Introduction

The RFplus package implements a novel spatial extrapolation and bias correction framework, integrating Random Forest (RF) and Quantile Mapping (QM) in a multi-stage process to improve the accuracy of satellite precipitation estimates. The methodology consists of three key stages:

1. Spatial Extrapolation of Precipitation: The first stage employs a Random Forest model to extrapolate the spatial distribution of precipitation. The model is trained using in-situ measurements as the response variable and a diverse set of satellite precipitation products and environmental covariates as predictors. This approach enables the generation of an initial precipitation field that extends observed precipitation patterns across unmonitored regions with high spatial flexibility, allowing applications at different temporal scales (e.g., daily, monthly, or annual).

2. Residual Correction through a Secondary RF Model: To enhance predictive accuracy, a second Random Forest model is trained to estimate residual errors from the initial predictions. The residuals are defined as the difference between observed and modeled precipitation values at station locations. By modeling these residuals as a function of the same covariates used in the first stage, systematic biases are identified and corrected iteratively. The corrected precipitation estimate is obtained by summing the residual predictions to the initial RF-based precipitation estimates, leading to a refined precipitation product with reduced bias and improved spatial coherence.

3. Bias Adjustment via Non-Parametric Quantile Mapping (QM): In the third stage, a nonparametric quantile mapping (QM) is applied to adapt the distribution of each time series to the in situ observations of the nearest station. The QM correction will be applied to those pixels that meet the proximity criterion, which states that only pixels within a predefined radius of influence (e.g., ≤15 km) are QM corrected.

The RFplus package is designed to be highly adaptable and can be utilized across various satellite precipitation products and geographic regions. Although initially developed for precipitation bias correction, its methodology is applicable to other environmental variables such as temperature, wind speed, and soil moisture. This versatility makes RFplus a powerful tool for enhancing the accuracy of remote sensing-based estimations across diverse environmental conditions.

# Load necessary libraries
library(RFplus)

## RFplus 1.4-0

## Type RFplusNews() to see new features/changes/bug fixes.

library(terra)

## Warning: package 'terra' was built under R version 4.4.3

## terra 1.8.29

library(data.table)

## 
## Attaching package: 'data.table'

## The following object is masked from 'package:terra':
## 
##     shift

# Load the in-situ data and the coordinates
data("BD_Insitu", package = "RFplus")
data("Cords_Insitu", package = "RFplus")

# Load the covariates
MSWEP = terra::rast(system.file("extdata/MSWEP.nc", package = "RFplus"))
CHIRPS = terra::rast(system.file("extdata/CHIRPS.nc", package = "RFplus"))
DEM = terra::rast(system.file("extdata/DEM.nc", package = "RFplus"))

# Adjust individual covariates to the covariate format required by RFplus
Covariates = list(MSWEP = MSWEP, CHIRPS = CHIRPS, DEM = DEM)

# Apply the RFplus -----------------------------------------------------------
# 1. Define categories to categorize rainfall intensity
Rain_threshold = list(
  no_rain = c(0, 1),
  light_rain = c(1, 5),
  moderate_rain = c(5, 20),
  heavy_rain = c(20, 40),
  violent_rain = c(40, 100)
)
# 2. Apply de the model
model = RFplus(BD_Insitu, Cords_Insitu, Covariates, n_round = 1, wet.day = 0.1 , ntree = 2000, seed = 123, training = 0.8, Rain_threshold = Rain_threshold, method = "RQUANT", ratio = 5, save_model = FALSE, name_save = NULL
)

## The training parameter has been introduced. The model will be trained with: 80 % data and validated with: 20 %

## Analysis in progress: Stage 1 of 2. Please wait...

## Analysis in progress: Stage 2 of 2. Correction by: RQUANT. Please wait...

## Applying correction method. This may take a while...

## Analysis completed.

## Validation process in progress. Please wait.

# Precipitation results within the study area
modelo_rainfall = model$Ensamble

# Validation statistic results 
# goodness-of-fit metrics
metrics_gof = model$Validation$gof

# Categorical Metrics
metrics_categoricxal = model$Validation$categorical_metrics
# Note: In the above example we used 80% of the data for training and 20% for model validation. 

# First layer of the QUANT method
plot(modelo_rainfall[[1]])

Rain_threshold = list(
  no_rain = c(0, 1), # No precipitation
  light_rain = c(1, 5), # Light rainfall
  moderate_rain = c(5, 20), # Moderate rainfall
  heavy_rain = c(20, 40), # Heavy rainfall
  violent_rain = c(40, 100) # violent rain
)