THREE-DIMENSIONAL HYDROTHERMAL MODEL
NEW YORK
OF
ONONDAGA LAKE,
By A. K. M. Quamrul Ahsan1 and Alan F. Blumberg,2 Members, ASCE
ABSTRACT: A three-dimensional time-dependent hydrodynamic model of Onondaga Lake, an inland lake in
central New York, emphasizing the simulation of dynamics and thermal structure has been developed. The model
is based on the ECOM family of models; this version, called ECOMsiz, employs a semi-implicit time splitting
algorithm and a z-level vertical coordinate system. Proper assignment of boundary conditions, especially surface
heat fluxes, has been found crucial in simulating the lake’s hydrothermal dynamics. Formulas for atmospheric
radiation and sensible and latent heat fluxes are introduced, which have been found most appropriate for evaluating the heat budget for this midlatitudinal urban lake. The ECOMsiz model has been calibrated and validated
against data for two years, 1985 and 1989, representing a wide spectrum of atmospheric and hydrographic
conditions in the lake. These two years, marked by significantly different freshwater inputs from tributary inflows,
ionic waste loadings, wind forcing, and atmospheric heating and cooling, form a firm basis for evaluating the
robustness of the hydrodynamic model. The simulation period chosen for both years, April through October,
spans the entire range of lake physical processes as it covers the well-mixed spring condition, the summer period
marked by strong vertical stratification, and the well-mixed fall period. Significant differences in thermal structure
have been observed in 1985 and 1989 as a result of different meteorological conditions. The mixed layer depth
in 1985 is about 3 m deeper (about 9 m) than that in 1989 (about 6 m), consistent with a stronger prevailing
wind in 1985. The model has successfully predicted the mixed layer depth for both the years. The model
computed total heat storage for both years is in good agreement with the observed conditions.
INTRODUCTION
Onondaga Lake has been a topic of intensive research for
the last few decades. Concern with the water quality of the
lake has prompted a continuing interest in developing a fullscale hydrodynamic and thermodynamic model capable of
simulating the dynamics and thermal structure of the lake.
Modeling an accurate thermal stratification is very important,
as this feature greatly regulates the biological and chemical
processes of the lake (Owens and Effler 1996). Transport and
mixing and, therefore, cycling of key water quality parameters
such as nutrients and dissolved oxygen are also significantly
influenced by the stratification regime (DiToro and Connolly
1980; Wodka et al. 1985). Atmospheric heating and cooling,
along with the wind stress, determine the formation, maintenance, and eventual destruction of the surface mixed layer and
control other large and small scale processes such as circulations and internal wave generations. Accurate estimation of the
heat exchanges between the water surface and the atmosphere
is extremely important to simulate the hydrothermal conditions
of the lake. Measurements of heat fluxes such as solar radiation, atmospheric radiation, sensible heat, and latent heat are
very difficult and costly to make and are often parameterized
to obtain the fluxes using the most commonly available meteorological and atmospheric data.
Onondaga Lake has been a recipient of a wide spectrum of
chemical, thermal, and biological pollution from natural and
manmade sources. It is underlain with NaCl brine and has
received large quantities of Cl-enriched ionic waste and thermal loads from a nearby chlor-alkali plant. Several researchers
(Effler and Owens 1986; Owens and Effler 1996) have found
that the density stratification in Onondaga Lake has been influenced by a positively buoyant thermal loading from this
plant until its closure in early 1986. They also claimed that
negatively buoyant inflows with elevated chloride concentration also may have impact on the stratification regime of the
lake (Doerr et al. 1994). Chemical pollution, such as Ca, Cl,
Alk, and TIC, as well as nutrient loadings that trigger algal
blooms, cause changes in light penetration, thereby affecting
the development and maintenance of the thermal structure of
the lake. Owens and Effler (1996) suggest that the salinity
component accounts for 30% of the overall density stratification in the lake based on the data for the period 1968–1986.
However, progressive decreases in the salinity component of
stratification have been observed during most of the years after
the closure of the plant in 1986, although the residual waste
loadings from the nearby abandoned waste bed continues to
impact the density stratification (Owens and Effler 1996) on
an occasional basis.
The principal objective of this paper is to document the
development, calibration, and application of a modeling framework needed to evaluate the hydrothermal conditions of Onondaga Lake. It will not address the issue of partitioning density stratification between the contribution of temperature and
salinity; rather, that issue will remain the subject of future
study. Parameterization of heat fluxes based on the bulk formulas suggested by Cole and Buchak (1995) and Edinger et
al. (1974) and characterization of turbulence kinetic energy
based on Mellor and Yamada (1982) are used in the modeling
framework. The model is calibrated against 1985 (before the
closure of chlor-alkali plant) and 1989 lake temperature data.
These two years, selected for calibration and validation of the
hydrodynamic model, provide a marked range in hydrographic
regimes and significantly different freshwater inputs from tributary inflows, ionic waste loadings, and wind forcing.
HYDROLOGY AND HYDROGRAPHY OF ONONDAGA
LAKE
1
Proj. Engr., HydroQual, Inc., 1 Lethbridge Plaza, Mahwah, NJ 07430.
Exec. Vice Pres. and Prin. Sci., HydroQual, Inc., 1 Lethbridge Plaza,
Mahwah, NJ.
Note. Discussion open until February 1, 2000. To extend the closing
date one month, a written request must be filed with the ASCE Manager
of Journals. The manuscript for this paper was submitted for review and
possible publication on April 27, 1998. This paper is part of the Journal
of Hydraulic Engineering, Vol. 125, No. 9, September, 1999. 䉷ASCE,
ISSN 0733-9429/99/0009-0912–0923/$8.00 ⫹ $.50 per page. Paper No.
18389.
2
912 / JOURNAL OF HYDRAULIC ENGINEERING / SEPTEMBER 1999
Onondaga Lake is located in Onondaga County in central
New York State, adjacent to the city of Syracuse. Fig. 1 illustrates the study area and shoreline and bathymetric features of
the lake. The outflow from the lake exits via a single outlet at
its northern end and enters the Seneca River. The Seneca River
combines with the Oneida River to form the Oswego River,
which flows north, ultimately entering Lake Ontario. Onondaga Lake is oriented along a northwest-southwest axis. It has
FIG. 1.
Hydrological and Morphological Descriptions of Onondaga Lake
a length of 7.6 km and a maximum width of 2 km. The lake
comprises two basins, the north and the south basins, that are
separated by a slight saddle region. The north basin has a
maximum measured depth of 19 m, and the south basin has a
maximum depth of 20 m. The volume of the lake is estimated
to be 139 ⫻ 106 m3, with a surface area of 11.8 km2. The lake
bathymetry is characterized by a relatively shallow area along
the lake shoreline ranging from 0 to 8 meters within a few
hundred meters from the shore. Changes in bottom depths of
as much as 12 meters can occur within 200 meter widths.
Onondaga Lake receives surface runoff from a drainage basin estimated to cover approximately 620 km2. The major surface water inflows to Onondaga Lake are Ninemile Creek, Onondaga Creek, Ley Creek, and Harbor Brook. Other minor
tributaries include Bloody Brook, Sawmill Creek, Tributary
5A, and the East Flume. Water is also contributed to the lake
by the Metropolitan Syracuse Sewage Treatment Plant
(METRO) facility and through intermittent bidirectional flows
from the Seneca River at the outlet of the lake (Effler 1987).
Long term annually averaged inflows to the lake from the major tributaries for the period January 1, 1970, through December 21, 1989, along with flows in 1985 and 1989 (study periods), are presented in Table 1. The average total inflows of
tributaries, listed in Table 1, to the lake based on an annual
basis for the period 1970–1989 was 15.23 m3/s. It is clearly
evident from the table that years 1985 and 1989 represent two
quite different hydrological conditions of dry and average flow
periods, respectively.
There is a strong seasonal pattern in the tributary inflows to
Onondaga Lake. High flows are found to occur in March and
April, and the lowest flows occur in August. Because of the
seasonal variation in tributary inflow and the relatively constant METRO flow, the contribution of METRO varies from
a low of 10–20% of the total lake inflow in March and April
TABLE 1. Annual Average Inflows of Major Tributaries into
Onondaga Lake
Source
(1)
Average flow a
(m3/s)
(2)
1985 flow b
(m3/s)
(3)
1989 flow b
(m3/s)
(4)
Onondaga Creek
Ninemile Creek
METRO
Ley Creek
Harbor Brook
Total
5.25
5.29
2.99
1.32
0.38
15.23
2.68
2.17
3.29
0.75
0.19
9.08
5.67
5.15
3.33
1.23
0.27
15.65
a
Averaging period, 1971–1989.
Averaged over model simulation period, Apr–Oct.
b
to a high of between 25 and 40% during the low flow summer
months.
An extensive database comprising a wide spectrum of data
exists for the lake. These data were collected, beginning in
1968 and continuing to present times, by various agencies,
including the Onondaga County Department of Drainage and
Sanitation (D&S), the Onondaga County Department of Health
(DOH), the Upstate Freshwater Institute (UFI), and the U.S.
Geological Survey (USGS). Walker (1991) has documented
and compiled these data into a unified database. This unified
database has been the source of data for the present study.
D&S and UFI collected data principally in two locations in
the lake (Fig. 1) during periods without ice cover, one in the
north basin and the other in the south basin (in proximity to
the deepest locations of the lake). The D&S data were taken
at 3 m intervals at the two major sampling locations. D&S
collected data approximately every two weeks at the south
basin station and more sporadically at the north basin station.
UFI sampled at 1 m depth intervals at both locations approxJOURNAL OF HYDRAULIC ENGINEERING / SEPTEMBER 1999 / 913
imately every week. The conditions at the south basin station
have been considered as well representative of the entire lake
(Devan and Effler 1984; Wodka et al. 1985).
MODEL DESCRIPTION
The model used for this study is based upon the well tested
and extensively used 3D hydrodynamic circulation model
ECOM, developed by Blumberg and Mellor (1987). It incorporates the Mellor and Yamada (1982) level 2-1/2 turbulent
closure model to provide a realistic parameterization of vertical mixing, and a free surface to simulate water level
changes. A system of curvilinear coordinates is used in the
horizontal which allows for a smooth representation of variable shoreline geometry. Unlike the ECOM (Blumberg and
Mellor 1987) vertical sigma coordinate transformation,
though, this new version of the model features an untransformed vertical coordinate (z-levels) system. It is this later
aspect which permits accurate solutions over steep bathymetry
without the need for high horizontal resolution. However,
without high vertical resolution, there is, relative to a sigma
coordinate system, some loss of accuracy in the density-driven
baroclinic circulation and a considerable degradation of predictive power in the bottom boundary layer. In a sense, this zlevel model is a reformulation of the version developed by
Blumberg and Mellor (1985), which was used to simulate the
dynamics of the Gulf of Mexico. A second major departure
from the ECOM model has to do with the time integration
scheme. This version uses a semi-implicit method where the
barotropic pressure gradient in the momentum equations and
the horizontal velocity divergence in the continuity equation
are treated implicitly. The implicit numerical algorithm permits
time steps many times greater than those based upon the Courant-Friedrichs-Levy (CFL) condition. This version of ECOM
will be called ECOMsiz to better reflect the new model features.
In a system of orthogonal Cartesian (for simplicity) coordinates with x increasing eastward, y increasing northward, and
z increasing upward, the equations governing the model, under
the simplifying assumption that the pressure is hydrostatic, are
⭸u
⭸v
⭸w
⫹
⫹
=0
⭸x
⭸y
⭸z
(1)
⭸u
⭸u2
⭸uv
⭸uw
⭸␩
⫹
⫹
⫹
⫺ fv ⫹ g
⭸t
⭸x
⭸y
⭸z
⭸x
=
⭸
⭸z
冉 冊
KM
⭸u
⭸z
⫺
g ⭸
␳0 ⭸x
冕
冉 冊
⭸v
KM
⭸z
g ⭸
⫺
␳0 ⭸y
␩
␳ dz ⫹ Fx
(2)
z
冕
␩
␳ dz ⫹ Fy
z
⭸T
⭸uT
⭸vT
⭸wT ⭸
⫹
⫹
⫹
=
⭸t
⭸x
⭸y
⭸z
⭸z
(3)
冉 冊
冉 冊
KH
⭸T
⭸z
⭸S
⭸uS
⭸vS
⭸wS ⭸
⫹
⫹
⫹
=
⭸t
⭸x
⭸y
⭸z
⭸z
FX =
⭸
⭸x
Fy =
⭸
⭸y
FT,S =
冉 冊 冋 冉
冉 冊 冋 冉
冉 冊 冉
⫹
KH
1 ⭸I
⫹ FT
␳0Cp ⭸z
(4)
⭸S
⭸z
(5)
⫹ FS
where ␩ = free surface height (upward positive from mean
water level); u, v, and w = velocity components along the x,
y, and z directions, respectively; ␳0 and ␳ = reference density
and in situ density of water, respectively; g = gravitational
acceleration; f = Coriolis parameter; KM = vertical viscosity for
momentum mixing; Fx and Fy = horizontal momentum diffusion in x and y directions, respectively; T is water temperature
and S is salinity; KH = vertical diffusivity for turbulent mixing
914 / JOURNAL OF HYDRAULIC ENGINEERING / SEPTEMBER 1999
冊册
冊册
冊
2AM
⭸u
⭸x
⫹
⭸
⭸y
AM
⭸u
⭸v
⫹
⭸y
⭸x
(6)
2AM
⭸v
⭸y
⫹
⭸
⭸x
AM
⭸u
⭸v
⫹
⭸y
⭸x
(7)
⭸
⭸y
AH
⭸
⭸x
AH
⭸(T, S)
⭸x
⫹
⭸(T, S)
⭸y
(8)
where the horizontal viscosity, AM, is calculated according to
Smagorinsky (1963) as
AM = C⌬x⌬y
冋冉 冊 冉 冊 冉
⭸u
⭸x
2
⭸v
⭸y
⫹
2
冊册
⭸u
⭸v
⫹
⭸y
⭸x
1
⫹
2
2
1/2
(9)
The parameter C is typically equal to 0.10; it ranges from 0.01
to 0.5 in various applications. Here, AH = AM, but the code
itself has provision to relax this constraint.
The vertical kinematic viscosity KM and diffusivity KH are
obtained by appealing to a 2-1/2 order turbulence closure
model (Mellor and Yamada 1982) and are given by
ˆ M ⫹ ␯M,
KM = K
ˆ M = qᐍSM,
K
ˆ H ⫹ ␯H
KH = K
(10)
ˇ H = qᐍSH
K
(11)
where q /2 = turbulent kinetic energy; ᐍ = turbulence length
scale; SM and SH = stability functions defined by solutions to
algebraic equations given by Mellor and Yamada (1982) as
modified by Galperin et al. (1988); and ␯M and ␯H = constants.
The variables q2 and ᐍ are found from the equations
2
⭸q2
⭸uq2
⭸vq2
⭸wq2 ⭸
⫹
⫹
⫹
=
⭸t
⭸x
⭸y
⭸z
⭸z
⫹ 2KM
冋冉 冊 冉 冊 册
⭸u
⭸z
2
⭸v
⭸z
⫹
2
⫹
冉 冊
Kq
⫹ E1ᐍ
再 冋冉 冊 冉 冊 册
KM
⭸u
⭸z
2
⫹
⭸v
⭸z
⭸q2
⭸z
2g
⭸␳
q3
KH
⫺2
⫹ Fq
␳0
⭸z
B1ᐍ
2q2ᐍ
2uq2ᐍ
⭸vq2ᐍ
2wq2ᐍ ⭸
⫹
⫹
⫹
=
⭸t
⭸x
⭸y
⭸z
⭸z
⭸v
⭸uv
⭸v 2
⭸vw
⭸␩
⫹
⫹
⫹
⫹ fu ⫹ g
⭸t
⭸x
⭸y
⭸z
⭸y
⭸
=
⭸z
of temperature and salinity; FT and Fs = horizontal diffusion
terms for temperature and salinity, respectively; ⭸I/⭸z = solar
radiation forcing term; and Cp = specific heat. The density of
water is calculated from temperature and salinity using an
equation of state (Fofonoff 1962).
The terms in the governing equations related to small-scale
mixing processes not directly resolved by the model are parameterized as horizontal diffusion:
2
⫹
冉
Kq
⭸q2ᐍ
⭸z
g
⭸p
KH
␳0
⭸z
冎
(12)
冊
⫺
q3 ˆ
W ⫹ Fᐍ
B1
(13)
where Kq = 0.2ᐍq, the eddy diffusion coefficient for turbulent
kinetic energy; Fq and Fᐍ represent horizontal diffusion of the
turbulent kinetic energy and turbulence length scale and are
parameterized in a manner analogous to either (10) or (11); Ŵ
= wall proximity function defined as Ŵ = 1 ⫹ E2(l/␬L)2; (L)⫺1
= (␩ ⫺ z)⫺1 ⫹ (H ⫹ z)⫺1; ␬ = von Kármán constant; H =
water depth, ␩ = free surface elevation; and E1, E2, and B1 =
empirical constants set in the closure model.
The boundary conditions on the continuity equation, (1), are
w(␩) =
⭸␩
⭸␩
⭸␩
⫹u
⫹v
⭸t
⭸x
⭸y
(14)
w(⫺H) = 0
(15)
The boundary conditions on (2) and (3) are
KM
冋 册
⭸u ⭸v
,
⭸z ⭸z
= ⫺(␶ox, ␶oy)/␳o,
z→␩
(16)
where the right-hand side of (16) corresponds to the input
values of the surface wind stress and at the bottom boundary
KM
冋 册
⭸u ⭸v
,
⭸z ⭸z
= Cz(u2 ⫹ v 2)1/2(u, v),
where
Cz = MAX
冋
␬2
,
(ln(z/zo))2
z → ⫺H
册
BFRIC
(17)
KH
冋 册
冋 册
⭸T ⭸S
,
⭸z ⭸z
= ⫺(Io, 0),
⭸T ⭸S
,
⭸z ⭸z
= (0, 0),
and
z→␩
(19)
z → ⫺H
(20)
where Io = surface heat flux.
The boundary conditions on (12) and (13) are
2
(q2, q2ᐍ) = (B12/3u␶S
, 0),
(q , q ᐍ) = (B u , 0),
2
2
2/3 2
1
␶B
(u)n⫹1 = F(u) ⫺ g
⭸␩n⫹1
⭸x
(25)
(v)n⫹1 = F(v) ⫺ g
⭸␩n⫹1
⭸y
(26)
冕
(27)
(18)
␬ = 0.4 is the von Kármán constant; zo = roughness parameter;
and BFRIC is a user-specified friction coefficient. Numerically,
(17) and (18) are applied to the first grid point nearest the
bottom. The bottom stress is determined by matching the bottom velocities with the logarithmic law of wall. Where the
bottom is not well resolved (z/zo is large), (18) reverts to an
ordinary drag coefficient formulation.
The boundary conditions on (4) and (5) are
KH
where ADVU and ADVV represent all the remaining terms in (2)
and (3). The time differencing leads to:
z→␩
(21)
z → ⫺H
(22)
where B1 = one of the turbulence closure constants as defined
earlier; and u␶S and u␶B = friction velocity at the surface and
bottom as denoted.
The boundary conditions along the vertical sidewalls at the
shoreline are that the normal component of the flow is zero
and a free slip condition is used for the tangential component.
The normal gradient of all the scalar parameters (T, S, q2, l)
are also zero.
The shortwave solar radiation gradient term ⭸I/⭸z in (4) is
determined based on the parameterization of downward irradiance described as I = Ioekz, where Io = incoming solar radiation at the water surface; k = extinction coefficient; and z =
depth. It has been found that proper parameterization of downward irradiance is crucial for accurate prediction of upper layer
thermal structure. In the present study, the value of k has been
used based on photometric measurement conducted at the
southern deepest station of the Onondaga Lake by Effler and
Perkins (1996).
The equations that form the circulation model, together with
their boundary conditions and after transformation to orthogonal, horizontal curvilinear coordinates, are solved by finitedifference techniques that are very similar to those of Blumberg and Mellor (1987), so stability conditions contained
therein apply here as well. The same horizontally and vertically staggered lattice of grid points is used for the computations. An implicit numerical scheme in the vertical direction
and a semi-implicit scheme in the horizontal direction (Casulli
1990) are new here. The semi-implicit treatment is patterned
after Casulli (1990) and Casulli and Cheng (1992). Basically,
the treatment involves taking the free surface gradient in momentum equations (2) and (3) and solving the velocity divergence in continuity equation (1) implicitly. Consider the Reynolds equations [(2) and (3)] in the forms
⭸u
⭸␩
⫹ ADVU ⫹ g
=0
⭸t
⭸x
(23)
⭸v
⭸␩
⫹ ADVV ⫹ g
=0
⭸t
⭸y
(24)
⭸␩
⭸
⫹
⭸t
⭸x
冕
␩
n⫹1
(u)
⫺H
⭸
dz ⫹
⭸y
␩
(v)n⫹1 dz = 0
⫺H
The F(u, v) terms in (25) and (26) represent the solution to
(23) and (24) at time level n ⫹ 1, where the contribution from
the ⭸␩/⭸x and ⭸␩/⭸y terms has been deferred until now (operator splitting). Substituting momentum equations (25) and
(26) into free surface equation (27), leads to a linear fivediagonal system that is solved for the water surface elevation
at time level n ⫹ 1 over the domain of interest. Such a linear
system is symmetric, positive definite and is solved by an efficient preconditioned conjugate gradient method (Casulli and
Cheng 1992).
This new model was constructed out of the ECOM computer code making as few changes as possible. The basic structure of the model variable names and variable indexing all
have been retained. The veracity of the z-level model introduced in the present study has been established by performing
several tests involving idealized geometries and forcing functions. Many tests are quite simplistic, checking the model’s
ability to conserve its various constituents, e.g., mass, heat and
salt. Other tests involve wave propagation over flat and gently
sloping bathymetry. More rigorous tests involve both the barotropic and baroclinic responses of an idealized coastal basin
with or without topography, sufficiently large to evolve large
scale oceanographic phenomena such as Ekman layer drift,
upwelling and downwelling, etc. The results from the flat bottom case demonstrate that the model reproduces the expected
physics and produces identical results to those from the well
tested ECOM model. In the second test, forced flow over an
undersea mountain in stratified conditions, the model results
show a stationary anticyclonic feature above the topographic
hump and a counter-cyclonic eddy that is eventually advected
by the downstream currents. This result is in agreement with
theory and the ECOM model results. The above two tests provide a high degree of confidence that the present model has
been properly developed.
MODEL GRID
As discussed earlier, Onondaga Lake is characterized by
marked varying depths from 0 m to as deep as 19.5 m in the
deepest section of the lake. In particular, a steep vertical gradient of about 0.05–0.06 exists along the periphery of the lake,
wherein the depth increases 12 m within a few hundred meters.
A 14 ⫻ 24 boundary fitted orthogonal curvilinear grid is developed, as shown in Fig. 2. The grid, which follows the lake
bathymetric contours, allows the mesh resolution to vary spatially having a minimum grid spacing of 90 m and a maximum
spacing of 600 m. The model uses a z-coordinate system that
discretizes the vertical domain of the lake into 19 levels, each
of 1 m thickness. These levels are spatially and temporally
constant, except the top level thickness, which varies with water level fluctuations.
FORCING FUNCTIONS
The major objective of the present study is to reproduce the
hydrodynamic and thermal features of the lake, particularly
JOURNAL OF HYDRAULIC ENGINEERING / SEPTEMBER 1999 / 915
FIG. 2.
Orthogonal Curvilinear Grid (14 ⫻ 24) of Onondaga Lake
during the summer months, where marked temperature and
salinity vertical structure exist. The model requires appropriate
forcing functions, necessary to reproduce the observed physics
of the lake. The model forcing information consists of freshwater inflows, temperature and salinity, surface wind stress,
and surface heat fluxes.
In the present study, emphasis has been on calibrating the
model for the year 1985 (a year marked by the elevated thermal and ionic discharges from the chlor-alkali facilities) and
then validate the model for the year 1989 (after the closure of
the chlor-alkali plant), when the ionic waste discharges have
been reduced substantially. In addition, this study is further
intended to evaluate lake hydrothermal dynamics during the
most stratified period of the year. In particular, this study focuses on the time period between April and October. This period is marked by well mixed conditions in the spring, strong
vertical stratification in the summer, and the recurrence of
mixed conditions in the fall.
Freshwater Inflows
The major tributaries that have been included in the present
modeling framework are Ninemile Creek, Harbor Brook, Onondaga Creek, and Ley Creek (Fig. 1). Since tributaries such
as Bloody Brook and Sawmill Creek have insignificant hydrological loading compared with the previously mentioned tributaries, they are not considered. Of the municipal and industrial discharges, only METRO and, for 1985, the chlor-alkali
plant’s intake and effluent discharges are included in the modeling framework.
Year-to-year variations in freshwater inflow are attributed to
916 / JOURNAL OF HYDRAULIC ENGINEERING / SEPTEMBER 1999
variations in snowfall and precipitation (Effler and Whitehead
1996). The highest rates of inflow usually occur in March and
April, just after snowmelt. Inflow decreases through the late
spring and summer. The minimum usually occurs during late
summer and early fall. Inflow, however, can increase to intermediate levels due to rainfall in late fall and winter.
A significant difference in freshwater inflows is observed in
1985 and 1989, as shown in Fig. 3. This difference is attributed to higher precipitation in 1989 (36.9 in. as compared with
32.5 in. in 1985). Strong seasonal variations in tributary flows
are also observed in these years. As can be seen in Fig. 3,
high flows are observed in 1989 in all tributaries during May,
June, September, and October. These high flows are associated
with high precipitation of 4.27, 5.41, 5.96, and 4.08 in., respectively, during those months. Inflow from the METRO facility is relatively uniform, although there are small increases
in flow during the August–September period of both years.
The chlor-alkali plant discharge is included in the 1985 calibration; this flow is zero in 1989, as the plant had ceased
operation in 1986.
The model ends at the connection to the Seneca River.
Flows at this boundary are computed using the principle of
water mass balances of the lake involving net flows into the
lake and the rate of change of the lake water level measured
at the marina (Fig. 1). The boundary conditions at the lake
outlet allow flow reversals, depending on the freshwater inflow
and water level conditions in the lake. However, bidirectional
vertical distribution of flows were not considered, as little information on them was available. Effler (1987), for example,
has confirmed that occasionally these vertical flow distributions exist in the area of the lake outlet.
FIG. 3.
Hydrologic and Hydrographic Inputs to Model
Tributary discharges were distributed equally in all 19
model layers. However, the point source discharges and withdrawals were made at different levels depending on their actual vertical positions. For example, the chlor-alkali plant cooling water withdrawals were made at model layers 11, 12, and
13 (10.75 m, 11.75 m, and 12.75 m) and discharges were
introduced at layers 3, 4, and 5 (2.75 m, 3.75 m and 4.75 m);
the METRO discharges were introduced at layers 5, 6, and 7
(4.75 m, 5.75 m and 6.75 m).
Temperature and Salinity
The model is forced by the temperature and salinity loads
accompanying the tributary, municipal, and industrial inflows.
Fig. 3 provides information on salinity and temperature associated with all tributary inflows as well as at METRO and the
East Flume (chlor-alkali) discharges for 1985 and 1989. As
can be seen from this figure, 1985 has significantly higher
salinity as compared with 1989. Ninemile Creek was the largest source of salinity discharged to the lake contributing between 65 and 80% of the total load, followed by Onondaga
Creek, which contributed between 5 and 25% of the salinity
loading to the lake. METRO salinity in 1985 is higher as compared with 1989. This resulted from the diversion of a portion
of the chlor-alkali process waste stream to the METRO facility
to assist in the removal of phosphorus from its discharge.
METRO salinity in 1989 again reflects the closure of the chloralkali facility. Fig. 3 also illustrates the temporal variations of
inflow temperature for the years 1985 and 1989. Seasonal variations in temperature in 1985 and 1989 are evident in all
sources, with low temperature during winter and spring and
high temperature during summer. The temporal variation in
temperature in the tributaries and at METRO have similar patterns for both years except for a marked deviation of about
5⬚C in tributary temperatures at the beginning of April in 1989.
In 1985, the East Flume discharged an elevated thermal load
to the lake. This load is associated with the chlor-alkali plant’s
use of lake water for cooling processes. The East Flume thermal load is absent in 1989, because the chlor-alkali had ceased
operation in 1986.
Ninemile Creek received chloride and other ionic wastes
associated with runoff and leachates of waste beds adjacent to
the chlor-alkali plant until its closure in early 1986. The creek
still continues to receive leachate from these waste beds, albeit
at a reduced rate. These leachates account for the elevated
salinity in Ninemile Creek discharges in 1989. Salinity in Onondaga Creek was consistent in 1985 and 1989 with small
increases in July, August, and early September. For accurate
modeling, daily loads of temperature and salinity need to be
provided as input to the model. Unfortunately the tributary
temperature and salinity data were only collected biweekly by
the D&S, while the USGS flow data used in the model were
recorded on a daily basis at the same gauged locations. Model
results will be very sensitive to loadings; therefore, it was important to estimate thermal and salinity loadings using a regression analysis. The temperature of the tributary flow, however, reflects the seasonal variation of temperature and is
therefore not expected to be correlated with tributary flow.
Attempts were made to find correlations between flow and
chloride concentrations in all tributaries, including METRO
JOURNAL OF HYDRAULIC ENGINEERING / SEPTEMBER 1999 / 917
inflows. No correlation exists between flow and Cl concentration for METRO, Harbor Brook, Ley Creek, or Onondaga
Creek. However, a strong correlation between flow and Cl
concentration was observed for Ninemile Creek (Doerr et al.
1994). Therefore, for Ninemile Creek, the regression formula
was used to estimate the Cl concentration associated with daily
flow measurements, and, for other tributaries, biweekly Cl
concentration data were used for loading computations.
Surface Wind Stress
Wind data available from the nearby Syracuse International
Airport (Hancock Airport), located 8.5 km northeast of Onondaga Lake, have been used to force the model. It is well
known that atmospheric data collected at land-based stations
does not represent over-water conditions (Hsu 1988), particularly with regard to wind speed. This is because there are
large gradients in heat, moisture, and momentum transfers that
occur between land and water. In particular, the air-water temperature difference contributes significantly to wind speed and
direction. On the other hand, the frictional effects of land orography may be very different from over-water conditions. For
a significantly large open water body, it has been demonstrated
(Hsu 1988) that over-water wind speed is increased substantially over land wind. However, for a small lake, such as Onondaga Lake, it may be reasonable to assume that ‘‘canopy’’
effects, from surrounding highlands, forests, and/or buildings,
may substantially reduce high frequency gusty wind fields. It
was therefore assumed that, due to the canopy effects from
the lake surroundings, the high frequency signals present in
the data at the airport were not present at the lake surface.
Thus, in the present study, winds have been filtered to remove
fluctuations with periods less than 12 hours.
Surface Heat Fluxes
The energy content in lakes and reservoirs is primarily governed by the surface energy exchanges. However, for shallow
and transparent lakes and reservoirs, the heat exchanges
through water-sediment interface may also play an important
role in the heat budget (Tsay et al. 1992). Measurements of
heat fluxes such as solar radiations, atmospheric radiation, sensible heat, and latent heat fluxes are very difficult and costly
to make and are often parameterized to obtain the fluxes, using
the commonly available meterological and atmospheric data.
The processes that control the heat exchange between the water and atmosphere are well documented (Clark et al. 1974;
Edinger et al. 1974; Large and Pond 1982; Fung et al. 1984;
Schertzer 1987; Rosati and Miyakoda 1988; Hondzo and Stefan 1993; Cole and Buchak 1995). All of these works relied
mostly on the bulk formulas to evaluate the components of
the heat budget. It is important to note here that most of the
bulk formulas available in literature for calculations of radiative fluxes are based on basically the same principles and generally agree with one another in general patterns of temporal
and spatial variations of fluxes. However, significant differences in their magnitudes exist, depending on the time period
of the year and the latitudinal position of the study area.
Estimation of net heat fluxes requires a great deal of judgement in choosing the bulk formulas, which are dependent on
many uncertain atmospheric parameters like cloud cover, humidity, and temperature. Four major heat flux components,
such as short wave solar radiations, longwave atmospheric radiations, sensible heat, and latent heat fluxes have been used
in the present study, largely based on the formulas reported in
Cole and Buchak (1995) suggested by Edinger et al. (1974).
Fig. 4 shows the schematic diagram of these processes. The
solar radiation data for the years 1985 and 1990 are provided
by the National Climatic Data Center and are directly used by
918 / JOURNAL OF HYDRAULIC ENGINEERING / SEPTEMBER 1999
FIG. 4. Schematic Diagram of Heat Budget Showing Heat Flux
Components
the model; therefore, no estimation for solar radiation was necessary in the current application. Details of the formulation of
other pieces of heat fluxes are described below.
Atmospheric Radiation
The net atmospheric radiation at the surface is the result of
two processes: the downward radiation from the atmosphere
and the upward radiation emitted by the water surface. This
longwave radiation ranges in wavelength between 4 and 120
␮ and has a peak intensity at about 10 ␮. Atmospheric radiation depends primarily on the air temperature, humidity, and
cloud cover. The magnitude of the atmospheric radiation
largely depends on the moisture content of the air and constitutes the major component of heat exchange processes during
the night and during cloudy conditions (Edinger et al. 1974).
The physics of the longwave radiation is simply a black body
radiation, and the magnitude is directly proportional to the
fourth power of the absolute temperature. Nevertheless, the
computation for the downflux is more complicated, as it evaluates the effects of changes in atmospheric temperature, humidity, cloud, aerosol distribution, carbon dioxide, and other
atmospheric constituents. Among several commonly referenced bulk formulas, Brunt (1932) suggested that the downflux depends on the square root of the near-surface vapor pressure (ea). In the present study, a Swinbank (1963) formulation
has been used, which suggests that ea is strongly correlated
with the air temperature (Ta) and evaluates the downflux as a
function of Ta alone. The net atmospheric flux is given as
Ha = ε␴((9.37 ⫻ 10⫺6T 6a)(1 ⫹ 0.17C 2) ⫺ T 4S)
(28)
Here, Ha = net longwave atmospheric radiations (Wm ); ε =
emissivity of the water body (0.97); ␴ = Stefan-Boltzmann
constant (5.67 ⫻ 10⫺8 Wm⫺2K⫺4); Ta = atmospheric temperature in ⬚K; TS = water temperature in ⬚K; and C = cloud
fraction (0–1).
Swinbank’s formulation is sometimes found more attractive
when surface humidity observations are not as readily available as air temperatures (Fung et al. 1984). This may also be
attractive when a land-based meteorological station is too far
from the lake and may not provide site-representative relative
humidity data.
⫺2
Sensible Heat Flux, Hc
Heat exchange can occur between the atmosphere and a
water body through conduction. The heat flux may be in either
direction, depending on the sense of the temperature differences between the air and the water body. It has been shown
(Edinger et al. 1974) that the daily rate of heat conduction is
about an order of magnitude less than other dominant processes. The flux of conduction heat is commonly parameterized by the bulk transfer formula with dependencies on wind
speed as suggested by Edinger et al. (1974):
Hc = Cc f (W )(Ts ⫺ Ta)
(29)
where Hc = sensible (conduction) heat fluxes (Wm⫺2); Cc =
Bowen’s coefficient (0.62 mb/K); f (W ) = wind speed function,
defined as a0 ⫹ a1W ⫹ a2W (Wm⫺2mb⫺1); and Ts and Ta =
water and air temperature, respectively, as defined earlier.
The coefficients a0, a1 and a2 are chosen based on Brady et
al. (1969) and suggested by Edinger et al. (1974). Significant
discrepancies in formulating the wind speed function have
been reported in the latter studies, suggesting a wide variety
of opinions among researchers. Suggestions have been made
as to whether conduction processes will remain to a negligible
molecular scale in the absence of wind or if other small scale
processes, such as conduction currents due to density instabilities, may dominate. The latter concept has gained significant favor due to the fact that density instabilities exist during
conduction and evaporation from thermally loaded water surface or during the night when the air temperature may be less
than the water temperature. Following Brady et al. (1969) and
Edinger et al. (1974), a slightly conservative formulation has
been adopted in this study:
f (W ) = 6.9 ⫹ 0.345W 2
(Wm⫺2 mb⫺1)
(30)
where W = wind speed in m/s, measured at 7 m above the
water surface. For both the sensible and the evaporative heat
flux computations, the evaporative wind speed function f (W )
is a somewhat uncertain parameter (Cole and Buchak 1995).
Various formulations of f (W ) have been examined in Edinger
et al. (1974). Cole and Buchak (1995) termed the wind speed
in this function as a ‘‘ventilation speed’’ rather than a vector
velocity speed, as used in the wind stress computations. This
ventilation speed is somewhat lower than the actual wind
speed measured in a distant land-based meteorological station,
which accounts for the sheltering and canopy effect by the
surroundings of a water body. A wind shelter coefficient has
been introduced by Cole and Buchak (1995) that has a range
of 0 to 1, depending on the shape and size of the water body.
For the Onondaga Lake model, a shelter coefficient of 0.85
has been used for both the simulation years, 1985 and 1989.
the model used in the present study. In particular, this study
is intended to evaluate the lake dynamics under various forcing
conditions during the most stratified period of the year. The
period chosen, April through October, spans the entire range
of lake physical processes, as it covers the well-mixed spring
condition, the summer period, marked by strong vertical stratification, and the well-mixed fall period. In order to realistically reproduce the lake temperature and salinity data, the
model is forced by tributary inflows, with their attendant temperature and salinity loads, surface winds, and surface heat
flux. The tributary and industrial thermal loads and prevailing
wind fields dictate the dynamics and, therefore, the patterns of
the lake surface temperature; however, the amplitude is greatly
influenced by the surface heat flux and its penetration through
the water column. Any systematic error in the heat flux computations would result in unrealistic lake surface temperature
obtained by the model simulations.
Model simulations have been performed for seven months
from April through October for both the years 1985 and 1989
using the forcing functions described earlier. Selected features
of the model-simulated stratification regimes of the lake have
been compared with the observed data. Fig. 5 illustrates the
model-computed surface and bottom temperatures compared
with the observed data from those respective depths. It is
clearly evident that the model reproduces the surface and bottom temperature of the lake very well. The difference in temperature between the water surface and the lake bottom is substantial during the summer months for both years. Moreover,
considerable variations of temperature differences also exist
between these two years with the model predicting such differences accurately. In 1985, stratification was rapidly established at end of April, and the model successfully predicted
Evaporative Heat Flux, He
The evaporative heat fluxes are related to the conductive
heat fluxes by the Bowen ratio and can be given as a function
of wind speed and the difference between the saturated water
vapor pressure at the water surface temperature and the water
vapor pressure in the overlying air (Edinger et al. 1974):
He = f (W )(es ⫺ ea)
(31)
⫺2
where He = evaporative heat flux (Wm ); es = saturated vapor
pressure at temperature Ts (mb); and ea = air-vapor pressure at
temperature Ta (mb).
MODEL CALIBRATION AND VALIDATION
The two years, 1985 and 1989, selected for calibration and
validation of the model provide a marked range in hydrographic regimes within the lake and also significantly different
freshwater inflows, ionic loadings, and wind forcing. It is,
therefore, anticipated that calibrating and validating the model
for these two years would firmly establish the robustness of
FIG. 5. Comparison of Model Computed Surface and Bottom
Temperatures with Observed Data for: (a) 1985; (b) 1989 Simulation Periods
JOURNAL OF HYDRAULIC ENGINEERING / SEPTEMBER 1999 / 919
its onset. In contrast, the surface and bottom temperature stratification in 1989 started to establish itself at the beginning of
April; however, the thermal stratification was very weak and
was readily mixed by the wind events at the surface. After
several mixing events in April and early May, a permanent
stratification became established. The model has been able to
reproduce all these events successfully. Prediction of the fall
turnover in 1985 was another physical feature of lake dynamics simulated fairly well by the model. In 1985, the model’s
turnover was fairly accurate (about a week earlier than the data
shows); however, in 1989 the model predicted a fall turnover
that occurred at about two weeks later than observed.
An analysis of the wind data used to force the model during
this latter year revealed that, during the overturn period, the
wind was blowing across the lake, imparting less energy into
lake mixing than had blown along the longitudinal axis of the
lake. It may be noted here that the wind-induced mixing occurs
in two ways: (1) by producing turbulence at the surface, which
in turn propagates through the mixed layer to erode the thermocline; and (2) by producing a bulk movement of water that
generates velocity shear across the density interface, introducing instability in the water column and causing enormous mixing. The bulk movement of water or velocity shear is largely
controlled by the length scale of a physical system. Along the
longitudinal direction, the bulk movement appears considerably larger than of that in the lateral direction. It has been
shown in several studies, e.g., Blumberg and Goodrich (1990),
that the mixing events are associated more strongly with internal velocity shear than the surface turbulence generated by
the wind. Therefore, it is anticipated that a slight change in
wind direction along the longitudinal axis could easily result
in an earlier overturn. This underscores the need for measuring
winds that occur over the lake rather than at a distant landbased measuring station where the wind field may be significantly different in terms of both magnitude and direction.
Fig. 6 illustrates vertical profiles of predicted temperature
compared with data starting from the well mixed spring condition through the fall turnover for the years 1985 and 1989,
respectively. Solid lines represent model-computed temperature profiles. The numbers at the top and bottom of each profile indicate the surface and bottom temperature in degrees
Celsius. The time of the vertical profile can be found by considering the horizontal position of the bottom temperature profile. It is quite apparent from these two figures that the upper
mixed layer depth in 1985 is deeper as compared with the
1989 mixed layer, a result of the stronger winds which prevailed in 1985. These figures demonstrate the model’s ability
to reproduce the entire vertical profile of the observed water
temperature. In general, the model captures both the seasonal
and vertical distributions observed in the data.
It is also useful to assess how well the model can predict
the observed salinity structure of the lake, since it plays an
important role in determining the vertical density structure.
Fig. 7 illustrates a comparison of the seasonal variation of the
vertical density distribution (␴t) in the water column from the
model and from observed data. The profile is taken at the
deepest section of the southern basin of the lake for the years
1985 and 1989, respectively (see Fig. 1 for station location).
Both the model and the data begin with a well mixed water
column during April. As can be seen from the figures, both
the model and the data show the formation of pycnocline at
depths of about 9 m and about 6 m during 1985 and 1989,
respectively. However, it appears that the thermal deepening
in the model is slightly slower than in the observations. In
1985, the model predicts formation of pycnocline in late August, while the data shows it to form in late June. The fall
turnover occurs in mid-October in both the model results and
observations. In 1989, the model-simulated pycnocline and the
data are shown to form at about the same time in June. However, the fall turnover occurs at the end of October, while the
observations suggest it to occur during the middle of October.
Overall, the model appears to reproduce the characteristics of
the lake’s density dynamics both spatially and temporally.
Finally, the model-computed lake-wide heat storage shown
in Fig. 8 is in good agreement with observations for both
years. Both the model and the data show a distinct seasonality
FIG. 6. Model Calibration of Vertical Temperature Structure with Observed Data (Open Circle) at South Basin Station for: (a) 1985; (b)
1989 Simulation Periods (Numbers Indicated at Top and Bottom of Each Profile Represent Surface and Bottom Temperature in Degrees
Celsius; Time of Vertical Profiles Can Be Found by Considering Horizontal Position of Bottom Temperature Profile)
920 / JOURNAL OF HYDRAULIC ENGINEERING / SEPTEMBER 1999
FIG. 7. Comparison of Model Computed Temporal and Vertical Distribution of Isopycnal with Observed Data during: (a) 1985; (b)
1989 Simulation Periods
of heat storage with low storage in spring time and a substantial gain in heat storage during the summer heating months.
The lake heat storage starts depleting during the fall and winter, when significant heat loss occurs.
DISCUSSION AND CONCLUSIONS
As part of the efforts to simulate the hydrothermal conditions of a small urban lake, a newly developed 3D hydrodynamic model was applied for the years 1985 and 1989. The
model is based on the extensively used estuarine, coastal, and
ocean model developed by Blumberg and Mellor (1987). It
incorporates the Mellor and Yamada (1982) level 2-1/2 turbulent closure model to provide a realistic parameterization of
vertical mixing. Unlike the original Blumberg and Mellor
(1987) model, this model features an untransformed vertical
coordinate (z-level) system and uses a semi-implicit integration scheme. The two years selected for calibration and validation of the hydrodynamic model provide a marked range in
hydrographic regimes within the lake as well as significantly
different freshwater inflows, ionic loadings, and wind forcing,
which helped establish the robustness of the model used in the
study.
The model is capable of reproducing the major physical
processes operating in the lake. It reproduces the overall seasonal variation of the temperature very well. The model has
successfully been able to predict the mixed layer depth for
both 1985 and 1989. The mixed layer depth in 1985 is about
3 m deeper (about 9 m) than that in 1989 (6 m). The cause
of this difference is identified as the stronger wind that prevailed in 1985. This was confirmed by performing two model
simulations, switching 1989 meterological conditions (much
weaker winds than those of 1985) for the 1985 simulation and
1985 meteorological conditions for the 1989 simulation. All
other forcing functions, including inflows and salinity and
temperature loadings associated with these flows, were kept
the same. The model predicted shallower mixed layer depths
and hotter surface temperatures in 1985 and deeper mixed
layer depths and cooler surface temperatures in 1989, suggesting that the wind is the dominant forcing function in determining the mixed layer depth. Hotter and cooler surface
temperatures in 1985 and 1989, respectively, are mostly because of a smaller and larger volume of upper mixed layer.
Heat distributed over a larger volume (large mixed layer depth)
of water will result in a lower temperature than if distributed
in a smaller volume (small mixed layer depth) of water. Another possible cause of surface temperature differences in these
two years of test simulations could be associated with less and
more evaporative heat losses in 1985 (weaker wind) and 1989
(stronger wind), respectively. No changes in fall turnover periods were predicted by the model in either of the years.
Although the model captures the vertical thermal and density structure very well, the thermal deepening of the model
was slower than the observations. The model-computed lakewide heat storage is in good agreement with the observation
for both years, suggesting the use of an appropriate formulation for heat flux computations for the lake.
The hydrodynamic model developed in this study is capable
of accurately simulating the dynamics and thermal structure of
the lake, which are considered to be important features regulating biological and chemical processes of a surface water
body. The model-computed transport and mixing fields, along
with thermal and salinity structure, can be used by a coupled
water quality model simulating biological and chemical processes of a natural system. The current model can be used for
both small and large lakes and reservoirs where knowledge of
temperature and density stratification is important for assessing
the water quality of the lake.
JOURNAL OF HYDRAULIC ENGINEERING / SEPTEMBER 1999 / 921
FIG. 8.
Model Computed Lake Wide Heat Storage Compared with Observed Data for (a) 1985; (b) 1989 Simulation Periods
ACKNOWLEDGMENTS
The writers thank James J. Fitzpatrick for sharing his great insight into
the physical, chemical, and biological processes of Onondaga Lake with
them. Dr. C. Kirk Ziegler contributed to the coding of the model in its
early stages of development. The writers also thank John G. Sondey, who
contributed to improving the quality of figures. This study was partially
supported by HydroQual’s Research and Development program through
project #RD950054.
APPENDIX.
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