rm(list=ls())
library(sf)
## Warning: package 'sf' was built under R version 4.1.2
## Linking to GEOS 3.9.1, GDAL 3.2.1, PROJ 7.2.1; sf_use_s2() is TRUE
library(rgdal)
## Warning: package 'rgdal' was built under R version 4.1.2
## Loading required package: sp
## Warning: package 'sp' was built under R version 4.1.2
## Please note that rgdal will be retired by the end of 2023,
## plan transition to sf/stars/terra functions using GDAL and PROJ
## at your earliest convenience.
##
## rgdal: version: 1.5-28, (SVN revision 1158)
## 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/JUPA/Documents/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/JUPA/Documents/R/win-library/4.1/rgdal/proj
## PROJ CDN enabled: FALSE
## Linking to sp version:1.4-6
## To mute warnings of possible GDAL/OSR exportToProj4() degradation,
## use options("rgdal_show_exportToProj4_warnings"="none") before loading sp or rgdal.
## Overwritten PROJ_LIB was C:/Users/JUPA/Documents/R/win-library/4.1/rgdal/proj
library(rasterVis)
## Loading required package: lattice
## Warning: package 'lattice' was built under R version 4.1.2
library(dplyr)
##
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
##
## filter, lag
## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union
library(raster)
##
## Attaching package: 'raster'
## The following object is masked from 'package:dplyr':
##
## select
library(gstat)
## Warning: package 'gstat' was built under R version 4.1.2
library(geoR)
## Warning: package 'geoR' was built under R version 4.1.2
## --------------------------------------------------------------
## 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
## --------------------------------------------------------------
library(berryFunctions)
## Warning: package 'berryFunctions' was built under R version 4.1.2
##
## Attaching package: 'berryFunctions'
## The following object is masked from 'package:raster':
##
## distance
## The following object is masked from 'package:dplyr':
##
## between
(s <- st_read("C:/Users/JUPA/Documents/geomatica/68_SANTANDER/ADMINISTRATIVO/MGN_MPIO_POLITICO.shp"))
## Reading layer `MGN_MPIO_POLITICO' from data source
## `C:\Users\JUPA\Documents\geomatica\68_SANTANDER\ADMINISTRATIVO\MGN_MPIO_POLITICO.shp'
## using driver `ESRI Shapefile'
## Simple feature collection with 87 features and 9 fields
## Geometry type: POLYGON
## Dimension: XY
## Bounding box: xmin: -74.52895 ymin: 5.707536 xmax: -72.47706 ymax: 8.14501
## Geodetic CRS: WGS 84
## Simple feature collection with 87 features and 9 fields
## Geometry type: POLYGON
## Dimension: XY
## Bounding box: xmin: -74.52895 ymin: 5.707536 xmax: -72.47706 ymax: 8.14501
## Geodetic CRS: WGS 84
## First 10 features:
## DPTO_CCDGO MPIO_CCDGO MPIO_CNMBR MPIO_CRSLC
## 1 68 68001 BUCARAMANGA 1623
## 2 68 68013 AGUADA 1775
## 3 68 68020 ALBANIA Ordenanza 33 de 1919
## 4 68 68051 ARATOCA 1750
## 5 68 68077 BARBOSA Ordenanza 30 del 25 de Abril de 1936
## 6 68 68079 BARICHARA 1799
## 7 68 68081 BARRANCABERMEJA Ordenanza 13 del 17 de Abril de 1922
## 8 68 68092 BETULIA 1874
## 9 68 68101 BOLIVAR 1844
## 10 68 68121 CABRERA 1869
## MPIO_NAREA MPIO_NANO DPTO_CNMBR Shape_Leng Shape_Area
## 1 152.90497 2017 SANTANDER 0.6922752 0.012513526
## 2 75.23125 2017 SANTANDER 0.4758098 0.006146093
## 3 166.21697 2017 SANTANDER 0.8761299 0.013570466
## 4 169.79155 2017 SANTANDER 0.6746922 0.013882031
## 5 46.66489 2017 SANTANDER 0.2703415 0.003810882
## 6 137.27581 2017 SANTANDER 0.5610888 0.011223345
## 7 1326.83512 2017 SANTANDER 2.7351901 0.108590745
## 8 431.24871 2017 SANTANDER 1.2718180 0.035286963
## 9 1010.11035 2017 SANTANDER 4.3603864 0.082514928
## 10 65.57431 2017 SANTANDER 0.3515706 0.005360404
## geometry
## 1 POLYGON ((-73.08418 7.23063...
## 2 POLYGON ((-73.56261 6.24032...
## 3 POLYGON ((-73.73616 5.87092...
## 4 POLYGON ((-72.98158 6.76065...
## 5 POLYGON ((-73.58988 5.99809...
## 6 POLYGON ((-73.22126 6.73288...
## 7 POLYGON ((-73.6939 7.254447...
## 8 POLYGON ((-73.53993 7.15392...
## 9 POLYGON ((-74.50132 6.27574...
## 10 POLYGON ((-73.25696 6.6213,...
(precip <- raster("C:/Users/JUPA/Documents/geomatica/chirps-v2.0.2021.12.6.tif"))
## 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-v2.0.2021.12.6.tif
## names : chirps.v2.0.2021.12.6
names(precip) <- "X2019.07"
(precip.mask <- mask(x = precip, mask = s))
## 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 : memory
## names : X2019.07
## values : 3.385371, 108.3905 (min, max)
(precip.points <- rasterToPoints(precip.mask, spatial = TRUE))
## 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 : X2019.07
## min values : 3.38537120819092
## max values : 108.390510559082
names(precip.points) <- "rain"
(p.sf.magna <- st_transform(st_as_sf(precip.points), crs=32618))
## Simple feature collection with 998 features and 1 field
## Geometry type: POINT
## Dimension: XY
## Bounding box: xmin: 558072.6 ymin: 638434.8 xmax: 773662.3 ymax: 898320.7
## Projected CRS: WGS 84 / UTM zone 18N
## First 10 features:
## rain geometry
## 1 6.887183 POINT (634962.7 898320.7)
## 2 6.587838 POINT (629469.2 892775.7)
## 3 7.148966 POINT (634979.3 892791.9)
## 4 6.219973 POINT (629485.1 887246.9)
## 5 6.712508 POINT (634995.9 887263.1)
## 6 11.947132 POINT (629500.9 881718.2)
## 7 13.916090 POINT (635012.3 881734.3)
## 8 5.177318 POINT (640523.9 881750.9)
## 9 15.970965 POINT (629516.6 876189.6)
## 10 16.666206 POINT (635028.7 876205.5)
(san.sf.magna <- st_transform(s, crs=32618))
## Simple feature collection with 87 features and 9 fields
## Geometry type: POLYGON
## Dimension: XY
## Bounding box: xmin: 552105.4 ymin: 630996 xmax: 778842.2 ymax: 900533.3
## Projected CRS: WGS 84 / UTM zone 18N
## First 10 features:
## DPTO_CCDGO MPIO_CCDGO MPIO_CNMBR MPIO_CRSLC
## 1 68 68001 BUCARAMANGA 1623
## 2 68 68013 AGUADA 1775
## 3 68 68020 ALBANIA Ordenanza 33 de 1919
## 4 68 68051 ARATOCA 1750
## 5 68 68077 BARBOSA Ordenanza 30 del 25 de Abril de 1936
## 6 68 68079 BARICHARA 1799
## 7 68 68081 BARRANCABERMEJA Ordenanza 13 del 17 de Abril de 1922
## 8 68 68092 BETULIA 1874
## 9 68 68101 BOLIVAR 1844
## 10 68 68121 CABRERA 1869
## MPIO_NAREA MPIO_NANO DPTO_CNMBR Shape_Leng Shape_Area
## 1 152.90497 2017 SANTANDER 0.6922752 0.012513526
## 2 75.23125 2017 SANTANDER 0.4758098 0.006146093
## 3 166.21697 2017 SANTANDER 0.8761299 0.013570466
## 4 169.79155 2017 SANTANDER 0.6746922 0.013882031
## 5 46.66489 2017 SANTANDER 0.2703415 0.003810882
## 6 137.27581 2017 SANTANDER 0.5610888 0.011223345
## 7 1326.83512 2017 SANTANDER 2.7351901 0.108590745
## 8 431.24871 2017 SANTANDER 1.2718180 0.035286963
## 9 1010.11035 2017 SANTANDER 4.3603864 0.082514928
## 10 65.57431 2017 SANTANDER 0.3515706 0.005360404
## geometry
## 1 POLYGON ((711536.6 799690.4...
## 2 POLYGON ((659020.5 689987.2...
## 3 POLYGON ((639912.4 649094.1...
## 4 POLYGON ((723092.9 747753.2...
## 5 POLYGON ((656073.2 663194.6...
## 6 POLYGON ((696604.3 744578.2...
## 7 POLYGON ((644192.4 802084.8...
## 8 POLYGON ((661229.3 791020.9...
## 9 POLYGON ((555160.7 693712.8...
## 10 POLYGON ((692700.7 732223.3...
precip2 <- as(p.sf.magna, 'Spatial')
san2 <- as(san.sf.magna, 'Spatial')
precip2@bbox <- san2@bbox
train_index <- sample(1:nrow(precip2), 0.7 * nrow(precip2))
test_index <- setdiff(1:nrow(precip2), train_index)
ptos_train <- precip2[train_index, ]
ptos_test <- precip2[test_index,]
ptos_train
## class : SpatialPointsDataFrame
## features : 698
## extent : 558072.6, 773662.3, 638445, 898320.7 (xmin, xmax, ymin, ymax)
## crs : +proj=utm +zone=18 +datum=WGS84 +units=m +no_defs
## variables : 1
## names : rain
## min values : 3.38537120819092
## max values : 108.390510559082
library(gstat)
grd <- as.data.frame(spsample(precip2, "regular", n=319000))
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))
## Coordinate Reference System:
## Deprecated Proj.4 representation:
## +proj=utm +zone=18 +datum=WGS84 +units=m +no_defs
## WKT2 2019 representation:
## PROJCRS["WGS 84 / UTM zone 18N",
## BASEGEOGCRS["WGS 84",
## DATUM["World Geodetic System 1984",
## ELLIPSOID["WGS 84",6378137,298.257223563,
## LENGTHUNIT["metre",1]]],
## PRIMEM["Greenwich",0,
## ANGLEUNIT["degree",0.0174532925199433]],
## ID["EPSG",4326]],
## CONVERSION["UTM zone 18N",
## METHOD["Transverse Mercator",
## ID["EPSG",9807]],
## PARAMETER["Latitude of natural origin",0,
## ANGLEUNIT["degree",0.0174532925199433],
## ID["EPSG",8801]],
## PARAMETER["Longitude of natural origin",-75,
## ANGLEUNIT["degree",0.0174532925199433],
## ID["EPSG",8802]],
## PARAMETER["Scale factor at natural origin",0.9996,
## SCALEUNIT["unity",1],
## ID["EPSG",8805]],
## PARAMETER["False easting",500000,
## LENGTHUNIT["metre",1],
## ID["EPSG",8806]],
## PARAMETER["False northing",0,
## LENGTHUNIT["metre",1],
## ID["EPSG",8807]]],
## CS[Cartesian,2],
## AXIS["(E)",east,
## ORDER[1],
## LENGTHUNIT["metre",1]],
## AXIS["(N)",north,
## ORDER[2],
## LENGTHUNIT["metre",1]],
## USAGE[
## SCOPE["Engineering survey, topographic mapping."],
## AREA["Between 78°W and 72°W, northern hemisphere between equator and 84°N, onshore and offshore. Bahamas. Canada - Nunavut; Ontario; Quebec. Colombia. Cuba. Ecuador. Greenland. Haiti. Jamica. Panama. Turks and Caicos Islands. United States (USA). Venezuela."],
## BBOX[0,-78,84,-72]],
## ID["EPSG",32618]]
sp::proj4string(grd) <- y
P.idw <- gstat::idw(rain ~ 1, ptos_train, newdata=grd, idp=2.0)
## [inverse distance weighted interpolation]
r <- raster(P.idw)
(r.m <- raster::mask(r, san2))
## class : RasterLayer
## dimensions : 616, 518, 319088 (nrow, ncol, ncell)
## resolution : 437.6985, 437.6985 (x, y)
## extent : 552216.4, 778944.2, 631035.9, 900658.2 (xmin, xmax, ymin, ymax)
## crs : +proj=utm +zone=18 +datum=WGS84 +units=m +no_defs
## source : memory
## names : var1.pred
## values : 3.454439, 108.0989 (min, max)
library(leaflet)
library(RColorBrewer)
pal <- colorNumeric(c("#B2182B", "#FFE4A9", "#afc9a9", "#86bbdb", "#2e0091"), values(r.m),
na.color = "transparent")
leaflet() %>% addTiles() %>%addRasterImage(r.m, colors = pal, opacity = 0.6) %>%addLegend(pal = pal, values = values(r.m), title = "Interpolación IDW [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
p.sf.magna
## Simple feature collection with 998 features and 1 field
## Geometry type: POINT
## Dimension: XY
## Bounding box: xmin: 558072.6 ymin: 638434.8 xmax: 773662.3 ymax: 898320.7
## Projected CRS: WGS 84 / UTM zone 18N
## First 10 features:
## rain geometry
## 1 6.887183 POINT (634962.7 898320.7)
## 2 6.587838 POINT (629469.2 892775.7)
## 3 7.148966 POINT (634979.3 892791.9)
## 4 6.219973 POINT (629485.1 887246.9)
## 5 6.712508 POINT (634995.9 887263.1)
## 6 11.947132 POINT (629500.9 881718.2)
## 7 13.916090 POINT (635012.3 881734.3)
## 8 5.177318 POINT (640523.9 881750.9)
## 9 15.970965 POINT (629516.6 876189.6)
## 10 16.666206 POINT (635028.7 876205.5)
(the_crs <- crs(p.sf.magna))
## Coordinate Reference System:
## Deprecated Proj.4 representation:
## +proj=utm +zone=18 +datum=WGS84 +units=m +no_defs
## WKT2 2019 representation:
## PROJCRS["WGS 84 / UTM zone 18N",
## BASEGEOGCRS["WGS 84",
## DATUM["World Geodetic System 1984",
## ELLIPSOID["WGS 84",6378137,298.257223563,
## LENGTHUNIT["metre",1]]],
## PRIMEM["Greenwich",0,
## ANGLEUNIT["degree",0.0174532925199433]],
## ID["EPSG",4326]],
## CONVERSION["UTM zone 18N",
## METHOD["Transverse Mercator",
## ID["EPSG",9807]],
## PARAMETER["Latitude of natural origin",0,
## ANGLEUNIT["degree",0.0174532925199433],
## ID["EPSG",8801]],
## PARAMETER["Longitude of natural origin",-75,
## ANGLEUNIT["degree",0.0174532925199433],
## ID["EPSG",8802]],
## PARAMETER["Scale factor at natural origin",0.9996,
## SCALEUNIT["unity",1],
## ID["EPSG",8805]],
## PARAMETER["False easting",500000,
## LENGTHUNIT["metre",1],
## ID["EPSG",8806]],
## PARAMETER["False northing",0,
## LENGTHUNIT["metre",1],
## ID["EPSG",8807]]],
## CS[Cartesian,2],
## AXIS["(E)",east,
## ORDER[1],
## LENGTHUNIT["metre",1]],
## AXIS["(N)",north,
## ORDER[2],
## LENGTHUNIT["metre",1]],
## USAGE[
## SCOPE["Engineering survey, topographic mapping."],
## AREA["Between 78°W and 72°W, northern hemisphere between equator and 84°N, onshore and offshore. Bahamas. Canada - Nunavut; Ontario; Quebec. Colombia. Cuba. Ecuador. Greenland. Haiti. Jamica. Panama. Turks and Caicos Islands. United States (USA). Venezuela."],
## BBOX[0,-78,84,-72]],
## ID["EPSG",32618]]
p.sf.magna$x <- st_coordinates(p.sf.magna)[,1]
p.sf.magna$y <- st_coordinates(p.sf.magna)[,2]
geoprec <- as.geodata(cbind(p.sf.magna$x,p.sf.magna$y,p.sf.magna$rain))
vario <- variog(geoprec, max.dist=300000)
## variog: computing omnidirectional variogram
fit <- variofit(vario)
## variofit: covariance model used is matern
## variofit: weights used: npairs
## variofit: minimisation function used: optim
## Warning in variofit(vario): initial values not provided - running the default
## search
## variofit: searching for best initial value ... selected values:
## sigmasq phi tausq kappa
## initial.value "675.93" "80837.89" "0" "0.5"
## status "est" "est" "est" "fix"
## loss value: 2513059167.82307
plot(vario) ; lines(fit)
d <- sapply(1:nrow(p.sf.magna), function(i) min(berryFunctions::distance(
p.sf.magna$x[i], p.sf.magna$y[i], p.sf.magna$x[-i], p.sf.magna$y[-i])))
hist(d/1000, breaks=20, main="distance to closest gauge [km]")
res <- 1000 # 0.5 km, since stations are 4.6 km apart on average
grid <- expand.grid(seq(min(p.sf.magna$x),max(p.sf.magna$x),res),
seq(min(p.sf.magna$y),max(p.sf.magna$y),res))
krico <- krige.control(type.krige="OK", obj.model=fit)
krobj <- krige.conv(geoprec, locations=grid, krige=krico)
## krige.conv: model with constant mean
## krige.conv: Kriging performed using global neighbourhood
grid_sf <- sf::st_as_sf(grid, coords=1:2, crs=sf::st_crs(san.sf.magna))
isinp <- sapply(sf::st_within(grid_sf, san.sf.magna), length) > 0
krobj2 <- krobj
krobj2$predict[!isinp] <- NA
(k_raster <- raster::rasterFromXYZ(cbind(grid, temp=krobj2$predict),
crs=y))
## class : RasterLayer
## dimensions : 260, 216, 56160 (nrow, ncol, ncell)
## resolution : 1000, 1000 (x, y)
## extent : 557572.6, 773572.6, 637934.8, 897934.8 (xmin, xmax, ymin, ymax)
## crs : +proj=utm +zone=18 +datum=WGS84 +units=m +no_defs
## source : memory
## names : temp
## values : 3.415321, 108.1598 (min, max)
leaflet() %>% addTiles() %>%
addRasterImage(k_raster$temp, colors = pal, opacity = 0.8) %>%
addLegend(pal = pal, values = values(r.m$var1.pred),
title = "Precipitaciones abril 2021 [mm]")
## Warning in colors(.): Some values were outside the color scale and will be
## treated as NA
P <- ptos_train
IDW.out <- vector(length = length(P))
for (i in 1:length(P)) {
IDW.out[i] <- gstat::idw(rain ~ 1, P[-i,], P[i,], idp=2.0)$var1.pred
}
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]