Gaussian Process Retrieval of Chlorophyll Content From Imaging Spectroscopy Data

Abstract

Precise and spatially-explicit knowledge of leaf chlorophyll content <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$(Chl)$</tex></formula> is crucial to adequately interpret the chlorophyll fluorescence <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$(ChF)$</tex></formula> signal from space. Accompanying information about the reliability of the <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$Chl$</tex></formula> estimation becomes more important than ever. Recently, a new statistical method was proposed within the family of nonparametric Bayesian statistics, namely Gaussian Processes regression (GPR). GPR is simpler and more robust than their machine learning family members while maintaining very good numerical performance and stability. Other features include: i) GPR requires a relatively small training data set and can adopt very flexible kernels, ii) GPR identifies the relevant bands and observations in establishing relationships with a variable, and finally iii) along with pixelwise estimations GPR provides accompanying confidence intervals. We used GPR to retrieve <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$Chl$</tex> </formula> from hyperspectral reflectance data and evaluated the portability of the regression model to other images. Based on field <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$Chl$</tex></formula> measurements from the SPARC dataset and corresponding spaceborne CHRIS spectra (acquired in 2003, Barrax, Spain), GPR developed a regression model that was excellently validated ( <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$r^{2}$</tex></formula> : 0.96, RMSE: 3.82 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\mu{\rm g/cm}^{2}$</tex> </formula> ). The SPARC-trained GPR model was subsequently applied to CHRIS images (Barrax, 2003, 2009) and airborne CASI flightlines (Barrax 2009) to generate <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$Chl$</tex></formula> maps. The accompanying confidence maps provided insight in the robustness of the retrievals. Similar confidences were achieved by both sensors, which is encouraging for upscaling <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$Chl$</tex> </formula> estimates from field to landscape scale. Because of its robustness and ability to deliver confidence intervals, GPR is evaluated as a promising candidate for implementation into <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$ChF$</tex> </formula> processing chains.