Date of Award

December 2015

Degree Type

Dissertation

Degree Name

Doctor of Philosophy

Department

Mathematics

First Advisor

Sergey V. Kravtsov

Second Advisor

Paul J. Roebber

Committee Members

Sergey Kravtsov, Paul Roebber, Kyle Swanson, Clark Evans, Istvan Lauko

Keywords

Climate Dynamics, Lake-atmosphere Interactions, Lake Modeling, The Ice-Albedo Feedback, The Laurentian Great Lakes

Abstract

For the last couple of decades, the Great Lakes have undergone rapid surface warming. In particular, the magnitude of the summer surface-warming trends of the Great Lakes have been much greater than those of surrounding land (Austin and Colman, 2007). Among the Great Lakes, the deepest Lake Superior exhibited the strongest warming trend in its annual, as well as summer surface water temperature. We find that many aspects of this behavior can be explained in terms of the tendency of deep lakes to exhibit multiple regimes characterized, under the same seasonally varying forcing, by the warmer and colder seasonal cycles exhibiting different amounts of wintertime lake-ice cover and corresponding changes in the summertime lake-surface temperatures. In this thesis, we address the problem of the Great Lakes' warming using one-dimensional lake modeling to interpret diverse observations of the recent lake behavior.

For a one-dimensional model to be able to faithfully simulate the dynamics of the Great Lakes' rapid warming and multiple climate regimes, it needs to accurately represent the lake's climatological seasonal cycle. However, these models (e.g., Hostetler and Bartlein 1990) have been known to simulate seasonal temperature cycles of deep lakes (> 200m) poorly. A number of attempts have aimed to improve the Hostetler and Bartlein (1990) model by parameterizing unresolved physical processes in the form of the so-called "enhanced minimum diffusion." In this thesis, we developed an ad hoc modification to the parametrization of the enhanced minimum diffusion, which led to the 1-D simulations of the lakes' seasonal cycle comparable in quality to those obtained by recent 3-D lake models.

To address the problem of Great Lakes climate dynamics, we considered multi-column generalizations of the improved one-dimensional lake model, which were also coupled to an idealized two-layer atmosphere. The variable temperature of the upper atmospheric layer in this model was a proxy for the large-scale atmospheric forcing, and consisted, in the most general case, of a linear trend mimicking the global warming, and random noise representing atmospheric intrinsic variability, both on top of the prescribed seasonal cycle of the upper-atmosphere temperature. The lower atmospheric layer of the coupled model is able to respond actively to the variability in the lake's surface temperature simulated by the multi-column lake component, and exchanges heat laterally between the lower-atmospheric columns via a diffusive heat transport.

The single-column models were shown to exhibit two possible steady seasonal cycles -- with and without lake-ice occurrence in winter and with corresponding cold and warm temperatures in the following summer, respectively, all under an identical external seasonally varying forcing. The basins of attraction of the warm and cold seasonal cycles depend on the annual-mean upper-atmosphere temperature, with warmer temperature leading to the preference of the warm regime and vice versa. The quantitative characteristics of the simulated lake regimes also depend on the depth of the lake column considered: in particular, the distinction in summertime heat content between warm (wintertime ice free) and cold (wintertime ice-covered) regimes is the largest for the deepest lakes. This property ultimately has to do with a shorter dynamical memory of the shallow lakes, which are climatologically characterized by longer duration of the summertime mixed layer; hence, the surface temperature (heat content) anomalies arising due to varying degrees of wintertime ice cover are being lost to the atmosphere over a longer period of time than for deeper lake columns.

A short dynamical memory of shallow lakes and a longer memory of deep lakes also explain the different character of regime transitions under the action of stochastic forcing associated with intrinsic atmospheric variability. Namely, shallow lakes may exhibit frequent and non-persistent year-to-year transitions from one regime to the other and back due to stochastic agitation. On the other hand, longer-memory deeper lakes tend to exhibit more persistent behavior with inter-annual preference of one regime over the other, with jump-like transitions in between.

Experiments with multi-column coupled models demonstrate analogous regime behavior. The regime structure of the multi-column models of non-uniform depth is more complex and involves an intermediate, partially ice-covered regime. However, in the presence of the efficient lateral heat exchange between the lower atmospheric columns, the transitions between the regimes characterizing different lake columns (shallower and deeper lake regions) synchronize. Under the forcing associated with global warming and superimposed atmospheric intrinsic variability, the multi-column lakes exhibit progressively more frequent (for shallow lakes) or persistent (for deep lakes) transitions to the warmest regime, and eventually switch to the warmest regime for good. Upon the final transition, the largest changes in the summertime maximum temperature occur over the deeper portions of the lake, and the deep lakes warm more than shallower lakes.

We used these modeling results to interpret observations of the recent warming of the Great Lakes. We find that the reason Lake Superior exhibits the strongest warming trend among the Great Lakes is that the eastern part of the lake clearly exhibits distinct regional-climate regimes. As global warming drives Lake Superior's local climate away from the basin of attraction of its colder seasonal regime toward its warmer regime, the surface water temperature of the lake undergoes a more drastic change than the surface temperature of surrounding land. The regime transition takes the form of a discontinuous jump in the Lake Superior surface water temperature, evident, for example, in the August-mean surface water temperature time series at buoy stations in Lake Superior around the years 1997-98. Moreover, we find that the surface water temperature of Lake Superior warms faster than those of the other, shallower Great Lakes, which exhibit less clear indications of the existence of multiple regimes in their summertime temperatures, consistent with the behavior of one-dimensional lake models.

The apparent correlation between local lake depth and lake-surface temperature warming rates occurs not only between the different lakes, but also within the individual Great Lakes. Our modeling results provide clues to causes of this intriguing property of the Great Lakes warming. Simulations show that due to larger dynamical memory, deeper lakes experience a larger summertime temperature jump when they transition from the colder to the warmer regime than the shallower lakes. Likewise, it is easier for shallow lakes to transition back and forth between its multiple regimes. The more frequently the lake transitions between the warmer and colder climate regimes under the slow global warming, the smaller its associated summer warming trend becomes. In other words, in the presence of global warming, deeper lake regions generally exhibit larger warming trends than shallower lake regions.

Finally, the much discussed observed correlation between summertime surface water temperatures and the amount of wintertime ice cover of the Great Lakes is to be naturally expected within the multiple regimes framework, as these two quantities characterize the main distinctions between the warm and cold simulated climate regimes. We hypothesize that the existence of multiple seasonal-cycle regimes in our lake model and, by inference, in observations is largely due to nonlinearity associated with the ice-albedo feedback. In future work, we plan to map out the detailed dynamics of these nonlinear effects and demonstrate the robustness of the ensuing regime behavior with respect to the model's horizontal resolution.

Download

Share

COinS