Mechanisms contributing to the deep chlorophyll maximum in Lake Superior

The seasonal appearance of a deep chlorophyll maximum (DCM) in Lake Superior is a striking phenomenon that is widely observed; however its mechanisms of formation and maintenance are not well understood. As this phenomenon may be the reflection of an ecological driver, or a driver itself, a lack of understanding its driving forces limits the ability to accurately predict and manage changes in this ecosystem. Key mechanisms generally associated with DCM dynamics (i.e. ecological, physiological and physical phenomena) are examined individually and in concert to establish their role. First the prevailing paradigm, “the DCM is a great place to live”, is analyzed through an integration of the results of laboratory experiments and field measurements. The analysis indicates that growth at this depth is severely restricted and thus not able to explain the full magnitude of this phenomenon. Additional contributing mechanisms like photoadaptation, settling and grazing are reviewed with a one-dimensional mathematical model of chlorophyll and particulate organic carbon. Settling has the strongest impact on the formation and maintenance of the DCM, transporting biomass to the metalimnion and resulting in the accumulation of algae, i.e. a peak in the particulate organic carbon profile. Subsequently, shade adaptation becomes manifest as a chlorophyll maximum deeper in the water column where light conditions particularly favor the process. Shade adaptation mediates the magnitude, shape and vertical position of the chlorophyll peak. Growth at DCM depth shows only a marginal contribution, while grazing has an adverse effect on the extent of the DCM. The observed separation of the carbon biomass and chlorophyll maximum should caution scientists to equate the DCM with a large nutrient pool that is available to higher trophic levels. The ecological significance of the DCM should not be separated from the underlying carbon dynamics. When evaluated in its entirety, the DCM becomes the projected image of a structure that remains elusive to measure but represents the foundation of all higher trophic levels. These results also offer guidance in examine ecosystem perturbations such as climate change. For example, warming would be expected to prolong the period of thermal stratification, extending the late summer period of suboptimal (phosphorus-limited) growth and attendant transport of phytoplankton to the metalimnion. This reduction in epilimnetic algal production would decrease the supply of algae to the metalimnion, possibly reducing the supply of prey to the grazer community. This work demonstrates the value of modeling to challenge and advance our understanding of ecosystem dynamics, steps vital to reliable testing of management alternatives.

Planting and production of switchgrass (Panicum virgatum L.) as a bioenergy crop in Michigan's Upper Peninsula

Switchgrass (Panicum virgatum L.) is a perennial grass holding great promise as a biofuel resource. While Michigan’s Upper Peninsula has an appropriate land base and climatic conditions, there is little research exploring the possibilities of switchgrass production. The overall objectives of this research were to investigate switchgrass establishment in the northern edge of its distribution through: investigating the effects of competition on the germination and establishment of switchgrass through the developmental and competitive characteristics of Cave-in-Rock switchgrass and large crabgrass (Digitaria sanguinalis L.) in Michigan’s Upper Peninsula; and, determining the optimum planting depths and timing for switchgrass in Michigan’s Upper Peninsula. For the competition study, a randomized complete block design was installed June 2009 at two locations in Michigan’s Upper Peninsula. Four treatments (0, 1, 4, and 8 plants/m2) of crabgrass were planted with one switchgrass plant. There was a significant difference between switchgrass biomass produced in year one, as a function of crabgrass weed pressure. There was no significant difference between the switchgrass biomass produced in year two versus previous crabgrass weed pressure. There is a significant difference between switchgrass biomass produced in year one and two. For the depth and timing study, a completely randomized design was installed at two locations in Michigan’s Upper Peninsula on seven planting dates (three fall 2009, and four spring 2010); 25 seeds were planted 2 cm apart along 0.5 m rows at depths of: 0.6 cm, 1.3 cm, and 1.9 cm. Emergence and biomass yields were compared by planting date, and depths. A greenhouse seeding experiment was established using the same planting depths and parameters as the field study. The number of seedlings was tallied daily for 30 days. There was a significant difference in survivorship between the fall and spring planting dates, with the spring being more successful. Of the four spring planting dates, there was a significant difference between May and June in emergence and biomass yield. June planting dates had the most percent emergence and total survivorship. There is no significant difference between planting switchgrass at depths of 0.6 cm, 1.3 cm, and 1.9 cm. In conclusion, switchgrass showed no signs of a legacy effect of competition from year one, on biomass production. Overall, an antagonistic effect on switchgrass biomass yield during the establishment period has been observed as a result of increasing competing weed pressure. When planting switchgrass in Michigan’s Upper Peninsula, it should be done in the spring, within the first two weeks of June, at any depth ranging from 0.6 cm to 1.9 cm.

Maximum principle preserving high order schemes for convection-dominated diffusion equations

The maximum principle is an important property of solutions to PDE. Correspondingly, it's of great interest for people to design a high order numerical scheme solving PDE with this property maintained. In this thesis, our particular interest is solving convection-dominated diffusion equation. We first review a nonconventional maximum principle preserving(MPP) high order finite volume(FV) WENO scheme, and then propose a new parametrized MPP high order finite difference(FD) WENO framework, which is generalized from the one solving hyperbolic conservation laws. A formal analysis is presented to show that a third order finite difference scheme with this parametrized MPP flux limiters maintains the third order accuracy without extra CFL constraint when the low order monotone flux is chosen appropriately. Numerical tests in both one and two dimensional cases are performed on the simulation of the incompressible Navier-Stokes equations in vorticity stream-function formulation and several other problems to show the effectiveness of the proposed method.