SciPy is an open-source scientific computing library for the Python programming language. Since its initial release in 2001, SciPy has become a de facto standard for leveraging scientific algorithms in Python, with over 600 unique code contributors, thousands of dependent packages, over 100,000 dependent repositories and millions of downloads per year. In this work, we provide an overview of the capabilities and development practices of SciPy 1.0 and highlight some recent technical developments.

Abstract. The geosciences are a highly suitable field of application for optimizing model parameters and experimental designs especially because many data are collected.In this paper, the weighted least squares estimator for optimizing model parameters is presented together with its asymptotic properties. A popular approach to optimize experimental designs called local optimal experimental designs is described together with a lesser known approach which takes into account the potential nonlinearity of the model parameters. These two approaches have been combined with two methods to solve their underlying discrete optimization problem.All presented methods were implemented in an opensource MATLAB toolbox called the Optimal Experimental Design Toolbox whose structure and application is described.In numerical experiments, the model parameters and experimental design were optimized using this toolbox. Two existing models for sediment concentration in seawater and sediment accretion on salt marshes of different complexity served as an application example. The advantages and disadvantages of these approaches were compared based on these models.Thanks to optimized experimental designs, the parameters of these models could be determined very accurately with significantly fewer measurements compared to unoptimized experimental designs. The chosen optimization approach played a minor role for the accuracy; therefore, the approach with the least computational effort is recommended.

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A new algorithm to approximate Hermitian matrices by positive semidefinite matrices based on modified Cholesky decompositions is presented. The approximation error and the condition number of the approximation can be controlled by parameters of the algorithm. The algorithm tries to minimize the approximation error in the Frobenius norm. It has no significant runtime and memory overhead compared to the computation of an unmodified Cholesky decomposition. Sparsity and positive diagonal entries can be preserved. A Cholesky decomposition of the approximation matrix is calculated as a byproduct.

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Methods for model parameter estimation, uncertainty quantification and experimental design are summarized in this paper. They are based on the generalized least squares estimator and different approximations of its covariance matrix using the first and second derivative of the model regarding its parameters. The methods have been applied to a model for phosphate and dissolved organic phosphorus concentrations in the global ocean. As a result, model parameters have been determined which considerably improved the consistency of the model with measurement results. The uncertainties regarding the estimated model parameters caused by uncertainties in the measurement results have been quantified as well as the uncertainties associated with the corresponding model output implied by the uncertainty in the model parameters. This allows to better assess the model parameters as well as the model output. Furthermore, it has been determined to what extent new measurements can reduce these uncertainties. For this, the information content of new measurements has been predicted depending on the measured process as well as the time and the location of the measurement. This is very useful for planning new measurements.

Abstract. The weighted least squares estimator for model parameters was presented together with its asymptotic properties. A popular approach to optimize experimental designs called local optimal experimental designs was described together with a lesser known approach which takes into account a potential nonlinearity of the model parameters. These two approaches were combined with two different methods to solve their underlying discrete optimization problem. All presented methods were implemented in an open source MATLAB toolbox called the Optimal Experimental Design Toolbox whose structure and handling was described. In numerical experiments, the model parameters and experimental design were optimized using this toolbox. Two models for sediment concentration in seawater of different complexity served as application example. The advantages and disadvantages of the different approaches were compared, and an evaluation of the approaches was performed.

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