Interpolación espacial del contenido de nitrógeno total en el departamento del Putumayo
Victor Zarate
2026-07-24
1 Introducción
La interpolación espacial es una herramienta fundamental dentro de los Sistemas de Información Geográfica (SIG) para estimar el valor de una variable continua en localizaciones donde no se dispone de mediciones directas, a partir de un conjunto de puntos muestreados. En el caso de las propiedades del suelo, como el contenido de nitrógeno total, esta técnica permite generar superficies continuas útiles para la planificación agrícola, la evaluación de la fertilidad y el ordenamiento del territorio.
En este cuaderno se desarrolla un ejercicio de interpolación espacial del contenido de nitrógeno total (g/kg) para el departamento del Putumayo, comparando dos métodos: la Ponderación por Distancia Inversa (IDW, por sus siglas en inglés), de naturaleza determinística, y el Kriging Ordinario (OK), de naturaleza probabilística. Los datos de entrada corresponden a una capa raster de nitrógeno total obtenida de SoilGrids 250m, a la profundidad de 15-30 cm.
El objetivo de esta práctica es aplicar ambas técnicas de interpolación, evaluar su desempeño mediante validación cruzada, e identificar cuál resulta más adecuada para representar la distribución espacial del nitrógeno en el área de estudio.
2 Preparación del espacio de trabajo
Antes de iniciar el análisis se cargan las librerías necesarias para el manejo de datos espaciales, la interpolación geoestadística y la visualización de resultados.
rm(list = ls())
library(terra)
library(stars)
library(sf)
library(gstat)
library(automap)
library(sp)
library(mapview)
library(RColorBrewer)Las principales librerías utilizadas fueron las siguientes:
| Librería | Descripción |
|---|---|
| terra | Lectura, reproyección y manejo de datos raster (el raster de nitrógeno). |
| stars | Estructura de datos raster/vectorial usada como formato de entrada y
salida en las interpolaciones de gstat. |
| sf | Manejo de las capas vectoriales de puntos de muestreo. |
| gstat | Motor geoestadístico: construcción del variograma, IDW y Kriging Ordinario. |
| automap | Ajuste automático del modelo de variograma a partir del variograma empírico. |
| sp | Formato intermedio requerido por automap para el ajuste
del variograma. |
| mapview | Visualización interactiva de las superficies interpoladas. |
| RColorBrewer | Paletas de color para la representación cartográfica. |
Nota sobre visualización: mapview
incrusta los datos directamente dentro del archivo HTML generado (no
depende de un servidor externo de tiles), por lo que mapas construidos a
partir de rasters de gran tamaño o de miles de puntos pueden inflar
considerablemente el peso del documento final, al punto de superar el
límite de subida de plataformas como RPubs. Para evitar esto, a lo largo
del cuaderno se usan versiones reducidas de los rasters
y muestras de los puntos únicamente para la
visualización interactiva, mientras que todos los cálculos
(interpolación, variograma, validación cruzada) se realizan siempre
sobre los datos completos.
3 Lectura y preparación de los datos de entrada
3.1 Lectura del raster de nitrógeno
El insumo principal es una capa raster de nitrógeno total obtenida de
SoilGrids 250m. Debido a que el área de estudio (Putumayo) supera la
cobertura de una sola descarga, el raster utilizado corresponde al
mosaico de dos capas (Nitro1.tif y Nitro2.tif)
unidas previamente en QGIS, resultando en el archivo
Nitro.tif, que además ya fue reproyectado a WGS84
(EPSG:4326) desde ese mismo software.
ruta <- "C:/Users/ASUS/OneDrive/Documents/unal/GB2/proyecto 5"
n_raw <- rast(file.path(ruta, "Nitro.tif"))
n_raw## class : SpatRaster
## size : 904, 1770, 1 (nrow, ncol, nlyr)
## resolution : 0.002259887, 0.002389381 (x, y)
## extent : -77.16, -73.16, -0.58, 1.58 (xmin, xmax, ymin, ymax)
## coord. ref. : lon/lat WGS 84 (EPSG:4326)
## source : Nitro.tif
## name : Nitro
## min value : 0
## max value : 1036crs(n_raw)## [1] "GEOGCRS[\"WGS 84\",\n ENSEMBLE[\"World Geodetic System 1984 ensemble\",\n MEMBER[\"World Geodetic System 1984 (Transit)\"],\n MEMBER[\"World Geodetic System 1984 (G730)\"],\n MEMBER[\"World Geodetic System 1984 (G873)\"],\n MEMBER[\"World Geodetic System 1984 (G1150)\"],\n MEMBER[\"World Geodetic System 1984 (G1674)\"],\n MEMBER[\"World Geodetic System 1984 (G1762)\"],\n MEMBER[\"World Geodetic System 1984 (G2139)\"],\n MEMBER[\"World Geodetic System 1984 (G2296)\"],\n ELLIPSOID[\"WGS 84\",6378137,298.257223563,\n LENGTHUNIT[\"metre\",1]],\n ENSEMBLEACCURACY[2.0]],\n PRIMEM[\"Greenwich\",0,\n ANGLEUNIT[\"degree\",0.0174532925199433]],\n CS[ellipsoidal,2],\n AXIS[\"geodetic latitude (Lat)\",north,\n ORDER[1],\n ANGLEUNIT[\"degree\",0.0174532925199433]],\n AXIS[\"geodetic longitude (Lon)\",east,\n ORDER[2],\n ANGLEUNIT[\"degree\",0.0174532925199433]],\n USAGE[\n SCOPE[\"Horizontal component of 3D system.\"],\n AREA[\"World.\"],\n BBOX[-90,-180,90,180]],\n ID[\"EPSG\",4326]]"3.2 Conversión de unidades
SoilGrids almacena el nitrógeno total como enteros en centigramos por kilogramo (cg/kg) para optimizar el espacio de almacenamiento. Para obtener las unidades convencionales (g/kg) es necesario dividir por el factor de conversión indicado en la documentación oficial de SoilGrids, que para esta variable es 100.
n_wgs84 <- n_raw / 100
names(n_wgs84) <- "nitrogeno"Para la vista previa del raster se usa una versión reducida (agregada), suficiente para inspeccionar visualmente la distribución general sin generar un mapa pesado:
n_wgs84_viz <- aggregate(n_wgs84, fact = 4)
mapview(n_wgs84_viz, col.regions = colorRampPalette(brewer.pal(9, "YlOrBr"))(100))4 Muestreo
A diferencia del flujo original de la guía —donde el muestreo
aleatorio se genera directamente en R con spatSample()— en
este ejercicio los puntos de muestreo (500 puntos aleatorios) y la
extracción del valor de nitrógeno en cada uno se realizaron previamente
en QGIS, y se almacenaron en el archivo Muestreo.gpkg. Este
archivo contiene el campo Muestreo1 con el valor crudo (en
cg/kg) extraído del raster en cada punto.
muestras_sf <- st_read(file.path(ruta, "Muestreo.gpkg"))## Reading layer `muestreo' from data source
## `C:\Users\ASUS\OneDrive\Documents\unal\GB2\proyecto 5\Muestreo.gpkg'
## using driver `GPKG'
## Simple feature collection with 3000 features and 2 fields
## Geometry type: POINT
## Dimension: XY
## Bounding box: xmin: -77.1575 ymin: -0.579858 xmax: -73.16057 ymax: 1.579529
## Geodetic CRS: WGS 84names(muestras_sf)## [1] "id" "Muestreo1" "geom"head(muestras_sf)## Simple feature collection with 6 features and 2 fields
## Geometry type: POINT
## Dimension: XY
## Bounding box: xmin: -76.52961 ymin: -0.380556 xmax: -73.97164 ymax: 1.399762
## Geodetic CRS: WGS 84
## id Muestreo1 geom
## 1 0 481 POINT (-76.52961 -0.380556)
## 2 1 410 POINT (-75.70385 -0.315392)
## 3 2 388 POINT (-75.4013 1.399762)
## 4 3 355 POINT (-75.28065 0.3788805)
## 5 4 415 POINT (-75.89192 0.9801482)
## 6 5 344 POINT (-73.97164 -0.2236016)Se convierte el valor muestreado a las mismas unidades convencionales (g/kg) usadas para el raster, y se remueven los registros sin dato (NA), que pueden ocurrir cuando un punto aleatorio cae fuera de la extensión válida del raster:
muestras_sf$nitrogeno <- muestras_sf$Muestreo1 / 100
sum(is.na(muestras_sf$nitrogeno))## [1] 0muestras_sf <- muestras_sf[!is.na(muestras_sf$nitrogeno), ]
muestras_sf$id <- 1:nrow(muestras_sf)
head(muestras_sf)## Simple feature collection with 6 features and 3 fields
## Geometry type: POINT
## Dimension: XY
## Bounding box: xmin: -76.52961 ymin: -0.380556 xmax: -73.97164 ymax: 1.399762
## Geodetic CRS: WGS 84
## id Muestreo1 geom nitrogeno
## 1 1 481 POINT (-76.52961 -0.380556) 4.81
## 2 2 410 POINT (-75.70385 -0.315392) 4.10
## 3 3 388 POINT (-75.4013 1.399762) 3.88
## 4 4 355 POINT (-75.28065 0.3788805) 3.55
## 5 5 415 POINT (-75.89192 0.9801482) 4.15
## 6 6 344 POINT (-73.97164 -0.2236016) 3.44Para visualizar los puntos de muestreo se usa una submuestra aleatoria (500 puntos como máximo), suficiente para apreciar su distribución espacial sin sobrecargar el mapa interactivo:
set.seed(123)
n_viz <- min(500, nrow(muestras_sf))
muestras_viz <- muestras_sf[sample(nrow(muestras_sf), n_viz), ]
mapview(muestras_viz, zcol = "nitrogeno")4.1 Reproyección a un sistema de coordenadas plano
Tanto los puntos de muestreo como el raster se encuentran en
coordenadas geográficas (WGS84, en grados). Para la interpolación esto
es problemático por dos razones: primero, gstat calcula
distancias entre puntos de forma euclidiana, por lo que trabajar en
grados distorsiona las distancias reales (un mismo delta de coordenada
no representa la misma distancia en metros en diferentes latitudes);
segundo, el cálculo de distancias sobre coordenadas geográficas es
computacionalmente mucho más costoso, lo que hace que la interpolación
sobre un raster de gran tamaño sea extremadamente lenta.
Por esta razón, tanto los puntos como el raster se reproyectan al
sistema de coordenadas planas oficial de Colombia, MAGNA-SIRGAS 2018 /
Origen Nacional (EPSG:9377), apropiado para todo el
territorio continental, incluyendo Putumayo. Todos los cálculos
de interpolación se realizan sobre el raster completo, sin reducir su
resolución.
muestras_proj <- st_transform(muestras_sf, crs = 9377)
n_proj <- project(n_wgs84, "EPSG:9377")5 Interpolación
5.1 Creación del objeto gstat
El objeto gstat almacena la información necesaria para
realizar la interpolación: la fórmula del modelo (variable dependiente y
covariables), los datos de calibración (los puntos de muestreo) y, en el
caso del Kriging, el modelo de variograma. Cuando no se especifica un
modelo de variograma, gstat interpreta que se desea una
interpolación IDW; cuando sí se especifica, realiza Kriging
Ordinario.
En ambos casos se utiliza el argumento nmax, que limita
el número de vecinos más cercanos usados para predecir cada celda (en
lugar de usar todos los puntos de muestreo disponibles). Esto es
especialmente importante para el Kriging, ya que su costo computacional
crece de forma no lineal con el número de vecinos utilizados, al
requerir resolver un sistema de ecuaciones lineales en cada
predicción.
Como plantilla de predicción se utiliza un raster con la misma
extensión, resolución y sistema de coordenadas del raster de nitrógeno
reproyectado, convertido al formato stars requerido por
gstat:
rrr <- n_proj
values(rrr) <- 1
names(rrr) <- "valor"
stars.rrr <- st_as_stars(rrr)5.2 Interpolación IDW
g1 <- gstat(formula = nitrogeno ~ 1, data = muestras_proj, nmax = 20)
system.time(
z1 <- predict(g1, stars.rrr, debug.level = 0)
)## user system elapsed
## 13.80 0.22 14.20idw_n <- z1["var1.pred"]
names(idw_n) <- "nitrogeno"
pal <- colorRampPalette(brewer.pal(9, "YlOrBr"))(100)Para la visualización se genera una versión reducida de la superficie interpolada (agregada por un factor de 4), suficiente para apreciar el patrón espacial sin generar un mapa pesado:
idw_n_viz <- st_as_stars(aggregate(rast(idw_n), fact = 4))
mapview(idw_n_viz, col.regions = pal, layer.name = "IDW")5.3 Interpolación con Kriging Ordinario
El Kriging requiere, a diferencia del IDW, un modelo de variograma que cuantifique de forma objetiva el patrón de autocorrelación espacial de los datos, y a partir de él asignar los pesos de cada vecino en la predicción.
Primero se calcula el variograma empírico, que describe cómo cambia la semivarianza entre pares de puntos en función de la distancia que los separa:
v1 <- variogram(nitrogeno ~ 1, data = muestras_proj)
plot(v1)
Después se ajusta automáticamente un modelo teórico a ese variograma
empírico, usando la función autofitVariogram del paquete
automap (que requiere el objeto de puntos en formato
Spatial, no sf):
muestras_sp <- as(muestras_proj, "Spatial")
vmf <- autofitVariogram(nitrogeno ~ 1, muestras_sp)
plot(vmf)
vmf$var_model## model psill range kappa
## 1 Nug 0.2773807 0 0.0
## 2 Ste 22.5736338 17097786 0.4El modelo ajustado corresponde a un modelo Matérn (Ste), con un nugget de 0.28, un sill parcial de 22.57 (sill total ≈ 22.85) y un rango estimado de aproximadamente 17,098 km. Este último valor excede ampliamente la extensión real del área de estudio (Putumayo tiene una extensión máxima de apenas ~300 km), lo cual se explica observando el variograma empírico: la semivarianza crece de forma prácticamente lineal dentro del rango de distancias real observado (0-160 km), sin llegar a estabilizarse en una meseta. Esto indica que, si bien existe una autocorrelación espacial fuerte (relación nugget/sill ≈ 1.2%), el proceso de variación del nitrógeno ocurre a una escala espacial mayor a la del departamento, posiblemente asociada a gradientes regionales de uso del suelo, precipitación o cobertura vegetal.
Con el modelo de variograma ajustado, se construye el objeto
gstat para el Kriging Ordinario y se realiza la predicción
sobre la misma plantilla raster utilizada en el IDW, es decir, a
resolución completa:
g2 <- gstat(formula = nitrogeno ~ 1, data = muestras_proj, model = vmf$var_model, nmax = 20)
system.time(
z2 <- predict(g2, stars.rrr, debug.level = 0)
)## user system elapsed
## 134.17 0.65 136.84ok_n <- z2["var1.pred"]
names(ok_n) <- "nitrogeno"ok_n_viz <- st_as_stars(aggregate(rast(ok_n), fact = 4))
mapview(ok_n_viz, col.regions = pal, layer.name = "OK")6 Evaluación de resultados
6.1 Evaluación cualitativa
Se comparan visualmente las tres superficies: el raster original de nitrógeno, la interpolación IDW y la interpolación por Kriging Ordinario. Al igual que en los mapas individuales anteriores, se usan las versiones reducidas para mantener el documento liviano.
mapview(n_wgs84_viz, col.regions = pal, layer.name = "RealWorld") +
mapview(idw_n_viz, col.regions = pal, layer.name = "IDW") +
mapview(ok_n_viz, col.regions = pal, layer.name = "OK")6.2 Validación cruzada
Para evaluar objetivamente la precisión de cada método se realiza una
validación cruzada Leave-One-Out (LOOCV) mediante la función
gstat.cv, que retira sucesivamente cada punto de la
muestra, predice su valor a partir de los puntos restantes, y compara la
predicción con el valor observado. Esta validación se realiza sobre los
puntos de muestreo (no sobre el raster completo), por lo que no
representa un problema de tamaño y no requiere ninguna reducción.
suppressWarnings(suppressMessages(
cv1 <- gstat.cv(g1)
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## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
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## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]cv1_sf <- st_as_sf(cv1)
plot(cv1_sf["residual"])
rmse_idw <- sqrt(mean(cv1$residual^2, na.rm = TRUE))
rmse_idw## [1] 0.5834503suppressWarnings(suppressMessages(
cv2 <- gstat.cv(g2)
))## [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]
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## [using ordinary kriging]cv2_sf <- st_as_sf(cv2)
plot(cv2_sf["residual"])
rmse_ok <- sqrt(mean(cv2$residual^2, na.rm = TRUE))
rmse_ok## [1] 0.5850086Los resultados obtenidos fueron los siguientes:
- RMSE IDW = 0.583 g/kg
- RMSE OK = 0.585 g/kg
La diferencia entre ambos métodos es mínima (~0.3% de diferencia relativa), lo que indica una precisión prácticamente equivalente. Este resultado es consistente con lo observado en el variograma: al no estabilizarse la semivarianza dentro del rango de distancias real del área de estudio, el Kriging Ordinario no logra aprovechar plenamente su ventaja teórica sobre el IDW, ya que los pesos que asigna a los vecinos terminan comportándose de forma similar a una ponderación simple por distancia inversa. Adicionalmente, el mapa de residuales de ambos métodos no muestra un patrón espacial de agrupamiento evidente, lo que sugiere que el error remanente corresponde principalmente a variabilidad local no explicada, coherente con el nugget identificado en el variograma.
7 Discusión
El flujo de trabajo desarrollado permitió aplicar dos técnicas de
interpolación espacial —IDW y Kriging Ordinario— sobre datos de
nitrógeno total del suelo en el departamento del Putumayo, usando los
paquetes gstat, automap, terra,
stars y sf. Un aspecto clave del proceso fue
la reproyección de los datos a un sistema de coordenadas planas
(EPSG:9377), necesaria tanto para obtener distancias
euclidianas correctas como para reducir drásticamente el tiempo de
cómputo de la interpolación sobre un raster de más de 1.6 millones de
celdas.
Otro aspecto relevante fue el manejo del tamaño del documento final:
dado que mapview incrusta los datos directamente en el HTML
generado, fue necesario diferenciar entre los datos usados para el
cálculo (siempre completos, sin ninguna reducción) y
los usados para la visualización interactiva (rasters
agregados y muestras de puntos), evitando así que el documento superara
el límite de tamaño de publicación en RPubs sin comprometer la validez
de los resultados numéricos.
El análisis del variograma permitió identificar que, aunque el nitrógeno presenta una autocorrelación espacial fuerte, la escala a la que se estabiliza dicha autocorrelación supera la extensión del área de estudio, lo cual explica por qué el Kriging Ordinario no superó de forma significativa al IDW en la validación cruzada. Este hallazgo resalta la importancia de interpretar los parámetros del variograma en relación con la escala real del territorio analizado, y no únicamente como un resultado estadístico aislado.
8 Conclusiones
- Se procesó y preparó un raster de nitrógeno total del suelo para el departamento del Putumayo, obtenido de SoilGrids 250m, incluyendo su conversión a unidades convencionales (g/kg).
- Se utilizaron 500 puntos de muestreo aleatorio generados y extraídos
previamente en QGIS, integrados al flujo de trabajo en R mediante el
paquete
sf. - Se implementaron dos técnicas de interpolación espacial, IDW y Kriging Ordinario, evaluando su desempeño mediante validación cruzada Leave-One-Out.
- El modelo de variograma ajustado evidenció un rango muy superior a la extensión del área de estudio, lo que explica la similitud en el desempeño (RMSE) de ambos métodos de interpolación.
- Dado que ambos métodos presentaron una precisión estadísticamente comparable, se recomienda el uso de IDW para este conjunto de datos por su menor costo computacional y mayor simplicidad de implementación frente al Kriging Ordinario.
9 Referencias
Lizarazo, I., 2023. Spatial interpolation of soil organic carbon. Disponible en: https://rpubs.com/ials2un
ISRIC — World Soil Information, SoilGrids. Disponible en: https://www.isric.org/explore/soilgrids
10 Entorno de trabajo
sessionInfo()## R version 4.6.0 (2026-04-24 ucrt)
## Platform: x86_64-w64-mingw32/x64
## Running under: Windows 11 x64 (build 26200)
##
## Matrix products: default
## LAPACK version 3.12.1
##
## locale:
## [1] LC_COLLATE=Spanish_Colombia.utf8 LC_CTYPE=Spanish_Colombia.utf8
## [3] LC_MONETARY=Spanish_Colombia.utf8 LC_NUMERIC=C
## [5] LC_TIME=Spanish_Colombia.utf8
##
## time zone: America/Bogota
## tzcode source: internal
##
## attached base packages:
## [1] stats graphics grDevices utils datasets methods base
##
## other attached packages:
## [1] RColorBrewer_1.1-3 mapview_2.11.4 sp_2.2-3 automap_1.1-20
## [5] gstat_2.1-6 stars_0.7-2 sf_1.1-1 abind_1.4-8
## [9] terra_1.9-27
##
## loaded via a namespace (and not attached):
## [1] gtable_0.3.6 xfun_0.57 bslib_0.10.0
## [4] ggplot2_4.0.3 raster_3.6-32 htmlwidgets_1.6.4
## [7] lattice_0.22-9 leaflet.providers_3.0.0 vctrs_0.7.3
## [10] tools_4.6.0 crosstalk_1.2.2 generics_0.1.4
## [13] stats4_4.6.0 parallel_4.6.0 tibble_3.3.1
## [16] proxy_0.4-29 spacetime_1.3-3 xts_0.14.2
## [19] pkgconfig_2.0.3 KernSmooth_2.23-26 satellite_1.0.6
## [22] S7_0.2.2 uuid_1.2-2 leaflet_2.2.3
## [25] lifecycle_1.0.5 compiler_4.6.0 farver_2.1.2
## [28] FNN_1.1.4.1 textshaping_1.0.5 codetools_0.2-20
## [31] htmltools_0.5.9 class_7.3-23 sass_0.4.10
## [34] yaml_2.3.12 pillar_1.11.1 jquerylib_0.1.4
## [37] classInt_0.4-11 cachem_1.1.0 brew_1.0-10
## [40] tidyselect_1.2.1 digest_0.6.39 dplyr_1.2.1
## [43] fastmap_1.2.0 grid_4.6.0 cli_3.6.6
## [46] magrittr_2.0.5 base64enc_0.1-6 leafem_0.2.5
## [49] e1071_1.7-17 scales_1.4.0 rmarkdown_2.31
## [52] otel_0.2.0 zoo_1.8-15 png_0.1-9
## [55] evaluate_1.0.5 knitr_1.51 rlang_1.2.0
## [58] leafpop_0.1.0 Rcpp_1.1.1-1.1 glue_1.8.1
## [61] DBI_1.3.0 svglite_2.2.2 rstudioapi_0.18.0
## [64] reshape_0.8.10 jsonlite_2.0.0 R6_2.6.1
## [67] plyr_1.8.9 systemfonts_1.3.2 intervals_0.15.5
## [70] units_1.0-1