The eofs library provides a high-level Python interface for computing empirical orthogonal functions (EOFs) and related quantities, with a focus on correctness and ease of use. The library is implemented in a modular hierarchical fashion, allowing computations using plain arrays, or the inclusion of metadata. The software provides a convenient package for users wanting to perform EOF analysis in Python, and integrates with popular libraries from atmospheric and climate science. The software is available on Github

The windspharm library is a Python package for performing computations on global wind fields in spherical geometry. It provides a high-level interface for computing derivatives and integrals of vector wind fields over a sphere using spherical harmonics. The software allows for computations with plain arrays, or with structures that include metadata, integrating with several popular data analysis libraries from the atmospheric and climate science community. The software is available on Github

Numerical weather prediction models are including an increasing number of components of the Earth system. In particular, every forecast now issued by the European Centre for Medium-Range Weather Forecasts (ECMWF) runs with a 3D ocean model and a sea ice model below the atmosphere. Initialisation of different components using different methods and on different timescales can lead to inconsistencies when they are combined in the full system. Historically, the methods for initialising the ocean and the atmosphere have been typically developed separately. This paper describes an approach for combining the existing ocean and atmospheric analyses into what we categorise as a weakly coupled assimilation scheme. Here, we show the performance improvements achieved for the atmosphere by having a weakly coupled ocean–atmosphere assimilation system compared with an uncoupled system. Using numerical weather prediction diagnostics, we show that forecast errors are decreased compared with forecasts initialised from an uncoupled analysis. Further, a detailed investigation into spatial coverage of sea ice concentration in the Baltic Sea shows that a much more realistic structure is obtained by the weakly coupled analysis. By introducing the weakly coupled ocean–atmosphere analysis, the ocean analysis becomes a critical part of the numerical weather prediction system and provides a platform from which to build ever stronger forms of analysis coupling.

Reducing the numerical precision of the forecast model of the Integrated Forecasting System (IFS) of the European Centre for Medium‐Range Weather Forecasts (ECMWF) from double to single precision results in significant computational savings without negatively affecting forecast accuracy. The computational savings allow to increase the vertical resolution of the operational ensemble forecasts from 91 to 137 levels earlier than anticipated and before the next upgrade of ECMWF's high‐performance computing facility. This upgrade to 137 levels harmonises the vertical resolution of the medium‐range deterministic forecasts and the medium‐range and extended‐range ensemble forecasts. Increasing the vertical resolution of the ensemble forecasts substantially improves forecast skill for all lead times as well as the mean of the model climate. ECMWF's ensemble and deterministic forecasts will run operationally at single precision from IFS model cycle 47R2 onwards.