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New ground-breaking study puts climate models to the test – yields unexpected result of steps and pauses in the climate signal

© Skepticalscience.comA ground-breaking new paper has recently been published in Earth System Dynamics that really turns the idea of direct linear warming of the atmosphere on it’s ear, suggesting a “store and release mechanism” by the oceans, which explains why there seemed to be a shift in global temperature during the 1997/98 super El Nino followed by a “pause” in global temperatures.

Remember the “escalator” graph from wrongly named “Skeptical Science” designed to shame climate skeptics? Looks like that may have been an accidentally prescient backfire on their part based on the findings of this new paper.

The paper is: “Reconciling the signal and noise of atmospheric warming on decadal timescales”, Roger N. Jones and James H. Ricketts, Earth System Dynamics, 8 (1), 2017.

Abstract:

“Interactions between externally forced and internally generated climate variations on decadal timescales is a major determinant of changing climate risk. Severe testing is applied to observed global and regional surface and satellite temperatures and modelled surface temperatures to determine whether these interactions are independent, as in the traditional signal-to-noise model, or whether they interact, resulting in step-like warming.

“The multistep bivariate test is used to detect step changes in temperature data. The resulting data are then subject to six tests designed to distinguish between the two statistical hypotheses, hstep and htrend.

Test 1: since the mid-20th century, most observed warming has taken place in four events: in 1979/80 and 1997/98 at the global scale, 1988/89 in the Northern Hemisphere and 1968 – 70 in the Southern Hemisphere. Temperature is more step-like than trend-like on a regional basis. Satellite temperature is more step-like than surface temperature. Warming from internal trends is less than 40 % of the total for four of five global records tested (1880 – 2013/14).

Test 2: correlations between step-change frequency in observations and models (1880 – 2005) are 0.32 (CMIP3) and 0.34 (CMIP5). For the period 1950 – 2005, grouping selected events (1963/64, 1968 – 70, 1976/77, 1979/80, 1987/88 and 1996 – 98), the correlation increases to 0.78.

Test 3: steps and shifts (steps minus internal trends) from a 107-member climate model ensemble (2006 – 2095) explain total warming and equilibrium climate sensitivity better than internal trends.

Test 4: in three regions tested, the change between stationary and non-stationary temperatures is step-like and attributable to external forcing.

Test 5: step-like changes are also present in tide gauge observations, rainfall, ocean heat content and related variables.

Test 6: across a selection of tests, a simple stepladder model better represents the internal structures of warming than a simple trend, providing strong evidence that the climate system is exhibiting complex system behaviour on decadal timescales.

“This model indicates that in situ warming of the atmosphere does not occur; instead, a store-and-release mechanism from the ocean to the atmosphere is proposed. It is physically plausible and theoretically sound. The presence of step-like – rather than gradual – warming is important information for characterising and managing future climate risk.”

The results:© Roger N. Jones and James H. RickettsHere they outline their reasoning for finding steps in warming:

If climate changes in a stepwise manner, it would be expected that other variables would show signs of this (Test 5). Instances of step changes in the literature are widespread, and are mentioned elsewhere in this paper (e.g. Table 6). For rainfall, notable examples are a step change in the Sahel in 1970 (L’Hôte et al., 2002; Mahé and Paturel, 2009), south-west Western Australia (WA) in the late 1960s and early 1970s (Li et al., 2005; Power et al., 2005; Hope et al., 2010) and the western US in the 1930s (Narisma et al., 2007). Similar changes have been detected in streamflow records worldwide, showing that regime changes in moisture have been a long-standing aspect of climate variability (Whetton et al., 1990).

A few more recent changes have been directly attributed to increasing gases, although south-west WA is an exception (Cai and Cowan, 2006; Timbal et al., 2006; Delworth and Zeng, 2014), with large-scale shifts in synoptic types accompanying a rapid decrease in rainfall (Hope et al., 2006). The bivariate test identifies a step change in southwest WA winter rainfall in 1969 (shown in Fig. 6a), with an upward step in summer rainfall in northern Australia 1 year later. Ocean heat content of the upper ocean also shows step changes occurring in 1977, 1996 and 2003 (Fig. 6b).

Changes in long-run tide gauge records also show a stepladder-like process of sea level rise, with the San Francisco record, quality controlled and dating back to 1855, being a good example; it shows step changes in 1866, 1935, 1957 and 1982 (Fig. 6c). Step changes in the Fremantle tide gauge data records, one of the longest in the Southern Hemisphere, shows that most of the decline in the average return intervals of extreme events noted by Church et al. (2006) before and after 1950 occurred in two events (Fig. 6d) in the late 1940s and the late 1990s. This variation in rise was noted by White et al. (2014). None of the internal trends in Fig. 6a – d attain p < 0.05, showing the dynamic nature of change and limited trend-like behaviour in these examples.

© Roger N. Jones and James H. RickettsThey did quite a bit of testing to separate the idea of steps from trends, and identified specific dates of steps, and in the case of the 97/98 super El Nino, a regime change:

Table 6 summarises the major tests undertaken with expected outcomes for htrend and hstep. While objections could be made to each of these on an individual basis, collectively they show that for externally forced warming on decadal scales, hstep is better supported than htrend.

In summary, these tests show that hstep is a close approximation of the data when analysing decadal-scale warming. Over the long term, this warming conforms to a complex trend that can be simplified as a monotonic curve, but the actual pathway is step-like. As outlined in Sect. 3.3, this rules out gradual warming, either in situ in the atmosphere or as a gradual release from the ocean, in favour of a more abrupt process of storage and release. This conclusion supports the substantive hypothesis H2 over H1, where the climate change and variability interact, rather than varying independently.

© Roger N. Jones and James H. RickettsHere, they defend the step mechanism as be part of the Earth climate system, but ignored in favor of searching for linear trends:

Proposed mechanisms for step-like warming The correlation between step-like warming and ECS in the models, between the timing of steps in model hindcasts and observations and between steps and known regime changes in observations (Table 6), provides strong evidence that warming is non-gradual on decadal timescales.

The high correlations of steps and shifts with model ECS indicate that atmospheric feedback processes respond to abrupt releases of heat into the atmosphere. The presence of negligible internal trends occurring over some oceanic regions, the region 30 – 60◦ N, and in tropospheric satellite temperatures, suggests that little of the heat being trapped in the atmosphere by anthropogenic greenhouse gases actually remains there. One justification given for rejecting externally driven steplike warming is that it is presumed that there is no plausible physical mechanism for this (Cahill et al., 2015; Foster and Abraham, 2015). However, to suggest that the stepwise release of heat energy is physically implausible overlooks the energetics of the ocean – atmosphere system. Hydrodynamic processes are quite capable of supplying the energy required (Ozawa et al., 2003; Lucarini and Ragone, 2011; Ghil, 2012).

The atmosphere contains as much heat energy as the top 3.2 m of ocean (Bureau of Meteorology, 2003). About 93 % of historically added heat currently resides in the ocean (Levitus et al., 2012; Roemmich et al., 2015), whereas the atmosphere contains about 3 % of the total. A similar amount of the heat has been stored within the land mass (Balmaseda et al., 2013) and on an annual basis a similar flux is absorbed in melting ice (Hansen et al., 2011). A physical reorganisation of the ocean – atmosphere system, as part of a regime change, is therefore large enough to provide the relatively small amount of energy required to cause abrupt sea surface and atmospheric warming (Roemmich et al., 2015; Reid et al., 2016), as shown by rapid changes in shallow ocean heat content (Fig. 6b; Roemmich and Gilson, 2011; Reid, 2016).

For example, Reid et al. (2016) in describing the late 1980s regime change, show it was associated with large-scale shifts in temperature and multiple impacts across terrestrial and marine systems, mainly in the Northern Hemisphere. Changes in the North Pacific in 1977 were considered even more extensive (Hare and Mantua, 2000), as were those in 1997/98 involving both the Pacific and Atlantic oceans (Chikamoto et al., 2012a, b). In developing tests for detection and attribution, Jones (2012) noted two types of regime change over land: one where codependent variables such as maximum temperature and rainfall undergo a step change but remain in a stationary relationship, and the other, nonstationary change, where warming undergoes a step change independent of rainfall change. This suggests that although regime changes are a normal part of internal climate variability, they can be enhanced, releasing extra heat. The step changes summarised in Table 6 coincide with El Niño events but the heat emitted by other El Niño events dissipates and is absorbed back into the ocean within months; thus, an added mechanism is required.

We propose that there is negligible in situ atmospheric warming and that almost all of the added heat trapped by anthropogenic greenhouse gases is absorbed by and stored in the ocean. It is subsequently released through the action of oscillatory mechanisms associated with regime shifts. Most heat (long-wave radiation) is trapped near the ground or ocean surface and much of that is radiated downwards (Trenberth, 2011). The atmosphere as a whole has little intrinsic heat memory and does not warm independently of the surface.

This is supported by observations on land where the overpassing air mass takes on the characteristics of the underlying surface, achieving energy balance within a 300 m distance (Morton, 1983). When passing from land to water, this will see all of the available heat energy taken up by water if the temperature of the air mass exceeds that of water (Morton, 1983, 1986), with the temperature of the overpassing air mass reaching equilibrium with the water beneath within a very short time. Very little of the heat trapped over land can be absorbed by the land surface, but will be transported from land to ocean within a few days to a few weeks, where it can be absorbed (the high latitudes being an exception).

Given that the atmosphere interacts with the top 70 m of ocean over an annual cycle (Hartmann, 1994), there is ample opportunity for the majority of available heat trapped over land that is not absorbed by land, lakes and ice to be absorbed by the ocean.

That’s a serious and credible argument. Here is an exceprt from their conclusion discussion:

Our conclusion that the atmosphere does not warm in situ will challenge many who consider that to be a basic part of the greenhouse effect. However, an exhaustive search of the literature failed to find any direct evidence that this actually takes place. We find it hard to perceive how an additional increment of long-wave radiation on the order of ∼ 0.2 Wm−2 (direct forcing and feedback derived from Schmidt et al. 2010) can behave differently to the ∼ 155 Wm−2 produced in the atmosphere year to year without being absorbed by the wider climate system.

Given that climate models exhibit step-like warming, where the abrupt component carries the greater part of the signal than internal trends, they produce emergent behaviour that is not identified by mainstream analytic approaches. Overwhelmingly, model- and statistically based studies represent the global warming signal as changing gradually. Some are prescriptive because of their structure or because they apply simplified assumptions about a more complex climate system, other models examine a small part of the system, and some have a historical legacy bestowing familiarity and reliability.

Modern climate models are almost as complex as the climate, and thus need to be understood through simpler models (Held, 2005; Benestad, 2016), forming a nested modelling approach from simple through to complex (Schneider and Dickinson, 1974; Ghil, 2015). The linking of trend analysis methods with gradual change may overlook the distinction between process-based and diagnostic models.

A diagnostic model may identify a trend without necessarily indicating a gradual process. A large part of the climate wars has been fought over this very point. Nonlinear responses in climate are being investigated by researchers, with an interest in complex system behaviour via dynamical systems and related theory. Our conclusions suggest that the processes of radiative transfer and subsequent warming take place in two separate domains of the climate system, separated by a delay. The absorption of radiation is a linear process that is quite separate from the behaviour of turbulent dissipation of heat energy within the climate system, which is fundamentally nonlinear (Ozawa et al., 2003). Developments based on deterministic nonlinear and stochastic linear behaviour originating from work by Lorenz (1963) and Hasselmann (1976) respectively explore a range of interrelated phenomena, such as non-equilibrium stable states, oscillators, strange attractors, bifurcations and entropy production, in order to develop a unified theory of climate (Ozawa et al., 2003; Lucarini et al., 2014; Franzke et al., 2015; Ghil, 2015). Studying how the free and forced aspects of change combine to alter the statistical properties of climate is a specific goal (Lucarini and Sarno, 2011; Ghil, 2012, 2015).

Our focus is on understanding the role of linear and nonlinear behaviour in changing climate risk over decadal timescales, specifically how initial condition and boundary-limited uncertainties (as described by Lorenz, 1975 and Hasselmann, 2002) combine. Initial-condition uncertainty is boundary limited, varying within a certain amplitude, with the outcome depending on the pathway taken within those limits (Lorenz, 1975).

There is also a time-dependent window that serves as a predictability barrier. Changing boundary conditions are intransitive, with the outcome being insensitive to initial conditions. The nested nature of climate phenomena over different timescales results in decadalscale climates being both an initial-condition and intransitive process, combining to produce stochastically driven step changes in warming that integrate into a long-term complex trend.

The coincident timing of step changes in both observations and models (Fig. 7) suggests that other factors, such as short-term volcanic forcing, can also influence the timing of step changes. Lorenz (1968) referred to the outcome of forced climate change on century timescales as almost intransitive. The “almost” is due to initial condition uncertainties operating within the boundary limitations of decadal variability. The almost-intransitive model (Lorenz, 1968) is described via linear response theory (Lucarini et al., 2014; Ragone et al., 2016) and shown to be robust for concepts such as effective radiative forcing (Hansen et al., 2005) and effective climate sensitivity (Andrews et al., 2015), although these phenomena would be sensitive to bifurcations if they were to occur (Hasselmann, 2002).

This is the first paper I’ve ever read that ties together models, observations, and chaos theory of the atmosphere from Lorenz. It makes many excellent points, and it will be interesting to see if those at the top of the climate science food chain like Mann, Trenberth, and Schmidt accept these new ideas, or dismiss them and call anyone who believes them “linear trend deniers”.

Besides these new findings, what is refreshing is that the paper had open peer review, with both editor and reviewer comments published here.

The final revised paper is available here. Well worth a read! I look forward to seeing the reactions.

And, they published data and code! Code is included with the Supplement as a zip file (Python and R modules). Data availability. Included with the Supplement as Excel files.

h/t to Larry Kummer of Fabius Maximus who has a long list of papers on the subject of testing models (with links) at the end of this post.

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New ground-breaking study puts climate models to the test – yields unexpected result of steps and pauses in the climate signal

© Skepticalscience.comA ground-breaking new paper has recently been published in Earth System Dynamics that really turns the idea of direct linear warming of the atmosphere on it’s ear, suggesting a “store and release mechanism” by the oceans, which explains why there seemed to be a shift in global temperature during the 1997/98 super El Nino followed by a “pause” in global temperatures.

Remember the “escalator” graph from wrongly named “Skeptical Science” designed to shame climate skeptics? Looks like that may have been an accidentally prescient backfire on their part based on the findings of this new paper.

The paper is: “Reconciling the signal and noise of atmospheric warming on decadal timescales”, Roger N. Jones and James H. Ricketts, Earth System Dynamics, 8 (1), 2017.

Abstract:

“Interactions between externally forced and internally generated climate variations on decadal timescales is a major determinant of changing climate risk. Severe testing is applied to observed global and regional surface and satellite temperatures and modelled surface temperatures to determine whether these interactions are independent, as in the traditional signal-to-noise model, or whether they interact, resulting in step-like warming.

“The multistep bivariate test is used to detect step changes in temperature data. The resulting data are then subject to six tests designed to distinguish between the two statistical hypotheses, hstep and htrend.

Test 1: since the mid-20th century, most observed warming has taken place in four events: in 1979/80 and 1997/98 at the global scale, 1988/89 in the Northern Hemisphere and 1968 – 70 in the Southern Hemisphere. Temperature is more step-like than trend-like on a regional basis. Satellite temperature is more step-like than surface temperature. Warming from internal trends is less than 40 % of the total for four of five global records tested (1880 – 2013/14).

Test 2: correlations between step-change frequency in observations and models (1880 – 2005) are 0.32 (CMIP3) and 0.34 (CMIP5). For the period 1950 – 2005, grouping selected events (1963/64, 1968 – 70, 1976/77, 1979/80, 1987/88 and 1996 – 98), the correlation increases to 0.78.

Test 3: steps and shifts (steps minus internal trends) from a 107-member climate model ensemble (2006 – 2095) explain total warming and equilibrium climate sensitivity better than internal trends.

Test 4: in three regions tested, the change between stationary and non-stationary temperatures is step-like and attributable to external forcing.

Test 5: step-like changes are also present in tide gauge observations, rainfall, ocean heat content and related variables.

Test 6: across a selection of tests, a simple stepladder model better represents the internal structures of warming than a simple trend, providing strong evidence that the climate system is exhibiting complex system behaviour on decadal timescales.

“This model indicates that in situ warming of the atmosphere does not occur; instead, a store-and-release mechanism from the ocean to the atmosphere is proposed. It is physically plausible and theoretically sound. The presence of step-like – rather than gradual – warming is important information for characterising and managing future climate risk.”

The results:© Roger N. Jones and James H. RickettsHere they outline their reasoning for finding steps in warming:

If climate changes in a stepwise manner, it would be expected that other variables would show signs of this (Test 5). Instances of step changes in the literature are widespread, and are mentioned elsewhere in this paper (e.g. Table 6). For rainfall, notable examples are a step change in the Sahel in 1970 (L’Hôte et al., 2002; Mahé and Paturel, 2009), south-west Western Australia (WA) in the late 1960s and early 1970s (Li et al., 2005; Power et al., 2005; Hope et al., 2010) and the western US in the 1930s (Narisma et al., 2007). Similar changes have been detected in streamflow records worldwide, showing that regime changes in moisture have been a long-standing aspect of climate variability (Whetton et al., 1990).

A few more recent changes have been directly attributed to increasing gases, although south-west WA is an exception (Cai and Cowan, 2006; Timbal et al., 2006; Delworth and Zeng, 2014), with large-scale shifts in synoptic types accompanying a rapid decrease in rainfall (Hope et al., 2006). The bivariate test identifies a step change in southwest WA winter rainfall in 1969 (shown in Fig. 6a), with an upward step in summer rainfall in northern Australia 1 year later. Ocean heat content of the upper ocean also shows step changes occurring in 1977, 1996 and 2003 (Fig. 6b).

Changes in long-run tide gauge records also show a stepladder-like process of sea level rise, with the San Francisco record, quality controlled and dating back to 1855, being a good example; it shows step changes in 1866, 1935, 1957 and 1982 (Fig. 6c). Step changes in the Fremantle tide gauge data records, one of the longest in the Southern Hemisphere, shows that most of the decline in the average return intervals of extreme events noted by Church et al. (2006) before and after 1950 occurred in two events (Fig. 6d) in the late 1940s and the late 1990s. This variation in rise was noted by White et al. (2014). None of the internal trends in Fig. 6a – d attain p < 0.05, showing the dynamic nature of change and limited trend-like behaviour in these examples.

© Roger N. Jones and James H. RickettsThey did quite a bit of testing to separate the idea of steps from trends, and identified specific dates of steps, and in the case of the 97/98 super El Nino, a regime change:

Table 6 summarises the major tests undertaken with expected outcomes for htrend and hstep. While objections could be made to each of these on an individual basis, collectively they show that for externally forced warming on decadal scales, hstep is better supported than htrend.

In summary, these tests show that hstep is a close approximation of the data when analysing decadal-scale warming. Over the long term, this warming conforms to a complex trend that can be simplified as a monotonic curve, but the actual pathway is step-like. As outlined in Sect. 3.3, this rules out gradual warming, either in situ in the atmosphere or as a gradual release from the ocean, in favour of a more abrupt process of storage and release. This conclusion supports the substantive hypothesis H2 over H1, where the climate change and variability interact, rather than varying independently.

© Roger N. Jones and James H. RickettsHere, they defend the step mechanism as be part of the Earth climate system, but ignored in favor of searching for linear trends:

Proposed mechanisms for step-like warming The correlation between step-like warming and ECS in the models, between the timing of steps in model hindcasts and observations and between steps and known regime changes in observations (Table 6), provides strong evidence that warming is non-gradual on decadal timescales.

The high correlations of steps and shifts with model ECS indicate that atmospheric feedback processes respond to abrupt releases of heat into the atmosphere. The presence of negligible internal trends occurring over some oceanic regions, the region 30 – 60◦ N, and in tropospheric satellite temperatures, suggests that little of the heat being trapped in the atmosphere by anthropogenic greenhouse gases actually remains there. One justification given for rejecting externally driven steplike warming is that it is presumed that there is no plausible physical mechanism for this (Cahill et al., 2015; Foster and Abraham, 2015). However, to suggest that the stepwise release of heat energy is physically implausible overlooks the energetics of the ocean – atmosphere system. Hydrodynamic processes are quite capable of supplying the energy required (Ozawa et al., 2003; Lucarini and Ragone, 2011; Ghil, 2012).

The atmosphere contains as much heat energy as the top 3.2 m of ocean (Bureau of Meteorology, 2003). About 93 % of historically added heat currently resides in the ocean (Levitus et al., 2012; Roemmich et al., 2015), whereas the atmosphere contains about 3 % of the total. A similar amount of the heat has been stored within the land mass (Balmaseda et al., 2013) and on an annual basis a similar flux is absorbed in melting ice (Hansen et al., 2011). A physical reorganisation of the ocean – atmosphere system, as part of a regime change, is therefore large enough to provide the relatively small amount of energy required to cause abrupt sea surface and atmospheric warming (Roemmich et al., 2015; Reid et al., 2016), as shown by rapid changes in shallow ocean heat content (Fig. 6b; Roemmich and Gilson, 2011; Reid, 2016).

For example, Reid et al. (2016) in describing the late 1980s regime change, show it was associated with large-scale shifts in temperature and multiple impacts across terrestrial and marine systems, mainly in the Northern Hemisphere. Changes in the North Pacific in 1977 were considered even more extensive (Hare and Mantua, 2000), as were those in 1997/98 involving both the Pacific and Atlantic oceans (Chikamoto et al., 2012a, b). In developing tests for detection and attribution, Jones (2012) noted two types of regime change over land: one where codependent variables such as maximum temperature and rainfall undergo a step change but remain in a stationary relationship, and the other, nonstationary change, where warming undergoes a step change independent of rainfall change. This suggests that although regime changes are a normal part of internal climate variability, they can be enhanced, releasing extra heat. The step changes summarised in Table 6 coincide with El Niño events but the heat emitted by other El Niño events dissipates and is absorbed back into the ocean within months; thus, an added mechanism is required.

We propose that there is negligible in situ atmospheric warming and that almost all of the added heat trapped by anthropogenic greenhouse gases is absorbed by and stored in the ocean. It is subsequently released through the action of oscillatory mechanisms associated with regime shifts. Most heat (long-wave radiation) is trapped near the ground or ocean surface and much of that is radiated downwards (Trenberth, 2011). The atmosphere as a whole has little intrinsic heat memory and does not warm independently of the surface.

This is supported by observations on land where the overpassing air mass takes on the characteristics of the underlying surface, achieving energy balance within a 300 m distance (Morton, 1983). When passing from land to water, this will see all of the available heat energy taken up by water if the temperature of the air mass exceeds that of water (Morton, 1983, 1986), with the temperature of the overpassing air mass reaching equilibrium with the water beneath within a very short time. Very little of the heat trapped over land can be absorbed by the land surface, but will be transported from land to ocean within a few days to a few weeks, where it can be absorbed (the high latitudes being an exception).

Given that the atmosphere interacts with the top 70 m of ocean over an annual cycle (Hartmann, 1994), there is ample opportunity for the majority of available heat trapped over land that is not absorbed by land, lakes and ice to be absorbed by the ocean.

That’s a serious and credible argument. Here is an exceprt from their conclusion discussion:

Our conclusion that the atmosphere does not warm in situ will challenge many who consider that to be a basic part of the greenhouse effect. However, an exhaustive search of the literature failed to find any direct evidence that this actually takes place. We find it hard to perceive how an additional increment of long-wave radiation on the order of ∼ 0.2 Wm−2 (direct forcing and feedback derived from Schmidt et al. 2010) can behave differently to the ∼ 155 Wm−2 produced in the atmosphere year to year without being absorbed by the wider climate system.

Given that climate models exhibit step-like warming, where the abrupt component carries the greater part of the signal than internal trends, they produce emergent behaviour that is not identified by mainstream analytic approaches. Overwhelmingly, model- and statistically based studies represent the global warming signal as changing gradually. Some are prescriptive because of their structure or because they apply simplified assumptions about a more complex climate system, other models examine a small part of the system, and some have a historical legacy bestowing familiarity and reliability.

Modern climate models are almost as complex as the climate, and thus need to be understood through simpler models (Held, 2005; Benestad, 2016), forming a nested modelling approach from simple through to complex (Schneider and Dickinson, 1974; Ghil, 2015). The linking of trend analysis methods with gradual change may overlook the distinction between process-based and diagnostic models.

A diagnostic model may identify a trend without necessarily indicating a gradual process. A large part of the climate wars has been fought over this very point. Nonlinear responses in climate are being investigated by researchers, with an interest in complex system behaviour via dynamical systems and related theory. Our conclusions suggest that the processes of radiative transfer and subsequent warming take place in two separate domains of the climate system, separated by a delay. The absorption of radiation is a linear process that is quite separate from the behaviour of turbulent dissipation of heat energy within the climate system, which is fundamentally nonlinear (Ozawa et al., 2003). Developments based on deterministic nonlinear and stochastic linear behaviour originating from work by Lorenz (1963) and Hasselmann (1976) respectively explore a range of interrelated phenomena, such as non-equilibrium stable states, oscillators, strange attractors, bifurcations and entropy production, in order to develop a unified theory of climate (Ozawa et al., 2003; Lucarini et al., 2014; Franzke et al., 2015; Ghil, 2015). Studying how the free and forced aspects of change combine to alter the statistical properties of climate is a specific goal (Lucarini and Sarno, 2011; Ghil, 2012, 2015).

Our focus is on understanding the role of linear and nonlinear behaviour in changing climate risk over decadal timescales, specifically how initial condition and boundary-limited uncertainties (as described by Lorenz, 1975 and Hasselmann, 2002) combine. Initial-condition uncertainty is boundary limited, varying within a certain amplitude, with the outcome depending on the pathway taken within those limits (Lorenz, 1975).

There is also a time-dependent window that serves as a predictability barrier. Changing boundary conditions are intransitive, with the outcome being insensitive to initial conditions. The nested nature of climate phenomena over different timescales results in decadalscale climates being both an initial-condition and intransitive process, combining to produce stochastically driven step changes in warming that integrate into a long-term complex trend.

The coincident timing of step changes in both observations and models (Fig. 7) suggests that other factors, such as short-term volcanic forcing, can also influence the timing of step changes. Lorenz (1968) referred to the outcome of forced climate change on century timescales as almost intransitive. The “almost” is due to initial condition uncertainties operating within the boundary limitations of decadal variability. The almost-intransitive model (Lorenz, 1968) is described via linear response theory (Lucarini et al., 2014; Ragone et al., 2016) and shown to be robust for concepts such as effective radiative forcing (Hansen et al., 2005) and effective climate sensitivity (Andrews et al., 2015), although these phenomena would be sensitive to bifurcations if they were to occur (Hasselmann, 2002).

This is the first paper I’ve ever read that ties together models, observations, and chaos theory of the atmosphere from Lorenz. It makes many excellent points, and it will be interesting to see if those at the top of the climate science food chain like Mann, Trenberth, and Schmidt accept these new ideas, or dismiss them and call anyone who believes them “linear trend deniers”.

Besides these new findings, what is refreshing is that the paper had open peer review, with both editor and reviewer comments published here.

The final revised paper is available here. Well worth a read! I look forward to seeing the reactions.

And, they published data and code! Code is included with the Supplement as a zip file (Python and R modules). Data availability. Included with the Supplement as Excel files.

h/t to Larry Kummer of Fabius Maximus who has a long list of papers on the subject of testing models (with links) at the end of this post.

Lincoln Report

Bioterrorism Phrophecy Vets Bill Gates Propaganda as Doomsday Clock Nears Midnight

Bioterrorism Phrophecy Vets Bill Gates Propaganda as Doomsday Clock Nears Midnight TWENTY YEAR ANNIVERSARY OF BIOTERRORISM PROPHECY: MASS DEPOPULATION COINCIDES WITH BILL GATES PROPAGANDA, "DOOMSDAY CLOCK" WARNING, AND TRUMP WALL BUILDING  

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