An improved strategy for regression of biophysical variables and Landsat ETM+ data

Empirical models are important tools for relating field-measured biophysical variables to remote sensing data. Regression analysis has been a popular empirical method of linking these two types of data to provide continuous estimates for variables such as biomass, percent woody canopy cover, and leaf area index (LAI). Traditional methods of regression are not sufficient when resulting biophysical surfaces derived from remote sensing are subsequently used to drive ecosystem process models. Most regression analyses in remote sensing rely on a single spectral vegetation index (SVI) based on red and near-infrared reflectance from a single date of imagery. There are compelling reasons for utilizing greater spectral dimensionality, and for including SVIs from multiple dates in a regression analysis. Moreover, when including multiple SVIs and/or dates, it is useful to integrate these into a single index for regression modeling. Selection of an appropriate regression model, use of multiple SVIs from multiple dates of imagery as predictor variables, and employment of canonical correlation analysis (CCA) to integrate these multiple indices into a single index represent a significant strategic improvement over existing uses of regression analysis in remote sensing.To demonstrate this improved strategy, we compared three different types of regression models to predict LAI for an agro-ecosystem and live tree canopy cover for a needleleaf evergreen boreal forest: traditional (Y on X) ordinary least squares (OLS) regression, inverse (X on Y) OLS regression, and an orthogonal regression method called reduced major axis (RMA). Each model incorporated multiple SVIs from multiple dates and CCA was used to integrate these. For a given dataset, the three regression-modeling approaches produced identical coefficients of determination and intercepts, but different slopes, giving rise to divergent predictive characteristics. The traditional approach yielded the lowest root mean square error (RMSE), but the variance in the predictions was lower than the variance in the observed dataset. The inverse method had the highest RMSE and the variance was inflated relative to the variance of the observed dataset. RMA provided an intermediate set of predictions in terms of the RMSE, and the variance in the observations was preserved in the predictions. These results are predictable from regression theory, but that theory has been essentially ignored within the discipline of remote sensing.