My seventh Notebook

##1. Introduction

Pre procesamiento Interpolacion, tomar varios puntos que sirven de muestreo, geometria de puntos con los valores de la propiedad, esos datos corresponden a un formato vectorial (shapefile, geopacket, geoJSON)
En campo Medicion, muestreo de la propiedad de interes y se obtienen datos, aqui descargamos los datos a traves de sitios como CHIRPS

##2. Downloading global precipitation data

CHIRPS, datos de precipitacion tomados con un sensor infrarrojo complementados con datos de estaciones, globales, diarios con un periodo ampli de 1981 y semanas atras al presente, producido por la Universidad de California en Santa Barbara, dato rastrer miden 0,05° de tamaño del pixel corresponde a 5,8 km
Baja resolucion pero utiles en Colombia un lugar donde la mitad de la zona no tiene estaciones meteorologicas
Los datos estan en formato raster, por ello hay que pasar de celdas a puntos para obtener datos con mayor resolucion
Datos .tiff, casi todos los rastrer viene en .tiff y son muy usados en geomatica
Libreria rgdal permite leer y entender datos raster, esta originalmente escriba en C++
Libreria gstat, responsable de geoestadistica e interpolaciones

library(rgdal)

## Loading required package: sp

## rgdal: version: 1.5-23, (SVN revision 1121)
## Geospatial Data Abstraction Library extensions to R successfully loaded
## Loaded GDAL runtime: GDAL 3.2.1, released 2020/12/29
## Path to GDAL shared files: C:/Users/morea/OneDrive - Universidad Nacional de Colombia/Documentos/R/win-library/4.1/rgdal/gdal
## GDAL binary built with GEOS: TRUE 
## Loaded PROJ runtime: Rel. 7.2.1, January 1st, 2021, [PJ_VERSION: 721]
## Path to PROJ shared files: C:/Users/morea/OneDrive - Universidad Nacional de Colombia/Documentos/R/win-library/4.1/rgdal/proj
## PROJ CDN enabled: FALSE
## Linking to sp version:1.4-5
## To mute warnings of possible GDAL/OSR exportToProj4() degradation,
## use options("rgdal_show_exportToProj4_warnings"="none") before loading rgdal.
## Overwritten PROJ_LIB was C:/Users/morea/OneDrive - Universidad Nacional de Colombia/Documentos/R/win-library/4.1/rgdal/proj

library(raster)
library(sf)

## Linking to GEOS 3.9.0, GDAL 3.2.1, PROJ 7.2.1

library(tidyverse)

## -- Attaching packages --------------------------------------- tidyverse 1.3.1 --

## v ggplot2 3.3.5     v purrr   0.3.4
## v tibble  3.1.2     v dplyr   1.0.7
## v tidyr   1.1.3     v stringr 1.4.0
## v readr   1.4.0     v forcats 0.5.1

## -- Conflicts ------------------------------------------ tidyverse_conflicts() --
## x tidyr::extract() masks raster::extract()
## x dplyr::filter()  masks stats::filter()
## x dplyr::lag()     masks stats::lag()
## x dplyr::select()  masks raster::select()

library(knitr)
library(tmap)
library(gstat)
library(sp)
library(leaflet)
library(RColorBrewer)
library(spatstat)

## Loading required package: spatstat.data

## Loading required package: spatstat.geom

## Registered S3 method overwritten by 'spatstat.geom':
##   method     from
##   print.boxx cli

## spatstat.geom 2.2-2

## 
## Attaching package: 'spatstat.geom'

## The following objects are masked from 'package:raster':
## 
##     area, rotate, shift

## Loading required package: spatstat.core

## Loading required package: nlme

## 
## Attaching package: 'nlme'

## The following object is masked from 'package:dplyr':
## 
##     collapse

## The following object is masked from 'package:raster':
## 
##     getData

## Loading required package: rpart

## spatstat.core 2.3-0

## 
## Attaching package: 'spatstat.core'

## The following object is masked from 'package:gstat':
## 
##     idw

## Loading required package: spatstat.linnet

## spatstat.linnet 2.3-0

## 
## spatstat 2.2-0       (nickname: 'That's not important right now') 
## For an introduction to spatstat, type 'beginner'

library(spatstat.data)
library(geoR)

## --------------------------------------------------------------
##  Analysis of Geostatistical Data
##  For an Introduction to geoR go to http://www.leg.ufpr.br/geoR
##  geoR version 1.8-1 (built on 2020-02-08) is now loaded
## --------------------------------------------------------------

##3. Pre prcesamiento de CHIRPS data

Leemos los datos CHIRPS

precip<-raster("C:/Users/morea/OneDrive - Universidad Nacional de Colombia/Documentos/UNAL/2021 - 1S/GeomaticaBasica/ImportFiles/chirps-v2.0.2021.06.6.tif/chirps-v2.0.2021.06.6.tif")

Capa raster con 2000 filas, 7200 columnas, 14400000 celdas, una resolucion de 0,05° cubriendo todo el globo, con interes en una region del territorio colombiano

precip

## class      : RasterLayer 
## dimensions : 2000, 7200, 14400000  (nrow, ncol, ncell)
## resolution : 0.05, 0.05  (x, y)
## extent     : -180, 180, -50, 50  (xmin, xmax, ymin, ymax)
## crs        : +proj=longlat +datum=WGS84 +no_defs 
## source     : chirps-v2.0.2021.06.6.tif 
## names      : chirps.v2.0.2021.06.6

Cargamos la zona de estudio

santander<-shapefile("C:/Users/morea/OneDrive - Universidad Nacional de Colombia/Documentos/UNAL/2021 - 1S/GeomaticaBasica/MGN2017_68_SANTANDER/68_SANTANDER/ADMINISTRATIVO/MGN_MPIO_POLITICO.shp")

santander

## class       : SpatialPolygonsDataFrame 
## features    : 87 
## extent      : -74.52895, -72.47706, 5.707536, 8.14501  (xmin, xmax, ymin, ymax)
## crs         : +proj=longlat +datum=WGS84 +no_defs 
## variables   : 9
## names       : DPTO_CCDGO, MPIO_CCDGO, MPIO_CNMBR,           MPIO_CRSLC,    MPIO_NAREA, MPIO_NANO, DPTO_CNMBR,     Shape_Leng,       Shape_Area 
## min values  :         68,      68001,     AGUADA,                 1539,   19.69444164,      2017,  SANTANDER, 0.270018178002, 0.00160984367921 
## max values  :         68,      68895,   ZAPATOCA, Ordenanza 33 de 1968, 3174.27867176,      2017,  SANTANDER,  4.36038638488,   0.259459176725

Recortamos los datos para que cubra solo al zona de interes

precip.crop <- raster::crop(precip, extent(santander))

Cuando recortamos un raster, nos sale un rectangulo como extension del objeto, si queremos que fuera de los limites no hayan datos y solo cubra la zona de interes creamos una mascara

precip.mask<-mask(x=precip.crop,mask=santander)

precip.mask

## class      : RasterLayer 
## dimensions : 49, 41, 2009  (nrow, ncol, ncell)
## resolution : 0.05, 0.05  (x, y)
## extent     : -74.55, -72.5, 5.699999, 8.149999  (xmin, xmax, ymin, ymax)
## crs        : +proj=longlat +datum=WGS84 +no_defs 
## source     : memory
## names      : chirps.v2.0.2021.06.6 
## values     : 2.722229, 61.97764  (min, max)

Ploteamos

plot(precip.mask, main= "CHIRPS rainfall in Santander from 26.03. to 30.03 in 2020 [mm]")
plot(santander, add=TRUE)

pal <- colorNumeric(c("red", "orange", "yellow", "blue", "darkblue"), values(precip.mask),
  na.color = "transparent")

leaflet() %>% addTiles() %>%
  addRasterImage(precip.mask, colors = pal, opacity = 0.6) %>%
  addLegend(pal = pal, values = values(precip.mask),
    title = "CHIRPS rainfall in Santander From 26.03 to 30.03 in 2020 [mm]")

## Warning in showSRID(uprojargs, format = "PROJ", multiline = "NO", prefer_proj =
## prefer_proj): Discarded ellps WGS 84 in Proj4 definition: +proj=merc +a=6378137
## +b=6378137 +lat_ts=0 +lon_0=0 +x_0=0 +y_0=0 +k=1 +units=m +nadgrids=@null
## +wktext +no_defs +type=crs

## Warning in showSRID(uprojargs, format = "PROJ", multiline = "NO", prefer_proj =
## prefer_proj): Discarded datum World Geodetic System 1984 in Proj4 definition

## Warning in showSRID(uprojargs, format = "PROJ", multiline = "NO", prefer_proj =
## prefer_proj): Discarded ellps WGS 84 in Proj4 definition: +proj=merc +a=6378137
## +b=6378137 +lat_ts=0 +lon_0=0 +x_0=0 +y_0=0 +k=1 +units=m +nadgrids=@null
## +wktext +no_defs +type=crs

## Warning in showSRID(uprojargs, format = "PROJ", multiline = "NO", prefer_proj =
## prefer_proj): Discarded datum World Geodetic System 1984 in Proj4 definition

La interpolacion necesita puntos entonces procedemos (spatial=T es que queremos que sean datos espaciales)
precip.points no siempre es eficiente

precip.points <- rasterToPoints(precip.mask, spatial = TRUE)

precip.points

## class       : SpatialPointsDataFrame 
## features    : 998 
## extent      : -74.475, -72.525, 5.774999, 8.124999  (xmin, xmax, ymin, ymax)
## crs         : +proj=longlat +datum=WGS84 +no_defs 
## variables   : 1
## names       : chirps.v2.0.2021.06.6 
## min values  :      2.72222924232483 
## max values  :      61.9776382446289

Cambiamos el nombre del atributo

names(precip.points)<-"rain"

precip.points

## class       : SpatialPointsDataFrame 
## features    : 998 
## extent      : -74.475, -72.525, 5.774999, 8.124999  (xmin, xmax, ymin, ymax)
## crs         : +proj=longlat +datum=WGS84 +no_defs 
## variables   : 1
## names       :             rain 
## min values  : 2.72222924232483 
## max values  : 61.9776382446289

Vemos la estructura para saber como estan los datos organizados

str(precip.points)

## Formal class 'SpatialPointsDataFrame' [package "sp"] with 5 slots
##   ..@ data       :'data.frame':  998 obs. of  1 variable:
##   .. ..$ rain: num [1:998] 31.8 30.6 31.4 32.4 33.6 ...
##   ..@ coords.nrs : num(0) 
##   ..@ coords     : num [1:998, 1:2] -73.8 -73.8 -73.8 -73.8 -73.8 ...
##   .. ..- attr(*, "dimnames")=List of 2
##   .. .. ..$ : NULL
##   .. .. ..$ : chr [1:2] "x" "y"
##   ..@ bbox       : num [1:2, 1:2] -74.47 5.77 -72.52 8.12
##   .. ..- attr(*, "dimnames")=List of 2
##   .. .. ..$ : chr [1:2] "x" "y"
##   .. .. ..$ : chr [1:2] "min" "max"
##   ..@ proj4string:Formal class 'CRS' [package "sp"] with 1 slot
##   .. .. ..@ projargs: chr "+proj=longlat +datum=WGS84 +no_defs"
##   .. .. ..$ comment: chr "GEOGCRS[\"WGS 84 (with axis order normalized for visualization)\",\n    DATUM[\"World Geodetic System 1984\",\n"| __truncated__

Ploteamos las celdas de la zona de interes y los puntos

plot(precip.mask, main= "CHIRPS rainfall from 26 to 30.03.2020 [mm]")
plot(santander, add=TRUE)
points(precip.points$x, precip.points$y, col = "red", cex = 0.6)

- Convertimos a objeto espacial

santander_sf<-sf::st_as_sf(santander)

Disuele limites externos

(border_sf <-
  santander_sf %>%
  summarise(area = sum(MPIO_NAREA)))

Hacemos una conversion inversa de sp a sf y cambiamos los nombres de los atributos para mayor facilidad en el reconocimiento con la funcion mutate

(santander.sf <- st_as_sf(santander) %>% mutate(MUNIC = MPIO_CNMBR, CODIGO = MPIO_CCDGO) %>% select(MUNIC, CODIGO))

p.sf <- st_as_sf(precip.points)

Interseccion, poner los poligonos con los puntos y guardar la informacion de los poligonos en los puntos

(precip.sf = st_intersection(santander.sf, p.sf))

## Warning: attribute variables are assumed to be spatially constant throughout all
## geometries

¿En que sistema de coordenadas vamos a usar?, en interpolacion es recomendable transformar de coordenadas geograficas a planas, en sentido estricto la interpolacion sucede en esa reproyeccion del plano y no en una esfera, en Colombia trabajamos con escalas medianas y pequeñas y por ello usamos un sistema de coordenadad magnacircas

(p.sf.magna <- st_transform(st_as_sf(precip.points), crs=32618))

(santander.sf.magna <- st_transform(santander.sf, crs=32618))

precip2 <- as(p.sf.magna, 'Spatial')

santander2 <- as(santander.sf.magna, 'Spatial')

precip2@bbox<-santander2@bbox

santander2

## class       : SpatialPolygonsDataFrame 
## features    : 87 
## extent      : 552105.4, 778842.2, 630996, 900533.3  (xmin, xmax, ymin, ymax)
## crs         : +proj=utm +zone=18 +datum=WGS84 +units=m +no_defs 
## variables   : 2
## names       :    MUNIC, CODIGO 
## min values  :   AGUADA,  68001 
## max values  : ZAPATOCA,  68895

Ploteamos la precipitacion en cada municipio y asi entender una distribucion espacial, obtenemos los puntos divididos en un sistema de grilla, esto no es comun, usualmente se ponen sistemas de muestreo aleatorio dependiendo de la variabilidad de la propiedad

[mapa inentendible, dejo codigo para proximas aplicaciones] tm_shape(santander2) + tm_polygons() + tm_shape(precip2) + tm_dots(col=“rain”, palette = “RdBu”, midpoint = 3.0, title=“Sampled precipitation (in mm)”, size=0.2) + tm_text(“rain”, just=“center”, xmod=.6, size = 0.5) + tm_legend(legend.outside=TRUE)

##4. Interpolando los datos de precipitacion #4.1 Poligonos de Thiessen

#4.2 Interpolacion por la Distancia Inversa Ponderada [IDW]

Creamos una grilla vacia, mejoramos la resolucion espacial al colocal 300.000 celdas y esto me permite controlar el espaciamiento de la grilla

grd<-as.data.frame(spsample(precip2, "regular", n=300000))
names(grd)<-c("X","Y")
coordinates(grd) <- c("X", "Y")
gridded(grd)<- TRUE  
fullgrid(grd)<- TRUE

x<-CRS(SRS_string='EPSG:32618')
wkt<-comment(x)
y<-CRS(SRS_string=wkt)

sp::proj4string(grd)<-y

P.idw <- gstat::idw(rain~1, precip2, newdata=grd, idp=2.0)

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r<-raster(P.idw)
(r.m<-raster::mask(r,santander2))

## class      : RasterLayer 
## dimensions : 597, 503, 300291  (nrow, ncol, ncell)
## resolution : 451.3462, 451.3462  (x, y)
## extent     : 551912.2, 778939.3, 630974.4, 900428.1  (xmin, xmax, ymin, ymax)
## crs        : +proj=utm +zone=18 +datum=WGS84 +units=m +no_defs 
## source     : memory
## names      : var1.pred 
## values     : 2.907161, 61.8175  (min, max)

leaflet() %>% addTiles() %>%
  addRasterImage(r.m$var1.pred, colors = pal, opacity = 0.8) %>%
  addLegend(pal = pal, values = values(r.m$var1.pred),
    title = "IDW rainfall in July 2019 [mm]")

## Warning in showSRID(uprojargs, format = "PROJ", multiline = "NO", prefer_proj =
## prefer_proj): Discarded ellps WGS 84 in Proj4 definition: +proj=merc +a=6378137
## +b=6378137 +lat_ts=0 +lon_0=0 +x_0=0 +y_0=0 +k=1 +units=m +nadgrids=@null
## +wktext +no_defs +type=crs

## Warning in showSRID(uprojargs, format = "PROJ", multiline = "NO", prefer_proj =
## prefer_proj): Discarded datum World Geodetic System 1984 in Proj4 definition

## Warning in showSRID(uprojargs, format = "PROJ", multiline = "NO", prefer_proj =
## prefer_proj): Discarded ellps WGS 84 in Proj4 definition: +proj=merc +a=6378137
## +b=6378137 +lat_ts=0 +lon_0=0 +x_0=0 +y_0=0 +k=1 +units=m +nadgrids=@null
## +wktext +no_defs +type=crs

## Warning in showSRID(uprojargs, format = "PROJ", multiline = "NO", prefer_proj =
## prefer_proj): Discarded datum World Geodetic System 1984 in Proj4 definition

tm_shape(r.m) + 
  tm_raster(n=10,palette = "RdBu", auto.palette.mapping = FALSE,
            title="Inverse Distance Weighted \nPredicted precipitation \n(in mm)") + 
  tm_shape(precip2) + tm_dots(size=0.01) +
  tm_legend(legend.outside=TRUE)

## Warning: The argument auto.palette.mapping is deprecated. Please use midpoint
## for numeric data and stretch.palette for categorical data to control the palette
## mapping.

P<-precip2

IDW.out<-vector(length=length(P))

Encontrar el parametro de potencia por un procedimiento automatico con muchos calculos y en cada calculo se saca 1 porcentaje de los puntos de muestreo y contra eso se chequea el error a traves de una validacion cruzada, entre mas cercana la linea roja a la negra mas pequeño es el error

for (i in 1:length(P)) {
  IDW.out[i] <- gstat::idw(rain ~ 1, P[-i,], P[i,], idp=2.0)$var1.pred
}

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OP <- par(pty="s", mar=c(4,3,0,0))
  plot(IDW.out ~ P$rain, asp=1, xlab="Observed", ylab="Predicted", pch=16,
       col=rgb(0,0,0,0.5))
  abline(lm(IDW.out ~ P$rain), col="red", lw=2,lty=2)
  abline(0,1)

Calculamos el error

par(OP)
sqrt( sum((IDW.out - P$rain)^2) / length(P))

## [1] 3.789831

#4.3 Kriging Interpolation

P$X <- coordinates(P)[,1]
P$Y <- coordinates(P)[,2]

f.1 <- as.formula(rain ~ X + Y) 
var.smpl <- variogram(f.1, P, cloud = FALSE, cutoff=100000, width=8990)
dat.fit  <- fit.variogram(var.smpl, fit.ranges = TRUE, fit.sills = TRUE,
                          vgm(psill=3, model="Mat", range=150000, nugget=0.0))

dat.fit

plot(var.smpl, dat.fit, xlim=c(0,130000))

f.1 <- as.formula(rain ~ X + Y) 
dat.krg <- krige( f.1, P, grd, dat.fit)

## [using universal kriging]

r <- raster(dat.krg)
r.m <- raster::mask(r, santander2)

r.m

## class      : RasterLayer 
## dimensions : 597, 503, 300291  (nrow, ncol, ncell)
## resolution : 451.3462, 451.3462  (x, y)
## extent     : 551912.2, 778939.3, 630974.4, 900428.1  (xmin, xmax, ymin, ymax)
## crs        : +proj=utm +zone=18 +datum=WGS84 +units=m +no_defs 
## source     : memory
## names      : var1.pred 
## values     : 2.832798, 61.79862  (min, max)

tm_shape(r.m) + 
  tm_raster(n=10, palette="RdBu", auto.palette.mapping=FALSE, 
            title="Universal Kriging\nPredicted precipitation \n(in mm)") +
  tm_shape(P) + tm_dots(size=0.02) +
  tm_legend(legend.outside=TRUE)

## Warning: The argument auto.palette.mapping is deprecated. Please use midpoint
## for numeric data and stretch.palette for categorical data to control the palette
## mapping.

pal <- colorNumeric(c("red", "orange", "yellow", "blue", "darkblue"), values(precip.mask),
  na.color = "transparent")

leaflet() %>% addTiles() %>%
  addRasterImage(r.m, colors = pal, opacity = 0.6) %>%
  addLegend(pal = pal, values = values(r.m),
    title = "Kriging interpolated rainfall in Montes\n From 26.03 to 30.03 in 2020 [mm]")

## Warning in showSRID(uprojargs, format = "PROJ", multiline = "NO", prefer_proj =
## prefer_proj): Discarded ellps WGS 84 in Proj4 definition: +proj=merc +a=6378137
## +b=6378137 +lat_ts=0 +lon_0=0 +x_0=0 +y_0=0 +k=1 +units=m +nadgrids=@null
## +wktext +no_defs +type=crs

## Warning in showSRID(uprojargs, format = "PROJ", multiline = "NO", prefer_proj =
## prefer_proj): Discarded datum World Geodetic System 1984 in Proj4 definition

## Warning in showSRID(uprojargs, format = "PROJ", multiline = "NO", prefer_proj =
## prefer_proj): Discarded ellps WGS 84 in Proj4 definition: +proj=merc +a=6378137
## +b=6378137 +lat_ts=0 +lon_0=0 +x_0=0 +y_0=0 +k=1 +units=m +nadgrids=@null
## +wktext +no_defs +type=crs

## Warning in showSRID(uprojargs, format = "PROJ", multiline = "NO", prefer_proj =
## prefer_proj): Discarded datum World Geodetic System 1984 in Proj4 definition

r   <- raster(dat.krg, layer="var1.var")
r.m <- raster::mask(r, santander2)

tm_shape(r.m) + 
  tm_raster(n=7, palette ="Reds",
            title="Kriging Interpolation\nVariance map \n(in squared mm)") +tm_shape(P) + tm_dots(size=0.02) +
  tm_legend(legend.outside=TRUE)

r   <- sqrt(raster(dat.krg, layer="var1.var")) * 1.96
r.m <- raster::mask(r, santander2)

tm_shape(r.m) + 
  tm_raster(n=7, palette ="Reds",
            title="Kriging Interpolation\n95% CI map \n(in mm)") +tm_shape(P) + tm_dots(size=0.02) +
  tm_legend(legend.outside=TRUE)