PROYECTO 2

1.INTRODUCCIÓN

1.1 CONTEXTO

El bosque tropical actualmente es considerado como la fuente de carbono mas importante del planeta y una fuente esencial de servicios ecosistémicos, suelos, agua, regulación del clima, generación de hábitats naturales, etc., (Tao et al. 2012). Esto hace que juegue un rol crucial en el ciclo del carbono terrestre, haciendo que su medición sea de gran importancia para apoyar procesos de mitigación al cambio climático,(Chazdon et al. 2016).

La reducción de las emisiones de carbono producto de la deforestación y la degradación de bosques en países en vía de desarrollo se ha convertido en un objetivo de vital importancia en los esfuerzos que se hacen por combatir el cambio climático a nivel mundial, debido a que se espera poder pagar por el valor de carbono almacenado en bosques con el fin de revertir la deforestación y así fortalecer el manejo forestal sostenible (Moros et al. 2019).

El programa Copernicus de agencia espacia europea (ESA) puso en marcha desde el año 2014 satélites que tienen la posibilidad de tomar imágenes en la superficie terrestre con una resolución espacial de hasta 10 metros, brindando nuevas posibilidades al acceso a información de manera libre, permitiendo la generación de metodologías para el monitoreo de los bosques y los fenómenos asociados a ellos en zonas tropicales (Lardeux et al. 2019).

Teniendo en cuenta las necesidades de los países latinoamericanos, se han definido diversas metodologías que integran sensores remotos en el cálculo de índices y variables ambientales (Ali et al. 2015). Contemplando el cálculo de índices de vegetación, datos de inventarios forestales y vinculando técnicas de estadística predictiva se han logrado definir técnicas que permiten cuantificar la degradación de los bosques y predecir fenómenos sobre los mismo mediante el uso e integración de variables ambientales con sensores remotos (Nzuza et al. 2020).

1.2 PROBLEMA

A través del tiempo se han encontrado grandes dificultades asociadas con el acceso a datos de características ambientales sobre el bosque natural debido a los costos y demanda de tiempo que conlleva realizar análisis sobre el territorio amazónico por sus extensas áreas, dificultad de acceso y poca información existente de inventarios forestales. (Gardner et al. 2008).

Los sensores remotos han brindado la posibilidad de obtener acercamientos al cálculo de algunas características ambientales (ej. stock de carbono en bosques) mediante la definición de algunos índices que hacen factible estimar datos mediante el análisis de patrones espaciales y temporales, (Xiao et al. 2019). Así, La integración de datos de campo con índices espectrales han dejado ver la necesidad de profundizar en el desarrollo de metodologías que idóneas para el cálculo de variables ambientales en zonas tropicales (Watzlawick et al. 2009).

Se ha evidenciado que la integración de sensores remotos en conjunto con métodos estadísticos y de manejo de datos permiten un acercamiento más detallado de las estimaciones algunas variables ambientales como la biomasa aérea (Zhang & Kondragunta 2006).

Otro elemento a tener en cuenta está relacionado a que las mediciones en estas zonas casi nunca pueden ser desarrolladas una medición que nunca de manera directa, lo que lleva a depender de estimaciones que alimentan cálculos remotos convirtiendo el proceso en “la estimación de la estimación”. Pese a los avances, aún existen limitaciones asociadas al muestreo, las especies, densidad de árboles, variaciones geográficas, etc., las cuales se suman a los errores propios de los procesos relacionados con sensores remotos. (Gonçalves et al. 2017).

Un ejemplo es de algunas aplicaciones desarrolladas que integran estas tecnologías puede lo realizado en el Parque Nacional Don Yong de Vietnam, donde se hallaron grandes potenciales al integrar una regresión basada en Random Forest con imágenes ópticas Sentinel 2 para el cálculo de biomasa aérea y las precisiones obtenidas fueron adecuadas, (Dang et al. 2019).

Un problema adicional es la variabilidad espacial de la biomasa aérea, la cual ha llevado a algunos investigadores a no implementar dentro de su estudio algoritmos clásicos de aprendizaje de máquinas como lo son Random Forest, sino que piensen en adicionar un enfoque geoestadístico. Este ejercicio se llevó a cabo en la provincia de Guandong en China, y comprobó que se fortalecen las estimaciones de biomasa aérea, ya que contempla las relaciones espaciales existentes entre las variables. Para tal fin, además de la integración de datos provenientes de inventarios forestales, sensores ópticos (ALOS), datos SAR (PALSAR) y algoritmos de aprendizaje de máquina, se llevó a cabo la aplicación de una técnica Random Forest/CoKriging (Su et al., 2020).

Lo anterior muestra la necesidad de evaluar metodologías que ayuden a la estimar de la biomasa aérea contemplando la variabilidad espacial .

1.3 OBJETIVOS

• Calcular algunos índices de vegetación utilizando imágenes ópticas Sentinel-2.

• Evaluar la regresión usando el algoritmo Random Forest

• Evaluar la regresión usando el algoritmo Random Forest Espacial (SpatialRF)

1.4 CONCEPTOS TEÓRICOS

La cuenca del amazonas es una de las mas extensas y dinámicas áreas de ecosistemas de bosque tropical en el mundo y puntualmente Colombia es una región con un alto porcentaje de bosque natural heterogéneo el cual de manera general ofrece una gran cantidad de servicios ecosistémicos como agua, madera, hábitat para plantas y animales, incluyendo humanos (comunidades indígenas), (Armenteras et al. 2019).

Sobre esos ecosistémicos recaen procesos de colonización que cambian el uso y cobertura de la tierra (LULC), que para ser controlados necesitan de herramientas que permitan su monitoreo. Dentro de estas herramientas se encuentran las imágenes de satélite las cuales ofrecen la posibilidad de monitorear de manera remota esos cambios. Las imágenes Sentinel 2 al ser una fue libre de información satelital la cual tiene grandes ventajas como lo son el que incluyen alta frecuencia de paso, entre 10 y 60 metros de resolución espacial, posee 13 bandas espectrales y con 4 bandas que rondan en el área del Red Edge, (Shang et al. 2021).

El trabajo con estas imágenes abre la posibilidad de acceder a información con escalas de trabajo mas detalladas y adicionalmente, las estimaciones realizadas tendrán un nivel de precisión mas elevado. Algunos de los estudio que mas se realizan en la estimación de la cobertura forestal es el cálculo de índices espectrales de vegetación, lo cuales son obtenidos mediante la combinación diferentes valores de reflectancia asociada a diferentes bandas, lo cuales permiten obtener parámetros que resumen la información multiespectral. Estos parámetros permiten así observar la presencia de vegetación en la superficie terrestre y sus variaciones, (Spadoni et al. 2020).

Algoritmos como el Random Forest permiten establecer relaciones entre todas estas variables independientes que son obtenidas a partir de sensores remotos para estimar unas variables dependientes como lo es la biomasa aérea (Ghosh & Behera, 2018).

2.MÉTODOS

2.1 ÁREA DE ESTUDIO

El estudio es realizado en el área boscosa al interior de la unidad de corta número 1 del Plan de Manejo Forestal (PMF) del municipio de Calamar en el departamento del Guaviare.

Esta región se encuentra en el municipio de Calamar y colinda con el Parque Nacional Natural Chiribiquete y tiene una topografía predominantemente plana cuyas pendientes oscilan entre el 0 y 7% a una altitud constante entre los 225 y 275 msnm. Esta zona se encuentra localizada entre el interfluvio de los ríos Unilla e Itilla, lo cual hace que sea parte de la zona hidrográfica del Orinoco. La temperatura media anual de la zona es de 25.7 ºC y dentro de los meses mas lluviosos están mayo y junio.

library(leaflet)
library (sp)
library (raster)
library (terra)
library (Rcpp)
library (sf)
library(PerformanceAnalytics)
library(dplyr)
library(rgdal)
library(stars)
library(rfUtilities)
library(randomForest)
library(tidyr)
library(leafem)
library(RColorBrewer)
library(spatialRF)
library(kableExtra)
library(rnaturalearth)
library(rnaturalearthdata)
library(randomForestExplainer)
library(pdp)

AE<- readOGR("E:/ESTUDIO/UN/MAESTRIA/PERCEPCION_REMOTA_2_AVANZADA/INFORME_2/SHP/BSQ_18N.shp")

## OGR data source with driver: ESRI Shapefile 
## Source: "E:\ESTUDIO\UN\MAESTRIA\PERCEPCION_REMOTA_2_AVANZADA\INFORME_2\SHP\BSQ_18N.shp", layer: "BSQ_18N"
## with 2 features
## It has 8 fields
## Integer64 fields read as strings:  OBJECTID_1 OBJECTID_2 OBJECTID

AE1<- readOGR("E:/ESTUDIO/UN/MAESTRIA/PERCEPCION_REMOTA_2_AVANZADA/INFORME_2/SHP/BSQ_WGS84.shp")

## OGR data source with driver: ESRI Shapefile 
## Source: "E:\ESTUDIO\UN\MAESTRIA\PERCEPCION_REMOTA_2_AVANZADA\INFORME_2\SHP\BSQ_WGS84.shp", layer: "BSQ_WGS84"
## with 2 features
## It has 8 fields
## Integer64 fields read as strings:  OBJECTID_1 OBJECTID_2 OBJECTID

e <- ext(AE)
censo <-  readOGR("E:/ESTUDIO/UN/MAESTRIA/PERCEPCION_REMOTA_2_AVANZADA/INFORME_2/SHP/PT_3_18N.shp")

## OGR data source with driver: ESRI Shapefile 
## Source: "E:\ESTUDIO\UN\MAESTRIA\PERCEPCION_REMOTA_2_AVANZADA\INFORME_2\SHP\PT_3_18N.shp", layer: "PT_3_18N"
## with 316 features
## It has 9 fields
## Integer64 fields read as strings:  OBJECTID_1 OBJECTID Join_Count TARGET_FID Id ORIG_FID

censo_st <-  st_read("E:/ESTUDIO/UN/MAESTRIA/PERCEPCION_REMOTA_2_AVANZADA/INFORME_2/SHP/PT_3_18N.shp")

## Reading layer `PT_3_18N' from data source 
##   `E:\ESTUDIO\UN\MAESTRIA\PERCEPCION_REMOTA_2_AVANZADA\INFORME_2\SHP\PT_3_18N.shp' 
##   using driver `ESRI Shapefile'
## Simple feature collection with 316 features and 9 fields
## Geometry type: POINT
## Dimension:     XY
## Bounding box:  xmin: 752184.3 ymin: 202803.9 xmax: 754964.4 ymax: 204724.6
## Projected CRS: WGS 84 / UTM zone 18N

AE_st<- readOGR("E:/ESTUDIO/UN/MAESTRIA/PERCEPCION_REMOTA_2_AVANZADA/INFORME_2/SHP/BSQ_18N.shp")

## OGR data source with driver: ESRI Shapefile 
## Source: "E:\ESTUDIO\UN\MAESTRIA\PERCEPCION_REMOTA_2_AVANZADA\INFORME_2\SHP\BSQ_18N.shp", layer: "BSQ_18N"
## with 2 features
## It has 8 fields
## Integer64 fields read as strings:  OBJECTID_1 OBJECTID_2 OBJECTID

loc <- leaflet(data=AE1)%>% 
  addPolygons() %>% 
  addTiles()
  addMiniMap(loc, tiles =  providers$OpenStreetMap,
             toggleDisplay = T, width = 180, height=120)

2.2 DATOS

Para el presente trabajo se utilizarán imágenes de satélite del Sensor Sentinel-2 con fecha de toma del 7 de septiembre de 2020 correspondiente al cuadrante 18NYH. Adicionalmente esta imagen tiene un nivel L2A, la cual ofrece una reflectancia (BOA).Esta imagen coincide con el segundo insumo que es a una muestra de 316 puntos los cuales fueron procesados para obtener biomasa aérea por punto y que a su vez representan la medición de 3 arboles en un área de 10x10 metros para hacerlos coincidir coN el tamaño de pixel de la imágen Sentinel-2.

#bands' load 10m

b2 <- rast('E:/ESTUDIO/UN/MAESTRIA/PERCEPCION_REMOTA_2_AVANZADA/INFORME_2/IMG_DATA/S2B_MSIL2A_20200907T151709_N0214_R125_T18NYH_20200907T204219.SAFE/GRANULE/L2A_T18NYH_A018312_20200907T152155/IMG_DATA/R10m/T18NYH_20200907T151709_B02_10m.jp2')
b3 <- rast('E:/ESTUDIO/UN/MAESTRIA/PERCEPCION_REMOTA_2_AVANZADA/INFORME_2/IMG_DATA/S2B_MSIL2A_20200907T151709_N0214_R125_T18NYH_20200907T204219.SAFE/GRANULE/L2A_T18NYH_A018312_20200907T152155/IMG_DATA/R10m/T18NYH_20200907T151709_B03_10m.jp2')
b4 <- rast('E:/ESTUDIO/UN/MAESTRIA/PERCEPCION_REMOTA_2_AVANZADA/INFORME_2/IMG_DATA/S2B_MSIL2A_20200907T151709_N0214_R125_T18NYH_20200907T204219.SAFE/GRANULE/L2A_T18NYH_A018312_20200907T152155/IMG_DATA/R10m/T18NYH_20200907T151709_B04_10m.jp2')
b8 <- rast('E:/ESTUDIO/UN/MAESTRIA/PERCEPCION_REMOTA_2_AVANZADA/INFORME_2/IMG_DATA/S2B_MSIL2A_20200907T151709_N0214_R125_T18NYH_20200907T204219.SAFE/GRANULE/L2A_T18NYH_A018312_20200907T152155/IMG_DATA/R10m/T18NYH_20200907T151709_B08_10m.jp2')

SentinelRGB<- c(b4,b3,b2)

plotRGB(SentinelRGB, axes = TRUE, stretch = "lin",  width = 200, height=200)

plot(censo_st["BA_KG_CL2"], key.pos = 1, axes = TRUE, key.width = lcm(1.3), key.length = 1.0, breaks= "jenks")

censo_st

## Simple feature collection with 316 features and 9 fields
## Geometry type: POINT
## Dimension:     XY
## Bounding box:  xmin: 752184.3 ymin: 202803.9 xmax: 754964.4 ymax: 204724.6
## Projected CRS: WGS 84 / UTM zone 18N
## First 10 features:
##    OBJECTID_1 OBJECTID Join_Count TARGET_FID Id        Y         X BA_KG_CL2
## 1           1    15720          3      15719  1 1.833383 -72.72400  4501.620
## 2           2    19031          3      19030  1 1.834302 -72.72486  4841.939
## 3           3    19045          3      19044  1 1.834244 -72.72363  4119.656
## 4           4    19710          3      19709  1 1.834458 -72.72348  3424.257
## 5           5    20708          3      20707  1 1.834757 -72.72335  5703.619
## 6           6    21033          3      21032  1 1.834833 -72.72395  1248.175
## 7           7    22681          3      22680  1 1.835278 -72.72503  5597.145
## 8           8    23351          3      23350  1 1.835449 -72.72452  2161.010
## 9           9    23356          3      23355  1 1.835482 -72.72401  2318.499
## 10         10    24029          3      24028  1 1.835609 -72.72320  1134.417
##    ORIG_FID                  geometry
## 1     15720 POINT (753194.9 202803.9)
## 2     19031 POINT (753104.8 202903.9)
## 3     19045   POINT (753244.8 202904)
## 4     19710   POINT (753254.8 202924)
## 5     20708   POINT (753274.8 202954)
## 6     21033   POINT (753204.8 202964)
## 7     22681 POINT (753084.8 203013.9)
## 8     23351 POINT (753144.8 203033.9)
## 9     23356   POINT (753194.8 203034)
## 10    24029   POINT (753284.8 203054)

2.3 ANÁLISIS ESTADÍSTICO DE LOS DATOS

Para el estudio se realiza un análisis de la imagen Sentinel 2 trabajada. Para esto se revisan las estadísticas por la imagen, puntualmente la distribución del histograma: Adicionalmente se realiza una composicíon en falso color RGB843, con el fin de evidenciar si la cobertura boscosa es predominante en la imagen seleccionada. Para este análisis se utilizan las bandas de la imagen que poseen una resolución espacial de 10 m.

Adicionalmente se realizó una evaluación de la distribución de los valores de biomasa aérea almacenados en cada uno de los arboles censados.

hist(censo_st$BA_KG_CL2,main = "Histograma de la variable Biomasa Aérea", 
     xlab = "Kg", ylab = "Frecuencia",
     col = "purple",breaks=150)

2.4 DEFINICIÓN DE ÍNDICES ESPECTRALES

Para el análisis se calculan los índices de vegetación EVI, SAVI y NDWI.

2.5 RANDOM FOREST (NO ESPACIAL)

Se ejecuto el algoritmo Random Forest en su versiñon clásica utilizando la librería “randomForest”. El algoritmo fue ejecutado utilizando como variable dependiente la biomasa aérea y como variables índependientes las bandas de la imágen Sentinel-2 y los índices espectrales calculados.

Se parametrizó el algoritmo Random Forest de diversas maneras para evaluar el cambio de los resultados obtenidos.

2.6 RANDOM FOREST ESPACIAL

Para el algoritmo Random Forest espacial fue utilizada la librería “SpatialRF”. Los parametros solicitados para la evaluación de un algoritmo de aprendizaje de maquinas espacial es la matriz de distancias, la cual permite que se evalue la correlación espacial contemplando el índice de Moran I.

Adicionalmente, se realiza una evaluación de los resultados obtenidos, incluyendo la clasificación de las variables independientes según su importancia en la estimación de la biomasa aérea.

2.7 CORRELACIÓN ENTRE ÍNDICES Y DATOS DEL CENSO FORESTAL

Se realiza un análisis sobre la correlación existente entre los datos del censo forestal para la variables biomasa aérea que ayude a validar los resultados obtenidos mediante los algoritmos de aprendizaje de máquina.

3.RESULTADOS

3.1 ANÁLISIS DE LA IMAGEN Y ESTADÍSTICAS

El área de objeto de estudio se encuentra se caracteriza por la densidad del bosque que se puede encontrar por ser parte de la región amazónica colombiana, lo cual es fácilmente comprobable al realizar una composición en falso color RGB843 para la detección de la vegetación. El color rojo en la mayoría de la imagen refleja lo anteriormente mencionado pero adicionalmente, se pueden apreciar algunos cuerpos de agua de gran tamaño al norte de la imagen asociados al río Guaviare y otros cuerpos que sobre él desembocan, y en el centro un gran núcleo de ocupación.

El área de estudio se encuentra localizada en la parte sur de la imagen satelital lo cual ofrece un área libre de nubes.

SentinelFC <- c(b8, b4, b3)
plotRGB(SentinelFC, axes=TRUE, stretch="lin", width = 200, height=200) #false color

par(mfrow =c(2,2)) #Plot in an arrangement 2x2
    plot(b2, main="BLUE",col=gray(0:100/100))
    plot(b3, main="GREEN",col=gray(0:100/100))
    plot(b4, main="RED",col=gray(0:100/100))
    plot(b8, main="NIR",col=gray(0:100/100))

Los histogramas de las bandas permiten corroborar lo antes observado en la imagen ya que los valores de reflectancia que se muestras en los histogramas evidencian que los valores de la banda 8 del infrarrojo cercano son mas elevados que en las otras bandas las cuales un comportamiento asimétrico positivo.

boa10m <- c(b2,b3,b4,b8)
names(boa10m) <- c('Blue', 'Green', 'Red','NIR') #rename bands

par(mfrow=c(2, 2))
hist(boa10m, 1, maxpixels=10000000, plot=TRUE, ylab="Frequency", col="darkblue", xlab="BOA reflectance" )
hist(boa10m, 2, maxpixels=10000000, plot=TRUE, ylab="Frequency", col="green",xlab="BOA reflectance" )
hist(boa10m, 3, maxpixels=10000000, plot=TRUE, ylab="Frequency", col="red", xlab="BOA reflectance" )
hist(boa10m, 4, maxpixels=10000000, plot=TRUE, ylab="Frequency", col="yellow", xlab="BOA reflectance")

Debido a que el área de interés se encuentra localizada al sur de la imagen se realiza un corte que permite evidenciar la imagen con mas detalle y así mismo las estadísticas. Este proceso se realiza para las bandas que tienen resolución espacial de 10 m.

Este corte se hace a la extensión del área objeto de estudio que para este caso es el área definida como bosque dentro de la unidad de corta 1 del plan de manejo forestal.

#crop 10m bands
b2c<-crop(b2,e)
b3c<-crop(b3,e)
b4c<-crop(b4,e)
b8c<-crop(b8,e)

El análisis sobre el corte de la imagen permite evidenciar mayor cantidad de elementos en la imagen. Adicionalmente, el sesgo de los histogramas es menos evidente para todas las bandas con el corte al área de estudio.

SentinelFC20 <- c(b8c, b4c, b3c)
plotRGB(SentinelFC20, axes=TRUE, stretch="lin") #false color

par(mfrow =c(2,2)) #Plot in an arrangement 2x2
    plot(b2c, main="BLUE",col=gray(0:100/100))
    plot(b3c, main="GREEN",col=gray(0:100/100))
    plot(b4c, main="RED",col=gray(0:100/100))
    plot(b8c, main="NIR",col=gray(0:100/100))

boac10m <- c(b2c,b3c,b4c,b8c)
names(boac10m) <- c('Blue', 'Green', 'Red','NIR') #rename bands

par(mfrow=c(2, 2))
hist(boac10m, 1, maxpixels=10000000, plot=TRUE, ylab="Frequency", col="darkblue", xlab="BOA reflectance",breaks=100 )
hist(boac10m, 2, maxpixels=10000000, plot=TRUE, ylab="Frequency", col="green",xlab="BOA reflectance" ,breaks=100)
hist(boac10m, 3, maxpixels=10000000, plot=TRUE, ylab="Frequency", col="red", xlab="BOA reflectance",breaks=100 )
hist(boac10m, 4, maxpixels=10000000, plot=TRUE, ylab="Frequency", col="yellow", xlab="BOA reflectance",breaks=100)

3.2 ÍNDICES ESPECTRALES

Los indices de vegetación que fueron obtenidos para lograr identificar relaciones entre ellas y la variable dependiente. Para ello se crearon el EVI, SAVI y NDWI.

El indice EVI permite visualizar mayores diferencias en la imagen con respecto a SAVI, el cual muestra una superficie demasiado homogénea. Por otra el NDWI permite ver con mayor facilidad los cuerpos de agua en el área de estudio.

EVI <-((2.5*(b8c - b4c))/(b8c + (6*b4c)-7.5*b2c))
plot(EVI, col=rev(terrain.colors(50)), main= "EVI resolución 10m")

SAVINUM <- (b8c - b4c)
SAVIDEN <- (b8c+b4c+0.428)
SAVI <- (SAVINUM/SAVIDEN)*1.428
plot((SAVI), col=rev(terrain.colors(50)), main= "SAVI resolución 10m")

NDWINUM <- (b3c - b8c)
NDWIDEN <- (b3c+b8c)
NDWI <- (NDWINUM/NDWIDEN)
plot((NDWI), col=blues9, main= "NDWI resolución 10m")

3.3 REGRESION USANDO RANDOM FOREST

Teniendo en cuenta que la variable dependiente (biomasa aérea), es numerica, la aplicación del algoritmo Random Forest se hace por medio de una regresión la cual tendrá como variables independientes los índices espectrales y las bandas de la imágen Sentinel 2.l

bandsc <- c(b2c,b3c,b4c,b8c,EVI,SAVI,NDWI)
names(bandsc) <- c('Blue', 'Green', 'Red','NIR','EVI','SAVI','NDWI') #rename bands
bandsn=c('Blue', 'Green', 'Red','NIR','EVI','SAVI','NDWI')

#Datos previamente preparados con el stack
x = read_stars("E:/ESTUDIO/UN/MAESTRIA/PERCEPCION_REMOTA_2_AVANZADA/INFORME_2/BANDS_COMP.tif", RasterIO = list(bandsn))

(x.spl = split(x, "band"))

## stars object with 2 dimensions and 7 attributes
## attribute(s):
##             Min.      1st Qu.       Median         Mean      3rd Qu.
## X1   160.0000000  251.0000000  271.0000000  303.8379481  325.0000000
## X2   255.0000000  416.0000000  455.0000000  503.1587991  553.0000000
## X3   135.0000000  227.0000000  251.0000000  324.9421833  339.0000000
## X4  1364.0000000 2667.0000000 2919.0000000 2971.4979211 3230.0000000
## X5     0.6139076    2.5183206    2.7314382    2.5596199    2.8358209
## X6     0.3997381    1.1329274    1.1996274    1.1456220    1.2290132
## X7    -0.8280740   -0.7532207   -0.7319893   -0.7092769   -0.6896552
##             Max.
## X1   907.0000000
## X2  1144.0000000
## X3  1422.0000000
## X4  5068.0000000
## X5     3.7173717
## X6     1.3018748
## X7    -0.3738369
## dimension(s):
##   from  to offset delta                refsys point values x/y
## x    1 319 752050    10 WGS_1984_UTM_Zone_18N FALSE   NULL [x]
## y    1 239 204820   -10 WGS_1984_UTM_Zone_18N FALSE   NULL [y]

st_extract(x, censo_st) %>% st_as_sf() -> datasample

datasample

## Simple feature collection with 316 features and 7 fields
## Geometry type: POINT
## Dimension:     XY
## Bounding box:  xmin: 752184.3 ymin: 202803.9 xmax: 754964.4 ymax: 204724.6
## Projected CRS: WGS 84 / UTM zone 18N
## First 10 features:
##    BANDS_COMP.tif.V1 BANDS_COMP.tif.V2 BANDS_COMP.tif.V3 BANDS_COMP.tif.V4
## 1                252               436               236              3373
## 2                245               443               235              3176
## 3                240               393               199              2397
## 4                263               409               236              3050
## 5                270               454               253              2843
## 6                248               381               216              2626
## 7                246               435               225              2775
## 8                259               412               236              3074
## 9                281               487               268              3227
## 10               260               405               231              2525
##    BANDS_COMP.tif.V5 BANDS_COMP.tif.V6 BANDS_COMP.tif.V7
## 1           2.705243          1.241093        -0.7710685
## 2           2.675096          1.231082        -0.7551810
## 3           3.068118          1.208870        -0.7182795
## 4           2.821336          1.222723        -0.7635155
## 5           2.771832          1.194447        -0.7245981
## 6           2.921921          1.210754        -0.7465913
## 7           2.796053          1.213627        -0.7289720
## 8           2.785084          1.224211        -0.7636259
## 9           2.712191          1.208851        -0.7377490
## 10          2.924528          1.188434        -0.7235495
##                     geometry
## 1  POINT (753194.9 202803.9)
## 2  POINT (753104.8 202903.9)
## 3    POINT (753244.8 202904)
## 4    POINT (753254.8 202924)
## 5    POINT (753274.8 202954)
## 6    POINT (753204.8 202964)
## 7  POINT (753084.8 203013.9)
## 8  POINT (753144.8 203033.9)
## 9    POINT (753194.8 203034)
## 10   POINT (753284.8 203054)

class(censo_st)

## [1] "sf"         "data.frame"

class(datasample)

## [1] "sf"         "data.frame"

datasample

## Simple feature collection with 316 features and 7 fields
## Geometry type: POINT
## Dimension:     XY
## Bounding box:  xmin: 752184.3 ymin: 202803.9 xmax: 754964.4 ymax: 204724.6
## Projected CRS: WGS 84 / UTM zone 18N
## First 10 features:
##    BANDS_COMP.tif.V1 BANDS_COMP.tif.V2 BANDS_COMP.tif.V3 BANDS_COMP.tif.V4
## 1                252               436               236              3373
## 2                245               443               235              3176
## 3                240               393               199              2397
## 4                263               409               236              3050
## 5                270               454               253              2843
## 6                248               381               216              2626
## 7                246               435               225              2775
## 8                259               412               236              3074
## 9                281               487               268              3227
## 10               260               405               231              2525
##    BANDS_COMP.tif.V5 BANDS_COMP.tif.V6 BANDS_COMP.tif.V7
## 1           2.705243          1.241093        -0.7710685
## 2           2.675096          1.231082        -0.7551810
## 3           3.068118          1.208870        -0.7182795
## 4           2.821336          1.222723        -0.7635155
## 5           2.771832          1.194447        -0.7245981
## 6           2.921921          1.210754        -0.7465913
## 7           2.796053          1.213627        -0.7289720
## 8           2.785084          1.224211        -0.7636259
## 9           2.712191          1.208851        -0.7377490
## 10          2.924528          1.188434        -0.7235495
##                     geometry
## 1  POINT (753194.9 202803.9)
## 2  POINT (753104.8 202903.9)
## 3    POINT (753244.8 202904)
## 4    POINT (753254.8 202924)
## 5    POINT (753274.8 202954)
## 6    POINT (753204.8 202964)
## 7  POINT (753084.8 203013.9)
## 8  POINT (753144.8 203033.9)
## 9    POINT (753194.8 203034)
## 10   POINT (753284.8 203054)

names(datasample)

## [1] "BANDS_COMP.tif.V1" "BANDS_COMP.tif.V2" "BANDS_COMP.tif.V3"
## [4] "BANDS_COMP.tif.V4" "BANDS_COMP.tif.V5" "BANDS_COMP.tif.V6"
## [7] "BANDS_COMP.tif.V7" "geometry"

datasample=rename(datasample,B2=BANDS_COMP.tif.V1,B3=BANDS_COMP.tif.V2,B4=BANDS_COMP.tif.V3,B8=BANDS_COMP.tif.V4,EVI=BANDS_COMP.tif.V5,SAVI=BANDS_COMP.tif.V6,NDWI=BANDS_COMP.tif.V7)

cbind(datasample,censo_st$BA_KG_CL2)

## Simple feature collection with 316 features and 8 fields
## Geometry type: POINT
## Dimension:     XY
## Bounding box:  xmin: 752184.3 ymin: 202803.9 xmax: 754964.4 ymax: 204724.6
## Projected CRS: WGS 84 / UTM zone 18N
## First 10 features:
##     B2  B3  B4   B8      EVI     SAVI       NDWI censo_st.BA_KG_CL2
## 1  252 436 236 3373 2.705243 1.241093 -0.7710685           4501.620
## 2  245 443 235 3176 2.675096 1.231082 -0.7551810           4841.939
## 3  240 393 199 2397 3.068118 1.208870 -0.7182795           4119.656
## 4  263 409 236 3050 2.821336 1.222723 -0.7635155           3424.257
## 5  270 454 253 2843 2.771832 1.194447 -0.7245981           5703.619
## 6  248 381 216 2626 2.921921 1.210754 -0.7465913           1248.175
## 7  246 435 225 2775 2.796053 1.213627 -0.7289720           5597.145
## 8  259 412 236 3074 2.785084 1.224211 -0.7636259           2161.010
## 9  281 487 268 3227 2.712191 1.208851 -0.7377490           2318.499
## 10 260 405 231 2525 2.924528 1.188434 -0.7235495           1134.417
##                     geometry
## 1  POINT (753194.9 202803.9)
## 2  POINT (753104.8 202903.9)
## 3    POINT (753244.8 202904)
## 4    POINT (753254.8 202924)
## 5    POINT (753274.8 202954)
## 6    POINT (753204.8 202964)
## 7  POINT (753084.8 203013.9)
## 8  POINT (753144.8 203033.9)
## 9    POINT (753194.8 203034)
## 10   POINT (753284.8 203054)

plot(datasample)

datasample$BA = censo_st$BA_KG_CL2 # no need for join, since the order did not change
datasample

## Simple feature collection with 316 features and 8 fields
## Geometry type: POINT
## Dimension:     XY
## Bounding box:  xmin: 752184.3 ymin: 202803.9 xmax: 754964.4 ymax: 204724.6
## Projected CRS: WGS 84 / UTM zone 18N
## First 10 features:
##     B2  B3  B4   B8      EVI     SAVI       NDWI                  geometry
## 1  252 436 236 3373 2.705243 1.241093 -0.7710685 POINT (753194.9 202803.9)
## 2  245 443 235 3176 2.675096 1.231082 -0.7551810 POINT (753104.8 202903.9)
## 3  240 393 199 2397 3.068118 1.208870 -0.7182795   POINT (753244.8 202904)
## 4  263 409 236 3050 2.821336 1.222723 -0.7635155   POINT (753254.8 202924)
## 5  270 454 253 2843 2.771832 1.194447 -0.7245981   POINT (753274.8 202954)
## 6  248 381 216 2626 2.921921 1.210754 -0.7465913   POINT (753204.8 202964)
## 7  246 435 225 2775 2.796053 1.213627 -0.7289720 POINT (753084.8 203013.9)
## 8  259 412 236 3074 2.785084 1.224211 -0.7636259 POINT (753144.8 203033.9)
## 9  281 487 268 3227 2.712191 1.208851 -0.7377490   POINT (753194.8 203034)
## 10 260 405 231 2525 2.924528 1.188434 -0.7235495   POINT (753284.8 203054)
##          BA
## 1  4501.620
## 2  4841.939
## 3  4119.656
## 4  3424.257
## 5  5703.619
## 6  1248.175
## 7  5597.145
## 8  2161.010
## 9  2318.499
## 10 1134.417

(datasample = as.data.frame(datasample))

##      B2  B3  B4   B8      EVI      SAVI       NDWI                  geometry
## 1   252 436 236 3373 2.705243 1.2410930 -0.7710685 POINT (753194.9 202803.9)
## 2   245 443 235 3176 2.675096 1.2310821 -0.7551810 POINT (753104.8 202903.9)
## 3   240 393 199 2397 3.068118 1.2088701 -0.7182795   POINT (753244.8 202904)
## 4   263 409 236 3050 2.821336 1.2227232 -0.7635155   POINT (753254.8 202924)
## 5   270 454 253 2843 2.771832 1.1944473 -0.7245981   POINT (753274.8 202954)
## 6   248 381 216 2626 2.921921 1.2107537 -0.7465913   POINT (753204.8 202964)
## 7   246 435 225 2775 2.796053 1.2136269 -0.7289720 POINT (753084.8 203013.9)
## 8   259 412 236 3074 2.785084 1.2242115 -0.7636259 POINT (753144.8 203033.9)
## 9   281 487 268 3227 2.712191 1.2088511 -0.7377490   POINT (753194.8 203034)
## 10  260 405 231 2525 2.924528 1.1884338 -0.7235495   POINT (753284.8 203054)
## 11  263 439 262 2988 2.633816 1.1976048 -0.7437993   POINT (753254.8 203064)
## 12  271 461 239 2714 2.924840 1.1966772 -0.7096063 POINT (753094.7 203073.9)
## 13  228 364 218 2676 2.702287 1.2126831 -0.7605263 POINT (752944.7 203083.8)
## 14  318 491 267 3119 3.052226 1.2026407 -0.7279778 POINT (753134.7 203083.9)
## 15  280 435 271 2596 2.739161 1.1578670 -0.7129660   POINT (753184.7 203094)
## 16  356 594 398 2976 2.392353 1.0909654 -0.6672269   POINT (753274.7 203094)
## 17  254 390 260 2339 2.606570 1.1421020 -0.7141810 POINT (752964.7 203103.9)
## 18  267 502 287 3149 2.494335 1.1892977 -0.7250068   POINT (753314.7 203134)
## 19  294 423 287 2552 2.736829 1.1391097 -0.7156302 POINT (752974.7 203163.9)
## 20  221 340 187 2468 2.950841 1.2266452 -0.7578347 POINT (753344.7 203174.1)
## 21  304 460 261 2851 3.029948 1.1883070 -0.7221383 POINT (753354.7 203184.1)
## 22  282 436 278 2375 2.719139 1.1285461 -0.6897901   POINT (753194.7 203194)
## 23  269 482 263 3149 2.662853 1.2077055 -0.7345084   POINT (753214.7 203204)
## 24  261 442 213 3115 2.978854 1.2450490 -0.7514760   POINT (753264.7 203224)
## 25  275 461 243 2618 2.948845 1.1852474 -0.7005521 POINT (753324.7 203224.1)
## 26  201 316 182 2700 2.755526 1.2474567 -0.7904509   POINT (753254.7 203234)
## 27  254 456 240 3112 2.712505 1.2233570 -0.7443946   POINT (753294.7 203234)
## 28  263 455 241 3437 2.745233 1.2407169 -0.7661871 POINT (752404.6 203243.6)
## 29  245 360 217 2547 2.895849 1.2035908 -0.7523220 POINT (752444.6 203253.6)
## 30  245 431 235 3120 2.678737 1.2277957 -0.7572515 POINT (752954.6 203253.9)
## 31  263 438 226 3275 2.867218 1.2434846 -0.7640722   POINT (753284.7 203254)
## 32  252 419 217 2687 2.941877 1.2144078 -0.7301996 POINT (752544.6 203263.7)
## 33  278 394 231 3351 2.941176 1.2436705 -0.7895861 POINT (752864.6 203263.8)
## 34  255 432 196 2950 3.110459 1.2498974 -0.7445298   POINT (753114.6 203264)
## 35  270 418 250 2641 2.824905 1.1808518 -0.7267081 POINT (752404.6 203273.6)
## 36  256 404 211 3229 2.930097 1.2526650 -0.7775943 POINT (752854.6 203273.8)
## 37  219 406 207 3185 2.673730 1.2535517 -0.7738792 POINT (752804.6 203283.8)
## 38  250 446 253 2822 2.605477 1.1928525 -0.7270502 POINT (752884.6 203303.8)
## 39  305 500 287 2806 2.810756 1.1628304 -0.6975197 POINT (752894.6 203303.8)
## 40  259 412 238 2997 2.778449 1.2177221 -0.7582869 POINT (752944.6 203303.9)
## 41  256 436 260 2699 2.606883 1.1768801 -0.7218501   POINT (753264.6 203304)
## 42  264 477 242 3319 2.756181 1.2337624 -0.7486828 POINT (752884.6 203313.8)
## 43  247 431 229 3276 2.722967 1.2412510 -0.7674670 POINT (752944.6 203313.9)
## 44  321 457 301 2932 2.822356 1.1619458 -0.7303039 POINT (752954.6 203323.9)
## 45  262 429 235 2963 2.832226 1.2179683 -0.7470519 POINT (753004.6 203323.9)
## 46  238 406 216 3242 2.747911 1.2494485 -0.7774123 POINT (752814.6 203343.8)
## 47  252 424 226 3299 2.778481 1.2447407 -0.7722267 POINT (752934.6 203343.9)
## 48  260 379 246 2640 2.763158 1.1843815 -0.7489235 POINT (752414.5 203353.6)
## 49  284 435 267 2580 2.817982 1.1599816 -0.7114428 POINT (752424.5 203353.6)
## 50  252 444 251 2987 2.627737 1.2064520 -0.7411833 POINT (752874.6 203353.8)
## 51  266 405 247 2698 2.804348 1.1882918 -0.7389623 POINT (752414.5 203363.6)
## 52  285 496 267 3174 2.754406 1.2062423 -0.7297003   POINT (753264.6 203364)
## 53  248 462 220 3162 2.805111 1.2420592 -0.7450331 POINT (752354.5 203383.6)
## 54  265 404 309 2356 2.302587 1.0966779 -0.7072464   POINT (753174.6 203394)
## 55  243 399 203 2831 2.950820 1.2367352 -0.7529412 POINT (754454.7 203394.7)
## 56  253 449 226 3110 2.807086 1.2343596 -0.7476819 POINT (752474.5 203403.6)
## 57  239 410 194 3261 2.912631 1.2674772 -0.7766276 POINT (752344.5 203413.6)
## 58  257 406 217 2973 2.935037 1.2335548 -0.7596922 POINT (752984.5 203413.9)
## 59  279 424 273 2666 2.705178 1.1625404 -0.7255663 POINT (753384.6 203414.1)
## 60  425 626 518 2643 2.072362 0.9598510 -0.6170083 POINT (754494.7 203424.7)
## 61  240 440 210 2895 2.850318 1.2346704 -0.7361319 POINT (752334.5 203433.6)
## 62  259 412 231 2909 2.845909 1.2177271 -0.7518820 POINT (752354.5 203433.6)
## 63  230 366 212 2626 2.777267 1.2144723 -0.7553476 POINT (752914.5 203433.9)
## 64  235 377 191 3275 2.900132 1.2704582 -0.7935378 POINT (752874.5 203453.9)
## 65  269 450 248 2741 2.818223 1.1908646 -0.7179568 POINT (752984.5 203453.9)
## 66  244 343 215 3007 2.829347 1.2372583 -0.7952239 POINT (752684.5 203463.8)
## 67  220 339 191 2695 2.857143 1.2388017 -0.7765326 POINT (752894.5 203463.9)
## 68  225 370 198 2608 2.857482 1.2262847 -0.7515111 POINT (753344.6 203464.1)
## 69  237 375 234 2517 2.662701 1.1848843 -0.7406639 POINT (753364.6 203464.1)
## 70  229 377 206 2364 2.865870 1.1988758 -0.7249179 POINT (753834.6 203464.4)
## 71  248 406 225 2665 2.830626 1.2054685 -0.7355910 POINT (752804.5 203483.8)
## 72  299 480 255 3045 2.990354 1.2071525 -0.7276596 POINT (753294.5 203484.1)
## 73  288 413 264 2756 2.857798 1.1781695 -0.7393500 POINT (753914.6 203484.4)
## 74  231 387 239 2340 2.572863 1.1631370 -0.7161716 POINT (753394.6 203494.1)
## 75  242 389 222 2577 2.811604 1.2012954 -0.7376938 POINT (753814.6 203494.3)
## 76  266 412 255 2854 2.719757 1.1935867 -0.7477036 POINT (752954.5 203503.9)
## 77  291 487 283 3220 2.684153 1.1971235 -0.7372538 POINT (753674.6 203514.3)
## 78  287 426 241 3257 2.956283 1.2310809 -0.7686669 POINT (752864.5 203523.9)
## 79  275 463 246 2983 2.855206 1.2102565 -0.7312827 POINT (752284.4 203533.6)
## 80  298 473 317 2599 2.517652 1.1173587 -0.6920573 POINT (753024.5 203533.9)
## 81  285 433 258 2915 2.856375 1.1956143 -0.7413381 POINT (753344.5 203544.1)
## 82  252 411 236 2813 2.754382 1.2067692 -0.7450372 POINT (753564.5 203544.2)
## 83  232 367 201 2522 2.918763 1.2169912 -0.7459329   POINT (753164.5 203554)
## 84  255 424 218 3496 2.834169 1.2602166 -0.7836735 POINT (752744.4 203563.8)
## 85  262 422 235 2648 2.882226 1.1950234 -0.7250814 POINT (753774.6 203564.3)
## 86  266 425 255 2347 2.778959 1.1479188 -0.6933622 POINT (752704.4 203583.8)
## 87  265 414 238 2820 2.855563 1.2055527 -0.7439703 POINT (753274.5 203584.1)
## 88  249 453 228 3581 2.720266 1.2569036 -0.7754090 POINT (754464.6 203584.7)
## 89  264 412 215 2633 3.111168 1.2122139 -0.7293925 POINT (752714.4 203593.8)
## 90  296 461 245 3204 3.014466 1.2249718 -0.7484311 POINT (753604.5 203594.2)
## 91  249 446 212 3839 2.795591 1.2784026 -0.7918320 POINT (752404.4 203603.6)
## 92  258 453 258 2841 2.631418 1.1900660 -0.7249545 POINT (753654.5 203604.3)
## 93  303 453 337 2380 2.398450 1.0735902 -0.6801977 POINT (753974.6 203604.4)
## 94  254 422 228 3741 2.741105 1.2638003 -0.7972616 POINT (752404.4 203613.6)
## 95  272 431 259 2609 2.767310 1.1699091 -0.7164474 POINT (752594.4 203613.7)
## 96  243 412 206 2824 2.925140 1.2336555 -0.7453647 POINT (752764.4 203613.8)
## 97  280 421 267 2524 2.785044 1.1546048 -0.7140917 POINT (752264.4 203623.6)
## 98  270 517 269 3454 2.616661 1.2215034 -0.7396122 POINT (753774.5 203634.3)
## 99  306 485 303 2721 2.693850 1.1416718 -0.6974423 POINT (753864.5 203634.4)
## 100 267 447 254 2731 2.749168 1.1848071 -0.7186910 POINT (753874.5 203634.4)
## 101 276 507 239 3156 2.893849 1.2267897 -0.7231777 POINT (754504.6 203634.7)
## 102 260 437 215 3533 2.887226 1.2640243 -0.7798489 POINT (752404.4 203653.6)
## 103 271 424 254 2639 2.798639 1.1770744 -0.7231472 POINT (753284.5 203654.1)
## 104 241 392 222 2774 2.775723 1.2162001 -0.7523689 POINT (753894.5 203654.4)
## 105 251 389 241 2664 2.719416 1.1908896 -0.7451687 POINT (753904.5 203654.4)
## 106 229 362 184 2833 2.983780 1.2536411 -0.7733960 POINT (752294.3 203663.6)
## 107 236 434 226 2788 2.697978 1.2136750 -0.7306021 POINT (752964.4 203663.9)
## 108 318 486 347 2797 2.455894 1.1126348 -0.7039293 POINT (753574.5 203664.2)
## 109 325 536 338 3162 2.564941 1.1520511 -0.7101136 POINT (754484.6 203664.7)
## 110 258 442 230 2820 2.858720 1.2124593 -0.7290006 POINT (752924.4 203673.9)
## 111 243 362 212 2061 3.060245 1.1614056 -0.7011968 POINT (753224.4 203674.1)
## 112 243 408 231 2478 2.751653 1.1842780 -0.7172557 POINT (753294.4 203674.1)
## 113 295 507 309 2907 2.548558 1.1534361 -0.7029877 POINT (753494.5 203674.2)
## 114 271 415 266 2625 2.694768 1.1650479 -0.7269737 POINT (753914.5 203674.4)
## 115 270 443 230 3050 2.931393 1.2275715 -0.7463499 POINT (753004.4 203683.9)
## 116 250 420 236 2730 2.745486 1.2005793 -0.7333333 POINT (753314.4 203684.1)
## 117 274 455 283 2896 2.572863 1.1735960 -0.7284393 POINT (753754.5 203684.3)
## 118 279 406 245 2465 3.012212 1.1696160 -0.7171717 POINT (752184.3 203693.5)
## 119 274 430 228 3060 2.983565 1.2297962 -0.7535816 POINT (754474.6 203694.7)
## 120 233 397 206 3913 2.724533 1.2850318 -0.8157772 POINT (752384.3 203703.6)
## 121 238 386 225 2889 2.713936 1.2214737 -0.7642748 POINT (752704.4 203703.8)
## 122 267 438 254 2784 2.743440 1.1890491 -0.7281192 POINT (753574.5 203714.2)
## 123 263 411 233 2799 2.883794 1.2083545 -0.7439252 POINT (752724.4 203723.8)
## 124 316 495 364 2592 2.315046 1.0761582 -0.6793003   POINT (753044.4 203724)
## 125 226 373 201 2993 2.787540 1.2481033 -0.7783719 POINT (753264.4 203724.1)
## 126 263 420 246 2584 2.800000 1.1795615 -0.7203729 POINT (752784.4 203733.8)
## 127 265 390 217 2684 3.086065 1.2141869 -0.7462590   POINT (753004.4 203734)
## 128 259 454 279 2976 2.490305 1.1830444 -0.7352770 POINT (753334.4 203734.1)
## 129 262 424 250 2893 2.721376 1.2006650 -0.7443473 POINT (752264.3 203743.6)
## 130 215 329 188 2303 2.907616 1.2122445 -0.7500000 POINT (752324.3 203743.6)
## 131 300 441 286 2546 2.808151 1.1394041 -0.7047204   POINT (753004.4 203744)
## 132 279 490 272 3116 2.677462 1.1985593 -0.7282307 POINT (754544.6 203744.8)
## 133 281 420 248 3194 2.860750 1.2220700 -0.7675706 POINT (752994.4 203753.9)
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## 134 13356.9700
## 135  2733.5023
## 136  2360.8720
## 137  3289.9524
## 138  1535.5740
## 139  9305.0593
## 140   445.7899
## 141  3005.8943
## 142   760.6294
## 143  2894.3493
## 144  3675.2393
## 145  2664.0083
## 146   961.8129
## 147 14349.7876
## 148  3639.8529
## 149  3876.3722
## 150   994.4146
## 151  1614.2396
## 152  2834.3202
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## 154  2212.3933
## 155   325.9574
## 156   866.2425
## 157  4163.6910
## 158  5849.4201
## 159  2292.1962
## 160  3764.3400
## 161  2655.1219
## 162   737.8567
## 163  1118.6338
## 164  1938.0831
## 165  4033.5201
## 166   443.0315
## 167  2905.7114
## 168  2749.2294
## 169  3248.6994
## 170  5274.3971
## 171  2160.4039
## 172  2705.6670
## 173  9269.2749
## 174 11901.4778
## 175   879.6138
## 176 10311.7303
## 177  1522.6306
## 178  1014.1920
## 179   974.7489
## 180  3034.5201
## 181  3173.4372
## 182   755.5188
## 183  3017.9359
## 184  4065.1585
## 185  8079.6946
## 186  3006.9818
## 187  6127.2347
## 188  1229.7229
## 189  2621.6946
## 190  2798.7231
## 191  2547.9649
## 192 12273.6459
## 193   921.3183
## 194  2966.1151
## 195  2365.2026
## 196  2198.5227
## 197  6562.0846
## 198  2722.2631
## 199  1075.8396
## 200   820.0357
## 201  2643.8456
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## 203  6673.8428
## 204  3321.9128
## 205  2961.6426
## 206 11788.6721
## 207   665.2819
## 208   663.3866
## 209  1915.4839
## 210  1161.1671
## 211  3304.9824
## 212  3995.0021
## 213  6864.7417
## 214   329.2807
## 215  4709.1538
## 216   749.4275
## 217  2559.0108
## 218 12516.6412
## 219  2112.3679
## 220  2336.8591
## 221   871.9550
## 222  6197.6635
## 223  3955.7184
## 224  2542.6072
## 225   858.9281
## 226  1762.8147
## 227  1985.3408
## 228 17066.9211
## 229  9624.2174
## 230   851.3327
## 231   921.1481
## 232 23094.7291
## 233   970.3911
## 234  2566.6497
## 235  1514.5650
## 236   808.4666
## 237  2524.6490
## 238  1344.3844
## 239  1043.8237
## 240  2451.5011
## 241  7084.6965
## 242   722.4257
## 243  1270.7759
## 244   470.4342
## 245  1783.6000
## 246   778.6155
## 247  2183.7887
## 248  4382.1974
## 249  1665.7019
## 250  4472.6914
## 251  2024.4881
## 252   561.2806
## 253  1398.7354
## 254  3675.2393
## 255   768.6404
## 256   674.1970
## 257  1484.3963
## 258  4830.4703
## 259  3388.7845
## 260  6871.3674
## 261 27486.9998
## 262  2373.6471
## 263  2282.0362
## 264  7002.2081
## 265  2615.9775
## 266  5013.2299
## 267   343.9435
## 268  2615.8996
## 269  1155.5617
## 270  1745.2707
## 271  8519.8597
## 272  3942.3537
## 273  2599.3845
## 274  1054.7122
## 275   765.8640
## 276  1681.8744
## 277  1953.7549
## 278  1016.3486
## 279   898.3130
## 280  3643.7179
## 281  1584.6627
## 282 16197.5598
## 283   910.0364
## 284  1315.7686
## 285   923.8850
## 286   825.1895
## 287 24731.7726
## 288  1057.7983
## 289  1131.0940
## 290  2315.5091
## 291 12018.4967
## 292  3825.8796
## 293   552.6132
## 294  1012.8931
## 295   306.3952
## 296  3248.1892
## 297  8159.3276
## 298  2734.7736
## 299  3213.8994
## 300   325.9574
## 301   353.2873
## 302   584.4932
## 303  1037.7343
## 304  1770.0547
## 305  4070.6383
## 306   894.6439
## 307  7330.5474
## 308  8802.2383
## 309  1948.6141
## 310  1644.9115
## 311  2516.1042
## 312  3293.3623
## 313  7416.3767
## 314  2446.7283
## 315  2930.6781
## 316  1340.9834

datasample %>% drop_na() -> nsample

nsample

##      B2  B3  B4   B8      EVI      SAVI       NDWI                  geometry
## 1   252 436 236 3373 2.705243 1.2410930 -0.7710685 POINT (753194.9 202803.9)
## 2   245 443 235 3176 2.675096 1.2310821 -0.7551810 POINT (753104.8 202903.9)
## 3   240 393 199 2397 3.068118 1.2088701 -0.7182795   POINT (753244.8 202904)
## 4   263 409 236 3050 2.821336 1.2227232 -0.7635155   POINT (753254.8 202924)
## 5   270 454 253 2843 2.771832 1.1944473 -0.7245981   POINT (753274.8 202954)
## 6   248 381 216 2626 2.921921 1.2107537 -0.7465913   POINT (753204.8 202964)
## 7   246 435 225 2775 2.796053 1.2136269 -0.7289720 POINT (753084.8 203013.9)
## 8   259 412 236 3074 2.785084 1.2242115 -0.7636259 POINT (753144.8 203033.9)
## 9   281 487 268 3227 2.712191 1.2088511 -0.7377490   POINT (753194.8 203034)
## 10  260 405 231 2525 2.924528 1.1884338 -0.7235495   POINT (753284.8 203054)
## 11  263 439 262 2988 2.633816 1.1976048 -0.7437993   POINT (753254.8 203064)
## 12  271 461 239 2714 2.924840 1.1966772 -0.7096063 POINT (753094.7 203073.9)
## 13  228 364 218 2676 2.702287 1.2126831 -0.7605263 POINT (752944.7 203083.8)
## 14  318 491 267 3119 3.052226 1.2026407 -0.7279778 POINT (753134.7 203083.9)
## 15  280 435 271 2596 2.739161 1.1578670 -0.7129660   POINT (753184.7 203094)
## 16  356 594 398 2976 2.392353 1.0909654 -0.6672269   POINT (753274.7 203094)
## 17  254 390 260 2339 2.606570 1.1421020 -0.7141810 POINT (752964.7 203103.9)
## 18  267 502 287 3149 2.494335 1.1892977 -0.7250068   POINT (753314.7 203134)
## 19  294 423 287 2552 2.736829 1.1391097 -0.7156302 POINT (752974.7 203163.9)
## 20  221 340 187 2468 2.950841 1.2266452 -0.7578347 POINT (753344.7 203174.1)
## 21  304 460 261 2851 3.029948 1.1883070 -0.7221383 POINT (753354.7 203184.1)
## 22  282 436 278 2375 2.719139 1.1285461 -0.6897901   POINT (753194.7 203194)
## 23  269 482 263 3149 2.662853 1.2077055 -0.7345084   POINT (753214.7 203204)
## 24  261 442 213 3115 2.978854 1.2450490 -0.7514760   POINT (753264.7 203224)
## 25  275 461 243 2618 2.948845 1.1852474 -0.7005521 POINT (753324.7 203224.1)
## 26  201 316 182 2700 2.755526 1.2474567 -0.7904509   POINT (753254.7 203234)
## 27  254 456 240 3112 2.712505 1.2233570 -0.7443946   POINT (753294.7 203234)
## 28  263 455 241 3437 2.745233 1.2407169 -0.7661871 POINT (752404.6 203243.6)
## 29  245 360 217 2547 2.895849 1.2035908 -0.7523220 POINT (752444.6 203253.6)
## 30  245 431 235 3120 2.678737 1.2277957 -0.7572515 POINT (752954.6 203253.9)
## 31  263 438 226 3275 2.867218 1.2434846 -0.7640722   POINT (753284.7 203254)
## 32  252 419 217 2687 2.941877 1.2144078 -0.7301996 POINT (752544.6 203263.7)
## 33  278 394 231 3351 2.941176 1.2436705 -0.7895861 POINT (752864.6 203263.8)
## 34  255 432 196 2950 3.110459 1.2498974 -0.7445298   POINT (753114.6 203264)
## 35  270 418 250 2641 2.824905 1.1808518 -0.7267081 POINT (752404.6 203273.6)
## 36  256 404 211 3229 2.930097 1.2526650 -0.7775943 POINT (752854.6 203273.8)
## 37  219 406 207 3185 2.673730 1.2535517 -0.7738792 POINT (752804.6 203283.8)
## 38  250 446 253 2822 2.605477 1.1928525 -0.7270502 POINT (752884.6 203303.8)
## 39  305 500 287 2806 2.810756 1.1628304 -0.6975197 POINT (752894.6 203303.8)
## 40  259 412 238 2997 2.778449 1.2177221 -0.7582869 POINT (752944.6 203303.9)
## 41  256 436 260 2699 2.606883 1.1768801 -0.7218501   POINT (753264.6 203304)
## 42  264 477 242 3319 2.756181 1.2337624 -0.7486828 POINT (752884.6 203313.8)
## 43  247 431 229 3276 2.722967 1.2412510 -0.7674670 POINT (752944.6 203313.9)
## 44  321 457 301 2932 2.822356 1.1619458 -0.7303039 POINT (752954.6 203323.9)
## 45  262 429 235 2963 2.832226 1.2179683 -0.7470519 POINT (753004.6 203323.9)
## 46  238 406 216 3242 2.747911 1.2494485 -0.7774123 POINT (752814.6 203343.8)
## 47  252 424 226 3299 2.778481 1.2447407 -0.7722267 POINT (752934.6 203343.9)
## 48  260 379 246 2640 2.763158 1.1843815 -0.7489235 POINT (752414.5 203353.6)
## 49  284 435 267 2580 2.817982 1.1599816 -0.7114428 POINT (752424.5 203353.6)
## 50  252 444 251 2987 2.627737 1.2064520 -0.7411833 POINT (752874.6 203353.8)
## 51  266 405 247 2698 2.804348 1.1882918 -0.7389623 POINT (752414.5 203363.6)
## 52  285 496 267 3174 2.754406 1.2062423 -0.7297003   POINT (753264.6 203364)
## 53  248 462 220 3162 2.805111 1.2420592 -0.7450331 POINT (752354.5 203383.6)
## 54  265 404 309 2356 2.302587 1.0966779 -0.7072464   POINT (753174.6 203394)
## 55  243 399 203 2831 2.950820 1.2367352 -0.7529412 POINT (754454.7 203394.7)
## 56  253 449 226 3110 2.807086 1.2343596 -0.7476819 POINT (752474.5 203403.6)
## 57  239 410 194 3261 2.912631 1.2674772 -0.7766276 POINT (752344.5 203413.6)
## 58  257 406 217 2973 2.935037 1.2335548 -0.7596922 POINT (752984.5 203413.9)
## 59  279 424 273 2666 2.705178 1.1625404 -0.7255663 POINT (753384.6 203414.1)
## 60  425 626 518 2643 2.072362 0.9598510 -0.6170083 POINT (754494.7 203424.7)
## 61  240 440 210 2895 2.850318 1.2346704 -0.7361319 POINT (752334.5 203433.6)
## 62  259 412 231 2909 2.845909 1.2177271 -0.7518820 POINT (752354.5 203433.6)
## 63  230 366 212 2626 2.777267 1.2144723 -0.7553476 POINT (752914.5 203433.9)
## 64  235 377 191 3275 2.900132 1.2704582 -0.7935378 POINT (752874.5 203453.9)
## 65  269 450 248 2741 2.818223 1.1908646 -0.7179568 POINT (752984.5 203453.9)
## 66  244 343 215 3007 2.829347 1.2372583 -0.7952239 POINT (752684.5 203463.8)
## 67  220 339 191 2695 2.857143 1.2388017 -0.7765326 POINT (752894.5 203463.9)
## 68  225 370 198 2608 2.857482 1.2262847 -0.7515111 POINT (753344.6 203464.1)
## 69  237 375 234 2517 2.662701 1.1848843 -0.7406639 POINT (753364.6 203464.1)
## 70  229 377 206 2364 2.865870 1.1988758 -0.7249179 POINT (753834.6 203464.4)
## 71  248 406 225 2665 2.830626 1.2054685 -0.7355910 POINT (752804.5 203483.8)
## 72  299 480 255 3045 2.990354 1.2071525 -0.7276596 POINT (753294.5 203484.1)
## 73  288 413 264 2756 2.857798 1.1781695 -0.7393500 POINT (753914.6 203484.4)
## 74  231 387 239 2340 2.572863 1.1631370 -0.7161716 POINT (753394.6 203494.1)
## 75  242 389 222 2577 2.811604 1.2012954 -0.7376938 POINT (753814.6 203494.3)
## 76  266 412 255 2854 2.719757 1.1935867 -0.7477036 POINT (752954.5 203503.9)
## 77  291 487 283 3220 2.684153 1.1971235 -0.7372538 POINT (753674.6 203514.3)
## 78  287 426 241 3257 2.956283 1.2310809 -0.7686669 POINT (752864.5 203523.9)
## 79  275 463 246 2983 2.855206 1.2102565 -0.7312827 POINT (752284.4 203533.6)
## 80  298 473 317 2599 2.517652 1.1173587 -0.6920573 POINT (753024.5 203533.9)
## 81  285 433 258 2915 2.856375 1.1956143 -0.7413381 POINT (753344.5 203544.1)
## 82  252 411 236 2813 2.754382 1.2067692 -0.7450372 POINT (753564.5 203544.2)
## 83  232 367 201 2522 2.918763 1.2169912 -0.7459329   POINT (753164.5 203554)
## 84  255 424 218 3496 2.834169 1.2602166 -0.7836735 POINT (752744.4 203563.8)
## 85  262 422 235 2648 2.882226 1.1950234 -0.7250814 POINT (753774.6 203564.3)
## 86  266 425 255 2347 2.778959 1.1479188 -0.6933622 POINT (752704.4 203583.8)
## 87  265 414 238 2820 2.855563 1.2055527 -0.7439703 POINT (753274.5 203584.1)
## 88  249 453 228 3581 2.720266 1.2569036 -0.7754090 POINT (754464.6 203584.7)
## 89  264 412 215 2633 3.111168 1.2122139 -0.7293925 POINT (752714.4 203593.8)
## 90  296 461 245 3204 3.014466 1.2249718 -0.7484311 POINT (753604.5 203594.2)
## 91  249 446 212 3839 2.795591 1.2784026 -0.7918320 POINT (752404.4 203603.6)
## 92  258 453 258 2841 2.631418 1.1900660 -0.7249545 POINT (753654.5 203604.3)
## 93  303 453 337 2380 2.398450 1.0735902 -0.6801977 POINT (753974.6 203604.4)
## 94  254 422 228 3741 2.741105 1.2638003 -0.7972616 POINT (752404.4 203613.6)
## 95  272 431 259 2609 2.767310 1.1699091 -0.7164474 POINT (752594.4 203613.7)
## 96  243 412 206 2824 2.925140 1.2336555 -0.7453647 POINT (752764.4 203613.8)
## 97  280 421 267 2524 2.785044 1.1546048 -0.7140917 POINT (752264.4 203623.6)
## 98  270 517 269 3454 2.616661 1.2215034 -0.7396122 POINT (753774.5 203634.3)
## 99  306 485 303 2721 2.693850 1.1416718 -0.6974423 POINT (753864.5 203634.4)
## 100 267 447 254 2731 2.749168 1.1848071 -0.7186910 POINT (753874.5 203634.4)
## 101 276 507 239 3156 2.893849 1.2267897 -0.7231777 POINT (754504.6 203634.7)
## 102 260 437 215 3533 2.887226 1.2640243 -0.7798489 POINT (752404.4 203653.6)
## 103 271 424 254 2639 2.798639 1.1770744 -0.7231472 POINT (753284.5 203654.1)
## 104 241 392 222 2774 2.775723 1.2162001 -0.7523689 POINT (753894.5 203654.4)
## 105 251 389 241 2664 2.719416 1.1908896 -0.7451687 POINT (753904.5 203654.4)
## 106 229 362 184 2833 2.983780 1.2536411 -0.7733960 POINT (752294.3 203663.6)
## 107 236 434 226 2788 2.697978 1.2136750 -0.7306021 POINT (752964.4 203663.9)
## 108 318 486 347 2797 2.455894 1.1126348 -0.7039293 POINT (753574.5 203664.2)
## 109 325 536 338 3162 2.564941 1.1520511 -0.7101136 POINT (754484.6 203664.7)
## 110 258 442 230 2820 2.858720 1.2124593 -0.7290006 POINT (752924.4 203673.9)
## 111 243 362 212 2061 3.060245 1.1614056 -0.7011968 POINT (753224.4 203674.1)
## 112 243 408 231 2478 2.751653 1.1842780 -0.7172557 POINT (753294.4 203674.1)
## 113 295 507 309 2907 2.548558 1.1534361 -0.7029877 POINT (753494.5 203674.2)
## 114 271 415 266 2625 2.694768 1.1650479 -0.7269737 POINT (753914.5 203674.4)
## 115 270 443 230 3050 2.931393 1.2275715 -0.7463499 POINT (753004.4 203683.9)
## 116 250 420 236 2730 2.745486 1.2005793 -0.7333333 POINT (753314.4 203684.1)
## 117 274 455 283 2896 2.572863 1.1735960 -0.7284393 POINT (753754.5 203684.3)
## 118 279 406 245 2465 3.012212 1.1696160 -0.7171717 POINT (752184.3 203693.5)
## 119 274 430 228 3060 2.983565 1.2297962 -0.7535816 POINT (754474.6 203694.7)
## 120 233 397 206 3913 2.724533 1.2850318 -0.8157772 POINT (752384.3 203703.6)
## 121 238 386 225 2889 2.713936 1.2214737 -0.7642748 POINT (752704.4 203703.8)
## 122 267 438 254 2784 2.743440 1.1890491 -0.7281192 POINT (753574.5 203714.2)
## 123 263 411 233 2799 2.883794 1.2083545 -0.7439252 POINT (752724.4 203723.8)
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## 125 226 373 201 2993 2.787540 1.2481033 -0.7783719 POINT (753264.4 203724.1)
## 126 263 420 246 2584 2.800000 1.1795615 -0.7203729 POINT (752784.4 203733.8)
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## 128 259 454 279 2976 2.490305 1.1830444 -0.7352770 POINT (753334.4 203734.1)
## 129 262 424 250 2893 2.721376 1.2006650 -0.7443473 POINT (752264.3 203743.6)
## 130 215 329 188 2303 2.907616 1.2122445 -0.7500000 POINT (752324.3 203743.6)
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## 134 263 408 227 2475 3.014213 1.1878740 -0.7169615 POINT (753474.4 203754.2)
## 135 250 364 226 2494 2.870886 1.1905127 -0.7452764 POINT (753624.4 203754.3)
## 136 246 401 207 3067 2.901786 1.2472652 -0.7687428 POINT (753314.4 203764.1)
## 137 247 405 255 2721 2.570356 1.1831121 -0.7408829 POINT (754474.5 203764.7)
## 138 247 347 195 2336 3.237073 1.2077563 -0.7413343 POINT (753494.4 203774.2)
## 139 307 510 312 2996 2.615474 1.1584814 -0.7090701 POINT (754464.5 203774.7)
## 140 257 411 204 3350 2.971850 1.2639130 -0.7814411 POINT (753424.4 203784.2)
## 141 245 444 234 2915 2.700987 1.2156074 -0.7356356 POINT (754624.5 203784.8)
## 142 272 437 253 2806 2.794440 1.1916227 -0.7304965 POINT (752194.3 203793.5)
## 143 226 400 216 3334 2.655877 1.2540753 -0.7857525 POINT (752214.3 203813.6)
## 144 249 426 239 2796 2.705820 1.2029263 -0.7355680 POINT (753564.4 203814.3)
## 145 245 429 253 2558 2.574269 1.1707716 -0.7127553 POINT (753494.4 203834.2)
## 146 271 466 269 2785 2.657934 1.1762753 -0.7133190 POINT (753394.4 203844.2)
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## 154 240 413 228 2331 2.768562 1.1733419 -0.6989796 POINT (753504.4 203884.2)
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nsample$geometry = NULL 

nsample

##      B2  B3  B4   B8      EVI      SAVI       NDWI         BA
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## 3   240 393 199 2397 3.068118 1.2088701 -0.7182795  4119.6558
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## 8   259 412 236 3074 2.785084 1.2242115 -0.7636259  2161.0103
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## 240 258 518 238 3248 2.745348 1.2328607 -0.7249070  2451.5011
## 241 233 392 210 2700 2.813559 1.2217172 -0.7464424  7084.6965
## 242 252 461 249 3453 2.620216 1.2357599 -0.7644354   722.4257
## 243 242 388 224 2536 2.799031 1.1960232 -0.7346101  1270.7759
## 244 248 437 220 2958 2.830852 1.2301251 -0.7425626   470.4342
## 245 245 382 222 2507 2.854110 1.1954813 -0.7355486  1783.6000
## 246 248 417 220 3332 2.786533 1.2509574 -0.7775407   778.6155
## 247 302 501 286 3138 2.753959 1.1892953 -0.7246496  2183.7887
## 248 235 353 221 2385 2.776495 1.1856042 -0.7421476  4382.1974
## 249 273 475 234 4015 2.803648 1.2705870 -0.7884187  1665.7019
## 250 265 393 239 2552 2.893420 1.1832525 -0.7331070  4472.6914
## 251 274 410 246 2835 2.869016 1.1997982 -0.7473035  2024.4881
## 252 255 426 227 3385 2.785324 1.2483637 -0.7764366   561.2806
## 253 281 508 225 3253 3.033460 1.2430856 -0.7298591  1398.7354
## 254 251 401 224 3338 2.780854 1.2482475 -0.7855042  3675.2393
## 255 255 476 236 3240 2.737379 1.2339424 -0.7438105   768.6404
## 256 257 479 230 3082 2.813178 1.2295078 -0.7309744   674.1970
## 257 236 452 227 2871 2.683719 1.2185638 -0.7279567  1484.3963
## 258 271 513 242 3066 2.840475 1.2189088 -0.7133278  4830.4703
## 259 236 372 200 2709 2.932445 1.2314627 -0.7585199  3388.7845
## 260 265 390 223 2758 3.005691 1.2141765 -0.7522236  6871.3674
## 261 234 323 217 2197 2.838303 1.1710600 -0.7436508 27486.9998
## 262 266 426 224 3096 2.936605 1.2351468 -0.7580920  2373.6471
## 263 247 452 229 3110 2.737032 1.2319679 -0.7462100  2282.0362
## 264 233 375 226 2656 2.682711 1.2038600 -0.7525569  7002.2081
## 265 290 434 251 2984 2.951404 1.2062466 -0.7460503  2615.9775
## 266 208 387 179 2196 2.948830 1.2125293 -0.7003484  5013.2299
## 267 265 423 225 2980 2.940235 1.2273369 -0.7513958   343.9435
## 268 248 398 222 2984 2.811482 1.2300715 -0.7646363  2615.8996
## 269 228 374 198 2548 2.899803 1.2218781 -0.7440109  1155.5617
## 270 263 392 237 2714 2.862260 1.1984558 -0.7475853  1745.2707
## 271 241 412 224 2653 2.773464 1.2054557 -0.7311583  8519.8597
## 272 254 421 230 2909 2.809354 1.2185698 -0.7471471  3942.3537
## 273 252 387 210 2966 2.949486 1.2389917 -0.7691619  2599.3845
## 274 251 415 245 3090 2.656396 1.2180326 -0.7631955  1054.7122
## 275 246 455 254 2928 2.564250 1.1998613 -0.7310080   765.8640
## 276 324 532 347 2721 2.501054 1.1048237 -0.6729173  1681.8744
## 277 237 444 213 3133 2.771976 1.2460331 -0.7517473  1953.7549
## 278 279 432 260 2607 2.828392 1.1688231 -0.7156960  1016.3486
## 279 252 441 234 2967 2.753930 1.2190572 -0.7411972   898.3130
## 280 300 451 285 2819 2.779728 1.1656100 -0.7241590  3643.7179
## 281 242 391 227 2714 2.749889 1.2073849 -0.7481481  1584.6627
## 282 272 435 278 2687 2.601512 1.1600524 -0.7213325 16197.5598
## 283 250 433 218 3100 2.844453 1.2401944 -0.7548825   910.0364
## 284 316 532 299 3140 2.770086 1.1795415 -0.7102396  1315.7686
## 285 303 506 281 3016 2.814365 1.1844323 -0.7126632   923.8850
## 286 260 420 242 2789 2.779354 1.1998029 -0.7382362   825.1895
## 287 259 424 254 3055 2.655983 1.2086161 -0.7562518 24731.7726
## 288 259 448 238 3017 2.776224 1.2190139 -0.7414141  1057.7983
## 289 244 399 219 3151 2.781784 1.2422446 -0.7752113  1131.0940
## 290 230 420 217 3294 2.679380 1.2513303 -0.7738287  2315.5091
## 291 275 473 254 3216 2.765640 1.2187937 -0.7435619 12018.4967
## 292 320 480 288 2922 2.926667 1.1716045 -0.7178131  3825.8796
## 293 255 426 217 2856 2.938098 1.2261527 -0.7404022   552.6132
## 294 305 498 271 2897 2.936703 1.1835295 -0.7066274  1012.8931
## 295 267 441 234 3109 2.862976 1.2279314 -0.7515493   306.3952
## 296 282 469 261 3038 2.789273 1.2018920 -0.7325349  3248.1892
## 297 262 401 239 2796 2.822296 1.2029263 -0.7491398  8159.3276
## 298 274 443 252 2893 2.809574 1.1989936 -0.7344125  2734.7736
## 299 269 444 234 2968 2.902952 1.2191225 -0.7397421  3213.8994
## 300 212 291 181 2151 2.990285 1.2061080 -0.7616708   325.9574
## 301 267 434 269 3027 2.613227 1.1947551 -0.7492054   353.2873
## 302 239 436 242 3152 2.587587 1.2242062 -0.7569677   584.4932
## 303 228 354 211 2643 2.764893 1.2166697 -0.7637638  1037.7343
## 304 267 446 233 3386 2.833903 1.2439767 -0.7672234  1770.0547
## 305 256 425 224 2736 2.907408 1.2116951 -0.7310978  4070.6383
## 306 256 386 241 2335 2.813004 1.1606115 -0.7162808   894.6439
## 307 282 478 253 3007 2.856847 1.2061950 -0.7256815  7330.5474
## 308 236 364 217 2980 2.749801 1.2339805 -0.7822967  8802.2383
## 309 228 404 209 2787 2.764908 1.2285908 -0.7467878  1948.6141
## 310 263 433 240 2745 2.830508 1.1982001 -0.7275016  1644.9115
## 311 323 541 321 2940 2.679558 1.1467161 -0.6891698  2516.1042
## 312 231 401 217 3018 2.706280 1.2362593 -0.7654285  3293.3623
## 313 247 379 227 2674 2.801695 1.2043436 -0.7517196  7416.3767
## 314 261 341 210 2552 3.157185 1.2106653 -0.7642586  2446.7283
## 315 265 422 241 2763 2.838172 1.1987027 -0.7350078  2930.6781
## 316 324 497 357 2795 2.431193 1.1043754 -0.6980559  1340.9834

Se ejecuta el algoritmo random Forest haciendo uso de sus valores por defecto para establecer que tanto el modelo es capaz de explicar la biomasa aérea. El porcentaje explicado es del -9.89% usando 500 arboles de decición y usando dos variables en cada división.

BA.rf = randomForest(BA ~ ., nsample, importance = TRUE) # 

BA.rf

## 
## Call:
##  randomForest(formula = BA ~ ., data = nsample, importance = TRUE) 
##                Type of random forest: regression
##                      Number of trees: 500
## No. of variables tried at each split: 2
## 
##           Mean of squared residuals: 21306447
##                     % Var explained: -9.57

El ploteo de los errores evidencia que los valores mas altos se encuentran entre los primeros 150 árboles.

plot(BA.rf)

Teniendo en cuenta lo anterior se procede a ejecutar el algoritmo pero ajustando parámetros para ver si es posible mejorar la respuesta de la variable. Para tal fin se ajustan los valores asociados al número de arboles ejecutados y al número de variables en cada uno de los arboles.

#usando 150 árboles

BA.rf2 = randomForest(BA ~ ., nsample, importance = TRUE,ntree =150)
BA.rf2

## 
## Call:
##  randomForest(formula = BA ~ ., data = nsample, importance = TRUE,      ntree = 150) 
##                Type of random forest: regression
##                      Number of trees: 150
## No. of variables tried at each split: 2
## 
##           Mean of squared residuals: 22085223
##                     % Var explained: -13.57

#Usando 500 arboles y 3 variables en cada arbol
BA.rf3 = randomForest(BA ~ ., nsample, importance = TRUE,ntree =500,mtry =3)
BA.rf3

## 
## Call:
##  randomForest(formula = BA ~ ., data = nsample, importance = TRUE,      ntree = 500, mtry = 3) 
##                Type of random forest: regression
##                      Number of trees: 500
## No. of variables tried at each split: 3
## 
##           Mean of squared residuals: 21630245
##                     % Var explained: -11.23

Debido a que el porcentaje explicado por el modelo no cambia de manera positiva ajustando el número de árboles ni tampoco la cantidad de variables usadas en cada árbol, se ejecutará ajustando las variables dependientes. Para tal fin se utilizarán primero solo las bandas de la imágen como variable de respuesta y luego usando solo los índices espectrales.

BA.rf4 = randomForest(BA ~ ., cbind(nsample[8],nsample[1:4]), importance = TRUE)
BA.rf4

## 
## Call:
##  randomForest(formula = BA ~ ., data = cbind(nsample[8], nsample[1:4]),      importance = TRUE) 
##                Type of random forest: regression
##                      Number of trees: 500
## No. of variables tried at each split: 1
## 
##           Mean of squared residuals: 21119426
##                     % Var explained: -8.61

BA.rf5 = randomForest(BA ~ ., nsample[5:8], importance = TRUE)
BA.rf5

## 
## Call:
##  randomForest(formula = BA ~ ., data = nsample[5:8], importance = TRUE) 
##                Type of random forest: regression
##                      Number of trees: 500
## No. of variables tried at each split: 1
## 
##           Mean of squared residuals: 21556711
##                     % Var explained: -10.85

Los valores de ajuste sobre el modelo no cambian de manera significativa al cambiar las variables predictoras ni parámetros del algoritmo por lo que se realiza una validación cruzada para evaluar su exactitud sobre el primer modelo que había sido ejecutado contemplando únicamente los parámetros por defecto del algoritmo. Se usó 30% de los datos para validar los resultados con 500 arboles.

( rf.cv <- rf.crossValidation(BA.rf, nsample[,1:7], 
                              p=0.30, n=50, ntree=500,plot=TRUE))

## running: regression cross-validation with 50 iterations

## Fit MSE = 21599769 
## Fit percent variance explained = -9.57 
## Median permuted MSE = 23572324 
## Median permuted percent variance explained = -12.145 
## Median cross-validation RMSE = 4246.254 
## Median cross-validation MBE = 233.1046 
## Median cross-validation MAE = 2897.18 
## Range of ks p-values = 1.110223e-16 0.0003580621 
## Range of ks D statistic = 0.2105263 0.5578947 
## RMSE cross-validation error variance = 479634.1 
## MBE cross-validation error variance = 326176.6 
## MAE cross-validation error variance = 52810.23

#IMPORTANCIA DE LAS VARIABLES
round(importance(BA.rf), 2)

##      %IncMSE IncNodePurity
## B2      9.24     702876400
## B3      8.57     744111423
## B4      8.75     609858441
## B8      8.34     836967225
## EVI     4.05     735401486
## SAVI   13.46     770848192
## NDWI   12.83     751287701

par(mfrow=c(2,2))
   plot(rf.cv)  
   plot(rf.cv, stat = "mse")
   plot(rf.cv, stat = "var.exp")
plot(rf.cv, stat = "mae")

3.4 RANDOM FOREST ESPACIAL

Para aplicar el algoritmo Random Forest Espacial, es necesario generar una matriz de distancias entre las muestras.

censo_dist <- as.matrix(dist(cbind(censo_st$X, censo_st$Y)))

head(censo_dist)

##              1           2            3            4            5            6
## 1 0.0000000000 0.001258635 0.0009387209 0.0011959101 0.0015221370 0.0014511199
## 2 0.0012586346 0.000000000 0.0012353623 0.0013927642 0.0015818502 0.0010596462
## 3 0.0009387209 0.001235362 0.0000000000 0.0002613350 0.0005849188 0.0006688871
## 4 0.0011959101 0.001392764 0.0002613350 0.0000000000 0.0003264384 0.0005989274
## 5 0.0015221370 0.001581850 0.0005849188 0.0003264384 0.0000000000 0.0006028101
## 6 0.0014511199 0.001059646 0.0006688871 0.0005989274 0.0006028101 0.0000000000
##             7            8            9           10          11          12
## 1 0.002154449 0.0021287379 0.0020990288 0.0023667471 0.002431272 0.002592693
## 2 0.000989849 0.0011983397 0.0014536853 0.0021159265 0.002015616 0.001489143
## 3 0.001739643 0.0014962600 0.0012964833 0.0014311272 0.001518880 0.002046918
## 4 0.001752655 0.0014343814 0.0011553359 0.0011845679 0.001296076 0.002000316
## 5 0.001758932 0.0013576038 0.0009844699 0.0008649306 0.001003842 0.001924779
## 6 0.001169935 0.0008392592 0.0006525527 0.0010771188 0.001039039 0.001402462
##            13          14          15          16          17          18
## 1 0.003420424 0.002619017 0.002629878 0.002729073 0.003398607 0.003103847
## 2 0.002162247 0.001653697 0.001860224 0.002294625 0.002148643 0.002764278
## 3 0.003146783 0.001947098 0.001834602 0.001811237 0.003059624 0.002168120
## 4 0.003169548 0.001851017 0.001681462 0.001581559 0.003063424 0.001919767
## 5 0.003163506 0.001715469 0.001474887 0.001278047 0.003034743 0.001597098
## 6 0.002584378 0.001278554 0.001190684 0.001337674 0.002470063 0.001773104
##            19          20          21          22          23          24
## 1 0.003794265 0.003604719 0.003710007 0.003552835 0.003620891 0.003851880
## 2 0.002571033 0.003276390 0.003374144 0.002746958 0.002871329 0.003241632
## 3 0.003351722 0.002666517 0.002771834 0.002728531 0.002769948 0.002950610
## 4 0.003317678 0.002413489 0.002518831 0.002548868 0.002576351 0.002727834
## 5 0.003239438 0.002087913 0.002193245 0.002297718 0.002308564 0.002427198
## 6 0.002719006 0.002289863 0.002392159 0.002106267 0.002169830 0.002418407
##            25          26          27          28          29          30
## 1 0.003921573 0.003938664 0.003936880 0.008150123 0.007889355 0.004599872
## 2 0.003469328 0.003272666 0.003393851 0.006964519 0.006686230 0.003394714
## 3 0.002990819 0.003051387 0.003019682 0.008116585 0.007818480 0.004093041
## 4 0.002746885 0.002836593 0.002786317 0.008178504 0.007870936 0.004029950
## 5 0.002426778 0.002544030 0.002475182 0.008203363 0.007884214 0.003911026
## 6 0.002544832 0.002494755 0.002523850 0.007612306 0.007297858 0.003438628
##            31          32          33          34          35          36
## 1 0.004142369 0.007177480 0.005122708 0.004246611 0.008332947 0.005241935
## 2 0.003537034 0.005948929 0.003875122 0.003251500 0.007133698 0.003994400
## 3 0.003235975 0.007042241 0.004723483 0.003512095 0.008269317 0.004840366
## 4 0.003009267 0.007078975 0.004691683 0.003367485 0.008322702 0.004807099
## 5 0.002704125 0.007073744 0.004608073 0.003153313 0.008336502 0.004721214
## 6 0.002712583 0.006496452 0.004093048 0.002852718 0.007750005 0.004208603
##            37          38          39          40          41          42
## 1 0.005624888 0.005331451 0.005224363 0.005092178 0.004588868 0.005383870
## 2 0.004370293 0.004105304 0.004002380 0.003897947 0.003921342 0.004160976
## 3 0.005258305 0.004856671 0.004740982 0.004553877 0.003693093 0.004899901
## 4 0.005233782 0.004799419 0.004681520 0.004476790 0.003471712 0.004839344
## 5 0.005157096 0.004684186 0.004564048 0.004338701 0.003171076 0.004719936
## 6 0.004634860 0.004206188 0.004089045 0.003892516 0.003148142 0.004247334
##            43          44          45          46          47          48
## 1 0.005149023 0.005156499 0.005055712 0.005957524 0.005410452 0.008585948
## 2 0.003963369 0.003973243 0.003922419 0.004713749 0.004225548 0.007357772
## 3 0.004594829 0.004598211 0.004429939 0.005529069 0.004850222 0.008445047
## 4 0.004511959 0.004513885 0.004322275 0.005483595 0.004763857 0.008476590
## 5 0.004366722 0.004366881 0.004147938 0.005380439 0.004613466 0.008462603
## 6 0.003931193 0.003934063 0.003761129 0.004887167 0.004185473 0.007890694
##            49          50          51          52          53          54
## 1 0.008580618 0.005715185 0.008658195 0.005078436 0.009231124 0.005327586
## 2 0.007350065 0.004495093 0.007427206 0.004362767 0.008006434 0.004450117
## 3 0.008432122 0.005219059 0.008507949 0.004191531 0.009098517 0.004501496
## 4 0.008461549 0.005152808 0.008536721 0.003974061 0.009131092 0.004312833
## 5 0.008444927 0.005025412 0.008519177 0.003676616 0.009117592 0.004044994
## 6 0.007874631 0.004563259 0.007949468 0.003632069 0.008545496 0.003882964
##           55          56          57          58          59         60
## 1 0.01245329 0.008441380 0.009420477 0.005860020 0.005708837 0.01286794
## 2 0.01289500 0.007193532 0.008190171 0.004733908 0.005191755 0.01329951
## 3 0.01176412 0.008224262 0.009269635 0.005212276 0.004777880 0.01217350
## 4 0.01154518 0.008234510 0.009296760 0.005092939 0.004532556 0.01195319
## 5 0.01131596 0.008194253 0.009276237 0.004902292 0.004210792 0.01172153
## 6 0.01185345 0.007640249 0.008708537 0.004543757 0.004319127 0.01225596
##            61          62          63          64          65          66
## 1 0.009585512 0.009484008 0.006183983 0.006567516 0.006179416 0.007489736
## 2 0.008352595 0.008247203 0.005010719 0.005376209 0.005061859 0.006237627
## 3 0.009425354 0.009310319 0.005593823 0.006002042 0.005517812 0.007086249
## 4 0.009449568 0.009330886 0.005493751 0.005909140 0.005392291 0.007043193
## 5 0.009425234 0.009302123 0.005324832 0.005747764 0.005193687 0.006939392
## 6 0.008860047 0.008739924 0.004925926 0.005335674 0.004850126 0.006446466
##            67          68          69          70          71          72
## 1 0.006578943 0.006116066 0.006156644 0.008211121 0.007056572 0.006217908
## 2 0.005399468 0.005500427 0.005567569 0.008240904 0.005836396 0.005506574
## 3 0.005993691 0.005198232 0.005234058 0.007338483 0.006544600 0.005321471
## 4 0.005893967 0.004962008 0.004994725 0.007082484 0.006468087 0.005097428
## 5 0.005724545 0.004646827 0.004677100 0.006783608 0.006325078 0.004792739
## 6 0.005325899 0.004694212 0.004743019 0.007191077 0.005884010 0.004774871
##            73          74          75          76          77          78
## 1 0.008864150 0.006453755 0.008325288 0.006643217 0.007695984 0.007130332
## 2 0.008938082 0.005904142 0.008309738 0.005519350 0.007503546 0.005946811
## 3 0.008006569 0.005524718 0.007440320 0.005983348 0.006773360 0.006545972
## 4 0.007753006 0.005280652 0.007182398 0.005857054 0.006512027 0.006444937
## 5 0.007459969 0.004959580 0.006878221 0.005656604 0.006192068 0.006272902
## 6 0.007884213 0.005054939 0.007266361 0.005315723 0.006498203 0.005878026
##            79          80          81          82          83          84
## 1 0.010494723 0.006738462 0.006812307 0.007492233 0.006802270 0.007983338
## 2 0.009250715 0.005682872 0.006162829 0.007147804 0.005904384 0.006760542
## 3 0.010288305 0.006011176 0.005898516 0.006554839 0.005972251 0.007470115
## 4 0.010297933 0.005859548 0.005664351 0.006296348 0.005778901 0.007390787
## 5 0.010254593 0.005630125 0.005350611 0.005970302 0.005504080 0.007242878
## 6 0.009703186 0.005353267 0.005383492 0.006195723 0.005357380 0.006808471
##            85          86          87         88          89          90
## 1 0.008603332 0.008309569 0.007112432 0.01337475 0.008312627 0.007968342
## 2 0.008482206 0.007077805 0.006353248 0.01367803 0.007085635 0.007634248
## 3 0.007694565 0.007818359 0.006225489 0.01261491 0.007808000 0.007031736
## 4 0.007433829 0.007745475 0.006005550 0.01237984 0.007730760 0.006772694
## 5 0.007119510 0.007604725 0.005704170 0.01212261 0.007584852 0.006446943
## 6 0.007460138 0.007159638 0.005664499 0.01262051 0.007147283 0.006679365
##            91          92          93          94          95          96
## 1 0.010204528 0.008268779 0.010015782 0.010216631 0.009130862 0.008239060
## 2 0.008946374 0.007987467 0.010035103 0.008958440 0.007882087 0.007031271
## 3 0.009892220 0.007336278 0.009143682 0.009903352 0.008698301 0.007690119
## 4 0.009871333 0.007075793 0.008887497 0.009882157 0.008642468 0.007598448
## 5 0.009790830 0.006751664 0.008587788 0.009801268 0.008520966 0.007435670
## 6 0.009272407 0.007012903 0.008988616 0.009283232 0.008049423 0.007024285
##            97          98          99         100        101         102
## 1 0.011206988 0.009095775 0.009574701 0.009648314 0.01388447 0.010430273
## 2 0.009954297 0.008910728 0.009476667 0.009557855 0.01416817 0.009171644
## 3 0.010950620 0.008176338 0.008672248 0.008747622 0.01311606 0.010091316
## 4 0.010944840 0.007915025 0.008412049 0.008487601 0.01287903 0.010062118
## 5 0.010881926 0.007596176 0.008100082 0.008176337 0.01261820 0.009971321
## 6 0.010346872 0.007906525 0.008450935 0.008530553 0.01310960 0.009463556
##           103         104         105         106         107         108
## 1 0.007688051 0.009917355 0.009944104 0.011219494 0.008039652 0.008410870
## 2 0.006929509 0.009828675 0.009859148 0.009962762 0.006952830 0.007992097
## 3 0.006798549 0.009017444 0.009045063 0.010926941 0.007329855 0.007472151
## 4 0.006576920 0.008757492 0.008785205 0.010910522 0.007182277 0.007216416
## 5 0.006273746 0.008446475 0.008474535 0.010834589 0.006955720 0.006890005
## 6 0.006240748 0.008801368 0.008831069 0.010311660 0.006669136 0.007076530
##          109         110         111         112         113         114
## 1 0.01392493 0.008193898 0.007825633 0.007870885 0.008314586 0.010084946
## 2 0.01418687 0.007083464 0.006985355 0.007111720 0.007795398 0.009996872
## 3 0.01314675 0.007506550 0.006964100 0.006980909 0.007379825 0.009185401
## 4 0.01290767 0.007366945 0.006755631 0.006758930 0.007130510 0.008925481
## 5 0.01264306 0.007149151 0.006464821 0.006455372 0.006806195 0.008614569
## 6 0.01312761 0.006842314 0.006374672 0.006423679 0.006933499 0.008969662
##           115         116         117        118        119         120
## 1 0.008171372 0.007992072 0.009362538 0.01214628 0.01396998 0.010978471
## 2 0.007118728 0.007260376 0.009121107 0.01089392 0.01419973 0.009720155
## 3 0.007430731 0.007093860 0.008435416 0.01188977 0.01317791 0.010621533
## 4 0.007271395 0.006867637 0.008174253 0.01188286 0.01293595 0.010586166
## 5 0.007031705 0.006560267 0.007852241 0.01181788 0.01266596 0.010487451
## 6 0.006777069 0.006548648 0.008135075 0.01128471 0.01314009 0.009988318
##           121         122         123         124         125         126
## 1 0.009243697 0.008837856 0.009324185 0.008448810 0.008304349 0.009177643
## 2 0.008030623 0.008393703 0.008120653 0.007432083 0.007504646 0.007998005
## 3 0.008699928 0.007899333 0.008760247 0.007679147 0.007425886 0.008572595
## 4 0.008608150 0.007644706 0.008661653 0.007508291 0.007209225 0.008460362
## 5 0.008444081 0.007318447 0.008489573 0.007255865 0.006910396 0.008272679
## 6 0.008034155 0.007491887 0.008092889 0.007034808 0.006854060 0.007903731
##           127         128        129        130         131        132
## 1 0.008549973 0.008503926 0.01196442 0.01159918 0.008628039 0.01477969
## 2 0.007505970 0.007783604 0.01070633 0.01034056 0.007583532 0.01501324
## 3 0.007800213 0.007601298 0.01164796 0.01125494 0.007878258 0.01398994
## 4 0.007636897 0.007372537 0.01162358 0.01122265 0.007714836 0.01374833
## 5 0.007392540 0.007062854 0.01153743 0.01112718 0.007470302 0.01347887
## 6 0.007149336 0.007062970 0.01102474 0.01062442 0.007227426 0.01395359
##           133         134         135         136        137         138
## 1 0.008816435 0.008952178 0.009413084 0.008747205 0.01441830 0.009135195
## 2 0.007763672 0.008383338 0.008995570 0.007992292 0.01460407 0.008580952
## 3 0.008072286 0.008021501 0.008474387 0.007853285 0.01360863 0.008202805
## 4 0.007910771 0.007775615 0.008218109 0.007628882 0.01336310 0.007955522
## 5 0.007668165 0.007453146 0.007891671 0.007322904 0.01308613 0.007632240
## 6 0.007419913 0.007553238 0.008081737 0.007301255 0.01354518 0.007742021
##          139         140        141        142        143         144
## 1 0.01429930 0.009074543 0.01556157 0.01272799 0.01267330 0.009725251
## 2 0.01447467 0.008434137 0.01579976 0.01147029 0.01141483 0.009222128
## 3 0.01348545 0.008153837 0.01477444 0.01241737 0.01234418 0.008788565
## 4 0.01323912 0.007914708 0.01453324 0.01239395 0.01231530 0.008537044
## 5 0.01296058 0.007596728 0.01426446 0.01230847 0.01222325 0.008211709
## 6 0.01341615 0.007652723 0.01474012 0.01179508 0.01171676 0.008353953
##           145         146        147         148         149         150
## 1 0.009659223 0.009536994 0.01519236 0.010188206 0.009521518 0.009843578
## 2 0.009073462 0.008850975 0.01535026 0.009030519 0.008628633 0.009246741
## 3 0.008729807 0.008624263 0.01437255 0.009546379 0.008676072 0.008915367
## 4 0.008484775 0.008389694 0.01412497 0.009420180 0.008473468 0.008671179
## 5 0.008162780 0.008075100 0.01384383 0.009215760 0.008187670 0.008349696
## 6 0.008255532 0.008104168 0.01429272 0.008878401 0.008073192 0.008436396
##           151        152         153         154        155        156
## 1 0.009564883 0.01156662 0.010036059 0.010113044 0.01632137 0.01670584
## 2 0.008675767 0.01135775 0.009442924 0.009528626 0.01651102 0.01690720
## 3 0.008717581 0.01064591 0.009107196 0.009183061 0.01551472 0.01590416
## 4 0.008514155 0.01038457 0.008862517 0.008937553 0.01526955 0.01565992
## 5 0.008227535 0.01006496 0.008540719 0.008615247 0.01499308 0.01538522
## 6 0.008116155 0.01036466 0.008630413 0.008710518 0.01545220 0.01584806
##           157         158         159         160        161         162
## 1 0.009896863 0.011084197 0.010367511 0.010386226 0.01203640 0.011177928
## 2 0.009000822 0.010713513 0.009770361 0.009350790 0.01177389 0.010723087
## 3 0.009051713 0.010147031 0.009438858 0.009621906 0.01110868 0.010239308
## 4 0.008849014 0.009888373 0.009194290 0.009451223 0.01084758 0.009984255
## 5 0.008562993 0.009562414 0.008872543 0.009197818 0.01052520 0.009657915
## 6 0.008448670 0.009780875 0.008960972 0.008976474 0.01079935 0.009831073
##           163        164         165        166        167         168
## 1 0.010875464 0.01172551 0.011000149 0.01256555 0.01225651 0.011381135
## 2 0.009757221 0.01052444 0.009880969 0.01233178 0.01194366 0.010847811
## 3 0.010183607 0.01114701 0.010308869 0.01164187 0.01132366 0.010445646
## 4 0.010039143 0.01104070 0.010164502 0.01138057 0.01106329 0.010195360
## 5 0.009813901 0.01085793 0.009939300 0.01105973 0.01073893 0.009870510
## 6 0.009520828 0.01047859 0.009646031 0.01134794 0.01098832 0.009999691
##          169         170        171        172        173        174        175
## 1 0.01586093 0.011099014 0.01251257 0.01255439 0.01227704 0.01228251 0.01692553
## 2 0.01591311 0.010078711 0.01215996 0.01216738 0.01180737 0.01179989 0.01697974
## 3 0.01500492 0.010321411 0.01157679 0.01161684 0.01133856 0.01134433 0.01607083
## 4 0.01475083 0.010145155 0.01131735 0.01135849 0.01108397 0.01109046 0.01581690
## 5 0.01445567 0.009885570 0.01099190 0.01103240 0.01075770 0.01076435 0.01552204
## 6 0.01486559 0.009681112 0.01122134 0.01124405 0.01092457 0.01092406 0.01593231
##          176        177        178        179        180        181        182
## 1 0.01701447 0.01808647 0.01670825 0.01715486 0.01780005 0.01291233 0.01680970
## 2 0.01706526 0.01819789 0.01671186 0.01718387 0.01786722 0.01243126 0.01680097
## 3 0.01615875 0.01725158 0.01583812 0.01629248 0.01695003 0.01197403 0.01593612
## 4 0.01590465 0.01700099 0.01558177 0.01603730 0.01669683 0.01171989 0.01567926
## 5 0.01560937 0.01671340 0.01528107 0.01573949 0.01640357 0.01139372 0.01537724
## 6 0.01601832 0.01714434 0.01567189 0.01614005 0.01681840 0.01155528 0.01576315
##          183        184        185        186        187        188        189
## 1 0.01721984 0.01836143 0.01984012 0.01650584 0.01932886 0.01960018 0.01659617
## 2 0.01724555 0.01845303 0.01999952 0.01643503 0.01943975 0.01972711 0.01652208
## 3 0.01635651 0.01751984 0.01902369 0.01561582 0.01849442 0.01877159 0.01570540
## 4 0.01610117 0.01726805 0.01877635 0.01535677 0.01824383 0.01852204 0.01544627
## 5 0.01580298 0.01697788 0.01849535 0.01504854 0.01795618 0.01823654 0.01513774
## 6 0.01620225 0.01740153 0.01894254 0.01540929 0.01838649 0.01867247 0.01549711
##          190        191        192        193        194        195        196
## 1 0.01967291 0.01399529 0.02006073 0.02023655 0.01910944 0.01708239 0.01770994
## 2 0.01979895 0.01359761 0.02019424 0.02037990 0.01918697 0.01702012 0.01769471
## 3 0.01884403 0.01305756 0.01923474 0.01941427 0.01826349 0.01619478 0.01683503
## 4 0.01859442 0.01279938 0.01898564 0.01916582 0.01801091 0.01593601 0.01657794
## 5 0.01830880 0.01247323 0.01870103 0.01888257 0.01771898 0.01562863 0.01627530
## 6 0.01874439 0.01268073 0.01913913 0.01932406 0.01813722 0.01599282 0.01665839
##          197        198        199        200        201        202        203
## 1 0.01623864 0.01998591 0.01580352 0.01411737 0.01458904 0.01580506 0.01593659
## 2 0.01608515 0.02009322 0.01559759 0.01365172 0.01421747 0.01558786 0.01573075
## 3 0.01533036 0.01915052 0.01488568 0.01317872 0.01365261 0.01488543 0.01501882
## 4 0.01506953 0.01889973 0.01462438 0.01292349 0.01339350 0.01462410 0.01475752
## 5 0.01475437 0.01861162 0.01430562 0.01259712 0.01306780 0.01430467 0.01443879
## 6 0.01507978 0.01904043 0.01460750 0.01276867 0.01328922 0.01460138 0.01474072
##          204        205        206        207        208        209        210
## 1 0.01674388 0.01835013 0.01923280 0.02016491 0.02037332 0.02021349 0.01379953
## 2 0.01661993 0.01835114 0.01928316 0.02026628 0.02048796 0.02031180 0.01320884
## 3 0.01584185 0.01748012 0.01837810 0.01932753 0.01954068 0.01937507 0.01286811
## 4 0.01558152 0.01722373 0.01812406 0.01907638 0.01929036 0.01912374 0.01262123
## 5 0.01526871 0.01692286 0.01782883 0.01878750 0.01900321 0.01883447 0.01229803
## 6 0.01560695 0.01731220 0.01823690 0.01921412 0.01943453 0.01925996 0.01239873
##          211        212        213        214        215        216        217
## 1 0.01584235 0.01648143 0.01766976 0.01823189 0.02021109 0.01667361 0.01780814
## 2 0.01560768 0.01630712 0.01760455 0.01820697 0.02030586 0.01650986 0.01773951
## 3 0.01492011 0.01556933 0.01678171 0.01735457 0.01937146 0.01576356 0.01691930
## 4 0.01465878 0.01530825 0.01652287 0.01709714 0.01911991 0.01550260 0.01666037
## 5 0.01433836 0.01499164 0.01621527 0.01679352 0.01883018 0.01518675 0.01635246
## 6 0.01462700 0.01530784 0.01657814 0.01717264 0.01925439 0.01550764 0.01671390
##          218        219        220        221        222        223        224
## 1 0.02042826 0.02056809 0.01480913 0.01615283 0.01632910 0.01585109 0.01610370
## 2 0.02052385 0.02067440 0.01439491 0.01592240 0.01611764 0.01556248 0.01584606
## 3 0.01958900 0.01973260 0.01387095 0.01523133 0.01541058 0.01492193 0.01517838
## 4 0.01933751 0.01948176 0.01361329 0.01496999 0.01514927 0.01466098 0.01491714
## 5 0.01904789 0.01919353 0.01328699 0.01464984 0.01483023 0.01433796 0.01459555
## 6 0.01947233 0.01962180 0.01348657 0.01494051 0.01512965 0.01460111 0.01487351
##          225        226        227        228        229        230        231
## 1 0.01932030 0.01517649 0.01525900 0.01545549 0.01579609 0.01603683 0.02025713
## 2 0.01932165 0.01476237 0.01485493 0.01508409 0.01546961 0.01574344 0.02030367
## 3 0.01845084 0.01423835 0.01432119 0.01451923 0.01486315 0.01510719 0.01940167
## 4 0.01819450 0.01398064 0.01406309 0.01426003 0.01460283 0.01484631 0.01914747
## 5 0.01789372 0.01365435 0.01373691 0.01393439 0.01427840 0.01452310 0.01885182
## 6 0.01828297 0.01385428 0.01394212 0.01415647 0.01452310 0.01478402 0.01925818
##          232        233        234        235        236        237        238
## 1 0.01828422 0.01890582 0.02030141 0.01546951 0.01571277 0.01733858 0.01570799
## 2 0.01819811 0.01886264 0.02034263 0.01506982 0.01535242 0.01715850 0.01531935
## 3 0.01739138 0.01802394 0.01944430 0.01453188 0.01477722 0.01642578 0.01477086
## 4 0.01713197 0.01776586 0.01918984 0.01427360 0.01451770 0.01616467 0.01451218
## 5 0.01682251 0.01746046 0.01889357 0.01394749 0.01419231 0.01584775 0.01418624
## 6 0.01717663 0.01783211 0.01929792 0.01415512 0.01442013 0.01616141 0.01439971
##          239        240        241        242        243        244        245
## 1 0.01901243 0.02060239 0.01519101 0.01588662 0.01735991 0.01840333 0.01871127
## 2 0.01895741 0.02065138 0.01469941 0.01552091 0.01716505 0.01829811 0.01862522
## 3 0.01812754 0.01974784 0.01425277 0.01495077 0.01644453 0.01750613 0.01781862
## 4 0.01786907 0.01949378 0.01399873 0.01469138 0.01618330 0.01724625 0.01755923
## 5 0.01756253 0.01919843 0.01367256 0.01436588 0.01586541 0.01693513 0.01724980
## 6 0.01792936 0.01960563 0.01383118 0.01459110 0.01617246 0.01728124 0.01760390
##          246        247        248        249        250        251        252
## 1 0.01875468 0.02085710 0.01484720 0.01576293 0.01817364 0.01865431 0.01890828
## 2 0.01867705 0.02090754 0.01426041 0.01536191 0.01803801 0.01856067 0.01882821
## 3 0.01786406 0.02000312 0.01391500 0.01482528 0.01726978 0.01775986 0.01801714
## 4 0.01760490 0.01974913 0.01366746 0.01456702 0.01700927 0.01750027 0.01775791
## 5 0.01729624 0.01945397 0.01334389 0.01424090 0.01669567 0.01719017 0.01744904
## 6 0.01765383 0.01986165 0.01344855 0.01444805 0.01702881 0.01754111 0.01780560
##          253        254        255        256        257        258        259
## 1 0.01917947 0.01941410 0.02023258 0.02030547 0.02082746 0.01567378 0.02070572
## 2 0.01911709 0.01937064 0.02023454 0.02030819 0.02086182 0.01522348 0.02072837
## 3 0.01829278 0.01853236 0.01936366 0.01943680 0.01996844 0.01473507 0.01984309
## 4 0.01803409 0.01827429 0.01910738 0.01918055 0.01971365 0.01447884 0.01958775
## 5 0.01772686 0.01796890 0.01880671 0.01887997 0.01941661 0.01415240 0.01928937
## 6 0.01809067 0.01834035 0.01919601 0.01926955 0.01981824 0.01433371 0.01968656
##          260        261        262        263        264        265        266
## 1 0.01670772 0.01532917 0.01712543 0.01812504 0.01866459 0.01917286 0.01626888
## 2 0.01638532 0.01476013 0.01683525 0.01793408 0.01851015 0.01906462 0.01582800
## 3 0.01577536 0.01439518 0.01619645 0.01721060 0.01775711 0.01827528 0.01533026
## 4 0.01551491 0.01414615 0.01593549 0.01694941 0.01749632 0.01801535 0.01507352
## 5 0.01519069 0.01382182 0.01561252 0.01663184 0.01718133 0.01770405 0.01474710
## 6 0.01543778 0.01393735 0.01587532 0.01694069 0.01750631 0.01804881 0.01493387
##          267        268        269        270        271        272        273
## 1 0.01928645 0.01600910 0.02086731 0.01545177 0.01980707 0.02036458 0.01607545
## 2 0.01917634 0.01550637 0.02084952 0.01481940 0.01971056 0.02031271 0.01555204
## 3 0.01838850 0.01507111 0.01999305 0.01452475 0.01891240 0.01948102 0.01513830
## 4 0.01812853 0.01481755 0.01973597 0.01428091 0.01865276 0.01922270 0.01488597
## 5 0.01781707 0.01449150 0.01943325 0.01395944 0.01834250 0.01891655 0.01456028
## 6 0.01816104 0.01464488 0.01981469 0.01403825 0.01869214 0.01928446 0.01470235
##          274        275        276        277        278        279        280
## 1 0.01663468 0.01861118 0.01543958 0.01614772 0.01758326 0.01883479 0.02085667
## 2 0.01621333 0.01840987 0.01472872 0.01561272 0.01727048 0.01864161 0.02080568
## 3 0.01569646 0.01769513 0.01452613 0.01521116 0.01665201 0.01792020 0.01997351
## 4 0.01543887 0.01743388 0.01429028 0.01495956 0.01639136 0.01765900 0.01971523
## 5 0.01511256 0.01711569 0.01397430 0.01463413 0.01606753 0.01734135 0.01940919
## 6 0.01530979 0.01741994 0.01400527 0.01476984 0.01631962 0.01764925 0.01977740
##          281        282        283        284        285        286        287
## 1 0.01678901 0.02026207 0.02045139 0.02002346 0.02015406 0.02017235 0.02065425
## 2 0.01633651 0.02016199 0.02036044 0.01989030 0.02002955 0.02003213 0.02054751
## 3 0.01585031 0.01936673 0.01955823 0.01912077 0.01925325 0.01926824 0.01975752
## 4 0.01559403 0.01910702 0.01929876 0.01886035 0.01899300 0.01900770 0.01949766
## 5 0.01526759 0.01879648 0.01898902 0.01854709 0.01868043 0.01869390 0.01918659
## 6 0.01544862 0.01914459 0.01934092 0.01888122 0.01901825 0.01902500 0.01953188
##          288        289        290        291        292        293        294
## 1 0.02079834 0.01662810 0.01662990 0.01734306 0.01811881 0.01828027 0.01842729
## 2 0.02069609 0.01603447 0.01604249 0.01688064 0.01776330 0.01795149 0.01811543
## 3 0.01990268 0.01569607 0.01569725 0.01640434 0.01718400 0.01734764 0.01749630
## 4 0.01964293 0.01544860 0.01544930 0.01614846 0.01692421 0.01708726 0.01723561
## 5 0.01933225 0.01512505 0.01512549 0.01582203 0.01659908 0.01676293 0.01691188
## 6 0.01967940 0.01522807 0.01523209 0.01599822 0.01683046 0.01700748 0.01716467
##          295        296        297        298        299        300        301
## 1 0.02069308 0.01857306 0.01898629 0.01903597 0.01958007 0.02027118 0.02045309
## 2 0.02057406 0.01825626 0.01865901 0.01871321 0.01932002 0.02006883 0.02026017
## 3 0.01979364 0.01764161 0.01805393 0.01810404 0.01865540 0.01935544 0.01953902
## 4 0.01953351 0.01738100 0.01779349 0.01784351 0.01839414 0.01909419 0.01927783
## 5 0.01922142 0.01705710 0.01746925 0.01751943 0.01807273 0.01877606 0.01896032
## 6 0.01956153 0.01730755 0.01771476 0.01776714 0.01835028 0.01907996 0.01926843
##          302        303        304        305        306        307        308
## 1 0.02024941 0.01794731 0.02055660 0.01753412 0.01900608 0.01924406 0.01739456
## 2 0.02003912 0.01745327 0.02035603 0.01694692 0.01864681 0.01891450 0.01676104
## 3 0.01933234 0.01700895 0.01964124 0.01660125 0.01807113 0.01831154 0.01646701
## 4 0.01907105 0.01675462 0.01938000 0.01635308 0.01781139 0.01805113 0.01622272
## 5 0.01875243 0.01642839 0.01906201 0.01602915 0.01748621 0.01772683 0.01590095
## 6 0.01905277 0.01658812 0.01936672 0.01613684 0.01771607 0.01797132 0.01598164
##          309        310        311        312        313        314        315
## 1 0.01802717 0.01890955 0.01916589 0.02080077 0.01722972 0.01819697 0.01881812
## 2 0.01752437 0.01850830 0.01879683 0.02059705 0.01649242 0.01769118 0.01838806
## 3 0.01708904 0.01797219 0.01823029 0.01988493 0.01632111 0.01725891 0.01787980
## 4 0.01683517 0.01771369 0.01797080 0.01962368 0.01608767 0.01700520 0.01762236
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##          316
## 1 0.01864939
## 2 0.01815024
## 3 0.01771112
## 4 0.01745698
## 5 0.01713078
## 6 0.01728826

datasample

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##             BA
## 1    4501.6203
## 2    4841.9386
## 3    4119.6558
## 4    3424.2565
## 5    5703.6193
## 6    1248.1745
## 7    5597.1450
## 8    2161.0103
## 9    2318.4994
## 10   1134.4166
## 11   1460.3116
## 12   3320.6009
## 13   4798.3154
## 14   4179.9386
## 15   2468.5044
## 16   3128.9569
## 17   2413.1796
## 18   3156.7831
## 19    842.5841
## 20  19116.5175
## 21   2973.9691
## 22   2904.3404
## 23    461.0414
## 24   3795.4481
## 25   1342.7311
## 26    260.5406
## 27   1059.4957
## 28   2589.3966
## 29   5311.0359
## 30   4782.4172
## 31   1370.1102
## 32   6077.8745
## 33   1882.9693
## 34   6018.8835
## 35   2750.0550
## 36   1544.0163
## 37   1164.9061
## 38   2170.6665
## 39   2284.6087
## 40   1599.8240
## 41   4566.4268
## 42   1490.1330
## 43    994.6543
## 44   1154.9232
## 45   1878.6013
## 46   5810.1237
## 47   4981.8019
## 48   1076.0557
## 49  15068.1014
## 50   2092.9910
## 51   7584.6462
## 52   2886.7378
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## 54   1845.1302
## 55   2426.3008
## 56    422.6499
## 57    634.7820
## 58    900.1417
## 59   4219.7647
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## 62   2900.6666
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## 67   1281.9443
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## 315  2930.6781
## 316  1340.9834

censo_st

## Simple feature collection with 316 features and 9 fields
## Geometry type: POINT
## Dimension:     XY
## Bounding box:  xmin: 752184.3 ymin: 202803.9 xmax: 754964.4 ymax: 204724.6
## Projected CRS: WGS 84 / UTM zone 18N
## First 10 features:
##    OBJECTID_1 OBJECTID Join_Count TARGET_FID Id        Y         X BA_KG_CL2
## 1           1    15720          3      15719  1 1.833383 -72.72400  4501.620
## 2           2    19031          3      19030  1 1.834302 -72.72486  4841.939
## 3           3    19045          3      19044  1 1.834244 -72.72363  4119.656
## 4           4    19710          3      19709  1 1.834458 -72.72348  3424.257
## 5           5    20708          3      20707  1 1.834757 -72.72335  5703.619
## 6           6    21033          3      21032  1 1.834833 -72.72395  1248.175
## 7           7    22681          3      22680  1 1.835278 -72.72503  5597.145
## 8           8    23351          3      23350  1 1.835449 -72.72452  2161.010
## 9           9    23356          3      23355  1 1.835482 -72.72401  2318.499
## 10         10    24029          3      24028  1 1.835609 -72.72320  1134.417
##    ORIG_FID                  geometry
## 1     15720 POINT (753194.9 202803.9)
## 2     19031 POINT (753104.8 202903.9)
## 3     19045   POINT (753244.8 202904)
## 4     19710   POINT (753254.8 202924)
## 5     20708   POINT (753274.8 202954)
## 6     21033   POINT (753204.8 202964)
## 7     22681 POINT (753084.8 203013.9)
## 8     23351 POINT (753144.8 203033.9)
## 9     23356   POINT (753194.8 203034)
## 10    24029   POINT (753284.8 203054)

predictor.variable.names <- colnames(datasample)[1:7]
predictor.variable.names

## [1] "B2"   "B3"   "B4"   "B8"   "EVI"  "SAVI" "NDWI"

Se ejecuta el algoritmo Random Forest Espacial, el cual arroja como resultado que no existe correlación espacial entre los datos tomados y por ende no es necesario ajustar el modelo.

spatial.model <- spatialRF::rf_spatial(
  data = (as.data.frame(datasample)),
  dependent.variable.name = "BA",
  predictor.variable.names = predictor.variable.names,
  distance.matrix = censo_dist
  )

## The model residuals are not spatially correlated, there is no need to fit a spatial model

Se muestran los parametros bajo los cuales el modelo fue intentó estimar la biomasa aérea. Con la intención de poder comprar los resultados, se trabaja con los parametros por defecto ya que corresponden tanto en número de arboles, variables por arbol y variables predictoras.

spatial.model

## Model type
##   - Fitted with:                     ranger()
##   - Response variable:               BA
## 
## Random forest parameters
##   - Type:                            Regression
##   - Number of trees:                 500
##   - Sample size:                     316
##   - Number of predictors:            7
##   - Mtry:                            2
##   - Minimum node size:               5
## 
## 
## Model performance 
##   - R squared (oob):                  -0.1054475
##   - R squared (cor(obs, pred)^2):     0.8931268
##   - Pseudo R squared (cor(obs, pred)):0.9450539
##   - RMSE (oob):                       4643.8
##   - RMSE:                             2301.5
##   - Normalized RMSE:                  0.7329261
## 
## Model residuals 
##   - Stats: 
##          +------------------------------------------------------------+
##          ¦ Min.     ¦ 1st Q.   ¦ Median  ¦ Mean   ¦ 3rd Q. ¦ Max.     ¦
##          +----------+----------+---------+--------+--------+----------¦
##          ¦ -7489.86 ¦ -1135.17 ¦ -553.70 ¦ -65.78 ¦ 303.77 ¦ 19099.53 ¦
##          +------------------------------------------------------------+
##   - Normality: 
##       - Shapiro-Wilks W: 0.726 
##       - p-value        : 0 
##       - Interpretation : Residuals are not normal 
## 
##   - Spatial autocorrelation: 
##              +---------------------------------------------------+
##              ¦ Distance ¦ Moran's I ¦ P value ¦ Interpretation   ¦
##              +----------+-----------+---------+------------------¦
##              ¦      0.0 ¦     0.001 ¦   0.646 ¦ No spatial       ¦
##              ¦          ¦           ¦         ¦ correlation      ¦
##              +----------+-----------+---------+------------------¦
##              ¦      0.0 ¦     0.001 ¦   0.646 ¦ No spatial       ¦
##              ¦          ¦           ¦         ¦ correlation      ¦
##              +----------+-----------+---------+------------------¦
##              ¦      0.0 ¦     0.001 ¦   0.646 ¦ No spatial       ¦
##              ¦          ¦           ¦         ¦ correlation      ¦
##              +----------+-----------+---------+------------------¦
##              ¦      0.0 ¦     0.001 ¦   0.646 ¦ No spatial       ¦
##              ¦          ¦           ¦         ¦ correlation      ¦
##              +---------------------------------------------------+
## 
## Variable importance: 
##                            +-----------------------+
##                            ¦ Variable ¦ Importance ¦
##                            +----------+------------¦
##                            ¦ SAVI     ¦   3410.627 ¦
##                            +----------+------------¦
##                            ¦ NDWI     ¦   2819.098 ¦
##                            +----------+------------¦
##                            ¦ B4       ¦   2377.067 ¦
##                            +----------+------------¦
##                            ¦ B2       ¦   2182.772 ¦
##                            +----------+------------¦
##                            ¦ B8       ¦   2016.374 ¦
##                            +----------+------------¦
##                            ¦ B3       ¦   1626.462 ¦
##                            +----------+------------¦
##                            ¦ EVI      ¦    962.582 ¦
##                            +-----------------------+

Para validar que efectivamente que no hay correlación espacial, se realiza un scatter-plot de la variable biomasa aérea contra cada uno de las variables independientes.

Esto muestra que no hay un comportamiento de aumento o cambio de la variable dependiente en función de las independientes.

spatialRF::plot_training_df(
  data = (as.data.frame(datasample)),
  dependent.variable.name =  "BA",
  predictor.variable.names = predictor.variable.names,
  ncol = 3,
  point.color = viridis::viridis(100, option = "F"),
  line.color = "gray30"
  )

XY<-cbind(censo_st$X,censo_st$Y)
XY<- as.data.frame(XY)
XY<-rename(XY,x=V1,y=V2)
XY

##             x        y
## 1   -72.72400 1.833383
## 2   -72.72486 1.834302
## 3   -72.72363 1.834244
## 4   -72.72348 1.834458
## 5   -72.72335 1.834757
## 6   -72.72395 1.834833
## 7   -72.72503 1.835278
## 8   -72.72452 1.835449
## 9   -72.72401 1.835482
## 10  -72.72320 1.835609
## 11  -72.72347 1.835754
## 12  -72.72497 1.835787
## 13  -72.72629 1.835930
## 14  -72.72460 1.835934
## 15  -72.72413 1.836010
## 16  -72.72336 1.836035
## 17  -72.72608 1.836070
## 18  -72.72296 1.836306
## 19  -72.72601 1.836603
## 20  -72.72266 1.836729
## 21  -72.72263 1.836828
## 22  -72.72408 1.836935
## 23  -72.72389 1.837002
## 24  -72.72338 1.837184
## 25  -72.72286 1.837134
## 26  -72.72354 1.837294
## 27  -72.72313 1.837223
## 28  -72.73114 1.837313
## 29  -72.73075 1.837472
## 30  -72.72622 1.837415
## 31  -72.72327 1.837460
## 32  -72.72985 1.837550
## 33  -72.72705 1.837501
## 34  -72.72481 1.837553
## 35  -72.73118 1.837624
## 36  -72.72712 1.837599
## 37  -72.72755 1.837751
## 38  -72.72680 1.837920
## 39  -72.72669 1.837861
## 40  -72.72632 1.837917
## 41  -72.72337 1.837928
## 42  -72.72678 1.837993
## 43  -72.72626 1.838011
## 44  -72.72624 1.838029
## 45  -72.72578 1.838115
## 46  -72.72744 1.838247
## 47  -72.72636 1.838255
## 48  -72.73102 1.838335
## 49  -72.73097 1.838389
## 50  -72.72691 1.838306
## 51  -72.73103 1.838444
## 52  -72.72346 1.838432
## 53  -72.73161 1.838611
## 54  -72.72422 1.838706
## 55  -72.71274 1.838694
## 56  -72.73047 1.838806
## 57  -72.73167 1.838861
## 58  -72.72596 1.838908
## 59  -72.72236 1.838850
## 60  -72.71240 1.838955
## 61  -72.73175 1.839028
## 62  -72.73158 1.839083
## 63  -72.72653 1.839028
## 64  -72.72690 1.839279
## 65  -72.72597 1.839242
## 66  -72.72859 1.839303
## 67  -72.72675 1.839361
## 68  -72.72270 1.839358
## 69  -72.72255 1.839365
## 70  -72.71831 1.839303
## 71  -72.72755 1.839481
## 72  -72.72319 1.839547
## 73  -72.71760 1.839517
## 74  -72.72224 1.839591
## 75  -72.71845 1.839584
## 76  -72.72616 1.839668
## 77  -72.71976 1.839805
## 78  -72.72702 1.839845
## 79  -72.73219 1.839944
## 80  -72.72553 1.839945
## 81  -72.72268 1.840066
## 82  -72.72068 1.840098
## 83  -72.72429 1.840179
## 84  -72.72806 1.840261
## 85  -72.71880 1.840237
## 86  -72.72843 1.840417
## 87  -72.72330 1.840461
## 88  -72.71263 1.840423
## 89  -72.72831 1.840491
## 90  -72.72037 1.840477
## 91  -72.73117 1.840651
## 92  -72.71991 1.840566
## 93  -72.71702 1.840566
## 94  -72.73117 1.840667
## 95  -72.72943 1.840729
## 96  -72.72788 1.840655
## 97  -72.73238 1.840831
## 98  -72.71885 1.840879
## 99  -72.71802 1.840859
## 100 -72.71793 1.840877
## 101 -72.71231 1.840862
## 102 -72.73111 1.841020
## 103 -72.72320 1.841029
## 104 -72.71773 1.841066
## 105 -72.71769 1.841067
## 106 -72.73208 1.841167
## 107 -72.72611 1.841143
## 108 -72.72067 1.841104
## 109 -72.71241 1.841091
## 110 -72.72642 1.841212
## 111 -72.72380 1.841206
## 112 -72.72317 1.841210
## 113 -72.72136 1.841267
## 114 -72.71761 1.841186
## 115 -72.72575 1.841365
## 116 -72.72295 1.841305
## 117 -72.71904 1.841320
## 118 -72.73310 1.841428
## 119 -72.71258 1.841418
## 120 -72.73133 1.841556
## 121 -72.72844 1.841490
## 122 -72.72064 1.841556
## 123 -72.72827 1.841672
## 124 -72.72541 1.841714
## 125 -72.72342 1.841667
## 126 -72.72775 1.841760
## 127 -72.72572 1.841759
## 128 -72.72276 1.841795
## 129 -72.73242 1.841889
## 130 -72.73189 1.841889
## 131 -72.72574 1.841835
## 132 -72.71187 1.841817
## 133 -72.72586 1.842001
## 134 -72.72148 1.841972
## 135 -72.72019 1.841991
## 136 -72.72299 1.842071
## 137 -72.71250 1.842076
## 138 -72.72131 1.842111
## 139 -72.71267 1.842104
## 140 -72.72199 1.842231
## 141 -72.71117 1.842188
## 142 -72.73303 1.842353
## 143 -72.73281 1.842500
## 144 -72.72069 1.842528
## 145 -72.72137 1.842677
## 146 -72.72224 1.842756
## 147 -72.71207 1.842787
## 148 -72.72773 1.842867
## 149 -72.72417 1.842903
## 150 -72.72140 1.842877
## 151 -72.72413 1.842947
## 152 -72.71749 1.842943
## 153 -72.72131 1.843051
## 154 -72.72121 1.843103
## 155 -72.71090 1.843117
## 156 -72.71049 1.843207
## 157 -72.72419 1.843278
## 158 -72.71903 1.843291
## 159 -72.72124 1.843375
## 160 -72.72589 1.843596
## 161 -72.71764 1.843600
## 162 -72.71969 1.843697
## 163 -72.72724 1.843764
## 164 -72.72926 1.843863
## 165 -72.72729 1.843879
## 166 -72.71709 1.843878
## 167 -72.71794 1.844036
## 168 -72.72031 1.844149
## 169 -72.71240 1.844199
## 170 -72.72578 1.844339
## 171 -72.71816 1.844447
## 172 -72.71845 1.844644
## 173 -72.71936 1.844747
## 174 -72.71948 1.844802
## 175 -72.71158 1.844874
## 176 -72.71154 1.844966
## 177 -72.71015 1.845010
## 178 -72.71221 1.845217
## 179 -72.71164 1.845274
## 180 -72.71079 1.845308
## 181 -72.71920 1.845370
## 182 -72.71225 1.845402
## 183 -72.71162 1.845350
## 184 -72.71012 1.845401
## 185 -72.70829 1.845495
## 186 -72.71307 1.845747
## 187 -72.70918 1.845782
## 188 -72.70880 1.845755
## 189 -72.71304 1.845841
## 190 -72.70875 1.845810
## 191 -72.71786 1.845960
## 192 -72.70837 1.845952
## 193 -72.70813 1.845933
## 194 -72.70968 1.846033
## 195 -72.71258 1.846087
## 196 -72.71166 1.846086
## 197 -72.71408 1.846234
## 198 -72.70869 1.846231
## 199 -72.71489 1.846293
## 200 -72.71853 1.846398
## 201 -72.71730 1.846341
## 202 -72.71500 1.846376
## 203 -72.71481 1.846398
## 204 -72.71344 1.846377
## 205 -72.71103 1.846363
## 206 -72.70986 1.846421
## 207 -72.70861 1.846415
## 208 -72.70831 1.846379
## 209 -72.70861 1.846483
## 210 -72.72007 1.846609
## 211 -72.71516 1.846531
## 212 -72.71414 1.846586
## 213 -72.71220 1.846537
## 214 -72.71139 1.846545
## 215 -72.70865 1.846525
## 216 -72.71390 1.846651
## 217 -72.71215 1.846669
## 218 -72.70847 1.846651
## 219 -72.70825 1.846604
## 220 -72.71766 1.846764
## 221 -72.71494 1.846751
## 222 -72.71463 1.846752
## 223 -72.71574 1.846910
## 224 -72.71526 1.846906
## 225 -72.71032 1.847022
## 226 -72.71749 1.847089
## 227 -72.71733 1.847107
## 228 -72.71687 1.847093
## 229 -72.71619 1.847111
## 230 -72.71569 1.847097
## 231 -72.70913 1.847136
## 232 -72.71201 1.847181
## 233 -72.71110 1.847204
## 234 -72.70915 1.847228
## 235 -72.71718 1.847268
## 236 -72.71661 1.847250
## 237 -72.71366 1.847301
## 238 -72.71694 1.847414
## 239 -72.71116 1.847401
## 240 -72.70884 1.847333
## 241 -72.71838 1.847497
## 242 -72.71659 1.847433
## 243 -72.71381 1.847439
## 244 -72.71214 1.847450
## 245 -72.71171 1.847493
## 246 -72.71159 1.847442
## 247 -72.70863 1.847482
## 248 -72.71968 1.847586
## 249 -72.71706 1.847534
## 250 -72.71263 1.847559
## 251 -72.71184 1.847525
## 252 -72.71151 1.847578
## 253 -72.71112 1.847596
## 254 -72.71075 1.847567
## 255 -72.70964 1.847638
## 256 -72.70958 1.847679
## 257 -72.70884 1.847658
## 258 -72.71769 1.847727
## 259 -72.70906 1.847717
## 260 -72.71566 1.847858
## 261 -72.71929 1.847970
## 262 -72.71505 1.847983
## 263 -72.71330 1.848009
## 264 -72.71253 1.848105
## 265 -72.71166 1.848051
## 266 -72.71731 1.848210
## 267 -72.71160 1.848154
## 268 -72.71819 1.848301
## 269 -72.70941 1.848302
## 270 -72.72008 1.848329
## 271 -72.71109 1.848403
## 272 -72.71018 1.848333
## 273 -72.71843 1.848463
## 274 -72.71690 1.848424
## 275 -72.71312 1.848482
## 276 -72.72117 1.848561
## 277 -72.71856 1.848585
## 278 -72.71507 1.848531
## 279 -72.71289 1.848587
## 280 -72.70982 1.848674
## 281 -72.71722 1.848743
## 282 -72.71083 1.848776
## 283 -72.71059 1.848819
## 284 -72.71139 1.848937
## 285 -72.71120 1.848948
## 286 -72.71138 1.849121
## 287 -72.71065 1.849137
## 288 -72.71049 1.849196
## 289 -72.71919 1.849299
## 290 -72.71910 1.849274
## 291 -72.71712 1.849300
## 292 -72.71534 1.849295
## 293 -72.71491 1.849239
## 294 -72.71461 1.849236
## 295 -72.71077 1.849296
## 296 -72.71460 1.849397
## 297 -72.71451 1.849828
## 298 -72.71443 1.849835
## 299 -72.71329 1.849773
## 300 -72.71212 1.849806
## 301 -72.71188 1.849859
## 302 -72.71224 1.849864
## 303 -72.71730 1.850032
## 304 -72.71192 1.850015
## 305 -72.71880 1.850128
## 306 -72.71494 1.850088
## 307 -72.71441 1.850065
## 308 -72.71954 1.850195
## 309 -72.71739 1.850155
## 310 -72.71557 1.850307
## 311 -72.71499 1.850299
## 312 -72.71182 1.850239
## 313 -72.72121 1.850385
## 314 -72.71737 1.850328
## 315 -72.71602 1.850423
## 316 -72.71709 1.850705

model.spatial.eva <- spatialRF::rf_evaluate(
  model = spatial.model,
  xy =XY,                  #data coordinates
  repetitions = 30,         #number of spatial folds
  training.fraction = 0.70, #training data fraction on each fold
  metrics = "r.squared",
  seed = 1,
  verbose = FALSE
)

model.spatial.eva

## Model type
##   - Fitted with:                     ranger()
##   - Response variable:               BA
## 
## Random forest parameters
##   - Type:                            Regression
##   - Number of trees:                 500
##   - Sample size:                     316
##   - Number of predictors:            7
##   - Mtry:                            2
##   - Minimum node size:               5
## 
## 
## Model performance 
##   - R squared (oob):                  -0.1054475
##   - R squared (cor(obs, pred)^2):     0.8931268
##   - Pseudo R squared (cor(obs, pred)):0.9450539
##   - RMSE (oob):                       4643.8
##   - RMSE:                             2301.5
##   - Normalized RMSE:                  0.7329261
## 
## Model residuals 
##   - Stats: 
##          +------------------------------------------------------------+
##          ¦ Min.     ¦ 1st Q.   ¦ Median  ¦ Mean   ¦ 3rd Q. ¦ Max.     ¦
##          +----------+----------+---------+--------+--------+----------¦
##          ¦ -7489.86 ¦ -1135.17 ¦ -553.70 ¦ -65.78 ¦ 303.77 ¦ 19099.53 ¦
##          +------------------------------------------------------------+
##   - Normality: 
##       - Shapiro-Wilks W: 0.726 
##       - p-value        : 0 
##       - Interpretation : Residuals are not normal 
## 
##   - Spatial autocorrelation: 
##              +---------------------------------------------------+
##              ¦ Distance ¦ Moran's I ¦ P value ¦ Interpretation   ¦
##              +----------+-----------+---------+------------------¦
##              ¦      0.0 ¦     0.001 ¦   0.646 ¦ No spatial       ¦
##              ¦          ¦           ¦         ¦ correlation      ¦
##              +----------+-----------+---------+------------------¦
##              ¦      0.0 ¦     0.001 ¦   0.646 ¦ No spatial       ¦
##              ¦          ¦           ¦         ¦ correlation      ¦
##              +----------+-----------+---------+------------------¦
##              ¦      0.0 ¦     0.001 ¦   0.646 ¦ No spatial       ¦
##              ¦          ¦           ¦         ¦ correlation      ¦
##              +----------+-----------+---------+------------------¦
##              ¦      0.0 ¦     0.001 ¦   0.646 ¦ No spatial       ¦
##              ¦          ¦           ¦         ¦ correlation      ¦
##              +---------------------------------------------------+
## 
## Variable importance: 
##                            +-----------------------+
##                            ¦ Variable ¦ Importance ¦
##                            +----------+------------¦
##                            ¦ SAVI     ¦   3410.627 ¦
##                            +----------+------------¦
##                            ¦ NDWI     ¦   2819.098 ¦
##                            +----------+------------¦
##                            ¦ B4       ¦   2377.067 ¦
##                            +----------+------------¦
##                            ¦ B2       ¦   2182.772 ¦
##                            +----------+------------¦
##                            ¦ B8       ¦   2016.374 ¦
##                            +----------+------------¦
##                            ¦ B3       ¦   1626.462 ¦
##                            +----------+------------¦
##                            ¦ EVI      ¦    962.582 ¦
##                            +-----------------------+
## 
## Spatial evaluation 
##   - Training fraction:             0.7
##   - Spatial folds:                 29
## 
##     Metric Median   MAD Minimum Maximum
##  r.squared  0.001 0.001       0   0.071

3.5 CORRELACIONES ENTRE DATOS DEL CENSO FORESTAL E ÍNDICES

Los indices calculados permitieron comparar los datos de campo con los indices espectrales, sin embargo los resultados indican que las correlaciones existentes entre el la medición de bioimasa aérea, no tienen correspondencia alguna con índices calculados. Los valores obtenidos en cada uno de los resultados fue muy cercano a 0.

xy <- as.matrix(geom(censo)[,c('x','y')])
CompSAVI <- raster::extract(SAVI, xy)


x0y0 <- as.matrix(geom(censo)[,c('x','y')])
CompEVI <- raster::extract(EVI, x0y0)


x1y1 <- as.matrix(geom(censo)[,c('x','y')])
CompNDWI <- raster::extract(NDWI, x1y1)


x2y2 <- as.matrix(geom(censo)[,c('x','y')])
CompB2 <- raster::extract(b2c, x2y2)


x3y3 <- as.matrix(geom(censo)[,c('x','y')]) 
CompB3 <- raster::extract(b3c, x3y3)


x4y4 <- as.matrix(geom(censo)[,c('x','y')]) 
CompB4 <- raster::extract(b4c, x4y4)



x5y5 <- as.matrix(geom(censo)[,c('x','y')]) 
CompB8 <- raster::extract(b8c, x5y5)


CompSAVI<- as.matrix(CompSAVI)
CompSAVI<- as.data.frame(CompSAVI)

CompEVI<- as.matrix(CompEVI)
CompEVI<- as.data.frame(CompEVI)

CompNDWI<- as.matrix(CompNDWI)
CompNDWI<- as.data.frame(CompNDWI)

CompB2<- as.matrix(CompB2)
CompB2<- as.data.frame(CompB2)

CompB3<- as.matrix(CompB3)
CompB3<- as.data.frame(CompB3)

CompB4<- as.matrix(CompB4)
CompB4<- as.data.frame(CompB4)

CompB8<- as.matrix(CompB8)
CompB8<- as.data.frame(CompB8)


Censodf<- as.data.frame(censo_st)

datossavi <- cbind.data.frame(Censodf,CompSAVI)
datosevi <- cbind.data.frame(Censodf,CompEVI)
datosndwi <- cbind.data.frame(Censodf,CompNDWI)
datosb2 <- cbind.data.frame(Censodf,CompB2)
datosb3 <- cbind.data.frame(Censodf,CompB3)
datosb4 <- cbind.data.frame(Censodf,CompB4)
datosb8 <- cbind.data.frame(Censodf,CompB8)

names(datossavi)

##  [1] "OBJECTID_1"                     "OBJECTID"                      
##  [3] "Join_Count"                     "TARGET_FID"                    
##  [5] "Id"                             "Y"                             
##  [7] "X"                              "BA_KG_CL2"                     
##  [9] "ORIG_FID"                       "geometry"                      
## [11] "T18NYH_20200907T151709_B08_10m"

datossavi=rename(datossavi,SAVI=T18NYH_20200907T151709_B08_10m)

datossavi

##     OBJECTID_1 OBJECTID Join_Count TARGET_FID Id        Y         X  BA_KG_CL2
## 1            1    15720          3      15719  1 1.833383 -72.72400  4501.6203
## 2            2    19031          3      19030  1 1.834302 -72.72486  4841.9386
## 3            3    19045          3      19044  1 1.834244 -72.72363  4119.6558
## 4            4    19710          3      19709  1 1.834458 -72.72348  3424.2565
## 5            5    20708          3      20707  1 1.834757 -72.72335  5703.6193
## 6            6    21033          3      21032  1 1.834833 -72.72395  1248.1745
## 7            7    22681          3      22680  1 1.835278 -72.72503  5597.1450
## 8            8    23351          3      23350  1 1.835449 -72.72452  2161.0103
## 9            9    23356          3      23355  1 1.835482 -72.72401  2318.4994
## 10          10    24029          3      24028  1 1.835609 -72.72320  1134.4166
## 11          11    24358          3      24357  1 1.835754 -72.72347  1460.3116
## 12          12    24674          3      24673  1 1.835787 -72.72497  3320.6009
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## 265    69974 POINT (754574.2 204434.8) 1.2062466
## 266    70243 POINT (753944.1 204444.5) 1.2125293
## 267    70306 POINT (754574.2 204444.8) 1.2273369
## 268    70565 POINT (753844.1 204454.5) 1.2300716
## 269    70663   POINT (754824.2 204455) 1.2218780
## 270    70876 POINT (753634.1 204464.4) 1.1984558
## 271    70976 POINT (754634.2 204464.9) 1.2054557
## 272    70986 POINT (754734.2 204464.9) 1.2185698
## 273    71226 POINT (753814.1 204474.5) 1.2389917
## 274    71243 POINT (753984.1 204474.5) 1.2180326
## 275    71285 POINT (754404.2 204474.8) 1.1998612
## 276    71528 POINT (753514.1 204484.3) 1.1048237
## 277    71557 POINT (753804.1 204484.5) 1.2460331
## 278    71596 POINT (754194.1 204484.7) 1.1688231
## 279    71620 POINT (754434.2 204484.8) 1.2190572
## 280    71986   POINT (754774.2 204495) 1.1656099
## 281    72236 POINT (753954.1 204504.5) 1.2073850
## 282    72639 POINT (754664.2 204514.9) 1.1600524
## 283    72642 POINT (754694.2 204514.9) 1.2401945
## 284    72965 POINT (754604.2 204524.9) 1.1795415
## 285    72967 POINT (754624.2 204524.9) 1.1844322
## 286    73629 POINT (754604.1 204544.9) 1.1998029
## 287    73969 POINT (754684.1 204554.9) 1.2086161
## 288    73971 POINT (754704.2 204554.9) 1.2190139
## 289    74206   POINT (753734 204564.4) 1.2422446
## 290    74207   POINT (753744 204564.4) 1.2513302
## 291    74229 POINT (753964.1 204564.5) 1.2187938
## 292    74249 POINT (754164.1 204564.6) 1.1716045
## 293    74254 POINT (754214.1 204564.7) 1.2261527
## 294    74257 POINT (754244.1 204564.7) 1.1835295
## 295    74300 POINT (754674.1 204564.9) 1.2279313
## 296    74589 POINT (754244.1 204574.7) 1.2018920
## 297    76250 POINT (754254.1 204624.7) 1.2029262
## 298    76251 POINT (754264.1 204624.7) 1.1989936
## 299    76264 POINT (754394.1 204624.8) 1.2191225
## 300    76277 POINT (754524.1 204624.8) 1.2061080
## 301    76279 POINT (754544.1 204624.9) 1.1947551
## 302    76607 POINT (754504.1 204634.8) 1.2242063
## 303    76883   POINT (753944 204644.5) 1.2166697
## 304    76943 POINT (754544.1 204644.9) 1.2439767
## 305    77198   POINT (753774 204654.5) 1.2116951
## 306    77241   POINT (754204 204654.7) 1.1606115
## 307    77247   POINT (754264 204654.7) 1.2061950
## 308    77522   POINT (753694 204664.4) 1.2339806
## 309    77546   POINT (753934 204664.5) 1.2285908
## 310    77898   POINT (754134 204674.6) 1.1982001
## 311    77905   POINT (754204 204674.7) 1.1467161
## 312    77940 POINT (754554.1 204674.9) 1.2362593
## 313    78167 POINT (753503.9 204684.3) 1.2043435
## 314    78210   POINT (753934 204684.5) 1.2106654
## 315    78557   POINT (754084 204694.6) 1.1987027
## 316    79541   POINT (753964 204724.6) 1.1043754

names(datosevi)

##  [1] "OBJECTID_1"                     "OBJECTID"                      
##  [3] "Join_Count"                     "TARGET_FID"                    
##  [5] "Id"                             "Y"                             
##  [7] "X"                              "BA_KG_CL2"                     
##  [9] "ORIG_FID"                       "geometry"                      
## [11] "T18NYH_20200907T151709_B08_10m"

datosevi=rename(datosevi,EVI=T18NYH_20200907T151709_B08_10m)

names(datosndwi)

##  [1] "OBJECTID_1"                     "OBJECTID"                      
##  [3] "Join_Count"                     "TARGET_FID"                    
##  [5] "Id"                             "Y"                             
##  [7] "X"                              "BA_KG_CL2"                     
##  [9] "ORIG_FID"                       "geometry"                      
## [11] "T18NYH_20200907T151709_B03_10m"

datosndwi=rename(datosndwi,NDWI=T18NYH_20200907T151709_B03_10m)

names(datosb2)

##  [1] "OBJECTID_1"                     "OBJECTID"                      
##  [3] "Join_Count"                     "TARGET_FID"                    
##  [5] "Id"                             "Y"                             
##  [7] "X"                              "BA_KG_CL2"                     
##  [9] "ORIG_FID"                       "geometry"                      
## [11] "T18NYH_20200907T151709_B02_10m"

datosb2=rename(datosb2,B2=T18NYH_20200907T151709_B02_10m)

names(datosb3)

##  [1] "OBJECTID_1"                     "OBJECTID"                      
##  [3] "Join_Count"                     "TARGET_FID"                    
##  [5] "Id"                             "Y"                             
##  [7] "X"                              "BA_KG_CL2"                     
##  [9] "ORIG_FID"                       "geometry"                      
## [11] "T18NYH_20200907T151709_B03_10m"

datosb3=rename(datosb3,B3=T18NYH_20200907T151709_B03_10m)

names(datosb4)

##  [1] "OBJECTID_1"                     "OBJECTID"                      
##  [3] "Join_Count"                     "TARGET_FID"                    
##  [5] "Id"                             "Y"                             
##  [7] "X"                              "BA_KG_CL2"                     
##  [9] "ORIG_FID"                       "geometry"                      
## [11] "T18NYH_20200907T151709_B04_10m"

datosb4=rename(datosb4,B4=T18NYH_20200907T151709_B04_10m)

names(datosb8)

##  [1] "OBJECTID_1"                     "OBJECTID"                      
##  [3] "Join_Count"                     "TARGET_FID"                    
##  [5] "Id"                             "Y"                             
##  [7] "X"                              "BA_KG_CL2"                     
##  [9] "ORIG_FID"                       "geometry"                      
## [11] "T18NYH_20200907T151709_B08_10m"

datosb8=rename(datosb8,B8=T18NYH_20200907T151709_B08_10m)

V_SAVI<- subset(x = datossavi, select = c("BA_KG_CL2", "SAVI"))
V_EVI<- subset(x = datosevi, select = c("BA_KG_CL2", "EVI"))
V_NDWI<- subset(x = datosndwi, select = c("BA_KG_CL2", "NDWI"))
V_B2<- subset(x = datosb2, select = c("BA_KG_CL2", "B2"))
V_B3<- subset(x = datosb3, select = c("BA_KG_CL2", "B3"))
V_B4<- subset(x = datosb4, select = c("BA_KG_CL2", "B4"))
V_B8<- subset(x = datosb8, select = c("BA_KG_CL2", "B8"))

• Correlaciones

chart.Correlation(V_SAVI)

chart.Correlation(V_EVI)

chart.Correlation(V_NDWI)

chart.Correlation(V_B2)

chart.Correlation(V_B3)

chart.Correlation(V_B4)

chart.Correlation(V_B8)

4.DISCUSIÓN

Durante la ejecuciones de los algoritmos de aprendizaje de maquinas en su versión no espacial y espacial, se evidencia la necesidad de tener claro que la variable dependiente pueda ser resuelta por las independientes siguiendo la lógica de percepción remota. En este caso el análisis a nivel de pixel quizá no sea el mas adecuado, a lo que se suma que los valores de biomasa aérea calculados con la ecuación alométrica responde árbol a árbol y en un solo pixel pueden haber mucho arboles que posiblemente no fueron medidos. Sumado a lo dicho, se desconoce el impacto de los pixeles vecinos sobre el pixel a evaluar.

Teniendo en cuenta lo anterior las regresiones realizadas a partir de Random Forest no lograron brindar resultados para una buena estimación de la variable dependiente, sin embargo se logró evidenciar que al remover los índices espectrales e intentar estimar la biomasa aérea únicamente usando las bandas de la imagen Sentinel-2, el porcentaje de ajuste del modelo aumento ligeramente con respecto a las otras parametrizaciones realizadas.

El uso de Random Forest Espacial, no permitió realizar un análisis a profundidad debido a que la naturaleza de los datos de entrada no mostro una correlación espacial, mostrando un p-value de 0 al intentar ejecutar el índice de Moran.

Los valores de R2 para ambos modelos son muy bajos, cercanos a cero y negativos. Lo que evidencia que el modelo no se ajusta a los datos.

#NO ESPACIAL
mean(BA.rf$rsq)

## [1] -0.1333619

#ESPACIAL
mean(spatial.model$r.squared)

## [1] -0.1054475

5.CONCLUSIONES

-Es necesario evaluar la naturaleza de los datos previo a realizar un ejercicio de clasificación o regresión al utilizar algoritmos de aprendizaje de maquina.

-Tener en cuenta indicadores como el R2 permiten evaluar que tan bien o mal nuestro modelo logra predecir la variable dependiente.

-Debido a la naturaleza de los datos no fue posible estimar algunos parámetros como el análisis de colinearidad entre variables y el índice de Moran por cada variable independiente según la distancia de los elementos

-Tener en cuenta las relaciones espaciales e puede ayudar a fortalecer estimaciones de la variable dependiente.

-En la aplicación de ambos métodos, los índices NDWI y SAVI, tienen la mayor representatividad, mientras que el índice EVI tiene el menor valor.

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