Journal cover Journal topic
Geoscientific Model Development An interactive open-access journal of the European Geosciences Union
doi:10.5194/gmd-2016-314
© Author(s) 2017. This work is distributed
under the Creative Commons Attribution 3.0 License.
Development and technical paper
09 Feb 2017
Review status
This discussion paper is under review for the journal Geoscientific Model Development (GMD).
Regional and seasonal truncation errors of trajectory calculations using ECMWF high-resolution operational analyses and forecasts
Thomas Rößler1,a, Olaf Stein1, Yi Heng2, and Lars Hoffmann1 1Forschungszentrum Jülich, Jülich Supercomputing Centre, Jülich, Germany
2School of Chemical Engineering and Technology, Sun Yat-sen University, Guangzhou, China
anow at: Department of Mathematics, University of Wisconsin–Milwaukee, Milwaukee, Wisconsin, United States
Abstract. Lagrangian particle dispersion models (LPDMs) are indispensable tools to study atmospheric transport processes. The accuracy of trajectory calculations, which form an essential part of LPDM simulations, depends on various factors. Here we focus on truncation errors that originate from the use of numerical integration schemes to solve the kinematic equation of motion. The optimization of numerical integration schemes to minimize truncation errors and to maximize computational speed is of great interest regarding the computational efficiency of large-scale LPDM simulations. In this study we analyzed truncation errors of six explicit integration schemes of the Runge Kutta family, which we implemented in the Massive-Parallel Trajectory Calculations (MPTRAC) model. The simulations were driven by wind fields of the latest operational analysis and forecasts of the European Centre for Medium-range Weather Forecasts (ECMWF) at T1279L137 spatial resolution and 3 h temporal sampling. We defined separate test cases for 15 distinct domains of the atmosphere, covering the polar regions, the mid-latitudes, and the tropics in the free troposphere, in the upper troposphere and lower stratosphere (UT/LS) region, and in the lower and mid stratosphere. For each domain we performed simulations for the months of January, April, July, and October for the years of 2014 and 2015. In total more than 5000 different transport simulations were performed. We quantified the accuracy of the trajectories by calculating transport deviations with respect to reference simulations using a 4th-order Runge-Kutta integration scheme with a sufficiently fine time step. We assessed the transport deviations with respect to error limits based on turbulent diffusion. Independent of the numerical scheme, the truncation errors vary significantly between the different domains and seasons. Especially the differences in altitude stand out. Horizontal transport deviations in the stratosphere are typically an order of magnitude smaller compared with the free troposphere. We found that the truncation errors of the six numerical schemes fall into three distinct groups, which mostly depend on the numerical order of the scheme. Schemes of the same order differ little in accuracy, but some methods need less computational time, which gives them an advantage in efficiency. The selection of the integration scheme and the appropriate time step should possibly take into account the typical altitude ranges as well as the total length of the simulations to achieve the most efficient simulations. However, trying to generalize, we recommend the 3rd-order Runge Kutta method with a time step of 170 s or the midpoint scheme with a time step of 100 s for efficient simulations of up to 10 days time based on ECMWF's high-resolution meteorological data.

Citation: Rößler, T., Stein, O., Heng, Y., and Hoffmann, L.: Regional and seasonal truncation errors of trajectory calculations using ECMWF high-resolution operational analyses and forecasts, Geosci. Model Dev. Discuss., doi:10.5194/gmd-2016-314, in review, 2017.
Thomas Rößler et al.
Thomas Rößler et al.
Thomas Rößler et al.

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Short summary
In this study we performed a detailed assessment of truncation errors and the computational efficiency of atmospheric trajectory calculations of six popular numerical integration schemes of the Runge Kutta family. More than 5000 individual transport simulations were conducted with the latest version of ECMWF operational analyses and forecasts. The assessment covers different seasons and regions of the free troposphere and stratosphere.
In this study we performed a detailed assessment of truncation errors and the computational...
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