Journal of Great Lakes Research 42 (2016) 511–523

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Journal of Great Lakes Research

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Simulating the thermal behavior in Lake Ontario using EFDC

Rumana Reaz Arifin a,b,⁎, Scott C. James c, Dilkushi A. de Alwis Pitts b,1, Alan F. Hamlet a,Ashish Sharma d, Harindra J.S. Fernando a

a University of Notre Dame, Department of Civil & Environmental Engineering and Earth Sciences (CEEES), 156 Fitzpatrick Hall, Notre Dame, IN 46556, USAb Center for Research Computing (CRC), University of Notre Dame, P.O. Box 539, Notre Dame, IN 46556, USAc Baylor University, Departments of Geosciences and Mechanical Engineering, Center for Reservoir & Aquatic Systems Research, The Institute of Ecological, Earth & Environmental Science,One Bear Place #97354, Waco, TX 76798-7354, USAd Environmental Change Initiative (ECI), University of Notre Dame, 1400 East Angela Boulevard, Unit 117, South Bend, IN 46617, USA

⁎ Corresponding author at: University of Notre DEnvironmental Engineering and Earth Sciences (CEEESDame, IN 46556, USA. Tel.: +1 574 387 9326.

E-mail address: rarifin@nd.edu (R.R. Arifin).1 Present address: University of Cambridge, UK.

http://dx.doi.org/10.1016/j.jglr.2016.03.0110380-1330/© 2016 International Association for Great Lak

a b s t r a c t

a r t i c l e i n f o

Article history:Received 7 August 2015Accepted 13 March 2016Available online 19 April 2016

Communicated by Ram Yerubandi

The thermal behavior of LakeOntario (springwarming, thermal bar formation, and summer stratification) is sim-ulated using the three-dimensional thermo-hydrodynamic model, Environmental Fluid Dynamics Code (EFDC).The model is forced with hourly meteorological data from weather stations around the lake and flow data fromNiagara and St. Lawrence Rivers. The simulation is performed from April to July 2011 on a curvilinear grid, withcells approximately 2 × 2 km2 and bathymetry interpolated onto the grid. We implement model improvementsby (a) updating the evaporation algorithm to ensure accurate simulation of evaporation rates and latent heatfluxes and (b) specifying appropriate solar radiation attenuation coefficients to ensure sufficient absorption of in-coming solar radiation by thewater column. The study also calibrated horizontal and verticalmixing coefficients.Results show that themodel accurately simulated the overall surface temperature profileswith RMSEs between 1and 2 °C and the vertical temperature profiles during the lake mixed phase with RMSEs b0.5 °C. Overall, themodified EFDC model successfully replicated thermal bar evolution.

© 2016 International Association for Great Lakes Research. Published by Elsevier B.V. All rights reserved.

Index words:EFDCLake OntarioNumerical water temperature simulationThermal mixing and stratificationThermal bar

Introduction

Lake Ontario, located at a temperate latitude and having the greatestdepth to surface area ratio of the five Great Lakes, displays thermal barphysics. This phenomenon was first reported on Lake Ontario byRodgers (1968). A thermal bar is a plume of dense, sinking water at4 °C, the temperature of maximum density, which forms in temperatelakes in the spring and/or fall (de Alwis, 1999; Rao and Schwab,2007). As spring heating proceeds from nearly 0 °C, the water warmsby solar and convective heating.When temperatures reach 4 °C in near-shore areas, the deeper portions of the lake still experience convectionas temperatures remain below 4 °C. Therefore, double-cell convectiondevelops with a dense downwelling current at ~4 °C in the narrowzone between the convection cells known as the thermal bar (Raoet al., 2004; Zilitinkevich et al., 1992). The thermal bar moves progres-sively towards the deepest portion of the lake until it finally disappearsas summer stratification develops throughout the lake in late May orearly June (de Alwis, 1999).

ame, Department of Civil &), 156 Fitzpatrick Hall, Notre

es Research. Published by Elsevier B

During summer stratification, near-surfacewater (the epilimnion) isheated through direct solar radiation and by wind mixing; the dense,cold water remains at the bottom of the lake (hypolimnion). Summertemperature differences establish vertical density gradients (thermo-cline) that act as a barrier between the epilimnion and hypolimnion.The thermocline is not an absolute barrier as strong winds can disruptit (Seker-Elci, 2004). During strong wind or storm events, turbulentmixing within the water column disrupts the thermocline and wind-driven mixing and heat flux penetrate deeper into the water column.

Lake thermal characteristics such as the spring thermal bar and sum-mer thermocline formation have significant environmental impacts onthe nearshore lake health and nutrient exchange rates. The thermalbar traps any shore- or river-released nutrients near the edges of thelake compounding eutrophication problems associatedwith high nutri-ent loading and limited horizontal mixing (Holland and Kay, 2003).Transient wind-driven upwelling or downwelling of the thermoclinein coastal waters is another physical process that affects mixing andtransport of contaminated waters in the nearshore by bringingnutrient-rich subsurface waters to the surface during upwelling (Raoand Schwab, 2007). It is noted that despite significant water-qualityimprovement in the open waters of Lake Ontario, nearshore waterscan still suffer from a number of impairments that limit their recreation-al use and ultimately affect the economic development of the region(Makarewicz and Howell, 2007).

.V. All rights reserved.

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Lake Ontario's thermal behavior has been previously investigatedbecause of its environmental significance. Thermal bar formation andits characteristics (propagation,flow circulation, andmixing coefficientsassociated with thermal bar) have been investigated with laboratory-scalemodels (Elliott and Elliott, 1970), theoretical analyses, and numer-ical models (Csanady, 1971; Gbah and Murthy, 1998; Malm, 1995;Scavia and Bennett, 1980; Zilitinkevich et al., 1992). Propagation of thethermal bar has been characterized by Elliott and Elliott (1970),Zilitinkevich et al. (1992), and Malm et al. (1993). The formation ofthermal bar in Lake Ontario was simulated for 1997–1999 using thetime-dependent, 3D hydrodynamic model ALGE by de Alwis (1999).Simulated lake surface temperatures were compared and validatedwith Advanced Very High Resolution Radiometer (AVHRR) satelliteimages. Rao et al. (2004) used observations from thermistors andcurrent meters in Lake Ontario to study spring thermal bar circulationand its effects on horizontal and vertical mixing processes. Their studydescribed that the thermal bar decreased the magnitude of bothalongshore and cross-shore horizontal exchange coefficients therebyinhibiting horizontal exchange of water.

In recent studies of Lake Ontario, the influence of atmospheric condi-tions on summer thermal stratification patterns has been of keen inter-est. Huang et al. (2010a) described thermal modeling on Lake Ontariousing the Princeton Ocean Model (POM) and simulated variations oflake surface temperatures and vertical stratification at seasonal and syn-optic time scales. They found that surface net heat flux had a significantimpact on simulated water temperatures in the surface and near-surface layers, whereas lack of proper implementation of wind stressin the epilimnion caused significant deviations from the measuredthermocline. Processes at the air/water interface such as wind, waves,and heat flux govern the exchanges of heat, kinetic energy, momentum,and concentrations (e.g. TSS and chlorophyll-a) (Hall, 2008;Wüest andLorke, 2003). In large lakes, thermal structures are driven byatmospheric conditions such as air temperature, heat transfer at theair–lake interface, precipitation, evaporation, and winds (Gibson et al.,2006; Huang et al., 2010b).

In this paper, we investigate the thermal characteristics of Lake On-tario, specifically spring warming, thermal bar formation, and summerstratification using the 3D hydrodynamic model, Environmental FluidDynamics Code (EFDC). In particular we evaluate the suitability ofEFDC for thermal hydrodynamic modeling of large, deep, temperatelakes like Lake Ontario. The heat flux components were explored toimprove EFDC model skill in matching observed temperatures. In theMethods section, (1) evaporation algorithm was updated to ensurecorrect evaporation rate and net surface heat flux computation,(2) solar radiation attenuation coefficients were calibrated to ensuresufficient absorption of incoming solar radiation. Finally, the formationof the thermal bar is presented to demonstrate the utility of the model.

EFDC is a surface water model that incorporates fully integratedhydrodynamics, sediment dynamics, and water quality components(Hamrick, 2007a, 2007b). The model uses the hydrostatic assumptionwhen simulating vertical flows. Despite its significant depth, LakeOntario has a low depth to length ratio, the vertical scale of mean prop-erties like turbulence intensity and turbulent length scale are muchsmaller than the corresponding horizontal properties. Small scale non-hydrostatic processes like internal waves and mixing are representedwith appropriate parameterization through calibration. Hence, use ofthe hydrostatic assumption is justified.

Methods

Overview of the hydrodynamic and heat models

Although there is a proprietary version of EFDCmaintained by TetraTech, Inc., the open source version, developed at Sandia National Labo-ratories (SNL) in California, SNL-EFDC (James and Boriah, 2010; Jameset al., 2013; Thanh et al., 2008) was used. This version is coupled to

updated versions of the USACE water quality code, CE-QUAL-ICM(Cerco and Cole, 1995; Cole andWells, 2006), and the sediment dynam-ics code, SEDZLJ (James et al., 2011; Jones, 2001).

EFDC (and SNL-EFDC) solves the three-dimensional, vertically hy-drostatic, free surface equations formulated using the turbulence-averaged equations of motion with the Boussinesq approximation andMellor–Yamada (Mellor and Yamada, 1982) turbulence closure(Hamrick, 1992). The code also solves scalar transport equations inthe water column (e.g., temperature, salinity, dye). Horizontal flowsare simulated usingmomentum equations with no-flow boundary con-ditions at lateralwalls. Density-dependent vertical flows are establishedby satisfyingmass conservation at each cellwith a specifiedflowbound-ary condition at the top because of precipitation and evaporation/condensation and at the bottom because of groundwater exchange.

The full heat balance model (Ji, 2008) includes: (a) radiativeprocesses including incoming shortwave and longwave solar radiationand outgoing longwave radiation emitted by the water surface,(b) latent heat transfer due to evaporation (or condensation) at thewater surface and sensible heat transfer between the water surfaceand the atmosphere, (c) heat addition/removal from inflows/outflows,and (d) heat exchange with the sediment bed.

Hnet ¼ HS þ HL−HB−HE−HC þ HQ þ HB ð1Þ

whereHS is the incoming shortwave radiation heatflux,HL is the incom-ing longwave radiation heat flux, HB is the outgoing longwave radiationheat flux, HE is the latent heat flux due to evaporation/condensation, HC

is the heat flux due to conduction,HQ is the heat addition/removal frominflows/outflows, and HB is the heat exchange through the sedimentbed.

Model development

Lake Ontario has surface area of 19,000 km2with amaximum lengthof 311 km and amaximumwidth of 85 km; average depth is 86m, witha maximum depth of 244 m. The Lake Ontario model was built with astructured curvilinear grid at approximately 2-kmhorizontal resolutioninterpolated with bathymetry data from the National Oceanic and At-mospheric Administration (NOAA). Twenty equally thick vertical layerscomprise the bathymetry following sigma vertical coordinates. Thesimulation was performed from April 4th to July 31st, 2011. Themodel was forced with hourly meteorological data (2011) from sevenweather stations surrounding Lake Ontario. Fig. 1 shows the interpolat-ed Lake Ontario bathymetry, local weather stations, and locations forobserved temperature profiles. The model flow boundaries includeinflow from the Niagara River at the southwest and outflow into theSt. Lawrence River at the northeast.

Modeling large lake systems requires significantmeteorological andhydrological data sets (Huang et al., 2010a, 2010b). Five buoys in LakeOntario record weather data, but they are removed in winter whenthe lake can freeze and damage the buoys. Hence, hourly atmosphericdata are used from land stations at Buffalo, Rochester, Oswego, Water-town, Hamilton, Toronto, and Kingston comprising: (1) wind speedand direction, (2) air temperature, (3) air pressure, (4) relative humid-ity, (5) shortwave solar radiation, (6) cloud cover, and (7) precipitation.Evaporation and condensation are internally computed from these data.All meteorological data were interpolated over the lake using inversedistance weighting. Hourly river volumetric flow rate data specify in-flow Niagara River and outflow St. Lawrence River with temperaturedata also available for inflow. The model's time integration used asecond-order accurate two-time level explicit finite difference schemewith an internal/external mode splitting technique. The mode ranwith a constant, 2-second time step to satisfy the stability criterion ofCourant–Fredrichs–Lewy condition.

Fig. 1. Lake Ontario bathymetry, inflow/outflow, seven weather stations around the lake, and monitoring buoy locations.

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Initial condition

SNL-EFDC does not include a rigorous ice model although one isavailable in the proprietary version. Hence, simulations commencedonce the lake was ice free. The weekly total ice coverage (percentage)over Lake Ontario for the winter of 2010–2011 (from EnvironmentCanada) indicated that the lake was ice free by early April 2011. Lakesurface AVHRR images and vertical profiles were obtained from theNOAA Great Lakes Environmental Research Laboratory (NOAA-GLERL)to determine initial temperature. Between April 4th and 8th, 2011,lake temperature was 3 °C. The hydrodynamic model was run from Jan-uary 1st and flows were recorded in a restart file on April 4th. This file

Fig. 2. (a)Deviation of simulated and observed (GLOS) surface temperatures, (b) anomalous cumthose from NOAA (April–May 2011) in Lake Ontario.

contains the initial flow conditions for the full thermo-hydrodynamicsimulation beginning at midnight on April 4th, 2011.

Updated evaporation rate algorithm and latent heat flux estimates

Using the existing EFDC heat algorithm, an anomalous increase insimulated surface temperatures was observed starting in mid-May2011 as shown in Fig. 2(a). Heat flux components (longwave incomingand outgoing, sensible and latent heat fluxes) and meteorological data(air temperature, shortwave solar radiation, wind speed, precipitationand evaporation) were individually extracted from themodel to identi-fy the source of the elevated simulated temperatures. Comparing the

ulative daily evaporation computed by EFDC (before the updated algorithm) compared to

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simulated evaporation rates to those from the NOAA Great Lakes Evap-oration Model revealed that spurious condensation caused the temper-ature discrepancies as shown in Fig. 2(b). The Great Lakes do experiencecondensation, notably in summer months when overlying air tempera-tures are significantly higher than surface water temperatures, butcontinuous condensation is not observed.

Of the various evaporation algorithms investigated (Croley, 1989;Derecki, 1976; Harbeck, 1954; Phillips, 1978; Quinn, 1979), the bulkaerodynamic approach of Quinn (1979)with thewind speed factor em-pirical formula of Croley (1989) yielded the best agreement betweenthe simulation and the NOAA Great Lakes Evaporation Model. Becauseno observed evaporation data are available for Lake Ontario, computedevaporation rates using the Quinn (1979) and Croley (1989) algorithmswere verified against observed evaporation rates at Long Point on LakeErie for May 2012–November 2013. Long Point on Lake Erie is thenearest location to Lake Ontario where evaporation data are availablefrom Environment Canada. Evaporation rates at Long Point werecomputed using over-land meteorological data using a calibrated bulkevaporation coefficient of 8 × 10−4. As shown in Fig. 3, evaporationrates computed from the algorithms of Quinn (1979) and Croley(1989) fit the observed data much better than the rates computed bythe original EFDC algorithm.

In the approach byQuinn (1979) evaporation from thewater surfaceis related to the difference between specific humidity near the watersurface and the overlying air as:

E ¼ ρa

ρw

� �Cewsp qsw−qaað Þ ð2Þ

where E (m/s) is the evaporation rate, ρa (kg/m3) is the air density, ρw(kg/m3) is the water density, Ce is the bulk evaporation coefficient, wsp

(m/s) is thewind speed 10mabove the lake, qsw is the specific humidityof water based on the saturation vapor pressure at the water surface,and qaa is the specific humidity of air based on the vapor pressure ofthe overlying air:

qsw ¼ 0:622eswPatm−0:378esw

ð3Þ

qaa ¼0:622eaa

Patm−0:378eaað4Þ

where esw (mbar) is the saturated vapor pressure at the water surfacetemperature, Tw (°C); eaa (mbar) is the actual vapor pressure at the

Fig. 3. Simulated evaporation rates (with original and updated algorithms)

overlying air temperature, Ta (°C); and Patm (mbar) is the atmosphericpressure. This bulk aerodynamic approach accounts for atmosphericstability through the iteratively computed evaporation coefficient, Ce,as a function of non-dimensional wind speed, potential temperaturegradients, and the Monin–Obukhov length (Stull, 1988). For thisstudy, however, we used the calibrated value (calibrated for LongPoint, Lake Erie) of bulk evaporation coefficient, Ce (8 × 10−4).

Croley (1989) suggested an adjustment to thewind speed in Quinn's(1979) algorithm to implement an over-land to over-lake bias correc-tion for the Great Lakes. Phillips and Irbe (1978) used over 7000 obser-vations from Lake Ontario in 1972 to come up with a regressionequation for an adjusted wind speed factor:

FWup ¼ 1:607þ 0:92wsp−0:28 Ta−Twð Þ: ð5Þ

The preceding equation includes the effects of temperature differ-ences between the overlying air and water surface along with windspeed. This adjusted wind speed factor better determines the evapora-tion (condensation) rate because the evaporation rate is not only linear-ly related to the wind speed but also to the temperature difference atair–water interface.

Combining Croley's (1989) adjustment for wind speed with Quinn's(1979) algorithm yields updated equations for the evaporation rate andlatent heat flux:

E ¼ ρa

ρw

� �Ce FWup qsw−qaað Þ ð6Þ

HE ¼ ρwEλv ð7Þ

where HE (MW/m2) is the latent heat flux and λv (MJ/kg) is the latentheat of vaporization:

λv ¼ 2:50−2:36� 10−3Tw: ð8Þ

The original evaporation algorithm in EFDC is based on amass trans-fer approach with governing equations:

E ¼ Cewsp esw−eaað Þ ð9Þ

HE ¼ FWefdc esw−eaað Þ ð10Þ

FWefdc ¼ 9:2þ 0:46w2sp: ð11Þ

compared to those observed at Long Point in Lake Erie (2012–2013).

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Both the original EFDC evaporation algorithm and the evaporationalgorithm by Quinn (1979) and Croley (1989) are fundamentallybased on amass transfer approach. However, an over-water adjustmentfor wind speed was developed in the latter, (Eq. (5)), which considersthe difference between the overlying air and water temperatures. Thisapproach improves the accuracy of estimated evaporation (condensa-tion) processes. Using FWup also improves estimates of sensible heatflux. In the original EFDC algorithm, FWefdc is quadratically related tothe wind speed in (Eq. (11)), resulting in an overestimation of evapora-tion (or condensation). The latent heat flux computation in the originalEFDC algorithm does not explicitly consider λv in (Eq. (10)), which isnecessary for accurate simulation of latent heat fluxes. Hence, in theoriginal EFDC algorithm, rates of evaporation and evaporative heatflux are computed separately in two different subroutines and valuesdo not correspond. Fig. 4 compares the evaporation rates in Lake Ontar-io, calculated using the original and updated EFDC formulations to theevaporation rates obtained from the NOAA Great Lakes EvaporationModel. This updated algorithm outperformed the original EFDC formu-lation and improved surface temperature simulations.

Sensitivity analysis of the solar radiation attenuation coefficients

In awater body, the distribution of solar radiation through thewatercolumn is described as an exponential function of water depth accord-ing to the Beer–Lambert law (Ji, 2008):

HS ¼ ISRnet f r exp−β f H 1−Ζð Þ þ 1− f rð Þ exp−βsH 1−Ζð Þ

h ið12Þ

where Hs (W/m2) is the shortwave incoming solar radiation heat flux,ISRnet (W/m2) is the incoming net shortwave solar radiation heat flux,βf (1/m) is the fast-scale light attenuation coefficient, βs (1/m) is theslow-scale light attenuation coefficient, fr is the fast-to-slowdistributionfraction between 0 and 1,H (m) is thewater depth, and Z is the normal-ized vertical sigma layer depth.

Solar radiation attenuation coefficients describe the light energy de-pletion rate through thewater column (Lee and Rast, 1997) that play animportant role in determining the depth of the thermocline and thedegree of temperature stratification. EFDC requires user-specifiedvalues for the attenuation coefficients to estimate downwelling irradi-ance in the water column. For this study, the solar radiation attenuationcoefficients for Lake Ontario were based only on TSS (mg/m3) and

Fig. 4. Simulated evaporation rates (with original and updated algorithm

chlorophyll-a (μg/l) concentrations (Armengol et al., 2003; Gallegosand Moore, 2000). The solar radiation attenuation coefficient based onTSS is (Armengol et al., 2003):

β ¼ 6:45� 10−5 � TSSþ 0:4806 ð13Þ

while the combination of TSS and chlorophyll-a concentrations yields(Gallegos and Moore, 2000):

β ¼ 0:32þ 0:016 � Chl‐aþ 0:094 � TSS: ð14Þ

Table 1 lists estimated concentrations of TSS and chlorophyll-a forLake Ontario and the corresponding solar radiation coefficients. Theestimated solar radiation attenuation coefficients range from 0.4 to1.45/m, and vary both spatially (nearshore/offshore) and periodically(annual/seasonal). The higher the radiation attenuation coefficient,the less radiation is absorbed deeper in the water column — more isabsorbed near the surface. Constrained by the range of solar radiationattenuation coefficients (Table 1), the values for this study were cali-brated to yield best matches to observed temperatures.

Malkin et al. (2010) analyzed the solar radiation attenuation coeffi-cients for Lake Ontario based on Secchi depths from 1995 to 2008.Their study showed that the summer solar radiation attenuation coeffi-cient values were higher than the spring values. Therefore, anothersensitivity analysis was performed with a temporally varying βf. Weset βf = 0.3/m for spring (April–May) and βf = 0.5/m for summer(June–July).

Fig. 5 compares simulated vertical temperature profiles in a shallowregion of the lake to those of Environment Canada. The RMSEswere lessthan 0.5 °C in themixed phase (April 25th toMay 10th) for all combina-tions of solar radiation attenuation coefficients. As the lake becamestratified in the nearshore later in May (after May 10th), RMSEs in-creased. The temporally varying fast-scale attenuation coefficients,βf = 0.3/m (spring, April–May), βf = 0.5/m (summer, June–July), andtemporally non-varying fast-scale attenuation coefficient, βf = 0.5/mboth yielded the similarly low RMSEs (b0.5 °C) during the lake mixedphase. However, temporally varying βf were selected for productionruns to be consistent with the fact that summer attenuation coefficientvalues are typically higher than those in the spring (Malkin et al., 2010).

s) compared to those from NOAA (April–July 2011) in Lake Ontario.

Table 1Solar radiation attenuation coefficients for Lake Ontario computed based on TSS and chlorophyll-a concentrations.

Time period and location TSS(mg/l)

Chlorophyll-a(μg/l)

Computed β (m−1)(TSS only)

Computed β (m−1)(TSS and Chl-a)

References

Lake spatial average in summer, 2011 2.2 1.75 0.62 0.55 Limnotech (2011), Yurista et al. (2012)Nearshore annual (2002–2010)mean (from tributaries)

11.62 1.75 (lake spatial average) 1.23 1.44 Coleates and Hale (2008), Yurista et al. (2012),Zevin et al. (2011)

Nearshore annual (2003–2009)mean (30 m depth)

0.7 2.1 0.52 0.42 Makarewicz et al. (2012)

Offshore annual (2003–2009)mean (100 m depth)

0.8 2.7 0.53 0.44 Makarewicz et al. (2012)

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Calibration

After early manual calibration efforts, the automated Parameter ES-Timation software, PEST (Doherty, 2009, 2010), was applied to the LakeOntario model. The software is based on a robust implementation ofGauss–Marquardt–Levenberg algorithmand adjusts themodel parame-ters by weighted least squares and yields parameter uncertainty andsensitivity information during estimation (Doherty, 2009).

Observed temperature data are supplied to PEST and adjustableparameters are iteratively updated to yield the closest match to thesedata (minimized weighted squared residuals between simulatedand observed temperatures). The parameter range that PEST wasconstrained to interrogate, the initial values, and calibrated parametersare listed in Table 2. Unit weight was applied to each observation.

Solar radiation attenuation coefficients were calibrated throughPEST to appropriately reflect the absorption of incoming radiationthroughwater column. The PEST-calibrated valueswere similar toman-ually calibrated values (Table 2). In addition, horizontal and verticalmixing coefficients were calibrated. These coefficients were interrogat-ed from a range of 0 to 0.25 m2/s for the background horizontal eddyviscosity (Smagorinsky coefficient) and from0.1 to 5 for the dimension-less horizontal momentum diffusivity. The simulated temperature

Fig. 5. Simulated and observed (Environment Canada) vertical temperature profiles in Lake Onation attenuation coefficients.

profiles were least sensitive to the horizontal mixing coefficients;therefore, they were fixed at a horizontal eddy viscosity of 0.1 m2/sand a dimensionless horizontal momentum diffusivity of 1. Calibrationof vertical mixing coefficients spanned ranges of 10−4–0.1 m2/s forvertical eddy viscosity and 10−8–0.01 m2/s for vertical diffusivity.Best results were achieved when vertical eddy viscosity was8.35 × 10−3 m2/s and vertical diffusivity was 1.05 × 10−6 m2/s.

The most sensitive parameters are, not surprisingly, the solar radia-tion attenuation coefficients because these directly affect the tempera-ture profiles. Next most sensitive are the vertical mixing parameters,which is intuitive given the importance of their role in establishing ordiminishing vertical temperature gradients. Temperature profiles wereleast sensitive to horizontal mixing parameters. In future efforts to re-fine this calibration, the focus will be on establishing improved verticalmixing parameters through implementation of a new vertical mixingalgorithm in EFDC.

Results and discussion

Simulated temperatures were compared against: (1) observedsurface time-series temperatures from three buoys that were part ofthe Great Lakes Observation System (GLOS), (2) observed vertical

tario, late April–July 2011 at shallow location showing the effect of varying the solar radi-

Table 2PEST calibration parameters for the EFDC Lake Ontario model.

Parameter type Parameter name Range Initial value Calibrated value

Solar radiation attenuation coefficients Fast-scale coefficient, βf 0.2–1.3 m−1 0.5 m−1 0.53 m−1

Slow-scale coefficient, βs 0.1–0.5 m−1 0.15 m−1 0.14 m−1

Distribution factor, fr 0.3–1.0 0.5 0.7Vertical mixing parameters Vertical eddy viscosity 10−4–0.1 m2/s 10−2 m2/s 8.35 × 10−3 m2/s

Vertical diffusivity 10−8–0.01 m2/s 10−6 m2/s 1.05 × 10−6 m2/sHorizontal mixing parameters Background horizontal eddy viscosity 0–0.25 m2/s 0.25 m2/s 0.1 m2/s

Dimensionless momentum diffusivity 0.1–5.0 1.0 1.0

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temperature profiles from two buoys monitored by EnvironmentCanada, and (3) lake-wide surface temperatures from remotely sensedAVHRR images from NOAA similar to the approach used by de Alwis(1999). Monitoring buoy locations are shown in Fig. 1. Surface temper-atures were compared at nearshore locationsWest Grimsby (WG, 25mdeep) and Prince Edward Point (PEP, 74 m deep) and offshore location20NM Buoy (20NMB, 140 m deep). Vertical temperature profiles werecompared at a nearshore location, Shallow Point (SP, 19 m deep), andan offshore location, Deep Point (DP, 177 m deep).

Simulated temperature profiles for Lake Ontario

After all of the adjustments to the EFDCmodel, the simulated surfacetemperature profiles are compared to observed surface temperatureprofiles from April to July 2011 in Fig. 6. At nearshore location WG, theRMSEwas 1.2 °C indicatingwell-matched temperature profiles. At near-shore location PEP, RMSE was 1.88 °C and at offshore location 20NMB,

Fig. 6. Simulated and observed (GLOS) surface temp

RMSE was 1.93 °C. Historically, RMSEs below 2 °C are considered as ac-ceptable for Lake Ontario (Hall, 2008; Huang et al., 2010a; Rao et al.,2004; Wilson et al., 2013). At nearshore location PEP and at offshorelocation 20NMB, increased discrepancies between the simulated andobserved temperature profiles were noticed in July (see Fig. 6) whenthe lake was fully stratified. The model underestimated the surfacetemperatures of the stratified lake in July hence the overall RMSEsincreased at PEP and 20NMB buoys.

Simulated vertical temperature profiles are compared to observa-tions at SP and DP buoys in Fig. 7(a) and (b). The simulated tempera-tures compared well with observed temperatures when the lake wasin the mixed phase (the overall RMSEs for both the SP and DP werebelow 0.5 °C). The lake began to stratify at SP and DP by May 20th andJune 10th, respectively, but the model failed to capture this transitionon these dates. At SP, the RMSE began to increase around May 20thand was 6.05 °C by July 10th. At DP, the RMSE increased after June10th, and by July 10th, the RMSE was 3.18 °C. The vertical profiles in

eratures in Lake Ontario, late April–July 2011.

Fig. 7. Simulated and observed (Environment Canada) vertical temperature profiles in Lake Ontario, late April–July 2011 (a) at SP, (b) at DP.

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Fig. 7(a) and (b) show that the model captured the mixed phase (ther-mal bar formation phase) better than the stratified phase. The greatestRMSEs occurred when the lake transitioned to the stratified phase(late May/early June). Deviations were observed primarily for depthsless than 20 m, regardless of the local depth of the lake. This is thedepth over which wind mixing imparts kinetic energy that mixes solarheating. This mixing mechanism governs the epilimnion transition.When wind-driven mixing decreases, the potential energy of the lakeis re-oriented to re-stratify the lake; warm, lighter water migrates tothe top, while colder, denser water sinks and a density-based thermo-cline appears. The model will benefit from an improved wind-driven

mixing algorithm in the epilimnion and this is the subject of ongoing re-search efforts.

Because the model captured temperature profiles well in the mixedphase, lake-wide surface temperatures were compared with remotelysensed AVHRR images fromNOAA (Fig. 8) during formation of the ther-mal bar (late April to late May). NOAA images were georeferenced andsuperimposed upon images of EFDC simulated temperatures and thespatial distribution of temperature differences between the two sets ofimages are shown in Fig. 8. From Fig. 8, simulated temperatures weretypically lower than the NOAA satellite measurements by 0.5 to 1 °C.However, the simulated nearshore temperatures near the north shore

Fig. 8. Lake-wide surface temperatures compared with satellite images from NOAA, late April–late May 2011 when the lake is in the mixed phase (during thermal bar evolution).

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were warmer than the corresponding NOAA data by 0.5 to 2 °C. Notethat near the north shore, colder, deeper water upwells because of pre-vailing winds (Hall, 2008). Although upward velocities were simulatedin this region, themodel did not capture themagnitude of local upwell-ing events. The simulated temperatures in the deeper areas of the lakeand in the south nearshore area were cooler than those measured byNOAA by 0.5 °C from late April to early May. Later in May, differencebetween the two increased to 1 °C in the deeper area and to 2 °Calong the south shore of the lake. Consistent with Figs. 6 and 7, themodel under-predicted temperatures in deeper areas as the lakemoved into the stratified phase. Nevertheless, the simulated surfacetemperatures were accurate (0.5 to 1 °C different from NOAA) whenthe lake was in the mixed phase.

Formation of the thermal bar in Lake Ontario

The EFDC Lake Ontario model captures the temperature profileswell in the mixed phase (RMSEs were below 0.5 °C for vertical tem-perature profiles) and so the evolution of the thermal bar was ex-plored through simulated temperature profiles from late April toMay 2011.

Fig. 9 shows the thermal bar formation (4 °C temperature through-out the water column) at SP consistent with observed data. Bothmodel-simulated and observed thermal bar formation started approxi-mately at day 113 (April 23rd). The simulated thermal bar was

stationary at SP until day 119 (April 29th) in the simulated profile anduntil day 118 (April 28th) in the observed data. The simulated lakemixed phase continued until day 125 (May 5th) and until day 127(May 7th) for observed data after which the lake began to stratify atthis nearshore location. Wind speed data (obtained from land-basedstations) during the thermal bar period at SP was low to moderate (3to 8 m/s for days 113 to 135) and hence the simulated wind stresswas low as well (0.015 to 0.15 N/m2). There were no strong winds topush the thermal bar into deep waters and minimal wind-energy-induced turbulent heat and mass exchange at the air–water interface.The wind direction was predominantly easterly. The simulated surfacenet heat flux (SNHF) at this location from day 113 to 125 was negativeon some days and positive on other days (the values were between−30 and +65 W/m2), so there was no sudden heat loss or gain atsurface. After day 125, the simulated SNHF was positive (+25 to+105 W/m2 for days 126–135) supporting thermal stratification atSP and facilitating progression of the thermal bar into deeper areas.

Fig. 10 illustrates the thermal bar progression rate at SP using time-series temperature profiles (simulated and observed). Using the analyt-ical formulation of Elliott and Elliott (1970), thermal bar progressionrate is estimated as the ratio of bar displacement from its current posi-tion to another deeper location based on the assumption that heat en-tering the surface of a unit column remains within the column and thehorizontal heat fluxes are negligible. By distributing the surface heatflux (considered constant in space and time) over the local depth and

Fig. 9. Time series (late April–late May 2011) of vertical temperature distributions and thermal bar formation (shaded in diagonal lines) at SP.

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balancing this against the rate of temperature increase, Elliott and Elliott(1970) estimated the speed of the thermal bar as:

S ¼ QsLΔTρcpD

ð15Þ

where Qs (cal/cm/s) is the heat flux through surface, L (cm) is the hori-zontal distance between the bar and some deeper reference positionwhere the mean temperature is known, D (cm) is the depth at thedeeper position, ΔT (°C) is the temperature difference between 4 °C

Fig. 10. Estimated thermal bar progression rate using simulated and observed (Env

and themean temperature at the deeper position, and ρcp is the densityof water times its specific heat (1 cal/°C/cm).

Fig. 10 shows that the thermal bar progression rate was slightly overestimated using the simulated time-series temperature profiles com-pared to the rate estimated using observed temperature profiles. Thisslight difference may be because the simulated temperature profilesneglected local mixing in the thermal bar zone. The estimated progres-sion rates (in Fig. 10) show two distinct phases of thermal bar progres-sion (Malm et al., 1993; Zilitinkevich et al., 1992): an initial slow phase(until mid-May) and a subsequent fast phase (late May). However,theoretical models over-estimate the progression rate of the thermal

ironment Canada) time-series (late April–late May 2011) temperature profiles.

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bar during the early phase. In the later phase, models that incorporatethe effect of horizontal heat flux in the thermal bar region (Malmet al., 1993; Zilitinkevich et al., 1992) capture the significant increasein progression rate (Rao and Schwab, 2007; Rao et al., 2004). Directlyobserved progression rates of the thermal bar were not available tocompare with our estimated rates. The estimated progression ratedidn't capture the thermal bar stationary phase at SP (April 23rd toApril 29th). This is probably due to the fact that an average heat fluxwas used and horizontal heat fluxes were not considered in the analyt-ical formula.

Fig. 11(a) shows the surface flow circulation on LakeOntario onMay7th when the lake was in the mixed phase and the thermal bar formednearshore. Fig. 11(b) shows vertical temperature profiles during ther-mal bar formation at north shore (25 m deep) and south shore (33 mdeep) locations (locations marked as N and S in Fig. 11(a)). Both atnorth and south shore the water column is homogeneously mixedwith ~4 °C temperature indicating the thermal bar formation at respec-tive locations. Fig. 9 depicts the thermal bar formation at SP from April23rd to April 29th. The north shore location in Fig. 11(b) is about~10 km from SP. As stratification began with positive heat flux at SP inearly May, the thermal bar progressed towards deeper position.Fig. 11(a) shows surface flows converging towards the thermal bar inopposite directions: counter-clockwise in stratified nearshore andclockwise in deepwater where water is still mixing. Converging surfaceflow patterns towards thermal bar have been observed and analyzed in

Fig. 11. (a) Surface velocity profile at Lake Ontario during the thermal bar formation at nearsh

several studies (Holland and Kay, 2003;Malm, 1995; Zilitinkevich et al.,1992). In general, density-induced horizontal circulation in large,temperate lakes in the northern hemisphere is counterclockwise inthe stably stratified nearshore region, and clockwise in the deep waterregion (Rao and Schwab, 2007). In the study by Rao et al. (2004), itwas confirmed that the observed circulation within a zone betweenthe shore and the thermal bar is predominantly shore-parallel andcounter-clockwise. This two-cell thermal bar circulation is importantbecause flows converging at the thermal bar suppress most cross-frontal exchange thereby inhibiting horizontal mixing (Gbah andMurthy, 1998; Holland and Kay, 2003).

Fig. 12 demonstrates the effect of thermal bar formation on horizon-tal mixing coefficients in nearshore areas. Fig. 12 shows that horizontaleddy viscosity (m2/s) significantly decreased during the thermal barphase (18 m2/s) compared to pre-thermal bar (30 m2/s) and post ther-mal bar periods (25 m2/s) at SP, whereas thermal bar formation has noconsiderable effect on horizontal eddy viscosity value (5–12 m2/s) atDP. At SP, horizontal mixing coefficients are higher near the surface(18–30 m2/s) than corresponding subsurface values during pre-, post-and thermal-bar periods. At DP, horizontal mixing coefficients areelevated near the water surface and at bottom (8–12 m2/s) withlower values (3–7m2/s) in themid-water column. Lower values of hor-izontalmixing coefficient at SP during the thermal bar phase, comparedwith the pre- and post-thermal bar periods, support the hypothesis thatthe thermal bar plays an important role in reducing horizontalmixing in

ore. (b) Vertical temperature profiles at north shore (N in (a)) and south shore (S in (a)).

Fig. 12. Depth variation of horizontal mixing coefficient (eddy viscosity, m2/s) during the pre-thermal bar, thermal bar, and post-thermal bar periods at SP and DP.

522 R.R. Arifin et al. / Journal of Great Lakes Research 42 (2016) 511–523

nearshore areas. Similar observationswere reported by Rao et al. (2004)as they found that during the thermal bar phase, the magnitude of bothalongshore and cross-shore exchange coefficients decreased when thebar was in the nearshore.

Conclusions

We present an EFDC model for simulating temperature profiles inLake Ontario and for exploring spring thermal bar evolution. Laketemperature profiles were simulated as closely as possible to those ofthe observed profiles after an update to the evaporation algorithm andparameter calibration.

Overall, the Lake Ontario model performed well when the lake wasin the mixed phase (thermal bar evolution period). The RMSEs for ver-tical profiles were below 0.5 °C (late April to lateMay 2011). The modelcaptured surface temperature profiles with RMSEs of 0.5 to 2 °C for theentire simulation period (April 4th through July 31st, 2011). Lake-widesurface temperatureswere compared to data from satellite images fromNOAA and the temperature differences between the two sets rangedfrom 0.5 to 1 °C when the lake was in the mixed phase (thermal barevolution period).

The EFDC Lake Ontario model was improved with an update to theevaporation algorithm because EFDC's original evaporation algorithmyielded anomalous evaporation rates and latent heat fluxes. This updateis recommended when EFDC is used to simulate similar lakes.

Lake Ontario is a mesotrophic lake and appropriate solar radiationattenuation coefficients must be specified to ensure accurate solarradiation absorption by the water column. In this study, solar radiationattenuation coefficients specifically applicable for Lake Ontario werebased on TSS and chlorophyll-a concentrations and were 0.3/m (spring,April–May) and 0.5/m (summer, June–July) for βf.

Because themodel accurately simulated temperature profiles duringthe mixed phase (late April to late May 2011), thermal bar formationwas explored nearshore. The simulated thermal bar showed the expect-ed characteristics: a thoroughly mixed water column at 4 °C, stationaryfrom days 113 to 119 (April 23rd to 29th) at SP, two-phase thermal-barprogression rate, surface flow convergence towards the thermal bar,and decreased horizontal eddy viscosity during the thermal bar period.

The model did not closely simulate the summer temperatures whenthe lake transitioned to the stratified phase (lateMay/early June and on-ward). Thermocline formation was not well captured in the simulatedvertical profiles, calling for an improved wind-driven mixing algorithm

for the epilimnion. Such an algorithm will allow EFDC to capture wind-driven mixing and density-driven stratification and this update is inprogress.

Acknowledgments

This research is funded by the Center for Research Computing at theUniversity of Notre Dame with the generous support from Dr. Jaroslaw(Jarek) Nabrzyski, (Director, Center for Research Computing). Wewould like to thank Mark Suhovecky (University of Notre Dame) forcompiling the EFDC source code; Dr. Dodi Heryadi and Dr. In-SaengSuh (Center for Research Computing) for providing computer-serversupport for running the simulations. We are indebted to several peopleincluding Dr. RamYerubandi Rao (Environment Canada, Burlington) forproviding measured vertical temperature profiles, Tim Hunter (NOAA-Great Lakes Environmental Research Laboratory, Ann Arbor, MI) forproviding daily evaporation data (NOAA Great Lakes EvaporationModel), Dr. Christopher Spence (Environment Canada, National Hydrol-ogy ResearchCenter) for providing Lake Erie daily observed evaporationdata, Paul M. Yu, PE, (U.S. Army Corps of Engineers, Buffalo District, NY)for providing Niagara River inflow data, Brent Whitcomb (New YorkPower Authority, NY) for providing St. Lawrence River outflow data,George A. Leshkevich (NOAA-Great Lakes Environmental ResearchLaboratory, Ann Arbor, MI) for providing remotely sensed surface tem-perature images for Lake Ontario, and Gregory Lang (NOAA-Great LakesEnvironmental Research Laboratory Federal) for providing temperaturetransect profiles (Great Lakes Coastal Forecasting System). Meteorolog-ical data were sourced from the National Climate Data Center, theNational Solar Radiation Database, the National Weather Service, theIowa Environmental Mesonet Weather Service, the EnvironmentCanada, the National Climate Data & Information Archive, and theGreat Lakes Observing system. The first author is grateful to ZachariahSilver (Department of Civil & Environmental Engineering and Earth Sci-ences, University of Notre Dame) and Dr. S. M. Niaz Arifin (Departmentof Computer Science and Engineering, University of Notre Dame) fortheir overall support.

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