A –Streams of Thought– contribution by Kevin Roche.
Andrea Rinaldo is director of the Laboratory of EcoHydrology at the École Polytechnique Fédérale de Lausanne (EPFL). Throughout his career, Professor Rinaldo has leveraged the tools of statistical physics to glean understanding of how river networks evolve and foster biodiversity. He is a former recipient of AGU’s Horton Award (Hydrology Section), an AGU Fellow, and a member of the National Academies of Engineering and Sciences. He received his Dott. Ing. from the University of Padova in Civil Engineering and his Ph.D. in fluid dynamics from Purdue University. You can find more information about Professor Rinaldo and his research on his EPFL webpage and his 2014 PNAS profile (Gabrielson, 2014).
Fig. 1. Professor Rinaldo and his craft.
When did you begin researching large scale hydrological processes?
I went to a conference led by Ignacio Rodriguez-Iturbe, now at Princeton University, who became my friend and collaborator for almost thirty years. It was titled Chaos in Rainfall, and I found it awesome. At the time I was bored with fluid mechanics research and in search for new ideas. After a short while, I started working with Ignacio, and here I am.
How did you establish the linkages between rivers and complex networks?
Actually, the linkage is rooted in empirical observations. In those times our ability to remotely acquire objective information about the hydrological world—for instance, river networks—as well as the arrival of big data, opened up a world that physicists had described in different contexts. So it came naturally; and I had no trouble making connections, because fluid mechanics gave me a proper technical ability.
Can you explain these linkages in more detail?
Point at a randomly chosen site within a map of a catchment. Measure the total catchment area that drains into that site (this can be done by remotely acquired and objectively manipulated information across several orders of magnitude). Repeat the exercise many times. Count the relative occurrence of total contributing area at any site. You will soon realize from your measurements that there exist catchment areas of all sizes. There is no preferential size of the catchment. Such a phenomenon can be described by power law distributions, in this case the relative proportion of areas endowed with a given size. Power laws are interesting mathematical objects, because in certain cases they can have no mean or variance under conditions.
In brief, they suffer from the syndrome of infinite variance. As dubbed by Benoit Mandelbrot, if the variance of your measurements is found to depend on the size of your sample, you’re essentially saying your phenomenon suffers from such syndrome. (An infinitely long signal will have an infinite variance.) Power laws are the tool that mathematically addresses what fractal geometry pioneer Benoit Mandelbrot had realized, which was that we’ve been looking at nature with the wrong set of eyes. Mountains are no cones, clouds are not spheres nor lightning travels in a straight line. These are the ingredients of self-organized critical phenomena where river network evolution belongs.
Fig. 2. River networks exhibit similar patterns, regardless of the area of your observation. Image courtesy of paulbourke.net.
What are the fundamental questions in hydrology that this framework can address?
Why in the world do river networks look the same, regardless of catchment size, vegetation, exposed lithology, and so on? What is turning the celestial screwdriver that tunes millions of parameters to reveal the same exact structures? It’s reasonable to think the outcome is inevitable, instead. Self-organization deals with just that. How can an open, dissipative natural system with a large number of degrees of freedom naturally settle into stable states that are statistically alike, regardless of initial conditions, parameter values, quenched randomness ? Rivers are perfect examples of self-organization because you can observe them from the scale of one meter to thousands of kilometers. Not even in planetary sciences do we have datasets this accurate across up to six orders of magnitude.
Are the current spatial datasets sufficient to test these theories?
Absolutely. Those datasets gave us the quantum step forward in understanding how the natural world operates, seen through the narrow-angled lens of the hydrological world I’m interested in.
Fig. 3. When scaled correctly, catchments of any size will possess the same statistical distribution, exhibiting finite-size scaling features, of total contributing drainage areas [Rinaldo et al., 2014].
In my view, the next step —where the gold medal in research lies in my view — is in water controls on biota: species (hence biodiversity), populations (hence migrations), and pathogens (hence spread of waterborne and water-based disease). Half of my group is working on the modeling the spread of epidemic cholera. Why? The pathway for the spread of biota is not an abstract network, but a river network and a human mobility one. Whether a pathogen is diffusing in a constrained space or in a very constrained one, the outcome proves completely different.
Humans no longer need to “follow the water” to navigate the planet. We can cross a continent without a sip of water. How do we reconcile this idea with the current pace of human mobility?
First, historic population migrations are important for meta-history. Second, we now have to understand two networks. Pathogens disperse over natural waterways, but humans inject pathogens at random nodes of the waterways network because of human mobility (asymptomatic infected individuals who move abound) generally not following those pathways. The two are completely different, but both can be measured – the latter by tracking cell phones for instance – and it is amazing the fact that a decent sanitation still cannot be deployed throughout developing countries whereas Nokia I-90 did pervasively.
Even on my visit to Haiti, a man in Carrefour, one of the poorest neighborhoods in Port-au-Prince, showed me on his Nokia 1900, an SMS message showing proof of payment for a cabbage. [The ubiquity of cell phones] means that we can track human mobility without having to model it. They’re inputs, which allow us to make spatially explicit models of epidemics.
Could you provide an example of how you expect these models to be used?
If you have an outbreak of infections now, like what happened in Haiti in 2010, it’s not obvious where you will have infections six months from now, and if you want to deploy medical staff, life-saving medical supplies, etc., you can’t ignore spatial effects in the propagation of the epidemics. Water controls become central then. So for me, the next step forward —the most important current challenge to hydrologists— is to take what we have learned about the water world and ask how it affects biota, biodiversity, population migrations, societal issues, water wars, etc. In all of these topics, water remains central.
Fig. 4. Population density in Haiti is highly heterogeneous and linked to water resources [Rinaldo et al., 2012].
Read broadly. Don’t confine yourself to your own original research field, say that of your doctoral thesis. If you’re a physical scientist, read biological literature. I found great inspiration in Jared Diamond’s and Stephen J. Gould’s books, for instance. There you find the very idea of a meta-history, the way environmental factors influence the development, rise and collapse, of human societies. For hydrologists, modeling this is great fun, and sometimes even instructive.
Could you share any insights on how you approach creativity?
To be truly creative there’s a necessary condition: know the technical tools of your trade perfectly well. Like a musician, you have to achieve technical perfection, then you sit down and think. Only then comes possible innovation.
We, as teachers and thesis advisors, should never constrain the student’s curiosity especially in the early phases of intellectual maturity, chiefly during her/his PhD research. Your research path should be always curiosity-driven. From this curiosity come the side projects borne from a main theme but reaching out, and these can be so interesting. You’ll never have such a quiet period in your life to sit down and think, and you will never regret doing it actually.
References
Gabrielson, P.: “Profile of Andrea Rinaldo” Proceedings of the National Academy of Sciences 111.11, 3900-3902. DOI:10.1073/pnas.1401995111, (2014).
Rinaldo, A., et al.: “Reassessment of the 2010–2011 Haiti cholera outbreak and rainfall-driven multiseason projections.” Proceedings of the National Academy of Sciences 109.17 6602-6607. DOI:10.1073/pnas.1203333109, (2012).
Rinaldo, A., et al.: “Evolution and selection of river networks: Statics, dynamics, and complexity.” Proceedings of the National Academy of Sciences 111.7 2417-2424. DOI:10.1073/pnas.1322700111,(2014).
For more information on fractal river basins:
Rodríguez-Iturbe, I., and Rinaldo, A. “Fractal River Basins: Chance and Self-Organization” Cambridge University Press, (2001).
About the author
Kevin Roche is a PhD researcher at the University of Northwestern, Department of Civil and Environmental Engineering and active member of the YHS-AGU branch.
Young Hydrologic Society 