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ABSTRACT Several iterative soft‐thresholding algorithms, such as FISTA, have been proposed in the literature for solving regularized linear discrete inverse problems that arise in various applications in science and engineering. These algorithms are easy to implement, but their rates of convergence may be slow. This paper describes novel approaches to reduce the computations required for each iteration by using Krylov subspace techniques. Specifically, we propose to impose sparsity on the coefficients in the representation of the computed solution in terms of a Krylov subspace basis. Several numerical examples from image deblurring and computerized tomography are used to illustrate the efficiency and accuracy of the proposed methods. 

Abstract. The widely used open-source community Noah with multi-parameterization options (Noah-MP) land surface model (LSM) isdesigned for applications ranging from uncoupled land surfacehydrometeorological and ecohydrological process studies to coupled numericalweather prediction and decadal global or regional climate simulations. It hasbeen used in many coupled community weather, climate, and hydrology models. Inthis study, we modernize and refactor the Noah-MP LSM by adopting modern Fortrancode standards and data structures, which substantially enhance the modelmodularity, interoperability, and applicability. The modernized Noah-MP isreleased as the version 5.0 (v5.0), which has five key features: (1) enhanced modularization as a result of re-organizing model physics into individualprocess-level Fortran module files, (2) an enhanced data structure with newhierarchical data types and optimized variable declaration andinitialization structures, (3) an enhanced code structure and calling workflowas a result of leveraging the new data structure and modularization, (4) enhanced(descriptive and self-explanatory) model variable naming standards, and (5) enhanced driver and interface structures to be coupled with the hostweather, climate, and hydrology models. In addition, we create a comprehensivetechnical documentation of the Noah-MP v5.0 and a set of model benchmark andreference datasets. The Noah-MP v5.0 will be coupled to variousweather, climate, and hydrology models in the future. Overall, the modernizedNoah-MP allows a more efficient and convenient process for future modeldevelopments and applications.