With DSM2, the Delta is modeled assuming a one-way coupling
between hydrodynamics and salinity. Flow and stage results from HYDRO are used
to drive the salinity transport model QUAL, but ignore feedback that
salinity-induced density gradients have on hydrodynamics. The assumption of no
feedback is made for convenience, but is supported by order-of-magnitude
arguments that play down the importance of baroclinic terms in the governing
equations. DSM2 does not support a coupled solution of hydrodynamics and
Numerical testing of the effects of variable density is a task
that is revisited from time to time. Recent motivation for investigation came
from the 1999-2000 IEP PWT calibration project, where certain mild systematic
errors were thought to be attributable to density. This report documents a
simple numerical experiment on the importance of longitudinal density variation
on 1-D hydrodynamics in DSM2 (no representation is made that this captures all
the nuances of baroclinic hydrodynamics).
The experiment was from September 15, 1997 to October 31,
1998. The original idea was to span two IEP calibration periods, one in April
1998 and another in September 1998, plus a warm-up period for the quality model.
Salinity varied considerably over this period, as demonstrated by the tidally
averaged (EC) plot of Figure 6-1. However, the most important high salinity
periods occurred before the first IEP calibration periods. The April 1998
calibration period had almost zero salinity, and in the September 1998 period
salinity was low to medium.
Figure 6-1: EC at Mallard (RSAC075) during the study period.
Internally, DSM2 is able to incorporate variable density into
the flow equations -- this capability is a legacy of the FourPt model written by
Lew de Long. However, there is no supporting input/output system for
inserting density information and DSM2 does not solve the full hydrodynamic and
salt transport system simultaneously.
For the present project, EC output from QUAL was used to
calculate a density estimate offline, which was then reinserted into HYDRO using
a crude input system designed for this experiment.
Three model runs were carried out for the experiment:
- a preliminary HYDRO run to establish a flow field;
- a QUAL run to estimate salinity; and
- a follow-up HYDRO run.
The feedback cycle could, of course, be repeated ad nauseum
with successively improved flow fields passing from HYDRO to QUAL, and improved
density fields returning from QUAL to HYDRO. The scheme is not guaranteed
to converge, but due to the small changes over one cycle it seems likely to do
so very rapidly. Such detail was not required here, and if density effects
were to be incorporated formally into DSM2, the iterative process would probably
be replaced by simultaneous solution of hydrodynamics and salt transport.
Density was estimated by converting EC to total dissolved
solids (TDS) and then adding the TDS concentration to the density of water to
obtain the density in solution. The conversion from EC to TDS was
calculated using regression results from the Suisun Marsh Reports (
A single conversion formula for Mallard Island (RSAC075) was applied over the
TDS (mg/l) = -60.06 + 0.614 * EC (umhos/cm)
The range of density over space and time was between 1.0 g/cc
and 1.022 g/cc, the latter is about two-thirds of the value quoted by Fischer
(1972) for seawater. The variable density results were compared to a base
case with fixed density – none of the results were compared to field
The main difference between the "base case" (with
constant density) and the "variable density case" is that stage in the
variable density case is up to several tenths of a foot higher. Figure 6-2
shows stage at Mallard (RSAC075) and Figure 6-3 shows flow on the Sacramento
near Sherman Lake (RSAC084) for a typical time segment during the early part of
the experiment, when salinity was high. Proportionally, the difference in stage
is larger than the difference in flow.
Figure 6-2: (Top) Stage results for Mallard (RSAC075). (Bottom) Difference
between the two cases (variable density minus base) and its tidal average.
Figure 6-3: (Top) Flow near Sherman Lake. (Bottom) Difference between
cases (variable density minus base) and its tidal average.
The right side of Figure 6-2 shows the evolution of stage and
flow differences during the experiment (variable density minus base). This
difference varies tidally, and a filtered (tidally averaged) line has been added
to give some idea of the "average" difference between the two cases.
Not unexpectedly, the difference between the two cases depends on how much salt
is in the Delta (compare to Figure 6-1).
The stage differences between the base and variable density
cases are fairly uniform over the Delta. Figure 6-4 shows stage difference on
the Sacramento at Collinsville (RSAC081), Rio Vista (RSAC101), Delta Cross
Channel (RSAC128), and at the head of Old River (ROLD074). The amount of tidal
variation is different from location to location, but the trends are the same
and have a similar magnitude.
Figure 6-4: Stage difference (variable density minus base) at four locations:
Collinsville (RSAC081), Rio Vista (RSAC101), Delta Cross Channel (RSAC128), and
Old River at Head (ROLD074).
The lack of spatial variation is not surprising. Density is
highest and the density gradient steepest near Martinez –magnitude and
gradient decrease precipitously more than 20-30 km toward the east and south.
West of Emmaton or Jersey Point the density gradients induced by salinity are
always gentle and insufficient to produce hydrodynamic change on their own.
Instead, the changes that are induced in most of the Delta are just due to the
propagation inward of changes near the western boundary. It is as if the
"boundary condition" had been changed.
The inclusion of density gradients influences model results.
Whether the magnitude of the effect is important will depend on application, but
it can be called "mild" compared to other sources of model error.
Baroclinic effects depend strongly on the timing of hydrology (they are almost
nil when salinity is low), but only weakly on location. Because the IEP
calibration periods in 1998 are times of low salinity, longitudinal baroclinic
effects were probably not the cause of the errors that motivated this
Fischer, H.B., E.J. List, R.C.Y. Koh, J. Imberger and N.H.
Brooks. (1972). Mixing in Inland and Coastal Waters, Academic Press, San
Author: Eli Ateljevich
Back to Delta Modeling Section 2000 Annual Report Table of Contents
Last revised: 2000-10-23
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