as nearly every vegetation index was developed / published by different researchers they have completely different value ranges. Many of them create data between 0 and 1 but this is no consistent standard.
Please also note that, strictly speaking, NDVI doesn't measure chlorophyll concentration but is a measure for general vitality and any value below 0 indicates water.
Article A review of vegetation indices
Conference Paper A review of multispectral vegetation indices for biomass estimation
Vegetation indices constitute a generally poor and rather obsolete approach to the analysis of satellite remote sensing data. However, if you really want to use them, you can find out for yourself their range of variability by inserting extreme values of the various channels into the formulas.
NDVI = (NIR - RED) / (NIR + RED)
where RED and NIR are the (positive) red and near-infrared reflectance, which themselves typically vary within the range [0.0, 1.0]. So,
* if RED = 0.0, NDVI = 1.0
* if NIR = 0.0, NDVI = -1.0
* if RED = NIR, NDVI = 0.0
Hence, NDVI cannot exceed [-1.0, 1.0] by definition, as you noted in your question.
Similarly, the Simple Ratio
SR = NIR/RED
can take on values in the range [0.0, infinity]:
* if RED -> 0, SR -> infinity
* if NIR -> 0, SR -> 0.0
If you plan to use another vegetation index, plug the minimum and maximum values of the input data in the formula and determine the range of the index.
Further to the theory explained by Michel so well, in practice, NDVI calculated from RED and NIR spectral bands measured from ASTER/LANDSAT satellites or at the ground seems not have been lower than -0.3 (both attachments). I would be interested to be referred to lower measured values.
Various regression techniques applied to available spectral band measurements have produced long ago (1985 attached) and recently (e.g. my mangrove papers) the better proxies of green biomass and other land cover features.
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