Visualizing the ill-posedness of the inversion of a canopy radiative transfer model: A case study for Sentinel-2 |
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| Institution: | 1. Department of Earth & Environment, Boston University, Boston, MA, USA;2. Environmental & Climate Sciences Department, Brookhaven National Laboratory, Upton, NY, USA;3. Sustainability Studies, Stony Brook University, Stony Brook, NY, USA;4. Department of Forest and Wildlife Ecology, University of Wisconsin-Madison, Madison, WI, USA;1. Departament de Física de la Terra i Termodinàmica, Facultat de Física, Universitat de València, Dr. Moliner, 50, Burjassot 46100, València, Spain;2. Image Processing Laboratory (IPL), Universitat de València, Catedrático A. Escardino, 9, Paterna 46980, València, Spain;3. Institute for Electromagnetic Sensing of the Environment, Italian National Research Council, Via Bassini 15, Milan 20133, Italy |
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| Abstract: | Monitoring biophysical and biochemical vegetation variables in space and time is key to understand the earth system. Operational approaches using remote sensing imagery rely on the inversion of radiative transfer models, which describe the interactions between light and vegetation canopies. The inversion required to estimate vegetation variables is, however, an ill-posed problem because of variable compensation effects that can cause different combinations of soil and canopy variables to yield extremely similar spectral responses. In this contribution, we present a novel approach to visualise the ill-posed problem using self-organizing maps (SOM), which are a type of unsupervised neural network. The approach is demonstrated with simulations for Sentinel-2 data (13 bands) made with the Soil-Leaf-Canopy (SLC) radiative transfer model. A look-up table of 100,000 entries was built by randomly sampling 14 SLC model input variables between their minimum and maximum allowed values while using both a dark and a bright soil. The Sentinel-2 spectral simulations were used to train a SOM of 200 × 125 neurons. The training projected similar spectral signatures onto either the same, or contiguous, neuron(s). Tracing back the inputs that generated each spectral signature, we created a 200 × 125 map for each of the SLC variables. The lack of spatial patterns and the variability in these maps indicate ill-posed situations, where similar spectral signatures correspond to different canopy variables. For Sentinel-2, our results showed that leaf area index, crown cover and leaf chlorophyll, water and brown pigment content are less confused in the inversion than variables with noisier maps like fraction of brown canopy area, leaf dry matter content and the PROSPECT mesophyll parameter. This study supports both educational and on-going research activities on inversion algorithms and might be useful to evaluate the uncertainties of retrieved canopy biophysical and biochemical state variables. |
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| Keywords: | Self-organizing map Radiative transfer modelling Model inversion SLC Vegetation biophysical and biochemical variables |
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