En este cuaderno se muestra uno de los métodos de interpolación espacial aplicado a un conjunto de datos de precipitación correspondientes al departamento de Boyacá.

Polígonos de Thiessen

Los polígonos de Thiessen (o interpolación de proximidad) se pueden crear utilizando la función dirichlet del faquete spatstat.

#LLamar las librerías necesarias
library(spatstat)#Utilizado para la función de teselación dirichlet
## Loading required package: spatstat.data
## Loading required package: nlme
## Loading required package: rpart
## 
## spatstat 1.64-1       (nickname: 'Help you I can, yes!') 
## For an introduction to spatstat, type 'beginner'
library(maptools)#Utilizado para la conversión de SPDF a ppp
## Loading required package: sp
## Checking rgeos availability: TRUE
library(raster)# Se utiliza para recortar polígonos de Thiessen
## 
## Attaching package: 'raster'
## The following objects are masked from 'package:spatstat':
## 
##     area, rotate, shift
## The following object is masked from 'package:nlme':
## 
##     getData

Es importante subir el mapa de puntos de precipitacion y el archivo que represente nuestra área de interés:

Boyaca<-shapefile("C:/Users/Brian/Desktop/Daniela/geomatica/Informe final/boyaca2.shp")
Precipitacion <- shapefile('C:/Users/Brian/Desktop/Daniela/geomatica/Informe final/precipitacion2.shp')

Debemos asegurarnos de que las dos extensiones coincidan:

Precipitacion@bbox <-Boyaca@bbox
# Crear una superficie teselada
th  <-  as(dirichlet(as.ppp(Precipitacion)), "SpatialPolygons")
## 
##      PLEASE NOTE:  The components "delsgs" and "summary" of the
##  object returned by deldir() are now DATA FRAMES rather than
##  matrices (as they were prior to release 0.0-18).
##  See help("deldir").
##  
##      PLEASE NOTE: The process that deldir() uses for determining
##  duplicated points has changed from that used in version
##  0.0-9 of this package (and previously). See help("deldir").
# La función dirichlet no transfiere información de proyección, lo que requiere que esta información se agregue manualmente
crs(th) <- crs(Precipitacion)
crs(Boyaca) <- crs(Precipitacion)
crs(th) 
## CRS arguments:
##  +proj=tmerc +lat_0=4.59620041666667 +lon_0=-74.0775079166667 +k=1
## +x_0=1000000 +y_0=1000000 +ellps=GRS80 +units=m +no_defs
crs(Precipitacion)
## CRS arguments:
##  +proj=tmerc +lat_0=4.59620041666667 +lon_0=-74.0775079166667 +k=1
## +x_0=1000000 +y_0=1000000 +ellps=GRS80 +units=m +no_defs

La superficie teselada no almacena información de atributos de la capa de datos de puntos. Usaremos la función over () (del paquete sp) para unir los atributos de punto a la superficie teselada a través de una unión espacial. La función over () crea un marco de datos que deberá agregarse al objeto th, creando así un objeto SpatialPolygonsDataFrame.

th.z     <- over(th, Precipitacion, fn=mean)
## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
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th.spdf  <-  SpatialPolygonsDataFrame(th, th.z)

Finalmente, recortaremos la superficie teselada a los límites de Boyacá:

th.clp   <- raster::intersect(Boyaca,th.spdf)
## Loading required namespace: rgeos

Ahora solo queda mapear los datos, así:

library(tmap)
tm_shape(th.clp) + 
  tm_polygons(col="lluvia", palette="RdBu", midpoint=50,
              title="Polígonos Thiessen  \nPrecipitación prevista \n(enn mm)") +
  tm_legend(legend.outside=TRUE)

sessionInfo()
## R version 3.6.3 (2020-02-29)
## Platform: x86_64-w64-mingw32/x64 (64-bit)
## Running under: Windows 8.1 x64 (build 9600)
## 
## Matrix products: default
## 
## locale:
## [1] LC_COLLATE=Spanish_Colombia.1252  LC_CTYPE=Spanish_Colombia.1252   
## [3] LC_MONETARY=Spanish_Colombia.1252 LC_NUMERIC=C                     
## [5] LC_TIME=Spanish_Colombia.1252    
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
## [1] tmap_3.0            raster_3.0-12       maptools_0.9-9     
## [4] sp_1.4-1            spatstat_1.64-1     rpart_4.1-15       
## [7] nlme_3.1-144        spatstat.data_1.4-3
## 
## loaded via a namespace (and not attached):
##  [1] xfun_0.12             sf_0.9-3              splines_3.6.3        
##  [4] lattice_0.20-38       colorspace_1.4-1      spatstat.utils_1.17-0
##  [7] htmltools_0.4.0       stars_0.4-1           viridisLite_0.3.0    
## [10] base64enc_0.1-3       yaml_2.2.1            mgcv_1.8-31          
## [13] XML_3.99-0.3          rlang_0.4.5           e1071_1.7-3          
## [16] foreign_0.8-75        DBI_1.1.0             RColorBrewer_1.1-2   
## [19] lifecycle_0.2.0       stringr_1.4.0         rgeos_0.5-2          
## [22] munsell_0.5.0         htmlwidgets_1.5.1     codetools_0.2-16     
## [25] leafsync_0.1.0        evaluate_0.14         knitr_1.28           
## [28] crosstalk_1.1.0.1     parallel_3.6.3        class_7.3-15         
## [31] leafem_0.1.1          Rcpp_1.0.3            KernSmooth_2.23-16   
## [34] tensor_1.5            scales_1.1.0          classInt_0.4-3       
## [37] lwgeom_0.2-1          leaflet_2.0.3         abind_1.4-5          
## [40] deldir_0.1-25         png_0.1-7             digest_0.6.25        
## [43] stringi_1.4.6         tmaptools_3.0         polyclip_1.10-0      
## [46] grid_3.6.3            rgdal_1.4-8           tools_3.6.3          
## [49] magrittr_1.5          goftest_1.2-2         dichromat_2.0-0      
## [52] Matrix_1.2-18         rmarkdown_2.1         R6_2.4.1             
## [55] units_0.6-5           compiler_3.6.3