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I have remote sensing data which I have got from landsat 7. The area which I am working on is combination of farms and natural area (Bare earth; without any vegetation). I want to estimate the Evatransporation for whole area to put in my hydrological model.

Can I use NDVI index for this purpose?

As I know NDVI helps us to find evatransporation in the vegetated area.

How can I estimate the evaporation from bare earth regions?

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You could use the S-SEBI index, which calculates the energy balance divided in its components, one of which is the Latent Heat Flux. You should read about it in the original paper published by Roerink et al, 2002.

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