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@ARTICLE{Rler:843657,
      author       = {Rößler, Thomas and Stein, Olaf and Heng, Yi and
                      Baumeister, Paul F. and Hoffmann, Lars},
      title        = {{T}rajectory errors of different numerical integration
                      schemes diagnosed with the {MPTRAC} advection module driven
                      by {ECMWF} operational analyses},
      journal      = {Geoscientific model development},
      volume       = {11},
      number       = {2},
      issn         = {1991-9603},
      address      = {Katlenburg-Lindau},
      publisher    = {Copernicus},
      reportid     = {FZJ-2018-01226},
      pages        = {575 - 592},
      year         = {2018},
      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.},
      cin          = {JSC},
      ddc          = {910},
      cid          = {I:(DE-Juel1)JSC-20090406},
      pnm          = {511 - Computational Science and Mathematical Methods
                      (POF3-511)},
      pid          = {G:(DE-HGF)POF3-511},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000424636400002},
      doi          = {10.5194/gmd-11-575-2018},
      url          = {https://juser.fz-juelich.de/record/843657},
}