Small Models Big Results
Alan Manne, a renowned economist, once said, “To get a large model to work you must start with a small model that works, not a large model that doesn’t work.” This philosophy, rooted in pragmatism and incremental development, holds important implications for various fields, including groundwater modeling. Groundwater modeling is a complex and often critical field of study that helps in understanding, predicting, and managing water resources in the subsurface environment. Applying Manne’s wisdom to this field offers a strategic approach to tackling its inherent challenges.
The Benefits of Small Models
Consider the simple act of making a paper airplane. Even a basic design, with just a few folds, can glide beautifully through the air. It doesn’t look like a real plane, but it “flies”. This may seem like child’s play, but scientists and engineers have used paper airplanes as prototypes to study aerodynamics and flight stability. Researchers turn to these simple (‘small’) models because there is “no good mathematical model for predicting this seemingly simple but subtle gliding flight”. So, although these simple paper models represent limited and very specific components for flight design, they provide valuable insights because they allow for quick incremental design changes, which really speeds up the research. For researchers in this field, having a more complex model which is difficult to adjust and comprises more parts, needlessly complicates their study with slower prototyping and more interacting variables to consider.
https://www.nyu.edu/about/news-publications/news/2022/march/for-new-insights-into-aerodynamics–scientists-turn-to-paper-air.html
Starting Small with Groundwater Models
Groundwater modeling often (but not always!) involves simulating the physical and chemical processes that occur in the subsurface environment. The challenge is that, unlike an airplane (paper or otherwise), we cannot see groundwater moving so we must infer, interpolate, estimate, and even guess what is happening in the real world based on a limited set (sometimes very limited!) of observations. Compounding this challenge is the fact that our ability to measure some of the important variables is inherently limited, it is expensive to make observations and some of the variables can be combined in many potential ways to explain the observations. For some, the complexity of groundwater systems often leads to the temptation to construct large, all-encompassing models right from the outset. Manne’s quote should serve as a reminder of the value of simplicity and the power of starting small.
Small models offer several advantages:
• Manageability: Smaller models are easier to manage and understand. They allow the researcher to focus on key processes and interactions without getting overwhelmed by the complexity of a full system.
• Testing: It is easier to test small models. They can be more readily compared with observed data with much more transparency in the cause and effect of the modelled variables.
• Building Blocks: Small comprehensible models can serve as building blocks for larger models. This step-by-step approach ensures that the foundation of the model is sound before adding complexity.
• Flexibility and Adaptation: Small models are more adaptable. Like all good prototypes they can be quickly modified and tested again.
Once a small model has been tested and deemed both insightful and useful, it can be scaled up incrementally. This scaling process involves gradually adding complexity, such as more detailed hydrogeological layers, varied water use scenarios, or climate change impacts. Of course, each added layer of complexity must be tested to ensure the model remains useful to its purpose.
The iterative process of scaling up has several benefits:
• Reduced Risk of Overfitting: By gradually increasing complexity, there’s less risk of creating a model that is too finely tuned to specific data sets and fails to generalize well to new situations.
• Enhanced Understanding: Each step in the scaling-up process offers an opportunity to deepen understanding of the groundwater system, leading to more informed decision-making.
• Stakeholder Engagement: This phased approach allows for continuous engagement with stakeholders, ensuring the model remains relevant and useful for decision-making.
Challenges and Considerations
While the approach of starting small and scaling up is advantageous, it is not without challenges:
• Communication: A simpler model is usually much easier to explain. However, researchers may tend to focus on communicating the most complex version of the model. This is a lost opportunity to demonstrate the evolution of thoughts and the most convincing arguments about how the real-world works via the model.
• Time and Resource Constraints: Incremental development might require more time and resources compared to building a large model outright. Plan accordingly.
Fold it Up
Alan Manne’s advice to start with a small, working model is bit like choosing to first make a paper airplane that flies rather than starting with a detailed toy plane that doesn’t (assuming that you want to learn about flight of course). In groundwater modeling, as in many scientific and engineering disciplines, the wisdom of Manne’s advice of starting with a small model cannot be overstated. In groundwater modeling, this approach ensures that we build models that start “small” and grow until they are suitably detailed for our purpose. This approach encourages prototyping which makes models easier to understand, easier to test, easier to modify and provides a much better understanding of how the system works. Ultimately, by following Alan Manne’s advice, groundwater researchers can navigate the complexities of the subsurface with greater confidence and success.