Table 1 The formulation of the seven indices and RCIE used in the study.

NDVI⁴⁸

\({\rm{NDVI}}=\frac{{\rho }_{{NIR}}-{\rho }_{{Red}}}{{\rho }_{{NIR}}+{\rho }_{{Red}}}\)

To monitor rice canopy dynamics via vegetation greenness.

EVI⁴⁹

\({\rm{EVI}}=2.5\times \frac{{\rho }_{{NIR}}-{\rho }_{{Red}}}{{\rho }_{{NIR}}+6\times {\rho }_{{Red}}-{\rho }_{{Blue}}+1}\)

Highly sensitive to rice canopy density, it effectively detects peak growth.

EVI2⁵⁰

\({\rm{EVI}}2=2.5\times \frac{{\rho }_{{NIR}}-{\rho }_{{Red}}}{{\rho }_{{NIR}}+2.4\times {\rho }_{{Red}}+1}\)

A simplified form adapted to band-limited sensors, with similar effectiveness in rice monitoring.

LSWI⁵¹

\({\rm{LSWI}}=\frac{{\rho }_{{NIR}}-{\rho }_{{SWIR}1}}{{\rho }_{{NIR}}+{\rho }_{{SWIR}1}}\)

Sensitive to surface water, effective for detecting paddy fields during transplanting and early growth.

NDSVI⁵²

\({\rm{NDSVI}}=\frac{{\rho }_{{SWIR}1}-{\rho }_{{Red}}}{{\rho }_{{SWIR}1}+{\rho }_{{Red}}}\)

Distinguishes bare soil from vegetation, useful for detecting field prep and early rice growth.

NDTI⁵³

\({\rm{NDTI}}=\frac{{\rho }_{{SWIR}1}-{\rho }_{{SWIR}2}}{{\rho }_{{SWIR}1}+{\rho }_{{SWIR}2}}\)

Indicates soil moisture, aiding irrigation monitoring and rice area identification.

GCVI⁵⁴

\({\rm{GCVI}}=\frac{{\rho }_{{NIR}}}{{\rho }_{{Green}}}-1\)

Suitable for monitoring rice condition during mid and late growth based on chlorophyll content.

RCIE²¹

\({\rm{RCIE}}=\frac{\triangle {LSWI}}{\triangle {EVI}2}\)

Captures rice-specific growth and moisture features for better identification.