Table 1 Spectral indices used to model impervious cover across the four countries.

Built-up area extraction index

BAEI

\({baei}=\frac{{Red}+0.3}{{Green}+{Swir}1}\)

⁵¹

Biophysical composition index

BCI

\({bci}=\frac{{TCB}+{TCW}\div2-{TCG}}{{TCB}+{TCW}\div2+{TCG}}\)

⁵²

Band ratio for built-up area index

BRBA

\({brba}=\frac{{Red}}{{Swir}1}\)

⁵³

Bare soil index

BSI

\({bsi}=\frac{\left({Red}+{Swir}1\right)-({Nir}+{Blue})}{({Red}+{Swir}1)+({Nir}+{Blue})}\)

⁵⁹

Combinational biophysical composition index

CBCI

\({cbci}=1.5* {mbsi}-{osavi}+0.5\)

⁵⁴

Normalized built-up area index

NBAI

\({nbai}=\frac{({Swir}2-{Swir}1)/{Green}}{({Swir}2+{Swir}1)/{Green}}\)

⁵³

Normalized burned ratio index

NBRI

\({nbri}=\frac{{Nir}-{Swir}1}{{Nir}+{Swir}1}\)

⁶⁰

Normalized difference built-up index

NDBI

\({ndbi}=\frac{{Swir}1-{Nir}}{{Swir}1+{Nir}}\)

⁵⁵

Normalized difference vegetation index

NDVI

\({ndvi}=\frac{{Nir}-{Red}}{{Nir}+{Red}}\)

⁵⁸

Urban index

UI

\({uid}=\frac{{Swir}2-{Nir}}{{Swir}2+{Nir}}\)

⁵⁶

Visible red-based built-up index

VRBI

\({vrbi}=\frac{{Red}-{Nir}}{{Red}+{Nir}}\)

⁵⁷