Imagine a large, vibrant lake ecosystem like Lake Erie. It's teeming with life, but also faces challenges. One major stressor? Dams built on the rivers and streams that flow into the lake. While dams can provide benefits like hydropower or water supply, many older dams no longer serve their original purpose and block fish from reaching crucial historic spawning grounds.
Removing these dams seems like a good idea for restoring fish populations, right? Well, it's complicated. This article explores the core ideas from a research paper by Zheng, Hobbs, and Koonce (2009) which tackles this very problem: How do we decide which dams to remove to get the most ecological benefit, considering the costs and the potential downsides?
Dam removal isn't a simple win-win scenario. The paper highlights several key trade-offs:
With thousands of dams in the Lake Erie basin, many being potential candidates for removal, figuring out the *best combination* (or "portfolio") of dams to remove becomes a complex optimization problem.
To make informed decisions, we first need to quantify the effects of dam removal.
Scientists use concepts like the Habitat Suitability Index (HSI) to score how good a particular river section is for a specific species and life stage (like spawning walleye or juvenile sea lamprey). HSI typically ranges from 0 (unsuitable) to 1 (perfectly suitable), considering factors like water depth, flow speed, and the type of riverbed material (rocks, sand, mud).
Removing a dam doesn't just open up *any* upstream area; it opens up area with varying degrees of suitability. The paper calculates the *amount* of suitable habitat ($H$) made accessible for both walleye (area, $km^2$) and sea lamprey (length, $km$) if a specific dam $j$ is removed.
More habitat is generally good, but how does it translate to the overall health of the Lake Erie ecosystem? The researchers used a complex simulation model called the Lake Erie Ecological Model (LEEM). This model simulates the interactions between different fish species, their food sources, and environmental factors.
By feeding the *change* in walleye spawning potential (derived from the new habitat) into LEEM, they could estimate the impact on various lake-wide indicators ($x_1, ..., x_8$ in the paper), such as:
With multiple ecological indicators changing (some improving, some potentially worsening), how do we get a single measure of overall benefit? The paper uses Multi-Criteria Value Analysis (MVA). Think of it like grading a student: you assign weights to homework, tests, and participation based on their importance, and then combine the scores into a final grade.
Here, each ecological indicator $x_i$ gets a weight $W_i$ reflecting its importance to managers and stakeholders. Each indicator's value is also converted to a 0-1 scale using a *value function* $V_i(x_i)$, where 0 is the worst outcome and 1 is the best. The overall ecological health score $z_1$ is then a weighted sum:
$$ z_1 = \sum_{i=1}^{8} W_i V_i(x_i) $$A higher $z_1$ means a better ecological outcome according to the defined priorities.
Restoration isn't free. The model considers two main costs:
The total economic cost ($x_9$) for a portfolio of removed dams is the sum of removal and lamprey control costs for all selected dams.
Now we put it all together. The goal is to choose a set of dams to remove that maximizes the ecological health score ($z_1$) without exceeding a total budget ($B$). This is formulated as a Mixed Integer Linear Program (MILP).
The key decision variable is $d_j$ for each candidate dam $j$: $d_j = 1$ if dam $j$ is removed, and $d_j = 0$ if it's kept.
Imagine a simple river system with a few dams. Each has a removal cost, a potential walleye habitat gain, and a potential lamprey habitat gain (leading to control costs). There's also an upstream dependency. Given a budget, which dams should be removed to maximize walleye gain while respecting the budget and dependency?
The researchers didn't just find one "best" solution. They ran the MILP model many times, varying the budget constraint ($B$) from zero up to the cost of removing all candidate dams. This traces out an efficiency frontier (also called a Pareto front or trade-off curve).
This curve shows the maximum possible ecological health score ($z_1$) achievable for any given budget ($x_9$). It visualizes the diminishing returns – the first few million dollars spent yield large ecological gains, but achieving the highest possible score requires much larger investments for smaller incremental benefits.
The specific dams included in the optimal portfolio change as the budget changes. Initially, the model tends to pick smaller, cheaper dams that open up significant walleye habitat without too much lamprey habitat. As the budget increases, larger or more expensive dams might be included if they offer substantial ecological benefits.
The model also allows exploring "what if" scenarios. For example, what if stakeholders become much more concerned about preventing sea lamprey spread? The paper explored this by adding a negative weight to lamprey habitat creation in the objective function. Unsurprisingly, this leads to different portfolios being chosen – prioritizing dams that open less lamprey habitat, even if they offer slightly less walleye benefit or cost more (see Figure 5 in the paper).
The MILP model developed by Zheng, Hobbs, and Koonce provides a powerful framework for navigating the complex trade-offs involved in multiple dam removals. Key takeaways:
Deciding which dams to remove is a complex environmental challenge with significant ecological and economic consequences. Mathematical optimization, coupled with ecological modeling and careful consideration of stakeholder values, offers a valuable way to make these decisions more transparent, efficient, and effective.
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.