl> <POINT [°]> <list>
#> 1 P_05284 889. 25.2 313. (2.320167 42.24139) <tibble [30 × 13]>
#> 2 P_06572 680. 18.0 79.9 (2.552233 42.02596) <tibble [30 × 13]>
#> 3 P_07201 141. 4.17 52.9 (2.721874 41.88258) <tibble [30 × 13]>
#> 4 P_07512 254. 14.3 261. (2.98657 41.9006) <tibble [30 × 13]>
#> 5 P_08207 1860. 36.4 293. (2.209903 42.33968) <tibble [30 × 13]>
#> 6 P_08299 183. 4.12 92.9 (2.817143 42.24325) <tibble [30 × 13]>
#> 7 P_09341 819 23.4 128. (1.126766 42.42612) <tibble [30 × 13]>
#> 8 P_10272 860 34.8 347. (1.398528 42.26791) <tibble [30 × 13]>
#> 9 P_10861 706 22.4 22.6 (0.9314126 42.04226) <tibble [30 × 13]>
#> 10 P_11651 585 22.0 199. (0.7578958 41.8612) <tibble [30 × 13]>
#> 11 P_12150 674. 30.3 154. (1.481719 41.81838) <tibble [30 × 13]>
#> 12 P_12227 752. 6.04 27.7 (1.283161 41.591) <tibble [30 × 13]>
#> 13 P_12417 702 11.6 63.1 (0.8727224 41.35875) <tibble [30 × 13]>
#> 14 P_13007 972. 4.21 338. (1.120383 42.6336) <tibble [30 × 13]>
#> 15 P_14029 556. 14.1 41.4 (1.480716 41.31541) <tibble [30 × 13]>
#> # ℹ 3 more variables: weekly_mean <list>, monthly_max <list>,
#> # monthly_erosivity <list>
We can use the interpolate_data()
function in a raster
type of data. All we need in this case is the topography information in
a stars
object, with elevation
,
aspect
and slope
variables as raster
attributes:
raster_to_interpolate_example
#> stars object with 2 dimensions and 3 attributes
#> attribute(s):
#> Min. 1st Qu. Median Mean 3rd Qu. Max.
#> elevation 240.000000 370.000000 447.00000 460.32231 525.00000 786.0000
#> slope 1.432096 5.720433 11.34812 13.07343 19.75851 31.0719
#> aspect 5.194427 74.744881 174.36932 181.67923 291.03751 360.0000
#> dimension(s):
#> from to offset delta refsys x/y
#> x 155 165 0.03648 0.01058 WGS 84 [x]
#> y 110 120 42.92 -0.01058 WGS 84 [y]
In this case, the raster is a 0.01 degree grid (10x10 cells) in central Catalonia. As the raster is inside the area covered by the interpolator object we created before, we will use it.
raster_interpolated <- raster_to_interpolate_example |>
interpolate_data(interpolator)
#> ℹ Starting interpolation...
#> ℹ Temperature interpolation is needed also...
#> • Interpolating temperature...
#> ℹ Precipitation interpolation is needed also...
#> • Interpolating precipitation...
#> ℹ Relative humidity interpolation is needed also...
#> • Interpolating relative humidity...
#> ℹ Radiation calculation is needed also...
#> • Calculating radiation...
#> ℹ Wind interpolation is needed also...
#> • Interpolating wind...
#> • Calculating PET...
#> ✔ Interpolation done...
#> ℹ Binding together interpolation results
#> ✔ Interpolation process finished
raster_interpolated
#> stars object with 3 dimensions and 14 attributes
#> attribute(s):
#> Min. 1st Qu. Median Mean
#> MeanTemperature 3.28710017 11.4127317 13.905175 13.419200
#> MinTemperature -4.21944950 3.9207208 6.575382 5.306937
#> MaxTemperature 6.96679206 14.9159502 19.225056 18.693510
#> Precipitation 0.00000000 0.0000000 0.000000 1.217155
#> MeanRelativeHumidity 32.89385498 58.0844689 64.649229 65.957527
#> MinRelativeHumidity 25.19625829 38.4317461 44.433889 47.943580
#> MaxRelativeHumidity 49.75939189 100.0000000 100.000000 97.027820
#> Radiation 7.38449673 16.1504318 20.815039 19.742938
#> WindSpeed 0.02164994 0.9119314 1.252240 1.385929
#> WindDirection 0.18621266 71.4293342 198.955399 181.615512
#> PET 1.09428184 2.4611166 3.196850 3.110504
#> elevation 240.00000000 370.0000000 447.000000 460.322314
#> slope 1.43209624 5.7204332 11.348120 13.073426
#> aspect 5.19442749 74.7448807 174.369324 181.679232
#> 3rd Qu. Max. NA's
#> MeanTemperature 16.0215966 20.225457 0
#> MinTemperature 7.6128811 11.721902 0
#> MaxTemperature 22.3273620 29.104431 0
#> Precipitation 0.2922964 21.000409 0
#> MeanRelativeHumidity 75.6627580 100.000000 0
#> MinRelativeHumidity 55.1586632 91.663163 0
#> MaxRelativeHumidity 100.0000000 100.000000 0
#> Radiation 23.8148915 28.126824 0
#> WindSpeed 1.7444530 5.811866 30
#> WindDirection 264.0404014 359.908196 1350
#> PET 3.7822172 5.598250 0
#> elevation 525.0000000 786.000000 0
#> slope 19.7585106 31.071896 0
#> aspect 291.0375061 360.000000 0
#> dimension(s):
#> from to offset delta refsys point x/y
#> x 1 11 1.671 0.01058 WGS 84 FALSE [x]
#> y 1 11 41.76 -0.01058 WGS 84 FALSE [y]
#> date 1 30 2022-04-01 UTC 1 days POSIXct FALSE
As we can see, the returned object is the same stars
raster provided to the function, with the interpolated meteorological
variables as new attributes. Dimensions now include the date, besides
the input’s latitude and longitude.
Like with the point location example, interpolated data in raster format can also be aggregated temporally.
summarise_interpolated_data(
raster_interpolated,
fun = "mean",
frequency = "week"
)
#> stars object with 3 dimensions and 11 attributes
#> attribute(s):
#> Min. 1st Qu. Median Mean
#> MeanTemperature 3.8085157 11.46543487 13.276586 12.702695
#> MinTemperature -2.1490631 2.77153554 6.299540 4.640385
#> MaxTemperature 7.6274425 16.18746065 18.457836 17.944528
#> Precipitation 0.0000000 0.04039901 0.372891 1.068806
#> MeanRelativeHumidity 42.9062182 60.53136706 64.595298 63.904152
#> MinRelativeHumidity 29.2592761 40.80836041 45.249846 46.333339
#> MaxRelativeHumidity 75.1187263 96.67327485 99.376895 95.009647
#> Radiation 11.7245475 17.90842114 19.929736 19.765548
#> WindSpeed 0.6861051 0.87245304 1.343451 1.515442
#> WindDirection 122.7681189 152.95041467 168.597605 184.990642
#> PET 1.6176152 2.74501755 3.084015 3.091572
#> 3rd Qu. Max. NA's
#> MeanTemperature 15.8981470 17.107689 0
#> MinTemperature 7.0401778 8.721007 0
#> MaxTemperature 21.3502767 24.825805 0
#> Precipitation 0.9568111 4.916280 0
#> MeanRelativeHumidity 69.2639299 88.634437 0
#> MinRelativeHumidity 52.5994550 72.780577 0
#> MaxRelativeHumidity 100.0000000 100.000000 0
#> Radiation 21.8800875 25.287348 0
#> WindSpeed 1.8527502 4.348124 5
#> WindDirection 234.5482210 246.486142 365
#> PET 3.4728443 5.069591 0
#> dimension(s):
#> from to offset delta refsys point x/y
#> time 1 5 2022-03-28 CEST 7 days POSIXct NA
#> x 1 11 1.671 0.01058 WGS 84 FALSE [x]
#> y 1 11 41.76 -0.01058 WGS 84 FALSE [y]
In this case the result is the aggregated variables as attributes, and the time dimension is aggregated in the desired frequency.
As with points, raster interpolation and utilities can also be piped. This way, if we are only interested in the mean monthly temperature in our study area, we can do:
monthly_mean_temperature <- raster_to_interpolate_example |>
interpolate_data(interpolator, variables = "Temperature") |>
summarise_interpolated_data(
fun = "max",
frequency = "month",
variable = "MeanTemperature"
)
#> ℹ Starting interpolation...
#> • Interpolating temperature...
#> ✔ Interpolation done...
#> ℹ Binding together interpolation results
#> ✔ Interpolation process finished
plot(monthly_mean_temperature)
Function (< 2.0.0) | Equivalence (>= 2.0.0) | deprecated |
---|---|---|
averagearea |
No equivalence, aggregating by area can be done with the
sf package |
TRUE |
correctionpoint , correctionpoints ,
correctionpoints.errors , correction_series ,
defaultCorrectionParams |
No equivalence, better bias correction methods are provided by other
packages (see package MBC for example) |
TRUE |
defaultInterpolationParams |
No change | FALSE |
download_* functions |
No equivalence, weather download functions are now provided by
meteospain package |
TRUE |
extractdates , extractgridindex ,
extractgridpoints , extractNetCDF ,
extractvars |
No equivalence, not needed as the meteo objects are now
sf objects |
TRUE |
humidity_* conversion tools |
No change | FALSE |
interpolation.calibration |
interpolator_calibration |
TRUE |
interpolation.calibration.fmax |
interpolator_calibration |
TRUE |
interpolation.coverage |
No equivalence | TRUE |
interpolation.cv |
interpolation_cross_validation |
TRUE |
interpolationgrid , interpolationpixels ,
interpolationpoints |
interpolate_data |
TRUE |
mergegrid , mergepoints |
No equivalence, meteorological objects are now sf
objects and can be merged, joined or filtered as any data.frame |
TRUE |
meteocomplete |
complete_meteo |
TRUE |
meteoplot |
No equivalence, meteo objects are now sf objects and can be plotted as any other data.frame | TRUE |
Meteorology_*_Data |
No equivalence, spatial classes based on sp are now
deprecated in meteoland |
TRUE |
penman , penmanmonteith |
No changes | FALSE |
plot.interpolation.cv |
No equivalence | TRUE |
precipitation_concentration |
No equivalence, precipitation_concentration utility is deprecated and will be removed in future versions | TRUE |
precipitation_rainfallErosivity |
precipitation_rainfall_erosivity |
TRUE |
radiation_* utility functions |
No change | FALSE |
readmeteorology* |
No equivalence, spatial classes based on sp are now
deprecated in meteoland |
TRUE |
readNetCDF* |
No equivalence, NetCDF files can be managed with more recent and up to date R packages (ncmeta, stars…) | TRUE |
readWindNinjaWindFields |
No equivalence | TRUE |
reshapemeteospain |
meteospain2meteoland |
TRUE |
reshapeworldmet |
worldmet2meteoland |
TRUE |
reshapeweathercan |
No equivalence, weathercan package was removed from
CRAN and the functions are deprecated |
TRUE |
Spatial**Meteorology ,
Spatial**Topography |
No equivalence, spatial classes based on sp are now
deprecated in meteoland |
TRUE |
summary* |
summarise_interpolate_data ,
summarise_interpolator |
TRUE |
utils_* |
No change | FALSE |
weathergeneration ,
defaultGenerationParams |
No equivalence, current weather generation methods are currently deprecated because they operate with classes that are deprecated themselves, but for future versions, we plan to keep the functionality in new functions. | TRUE |
writemeteorology* |
No equivalence, spatial classes based on sp are now
deprecated in meteoland |
TRUE |
These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
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