Radiative transfer emulation for hyperspectral imaging retrievals with advanced Kernel Flows-based Gaussian Process emulation

Changes in geophysical properties on the surface of the Earth can be monitored with remote imaging spectroscopy, and in the coming years several space-borne imaging spectrometers, such as SBG, EnMAP, and CHIME, will start producing large amounts of data. The quantities of interest that can be inferred from these measurements include, for example, plant traits, emission point sources, algae concentration, mineral content, etc. These quantities are derived from surface reflectance, which needs to be obtained in a first-stage retrieval from measured radiance spectra. Performing this retrieval requires solving a non-linear inverse problem and the quality of the subsequent second-stage retrievals of the biophysical properties depends on how well the first-stage retrieval is performed. A major computational bottleneck for these retrievals is radiative transfer: for each retrieval a radiative transfer model (RTM) needs to be queried several times, and these models are in general computationally costly. A standard way to resolve this issue is to construct a lookup table representation of the RTM, which is then interpolated. While kriging (one of the most commonly used interpolation methods) offers a simple solution, its accuracy and the underlying uncertainties are highly sensitive to the prior selection of an underlying kernel. We solve this problem by using the Kernel Flows (KF) algorithm to learn a data-dependent kernel, with which we construct a Gaussian process emulator for the RTM. This emulator can then be used in retrievals. In this presentation we discuss the KF algorithm implementation and the emulator design for the reflectance retrieval problem. We describe the computational details, evaluate the performance of the emulator, and describe what effects keeping track of uncertainties in approximating radiative transfer has on the retrieved surface reflectances.