Transactions on Ecology and the Environment vol 14, © 1997 WIT Press, www.witpress.com, ISSN 1743-3541
3D Mathematical Modelling of the Po River
Inflow into the Northern Adriatic
M. Cetina
University of Ljubljana, Faculty of Civil and Geodetic Engineering,
Slovenia
EMail: mcetina@fagg. uni-lj. si
Abstract
A three-dimensional mathematical model LMT3D, which has been developed at the University
of Ljubljana (FGG) for flow and mass transport simulations in lakes and coastal seas, is
presented in the paper. The model is composed of a hydrodynamic module and of a transportdispersion module. Since the model is baroclinic coupled, it was possible to apply it to the
practical flow situation of the Po river inflow into the Northern Adriatic. The results were
compared with the field measurements of temperature and salinity in a zone facing the Po
river mouth, which were collected during the cruise ASCOP19 in March 1991. The simulated
plume of the fresh water coming from the Po river was qualitatively well predicted but
quantitatively the computed values of the surface salinity were overestimated. To improve the
accuracy of the results it would be necessary to use a greater number of vertical layers near the
surface and to perform more detailed calibration of the vertical eddy viscosity/difiusivity
coefficients by using powerful computers.
1 Introduction
The general circulation in the Northern Adriatic Sea is not very favourable:
different measurements and simulations (Orlic [5]) have shown that in winter
and spring time this region is mainly flushed by circulation coming from the
Middle Adriatic along the East (Croatian) coast and returning toward South
along the West (Italian) coast. But in the summer and autumn there is partly
closed circulation in this part of the sea and the water quality may be very bad.
This was proven by an extensive blooming of algae in 1988 and 1989.
The major source of pollutants in the Northern Adriatic is the Po River,
which has a fundamental role in driving the circulation and with itsfreshwater
strongly influences the bio-chemical cycles in the aquatic environment.
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To determine the transport and dispersion of pollutants from the Po River,
especially to see what part of the pollutants approach the Slovenian coastal
waters, we have simulated the circulation at different weather conditions, in first
phase wind induced circulation (Rajar&Cetina [9], [10], Rajar [7], [8]).
In the second phase of the work, which is presented in this paper, our
attention was focused on the behaviour of the Po River plume. The main aim of
the work was to test the simulations of the Po River outflow as obtained by the
existing three-dimensional (3D) model LMT3D, developed at FGG, University
of Ljubljana. In order to do this, data collected by the Osservatorio Geofisico
Sperimentale (OGS, Trieste) in the Northern Adriatic during March 1991, have
been used to initialise and compare model's results as well as to calibrate model'
s parameters.
2 Field Measurements
These data are obtained from an intensive measurement program in a zone
facing the Po River mouth. The cruise ASCOP19 was carried out by OGS from
March 23"* to March 29*, 1991. A total of 72 hydrological stations were treated
during the cruise, which is shown in Fig. 1. A dense grid of 49 stations was set
near the mouth in a square of 15x15 and a grid interval of 2.5 nautical miles. At
each station thermocline measurements were carried out with CTD.
What is fundamental for this study is that the plume of fresh water coming
from the Po River is very evident in every station. This plume has a thickness of
about 3 meters and spreads towards the middle of the basin, which can be clearly
seen from the vertical distribution of temperature and salinity hi Figs. 2 and 3.
This data set is very suitable to test the model's capacity to reproduce the
spreading of the fresh water into the Adriatic ambient water. Before showing
some results, a brief description of the model is given.
Fig. 1. The computational area with
hydrological stations
Fig. 2. Vertical profiles of the average
temperature and salinity
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D06
D07
4
D06
DOB
6
DO?
10
D09
12
D08
10
14
DIG
16
D09
12
14
18
Dll
20
D10
16
18
22
D12
24
Dll
20
22
26
D12
24
26
Fig. 3. Measured temperature (a.) and salinity (b.) at the vertical cross-section D
3 Mathematical model
3.1 General description
Since the mathematical model LMT3D has already been described elsewhere
(Rajar [8], Rajar&Cetina [9], [10]), only some basic features are given here.
The model is three-dimensional (3D) and fully non-linear. The continuity
equation, together with the two momentum equations in the xy plane, the
simplified dynamic equation in the z direction expressing hydrostatic pressure
distribution and the kinematic condition for the surface are used to compute
three velocity components, water elevation and pressure. Transport-dispersion
(advection-diffusion) equations for salinity and heat (and/or any pollutant) are
further used to compute the distribution of these parameters, which influence the
density by the equation of state. The variable density influences the velocity field
in the next time step. Thus, the model is baroclinic - coupled. No co-ordinate
transformation in the z direction is used.
Until now, the model has thefirsthydrodynamic (HD) and the second
transport dispersion (TD) module also including the sedimentation module of
suspended particles. The third bio-chemical (BK) module is being prepared for
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some specific matter (oil slick, mercury forms) by introducing the so called
sink/source terms into transport equations.
3.2 Turbulence model
In the momentum equations the known Boussinesq approximation is used for
determination of Reynolds stresses between the control volumes. Due to large
differences between horizontal and vertical dimensions of the computational
domain, different eddy viscosities Nh and Nv are used for both directions. The
Prandtl-Schmidt number a is used to correlate N and eddy difiusivity D, such
that Dh=Nh/a and Dh=Nh/a (Rodi [12]).
We used a constant value for "horizontal" eddy viscosity NH since for
circulation in large water bodies several studies have shown (e.g. Rajar&Cetina
[9], [11]) that Nh does not have an important influence and that good results can
be obtained using the constant Nh (in space and time) if its order of magnitude is
properly determined.
Many studies (Koutitas&O'Connor [2]), Rajar [8]) confirm that the
accuracy of the simulation depends much more on the value and distribution of
the "vertical" eddy viscosity coefficient Nv. Therefore, a turbulence model after
Koutitas&O'Connor [2] is used to compute it. This model is based on the
simplified equation of the turbulence kinetic energy. The distribution of Nv along
the depth is parabolic, the maximum value being attained at 0.6xH, and the
minimum values being zero at the bottom and at the surface. The maximum
value depends on the depth H, on the surface wind stress according to a
reference wind velocity Vw, and on the calibration constant F, which is
theoretically of the order of 1.0.
The stable density stratification can strongly diminish the values of NV and
Dv and can also change the velocity field considerably. The Munk-Anderson
relation with Nv and Dv dependent on the Richardson number (Rodi [12]) is
used in the model.
3.3 Numerical method and computer code
For the solution of basic equations, the known "finite volume" method of
Patankar [6] is used. The main characteristics of this method are a staggered
grid and a hybrid scheme in space, a fully implicit scheme in time and the use of
the SIMPLE procedure of pressure corrections to solve the system of equations.
The source computer code of LMT3D is written in FORTRAN??
language and is adopted to run on Intel compatible PC computers as well as on
IBM RISC/6000 and DEC/Alpha workstations. The computations within this
study were mainly performed on IBM RISC 6000/340 workstation at OGS.
3.4 Boundary conditions
In the mathematical model, the following boundary conditions are taken into
account: a) solid boundaries (with zero normal velocities); b) wind stress at the
Transactions on Ecology and the Environment vol 14, © 1997 WIT Press, www.witpress.com, ISSN 1743-3541
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surface; c) inflow of rivers; d) variable atmospheric pressure; e) known tidal
functions at the open boundary; f) the "radiation condition" at the open
boundary; g) the "continuity" boundary condition at the open boundary; h)
known distribution of velocities at the open boundaries (e. g. obtained from
computation of larger flow field); i) known temperature and salinity conditions
at the boundaries (e. g. at the river inflow).
The "continuity" boundary condition f was introduced after an idea of
Stravisi [13]. The basic principle is that at the open boundary the inflow into the
region equals the outflow, although vertically averaged velocities are used at the
open boundary cross-section.
4 Model Simulations
4.1 Input data
Wind measurements and Po River discharge data for the period from February
1* to March 31** 1991 were used to run the model.
Daily average wind speeds and directions prepared by the Institute
Talassografico CNR, Trieste, were used in the simulations. An important feature
to note is that a non uniform distribution along the Istrian peninsula proposed by
Kuzmic&Orlic [3] was taken into account in the case of the Burja wind. For
other wind directions, a uniform velocity distribution over the whole sea surface
area was proposed.
The data on the Po River discharge were obtained from an environmental
study carried out by the county of the Emilia-Romagna Region [1]. In this case,
the daily mean values have been used in the model. For the whole simulated
period, a temperature T = 15 °C and a salinity s = 18 %o for thefreshinflow
water of the Po River were assumed.
In all cases, a non uniform horizontal numerical grid of 33x32 cells was
used (Figs. 1 and 4 to 9). The space step was thus Ax = Ay = 7500 m, except in
the vicinity of the Po River mouth where three cells with Ax = Ay = 1500 m
were used to simulate the momentum of the Po River water more accurately. In
most computed cases we used 7 vertical layers situated at 0.7, 4, 10, 20, 30, 40
and 50 meters in depth, except in run PO5 where 9 vertical layers situated at 0.7,
1.5, 2.5, 4.0, 10, 20, 30, 40 and 50 meters were used. The time step which
resulted from the stability criteria At < (Az)*/ (2*Nv) was At = 180 s.
The initial vertical temperature and salinity profile were taken from the
measurements of the cruise ASCOP19 to represent an average of several
hydrological stations (Fig. 2) neglecting the initial influence of the Po River
plume. Thus, a constant temperature T = 9.2 °C and salinity s = 38.2 %o were
assumed over this depth. At the open boundary the radiation condition was
applied over the whole simulated period.
The constant horizontal eddy viscosity and diffiisivity coefficients were
given with the values NH = DH = 100 nf/s (Malanotte-Rizzoli&Bergamasco [4]).
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The distribution of vertical eddy viscosity and diffusivity Nv and Dv was
calculated using
a one-equation turbulent model proposed
by
Koutitas&O Connor [2] (Chapter 3.2) in which the values of F, Vw and a were
varied. This is briefly summarised below and also shows the results of the runs.
4.2 Results
Run POL Thefirstrun was performed using the values of F = 0.7, a = 1.0 and a
reference wind velocity for Nv computation of Vw = 2.2 m/s which changed after
7 days of the simulation to Vw = 7 m/s. The period from March 1* to March 31*
was simulated.
The computed velocityfieldsand salinity distributions on March 25*, 27*
and 29* which, due to lack of space are not presented in this paper, showed only
qualitative agreement with the measurements. Quantitatively, the computed
surface area of the Po River plume was too small and surface salinity too high in
comparison with measured data. To improve the results we tried to decrease the
values of the vertical eddy viscosity/diffusivity in the next run, PO3
Run PO3 We changed the value of a to 10 and kept Vw = 2.2 m/s during
the whole simulated period. The simulation from March l^to March 31** took 28
h CPU time on IBM RISC 6000/340 workstation.
The computed velocityfieldsin the surface layer (Figs. 4a and 5 a) and in
the vertical cross-sections on March 23"*, 27*, 29* and 31* have shown that the
surface velocities were strongly wind dependent and that the magnitudes were
evidently greater than in the case of run POL These differences can be explained
by the decrease of the coefficients Nv and Dy. The average values in the surface
layer, which were strongly diminished by the stable stratification according to
the Munk-Anderson relation [12], were Nv=1.5 and Dv=0.03 cmVs.
/I/
b)
Fig. 4. Run PO3: surface velocities (a.) and salinity (b.) on March 23"*, 1991
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Fig. 5. Run PO3: surface velocities (a.) and salinity (b.) on March 27*, 1991
0
height
30m
Fig. 6. Run PO3: salinity distribution in the vertical cross-section YZ24 on
March 27*, 1991
On March 28*, a strong Burja ENE wind with an intensity of Vw = 8.7
m/s started to blow. As a consequence, on March 29* the surface velocity field
changed considerably in comparison with the period from March 1** to 28* and
the magnitudes of the surface velocities increased by up to 40 cm/s.
As far as the spreading of the Po river plume is concerned, the surface
salinity distribution (Figs. 4b, 5b and 6) showed slightly better agreement with
the measurements than on run POL In general, the results were still not very
satisfactory because the salinity values were too high. This means that the
spreading of the Po river fresh water plume in the horizontal directions was too
weak.
Run PO5. Since relatively thin surface layer of about 3 m and a vertical
distribution of Nv and Dv near the surface play a crucial role in the proper
simulation of the impact of the Po River plume in the sea, nine vertical layers
were taken into account in this run. We used the calibration constant F = 0.5 and
a realistic wind velocity as the reference value Vw if the absolute value of the
wind velocity was greater than 0.5 m/s. Otherwise, Vw = 0.5 m/s was used.
The computed velocities in the surface layer on March 10* and 27* (Figs.
7a and 8a) are very similar to those obtained at the run PO3
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Fig. 7. Run PO5: surface velocities (a.) and salinity (b.) on March 10*, 1991
b)
Fig. 8. Run PO5: surface velocities (a.) and salinity (b.) on March 27*, 1991
0 ^th 30km
0
height
30m
Fig. 9. Run PO5: salinity distribution in the vertical cross-section YZ24 on
March 27*, 1991
Much better agreement between measurements was obtained for the computed
salinity distribution (Figs. 7b, 8b and 9). On March 27*, the spreading of the Po
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River plume was qualitatively quite well reproduced. Quantitatively, the values
of the surface salinity in the Po River plume region are closer to the
measurements than those computed in run P03, but were still too high. One of
the possible reasons for this disagreement is that we started the computation
from an initially homogeneous temperature and salinity profile over the whole
area, while, in reality, the Po River plume was already spread out before the
simulated period.
Run PO7. In order to use initial conditions which were closer to the
reality, we simulated the two month period from February 1* to March 31*.
However, due to extremely long computational time of several days we used
only seven vertical layers. The value of T was changed to 0.7 and we used the
upper limit of Vw = 7.0 m/s to avoid possible numerical stability problems due to
rapid changes in Nv and DV.
The results of this run are not presented in the paper since a better
agreement with the measured data as compared to run PO5 was expected, but
not achieved. This is probably due to the smaller number of vertical layers used
and slightly higher value off and thus Nv and DV.
5 CONCLUSIONS
The main goal of this research was to apply the 3D baroclinic hydrodynamic and
transport-dispersion model in order to better understand current velocities and
dispersion of contaminants in the Northern Adriatic. Since this region is strongly
influenced by the Po River inflow and very detailed measurements of this
phenomenon were carried on the cruise ASCOP19, performed by OGS in March
1991, the spreading of the plume was simulated.
We succeeded only partially in improving calibration of the model. The
plume of the Po River was qualitatively well simulated, but, quantitatively, the
computed values of the surface salinity were still too high.
The research has given the following indications for further work on the
problem. To improve the results we should increase the number of the vertical
layers near the surface and slightly decrease the values of vertical eddy viscosity
and diffiisivity. In order to start the computations from more realistic initial
conditions it would also be necessary to simulate a longer period of the Po River
inflow of at least two months. One of the possible causes of the discrepancy is
also the numerical diffusion of the hybrid scheme. This can be partly diminished
by using a more dense numerical grid. We are working on the implementation of
a third order numerical method, QUICKEST, in the model.
For future work it is crucial to use even faster computers to execute a
detailed sensitivity analysis of several not well known parameters (F, Nv, DV).
Acknowledgements
This paper is based on research work which was carried out at the Institute
Geofisico Sperimentale (OGS), Trieste, during the author's four months stay at
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OGS. The fellowship was funded by the Commission of the European
Communities (COST Programme, Contract No. ERB-CEPA-CT-92-0364). The
author wish to thank the OGS for making experimental data available and
especially to Dr. Renzo Mosetti for his valuable advice on modelling.
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