Taller interpolacion Carlos German Sanchez Rivera
Interpolacion IDW
1.1 Instalacion librerias y paquetes
library(sf)
library(stars)
library(leaflet)
library(gstat)
library(automap)
library(raster)
library(RColorBrewer)1.2 Verificacion y lugar de guardado
getwd()[1] "/Users/carlitos/Documents/University/Geomatica/drive-download-20250223T004732Z-001" setwd("/Users/carlitos/Documents/University/Geomatica/drive-download-20250223T004732Z-001")1.3 Declarar las variables
ruta_aoi="./municipios_muestreo.shp"
ruta_puntos="./puntos_muestreo.shp"
ruta_raster="./dem_srtm_9377.tif"1.4 Visualizar los archivos de datos (shp y tif) (tablas atributos)
raster_dem=read_stars(ruta_raster, RasterIO = list(bands = 1))
raster_demstars 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): plot(raster_dem)downsample set to 2
puntos = st_read(ruta_puntos)Reading layer `puntos_muestreo' from data source `/Users/carlitos/Documents/University/Geomatica/drive-download-20250223T004732Z-001/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-Nacional gs_crs = st_crs(raster_dem)
puntos = st_transform(puntos, crs = gs_crs)
(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 NO3.ppm K2O.ppm P2O5.ppm SOC.pct Sand.pct Silt.pct Clay.pct Slope.pct geometry
1 Santander Confines 6.331580 -73.25827 1533 4.8 0.08 10.3 8.4 173.5 10.1 2.46 40.7 32.6 26.6 10.5 POINT (4971447 2257635)
2 Santander Confines 6.345463 -73.28759 1489 4.9 0.07 10.3 5.4 122.9 8.9 1.62 51.2 26.1 22.6 9.2 POINT (4968206 2259171)
3 Santander Confines 6.357339 -73.28138 1482 4.8 0.08 18.2 0.9 119.3 6.2 2.95 51.9 35.4 12.7 7.4 POINT (4968893 2260483)
4 Santander Confines 6.360368 -73.24903 1581 4.7 0.07 6.7 2.3 181.9 12.1 1.02 37.3 36.1 26.5 12.6 POINT (4972470 2260816)
5 Santander Confines 6.340922 -73.20868 1878 4.8 0.15 24.0 12.3 130.1 7.3 2.48 65.6 30.3 4.1 8.5 POINT (4976930 2258665)
6 Santander Confines 6.357226 -73.23005 1742 4.8 0.09 11.7 1.2 131.3 4.8 1.60 40.8 46.5 12.6 7.5 POINT (4974568 2260467)
7 Santander Confines 6.339062 -73.23301 1752 4.9 0.09 9.4 2.0 73.5 11.5 3.65 55.0 42.5 2.5 5.6 POINT (4974240 2258460)
8 Santander Confines 6.402768 -73.22524 1715 4.8 0.08 9.4 5.9 194.0 6.6 2.12 33.7 45.4 20.9 13.7 POINT (4975101 2265500)
9 Santander Confines 6.365608 -73.21098 1878 4.8 0.10 19.3 0.3 273.5 3.4 3.81 64.4 24.9 10.6 1.5 POINT (4976677 2261393)
10 Santander Paramo 6.384360 -73.19552 1912 4.9 0.12 19.1 0.1 128.9 18.8 3.14 39.1 50.7 10.3 15.8 POINT (4978386 2263464)1.5 Verificacion sistema de coordenadas y reproyeccion de puntos
st_crs(puntos)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]] st_crs(raster_dem)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]] 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)
}El sistema de referencia de coordenadas del raster y de los puntos es el mismo:
Coordinate Reference System:
User input: MAGNA-SIRGAS / Origen-Nacional
wkt:
PROJCRS["MAGNA-SIRGAS / Origen-Nacional",
BASEGEOGCRS["MAGNA-SIRGAS",
DATUM["Marco Geocentrico Nacional de Referencia",
ELLIPSOID["GRS 1980",6378137,298.257222101,
LENGTHUNIT["metre",1]]],
PRIMEM["Greenwich",0,
ANGLEUNIT["degree",0.0174532925199433]],
ID["EPSG",4686]],
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."],
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_reproj <- st_transform(puntos, crs_raster)
(puntos_reproj)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-Nacional
First 10 features:
Department Municipali Latitude.D Longitude. Altitude.m pH EC.dSm NH4.ppm NO3.ppm K2O.ppm P2O5.ppm SOC.pct Sand.pct Silt.pct Clay.pct Slope.pct geometry
1 Santander Confines 6.331580 -73.25827 1533 4.8 0.08 10.3 8.4 173.5 10.1 2.46 40.7 32.6 26.6 10.5 POINT (4971447 2257635)
2 Santander Confines 6.345463 -73.28759 1489 4.9 0.07 10.3 5.4 122.9 8.9 1.62 51.2 26.1 22.6 9.2 POINT (4968206 2259171)
3 Santander Confines 6.357339 -73.28138 1482 4.8 0.08 18.2 0.9 119.3 6.2 2.95 51.9 35.4 12.7 7.4 POINT (4968893 2260483)
4 Santander Confines 6.360368 -73.24903 1581 4.7 0.07 6.7 2.3 181.9 12.1 1.02 37.3 36.1 26.5 12.6 POINT (4972470 2260816)
5 Santander Confines 6.340922 -73.20868 1878 4.8 0.15 24.0 12.3 130.1 7.3 2.48 65.6 30.3 4.1 8.5 POINT (4976930 2258665)
6 Santander Confines 6.357226 -73.23005 1742 4.8 0.09 11.7 1.2 131.3 4.8 1.60 40.8 46.5 12.6 7.5 POINT (4974568 2260467)
7 Santander Confines 6.339062 -73.23301 1752 4.9 0.09 9.4 2.0 73.5 11.5 3.65 55.0 42.5 2.5 5.6 POINT (4974240 2258460)
8 Santander Confines 6.402768 -73.22524 1715 4.8 0.08 9.4 5.9 194.0 6.6 2.12 33.7 45.4 20.9 13.7 POINT (4975101 2265500)
9 Santander Confines 6.365608 -73.21098 1878 4.8 0.10 19.3 0.3 273.5 3.4 3.81 64.4 24.9 10.6 1.5 POINT (4976677 2261393)
10 Santander Paramo 6.384360 -73.19552 1912 4.9 0.12 19.1 0.1 128.9 18.8 3.14 39.1 50.7 10.3 15.8 POINT (4978386 2263464)1.6 Interpolacion por metodo IDW
var="pH"
puntos[var]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 2018 / 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)
st_crs(puntos_reproj) Coordinate Reference System:
User input: MAGNA-SIRGAS / Origen-Nacional
wkt:
PROJCRS["MAGNA-SIRGAS / Origen-Nacional",
BASEGEOGCRS["MAGNA-SIRGAS",
DATUM["Marco Geocentrico Nacional de Referencia",
ELLIPSOID["GRS 1980",6378137,298.257222101,
LENGTHUNIT["metre",1]]],
PRIMEM["Greenwich",0,
ANGLEUNIT["degree",0.0174532925199433]],
ID["EPSG",4686]],
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."],
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] NA
g = gstat(formula = pH ~ 1, data = puntos_reproj,set=list(idp=2))
z = predict(g, raster_dem)[inverse distance weighted interpolation] 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. 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):1.7 Formula establecida interpolacion
g = gstat(formula = pH ~ 1, data = puntos_reproj,set=list(idp=2))1.8 Definicion parametros
z = predict(g, raster_dem)[inverse distance weighted interpolation]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. 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):z = z["var1.pred",,]
1.9 Visualizacion resultados interpolacion
names(z) = "pH"
b = seq(4, 7.5, 0.1)plot(z, breaks = b, col = hcl.colors(length(b)-1, "Spectral"), reset = FALSE)downsample set to 2 plot(st_geometry(puntos_reproj), pch = 3, add = TRUE) contour(z, breaks = b, add = TRUE)
1.10 Asignacion variable
interpolacion_idw="./ph_idw.tif"1.11 Almacenar raster en archivo geotiff
write_stars(z, dsn = interpolacion_idw)1.12 Zonas optimas jitomate
zona_optima = prediccion
zona_optima[zona_optima < 6.0 | zona_optima > 6.8] <- NA
plot(zona_optima, col = hcl.colors(10, "blues"), main = "Zonas óptimas para jitomate")downsample set to 2
Interpolacion por kriging
2.1 Creacion variograma empirico
v_emp_ok = variogram(pH ~ 1, puntos_reproj)
plot(v_emp_ok)
2.2 Ajuste variograma a funcion
v_mod_ok = autofitVariogram(pH ~ 1, as(puntos_reproj, "Spatial"))
plot(v_mod_ok)
2.3 Formula interpolacion
g2 = gstat(formula = pH ~ 1, model = v_mod_ok$var_model, data = puntos_reproj)2.4 Prediccion kriging
z = predict(g2, 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):2.5 Visualizacion kriging
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)downsample set to 2
2.6 Visual varianza
varianza = z["var1.var",,]
names(varianza) = "varianza pH"
b_var = seq(0.1, 1.4, 0.1)2.7 Distribucion varianza
plot(varianza, breaks = b_var, col = hcl.colors(length(b_var)-1, "Spectral"), reset = FALSE)downsample set to 2 plot(st_geometry(puntos_reproj), pch = 3, add = TRUE)
2.8 Asignacion formulas IDW y Kriging (g, g2) y grafico de burbujas
cv2 = gstat.cv(g2)
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sp::bubble(as(cv2[, "residual"], "Spatial"))
cv3 = gstat.cv(g)
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|========================================================================================================================================================== | 86%[inverse distance weighted interpolation]
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|============================================================================================================================================================ | 88%[inverse distance weighted interpolation]
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|=============================================================================================================================================================== | 89%[inverse distance weighted interpolation]
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|================================================================================================================================================================== | 91%[inverse distance weighted interpolation]
|
|===================================================================================================================================================================== | 92%[inverse distance weighted interpolation]
|
|======================================================================================================================================================================= | 94%[inverse distance weighted interpolation]
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|========================================================================================================================================================================== | 95%[inverse distance weighted interpolation]
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|============================================================================================================================================================================= | 97%[inverse distance weighted interpolation]
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|=============================================================================================================================================================================== | 98%[inverse distance weighted interpolation]
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|==================================================================================================================================================================================| 100%[inverse distance weighted interpolation] cv3 = st_as_sf(cv3)
sp::bubble(as(cv3[, "residual"], "Spatial"))
NA2.9 Calculo RMSE
sqrt(sum((cv2$var1.pred - cv2$observed)^2) / nrow(cv2))[1] 0.7066087sqrt(sum((cv3$var1.pred - cv3$observed)^2) / nrow(cv3))[1] 0.7196336FIN
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