Interpolación espacial del carbono organico del suelo
Nicolas Cely
2023-06-14
Introducción
En este cuaderno se exponen dos tecnicas de interpolación, estas son: IDW (Distancia Inversa Ponderada) y OK (kriging Ordinario). Ambas tecnicas se usan para tener una superficie continua del carbono organico del suelo (SOC) a una profundidad de 15 - 30 cm a partir de muestras obtenidas de SoilGrids 250m.
Configuración
Primero limpiremos la memeoria
rm(list=ls())Cargar la librerias necesarias para el trabajo. Antes de cargarlas, verifica que estas hayan sido instaladas previamente.
library(sp)
library(terra)
library(sf)
library(stars)
library(gstat)
library(automap)
library(leaflet)
library(leafem)
library(ggplot2)
library(dplyr)library(curl)h <- new_handle()
handle_setopt(h, http_version = 2)Leer los datos de entrada
Con el fin de imitar los datos del mundo real, vamos a leer la capa SOC que descargamos de ISRIC hacinedo uso de la libreria terra.
archivo <- ('C:/Users/LENOVO/Desktop/Geomatica/R/SOC15.tif')(soc <- rast(archivo))## class : SpatRaster
## dimensions : 728, 816, 1 (nrow, ncol, nlyr)
## resolution : 0.002261029, 0.00239011 (x, y)
## extent : -76.4, -74.555, 4.06, 5.8 (xmin, xmax, ymin, ymax)
## coord. ref. : lon/lat WGS 84 (EPSG:4326)
## source : SOC15.tif
## name : SOC15Ahora convertiremos los datos de SOC en porcentaje.
soc.perc <- soc/10Transformación de este CRS al CRS WGS84
geog ="+proj=longlat +datum=WGS84"
(geog.soc = project(soc.perc, geog))## class : SpatRaster
## dimensions : 750, 796, 1 (nrow, ncol, nlyr)
## resolution : 0.002319123, 0.002319123 (x, y)
## extent : -76.4, -74.55398, 4.060658, 5.8 (xmin, xmax, ymin, ymax)
## coord. ref. : +proj=longlat +datum=WGS84 +no_defs
## source(s) : memory
## name : SOC15
## min value : 0.0000
## max value : 287.2864Convirtamos la capa SpatRaster en un stars object
stars.soc = st_as_stars(geog.soc)Ahora relizamos un mapa
m <- leaflet() %>%
addTiles() %>%
leafem:::addGeoRaster(
stars.soc,
opacity = 0.8,
colorOptions = colorOptions(palette = c("orange", "yellow", "cyan", "green"),
domain = 8:130)
)
m Muestreo del mundo real
A continuación obtendremos una muestra de aproximadamente 500 sitios del mundo real utilizando una muestra localizada aleatoriamente.
set.seed(123456)
# Muestreo aleatoreo de 500 puntos
(samples <- spatSample(geog.soc, 500, "random", as.points=TRUE))## class : SpatVector
## geometry : points
## dimensions : 500, 1 (geometries, attributes)
## extent : -76.39884, -74.55514, 4.061817, 5.79884 (xmin, xmax, ymin, ymax)
## coord. ref. : +proj=longlat +datum=WGS84 +no_defs
## names : SOC15
## type : <num>
## values : 201.5
## 72.28
## 20.74Debemos describir las principales caracteristicas del objeto muestra
Ahora, tenemos que convertir el objeto SpatVector en un objeto feature simple
(muestras <- sf::st_as_sf(samples))## Simple feature collection with 500 features and 1 field
## Geometry type: POINT
## Dimension: XY
## Bounding box: xmin: -76.39884 ymin: 4.061817 xmax: -74.55514 ymax: 5.79884
## Geodetic CRS: GEOGCRS["unknown",
## DATUM["World Geodetic System 1984",
## ELLIPSOID["WGS 84",6378137,298.257223563,
## LENGTHUNIT["metre",1]],
## ID["EPSG",6326]],
## PRIMEM["Greenwich",0,
## ANGLEUNIT["degree",0.0174532925199433],
## ID["EPSG",8901]],
## CS[ellipsoidal,2],
## AXIS["longitude",east,
## ORDER[1],
## ANGLEUNIT["degree",0.0174532925199433,
## ID["EPSG",9122]]],
## AXIS["latitude",north,
## ORDER[2],
## ANGLEUNIT["degree",0.0174532925199433,
## ID["EPSG",9122]]]]
## First 10 features:
## SOC15 geometry
## 1 201.52055 POINT (-76.32695 5.662012)
## 2 72.27789 POINT (-76.19244 5.703756)
## 3 20.73886 POINT (-74.62703 5.50895)
## 4 47.95502 POINT (-75.63121 5.251527)
## 5 124.67467 POINT (-76.1878 5.272399)
## 6 76.56056 POINT (-75.13724 5.629544)
## 7 40.15657 POINT (-75.6544 4.910616)
## 8 69.90199 POINT (-75.49902 4.989466)
## 9 59.86207 POINT (-75.5454 4.263581)
## 10 71.97430 POINT (-74.99809 5.290952)nmuestras <- na.omit(muestras)Visualicemos las muestras
longit <- st_coordinates(muestras)[,1]
latit <- st_coordinates(muestras)[,2]
soc <- muestras$`SOC15`id <- seq(1,500,1)(sitios <- data.frame(id, longit, latit, soc))## id longit latit soc
## 1 1 -76.32695 5.662012 201.52055
## 2 2 -76.19244 5.703756 72.27789
## 3 3 -74.62703 5.508950 20.73886
## 4 4 -75.63121 5.251527 47.95502
## 5 5 -76.18780 5.272399 124.67467
## 6 6 -75.13724 5.629544 76.56056
## 7 7 -75.65440 4.910616 40.15657
## 8 8 -75.49902 4.989466 69.90199
## 9 9 -75.54540 4.263581 59.86207
## 10 10 -74.99809 5.290952 71.97430
## 11 11 -75.05839 4.636960 50.51255
## 12 12 -76.37333 4.428239 57.62215
## 13 13 -75.02360 5.056721 38.62682
## 14 14 -75.81674 4.261262 43.72710
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## 17 17 -75.26711 5.471844 46.19360
## 18 18 -74.73835 4.428239 28.56844
## 19 19 -75.89327 4.785384 21.73819
## 20 20 -75.91414 5.052083 36.93518
## 21 21 -76.23186 4.799298 80.77451
## 22 22 -76.11823 5.397632 71.49570
## 23 23 -74.72211 4.794660 31.32504
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## 341 341 -75.77036 4.268219 55.29541
## 342 342 -76.31999 4.061817 21.68181
## 343 343 -74.80328 4.456068 23.13152
## 344 344 -74.91692 5.228336 21.72222
## 345 345 -75.20217 5.265442 82.00424
## 346 346 -75.65904 4.792341 40.78756
## 347 347 -74.63167 4.834085 32.56137
## 348 348 -75.67759 5.200507 29.60692
## 349 349 -75.06998 5.207464 48.28332
## 350 350 -75.57323 5.001062 37.90054
## 351 351 -74.73835 5.119337 22.98896
## 352 352 -76.33390 5.237613 95.89774
## 353 353 -75.42249 4.681023 66.80602
## 354 354 -76.19012 5.198188 73.31627
## 355 355 -76.05329 5.527503 113.80224
## 356 356 -76.16229 4.277496 20.91250
## 357 357 -74.82416 4.358665 20.79509
## 358 358 -74.95635 5.207464 31.42168
## 359 359 -75.84689 5.063678 25.67172
## 360 360 -75.32972 4.611449 61.83695
## 361 361 -76.29680 5.784926 65.58174
## 362 362 -76.08808 4.333155 25.45052
## 363 363 -76.13910 4.572024 71.84538
## 364 364 -75.43872 4.432877 53.62717
## 365 365 -75.01896 4.249666 19.92265
## 366 366 -74.90301 4.284453 16.84386
## 367 367 -76.11591 5.754777 68.60464
## 368 368 -74.58065 4.456068 24.65936
## 369 369 -75.04447 4.451430 19.79432
## 370 370 -74.57369 5.272399 23.92711
## 371 371 -74.68733 4.108200 32.01759
## 372 372 -76.31071 4.889744 99.67415
## 373 373 -74.76850 5.450972 24.33921
## 374 374 -75.88168 5.089189 23.19234
## 375 375 -75.72398 4.616088 34.90303
## 376 376 -75.14883 5.655055 47.94374
## 377 377 -75.74021 5.010339 38.22617
## 378 378 -76.35014 4.792341 49.16828
## 379 379 -75.54540 5.123976 48.50538
## 380 380 -75.00969 4.984828 27.40895
## 381 381 -76.19940 4.091966 0.00000
## 382 382 -74.85430 4.284453 20.18382
## 383 383 -76.33622 5.423142 222.05420
## 384 384 -75.41553 5.597077 66.81011
## 385 385 -75.78427 4.347069 27.65158
## 386 386 -75.16739 5.012658 63.05899
## 387 387 -75.25551 5.685203 91.89825
## 388 388 -76.00459 5.692161 70.78352
## 389 389 -75.58019 5.212102 50.89899
## 390 390 -76.00459 4.270538 25.20052
## 391 391 -75.41089 4.799298 59.24374
## 392 392 -74.69892 5.446334 28.56255
## 393 393 -75.96285 4.539557 20.62407
## 394 394 -76.03474 5.100784 107.95598
## 395 395 -75.56164 4.548833 62.48239
## 396 396 -75.84689 5.381398 68.31615
## 397 397 -74.75922 4.258943 25.30676
## 398 398 -76.12982 5.272399 89.91652
## 399 399 -75.34828 4.238071 56.97986
## 400 400 -75.27870 5.049764 69.88731
## 401 401 -75.08390 5.304867 51.82898
## 402 402 -76.16461 5.460248 73.35531
## 403 403 -74.95866 5.168039 41.97486
## 404 404 -74.71284 5.244570 18.95735
## 405 405 -76.05793 4.149944 35.51830
## 406 406 -75.30885 5.411547 77.49171
## 407 407 -74.97026 5.151805 71.02966
## 408 408 -76.21331 5.270080 72.28096
## 409 409 -76.35246 5.163401 164.32655
## 410 410 -76.15533 4.126753 24.60173
## 411 411 -75.23696 5.186592 67.46825
## 412 412 -75.29726 5.318782 55.75346
## 413 413 -75.04215 4.402728 18.94314
## 414 414 -74.88677 5.031211 18.69214
## 415 415 -75.88168 5.791883 39.73401
## 416 416 -74.58761 4.523323 34.50966
## 417 417 -75.86312 5.501993 93.30278
## 418 418 -75.64513 4.834085 41.15916
## 419 419 -75.71470 5.003381 31.00526
## 420 420 -75.01200 4.245028 18.53606
## 421 421 -74.90996 4.245028 21.53582
## 422 422 -76.15069 4.699576 34.85075
## 423 423 -74.87286 5.536780 24.26187
## 424 424 -75.53149 4.384175 58.82573
## 425 425 -75.15811 4.903659 71.30268
## 426 426 -75.00273 4.136029 14.37605
## 427 427 -75.75181 5.367484 61.64387
## 428 428 -74.91692 5.594758 28.67395
## 429 429 -75.15347 5.750139 86.83689
## 430 430 -74.62703 4.739001 33.26605
## 431 431 -74.74531 4.110519 15.55320
## 432 432 -76.39884 5.056721 184.73198
## 433 433 -75.56628 4.743639 52.50283
## 434 434 -76.28057 4.126753 18.43217
## 435 435 -75.44800 4.474621 89.49364
## 436 436 -74.72907 4.437515 22.99113
## 437 437 -75.08390 4.105881 31.50039
## 438 438 -74.57833 5.314144 63.08957
## 439 439 -75.41785 5.471844 66.73744
## 440 440 -75.84921 4.407367 26.74456
## 441 441 -75.85385 4.548833 26.42059
## 442 442 -74.95171 4.138348 18.34733
## 443 443 -76.28057 4.678704 51.70436
## 444 444 -75.93965 4.407367 27.72754
## 445 445 -75.55236 4.736682 56.53277
## 446 446 -75.39930 5.687523 40.03516
## 447 447 -74.87054 5.226017 21.21263
## 448 448 -75.44568 5.144848 69.67031
## 449 449 -75.25087 4.189369 26.73174
## 450 450 -75.86544 4.080370 55.80783
## 451 451 -75.70078 5.302548 92.06828
## 452 452 -75.43872 4.732044 65.55432
## 453 453 -75.47119 5.251527 52.35936
## 454 454 -75.55236 4.061817 50.73089
## 455 455 -75.98604 5.450972 72.99322
## 456 456 -76.28984 4.175454 21.21450
## 457 457 -74.57369 4.676385 34.84175
## 458 458 -75.99995 5.481121 85.66775
## 459 459 -75.90487 5.752458 39.53645
## 460 460 -76.27129 4.989466 63.06372
## 461 461 -74.61543 4.954680 27.96161
## 462 462 -74.66182 4.905978 28.52035
## 463 463 -74.98881 5.775649 42.95164
## 464 464 -75.02824 5.437057 53.05967
## 465 465 -75.27175 5.195868 74.47117
## 466 466 -76.31535 4.333155 43.04797
## 467 467 -74.90069 5.017296 22.65612
## 468 468 -75.11173 4.815532 64.20106
## 469 469 -76.27129 4.956999 77.76530
## 470 470 -75.04215 4.490855 20.94310
## 471 471 -74.57601 5.302548 27.51717
## 472 472 -75.57323 4.219518 69.09544
## 473 473 -75.23928 4.421281 26.37920
## 474 474 -76.30839 5.571566 190.69368
## 475 475 -74.96098 4.685661 23.85669
## 476 476 -75.50830 4.395771 52.45917
## 477 477 -76.25505 5.497354 171.58464
## 478 478 -75.05143 4.312282 13.95514
## 479 479 -75.12796 5.476482 57.76789
## 480 480 -76.06257 4.476940 26.75782
## 481 481 -75.23696 5.553013 87.20108
## 482 482 -75.55468 5.142529 38.09097
## 483 483 -74.79169 4.544195 17.88832
## 484 484 -75.60338 4.676385 50.12939
## 485 485 -75.48974 4.643917 66.56770
## 486 486 -75.43640 4.704214 63.59487
## 487 487 -75.94429 4.701895 17.68264
## 488 488 -74.94243 5.548375 55.45159
## 489 489 -75.66368 5.177315 26.25048
## 490 490 -75.99299 5.369803 38.65867
## 491 491 -75.39466 5.328058 73.23988
## 492 492 -75.81906 4.931488 36.25452
## 493 493 -75.96285 4.984828 33.63740
## 494 494 -74.64095 5.191230 33.01804
## 495 495 -76.30376 4.490855 42.95618
## 496 496 -75.79123 4.838723 26.77345
## 497 497 -76.16693 4.316921 23.02101
## 498 498 -74.94475 5.515907 48.53756
## 499 499 -75.55700 5.796521 39.42776
## 500 500 -74.78937 5.019615 32.81052Ahora borraremos los valores NA
sitios <- na.omit(sitios)head(sitios)## id longit latit soc
## 1 1 -76.32695 5.662012 201.52055
## 2 2 -76.19244 5.703756 72.27789
## 3 3 -74.62703 5.508950 20.73886
## 4 4 -75.63121 5.251527 47.95502
## 5 5 -76.18780 5.272399 124.67467
## 6 6 -75.13724 5.629544 76.56056Visualizemos las muestras
m <- leaflet() %>%
addTiles() %>%
leafem:::addGeoRaster(
stars.soc,
opacity = 0.7,
colorOptions = colorOptions(palette = c("orange", "yellow", "cyan", "green"),
domain = 8:130)
) %>%
addMarkers(lng=sitios$longit,lat=sitios$latit, popup=sitios$soc, clusterOptions = markerClusterOptions())
m # Print the mapInterpolación
Creación de objeto´gstat
Para interpolar, primero necesitamos crear un objeto de la clase gstat.
Un objeto gstat contiene toda la información necesaria para realizar la interpolación espacial.
Vamos a utilizar tres parámetros de la función gstat: - Fórmula: la “fórmula” de predicción que especifica las variables dependientes e independientes - Data: los datos de calibración - Modelo: el modelo de variograma
Interpolación IDW
Para interpolar utilizando este metodo creamos el siguinte objeto gstat, especificando unicamente la formula y los datos:
g1 = gstat(formula = SOC15 ~ 1, data = nmuestras)Ahora que el modelo de interpolación g1 está definido, podemos utilizar la función predict para interpolar.
Vamos a crear un objeto raster con valores de celda iguales a 1:
rrr = aggregate(geog.soc, 4)¿Que es rrr?
rrr## class : SpatRaster
## dimensions : 188, 199, 1 (nrow, ncol, nlyr)
## resolution : 0.009276493, 0.009276493 (x, y)
## extent : -76.4, -74.55398, 4.056019, 5.8 (xmin, xmax, ymin, ymax)
## coord. ref. : +proj=longlat +datum=WGS84 +no_defs
## source(s) : memory
## name : SOC15
## min value : 0.0000
## max value : 255.0888Definiremos nuevos valores para rrr
values(rrr) <-1Definiremos nuevos nombres para rrr
names(rrr) <- "valor"Ahora rrr es:
rrr## class : SpatRaster
## dimensions : 188, 199, 1 (nrow, ncol, nlyr)
## resolution : 0.009276493, 0.009276493 (x, y)
## extent : -76.4, -74.55398, 4.056019, 5.8 (xmin, xmax, ymin, ymax)
## coord. ref. : +proj=longlat +datum=WGS84 +no_defs
## source(s) : memory
## name : valor
## min value : 1
## max value : 1stars.rrr = st_as_stars(rrr)El siguiente codigo interpola los valores SOC según el modelo definido en g1 y la plantilla raster definida en stars.rrr:
z1 = predict(g1, stars.rrr)## [inverse distance weighted interpolation]¿Que es Z1?
z1## stars object with 2 dimensions and 2 attributes
## attribute(s):
## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## var1.pred 0.9032976 34.64183 48.23325 51.72116 60.39388 242.9888 0
## var1.var NA NA NA NaN NA NA 37412
## dimension(s):
## from to offset delta refsys x/y
## x 1 199 -76.4 0.00927649 +proj=longlat +datum=WGS8... [x]
## y 1 188 5.8 -0.00927649 +proj=longlat +datum=WGS8... [y]El objeto z1 dos atributos, podemos subconjuntar sólo el primer atributo y renombrarlo a “soc”:
z1 = z1["var1.pred",,]
names(z1) = "soc"Necesitrampos una paleta de colores
paleta <- colorNumeric(palette = c("red", "yellow", "cyan", "green"), domain = 10:100, na.color = "transparent")El raster SOC interpolado lo podemos observar a continuación:
m <- leaflet() %>%
addTiles() %>%
leafem:::addGeoRaster(
z1,
opacity = 0.7,
colorOptions = colorOptions(palette = c("red", "yellow", "cyan", "green"),
domain = 11:55)
) %>%
addMarkers(lng=sitios$longit,lat=sitios$latit, popup=sitios$soc, clusterOptions = markerClusterOptions()) %>%
addLegend("bottomright", pal=paleta, values= z1$soc,
title = "IDW SOC interpolation [%]"
)## Warning in pal(c(r[1], cuts, r[2])): Some values were outside the color scale
## and will be treated as NAm # Print the mapInterpolación OK
Primeramente calcularemos y examinaremos el variograma empírico utilizando laa función Variogram.
La función requiere dos argumentos: formula y datos
El siguiente codigo calcula el variograma empirico de muestras, sin covariables.
v_emp_ok = variogram(SOC15 ~ 1, data=nmuestras)Ilustermos el variograma:
plot(v_emp_ok) 
Utilizaremos la función autofitVariogram para ajustar un modelo de variograma a un variograma empirico.
v_mod_ok = autofitVariogram(SOC15 ~ 1, as(nmuestras, "Spatial"))La función elige el tipo de modelo que mejor se ajusta y también afina sus parámetros.
El modelo ajustado puede representarse con plot:
plot(v_mod_ok)
El objeto resultante es en realidad una lista con varios componentes, incluyendo el variograma empírico y el modelo de variograma ajustado. El componente $var_model del objeto resultante contiene el modelo real:
v_mod_ok$var_model## model psill range kappa
## 1 Nug 20.52881 0.00000 0.0
## 2 Ste 1171.51991 79.38399 0.3El modelo puedo pasarse a la función gstat para asi poder continuar con la interpolación OK:
g2 = gstat(formula = SOC15 ~ 1, model = v_mod_ok$var_model, data = nmuestras)
z2= predict(g2, stars.rrr)## [using ordinary kriging]Nuevamente vamos a subconjuntar el atributo de valores predichos y cambiaremos el nombre:
z2 = z2["var1.pred",,]
names(z2) = "soc"Las prediciones de Kriging ordinario se puede ver a continuación.
m <- leaflet() %>%
addTiles() %>%
leafem:::addGeoRaster(
z2,
opacity = 0.7,
colorOptions = colorOptions(palette = c("orange", "yellow", "cyan", "green"),
domain = 11:55)
) %>%
addMarkers(lng=sitios$longit,lat=sitios$latit, popup=sitios$soc, clusterOptions = markerClusterOptions()) %>%
addLegend("bottomright", pal = paleta, values= z2$soc,
title = "OK SOC interpolation [%]"
)## Warning in pal(c(r[1], cuts, r[2])): Some values were outside the color scale
## and will be treated as NAm # Print the mapEvaluación de los resultados
Evaluación cualitativa
Otra forma de visualizar los tres resultados de interpolación:
colores <- colorOptions(palette = c("orange", "yellow", "cyan", "green"), domain = 10:100, na.color = "transparent")m <- leaflet() %>%
addTiles() %>%
addGeoRaster(stars.soc, opacity = 0.8, colorOptions = colores, group="RealWorld") %>%
addGeoRaster(z1, colorOptions = colores, opacity = 0.8, group= "IDW") %>%
addGeoRaster(z2, colorOptions = colores, opacity = 0.8, group= "OK") %>%
# Add layers controls
addLayersControl(
overlayGroups = c("RealWorld", "IDW", "OK"),
options = layersControlOptions(collapsed = FALSE)
) %>%
addLegend("bottomright", pal = paleta, values= z1$soc,
title = "Soil organic carbon [%]"
)## Warning in pal(c(r[1], cuts, r[2])): Some values were outside the color scale
## and will be treated as NAm # Print the mapValidación cruzada
Validación cruzada Leave-One-Out
cv1 = gstat.cv(g1)## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
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## [inverse distance weighted interpolation]cv2 = gstat.cv(g2)## [using ordinary kriging]
## [using ordinary kriging]
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## [using ordinary kriging]cv1 = na.omit(cv1)cv1## class : SpatialPointsDataFrame
## features : 500
## extent : -76.39884, -74.55514, 4.061817, 5.79884 (xmin, xmax, ymin, ymax)
## crs : +proj=longlat +datum=WGS84 +no_defs
## variables : 6
## names : var1.pred, var1.var, observed, residual, zscore, fold
## min values : 17.2576789621635, NA, 0, -83.6916712396385, NA, 1
## max values : 184.56223330443, NA, 246.571563720703, 118.695562119791, NA, 500Convertiremos el objeto cv1
cv1 = st_as_sf(cv1)Ahora trazemos los residuales
sp::bubble(as(cv1[, "residual"], "Spatial"))
Ahora calcularemos los indices de precisión de la predicción, como tambien el error cuadratico medio (RMSE)
sqrt(sum((cv1$var1.pred - cv1$observed)^2) / nrow(cv1))## [1] 21.26027repetiremos el proceso para los resultados de OK
Conversión:
cv2 = st_as_sf(cv2)calculo de RSME para OK
sqrt(sum((cv2$var1.pred - cv2$observed)^2) / nrow(cv2))## [1] 18.94742Referencias
Este trabajo se realizó tomando como guía el cuaderno: Lizarazo, I. 2023, Spatial interpolation of soil organic carbon.
Cite este trabajo así: Cely, N., 2023. Interpolación espacial del carbono organico del suelo. Disponible en https://rpubs.com/ncely/1048046