1. INTRODUCCION

En este cuaderno ilustraremos dos técnicas de interpolación espacial: distancia ponderada inversa (IDW) y Kriging ordinario (OK). IDW es una técnica determinista. OK es probabilístico. Ambas técnicas se utilizan aquí para obtener una superficie continua de SOC a 15-30 cm a partir de muestras obtenidas de SoilGrids 250 m.

2. CONFIGURACION

Primero, limpiamos la memoria:

rm(list=ls())

Luego, nos asegúramos de haber instalado previamente las bibliotecas necesarias.

Luego, cargamos las bibliotecas:

library(sp)
library(terra)
## terra 1.7.55
library(sf)
## Warning: package 'sf' was built under R version 4.3.2
## Linking to GEOS 3.11.2, GDAL 3.7.2, PROJ 9.3.0; sf_use_s2() is TRUE
library(stars)
## Loading required package: abind
library(gstat)
## Warning: package 'gstat' was built under R version 4.3.2
library(automap)
## Warning: package 'automap' was built under R version 4.3.2
library(leaflet)
library(leafem)
library(ggplot2)
library(dplyr)
## Warning: package 'dplyr' was built under R version 4.3.2
## 
## Attaching package: 'dplyr'
## The following objects are masked from 'package:terra':
## 
##     intersect, union
## The following objects are masked from 'package:stats':
## 
##     filter, lag
## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union
library(curl)
## Using libcurl 8.3.0 with Schannel
h <- new_handle()
handle_setopt(h, http_version = 2)

3. LEER LOS DATOS DE ENTRADA

Necesitamos leer un conjunto de datos para imitar datos del mundo real. Por lo tanto, leamos la capa SOC que descargamos de ISRIC) usando la biblioteca terra:

archivo <- ("soc_igh_15_30.tif")
(soc <- rast(archivo))
## class       : SpatRaster 
## dimensions  : 938, 809, 1  (nrow, ncol, nlyr)
## resolution  : 250, 250  (x, y)
## extent      : -8344750, -8142500, 415500, 650000  (xmin, xmax, ymin, ymax)
## coord. ref. : Interrupted_Goode_Homolosine 
## source      : soc_igh_15_30.tif 
## name        : soc_igh_15_30

Ahora, convertimos los datos del SOC en porcentaje y revisamos el factor de escala de SOC en el sitio web de SoilGrids y los anotamos.

soc.perc <-  soc/10

¿Cuál es el CRS de los datos del mundo real?

Rta: CRS significa sistema de referencias de coordenadas, define la posicion de puntos en el espacio, tambien son esenciales para la representacion precisa de datos geoespaciales y facilitan la interoperabilidad entre los sistemas y aplicaciones cartograficas.

El sistema de coordenadas mas usadas en el mundo es WGS84, su finalidad es poder señalar cualquier punto que este situado en la tierra a travez de (x,y,z) sin la necesidad de otro punto de referencia, de igual modo es usado para la cartografia y la geodesia y el GPS lo usa como sistema de referencia.

Parece que necesitamos una transformación de dicho CRS al conocido CRS WGS84:

geog ="+proj=longlat +datum=WGS84"
(geog.soc = project(soc.perc, geog))
## class       : SpatRaster 
## dimensions  : 954, 862, 1  (nrow, ncol, nlyr)
## resolution  : 0.002207491, 0.002207491  (x, y)
## extent      : -74.90894, -73.00609, 3.733103, 5.839049  (xmin, xmax, ymin, ymax)
## coord. ref. : +proj=longlat +datum=WGS84 +no_defs 
## source(s)   : memory
## name        : soc_igh_15_30 
## min value   :      9.127214 
## max value   :    270.960205

Convertimos la capa SpatRaster en un objeto de estrellas:

stars.soc = st_as_stars(geog.soc)
m <- leaflet() %>%
  addTiles() %>%  
  leafem:::addGeoRaster(
      stars.soc,
      opacity = 0.8,                
      colorOptions = colorOptions(palette = c("#43CD80", "#CD6889", "#CD853F", "#68838B"), 
                                  domain = 8:130)
    ) 
#
m  # Print the map

4. MUESTREO DEL MUNDO

Conseguimos una muestra de aprox. 500 sitios a partir de datos del mundo real utilizando una muestra ubicada aleatoriamente:

set.seed(123456)

# Random sampling of 500 points
(samples <- spatSample(geog.soc, 500, "random", as.points=TRUE))
##  class       : SpatVector 
##  geometry    : points 
##  dimensions  : 500, 1  (geometries, attributes)
##  extent      : -74.90784, -73.0094, 3.736414, 5.835738  (xmin, xmax, ymin, ymax)
##  coord. ref. : +proj=longlat +datum=WGS84 +no_defs 
##  names       : soc_igh_15_30
##  type        :         <num>
##  values      :         39.05
##                           NA
##                        62.52

Describimos las características principales del objeto de muestra.

Ahora, necesitamos convertir el objeto spatVector en un objeto de característica simple:

(muestras <- sf::st_as_sf(samples))
nmuestras <- na.omit(muestras)

Visualizamos las muestras:

longit <- st_coordinates(muestras)[,1]
latit <- st_coordinates(muestras)[,2]
soc <- muestras$soc_igh_15_30
id <- seq(1,500,1) 
(sitios <- data.frame(id, longit, latit, soc))

Eliminamos los valores de NA:

sitios <- na.omit(sitios)
head(sitios)

Visualizamos las muestras:

m <- leaflet() %>%
  addTiles() %>%  
  leafem:::addGeoRaster(
      stars.soc,
      opacity = 0.7,                
      colorOptions = colorOptions(palette = c("#43CD80", "#CD6889", "#CD853F", "#68838B"), 
                                  domain = 8:130)
    ) %>%
  addMarkers(lng=sitios$longit,lat=sitios$latit, popup=sitios$soc, clusterOptions = markerClusterOptions())
m  # Print the map

Ahora estamos listos para realizar las tareas de interpolación.

5. INTERPOLACION

5.1 Creación del objeto gstat

Para interpolar, primero necesitamos crear un objeto de clase gstat, usando una función del mismo nombre: gstat.

Un objeto gstat contiene toda la información necesaria para realizar la interpolación espacial, a saber:

La definición del modelo. Los datos de calibración Según sus argumentos, la función gstat “entiende” qué tipo de modelo de interpolación queremos usar:

Sin modelo de variograma → IDW Modelo de variograma, sin covariables → Kriging ordinario Vamos a utilizar tres parámetros de la función gstat:

fórmula: la “fórmula” de predicción que especifica las variables dependientes e independientes (también conocidas como covariables) datos: los datos de calibración (también conocidos como los datos del tren) modelo: el modelo de variograma

5.2 interpolación IDW

Para interpolar SOC usando el método IDW creamos el siguiente objeto gstat, especificando solo la fórmula y los datos:

g1 = gstat(formula = soc_igh_15_30 ~ 1, data = nmuestras)

Ahora que nuestro modelo de interpolación g1 está definido, podemos usar la función de predicción para interpolar, es decir, estimar los valores de precipitación.

La función de predicción acepta:

-Un objeto ráster: estrellas, como dem -Un modelo: objeto gstat, como g1 -El ráster sirve para dos propósitos:

Especificar las ubicaciones donde queremos hacer predicciones (en todos los métodos) Especificación de valores de covariables (solo en Universal Kriging) Creemos un objeto ráster con valores de celda iguales a 1:

# a simple copy
VVV = aggregate(geog.soc, 4)

Que es vvv?

VVV
## class       : SpatRaster 
## dimensions  : 239, 216, 1  (nrow, ncol, nlyr)
## resolution  : 0.008829966, 0.008829966  (x, y)
## extent      : -74.90894, -73.00167, 3.728688, 5.839049  (xmin, xmax, ymin, ymax)
## coord. ref. : +proj=longlat +datum=WGS84 +no_defs 
## source(s)   : memory
## name        : soc_igh_15_30 
## min value   :      10.48266 
## max value   :     120.18581

Definimos nuevos valores:

values(VVV) <-1

Definimos nuevos nombres:

names(VVV) <- "valor"

Qué es VVV ahora?

VVV
## class       : SpatRaster 
## dimensions  : 239, 216, 1  (nrow, ncol, nlyr)
## resolution  : 0.008829966, 0.008829966  (x, y)
## extent      : -74.90894, -73.00167, 3.728688, 5.839049  (xmin, xmax, ymin, ymax)
## coord. ref. : +proj=longlat +datum=WGS84 +no_defs 
## source(s)   : memory
## name        : valor 
## min value   :     1 
## max value   :     1
stars.vvv = st_as_stars(VVV)

Por ejemplo, la siguiente expresión interpola los valores SOC según el modelo definido en g1 y la plantilla ráster definida en stars.VVV:

## [inverse distance weighted interpolation]
z1 = predict(g1, stars.vvv)
## [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  11.10414 30.82191 40.16246 38.92314 45.78968 84.77748     0
## var1.var         NA       NA       NA      NaN       NA       NA 51624
## dimension(s):
##   from  to offset    delta                       refsys x/y
## x    1 216 -74.91  0.00883 +proj=longlat +datum=WGS8... [x]
## y    1 239  5.839 -0.00883 +proj=longlat +datum=WGS8... [y]

Tomamos nota de los nombres de los dos atributos incluidos dentro del objeto z1. 1.Columna x: Esta variable representa cada geometria, sus valores son 1, 216, -74.91. 2. Columna y: Esta variable reepresneta cada geometria, sus valores para cada una son: 1, 239, 5.839.

Podemos crear un subconjunto solo del primer atributo y cambiarle el nombre a “soc”:

z1 = z1["var1.pred",,]
names(z1) = "soc"

Necesitamos una paleta de colores:

paleta <- colorNumeric(palette = c("#43CD80", "#CD6889", "#CD853F", "#68838B"), domain = 10:100, na.color = "transparent")

El ráster SOC interpolado, utilizando IDW, se muestra en la siguiente figura:

m <- leaflet() %>%
  addTiles() %>%  
  leafem:::addGeoRaster(
      z1,
      opacity = 0.7,                
      colorOptions = colorOptions(palette = c("#43CD80", "#CD6889", "#CD853F", "#68838B"), 
                                  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 [%]"
    )
m  # Print the map

5.3 Interpolación correcta

Los métodos de Kriging requieren un modelo de variograma. El modelo de variograma es una forma objetiva de cuantificar el patrón de autocorrelación en los datos y asignar ponderaciones en consecuencia al hacer predicciones.

Como primer paso, podemos calcular y examinar el variograma empírico utilizando la función de variograma.

La función requiere dos argumentos:

-fórmula: especifica la variable dependiente y las covariables, como en gstat -datos: la capa de puntos con la variable dependiente y covariables como atributos de puntos Por ejemplo, la siguiente expresión calcula el variograma empírico de muestras, sin covariables:

v_emp_ok = variogram(soc_igh_15_30 ~ 1, data=nmuestras)

Tracemos el variograma:

plot(v_emp_ok)

Hay varias formas de ajustar un modelo de variograma a un variograma empírico. Usaremos el más simple: ajuste automático usando la función autofitVariogram del paquete automap:

v_mod_ok = autofitVariogram(soc_igh_15_30 ~ 1, as(nmuestras, "Spatial"))

La función elige el tipo de modelo que mejor se adapta y también ajusta sus parámetros. Puede utilizar show.vgms() para mostrar los tipos de modelos de variograma.

Tengamos en cuenta que la función autofitVariogram no funciona en objetos sf, por lo que convertimos el objeto en un SpatialPointsDataFrame (paquete sp).

El modelo ajustado se puede trazar con plot:

plot(v_mod_ok)

El objeto resultante es en realidad una lista con varios componentes, incluido 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

Explicamos el significado de cada elemento del modelo anterior.

Rta: 1. Columna model: Hay dos tipos de modelos en el variograma “Nug” y “Ste” representando los modelos de pepita y esferico. 2. Columna psill: Representa el sill que es la variabilidad maxima que se alcanza a medida que la distancia entre las ubicaciones aumenta o meseta del variograma, el modelo Nug tiene un valor de 4.174328 y el modelo Ste tiene un valor de 760.508247. 3. Columna range: Es el rango de la variograma indicando la distancia en donde la variabilidad espacial alcanza un 95% del sill. El modelo “Nug” tiene un valor de 0.000 lo que indica que se alcanza instantaneamente y el modelo “Ste” tiene un valor de 464.1041. 4. Columna kappa: Este representa el parametro de la suavidad, que controla la forma del variograma esferico y afecta la rapidez con lo que la correlacion disminuye cuando aumenta la distancia. El modelo “Nug” tiene un valor de 0.00 indicando que no hay suavidad y el modelo “Ste” tiene un valor de 0.3 indicando que si hay suavidad.

Ahora, el modelo de variograma se puede pasar a la función gstat y podemos continuar con la interpolación Kriging ordinaria:

## [using ordinary kriging]
g2 = gstat(formula = soc_igh_15_30 ~ 1, model = v_mod_ok$var_model, data = nmuestras)
z2= predict(g2, stars.vvv)
## [using ordinary kriging]

Nuevamente, crearemos un subconjunto del atributo de valores predichos y le cambiaremos el nombre:

z2 = z2["var1.pred",,]
names(z2) = "soc"

Las predicciones de Kriging ordinario se muestran en la siguiente figura:

m <- leaflet() %>%
  addTiles() %>%  
  leafem:::addGeoRaster(
      z2,
      opacity = 0.7,                
      colorOptions = colorOptions(palette = c("#43CD80", "#CD6889", "#CD853F", "#68838B"), 
                                  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 [%]"
    )
m  # Print the map

##6. EVALUACION DE RESULTADOS ###6.1 Evaluación cualitativa Otra vista de las tres salidas de interpolación:

colores <- colorOptions(palette = c("#43CD80", "#CD6889", "#CD853F", "#68838B"), 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 [%]"
)
m  # Print the map

6.2 Validación cruzada

Hemos estimado las superficies climáticas utilizando dos métodos diferentes: IDW y Kriging Ordinario. Aunque es útil examinar y comparar los resultados gráficamente, también necesitamos una forma objetiva de evaluar la precisión de la interpolación. De esa manera, podemos elegir objetivamente el método más preciso entre los métodos de interpolación disponibles.

En la validación cruzada Leave-One-Out nosotros:

-Saque un punto de los datos de calibración. -Haz una predicción para ese punto. -Repita para todos los puntos. Al final, lo que obtenemos es una tabla con un valor observado y un valor predicho para todos los puntos. -Podemos ejecutar la validación cruzada Leave-One-Out usando la función gstat.cv, que acepta un objeto gstat.

Al escribir el siguiente fragmento, oculte el mensaje y los resultados.

### run the following code from the console -- line-by-line
cv1 = gstat.cv(g1)
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## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
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## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
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## [inverse distance weighted interpolation]
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## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
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## [inverse distance weighted interpolation]
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## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
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## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
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## [inverse distance weighted interpolation]
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## [inverse distance weighted interpolation]
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## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
#cv2 = gstat.cv(g2)

El resultado de gstat.cv tiene los siguientes atributos:

var1.pred: valor previsto var1.var: varianza (solo para Kriging) observado: valor observado residual: observado-predicho zscore: puntuación Z (solo para Kriging) plegar: ID de validación cruzada

cv1 = na.omit(cv1)
cv1
## class       : SpatialPointsDataFrame 
## features    : 470 
## extent      : -74.89459, -73.02926, 3.736414, 5.826908  (xmin, xmax, ymin, ymax)
## crs         : +proj=longlat +datum=WGS84 +no_defs 
## variables   : 6
## names       :        var1.pred, var1.var,         observed,          residual, zscore, fold 
## min values  :  16.672899371437,       NA, 10.9684953689575, -19.0217881022598,     NA,    1 
## max values  : 67.4365390094691,       NA, 86.4442977905273,  39.1708320325544,     NA,  470

Convirtamos el objeto cv1:

cv1 = st_as_sf(cv1)

Ahora, grafiquemos los residuos:

sp::bubble(as(cv1[, "residual"], "Spatial"))

Ahora, calculamos índices de precisión de predicción, como el error cuadrático medio (RMSE):

# This is the RMSE value for the IDW interpolation
sqrt(sum((cv1$var1.pred - cv1$observed)^2) / nrow(cv1))
## [1] 9.594338

Ahora, repita el proceso con los resultados correctos:

Tiempo de conversión:

cv2 = gstat.cv(g2)
## [using ordinary kriging]
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## [using ordinary kriging]
## [using ordinary kriging]
## [using ordinary kriging]
## [using ordinary kriging]
## [using ordinary kriging]
## [using ordinary kriging]
## [using ordinary kriging]
## [using ordinary kriging]
## [using ordinary kriging]
## [using ordinary kriging]
## [using ordinary kriging]
## [using ordinary kriging]
## [using ordinary kriging]
## [using ordinary kriging]
## [using ordinary kriging]
## [using ordinary kriging]
## [using ordinary kriging]
## [using ordinary kriging]
## [using ordinary kriging]
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## [using ordinary kriging]
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## [using ordinary kriging]
## [using ordinary kriging]
cv2 = st_as_sf(cv2)

Calcule RSME para obtener resultados correctos

sqrt(sum((cv2$var1.pred - cv2$observed)^2) / nrow(cv2))
## [1] 8.379492

Los resultados de las tecnicas de interpolacion indican como se estiman valores intermedios entre puntos de datos conocidos, la tecnica de interpolacion de kriging ordinario (OK) es una tecnica de interpolacion espacial utilizada en estadisticas geoespaciales y geoestadisticas, en este caso muestra una mayor precision en comparacion con la tecnica de inverso de la distancia ponderado (IDW) es un metodo comun en el ambito de la interpolacion espacial. El RMSE para la interpolacion OK es de 8.379492, mientras que para la interpolacion IDW es de 9.594338. El RMSE es una medida utilizada para evaluar la precision de un modelo predilecto, y en este caso, valores mas bajos indican una mayor precision. Por lo tanto,podemos concluir que el RMSE mas bajo asociado con la interpolacion OK siguiere que esta tecnica proporciona predicciones mas precisas en comparacion con IDW. La eleccion entre tecnicas de interpolacion depende mucho de la naturaleza especifica de los datos y los patrones espaciales, OK tiene el metodo mas preciso.

7. REFERENCIAS

Lizarazo, I., 2023. Spatial interpolation of soil organic carbon. Available at https://rpubs.com/ials2un/soc_interp.

sessionInfo()
## R version 4.3.1 (2023-06-16 ucrt)
## Platform: x86_64-w64-mingw32/x64 (64-bit)
## Running under: Windows 10 x64 (build 19045)
## 
## Matrix products: default
## 
## 
## locale:
## [1] LC_COLLATE=Spanish_Mexico.utf8  LC_CTYPE=Spanish_Mexico.utf8   
## [3] LC_MONETARY=Spanish_Mexico.utf8 LC_NUMERIC=C                   
## [5] LC_TIME=Spanish_Mexico.utf8    
## 
## time zone: America/Bogota
## tzcode source: internal
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
##  [1] curl_5.1.0    dplyr_1.1.4   ggplot2_3.4.4 leafem_0.2.3  leaflet_2.2.0
##  [6] automap_1.1-9 gstat_2.1-1   stars_0.6-4   abind_1.4-5   sf_1.0-14    
## [11] terra_1.7-55  sp_2.1-1     
## 
## loaded via a namespace (and not attached):
##  [1] gtable_0.3.4       xfun_0.40          bslib_0.5.1        raster_3.6-26     
##  [5] htmlwidgets_1.6.2  lattice_0.22-5     vctrs_0.6.4        tools_4.3.1       
##  [9] crosstalk_1.2.0    generics_0.1.3     parallel_4.3.1     tibble_3.2.1      
## [13] proxy_0.4-27       spacetime_1.3-0    fansi_1.0.5        xts_0.13.1        
## [17] pkgconfig_2.0.3    KernSmooth_2.23-21 lifecycle_1.0.3    farver_2.1.1      
## [21] compiler_4.3.1     FNN_1.1.3.2        munsell_0.5.0      codetools_0.2-19  
## [25] htmltools_0.5.6.1  class_7.3-22       sass_0.4.7         yaml_2.3.7        
## [29] pillar_1.9.0       jquerylib_0.1.4    ellipsis_0.3.2     classInt_0.4-10   
## [33] cachem_1.0.8       tidyselect_1.2.0   digest_0.6.33      fastmap_1.1.1     
## [37] grid_4.3.1         colorspace_2.1-0   cli_3.6.1          magrittr_2.0.3    
## [41] base64enc_0.1-3    utf8_1.2.4         e1071_1.7-13       withr_2.5.1       
## [45] scales_1.2.1       rmarkdown_2.25     zoo_1.8-12         png_0.1-8         
## [49] evaluate_0.22      knitr_1.44         rlang_1.1.1        Rcpp_1.0.11       
## [53] glue_1.6.2         DBI_1.1.3          rstudioapi_0.15.0  reshape_0.8.9     
## [57] jsonlite_1.8.7     R6_2.5.1           plyr_1.8.9         intervals_0.15.4  
## [61] units_0.8-4