Interpolacion
Jersson Quintero
2025-02-12
1. Introducción
Este cuaderno ofrece un acercamiento a la interpolación de datos geoespaciales, dado que es muy costoso, riguroso y demorado, el proceso de muestreo del suelo, se ha dispuesto de una tecnica que permite hacer una estimación de variables cuantitativas de un espacio geoespacial por medio de interpolación de datos, en este cuadernillo se presentaran dos tecnicas de interpolación espacial: 1. la técnica de ponderación de distancia inversa (IDW) 2. la técnica de kriging ordinario (OK).
La IDW es una técnica determinista, mientras que la OK es una técnica probabilística. Ambas técnicas se utilizan aquí para obtener una superficie continua de carbono orgánico del suelo (SOC) a una profundidad de 15-30 cm de muestras obtenidas de SoilGrids a 250 m. se utiliza estas distancia dado que gran parte de las plantas de cultivos se encuentran ubicadas en este rango de profundidad del suelo.
2. Configuración
Limpiar el area de trabajo:
rm(list=ls())Si bien en cuadernos anteriores hemos visto el funcionamiento de algunas librerias como terra (para archivos raster) y sf (para archivos de vectores), si desea conocer un poco mas de los algoritmos anteriores lo invitamos a ver la bibliografia, pues puede disponer de estos link en dicha sección.
Ahora se procede a dar una breve explicación de la interpolación espacial, utilizaremos las bibliotecas gstat y automap. Para la visualización, utilizaremos ggplot, leaflet y tmap.
Primero, debemos instalar las bibliotecas necesarias. Hazlo desde la consola R, no desde este notebook.
# DO NOT INSTALL PACKAGES THAT YOU ALREADY INSTALLED
#paquetes = c('terra', 'sf', 'sp', 'stars', 'gstat', 'automap', 'leaflet', 'leafem')
#install.packages(paquetes)El proceso de instalación puede demorar un poco, por favor verifique que todas las librerias quedaron instaladas
Importamos las librerias previamente instaladas
library(terra)## terra 1.8.21library(sf)## Linking to GEOS 3.12.2, GDAL 3.9.3, PROJ 9.4.1; sf_use_s2() is TRUElibrary(sp)
library(ggplot2)
library(stars)## Cargando paquete requerido: abindlibrary(gstat)
library(automap)
library(RColorBrewer)
library(leaflet)
library(leafem)3. Leer los datos de entrada
Esta sección es una de las importantes, pues se desea consultar los datos de Carbono Organico en el Suelo conocido de ahora en adelante como SOC.
Como se indica en la introducción, nuestras muestras son valores de SOC a una profundidad de 15-30 cm. Se obtuvieron de SoilGrids 250 m utilizando un cuaderno anterior. Guardamos dichas muestras en formato geopackage. Luego leemos las muestras usando sf:
samples <- sf::st_read("C:/Users/ASUS/Desktop/Agronomia/3 Semestre/Geomatica_basica/notebook_adicionales/codigos_clase/Eje_cafetero_soc_stder.gpkg")## Reading layer `Eje_cafetero_soc_stder' from data source
## `C:\Users\ASUS\Desktop\Agronomia\3 Semestre\Geomatica_basica\notebook_adicionales\codigos_clase\Eje_cafetero_soc_stder.gpkg'
## using driver `GPKG'
## Simple feature collection with 1903 features and 1 field
## Geometry type: POINT
## Dimension: XY
## Bounding box: xmin: -76.24417 ymin: 4.078827 xmax: -74.62737 ymax: 5.779554
## Geodetic CRS: +proj=longlat +datum=WGS84 +no_defsComo se puede ver tenemos las coordenales de latitud y longitud del eje cafetero y el formato CRS WGS84
Como nuestra zona de estudio es el Eje cafetero, tiene sentido leer también el geopaquete de municipios correspondiente:
munic <- sf::st_read("C:/Users/ASUS/Desktop/Agronomia/3 Semestre/Geomatica_basica/notebook_adicionales/codigos_clase/Eje_cafetero.gpkg")## Reading layer `eje_cafetero' from data source
## `C:\Users\ASUS\Desktop\Agronomia\3 Semestre\Geomatica_basica\notebook_adicionales\codigos_clase\Eje_cafetero.gpkg'
## using driver `GPKG'
## Simple feature collection with 53 features and 6 fields
## Geometry type: MULTIPOLYGON
## Dimension: XY
## Bounding box: xmin: -76.21143 ymin: 4.075311 xmax: -74.62746 ymax: 5.779182
## Geodetic CRS: MAGNA-SIRGASPodemos ver que el archivo de los municipios del eje cafetero esta en formato CRS Magna-sirgas.
(munic_wgs84 <- st_transform(munic, crs = 4326))## Simple feature collection with 53 features and 6 fields
## Geometry type: MULTIPOLYGON
## Dimension: XY
## Bounding box: xmin: -76.21143 ymin: 4.075311 xmax: -74.62746 ymax: 5.779182
## Geodetic CRS: WGS 84
## First 10 features:
## dpto_ccdgo mpio_ccdgo mpio_cdpmp dpto_cnmbr mpio_cnmbr mpio_tipo
## 1 17 001 17001 CALDAS MANIZALES MUNICIPIO
## 2 17 013 17013 CALDAS AGUADAS MUNICIPIO
## 3 17 042 17042 CALDAS ANSERMA MUNICIPIO
## 4 17 050 17050 CALDAS ARANZAZU MUNICIPIO
## 5 17 088 17088 CALDAS BELALCÁZAR MUNICIPIO
## 6 17 174 17174 CALDAS CHINCHINÁ MUNICIPIO
## 7 17 272 17272 CALDAS FILADELFIA MUNICIPIO
## 8 17 380 17380 CALDAS LA DORADA MUNICIPIO
## 9 17 388 17388 CALDAS LA MERCED MUNICIPIO
## 10 17 433 17433 CALDAS MANZANARES MUNICIPIO
## geom
## 1 MULTIPOLYGON (((-75.66009 5...
## 2 MULTIPOLYGON (((-75.59452 5...
## 3 MULTIPOLYGON (((-75.78565 5...
## 4 MULTIPOLYGON (((-75.49097 5...
## 5 MULTIPOLYGON (((-75.80145 5...
## 6 MULTIPOLYGON (((-75.70642 5...
## 7 MULTIPOLYGON (((-75.60607 5...
## 8 MULTIPOLYGON (((-74.67154 5...
## 9 MULTIPOLYGON (((-75.57209 5...
## 10 MULTIPOLYGON (((-75.11849 5...4. Explorando los datos de entrada
Veamos un resumen de los datos descargados y el comportamiento de la variable para el Eje cafetero.
summary(samples)## soc geom
## Min. : 12.73 POINT :1903
## 1st Qu.: 27.89 epsg:NA : 0
## Median : 44.45 +proj=long...: 0
## Mean : 48.49
## 3rd Qu.: 66.23
## Max. :210.91Se puede observar que el valor promedio es 48.49, y sus valores maximos y minimos pueden ofrecer el comportamiento general de los datos, se observa que los datos distribuidos con asimetria positiva orientando los valores cercanos a 0, indicando que si bien hay contenido de SOC, ese es bajo.
hist(samples$soc)
Esta misma información es corrobora por medio del histograma anterior el
cual confirma la informacion presentada anteriormente.
Redondeemos los valores SOC a dos dígitos:
samples$soc = round(samples$soc,2)Ahora, visualicemos las muestras para conocer su distribución espacial. Visite este sitio para comprender cómo funciona Leaflet.
pal <- colorNumeric(
c("#66CD00", "#BCEE68", "#FFD700", "#FF4500", "#FF0000"),
# colors depend on the count variable
domain = samples$soc,
)# This a simple visualization
# Change the code to suit your preferences
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 = 0.3) %>%
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'Se puede observar el numero de nuestras para el eje cafetero contando con 1903 muestras, entre las cuales su valor promedio esta en color Verde oscuro y verde claro, se podria considerar que la geografia tiene una relación con la cantidad de Carbono Organico disponible en el suelo, ya que donde hay mejor concentración en las cordilleras de los andes y entre ellas (valle de las cordilleras) el nivel de SOC aumenta, con estos valores se procedera a realizar las interpolaciones correspondientes.
5. Interpolación de datos
5.1 Creación del objeto gstat
La función gstat() en R permite definir un objeto de interpolación espacial. Este objeto almacena toda la información necesaria para realizar predicciones en ubicaciones no muestreadas.
¿Qué Contiene un Objeto gstat?
La función gstat() en R pertenece al paquete gstat y se utiliza para la interpolación espacial basada en geoestadística. Permite definir modelos de interpolación como Kriging y IDW (Inverse Distance Weighting).
- Principales Usos de gstat()
- Definir un modelo de interpolación: Se usa para configurar una interpolación espacial con los datos de entrada.
- Especificar el método de interpolación: Puede ser Kriging ordinario (OK), Kriging universal (UK), IDW, entre otros.
- Ajustar un modelo de semivarianza: Para Kriging, gstat() puede estimar el semivariograma y modelarlo automáticamente.
- Predecir valores en ubicaciones no muestreadas: Se usa para generar una superficie interpolada.
Tipos de Modelos que gstat() Puede Usar
Dependiendo de los argumentos que le pasemos, gstat() automáticamente entiende qué tipo de interpolación aplicar:
- Sin modelo de variograma → Distancia de ponderación inversa (IDW)
- Se usa cuando no se define un modelo de variograma.
- Calcula la estimación en función de la distancia de los puntos conocidos.
- Con modelo de variograma, sin covariables → Kriging Ordinario (OK)
- Se usa cuando se especifica un modelo de variograma.
- Asume que la media del proceso es constante en toda el área.
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): formula = soc ~ 1 (para IDW) * formula = soc ~ elev + slope
datos: los datos de calibración (también conocidos como los datos de entrenamiento en formato Dataframe o en objeto sf, sp)
modelo: el modelo de variograma, si no se define se usa el metodo IDW, si se define se usa el modelo kriging.
5.2 Interpolación IDW
Para interpolar el SOC mediante el método IDW, creamos el siguiente objeto gstat, especificando solo la fórmula y los datos:
g1 = gstat(formula = soc ~ 1, data = samples)Ahora que nuestro modelo de interpolación g1 está definido, podemos usar la función de predicción para interpolar realmente, es decir, para estimar los valores de SOC.
La función de predicción acepta:
Un objeto ráster: estrellas, como dem Un objeto modelo: gstat, como g1 El ráster sirve para dos propósitos:
Especificar las ubicaciones donde queremos hacer predicciones (en todos los métodos) Especificar valores de covariables (solo en Universal Kriging) Usemos la biblioteca terra para crear un objeto ráster con valores de celda iguales a 1. La extensión de este ráster debe cubrir nuestra área de interés.
Nota: Puede usar los metadatos de cualquier ráster que cubra su departamento (por ejemplo, un modelo de elevación digital) para definir los parámetros de creación del ráster:
(rrr <- terra::rast(xmin=-76.21143, xmax=-74.62746, ymin=4.075311, ymax=5.779182, nrows=370, ncols = 329, vals = 1, crs = "epsg:4326"))## class : SpatRaster
## dimensions : 370, 329, 1 (nrow, ncol, nlyr)
## resolution : 0.004814498, 0.004605057 (x, y)
## extent : -76.21143, -74.62746, 4.075311, 5.779182 (xmin, xmax, ymin, ymax)
## coord. ref. : lon/lat WGS 84 (EPSG:4326)
## source(s) : memory
## name : lyr.1
## min value : 1
## max value : 1Nota: Si su computadora tiene recursos limitados (por ejemplo, poca memoria), use una resolución espacial más baja (por ejemplo, 0,008 o 0,01 grados).
Ahora, necesitamos convertir este SpatRaster en un objeto stars:
stars.rrr <- stars::st_as_stars(rrr)pero, ¿Por qué usar stars en lugar de terra o raster? Soporta datos ráster y vectoriales en un solo objeto. Facilita la conversión y manipulación de datos espaciales con sf (paquete de datos vectoriales). Permite manejar múltiples dimensiones (por ejemplo, datos de tiempo y espacio en una sola estructura).
Ahora hacemos la respectiva predicción, con al funcion predict() ya que esta instrucción realiza una interpolación espacial sobre una cuadrícula (stars.rrr) utilizando un modelo previamente definido (g1) que en este caso es IDW
## [inverse distance weighted interpolation IDW]
## running this code takes several minutes
z1 = predict(g1, stars.rrr)## [inverse distance weighted interpolation]Ahora analicemos un poco ¿Qué es z1? como sabemos Z1 es la predicción del modelo IDW con los datos de SOC en nuestra zona de interes es el Eje Cafetero, recordando que la variable de interes es la cantidad de Carbono Organico en el suelo, z1 tiene los valores estimados de SOC segun los datos conocidos, revicemos un poco que contiene z1
z1## stars object with 2 dimensions and 2 attributes
## attribute(s):
## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## var1.pred 14.01486 33.70745 46.8275 47.81982 60.22275 203.0913 0
## var1.var NA NA NA NaN NA NA 121730
## dimension(s):
## from to offset delta refsys x/y
## x 1 329 -76.21 0.004814 WGS 84 [x]
## y 1 370 5.779 -0.004605 WGS 84 [y]z1 tiene valores min de 14.01486 y valores maximos de 203.0913 , podemos ver que en su promedio esta sobre 47.81982, valor con mayor presencia de datos de muestra, valores que pudismos ver en el histograma inicial, por otro lado, dicho modelo no ofrece una varianza conocida.
Podemos crear un subconjunto solo del primer atributo que son los valores estimados de SOC y los valores de N/A asignamos el valor de 0 y cambiarle el nombre a Z1 por el valor de la variable de estimación “soc”
a <- which(is.na(z1[[1]]))
z1[[1]][a] = 0.0
z1## stars object with 2 dimensions and 2 attributes
## attribute(s):
## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## var1.pred 14.01486 33.70745 46.8275 47.81982 60.22275 203.0913 0
## var1.var NA NA NA NaN NA NA 121730
## dimension(s):
## from to offset delta refsys x/y
## x 1 329 -76.21 0.004814 WGS 84 [x]
## y 1 370 5.779 -0.004605 WGS 84 [y]names(z1) = "soc"Ahora se procede a revisar el rango del valor de la prediccion Z1 y del los datos de entrada:
range(z1$soc, na.rm = TRUE)## [1] 14.01486 203.09131range(samples$soc, na.rm = TRUE)## [1] 12.73 210.91Se pude observar que los datos predichos estan dentro del rango de los valores de entrada.
Para trazar la superficie interpolada, necesitamos una paleta de colores:
# change this chunk to meet your preferences
paleta <- colorNumeric(palette = c("#66CD00", "#BCEE68", "#FFD700", "#FF4500", "#FF0000"), domain = 0:210, na.color = "transparent")Ahora, visualicemos la salida de la interpolación:
color = ~paleta(soc)m <- leaflet() %>%
addTiles() %>%
leafem:::addGeoRaster(
z1,
opacity = 0.7,
colorOptions = colorOptions(palette = c("#66CD00", "#BCEE68", "#FFD700", "#FF4500", "#FF0000"),
domain = 0:210)
) %>%
addCircleMarkers(
data = samples,
radius= 1.5,
label = ~soc,
color = ~paleta(soc),
fillOpacity = 1,
stroke = F
) %>%
addLegend("bottomright", pal=paleta, values= z1$soc,
title = "Interpolación IDW de SOC [%]"
)## Warning in paleta(soc): Some values were outside the color scale and will be
## treated as NA
## Warning in paleta(soc): Some values were outside the color scale and will be
## treated as NA## Warning in write_stars.stars(x, dsn = fl): all but first attribute are ignoredm # Print the map5.3 Interpolación OK
El kriging ordinario (OK) requiere un modelo de variograma para cuantificar la autocorrelación espacial de los datos. Esto nos permite asignar pesos óptimos al hacer predicciones espaciales.
- Cálculo del variograma empírico El variograma empírico representa la relación entre la distancia entre puntos y la diferencia en sus valores. Lo calculamos con la función variogram(), que requiere:
- Formula: la variable a interpolar
- Data: el conjunto de datos con coordenadas espaciales
La siguiente expresión calcula el variograma empírico de muestras, sin covariables:
v_emp_ok = variogram(soc ~ 1, data=samples)Dibujemos el variograma empírico:
plot(v_emp_ok)
Como se puede ver en la grafica anterior, los semivarianza esta en
funcion de la distancia donde nos permite ver cómo la variable soc
cambia con la distancia, cabe resaltar que este es el primer paso antes
de ajustar un modelo de variograma para realizar interpolación con
Kriging.
Existen varias formas de ajustar un modelo de variograma a un variograma empírico. Aquí, utilizaremos la más sencilla: el ajuste automático mediante la función autofit Variogram del paquete automap, el cual permite evaluar varios modelos de variogramas sean esférico, exponencial, gaussiano, etc., despues de hacer la respectiva evaluación, elije el modelo que mejor se menor diferencia existe entre el valor empirico y el valor teorico, y los parametros encontrados son los optimos para realizar la interpolación de Kriging
#make sure you understand the parameters needed to run this fitting function
v_mod_ok = automap::autofitVariogram(soc ~ 1, as(samples, "Spatial"))Tenga en cuenta que la función autofitVariogram no funciona en objetos sf y dado que sample es un raster de tipo sf, es necesario hacer la conversion a, por lo que convertimos el objeto samples en un SpatialPointsDataFrame (paquete sp).
Para conocer con mayor detalle cuales son los tipos de modelos que utiliza autofitVariagram, se utiliza la funcion show.vgms() obteniendo la grafica de 17 modelos y la funcion autofitVariogram compara con cada uno de ellos con el valor experimental para identifir cual se aproxima mas al valor experimental.
show.vgms()
El modelo ajustado con mejor estimación se puede representar gráficamente con plot:
plot(v_mod_ok)
En la grafica anterior se puede ver que el modelo escogido por la
función autofitVariogram es Sph, con Nugget de 77, sill de 77 y range de
67.
la función autofitVariogram() ajusta un modelo de variograma a los datos espaciales y devuelve una lista con varios componentes. Uno de esos componentes es var_model, que contiene una tabla con los parámetros del modelo ajustado.
v_mod_ok$var_model## model psill range
## 1 Nug 76.54907 0.00000
## 2 Sph 458.33214 67.14237Ahora, el modelo de variograma se puede pasar a la función gstat y podemos continuar con la interpolación de Kriging ordinario:
g2 = gstat(formula = soc ~ 1, model = v_mod_ok$var_model, data = samples)
z2= predict(g2, stars.rrr)## [using ordinary kriging]Aquí se está definiendo un nuevo objeto gstat (g2) para realizar la interpolación espacial mediante Kriging Ordinario (OK) con lo siguientes paramentros * formula = soc ~ 1: Indica que estamos interpolando la variable soc (contenido de carbono orgánico en el suelo) sin covariables. * model = v_mod_ok\(var_model: Se usa el modelo de variograma (v_mod_ok\)var_model) previamente ajustado con autofitVariogram(). * data = samples: samples es el conjunto de datos de entrenamiento (datos de muestreo con valores conocidos de soc en diferentes ubicaciones).
La instruccion 2, hace una Interpolar de valores en una grilla espacial (raster), Ahora aplicamos la interpolación Kriging Ordinario (g2) a un objeto ráster (stars.rrr), lo que genera un nuevo conjunto de datos interpolados (z2). * Realiza la predicción de valores de soc en los píxeles del ráster stars.rrr, usando el modelo de Kriging definido en g2. * stars.rrr especifica la extensión espacial donde queremos hacer la predicción. * El resultado, z2, contiene los valores estimados de soc en una grilla espacial.
Nuevamente, crearemos un subconjunto del atributo de valores predichos y lo renombraremos soc, ademas eliminamos los valores nulos:
a <- which(is.na(z2[[1]]))
z2[[1]][a] = 0.0
names(z2) = "soc"Aquí se está buscando cuáles valores en z2[[1]] son NA (valores faltantes) y devuelve la dirección de los nulos. donde z2[[1]] son los valores de SOC estimados, ahora los NA son cambiados por 0.0, y camvbia el valor de z2 a SOC
Ahora se procede a revisar el rango del valor de la prediccion Z2 y del los datos de entrada:
range(z2$soc, na.rm = TRUE)## [1] 14.9849 159.3328range(samples$soc, na.rm = TRUE)## [1] 12.73 210.91Se pude observar que los datos predichos estan dentro del rango de los valores de entrada.
Ahora se procede a Visualizar por medio de un histograma el cual permite comparar el comportamiento de los datos y observar que si tienen la misma distribución y tendencia.
# Extraer los valores de Z2 y de samples$soc
valores_z2 <- as.vector(z2$soc)
valores_samples <- samples$soc
# Crear un data frame con ambas variables
df_hist <- data.frame(
Tipo = rep(c("Z2", "Samples"), c(length(valores_z2), length(valores_samples))),
Valores = c(valores_z2, valores_samples)
)
# Graficar histogramas en un solo panel
ggplot(df_hist, aes(x = Valores, fill = Tipo)) +
geom_histogram(position = "identity", alpha = 0.5, bins = 15) +
facet_wrap(~Tipo, scales = "free") +
theme_minimal() +
labs(title = "Distribución de Valores",
x = "Carbono Organico Disponible - SOC",
y = "Cantidad de valres")
Se puede observar que los datos tienden a tener la misma distribución de
datos.
#palette = c("#66CD00", "#BCEE68", "#FFD700", "#FF4500", "#FF0000"),domain = range(samples$soc, na.rm = TRUE)))
paleta1 <- colorNumeric(palette = c("#66CD00", "#BCEE68", "#FFD700", "#FF4500", "#FF0000"), samples$soc, na.color = "transparent")Ahora se procede a observar en nuestra area de interes las predicciones de metodo de Kriging Ordinario:
m <- leaflet() %>%
addTiles() %>%
leafem:::addGeoRaster(
z2, # Raster sin puntos
opacity = 0.7,
colorOptions = colorOptions(palette = c("#66CD00", "#BCEE68", "#FFD700", "#FF4500", "#FF0000"),
domain = range(samples$soc, na.rm = TRUE)) # Ajusta el dominio a los valores de z2$soc
) %>%
addCircleMarkers( # Aquí sí mostramos los puntos
data = samples,
radius = 1.5,
label = ~soc,
color = ~paleta1(soc),
fillOpacity = 1,
stroke = FALSE
) %>%
addLegend("bottomright", pal = paleta, values = samples$soc,
title = "OK SOC interpolation"
)## Warning in pal(c(r[1], cuts, r[2])): Some values were outside the color scale
## and will be treated as NA## Warning in write_stars.stars(x, dsn = fl): all but first attribute are ignoredm # Mostrar el mapaSe puede observar que los valores de SOC estimados visualmente y entran dentro del rango de SOC de entrada.
6. Evaluación de resultados
6.1 Evaluación cualitativa
Ahora se procede a asignar otra paleta de colores para el siguiente analisis
colores <- colorOptions(palette = c("orange", "yellow", "cyan", "green"), domain = samples$soc, na.color = "transparent")m <- leaflet() %>%
addTiles() %>%
leafem:::addGeoRaster(z1, colorOptions = colorOptions(palette = c("#66CD00", "#BCEE68", "#FFD700", "#FF4500", "#FF0000"),
domain = range(samples$soc, na.rm = TRUE)), opacity = 0.8, group= "IDW") %>%
leafem:::addGeoRaster(z2, colorOptions = colorOptions(palette = c("#66CD00", "#BCEE68", "#FFD700", "#FF4500", "#FF0000"),
domain = range(samples$soc, na.rm = TRUE)), opacity = 0.8, group= "OK") %>%
# Add layers controls
addLayersControl(
overlayGroups = c("IDW", "OK"),
options = layersControlOptions(collapsed = FALSE)
) %>%
addLegend("bottomright", pal = paleta1, values= samples$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 ignoredm6.2 Validación cruzada
Hemos estimado las superficies SOC 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, para ello se usa la tecnica de validación cruzada, siendo esta una tecnica estadistica utilizada para evaluar el rendimiento de un modelo predictivo. Su objetivo principal es medir qué tan bien el modelo generaliza a datos nuevos, evitando el sobreajuste (overfitting).
Se basa en dividir los datos en varias partes (folds), entrenando el modelo con una parte de los datos y evaluándolo con la otra. Luego, el proceso se repite varias veces con diferentes particiones, y los resultados se promedian para obtener una métrica más confiable.
Existen varios tipos, pero los más comunes son: * Validación Simple (Hold-Out) * Validación Cruzada k-Fold * Validación Leave-One-Out (LOO)
En la validación cruzada Leave-One-Out:
- Eliminamos un punto de los datos de calibración
- Hacemos una predicción para ese punto
- Repetimos para todos los puntos Al final, lo que obtenemos es una tabla con un valor observado y un valor predicho para todos los puntos.
Para este caso se realizara la validación cruzada Leave-One-Out utilizando la función gstat.cv, que acepta un objeto gstat.
Al escribir el siguiente fragmento, oculta el mensaje y los resultados.
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## this code should be run from the console not from here
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## [using ordinary kriging]El codigo anterior permite almacenar los resultados en cv2, que contiene las predicciones en los puntos de muestreo y los errores de predicción. ahora bien esta variable contiene las siguientes columnas o atributos:
- var1.pred: Valores predichos por el modelo de Kriging (g2) en esos mismos puntos.
- var1.var: varianza (solo para Kriging)
- observed: Valores reales de soc en los puntos de muestreo (samples).
- residual: Diferencia entre el valor observado y el predicho
- zscore: Residual normalizado (se usa para detectar errores sistemáticos en la interpolación).
- fold: ID de validación cruzada
- geometry: Punto espacial que fue extraido para hacer la validación cruzada
Ahora bien, se usa para transformar objetos espaciales de otros formatos (como SpatialPointsDataFrame de sp) a una estructura compatible con sf, Convertiendo el objeto cv2:
# run from the console
cv2 = st_as_sf(cv2)Ahora hacer una grafica del error de la estimación, en este caso de la variable residual:
# run from the console
sp::bubble(as(cv2[, "residual"], "Spatial"))
Se puede observar que en la grafica de burbujass hay puntos de color
morado y otros de color verde, que representa la diferentecia (error)
entre los datos reales y los estimados de la interpolación utilizando
Kriging Ordinario (OK).
Pero ¿Qué significa estos valores?
Los colores: * Verde: Residuales positivos (sobreestimaciones del modelo). * Magenta: Residuales negativos (subestimaciones del modelo).
Tamaño de las burbujas:
- Burbujas más grandes indican errores más grandes en la predicción.
- Burbujas más pequeñas representan errores menores.
Ahora bien ¿por qué las burbujas estan distribuidas en un plano?
Este plano representa nuestra zona de interes (Eje Cafetero) y se puede observar que si bien hay datos distribuidos en todo el plano, los mayores errorese se encuentran en en la zona de las cordilleras de los andes, pues hay una gran cantidad de variaciónes geomorfologicas.
# This is the RMSE value for the OK interpolation
# run from the console
sqrt(sum((cv2$var1.pred - cv2$observed)^2) / nrow(cv2))## [1] 10.46955El RMSE mide qué tan bien el modelo predice los valores reales, dandole mas importancia a los valores grandes, en este caso el RMSE es de 10.47.
Una vez finalizado el proceso para el modelo kriging ordinario (g2), se realiza el mismo proceso con los resultados de interpolación IDW (g1).
###
## this code should be run from the console not from here
cv1 = gstat.cv(g1)## [inverse distance weighted interpolation]
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## [inverse distance weighted interpolation]# run from the console
cv1 = st_as_sf(cv1)Grafiquemos los residuos:
# run from the console
sp::bubble(as(cv1[, "residual"], "Spatial"))
Se puede ver en la grafica los resultados del modelo IDW, que las
burbujas son mas grandes y los valores de sobrestimación son mayores que
para el modelo de kriging ordinario. ahora se procede a sacar el valor
RMSE para identificar cual es el mejor metodo para nuestra zona de
interes.
# This is the RMSE value for the OK interpolation
# run from the console
sqrt(sum((cv1$var1.pred - cv1$observed)^2) / nrow(cv1))## [1] 12.48305Se puede visualizar que el valor de RMSE es mayor para el caso del modelo de kriging ordinario, ya que tiene valores de estimación mas cercanos a los valores reales.
Esto se debe al que el modelo de kriging ordinario permite analizar el comportamiento de los datos geoespacioales mostrando la dependencia entre datos. mientras que el metodo de interpolación por ponderación inversa de la distancia (IDW), nos permite darle mayor importancia a los valores cercanos.
ademas, el metodo de kriging ordinario estima valores óptimos usando una función matematica basada en la variabilidd espacial. y ajusta el variograma para modelar como varian los valores con la distancia. lo que ayuda a tener presente las tendencias espaciales.
un ejemplo practica de esta comparacion es: Si hay una tendencia en los datos (por ejemplo, una zona donde el carbono del suelo aumenta gradualmente), IDW no la detectará porque solo usa distancias, mientras que Kriging sí lo hará porque modela la correlación espacial.
Sin embargo, una de las limitaciones que tiene el metodo de Kriging ordinario es el costo computacional para estimar datos ya que debe tener encuenta varios datos y correlaciones, situación que no sucede con el metodo de interpolación por ponderación inversa de la distancia (IDW)
7. Guardar las salidas de interpolación
write_stars(
z1, dsn = "C:/Users/ASUS/Desktop/Agronomia/3 Semestre/Geomatica_basica/notebook_adicionales/codigos_clase/IDW_soc_eje_cafetero.tif", layer = 1
)write_stars(
z2, dsn = "C:/Users/ASUS/Desktop/Agronomia/3 Semestre/Geomatica_basica/notebook_adicionales/codigos_clase/OK_soc_eje_cafetero.tif", layer = 1
)8. Conclusiones
En el sector agrario, el análisis de variables geomorfológicas presenta diversas limitaciones, ya que la disponibilidad de datos es un factor clave para realizar estudios detallados. Contar con un amplio número de variables permite obtener una visión integral de una región específica. Sin embargo, en países en vía de desarrollo como Colombia, la cantidad de variables disponibles para análisis detallados suele ser más reducida. Por ello, una alternativa para disponer de información en todo el territorio colombiano es la estimación de atributos como el tipo de suelo, la materia orgánica y la capacidad de intercambio catiónico, entre otros.
La estimación de variables en una zona de interés es una práctica cada vez más utilizada, con diferentes modelos según el nivel de precisión requerido. En este estudio, se emplearon dos métodos para la estimación del carbono orgánico en el suelo (SOC):
- El metodo de interpolación por ponderación inversa de la distancia (IDW)
- kriging ordinario.
A partir de 1.903 muestras tomadas en el Eje Cafetero, se inició el proceso de estimación. Los mapas generados revelaron dos tendencias principales: valores que oscilaban entre 0 y 50 g/kg y entre 50 y 100 g/kg. Sin embargo, algunos puntos específicos alcanzaron valores de hasta 200 g/kg, especialmente en la zona noreste del mapa, con mayor precisión en el municipio de Puerto Rico, Risaralda.
Tras realizar las estimaciones y sus respectivas validaciones, los gráficos de error evidenciaron que las mayores discrepancias se concentraron en esta región, así como en la zona montañosa de la Cordillera de los Andes. A continuación, se presentan algunos factores que influyeron en esta variabilidad:
- Variabilidad geomorfológica: La presencia de cordilleras y valles en la misma zona de estudio afecta la continuidad del SOC, generando fluctuaciones en los valores estimados.
- Limitaciones en los datos fronterizos: Solo se consideraron datos del Eje Cafetero, lo que impidió incluir información de regiones vecinas que podría haber mejorado la estimación en los límites departamentales. Esto plantea interrogantes como:
** ¿Cuánta área adicional deberíamos incluir para mejorar la estimación en nuestra zona de interés? ** ¿Qué relación costo computacional vs. calidad de estimación es aceptable para el estudio? ** ¿En qué dirección debería expandirse la zona de estudio para optimizar la precisión de los datos?
Finalmente, al evaluar los modelos mediante la métrica de RMSE (Root Mean Square Error), se observó una diferencia significativa en la precisión de las estimaciones. El método de Kriging Ordinario demostró ser más preciso en la estimación del SOC en el Eje Cafetero, reduciendo el error en promedio en 2 g/kg en comparación con el modelo IDW. Sin embargo, sería conveniente explorar métricas adicionales como MAE (Mean Absolute Error), precisión, exactitud y especificidad, entre otras, para determinar con mayor certeza cuál es el modelo que mejor se ajusta a los datos originales.
9. Referencia
Lizarazo, I. 2025. Interpolación espacial. Disponible en: https://rpubs.com/ials2un/Spatial_Interpolation
Lizarazo, I. 2025. Descarga de datos de SoilGrids. Disponible en: https://rpubs.com/ials2un/downloadSoilGrids
sessionInfo()## R version 4.4.2 (2024-10-31 ucrt)
## Platform: x86_64-w64-mingw32/x64
## Running under: Windows 11 x64 (build 26100)
##
## Matrix products: default
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## 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] leafem_0.2.3 leaflet_2.2.2 RColorBrewer_1.1-3 automap_1.1-16
## [5] gstat_2.1-3 stars_0.6-8 abind_1.4-8 ggplot2_3.5.1
## [9] sp_2.2-0 sf_1.0-19 terra_1.8-21
##
## loaded via a namespace (and not attached):
## [1] gtable_0.3.6 xfun_0.49 bslib_0.8.0
## [4] raster_3.6-31 htmlwidgets_1.6.4 lattice_0.22-6
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## [13] tibble_3.2.1 proxy_0.4-27 spacetime_1.3-3
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## [28] yaml_2.3.10 pillar_1.10.0 jquerylib_0.1.4
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## [34] digest_0.6.37 dplyr_1.1.4 labeling_0.4.3
## [37] fastmap_1.2.0 grid_4.4.2 colorspace_2.1-1
## [40] cli_3.6.3 magrittr_2.0.3 base64enc_0.1-3
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## [46] rmarkdown_2.29 zoo_1.8-12 png_0.1-8
## [49] evaluate_1.0.1 knitr_1.49 rlang_1.1.4
## [52] Rcpp_1.0.13-1 glue_1.8.0 DBI_1.2.3
## [55] rstudioapi_0.17.1 reshape_0.8.9 jsonlite_1.8.9
## [58] R6_2.5.1 plyr_1.8.9 intervals_0.15.5
## [61] units_0.8-5