Semester planning & Project planning Review from Nov 1 lecture! Gaia - biogeophysical feedbacks Gaia - nonlinear dynamics Forest Fire example Summary

Transcription

1 Wednesday 15 Nov, 2017 Lecture #33 Today s Topics Semester planning & Project planning Review from Nov 1 lecture! Gaia - biogeophysical feedbacks Gaia - nonlinear dynamics Forest Fire example Summary 1

2 Semester Schedule Wed 11/15 lect 33 Uma Gaia-modeling Fri 11/17 AM lect 34 Dan lecture Friday 11/17 PM How to give a bad/good talk Mon 11/20 lect 35 Dan lecture Wed 11/22 lect 36 Dan lecture Thanksgiving Break Mon 11/27 lecture 37 Dan Lecture Wed 11/29 lecture 38 Uma lecture Fri AM/PM 12/1 student presenta[ons all on this day, 5 presenta[ons. This is 2 weeks from this Friday. Mon 12/4 lecture 39 Uma lecture Wed 12/6 lecture 40 Uma lecture Fri 12/9 Final part a AM (Paleo), part b PM (climate dyn.)

3 Project Deadlines Deadline 3: Key project papers, 20 points Deadline 4: Presentation outline, 11/22, 40 points Deadline 5: go over slides, 11/29, 30 points above early deadlines are 20% of your grade How to give talks Go over talk outline with Dan or Uma Go over slides by today with Dan or Uma Presentation Day

4 Review What is a parameteriza?on? What is a model? What is a climate model? 4

5 Originated in 1983 by A. Watson and J. Lovelock. This very simple model was developed to respond to the cri?cisms of the Gaia Hypothesis. Daisyworld Imaginary grey world; same distance from sun as earth The environment of Daiseyworld has one variable, Temperature. The biota has black and white daisies The planet is well watered and has nutrients so temperature determines the growth of daisies. A key point about Daisyworld is that the daisies alter the same environmental variable (temperature) in the same direc?on at the local level and the global level. Much of the theore?cal interests is model centers on establishing the condi?ons in which regula?on does, and does not, emerge. Daisyworld online model you can play with:

6 Daisyworld Two types of daisies compete for space on a planet and grow similarly as a func?on of temperature. Because of the albedo effect they can tolerate different amounts of solar radia?on. Black daisies can tolerate lower solar luminosity while white daisies can tolerate higher solar luminosity. The albedo governs local temperature which controls the amount of area covered. Companion website: Model on web: h_p://

7 Daisyworld α g = f bare α bare + f W α W + f B α B Global albedo is a func?on of bare ground, white daisies and black daisies. As the local temperature changes in response to changes in solar luminosity, the growth rates of the daisies change and this changes the albedo of the planet. Daisies can grow to cover arable land based on a growth rate that depends on temperature. The growth rate is largest at op?mal temperature and drops off at local temperatures that are warmer or colder. G r = 1 k g (T optimum T local ) 2 When luminosity is low black daisies dominate but as luminosity increases, white daisies begin to dominate. This model provides a framework for the expira[on of how organisms can selfregulate their environment.

8 The CLAW paper Considered the first testable Gaia Hypothesis (that living things work to modify the climate) To counteract the warming due to doubling CO2, we need to double the number of CCN.

9 DMS Mechanism Dimethylsulfide (DMS), produced by ocean plankton and oxidized in atmosphere to form a sulfate aerosol. Aerosols cool climate overall by increasing albedo In Gaian terms, the plankton act to reduce the disturbance to the climate.' Processes Measurable Quantities Sign here uncertain

10 Aside Roots of the DMS Mechanism Dr. Robert Charlson, Prof Emeritus UW Dr. Glenn Shaw, Prof Emeritus UAF

11 Gaia The field has now matured to the extent that the viability of the Gaia theory is no longer directly?ed to the validity of the Daisyworld model, as was some?mes the case in the early years a^er its incep?on. Hence we treat Daisyworld as an interes?ng mathema?cal model in its own right. It may inform the debate on Gaia, but they are not inextricably?ed. There have been many offshoots to other areas of science, including nonlinear dynamics, ecosystem and food web theory, evolu[onary theory, physiology, maximum entropy produc[on, and ar[ficial life. Thanks to its rela?vely simple mathema?cal formula?on, Daisyworld is also widely used in the teaching of Earth system science [e.g., Kump et al., 1999; McGuffie and Henderson-Sellers, 1997; Ford, 1999]. (from Wood et al. 2008) Now it is?me to move on to develop new conceptual models to address ques?ons regarding planetary self-regula?on and the coupling of life and the environment. Reference: Wood, A. J., G. J. Ackland, J. G. Dyke, H. T. P. Williams, and T. M. Lenton (2008), Daisyworld: A review, Rev. Geophys., 46, RG1001, doi: /2006rg000217

12 Gaia How daisies adapt within the bounds of feedback loops defined in the original model. But what the nature of the feedbacks in the model are altered to see how this effects the evolu?on of the components of the system. Watson and Lovelock [1983] reversed the sign of interac?on between daisy color and planetary temperature by assuming that convec[on generated over the warm spots of the black daisy clumps generates white clouds above them. In this case the black daisies are s?ll locally warmer than the white daisies, but both daisy types now cool the planet. Hence the black daisies always have a selec[ve advantage over their white compatriots, which they drive to ex[nc[on. Yet planetary temperature is s[ll regulated, albeit on the cold side of the op?mum for growth.

13 Non-linear Dynamics: Basins of A_rac[on stable state A or B Change environment so basin is shallower so A is less stable, a small push moves it to B. A big push needed to move it to B.

14 Forest Fire Models as another Example Drossel and Schwabl forest-fire model: A burning tree becomes an empty site. A green tree becomes a burning tree if at least one of its neighbors is burning. At an empty site a tree grows with probability p. A tree without a burning nearest neighbor becomes a burning tree by lightning with a probability f. Cri?cal parameter is f/p (for p << f/p) and it is small Forest fire model slides thanks to David Newman

15 Forest Fire Models Forest fire model becomes cri?cal by the introduc?on of the lightning parameter f. There is only one relevant parameter in the system f/p. If ρ is the averaged density of trees in steady state, the average number of trees destroyed by a lightning stroke is s = f p 1 1 ρ ρ There is a self-organized cri?cal state for f 0. Forest fire model slides thanks to David Newman

16 Spreading rate and dynamics governed by f/p (and p) Small f/p leads to front like (ordered) propaga[ng fires, probability of growth is large f: probability of lightning p: probability of regrowth Not a very realis?c looking forest. Forest fire model slides thanks to David Newman

17 Forest with patchy distribu[on Larger f/p (through reduc[on in p) gives a more physical picture of a forest Forest fire model slides thanks to David Newman More realis[c looking forest than previous slide.

18 Low Risk Control Strategy can be Counter Produc[ve System undergoes dynamical self-organiza[on Self-similar in the patchiness and in the number of fires. The system organizes itself to sit at a cri[cal point. Trees burned Trees burned-control1 Trees burned-nocontrol Forest fire model slides thanks to David Newman Time Control of small fires (fire figh[ng) can lead to increased density and increased chance of major fires similar to decreased f/p figure

19 Aside: Self-similarity Property in Nature In mathema?cs, a self-similar object is exactly or approximately similar to a part of itself (i.e. the whole has the same shape as one or more of the parts). You see this in streams to rivers, similar shapes but different scales. You see this in coastlines. A Fern or Romanescu Broccoli are examples of something self-similar.

20 If you control Forest Fires => More Big fires Tail of Probability Distribu[on Func[on of fires gets larger Regular Scale Trees burned-control1 Trees burned-nocontrol 10 4 Log Scale Trees burned-control1 Trees burned-nocontrol Events Events More Big fires Size Size Forest fire model slides thanks to David Newman

21 Mul[ple Time Scales in the Dynamics System has correla[ons over many [me scales dynamical not probabilis[c effect Density of green trees Density Trees burned Time steps This is an example of a self regula[ng system. Number of trees burned per step Forest fire model slides thanks to David Newman

22 Add Seasonality to Gaia

23 Conclusions It is not just life alone that but the whole Earth system that tends to regulate climate. This idea of GAIA makes complete sense to nonlinear dynamics community but they view it somewhat differently than mother earth & Unicorns & macrame etc.. But selfregula?on within a certain parameter space, beyond which you will go into a different state which could be or may not be ok.