Author: Matteo Marcantonio, Duccio Rocchini
Date: 2025-09-02

# Indices of diversity from NDVI.

#### Matteo Marcantonio, Duccio Rocchini

#### 2025-09-02

    require(rasterdiv)
    require(terra)
    require(rasterVis)
    require(RColorBrewer)

This vignette uses rasterdiv to build global series of indices of diversity based on Information Theory. The input dataset is the Copernicus Long-term (1999-2017) average Normalised Difference Vegetation Index for the 21st of June (copNDVI).

    copNDVI <- load_copNDVI()

## Overview

A SpatRaster called copNDVI is loaded together with the package rasterdiv. copNDVI is a 8-bit raster, meaning that pixel values range from 0 to 255. You could stretch it to match a more familiar (-1,1) values range using `terra::stretch(copNDVI,minv=-1,maxv=1)`. The original dataset was resampled to 1/20th its spatial resolution and pixels with values 253, 254 and 255 (water) were set as NA’s.

    #Resample using terra::aggregate and a linear factor of 10
    copNDVI <- terra::aggregate(copNDVI, fact=20)

## Compute all indexes in rasterdiv on copNDVI

rasterdiv allows the computation of 8 diversity indexes based on information theory. In the following section, all these indexes will be computed for copNDVI using a moving window of 81 pixels (9 px side). Alpha values for the Hill, Rényi and parametric Rao indexes will be set from 0 to 2 every 0.5. In addition, we will set `na.tolerance=0.2`, meaning that all moving windows with more than 10% of pixels equal NA will be set to NA.

    #Shannon's Diversity
    sha <- Shannon(copNDVI,window=9,na.tolerance=0.2,np=1)

    #Pielou's Evenness
    pie <- Pielou(copNDVI,window=9,na.tolerance=0.2,np=1)

    #Berger-Parker's Index
    ber <- BergerParker(copNDVI,window=9, na.tolerance=0.2, np=1)

    #Parametric Rao's quadratic entropy with alpha ranging from 1 to 3
    prao <- paRao(copNDVI, window=9, alpha=c(1:3), na.tolerance=0.8, dist_m="euclidean", np=1)

    #Cumulative residual entropy
    cre <- CRE(copNDVI, window=9, na.tolerance=1, np=1, simplify=0)

    #Hill's numbers
    hil <- Hill(copNDVI, window=9, alpha=seq(0,1,0.5), na.tolerance=0.2, np=1)

    #Rényi's Index
    ren <- Renyi(copNDVI, window=9, alpha=seq(0,1,0.5), na.tolerance=0.2, np=1)

## Visualise output `SpatRasters` (the shape of continents is deformed by the NAs in the 9x9 moving windows)

    #Shannon's Diversity
    levelplot(sha, main="Shannon's entropy from Copernicus NDVI 5 km (9 px-side moving window)", as.table = T,layout=c(0,1,1), ylim=c(-60,75), margin = list(draw = TRUE))

    #Pielou's Evenness
    levelplot(pie, main="Pielou's evenness from Copernicus NDVI 5 km (9 px-side moving window)", as.table = T, layout=c(0,1,1), ylim=c(-60,75), margin = list(draw = TRUE))

    #Berger-Parker' Index
    levelplot(ber, main="Berger-Parker's index from Copernicus NDVI 5 km (9 px-side moving window)", as.table = T, layout=c(0,1,1), ylim=c(-60,75), margin = list(draw = TRUE))

    #Parametric Rao's quadratic Entropy
    levelplot(rast(prao[[1]]), main="Parametric Rao's quadratic entropy from Copernicus NDVI 5 km (9 px-side moving window)", as.table = T,layout=c(0,3,1), ylim=c(-60,75), margin = list(draw = TRUE))

    #Cumulative residual entropy
    levelplot(cre, main="Cumulative residual entropy from Copernicus NDVI 5 km (9 px-side moving window)", as.table = T, layout=c(0,1,1), ylim=c(-60,75), margin = list(draw = TRUE))

    #Hill's numbers (alpha=0, 0.5 and 1)
    levelplot(terra::rast(hil), main="Hill's numbers from Copernicus NDVI 5 km (9 px-side moving window)", as.table = T, layout=c(0,3,1), ylim=c(-60,75))

    #Renyi' Index (alpha=0, 0.5 and 1)
    levelplot(terra::rast(ren), main="Renyi's entropy from Copernicus NDVI 5 km (9 px-side moving window)", as.table = T,layout=c(0,3,1), names.attr=paste("alpha",seq(0,1,0.5),sep=" "), ylim=c(-60,75), margin = list(draw = FALSE))