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Feedbacks and climate sensitivity Program on Climate Change, Summer Institute.

Feedbacks and climate sensitivity Program on Climate Change, Summer Institute. Feedbacks are found in many forms: Mechanical feedbacks used in water clocks in ancient Greece. Float valve, Greek Clepsydra (“water thief”). Feedbacks are found in many forms: A feedback in every bathroom….

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Feedbacks and climate sensitivity Program on Climate Change, Summer Institute.

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  1. Feedbacks and climate sensitivity Program on Climate Change, Summer Institute.

  2. Feedbacks are found in many forms: Mechanical feedbacks used in water clocks in ancient Greece. Float valve, Greek Clepsydra (“water thief”)

  3. Feedbacks are found in many forms: A feedback in every bathroom…. Ballcock assembly

  4. Feedbacks are found in many forms: James Watt’s governor “Science” Holborn viaduct, London

  5. Feedbacks are found in many forms: Centrifugal governors in windmills since 16th century. Centrifugal governor, Dutch Mill “On governors” Maxwell, 1869

  6. Feedback analysis Formalized framework for the evaluation of interactions in dynamical systems. • introduced the concept of negative • feedback. • got the idea on Lackawanna • ferry on his way to work. Harold S. Black (1898-1983) • took nine years to get granted • a patent. • “Our patent application was treated in the • same manner one would a perpetual motion • machine” Black, H.S. IEEE Spectrum, 1977 Original notes scribbled on NY Times

  7. Feedback analysis The language of feedbacks is ubiquitous in Earth Sciences (Maxwell, 1863; Black, 1927; Cess, 1975; Charney et al., 1979; Hansen et al., 1984; Schlesinger & Mitchell, 1985) But the language is confused and abused… U.S. National Research Council report, 2003 • gets definitions of feedbacks wrong… • - Worth standardizing terminology

  8. Feedback analysis Definition of reference system is intrinsic to feedbacks reference climate system forcing, DR response, DT Climate sensitivity parameter defined by: DT0 = l0DR

  9. Feedback analysis Adding a feedback reference climate system DR DT c1DT So now DT = l0(DR + c1DT)

  10. Feedback analysis Adding a feedback reference climate system DR DT c1DT So now DT = l0(DR + c1DT) Additional radn forcing due to system response to DR

  11. Feedback analysis Adding a feedback reference climate system DR DT c1DT So now DT = l0(DR + c1DT) Rearrange for DT 

  12. Feedback analysis Technobabble Feedback factor: f = c1l0(f  to fraction of output fed back into input) (Gain is proportion by which system has gained) From before : And since

  13. Feedback analysis The gain curve Range of possibilities: - < f < 0: G < 1  response damped  NEGATIVE fdbk. 0 < f < 1: G > 1  response amplified  POSITIVE fdbk. f > 1: G undef.  Planet explodes…

  14. Aspects of feedbacks I. The compounding effect of multiple feedbacks DR DT reference climate system c1DT c2DT DT = l0(DR + c1DT+c2DT) Now have (two nudges) The effect of one feedback is influenced by the strength of the others..

  15. Aspects of feedbacks II. Comparing different feedbacks DR DT reference climate system c1DT c2DT The relative importance of two different feedbacks must be evaluated relative to the same reference system. There is a danger is comparing separate studies where only one piece of physics has been isolated.

  16. Aspects of feedbacks III. How does uncertainty in feedbacks translate into uncertainty in the system response? ∆T = ∆T0 1 - f T for 2 x CO2 (oC)

  17. Aspects of feedbacks III. How does uncertainty in feedbacks translate into uncertainty in the system response? ∆T = ∆T0 1 - f T for 2 x CO2 (oC) f

  18. Aspects of feedbacks III. How does uncertainty in feedbacks translate into uncertainty in the system response? ∆T = ∆T0 1 - f T for 2 x CO2 (oC) T f

  19. Aspects of feedbacks III. How does uncertainty in feedbacks translate into uncertainty in the system response? ∆T = ∆T0 1 - f T for 2 x CO2 (oC) T f f

  20. Aspects of feedbacks III. How does uncertainty in feedbacks translate into uncertainty in the system response? ∆T = ∆T0 1 - f T T for 2 x CO2 (oC) T f f Systems of strong positive feedbacks inherently less predictable

  21. Aspects of feedbacks IV. The relationship between feedbacks and response time climate model response (mean & 95% bounds) to step function in forcing Positive feedback systems have inherently long response times

  22. Aspects of feedbacks V. Diagnosing feedbacks from models and observations For ith climate variable: So feedback factors: i - can be a lumped property (like clouds, sea ice, etc.), - or individual model parameter (like entrainment coefficient) - can also calculate spatial variations in fi if desired.

  23. Aspects of feedbacks V. Diagnosing feedbacks from models and observations Springtime snow albedo feedback (Fernandes et al., 2009) Feedback factor of ice albedo on sea-ice thickness (Bitz, 2008)

  24. Aspects of feedbacks VI. The variable of interest matters… The same physical process can be a positive or negative feedback depending on the variable of interest. e.g., dynamic sea-ice is - a positive feedback on surface air temperatures - a negative feedback on mixed layer temperature

  25. Strengths of feedback analysis. • Good points: • Feedback analysis powerful representation of system dynamics • -system will try to adjust via most negative feedback. • Can be used to propagate how uncertainty in one process • controls uncertainty in system response. • Puts different mechanisms in the same non-dimensional • language. • e.g., Gaia is just a number…. • fGaia ~ -0.65 (which is pretty absurd)

  26. Issues with feedback analysis. Not always a useful technique... - Is the system linear enough that is makes sense to isolate the individual feedbacks? (The Humpty Dumpty test) - Is the reference system and variable of interest clear when comparing different feedbacks? - Feedback analysis can get blurry when physics has different timescales (what’s a forcing, and what’s a feedback?)

  27. Climate sensitivity. A benchmark of climate change. An envelope of uncertainty. 1,200,000+ integrations, 75,000,000+ yrs model time(!); Eqm. response of global, annual mean sfc. T to 2 x CO2. 6,000 model runs, perturbed physics. Slab ocean, Q-flux 12 model params. varied What governs the shape of this distribution: a) in observations? b) in models?

  28. Climate sensitivity. Estimates from observations. Global energy budget: forcing storage (ocean) atmospheric response = + In principle, get Rf, F, DT from observations, solve for l, then:

  29. Climate sensitivity. Estimates from modern observations. IPCC 2007 (mainly, plus a bit from Kyle) Forcing change Temperature change

  30. Climate sensitivity. Estimates from modern observations. IPCC 2007 (mainly, plus a bit from Kyle) Forcing change Temperature change

  31. Climate sensitivity. Estimates from modern observations.

  32. Climate sensitivity. Estimates from last glacial maximum observations. Hansen et al.1984 n.b. F is assumed zero (not necessarily true)

  33. Climate sensitivity. Estimates from models. Individual feedbacks uncorrelated among models, so can be simply combined: Soden & Held (2006): Colman (2003): • How does this uncertainty in physics translate to uncertainty in climate sensitivity?

  34. Climate sensitivity. Estimates from models. for:

  35. Climate sensitivity. Estimates from models. for:

  36. Climate sensitivity. Estimates from models. • GCMs produce climate sensitivity consistent with the • compounding effect of essentially-linear feedbacks.

  37. Climate sensitivity. An aside: nonlinearity of feedbacks From basic analysis: But can take quadratic terms… giving… Taking ~12 different studies:

  38. Climate sensitivity. An aside: nonlinearity of feedbacks So not a big deal…..

  39. Climate sensitivity. Models and observations. • All look pretty similar. • How to do better?

  40. Climate sensitivity. How to do better? 1. Combine different estimates? Very hard to establish the degree of independence of individual estimates. 2. Use other observations? (e.g., NH vs. SH; pole-to-eq. DT; seasonality, trop. water vapor) Structural errors among models highly uncertain (see Knutti et al, 2010). 3. Transient climate response? Clim. Sens. is an equilibrium property, short observations only have limited resolving power.

  41. Fortunately... Feedbacks don’t exist, and climate sensitivity doesn’t matter!

  42. Feedbacks don’t exist. They are just a Taylor series in disguise reference climate system DR DT c1DT c2DT reference system (Thanks Kyle and Aaron)

  43. Feedbacks don’t exist. They are just a Taylor series in disguise reference climate system DR DT c1DT c2DT why not this? (Thanks Kyle and Aaron)

  44. Feedbacks don’t exist. They are just a Taylor series in disguise. reference climate system DR DT c1DT c2DT or this?? • Feedbacks are entirely in the eye of the beholder! (Thanks Kyle and Aaron)

  45. Climate sensitivity doesn’t matter. Constraining climate sensitivity is not terribly relevant for projecting climate change… (Allen and Frame, 2007) Stabilization target of 450 ppm at 2100 High end sensitivities take a long, long time to be realized…

  46. Climate sensitivity doesn’t matter. Constraining climate sensitivity is not terribly relevant for projecting climate change… (Allen and Frame, 2007) Concentration target adjusted at 2050. Geoengineering = the human feedback.

  47. Miscellany

  48. Time dependent climate change: The role of the ocean • The ocean heat uptake acts as a (transient) negative feedback.

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