space oddity: estimating earth biodiversity from a satellite · 2020-05-04 · space oddity:...

Information theorySolving non-dimensionality

Solving point description

Space oddity: estimating Earth biodiversity froma satellite

Duccio Rocchini

Alma Mater Studiorum University of Bologna, ItalyCzech University of Life Sciences Prague, Czech Republic

Information theorySolving non-dimensionality

Solving point description

Aim

Showing the most powerful approaches to measure the diversity oflife from space.

Information theorySolving non-dimensionality

Solving point description

Aim

Information theorySolving non-dimensionality

Solving point description

Outline

1 Information theory

2 Solving non-dimensionality

3 Solving point description

Information theorySolving non-dimensionality

Solving point description

Information Theory

H ′ = −∑

pi × ln(pi ) (1)

Information theorySolving non-dimensionality

Solving point description

Issues

Main issues related to the use of Shannon’s H’ in remote sensing:

Non-dimensionality: H’ is only based on relative abundanceand not on numbers, i.e. pixel values

Point description: H’, as many other indices, represents onlya part of the whole diversity spectrum

Information theorySolving non-dimensionality

Solving point description

Outline

1 Information theory

2 Solving non-dimensionality

3 Solving point description

Information theorySolving non-dimensionality

Solving point description

Distance matrices and relative abundance: the Rao’s Qdiversity

H ′ = −∑

pi × ln(pi ) (2)

Q =∑∑

dij × pi × pj (3)d1,1 d1,2 · · · d1,n

d2,1 d2,2 · · · d2,n...

.... . .

...dn,1 dn,2 · · · dn,n

Information theorySolving non-dimensionality

Solving point description

Distance matrices and relative abundance: the Rao’s Qdiversity

H ′ = −∑

pi × ln(pi ) (2)

Q =∑∑

dij × pi × pj (3)d1,1 d1,2 · · · d1,n

d2,1 d2,2 · · · d2,n...

.... . .

...dn,1 dn,2 · · · dn,n

Information theorySolving non-dimensionality

Solving point description

Rao’s Q diversity

Rocchini et al. (Ecol. Indic, 2017)

Information theorySolving non-dimensionality

Solving point description

Outline

1 Information theory

2 Solving non-dimensionality

3 Solving point description

Information theorySolving non-dimensionality

Solving point description

Solving point description: the Renyi Generalised Entropy

Renyi (1970) generalised entropy:

Hα =1

1− αln∑

pα (4)

where p=relative abundance of each spectral reflectance value (DN).Such measure is extremely flexible and powerful since many popular diversity indicesare simply special cases of Hα.

Hα =

α = 0,H0 = ln(N)

α→ 1,H1 = −∑

p × ln(p)

α = 2,H2 = ln(1/D)

(5)

Information theorySolving non-dimensionality

Solving point description

Solving point description: the Renyi Generalised Entropy

Information theorySolving non-dimensionality

Solving point description

R package: rasterdiv

Information theorySolving non-dimensionality

Solving point description

Many thanks!

Contact:Duccio Rocchini, PhD - Full Professor @:Alma Mater Studiorum University of Bologna, Italyduccio.rocchini@unibo.it

This presentation has been made by only relying on Free and Open Source philosophy: Linux, LATEX, R, GRASS GIS.