Lake Erie, the shallowest and most biologically productive of the Great Lakes, faces numerous environmental challenges. Historically, the damming of its tributaries fragmented river habitats, contributing to the decline of native fish populations like the prized walleye. Recently, removing aging or obsolete dams has gained traction as a river restoration strategy. But is it always a good idea? How do we decide which dams to remove, especially when removal has costs and potential downsides?
This article explores the core ideas from the paper "Optimizing multiple dam removals under multiple objectives: Linking tributary habitat and the Lake Erie ecosystem" by Zheng, Hobbs, and Koonce (2009). The researchers developed a mathematical model to help navigate the complex trade-offs involved in selecting *portfolios* of dams for removal in Lake Erie's U.S. watersheds.
Dam removal isn't simple. While it can reopen historical habitat for desirable native fish like walleye, it also comes with significant costs. Furthermore, removing a dam might inadvertently help invasive species, like the parasitic sea lamprey, access new spawning grounds. Some dams also serve functions like flood control or recreation, whose loss represents another cost.
Decisions are further complicated because:
The paper tackles this using multiobjective optimization, a mathematical framework for making decisions when you have multiple, often conflicting, goals.
Imagine a simple scale. On one side, we have the potential benefits of dam removal, primarily improved habitat for native fish. On the other, we have the costs: removal expenses, lost dam services, and potential harm like expanded habitat for invasive species.
The goal is to find a set of dam removals that achieves the "best" balance, but what "best" means depends on how much we value each objective.
To build an optimization model, we first need ways to measure the effects of removing a dam.
Removing a dam can reconnect fragmented river sections, making upstream areas accessible again. The quality of this newly accessible habitat varies. Ecologists use tools like the Habitat Suitability Index (HSI) to quantify how suitable a particular river reach is for a specific species (like walleye or sea lamprey) based on factors like water depth, flow velocity, and substrate (the river bottom material).
Click on a dam to simulate its removal and see how it opens up upstream habitat. Observe the potential habitat quality (HSI) for Walleye and Sea Lamprey in the newly accessible segment.
The paper calculates potential habitat gains ($H^{walleye}_j$, $H^{lamprey}_j$) for removing each dam $j$. These habitat changes are then linked to the broader Lake Erie ecosystem using the Lake Erie Ecological Model (LEEM), a complex simulation estimating how changes in tributary habitat (especially for walleye young-of-year, YOY) affect lake-wide fish populations and community structure.
Removing dams costs money. The paper estimates this cost ($C^{dam}_j$) using a statistical model based on past removals, considering factors like:
Additionally, if removing a dam opens up habitat for sea lamprey, there's an associated cost ($C^{lamprey}_j$) for controlling them, typically by applying lampricides. This cost depends on the length of suitable lamprey nursery habitat created.
Adjust the sliders to see how different dam characteristics influence the estimated removal and potential lamprey control costs, based on the paper's models (Equations 14 & 15, simplified).
The core of the paper is a Mixed Integer Linear Program (MILP). This sounds complex, but the basic idea is to make a series of yes/no decisions – whether to remove each specific dam ($d_j=1$) or keep it ($d_j=0$) – to achieve the best possible outcome according to defined objectives and constraints.
The model aims to:
A key constraint is the budget ($B$). The total cost cannot exceed the available budget: $x_9 \le B$. Another constraint ensures logical consistency: a dam cannot be removed unless any dam immediately downstream of it is also removed.
Since maximizing health and minimizing cost are conflicting goals, there isn't a single "perfect" solution. Instead, there's a set of "efficient" or "Pareto optimal" solutions. A solution (a portfolio of dams to remove) is efficient if you cannot improve one objective (e.g., increase ecosystem health) without worsening another objective (e.g., increasing cost).
The paper uses the constraint method to find these efficient solutions. They solve the MILP repeatedly, maximizing ecosystem health ($z_1$) for different budget levels ($B$). Plotting the resulting health scores against their corresponding costs reveals the efficient frontier – the curve representing the best possible trade-offs.
This chart shows the trade-off between total cost and the aggregate ecosystem health index (scaled from 0% = no removal, to 100% = max potential improvement found). Each point represents an efficient portfolio of dam removals found by the model for a specific budget. Use the slider to set a budget limit ($B$). The points meeting the budget turn blue, and the best portfolio achievable within that budget is highlighted in orange.
The shape of the efficient frontier is important. Often, it shows diminishing returns: the initial investments yield large gains in ecosystem health, but achieving further improvements becomes increasingly expensive.
What if stakeholders are particularly worried about sea lamprey? The initial model weights might not fully capture this concern. The paper explores this using sensitivity analysis.
They introduce a weight ($WL$) representing the importance placed on *avoiding* increases in potential sea lamprey habitat ($z_3$). The objective function is modified to maximize a weighted combination: $(1 - WL)z_1 - WL z_3$. A higher $WL$ means lamprey avoidance is prioritized more heavily.
Let's fix the budget at $15M (the orange point in the previous chart). Now, use the slider to adjust the weight ($WL$) given to avoiding lamprey habitat expansion. Observe how the *chosen portfolio* (highlighted in red) changes as priorities shift. Compare it to the original $15M portfolio (orange).
Notice that as $WL$ increases, the model selects portfolios that open up less lamprey habitat, even if it means achieving a lower score on the original ecosystem health index ($z_1$). This often involves removing a different set of dams, potentially more numerous but smaller or located in areas less suitable for lamprey.
Simplified Map: Dams selected with WL = 0.0 shown in red. Original $15M portfolio dams (WL=0) shown in yellow for comparison.
The MILP model developed by Zheng, Hobbs, and Koonce provides a powerful framework for analyzing the complex trade-offs in multi-dam removal decisions. By integrating ecological impacts (via habitat models and ecosystem simulations) and economic costs within an optimization framework, it can:
It's crucial to remember that such models are *screening tools*. They help identify promising strategies and understand system dynamics. However, due to uncertainties in data and model parameters (habitat quality, costs, ecosystem responses), any potential dam removal identified by the model would require detailed site-specific study before action is taken.
This work highlights the value of quantitative, multiobjective approaches in tackling complex environmental management problems, providing a structured way to navigate trade-offs and inform negotiations among diverse stakeholders.
Based on: Zheng, P. Q., B. F. Hobbs, and J. F. Koonce (2009), Optimizing multiple dam removals under multiple objectives: Linking tributary habitat and the Lake Erie ecosystem, Water Resour. Res., 45, W12417, doi:10.1029/2008WR007589.