regspas 9

library(sp)

## Warning: package 'sp' was built under R version 4.5.2

library(sf)

## Warning: package 'sf' was built under R version 4.5.2

## Linking to GEOS 3.13.1, GDAL 3.11.4, PROJ 9.7.0; sf_use_s2() is TRUE

library(gstat)

## Warning: package 'gstat' was built under R version 4.5.3

library(ggplot2)

## Warning: package 'ggplot2' was built under R version 4.5.3

library(tidyr)

## Warning: package 'tidyr' was built under R version 4.5.2

data(meuse)
data(meuse.grid)

meuse_sf <- st_as_sf(meuse, coords = c("x", "y"), crs = 28992)
meuse.grid_sf <- st_as_sf(meuse.grid, coords = c("x", "y"), crs = 28992)

target_formula <- zinc ~ 1


print("Memproses Cross-Validation, mohon tunggu sebentar...")

## [1] "Memproses Cross-Validation, mohon tunggu sebentar..."

set.seed(16180339)

cv_closest <- krige.cv(target_formula, meuse_sf, nmax = 1)

cv_nn <- krige.cv(target_formula, meuse_sf, nmax = 5, set = list(idp = 0))

cv_idw <- krige.cv(target_formula, meuse_sf)

v <- variogram(target_formula, meuse_sf)
v_fit <- fit.variogram(v, vgm(psill = var(meuse_sf$zinc), model = "Sph", range = 900, nugget = min(v$gamma)))
cv_kriging <- krige.cv(target_formula, meuse_sf, model = v_fit)

ensemble_cv_pred <- (cv_idw$var1.pred + cv_kriging$var1.pred + cv_nn$var1.pred) / 3


calc_rmse <- function(observed, predicted) {
  sqrt(mean((observed - predicted)^2))
}
obs_aktual <- meuse_sf$zinc

tabel_rmse <- data.frame(
  Metode_Interpolasi = c("Closest Obs", "Nearest Neighbor", "IDW", "Kriging", "Ensembel"),
  RMSE = c(
    calc_rmse(obs_aktual, cv_closest$var1.pred),
    calc_rmse(obs_aktual, cv_nn$var1.pred),
    calc_rmse(obs_aktual, cv_idw$var1.pred),
    calc_rmse(obs_aktual, cv_kriging$var1.pred),
    calc_rmse(obs_aktual, ensemble_cv_pred)
  )
)

print("--- Hasil Perbandingan RMSE Cross Validation ---")

## [1] "--- Hasil Perbandingan RMSE Cross Validation ---"

print(tabel_rmse[order(tabel_rmse$RMSE), ])

##   Metode_Interpolasi     RMSE
## 4            Kriging 224.8003
## 5           Ensembel 247.1181
## 2   Nearest Neighbor 263.9874
## 3                IDW 278.2734
## 1        Closest Obs 309.9685

print("Memproses prediksi grid untuk plot...")

## [1] "Memproses prediksi grid untuk plot..."

pred_closest <- krige(target_formula, meuse_sf, meuse.grid_sf, nmax = 1)

## [inverse distance weighted interpolation]

pred_nn      <- krige(target_formula, meuse_sf, meuse.grid_sf, nmax = 5, set = list(idp = 0))

## [inverse distance weighted interpolation]

pred_idw     <- krige(target_formula, meuse_sf, meuse.grid_sf)

## [inverse distance weighted interpolation]

pred_kriging <- krige(target_formula, meuse_sf, meuse.grid_sf, model = v_fit)

## [using ordinary kriging]

pred_ensemble <- (pred_idw$var1.pred + pred_kriging$var1.pred + pred_nn$var1.pred) / 3


print("Men-generate plot...")

## [1] "Men-generate plot..."

grid_coords <- st_coordinates(meuse.grid_sf)

df_plot <- data.frame(
  x = grid_coords[, "X"],
  y = grid_coords[, "Y"],
  Closest_Obs = pred_closest$var1.pred,
  Nearest_Neighbor = pred_nn$var1.pred,
  IDW = pred_idw$var1.pred,
  Kriging = pred_kriging$var1.pred,
  Ensembel = pred_ensemble
)

metode_list <- c(
  "Closest_Obs" = "Closest Observation (1-NN)",
  "Nearest_Neighbor" = "Nearest Neighbor (5-NN Rata-rata)",
  "IDW" = "Inverse Distance Weighting (IDW)",
  "Kriging" = "Ordinary Kriging",
  "Ensembel" = "Ensembel (IDW + Kriging + 5-NN)"
)

for (kolom in names(metode_list)) {
  
  p <- ggplot(df_plot, aes(x = x, y = y, fill = .data[[kolom]])) +
    geom_tile() + 
    scale_fill_viridis_c(option = "magma", direction = -1) +
    theme_minimal() +
    coord_equal() + 
    labs(
      title = paste("Prediksi Spasial:", metode_list[[kolom]]),
      x = "Koordinat X",
      y = "Koordinat Y",
      fill = "Zinc (ppm)"
    ) +
    theme(
      plot.title = element_text(face = "bold", size = 14),
      legend.position = "right", 
      legend.title = element_text(face = "bold")
    )
  
  print(p)
}

Berdasarkan hasil analisis interpolasi spasial terhadap konsentrasi zinc menggunakan metode Cross-Validation, diperoleh perbedaan tingkat akurasi antara metode Closest Observation (1-NN), Nearest Neighbor (5-NN), Inverse Distance Weighting (IDW), Ordinary Kriging, dan Ensembel (gabungan IDW, Kriging, dan 5-NN). Metode dengan nilai Root Mean Square Error (RMSE) terendah menunjukkan tingkat akurasi prediksi terbaik, sedangkan metode dengan nilai RMSE tertinggi menunjukkan tingkat kesalahan prediksi terbesar. Dari hasil visualisasi peta spasial, metode Ensembel mampu menggambarkan persebaran konsentrasi zinc dengan pola gradasi warna yang memperlihatkan variasi konsentrasi pada berbagai lokasi pengamatan. Area dengan warna lebih gelap menunjukkan konsentrasi zinc yang relatif tinggi, sedangkan area dengan warna lebih terang menunjukkan konsentrasi yang relatif rendah. Perbedaan pola visualisasi antarmetode menunjukkan bahwa setiap pendekatan interpolasi memiliki karakteristik tersendiri dalam menggambarkan variasi konsentrasi zinc secara spasial.