If you’re like me, you’ve spent a little extra time reading the news and following social media the last few weeks. I have found myself hitting refresh on NPR looking for the newest updates on the COVID-19 pandemic. One thing I have noticed in my addiction to the news is that mathematical models, usually reserved to engineers or scientist, have come to the forefront of the mainstream news media. In particular, there is one plot I have seen over and over again:
Despite not being a public health expert this graph looks extremely familiar to me. A couple things stand out: the log scale on the y-axis and the straight line projections in log scale (dashed lines). In a normal-normal scale these projection would show exponential growth.
Why do these attributes look so familiar to a groundwater modeler? Well, here is an example of a drawdown curve from an aquifer test with a straight line projection in log time. Can you see the similar features? There is an axis in normal scale (drawdown) and a log scale (time in minutes), and a straight line projection into the future, just like in the graph above. Both of these graphs are examples of mathematical model results. Mathematical models are numerical simulations of real world physics, with simulations of past events (actual deaths from COVID-19 or groundwater drawdown), and a projections into the future based on the observations (increases in COVID-19 or groundwater drawdown).
At LRE we use these drawdown models and projections to recommend the design rate and total dynamic head for pump selection in a groundwater wells. Without these models we would select pumps blind and potentially oversize the pump, resulting in excessive drawdown and the pump burning out, or undersize the pump, resulting in a well that produces less than its potential.
Another model we have all seen recently is the “flattening the curve” model. These curves are representative of predictive models of COVID-19 infections at a specific time under differing social distancing measures. This model looked very similar to the results of numerical groundwater flow and transport model LRE Water just finished constructing! Below is the results of this model, used for the selection of a horizontal well type and location. This plot shows the distribution of modeled times for particles to flow from a river to different alluvial groundwater wells. We looked at transport times for different horizontal well types at varying locations to help our client decide what type of well and well location met their water quality and groundwater yield design requirements.
Seeing these kind of predictive models in the news has been eye opening to me as a modeler. I am inspired by how these scientists are using models to drive meaningful action across the globe and that these actions have the potential to save hundreds of thousands of lives. I am thankful for the efforts of the health experts in keeping our community safe.
I also see common threads in these models and the groundwater models I develop every day at LRE water in the inherent responsibility that comes with modeling and model predictions. The groundwater flow and transport models LRE Water developed will be used to drive decisions regarding a multi-million dollar well field that will provide drinking water to a major community. The recommendations we made based on these model results will significantly affect our client’s finances as well as the public health. There is a lot or responsibility inherent in modeling because of the consequential decisions that are made based upon the results. A weatherman makes a snow prediction that drives the closing of stores and schools which has significant consequences on local lives and the economy. And the health experts that are now running the COVID-19 pandemic models provided predictions that have driven the partial shutdown of the global economy.
When making predictive models, there is never a counter-factual. For example, if social distancing works, it is inevitable that people will ask “was it necessary?” because the outcome of the pandemic if we didn’t social distance will never be known. The same is true in groundwater modeling or any other scientific predictive modeling. There is trust in modelers as experts that the models we produce are accurate. Predictive models are powerful tools, and can be used to save lives, protect the environment, and help manage water resources. But the decisions made are also highly consequential, and these consequences highlight the responsibility that we have as modelers to our clients and the public.
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