Soil Sampling Optimization: cLHS + Random Forest

An R-based workflow that optimizes spatial sampling designs by combining Conditioned Latin Hypercube Sampling (cLHS) with Random Forest (RF) optimization using simulated annealing.

📊 Results Preview

Performance Improvement: The RF-optimized design achieved a 46.59% reduction in MSE compared to the cLHS baseline.

Method	MSE	Samples	Improvement
cLHS	0.0038	100	0%
RF Optimized	0.0020	100	46.59%

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🎯 Overview

This project implements a two-stage optimization approach for spatial sampling:

1. Stage 1: cLHS Sampling - Generates representative samples covering the full range of environmental conditions
2. Stage 2: RF Optimization - Uses simulated annealing with Random Forest MSE as the objective function to refine sample locations

The result is a sampling design that is both environmentally representative and predictively optimal.

🔬 Methodology

Conditioned Latin Hypercube Sampling (cLHS)

• Ensures samples cover the full distribution of environmental covariates
• Provides a statistically representative baseline design
• Guarantees coverage across the environmental feature space

Random Forest Optimization

• Algorithm: Simulated annealing with Metropolis acceptance criterion
• Objective Function: Cross-validated Random Forest MSE (5-fold CV)
• Mechanism: Iteratively swaps sample points to minimize prediction error
• Parameters:
  • Initial temperature: 1000
  • Cooling rate: 0.95
  • Default iterations: 500

📋 Requirements

R Packages

install.packages(c("terra", "clhs", "randomForest", "ggplot2", "gridExtra"))

• terra - Spatial raster data handling
• clhs - Conditioned Latin Hypercube Sampling
• randomForest - Random Forest modeling
• ggplot2 - Visualization
• gridExtra - Plot arrangement

🚀 Quick Start

Basic Usage

# Source the script
source("clhs_rf_optimized.R")

# Run with default parameters
results <- run_sampling_optimization(
  raster_file = "data/predictors.tif",
  n_samples = 100,
  n_iterations = 500,
  seed = 123
)

Custom Configuration

# Advanced usage with custom parameters
results <- run_sampling_optimization(
  raster_file = "data/predictors.tif",
  n_samples = 150,              # Number of sample points
  n_iterations = 1000,          # Optimization iterations
  output_dir = "outputs/",      # Output directory
  seed = 42,                    # Random seed for reproducibility
  target_var = NULL,            # Specific target variable
  export_results = TRUE         # Export CSV and plots
)

📂 Input Data

The script expects a multi-band GeoTIFF raster file with environmental covariates:

• Format: GeoTIFF (.tif)
• Structure: Multi-band raster where each band represents an environmental variable
• Example: data/predictors.tif

Supported covariates: DEM, slope, aspect, NDVI, TWI, soil properties, climate variables, etc.

📤 Output Files

All outputs are saved to the outputs/ directory:

CSV Files

1. clhs_sample_locations.csv - cLHS sample coordinates and covariate values
2. rf_optimized_locations.csv - RF-optimized sample coordinates and covariate values
3. sampling_comparison_table.csv - Performance metrics comparison

Visualizations

4. sampling_comparison_plots.png - Side-by-side comparison plots showing:
   • Left: cLHS sampling design (red points)
   • Right: RF optimized design (blue points)

🔧 Workflow Steps

The optimization workflow consists of 5 main steps:

1. Data Preparation - Load and validate raster covariates
2. cLHS Sampling - Generate representative baseline samples
3. RF Optimization - Refine samples using simulated annealing
4. Visualization - Create comparison plots
5. Export Results - Save CSV files and visualizations

📊 Understanding the Results

Returned Object

The function returns a list containing:

results <- run_sampling_optimization(...)

# Access results
results$clhs_samples            # cLHS sample locations
results$rf_optimized_samples    # Optimized sample locations
results$comparison_table        # Performance comparison table
results$plots                   # ggplot2 plot objects
results$improvement             # Improvement percentage

Interpretation

• Lower MSE = Better sampling design - Samples provide more accurate predictions
• Improvement % - How much the RF optimization reduced prediction error
• Visual comparison - Observe spatial redistribution of sample points

🎲 Reproducibility

The script uses separate seeds for different operations:

• cLHS: Uses the provided seed
• RF Optimization: Uses seed + 1

This ensures reproducible results while maintaining independence between sampling stages.

🔍 Algorithm Details

Simulated Annealing Process

1. Initialize with cLHS samples
2. For each iteration:
   • Randomly select one sample point to replace
   • Choose a new point from remaining locations
   • Calculate MSE of candidate design
   • Accept or reject based on Metropolis criterion:
     • Always accept if MSE improves
     • Probabilistically accept if MSE worsens: P(accept) = exp(-Δ/T)
   • Cool temperature: T = T × 0.95
3. Track the best solution throughout the process

Cross-Validation Strategy

• Method: k-fold cross-validation (default: 5 folds)
• Model: Random Forest with 100 trees
• Metric: Mean Squared Error (MSE) averaged across folds
• Target: Third covariate by default (customizable with target_var)

📈 Use Cases

This workflow is ideal for:

• Environmental monitoring - Optimizing soil sampling locations
• Precision agriculture - Strategic crop monitoring points
• Ecological surveys - Biodiversity assessment locations
• Geological exploration - Mineral or resource sampling
• Climate studies - Weather station placement

🤝 Contributing

For suggestions or improvements, please open an issue or submit a pull request.

📄 License

This project is open-source and available for educational and research purposes.

📚 References

Key Papers

• Wadoux, A. M. J. C., Brus, D. J., & Heuvelink, G. B. M. (2019). Sampling design optimization for soil mapping with random forest. Geoderma, 355, Article 113913. https://doi.org/10.1016/j.geoderma.2019.113913
• Minasny, B., & McBratney, A. B. (2006). A conditioned Latin hypercube method for sampling in the presence of ancillary information. Computers & Geosciences, 32(9), 1378-1388. https://doi.org/10.1016/j.cageo.2006.04.009
• Breiman, L. (2001). Random forests. Machine Learning, 45(1), 5-32. https://doi.org/10.1023/A:1010933404324
• Kirkpatrick, S., Gelatt, C. D., & Vecchi, M. P. (1983). Optimization by simulated annealing. Science, 220(4598), 671-680. https://doi.org/10.1126/science.220.4598.671

R Packages

• Roudier, P., Beaudette, D. E., & Hewitt, A. E. (2012). A conditioned Latin hypercube sampling algorithm incorporating operational constraints. 5th Global Workshop on Digital Soil Mapping.

📧 Contact

For questions or collaboration opportunities, please reach out through GitHub issues.

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Note: This workflow automatically executes when the script is sourced. Comment out the last line in clhs_rf_optimized.R to disable automatic execution.