Normal-mode function representation of global 3-D data sets: Open-access software for the atmospheric research community

This article presents new software for the analysis of global dynamical fields in (re)analyses, weather forecasts and climate models. A new diagnostic tool, developed within the MODES project, allows one to diagnose properties of balanced and inertio-gravity (IG) circulations across many scales. In particular, the IG spectrum, which has only recently become observable, can be studied simultaneously in the mass and wind fields while considering the whole model depth in contrast to the majority of studies. The paper includes the theory of normal-mode function (NMF) expansion, technical details of the Fortran 90 code, examples of namelists which control the software execution and outputs of the software application on the ERA Interim reanalysis data set. The applied libraries and default compiler are from the open-source domain. A limited understanding of Fortran suffices for the successful implementation of the software. The presented application of the software to the ERA Interim data set reveals several aspects of the large-scale circulation after it has been partitioned into the linearly balanced and IG components. The global energy distribution is dominated by the balanced energy while the IG modes contribute around 10% of the total wave energy. However, on sub-synoptic scales, IG energy dominates and it is associated with the main features of tropical variability on all scales. The presented energy distribution and features of the zonally averaged and equatorial circulation provide a reference for the validation of climate models.