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.

On my morning walks by the river I take note of how much water appears to be flowing in the river. Lately the flows have not been that high because most of the snow has already melted and there has not been that much rain or snow for the last few weeks. Previously, when the snow melted the riverbanks overflowed onto roads and it was a very different river.

How do you explain and/or predict the flow of a river?

To predict flow you need to start by having a good measurement of existing flow. A standard technique is to measure the width of the stream and the depths of the stream at various regular intervals then sum over these trapezoidal area estimates (A = Σ a_i). You would then have to measure the velocity v of the water perhaps by floating a cork in water between two markers and timing how long it takes. Once you had area and velocity measurements you could compute a flow volume (Q = A x v). This flow volume would vary from day to day.

What factors might you use to explain and predict a river flow?

Explaining a river flow is different than predicting a river flow. A big factor in explaining a river flow volume is the number and size of tributaries leading into it. This factor stays fairly constant from day to day so is not very useful in predicting the daily variation in river flow. Other factors like precipitation, ground saturation, ground permeability, evaporation, etc. might be more useful in predicting the day to day expected flows.

Most cities are built along a river. Around half of those cities withdraw a major part of their water supply from upriver. Depending on the size of the city and its seasonal demand for water, this extracted volume could be a significant factor influencing flow rate.

A home property can also be the focus of an investigation into daily flow volumes. What factors explain and predict the amount of water you use on your property on a daily basis? Those on metered water have an advantage over non-metered users in that they can figure out those factors better because they have accurate flow measurements to go by (depending on how that usage is reported).

Cashflow is another type of flow that concerns entrepreneurs and investors. What are the factors that explain and predict the cashflow of a company? What is the time frame of concern in our cashflow projections - a day, a week, a month, quarterly, etc... The time frame determines how frequently we would have to measure cashflow to determine if the cashflow model is correct. Comparing cashflow models to riverflow models offers potential insights.

Stock and flow diagrams are commonly used in systems theory to model systems dynamics. The simplist stock and flow diagram looks like this bathtub model used to explain and predict the level of water in a bathtub:

Donnella Meadows in her book Thinking In Systems: A Primer (3rd Edition, 2008) uses a slightly more complex stock and flow diagram to explain and predict the volume of living wood in a forest and also the lumber inventory associated with that forest:

There are many mathematical and graphical techniques you can use to explain and predict flows. The study of river flows offers a useful foundational metaphor for thinking about other types of flows (e.g., the flow of electricity is often understood in terms of water flows). The techniques needed to explain and predict stream flows might also be used to explain and predict these other types of flows as well. Something to think about the next time you are walking beside a river and looking for something to occupy your mind.

FLORIDA INVESTMENT NETWORK

Home

Contact

Entrepreneurs | Investors | About | Our Privacy Policy

© 2004-2024, Dealflow Solutions Ltd. All rights reserved.

Connecting Florida Entrepreneurs and Investors.