Step 1: Understanding the Question:
This question tests knowledge of vegetation indices used in remote sensing.
Step 2: Detailed Explanation:
The Transformed Vegetation Index (TVI) is expressed as \(\sqrt{\mathrm{NDVI}}\).
The Normalized Difference Vegetation Index (NDVI) is calculated as:
\[
\mathrm{NDVI} = \frac{\mathrm{NIR} - \mathrm{RED}}{\mathrm{NIR} + \mathrm{RED}}
\]
TVI is a transformation of NDVI that reduces the effect of soil background and enhances the correlation with vegetation cover.
Other options:
- (NDVI)$^2$ (B): Not TVI.
- \(\sqrt{\mathrm{GVI}}\) (C): Green Vegetation Index (not TVI).
- \(\sqrt{0.5 + \mathrm{NDVI}}\) (D): Not TVI.
Thus, TVI is \(\sqrt{\mathrm{NDVI}}\).
Step 3: Final Answer:
Thus, the Transformed Vegetation Index is \(\sqrt{\mathrm{NDVI}}\), which corresponds to option (A).
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