Trajectory errors of different numerical integration schemes diagnosed with the MPTRAC advection module driven by ECMWF operational analyses

Abstract

Abstract. The accuracy of trajectory calculations performed by Lagrangian particle dispersion models (LPDMs) depends on various factors. The optimization of numerical integration schemes used to solve the trajectory equation helps to maximize the computational efficiency of large-scale LPDM simulations. We analyzed global truncation errors of six explicit integration schemes of the Runge-Kutta family, which we implemented in the Massive-Parallel Trajectory Calculations (MPTRAC) advection module. The simulations were driven by wind fields from 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 regions of the atmosphere, covering the polar regions, the midlatitudes, and the tropics in the free troposphere, in the upper troposphere and lower stratosphere (UT/LS) region, and in the middle stratosphere. In total, more than 5000 different transport simulations were performed, covering the months of January, April, July, and October for the years 2014 and 2015. We quantified the accuracy of the trajectories by calculating transport deviations with respect to reference simulations using a fourth-order Runge-Kutta integration scheme with a sufficiently fine time step. Transport deviations were assessed with respect to error limits based on turbulent diffusion. Independent of the numerical scheme, the global truncation errors vary significantly between the different regions. 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 summarize, we recommend the third-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 of simulation time for the specific ECMWF high-resolution data set considered in this study. Purely stratospheric simulations can use significantly larger time steps of 800 and 1100 s for the midpoint scheme and the third-order Runge-Kutta method, respectively.

From ERA-Interim to ERA5: the considerable impact of ECMWF's next-generation reanalysis on Lagrangian transport simulations

“…Hoffmann et al (2017) presented an intercomparison of meteorological analyses and an evaluation of MPTRAC trajectory calculations with super-pressure balloon observations for the Antarctic lower stratosphere. Rößler et al (2018) evaluated trajectory errors of different numerical integration schemes diagnosed with the MPTRAC advection module driven by highresolution ECMWF operational analyses and forecasts.…”

From ERA-Interim to ERA5: considerable impact of ECMWF's next-generation reanalysis on Lagrangian transport simulations

“…Roughly, these layers cover the free troposphere (2 -8 km), the upper troposphere and lower stratosphere (UT/LS, 8 -16 km), the lower and middle stratosphere (16 -32 km), and the middle and upper stratosphere (32 -48 km). Rößler et al (2018) found that trajectory errors within different height layers also vary with latitude and season. We therefore evaluated the simulation results not only globally, but also in three latitude bands, covering .…”

“…Hoffmann et al (2017) presented an intercomparison of meteorological analyses and an evaluation of MPTRAC trajectory calculations with superpressure balloon observations for the Antarctic lower stratosphere. Rößler et al (2018) evaluated trajectory errors of different numerical inte-Atmos. Chem.…”

“…Following the approach of Rößler et al (2018), we evaluated the simulation results separately in different height ranges and latitude bands. Considering that the trajectory errors depend on the height level within the atmosphere, we split the full log-pressure altitude range of 2 -48 km into four layers.…”

“…Experiment IV was set up to achieve a spatiotemporal sampling similar to ERA-Interim. We quantified the differences of the Lagrangian transport simulations using the downsampled and the full resolution ERA5 data by calculating transport deviations after 1 day, as these are most sensitive to the specific uncertainties and less dependent on the individual meteorological conditions and flow conditions (Rößler et al, 2018). Figures 12 and 13 show the results of these four experiments.…”