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  • View in gallery

    Schematic of one-dimensional lake model, depicting typical summer and winter lake conditions and air–lake heat fluxes. LWAVE and SWAVE stand for longwave and shortwave radiation, respectively. QW is conductive heat flux between ice and the water below.

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    (left) Model domain topography and extent. (right) Model lake bathymetry (m) and NDBC station locations.

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    Observed (black) and simulated (blue, DEF; red, MOD) mean seasonal cycle of lake surface temperature at the nine Great Lakes NDBC stations (Fig. 2). Buoy stations are sorted according to local lake depth, shallowest to deepest. Line widths depict interannual variability (standard deviation) in local lake surface temperature.

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    Lakewide mean lake surface temperatures from the GLSEA satellite data product (1995–2009, black), simulated by the default lake model (1985–2009, blue) and simulated by the modified lake model (1985–2009, red).

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    Mean lake surface temperatures for shallow lake portions (0–49 m; solid lines) and deeper lake portions (50+ m; dashed lines) for Lakes (a) Superior, (b) Michigan, (c) Huron, and (d) Ontario. The default model is depicted in blue, and the modified lake model results are shown in red. Lake Erie has no model lake points deeper than 49 m, so it is not included here.

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    Mean vertical thermal structure (1985–2009) of (left) shallow (0–49 m) and (right) deep (50+ m) lake points for each of the Great Lakes as simulated by DEF. Note the logarithmic axes for depth, in order to visualize upper-layer vertical thermal structure. Time series of shallow and deep percentage of ice coverage is shown in black.

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    As in Fig. 6, but for MOD.

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    Mean number of days of winter ice as simulated by (a) DEF and (b) MOD and (c) observed. A winter ice day is considered any day with at least 10% ice cover in observations. The interannual variability [standard deviation (STD)] in winter ice days is shown in (d) DEF, (e) MOD, and (f) observed.

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    DJFMA for (a) the Great Lakes as a whole, (b) Lake Superior, (c) Lake Michigan, (d) Lake Huron, (e) Lake Erie, and (f) Lake Ontario as observed (black) and simulated by the default (blue) and modified (red) lake models. Correlations to observations noted within each subplot.

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    Mean seasonal (1985–2009) air temperature changes (modified minus default) near the surface (2 m) caused by lake model modifications within RegCM4.3 for (a) DJF, (b) MAM, (c) JJA, and (d) SON.

  • View in gallery

    Near-surface air temperature (2 m) bias in DEF (1985–2006) compared to gridded station observation dataset UDEL for (a) winter, (b) spring, (c) summer, and (d) fall. Seasonal precipitation biases (cm month−1; 1985–99) for (e) winter, (f) spring, (g) summer, and (h) fall as simulated by the default model. Precipitation is compared to the undercatchment-corrected gridded station observations of UDEL. (i) Domain-wide, mean monthly biases (1985–2006) in near-surface temperature for DEF (blue) and MOD (red). (j) The seasonal cycle of domain-wide precipitation biases (mm month−1) for the default (blue) and modified (red) model for 1985–99.

  • View in gallery

    Mean (1985–2009) above-lake air temperatures (model at 2 m) at the nine NDBC buoy locations on the Great Lakes. Observed (black), simulated by default (blue) and modified (red) lake model within RegCM4.3. Observations at ~7 m. Buoy observations did not begin on Lake Ontario until 2004. Line widths depict a single standard deviation across years. Note large variability in observed temperatures in winter/early spring may be due to inadequate number of years of observation, since buoys usually deployed from April to November.

  • View in gallery

    Statistically significant changes in seasonal mean (1985–2009) sea level pressure (hPa) and winds (m s−1) at 10-m height caused by lake model modifications within RegCM4.3 are shown for (a) winter, (b) spring, (c) summer, and (d) fall. Changes are shown as MOD minus DEF.

  • View in gallery

    Statistically significant mean changes (modified default) in (a) winter, (b) spring, (c) summer, and (d) fall and (e) annual precipitation (1985–2009) caused by lake model modifications. Changes are shown as MOD minus DEF.

  • View in gallery

    Changes in mean (1985–2009) monthly snow totals (cm month−1) caused by lake model modifications within RegCM4.3 are shown for (a) December, (b) January, (c) February, and (d) March. Changes are shown as MOD minus DEF.

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    Interannual variability in lakewide surface temperatures (1995–2009) for Lakes (a) Superior, (b) Michigan, (c) Huron, (d) Ontario, and (e) Erie as simulated by DEF (blue) and MOD (red) and estimated by the GLSEA satellite product (black).

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Improving Climate Sensitivity of Deep Lakes within a Regional Climate Model and Its Impact on Simulated Climate

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  • 1 Nelson Institute Center for Climatic Research, University of Wisconsin–Madison, Madison, Wisconsin
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Abstract

Regional climate models aim to improve local climate simulations by resolving topography, vegetation, and land use at a finer resolution than global climate models. Lakes, particularly large and deep lakes, are local features that significantly alter regional climate. The Hostetler lake model, a version of which is currently used in the Community Land Model, performs poorly in deep lakes when coupled to the regional climate of the International Centre for Theoretical Physics (ICTP) Regional Climate Model, version 4 (RegCM4). Within the default RegCM4 model, the lake fails to properly stratify, stifling the model’s ability to capture interannual variability in lake temperature and ice cover. Here, the authors improve modeled lake stratification and eddy diffusivity while correcting errors in the ice model. The resulting simulated lake shows improved stratification and interannual variability in lake ice and temperature. The lack of circulation and explicit mixing continues to stifle the model’s ability to simulate lake mixing events and variability in timing of stratification and destratification. The changes to modeled lake conditions alter seasonal means in sea level pressure, temperature, and low-level winds in the entire model domain, highlighting the importance of lake model selection and improvement for coupled simulations. Interestingly, changes to winter and spring snow cover and albedo impact spring warming. Unsurprisingly, regional climate variability is not significantly altered by an increase in lake temperature variability.

Corresponding author address: Val Bennington, Nelson Institute Center for Climatic Research, University of Wisconsin–Madison, 1225 West Dayton St., Madison, WI 53706. E-mail: benesh@wisc.edu

Abstract

Regional climate models aim to improve local climate simulations by resolving topography, vegetation, and land use at a finer resolution than global climate models. Lakes, particularly large and deep lakes, are local features that significantly alter regional climate. The Hostetler lake model, a version of which is currently used in the Community Land Model, performs poorly in deep lakes when coupled to the regional climate of the International Centre for Theoretical Physics (ICTP) Regional Climate Model, version 4 (RegCM4). Within the default RegCM4 model, the lake fails to properly stratify, stifling the model’s ability to capture interannual variability in lake temperature and ice cover. Here, the authors improve modeled lake stratification and eddy diffusivity while correcting errors in the ice model. The resulting simulated lake shows improved stratification and interannual variability in lake ice and temperature. The lack of circulation and explicit mixing continues to stifle the model’s ability to simulate lake mixing events and variability in timing of stratification and destratification. The changes to modeled lake conditions alter seasonal means in sea level pressure, temperature, and low-level winds in the entire model domain, highlighting the importance of lake model selection and improvement for coupled simulations. Interestingly, changes to winter and spring snow cover and albedo impact spring warming. Unsurprisingly, regional climate variability is not significantly altered by an increase in lake temperature variability.

Corresponding author address: Val Bennington, Nelson Institute Center for Climatic Research, University of Wisconsin–Madison, 1225 West Dayton St., Madison, WI 53706. E-mail: benesh@wisc.edu

1. Introduction

a. Regional climate models

Global climate models (GCMs) have the ability to simulate the coupled ocean–land–atmosphere system across the globe for extended periods of time, though horizontal resolution is often sacrificed. Significant regional features, such as mountain chains and lakes, are poorly characterized by global climate models. Lake area and depth are often misrepresented in global climate models because of the grid spacing. Even large lakes, such as the Laurentian Great Lakes, with a combined surface area of more than 244 000 km2 and average depths ranging from ~15 m in Lake Erie to ~150 m in Lake Superior, are rarely incorporated into global climate models. Global climate models, which do include lake points such as Community Climate System Model, version 4 (CCSM4), generally assign all lake points a uniform depth of 50 m and poorly simulate deep lake temperatures (Subin et al. 2012).

Regional climate models (RCMs) aim to improve upon global climate models by including finer-scale topography, vegetation, and land cover and improved convective schemes, while utilizing GCM output as lateral boundary conditions. The finer grid spacing (tens of kilometers) generally improves simulated temperature, airflow, moisture, and precipitation in regions of heterogeneous vegetation, land cover, or topography. RCMs have been found to outperform reanalysis and GCM simulations in numerous studies (Giorgi and Bates 1989; Liang et al. 2008; Diffenbaugh et al. 2005; Zhu and Liang 2007; Wang et al. 2009). To understand the mean influence of these finer-scale features on regional climate and many other scientific questions, it may be adequate to prescribe a mean seasonal cycle to the land or lake surface state at high spatial resolution. In this case, it is far less computationally expensive to prescribe surface boundary conditions. However, depending on the scientific question to be addressed, it may be necessary to reasonably simulate the magnitude of interannual variability and trends in the land or lake state (surface boundary conditions). In some cases, variability of the system itself exceeds the mean state value, particularly in the midlatitudes. For instance, year-to-year variability (standard deviation) in fractional ice coverage of the Laurentian Great Lakes exceeds the annual mean ice fraction for the period 1973–2010 (Wang et al. 2012).

b. Lakes

Lakes alter local and regional climates through differences in moisture, surface roughness, and specific heat when compared to the surrounding vegetation. The large specific heat of water causes a delayed spring warming and autumn cooling of the lake, decreasing both daily and seasonal temperature ranges for the region (Notaro et al. 2013a), with this effect dependent on lake size, depth, and latitude. Lakes can act as a source of moisture during the ice-free, cool seasons through synoptic episodes of evaporation, with large, deeper lakes able to continuously supply water to the overlying air (Blanken et al. 2011). The decreased surface roughness of lakes acts to enhance over-lake wind speeds and can create shoreline convergence and precipitation (George 1940; Lemire 1961). As relatively warm (cool) air travels over a lake during summer (winter), the cool (warm) lake surface acts to enhance (decrease) atmospheric stability and decrease (increase) deep convection, cloud cover, and precipitation (Lyons 1966; Changnon and Jones 1972; Scott and Huff 1997; Holman et al. 2012). Additionally, the decrease in boundary layer height above the lake caused by the cold lake surface reduces the transport of momentum from higher altitudes down toward the lake surface, and above-lake wind speeds are reduced (Desai et al. 2009). Furthermore, the large Laurentian Great Lakes weaken winter anticyclones and summer cyclones (Notaro et al. 2013a; Cox 1917; Petterssen and Calabrese 1959) through this mechanism. Regional sea level pressure, temperature, wind direction, and moisture are all modified by the large lake presence in the Great Lakes region (Notaro et al. 2013a). Summertime evaporation from lakes is often less than evapotranspiration over surrounding forests; thus, large lakes can reduce summer moisture supply to the atmosphere, compared to terrestrial vegetation. Regional albedo is also influenced by the presence of ice cover during winter.

Lakes around the globe are currently changing. Lake ice cover has significantly declined around the globe (Magnuson et al. 2000); summer temperatures in the Laurentian Great Lakes (Austin and Colman 2007) and African Great Lakes have rapidly increased (Tierney et al. 2010). As we try to decipher likely projections of global and regional climates, these lake changes will likely be of importance to the regional atmosphere. As lake ice declines, regional albedo and latent and sensible heat fluxes will likely change. Warmer summer lake surface temperatures may directly impact surface fluxes of heat and momentum. Decreases in atmospheric stability above Lake Superior have already resulted in increased wind speed above the lake (Desai et al. 2009). As lakes continue to change in the future, we must have confidence that lake models utilized within climate models are physically based and capture the two-way lake–atmosphere interactions.

Although many multiyear regional climate model simulations now include interactive lake models (Lofgren 2002; Holman et al. 2012; Vavrus et al. 2013), there has been little effort to evaluate deep lake model performance within coupled regional climate models beyond a 10-day simulation (Hostetler et al. 1993), particularly the lake’s physical structure and ability to capture observed variability. When a study is explicitly focused on variability and/or trends, the lake model must capture year-to-year variability in temperature and ice cover to accurately simulate local climate features impacted by lake conditions (i.e., lake-effect snow). The International Centre for Theoretical Physics (ICTP) Regional Climate Model, version 4 (RegCM4), a widely utilized regional climate model (Giorgi et al. 2012), couples the one-dimensional, energy-balance lake model of Hostetler and Bartlein (1990) to the ice model of Patterson and Hamblin (1988) to the hydrostatic fifth-generation Penn State/National Center for Atmospheric Research (NCAR) Mesoscale Model (MM5) in order to simulate both short periods of weather and the long-term climate of a region. The Hostetler model is used in both offline and coupled lake simulations (Notaro et al. 2013a,b; Vavrus et al. 2013; Bates et al. 1995; Bonan 1995; Hostetler and Bartlein 1990; Hostetler et al. 1994; Stepanenko et al. 2010), as well as in global climate models as part of the land surface component. In a region where lakes significantly alter the regional climate, such as the Great Lakes region in North America, a reasonable representation of lake conditions is necessary to sufficiently capture regional phenomenon such as lake-effect snow (Notaro et al. 2013b; Gula and Peltier 2012). The Hostetler model coded within previous versions of RegCM was evaluated for the Great Lakes using a 10-day winter simulation (Hostetler et al. 1993; Bates et al. 1993) at 60-km horizontal resolution. This analysis could not investigate the model’s ability to capture year-to-year variability or lake vertical structure, given its duration, season, and chosen initial conditions. However, there was no indication that the model was not behaving as intended. The mean lake state simulated by RegCM4 was evaluated by Notaro et al. (2013a) and showed a damped seasonal cycle for the deep Great Lakes and an inability to simulate ice at deep lake points. We ask: Why is the seasonal cycle of deep lakes dampened within RegCM4.3? How does improving the physicality of modeled lake conditions alter the mean state and variability of the simulated regional climate? When is it appropriate to use an explicit lake model?

In this paper, we focus on improving the lake and lake ice models within RegCM4. We introduce the default lake (Hostetler et al. 1993) and ice models (Patterson and Hamblin 1988) as the models are currently coded into RegCM4, discuss model performance concerns, and suggest model alterations that improve the physicality of both lake temperature and lake ice simulations. We apply the lake temperature and ice models to the Laurentian Great Lakes, the largest collection of freshwater lakes in the world, because of the great depth and large influence of these lakes on regional climate. Lake models coupled to climate models tend to perform poorly for deep lakes (Subin et al. 2012; Martynov et al. 2010). We separately simulate and compare the regional climate using the default lake model (DEF) and the improved lake model (MOD). We believe that the model adjustments presented here may possibly be applied to other one-dimensional lake models within climate models. More importantly, we believe the work highlights the importance of lake model evaluation in all coupled models. In section 2, we introduce the default lake and ice models and the alterations made. In section 3, we discuss the impacts of model changes on lake temperature, ice, and simulated regional climate. In section 4, we discuss the implications of lake model improvements and remaining model inadequacies.

2. Methods

a. Model descriptions

RegCM4 (Giorgi et al. 2012) couples a modified version of the Hostetler lake model (Hostetler and Bartlein 1990) and the Patterson and Hamblin (1988) ice model to a modified version of the hydrostatic NCAR MM5 for both short- and long-term regional climate simulations. The Hostetler model and modified versions of the Hostetler model are used in both offline (i.e., lake does not feed back on atmosphere) and coupled lake simulations, as well as in global climate models as part of the land surface component Community Land Model (Subin et al. 2012).

1) Default lake model

The lake model (Hostetler and Bartlein 1990) is a one-dimensional lake model, implemented with 1-m vertical resolution in RegCM4. When coupled to a regional climate model, a large lake is represented by a collection of independent one-dimensional lake models, each with a depth defined by the local lake bathymetry. Thus, there is no direct exchange of heat or momentum between neighboring lake grid cells and no horizontal lake circulation. Figure 1 depicts a typical simulated summer and winter lake thermal structure and heat fluxes included within the lake model within RegCM4.3.

Fig. 1.
Fig. 1.

Schematic of one-dimensional lake model, depicting typical summer and winter lake conditions and air–lake heat fluxes. LWAVE and SWAVE stand for longwave and shortwave radiation, respectively. QW is conductive heat flux between ice and the water below.

Citation: Journal of Climate 27, 8; 10.1175/JCLI-D-13-00110.1

(i) Lake heating

During ice-free conditions, the lake surface and overlying atmosphere interact at each time step via downward solar radiation, atmospheric longwave radiation, longwave radiation emitted by the lake, and sensible and latent heat fluxes. Shortwave radiation is the only surface flux able to directly penetrate below the lake surface layer and input energy deep within the lake column, where the depth of penetration is calculated according to Beer’s Law. Within RegCM4, the attenuation coefficient is set to 0.5 m−1 for lake depths of less than 50 m, 0.3 m−1 for lake depths between 50 and 100 m, and 0.1 m−1 for lake depths greater than 100 m. The assumption that shortwave absorption varies according to depth is reasonable, as smaller lakes tend to be shallower and inundated with terrestrial colored matter that strongly absorbs shortwave radiation, visible in satellite imagery of the lakes (Mouw et al. 2013). Deep lake points are generally farther from shore, less nutrient rich, and less impacted by the shoreline, although the three discrete values of attenuation coefficients can lead to adjacent lake grid cells with very different optical properties that would, in reality, be smoothed by the horizontally mixing caused by circulation. During each time step under ice-free conditions, eddy diffusion is calculated, surface fluxes and diffusion act to warm or cool the lake layers, and convective mixing is possible. During ice-covered conditions, the surface water layer temperature is set to 1.778°C, no shortwave radiation is permitted to reach the water, and all surface fluxes occur between the ice layer and the overlying atmosphere.

(ii) Diffusion
The model parameterizes wind-driven eddy turbulence as enhanced diffusion and solves the vertical thermal diffusion Eq. (1) based on Henderson-Sellers (1986):
e1
where T is the temperature, z is the depth, km is the molecular diffusion of water, K is the local eddy diffusion, and cw is the specific heat of water. Eddy diffusion is determined by the wind speed and latitude in Eq. (2),
e2
where κ is the von Kármán constant, υs is the surface shear velocity [Eq. (3)], z is the depth in meters, Pr is the turbulent Prandtl number, ks is the Ekman profile parameter [Eq. (4)], and Ri is the local Richardson number [Eq. (5)], assuming an Ekman profile of velocities determined by the instantaneous winds:
e3
e4
e5
The variable u2m is the wind speed 2 m above the lake, lat is the latitude in radians, g is the gravitational constant, and ρ is local water density. As z is positive downward in the lake model within RegCM4, ρ/z > 0 when denser water lies below lighter water. The term under the square root is restricted to zero or greater. A maximum diffusivity allowable as the sum of molecular and eddy is set to 0.5 × 0.99 × dz2/dt2. For a time step of 60 (120) s, this corresponds to a maximum diffusivity of 0.008 25 m2 s−1 (0.004 125 m2 s−1). When ice is present, the only diffusion permitted is molecular diffusion.
(iii) Convection

Convection occurs when denser water lies on top of less dense water. In the Hostetler model, a buoyancy-induced instability anywhere within the water column forces the lake model to mix all layers from the surface down to the unstable layer. Mixing is an instantaneous reassignment of temperature in all of the mixing layers to the mean temperature from the lake top to the mixing depth, accounting for layer thicknesses. In RegCM4.3, convection and eddy mixing are only permitted when the lake point is ice-free.

2) Ice model

The ice model of Patterson and Hamblin (1988) is coupled to the lake model in RegCM4.3. Ice forms on the lake when lake surface temperatures are below −0.002°C and the net surface heat flux is a loss great enough to create 1 cm of ice. The model has a single growing ice layer and, when present, a growing snow layer. The ice bottom temperature is the freezing temperature (Tf), and a temperature gradient exists within the ice layer to the cooler ice top [Ti(z)]. This temperature gradient causes a conductive heat flux within the ice layer. When snow is present, the bottom of the snow is set to the temperature of the ice top. Positive heat fluxes are directed into the ice/lake.

The ice model uses two spectral bands for shortwave radiation, each with separate attenuation coefficients for both ice and snow (Table 1). At the surface, longwave radiation from the atmosphere (LD) warms the surface. Outgoing longwave radiation (LU) and conduction from within the ice/snow (q0) act to cool the surface. Depending on atmospheric temperature and humidity, latent (LH) and sensible (SH) heat fluxes may act in either direction. Once ice is formed, the surface temperature (T0) that balances heat fluxes at the surface [Eq. (6)] is iteratively solved for using a Newtonian method. This is required because four parts of the equation are dependent on the ice surface temperature itself. If the surface temperature is below zero, ice growth is possible, dependent on the ice bottom conditions, and the ice thickness (hi) increases. Ice melt occurs when the ice surface temperature exceeds 0°C [Eq. (7)]. Snow can accumulate on the ice when precipitation occurs during cold atmospheric conditions. When snow is present, the model solves for snow surface temperatures and melts snow before melting ice:
e6
e7
The variable T0 is the ice/snow surface temperature, ρi is the density of ice, and Lf is the latent heat of fusion. The Stefan–Boltzmann law describes the magnitude of longwave radiation emitted to space by the ice/snow layer. Sensible and latent heat fluxes are calculated with bulk formulae equations within RegCM4.3. The variable q0 is a function of the ice/snow surface temperature and the incoming solar radiation:
e8
e9
The variable Tf is the freezing temperature, ki is the thermal conductivity of ice, ks is the thermal conductivity of snow, hi is ice thickness, hs is snow thickness, I0 is the incoming solar radiation at the ice surface, A1 is the fraction of shortwave radiation in spectral band 1, A2 is the fraction of shortwave radiation in spectral band 2, λi1 and λi2 are the attenuation coefficients for spectral bands 1 and in ice, and λs1 and λs2 are the attenuation coefficients for spectral bands 1 and 2 in snow. The variable qpen is the analytical solution to Eqs. (8) and (9), describing the temperature distribution within the snow and ice layers and the boundary conditions, as discussed by Patterson and Hamblin (1988).
Table 1.

Lake and ice model parameters.

Table 1.
At the ice bottom, heat is conducted toward the cooler ice surface (qf). The net upward heat from the ice bottom (qf) is the solar radiation absorbed by the ice and snow layers not conducted out from the surface [Eq. (10)]. Heat is conducted to the ice from the warmer water below (qw) [Eq. (11)]:
e10
e11
where Tw is the water temperature, kw is the thermal conductivity of water, Cs is the Stanton number, Cp is the specific heat of water, and U is the speed of lake currents at the surface.
In RegCM4.3, U = 0, qw is set to a constant value of 1.389 W m−2, and the water temperature below the ice is set to a constant value of 1.778°C. When qw < qf, there is a net loss of heat at the ice–water interface and ice growth occurs:
e12
When thin ice is present, RegCM4.3 does not strictly conserve energy within the ice model. It calculates an amount of solar energy absorbed by the ice, but it does not use the energy penetrating through the ice to heat the underlying water. Similarly, when both snow and ice layers are present and there is melting, the model melts the snow first. RegCM4.3 assumes that no excess energy exists to melt the ice below.
Sensible and latent heat fluxes in the presence of ice.
The default lake model within RegCM4.3 sets the ground temperature to the mean temperature of the ice and lake water surface temperature (twi, ~2°C) when ice is present. Thus, the atmospheric model sees ~0–2°C water when calculating latent heat fluxes during the ice-covered season [Eq. (13)], not ice surface temperatures, which easily fall below 0°C:
e13
where qa is the specific humidity of the overlying atmosphere, qw is the specific humidity of the saturated air immediately above the lake surface (twi), and Ct is the transfer coefficient, modified by atmospheric stability, wind speed, and surface roughness.
For calculating sensible heat fluxes between the ice-covered lake and atmosphere, the atmosphere sees 2°C water to calculate the energy flux. This flux is then reduced according to the ice and snow thickness:
e14
where ρa is the density of the atmosphere, Cpa is the specific heat of air, Cd is the transfer coefficient, Ta is the atmospheric temperature, href is the reference height, and steepf is the steepness function.

3) Model changes

Here we describe how the lake model is altered.

(i) Lake heating
The shortwave attenuation coefficients (a) in RegCM4.3 are reasonable, but the values jump as a step function of depth (d) [section 2a(1)]. We update the values of attenuation coefficients to a continuous function of local depth according to Håkanson (1995), as done by Subin et al. (2012):
e15
In the default model, shortwave radiation is cut off from lake water when ice is present, and energy is not strictly conserved within the ice model. We modify this to permit shortwave radiation that is not absorbed within the snow and ice layers [second term on the right side of Eq. (10)] to warm the lake, although the conductive heat loss to ice (qw) may act to cool the water surface.
(ii) Diffusion
Although a one-dimensional lake model does not have currents, real lakes are always in motion, and eddy diffusion is much larger than molecular diffusion, even without strong winds or instabilities. Deep lakes, with the capacity to store greater amounts of heat, are poorly simulated when low diffusivities are used in offline simulations (Martynov et al. 2010). We update the model to enhance diffusion according to Subin et al. (2012), as suggested by Fang and Stefan (1996), using under-ice measurements of diffusivity conducted by Ellis et al. (1991). We enhance minimum diffusivity by a factor of 1000 (Martynov et al. 2010):
e16
where N2 is the Brunt–Väisälä frequency, limited to a minimum of 7.5 × 10−5 s−2 (Fang and Stefan 1996). As discussed by Subin et al. (2012), this enhancement of diffusivity is only important to deep lake points, and as such, is limited to lake points with a depth greater than 50 m. This change increases heat vertical heat transport within the column, particularly during periods of high winds. Eddy-enhanced diffusion under ice is now permitted.
(iii) Convection

Within RegCM4.3, the Hostetler convective mixing scheme causes problems with stratification (see section 2c). When a buoyancy-driven instability exists between two lake layers, for example, the Hostetler model forces complete mixing from the top of the layer to the bottom. The small density variations possible within a single time step within RegCM4.3 causes perpetual mixing at many simulated lake points, unrealistic deep water temperatures, severe sensitivity to initialized lake temperatures, and a seriously dampened seasonal cycle of surface temperatures. To improve stratification within RegCM4.3, the convective scheme is modified. Instead of mixing from the top to any region of instability, the model now iteratively moves from top to bottom, finds whether any layers are unstable relative to that layer, and mixes only the unstable layers (and those between them). Thus, when instability exists between several layers within the thermocline, mixing now occurs only between those layers, not from the lake surface to the thermocline. Mixing in both the Hostetler model and in this modified lake model is an instantaneous reassignment of temperature in the selected layers to the mean temperature of those layers, accounting for layer thicknesses. We now permit buoyancy-driven convection under ice, should the conditions exist.

(iv) Ice

Errors within the ice model of RegCM4.3 are corrected. The variable I0, the incoming solar radiation at the ice/snow surface, was mistakenly modified by qpen (the penetrating solar radiation) in RegCM4.3, causing problems in both melting and growing calculations. This is corrected, as I0 is not modified by any conditions below the surface. Energy is now conserved within the ice model. Lake surface temperatures and the conductive flux from water to ice (qw) are no longer held constant, and qw now varies according to Eq. (11). When both snow and ice are present and the layers are melting, snow melts first. If all snow is melted, any excess energy is now used to melt ice. The maximum snow depth suggested by Patterson and Hamblin (1988), dependent on ice thickness, is now utilized. Basal melting is now permitted, conserving energy, such that the heat flux between the water and ice may either melt or grow ice. Eddy-enhanced diffusion under ice is now permitted.

b. Model runs

RegCM4.3 (Pal et al. 2007; Elguindi et al. 2011) was configured at 20-km horizontal resolution for the Laurentian Great Lakes region. The domain is centered at 44°N, 85°W and has a zonal extent of 3040 km and a meridional extent of 2560 km (Fig. 2a). Individual lake grid points and corresponding depths are depicted in Fig. 2b. The atmosphere includes 18 terrain-following vertical sigma layers, by default, and atmospheric dynamics that are based on MM5 (Grell et al 1994). RegCM4.3 is a compressible hydrostatic model. The Biosphere–Atmosphere Transfer Scheme (BATS; Dickinson et al. 1986, 1993), which includes three soil layers and 20 types of land cover, simulates the heat, moisture, and momentum fluxes between the atmosphere and land surface. The lake and accompanying ice models are turned on, an option within RegCM4.3. Convective precipitation is parameterized using the Grell scheme (Grell 1993). Lateral boundary conditions from the National Centers for Environmental Precipitation (NCEP)–NCAR Reanalysis (Kalnay et al. 1996) and the National Oceanic and Atmospheric Administration (NOAA) Optimum Interpolation (OI) Sea Surface Temperature (OISST; Reynolds et al. 2002) are imposed every 6 h within the 15 grid cells nearest the domain boundary. The relaxation to boundary conditions of temperature and wind linearly decreases to zero, moving away from the boundary. We run the model from 1975 to 2009 using RegCM4’s default lake model (DEF) and with the modifications described above (MOD). Nothing else differs between the two runs. We treat 1975–84 as a spinup period for the deep lakes and compare the simulations for 1985–2009.

Fig. 2.
Fig. 2.

(left) Model domain topography and extent. (right) Model lake bathymetry (m) and NDBC station locations.

Citation: Journal of Climate 27, 8; 10.1175/JCLI-D-13-00110.1

c. Observations

1) Lake temperature

To evaluate model performance, we utilize the National Data Buoy Center (NDBC) buoy data on each of the Laurentian Great Lakes, (Fig. 2b). The NDBC places between one and three buoys on each of the Great Lakes every spring (usually in April) and removes them each fall (usually in November). The buoys measure lake surface temperature, air temperature, wind speed and direction, and dewpoint at half-hourly resolution. These direct measurements have little uncertainty when the equipment is operating properly. No buoys are present during winter, so we utilize NOAA Great Lakes Environmental Research Laboratory (GLERL) satellite-derived Great Lakes Surface Environmental Analysis (GLSEA) product (Schwab et al. 1992) that provides a lakewide daily mean lake skin temperature for each lake from 1995 to the present (available at http://coastwatch.glerl.noaa.gov/glsea/). Given significant cloud coverage over the lakes, particularly in winter, and interpolation in both space and time within this product, uncertainties are on the order of a couple degrees.

2) Lake ice

To evaluate model ice performance, we regrid the Great Lakes Ice Atlas (Assel 2003, 2005; Wang et al. 2012) to the model grid. Beginning in the 1970s, ice concentrations and age were estimated by visual and radar observations by Environment Canada, NOAA GLERL, and the U.S. Coast Guard. These observations were rounded to the nearest 10% of ice coverage and charted by hand. Assel (1983) used these charts to create the Great Lakes Ice Atlas by interpolating ice coverage over both time and space. Here we note that observational data were partitioned into half-month periods, because of data availability, and were later interpolated to create estimates of daily ice coverage, again rounded to the nearest 10%. Assel (2003, 2005) and Wang et al. (2012) continued this atlas through the winter of 2011. We utilize these observations for 1985–2009. When calculating the number of days with any ice, a day is considered an ice day when any ice (>10%) is present in observations, as the model is incapable of partial ice coverage in a grid cell. When calculating fractional ice coverage, the percent cover in each grid cell is retained.

3) Atmosphere

Temperature and precipitation are compared against monthly mean station observations gridded to 0.5° × 0.5° from the University of Delaware (UDEL; Willmott and Matsuura 1995). For precipitation, we utilize the undercatchment-corrected precipitation dataset (Matsuura and Willmott 2009). Precipitation uncertainty within the UDEL dataset is ~30%, comparing undercatchment corrected to the uncorrected dataset. Simulated above-lake atmospheric conditions are evaluated against NDBC buoy data.

3. Results

a. Lake temperature

Simulated surface lake temperature daily climatology is compared to available observations at the nine NDBC buoy locations (Fig. 3). The default lake model severely underestimates the seasonal variations in temperature at the five deepest buoy locations (45001, 45004, 45006, 45007, and 45012; Figs. 3e–i), with simulated amplitudes of the seasonal cycle that are 3°–6° when observed amplitudes are >20°. Here, simulated surface temperatures are far cooler than observed during summer and warmer in spring and fall. Thus, the default model fails to generate a reasonable seasonal cycle at any of the deep Lake Superior, Lake Ontario, or Lake Michigan buoy locations. The modified model improves the seasonal cycle at these buoy locations, without much change to shallow lake locations. At shallow locations, this increase in amplitude is primarily due to cooler spring temperatures, and at the Lake Erie buoy location, it is due to winter ice that remains until late spring. At deep locations, the impact of model revisions on lake temperatures is evident year round. Interestingly, although stratification occurs later in the modified lake model, the maximum surface temperatures are greater in the modified model. This may be due to increases in stability in the modified lake model, or warmer air resulting from an increase in lake temperatures at deep lake points. Lake surface temperatures at deep lake points remained above 4°C year round in the default model, but model revisions make freezing possible (as shown in Figs. 8, 9). Furthermore, surface temperatures warm too rapidly in spring and far exceed observed summer temperatures and atmospheric temperatures, a deficiency that is also present in shallow locations of the default model. This deficiency is present in both the offline and online Hostetler model runs by Martynov et al. (2010, 2012) as well, likely caused by the lack of explicit convection, absence of lake circulation, and the inability to disrupt summer stratification during storm events.

Fig. 3.
Fig. 3.

Observed (black) and simulated (blue, DEF; red, MOD) mean seasonal cycle of lake surface temperature at the nine Great Lakes NDBC stations (Fig. 2). Buoy stations are sorted according to local lake depth, shallowest to deepest. Line widths depict interannual variability (standard deviation) in local lake surface temperature.

Citation: Journal of Climate 27, 8; 10.1175/JCLI-D-13-00110.1

These issues with the default model in RegCM4.3 are not isolated to buoy locations. Figure 4 depicts the mean seasonal cycle of lake surface temperature for each of the five Great Lakes as simulated by the default (blue) and modified (red) model and the GLSEA observations. The dampened seasonal cycle of temperature in the default model is apparent in Lakes Superior, Michigan, and Ontario, and to a lesser extent, Huron. Lakes with a larger percentage of deep points show an increasingly dampened seasonal cycle in the default model, and the modified model decreases winter lake surface temperatures and increases summer lake surface temperatures. The modified model has the opposite issue of lake surface temperatures: too hot in summer compared to observations in the deep lakes.

Fig. 4.
Fig. 4.

Lakewide mean lake surface temperatures from the GLSEA satellite data product (1995–2009, black), simulated by the default lake model (1985–2009, blue) and simulated by the modified lake model (1985–2009, red).

Citation: Journal of Climate 27, 8; 10.1175/JCLI-D-13-00110.1

To determine whether model modifications are solely responsible for this overheating, we separate mean lake surface temperatures for shallow lake points (<50 m) and deep lake points (50+ m) for Lakes Superior, Michigan, Huron, and Ontario (Fig. 5). While the modified model causes a slight increase in lake surface temperatures at shallow lake points, the increase in lakewide mean surface temperatures seen in Fig. 4 is due to the increasing physicality of deep lake points in the modified model. Shallow lake points in the default model were also too warm, but the unphysical cool deep lake points in summer and hot deep lake points in winter helped to mask the problems of the default model, when utilizing lakewide mean temperatures. Figure 5 also highlights the fact that the modified Hostetler model within RegCM4.3 is able to capture the increased thermal inertia of deep lake points, with a delayed onset of stratification in spring and delayed winter mixing. Increased shallow lake temperatures during summer within the modified model may in part be due to the increase in surface temperatures at the now warmer deep lake points.

Fig. 5.
Fig. 5.

Mean lake surface temperatures for shallow lake portions (0–49 m; solid lines) and deeper lake portions (50+ m; dashed lines) for Lakes (a) Superior, (b) Michigan, (c) Huron, and (d) Ontario. The default model is depicted in blue, and the modified lake model results are shown in red. Lake Erie has no model lake points deeper than 49 m, so it is not included here.

Citation: Journal of Climate 27, 8; 10.1175/JCLI-D-13-00110.1

b. Lake stratification

Behavior of deep lake surface temperatures warrants an examination of lake vertical thermal structure. The lakewide mean seasonal cycle of thermal structure and percent ice cover as simulated by the default model is shown for each lake in Fig. 6. Lake Superior, a predominantly deep lake (Table 2), illustrates how the Hostetler model, as coded within RegCM4.3, is not compatible with RegCM4.3. Temperature is isothermal with depth nearly year round. Lake temperature at 100 m reaches a minimum of nearly 279 K (6°C) in late winter and increases to 282 K (9°C) in summer. The lake is not properly stratifying. Shallow points need not stratify for warm surface temperatures to occur. Thus, lakewide mean increases in surface temperatures are not necessarily caused by the presence of stratification, but rather by the ability to warm an entire column of shallow water in summer. As the fraction of shallow lake points increases, such as in Lakes Michigan, Huron, and Ontario, the discontinuity between shallow and deep lake temperatures is apparent near 80 m. Lake Erie contains zero deep lake points. Deep lake points are incapable of freezing, as cooling an entire 100-m column of water to 273 K does not occur. In the default model, lake ice onset begins in November and December, when lake points of 2-m thickness are able to cool and freeze. Ice coverage maximizes in March in Lakes Michigan, Huron, and Superior. Lakes Erie and Ontario reach a maximum ice extent in January and maintain these maxima into March.

Fig. 6.
Fig. 6.

Mean vertical thermal structure (1985–2009) of (left) shallow (0–49 m) and (right) deep (50+ m) lake points for each of the Great Lakes as simulated by DEF. Note the logarithmic axes for depth, in order to visualize upper-layer vertical thermal structure. Time series of shallow and deep percentage of ice coverage is shown in black.

Citation: Journal of Climate 27, 8; 10.1175/JCLI-D-13-00110.1

Table 2.

Model representation of the Great Lakes.

Table 2.

In the modified model, physicality of the vertical thermal structure is improved (Fig. 7). Stratification in summer occurs across the lakes, and a reverse stratification is present in winter below the ice. This stratification permits even deep lake points to freeze during winter, and the lakes form excessive ice (Fig. 8). Observed winter mixed layers are deeper than those simulated in Lake Superior, with mixing to ~100 m (J. Austin and D. Titze 2013, personal communication). Additionally, observed isothermal conditions persist for months during winter, which would delay ice onset. Thus, the lake model is still too stable in winter, and correction of this winter stability could significantly delay ice onset and would reduce simulated ice at deep lake points. Modeled ice coverage reaches 100% cover from mid-January through March on Lake Superior, from February through March on Lakes Huron and Ontario, and from mid-January to mid-March on Lake Erie. Individual grid cells may form deep ice that lasts well into spring, without any circulation to break up the ice.

Fig. 7.
Fig. 7.

As in Fig. 6, but for MOD.

Citation: Journal of Climate 27, 8; 10.1175/JCLI-D-13-00110.1

Fig. 8.
Fig. 8.

Mean number of days of winter ice as simulated by (a) DEF and (b) MOD and (c) observed. A winter ice day is considered any day with at least 10% ice cover in observations. The interannual variability [standard deviation (STD)] in winter ice days is shown in (d) DEF, (e) MOD, and (f) observed.

Citation: Journal of Climate 27, 8; 10.1175/JCLI-D-13-00110.1

The lack of stratification at deep lake points is responsible for the dampened seasonal cycle in temperatures seen in Fig. 4. Thus, the Hostetler model coupled to RegCM4 was failing to reasonably simulate the physical characteristics of the lakes, in which all lake points stratify. At shallow points, where stratification is unnecessary to capture the seasonal cycle of temperature, this issue goes unnoticed. The modified model captures stratification during both the winter and summer seasons, with summer mixed layer depths ranging from <10 m at shallow lake grid cells to >20 m at deep lake points, reasonable estimates when compared to Environmental Protection Agency (EPA) observations (www.epa.gov/glnpo/monitoring/data_proj/glenda).

c. Mean lake ice coverage

In the default model, lake ice development was impossible at deep lake points in RegCM4.3 that failed to stratify because of the unphysical vertical lake structure and resulting temperatures. Winter temperatures remain above 4°C at deep lake points even at their minimum (Figs. 3, 4), prohibiting ice formation. The modified model, which is capable of stratifying in both summer and winter, corrects this, but is limited by the one-dimensional model structure and lack of currents or explicit convection. Lake thermocline depth is completely determined by shortwave attenuation and wind speed, and thus, lake ice formation is controlled by shortwave attenuation (here determined by lake depth), wind speed, and latitude. The spatial structure and variability in ice coverage simulated in the default and modified models are evaluated against the Great Lakes Ice Atlas (Fig. 8). The modified model clearly improves the extent of ice cover in the deep portions of Lakes Superior, Huron, and Michigan but overestimates the mean number of winter ice days in the deep eastern basin of Lake Superior. Gula and Peltier (2012) simulated Great Lakes ice coverage using the FLake model within a regional climate model. The average ice duration simulated by Gula and Peltier (2012) is 135 days for the northern half of Lake Superior, a much larger bias than simulated here (75 days). The observations clearly reflect lake depth, latitude, and circulation, but model ice coverage is controlled only by depth and latitude. Increases in Lake Erie ice coverage may be due to domain cooling (see section 3d). The modified model also increases interannual variability in simulated ice coverage for Lakes Superior, Michigan, and Huron, which is more reasonable compared to observations, but still too low.

To consider partial ice coverage in the observations, we compare the mean fraction of the lake surface covered by ice during a given winter between observations and the model (Fig. 9). The modified model improves correlations with observations on all lakes except Ontario. Lake Superior correlations remain unchanged. Ice fraction variability is amplified on all lakes because of the ability of deep lake points to form ice during cold years. Ice cover on Lake Erie, the shallowest Great Lake, is well captured by both models. Although model revisions decrease winter temperatures at deep lake points, mean ice fractional coverage is only significantly changed on Lake Superior, the lake farthest north. Lake Ontario is sensitive to climatic variations that cause ice gain/loss at the deeper points on Lake Ontario because of the small number of lake points and their depth distribution (Table 2).

Fig. 9.
Fig. 9.

DJFMA for (a) the Great Lakes as a whole, (b) Lake Superior, (c) Lake Michigan, (d) Lake Huron, (e) Lake Erie, and (f) Lake Ontario as observed (black) and simulated by the default (blue) and modified (red) lake models. Correlations to observations noted within each subplot.

Citation: Journal of Climate 27, 8; 10.1175/JCLI-D-13-00110.1

Mean winter ice coverage is high in the modified model. There are several possible reasons for this deficiency. First, regional air temperatures are decreased by model modifications that will increase ice coverage. Second, to stratify at deep lake points within RegCM4.3, the lake convective scheme was altered to be more stable. Winter mixed layer depths are half of those observed in Lake Superior, and thus, the deep lake is able to cool the surface more rapidly in winter, having only to cool the top 50 m of the water column. Additionally, the entire water column is observed to sometimes cool below 4°C, requiring significantly more cooling than simulated before ice formation. Additionally, horizontal heat transport within the lake must be considered in the observations to the heat budget of deep lake points, and thus, lateral heating and cooling may be important here. Finally, lake circulation moves newly formed ice and inhibits ice formation and growth (Fujisaki et al. 2013), which cannot be considered here.

d. Regional air temperatures

We assess the impact of altered lake conditions on the regional 2-m air temperatures in Fig. 10. Decreased winter lake surface temperatures result in a regional cooling during December–February (DJF) of more than 2°C over the lakes. This temperature decrease is reduced farther from the lakes, with nearly no temperature change south of Illinois. During March–May (MAM), air temperatures are similarly decreased, but not by a change in lake temperatures. Increases in snow precipitation (section 3e) result in increased snow cover and higher albedos that persist later into spring than in the default model. This results in a cooling of spring temperatures in the modified model. During summer [June–August (JJA)], air temperatures directly above the deeper lakes are increased by more than 3°C. However, air temperatures farther from the lake are indirectly slightly decreased by this increase in summer lake temperatures. During fall [September–November (SON)], air temperatures are only significantly altered directly above the deep lakes, where increases are greater above deeper lake points.

Fig. 10.
Fig. 10.

Mean seasonal (1985–2009) air temperature changes (modified minus default) near the surface (2 m) caused by lake model modifications within RegCM4.3 for (a) DJF, (b) MAM, (c) JJA, and (d) SON.

Citation: Journal of Climate 27, 8; 10.1175/JCLI-D-13-00110.1

Mean simulated seasonal air temperatures 2 m above land in the default model are compared to UDEL data to understand biases, changes, and potential improvements due to lake model revisions (Fig. 11). UDEL gridded observations are available through 2006, so we compare seasonal temperatures for 1985–2006. During winter (DJF), the default model overestimates temperatures in the northern portion of the domain while underestimating eastern domain temperatures (Fig. 11), despite a large warm lake bias during winter (Notaro et al. 2013a). Model modifications cause winter cooling, and the northern warm bias during winter is now a cold bias.

Fig. 11.
Fig. 11.

Near-surface air temperature (2 m) bias in DEF (1985–2006) compared to gridded station observation dataset UDEL for (a) winter, (b) spring, (c) summer, and (d) fall. Seasonal precipitation biases (cm month−1; 1985–99) for (e) winter, (f) spring, (g) summer, and (h) fall as simulated by the default model. Precipitation is compared to the undercatchment-corrected gridded station observations of UDEL. (i) Domain-wide, mean monthly biases (1985–2006) in near-surface temperature for DEF (blue) and MOD (red). (j) The seasonal cycle of domain-wide precipitation biases (mm month−1) for the default (blue) and modified (red) model for 1985–99.

Citation: Journal of Climate 27, 8; 10.1175/JCLI-D-13-00110.1

Spring (MAM) temperature biases in the default model are small and similar in pattern to winter biases (Fig. 11). Temperature changes caused by the model modifications cause a 1°–2°C warm bias in the northern portion of the domain to a 1°–2°C cold bias. During summer (JJA), the default model severely overestimates regional air temperatures, with biases exceeding 5°C in the southwestern domain (Fig. 11). The modified model still has a warm bias in the western and southwestern portion of the domain during summer; this bias is decreased by 1°–2°C by the modifications. Warming of deep lake surface temperatures during summer results in a decrease in air temperatures away from the lake. The default model has a slight cold bias in fall (Fig. 11), which remains largely unchanged by modifications. This regional cooling is seen during all seasons in the model update, and a possible explanation is provided below.

To evaluate above-lake atmospheric temperatures simulated by both the default and modified models, we compare buoy observations of air temperature, at approximately 4 m above the lake surface, to modeled 2-m air temperature in the corresponding grid cells (Fig. 12). Considering the dramatic changes to lake surface temperatures caused by model modifications at buoy locations of great depth, the atmospheric temperatures at buoy locations are far less altered (Fig. 12). In fact, atmospheric temperatures are only increased by 5°C over the deepest portions of Lake Superior by model revisions from July through September, when lake surface temperatures were increased by 10°C during the same period (Fig. 3). This suggests that modeled above-lake temperatures are largely driven by regional atmospheric temperatures and dampened only slightly by modeled lake temperatures, pointing to a likely model deficiency in air–lake heat fluxes.

Fig. 12.
Fig. 12.

Mean (1985–2009) above-lake air temperatures (model at 2 m) at the nine NDBC buoy locations on the Great Lakes. Observed (black), simulated by default (blue) and modified (red) lake model within RegCM4.3. Observations at ~7 m. Buoy observations did not begin on Lake Ontario until 2004. Line widths depict a single standard deviation across years. Note large variability in observed temperatures in winter/early spring may be due to inadequate number of years of observation, since buoys usually deployed from April to November.

Citation: Journal of Climate 27, 8; 10.1175/JCLI-D-13-00110.1

e. Atmospheric dynamics

We depict the changes to sea level pressure and surface winds for each season caused by lake model revisions in Fig. 13. Winter lake surface temperatures are colder at lake points of great depth in the modified model because of the modified model’s ability to stratify. Lake surface temperatures decrease by more than 4°C in these deep regions, and ice is more extensive. Thus, colder surface temperatures and a higher surface albedo (section 3f) result in higher sea level pressure, with increases in excess of 1 hPa (Fig. 13a). Wind changes are controlled by a change in sea level pressure and a change in land surface roughness. While expected wind changes would show a geostrophic response according to sea level pressure changes, this is not the only mechanism that alters the wind fields during winter and early spring (Fig. 13a,b). Increases in snow coverage decrease the surface roughness the wind field experiences in the modified model, thereby increasing the mean wind speeds. Thus, south of the center of the anomalous high in Fig. 13a, where one might expect to see an easterly anomaly in winds, this easterly anomaly is smaller than the enhancement of the mean westerlies. This decrease in surface roughness also increases the magnitude of the anomalous westerlies in the northern portion of the domain.

Fig. 13.
Fig. 13.

Statistically significant changes in seasonal mean (1985–2009) sea level pressure (hPa) and winds (m s−1) at 10-m height caused by lake model modifications within RegCM4.3 are shown for (a) winter, (b) spring, (c) summer, and (d) fall. Changes are shown as MOD minus DEF.

Citation: Journal of Climate 27, 8; 10.1175/JCLI-D-13-00110.1

The cold temperature anomalies in spring caused by increased snow cover and surface albedo in the modified model causes an anomalous high in the northern and northeastern portions of the domain. The change in the wind field resembles the expected geostrophic response (Fig. 13b), with minor alterations due to land surface roughness changes during March. During summer, the model modifications result in warmer surface temperatures of the deep lakes and lower sea level pressure directly over the Great Lakes of ~0.75 hPa over deep Lake Superior (Fig. 13c). A cooler summer to the south, perhaps caused by the delay in spring warming and increased soil moisture, causes an anomalous high. Warming directly over the lakes causes a smaller anomalous low directly over the lakes. The anomalous sea level pressure in summer leads to anomalous northerly winds in the southern portion of the model domain, contributing to cooling of the area (Fig. 12c). Only minor sea level pressure changes are evident in fall, with smaller warming over the upper lakes resulting in lower sea level pressure there (Fig. 13d).

f. Precipitation

During winter, decreased lake surface temperatures and increased ice cover unsurprisingly reduce seasonal precipitation (Fig. 14) by 6–8 cm per season directly over eastern Lake Superior. Seasonal totals of spring precipitation in the domain remain largely unchanged (Fig. 14). During summer, precipitation is increased in the domain, particularly on the lake coasts, increasing the domain-wide wet bias (Fig. 11j). This is likely due to increased lake temperatures and the resulting increases in lake evaporation during summer, moistening the regional atmosphere. Precipitation remains slightly increased in fall over eastern Lake Superior (2–4 cm). Summer increases in precipitation dominate the mean annual change in precipitation of up to 15 cm near the lakes and to the east of the lakes. Increases in precipitation away from the lakes are due to increases in soil moisture and resulting evapotranspiration.

Fig. 14.
Fig. 14.

Statistically significant mean changes (modified default) in (a) winter, (b) spring, (c) summer, and (d) fall and (e) annual precipitation (1985–2009) caused by lake model modifications. Changes are shown as MOD minus DEF.

Citation: Journal of Climate 27, 8; 10.1175/JCLI-D-13-00110.1

Snowfall is decreased by model modifications over Lake Superior for January and February by increased lake ice cover (Fig. 15). Snowfall increases over the other lakes and to the east and southeast of the lakes from January through March. The increases in snowfall seen within the domain are caused by decreased air temperatures (Fig. 10) and a conversion of rain to snow by model modifications. The increase in snowfall leads to deeper snow cover throughout winter, delayed melt in spring, an increase in winter and early spring surface shortwave albedo, and a decrease in land surface roughness.

Fig. 15.
Fig. 15.

Changes in mean (1985–2009) monthly snow totals (cm month−1) caused by lake model modifications within RegCM4.3 are shown for (a) December, (b) January, (c) February, and (d) March. Changes are shown as MOD minus DEF.

Citation: Journal of Climate 27, 8; 10.1175/JCLI-D-13-00110.1

g. Interannual variability

The mean state of both the lake and surrounding regional climate are altered by model modifications, and thus, interannual variability may be altered. Simulated interannual variability in lake surface temperature simulated by the two model versions is compared between observations in Fig. 16. The modified model increases the variability in lakewide surface temperatures of all lakes throughout spring through fall, improving the simulated variability compared to the satellite data product estimates. Spring lake surface temperature variability is doubled for Lake Superior. However, stratification remains too early (June) and is not variable enough compared to observations, which show a peak of variability in July of more than 4°C (Fig. 16a). For Lake Michigan (Fig. 16b), lake surface temperature variability is improved by model modifications, particularly in May and June, during the timing of stratification, although still less variable than observed. Variability in Lake Huron is only slightly improved (0.25°–0.5°C) in spring through fall (Fig. 16c), but surface temperature variability in Lake Ontario agrees with observations in the modified model (Fig. 16d). Even variability in shallow Lake Erie agrees better with observations (Fig. 16e).

Fig. 16.
Fig. 16.

Interannual variability in lakewide surface temperatures (1995–2009) for Lakes (a) Superior, (b) Michigan, (c) Huron, (d) Ontario, and (e) Erie as simulated by DEF (blue) and MOD (red) and estimated by the GLSEA satellite product (black).

Citation: Journal of Climate 27, 8; 10.1175/JCLI-D-13-00110.1

Ice coverage is dependent on lake winter temperatures, as well as on correction of model bugs. Ice cover variability in the unmodified model is only possible at shallow lake points, where stratification is unnecessary to reach a freezing surface temperature and at random deep points where stratification occurs. Correlations between observed ice coverage (black) and simulated ice fraction are improved for all lakes but Superior and Ontario by the modified model (Fig. 9). Importantly, the magnitude of ice cover variability in the modified model is an improvement over the default model (11.4%, 12.1%, 10.5%, 13.8%, 14.1%, and 13% in the modified model compared to 4.4%, 4.2%, 4.9%, 6.0%, 14.2%, and 12.9% in the default model for Great Lakes, Superior, Michigan, Huron, Erie, and Ontario, respectively). The modified model reasonably captures the standard deviation in winter ice fraction (DJFMA) variability for all lakes but Ontario (9.5%, 11.9%, 5.9%, 11%, 13.6%, and 4% for all lakes, Superior, Michigan, Huron, Erie, and Ontario, respectively). Treating the lakes as a single, combined lake, the modifications increase the interannual variability in ice cover from 4.4% to 11.4%, more reasonable compared to the observations, 9.5%, during this period. The small surface area of Lake Ontario and strong depth contrasts within the small lake make simulating ice fraction on that lake challenging without a finer-resolution lake model.

Only minor changes in variability of regional (10 m) winds and temperature (2 m) are caused by model changes. The regional increase in winter westerly winds over land (0.1 m s−1), seen in Fig. 10, results in a 10%–20% increase in winter U-wind variability. Westerlies are decreased in summer, with a corresponding 10% decrease in U-wind variability. V-winds are impacted during winter and summer (Fig. 10), and an increase/reduction in southerly flow results in a small increase/decrease in winter/summer V-wind variability. Temperatures over land are decreased year round by model modifications, but variability remains unchanged. Changes to winds and moisture can be seen throughout the entire atmospheric column but are largest below 550 hPa. The increased magnitudes of lake ice and lake temperature variability do little to alter domain-wide regional climate variability.

4. Discussion and conclusions

The lake model within RegCM4.3 (Hostetler and Bartlein 1990) fails to reasonably simulate stratification at deep lake points, and thus, results in unphysical lake temperature and ice simulations at deep lake points, which influence regional climate. Instead of stratifying, the entire lake column warms and cools with the seasons, and thus, the seasonal range of temperatures is unreasonably small at deep lake points. The lack of winter cooling results in a failure to create ice at deep lake points during even the coldest of winters in the unmodified lake model. Interannual variability in lake temperature and ice are seriously dampened. Here, we improve the performance of the lake model with alterations to vertical diffusion, convection, and attenuation and correct coding bugs found within the Patterson and Hamblin (1988) ice model in RegCM4.3. We subsequently investigate how these changes alter the mean state and variability of the lakes themselves, as well as how these changes alter the regional climate.

We improve the amplitude of the seasonal cycle of surface lake temperatures at deep lake points by altering convection and diffusion within the lake model. Deep lake points are now able to stratify. The seasonal cycle of lake surface temperatures is improved in amplitude, resulting in colder lake surface temperatures in the deep lakes during winter and warmer lake surface temperatures in the deep lakes during summer. During winter, this cooling results in increased atmospheric pressure, centered over Lake Superior, resulting in anomalous easterly winds over the lakes and weaker net wind speeds. Less precipitation—but higher snowfall amounts in winter—increases snow cover and early spring albedo. This delays regional warming, as well as results in an increase in summer soil moisture. During summer, warmer lake surface temperatures over deep lake points cause a local warming and lower atmospheric pressure over the lakes, but the lingering effects of an altered spring and anomalous northerly flow in the southern part of the domain result in summer cooling away from the lakes.

While the evaluation of the Hostetler lake model in coupled regional climate model simulations has historically been limited by computational expense, the present study clearly illustrates the need for such investigations. For historic simulations, prescribing observed lake temperature and ice conditions, or a simple climatology of lake conditions, would be an improvement over the computationally expensive coupling of the default one-dimensional Hostetler lake model to RegCM4.3. However, this is clearly inadequate when one wishes to use the coupled model for future climate simulations or variability in lake-effect snow. We must ensure that the coupled model behaves physically, in the vertical structure and climate sensitivity, if we are to utilize coupled lake models for future regional climate simulations.

a. Variability

The lake model alterations improve seasonal and interannual variability in lake temperature and ice cover. Altering the mean state of the lake changes the simulated regional climate, both in the mean and its variability. Although lake variability is increased with model changes, the variability in the simulated regional climate does not increase. Unsurprisingly, lake conditions are driven by the regional climate, and lake variability is not a first-order control on the larger regional climate variability. Variability in lake ice conditions is important to local phenomena, such as lake effect snow (Notaro et al. 2013b). Additionally, colder winter temperatures and increased lake ice actually cause an increase in northern snowfall, winter and spring snow cover, and surface shortwave albedo. The impacts of a colder winter in the modified model are seen into spring and lead to increases in late spring and summer soil moisture across the entire domain. Thus, variability in lake ice conditions has the ability to impact the following spring and summer conditions, important to regional prediction. The synoptic variability dominates interannual variability in regional winds and sea level pressure. This suggests that hindcast simulations focused on the region as a whole may not require a dynamic lake model. However, for future climate simulations, where a new mean state is possible, this work illustrates the importance of capturing the lake’s new mean state.

b. Model limitations

The model is still limited in its representation of large lake systems because of the one-dimensional structure of the lake model, instantaneous mixing of instabilities, and limitations to eddy diffusivity. More than 400 individual lake models with a horizontal grid size of 20 km represent the Great Lakes in RegCM4.3; in reality, five lake systems exist. Each individual lake model only sees a neighboring lake grid cell indirectly, through neighboring grid cells’ impact on the overlying atmosphere, which appears insufficient within RegCM4.3.

Although lake temperature is largely controlled by freshwater heat capacity and shortwave attenuation, circulation plays a significant role in the redistribution of heat in the largest Great Lakes. Coastal currents in Lake Superior, for instance, move the shallow southern waters to the north. Upwelling along the northwestern shores of Lake Superior drives temperature in that region (Bennington et al. 2010). In observations, the interannual variability in ice cover on Lake Superior is smallest in the eastern gyre in observations, while model variability is clearly dominated by latitude (Fig. 8). In the Great Lakes, wind stress curl drives Ekman suction (pumping) that is a dominant control on thermocline depth and vertical processes (Beletsky et al. 2012). There are large areas of persistent upwelling and downwelling in the Great Lakes, and wind direction changes rapidly alter lake temperatures. Rapid coastal jets transport heat around the lakes, and frequent eddies mix near and off shore waters. Currents cause shear instabilities and mixing events. Ice movement impedes ice formation and accelerates its breakup (Fujisaki et al. 2013). The lack of circulation in simulations presented here increases winter ice, as nothing can prevent ice formation once the surface waters cool, even though winds and open lake surface currents are fastest during winter before extensive ice formation (Bennington et al. 2010).

In the one-dimensional model, the mixed layer depth is determined by the shortwave attenuation coefficient and wind speed. Here, attenuation of shortwave radiation is determined by depth only. In reality, distance from shore, watershed to lake area ratio, trophic status, and season impact the attenuation of shortwave radiation within the lake and are not static in time. Modeled deep lake points have a deeper mixed layer depth, and this is a primary mechanism for the modeled delayed warming/cooling at deep lake points.

In reality, deep mixing can occur for months when water temperatures are near 4°C, with mixed layers exceeding 200 m or reaching the lake bottom (J. Austin 2009, personal communication; see www.seagrant.umn.edu/newsletter/2009/12/mixup_over_lake_superiors_mixing.html). Here, the model redistributes instabilities instantly, and the modeled vertical structure is too stable. While synoptic storm events can break up the thermocline for days in observations (Chen et al. 2001; Bennington et al. 2010), modeled vertical eddy diffusion simply increases heat transport to below the thermocline, and the thermocline depth does not exhibit variability on synoptic time scales. This is due to the assumption of an Ekman velocity profile, which makes shear instabilities nearly impossible. The lack of explicit mixing causes rapid spring stratification and an overestimate of spring and summer lake temperatures at deep lake points. Modeled summer lake surface temperatures exceed the overlying atmosphere, highlighting the remaining inadequacies of the model. Once the model surface temperature reaches 4°C, stratification begins and the lake warms until fall. The observed period of winter and spring overturn lasts for weeks and delays both winter and spring stratification, reducing ice formation and summer maximum temperatures.

While Martynov et al. (2012) suggest an increase in vertical eddy diffusivity by a factor of 1000 for deep lake points, we find this to still be insufficient for the lake model within RegCM4.3. Prescribing excessive vertical diffusivities at deep lake points decreases surface temperature biases by increasing mixed layer depths (e.g., Martynov et al. 2010; Subin et al. 2012), but this causes nearshore thermoclines to be shallower than offshore. This is exactly opposite of what is observed. Shallow, nearshore waters exhibit deeper thermoclines, and shallow thermoclines are observed offshore, in cyclonic gyre centers (Beletsky et al. 2012). Thus, this one-dimensional lake model is incapable of a realistic physical response to atmospheric conditions. The uncertainties caused by “overtuning” of these models should be investigated.

Although the Hostetler lake model within RegCM4 is now able to capture a reasonable vertical structure of temperature, circulation and dynamics must be accounted for in the large, deep lakes. Interannual variability in lake conditions is increased with the model updates, but to less than half of the observed magnitude of temperature variability. Although we still do not anticipate that lake conditions are a first-order control of regional climate variability, lake temperature variability must increase to more realistic values if we are to capture a new mean state of the Laurentian Great Lakes in future climate simulations.

Acknowledgments

NOAA_OI_SST_V2 data were provided by the NOAA/OAR/ESRL/PSD, Boulder, Colorado, from their website at www.esrl.noaa.gov/psd/. This study was funded by the University of Michigan and the National Oceanic and Atmospheric Administration (NA07OAR4320006). We thank three reviewers for thoughtful comments that improved this manuscript.

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