(87g) Dynamic Optimization Strategies for Control of Algae Growth in Eutrophic LAKES with Nonpoint Nutrient Sources
We address the optimal planning of alternative restoration strategies of eutrophic water bodies, mainly affected by nonpoint nutrient sources, through advanced dynamic optimization techniques. Restoration strategies that involve chemical and physical processes and biological manipulation have been studied and implemented to reduce algal blooms and their consequences (Paerl and Otten, 2013; Jeppesen et al., 2012; Estrada et al., 2011) as eutrophication is the most serious environmental problem in many lakes and reservoirs.
Artificial wetlands have been largely used to decrease external nutrient loading from nonpoint sources and, in this way, carry out bottom up control on phytoplankton growth. However, biogeochemical processes that take place within water bodies delay restoration (phosphorus and nitrogen recycles, as well as nutrient release from sediments). Additional inlake strategies have been proposed and applied, such as hypolimnetic oxygenation and biomanipulation (Søndergaard et al., 2007). Moreover, macrophytes play an important role on biological processes of water bodies, since they capture nutrients from the water column and sediments, act as zooplankton refuge and, in some cases, produce substances that inhibit algal growth (Jeppesen et al., 2012; Asaeda and Bon, 1997).
We have implemented some of these strategies as different optimal control problems in previous work, by developing ecological water models integrated to optimization strategies to evaluate management strategies in both the short and long term (Estrada et al., 2011). In this work, we include mass balances for the macrophyte population, modeling roots and leaves biomass as different submodels. The net growth of macrophytes results from photosynthesis, respiration, dead, reserves and reallocation of dead biomass (Asaeda and Bon, 1997). The resulting dynamic optimization problems are subject to complex partial differential algebraic equations (PDAE) systems representing the main biogeochemical processes that take place within these water bodies. The PDAE systems result from dynamic mass balances for the different submodels for macrophytes, three phytoplankton groups (cyanobacteria, diatomea, chlorophyta); two zooplankton groups (cladocera, copepoda) and three size classes of local zooplanktivorous fish, as well as dissolved oxygen and main nutrients. Algebraic equations stand for forcing functions profiles, such as temperature, solar radiation, river inflows and concentrations, etc. Optimization variables (time dependent degrees of freedom) are associated to the reduction of nutrient loading by deviation to an artificial wetland (tributary flowrate to wetland profile) and in-lake restoration through fish removal rate for each of the class sizes. The dynamic optimization problem is formulated within a control vector parameterization framework (PSEnterprise, 2013). The present study has been performed on Paso de las Piedras Reservoir (38° 22´ S and 61° 12´ W), which is the drinking water source for two cities in Argentina. Numerical results provide optimal profiles for planning of the restoration actions, as well as a quantitative estimation of restoration effects on the water body, along a middle term time horizon.
Asaeda, T. and T. Van Bon (1997), Modeling the effects of macrophytes on algal blooming in eutrophic shallow lakes, Ecological Modeling, 104, 262-267.
Estrada V., J. Di Maggio, M.S. Diaz (2011), Water Sustainability: A Process Systems Engineering approach to the restoration of eutrophic lakes, Computers and Chemical Engineering, 35, 8, 1598-1613
Jeppesen, E., Søndergaard, M., Lauridsen, T., Davidson, T., Liu, Z., Mazzeo, N., Trochine, C., Özkan, K., Jensen, H., Tolle, D., Starling, F, Lazzaro, X., Johansson, L., Bjerring, R., Liboriussen, L., Larsen, S., Landkildehus, F., Egemose, S. & Meerhoff, M. (2012). Biomanipulation as a Restoration Tool to Combat Eutrophication: Recent Advances and Future Challenges. Advances in Ecological Research, 47.
Paerl, H. and Otten, T. (2013) Harmful Cyanobacterial Blooms: Causes, Consequences, and Controls. Environmental microbiology, 65, 995-1010.
Process Systems Enterprise (2013), gPROMS, www.psenterprise.com/gproms
Søndergaard, M., Jeppesen, E., Lauridsen, T. L., Skov, C., van Nes, E. H., Roijackers, R., Lammens, E. & Portielje, R. (2007). Lake restoration: successes, failures and long-term effects. Journal of Applied Ecology, 44, 1095–1105.