Calculate Aridity Index

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This chapter calculates the Aridity Index (AI). AI is a dryness indicator defined here as precipitation (\(P\)) divided by potential evapotranspiration (\(PET\)) (World Atlas of Desertification 1992). Lower values indicate drier conditions because potential evapotranspiration is larger relative to precipitation.

Several definitions of aridity index are used in the literature. In this chapter, the following equation is used:

\[AI = \frac{P}{PET}\]

where \(P\) is precipitation and \(PET\) is potential evapotranspiration.

Load libraries

library(sf)

Load data

In this repository, the PROJECT_DATA_DIR environment variable points to the directory where input and output data are stored. Change it as needed for your local environment.

data_dir <- Sys.getenv("PROJECT_DATA_DIR")
sf_climate <- readRDS(file.path(
  data_dir,
  "climate_mesh_data_joined/climate_mesh_data_with_pet.rds"
))

Calculate Aridity Index

First, calculate the annual Aridity Index and add it to the sf_climate object as a new aridity_index column. When PET is zero, negative, or missing, the Aridity Index is undefined, so the value is set to NA.

sf_climate$aridity_index <- ifelse(
  is.na(sf_climate$PET_year) | sf_climate$PET_year <= 0,
  NA_real_,
  sf_climate$precipitation_year / sf_climate$PET_year
)

Then, calculate monthly Aridity Index values. The monthly columns are named from aridity_index_Jan to aridity_index_Dec.

month_labels <- month.abb
for (month in seq_along(month_labels)) {
  month_label <- month_labels[month]
  precipitation_col <- paste0("precipitation_", month_label)
  pet_col <- paste0("PET", month)
  aridity_index_col <- paste0("aridity_index_", month_label)
  pet_values <- sf_climate[[pet_col]]

  sf_climate[[aridity_index_col]] <- ifelse(
    is.na(pet_values) | pet_values <= 0,
    NA_real_,
    sf_climate[[precipitation_col]] / pet_values
  )
}

Save data

Save the result in both RDS and CSV formats. Change the output path as needed.

saveRDS(
  sf_climate,
  file.path(
    data_dir,
    "climate_mesh_data_joined/climate_mesh_data_with_aridity_index.rds"
  )
)
df_climate <- st_drop_geometry(sf_climate)
write.csv(
  df_climate,
  file.path(
    data_dir,
    "climate_mesh_data_joined/climate_mesh_data_with_aridity_index.csv"
  ),
  row.names = FALSE
)

References

World Atlas of Desertification. 1992. UNEP.