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variables.Rmd
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variables.Rmd
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---
title: "Variables"
output: rmarkdown::html_vignette
vignette: >
%\VignetteIndexEntry{Variables}
%\VignetteEngine{knitr::rmarkdown}
%\VignetteEncoding{UTF-8}
---
## Description of variables
Each variable is computed using `terra`, `stars` and/or `gdalwarp`.
In the following table only others packages or functions are mentioned.
Solar radiation is calculated on equinox day (20th March).
Protected area are extracted from [protectedplanet.net](https://www.protectedplanet.net/en), enable to extract only countries.
| Name | Unit | Description | Particular package or function | Source |
| ---------------- | :--------------------: | ---------------------- | :----------------------------: | :----------------: |
| elevation | m | Elevation | gdalbuildvrt | [srtm.csi.cgiar.org](https://srtm.csi.cgiar.org/srtmdata/) |
| aspect | degrees | Aspect | gdaldem slope | [srtm.csi.cgiar.org](https://srtm.csi.cgiar.org/srtmdata/) |
| roughness | m | Roughness is the largest inter-cell difference of a central pixel and its surrounding cell, as defined in Wilson et al (2007, Marine Geodesy 30:3-35) | gdaldem roughness | [srtm.csi.cgiar.org](https://srtm.csi.cgiar.org/srtmdata/) |
| slope | degrees | slope values are in degrees | gdaldem slope | [srtm.csi.cgiar.org](https://srtm.csi.cgiar.org/srtmdata/) |
| srad | $Wh.m^{-2}$ | Solar irradiance : computes direct, diffuse and reflected solar irradiation from elevation, slope, roughness, aspect | rgrass (r.in.gdal, r.out.gdal, r.sun) | |
| SoilType | category | Types of soils according to World Reference Base (2006) Soil Groups | gdalbuildvrt gdal_translate | [soilgrids.org](https://soilgrids.org/) |
| forest | binary | Forest/No forest layer | gdal_translate | [forestatrisk.cirad.fr](https://forestatrisk.cirad.fr/rasters.html) |
| distanceForest | m | Minimal distance to forest | gdal_proximity | [forestatrisk.cirad.fr](https://forestatrisk.cirad.fr/rasters.html) |
| distanceSea | m | Minimal distance to sea compute from elevation layer | gdal_proximity | elevation layer |
| distanceRoad | m | Minimal distance to any road bigger than `terciary road` define on [openstreetmap.org](https://www.openstreetmap.org) | osmextract ogr2ogr gdal_proximity | [openstreetmap.org](https://www.openstreetmap.org) |
| distancePlace | m | Minimal distance to cities, town and village | osmextract ogr2ogr gdal_proximity | [openstreetmap.org](https://www.openstreetmap.org) |
| distancewater | m | Minimal distance to river, lake, or reservoir (except sewage and water storage) | osmextract ogr2ogr gdal_proximity | [openstreetmap.org](https://www.openstreetmap.org) |
| WDPA | category | Protected areas (all type of protection) | httr | [protectedplanet.net](https://www.protectedplanet.net/en) |
| tas | °C x 10 | Daily mean air temperature at 2 metres from hourly ERA5 data for each month | | [chelsa-climate.org](https://chelsa-climate.org)
| tasmin | °C x 10 | Daily minimum air temperature at 2 metres from hourly ERA5 data for each month | | [chelsa-climate.org](https://chelsa-climate.org)
| tasmax | °C x 10 | Daily maximum air temperature at 2 metres from hourly ERA5 data for each month | | [chelsa-climate.org](https://chelsa-climate.org)
| pr | $kg.m^{-2}$ | Precipitation amount | | [chelsa-climate.org](https://chelsa-climate.org) |
| clt | % | Cloud area fraction | | [chelsa-climate.org](https://chelsa-climate.org) |
| pet_penman | $kg.m^{-2}$ | Potential evapotranspiration calculated with the Penman-Monteith equation. | | [chelsa-climate.org](https://chelsa-climate.org) |
| pet_thornthwaite | $kg.m^{-2}$ | Potential evapotranspiration calculated with the Thornthwaite equation. | | [chelsa-climate.org](https://chelsa-climate.org) |
| cwd_penman | $kg.m^{-2}$ | Climatic Water Deficit calculated with pet_penman variable | | [chelsa-climate.org](https://chelsa-climate.org) |
| cwd_thornthwaite | $kg.m^{-2}$ | Climatic Water Deficit calculated with pet_thornthwaite variable | | [chelsa-climate.org](https://chelsa-climate.org) |
| ndm_penman | month | Number of Dry Month calculated with cwd_penman variable | | [chelsa-climate.org](https://chelsa-climate.org) |
| ndm_thornthwaite | month | Number of Dry Month calculated with cwd_thornthwaite variable | | [chelsa-climate.org](https://chelsa-climate.org) |
| bio1 | °C x 10 | mean annual daily mean air temperatures averaged over 1 year | | [chelsa-climate.org](https://chelsa-climate.org) |
| bio2 | °C x 10 | mean diurnal range of temperatures averaged over 1 year | | [chelsa-climate.org](https://chelsa-climate.org) |
| bio3 | °C x 10 | ratio of diurnal variation to annual variation in temperatures | | [chelsa-climate.org](https://chelsa-climate.org) |
| bio4 | °C x 10 | standard deviation of the monthly mean temperatures | | [chelsa-climate.org](https://chelsa-climate.org) |
| bio5 | °C x 10 | The highest temperature of any monthly daily mean maximum temperature | | [chelsa-climate.org](https://chelsa-climate.org) |
| bio6 | °C x 10 | The lowest temperature of any monthly daily mean maximum temperature | | [chelsa-climate.org](https://chelsa-climate.org) |
| bio7 | °C x 10 | Annual range of air temperature : the difference between the Maximum Temperature of Warmest month and the Minimum Temperature of Coldest month | | [chelsa-climate.org](https://chelsa-climate.org) |
| bio8 | °C x 10 | Mean daily mean air temperatures of the wettest quarter | | [chelsa-climate.org](https://chelsa-climate.org) |
| bio9 | °C x 10 | Mean daily mean air temperatures of the driest quarter | | [chelsa-climate.org](https://chelsa-climate.org) |
| bio10 | °C x 10 | Mean daily mean air temperatures of the warmest quarter | | [chelsa-climate.org](https://chelsa-climate.org) |
| bio11 | °C x 10 | Mean daily mean air temperatures of the coldest quarter | | [chelsa-climate.org](https://chelsa-climate.org) |
| bio12 | $kg.m^{-2}.year^{-1}$ | Accumulated precipitation amount over 1 year | | [chelsa-climate.org](https://chelsa-climate.org) |
| bio13 | $kg.m^{-2}.month^{-1}$ | The precipitation of the wettest month. | | [chelsa-climate.org](https://chelsa-climate.org) |
| bio14 | $kg.m^{-2}.month^{-1}$ | The precipitation of the driest month. | | [chelsa-climate.org](https://chelsa-climate.org) |
| bio15 | $kg.m^{-2}$ | Precipitation seasonality | | [chelsa-climate.org](https://chelsa-climate.org) |
| bio16 | $kg.m^{-2}.month^{-1}$ | Mean monthly precipitation amount of the wettest quarter | | [chelsa-climate.org](https://chelsa-climate.org) |
| bio17 | $kg.m^{-2}.month^{-1}$ | Mean monthly precipitation amount of the driest quarter | | [chelsa-climate.org](https://chelsa-climate.org) |
| bio18 | $kg.m^{-2}.month^{-1}$ | Mean monthly precipitation amount of the warmest quarter | | [chelsa-climate.org](https://chelsa-climate.org) |
| bio19 | $kg.m^{-2}.month^{-1}$ | Mean monthly precipitation amount of the coldest quarter | | [chelsa-climate.org](https://chelsa-climate.org) |
## Potential evapotranspiration
#### Penman-Monteith formula
$$\lambda ET = \frac{\Delta (R_n - G) + \rho_a c_p \frac{(e_s - e_a)}{r_a}}{\Delta + \gamma (1 + \frac{r_s}{r_a})} $$
where R_n is the net radiation, G is the soil heat flux, (e_s - e_a) represents the vapour pressure deficit of the air, r_a is the mean air density at constant pressure, c_p is the specific heat of the air, $\Delta$ represents the slope of the saturation vapour pressure temperature relationship, $\gamma$ is the psychrometric constant, and r_s and r_a are the (bulk) surface and aerodynamic resistances.
#### Thornthwaite formula
$PET_k$ is the estimated potential evapotranspiration (in mm/month) for month $k$. $T_k$ is the average daily temperature (in degrees Celsius) for month $k$. $L_k$ is the average day length (in hours) of the month $k$. $N_k$ is the number of days for month $k$. $I$ is a heat index which depends on the 12 monthly mean temperatures.
$$ I = \Sigma^{12}_{i = 1} (\frac{T_i}{5})^{1.514}$$
$$ \alpha = (6.75e-7) I^3 - (7.71e-5) I^2 + (1.792e-2) I + 0.49239 $$
$$ PET_k = 16 \frac{L_k}{12} \frac{N_k}{30} \left(\frac{10 T_k}{I}\right)^{\alpha} $$
## Water Deficit
#### Climatic water deficit
Climatic Water Deficit (CWD) is the sum of monthly differences between potential evapotranspiration and precipitation. CWD is a positive value. A higher value of CWD indicates a higher deficit in water.
The minimal monthly value of CWD is set to 0 when there is more precipitation than potential evapotranspiration and thus no water deficit.
$$ cwd = \Sigma^{12}_{i = 1} max(pet_i - pr_i, 0) $$
#### Number of dry months
Number of dry months (NDM) is the annual number of months for which potential evapotranspiration (pet) exceeds precipitation (pr). It's a number between 0 and 12.
$$ ndm = \Sigma^{12}_{i = 1} \unicode{x1D7D9}_{(pet_i - pr_i > 0)} $$