Geographical Convergent Cross Mapping (GCCM)
Wenbo Lv
2025-03-21
Source:vignettes/GCCM.Rmd
GCCM.Rmd1.1 Install the spEDM package
Install the stable version from CRAN with:
install.packages("spEDM", dep = TRUE)Alternatively, you can install the development version from R-universe with:
install.packages("spEDM",
repos = c("https://stscl.r-universe.dev",
"https://cloud.r-project.org"),
dep = TRUE)1.2 An example of spatial lattice data
Load the spEDM package and its county-level population
density data:
library(spEDM)
popd_nb = spdep::read.gal(system.file("case/popd_nb.gal",package = "spEDM"))
## Warning in spdep::read.gal(system.file("case/popd_nb.gal", package = "spEDM")):
## neighbour object has 4 sub-graphs
popd_nb
## Neighbour list object:
## Number of regions: 2806
## Number of nonzero links: 15942
## Percentage nonzero weights: 0.2024732
## Average number of links: 5.681397
## 4 disjoint connected subgraphs
popd = readr::read_csv(system.file("case/popd.csv",package = "spEDM"))
## Rows: 2806 Columns: 7
## ── Column specification ────────────────────────────────────────────────────────────────────────────
## Delimiter: ","
## dbl (7): x, y, popd, elev, tem, pre, slope
##
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
popd
## # A tibble: 2,806 × 7
## x y popd elev tem pre slope
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 117. 30.5 780. 8 17.4 1528. 0.452
## 2 117. 30.6 395. 48 17.2 1487. 0.842
## 3 117. 30.8 261. 49 16.0 1456. 3.56
## 4 116. 30.1 258. 23 17.4 1555. 0.932
## 5 116. 30.5 211. 101 16.3 1494. 3.34
## 6 117. 31.0 386. 10 16.6 1382. 1.65
## 7 117. 30.2 350. 23 17.5 1569. 0.346
## 8 117. 30.7 470. 22 17.1 1493. 1.88
## 9 117. 30.6 1226. 11 17.4 1526. 0.208
## 10 116. 30.9 137. 598 13.9 1458. 5.92
## # ℹ 2,796 more rows
popd_sf = sf::st_as_sf(popd, coords = c("x","y"), crs = 4326)
popd_sf
## Simple feature collection with 2806 features and 5 fields
## Geometry type: POINT
## Dimension: XY
## Bounding box: xmin: 74.9055 ymin: 18.2698 xmax: 134.269 ymax: 52.9346
## Geodetic CRS: WGS 84
## # A tibble: 2,806 × 6
## popd elev tem pre slope geometry
## * <dbl> <dbl> <dbl> <dbl> <dbl> <POINT [°]>
## 1 780. 8 17.4 1528. 0.452 (116.912 30.4879)
## 2 395. 48 17.2 1487. 0.842 (116.755 30.5877)
## 3 261. 49 16.0 1456. 3.56 (116.541 30.7548)
## 4 258. 23 17.4 1555. 0.932 (116.241 30.104)
## 5 211. 101 16.3 1494. 3.34 (116.173 30.495)
## 6 386. 10 16.6 1382. 1.65 (116.935 30.9839)
## 7 350. 23 17.5 1569. 0.346 (116.677 30.2412)
## 8 470. 22 17.1 1493. 1.88 (117.066 30.6514)
## 9 1226. 11 17.4 1526. 0.208 (117.171 30.5558)
## 10 137. 598 13.9 1458. 5.92 (116.208 30.8983)
## # ℹ 2,796 more rowsSelect the appropriate embedding dimension E:
simplex(popd_sf,"pre",lib = 1:2000,pred = 2001:nrow(popd_sf),k = 6,nb = popd_nb,trend.rm = TRUE)
## The suggested E and k for variable pre is 2 and 6
simplex(popd_sf,"popd",lib = 1:2000,pred = 2001:nrow(popd_sf),k = 6,nb = popd_nb,trend.rm = TRUE)
## The suggested E and k for variable popd is 5 and 6We choose the E with the highest rho and the lowest MAE and RMSE as
the most suitable one. Under the selected lib and pred, the optimal
embedding dimension E for the variable pre is 2, and for
the variable popdensity, it is 5.
Then, run GCCM:
startTime = Sys.time()
pd_res = gccm(data = popd_sf,
cause = "pre",
effect = "popd",
libsizes = seq(10, 2800, by = 100),
E = c(2,5),
k = 6,
nb = popd_nb,
progressbar = FALSE)
endTime = Sys.time()
print(difftime(endTime,startTime, units ="mins"))
## Time difference of 5.75923 mins
pd_res
## libsizes pre->popd popd->pre
## 1 10 0.05589905 0.01004636
## 2 110 0.18109636 0.03478543
## 3 210 0.24325566 0.04932428
## 4 310 0.27657692 0.06417637
## 5 410 0.30630281 0.07634983
## 6 510 0.34116169 0.08815848
## 7 610 0.38078810 0.09890353
## 8 710 0.41612716 0.10867846
## 9 810 0.44420437 0.11714337
## 10 910 0.46815429 0.12485229
## 11 1010 0.48876449 0.13194552
## 12 1110 0.50538462 0.13802611
## 13 1210 0.52300459 0.14335037
## 14 1310 0.53902632 0.14813342
## 15 1410 0.55309048 0.15284706
## 16 1510 0.56754023 0.15777314
## 17 1610 0.58387624 0.16301596
## 18 1710 0.60029184 0.16768202
## 19 1810 0.61631190 0.17202960
## 20 1910 0.63213899 0.17601166
## 21 2010 0.64785899 0.17979878
## 22 2110 0.66289302 0.18304365
## 23 2210 0.67740971 0.18596497
## 24 2310 0.69156193 0.18906187
## 25 2410 0.70541793 0.19196548
## 26 2510 0.71925253 0.19503355
## 27 2610 0.73287448 0.19819076
## 28 2710 0.74435871 0.20116518Visualize the result:
Figure 1. The cross-mapping
prediction outputs between population density and county-level
precipitation.
1.3 An example of spatial grid data
Load the spEDM package and its farmland NPP data:
library(spEDM)
npp = terra::rast(system.file("case/npp.tif", package = "spEDM"))
npp
## class : SpatRaster
## dimensions : 404, 483, 4 (nrow, ncol, nlyr)
## resolution : 10000, 10000 (x, y)
## extent : -2625763, 2204237, 1877078, 5917078 (xmin, xmax, ymin, ymax)
## coord. ref. : CGCS2000_Albers
## source : npp.tif
## names : npp, pre, tem, elev
## min values : 164.00, 384.3409, -47.8194, -122.2004
## max values : 16606.33, 23878.3555, 263.6938, 5350.4902
# configure the default colormap in terra
options(terra.pal = grDevices::terrain.colors(100,rev = T))
# visualize raster data
terra::plot(npp, nc = 2,
axes = FALSE,
legend = FALSE)
Figure 2. Maps of farmland NPP
and climate factors.
To save the computation time, we will aggregate the data by 3 times and select 1500 non-NA pixels to predict:
npp = terra::aggregate(npp, fact = 3, na.rm = TRUE)
npp
## class : SpatRaster
## dimensions : 135, 161, 4 (nrow, ncol, nlyr)
## resolution : 30000, 30000 (x, y)
## extent : -2625763, 2204237, 1867078, 5917078 (xmin, xmax, ymin, ymax)
## coord. ref. : CGCS2000_Albers
## source(s) : memory
## names : npp, pre, tem, elev
## min values : 187.50, 390.3351, -47.8194, -110.1494
## max values : 15381.89, 23734.5330, 262.8576, 5217.6431
terra::global(npp,"isNA")
## isNA
## npp 14815
## pre 14766
## tem 14766
## elev 14760
terra::ncell(npp)
## [1] 21735
nnamat = terra::as.matrix(npp[[1]], wide = TRUE)
nnaindice = which(!is.na(nnamat), arr.ind = TRUE)
dim(nnaindice)
## [1] 6920 2
set.seed(2025)
indices = sample(nrow(nnaindice), size = 1500, replace = FALSE)
libindice = nnaindice[-indices,]
predindice = nnaindice[indices,]Due to the high number of NA values in the npp raster data, we used all non-NA cell as the libraries when testing for the most suitable embedding dimensions.
simplex(npp,"pre",nnaindice,predindice,k = 8,trend.rm = TRUE)
## The suggested E and k for variable pre is 2 and 8
simplex(npp,"npp",nnaindice,predindice,k = 8,trend.rm = TRUE)
## The suggested E and k for variable npp is 10 and 8Under the selected lib and pred, the optimal embedding dimension E
for the variable pre is 2, and for the variable
npp, it is 10.
Then, run GCCM:
startTime = Sys.time()
npp_res = gccm(data = npp,
cause = "pre",
effect = "npp",
libsizes = as.matrix(expand.grid(seq(10,130,10),seq(10,160,10))),
E = c(2,10),
k = 8,
lib = nnaindice,
pred = predindice,
progressbar = FALSE)
endTime = Sys.time()
print(difftime(endTime,startTime, units ="mins"))
## Time difference of 9.433306 mins
npp_res
## libsizes pre->npp npp->pre
## 1 10 0.1295281 0.1013898
## 2 20 0.1990710 0.1605447
## 3 30 0.2607783 0.2286559
## 4 40 0.3219650 0.2744616
## 5 50 0.3788341 0.2956426
## 6 60 0.4512668 0.3272331
## 7 70 0.4961658 0.3394660
## 8 80 0.5366037 0.3378108
## 9 90 0.5972341 0.3376894
## 10 100 0.6670024 0.3405838
## 11 110 0.7358447 0.3412305
## 12 120 0.7981711 0.3500295
## 13 130 0.8386849 0.3663077
## 14 140 0.8460446 0.3687385
## 15 150 0.8483344 0.3696080
## 16 160 0.8503816 0.3695784Visualize the result:
plot(npp_res,xlimits = c(9, 161),ylimits = c(0.05,1)) +
ggplot2::theme(legend.justification = c(0.25,1))
Figure 3. The cross-mapping
prediction outputs between farmland NPP and precipitation.