Interpolación Espacial
Laura Isabel Silva Zarate
27.02.2025
1. Introducción
Este cuaderno aplica dos técnicas de interpolación espacial, Ponderación Inversa de la Distancia (IDW) y Kriging Ordinario (OK), con el objetivo de generar una superficie continua del carbono orgánico del suelo (SOC) a 15-30 cm de profundidad en Santander. Utilizando datos de SoilGrids 250 m, se configuran herramientas de análisis espacial en R, se cargan los datos geoespaciales, y se construyen modelos de interpolación para representar la distribución del SOC en la región. Los resultados se visualizan en mapas interactivos, permitiendo evaluar la variabilidad espacial del SOC en Santander y comparando la precisión de ambos métodos en la captura de patrones locales del suelo. A continuación, se analiza el propósito y funcionamiento de cada bloque de código.
Los pasos para la descarga de los datos se encuentran en el siguiente enlace: https://rpubs.com/Lsilvaz/1277756.
2.Configuración y carga de datos
Eliminación de objetos previos
rm(list=ls())Cargar bibliotecas
library(terra)
library(sf)
library(sp)
library(stars)
library(gstat)
library(automap)
library(RColorBrewer)
library(leaflet)
library(leafem)Se cargan paquetes esenciales para el análisis espacial y la visualización de datos, como terra, sf y stars para manipulación de datos espaciales, gstat y automap para interpolación y leaflet para generar mapas interactivos.
Listar Archivos en el Directorio de Datos
list.files(path="datos", pattern = "*.gpkg")## [1] "dpto_santander.gpkg" "mun_santander.gpkg"
## [3] "santander_cities.gpkg" "santander_roadas.gpkg"
## [5] "santander_water_areas.gpkg" "santander_water_lines.gpkg"
## [7] "soc_stder.gpkg" "water.gpkg"Se cargan los datos de SOC y los límites municipales en formato gpkg para su posterior análisis y visualización.
samples <- sf::st_read("datos/soc_stder.gpkg")## Reading layer `soc_stder' from data source
## `C:\Users\lausi\OneDrive\Documents\2024-2\GEOMATICA\GB02\Proyecto R\datos\soc_stder.gpkg'
## using driver `GPKG'
## Simple feature collection with 1850 features and 1 field
## Geometry type: POINT
## Dimension: XY
## Bounding box: xmin: -74.55196 ymin: 5.709403 xmax: -72.41505 ymax: 8.144378
## Geodetic CRS: +proj=longlat +datum=WGS84 +no_defsmunic <- sf::st_read("datos/dpto_santander.gpkg")## Reading layer `dpto_santandercorr' from data source
## `C:\Users\lausi\OneDrive\Documents\2024-2\GEOMATICA\GB02\Proyecto R\datos\dpto_santander.gpkg'
## using driver `GPKG'
## Simple feature collection with 87 features and 5 fields
## Geometry type: MULTIPOLYGON
## Dimension: XY
## Bounding box: xmin: -74.52895 ymin: 5.707536 xmax: -72.47706 ymax: 8.14501
## Geodetic CRS: MAGNA-SIRGASAca se obtiene un resumen estadístico de la variable SOC.
summary(samples)## soc geom
## Min. : 12.40 POINT :1850
## 1st Qu.: 24.89 epsg:NA : 0
## Median : 32.89 +proj=long...: 0
## Mean : 35.65
## 3rd Qu.: 43.70
## Max. :101.29***arreglar mas lindo Se genera un histograma para analizar la distribución de los valores de SOC.
hist(samples$soc)
samples$soc = round(samples$soc,2)3. Generación de Mapas Interactivos
Se define una paleta de colores para visualizar la variable SOC en los mapas
pal <- colorNumeric(
c("#66CD00", "#BCEE68", "#FFD700", "#CD6600", "#8B3A3A"),
domain = samples$soc,
)Se genera un mapa interactivo con leaflet, agregando los datos municipales y los puntos de SOC con la paleta de colores definida.
leaflet() %>%
addPolygons(
data = munic,
color = "gray",
# set the opacity of the outline
opacity = 1,
# set the stroke width in pixels
weight = 1,
# set the fill opacity
fillOpacity = 0.2) %>%
addCircleMarkers(
data = samples,
radius= 1.5,
label = ~soc,
color = ~pal(soc),
fillOpacity = 1,
stroke = F
) %>%
addLegend(
data = samples,
pal = pal,
values = ~soc,
position = "bottomleft",
title = "SOC:",
opacity = 0.9) %>%
addProviderTiles("OpenStreetMap")## Warning: sf layer has inconsistent datum (+proj=longlat +ellps=GRS80 +towgs84=0,0,0,0,0,0,0 +no_defs).
## Need '+proj=longlat +datum=WGS84'##5. Interpolación ###5.1 IDW interpolacion Se crea un modelo IDW con gstat utilizando SOC como variable dependiente.
g1 = gstat(formula = soc ~ 1, data = samples)Ahora que nuestro modelo de interpolación g1 está definido, podemos usar la función actually interpolate para estimar los valores de precipitación:
creamos un objeto ráster con valores de celda iguales a 1:
(rrr <- terra::rast(xmin=-74.55524, xmax=-72.38985, ymin=5.708308, ymax=8.145474, nrows=370, ncols = 329, vals = 1, crs = "epsg:4326"))## class : SpatRaster
## dimensions : 370, 329, 1 (nrow, ncol, nlyr)
## resolution : 0.006581733, 0.006586935 (x, y)
## extent : -74.55524, -72.38985, 5.708308, 8.145474 (xmin, xmax, ymin, ymax)
## coord. ref. : lon/lat WGS 84 (EPSG:4326)
## source(s) : memory
## name : lyr.1
## min value : 1
## max value : 1stars.rrr <- stars::st_as_stars(rrr)Se predicen los valores interpolados de SOC usando el modelo IDW y se asigna el nombre a la capa generada.
z1 = predict(g1, stars.rrr)## [inverse distance weighted interpolation]z1## stars object with 2 dimensions and 2 attributes
## attribute(s):
## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## var1.pred 12.73927 29.28242 34.54546 35.80878 42.00168 98.42292 0
## var1.var NA NA NA NaN NA NA 121730
## dimension(s):
## from to offset delta refsys x/y
## x 1 329 -74.56 0.006582 WGS 84 [x]
## y 1 370 8.145 -0.006587 WGS 84 [y]Se asigna el nombre “soc” a la capa de raster z1, que representa la interpolación del Carbono Orgánico del Suelo (SOC) utilizando IDW.
names(z1) = "soc"Se define una paleta de colores personalizada para representar los valores interpolados del SOC en el mapa.
paleta <- colorNumeric(palette = c("orange", "yellow", "cyan", "green"), domain = 10:120, na.color = "transparent")Se muestra en la siguiente figura el ráster SOC interpolado, usando IDW
m <- leaflet() %>%
addTiles() %>%
leafem:::addGeoRaster(
z1,
opacity = 0.7,
colorOptions = colorOptions(palette = c("orange", "yellow", "cyan", "green"),
domain = 10:100)
) %>%
addCircleMarkers(
data = samples,
radius= 1.5,
label = ~soc,
color = ~paleta(soc),
fillOpacity = 1,
stroke = F
) %>%
addLegend("bottomright", pal=paleta, values= z1$soc,
title = "IDW SOC interpolation [%]"
)## Warning in write_stars.stars(x, dsn = fl): all but first attribute are ignoredm # Print the mapLos métodos kriging requieren un modelo de variograma. El modelo de variograma es una forma objetiva de cuantificar el patrón de autocorrelación en los datos y asignar pesos en consecuencia al hacer predicciones.
###5.3 Interpolación OK Se calcula el variograma empírico de los datos de Carbono Orgánico del Suelo (SOC) usando la función variogram() de la librería gstat, sin covariables
v_emp_ok = variogram(soc ~ 1, data=samples)Se grafica el variograma empírico calculado en el paso anterior.
plot(v_emp_ok)
Se ajusta el modelo de variograma usando la función autofitVariogram del
paquete automap
v_mod_ok = automap::autofitVariogram(soc ~ 1, as(samples, "Spatial"))Observamos el modelo ajustado
plot(v_mod_ok)
El modelo NUG (Nugget) y STE (Sill-To-Effective) se utiliza en
geostadística para analizar la variabilidad espacial de un fenómeno. El
NUG representa la variabilidad mínima o los errores aleatorios en los
datos, mientras que el STE describe la variabilidad estructural a medida
que aumenta la distancia entre los puntos. Juntos, proporcionan una
descripción completa de la variabilidad espacial de los datos,
permitiendo ajustar el variograma y realizar interpolaciones para
predecir los valores en ubicaciones no muestreadas.
v_mod_ok$var_model## model psill range kappa
## 1 Nug 0.0000 0.0000 0.0
## 2 Ste 220.0229 119.6611 0.2Ahora, se pasa el modelo de variograma se puede pasar a la función gstat, y continuar con the Ordinary Kriging interpolation:
g2 = gstat(formula = soc ~ 1, model = v_mod_ok$var_model, data = samples)
z2= predict(g1, stars.rrr)## [inverse distance weighted interpolation]Se subdivide y renombra el atributo de valores.
a <- which(is.na(z2[[1]]))
z2[[1]][a] = 0.0
names(z2) = "soc"Se puede observar el Ordinary Kriging interpolation
m <- leaflet() %>%
addTiles() %>%
leafem:::addGeoRaster(
z2,
opacity = 0.7,
colorOptions = colorOptions(palette = c("orange", "yellow", "cyan", "green"),
domain = 10:100)
) %>%
addCircleMarkers(
data = samples,
radius= 1.5,
label = ~soc,
color = ~paleta(soc),
fillOpacity = 1,
stroke = F
) %>%
addLegend("bottomright", pal = paleta, values= z2$soc,
title = "OK SOC interpolation [%]"
)## Warning in write_stars.stars(x, dsn = fl): all but first attribute are ignoredm6. Evaluacion de resultados
6.1 Evaluación cualitativa
Se crea otra vista de las tres salidas de interpolación.
colores <- colorOptions(palette = c("orange", "yellow", "cyan", "green"), domain = 10:100, na.color = "transparent")Visualizar
m <- leaflet() %>%
addTiles() %>%
addGeoRaster(z1, colorOptions = colores, opacity = 0.8, group= "IDW") %>%
addGeoRaster(z2, colorOptions = colores, opacity = 0.8, group= "OK") %>%
# Add layers controls
addLayersControl(
overlayGroups = c("IDW", "OK"),
options = layersControlOptions(collapsed = FALSE)
) %>%
addLegend("bottomright", pal = paleta, values= z1$soc,
title = "Soil organic carbon [%]"
)## Warning in write_stars.stars(x, dsn = fl): all but first attribute are ignored
## Warning in write_stars.stars(x, dsn = fl): all but first attribute are ignoredm###6.2 Cross-validation
Se elije objetivamente el método más preciso entre los métodos de interpolación disponibles, a continuacion escribiremos el siguiente fragmento, ocultando el mensaje y los resultados:
cv2 = gstat.cv(g1)## [inverse distance weighted interpolation]
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## [inverse distance weighted interpolation]El resultado de gstat.cv tiene los siguientes atributos:
var1.pred—Predicted value var1.var—Variance (only for Kriging) observed—Observed value residual—Observed-Predicted zscore—Z-score (only for Kriging) fold—Cross-validation ID
Se convierte el objeto cv1
cv2 = st_as_sf(cv2)Se grafica los residuos
sp::bubble(as(cv2[, "residual"], "Spatial"))
Los residuos de interpolación en Santander muestra variaciones significativas entre los valores observados y estimados, evidenciadas por la dispersión y tamaño de los círculos en el gráfico. La presencia de residuos positivos y negativos en diferentes zonas sugiere que el modelo presenta tanto sobreestimaciones como subestimaciones, lo que indica que la interpolación no es completamente precisa en todas las áreas.
IDW es un método determinista que asigna valores según la distancia a los puntos de muestra, siendo sencillo y eficiente, pero con menor precisión en variaciones locales. En Santander, ofrece una estimación general del SOC sin capturar completamente la estructura del suelo. En contraste, Kriging Ordinario (OK) es un método geoestadístico que modela la dependencia espacial, logrando estimaciones más precisas y representando mejor la variabilidad del SOC, aunque su implementación es más compleja y requiere ajuste del modelo variográfico.
write_stars(
z1, dsn = "datos/IDW_soc_stder.tif", layer = 1
)write_stars(
z2, dsn = "datos/OK_soc_stder.tif", layer = 1
)7. Conclusión
Este cuaderno permitió explorar y comparar dos enfoques de interpolación espacial, IDW y Kriging Ordinario (OK), aplicados a la estimación del Carbono Orgánico del Suelo (SOC) en Santander. A lo largo del análisis, se evidenció la importancia de seleccionar un método adecuado según la naturaleza de los datos y el objetivo del estudio. Mientras que IDW resulta práctico y rápido de aplicar, su capacidad para capturar patrones espaciales complejos es limitada. En contraste, Kriging Ordinario, al incorporar la estructura de variabilidad espacial mediante un modelo variográfico, demostró mayor precisión en la representación del SOC, aunque con un mayor costo computacional y necesidad de parametrización.
Este trabajo brindó un aprendizaje sobre la utilidad de los sistemas de información geográfica. Se evidencia la relevancia de contar con datos georreferenciados de calidad y comprender la influencia de la distribución de puntos de muestreo en la precisión de los modelos. Además, el análisis de residuos mostró que, si bien la interpolación mejora la comprensión de la variabilidad espacial del SOC, ningún modelo es perfecto y siempre existen errores de estimación que deben ser considerados en la toma de decisiones.
Estó demostró la importancia de adaptar los métodos de interpolación a las características específicas del área de estudio. En el caso de Santander, donde la variabilidad del suelo es alta, Kriging Ordinario representa una herramienta valiosa para mejorar la planificación agrícola y la gestión sostenible de los suelos. La reflexión principal que deja este cuaderno es que el análisis espacial no solo permite generar mapas, sino que también proporciona información clave para comprender y gestionar los recursos naturales de manera más eficiente y fundamentada.
##Referencias Lizarazo, I., 2023. Spatial interpolation of soil organic carbon. Available at https://rpubs.com/ials2un/soc_interp.
sessionInfo()## R version 4.4.2 (2024-10-31 ucrt)
## Platform: x86_64-w64-mingw32/x64
## Running under: Windows 11 x64 (build 22631)
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## Matrix products: default
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## locale:
## [1] LC_COLLATE=English_United States.utf8
## [2] LC_CTYPE=English_United States.utf8
## [3] LC_MONETARY=English_United States.utf8
## [4] LC_NUMERIC=C
## [5] LC_TIME=English_United States.utf8
##
## time zone: America/Bogota
## tzcode source: internal
##
## attached base packages:
## [1] stats graphics grDevices utils datasets methods base
##
## other attached packages:
## [1] leafem_0.2.3 leaflet_2.2.2 RColorBrewer_1.1-3 automap_1.1-12
## [5] gstat_2.1-3 stars_0.6-8 abind_1.4-8 sp_2.1-4
## [9] sf_1.0-19 terra_1.8-10
##
## loaded via a namespace (and not attached):
## [1] generics_0.1.3 sass_0.4.9 class_7.3-22
## [4] KernSmooth_2.23-24 lattice_0.22-6 digest_0.6.37
## [7] magrittr_2.0.3 evaluate_1.0.1 grid_4.4.2
## [10] fastmap_1.2.0 plyr_1.8.9 jsonlite_1.8.9
## [13] e1071_1.7-16 reshape_0.8.9 DBI_1.2.3
## [16] crosstalk_1.2.1 scales_1.3.0 codetools_0.2-20
## [19] jquerylib_0.1.4 cli_3.6.3 rlang_1.1.4
## [22] units_0.8-5 munsell_0.5.1 intervals_0.15.5
## [25] base64enc_0.1-3 cachem_1.1.0 yaml_2.3.10
## [28] FNN_1.1.4.1 raster_3.6-31 tools_4.4.2
## [31] parallel_4.4.2 dplyr_1.1.4 colorspace_2.1-1
## [34] ggplot2_3.5.1 spacetime_1.3-3 png_0.1-8
## [37] vctrs_0.6.5 R6_2.5.1 zoo_1.8-12
## [40] proxy_0.4-27 lifecycle_1.0.4 classInt_0.4-11
## [43] leaflet.providers_2.0.0 htmlwidgets_1.6.4 pkgconfig_2.0.3
## [46] pillar_1.10.0 bslib_0.8.0 gtable_0.3.6
## [49] glue_1.8.0 Rcpp_1.0.14 tidyselect_1.2.1
## [52] tibble_3.2.1 xfun_0.49 rstudioapi_0.17.1
## [55] knitr_1.49 farver_2.1.2 htmltools_0.5.8.1
## [58] rmarkdown_2.29 xts_0.14.1 compiler_4.4.2