Paleo-hydrologists have adjusted for glacial isostatic uplift and compared the original elevations of paleo-water level indicators and basin outlets for Lake Huron, revealing that Huron lake levels fell tens of meters below its lowest possible outlet (becoming a terminal lake) about 7,900 14C years BP. This corresponds to when the upper Great Lakes stopped receiving glacial melt inflow and became dependent for water supply on precipitation alone, as at present. Since these researchers accounted for differential isostatic effects, they surmised that the upper Great Lakes were impacted by severe dry climate. To understand possible climate changes that led to the closure, the Great Lakes Environmental Research Laboratory applied their Advanced Hydrologic Prediction System to explore deviations from present climates that could force the upper Great Lakes to become terminal. GLERL modeled the steady-state water balance of the present upper Great Lakes with pre-development natural water flow conditions by employing lake outflow-depth rating curves (using estimated sill elevations) reasonable for a natural system and by using dynamic lake areas controlled by observed hypsometric relations for each lake. By using systematic shifts in precipitation and temperature relative to the present base climate, GLERL showed the temperature rises and precipitation drops required for a terminal lake; they may be less extreme if additional effects of past differences in wind speed and insolation are also considered.
Prior to 8,000 radiocarbon (14C) years before present (BP) the large upstream glacial Lake Agassiz in northwestern Ontario and Manitoba supplied melt water from the last glaciation to the upper Great Lakes through outlets to the Lake Nipigon basin and thence to the Superior and Huron-Michigan basins. About 8,000 14C years BP, Lake Agassiz merged with glacial Lake Ojibway in northern Ontario and northeastern Quebec, and drained into the Ottawa River valley and thence to the North Atlantic Ocean via the St. Lawrence River valley (Croley and Lewis, 2006), thereby bypassing the Great Lakes basin. At this stage Great Lakes water supply was no longer supplemented from upstream sources, but was supplied by precipitation alone, as at present. The upper Great Lakes then overflowed the North Bay outlet into the Mattawa River and thence to Ottawa and St. Lawrence River valleys.
Recent construction of an empirical exponential model of isostatic uplift for the Great Lakes region following the last glaciation allowed comparison of the elevations of rebounding lake outlets with reconstructed lake levels based on 14C-dated water level indicators such as abandoned shorelines, isolation basins, submerged tree stumps, and unconformities (Croley and Lewis, 2006). The early Holocene results for the Huron basin reveal lake levels lower than present due to overflow drainage through the isostatically depressed outlet area near North Bay, Ontario, to the Ottawa and St. Lawrence valleys. Surprisingly, lake levels fell below the Huron basin outlet after 8,000 14C years BP and during which the lowest water levels (between 7,500–7,900 14C years BP) were up to 30 m below the overflow sill at North Bay.
The inferred 7,900 14C years BP low stand of the Huron basin occurred after melt water drainage from upstream glacial Lake Agassiz began to bypass the Great Lakes basin, leaving it susceptible to the early dry Holocene climate. As the Great Lakes basin had then entered its present hydrological regime of water supply by precipitation only, and as differential glacial-isostatic crustal uplift was accounted for, the only known process that could explain the sub-outlet low levels is climatic reduction in water supply, either by enhanced evaporation or reduced precipitation or both. This episode of lowest levels appears as an extraordinarily severe impact of a dry climate, possibly of short duration, on the upper Great Lakes.
It would be helpful to understand the climate change required to drop lake levels below the lake outlet for assessment of the hypothesis that the 7,900 14C years BP Huron low stand was climate-driven. Accordingly, we used a hydrological model to explore the excursion from the present climate that would force Lake Huron into hydrologic closure in terms of increased temperature and reduction in precipitation. The purpose of this paper is to demonstrate that if a climate is extreme enough, Lake Huron water levels would drop sufficiently to cut off outflow, thereby making that lake terminal. We look at excursions in temperature and precipitation from the present climate to disclose those values that would drive upper Great Lakes hydrology to produce terminal lakes. This is not an attempt to simulate past hydrology exactly, but to explore the possible magnitude of changed climates that might produce terminal lakes.
Lake Superior flows through the St. Mary's River into Lake Huron where it is joined by water flowing from Lake Michigan through the Straits of Mackinac. Lakes Michigan and Huron are considered to be one lake hydraulically because of their connection through the deep Straits of Mackinac. These days, the water flows from Lake Huron through the St. Clair River, Lake St. Clair, and Detroit River system into Lake Erie. The drop in water surface between Lakes Michigan-Huron and Lake Erie is only about 2 m (8 ft). This could result in a backwater effect between Lakes Erie, St. Clair, and Huron; changes in Lakes St. Clair and Erie levels are transmitted upstream to Lake Huron. However 7,900 14C years BP Lake Huron outflow was through North Bay with no downstream backwater effects presumed. Lake Huron is very deep, reaching about 252 m at its deepest points within the upper main lake area.
We use the Great Lakes Environmental Research Laboratory (GLERL) Advanced Hydrologic Prediction System (AHPS), a system of hydrology, thermodynamic, and hydraulic models for the Great Lakes (Croley, 2005). GLERL uses these models to make probabilistic outlooks of Great Lakes hydrology and water levels (see http://www.glerl.noaa.gov/wr/ahps/curfcst/curfcst.html), and to assess climate change impacts in the Great Lakes. GLERL's AHPS includes daily runoff models for each of the 22 Lake Superior watersheds, 27 Michigan watersheds, and 29 Huron watersheds. It also includes lake thermodynamic models for each of these water bodies, hydraulic models for the connecting channels and lake outflows with operating plans encoded for Lake Superior, and simultaneous water balances on all the lakes. It is described in detailed overviews elsewhere (Croley, 2005). For the purpose of this study, we adjusted the present models to simulate the Great Lakes in their pre-European-settlement natural state by removing the influences of channel control works and regulation plans. We use the models here with water balances on all lakes and with lake outflow rating curves selected to represent “natural” or “pre-development” conditions. We account for lake area variations with changes in water level, but do not remove present-day diversions and consumptions as they are relatively insignificant for our purpose.
First we consider all lakes as interdependent (as they are now, but with “natural” outlet and connecting channel flows) to see if simulations with historical meteorology (1948–1999) produce hydrology comparable with the historical records. This allows us to assess the applicability of the modified models. Then, we model Lakes Superior, Michigan, and Huron (the upper Great Lakes). Next, we consider steady state hydrology by modeling over an extended period constructed by repeating the adjusted meteorological record until consecutive 52-year segments are identical.
The hydrology models use daily meteorological data from 1948–1999, compiled from about 1,800 stations for over-land meteorology (precipitation and air temperature) and about 40 stations for over-lake meteorology (air temperature, humidity, wind speed, and cloud cover). These data provide daily meteorological time series over each of the 78 riverine watersheds that drain into the Upper Great Lakes and the 4 Upper Great Lake water surfaces [Superior, Michigan, Huron (including Saginaw Bay), and Georgian Bay (including North Channel)]; see Figure 1 for a Lake Huron map. Annual average precipitation and air temperature are, respectively, 80.9 cm and 2.93°C (Superior basin) and 84.5 cm and 6.49°C (Michigan-Huron). We used historical meteorological data with our hydrology models to compute the “present” or “base case” scenario. We then applied selected precipitation ratios and air temperature differences to the Historical meteorology and used these modified data with our hydrology models to construct changed climate scenarios. All precipitation is adjusted by multiplying by a single precipitation ratio and all air temperatures are adjusted by adding a single temperature difference. In addition, for precipitation ratios below unity, which are all that are considered here, the absolute humidity is multiplied by the ratio. Thus, if precipitation is halved, then so is humidity.
GLERL's Large Basin Runoff Model (LBRM), the first AHPS component, consists of moisture storages arranged as a serial and parallel cascade of “tanks” coinciding with the upper and lower soil zones, a groundwater zone, and the surface channel system (Croley, 2002). Water enters the snow pack, which supplies the basin surface (degree-day snowmelt). Infiltration is proportional to this supply and inversely so to saturation of the upper soil zone (partial-area infiltration). Water percolates from the upper to the lower soil zone and from the lower to the groundwater zone (deep percolation). Water also flows from the upper, lower, and groundwater zones into the surface channel system, as surface runoff, interflow, and groundwater flow respectively. “Groundwater” refers to intra-, not inter-, watershed storage. Flows from all tanks are proportional to their amounts (linear-reservoir flows). Evapotranspiration is proportional to available water and to sensible heat (a complementary concept in that evapotranspiration reduces available sensible heat). Mass conservation applies for the snow pack and tanks; energy conservation applies to evapotranspiration. Complete analytical solutions exist. The model has been calibrated to each of the 78 watersheds contributing to the Upper Great Lakes by minimizing root mean square error between daily model outflows and adjusted outflow observations. Each calibration determined parameters for infiltration, snow melt, surface runoff, percolation, interflow, deep percolation, groundwater flow, surface storage, and evapotranspiration by systematically searching the parameter space (gradient-search). The model agrees quite well with weekly and monthly outflow observations (Croley, 2002). These parameters represent present-day hydrology and are not changed in the simulations.
GLERL's Lake Thermodynamic Model adjusts over-land data (original or adjusted as a changed-climate scenario) to estimate over-water meteorology for over-water or over-ice conditions based on empirical relationships between the two (Croley, 2005). Surface flux processes are represented for reflection and short-wave radiation, net long-wave radiation, and advection. Aerodynamic equation bulk transfer coefficients for sensible and latent heat are formulated with atmospheric stability effects. Energy conservation accounts for heat storage; superposition of heat additions or losses determines temperature-depth profiles. Each addition is parameterized by age and mixes throughout the volume. Mass and energy conservation account for ice formation and decay. The model has been calibrated to each of the four lake surfaces by minimizing root mean square error between daily model surface temperatures and observations. The model enables one-dimensional modeling of spatially averaged water temperatures over the lake depth and can be used to follow thermal development and turnovers in the lake.
Lake area adjustment
For each lake, precipitation is provided as a scenario-dependent boundary condition and runoff and evaporation are estimated with the runoff and evaporation models, respectively. They are expressed as depth rates over the lake surface in m day−1 and are based on lake areas as coordinated between the US and Canada (Croley and Lewis, 2006). That is, no variation of lake area is actually considered in their determination in the runoff and evaporation models. However, we adjust to actual lake area by converting these depth rates into volumetric flow rates in m3 s− 1. Precipitation and evaporation are directly converted by simply multiplying the overlake depth rates by actual lake area. Runoff is first multiplied by the coordinated lake area (over which it was expressed) to calculate the modeled runoff volume, then divided by the coordinated land area (to express it as the equivalent yield per unit of land area), and then multiplied by the actual land area to calculate the adjusted runoff volume. Thus adjusted runoff gets bigger as actual lake area gets smaller. Of course, there is some error involved with this procedure since the unadjusted depth rates actually depend on actual lake area too and should have been computed from models considering actual lake area and volume changes. Also, exposed land areas would not have the same properties as the original basin.
Unmanaged lake outflow depends on lake level and outflow sill elevation for Lakes Superior and Michigan-Huron. Southam (1989) described a quantitative empirical relationship between water elevation and outflow for each lake that represents “natural” conditions, prior to the introduction of societal developments including regulation of Lake Superior outflows, modification of connecting channels through dredging or shoreline changes, use of ice control measures, and diversion of water into and out of the lakes. Any impacts caused by land use modification, consumptive uses, and regulation of tributary rivers are viewed as reflected by changes in water supplies to the lakes and not by changes in elevation—outflow relationships, and were not considered in that study. We converted Southam's relationships from their original English units and IGLD'55 water level datum to metric units and IGLD'85 water level datum, respectively (Croley and Lewis, 2006). Note, outflows are zero when water levels are below the “sill” elevation of the lake; the sill is the lowest elevation where flow from the lake is still possible.
The Coordinating Committee on Great Lakes Basic Hydraulic and Hydrologic Data provided graphical relations, for each lake, between depth and volume; inspection reveals that simple power relations are a very good fit. By differentiating volume with respect to depth, we find lake area is also a simple power relation of depth. The power relation parameters are determined by requiring that the coordinated values of area and volume exist at the reference elevation (chart datum), where the depth is zero. These relations are transformed into functions of water elevation (Croley and Lewis, 2006).
We used over-lake precipitation, runoff to the lake, and lake evaporation in water balances for Lake Superior and Michigan-Huron with outflow from Superior appearing as inflow to Michigan-Huron. We jointly solved equations for lake outflows, surface elevations, surface areas and volumes, net basin supplies, and water balance for each lake simultaneously at each time step. Our numerical procedure at each time step is: i) given unadjusted (uncorrected for lake surface area) over lake precipitation, runoff, and evaporation and the water elevation at beginning of time step for all lakes; ii) calculate lake area and volume at beginning of time step for all lakes from hypsometric relations and outflow rate at beginning of time step for all water bodies from outflow relations; iii) approximate end-of-time-step water elevation as the beginning-of-time step value for all lakes; iv) calculate end-of-time-step lake area for all lakes from hypsometric relations and end-of-time-step outflow rate for all lakes from outflow relations; v) approximate outflow rates and lake areas over the time increment as linear and calculate averages of both for each lake; vi) adjust precipitation, runoff, and evaporation and calculate the changes in storage for all water bodies over the time interval by using these approximate outflow rates and lake areas in the water balances; and vii) approximate the end-of-time-step lake volume by adding the change in storage to the beginning-of-time-step lake volume for each lake and then find end-of-time-step water elevation by using end-of-time-step lake volume with hypsometric relations for each water body (for Lake Michigan-Huron, interpolate for end-of-time-step water elevation by using end-of-time-step lake volume with hypsometric relations applied to Lakes Michigan, Huron, and Georgian Bay and summed). Repeat steps iv– vii until end-of-time-step water elevation for all lakes change negligibly. Repeat steps i– vii for next time step.
We actually considered corrections to the water balance for backflow between the lakes. However, backflow does not occur when simulating the existing system with the existing climate (using natural channel conditions and lake outflows). It also does not occur when simulating the upper lake system (Superior, Michigan, and Huron) with any climate since the outflow is replaced with a relation that is a function of Michigan-Huron levels only (discussed subsequently). Backflow corrections are only required when simulating the existing system or the lower lake system (St. Clair, Erie, and Ontario) with warmer or dryer climates, which is not done here. The solution converges to an insignificant difference within 2-15 iterations (the difference between water elevations in successive iterations, summed over all lakes, is less than one thousandth of a millimeter).
To check the models and water balance approximations, we simulated the entire interconnected Great Lakes for the historical meteorological record. First, we compared simulated net basin supplies (precipitation + runoff – lake evaporation) resulting from the model, applied to the historical meteorological record with actual initial conditions, directly to historical net basin supplies (computed as a water balance residual from historical lake levels and flows). Figure 2 compares our estimates with historical NBS for Lakes Superior and Michigan-Huron and shows good agreement, as expected since historical meteorology data are used in the simulation. Differences are ascribed to water balance errors in the computation of residual NBS and to modeling errors in the computation of the NBS components.
Changed climate simulation
Before applying the simulations to changed climates (i.e. changed temperature and precipitation), we ascertained that the present-day diversions in the hydrology models were on the order of a few centimeters. Thus, they are negligible compared to the changes in net basin supplies or drops in water levels to be simulated with changed climates. Therefore, we ignore them; no effort was made to remove these diversions from the existing models. We use both the historical and modified meteorological time series with our models to simulate base case and climate change hydrology scenarios, respectively. We estimate steady state hydrology by modeling with arbitrary initial conditions (snow pack, water storages in the basins, thermal structure of the lakes, lake levels, and so forth) over an extended period constructed by repeating the adjusted meteorological record until consecutive 52-year segments are identical. (The models always converge no matter where started). Separating Lakes Superior, Michigan, and Huron from Lakes St. Clair, Erie, and Ontario, is accomplished by changing Lake Michigan-Huron outflow to a function only of the water level in Lake Michigan-Huron. We used a weir equation with present-day sill elevation (St. Clair River). We found the coefficient by matching a long-term water balance with historical levels.
When lake levels are always below the sill elevation, then the lake is terminal. We looked at 36 climate scenarios, each defined in terms of the precipitation drop from the base case (0–50% in steps of 10%) and the temperature rise above the base case (0–5°C in steps of 1°C). We calculated the steady-state average water level resulting from each and plotted it with precipitation drop and temperature rise as shown in Figure 3 for Lake Superior and Figure 4 for Lake Michigan-Huron. Note three regions in Figure 3 or 4: the region where all water levels are above the sill elevation in the lower left of the graphs, the region where all water levels are below the sill elevation in the upper right of the graphs, and the intermediate region where water levels are both above and below the sill elevation. We determined the boundaries of these regions by looking at maximum and minimum water levels in each simulation and comparing them to the sill elevations. Since behavior of steady-state average water levels is fundamentally different in each region, we restricted linear interpolation of isolines in each region to only values therein.
Note that the climate isolines for a terminal Lake Superior in Figure 3 drop about 1°C for every 4.7% change in precipitation. Figure 3 suggests that Lake Superior should be a terminal lake for climates with a temperature rise T (°C) and a precipitation drop P (%) such that 4.7T + P > 60. Likewise, the isolines in Figure 4 for a terminal Lake Michigan-Huron drop about 1°C for every 4.5% change in precipitation; Lake Huron should be terminal for climates with a temperature rise T (°C) and a precipitation drop P (%) such that 4.5T + P > 63.
Each climate considered herein is specified over the entire upper Great Lakes basin. That is, the same changes made to historical data, to construct a hypothetical climate, were used across all water bodies and their basins (Superior, Michigan, and Huron) in each analysis. For example, the 1°C increase applied to Lake Huron meteorological data was applied at the same time to the Lake Michigan and Lake Superior meteorological data in the analyses. Thus, no consideration is made of more complex changed climates (such as a 1°C change in Lake Huron air temperatures with a 2°C change in Lake Superior air temperatures). Given this limitation, the order of the upper lakes going terminal as climate gets warmer and drier is first Lake Superior and then Michigan-Huron. (The order varies a little depending on the path of the changes from the present climate taken in Figure 3 and Figure 4.) There may be climates (where meteorological conditions are different over say Lake Superior and Lake Michigan-Huron) that would yield a terminal Lake Huron with a non-terminal Lake Superior. Those climates were not investigated herein. As more is learned about past climates from paleoclimatic considerations, we can fine tune these observations.
Likewise, the climate changes considered herein were simplified. We multiplied all historical daily precipitation amounts, without regard to season of the year, by a constant ratio and we added to all historical daily air temperatures, again without regard to season of the year, a constant value. Undoubtedly, we could consider more reasonable changes by considering the season of the year, and even location. Again, as more is learned about past climates from paleoclimatic considerations, we can make these additional considerations. However, we think these results are generally indicative of how climate effects would influence Great Lakes terminal lake status. Indeed, Lofgren et al. (2002) summarized many of the past Great Lake climate impact assessments of water level sensitivity that used general circulation model or global climate model based climate change scenarios; those climates that were warmer and drier showed good agreement with Figure 4.
Since we used only the available 52 years of daily meteorological data, continuously repeated, to represent steady-state, we biased our results somewhat; only the storm events on record are represented. The “transitional zone” in Figure 3 and Figure 4 might be wider if a longer period were used since more marginal storm events would be included that allowed some small outflow at water levels close to sill elevations.
There are also many errors of approximation in this study; our calculations used over-lake precipitation, over-lake evaporation, and runoff to the lake from models that assumed fixed values (coordinated between the U.S. and Canada) for lake areas and volumes, and then adjusted them for the actual lake and basin areas obtained in a comprehensive water balance. Better consideration would modify the runoff and lake evaporation models directly to consider the actual lake areas and volumes in an integrated water balance that employs these models directly. Likewise, the hypsometric and outflow relations could be improved. Different sill elevations would shift the “terminal” lines in Figure 3 and Figure 4.
Finally, the results do not exactly represent past hydrology (for example, paleo-lake areas have not been incorporated) so that results should be interpreted as exploration of the effect of various climate scenarios on the hydrology of the pre-development Upper Great Lakes. This is an attempt to study the question of “What magnitude of drying and warming of the present climate might produce terminal lakes as a guide to possible climate that apparently produced hydrologic closure of at least some of the Great Lakes about 7,900 14C years BP?” It is possible that other aspects of climate may have been a factor in lowering lake levels about 7,900 14C years BP. Other studies summarized elsewhere (Croley and Lewis, 2006) indicate significant increases of mean annual temperature and summer relative humidity from 8,000 to 7,000 14C years BP. Others indicated that wind activity started about 8,000 14C years BP and was associated with relatively severe drought conditions. Thus future paleoclimate modeling focused on the 7,900 14C years BP Great Lakes low stand may need to explore potential impacts under cold/dry and windy conditions. Likewise, insolation would have been different at the time of the low stands than at present.
A new empirical model of glacial rebound and comparison of past lake level indicators with outlet elevations showed that lake levels in the Huron and Michigan basins had fallen below their outlets about 7,900 14C years BP (Lewis, Blasco, et al., 2007a; Lewis, Heil Jr. et al., 2007b). As glacial-isostatic depression of outlets was accounted for, the only alternate known process that could close the lakes is enhanced evaporation, reduced precipitation, or both, in a dry climate. These findings motivated us to explore temperature and precipitation excursions of the present climate that might close Lake Huron as a guide to better understanding possible conditions at 7,900 14C years BP. We demonstrate the possibility that changed climates could produce a terminal Lake Huron by using present hydrology with natural (pre-development) channel and outflow conditions. We first integrated existing comprehensive models for present-day large basin runoff applied to each of the 78 watersheds draining into the Upper Great Lakes, models of present-day large-lake thermodynamics applied to the four water bodies of the Upper Great Lakes, water balances of the lakes and their connecting channels, lake area adjustments relating supplies (lake precipitation, runoff, and evaporation) to the water balance, models of natural outflows and channel flows, present-day hypsometric relations, and a water balance of all lakes and connecting channels. We tested the integrated model with historical meteorological data (1948-1999) and found it to be a reasonable model of present Upper Great Lakes hydrology. We built alternate climates from the historical meteorological record by reducing precipitation by fixed ratios and increasing temperature by fixed increments. We applied the integrated hydrology model to the alternate climates, producing associated alternate lake level time series.
The changed climate scenarios used in this study were simple: spatially and temporally constant adjustments were applied to historical meteorology for each watershed and lake surface to estimate changed-climate meteorology for each watershed and lake surface. More complex climate change considerations in our study of terminal Great Lakes wait on improved paleoclimatic reconstructions. Our results are biased by the length of the historical meteorology record we used. Errors of approximation include linear adjustment of supplies for lake area, power equation hypsometric relations, and approximation of natural flow conditions and sill elevations for each Great Lake.
We modeled each alternate climate by repeating our 52 years of adjusted meteorology until there were no changes, in an effort to simulate steady-state conditions. It appears that Lake Superior would be a terminal lake if precipitation dropped 60% or more from the present or if air temperature increased 60/4.7 = 13°C or more above the present or some linear combination of the two, 4.7T + P > 60 where T and P are temperature rise (°C) and precipitation drop (%), respectively. Likewise, it appears Michigan-Huron would be a terminal lake for P > 63% or T > 14°C or 4.5T + P > 63.
Our study addresses only the question of climate change necessary to close the pre-development Great Lakes and does not represent past or present hydrology. We endeavored not to exactly model the hydrology of the lakes around 7,900 14C years BP, but to explore the potential magnitude of excursions in temperature and precipitation that could cause the lakes to drop so low as to become “terminal” lakes (with no outflow). Additional modeling could be done to accommodate the paleogeographic conditions of 7,900 14C years BP, such as incorporating changes in vegetation including those associated with changed lake areas. In addition, future modeling of the impacts of cold/dry and windier conditions as well as changed insolation are likely to be useful in understanding the Great Lakes low stands.
This is GLERL contribution no. 1457.