#Install and load googledrive package
install.packages("googledrive")
library(googledrive)
# This will prompt you to authenticate in the browser to get access to Google Drive files
drive_auth()

Installing package into ‘/usr/local/lib/R/site-library’
(as ‘lib’ is unspecified)

The googledrive package is requesting access to your Google account.
Enter '1' to start a new auth process or select a pre-authorized account.
1: Send me to the browser for a new auth process.
2: dmglandon@gmail.com

Selection: 2

#install packages
install.packages("lidR")
install.packages("terra")
install.packages("raster")
install.packages("caret")
install.packages("ggplot2")
install.packages("ggpointdensity")

#Load packages
library(lidR)
library(terra)
library(raster)
library(caret)
library(sp)
library(sf)
library(dplyr)
library(tools)
library(ggplot2)
library(ggpointdensity)

Installing package into ‘/usr/local/lib/R/site-library’
(as ‘lib’ is unspecified)

also installing the dependencies ‘proxy’, ‘wk’, ‘e1071’, ‘htmlwidgets’, ‘s2’, ‘units’, ‘abind’, ‘classInt’, ‘lazyeval’, ‘Rcpp’, ‘rgl’, ‘rlas’, ‘sf’, ‘stars’, ‘terra’, ‘BH’, ‘RcppArmadillo’


Installing package into ‘/usr/local/lib/R/site-library’
(as ‘lib’ is unspecified)

Installing package into ‘/usr/local/lib/R/site-library’
(as ‘lib’ is unspecified)

also installing the dependency ‘sp’


Installing package into ‘/usr/local/lib/R/site-library’
(as ‘lib’ is unspecified)

also installing the dependencies ‘listenv’, ‘parallelly’, ‘future’, ‘globals’, ‘shape’, ‘future.apply’, ‘numDeriv’, ‘progressr’, ‘SQUAREM’, ‘diagram’, ‘lava’, ‘prodlim’, ‘iterators’, ‘clock’, ‘gower’, ‘hardhat’, ‘ipred’, ‘timeDate’, ‘foreach’, ‘ModelMetrics’, ‘plyr’, ‘pROC’, ‘recipes’, ‘reshape2’


Installing package into ‘/usr/local/lib/R/site-library’
(as ‘lib’ is unspecified)

Installing package into ‘/usr/local/lib/R/site-library’
(as ‘lib’ is unspecified)

terra 1.7.71


Attaching package: ‘terra’


The following objects are masked from ‘package:lidR’:

    area, crs, crs<-, is.empty


Loading required package: sp


Attaching package: ‘sp’


The following object is masked from ‘package:lidR’:

    wkt


Attaching package: ‘raster’


The following objects are masked from ‘package:lidR’:

    projection, projection<-


Loading required package: ggplot2

Loading required package: lattice

Linking to GEOS 3.11.1, GDAL 3.6.4, PROJ 9.1.1; sf_use_s2() is TRUE


Attaching package: ‘sf’


The following object is masked from ‘package:lidR’:

    st_concave_hull


Attaching package: ‘dplyr’


The following objects are masked from ‘package:raster’:

    intersect, select, union


The following objects are masked from ‘package:terra’:

    intersect, union


The following objects are masked from ‘package:stats’:

    filter, lag


The following objects are masked from ‘package:base’:

    intersect, setdiff, setequal, union

#Make directory for inputs and results first

#Download LiDAR and SAR data under the folders "LiDAR" and "SAR"

dir.create("/content/sample_data/Data")
dir.create("/content/sample_data/Result")
dir.create("/content/sample_data/Data/LiDAR")
dir.create("/content/sample_data/Data/SAR")
dir.create("/content/sample_data/Result/CHM")
dir.create("/content/sample_data/Result/Grid_75m")

Warning message in dir.create("/content/sample_data/Data"):
“'/content/sample_data/Data' already exists”
Warning message in dir.create("/content/sample_data/Result"):
“'/content/sample_data/Result' already exists”
Warning message in dir.create("/content/sample_data/Data/LiDAR"):
“'/content/sample_data/Data/LiDAR' already exists”
Warning message in dir.create("/content/sample_data/Data/SAR"):
“'/content/sample_data/Data/SAR' already exists”
Warning message in dir.create("/content/sample_data/Result/CHM"):
“'/content/sample_data/Result/CHM' already exists”
Warning message in dir.create("/content/sample_data/Result/Grid_75m"):
“'/content/sample_data/Result/Grid_75m' already exists”

#This section is to download remote sensing datasets from Google Drive to Colab file

# List all folders in the root of Google Drive
drive_ls(path = "https://drive.google.com/drive/folders/135hqF1uEu7Jm4a6PT0FvbhklQZJvJDbp")

# List all files in the specified Google Drive SAR folder URL
files_SAR <- drive_ls(path = "https://drive.google.com/drive/folders/1Wiec_oIYPNdG70irKLj3O_7wT0I0LOp6")

# Loop through the list of file names in the SAR directory
for (i in 1:length(files_SAR[[2]])){
  print(i)
  # Print a message to the console indicating the start of the download process
  print(paste0("Downloading SAR file...",files_SAR[[1]][i]))
  # Retrieve the file object from Google Drive using its ID
  file <- drive_get(as_id(files_SAR[[2]][i]))
  # Download the file to a specified local path in the Colab environment
  drive_download(file, path = paste0("/content/sample_data/Data/SAR/",files_SAR[[1]][i]))
}

# List all files in the specified Google Drive LiDAR folder URL
files_LiDAR <- drive_ls(path = "https://drive.google.com/drive/folders/1LKoJxJMn-rSofrkNKEnFmidjq6U7vrlr")

# Loop through the list of file names in the LiDAR directory
for (i in 1:length(files_LiDAR[[2]])){
  # Print a message to the console indicating the start of the download process
  print(paste0("Downloading LiDAR file...",files_LiDAR[[1]][i]))
  # Retrieve the file object from Google Drive using its ID
  file <- drive_get(as_id(files_LiDAR[[2]][i]))
  # Download the file to a specified local path in the Colab environment
  drive_download(file, path = paste0("/content/sample_data/Data/LiDAR/",files_LiDAR[[1]][i]))
}

[1] 1
[1] "Downloading SAR file...SAR_0826_msf.tif.aux.xml"

Error in `drive_download()`:
! Local `path` already exists and overwrite is `FALSE`:
• /content/sample_data/Data/SAR/SAR_0826_msf.tif.aux.xml
Traceback:

1. drive_download(file, path = paste0("/content/sample_data/Data/SAR/", 
 .     files_SAR[[1]][i]))
2. drive_abort(c("Local {.arg path} already exists and overwrite is {.code FALSE}:", 
 .     bulletize(gargle_map_cli(path, "{.path <<x>>}"))))
3. cli::cli_abort(message = message, ..., .envir = .envir)
4. rlang::abort(message, ..., call = call, use_cli_format = TRUE, 
 .     .frame = .frame)
5. signal_abort(cnd, .file)

# ------------------------------------------------------------------------------------------------ #
# Batch preprocessing of LiDAR point cloud data to create Canopy Height Models (CHM)
dir <- "/content/sample_data/Data/LiDAR"          # Directory containing input LiDAR files
output = "/content/sample_data/Result/CHM"          # Output directory for the CHM TIFF files
las_files = list.files(dir, pattern = glob2rx('*.laz'), full.names = T)  # List all .laz files in the directory with full paths

for (i in las_files){  # Loop over each LiDAR file in the list
  out = file.path(output, paste0(basename(file_path_sans_ext(i)), ".tif"))  # Create a filepath for the output .tif file using the base name of the input file
  if (!file.exists(out))  # Check if the output file already exists to avoid overwriting
  {
    print(i)  # Print the current file being processed
    print("read ALS")  # Indicate start of reading the LiDAR (ALS) data
    las <- readLAS(i, select = "i,c,r")  # Read the .laz file with intensity, class, and return number
    print("normalize ALS")  # Indicate start of height normalization
    las = normalize_height(las, tin(), na.rm = TRUE)  # Normalize point cloud heights using a Triangulated Irregular Network (TIN)
    print("filter out ALS point cloud > 100m")  # Indicate filtering action
    las <- filter_poi(las, Z >= 0, Z <= 100)  # Filter points to include only those between 0 and 100 meters
    print("1m CHM generation")  # Indicate start of Canopy Height Model generation
    chm <- grid_canopy(las, 1, p2r())  # Generate a CHM with a grid cell size of 1 meter
    projection(chm) <- CRS("+proj=utm +zone=21 +south +datum=WGS84 +units=m +no_defs")  # Set the projection information for the CHM
    print("Output chm")  # Indicate CHM is being outputted
    writeRaster(chm, out, options=c('TFW=YES'), overwrite=TRUE)  # Write the CHM raster to file with a world file (.tfw) and allow overwriting if needed
  }
}

# ------------------------------------------------------------------------------------------------ #
# Batch process to mosaic individual CHM TIFF files into larger, merged CHM files by site

# Setting up directory paths for individual CHM files and output for merged CHM files
dir_chm = "/content/sample_data/Result/CHM"

# List files matching the current site name and ending with '.tif'
chm_files <- list.files(path = dir_chm, pattern = paste0("TAP_A03_2018", ".*\\.tif$"), full.names = TRUE)

# Load all matching CHM files as raster objects
rasters <- lapply(chm_files, raster)

# Merge all raster objects into a single raster using the 'merge' function
merged_raster <- do.call(merge, rasters)

# Write the merged raster to disk with a filename that includes the site name, in GeoTIFF format, and overwrite if exists
writeRaster(merged_raster, filename = file.path(dir_chm,"TAP_A03_2018_Merge.tif"), format = "GTiff", overwrite = TRUE)

# Set the size of plots in Google Colab
options(repr.plot.width=12, repr.plot.height=12)

#Let's visualize the mosaic CHM dataset for all LiDAR tiles
plot(raster("/content/sample_data/Result/CHM/TAP_A03_2018_Merge.tif"), main="2018 Mosaic LiDAR-based CHM map")

# Specify the output directory where the modified raster will be saved
output = "/content/sample_data/Result/CHM"

# Load the raster file from the specified directory
ras <- merged_raster

# Set raster values less than 1.5 and greater than 0 to 0 (e.g., treat as non-woody vegetation)
values(ras)[values(ras) < 1.5] <- 0

# Set raster values equal to or greater than 1.5 to 1 (e.g., treat as woody cover)
values(ras)[values(ras) >= 1.5] <- 1


# Write the modified raster back to file with the specified name and enable the TFW option, allowing overwriting of the existing file if necessary
writeRaster(ras, file.path(output, "TAP_A03_2018_cover.tif"), options=c('TFW=YES'), overwrite=TRUE)

# Set the size of plots in Google Colab
options(repr.plot.width=12, repr.plot.height=12)

#Let's visualize the woody cover for all LiDAR tiles
plot(raster("/content/sample_data/Result/CHM/TAP_A03_2018_cover.tif"), main="2018 Mosaic LiDAR-based woody cover map")

# Set the size of plots in Google Colab
options(repr.plot.width=12, repr.plot.height=12)

# Load the first raster file into the 'raster1' object from the specified path
raster1 <- raster("/content/sample_data/Data/SAR/SAR_0826.tif")

# Load the second raster file into the 'raster2' object from the specified path
raster2 <- raster("/content/sample_data/Data/SAR/SAR_0826_msf.tif")

# Plot the whole extent of the clipped ScanSAR data
plot(raster2, main="2018 MSF ScanSAR", zlim=c(-30,0), col=terrain.colors(255))

# Define a new spatial extent to be applied to both rasters
new_extent <- extent(759000, 760000, 9663600, 9664600)

# Crop 'raster1' to the defined spatial extent and store the result in 'raster1_cropped'
raster1_cropped <- crop(raster1, new_extent)

# Crop 'raster2' to the same defined spatial extent and store the result in 'raster2_cropped'
raster2_cropped <- crop(raster2, new_extent)

# Set the size of plots in Google Colab
options(repr.plot.width=6, repr.plot.height=6)

# Plot the cropped area of 'raster2' with a title and a terrain color scheme, indicating multi-spectral filtering (MSF)
plot(raster2_cropped, main="Subset of 2018 MSF ScanSAR", col=terrain.colors(255))

# Plot the cropped area of 'raster1' with a title and a terrain color scheme
plot(raster1_cropped, main="Subset of 2018 original ScanSAR", col=terrain.colors(255))

# ------------------------------------------------------------------------------------------------ #
# Create a 75m grid based on the extent of a LiDAR-derived 25m resolution raster
# Load the 25m resolution raster from a specified path
raster25m <- raster("/content/sample_data/Result/CHM/TAP_A03_2018_cover.tif")

# Create an empty raster with a 75m resolution using the extent and CRS of the 25m raster
raster75m <- raster(extent(raster25m), res=75, crs=crs(raster25m))

# Adjust the origin of the 75m raster to match that of the 25m raster
# This ensures that the grid cells of both rasters align perfectly if they cover the same area
origin(raster75m) <- origin(raster25m)

# Initialize the raster's values. Here, assigning a unique ID to each cell, which can be useful for tracking or identification
# This step is optional and could instead fill with random values or other data as needed
values(raster75m) <- 1:ncell(raster75m)

# Convert the 75m grid raster to polygons
# This creates a polygon for each unique value (cell) in the raster, dissolving all borders within the same value
polygons <- rasterToPolygons(raster75m, fun=NULL, dissolve=TRUE)

# Convert the resulting polygons from SpatialPolygonsDataFrame to an sf object for better handling in modern GIS operations
sf_object <- st_as_sf(polygons)

# Write the sf object to a shapefile, deleting any existing layer with the same name to avoid errors
st_write(sf_object, "/content/sample_data/Result/Grid_75m/Grid_75m.shp", delete_layer = TRUE)

# Set the size of plots in Google Colab
options(repr.plot.width=12, repr.plot.height=6)

# Plot the 75m grid in raster format
plot(sf_object, main="75m vector grid", col=rgb(runif(20), runif(20), runif(20)))

writing: substituting ENGCRS["Undefined Cartesian SRS with unknown unit"] for missing CRS

Writing layer `Grid_75m' to data source 
  `/content/sample_data/Result/Grid_75m/Grid_75m.shp' using driver `ESRI Shapefile'
Writing 1924 features with 1 fields and geometry type Polygon.

Warning message in plot.sf(sf_object, main = "75m vector grid", col = rgb(runif(20), :
“col is not of length 1 or nrow(x): colors will be recycled; use pal to specify a color palette”

# ------------------------------------------------------------------------------------------------ #
# Aggregate 25m SAR and 1m LiDAR-derived woody cover to 75m using zonal statistics

# Load the SAR raster data from a file, which will be analyzed to compute mean values within each zone
value_raster_SAR <- rast("/content/sample_data/Data/SAR/SAR_0826_msf.tif")

# Load the LiDAR-derived woody cover raster data from a file, which will be analyzed to compute sum values within each zone
value_raster_Cover <- rast("/content/sample_data/Result/CHM/TAP_A03_2018_cover.tif")

# Load the shapefile defining the zones for which statistics will be calculated
zones <- vect("/content/sample_data/Result/Grid_75m/Grid_75m.shp")

# Calculate mean zonal statistics for the SAR data within each 75m grid zone
zonal_stats_SAR <- zonal(value_raster_SAR, zones, "mean")

# Calculate sum zonal statistics for the LiDAR-derived cover data within each 75m grid zone
zonal_stats_Cover <- zonal(value_raster_Cover, zones, "sum")

# Normalize the summed LiDAR cover data by the total number of 1m pixels within a 75m pixel
# Assuming a 75m x 75m grid implies 5625 (75*75) 1m pixels per grid cell
zonal_stats_Cover$TAP_A03_2018_cover <- zonal_stats_Cover$TAP_A03_2018_cover / 5625

# Assign a unique ID to each zone for SAR statistics for later merging and comparison
zonal_stats_SAR$ID <- c(1:nrow(zonal_stats_SAR))

# Assign a unique ID to each zone for cover statistics for later merging and comparison
zonal_stats_Cover$ID <- c(1:nrow(zonal_stats_Cover))

# Merge the SAR and cover statistics into a single dataframe based on their IDs
Data_SAR_Cover <- merge(x = zonal_stats_SAR, y = zonal_stats_Cover, by.x = "ID", by.y = "ID")

# Remove all rows with NA values, which might result from zones not covered by both datasets
Data_SAR_Cover <- na.omit(Data_SAR_Cover)

# Rename columns to reflect the data they represent
names(Data_SAR_Cover) <- c("ID", "SAR", "Cover")

# Round the cover and SAR data to three decimal places for cleaner presentation and analysis
Data_SAR_Cover$Cover <- round(Data_SAR_Cover$Cover, 3)
Data_SAR_Cover$SAR <- round(Data_SAR_Cover$SAR, 3)

# Filter the data to include only rows where cover is greater than 0 and less than 1
# This step assumes cover is a proportion or percentage that should logically fall between 0 and 1
Data_SAR_Cover <- Data_SAR_Cover[Data_SAR_Cover$Cover > 0,]
Data_SAR_Cover <- Data_SAR_Cover[Data_SAR_Cover$Cover < 1,]

# Print or view the first 20 rows of cleaned, joined data table
head(Data_SAR_Cover, 10)

# Set the size of plots in Google Colab
options(repr.plot.width=12, repr.plot.height=12)

r2 <- round(cor(Data_SAR_Cover$SAR,Data_SAR_Cover$Cover)^2,3)
# Create a scatter plot with density coloring and add a linear regression line
ggplot(Data_SAR_Cover, aes(x = Cover, y = SAR)) +
  theme_bw() +  # Use a theme with a white background and no grid
  geom_pointdensity() +  # Create a density scatter plot
  geom_smooth(
    method = "lm",  # Linear model
    formula = y ~ x,  # Formula for the linear model
    se = FALSE,  # Do not include a confidence interval around the regression line
    size = 1.5,  # Set the size of the regression line
    linetype = "solid",  # Use a solid line
    colour = "red"  # Color the line red
  ) +
  annotate("text", x = 0.35, y = -21, hjust = 0, color = "red", size = 7,
           label = paste(expression(Linear ~ model ~ R^2), ": ", r2), parse = TRUE) +
  theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank()) +
  labs(
    x = "Mean of Woody cover (Mg/ha)",  # X-axis label
    y = "Mean of SAR backscatter (dB)"  # Y-axis label
  ) +
  theme(
    legend.position = "none",  # Remove the legend
    legend.title = element_blank(),  # Remove the legend title
    text = element_text(size = 25),  # Increase text size for better readability
    # Uncomment the following line to set a specific font family
    # text = element_text(family = "A"),
    plot.title = element_text(hjust = 0.5)  # Center the plot title
  )

Warning message:
“Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
ℹ Please use `linewidth` instead.”

# ------------------------------------------------------------------------------------------------ #
# Grouping data into intervals and ordering by group
Data_SAR_Cover <- Data_SAR_Cover %>%
  group_by(gr = cut(Cover, breaks = seq(0, 1, by = 0.1))) %>%
  arrange(as.numeric(gr))

# Initialize variables
i <- 1
rsqd_sample <- numeric(10)
bias_sample <- numeric(10)
RMSE_sample <- numeric(10)
raster_list <- vector("list", 10)

# Loop to perform operations 10 times
for (i in 1:10){
  # Partitioning the data into training and testing sets (70% training data)
  random_sample <- createDataPartition(Data_SAR_Cover$Cover, p = 0.7, list = FALSE)
  training_dataset <- Data_SAR_Cover[random_sample, ]
  testing_dataset <- Data_SAR_Cover[-random_sample, ]

  # Linear regression model
  reg <- lm(Cover ~ SAR, data = training_dataset)
  testing_dataset$preds <- predict(reg, newdata = testing_dataset)

  # Calculating performance metrics
  rsqd_sample[i] <- round(cor(testing_dataset$Cover, testing_dataset$preds)^2, 3)
  bias_sample[i] <- mean(testing_dataset$preds - testing_dataset$Cover)
  RMSE_sample[i] <- sqrt(mean((testing_dataset$preds - testing_dataset$Cover)^2))

  # Creating raster map using regression coefficients
  value_raster_SAR <- raster("/content/sample_data/Data/SAR/SAR_0826_msf.tif")
  SAR_cover <- value_raster_SAR * reg$coefficients[2] + reg$coefficients[1]
  raster_list[[i]] <- SAR_cover  # Storing raster in list
}

# Calculating average of the performance metrics
R2_testing <- mean(rsqd_sample)
bias_testing <- mean(bias_sample)
RMSE_testing <- mean(RMSE_sample)

# Print the results
cat("Average R-squared:", R2_testing, "
")
cat("Average Bias:", bias_testing, "
")
cat("Average RMSE:", RMSE_testing, "
")

Error in eval(expr, envir, enclos): object 'Data_SAR_Cover' not found
Traceback:

1. Data_SAR_Cover %>% group_by(gr = cut(Cover, breaks = seq(0, 1, 
 .     by = 0.1))) %>% arrange(as.numeric(gr))
2. arrange(., as.numeric(gr))
3. group_by(., gr = cut(Cover, breaks = seq(0, 1, by = 0.1)))

# ------------------------------------------------------------------------------------------------ #
# Stack raster layers from the list into a single raster stack
raster_stack <- stack(raster_list)

# Calculate the mean of all rasters in the stack
raster_mean <- mean(raster_stack)

#limit woody cover map to specific range
raster_mean[raster_mean < 0] <- 0
raster_mean[raster_mean > 1] <- 1

# Specify the file path and name for the output raster
output_SAR_cover <- "/content/sample_data/Result/SAR_cover_75m.tif"

# Write the mean raster to a GeoTIFF file at the specified location
# This saves the raster permanently to disk for further use
writeRaster(raster_mean, filename=output_SAR_cover, format="GTiff", overwrite=TRUE)

# Set the size of plots in Google Colab
options(repr.plot.width=12, repr.plot.height=12)

# Plot the mean woody cover raster to visualize the average values
plot(raster_mean, zlim=c(0, 1), main="Mean SAR-predicted woody cover map")

#remove stack raster from memory to avoid program crash
rm(raster_stack)

# ------------------------------------------------------------------------------------------------ #
# Define break points for bins from 0 to 1, at intervals of 0.1
breakbin = seq(0, 1, by = 0.1)

# Calculate the difference between predictions and actual cover values, store in new column 'Diff'
testing_dataset$Diff <- testing_dataset$preds - testing_dataset$Cover

# Group 'Diff' by binned 'Cover', calculate mean for each bin
a <- tapply(testing_dataset$Diff, cut(testing_dataset$Cover, breaks = breakbin, dig.lab = 1), mean)

# Generate sequence from 0 to 0.9 for x-axis labels, rounded to one decimal place
x <- round(seq(0, 0.9, by = 0.1), digits = 1)

# Combine 'x' and 'a' into a matrix
l <- cbind(x, a)

# Convert the matrix to a dataframe for plotting
df <- data.frame(l)

# Set the size of plots in Google Colab
options(repr.plot.width=12, repr.plot.height=12)

# Create a ggplot: bars shifted right by 0.05 for centering, using the dataframe 'df'
ggplot(df, aes(x = x + 0.05, y = a)) +
  geom_bar(stat = 'identity') +  # Plot bars representing data
  theme_bw() +  # Use a minimal theme with white background
  coord_cartesian(ylim = c(-0.2, 0.3)) +  # Set y-axis limits
  scale_y_continuous(minor_breaks = seq(-0.2, 0.3, 0.1), breaks = seq(-0.2, 0.3, 0.1)) +  # Define breaks for y-axis
  scale_x_continuous(minor_breaks = round(seq(0, 1, 0.1), digits = 1),  # Minor x-axis breaks
                     breaks = round(seq(0, 1, 0.1), digits = 1)) +  # Major x-axis breaks
  labs(x = expression("Woody cover interval"),  # X-axis label
       y = expression("Woody cover difference")) +  # Y-axis label
  theme(legend.position = "none") +  # Remove legend
  theme(legend.title = element_blank()) +  # Remove legend title
  theme(text = element_text(size = 25)) +  # Set text size for all text elements
  theme(plot.title = element_text(hjust = 0.5))  # Center the plot title horizontally

Error in eval(expr, envir, enclos): object 'testing_dataset' not found
Traceback:

# Statistics and plots using logarithmic model
# Calculate the R^2 value for the relationship between SAR and log(Cover) and round it to three decimal places
r2 <- round(cor(Data_SAR_Cover$SAR, log(Data_SAR_Cover$Cover))^2, 3)

# Create a ggplot of log(Cover) vs SAR with a density point
ggplot(Data_SAR_Cover, aes(x=Cover, y=SAR)) +
  theme_bw() +
  geom_pointdensity() +
  geom_smooth(
    method = "lm",
    formula = 'y ~ log(x)',
    se = FALSE,
    size = 1.5,
    linetype = "solid",
    colour = "red"
  ) +
  annotate("text", x = 0.7, y = -20, hjust = 0, color = "red", size = 7,
           label = paste(expression(Linear~model~R^2), ": ", r2), parse = TRUE) +
  theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank()) +
  labs(x = "Mean of Woody cover",
       y = "Mean of SAR backscatter (dB)") +
  theme(legend.position = "none") +
  theme(legend.title = element_blank()) +
  theme(text = element_text(size = 30)) +
  theme(plot.title = element_text(hjust = 0.5))

# Group and arrange the data based on Cover
Data_SAR_Cover <- Data_SAR_Cover %>%
  group_by(gr = cut(Cover, breaks = seq(0, 1, by = 0.1))) %>%
  arrange(as.numeric(gr))

# Initialize variables for storing metrics across subsets
rsqd_sample <- numeric(10)  # Store R-squared values
bias_sample <- numeric(10)  # Store bias values
RMSE_sample <- numeric(10)  # Store RMSE values
raster_list <- list()       # List to store raster data

# Loop over 10 subsets to calculate metrics for each
for (i in 1:10) {
  random_sample <- createDataPartition(Data_SAR_Cover$Cover, p = 0.7, list = FALSE)
  training_dataset <- Data_SAR_Cover[random_sample, ]
  testing_dataset <- Data_SAR_Cover[-random_sample, ]
  x <- testing_dataset$Cover
  y <- testing_dataset$SAR
  # Non-linear regression model
  mult_nls <- nls(x ~ a * exp(b * y), start = list(a = 20, b = 0.2), data = training_dataset)
  testing_dataset$preds <- coef(mult_nls)[1] * exp(coef(mult_nls)[2] * testing_dataset$SAR)

  # Calculate R-squared, bias, and RMSE for the testing dataset
  rsqd_sample[i] <- round(cor(testing_dataset$Cover, testing_dataset$preds)^2, 3)
  bias_sample[i] <- mean(testing_dataset$preds - testing_dataset$Cover)
  RMSE_sample[i] <- sqrt(mean((testing_dataset$preds - testing_dataset$Cover)^2))
}

# Calculate average R-squared, bias, and RMSE across all subsets
R2_testing <- mean(rsqd_sample)
bias_testing <- mean(bias_sample)
RMSE_testing <- mean(RMSE_sample)

# Print the results
cat("Average R-squared:", R2_testing, "
")
cat("Average Bias:", bias_testing, "
")
cat("Average RMSE:", RMSE_testing, "
")

Error in eval(expr, envir, enclos): object 'Data_SAR_Cover' not found
Traceback:

1. cor(Data_SAR_Cover$SAR, log(Data_SAR_Cover$Cover))
2. is.data.frame(y)

	ID	SAR	Cover
	<int>	<dbl>	<dbl>
39	39	-15.611	0.454
40	40	-15.333	0.580
41	41	-15.891	0.883
42	42	-14.203	0.881
59	59	-20.579	0.133
60	60	-21.045	0.073
61	61	-21.321	0.092
62	62	-19.601	0.123
63	63	-18.192	0.034
64	64	-16.344	0.102

ABSTRACT¶

Background¶

Data introduction, processing and analysis¶

Exercise 1¶

Exercise 2 (optional)¶

Reference¶

Cite this work¶

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