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Geoscientific Model Development An interactive open-access journal of the European Geosciences Union
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https://doi.org/10.5194/gmd-2020-154
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/gmd-2020-154
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.

Submitted as: development and technical paper 24 Jun 2020

Submitted as: development and technical paper | 24 Jun 2020

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A revised version of this preprint is currently under review for the journal GMD.

Numerical integrators for Lagrangian oceanography

Tor Nordam1,2 and Rodrigo Duran3,4 Tor Nordam and Rodrigo Duran
  • 1SINTEF Ocean, Trondheim, Norway
  • 2Department of Physics, Norwegian University of Science and Technology, Trondheim, Norway
  • 3National Energy Technology Laboratory, Albany, OR 97321, USA
  • 4Theiss Research, San Diego, CA 92037, USA

Abstract. A common task in Lagrangian oceanography is to calculate a large number of drifter trajectories from a velocity field pre-calculated with an ocean model. Mathematically, this is simply numerical integration of an Ordinary Differential Equation (ODE), for which a wide range of different methods exist. However, the discrete nature of the modelled ocean currents requires interpolation of the velocity field, and the choice of interpolation scheme has implications for the accuracy and efficiency of the different numerical ODE methods.

We investigate trajectory calculation in modelled ocean currents with 800 m, 4 km, and 20 km horizontal resolution, in combination with linear, cubic and quintic spline interpolation. We use fixed-step Runge-Kutta integrators of orders 1–4, as well as three variable-step Runge-Kutta methods (Bogacki-Shampine 3(2), Dormand-Prince 5(4) and 8(7)). Additionally, we design and test modified special-purpose variants of the three variable-step integrators, that are better able to handle discontinuous derivatives in an interpolated velocity field.

Our results show that the optimal choice of ODE integrator depends on the resolution of the ocean model, the degree of interpolation, and the desired accuracy. For cubic interpolation, the commonly used Dormand-Prince 5(4) is rarely the most efficient choice. We find that in many cases, our special-purpose integrators can improve accuracy by many orders of magnitude over their standard counterparts, with no increase in computational effort. The best results are seen for coarser resolutions (4 km and 20 km), thus the special-purpose integrators are particularly advantageous for research using regional to global ocean models to compute large numbers of trajectories. Our results are also applicable to trajectory computations from atmospheric models.

Tor Nordam and Rodrigo Duran

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Tor Nordam and Rodrigo Duran

Tor Nordam and Rodrigo Duran

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Latest update: 22 Sep 2020
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Short summary
In applied oceanography, a common task is to calculate the trajectory of objects floating at the sea surface, or submerged in the water. We have investigated different methods for doing such calculations, and discuss the benefits and challenges of some common methods. We then propose a small change to some common methods that make them more efficient for this particular application. This will allow researchers to obtain more accurate answers, with less computer resources.
In applied oceanography, a common task is to calculate the trajectory of objects floating at the...
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