INTERPOLACION
MARIA FERNANDA SANCHEZ CALDERON - DUVAN FELIPE CAMACHO BERMUDEZ
2023-06-21
1. INTRODUCCIÓN
Este cuaderno ilustra dos técnicas de interpolación espacial: Distancia ponderada inversa (IDW) y Kriging ordinario (OK). IDW es una técnica determinista. OK es probabilístico. Ambas técnicas se utilizan aquí para obtener una superficie continua de SOC a 15-30 cm de muestras obtenidas de SoilGrids 250 m.
2. SETUP
Primero, limpiemos la memoria:
rm(list=ls())Ahora, asegúrese de haber instalado previamente las bibliotecas requeridas.
Luego, carga las bibliotecas:
library(sp)
library(terra)
library(sf)
library(stars)
library(gstat)
library(automap)
library(leaflet)
library(leafem)
library(ggplot2)
library(dplyr)library(curl)## Using libcurl 7.84.0 with Schannel3. LEER LOS DATOS DE ENTRADA
Necesitamos leer un conjunto de datos para imitar los datos del mundo real. Por lo tanto, leamos la capa SOC que descargamos de ISRIC usando la biblioteca terra:
## class : SpatRaster
## dimensions : 837, 885, 1 (nrow, ncol, nlyr)
## resolution : 0.002259887, 0.002389486 (x, y)
## extent : -77.1284, -75.1284, 4.2754, 6.2754 (xmin, xmax, ymin, ymax)
## coord. ref. : lon/lat WGS 84 (EPSG:4326)
## source : RISARALDA.tif
## name : RISARALDA
## min value : 0
## max value : 3507Ahora, convierta los datos SOC en porcentaje. Revise el factor de escala de SOC en el sitio web de SoilGrids y anótelo aquí.
¿Qué es el CRS de los datos del mundo real?
Parece que necesitamos una transformación de dicho CRS en el conocido WGS84 CRS:
## class : SpatRaster
## dimensions : 861, 861, 1 (nrow, ncol, nlyr)
## resolution : 0.002321978, 0.002321978 (x, y)
## extent : -77.1284, -75.12918, 4.276177, 6.2754 (xmin, xmax, ymin, ymax)
## coord. ref. : +proj=longlat +datum=WGS84 +no_defs
## source(s) : memory
## name : RISARALDA
## min value : 0.0000
## max value : 343.6304Convirtamos la capa SpatRaster en un objeto de estrellas:
4. MUESTREO DEL MUNDO
Cogemos una muestra de aprox. 500 sitios de los datos del mundo real utilizando una muestra ubicada aleatoriamente:
## class : SpatVector
## geometry : points
## dimensions : 500, 1 (geometries, attributes)
## extent : -77.12724, -75.13034, 4.27966, 6.271917 (xmin, xmax, ymin, ymax)
## coord. ref. : +proj=longlat +datum=WGS84 +no_defs
## names : RISARALDA
## type : <num>
## values : 87.28
## 70.87
## 179.1Describa las características principales del objeto de muestras.
Ahora, necesitamos convertir el objeto spatVector en un objeto de característica simple:
## Simple feature collection with 500 features and 1 field
## Geometry type: POINT
## Dimension: XY
## Bounding box: xmin: -77.12724 ymin: 4.27966 xmax: -75.13034 ymax: 6.271917
## Geodetic CRS: GEOGCRS["unknown",
## DATUM["World Geodetic System 1984",
## ELLIPSOID["WGS 84",6378137,298.257223563,
## LENGTHUNIT["metre",1]],
## ID["EPSG",6326]],
## PRIMEM["Greenwich",0,
## ANGLEUNIT["degree",0.0174532925199433],
## ID["EPSG",8901]],
## CS[ellipsoidal,2],
## AXIS["longitude",east,
## ORDER[1],
## ANGLEUNIT["degree",0.0174532925199433,
## ID["EPSG",9122]]],
## AXIS["latitude",north,
## ORDER[2],
## ANGLEUNIT["degree",0.0174532925199433,
## ID["EPSG",9122]]]]
## First 10 features:
## RISARALDA geometry
## 1 87.27782 POINT (-75.18839 6.137242)
## 2 70.87183 POINT (-75.16285 6.179038)
## 3 179.05453 POINT (-77.06919 5.983992)
## 4 35.99824 POINT (-75.69226 5.726252)
## 5 207.07167 POINT (-76.39117 5.74715)
## 6 64.91766 POINT (-75.99411 6.104735)
## 7 80.68392 POINT (-76.06609 5.384921)
## 8 240.06917 POINT (-76.50959 5.463869)
## 9 195.00716 POINT (-77.07383 4.737089)
## 10 36.37814 POINT (-76.30061 4.514179)Visualicemos las muestras:
## id longit latit soc
## 1 1 -75.18839 6.137242 87.277817
## 2 2 -75.16285 6.179038 70.871826
## 3 3 -77.06919 5.983992 179.054535
## 4 4 -75.69226 5.726252 35.998238
## 5 5 -76.39117 5.747150 207.071671
## 6 6 -75.99411 6.104735 64.917656
## 7 7 -76.06609 5.384921 80.683922
## 8 8 -76.50959 5.463869 240.069168
## 9 9 -77.07383 4.737089 195.007156
## 10 10 -76.30061 4.514179 36.378139
## 11 11 -76.80216 5.891113 205.853424
## 12 12 -76.14272 6.271917 55.879570
## 13 13 -76.03823 4.295913 23.360821
## 14 14 -75.39969 5.849317 72.381210
## 15 15 -75.52740 4.792817 80.541985
## 16 16 -76.75108 4.790495 183.446838
## 17 17 -76.34705 4.797461 87.319481
## 18 18 -75.33467 5.946840 61.890442
## 19 19 -76.11486 4.412012 25.521173
## 20 20 -75.60867 4.502569 48.452229
## 21 21 -76.74179 5.480122 196.632309
## 22 22 -76.21935 4.330743 41.023312
## 23 23 -75.32771 5.273466 77.125450
## 24 24 -76.36563 5.872537 208.496933
## 25 25 -76.88111 5.268822 191.216629
## 26 26 -75.74102 4.820680 35.631210
## 27 27 -76.56764 5.315262 210.094818
## 28 28 -75.15124 5.995602 56.013706
## 29 29 -76.76733 4.976253 225.072723
## 30 30 -75.75959 4.432910 26.014748
## 31 31 -75.38576 5.194519 72.062981
## 32 32 -75.87569 5.821453 43.441902
## 33 33 -75.40665 5.626407 67.357910
## 34 34 -76.18684 5.220061 103.940125
## 35 35 -77.09705 5.798233 229.951843
## 36 36 -75.82229 6.090803 32.641544
## 37 37 -75.82693 5.057522 28.045456
## 38 38 -76.38421 5.175943 201.778885
## 39 39 -75.76656 6.062939 44.035587
## 40 40 -75.17446 5.468512 84.608299
## 41 41 -75.17446 5.454581 49.048431
## 42 42 -76.40975 6.174394 196.890533
## 43 43 -76.20774 5.556748 193.700241
## 44 44 -76.95541 6.251019 244.319626
## 45 45 -75.64349 5.373311 32.368717
## 46 46 -75.42523 5.027337 71.874161
## 47 47 -75.61563 5.888791 28.568874
## 48 48 -76.43993 5.470834 208.466125
## 49 49 -76.19613 5.788946 62.658966
## 50 50 -77.05526 5.960772 166.698105
## 51 51 -76.28436 6.109379 222.407120
## 52 52 -76.96470 4.525789 205.642426
## 53 53 -76.67910 4.760309 156.148117
## 54 54 -77.04597 4.565263 200.201370
## 55 55 -75.60867 4.641888 40.101250
## 56 56 -75.33003 4.894984 0.000000
## 57 57 -76.74876 5.064488 185.815292
## 58 58 -75.70851 4.509535 35.104443
## 59 59 -77.00882 5.250247 203.843887
## 60 60 -76.30061 6.062939 288.380951
## 61 61 -76.27739 4.769597 78.699577
## 62 62 -75.54829 6.093125 76.925827
## 63 63 -75.35325 5.912010 71.984009
## 64 64 -75.24876 5.858605 81.528076
## 65 65 -75.41362 5.373311 92.968369
## 66 66 -75.50650 4.518823 65.547867
## 67 67 -75.16517 4.295913 55.814148
## 68 68 -76.44458 4.651176 195.812576
## 69 69 -77.02507 5.624085 202.326523
## 70 70 -76.97863 6.209224 221.435608
## 71 71 -75.88962 5.886469 28.479691
## 72 72 -76.91826 4.495604 201.014664
## 73 73 -75.84551 5.108606 25.327795
## 74 74 -75.22322 5.115572 86.773308
## 75 75 -75.15820 5.445293 72.895035
## 76 76 -76.73018 5.366345 223.642273
## 77 77 -76.80913 5.484766 199.359970
## 78 78 -76.55603 4.929813 205.596039
## 79 79 -77.07151 4.692972 196.259552
## 80 80 -76.01966 5.844673 34.774796
## 81 81 -76.16594 5.798233 52.974453
## 82 82 -75.27894 5.526562 75.493874
## 83 83 -76.80216 4.581517 201.150421
## 84 84 -76.88808 4.458452 183.507446
## 85 85 -76.32383 4.881052 140.387985
## 86 86 -75.69458 4.330743 55.120678
## 87 87 -75.30216 5.429039 70.220596
## 88 88 -76.92523 4.627956 218.370407
## 89 89 -76.56996 5.391887 173.173492
## 90 90 -76.46315 6.262629 95.161697
## 91 91 -75.28127 4.850866 73.800232
## 92 92 -76.69535 5.756438 289.070099
## 93 93 -76.38653 5.384921 214.952652
## 94 94 -76.70232 4.990185 183.447861
## 95 95 -76.94612 5.617119 253.139038
## 96 96 -75.14427 4.762631 68.721733
## 97 97 -76.71160 5.568358 240.830170
## 98 98 -76.34009 5.596221 247.644684
## 99 99 -77.05526 6.134920 198.988907
## 100 100 -76.92058 4.869442 221.811432
## 101 101 -75.35325 4.892662 45.300129
## 102 102 -76.35866 5.048234 102.740791
## 103 103 -76.91594 4.442198 183.812271
## 104 104 -75.86408 5.454581 75.884384
## 105 105 -75.20232 5.426717 74.546555
## 106 106 -76.38188 5.577645 206.942291
## 107 107 -76.22631 4.367895 32.338093
## 108 108 -76.27275 4.897306 33.326439
## 109 109 -75.72476 5.624085 78.991058
## 110 110 -75.78514 5.967738 49.649998
## 111 111 -77.10170 6.206902 226.408997
## 112 112 -75.21161 5.366345 70.054619
## 113 113 -75.75031 6.028109 45.881828
## 114 114 -76.54442 5.633373 216.012711
## 115 115 -75.91981 4.333065 35.488617
## 116 116 -76.95541 4.857832 187.937622
## 117 117 -75.99411 5.155045 99.966354
## 118 118 -75.46470 4.321455 60.952976
## 119 119 -76.62105 4.600093 192.989853
## 120 120 -76.64195 5.217739 209.502823
## 121 121 -76.96006 4.971609 196.708542
## 122 122 -76.84628 4.542043 194.232269
## 123 123 -75.44845 5.858605 62.508076
## 124 124 -77.04365 5.647305 244.214203
## 125 125 -76.10789 4.971609 92.361557
## 126 126 -76.14969 5.902722 68.784134
## 127 127 -75.81532 5.387243 87.118263
## 128 128 -75.88730 5.596221 51.473667
## 129 129 -76.55603 4.946067 224.065216
## 130 130 -75.63885 4.532755 5.692451
## 131 131 -76.56300 4.939101 224.197113
## 132 132 -77.11331 5.494054 214.057968
## 133 133 -76.03127 5.833063 35.836510
## 134 134 -76.38885 4.829968 68.007111
## 135 135 -75.73870 5.844673 21.351812
## 136 136 -76.70696 5.828419 267.752472
## 137 137 -76.00340 4.860154 38.643814
## 138 138 -75.64349 4.453808 61.656082
## 139 139 -77.00185 4.544365 202.370667
## 140 140 -76.67213 5.020371 228.120956
## 141 141 -76.80216 5.740184 256.989563
## 142 142 -75.13034 5.329194 79.955940
## 143 143 -75.75727 4.618668 34.563599
## 144 144 -76.58622 5.758760 284.165039
## 145 145 -76.98328 4.846222 223.312775
## 146 146 -76.53978 4.316811 81.646233
## 147 147 -76.69303 4.291269 190.350418
## 148 148 -76.76269 5.138792 214.626511
## 149 149 -75.89427 5.874859 34.270996
## 150 150 -75.27198 6.141886 68.853416
## 151 151 -76.06609 5.389565 78.656265
## 152 152 -75.42291 4.751021 64.939735
## 153 153 -76.76037 4.827646 189.459061
## 154 154 -75.35093 4.860154 58.552708
## 155 155 -76.24257 5.867893 63.971790
## 156 156 -76.20077 4.769597 33.162369
## 157 157 -76.60479 5.556748 182.479019
## 158 158 -75.14427 5.236315 60.847794
## 159 159 -76.94148 4.381827 181.408890
## 160 160 -75.62260 6.255663 0.000000
## 161 161 -76.68142 4.463096 175.209641
## 162 162 -76.82306 6.058295 245.983688
## 163 163 -75.59473 4.704582 52.024014
## 164 164 -76.07770 4.660464 25.896441
## 165 165 -75.57151 6.088481 98.886787
## 166 166 -75.50882 4.904272 73.966110
## 167 167 -77.03436 5.001795 192.981842
## 168 168 -75.75727 5.733218 75.163071
## 169 169 -76.61176 5.456903 242.417786
## 170 170 -75.57384 5.271144 45.474922
## 171 171 -76.05681 4.918204 42.980415
## 172 172 -75.69226 4.662786 42.159878
## 173 173 -76.39349 4.370217 45.484161
## 174 174 -75.38343 4.409690 54.935192
## 175 175 -77.04829 5.603187 210.669647
## 176 176 -75.39737 5.326872 69.977554
## 177 177 -75.53901 5.305974 41.317051
## 178 178 -75.61331 6.095447 60.545502
## 179 179 -76.96238 6.151174 196.003723
## 180 180 -76.07770 5.429039 68.062508
## 181 181 -75.67832 4.681362 40.764973
## 182 182 -76.21470 5.531206 183.733475
## 183 183 -76.90433 6.197614 203.444778
## 184 184 -75.76192 5.433683 62.698158
## 185 185 -77.02507 5.294364 208.148956
## 186 186 -76.72786 6.195292 0.000000
## 187 187 -75.47631 6.260307 56.364750
## 188 188 -76.08467 5.115572 86.236153
## 189 189 -75.60402 4.439876 57.072392
## 190 190 -76.46780 4.428266 34.811321
## 191 191 -75.57616 6.093125 108.293594
## 192 192 -77.07383 4.878730 181.889145
## 193 193 -76.94845 5.384921 286.218872
## 194 194 -75.64117 5.247925 34.810215
## 195 195 -76.74179 4.398080 185.300751
## 196 196 -76.81842 5.380277 208.331055
## 197 197 -77.07616 6.151174 265.460754
## 198 198 -75.39272 5.863249 57.454773
## 199 199 -77.07151 5.881825 192.107697
## 200 200 -75.21625 4.365573 31.492250
## 201 201 -76.10557 4.437554 20.801600
## 202 202 -77.09705 5.626407 223.130951
## 203 203 -76.30061 4.925170 48.114456
## 204 204 -75.32074 5.124860 72.329727
## 205 205 -75.97786 4.744055 28.908651
## 206 206 -75.58545 4.804427 58.992214
## 207 207 -76.62105 5.468512 187.064987
## 208 208 -76.14736 5.018049 58.935280
## 209 209 -75.77585 4.295913 42.336060
## 210 210 -75.80603 5.101640 40.374447
## 211 211 -76.71393 6.139564 170.307999
## 212 212 -76.54907 5.921298 293.644226
## 213 213 -75.17446 4.771919 71.921738
## 214 214 -76.23560 5.011083 112.349197
## 215 215 -75.41362 5.675169 54.677170
## 216 216 -76.28900 4.987863 57.912689
## 217 217 -76.60712 4.384149 220.847443
## 218 218 -75.20696 4.525789 56.350460
## 219 219 -75.88498 4.857832 40.724785
## 220 220 -76.13111 6.267273 38.944817
## 221 221 -75.96161 4.813715 24.524565
## 222 222 -75.28591 4.913560 72.962448
## 223 223 -76.89736 6.118666 213.904556
## 224 224 -76.50030 4.474706 57.058369
## 225 225 -75.62724 5.498698 52.134880
## 226 226 -75.29055 5.364023 61.410500
## 227 227 -76.48405 6.093125 256.605530
## 228 228 -75.44613 5.988636 55.344032
## 229 229 -76.31687 4.881052 200.156555
## 230 230 -75.84551 5.322228 72.893082
## 231 231 -76.24489 4.992507 97.797073
## 232 232 -76.33544 5.756438 216.423492
## 233 233 -76.27043 6.248697 42.345409
## 234 234 -76.41439 5.612475 214.827301
## 235 235 -76.59318 5.477800 250.710831
## 236 236 -76.04520 4.502569 23.497158
## 237 237 -75.86176 5.809843 39.830582
## 238 238 -75.90588 5.837707 29.671490
## 239 239 -76.01733 5.644983 88.245499
## 240 240 -76.54907 5.570680 190.256638
## 241 241 -76.19148 5.656593 89.948776
## 242 242 -76.14040 4.934457 54.547821
## 243 243 -75.71315 4.288947 55.567383
## 244 244 -75.35789 4.934457 67.473732
## 245 245 -75.64349 5.935230 49.189754
## 246 246 -75.69458 5.192197 30.852612
## 247 247 -77.04133 5.078420 202.488434
## 248 248 -76.51656 5.173621 190.331253
## 249 249 -75.53901 4.692972 69.778122
## 250 250 -76.86950 6.093125 269.043304
## 251 251 -76.58390 5.721608 260.572662
## 252 252 -76.26811 4.632600 50.393631
## 253 253 -75.91052 4.595449 33.341091
## 254 254 -76.68606 5.187553 214.095978
## 255 255 -75.75959 4.899628 33.109276
## 256 256 -76.05216 5.663559 82.709930
## 257 257 -75.14659 4.769597 63.482723
## 258 258 -76.79055 5.744828 239.430206
## 259 259 -76.23328 4.964643 102.694824
## 260 260 -76.32151 6.125632 193.774536
## 261 261 -75.23018 4.428266 12.215521
## 262 262 -76.95773 4.537399 191.174042
## 263 263 -77.02507 6.053651 240.546600
## 264 264 -75.85247 4.992507 33.053726
## 265 265 -76.03591 4.922848 41.483849
## 266 266 -75.66439 5.401175 42.351475
## 267 267 -75.89891 6.181360 37.178616
## 268 268 -76.31455 4.802105 56.174278
## 269 269 -75.52507 5.853961 41.472160
## 270 270 -76.48637 4.553653 88.893906
## 271 271 -76.76037 5.424395 207.697159
## 272 272 -75.53204 4.493282 64.925697
## 273 273 -76.46083 5.018049 197.966248
## 274 274 -75.89891 4.748699 9.133649
## 275 275 -75.25108 5.422073 72.513191
## 276 276 -77.07848 5.134148 197.874222
## 277 277 -75.66439 5.872537 43.282372
## 278 278 -75.61563 5.631051 40.916744
## 279 279 -76.49566 5.698388 200.231339
## 280 280 -76.79752 5.726252 254.407394
## 281 281 -75.94071 4.425944 27.890051
## 282 282 -75.23018 5.247925 57.039967
## 283 283 -76.40975 5.963094 201.315338
## 284 284 -75.90356 6.248697 34.561378
## 285 285 -75.66439 6.232443 67.186867
## 286 286 -77.10170 4.349319 164.240326
## 287 287 -76.40046 6.218512 113.447212
## 288 288 -75.15820 5.928264 45.149586
## 289 289 -75.34628 5.494054 72.472862
## 290 290 -76.40975 5.749472 198.905350
## 291 291 -76.12182 5.382599 87.546562
## 292 292 -76.53978 5.916654 298.608063
## 293 293 -75.67832 6.262629 82.314064
## 294 294 -76.73715 5.754116 252.529572
## 295 295 -76.35866 5.220061 121.782722
## 296 296 -75.32538 4.755665 67.344757
## 297 297 -75.52740 5.545138 45.646076
## 298 298 -77.03668 6.216190 245.075378
## 299 299 -75.90123 5.243281 82.092606
## 300 300 -75.23483 5.064488 49.175484
## 301 301 -75.21857 5.631051 87.689713
## 302 302 -76.68142 5.055200 225.133911
## 303 303 -76.28668 5.018049 31.126347
## 304 304 -75.62027 5.071454 36.871635
## 305 305 -75.62956 4.669752 51.148991
## 306 306 -77.11795 4.607058 182.221008
## 307 307 -76.83699 4.948389 214.181381
## 308 308 -75.45774 5.770370 75.633087
## 309 309 -76.60944 5.726252 251.963226
## 310 310 -76.44226 5.229349 202.651321
## 311 311 -76.47244 4.711548 171.808685
## 312 312 -75.18607 4.969287 76.982536
## 313 313 -75.87569 4.525789 43.933056
## 314 314 -76.20774 5.603187 213.791321
## 315 315 -77.02739 4.444520 155.765228
## 316 316 -77.02275 4.323777 220.814011
## 317 317 -75.28591 6.146530 60.869904
## 318 318 -76.96934 6.141886 204.185410
## 319 319 -75.28359 4.957677 70.974709
## 320 320 -75.42987 5.944518 84.434509
## 321 321 -75.22786 4.648854 72.926079
## 322 322 -76.53978 4.660464 93.447433
## 323 323 -76.04520 5.596221 80.001259
## 324 324 -75.40897 4.328421 63.822693
## 325 325 -76.79287 4.395758 195.664047
## 326 326 -76.94148 5.535850 194.019272
## 327 327 -75.48792 5.858605 54.191631
## 328 328 -76.80216 6.004890 236.180237
## 329 329 -76.48173 5.514952 231.364075
## 330 330 -76.17291 6.055973 92.041641
## 331 331 -75.30913 5.466191 52.825386
## 332 332 -75.62492 5.631051 27.753708
## 333 333 -75.55062 5.164333 40.589798
## 334 334 -76.30526 4.699938 51.629807
## 335 335 -75.76424 6.093125 30.289902
## 336 336 -75.16517 5.076098 65.417824
## 337 337 -77.04597 5.591577 207.309708
## 338 338 -75.71315 5.359379 51.636051
## 339 339 -75.59241 5.545138 50.575562
## 340 340 -75.69458 6.130276 89.816437
## 341 341 -76.78823 5.668203 211.161392
## 342 342 -77.08544 4.908916 186.439377
## 343 343 -75.34164 4.825324 83.404503
## 344 344 -75.81764 6.183682 25.443794
## 345 345 -75.86176 4.542043 20.845411
## 346 346 -75.86873 5.396531 60.538235
## 347 347 -76.16594 4.293591 29.238165
## 348 348 -75.24411 4.393436 65.227852
## 349 349 -76.28204 5.600865 226.003143
## 350 350 -76.44690 5.851639 227.267914
## 351 351 -77.08544 5.245603 231.617310
## 352 352 -75.65975 4.460774 42.492775
## 353 353 -76.64195 5.322228 200.578125
## 354 354 -76.63962 5.319906 200.590851
## 355 355 -75.25572 5.240959 78.170418
## 356 356 -76.65820 4.997151 182.547989
## 357 357 -76.01501 5.498698 52.281391
## 358 358 -76.73482 6.035075 292.147217
## 359 359 -75.53436 5.259534 57.254555
## 360 360 -75.25805 6.248697 53.546909
## 361 361 -77.09473 5.429039 181.906586
## 362 362 -76.91826 6.251019 221.438538
## 363 363 -75.26501 4.846222 70.945671
## 364 364 -75.16285 5.150401 74.692635
## 365 365 -76.36099 5.289720 216.379593
## 366 366 -76.20774 4.753343 49.773190
## 367 367 -76.00572 4.820680 37.446877
## 368 368 -77.03436 5.022693 225.339752
## 369 369 -76.20309 6.202258 54.319843
## 370 370 -76.65820 4.741733 190.894958
## 371 371 -76.05216 4.535077 25.261669
## 372 372 -77.01578 4.929813 189.282654
## 373 373 -75.93606 5.703032 57.001339
## 374 374 -76.79984 5.740184 253.455872
## 375 375 -76.97631 5.266500 184.014420
## 376 376 -76.71393 5.308296 225.664993
## 377 377 -76.21238 5.675169 87.206345
## 378 378 -77.01114 5.682135 232.878967
## 379 379 -76.83003 5.475478 214.755295
## 380 380 -75.76888 5.593899 100.530823
## 381 381 -77.04597 4.302879 186.741501
## 382 382 -75.89427 5.712320 33.121578
## 383 383 -76.38653 5.155045 185.561539
## 384 384 -75.99876 4.509535 28.154982
## 385 385 -76.51888 5.672847 209.469696
## 386 386 -75.51811 6.002568 65.015587
## 387 387 -75.79907 4.751021 34.343311
## 388 388 -76.22863 4.832290 53.349560
## 389 389 -76.14040 5.682135 59.230343
## 390 390 -75.32074 5.538172 72.525467
## 391 391 -75.47167 5.085386 71.040176
## 392 392 -75.14427 6.260307 48.727314
## 393 393 -75.58777 4.806749 52.824501
## 394 394 -76.40743 5.045912 196.994644
## 395 395 -77.06919 4.906594 180.472092
## 396 396 -76.22863 4.723157 33.862190
## 397 397 -75.22322 4.757987 63.245056
## 398 398 -76.86718 6.230121 207.578659
## 399 399 -75.70851 4.929813 42.110050
## 400 400 -75.28823 4.925170 76.919319
## 401 401 -76.09396 5.747150 67.109093
## 402 402 -76.78359 4.400402 185.359756
## 403 403 -75.62724 4.532755 45.159241
## 404 404 -76.57693 5.364023 216.151154
## 405 405 -75.30216 5.925942 67.047798
## 406 406 -75.94767 5.563714 89.314125
## 407 407 -75.47863 5.090030 70.786232
## 408 408 -75.96393 6.130276 49.836746
## 409 409 -76.00108 5.484766 90.533813
## 410 410 -75.47863 5.266500 63.236668
## 411 411 -76.52585 4.502569 98.481201
## 412 412 -77.12724 5.598543 194.613068
## 413 413 -75.69922 5.459225 43.125355
## 414 414 -76.83931 4.565263 194.908432
## 415 415 -76.31455 4.281981 40.178741
## 416 416 -75.59473 4.720835 59.885208
## 417 417 -75.29055 6.072227 68.655807
## 418 418 -76.70928 4.820680 221.018097
## 419 419 -76.39117 5.487088 211.712784
## 420 420 -75.55526 6.160462 54.740356
## 421 421 -76.57461 6.167428 315.270142
## 422 422 -75.16285 5.686778 51.392376
## 423 423 -76.19148 4.744055 39.830322
## 424 424 -76.67445 5.273466 209.931610
## 425 425 -75.55526 4.316811 66.373589
## 426 426 -75.74334 5.013405 43.278378
## 427 427 -76.04984 5.575323 86.435020
## 428 428 -75.17910 5.022693 65.575272
## 429 429 -76.52120 5.856283 202.242172
## 430 430 -76.10789 4.732445 42.371986
## 431 431 -77.10170 5.747150 230.723480
## 432 432 -75.49489 4.711548 58.853077
## 433 433 -77.02739 5.524240 197.998489
## 434 434 -76.06609 5.779658 68.819992
## 435 435 -76.42832 5.935230 211.583618
## 436 436 -75.14891 5.642661 57.547813
## 437 437 -76.73947 4.298235 198.126160
## 438 438 -76.99024 5.045912 193.730087
## 439 439 -76.33544 4.623312 78.425835
## 440 440 -75.61331 4.391114 60.004860
## 441 441 -76.04055 6.127954 67.230019
## 442 442 -76.79055 5.498698 243.638382
## 443 443 -76.46780 4.690650 61.144131
## 444 444 -77.01578 5.354736 231.796890
## 445 445 -75.55758 4.279660 67.312622
## 446 446 -76.37492 5.661237 212.566864
## 447 447 -76.16594 4.402724 25.203529
## 448 448 -75.21393 5.703032 91.238350
## 449 449 -75.14195 4.616346 71.990791
## 450 450 -76.96470 5.591577 243.885223
## 451 451 -75.37415 4.997151 58.651077
## 452 452 -75.36718 4.316811 96.224907
## 453 453 -75.79675 5.977026 41.796757
## 454 454 -76.89504 5.308296 208.452820
## 455 455 -75.28127 5.477800 79.364182
## 456 456 -76.57925 4.451486 199.404572
## 457 457 -76.92987 5.466191 233.735001
## 458 458 -75.91981 6.016499 58.298122
## 459 459 -75.75031 4.850866 31.019745
## 460 460 -76.05681 6.011855 83.708138
## 461 461 -76.38188 4.857832 30.436731
## 462 462 -75.90820 5.377955 45.298435
## 463 463 -76.59551 4.609380 201.958633
## 464 464 -75.63653 5.842351 24.720390
## 465 465 -75.46470 6.069905 60.619854
## 466 466 -76.35634 6.225477 61.718830
## 467 467 -75.13730 5.213095 60.471573
## 468 468 -75.43916 4.583839 59.887680
## 469 469 -76.23560 5.531206 223.266830
## 470 470 -75.20928 5.217739 71.632484
## 471 471 -76.49798 4.600093 210.882889
## 472 472 -77.04829 4.948389 184.848846
## 473 473 -75.52972 4.911238 77.542526
## 474 474 -75.64349 4.579195 35.731258
## 475 475 -75.92910 5.788946 33.521137
## 476 476 -76.38653 5.946840 207.472382
## 477 477 -75.35789 4.881052 36.433659
## 478 478 -76.40510 5.022693 143.575638
## 479 479 -75.79675 4.611702 31.794424
## 480 480 -75.15124 5.152723 67.062492
## 481 481 -76.30061 4.881052 94.273346
## 482 482 -75.46470 5.210773 67.134506
## 483 483 -77.06222 6.162784 238.776031
## 484 484 -76.14969 5.700710 72.409843
## 485 485 -76.91826 5.619441 233.378830
## 486 486 -76.78126 4.662786 192.122864
## 487 487 -76.89040 4.553653 187.406357
## 488 488 -75.55062 5.777336 35.321281
## 489 489 -75.68297 5.206129 28.668873
## 490 490 -76.57461 5.726252 240.918289
## 491 491 -76.05681 4.535077 21.871252
## 492 492 -77.02507 5.925942 187.582047
## 493 493 -76.81609 4.648854 227.971176
## 494 494 -76.86718 5.150401 215.968491
## 495 495 -76.16594 5.956128 72.967430
## 496 496 -75.74566 6.227799 55.481659
## 497 497 -75.62956 5.463869 53.204323
## 498 498 -76.84396 5.429039 257.888580
## 499 499 -75.30681 5.380277 66.256256
## 500 500 -75.77120 6.251019 51.805077Quitemos los valores de NA:
head(sitios)## id longit latit soc
## 1 1 -75.18839 6.137242 87.27782
## 2 2 -75.16285 6.179038 70.87183
## 3 3 -77.06919 5.983992 179.05453
## 4 4 -75.69226 5.726252 35.99824
## 5 5 -76.39117 5.747150 207.07167
## 6 6 -75.99411 6.104735 64.91766Visualicemos las muestras:
Ahora, estamos listos para realizar las tareas de interpolación.
5. INTERPOLACIÓN
5.1 Creación del objeto gstat
Para interpolar, primero necesitamos crear un objeto de clase gstat, usando una función del mismo nombre: gstat.
Un objeto gstat contiene toda la información necesaria para realizar la interpolación espacial, a saber:
- La definición del modelo
- Los datos de calibración
Basándose en sus argumentos, la función gstat “entiende” qué tipo de modelo de interpolación queremos usar:
Sin modelo de variograma → IDW Modelo de variograma, sin covariables → Kriging ordinario
Vamos a utilizar tres parámetros de la función gstat:
- fórmula: la “fórmula” de predicción que especifica las variables dependientes e independientes (también conocidas como covariables)
- datos: los datos de calibración (también conocidos como los datos del tren)
- modelo: el modelo de variograma
5.2 interpolación IDW
Para interpolar SOC usando el método IDW, creamos el siguiente objeto gstat, especificando solo la fórmula y los datos:
Ahora que nuestro modelo de interpolación g1 está definido, podemos usar la función de predicción para interpolar realmente, es decir, para estimar los valores de precipitación.
La función de predicción acepta:
- Un raster—objeto de estrellas, como dem
- Un modelo: objeto gstat, como g1
El raster sirve para dos propósitos:
- Especificar las ubicaciones donde queremos hacer predicciones (en todos los métodos)
- Especificación de valores de covariables (solo en Universal Kriging)
Vamos a crear un objeto ráster con valores de celda iguales a 1:
¿Qué es rrr?
rrr## class : SpatRaster
## dimensions : 216, 216, 1 (nrow, ncol, nlyr)
## resolution : 0.009287914, 0.009287914 (x, y)
## extent : -77.1284, -75.12221, 4.269211, 6.2754 (xmin, xmax, ymin, ymax)
## coord. ref. : +proj=longlat +datum=WGS84 +no_defs
## source(s) : memory
## name : RISARALDA
## min value : 0.0000
## max value : 333.5054Definimos nuevos valores:
Definimos nuevos nombres
¿Qué es rrr ahora?
rrr## class : SpatRaster
## dimensions : 216, 216, 1 (nrow, ncol, nlyr)
## resolution : 0.009287914, 0.009287914 (x, y)
## extent : -77.1284, -75.12221, 4.269211, 6.2754 (xmin, xmax, ymin, ymax)
## coord. ref. : +proj=longlat +datum=WGS84 +no_defs
## source(s) : memory
## name : valor
## min value : 1
## max value : 1Por ejemplo, la siguiente expresión interpola los valores SOC según el modelo definido en g1 y la plantilla ráster definida en stars.rrr:
## [inverse distance weighted interpolation]¿Qué es z1?
z1## stars object with 2 dimensions and 2 attributes
## attribute(s):
## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## var1.pred 1.067947 64.9101 82.81908 116.7504 184.1278 314.8289 0
## var1.var NA NA NA NaN NA NA 46656
## dimension(s):
## from to offset delta refsys x/y
## x 1 216 -77.1284 0.00928791 +proj=longlat +datum=WGS8... [x]
## y 1 216 6.2754 -0.00928791 +proj=longlat +datum=WGS8... [y]Tome nota de los nombres de los dos atributos incluidos en el objeto z1.
Podemos crear un subconjunto solo del primer atributo y cambiarle el nombre a “soc”:
Tenemos que crear una paleta de color:
El ráster SOC interpolado, utilizando IDW, se muestra en la siguiente figura:
## Warning in pal(c(r[1], cuts, r[2])): Some values were outside the color scale
## and will be treated as NA5.3 Aceptar interpolación
Los métodos kriging requieren un modelo de variograma. El modelo de variograma es una forma objetiva de cuantificar el patrón de autocorrelación en los datos y asignar pesos en consecuencia al hacer predicciones.
Como primer paso, podemos calcular y examinar el variograma empírico utilizando la función de variograma.
La función requiere dos argumentos:
- fórmula: especifica la variable dependiente y las covariables, al igual que en gstat
- datos: la capa de puntos con la variable dependiente y las covariables como atributos de puntos
Por ejemplo, la siguiente expresión calcula el variograma empírico de muestras, sin covariables:
Tracemos el variograma:
plot(v_emp_ok)
Hay varias formas de ajustar un modelo de variograma a un variograma empírico. Usaremos el más simple: ajuste automático usando la función autofitVariogram del paquete automap:
La función elige el tipo de modelo que mejor se ajusta y también ajusta sus parámetros. Puede usar show.vgms() para mostrar los tipos de modelos de variograma.
Tenga en cuenta que la función autofitVariogram no funciona en objetos sf, por lo que convertimos el objeto en un SpatialPointsDataFrame (paquete sp).
El modelo ajustado se puede trazar con plot:
plot(v_mod_ok)
El objeto resultante es en realidad una lista con varios componentes, incluido el variograma empírico y el modelo de variograma ajustado. El componente $var_model del objeto resultante contiene el modelo real:
v_mod_ok$var_model## model psill range kappa
## 1 Nug 364.8009 0.000 0.0
## 2 Ste 107208.6010 1455.953 0.7En tu cuaderno, explica el significado de cada elemento del modelo anterior.
Ahora, el modelo de variograma se puede pasar a la función gstat, y podemos continuar con la interpolación de Kriging ordinario:
## [using ordinary kriging]Nuevamente, subdividiremos el atributo de valores predichos y lo renombraremos:
Las predicciones de Kriging ordinario se muestran en la siguiente figura:
## Warning in pal(c(r[1], cuts, r[2])): Some values were outside the color scale
## and will be treated as NA6. EVALUACIÓN DE RESULTADOS
6.1 Evaluación cualitativa
Otra vista de las tres salidas de interpolación:
## Warning in pal(c(r[1], cuts, r[2])): Some values were outside the color scale
## and will be treated as NA6.2 Validación cruzada
Hemos estimado superficies climáticas usando dos métodos diferentes: IDW y Kriging Ordinario. Aunque es útil examinar y comparar los resultados gráficamente, también necesitamos una forma objetiva de evaluar la precisión de la interpolación. De esa forma, podemos elegir objetivamente el método más preciso entre los métodos de interpolación disponibles.
En la validación cruzada Leave-One-Out:
- Saque un punto de los datos de calibración
- Haz una predicción para ese punto
- Repetir para todos los puntos Al final, lo que obtenemos es una tabla con un valor observado y un valor pronosticado para todos los puntos.
Podemos ejecutar la validación cruzada Leave-One-Out usando la función gstat.cv, que acepta un objeto gstat.
Al escribir el siguiente fragmento, oculte el mensaje y los resultados.
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## [using ordinary kriging]El resultado de gstat.cv tiene los siguientes atributos:
- var1.pred: valor previsto
- var1.var—Varianza (solo para Kriging)
- observado: valor observado
- residual—Observado-Predicho
- zscore—Z-score (solo para Kriging)
- fold: ID de validación cruzada
cv1## class : SpatialPointsDataFrame
## features : 500
## extent : -77.12724, -75.13034, 4.27966, 6.271917 (xmin, xmax, ymin, ymax)
## crs : +proj=longlat +datum=WGS84 +no_defs
## variables : 6
## names : var1.pred, var1.var, observed, residual, zscore, fold
## min values : 20.4784998080254, NA, 0, -189.763144203481, NA, 1
## max values : 281.610887917643, NA, 315.270141601562, 148.756393343835, NA, 500Convirtamos el objeto cv1:
Ahora, grafiquemos los residuos:
Ahora, calculamos índices de precisión de predicción, como el error cuadrático medio (RMSE):
## [1] 30.31076Ahora, repita el proceso con los resultados OK:
Tiempo de conversión:
Calcule RSME para obtener resultados correctos:
## [1] 26.50455El metodo de IDW tiene una forma de interpretar mas sencilla, pero genera resultados mas sesgandos, pero, el metodo OK es mas complejo de interpretar tanto en graficos como en datos, pero es mas preciso en el momento de los resultados, por esta razon el metodo OK es mucho mas optimo siempre y cuando se tenga una correlacion espacial de los datos lo cual puede llegar a una variabilidad espcial del fenomeno mejor representada como se tiene en este caso.
7. Reference
Citar este trabajo como: Lizarazo, I., 2023. Interpolación espacial del carbono orgánico del suelo. Disponible en https://rpubs.com/ials2un/soc_interp.
sessionInfo()## R version 4.2.2 (2022-10-31 ucrt)
## Platform: x86_64-w64-mingw32/x64 (64-bit)
## Running under: Windows 10 x64 (build 22621)
##
## Matrix products: default
##
## locale:
## [1] LC_COLLATE=Spanish_Colombia.utf8 LC_CTYPE=Spanish_Colombia.utf8
## [3] LC_MONETARY=Spanish_Colombia.utf8 LC_NUMERIC=C
## [5] LC_TIME=Spanish_Colombia.utf8
##
## attached base packages:
## [1] stats graphics grDevices utils datasets methods base
##
## other attached packages:
## [1] curl_5.0.0 dplyr_1.1.0 ggplot2_3.4.1 leafem_0.2.0 leaflet_2.1.2
## [6] automap_1.1-9 gstat_2.1-1 stars_0.6-1 abind_1.4-5 sf_1.0-12
## [11] terra_1.7-29 sp_1.6-0
##
## loaded via a namespace (and not attached):
## [1] Rcpp_1.0.10 lattice_0.20-45 FNN_1.1.3.2 png_0.1-8
## [5] class_7.3-20 zoo_1.8-12 digest_0.6.31 utf8_1.2.3
## [9] R6_2.5.1 plyr_1.8.8 evaluate_0.20 e1071_1.7-13
## [13] highr_0.10 pillar_1.8.1 rlang_1.0.6 rstudioapi_0.14
## [17] raster_3.6-20 jquerylib_0.1.4 rmarkdown_2.20 rgdal_1.6-6
## [21] htmlwidgets_1.6.2 munsell_0.5.0 proxy_0.4-27 compiler_4.2.2
## [25] xfun_0.37 pkgconfig_2.0.3 base64enc_0.1-3 htmltools_0.5.4
## [29] tidyselect_1.2.0 tibble_3.1.8 intervals_0.15.3 codetools_0.2-18
## [33] reshape_0.8.9 fansi_1.0.4 spacetime_1.3-0 withr_2.5.0
## [37] grid_4.2.2 jsonlite_1.8.4 lwgeom_0.2-11 gtable_0.3.1
## [41] lifecycle_1.0.3 DBI_1.1.3 magrittr_2.0.3 units_0.8-2
## [45] scales_1.2.1 KernSmooth_2.23-20 cli_3.6.0 cachem_1.0.6
## [49] farver_2.1.1 bslib_0.4.2 ellipsis_0.3.2 xts_0.13.1
## [53] generics_0.1.3 vctrs_0.5.2 tools_4.2.2 glue_1.6.2
## [57] crosstalk_1.2.0 parallel_4.2.2 fastmap_1.1.0 yaml_2.3.7
## [61] colorspace_2.1-0 classInt_0.4-9 knitr_1.42 sass_0.4.5