For the last couple of blogs I have been talking about rivers and flows (Part 1, Part 2). These blogs are inspired by my morning walks by the local river and by my reading of a book by Sean W. Fleming called Where The River Flows: Scientific Reflections on Earth's Waterways (2017).

The book covers different approaches to river science, more specifically flow prediction, involving neural networks, markov chains, information theory, spectral analysis, chaos theory (fractals), complexity theory (cellular automata) and monte carlo methods. I was a bit disappointed at first because I was looking for something a little more meaty about the mechanics of river flow and this seemed a bit too high level. I eventually picked up a book on hydrology for lower level details (Environmental Hydrology , 2015) which complimented Sean's faster-paced high level discussion of how river flow can be related to physics, geology and astronomy using modern tools and techniques. Sean discussed may interesting and complex topics is relatively short book (204 pages) in a way that was easy to read and entertaining. I recommend it if you have an interest in rivers and flow patterns.

To begin predicting river flow, it helps to have a time series consisting of a river flow measurement recorded at regular intervals of time (e.g., daily, monthly). Hydrologists try to predict these flows using different types of models. One type of model is an empirical one that statistically relates flow rates to dominant factors like rain fall, snow depth, temperature, previous day's streamflow, watershed topography, etc... These are often the types of models that are developed in practice for streamflow forecasting. Another type of model is a process model that uses physics equations to represent meteorological inputs and internal watershed characteristics. You run the model with the proper inputs and the model simulates expected stream flow. A final type of model is what I would call phenomenological that is based on extended observation and interaction with river flow. A beaver, for example, uses a phenomenological model to predict and alter river flows.

Humans are fortunate that we can develop empirical and process models of stream flow patterns, but it is interesting that a beaver can have a profound beneficial effect on water flows using only a phenomenological model based on observation and interaction with flows. In the Devon area of England, the wildlife trust has re-introduced beavers to an enclosed 6 acre area to study how they alter their immediate environment and downstream areas. Their main findings were that 1) beavers significantly increased biodiversity in that area, 2) they altered flow patterns so that downstream areas are less likely to flood because of the impounding and slow release of water from their dams, and 3) their dams act as a filter cleaning agricultural pollutants from the streamflow. Some of that research is reported in the Devon Wildlife Trust Beaver Project Update (PDF). I would like to draw you attention to one graph from that report that shows the evolution of the dams over time. Starting from 0 dams in 2011 they have constructed 13 dams and completely altered and enlarged the flow of water through the landscape

I think it is worth keeping the beaver in mind when we think about modelling the flow of automotive traffic through a streetscape, the flow of foot traffic through a mall or store, or other flows that are of concern to us. We can certainly construct sophisticated models to explain and predict these flow patterns, but phenomenological models developed through sustained observation and interaction can also be powerful ways to understand these flows for the purposes of modifying them in beneficial ways.