Chapter 7
TRACMASS—A Lagrangian Trajectory Model
Kristofer Döös, Joakim Kjellsson, and Bror Jönsson
Abstract A detailed description of the Lagrangian trajectory model TRACMASS
is presented. The theory behind the original scheme for steady state velocities is
derived for rectangular and curvilinear grids with different vertical coordinates for
the oceanic and atmospheric circulation models. Two different ways to integrate
the trajectories in time in TRACMASS are presented. These different time schemes
are compared by simulating inertial oscillations, which show that both schemes are
sufficiently accurate not to deviate from the analytical solution.
The TRACMASS are exact solutions to differential equations and can hence be
integrated both forward and backward with unique solutions. Two low-order trajectory subgrid parameterizations, which are available in TRACMASS, are explained.
They both enable an increase of the Lagrangian dispersion, but are, however, too
simple to simulate some of the Lagrangian properties that are desirable. The mass
conservation properties of TRACMASS are shown to make it possible to follow the
water or air masses both forward and backward in time, which also opens up for
all sorts of calculations of water/air mass exchanges as well as Lagrangian stream
functions.
7.1 Introduction
The specification of a flow field can be made in an Eulerian or a Lagrangian frame of
reference. The Eulerian method is when the fluid flow is observed from a point fixed
in space, while the Lagrangian method is instead working from the perspective of the
K. Döös (B) · J. Kjellsson
Department of Meteorology, Bolin Centre for Climate Research, Stockholm University, Svante
Arrhenius väg 16C, 106 91 Stockholm, Sweden
e-mail: doos@misu.su.se
J. Kjellsson
e-mail: joakim@misu.su.se
B. Jönsson
Department of Geosciences, Princeton University, Guyot Hall, Princeton, NJ 08544, USA
e-mail: bjonsson@princeton.edu
T. Soomere, E. Quak (eds.), Preventive Methods for Coastal Protection,
DOI 10.1007/978-3-319-00440-2_7,
© Springer International Publishing Switzerland 2013
225
TRACMASS—A Lagrangian Trajectory Model
Kristofer Döös, Joakim Kjellsson, and Bror Jönsson
Abstract A detailed description of the Lagrangian trajectory model TRACMASS
is presented. The theory behind the original scheme for steady state velocities is
derived for rectangular and curvilinear grids with different vertical coordinates for
the oceanic and atmospheric circulation models. Two different ways to integrate
the trajectories in time in TRACMASS are presented. These different time schemes
are compared by simulating inertial oscillations, which show that both schemes are
sufficiently accurate not to deviate from the analytical solution.
The TRACMASS are exact solutions to differential equations and can hence be
integrated both forward and backward with unique solutions. Two low-order trajectory subgrid parameterizations, which are available in TRACMASS, are explained.
They both enable an increase of the Lagrangian dispersion, but are, however, too
simple to simulate some of the Lagrangian properties that are desirable. The mass
conservation properties of TRACMASS are shown to make it possible to follow the
water or air masses both forward and backward in time, which also opens up for
all sorts of calculations of water/air mass exchanges as well as Lagrangian stream
functions.
7.1 Introduction
The specification of a flow field can be made in an Eulerian or a Lagrangian frame of
reference. The Eulerian method is when the fluid flow is observed from a point fixed
in space, while the Lagrangian method is instead working from the perspective of the
K. Döös (B) · J. Kjellsson
Department of Meteorology, Bolin Centre for Climate Research, Stockholm University, Svante
Arrhenius väg 16C, 106 91 Stockholm, Sweden
e-mail: doos@misu.su.se
J. Kjellsson
e-mail: joakim@misu.su.se
B. Jönsson
Department of Geosciences, Princeton University, Guyot Hall, Princeton, NJ 08544, USA
e-mail: bjonsson@princeton.edu
T. Soomere, E. Quak (eds.), Preventive Methods for Coastal Protection,
DOI 10.1007/978-3-319-00440-2_7,
© Springer International Publishing Switzerland 2013
225