Juan Carlos De Los Reyes

We carry out a rigorous analysis of four-dimensional variational data assimilation (4DVAR) problems for linear and semilinear parabolic partial differential equations. Continuity of the state with respect to the spatial variable is required since pointwise observations of the state variable appear in the cost functional. Using maximal parabolic regularity tools, we prove this regularity for initial conditions with Lβ-regularity guaranteed by control constraints, rather than Sobolev regularity of the controls ensured by artificial cost terms. We obtain existence of optimal controls and first-order necessary optimality conditions for both the convex and nonconvex problem with spatial dimension d = 2, 3, as well as second-order sufficient optimality conditions for the nonconvex problem for d = 2.

The assimilation of satellite spectral sounder data requires fast and accurate radiative transfer models. This study proposes a novel methodology to automatically parameterize atmospheric optical depths within the Radiative Transfer for TOVS (RTTOV) version 13 scheme using statistical thresholds across pressure levels and Least Absolute Shrinkage and Selection Operator (LASSO) regression to induce sparsity. Numerical experiments with Visible Infrared Imaging Radiometer Suite (VIIRS) infrared channels demonstrate that this approach significantly reduces computational costs while maintaining accuracy. The sparsity also facilitates the automatic selection of absorbing gases and predictors by channel and pressure level, making it particularly effective for multispectral instruments with numerous atmospheric variables. These findings highlight the potential of sparse regression methods to enhance the efficiency of radiative transfer models for satellite data assimilation.

The assimilation of satellite spectral sounder data requires fast and accurate radiative transfer models for retrieving surface and atmospheric variables. This study proposes a novel methodology to automatically parameterize atmospheric optical depths within the RTTOV scheme using statistical thresholds across pressure levels and LASSO regression to induce sparsity. Numerical experiments with VIIRS infrared channels demonstrate that this approach significantly reduces computational costs while maintaining accuracy. The sparsity also facilitates the automatic selection of absorbing gases and predictors by channel and pressure level, making it particularly effective for multispectral instruments with numerous atmospheric variables. These findings highlight the potential of sparse regression methods to enhance the efficiency of radiative transfer models for satellite data assimilation.

The assimilation of satellite spectral sounder data requires fast and accurate radiative transfer models for retrieving surface and atmospheric variables. This study proposes a novel methodology to automatically parameterize atmospheric optical depths within the RTTOV scheme using statistical thresholds across pressure levels and LASSO regression to induce sparsity. Numerical experiments with VIIRS infrared channels demonstrate that this approach significantly reduces computational costs while maintaining accuracy. The sparsity also facilitates the automatic selection of absorbing gases and predictors by channel and pressure level, making it particularly effective for multispectral instruments with numerous atmospheric variables. These findings highlight the potential of sparse regression methods to enhance the efficiency of radiative transfer models for satellite data assimilation.

The assimilation of satellite spectral sounder data requires fast and accurate radiative transfer models for retrieving surface and atmospheric variables. This study proposes a novel methodology to automatically parameterize atmospheric optical depths within the RTTOV scheme using statistical thresholds across pressure levels and LASSO regression to induce sparsity. Numerical experiments with VIIRS infrared channels demonstrate that this approach significantly reduces computational costs while maintaining accuracy. The sparsity also facilitates the automatic selection of absorbing gases and predictors by channel and pressure level, making it particularly effective for multispectral instruments with numerous atmospheric variables. These findings highlight the potential of sparse regression methods to enhance the efficiency of radiative transfer models for satellite data assimilation.

The assimilation of satellite spectral sounder data requires fast and accurate radiative transfer models for retrieving surface and atmospheric variables. This study proposes a novel methodology to automatically parameterize atmospheric optical depths within the RTTOV scheme using statistical thresholds across pressure levels and LASSO regression to induce sparsity. Numerical experiments with VIIRS infrared channels demonstrate that this approach significantly reduces computational costs while maintaining accuracy. The sparsity also facilitates the automatic selection of absorbing gases and predictors by channel and pressure level, making it particularly effective for multispectral instruments with numerous atmospheric variables. These findings highlight the potential of sparse regression methods to enhance the efficiency of radiative transfer models for satellite data assimilation.

The assimilation of satellite spectral sounder data requires fast and accurate radiative transfer models for retrieving surface and atmospheric variables. This study proposes a novel methodology to automatically parameterize atmospheric optical depths within the RTTOV scheme using statistical thresholds across pressure levels and LASSO regression to induce sparsity. Numerical experiments with VIIRS infrared channels demonstrate that this approach significantly reduces computational costs while maintaining accuracy. The sparsity also facilitates the automatic selection of absorbing gases and predictors by channel and pressure level, making it particularly effective for multispectral instruments with numerous atmospheric variables. These findings highlight the potential of sparse regression methods to enhance the efficiency of radiative transfer models for satellite data assimilation.

The assimilation of satellite spectral sounder data requires fast and accurate radiative transfer models for retrieving surface and atmospheric variables. This study proposes a novel methodology to automatically parameterize atmospheric optical depths within the RTTOV scheme using statistical thresholds across pressure levels and LASSO regression to induce sparsity. Numerical experiments with VIIRS infrared channels demonstrate that this approach significantly reduces computational costs while maintaining accuracy. The sparsity also facilitates the automatic selection of absorbing gases and predictors by channel and pressure level, making it particularly effective for multispectral instruments with numerous atmospheric variables. These findings highlight the potential of sparse regression methods to enhance the efficiency of radiative transfer models for satellite data assimilation.