A while back, I mentioned that 2013 will be a special year for programs on the Mathematics of Planet Earth. I also mentioned that the Centre de Recerca Matematica in Barcelona is inviting mathematicians to organize conferences and workshops on this theme.

They’re also inviting mathematicians to organize workshops on this theme at the Banff International Research Station for Mathematical Innovation and Discovery, or BIRS. This is a famous and beautiful research center in the Canadian Rockies.

The deadline is coming up on September 30th, and I want to apply. If you’d like to join me, please drop me a note, either here on this blog or by email!

I’m open to all sorts of ideas, and I’d love help from biologists or climate scientists. If you don’t give me a better idea, I’ll probably do an application on network theory. It might look a bit like this:

Diagrammatic languages for describing complex networks made of interacting parts are used throughout ecology, biology, climate science, engineering, and many other fields. Examples include Systems Biology Graphical Notation, Petri nets in computer science, stochastic Petri nets and chemical reaction networks in chemistry and biochemistry, bond graphs in electrical, chemical and mechanical engineering, Bayesian networks in probabilistic reasoning, box models in climate science, and Harold Odum’s Energy Systems Language for systems ecology. Often these diagrammatic languages are invented by practitioners in a given field without reference to previous work in other fields. Recently mathematicians have set up the theoretical infrastructure needed to formalize, rigorously relate, and some cases unify these various languages. Doing this will help interdisciplinary work of the sort that is becoming important in theoretical ecology, climate science and ‘the mathematics of planet Earth’. The goal of this workshop is to bring together experts on various diagrammatic languages and mathematicians who study the general theory of diagrammatic reasoning.

If you’d be interested in coming to a workshop on this subject, let me know. Banff provides accommodation, full board, and research facilities—but not, I believe, travel funds! So, “interested in coming” means “interested enough to pay for your own flight”.

Banff does “full workshops” with 42 people for 5 days, and “half workshops” with 20 people for 5 days. Part of why I’m asking you to express your interest is to gauge which seems more appropriate.

Here’s what they say:

With a growing global population competing for the same global resources, an increased frequency and intensity of dramatic climatic events, and evidence pointing to more long-term patterns of general climate change, the pressure to comprehend nature and its trends is greater than ever. Leaders in politics, sociology and economics have begun to seriously take note of issues which before were confined to the natural sciences alone, and mathematical modeling is at the heart of much of the research undertaken. The year 2013 has thus been earmarked by mathematical sciences institutes around the world as a time for a special emphasis on the study of the “Mathematics of Planet Earth” (MPE 13). This theme is to be interpreted as broadly as possible, in the aim of creating new partnerships with related disciplines and casting new light on the many ways in which the mathematical sciences can help to comprehend and tackle some of the world’s most pressing problems.

The Banff International Research Station (BIRS) is a full partner in this important initiative, as the goals of MPE 13 are completely in line with the station’s commitment to pursuing excellence in a broad range of mathematical sciences and applications. BIRS has already planned to host five workshops in 2012 which deal with the themes of MPE 13:

•

“Emergent Behavior in Multi-particle Systems with Non-local Interactions”(January 22-27).•

“Frontiers in the Detection and Attribution of Climate Change”(May 29–June 1).•

“Tissue Growth and Morphogenesis: from Genetics to Mechanics and Back”(July 22-27).•

“Model Reduction in Continuum Thermodynamics: Modeling, Analysis and Computation”(September 16-21).•

“Thin Liquid Films and Fluid Interfaces: Models, Experiments and Applications”(December 9-14).BIRS also invites interested applicants to use the opportunities of its 2013 program and submit proposals in line of the MPE 2013 theme, in conjunction with BIRS’ regular format for programming. Proposals should be made using the BIRS online submission process.

I would like to help!

Great! Of course I figured that…

Besides you and Blake, two people who’ve expressed interest are Dan Ghica and Jason Morton. Jason Morton is doing some cool work on dagger-compact categories and Bayesian networks—exactly the sort of thing I’m interested in these days. Dan Ghica works on things like using category theory and diagrammatic methods for hardware synthesis with programmable gate arrays, as I explained on the

n-Category Café. You can see a recent talk by him here.I’m interested!

The proposal as written seems a little too general; a greater focus or more detail on the ecology and climate science applications of network theory might make it more “mathematics for the Earth”.

I’m glad you’re interested, Blake! I hope by then we’ll have something cool written up about quantum field theory stochastic lattice Lotka–Volterra models. Maybe you can give a talk about it.

Yes, I should make the proposal more focused on “planet Earth”, and more detailed too.

It looks like the last few links are all broken …

Whoops – I grabbed that stuff off the BIRS website and those were relative links, not absolute ones. I stuck in some extra stuff—they work now.

And I should add those links to our list of conferences on math, physics and environmental issues!

I’d like to come to that.

Great!

Over on the

n-Café, Eugene Lerman has also expressed interest. He’s been using category theory to study dynamics on networks—exactly the sort of thing I’m interested in.I’d be up for this. I have a general interest in logic-cizing statistical hammers.

Great! And where you go, an army of grad students and postdocs follows.

So far it’s Jacob Biamonte, Bruce Bartlett, Dan Ghica, Eugene Lerman, Jason Morton, Cameron Smith, Blake Stacey, you and me. I still want more biologists, ecologists and climate scientists—my goal is to pull in insights from fields like this. I need to see if there are still any ‘systems ecologists’ following in the old footsteps of Howard T. Odum.

Maybe worth to give Tim Palmer a buzz, …

“an increased frequency and intensity of dramatic climatic events”

There is no proof for that whatsoever. Or it may depend on what they mean by “dramatic climatic event”, of course.

If it is an ordinary climatic event presented as “drama” (a situation or succession of events having the dramatic progression or emotional effect characteristic of a play), it may well be true, but it has nothing to do with the distribution of events on any objective “severity scale” and everything with how these events are dramatized (presented or viewed in a dramatic or melodramatic way).

Set “dramatic” := “one in a century (or centuries)”. Then have a look at recent extreme precipitation and drought. E.g. this anomaly from yesterday. More: Australian fires 2008/2009, Russian fires 2010, Pakistan drought 2009/2010 plus super deluge 2010, Texas drought 2011.

Texas drought 2011In fact no century-scale trend in Texas summers, see DOC > NOAA > NESDIS > NCDC

Texas Precipitation June 1895-2011 trend: +0.34″/cy

Texas Precipitation July 1895-2011 trend: -0.25″/cy

Texas Precipitation August 1895-2011 trend: +0.34″/cy

Texas Temperature June 1895-2011 trend: +0.3°F/cy

Texas Temperature July 1895-2011 trend: +0.4°F/cy

Texas Temperature August 1895-2011 trend: -0.2°F/cy

Texas PDSI June 1895-2011 trend: -0.3/cy

Texas PDSI July 1895-2011 trend: -0.3/cy

Texas PDSI August 1895-2011 trend: +0.3/cy

Berenyi Peter wrote:

Do you have evidence for your claim? I would like to see some.

Here’s what I’ve been able to find so far.

If anyone knows papers in referee journals about the changing frequency of floods, droughts, heat waves, fires etcetera over time, I would like to add them to the Azimuth Library!• Munich Re, Press Release, 27 September, 2010.

See also Munich Re’s graph of weather disasters over time.

• Steve Connor, Weather disasters in the poorest nations ‘have trebled since 1980s’,

The Independent, 23 May 2011.He suspects it’s smaller, but he feels it’s unlikely that it’s zero!

On a smaller scale, in a recent post I mentioned that 2011 holds the record for weather disasters costing over $1 billion in the United States, with 2008 coming in second place. Of course this doesn’t clearly separate the changing weather from the changing economic factors.

I can easily provide data proving that heat records are being broken at a rate that exceeds the rate at which cold records are being broken.

Staffan Liljgeren just pointed us to this:

• Dan Vergano, Climate report links extreme weather events to global warming,

USA Today, 8 September, 2011.Here’s a quote:

Do you have evidence for your claim? I would like to see some.John, you may want to have a look at A Chronological Listing of Early Weather Events by James A. Marusek. It covers the period between 6 AD – 1900 AD (with proper references).

It is indispensable for acquiring some historic perspective on what counts as “dramatic”.

You may also want to study recent history of global tropical cyclone activity and accumulated cyclone energy (ACE). Dr. Ryan N. Maue’s site is a good starting point. You could also link to some of his graphics in this thread, they are telling.

From the work mentioned above:

“In 851 and 855, there was so great a drought over all ofItalyandGermanyas caused such a famine that parents eat their own children and children their parents.”in:

Thomas Short, A General Chronological History of Air, Weather, Seasons, Meteors in Sultry Places and different Times, London, 1749.Now, that’s

dramatic.If I would be welcomed, I would certainly love to come!

You bet, Cameron! You’re an actual biologist! I don’t have travel funds for the participants lined up, but I’ll try to get some if the application for the workshop is accepted.

Do you know other biologists, ecologists, etcetera who might be interested in a workshop on network theory? Especially ones who actually work in this area?

I second that — am most keen in hearing what biologists, ecologists, etcetera have to say.

I should have thought of this before, but I am going to send a link to my friend Phillip Staniczenko, a physicist working on mathematical ecology and related ideas. He might be able to pass this around and drum up interest, particularly of people that have a non-zero probability of saying something anyone else has general interest in.

Just emailed the administrator at CABDyN whom hopefully will pass along this blog link to people at the centre that would likely be interested in this.

CABDyN stands for Complex Agent-Based Dynamic Networks:

http://www.cabdyn.ox.ac.uk/complexity_home.asp

Thanks, Jacob!

Great John! Even if travel funds wouldn’t become available, I have a yearly travel allowance I’d be happy to use for this so long as my institution wouldn’t put up any blocks. If you wouldn’t mind, I could give the information to my adviser who I am sure would be happy to circulate it more widely than I could myself among network theory-oriented biologists.

There are plenty of things mathematicians could do to promote climate science, providing proper tools to understand non-equilibrium quasi steady state thermodynamic processes in non-linear systems of many degrees of freedom being

.topmost priorityAs I see it, the climate system is obviously a heat engine, which is only radiatively coupled to its (cosmic) environment. Temperature of a tiny fraction of the celestial sphere is 5778 K, while the rest is 2.7 K – those are the relevant heat reservoirs we have, with infinite heat capacity each for all practical purposes. Now, the first thing to understand with a heat engine is its entropy processes. Paltridge had a good start in this direction, but this line of investigation is all but abandoned. It is pretty unfortunate, because the climate engine is mind-bogglingly complicated, therefore an analytic approach (pursued by computational climate models) is

a priorihopeless.But we have other means to approach such a system, like SOC (Self Organized Criticality), SAD (Sandpile Avalanche Dynamics), fractal geometry, MEPP (Maximum Entropy Production Principle), etc. The common trait is that they do not focus on minute details of the system, but treat it as a whole.

It is far from being clear how to proceed in this direction, nevertheless this is the only track that has a chance to bear fruit. With a non-linear system having an astronomical number of degrees of freedom any other approach is doomed to early failure.

For example it is crystal clear that most of the entropy production happens in the climate system when short wave radiation gets absorbed (either in the atmosphere, at the surface or at some depth in the ocean) and is converted to heat. It is also clear that the amount of flux absorbed depends on the planetary albedo, which is not constant. But it is not clear how MEPP or some related extremum principle could control the overall value of albedo (and also the effective emissivity of the system as seen from outside).

Anyway, the first thing to do is to actually *understand* what’s going on, by actively looking for a logical level on which the system is *understandable*.

BTW, I am pretty sure no one actually understands a computational climate model with its million lines of code, especially if it is not structured properly, not published, not documented and the code base itself is bogus in the first place.

ps. Fractal geometry is mentioned, because distribution of water vapor in the atmosphere is clearly fractal-like (even computer graphics people know that), its fractal dimension generally decreasing poleward. Calculating bulk quantities like reflectivity, absorptivity, emissivity, transmittance, etc. over fractals is not trivial and involves some mathematical insight. Simple gridding, if it is done on a single scale, can be quite misleading.

This sounds like a great idea for a workshop, Berényi. I’m

very much interested in these ideas, as this desperate attempt to understand extremal principles in nonequilibrium thermodynamics shows.

Unfortunately I’m not enough of an expert on these ideas (yet?) to feel confident that BIRS would approve an application by me for a workshop on this topic. I have a long history of studying diagrammatic techniques in physics, and I’ve been writing a series of expository articles about more practical applications of these ideas for a while now, so that seems like a better bet.

But if someone else organizes a workshop on nonequilibrium thermodynamics, or something like that, I’d love to go!

IWNET 2012 6th International Workshop on Nonequilibrium Thermodynamics

Røros, Norway, 19-24 August 2012

*

which is only radiatively coupled to its (cosmic) environmentThis is not entirely true. Tidal effects have a major role in the climate system, they provide a good portion of the (mechanical) energy needed for deep turbulent mixing of oceans (the other player is internal waves generated by wind stress, mostly over the southern ocean).

Without this (ill-quantified) deep turbulent mixing, which happens at some continental margins and mid-ocean ridges over rugged bottom features, the MOC (Meridional Overturning Circulation) would eventually stop, or at least slow down to a crawl supported only by geothermal heating at the bottom.

For MOC is

a heat engine, it does not convert thermal differences to work (mechanical energy), but it’s the other way around. If different parts of a fluid are heated and cooled at the same gravitational potential (depth/height), that never induces any macroscopic flow whatsoever.notOr, as cooling always happens close to the surface (even if one takes surface waves into account) while some heating goes down to several hundred meters (water is pretty transparent to light, especially in the UV and blue segments of the spectrum), it would provide for a very shallow overturning perhaps, unlike what is observed.

Therefore tidal coupling (and breaking) can’t be dismissed. True, it is only ~150 GW on average, but it is a pure mechanical energy input, which rearranges heat, salts, nutrients, dissolved oxygen & carbon dioxide in the oceans before dissipating (into minuscule amount of heat).

I fired off the proposal to BIRS today. Another person emailed me to express interest in the workshop: Michael Dietze of the Department of Plant Biology at the University of Illinois at Urbana-Champaign. His homepage says:

All this is great!

Today I got an email from Georghe Craciun expressing interest in the BIRS workshop.

Craciun helped prove the exciting theorem that Brendan and I discussed in Part 9 of the Network Theory posts. He works in the Department of Mathematics and the Department of Biomolecular Chemistry at the University of Wisconsin. He studies biochemical networks and biological interaction networks. He’s shown that some graphs associated to biological interaction networks give information about the qualitative properties of the associated dynamical systems: multistability, oscillations, persistence, and global stability. This is the exactly the sort of thing I’d like to hear about at the workshop, if it’s approved: using diagrams to help understand complex systems.

Today I got an email from Lee Deville saying he was interested in the proposed BIRS workshop.

Deville is at the Department of Mathematics at the University of Illinois at Urbana-Champaign. He’s cowrote the paper Dynamics on networks I. Combinatorial categories of modular continuous-time systems with Eugene Lerman. He’s also written about Dynamics of stochastic neuronal networks and the connections to random graph theory and Stability of distributed algorithms in the face of incessant faults. Good stuff!

My proposal for a workshop at Banff in 2013 was turned down, but they invited me to reapply for 2014, and I just did.

I’ll definitely be holding a special session Fall 2013 Meeting of the AMS Western Section here at U.C. Riverside on Saturday and Sunday, November 2 and 3, 2013. But more about that later!

Here’s the new proposal. Wish me luck:

Good luck!

Too bad about 2013 — but here’s hoping for the year after!