Scale invariance of fluctuations, the return time of climate events and anthropogenic warming*

Transcription

1 Scale invariance of fluctuations, the return time of climate events and anthropogenic warming* A mephiticly ectoplasmic emanation from the forces of darkness Viscount Christopher Monckton of Brenchley Une émanation éctoplasmique méphitique des forces des ténèbres. - Lord Christopher Monckton de Brenchley CNRS, Wimereux 12, May, 2014 Université Paris Sud, Orsay, 13, May, 2014 Institut Pierre Simon Laplace, ENS, 15, May, 2014 S. Lovejoy, McGill, Montreal * Transparencies in English presentation given in French

2 L invariance d échelle des fluctuations, le temps de retour des évènements climatiques et le réchauffement anthropique A mephiticly ectoplasmic emanation from the forces of darkness Viscount Christopher Monckton of Brenchley IPSL 15, Mai, 2014 Une émanation éctoplasmique méphitique des forces des ténèbres. - Lord Christopher Monckton de Brenchley S. Lovejoy, McGill, Montreal

3 From the age of the earth to the viscous dissipa on scale: 4.5x10 9 years - 1 ms: 20 orders of magnitude in me A voyage through scale

4 4 50 K Phanerazoic eon Age (Myr BP) δ 18 O 0 00 X K Cenozoic era X5.8 X K Quaternary Period Age (Myr BP)

5 T 5 present Middle and Late stages Pleistocene epoch (EPICA, Antarc ca) K 600 Age (kyr BP) ice ages δ 18 X8.8 O Upper stage Pleistocene epoch (GRIP 34 Summit 75 o N) 6 K T 1.0 interglacial (Holocene) X91 20 last glaciation Age (kyr BP) Last Millenium (Northern hemisphere) X K Date 2000

6 T (K) T (K) Anthropocene epoch (global, land ) 5 K Montreal 700 mb, 2 o x2 o K Date Annual cycle removed 0.85K T (K) K CNRS, May 12, Paris Sud, May 13, IPSL, May 15, K

7 o 10 C 5 Montreal Temperatures at increasing resolu on years - 25 o 5 C x years o 5 5 C x Fluctua ons mostly cancel years years 10 o C o 5 C years years months X 324,000 x2 x years year s Fluctua ons don t cancel much CNRS, May 12, Paris Sud, May 13, IPSL, May 15, 2015

8 How to understand the variability? Answer #1: Scale bound thinking

9 Antonie van Leeuwenhoek ( ) A new world in a drop of water..the discovery of micro- organisms Animalcules, described in depth by Leeuwenhoek, c By Anton van Leeuwenhoek

10 10 5 Log 10 E(ω) K 2 yr β = 1.8 The missing quadrillion macroclimate β = -0.6 β = 1.8 Atmospheric dynamics 1 hour yrs: Mitchell 1976 (grey, bottom) with modern data megaclimate climate macroweather weather β = 0.8 β = 0.2 β = 2.5 β = Log 10 ω (yr) CNRS, May 12, Paris Sud, May 13, IPSL, May 15, 2015

11 The NOAA NCDC Paleoclimate data site graph (inspired by Mitchell) The background is totally flat: error of The explana on of the figure: figure is intended as a mental model to provide a general "powers of ten" overview of climate variability, and to convey the basic complexi es of climate dynamics for a general science savvy audience. The site assures us that just because a par cular phenomenon is called an oscilla on, it does not necessarily mean there is a par cular oscillator causing the pa ern. Some prefer to refer to such processes as variability.

12 How to understand the variability? Answer #2 Scaling, scale invariance: ΔT Δt ( ) = ϕ Δt H

13 ΔT ( Δt) Δt H H Megaclimate Veizer: 290 Mys - 511Myrs BP (1.23Myr) Megaclimate Zachos: 0-67 Myrs (370 kyr) H H 0.4 T/ΔT max 0-1 Macroclimate Huybers: Myrs (14 kyrs) Climate Epica: BP kyrs (400 yrs) H Macroweather Berkeley: AD (1 month) H Weather Lander Wy.: July 4- July 11, 2005 (1 hour) CNRS, May 12, Paris Sud, May 13, IPSL, May 15, 2015 t

14 Difference, Anomaly, Haar fluctua ons Differences: The difference in temperature between t and t+δt Anomaly: Haar: The average of the temperature (with overall mean removed) between t and t+δt The difference between the average of the temperature from t and t+δt/2 and from t+δt/2 and t+δt Rela ons: When 1 > H > 0: Haar difference When 0 > H > -1: Haar tendency

15 Hourly Station scale 45 o N CR 75 o N 2 o x2 o grid -0.4 Log 10 <ΔT 2 > 1/2 (K) 20 K 10 K 5 K Composite Huybers Epica Veizer Zachos K Log 10 Δt (yrs) weather 0.2 K macroweather climate macroclimate megaclimate

16 Extrapolated from 1 hour, this is the NOAA update of Mitchell Log 10 <ΔT 2 > 1/2 (K) 20 K 10 K K 0.01 K 10-3 K 10-4 K 10 2 Epica Huybers 10 3 Veizer Zachos Extrapolated from 10 days, this is the NOAA update of Mitchell Log 10 Δt (yrs) Mitchell s background 10-5 K 10-6 K Gaussian white noise, slopes: CNRS, May 12, Paris Sud, May 13, IPSL, May 15, 2015

17 The macroweather regime Low frequency cascades Time scales >10 days (τ>τ w )

18 First principles predictions Atmosphere: The large scale winds and weather-climate transition scale Horizontal wind: Δv = ε 1/3 Δx 1/3 ε = Energy flux (Fourier space) also energy rate density Power / area: Solar heating, top of the atmosphere: 10 3 W/m 2 Absorbed 2X10 2 W/m 2 4% Converted to K.E. 8 W/m 2 Mass / area = Δp/g 8x10 3 Kg/m 2 Energy flux: ε 8/(8x10 3 ) =10-3 W/Kg Troposphere only Prediction using horizontal relation: Δv = ε 1/3 Δx 1/3 Scales: Length: L 2x10 7 m Velocity: V ε 1/3 L 1/3 21 m/s Time: T=L/V 10 6 s = 11 days c.f. empirical antipodes velocity difference 17.4±5.7 m/s

19 log 10 E( ω ) (K 2 s) β=0.6 climate Macroweather, Macro ocean weather, Martian macro weather Air over land SST Mars Macro Ocean weather Ocean weather Macroweather β = 0.2 β=1.8 Mars ε w 0.03 m 2 /s 3 τ w ε w 1/3 L -2/3 1.8 dys Weather extra -0.1 β=1.8 Theory (- 0.68) (100 yrs) - 1 Earth Ocean surface ε o 10-8 m 2 /s 3 τ o ε o 1/3 L -2/3 1 yr (6 yrs) - 1 (1 yr) - 1 (100 d) - 1 (30 d) - 1 (10 d) - 1 (2 d) - 1 log 10 ω Earth Atmosphere ε w 10-3 m 2 /s 3 τ w ε w 1/3 L -2/3 10 dys

20 - 0.4 Mars wind Wind: Mars-Earth comparison (No adjustable parameters) (60 days) -1 Log 10 E(ω) (1 day) -1 Red arrow shows shi of Mars due to theore cal parameters for le right shi : Units: Hz Log 10 ω τ Δ log 10 τ = log w,e 10 = 1 τ w,m 3 log ε e ε m 3 log r e 10 r m -3 Martian day Fairbanks, Ak blue surface pressure ε m = Δp e ε e Δp m Energy flux r e r m Planet radius 2 Distance from sun R e R m 2 m m m e Planet mass -4 1 α m 1 α e Planet albedo ( ) ( ) ε e E v,e ω E v,m ω 1/3 ε m 1/3 Nondimensional frequency CNRS, May 12, Paris Sud, May 13, IPSL, May 15, 2015 r e r m 4/3-5/3

21 Do GCM s predict the climate. Or Macroweather?

22 4 months 10 Log 10 Δt (yrs) 100 GISS E2-R North, land Log 10 < ΔT 2 > 1/2 (K) 1 K 0.5 K CRU: North, land CRU global CRU North Multi-Proxies North K macroweather (preindustrial) Climate preindustrial) 0.1 K macroweather (industrial) Climate (industrial) CNRS, May 12, Paris Sud, May 13, IPSL, May 15, 2015

23 Log 10 Δt (yrs) GISS- ER2 simula ons (Northern Hemisphere, land only) Versus mul proxies (northern hemisphere) K K Log 10 < ΔT 2 > 1/2 (K) 0.1 K Models versus data: <1900 Multi- Proxies Gao volcano Crowley volcano Solar only control

24 How well can we measure the global temperature? What is ε(t)?

25 Instruments versus multiproxies (global scale) Log <ΔT 2 > 1/ yrs 10 yrs 100 yrs K Log 10 Δ t 300 yrs 2.5 Pre 2003 multiproxies (5) ±0.18 K data-<data> All multiproxies (8) K -0.1 data-<data> -0.1 ±0.03 K ±0.09 K Post 2003 multiproxies (3) ±0.05 K Instrumental HadCRUT, NOAA, NASA, 20CR Note: 20CR uses no station temperatures!

26 Proving the truth of Anthropogenic Global Warming Diminishing returns - In its AR5 report last September, the IPCC upgraded the AR4 s (2007) qualification likely to conclude that it is extremely likely that human influence has been the dominant cause of the observed warming since the mid-20th century. extremely likely = % confidence - Climate sensitivity: o C Unchanged since Disproving natural global warming Relatively easy due to an asymmetry -No theory can ever be proven beyond reasonable doubt but a single decisive experiment can effectively disprove one. Requires no numerical models, needs Nonlinear Geophysics

27 Primary evidence for anthropogenic warming

28 T ( o C) 1.5 The Preindustrial versus industrial epoch Mul proxies Years since the start of the series

29 GCM-free quantification of Anthropogenic effects (including extremes)* Premise: if anthropogenic warming is as strong as claimed, then why do we need huge numerical models to demonstrate it? *Thanks to the Quebec Skeptical Society!

30 Log 2 ( ρ CO2 ( t) / ρ CO2, pre) Forcing (energy/ me) T ( o C) (anomaly) ppm Concentra on du CO 2 Increase in CO 2 since ppm 329 ppm 318 ppm 297 ppm 277 ppm date Increase in the global average temperature since 1880 Dec. 2012: 394.4ppm Mauna Loa

31 Natural variability as a perturbation to anthropogenic change Effective climate sensitivity (K/(W/m 2 )) Measurement error: ±0.03K T globe ( t) = λ 2 xco2,eff log 2 ρ CO2 t ( ) / ρ CO2, pre ( ) + T natural t ( ) + ε( t) Proportional to CO 2 radiative forcing (W/m 2 ) Linear Surrogate for all anthropogenic forcings (determinstic) Small fluctuations due to natural variability (stochastic). Includes responses to solar, volcanic and other natural forcings. Justified if: a) the anthropogenic effects do not effect the type of internal dynamic (variability), b) nor their responses to (natural) external forcing

32 CO 2 forcing as surrogate for all anthropogenic effects Roughly: you double the global economy, you double the emissions, land use and other changes, you double the effects

33 1.0 Non- dimensional The global economy and CO 2 forcing Sulfates (aerosols, cooling) Greenhouse Gases (warming) +79% Global GDP (Gross Domes c Product) CO 2 Radia ve Forcing (energy/ me) Correlation coefficients: (sulfate production), (total GHG forcing), (GDP). Log 2 (ρ CO2 /277)

34 2.0 CO 2 as a surrogate for all anthropogenic effects W/m 2 Historic emission reconstructions Slope= 1.79 corr. coef: All long lived Greenhouse Gases R F,GHG Slope= corr. coef: R F,anth 1880 All anthropogenic effects (including aerosol cooling) 1995 Data Source: from Myhre et al R F,CO2 CNRS, May 12, Paris Sud, May 13, IPSL, May 15, 2015 W/m 2

35 ΔT ( o C) (anomaly) ppm Lovejoy 2014 The Temperature is nearly linear with the CO 2 forcing 1945, 311ppm 1975, 330 ppm foring = increase of energy per unit of me Slope gives (95% uncertain es) λ = No forcing- response lag This direct method (no GCM s): Temperature increase with doubled CO 2 λ = o C (95% confidence, 0-20 yr lag) Log 2 ρ CO2 t 2004, 373 ppm ( ) / ρ CO2,pre ( ) Forcing (energy/time) -> IPCC1-3 ( ): o C IPCC4 (2007): o C IPCC5 (2013) : o C ( high confidence )

36 0.4 T (o C) (anomaly) Global Temperature Anthropogenic (0.85 o C) The CO 2 forcing Residual = Natural Variability Total Anthropogenic warming: 0.85±0.22 C c.f.: IPCC4: 0.74±0.18 C, over the period IPCC5: 0.85 ±0.20 C, over the period

37 T (K) 1.5 Preindustriel and Industrial epochs Year since start CNRS, May 12, Paris Sud, May 13, IPSL, May 15, Average of 3 mul proxies

38 Log 10 < ΔT 2 > 1/2 (K) 1 K 0.5 K 0.25 K Log 10 Δ t (yrs) Verification T natural ( ) ( t) = T globe ( t) λ 2 xco2,eff log 2 ρ CO2 ( t) / ρ CO2, pre Multiproxies K 0.1 K Dashed: Pre-industrial range of T natural Residuals of surface series, after removal of the CO 2 responses Note: flat line corresponds to long range dependencies: E(ω) ω -1

39 4log102 Blue arrows indicate H =0 CNRS, May 12, Paris Sud, May 13, IPSL, May 15, 2015

40 Log 10 < ΔT 2 > 1/2 (K) K 1 K 0.5 K 0.3 K 0.1 K Δ t (yrs) Extrapolating to 125 years: RMS difference fluctuations 10 years 100 years Surface Standard deviation at 125 years: 0.20±0.03K CNRS, May 12, Paris Sud, May 13, IPSL, May 15, 2015 Mul proxies

41 - 1 Probability of natural warming Lovejoy 2014 Anthropogenic Warming ( o C) 10% 1% 0.1% 0.01% 0.001% AR Empirical method No extremes Gaussian AR Strong extremes q D =4 Weak extremes q D =5 q D =6 ( q D = ) 90% 97.5% 99% 99.9% here 99.99% % Confidence with which we can reject the hypothesis of natural variability

42 The pause in the warming, return periods

43 Update to 2013 using NASA GISS data T globe (K) ppm ppm ppm ppm Global Post war cooling ppm ppm Prepause warming Pause cooling ppm Northern hemisphere Log 2 ρ CO2 ( t) / ρ CO2,pre ( )

44 Residues (natural variability) T nat (K) Global Post war cooling Prepause warming Pause cooling Northern hemisphere CNRS, May 12, Paris Sud, May 13, IPSL, May 15, 2015

45 4 Log 10 R (return period, years) yrs Anthropogenic warming Gaussian q D = yrs q D = yrs 100 yrs pause 20 yrs 10 yrs 4 yrs 8 yrs Pre- pause 16 yrs 32 yrs Pre- pause pause Postwar cooling Expected maximum yrs Anthropogenic warming Δ T (K) CNRS, May 12, Paris Sud, May 13, IPSL, May 15, 2015

46 Predictability and stochas c forecas ng

47 Forecas ng the climate ΔT ( Δt) Δt H T Macroweather up to 100 years H T ( ) = I ΔH γ = ( t t ) 1 ΔH T t t ( ) γ ( t )d t Frac onal integra on order ΔH Ignore intermi ency, take quasi- Gaussian model: H γ = - 1/2 Hyper Gaussian ΔH = H T H γ 0.4 To obtain independent noises: γ ( t) = I ΔH T ( t); t 0 Es mate past noise generator up to t=0 To predict to me t p, simply add independent noises from t = 0 to t = t p then frac onally integrate to obtain T(t) for t t p

48 T (K) Forecast from % 90% 70% 50% 30% 10% 1% 2.0 Postwar cooling T (K) 99% 90% 70% 50% 30% 10% 1% Prepause forecast T (K) 99% 90% 70% 50% 30% 10% 1% 1.5 T (K) The pause almost perfectly forecast 99% 90% 70% 50% 30% 10% 1%

49 Game over! Rather than trying to prove anthropogenic warming is true, we disprove natural warming. Note asymmetry: no theory can be proven beyond reasonable doubt, but a theory can be disproved by a decisive experiment. a) The main source of uncertainty is the lag: 0-> 20 years. With GCM s, it is cloud, radiation feedbacks. a) Only changes in global temperature over 125 year periods are important. Taking differences filters out the low frequencies so that historic temperatures such as the medieval warming event may be warmer than today if the changes were slow enough. The peons can roast! c) The multiproxies agree with each other up to about 200 year scales so that the probability distributions of 64 year changes are reliable. Using the observed scaling we scale them to 125 years. For 125 years periods all the hockey sticks are reliable. d) If we are prepared to accept the natural variability hypothesis at as low a level as 10% (reject it with only 90% confidence), then the change since 1880 must be less than 0.26 o C i.e. 3 to 4 times lower than the observations. Impossible to save natural variability even with fat tails/ black swan events. e) The pause (cooling) was expected: it followed a large prepause warming.

50 Conclusions 1. Using scaling fluctua on analysis to characterizing the climate by its type of variability: expect macroweather not climate 2. The need for GCM- free approaches: a) their climate not ours, b) disarming climate skep cs c) Using sta s cal hypothesis tes ng to rule out natural variability 3. Anthropogenic warming dominates macroweather at about 10 years rather than about 100 years (preindustrial). 4. The total anthropogenic warming is about 0.85 o C, for CO 2 doubling, 3.08±0.58 o C, GCM s: o C ( ). 5. The probability that the warming since 1880 is natural is <1% (most likely <0.1%). 6. The pause has a return period of years, the post war cooling 125 years: not surprising.