Interpolación Espacial
Andres_Cuasquer
2025-02-26
true
Introducción
Este documento presenta una sesión de práctica para aplicar conceptos de interpolación espacial, basado en el script del profesor Iván Lizarazo (2021) disponible en RPubs https://rpubs.com/ials2un/laaspint. Se utilizarán dos tipos de datos:
Muestreos de propiedades químicas y físicas del suelo en sistemas productivos de tomate en el departamento de Santander (shapefile y CSV).
Un DEM SRTM descargado de Google Earth Engine (archivo tif).
Se realizarán las siguientes actividades:
Instalación y carga de librerías.
Ajuste del directorio de trabajo.
Lectura y visualización de datos (shapefile y tif).
Interpolación de valores de pH utilizando IDW y Kriging.
Exportación de resultados en formato GeoTIFF.
Validación cruzada de los modelos mediante cálculo de RMSE.
1. Instalar los paquetes necesarios (solo ejecutar si aún no se han instalado)
install.packages(c("sf", "stars", "leaflet", "gstat", "automap", "raster", "RColorBrewer"), repos = "https://cloud.r-project.org/")## package 'sf' successfully unpacked and MD5 sums checked## package 'stars' successfully unpacked and MD5 sums checked
## package 'leaflet' successfully unpacked and MD5 sums checked
## package 'gstat' successfully unpacked and MD5 sums checked## package 'automap' successfully unpacked and MD5 sums checked
## package 'raster' successfully unpacked and MD5 sums checked## package 'RColorBrewer' successfully unpacked and MD5 sums checked
##
## The downloaded binary packages are in
## C:\Users\cuasq\AppData\Local\Temp\RtmpmoKqc2\downloaded_packages2. Cargar las librerías
library(sf)
library(stars)
library(leaflet)
library(gstat)
library(automap)
library(raster)
library(RColorBrewer)3. Ajustar el directorio de trabajo
getwd() # Muestra el directorio actual## [1] "D:/Documentos/5 Semestre/Geomatica Básica/R/Taller_de_Interpolacion"setwd("D:/Documentos/5 Semestre/Geomatica Básica/R/Taller_de_Interpolacion")
getwd() # Verificar el directorio actualizado## [1] "D:/Documentos/5 Semestre/Geomatica Básica/R/Taller_de_Interpolacion"4. Declarar las variables de entrada
ruta_aoi <- "./municipios_muestreo.shp"
ruta_puntos <- "./puntos_muestreo.shp" # Ruta del shapefile de puntos de muestreo
ruta_raster <- "./dem_srtm_9377.tif" # Ruta del DEM (archivo tif)5. Leer y visualizar los archivos de datos (shp y tif)
Leer el DEM con read_stars
raster_dem <- read_stars(ruta_raster, RasterIO = list(bands = 1))
print(raster_dem)## stars object with 2 dimensions and 1 attribute
## attribute(s), summary of first 1e+05 cells:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## dem_srtm_9377.tif -247 0 0 131.274 0 1673
## dimension(s):
## from to offset delta refsys point x/y
## x 1 1754 4966240 29.78 MAGNA-SIRGAS 2018 / Orige... FALSE [x]
## y 1 1428 2297460 -29.78 MAGNA-SIRGAS 2018 / Orige... FALSE [y]plot(raster_dem)
crs_raster <- st_crs(raster_dem)
print(crs_raster)## Coordinate Reference System:
## User input: MAGNA-SIRGAS 2018 / Origen-Nacional
## wkt:
## PROJCRS["MAGNA-SIRGAS 2018 / Origen-Nacional",
## BASEGEOGCRS["MAGNA-SIRGAS 2018",
## DATUM["Marco Geocentrico Nacional de Referencia 2018",
## ELLIPSOID["GRS 1980",6378137,298.257222101,
## LENGTHUNIT["metre",1]]],
## PRIMEM["Greenwich",0,
## ANGLEUNIT["degree",0.0174532925199433]],
## ID["EPSG",20046]],
## CONVERSION["Colombia Transverse Mercator",
## METHOD["Transverse Mercator",
## ID["EPSG",9807]],
## PARAMETER["Latitude of natural origin",4,
## ANGLEUNIT["degree",0.0174532925199433],
## ID["EPSG",8801]],
## PARAMETER["Longitude of natural origin",-73,
## ANGLEUNIT["degree",0.0174532925199433],
## ID["EPSG",8802]],
## PARAMETER["Scale factor at natural origin",0.9992,
## SCALEUNIT["unity",1],
## ID["EPSG",8805]],
## PARAMETER["False easting",5000000,
## LENGTHUNIT["metre",1],
## ID["EPSG",8806]],
## PARAMETER["False northing",2000000,
## LENGTHUNIT["metre",1],
## ID["EPSG",8807]]],
## CS[Cartesian,2],
## AXIS["northing (N)",north,
## ORDER[1],
## LENGTHUNIT["metre",1]],
## AXIS["easting (E)",east,
## ORDER[2],
## LENGTHUNIT["metre",1]],
## USAGE[
## SCOPE["Cadastre, topographic mapping."],
## AREA["Colombia - onshore and offshore. Includes San Andres y Providencia, Malpelo Islands, Roncador Bank, Serrana Bank and Serranilla Bank."],
## BBOX[-4.23,-84.77,15.51,-66.87]],
## ID["EPSG",9377]]Leer el shapefile de puntos de muestreo
puntos <- st_read(ruta_puntos)## Reading layer `puntos_muestreo' from data source
## `D:\Documentos\5 Semestre\Geomatica Básica\R\Taller_de_Interpolacion\puntos_muestreo.shp'
## using driver `ESRI Shapefile'
## Simple feature collection with 67 features and 16 fields
## Geometry type: POINT
## Dimension: XY
## Bounding box: xmin: 4968206 ymin: 2257635 xmax: 5005157 ymax: 2292361
## Projected CRS: MAGNA-SIRGAS_Origen-Nacionalcrs_puntos <- st_crs(puntos)
print(crs_puntos)## Coordinate Reference System:
## User input: MAGNA-SIRGAS_Origen-Nacional
## wkt:
## PROJCRS["MAGNA-SIRGAS_Origen-Nacional",
## BASEGEOGCRS["GCS_MAGNA-SIRGAS_2018",
## DATUM["Marco Geocentrico Nacional de Referencia 2018",
## ELLIPSOID["GRS 1980",6378137,298.257222101,
## LENGTHUNIT["metre",1]],
## ID["EPSG",1329]],
## PRIMEM["Greenwich",0,
## ANGLEUNIT["Degree",0.0174532925199433]]],
## CONVERSION["unnamed",
## METHOD["Transverse Mercator",
## ID["EPSG",9807]],
## PARAMETER["Latitude of natural origin",4,
## ANGLEUNIT["Degree",0.0174532925199433],
## ID["EPSG",8801]],
## PARAMETER["Longitude of natural origin",-73,
## ANGLEUNIT["Degree",0.0174532925199433],
## ID["EPSG",8802]],
## PARAMETER["Scale factor at natural origin",0.9992,
## SCALEUNIT["unity",1],
## ID["EPSG",8805]],
## PARAMETER["False easting",5000000,
## LENGTHUNIT["metre",1],
## ID["EPSG",8806]],
## PARAMETER["False northing",2000000,
## LENGTHUNIT["metre",1],
## ID["EPSG",8807]]],
## CS[Cartesian,2],
## AXIS["(E)",east,
## ORDER[1],
## LENGTHUNIT["metre",1,
## ID["EPSG",9001]]],
## AXIS["(N)",north,
## ORDER[2],
## LENGTHUNIT["metre",1,
## ID["EPSG",9001]]]]Comparar los sistemas de referencia
if (identical(crs_raster, crs_puntos)) {
cat("El sistema de referencia de coordenadas del raster y de los puntos es el mismo:\n")
print(crs_raster)
} else {
cat("Los sistemas de referencia de coordenadas son diferentes.\n")
cat("Raster:\n")
print(crs_raster)
cat("Puntos:\n")
print(crs_puntos)
}## Los sistemas de referencia de coordenadas son diferentes.
## Raster:
## Coordinate Reference System:
## User input: MAGNA-SIRGAS 2018 / Origen-Nacional
## wkt:
## PROJCRS["MAGNA-SIRGAS 2018 / Origen-Nacional",
## BASEGEOGCRS["MAGNA-SIRGAS 2018",
## DATUM["Marco Geocentrico Nacional de Referencia 2018",
## ELLIPSOID["GRS 1980",6378137,298.257222101,
## LENGTHUNIT["metre",1]]],
## PRIMEM["Greenwich",0,
## ANGLEUNIT["degree",0.0174532925199433]],
## ID["EPSG",20046]],
## CONVERSION["Colombia Transverse Mercator",
## METHOD["Transverse Mercator",
## ID["EPSG",9807]],
## PARAMETER["Latitude of natural origin",4,
## ANGLEUNIT["degree",0.0174532925199433],
## ID["EPSG",8801]],
## PARAMETER["Longitude of natural origin",-73,
## ANGLEUNIT["degree",0.0174532925199433],
## ID["EPSG",8802]],
## PARAMETER["Scale factor at natural origin",0.9992,
## SCALEUNIT["unity",1],
## ID["EPSG",8805]],
## PARAMETER["False easting",5000000,
## LENGTHUNIT["metre",1],
## ID["EPSG",8806]],
## PARAMETER["False northing",2000000,
## LENGTHUNIT["metre",1],
## ID["EPSG",8807]]],
## CS[Cartesian,2],
## AXIS["northing (N)",north,
## ORDER[1],
## LENGTHUNIT["metre",1]],
## AXIS["easting (E)",east,
## ORDER[2],
## LENGTHUNIT["metre",1]],
## USAGE[
## SCOPE["Cadastre, topographic mapping."],
## AREA["Colombia - onshore and offshore. Includes San Andres y Providencia, Malpelo Islands, Roncador Bank, Serrana Bank and Serranilla Bank."],
## BBOX[-4.23,-84.77,15.51,-66.87]],
## ID["EPSG",9377]]
## Puntos:
## Coordinate Reference System:
## User input: MAGNA-SIRGAS_Origen-Nacional
## wkt:
## PROJCRS["MAGNA-SIRGAS_Origen-Nacional",
## BASEGEOGCRS["GCS_MAGNA-SIRGAS_2018",
## DATUM["Marco Geocentrico Nacional de Referencia 2018",
## ELLIPSOID["GRS 1980",6378137,298.257222101,
## LENGTHUNIT["metre",1]],
## ID["EPSG",1329]],
## PRIMEM["Greenwich",0,
## ANGLEUNIT["Degree",0.0174532925199433]]],
## CONVERSION["unnamed",
## METHOD["Transverse Mercator",
## ID["EPSG",9807]],
## PARAMETER["Latitude of natural origin",4,
## ANGLEUNIT["Degree",0.0174532925199433],
## ID["EPSG",8801]],
## PARAMETER["Longitude of natural origin",-73,
## ANGLEUNIT["Degree",0.0174532925199433],
## ID["EPSG",8802]],
## PARAMETER["Scale factor at natural origin",0.9992,
## SCALEUNIT["unity",1],
## ID["EPSG",8805]],
## PARAMETER["False easting",5000000,
## LENGTHUNIT["metre",1],
## ID["EPSG",8806]],
## PARAMETER["False northing",2000000,
## LENGTHUNIT["metre",1],
## ID["EPSG",8807]]],
## CS[Cartesian,2],
## AXIS["(E)",east,
## ORDER[1],
## LENGTHUNIT["metre",1,
## ID["EPSG",9001]]],
## AXIS["(N)",north,
## ORDER[2],
## LENGTHUNIT["metre",1,
## ID["EPSG",9001]]]]Transformar (reproyectar) los puntos al CRS del raster
puntos_reproj <- st_transform(puntos, crs_raster)
print(puntos_reproj) # Muestra la tabla de atributos de los puntos## Simple feature collection with 67 features and 16 fields
## Geometry type: POINT
## Dimension: XY
## Bounding box: xmin: 4968206 ymin: 2257635 xmax: 5005157 ymax: 2292361
## Projected CRS: MAGNA-SIRGAS 2018 / Origen-Nacional
## First 10 features:
## Department Municipali Latitude.D Longitude. Altitude.m pH EC.dSm NH4.ppm
## 1 Santander Confines 6.331580 -73.25827 1533 4.8 0.08 10.3
## 2 Santander Confines 6.345463 -73.28759 1489 4.9 0.07 10.3
## 3 Santander Confines 6.357339 -73.28138 1482 4.8 0.08 18.2
## 4 Santander Confines 6.360368 -73.24903 1581 4.7 0.07 6.7
## 5 Santander Confines 6.340922 -73.20868 1878 4.8 0.15 24.0
## 6 Santander Confines 6.357226 -73.23005 1742 4.8 0.09 11.7
## 7 Santander Confines 6.339062 -73.23301 1752 4.9 0.09 9.4
## 8 Santander Confines 6.402768 -73.22524 1715 4.8 0.08 9.4
## 9 Santander Confines 6.365608 -73.21098 1878 4.8 0.10 19.3
## 10 Santander Paramo 6.384360 -73.19552 1912 4.9 0.12 19.1
## NO3.ppm K2O.ppm P2O5.ppm SOC.pct Sand.pct Silt.pct Clay.pct Slope.pct
## 1 8.4 173.5 10.1 2.46 40.7 32.6 26.6 10.5
## 2 5.4 122.9 8.9 1.62 51.2 26.1 22.6 9.2
## 3 0.9 119.3 6.2 2.95 51.9 35.4 12.7 7.4
## 4 2.3 181.9 12.1 1.02 37.3 36.1 26.5 12.6
## 5 12.3 130.1 7.3 2.48 65.6 30.3 4.1 8.5
## 6 1.2 131.3 4.8 1.60 40.8 46.5 12.6 7.5
## 7 2.0 73.5 11.5 3.65 55.0 42.5 2.5 5.6
## 8 5.9 194.0 6.6 2.12 33.7 45.4 20.9 13.7
## 9 0.3 273.5 3.4 3.81 64.4 24.9 10.6 1.5
## 10 0.1 128.9 18.8 3.14 39.1 50.7 10.3 15.8
## geometry
## 1 POINT (4971447 2257635)
## 2 POINT (4968206 2259171)
## 3 POINT (4968893 2260483)
## 4 POINT (4972470 2260816)
## 5 POINT (4976930 2258665)
## 6 POINT (4974568 2260467)
## 7 POINT (4974240 2258460)
## 8 POINT (4975101 2265500)
## 9 POINT (4976677 2261393)
## 10 POINT (4978386 2263464)Verificar atributos y CRS de los puntos
print(names(puntos))## [1] "Department" "Municipali" "Latitude.D" "Longitude." "Altitude.m"
## [6] "pH" "EC.dSm" "NH4.ppm" "NO3.ppm" "K2O.ppm"
## [11] "P2O5.ppm" "SOC.pct" "Sand.pct" "Silt.pct" "Clay.pct"
## [16] "Slope.pct" "geometry"print(st_crs(puntos))## Coordinate Reference System:
## User input: MAGNA-SIRGAS_Origen-Nacional
## wkt:
## PROJCRS["MAGNA-SIRGAS_Origen-Nacional",
## BASEGEOGCRS["GCS_MAGNA-SIRGAS_2018",
## DATUM["Marco Geocentrico Nacional de Referencia 2018",
## ELLIPSOID["GRS 1980",6378137,298.257222101,
## LENGTHUNIT["metre",1]],
## ID["EPSG",1329]],
## PRIMEM["Greenwich",0,
## ANGLEUNIT["Degree",0.0174532925199433]]],
## CONVERSION["unnamed",
## METHOD["Transverse Mercator",
## ID["EPSG",9807]],
## PARAMETER["Latitude of natural origin",4,
## ANGLEUNIT["Degree",0.0174532925199433],
## ID["EPSG",8801]],
## PARAMETER["Longitude of natural origin",-73,
## ANGLEUNIT["Degree",0.0174532925199433],
## ID["EPSG",8802]],
## PARAMETER["Scale factor at natural origin",0.9992,
## SCALEUNIT["unity",1],
## ID["EPSG",8805]],
## PARAMETER["False easting",5000000,
## LENGTHUNIT["metre",1],
## ID["EPSG",8806]],
## PARAMETER["False northing",2000000,
## LENGTHUNIT["metre",1],
## ID["EPSG",8807]]],
## CS[Cartesian,2],
## AXIS["(E)",east,
## ORDER[1],
## LENGTHUNIT["metre",1,
## ID["EPSG",9001]]],
## AXIS["(N)",north,
## ORDER[2],
## LENGTHUNIT["metre",1,
## ID["EPSG",9001]]]]6. Interpolar el valor de pH usando IDW
6.1. Revisar los valores de la variable pH
var <- "pH" # Definir la variable de interés
print(puntos[var]) # Extrae la columna pH## Simple feature collection with 67 features and 1 field
## Geometry type: POINT
## Dimension: XY
## Bounding box: xmin: 4968206 ymin: 2257635 xmax: 5005157 ymax: 2292361
## Projected CRS: MAGNA-SIRGAS_Origen-Nacional
## First 10 features:
## pH geometry
## 1 4.8 POINT (4971447 2257635)
## 2 4.9 POINT (4968206 2259171)
## 3 4.8 POINT (4968893 2260483)
## 4 4.7 POINT (4972470 2260816)
## 5 4.8 POINT (4976930 2258665)
## 6 4.8 POINT (4974568 2260467)
## 7 4.9 POINT (4974240 2258460)
## 8 4.8 POINT (4975101 2265500)
## 9 4.8 POINT (4976677 2261393)
## 10 4.9 POINT (4978386 2263464)6.2. Definir el modelo de interpolación IDW
st_crs(puntos_reproj)## Coordinate Reference System:
## User input: MAGNA-SIRGAS 2018 / Origen-Nacional
## wkt:
## PROJCRS["MAGNA-SIRGAS 2018 / Origen-Nacional",
## BASEGEOGCRS["MAGNA-SIRGAS 2018",
## DATUM["Marco Geocentrico Nacional de Referencia 2018",
## ELLIPSOID["GRS 1980",6378137,298.257222101,
## LENGTHUNIT["metre",1]]],
## PRIMEM["Greenwich",0,
## ANGLEUNIT["degree",0.0174532925199433]],
## ID["EPSG",20046]],
## CONVERSION["Colombia Transverse Mercator",
## METHOD["Transverse Mercator",
## ID["EPSG",9807]],
## PARAMETER["Latitude of natural origin",4,
## ANGLEUNIT["degree",0.0174532925199433],
## ID["EPSG",8801]],
## PARAMETER["Longitude of natural origin",-73,
## ANGLEUNIT["degree",0.0174532925199433],
## ID["EPSG",8802]],
## PARAMETER["Scale factor at natural origin",0.9992,
## SCALEUNIT["unity",1],
## ID["EPSG",8805]],
## PARAMETER["False easting",5000000,
## LENGTHUNIT["metre",1],
## ID["EPSG",8806]],
## PARAMETER["False northing",2000000,
## LENGTHUNIT["metre",1],
## ID["EPSG",8807]]],
## CS[Cartesian,2],
## AXIS["northing (N)",north,
## ORDER[1],
## LENGTHUNIT["metre",1]],
## AXIS["easting (E)",east,
## ORDER[2],
## LENGTHUNIT["metre",1]],
## USAGE[
## SCOPE["Cadastre, topographic mapping."],
## AREA["Colombia - onshore and offshore. Includes San Andres y Providencia, Malpelo Islands, Roncador Bank, Serrana Bank and Serranilla Bank."],
## BBOX[-4.23,-84.77,15.51,-66.87]],
## ID["EPSG",9377]]crs(raster_dem)## [1] NAg <- gstat(formula = pH ~ 1, data = puntos_reproj, set = list(idp = 2))6.3. Crear la superficie de predicción usando el raster como malla
z <- predict(g, raster_dem)## [inverse distance weighted interpolation]print(z) # Muestra el resultado; contiene 'var1.pred' y (para kriging) 'var1.var'## stars object with 2 dimensions and 2 attributes
## attribute(s), summary of first 1e+05 cells:
## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## var1.pred 5.04681 5.130046 5.162891 5.174822 5.238671 5.283381 0e+00
## var1.var NA NA NA NaN NA NA 1e+05
## dimension(s):
## from to offset delta refsys x/y
## x 1 1754 4966240 29.78 MAGNA-SIRGAS 2018 / Orige... [x]
## y 1 1428 2297460 -29.78 MAGNA-SIRGAS 2018 / Orige... [y]Para IDW se extrae solo el atributo de predicción
z <- z["var1.pred",,]
names(z) <- "pH"6.4. Visualizar la interpolación
b <- seq(4, 7.5, 0.1) # Secuencia para definir intervalos
plot(z, breaks = b, col = hcl.colors(length(b) - 1, "Spectral"), reset = FALSE)
plot(st_geometry(puntos_reproj), pch = 3, add = TRUE)
contour(z, breaks = b, add = TRUE)
6.5. Exportar el raster de la interpolación IDW a archivo GeoTIFF
interpolacion_idw <- "./ph_idw.tif"
write_stars(z, dsn = interpolacion_idw)7. Interpolar el valor de pH usando Kriging
7.1. Crear el variograma empírico
v_emp_ok <- variogram(pH ~ 1, puntos_reproj)
plot(v_emp_ok)
7.2. Ajustar el variograma empírico a una función
v_mod_ok <- autofitVariogram(pH ~ 1, as(puntos_reproj, "Spatial"))
plot(v_mod_ok)
7.3. Definir el modelo de interpolación usando el variograma ajustado
g <- gstat(formula = pH ~ 1, model = v_mod_ok$var_model, data = puntos_reproj)7.4. Realizar la predicción usando Kriging
z <- predict(g, raster_dem)## [using ordinary kriging]print(z)## stars object with 2 dimensions and 2 attributes
## attribute(s), summary of first 1e+05 cells:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## var1.pred 4.973535 5.0923192 5.1475910 5.1348409 5.18763 5.238132
## var1.var 0.604284 0.7349258 0.8883815 0.9006311 1.04760 1.302663
## dimension(s):
## from to offset delta refsys x/y
## x 1 1754 4966240 29.78 MAGNA-SIRGAS 2018 / Orige... [x]
## y 1 1428 2297460 -29.78 MAGNA-SIRGAS 2018 / Orige... [y]7.5. Visualizar la superficie de predicción
prediccion <- z["var1.pred",,]
names(prediccion) <- "pH"
b_predict <- seq(4, 7, 0.1)
plot(prediccion, breaks = b_predict, col = hcl.colors(length(b_predict) - 1, "Spectral"), reset = FALSE)
7.6. Visualizar la superficie de la varianza
varianza <- z["var1.var",,]
names(varianza) <- "varianza pH"
b_var <- seq(0.1, 1.4, 0.1)
plot(varianza, breaks = b_var, col = hcl.colors(length(b_var) - 1, "Spectral"), reset = FALSE)
Exportar los rasters de predicción y varianza a archivos GeoTIFF
ruta_prediccion_idw <- "./ph_idw_prediccion.tif"
ruta_varianza_idw <- "./ph_idw_varianza.tif"
ruta_prediccion_kriging <- "./ph_kriging_prediccion.tif"
ruta_varianza_kriging <- "./ph_kriging_varianza.tif"Exportar raster de predicción IDW
if (exists("z")) {
writeRaster(as(z, "Raster"), filename = ruta_prediccion_idw, format = "GTiff", overwrite = TRUE)
cat("Raster de predicción IDW exportado a:", ruta_prediccion_idw, "\n")
}## Raster de predicción IDW exportado a: ./ph_idw_prediccion.tifExportar raster de varianza IDW (si existe)
if ("var1.var" %in% names(z)) {
writeRaster(as(z["var1.var",,], "Raster"), filename = ruta_varianza_idw, format = "GTiff", overwrite = TRUE)
cat("Raster de varianza IDW exportado a:", ruta_varianza_idw, "\n")
}## Raster de varianza IDW exportado a: ./ph_idw_varianza.tifExportar raster de predicción Kriging
if (exists("prediccion")) {
writeRaster(as(prediccion, "Raster"), filename = ruta_prediccion_kriging, format = "GTiff", overwrite = TRUE)
cat("Raster de predicción Kriging exportado a:", ruta_prediccion_kriging, "\n")
}## Raster de predicción Kriging exportado a: ./ph_kriging_prediccion.tifExportar raster de varianza Kriging (si existe)
if (exists("varianza")) {
writeRaster(as(varianza, "Raster"), filename = ruta_varianza_kriging, format = "GTiff", overwrite = TRUE)
cat("Raster de varianza Kriging exportado a:", ruta_varianza_kriging, "\n")
}## Raster de varianza Kriging exportado a: ./ph_kriging_varianza.tifRutas de archivos y lectura de datos nuevamente (para la validación cruzada)
ruta_puntos <- "./puntos_muestreo.shp"
ruta_raster <- "./dem_srtm_9377.tif"
raster_dem <- read_stars(ruta_raster, RasterIO = list(bands = 1))
puntos <- st_read(ruta_puntos)## Reading layer `puntos_muestreo' from data source
## `D:\Documentos\5 Semestre\Geomatica Básica\R\Taller_de_Interpolacion\puntos_muestreo.shp'
## using driver `ESRI Shapefile'
## Simple feature collection with 67 features and 16 fields
## Geometry type: POINT
## Dimension: XY
## Bounding box: xmin: 4968206 ymin: 2257635 xmax: 5005157 ymax: 2292361
## Projected CRS: MAGNA-SIRGAS_Origen-Nacionalpuntos_reproj <- st_transform(puntos, st_crs(raster_dem))Filtrar puntos con pH entre 4.5 y 5.0
puntos_filtrados <- puntos_reproj[puntos_reproj$pH >= 4.5 & puntos_reproj$pH <= 5.0, ]Función para calcular RMSE
calcular_rmse <- function(observado, predicho) {
sqrt(mean((observado - predicho)^2))
}1. Validación Cruzada para IDW
cat("\n--- Validación Cruzada para IDW ---\n")##
## --- Validación Cruzada para IDW ---resultados_idw <- vector("numeric", length = nrow(puntos_filtrados))
for (i in 1:nrow(puntos_filtrados)) {
# Dejar un punto fuera para la validación
puntos_entrenamiento <- puntos_filtrados[-i, ]
punto_prueba <- puntos_filtrados[i, ]
# Modelo IDW
modelo_idw <- gstat(formula = pH ~ 1, data = puntos_entrenamiento, set = list(idp = 2))
prediccion_idw <- predict(modelo_idw, punto_prueba)
# Almacenar la predicción
resultados_idw[i] <- prediccion_idw$var1.pred
}## [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]Calcular RMSE para IDW
rmse_idw <- calcular_rmse(puntos_filtrados$pH, resultados_idw)
cat("RMSE IDW: ", rmse_idw, "\n")## RMSE IDW: 0.13821112. Validación Cruzada para Kriging
cat("\n--- Validación Cruzada para Kriging ---\n")##
## --- Validación Cruzada para Kriging ---resultados_kriging <- vector("numeric", length = nrow(puntos_filtrados))
for (i in 1:nrow(puntos_filtrados)) {
puntos_entrenamiento <- puntos_filtrados[-i, ]
punto_prueba <- puntos_filtrados[i, ]
# Crear variograma y ajustar modelo para Kriging
variograma <- variogram(pH ~ 1, puntos_entrenamiento)
modelo_variograma <- autofitVariogram(pH ~ 1, as(puntos_entrenamiento, "Spatial"))
# Modelo Kriging
modelo_kriging <- gstat(formula = pH ~ 1, model = modelo_variograma$var_model, data = puntos_entrenamiento)
prediccion_kriging <- predict(modelo_kriging, punto_prueba)
# Almacenar la predicción
resultados_kriging[i] <- prediccion_kriging$var1.pred
}## [using ordinary kriging]
## [using ordinary kriging]
## [using ordinary kriging]
## [using ordinary kriging]
## [using ordinary kriging]
## [using ordinary kriging]
## [using ordinary kriging]
## [using ordinary kriging]
## [using ordinary kriging]
## [using ordinary kriging]
## [using ordinary kriging]
## [using ordinary kriging]
## [using ordinary kriging]
## [using ordinary kriging]
## [using ordinary kriging]
## [using ordinary kriging]
## [using ordinary kriging]
## [using ordinary kriging]
## [using ordinary kriging]
## [using ordinary kriging]
## [using ordinary kriging]
## [using ordinary kriging]
## [using ordinary kriging]
## [using ordinary kriging]
## [using ordinary kriging]
## [using ordinary kriging]
## [using ordinary kriging]
## [using ordinary kriging]
## [using ordinary kriging]
## [using ordinary kriging]
## [using ordinary kriging]
## [using ordinary kriging]
## [using ordinary kriging]
## [using ordinary kriging]
## [using ordinary kriging]
## [using ordinary kriging]
## [using ordinary kriging]
## [using ordinary kriging]
## [using ordinary kriging]
## [using ordinary kriging]
## [using ordinary kriging]Calcular RMSE para Kriging
rmse_kriging <- calcular_rmse(puntos_filtrados$pH, resultados_kriging)
cat("RMSE Kriging: ", rmse_kriging, "\n")## RMSE Kriging: 0.14178865 (Revisión adicional): Mostrar atributos de los puntos de muestreo y su CRS
print(names(puntos))## [1] "Department" "Municipali" "Latitude.D" "Longitude." "Altitude.m"
## [6] "pH" "EC.dSm" "NH4.ppm" "NO3.ppm" "K2O.ppm"
## [11] "P2O5.ppm" "SOC.pct" "Sand.pct" "Silt.pct" "Clay.pct"
## [16] "Slope.pct" "geometry"print(st_crs(puntos))## Coordinate Reference System:
## User input: MAGNA-SIRGAS_Origen-Nacional
## wkt:
## PROJCRS["MAGNA-SIRGAS_Origen-Nacional",
## BASEGEOGCRS["GCS_MAGNA-SIRGAS_2018",
## DATUM["Marco Geocentrico Nacional de Referencia 2018",
## ELLIPSOID["GRS 1980",6378137,298.257222101,
## LENGTHUNIT["metre",1]],
## ID["EPSG",1329]],
## PRIMEM["Greenwich",0,
## ANGLEUNIT["Degree",0.0174532925199433]]],
## CONVERSION["unnamed",
## METHOD["Transverse Mercator",
## ID["EPSG",9807]],
## PARAMETER["Latitude of natural origin",4,
## ANGLEUNIT["Degree",0.0174532925199433],
## ID["EPSG",8801]],
## PARAMETER["Longitude of natural origin",-73,
## ANGLEUNIT["Degree",0.0174532925199433],
## ID["EPSG",8802]],
## PARAMETER["Scale factor at natural origin",0.9992,
## SCALEUNIT["unity",1],
## ID["EPSG",8805]],
## PARAMETER["False easting",5000000,
## LENGTHUNIT["metre",1],
## ID["EPSG",8806]],
## PARAMETER["False northing",2000000,
## LENGTHUNIT["metre",1],
## ID["EPSG",8807]]],
## CS[Cartesian,2],
## AXIS["(E)",east,
## ORDER[1],
## LENGTHUNIT["metre",1,
## ID["EPSG",9001]]],
## AXIS["(N)",north,
## ORDER[2],
## LENGTHUNIT["metre",1,
## ID["EPSG",9001]]]]summary(mtcars)## mpg cyl disp hp
## Min. :10.40 Min. :4.000 Min. : 71.1 Min. : 52.0
## 1st Qu.:15.43 1st Qu.:4.000 1st Qu.:120.8 1st Qu.: 96.5
## Median :19.20 Median :6.000 Median :196.3 Median :123.0
## Mean :20.09 Mean :6.188 Mean :230.7 Mean :146.7
## 3rd Qu.:22.80 3rd Qu.:8.000 3rd Qu.:326.0 3rd Qu.:180.0
## Max. :33.90 Max. :8.000 Max. :472.0 Max. :335.0
## drat wt qsec vs
## Min. :2.760 Min. :1.513 Min. :14.50 Min. :0.0000
## 1st Qu.:3.080 1st Qu.:2.581 1st Qu.:16.89 1st Qu.:0.0000
## Median :3.695 Median :3.325 Median :17.71 Median :0.0000
## Mean :3.597 Mean :3.217 Mean :17.85 Mean :0.4375
## 3rd Qu.:3.920 3rd Qu.:3.610 3rd Qu.:18.90 3rd Qu.:1.0000
## Max. :4.930 Max. :5.424 Max. :22.90 Max. :1.0000
## am gear carb
## Min. :0.0000 Min. :3.000 Min. :1.000
## 1st Qu.:0.0000 1st Qu.:3.000 1st Qu.:2.000
## Median :0.0000 Median :4.000 Median :2.000
## Mean :0.4062 Mean :3.688 Mean :2.812
## 3rd Qu.:1.0000 3rd Qu.:4.000 3rd Qu.:4.000
## Max. :1.0000 Max. :5.000 Max. :8.000mtcars## mpg cyl disp hp drat wt qsec vs am gear carb
## Mazda RX4 21.0 6 160.0 110 3.90 2.620 16.46 0 1 4 4
## Mazda RX4 Wag 21.0 6 160.0 110 3.90 2.875 17.02 0 1 4 4
## Datsun 710 22.8 4 108.0 93 3.85 2.320 18.61 1 1 4 1
## Hornet 4 Drive 21.4 6 258.0 110 3.08 3.215 19.44 1 0 3 1
## Hornet Sportabout 18.7 8 360.0 175 3.15 3.440 17.02 0 0 3 2
## Valiant 18.1 6 225.0 105 2.76 3.460 20.22 1 0 3 1
## Duster 360 14.3 8 360.0 245 3.21 3.570 15.84 0 0 3 4
## Merc 240D 24.4 4 146.7 62 3.69 3.190 20.00 1 0 4 2
## Merc 230 22.8 4 140.8 95 3.92 3.150 22.90 1 0 4 2
## Merc 280 19.2 6 167.6 123 3.92 3.440 18.30 1 0 4 4
## Merc 280C 17.8 6 167.6 123 3.92 3.440 18.90 1 0 4 4
## Merc 450SE 16.4 8 275.8 180 3.07 4.070 17.40 0 0 3 3
## Merc 450SL 17.3 8 275.8 180 3.07 3.730 17.60 0 0 3 3
## Merc 450SLC 15.2 8 275.8 180 3.07 3.780 18.00 0 0 3 3
## Cadillac Fleetwood 10.4 8 472.0 205 2.93 5.250 17.98 0 0 3 4
## Lincoln Continental 10.4 8 460.0 215 3.00 5.424 17.82 0 0 3 4
## Chrysler Imperial 14.7 8 440.0 230 3.23 5.345 17.42 0 0 3 4
## Fiat 128 32.4 4 78.7 66 4.08 2.200 19.47 1 1 4 1
## Honda Civic 30.4 4 75.7 52 4.93 1.615 18.52 1 1 4 2
## Toyota Corolla 33.9 4 71.1 65 4.22 1.835 19.90 1 1 4 1
## Toyota Corona 21.5 4 120.1 97 3.70 2.465 20.01 1 0 3 1
## Dodge Challenger 15.5 8 318.0 150 2.76 3.520 16.87 0 0 3 2
## AMC Javelin 15.2 8 304.0 150 3.15 3.435 17.30 0 0 3 2
## Camaro Z28 13.3 8 350.0 245 3.73 3.840 15.41 0 0 3 4
## Pontiac Firebird 19.2 8 400.0 175 3.08 3.845 17.05 0 0 3 2
## Fiat X1-9 27.3 4 79.0 66 4.08 1.935 18.90 1 1 4 1
## Porsche 914-2 26.0 4 120.3 91 4.43 2.140 16.70 0 1 5 2
## Lotus Europa 30.4 4 95.1 113 3.77 1.513 16.90 1 1 5 2
## Ford Pantera L 15.8 8 351.0 264 4.22 3.170 14.50 0 1 5 4
## Ferrari Dino 19.7 6 145.0 175 3.62 2.770 15.50 0 1 5 6
## Maserati Bora 15.0 8 301.0 335 3.54 3.570 14.60 0 1 5 8
## Volvo 142E 21.4 4 121.0 109 4.11 2.780 18.60 1 1 4 2