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David J. Schwab

Abstract

Two simple numerical models have been used to study the low-frequency (<0.6 cpd) current oscillations observed in Lake Michigan in order to learn more about what really limits our ability to simulate currents in large lakes. Both are based on the barotropic vorticity equation with the rigid-lid approximation. One model used observed wind to calculate the time-dependent response of the lake for eight months in 1976. The results agree reasonably well with observed currents, but only in the frequency range corresponding to the maximum energy in the forcing function, approximately 0.125–0.3 cpd. Over this frequency range, peaks in the energy spectrum of the forcing function also occur in both the model response and the observed currents at the same frequencies. At lower and higher frequencies, the model underestimates the observed kinetic energy of the currents. The second model calculate the response of the lake to purely oscillatory wind forcing. From 0.125 to 0.3 cpd, the spatial structure of the response is relatively insensitive to changes in forcing frequency. The response to a north–south oscillatory wind stress resembles a free topographic wave consisting of two counterrotating gyres in the southern basin of the lake, but is more complicated in the northern part. When compared to previous analytic and numerical studies of steady-state circulation, the steady-state (zero frequency) response is found to be consistent with Ekman dynamics for realistic values of linearized bottom stress. The results indicate that the barotropic rigid-lid model can simulate observed current fluctuations only in the 0.125–0.3 cpd frequency range. Over this range, the average response of the lake is nonresonant, showing no peaks in lakewide average kinetic energy. At higher and lower frequencies, baroclinicity and nonlinear effects may have to be included in order to improve the model results.

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David J. Schwab

Abstract

A numerical model based on the impulse response function method is used to hindcast and forecast storm surges on Lake Erie. The impulse response function method is more efficient then numerical integration of the dynamic equations when results are required at only a few grid points. Hindcasts use wind observations from seven weather stations around Lake Erie. The surge phenomenon depends on the two-dimensional structure of the wind field and on the stability of the atmospheric boundary layer over the lake. The overall correlation coefficient between computed and observed water level deviations for 15 five-day hindcast cases is 0.83 at eight water level recording stations. Operational Great Lakes wind forecasts are used to drive the model for water level forecasts at Buffalo, NY, and Toledo, OH. The accuracy of the water level forecasts is currently limited by the accuracy of the forecast winds.

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Urmas Raudsepp
,
Dmitry Beletsky
, and
David J. Schwab

Abstract

A two-dimensional circulation model has been used to test the hypothesis of whether the observed low-frequency current variations in the central Gulf of Riga, Baltic Sea, can be explained by basin-scale topographic wave response. A comparison of two-dimensional model results with measurements from a single current meter in the gulf showed good correlation. More sophisticated three-dimensional barotropic and baroclinic models provided only marginal improvement over the two-dimensional model. The model results indicate that wind-driven flow over variable bottom topography is the dominant process during moderate and strong winds. The double-gyre circulation pattern resembles the gravest basin-scale topographic wave. The free topographic wave propagates cyclonically around the basin, but does not complete a full cycle because of the shallowness of the Gulf of Riga. The evolution of the topographic wave under realistic wind conditions is analyzed using vorticity dynamics in a basin-scale sense. The topographic wave is reinforced by cyclonically rotating wind and can be destroyed most effectively by anticyclonically rotating wind. The topographic wave signature is more apparent in deep water and almost absent in shallow areas of the basin. During calm periods or under the influence of weak winds, the double-gyre circulation will evolve into predominantly cyclonic circulation.

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Desiraju B. Rao
and
David J. Schwab

Abstract

The mean circulation in large takes is nearly nondivergent in character. This paper takes advantage of this fact to represent the flow field in terms of the transport streamfunction. The horizontal velocity vector (v) and the vertical component of vorticity are then given by v = k × H −1 ΔΨ and ζ = Δ · H −1 ΔΨ, where Ψ is the transport streamfunction, Δ the horizontal gradient, and H = H(x,y) the equilibrium depth of the lake. If the vorticity field Ψ(x, y) is known, Ψ can be determined from the above inhomogeneous equation with H −1Ψ = 0 on the boundary. The current vector is then obtained from the other equation. In practice, however, currents are measured and not vorticity. Therefore, the proposed objective analysis procedure expands the transport streamfunction in terms of the eigenvectors of the self-adjoint problem Δ · H −1 ΔΨα = μαΨα with H −1Ψα = 0 on the boundary. The eigenvalues μα and eigenvectors Ψα are characteristic of the particular lake and are determined numerically by a Lanezos procedure. The expansion coefficients are determined by minimizing the squared error between the calculated v field and available current meter data. Since the Ψα functions for the entire domain of the basin are known, the currents can be reconstructed at any point. This method has been applied to data gathered in Lake Ontario during the winter months of 1972–73 as part of the International Field Year for the Great Lakes (IFYGL).

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Thomas R. Hultquist
,
Michael R. Dutter
, and
David J. Schwab

There has been considerable debate over the past three decades concerning the specific cause of the loss of the ship the Edmund Fitzgerald on Lake Superior on 10 November 1975, but there is little question that weather played a role in the disaster. There were only a few surface observations available during the height of the storm, so it is difficult to assess the true severity and meteorological rarity of the event. In order to identify likely weather conditions that occurred during the storm of 9–10 November 1975, high-resolution numerical simulations were conducted in an attempt to assess wind and wave conditions throughout the storm. Comparisons are made between output from the model simulations and available observational data from the event to assess the accuracy of the simulations. Given a favorable comparison, more detailed output from the simulations is presented, with a focus on high-resolution output over Lake Superior between 1800 UTC 9 November 1975 and 0600 UTC 11 November 1975. A detailed analysis of low-level sustained wind and significant wave height output is presented, illustrating the severity of the conditions and speed with which they developed and later subsided during the event. The high temporal and spatial resolution of the model output helps provide a more detailed depiction of conditions on Lake Superior than has previously been available.

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Paul C. Liu
,
David J. Schwab
, and
John R. Bennett

Abstract

We compare results from a simple parametric, dynamical, deep-water wave prediction model with two sets of measured wave height maps of Lake Michigan. The measurements were made with an airborne laser altimeter under two distinctly different wind fields during November 1977. The results show that the model predicted almost all of the synoptic features. Both the magnitude and the general pattern of the predicted wave-height contours compared well with the measurements. The model also predicts the direction for wave propagation in conjunction with the wave height map, which is useful for practical ship routing and can be significantly different form the prevailing wind direction.

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William P. O’Connor
,
David J. Schwab
, and
Gregory A. Lang

Abstract

This article has two purposes. The first is to describe how the Great Lakes Coastal Forecasting System (GLCFS) can be used to validate wind forecasts for the Great Lakes using observed and forecast water levels. The second is to evaluate how well two versions (40 km and 29 km) of the numerical weather prediction step-coordinate Eta Model are able to forecast winds for the Great Lakes region, using the GLCFS as a verification technique. A brief description is given of the 40- and 29-km versions of the Eta Model and their surface wind and wind stress output. A description is given of the GLCFS for Lake Erie. This includes the numerical Princeton Ocean Model (POM), observed winds from surface meteorological stations and buoys, and water level gauge data. The wind stresses obtained from both the 40-km Eta Model and the observed winds are used to force the POM for Lake Erie for several periods in 1993 when water level surges were recorded. The resulting POM water levels are then compared to observed water levels to provide an indication of the accuracy of 40-km Eta Model forecasts. The same experiments are made with the POM using wind stresses from the 29-km Eta Model and observed winds in 1997. Twin experiments are made with the GLCFS to determine: 1) how well it can predict (hindcast) water levels using observed winds as forcing, and 2) how well it can predict water levels using both the 40- and 29-km Eta Model forecast winds as forcing. The use of this forecast validation technique for other coastal forecasting systems is discussed.

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David J. Schwab
,
William P. O'Connor
, and
George L. Mellor

Abstract

This paper proposes a possible explanation for the mean cyclonic circulation in large stratified lakes The condition of no heat flux through the bottom boundary causes the isotherms to dip near the shores to intersect the sloping bottom orthogonally. This “doming” of the thermocline causes an internal pressure gradient in the surface layer with higher pressure nearshore and results in a geostrophic cyclonic circulation.

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Desiraju B. Rao
,
David J. Schwab
, and
C. H. Mortimer

Abstract

Periods and structures of several normal modes of Lake Michigan (including Green Bay) are calculated theoretically, taking into account the Lake's topography and the earth's rotation. The calculations are based on a Galerkin method developed by Rao and Schwab (1976). Even though the calculations give both rotational and gravitational modes, attention is focused primarily on the latter. The calculations show that there are several modes dominant in the main basin of Lake Michigan and some dominant in Green Bay. The lowest Lake Michigan mode has a period of 9.27 h. Green Bay exhibits a (co-oscillating or Hemlholtz) mode with a period 10.35 h. For the modes dominant in the main basin, the periods and structures obtained from theoretical calculations are compared to those deduced from spectral analyses of water level data from various stations around the Lake. The agreement is found satisfactory for several of the lowest modes.

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Dmitry Beletsky
,
William P. O’Connor
,
David J. Schwab
, and
David E. Dietrich

Abstract

Two three-dimensional primitive equation numerical ocean models are applied to the problem of internal Kelvin waves and coastal upwelling in the Great Lakes. One is the Princeton Ocean Model (POM) with a terrain-following (sigma) vertical coordinate, and the other is the Dietrich/Center for Air Sea Technology (DIECAST) model with constant z-level coordinates. The sigma coordinate system is particularly convenient for simulating coastal upwelling, while the z-level system might be better for representing abrupt topographic changes. The models are first tested with a stratified idealized circular lake 100 km in diameter and 100 m deep. Two bottom topographies are considered: a flat bottom and a parabolic depth profile. Three rectilinear horizontal grids are used: 5, 2.5, and 1.25 km. The POM was used with 13 vertical levels, while the DIECAST model was tested with both 13 and 29 vertical levels. The models are driven with an impulsive wind stress imitating the passage of a weather system.

In the case of the flat-bottom basin, the dynamical response to light wind forcing is a small amplitude internal Kelvin wave. For both models, the speed of the Kelvin wave in the model is somewhat less than the inviscid analytic solution wave speed. In the case of strong wind forcing, the thermocline breaks the surface (full upwelling) and a strong surface thermal front appears. After the wind ceases, the edges of this thermal front propagate cyclonically around the lake, quite similar to an internal Kelvin wave. In the case of parabolic bathymetry, Kelvin wave and thermal front propagation is modified by interaction with a topographic wave and a geostrophic circulation. In both models, higher horizontal resolution gives higher wave and frontal speeds. Horizontal resolution is much more critical in the full upwelling case than in the Kelvin wave case. Vertical resolution is not as critical.

The models are also applied to Lake Michigan to determine the response to strong northerly winds causing upwelling along the eastern shore. The results are more complex than for the circular basin, but clearly show the characteristics of cyclonically propagating thermal fronts. The resulting northward warm front propagation along the eastern shore compares favorably with observations of temperature fluctuations at municipal water intakes after a storm, although the model frontal speed was less than the observed speed.

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