Saturday, October 13, 2018

Controllability and Dynamical Systems

Wow! There is a lot of literature on dynamical systems. Originally, when i though to dynamical systems I identify them with the non linear dynamical systems which produced chaos (e.g. Strogatz, 1994) or to elegant geometric representations of mechanics (Arnold, 1983, 1989 ). Looking to lumped hydrological models as dynamical systems opened to me new perspectives. The more important one: learning dynamical systems from system dynamics. Said this way, it seems a joke or a tautology. However system dynamics is its own discipline. It can be think to originate from von Bertalanffy but it is conjugate as “System and Control” since Kalman (e.g. Kalman, 1968). Wilems (e.g. Polderman and Wilems, 1998) offers a little different (but interesting) perspective (and a terrible notation).
 
When one think to a systems of ordinary differential equations (ODEs), obviously the thoughts go to their solutions. Does exist a solution for such a system ? Is it unique ? A mantra that we learned since our first courses on calculus. However “System and Controls” steers towards different concepts (e.g. Luenberger, 1979 or Kalilath, 1980 or more mathematically, Sontag, 1998). In fact the concept of control implies to study the conditions under which the ODEs systems solution can be moved to a precise beahvior (Willems, 2007) by actuators, i.e., external inputs (fluxes ?) to the state variables. This condition was easily translated into the determination of the rank of a special matrix, first written by Kalman (e.g. Liu and Barabási, 2016). Other equivalent formulation include the Gramian integral. What exactly means this property said “controllability” ? It means no more that what is intended: that trough a number of external actions you can move the systems to any conceivable state. Let $x_1$ to $x_n$ these variables, then you have to be sure that that all the n-dimensional vector domain can be spanned under the action of actuators, and the Kalman result, just establish the condition under which this is possible. I did not mention however, that the above results are valid for linear systems: a great result but a little poor in scope, since most of the problem we have are nonlinear. Fortunately people piooneered studies on the controllability on non linear systems since the seventies (Heines and Hemes, 1970; Hermann and Kremer, 1977; Cornelius et al, 2013, Isidori, A., 2013).
The application field of controllability had its first application oh hydraulic and mechanical engineering (e.g. Polderman and Wilems, 1998) , but soon moved to other systems. Notably: ecology (Iglesias and Ingals, 2010), brain (Lynn and Basset, 2018) , internet connections ( Liu and Barabási, 2016). There is then hope that those studies also impact hydrological and earth system sciences.
I did not mentioned it but really entangled with the more recents developments of the matter, there is the study of graph theorethic methods applied to the dynamical system (Yamada and Fouls,1990). Barabasi and Liu (Liu and Barabási, 2016) wrote a recent review that practically starts from the illustration of the systems with graph.
Made the note that I believe that Petri Nets are more exppressive than those used by Barabasi, I found the graph methods more easy to grasp and intuitive. Possibly one can also see connections between the results here (in dynamical systems) and some of those in causality theory (Pearl et al., 2016). For instance the theorem regarding the structural controllability of systems described by graphs (see in Lu and Barabási, 2016) recall the theorems on correlations in causality theory. A system which is correlated, read as a causal graph, is not controllable (it seems). A-posteriori, this seems obvious, since correlation, means some type of limitation on the phase space explorability.


References

Thursday, October 4, 2018

Peter Germann's open book on preferential flow

Peter German (GS) first raised the issue of how preferential flow in soils due to preferential flow in a famous paper with Keith Beven (GS) in 1982, Macropores flow in soils. A benchmark paper from which uncountable studies followed. Now retired, he wrote a book entitled "Preferential flow: Stokes approach to infiltration and drainage".
Since 1982 there was a great debate on preferential flow modelling which is not yet concluded. Germann's book is evidently  a contribution from a protagonist of this story and he had the kindness to make it open. I am not sure about the content. Stokesian flows are those that happens when all acceleration is dissipated, so the subtitle is not very informative on the content. More detailed comments will arrive when I will have read it. For now you can get it by clicking on the Figure.

Wednesday, October 3, 2018

Kirchner 2016 model

I open a new series of posts that analyze simple (or less simple) lumped (reservoir based) Hydrological Models. They are Dynamical Systems and they are well represented through Petri Nets introduced in Reservoirology #3. The present is the case of a simple two reservoirs model presented in Kirchner 2016 (from now on, K2016b).


Because of  its simplicity, K2016b is a nice case study to test and verify various aspect treated more abstractly in Rigon et al., 2016.  The presentation that contains K2016 is here.

Reference

Kirchner, J. W. (2016). Aggregation in environmental systems-Part 2. Catchment mean transit times and young water fractions under hydrologic non-stationarity. Hess, 20, 299–328. http://doi.org/10.5194/hess-20-299-2016

Tuesday, October 2, 2018

Richard Rotunno on the predictability of Storms

In these days we have here in Trento,  at my Department, Richard Rotunno (GS), a pleasant person and an outstanding scientist. His field of interest is meteorology and micrometeorology and, in particular, the evolution of storms.  Here in Trento he gave various seminars and in particular one  on the predictability of storms, which he permitted to share with you.
As usual, by clicking on the above image, you will be able to access the presentation. He cited some interesting papers that you will find below. On the butterfly effect, you can also see this my previous post, to which I think the literature cited by Richards add something important.

References (In the order in which they are cited)

Monday, October 1, 2018

Floods in Alberto Viglione research

I had the honour to be in the committee that selected Alberto Viglione (GS) to become Associate Professor at Politecnico di Torino.  Alberto gave a nice seminar entitled "understanding and Estimating River Flood Hazards across Timescales" which covers some issues on flooding forecasting and variability in space-time.
I really appreciate his point of view which is different from mine and from which I can learn a lot, therefore I  asked him the permission to publish his presentation in my blog here. Please by clicking on the Figure above, find Alberto's presentation.

References

Archfield, S. A., R. M. Hirsch, A. Viglione, and G. Blöschl (2016), Fragmented patterns of flood change across the United States, Geophysical Research Letters, doi:10.1002/2016GL070590.

Barendrecht, M.H., A. Viglione and G. Blöschl (2017) A dynamic framework for
flood risk, Water Security, 1, 3-11, doi:10.1016/j.wasec.2017.02.001.

Blöschl, G., M. Sivapalan, T. Wagener, A. Viglione, and H. H. Savenije (2013b), Runoff Prediction in Ungauged Basins - Synthesis across Processes, Places and Scales, 484 pp., Cambridge University Press, ISBN:9781107028180.

Blöschl, G., et al. (2017), Changing climate shifts timing of European
floods, Science, 357 (6351), 588–590, doi:10.1126/science.aan2506.

Di Baldassarre, G., A. Viglione, G. Carr, L. Kuil, J. L. Salinas, and G. Blöschl (2013), Socio-hydrology: conceptualising
human-flood interactions, Hydrology and Earth System Sciences, 17, 3295–3303, doi:10.5194/hess-17-3295-2013.

Merz, R., and G. Blöschl (2008), Flood frequency hydrology: 1. Temporal, spatial, and causal expansion of information, Water Resources Research, 44, W08432, doi:10.1029/2007WR006744.

Salinas, J. L., A. Kiss, A. Viglione, R. Viertl, and G. Blöschl (2016), A fuzzy Bayesian approach to
flood frequency estimation with imprecise historical information, Water Resources Research, 52 (9), 6730–6750, doi:10.1002/2016WR019177.

Viglione, A., R. Merz, and G. Blöschl (2009), On the role of the runoff coefficient in the mapping of rainfall to flood  return periods, Hydrology and Earth System Sciences, 13 (5), 577–593, doi:10.5194/hess-13-577-2009.

Viglione, A., G. B. Chirico, R. A. Woods, and G. Blöschl (2010a), Generalised synthesis of space-time variability in flood response: An analytical framework, Journal of Hydrology, 394, 198–212, doi:10.1016/j.jhydrol.2010.05.047.

Viglione, A., G. B. Chirico, J. Komma, R. A. Woods, M. Borga, and G. Blöschl (2010b), Quantifying space-time dynamics of flood event types, Journal of Hydrology, 394, 213–229, doi:10.1016/j.jhydrol.2010.05.041.

Viglione, A., R. Merz, J. L. Salinas, and G. Blöschl (2013), Flood frequency hydrology: 3. A Bayesian analysis, Water Resources Research, 49 (2), 675–692, doi:10.1029/2011WR010782.

Viglione, A., G. D. Baldassarre, L. Brandimarte, L. Kuil, G. Carr, J. L. Salinas, A. Scolobig, and G. Blöschl (2014), Insights from socio-hydrology modelling on dealing with flood risk – Roles of collective memory, risk-taking attitude and trust, Journal of Hydrology, 518 (A), 71–82, doi:10.1016/j.jhydrol.2014.01.018.

Viglione, A. and M. Rogger (2015) Flood processes and hazards, Chapter 1.1 in: J.F. Schroder, P. Paron and G. Di Baldassarre (Eds.) HydroMeteorological Hazards and Disasters, Elsevier, pp. 3-33, doi:10.1016/
B978-0-12-394846-5.00001-1.

Viglione, A., B. Merz, N. V. Dung, J. Parajka, T. Nester, and G. Blöschl (2016), Attribution of regional flood changes based on scaling fingerprints, Water Resources Research, 52 (7), 5322–5340, doi:10.1002/2016WR019036

Sunday, September 30, 2018

Concentrations

Some notes on concentration of solutes in Hydrological Dynamical Systems  (a.k.a. lumped, a.k.a. compartmental ) Hydrological models.



The slides can be seen by clicking on the Figure above.  These slides pretend to be be quite intuitive in content but, obviously to people  who have some familiarity with the topic treated. A good lecture for  their introduction is Rigon et al. 2016. For understanding the graphs the blog posts entitled “Reservoirology”, especially Reservoirology #3 are also a preparatory lecture.

Thursday, September 27, 2018

Java 11 trap

As you know we use Java (R and python).  Version 11 is a major release because it has long-term support (LTS). But it comes with some traps. Here below, please find  "verbatim" a post from Stephen Colebourne's blog which inform about some problems that Oracles's new licensing strategy can cause. (From the same blog, also interesting the suggestions on how to move from Java 8 to Java 11).

" ... It is a But Oracle have also set it up to be a trap (either deliberately or accidentally).

The trap

For 23 years, developers have downloaded the JDK from Oracle and used it for $free. Type "JDK" into your favourite search engine, and the top link will be to an Oracle Java SE download page (I'm deliberately not providing a link). But that search and that link is now a trap.
Oracle JDK, the one all web searches take you to, is now commercial not $free.
The key part of the terms is as follows:

You may not: use the Programs for any data processing or any commercial, production, or internal business purposes other than developing, testing, prototyping, and demonstrating your Application;

The trap is as follows:
  • Download Oracle JDK (because that is what you've always done, and it is what the web-search tells you). 
  • Use it in production (because you didn't realise the license changed)
  • Get a nasty phone call from Oracle's license enforcement teams demanding lots of money
In other words, Oracle can rely on inertia from Java developers to cause them to download the wrong (commercial) release of Java. Unless you read the text/warnings/legalese very carefully you might not even realise Oracle JDK is now commercial, and that you are therefore liable to pay Oracle for Java.
Is this trap malicious behaviour on the part of Oracle? Readers will have their own opinions. I do suggest bearing in mind that Oracle invests huge amounts in developing Java, so it is reasonable to have a commercial plan available for those that want it. And they do provide a $free alternative...
The solution

The solution is simple!

Use an OpenJDK build.
As well as their commercial JDK, Oracle produce an OpenJDK build. It is free, zero-cot and GPL licensed (with Classpath exception, so safe for commercial use).

Download $free Java here.

Right now, the OpenJDK build from Oracle is the only one available. But more will be available soon such as from AdoptOpenJDK (probably later this week). And the OpenJDK build from groups other than Oracle will the the ones to use for Java 11 longer-term support. See Couleborne's post on zero-cost Java and the wide variety of OpenJDK builds for more details.


Summary

Do NOT download or use the Oracle JDK unless you intend to pay for it.
For Java 11, download and use an OpenJDK build, currently from here. (No comments on this post. There are plenty of other places to express opinions.)"