Algorithm descriptions


SICOR is subdivided into two sequential main algorithms: the retrieval of the three phases of water and the calculation of the surface reflectance. The latter requires the output from the water retrieval to accurately model the level 2a spectra. The input requires an EnMAP level 1b product generated by the EnPT EnMAP data reader and an options file in json format. Via the options file, the user is able to set the path to the atmospheric Look-Up-Table (LUT), decide whether the algorithm should retrieve vapor, liquid and ice or only vapor and liquid, and set the number of cpu’s used for processing. All other relevant parameters are retrieved from the EnMAP product metadata file during the EnPT reader process.

Three Phases of Water Retrieval

SICOR uses sufficient narrow bands in the NIR to identify and quantify water in different states. The path lengths of water vapor, liquid water and ice are simultaneously estimated by applying a physically-based inversion of an atmospheric radiative transfer model (RTM) which is linked to a well-parameterized surface reflectance model. The latter incorporates the Beer-Lambert law to express the radiation absorption as a function of the path length of pure liquid water and ice. While water vapor can be inferred from the RTM simulations, the surface reflectance model enables the retrieval of the other two phases. The approach is based on the decoupling of the overlapping absorption lines of water vapor, liquid water and ice. The lines of liquid water and ice are shifted towards longer wavelengths. This displacement, in combination with the moderate absorption energies enables a spectroscopic separation of the three phases.

Forward Operator (FO)

Both the retrieval of the three phases of water and the modeling of the surface reflectance are based on the inversion of a well-parameterized forward model (FO), which models the TOA radiance spectra. The water retrieval uses the FO to estimate the values of vapor, liquid and ice by minimizing the difference between modeled and measured spectra. The minimization uses a predefined cost function in an iterative optimization procedure. The modeling of the surface reflectance applies the FO based on the retrieved combined atmospheric and surface state vector. Besides the path lengths of the three water phases, the FO additionally requires state vector parameters such as observation geometry, surface elevation and aerosol optical thickness (AOT). All these additional parameters are obtained from the metadata of the input EnMAP dataset.

Atmospheric Model

Assuming clear sky and a plane-parallel atmosphere as well as a Lambertian surface, SICOR models the TOA radiance by a simplified solution of the radiative transfer equation following the approach of Chandrasekhar (1960). To decrease the computational burden and to increase the processing speed, the needed atmospheric components were previously calculated for different atmospheric cases and stored in a multidimensional LUT.

Surface Reflectance Model

For the three phases of water retrieval, SICOR models the surface reflectance as a linear change in reflectance with wavelength attenuated by the spectrally dependent absorption for liquid water and ice based on the Beer-Lambert law. The wavelength dependent absorption coefficients of liquid water and ice are calculated by using the imaginary part of the complex index of refraction k. To obtain k, SICOR uses the table of Kedenburg et al. (2012) for liquid water and the values from Warren (1984) for ice.


SICOR iteratively adjusts water vapor, liquid water, and ice path lengths to match modeled and measured spectra within the selected water absorption feature. For EnMAP datasets, the 1140 nm window is applied due to the VNIR and SWIR detector overlapping around the 940 nm feature. The matching of the spectra is evaluated by a predefined cost function and at each iteration step, the needed atmospheric parameters are obtained by a multidimensional interpolation within the LUT. SICOR applies optimal estimation according to Rodgers (2000) to the iteration procedure.

Optimal Estimation

Optimal estimation enables the possibility to incorporate an error vector in terms of measurement, forward model, and a priori uncertainties.