It you hit a climate problem with a Fourier analysis hammer you will get sine waves. If data such as long term Nile River flows are analysed from a Hurst perspective there is a different result – one resembling step functions. I like this very new study = by Marohasy and Abbott, 2017 – for the new method of 20th century surface temperature attribution – mostly natural. But thinking of climate as cyclic is far too limiting.
“Examination of many of these proxy temperature records shows they typically consist of complex oscillations or cycles about a mean value, with the amplitude and structure of the temperature signal depending on the geographical location considered. In the pre-industrial era, these oscillations represent the compound effect of natural phenomena both internal (e.g. North Atlantic Oscillation, El Nino Southern Oscillation) and external (e.g. solar, volcanic activity).”
The US ‘special report’ focuses on climate science talking points – surface temperature (instruments at 2m from the ground and ocean surface temperature), hydrology, climate sensitivity, sea level rise, acidification, etc. These are points that are endlessly discussed – but are ultimately indeterminate given the limitations of data and models. Both sides on these points – moreover – lack a theoretical underpinning that places transient phenomenon in the context of globally coupled fluid flows in the spatio/temporal chaotic Earth system.
“The story of British hydrologist and civil servant H.E. Hurst who earned the nickname “Abu Nil”, Father of the Nile, for his 62 year career of measuring and studying the river is now fairly well known. Pondering an 847 year record of Nile overflow data, Hurst noticed that the series was persistent in the sense that heavy flood years tended to be followed by heavier than average flood years while below average flood years were typically followed by light flood years. Working from an ancient formula on optimal dam design he devised the equation: log(R/S) = K*log(N/2) where R is the range of the time series, S is the standard deviation of year-to-year flood measurements and N is the number of years in the series.” Revelutions webspot –
Mandelbrot rediscovered and popularized Hurst’s work in the 1960’s – and renamed K to H. Persistence is a period of flows that hover about a mean with a specific variance – and then the system shifts to another flow regime with a different mean and variance.
Persistence can be easily seen in modern data on the globally coupled ENSO quasi standing wave in Earth’s spatio/temporal chaotic system. There is a sharp delineation between a La Nina (blue) dominated regime and an El Nino (red) dominated regime in 1976/77. The Pacific Ocean shifted again to a somewhat cooler state after 1998.
Figure 1: Modulation of ENSO in 20 to 30 year regimes seen in the MEI of Claus Wolter
Transitions in climate are typically abrupt. There are external triggers at thresholds and an immense and complex response in planetary ocean and atmospheric flow fields. There is no comfort for skeptics here – shifts are unpredictable and may be extreme. The next Pacific Ocean climate shift – if it runs true to the form shown over a millennia – is due in a 2018-2028 window. Predicting this more precisely – with it’s global implications for rainfall, biology and atmosphere and ocean heat content – is impossible.
And anthropogenic greenhouse gases may perturb the climate system flow sufficiently to cause some or major change in the global pattern of coupled quasi standing waves.
It seems clear to me that spatio-temporal chaos is the not so new climate paradigm. One that provides a far more powerful theoretical underpinning for consideration of climate processes. This graphic in the ‘special report summary gives a clue to follow.
Figure 2: ENSO and jet stream coupling
Turbulent flows in Earth’s oceans and atmosphere are driven by planetary spin and solar energy creating quasi standing waves everywhere. Several are involved in the ENSO-Jet Stream coupling. The proximate cause is the Northern Annular Mode (NAM). Higher surface pressure at the pole pushes winds and polar storms into lower latitudes. There is considerable interest in a sun and NAM (and SAM) connections via UV/ozone chemistry and modulating Earth system flows – especially equator to pole stratospheric and tropospheric pathways. (e.g. …)
Unlike many things in climate science – spatio/temporal chaos climate science can be seen in the wild. Within the turbulent flow of the mountain river vortices form and the location and size are relatively stable across both time and space. Oder emerging out of disorder. The first rule of chaos theory.
Figure 3: Turbulent flow in a mountain river
The governing regime of the river flow persists until the flow is perturbed and then shifts to another state – with different size and location of standing waves in the flow. Persistence and shifts are seem in climate wide regimes of quasi standing waves in the Earth system. Perturb the flow somehow and the river standing waves will shift in size and location. At the climate scale solar, orbital and greenhouse gas changes may perturb the fluid flow through the system and the energy dynamic of the entire planet.
On the different scale of society and energy – there are obvious solutions to this and broader problems that bring short term benefits to global communities and environments. This does entail fostering democracy and classic liberal economics. Uncertainties in climate from many sources suggest the need to refocus on no-regrets policy options rather than endlessly quibbling about climate talking points.
But to return to intellectually interesting questions of science – ENSO has fascinating dynamics that are globally coupled to rainfall regimes over many timescales.
Figure 4: Laguna Pallcacocha ENSO proxy – greater red intensity shows higher El Niño intensity (Source: Tsonis, 2009)
Moy et al (2002) present the Holocene record of sedimentation shown above which is strongly influenced by ENSO variability. The record has continuous high resolution coverage over 12,000 years. It is based on the presence of greater and less red sediment in a lake core. More sedimentation is associated with El Niño. It shows periods of high and low El Niño intensity alternating with a period of about 2,000 years. There was a shift from La Niña dominance to El Niño dominance that was identified by Tsonis 2009 as a chaotic bifurcation – and is associated with the drying of the Sahel. There is a period around 3,500 years ago of high El Niño intensity associated with the demise of the Minoan civilization (Tsonis et al, 2010). For comparison – red intensity in the Minoan period was regularly over 200 – red intensity was 99 in the 1997/98 El Niño. The record shows ENSO variability considerably in excess of that seen in the modern period. Great variability over millennia casts doubt on the statistical reliability of divining rainfall changes from modern records.
Earth’s climate is a coupled, nonlinear, isolated mechanism tending to maximum entropy over a long enough period. There are resonant frequencies, a driving force in solar energy and external beats in solar activity and orbits that modulate climate. Climate persists in a regime for minutes, days, years, centuries – it’s like Russian dolls or fractals better yet – and then shifts state as they say. Moreover there are broad but well studied temporal patterns.
Modern satellite instruments provide the most precise and comprehensive data ever on global atmospheric temeperature, incoming solar energy and changes in outgoing energy. Some 3,900 Argo floats measure temperature and salinity to 2000m in the oceans. There are a few simple terms in the 1st differential global energy storage equation.
Δ(h&w)/dt = energy in – energy out + heat of combustion + plus heat from the mantle
The change in heat and work in the system over a period is equal to the difference in the energy terms.
Now comes the fun of science as investigation in the world. Why is it so?
The change in heat and work in the planetary system is complicated by large changes in radiant flux at TOA due to changes in atmospheric and ocean circulation (Loeb et al 2012). Energy in is measured as an absolute value – although the number has changed in the recent past. Energy out is given in anomalies – it gives a sense of change in the energy budget – i.e. warming or cooling. The planet warms if energy in is greater over a period – the energy imbalance idea. As Earth’s energy content is mostly in the oceans – some 90% – energy imbalances are calculated from ocean heat records.
Figure 5: Unfiltered Argo data to June 2017 – source Argo Marine Global Atlas
The heat from Earth’s interior is a minor term – as is the heat of combustion – but may have implications for ideas of energy loss from the surface of the oceans, thermal inertia and thus radiant imbalances at top of atmosphere (TOA). The oceans are heated from the bottom up at a rate far greater than the instantaneous rate of increase in greenhouse gas forcing.
Earth radiant energy budget satellite records show warming of the ocean to 1998 over the 90’s. ” With this final correction, the ERBS Nonscanner-observed decadal changes in tropical mean LW, SW, and net radiation between the 1980s and the 1990s now stand at -0.7, +2.1, and +1.4 W/m2, respectively.” Wong et al 2006
Figure 6: Net radiant flux at top of atmosphere (TOA) v. ocean heat content rate of change
This paper gives an update on the observed decadal variability of the earth radiation budget (ERB) using the latest altitude-corrected Earth Radiation Budget Experiment (ERBE)/Earth Radiation Budget Satellite (ERBS) Nonscanner Wide Field of View (WFOV) instrument Edition3 dataset. The effects of the altitude correction are to modify the original reported decadal changes in tropical mean (20°N to 20°S) longwave (LW), shortwave (SW), and net radiation between the 1980s and the 1990s from 3.1, -2.4, and -0.7 to 1.6, -3.0, and 1.4 W m2 , respectively. In addition, a small SW instrument drift over the 15-yr period was discovered during the validation of the WFOV Edition3 dataset. A correction was developed and applied to the Edition3 dataset at the data user level to produce the WFOV Edition3_Rev1 dataset. With this final correction, the ERBS Nonscanner-observed decadal changes in tropical mean LW, SW, and net radiation
between the 1980s and the 1990s now stand at 0.7, 2.1, and 1.4 W m2
, respectively, which are similar to the observed decadal changes in the High-Resolution Infrared Radiometer Sounder (HIRS) Pathfinder OLR and the International Satellite Cloud Climatology Project (ISCCP) version FD record but disagree with the Advanced Very High Resolution Radiometer (AVHRR) Pathfinder ERB record. Furthermore,
the observed interannual variability of near-global ERBS WFOV Edition3_Rev1 net radiation is found to be remarkably consistent with the latest ocean heat storage record for the overlapping time period of 1993 to 1999. Both datasets show variations of roughly 1.5 W m2 in planetary net heat balance during the 1990s.” Wong et al 2006
Wong et al used Earth Radiation Budget Experiment data and compared that to more dense XPT data compiled by Joel Norris as annual ocean heat content. The older XPT data had 10% coverage and was averaged over 5 years. It shows ocean warming in the shortwave – SW – (and longwave – LW – cooling) in the 1990’s and a transient peak in ocean heat content. There were initial stumbles in all of the early satellite products – corrected as best as they could. The newer data is much more precise and stable.
These were downloaded from a NASA site today and it’s a mess. The graphs at – https://ceres.larc.nasa.gov/order_data.php – and are at least updated to January 2017. What’s happening with NASA? Don’t tell me Donald Trump is shutting down this critical Earth system monitoring program – in which the US is the world’s leader?
The solar energy peak of the 11 year cycle solar was at the start of the century – we have passed the last peak and are heading for a trough in this cycle. Solar activity varies in a tight band – incident energy at the surface is reduced by a factor of four. The sun may influence climate – not on an incident radiation basis – but on indirect effects through stratospheric/atmospheric pathways.
Figure 7: CERES data product – incoming solar irradiance
Reflected SW shows some stark trends. Declining appreciably to 2003, ambling along to 2013 and declining again since. Warming tendency then neutral and then warming again in the short but relatively precise record of anomalies. This is mostly cloud cover variation coupled with the state of the Pacific Ocean.
Figure 8: CERES data product – reflected SW power flux up
The LW record shows broad changes linked to cloud cover and water vapour. Infrared (LW) emissions rose in the early part of the record (cooling in LW), dipped in the middle section and rose again more recently.
Figure 9: CERES data product – emitted LW
This Loeb et al 2012 plot splices CERES to earlier data and highlights La Nina and El Nino years. The problem is splicing and whether you believe graph (a) or (b)? There was a step change in cloud around the turn of the century from satellite cloud products – or alternatively IR out ambled along without much apparent trend change over decades.
Figure 10: Spliced ERBE and CERES data
There is intriguing evidence from a brilliant little bit of astronomical engineering that shows a step change in cloud cover around the turn of the 21st century. The satellite and Project Earthshine results are at least consilient.
Figure 11: “Earthshine changes in albedo shown in blue, ISCCP-FD shown in black and CERES in red. A climatologically significant change before CERES followed by a long period of insignificant change“.
Net radiant flux is planetary warming upward by convention. Net flux = -SW- LW. So ambling along to 2008, some ENSO bumps to 2013 and a modest warming since.
Figure 12: CERES product – net radiant flux at TOA
Little can be determined from these short term records other than that there are large natural variations doe to variability in ocean and atmospheric flows – and thus the energy budget of the planet. Over a longer term – evidence of Earth’s underlying dynamic comes at many scales with coupled changes to the energy budget.
“Evidence is presented supporting the hypothesis of polar synchronization, which states that during the last ice age, and likely in earlier times, millennial-scale temperature changes of the north and south Polar Regions were coupled and synchronized. The term synchronization as used here describes how two or more coupled nonlinear oscillators adjust their (initially different) natural rhythms to a common frequency and constant relative phase. In the case of the Polar Regions heat and mass transfer through the intervening ocean and atmosphere provided the coupling. As a working hypothesis, polar synchronization brings new insights into the dynamic processes that link Greenland’s Dansgaard-Oeschger (DO) abrupt temperature fluctuations to Antarctic temperature variability. It is shown that, consistent with the presence of polar synchronization, the time series of the most representative abrupt climate events of the last glaciation recorded in Greenland and Antarctica can be transformed into one another by a π/2 phase shift, with Antarctica temperature variations leading Greenland’s. This, plus the fact that remarkable close simulations of the time series are obtained with a model consisting of a few nonlinear differential equations suggest the intriguing possibility that there are simple rules governing the complex behavior of global paleoclimate.” (J. A. Rial 2012)
Shorter periods of climate regimes – and it suggested that this is a better terminology than old fashioned cycles or oscillations – are revealed by spectral analysis.
“The driving forces of climate change were investigated and the results showed two independent degrees of freedom —a 3.36-year cycle and a 22.6-year cycle, which seem to be connected to the El Niño–Southern Oscillation cycle and the Hale sunspot cycle, respectively. Moreover, these driving forces were modulated in amplitude by signals with millennial timescales.” (Wang et al 2017)
So we have an ENSO cycle, a Hale solar magnetic (not sunspot) cycle and a 1000 year cycle that might be speculated to be greenhouse gases. Or perhaps volcanoes. Or something else.
But these powerful natural flow fields are bubbling along under the surface – and I use that term advisably. The 20 to 30 year Pacific regimes seem very likely to continue for a bit. The next one is due in a 2018 to 2028 window. And the Pacific state seems modulated by something.
The proxy below shows levels of salt a Law Dome ice core. More or less salt in the ice core. More salt is a cool Pacific state (less eastern margin upwelling) . It shows ENSO periodicity – and an intriguing change in tempo at the turn of the 20th century – as well as the familiar 20 to 30 year patterns of rainfall. Rain in this graph is eastern and northern Australian rainfall – but it has global implications.
Figure 13: Millennial ENSO proxy – Vance et al 2013
The Pacific state is modulated over a millennia. The details of the ocean and atmospheric links are fascinating – it is postulated that it starts with solar uv/ozone chemistry modulating ocean and atmospheric circulation throughout the system. The change in solar UV modulate surface pressure at the poles – changing the polar annular modes and influencing sub-polar gryes in all oceans thereby triggering triggering more or less upwelling on the eastern margin. (e.g. ,,,
Figure 14: Impact of polar wind fields on oceans gyres – NAS workshop report 2012
The Hale beat may be a switch of sorts – signalling changes in the Pacific State at the 20 to 30 year scale. And then literally shifts again to another state and these shifts add up over time to long term climate. At all scales. The second rule of spatio/temporal chaos is that it is scale independent. Again the modulator seems quite evidently solar. High sunspot numbers equate to higher solar activity and less upwelling in the eastern Pacific. Solar activity remained high throughout the 20th century.
Figure 15: Sunspot counts
“The sunspot cycle happens because of this pole flip — north becomes south and south becomes north—approximately every 11 years. Some 11 years later, the poles reverse again back to where they started, making the full solar cycle actually a 22-year phenomenon. The sun behaves similarly over the course of each 11-year cycle no matter which pole is on top, however, so this shorter cycle tends to receive more attention.” NASA
The Hale beat itself may be spatio/temporal chaos modulated though n-body gravity interactions in the solar system. The interior of the sun is turbulent flow modulating the small changes in solar output. The waxing and waning of the 11 year butterfly may set the tone of Earth climate’s resonant frequencies – with the 22 year regime seemingly having a synchronous resonance with the state of the Pacific Ocean.
Figure 15 – The solar butterfly – sourced from Wikipedia
On two hands we have butterflies – on the other we have the temperature anomalies as measured by microwave sounders at the O2 radiant frequency band.
Fugure 16: CMIP-5 models comparison with RSS tropospheric temperature anomalies
Surface records capture perhaps 1% of the global energy content. And there are appreciable artifacts in the record as a result of changing soil moisture and thus changing ratios of sensible and latent heat at 2m from the ground – plausibly causing an increasing land/ocean temperature divergence during periods of widespread drought.
The yellow is the results of a CMIP-5 opportunistic ensemble. Frankly – if you imagined that they wouldn’t diverge from reality – then you are on the wrong track entirely. There is not even one single solution to any of the general circulation models. Models have temporal chaos.
“Sensitive dependence and structural instability are humbling twin properties for chaotic dynamical systems, indicating limits about which kinds of questions are theoretically answerable. They echo other famous limitations on scientist’s expectations, namely the undecidability of some propositions within axiomatic mathematical systems (Gödel’s theorem) and the uncomputability of some algorithms due to excessive size of the calculation.” (James McWiliams 2007)
Models have what is called irreducible imprecision – reducing imprecision comes at a trade off. Reducing the grid size to reduce model uncertainty exponentially increases the computing power required due to the increasing size of the calculation. Improving initial values takes time and data. Each model has many divergent solutions within the limits of feasible initial values and structural instability induced by the changes in depth of model process coupling.
Figure 17: Schematic of a perturbed physics model ensemble – Slingo and Palmer 2012
“Lorenz was able to show that even for a simple set of nonlinear equations (1.1), the evolution of the solution could be changed by minute perturbations to the initial conditions, in other words, beyond a certain forecast lead time, there is no longer a single, deterministic solution and hence all forecasts must be treated as probabilistic. The fractionally dimensioned space occupied by the trajectories of the solutions of these nonlinear equations became known as the Lorenz attractor (figure 1), which suggests that nonlinear systems, such as the atmosphere, may exhibit regime-like structures that are, although fully deterministic, subject to abrupt and seemingly random change.” Slingo and Palmer 2011
Select one of the blue lines in the plots arbitrarily and put it into an opportunistic ensemble. Of course it’s warm. With the boys’ club of climate modelling – I’m surprised it’s not warmer.