Validating component substitution in ecological indicators: a structural floor on index-to-index correlation and an external validation route for RSEI

Authors:
  • JLJunjie Li
    Junjie Li
  • THTongyi Huang
    Tongyi Huang
  • XCXinrui Cui
    Xinrui Cui
  • MLMingshu Li
    Mingshu Li
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Abstract
The remote sensing ecological index (RSEI) is widely used to track regional ecological quality, and a growing literature revises it by substituting a satellite canopy height term for its greenness component. Such revisions are judged by how far the modified index departs from the original, a criterion that cannot work. For any index defined as the first principal component of k standardised components, replacing one component while retaining the rest leaves the two indices correlated above a floor fixed by the construction, even when the incoming component is orthogonal to everything already in the index. With retained components correlated at 0.4, the floor runs from 0.959 to 0.988 at k = 4 and reaches 0.990 by k = 8, so resolution falls away as indicators grow. We derive the bound analytically, then supply the validation it cannot provide, over 12,499,740 forest pixels at 30 m in the Three Gorges Reservoir Area, where growing-season NDVI varies by only 4.98% of its mean. A canopy height layer trained on GEDI RH98 scored R² = 0.158 on 350 locked footprints, against 0.024 for the published product. Three-dimensional greenness built from it raised the correlation of the index with measured canopy height from 0.176 to 0.225 (bootstrap 95% CI of the gain [0.0144, 0.0844]), although both explain under 6% of its variance. The two indices meanwhile correlated at 0.9520 against a floor of 0.9490. Revised indicators need validation against data lying outside the index.

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