Showing posts sorted by relevance for query solar ocean oscillations. Sort by date Show all posts
Showing posts sorted by relevance for query solar ocean oscillations. Sort by date Show all posts

Friday, May 22, 2015

New paper finds another solar amplification mechanism by which the Sun controls climate

A paper published today in Environmental Research Letters finds another potential solar amplification mechanism by which changes in solar UV activity over 11-year solar cycles are amplified to large-scale effects upon climate via modulations of the North Atlantic Oscillation [NAO]. 

The authors model a mechanism whereby large changes (up to 100%in solar UV over solar cycles affect heating rates of the upper stratosphere, which in turn affect winds and temperature gradients in the troposphere, and heat storage in North Atlantic Ocean. This results in a lagged effect of 3-4 years in the amplitude of the North Atlantic Oscillation, which in turn affects Arctic sea ice extent, other ocean oscillations, the jet stream, and weather patterns around the globe. The paper corroborates several others demonstrating solar influence upon the NAO, as well as other ocean oscillations. 

According to the authors,
Numerous studies have suggested an impact of the 11 year solar cycle on the winter North Atlantic Oscillation (NAO), with an increased tendency for positive [NAO signals to occur at maxima of the solar cycle, and negative NAO signals to occur at minima of the solar cycle]. Climate models have successfully reproduced this solar cycle modulation of the NAO, although the magnitude of the effect is often considerably weaker than implied by observations.  
A leading candidate for the mechanism of solar influence is via the impact of ultraviolet radiation variability on heating rates in the tropical upper stratosphere, and consequently on the meridional temperature gradient and zonal winds...On reaching the troposphere this produces a response similar to the winter NAO. Recent analyses of observations have shown that solar cycle–NAO link becomes clearer approximately three years after solar maximum and minimum. Previous modelling studies have been unable to reproduce a lagged response of the observed magnitude. 
In this study, the impact of solar cycle on the NAO is investigated using an atmosphere–ocean coupled climate model. We show that the model produces significant NAO responses peaking several years after extrema of the solar cycle, persisting even when the solar forcing becomes neutral. This confirms suggestions of a further component to the solar influence on the NAO beyond direct atmospheric heating and its dynamical response. Analysis of simulated upper ocean temperature anomalies confirms that the North Atlantic Ocean provides the memory of the solar forcing required to produce the lagged NAO response. These results have implications for improving skill in decadal predictions of the European and North American winter climate.

A simulated lagged response of the North Atlantic Oscillation to the solar cycle over the period 1960–2009

OPEN ACCESS

M B Andrews 1, J R Knight 1 and L J Gray 2
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M B Andrews et al 2015 Environ. Res. Lett. 10 054022
doi:10.1088/1748-9326/10/5/054022Published 22 May 2015

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Abstract

Numerous studies have suggested an impact of the 11 year solar cycle on the winter North Atlantic Oscillation (NAO), with an increased tendency for positive (negative) NAO signals to occur at maxima (minima) of the solar cycle. Climate models have successfully reproduced this solar cycle modulation of the NAO, although the magnitude of the effect is often considerably weaker than implied by observations. A leading candidate for the mechanism of solar influence is via the impact of ultraviolet radiation variability on heating rates in the tropical upper stratosphere, and consequently on the meridional temperature gradient and zonal winds. Model simulations show a zonal mean wind anomaly that migrates polewards and downwards through wave–mean flow interaction. On reaching the troposphere this produces a response similar to the winter NAO. Recent analyses of observations have shown that solar cycle–NAO link becomes clearer approximately three years after solar maximum and minimum. Previous modelling studies have been unable to reproduce a lagged response of the observed magnitude. In this study, the impact of solar cycle on the NAO is investigated using an atmosphere–ocean coupled climate model. Simulations that include climate forcings are performed over the period 1960–2009 for two solar forcing scenarios: constant solar irradiance, and time-varying solar irradiance. We show that the model produces significant NAO responses peaking several years after extrema of the solar cycle, persisting even when the solar forcing becomes neutral. This confirms suggestions of a further component to the solar influence on the NAO beyond direct atmospheric heating and its dynamical response. Analysis of simulated upper ocean temperature anomalies confirms that the North Atlantic Ocean provides the memory of the solar forcing required to produce the lagged NAO response. These results have implications for improving skill in decadal predictions of the European and North American winter climate.

1. Introduction

The variability of the Sun's output influences the heating of the stratosphere via the absorption of ultraviolet (UV) by ozone (Haigh1994, Gray et al 2009). Observational studies of the influence of the 11 year solar cycle show warm temperature anomalies in the equatorial upper stratosphere at solar maximum compared to solar minimum (Frame and Gray 2010, Mitchell et al 2014). Significant changes in the extratropical atmospheric circulation have been linked to these temperature anomalies (Kodera 1995, Kodera and Kuroda 2002), and this is supported by modelling studies (e.g. Matthes et al 2004, 2006, Ineson et al 2011). One of the mechanisms for 'top-down' solar influence (Gray et al 2010) involves equatorial stratospheric warm anomalies at solar maximum which increases the mean meridional temperature gradient, resulting in an increase in the mean Westerly wind in the mid-latitude stratosphere. This positive zonal wind anomaly is then amplified by forcing from planetary waves propagating upwards from the troposphere. Along with meridional advection, this wave feedback causes the poleward and downward migration and amplification of the wind anomaly to the mid- and high-latitude lower stratosphere, where it is able to influence tropospheric circulation. The resulting surface response involves sea-level pressure changes at solar maximum which are very similar to the positive phase of the Arctic Oscillation (AO), with anomalous low pressure over the North Pole bordered by anomalous high pressure in mid-latitudes (Thompson and Wallace 1998). Conversely, at solar minimum, a negative AO response results from reduced stratospheric meridional temperature gradients and the downward and poleward propagation of negative zonal wind anomalies. This top-down mechanism occurs on seasonal timescales since planetary wave propagation in the stratosphere is limited to the winter half-year.

This 'top-down' mechanism cannot explain the recently identified lag of approximately 3 years between solar maximum (minimum) and an increased tendency of a positive (negative) North Atlantic Oscillation (NAO) signal superimposed on the intrinsic year-to-year NAO variability (Gray et al 2013). The ability of the climate system to produce a multi-year lag in the winter NAO response necessitates the persistence of solar signals within the climate system from one winter to the next. Scaife et al (2013) showed that the North Atlantic Ocean is a prime candidate for the source of the lag. Model simulations have demonstrated that the sub-surface North Atlantic Ocean can be influenced by NAO changes related to the internal variability of stratospheric circulation (Reichler et al2012) and changes in multidecadal solar irradiance (Menary and Scaife 2014). On interannual timescales, Scaife et al (2013) presented a mechanism involving coupled atmosphere–ocean feedbacks. The NAO is known to be correlated with a tripole pattern in the North Atlantic sea-surface temperatures (SST), (Visbeck et al 2003), which extends below the surface into the ocean mixed layer. Due to the seasonal cycle in surface heat and turbulent fluxes, the mixed-layer-depth (MLD) is deeper in winter than in summer. This suggests that a winter sub-surface ocean signal, linked to solar variability, could persist by being isolated underneath the shallower summer mixed layer from the modifying influence of surface fluxes from the atmosphere. In autumn, as the summer mixed-layer erodes and the deeper winter mixed layer becomes established, any sub-surface solar signal would reconnect with the surface, giving it the potential to influence the atmosphere. This sequestration and re-emergence of signals from one winter to the next has been shown to operate in other contexts (Alexander et al 1999, Timlin et al 2002, Deser et al 2003, Taws et al 2011), and would give rise to a forcing of the NAO by the ocean (Rodwell and Folland 2002). Hanawa and Sugimoto (2004) identified several regions of re-emergence including areas of the North Atlantic relevant to this study. Scaife et al (2013) argue that a weak solar-related AO/NAO signal could build up over a number of years in the tripole region of the North Atlantic Ocean and feedback onto the atmosphere to produce a peak in the NAO signal after a few years.

Several studies have examined the simulated NAO response to solar forcings. Gray et al (2013) and Mitchell et al (2015) showed that Coupled Model Intercomparison Project Phase 5 (CMIP5) simulations were unable to reproduce the observed NAO response. On the other hand, Ineson et al (2011) were able to simulate a realistic amplitude of the NAO response by imposing a higher level of variability in UV-band irradiance. They reproduced the UV-induced 'top-down' mechanism, connecting the upper-stratosphere and the tropospheric NAO. The simulations from Ineson et al (2011) were further analysed by Scaife et al (2013), who showed that the implied ocean–atmosphere coupling in the model used by Ineson et al (2011) was too weak to produce the observed delay.

In this study we use historical simulations of the period 1960–2009 with CMIP5 evolving forcings to explore the influence of solar variability on the NAO. This is different to the experiments of Ineson et al (2011) which use constant forcings within their solar maximum and solar minimum scenarios. We use two ensembles, the first with solar irradiance held constant and the second with time-varying spectrally resolved solar variability. The difference in response of the ensembles should reveal the influence of the varying solar cycle on the atmosphere and oceans.

...
Figure 1. (a) Time-series of imposed TSI anomaly (black line), and UV-band irradiance anomaly (dashed blue line) with respect to the 1960–2009 mean. (b) Composites of upper stratospheric zonal mean temperature (dashed red line) and DJF NAO-index (black line) as a function of lag with respect to solar maximum minus solar minimum. The upper stratospheric temperature is calculated as the annual average of the region bounded by 0.5–5 hPa (approximately 40–55 km), and 30 °S–30 °N. The NAO-index is defined as the DJF surface pressure difference between the Azores and Iceland. The points where the NAO-index is significant at the 95% level are highlighted with squares.
We have investigated the NAO response to solar variability using a state-of-the-art atmosphere–ocean coupled model. Historical ensembles for the period 1960–2009 were performed with constant and time-varying solar irradiance. Analysis of the differences between the ensembles was performed to identify solar cycle responses in the atmosphere and ocean. The results demonstrate tropical upper stratospheric heating in response to the imposed UV change at solar maximum compared to solar minimum, and confirm the results of Ineson et al (2011), showing a subsequent surface winter NAO response via a 'top-down' mechanism. The response of the NAO peaks 3–4 years following the extreme phase of the solar cycle. This finding is consistent with a recent re-evaluation of observed responses to the solar cycle (Gray et al 2013) which shows the largest NAO signal at a similar lag. The in-phase response of the Aleutian Low is also in agreement with observational analyses.
We diagnose the source of the NAO lag in the model by examining its surface and sub-surface solar responses in the North Atlantic Ocean. We find evidence for amplification of 'top-down' solar-related NAO changes via an ocean feedback over a period of several years, as suggested by Scaife et al (2013). This feedback is analysed by examining solar cycle responses in the different nodes of the North Atlantic tripole SST pattern, as this pattern reflects NAO–ocean coupling. The Northern and Middle nodes of the tripole show temperature responses in the surface and sub-subsurface ocean with a similar lag to the NAO. The Southern node, however, does not show any lag. In the Middle node we find re-emergence of solar signals imprinted on the ocean from the previous winter. By remaining intact below the shallow ocean mixed-layer that forms in summer, these signals can re-emerge in winter and reinforce the 'top-down' forcing of the NAO via coupling with the atmosphere. This mechanism is not evident in the Northern and Southern nodes. The simulated re-emergence in the North Atlantic Ocean causes an accumulation of the solar signal, allowing the NAO to grow over several years. This growth is limited by the reversal of the solar cycle, resulting in a lag approximately equal to one quarter of its period. Although we do not explicitly demonstrate here that the growth in the NAO response arises through feedback from the solar SST signal in the Middle node the existence of this feedback is supported by previous studies (Rodwell and Folland 2002, Timlin et al 2002) that show the influence of tripole SSTs on the NAO.
The NAO (Hurrell et al 2003) is a key mode of regional climate variability that strongly influences the wintertime weather of Northern Europe and Eastern North America. The ability to reproduce the lagged NAO response to solar forcing in atmosphere–ocean coupled models offers the possibility of increased NAO predictability and hence skill in seasonal forecasts (Scaife et al 2014) and decadal forecasts up to a few years ahead (Smith et al 2012).

Friday, June 1, 2012

New paper explains how the Sun controls ocean oscillations

A paper published today in the Journal of Atmospheric and Solar-Terrestrial Physics finds that solar poloidal and toroidal fields have different long-term variations and opposite effects upon the North Atlantic Oscillation [NAO]. Several other papers have shown that solar changes are correlated with ocean oscillations. IPCC climate models do not incorporate the link between solar activity and ocean oscillations and thus are critically flawed and cannot be relied upon to forecast climate.

Fig. 2. Long-term variations of the sunspot-related (full circles, solid line) and non-sunspot-related (open circles, dashed line) geomagnetic activity, moving averages over 30 years with a step of 10 years (climatic normals).

Solar influences on atmospheric circulation

  • K. GeorgievaaCorresponding author contact informationE-mail the corresponding author
  • B. Kirova
  • P. Koucká-Knížováb
  • Z. Mošnab
  • D. Koubab
  • Y. Asenovskaa
  • a Space and Solar-Terrestrial Research Institute, Bulgarian Academy of Sciences
  • b Institute of Atmospheric Physics, Czech Academy of Sciences
Various atmospheric parameters are in some periods positively and in others negatively correlated with solar activity. Solar activity is a result of the action of solar dynamo transforming solar poloidal field into toroidal field and back. The poloidal and toroidal fields are the two faces of solar magnetism, so they are not independent, but we demonstrate that their long-term variations are not identical, and the periods in which solar activity agents affecting the Earth are predominantly related to solar toroidal or poloidal fields are the periods in which the North Atlantic Oscillation is negatively or positively correlated with solar activity, respectively. We find further that solar poloidal field-related activity increases the NAM index, while solar toroidal field-related activity decreases it. This is a possible explanation of the changing correlation between the North Atlantic Oscillation and solar activity.

Highlights

Solar poloidal and toroidal fields have different long-term variations. ► The correlation NAO/solar activity changes with the ratio poloidal/toroidal field. ► Solar poloidal field-related activity increases the NAM index. ► Solar toroidal field-related activity decreases the NAM index

Sunday, September 7, 2014

New paper finds another potential solar amplification mechanism via monsoon oscillations

A new paper published in Quaternary Science Reviews reconstructs the climate in NE China over the past 9000 years and finds climate variations related to Pacific ocean cycles and solar activity. According to the authors, there is a "strong link" between solar activity and monsoon rainfall/oscillations:
"The centennial monsoon oscillations could be linked to solar activity
Pacific Ocean is a main regulator for monsoon rainfall in northeastern China.
Spectral analysis...reveals significant periodicities of 87–89, 205–212, 1020–1050 and 1750–2041 years. On the centennial timescale, the quasi-periodicities around 88 and 210 years suggest a strong link between solar activity and monsoon rainfall... We suggest that the Pacific Ocean is a main regulator for summer monsoon rainfall in northeastern China at present and at different time scales during the Holocene."
Solar activity has also been shown to be a driver of Pacific [and other] ocean oscillations. Thus, these may be additional solar amplification mechanisms whereby small changes in solar activity are amplified via monsoonal and ocean oscillations to have large effects upon climate.

Interestingly, the paper shows increasing sea levels and ENSO activity during the Holocene up to the Medieval Warm Period ~1000 years ago, followed by a decrease to the end of the record. 



Wavelet graph shows periodicities of ~88, ~210, ~ 1030, and ~2000 years [areas of horizontal red bands corresponding to periods on vertical axis] corresponding to solar periodicities
SST=sea surface temperature, ENSO=El Nino Southern Oscillation, horizontal axis is years before the present. Interestingly, the paper shows increasing sea levels and ENSO activity to the Medieval Warm Period ~1000 years ago, followed by a decrease of both to the end of the record at the left side of graph. 

An n-alkane and compound-specific carbon isotope record of the past 9000 years 
New idea about the n-alkane distribution and lake evolution.
The centennial monsoon oscillations could be linked to solar activity.
The millennial monsoonal cycles are associated with SST variations.
Pacific Ocean is a main regulator for monsoon rainfall in northeastern China.

Abstract

We present an n-alkane and compound-specific carbon isotope record of the past 9 ka from the annually laminated sedimentary sequence of Lake Xiaolongwan, northeastern China. The n-alkane distribution suggests that Lake Xiaolongwan has undergone a shift from an oligotrophic state with low algal production and little emergent/submerged macrophytes in the early Holocene, to a eutrophic state with high algal production and abundant emergent/submerged macrophytes since the middle Holocene. The pattern of variation observed in the biomarker proxies ACL (the n-alkane average chain length), Paq (aquatic macrophyte versus aquatic macrophyte and terrestrial plant ratio), and LPTP (lake productivity/terrigenous organic production) is throughout the record similar to that of the total organic carbon. The variation of compound-specific carbon isotopic values in the middle- and short-chain alkanes was mainly regulated by lake productivity and the accumulating organic pool through time. In this forested region, where the vegetation is dominated by C3 plants, the long-chain n-alkanes (C27–C31) are predominantly derived from leaf wax lipids. The compound-specific δ13C27–31 value is sensitive to effective precipitation, and therefore represents a useful indicator of regional monsoonal precipitation. Spectral analysis on the δ13C27–31 time series reveals significant periodicities of 87–89, 205–212, 1020–1050 and 1750–2041 years. On the centennial timescale, the quasi-periodicities around 88 and 210 years suggest a strong link between solar activity and monsoon rainfall. The millennial monsoon cycle in northeastern China is associated with sea surface temperature (SST) variations in two active centers of the summer monsoon, the western Pacific Subtropical High (WPSH) and the Okhotsk High. Increasing SST in the subtropical sea may cause a northwards shift of the WPSH, which extends the monsoon rain band (Meiyu) to northeastern China, and thus increasing rainfall in that region. Meanwhile, decreasing SST in the Okhotsk Sea may strengthen the Okhotsk high, bringing more moisture into northeastern China. We suggest that the Pacific Ocean is a main regulator for summer monsoon rainfall in northeastern China at present and at different time scales during the Holocene.

Tuesday, January 1, 2013

Paper shows solar activity at end of 20th century was near highest levels of past 11,500 years

A paper published in Astronomy & Astrophysics reconstructs solar activity over the Holocene and finds solar activity at the end of the 20th century was near the highest levels of the entire 11,500 year record. Over the past 2,500 years, the paper shows a 'hockey stick' of solar activity, with a sharp increase following the end of the Little Ice Age in the 1800's. 

Multiple peer-reviewed publications have shown that small changes in solar activity can have greatly amplified effects upon climate via a variety of mechanisms, including:

1. Galactic cosmic rays/clouds


2. Ocean oscillations, which have been shown in multiple studies to be driven by solar activity
http://hockeyschtick.blogspot.com/search?q=solar+ocean+oscillations
3. Global brightening following the ice age scare of the 1970′s, due to decreased aerosols/clouds noted in multiple studies around the globe
http://hockeyschtick.blogspot.com/search?q=solar
4. Effects on ozone production from large changes in solar UV within and between solar cycles, which has large secondary effects on surface temperature
http://hockeyschtick.blogspot.com/search?q=ozone&max-results=20&by-date=false
5. Forcing due to changes in length of day [LOD]
http://hockeyschtick.blogspot.com/search?q=length+of+day

Reconstructed Total Solar Irradiance [TSI] over the past 11,500 years shown in top graph, and a blow-up of past 3000 years shown in bottom graph
A&A 531, A6 (2011)

Evolution of the solar irradiance during the Holocene,⋆⋆

L. E. A. Vieira1,2, S. K. Solanki1,3, N. A. Krivova1 and I. Usoskin4
1 Max-Planck-Institut für Sonnensystemforschung, Max-Planck-Str. 2, 37191 Katlenburg-Lindau, Germany
e-mail: luis.vieira@cnrs-orleans.fr
2 Laboratoire de Physique et Chimie de l’Environnement et de l’Espace (LPC2E/CNRS), 3A, Avenue de la Recherche, 45071 Orléans Cedex 2, France
3 School of Space Research, Kyung Hee University, Yongin, Gyeonggi, 446-701, Korea
4 Sodankyla Geophysical Observatory (Oulu Unit), POB 3000, Universiy of Oulu, Finland 
Abstract
Context. Long-term records of solar radiative output are vital for understanding solar variability and past climate change. Measurements of solar irradiance are available for only the last three decades, which calls for reconstructions of this quantity over longer time scales using suitable models.
Aims. We present a physically consistent reconstruction of the total solar irradiance for the Holocene.
Methods. We extend the SATIRE (Spectral And Total Irradiance REconstruction) models to estimate the evolution of the total (and partly spectral) solar irradiance over the Holocene. The basic assumption is that the variations of the solar irradiance are due to the evolution of the dark and bright magnetic features on the solar surface. The evolution of the decadally averaged magnetic flux is computed from decadal values of cosmogenic isotope concentrations recorded in natural archives employing a series of physics-based models connecting the processes from the modulation of the cosmic ray flux in the heliosphere to their record in natural archives. We then compute the total solar irradiance (TSI) as a linear combination of the jth and jth + 1 decadal values of the open magnetic flux. In order to evaluate the uncertainties due to the evolution of the Earth’s magnetic dipole moment, we employ four reconstructions of the open flux which are based on conceptually different paleomagnetic models.
Results. Reconstructions of the TSI over the Holocene, each valid for a different paleomagnetic time series, are presented. Our analysis suggests that major sources of uncertainty in the TSI in this model are the heritage of the uncertainty of the TSI since 1610 reconstructed from sunspot data and the uncertainty of the evolution of the Earth’s magnetic dipole moment. The analysis of the distribution functions of the reconstructed irradiance for the last 3000 years, which is the period that the reconstructions overlap, indicates that the estimates based on the virtual axial dipole moment are significantly lower at earlier times than the reconstructions based on the virtual dipole moment. We also present a combined reconstruction, which represents our best estimate of total solar irradiance for any given time during the Holocene.
Conclusions. We present the first physics-based reconstruction of the total solar irradiance over the Holocene, which will be of interest for studies of climate change over the last 11 500 years. The reconstruction indicates that the decadally averaged total solar irradiance ranges over approximately 1.5 W/m2 from grand maxima to grand minima.

Monday, July 14, 2014

Analysis: Solar activity & ocean cycles are the 2 primary drivers of climate, not CO2

Dan Pangburn has updated his analysis identifying the two primary drivers of global temperature:

1) the integral of solar activity 
2) ocean oscillations [which are in-turn driven by solar activity and perhaps lunar-tidal forcing]. 

The correlation of the integral of solar activity and ocean cycles to global temperature is 90.49%, and with the addition of CO2 the correlation only improves very slightly to 90.61%, demonstrating CO2 change has no significant effect on climate. The correlation of CO2 alone to global temperature is poor at only 44%, not to mention that CO2 follows temperature on short, intermediate, and long-term timescales, and the effect does not precede the cause. 

Comment by Dan Pangburn:

Two primary drivers of average global temperature have been identified. They very accurately explain the reported up and down measurements since before 1900 with coefficient of determination, R2>0.9 (correlation coefficient = 0.95) and provide credible estimates back to the low temperatures of the Little Ice Age (1610). 

R2 = 0.9049 considering only sunspots and ocean cycles.
R2 = 0.9061 considering sunspots, ocean cycles and CO2 change.

The tiny difference in R2, whether considering CO2 or not, demonstrates that CO2 change has no significant effect on climate.

The coefficients of determination are a measure of how accurately the calculated average global temperatures compare with measured. R2 > 0.9 is excellent.

The calculations use data since before 1900 which are official, accepted as valid and are publicly available. 

Solar cycle duration or magnitude fail to correlate but their combination, expressed as the time-integral of solar cycle anomalies, gives an excellent correlation. A solar cycle anomaly is the difference between the sunspot number for a year and an average sunspot number for many years. 

Everything not explicitly considered (such as the 0.09 K s.d. random uncertainty in reported annual measured temperature anomalies, aerosols, CO2, other non-condensing ghg, volcanoes, ice change, etc.) must find room in the unexplained 9.51%.

The method, equation, data sources, history and predictions are provided at http://agwunveiled.blogspot.com and references.


Introduction
This monograph is a clarification and further refinement of Reference 10 (references are listed at the end of this paper) which also considers only average global temperature. It does not discuss weather, which is a complex study of energy moving about the planet. It does not even address local climate, which includes precipitation. It does, however, consider the issue of Global Warming and the mistaken perception that human activity has a significant influence on it.

The word ‘trend’ is used here for temperatures in two different contexts. To differentiate, α-trend applies to averaging-out the uncertainties in reported average global temperature measurements to produce the average global temperature oscillation resulting from the net ocean surface oscillation. The term β-trend applies to the slower average temperature change of the planet which is associated with change to the temperature of the bulk volume of the material (mostly water) involved.

The first paper to suggest the hypothesis that the sunspot number time-integral is a proxy for a substantial driver of average global temperature change was made public 6/1/2009. The discovery started with application of the first law of thermodynamics, conservation of energy, and the hypothesis that the energy acquired, above or below break-even (appropriately accounting for energy radiated from the planet), is proportional to the time-integral of sunspot numbers. The derived equation revealed a rapid and sustained global energy rise starting in about 1941. The true average global temperature anomaly change β-trend is proportional to global energy change.

Subsequent analysis revealed that the significant factor in calculating the β-trend is the sunspot number anomaly time-integral. The sunspot number anomaly is defined as the difference between the sunspot number in a specific year and an average sunspot number for several years.
Measured temperature anomaly α-trends oscillate above and below the temperature anomaly β-trend calculated using only the sunspot number time-integral. The existence of ocean oscillations, especially the Pacific Decadal Oscillation, led to the perception that there must be an effective net surface temperature oscillation for the planet with all named and unnamed ocean oscillations as participants. Plots of measured average global temperatures indicate that the net surface temperature oscillation has a period of 64 years with the most recent maximum in 2005.

Combination of the effects results in the effect of the ocean surface temperature oscillation (α-trend) decline 1941-1973 being slightly stronger than the effect of the rapid rise from sunspots (β-trend) resulting in a slight decline of the trend of reported average global temperatures. The steep rise 1973-2005 occurred because the effects added. A high coefficient of determination, R2, demonstrates that the hypothesis is true.

Over the years, several refinements to this work (often resulting from other's comments which may or may not have been corroborative) slightly improved the accuracy and led to the equations and figures in this paper.

Prior work
The law of conservation of energy is applied effectively the same as described in Reference 2 in the development of a very similar equation that calculates temperature anomalies. The difference is that the variation in energy ‘OUT’ has been found to be adequately accounted for by variation of the sunspot number anomalies. Thus the influence of the factor [T(i)/Tavg]4 is eliminated.

Change to the level of atmospheric carbon dioxide has no significant effect on average global temperature. This was demonstrated in 2008 at Reference 6 and is corroborated at Reference 2 and again here.

As determined in Reference 3, reported average global temperature anomaly measurements have a random uncertainty with equivalent standard deviation ≈ 0.09 K.

Global Warming ended more than a decade ago as shown here, and in Reference 4 and also Reference 2.

Average global temperature is very sensitive to cloud change as shown in Reference 5.

The parameter for average sunspot number was 43.97 (average 1850-1940) in Ref. 1, 42 (average 1895-1940) in Ref. 9, and 40 (average 1610-2012) in Ref. 10. It is set at 34 (average 1610-1940) in this paper. The procession of values for average sunspot number produces slight but steady improvement in R2 for the period of measured temperatures and progressively greater credibility of average global temperature estimates for the period prior to direct measurements becoming available.

Initial work is presented in several papers at http://climaterealists.com/index.php?tid=145&linkbox=true

The sunspot number anomaly time-integral drives the temperature anomaly trend
It is axiomatic that change to the average temperature trend of the planet is due to change to the net energy retained by the planet.

Table 1 in reference 2 shows the influence of atmospheric carbon dioxide (CO2) to be insignificant (tiny change in R2 if considering CO2 or not) so it can be removed from the equation by setting coefficient ‘C’ to zero. With ‘C’ set to zero, Equation 1 in Reference 2 calculates average global temperature anomalies (AGT) since 1895 with 89.82% accuracy (R2= 0.898220).

The current analysis determined that 34, the approximate average of sunspot numbers from 1610-1940, provides a slightly better fit (in fact, the best fit) to the measured temperature data than did 43.97 and other values 9,10. The influence, of Stephan-Boltzmann radiation change due to AGT change, on energy change is adequately accounted for by the sunspot number anomaly time-integral. With these refinements to Equation (1) in Reference 2 the coefficients become A = 0.3588, B = 0.003461 and D = ‑ 0.4485.  R2 increases slightly to 0.904906 and the calculated anomaly in 2005 is 0.5045 K. Also with these refinements the equation calculates lower early temperature anomalies and projects slightly higher (0.3175 K vs. 0.269 K in 2020) future anomalies. The resulting equation for calculating the AGT anomaly for any year, 1895 or later, is then:

Anom(y) = (0.3588,y) + 0.003461/17 Σyi=1895 (s(i) – 34) – 0.4485

Where:
            Anom(y) = calculated temperature anomaly in year y, K
            (0.3588,y) = approximate contribution of ocean cycle effect to AGT in year y
            s(i) = average daily Brussels International sunspot number in year i

Measured temperature anomalies are from Figure 2 of Reference 3. The excellent match of the up and down trends since before 1900 of calculated and measured anomalies, shown here in Figure 1, demonstrates the usefulness and validity of the calculations.

Projections until 2020 use the expected sunspot number trend for the remainder of solar cycle 24 as provided 11 by NASA. After 2020 the limiting cases are either assuming sunspots like from 1925 to 1941 or for the case of no sunspots which is similar to the Maunder Minimum.

Some noteworthy volcanoes and the year they occurred are also shown on Figure 1. No consistent AGT response is observed to be associated with these. Any global temperature perturbation that might have been caused by volcanoes of this size is lost in the temperature measurement uncertainty. Much larger volcanoes can cause significant temporary global cooling from the added reflectivity of aerosols and airborne particulates. The Tambora eruption, which started on April 10, 1815 and continued to erupt for at least 6 months, was approximately ten times the magnitude of the next largest in recorded history and led to 1816 which has been referred to as ‘the year without a summer’. The cooling effect of that volcano exacerbated the already cool temperatures associated with the Dalton Minimum.
 
 Figure 1: Measured average global temperature anomalies with calculated prior and future trends using 34 as the average daily sunspot number.

As discussed in Reference 2, ocean oscillations produce oscillations of the ocean surface temperature with no significant change to the average temperature of the bulk volume of water involved. The effect on AGT of the full range of surface temperature oscillation is given by the coefficient ‘A’.

The influence of ocean surface temperature oscillations can be removed from the equation by setting ‘A’ to zero. To use all regularly recorded sunspot numbers, the integration starts in 1610. The offset, ‘D’ must be changed to -0.1993 to account for the different integration start point and setting ‘A’ to zero. Setting ‘A’ to zero requires that the anomaly in 2005 be 0.5045 - 0.3588/2 = 0.3251 K. The result, Equation (1) here, then calculates the trend 1610-2012 resulting from just the sunspot number time-integral.

Trend3anom(y) = 0.003461/17 * Σyi = 1610 [s(i)-34] – 0.1993                (1)

Where:
Trend3anom(y) = calculated temperature anomaly β-trend in year y, K degrees.
0.003461 = the proxy factor, B, W yr m-2.
17 = effective thermal capacitance of the planet, W Yr m-2 K-1
s(i) = average daily Brussels International sunspot number in year i
34 ≈ average sunspot number for 1610-1940.
-0.1993 is merely an offset that shifts the calculated trajectory vertically on the graph, without changing its shape, so that the calculated temperature anomaly in 2005 is 0.3251 K which is the calculated anomaly for 2005 if the ocean oscillation is not included.

Sunspot numbers back to 1610 are shown in Figure 2 of Reference 1.

Applying Equation (1) to the sunspot numbers of Figure 2 of Reference 1 produces the trace shown in Figure 2 below.

Figure 2: Anomaly trend from just the sunspot number time-integral using Equation (1).

Average global temperatures were not directly measured in 1610 (thermometers had not been invented yet). Recent estimates, using proxies, are few. The anomaly trend that Equation (1) calculates for that time is roughly consistent with other estimates. The decline in the trace 1610-1700 on Figure 2 results from the low sunspot numbers for that period as shown on Figure 2 of Reference 1. 

How this phenomenon could take place
Although the connection between AGT and the sunspot number time-integral is demonstrated, the mechanism by which this takes place remains somewhat theoretical.

Various papers have been written that indicate how the solar magnetic field associated with sunspots can influence climate on earth. These papers posit that decreased sunspots are associated with decreased solar magnetic field which decreases the deflection of and therefore increases the flow of galactic cosmic rays on earth.

Henrik Svensmark, a Danish physicist, found that decreased galactic cosmic rays caused decreased low level (< 3 km) clouds and planet warming. An abstract of his 2000 paper is at Reference 13. Marsden and Lingenfelter also report this in the summary of their 2003 paper 14 where they make the statement “…solar activity increases…providing more shielding…less low-level cloud cover… increase surface air temperature.”  These findings have been further corroborated by the cloud nucleation experiments 15 at CERN.

These papers associated the increased low-level clouds with increased albedo leading to lower temperatures. Increased low clouds would also result in lower average cloud altitude and therefore higher average cloud temperature. Although clouds are commonly acknowledged to increase albedo, they also radiate energy to space so increasing their temperature increases radiation to space which would cause the planet to cool. Increased albedo reduces the energy received by the planet and increased radiation to space reduces the energy of the planet. Thus the two effects work together to change the AGT of the planet.

Simple analyses 5 indicate that either an increase of approximately 186 meters in average cloud altitude or a decrease of average albedo from 0.3 to the very slightly reduced value of 0.2928 would account for all of the 20th century increase in AGT of 0.74 °C. Because the cloud effects work together and part of the temperature change is due to ocean oscillation, substantially less cloud change is needed.


Combined Sunspot Effect and Ocean Oscillation Effect
As a possibility, the period and amplitude of oscillations attributed to ocean cycles demonstrated to be valid after 1895 are assumed to maintain back to 1610. Equation (1) is modified as shown in Equation (2) to account for including the effects of ocean oscillations. Since the expression for the oscillations calculates values from zero to the full range but oscillations must be centered on zero, it must be reduced by half the oscillation range.

Trend4anom(y) = (0.3588,y) – 0.1794 + 0.003461/17 * Σyi = 1610 [s(i)-34] – 0.1993   (2)

The ocean oscillation factor, (0.3588,y) – 0.1794, is applied to the period prior to the start of temperature measurements as a possibility. The effective sea surface temperature anomaly, (A,y), is defined in Reference 2.

Applying Equation (2) to the sunspot numbers from Figure 2 of Reference 1 produces the trend shown in Figure 3 next below. Available measured average global temperatures from Figure 2 in Reference 3 are superimposed on the calculated values.
 
 Figure 3: Calculated temperature anomalies from the sunspot number anomaly time-integral plus ocean oscillation using Equation (2) with superimposed available measured data from Reference 3 and range estimates determined by Loehle.

Figure 3 shows that temperature anomalies calculated using Equation (2) estimate possible trends since 1610 and actual trends of reported temperatures since they have been accurately measured world wide. The match from 1895 on has R2 = 0.9049 which means that 90.49% of average global temperature anomaly measurements are explained. All factors not explicitly considered must find room in that unexplained 9.51%. Note that a coefficient of determination, R2 = 0.9049 means a correlation coefficient of 0.95.

A survey 12 of non-tree-ring global temperature estimates was conducted by Loehle including some for a period after 1610. A simplification of the 95% limits found by Loehle are also shown on Figure 3. The spread between the upper and lower 95% limits are fixed, but, since the anomaly reference temperatures might be different, the limits are adjusted vertically to approximately bracket the values calculated using the equations. The fit appears reasonable considering the uncertainty in all values.

Calculated temperature anomalies look reasonable back to 1700 but indicate higher temperatures prior to that than most proxy estimates. They are, however, consistent with the low  sunspot numbers in that period. They qualitatively agree with Vostok, Antarctica ice core data but decidedly differ from Sargasso Sea estimates during that time (see the graph for the last 1000 years in Reference 6). Credible worldwide assessments of average global temperature that far back are sparse. Ocean oscillations might also have been different from assumed.

Possible lower values for average sunspot number
Possible lower assumed values for average sunspot number, with coefficients adjusted to maximize R2, result in noticeably lower estimates of early (prior to direct measurement) temperatures with only a tiny decrease in R2. Calculated temperature anomalies resulting from using an average sunspot number value of 26 are shown in Figure 4. The projected temperature anomaly trend decline is slightly less steep (0.018 K warmer in 2020) than was shown in Figure 1.

Figure 4: Calculated temperature anomalies from the sunspot number anomaly time-integral plus ocean oscillation using 26 as the average sunspot number with superimposed available measured data from Reference 3 and range estimates determined by Loehle.

Carbon dioxide change has no significant influence
The influence that CO2 has on AGT can be calculated by including ‘C’ in Equation (1) of Reference 2 as a coefficient to be determined. The tiny increase in R2 demonstrates that consideration of change to the CO2 level has no significant influence on AGT. The coefficients and resulting R2 are given in Table 1.

Table 1: A, B, C, D, refer to coefficients in Equation 1 in Reference 2
Average daily SSN
ocean oscillation A
sunspots B
CO2C
Offset
D
Coefficient of determinationR2
% cause of 1909-2005 AGT change
Sunspots
Ocean oscillation
CO2change
26
0.3416
0.002787
0
-0.4746
0.903488
63.8
36.2
0
32
0.3537
0.003265
0
-0.4562
0.904779
62.7
37.3
0
34
0.3588
0.003461
0
-0.4485
0.904906
62.2
37.8
0
36
0.3642
0.003680
0
-0.4395
0.904765
61.7
38.3
0
34
0.3368
0.002898
0.214
-0.4393
0.906070
52.3
35.6
12.1

Further discussion of ocean cycles
The temperature contribution to AGT of ocean cycles is approximated by a function that has a saw-tooth trajectory profile. It is represented in equation (2) by (A,y) where A is the total amplitude and y is the year. The uptrends and down trends are each determined to be 32 years long for a total period of 64 years. The total amplitude resulting from ocean oscillations was found here to be 0.3588 K (case highlighted in Table 1).

Thus, for an ocean cycle surface temperature uptrend, the contribution of ocean oscillations to AGT is approximated by adding (to the value calculated from the sunspot integral) 0.3588 multiplied by the fraction of the 32 year period that has elapsed since a low. For an ocean cycle surface temperature down trend, the contribution is calculated by adding 0.3588 minus 0.3588 multiplied by the fraction of the 32 year period that has elapsed since a high. The lows were found to be in 1909 and 1973 and the highs in 1941 and 2005. The resulting trajectory, offset by half the amplitude, is shown as ‘approximation’ in Figure 5.

Temperature data is available for three named cycles: PDO, ENSO 3.4 and AMO. Successful accounting for oscillations is achieved for PDO and ENSO when considering these as forcings (with appropriate proxy factors) instead of direct measurements. As forcings, their influence accumulates with time. The proxy factors must be determined separately for each forcing. The measurements are available since 1900 for PDO 16 and ENSO3.4 17. This PDO data set has the PDO temperature measurements reduced by the average SST measurements for the planet.

The contribution of PDO and ENSO3.4 to AGT is calculated by:
PDO_NINO = Σyi=1900 (0.017*PDO(i) + 0.009 * ENSO34(i))        (3)

Where:
            PDO(i) = PDO index 16 in year i
            ENSO34(i) = ENSO 3.4 index 17 in year i


How this calculation compares to the idealized approximation use in Equation (2) is shown in Figure 5. The high coefficient of determination in Table 1 and the comparison in Figure 5 corroborate the assumption that the saw-tooth profile provides an adequate approximation of the influence of all named and unnamed ocean cycles in the calculated AGT anomalies.
Figure 5: Comparison of idealized approximation of ocean cycle effect and the calculated effect from PDO and ENSO.

Conclusions
Others that have looked at only amplitude or only duration factors for solar cycles got poor correlations with average global temperature. The good correlation comes by combining the two, which is what the time-integral of sunspot numbers does. As shown in Figure 2, the anomaly trend determined using the sunspot number time-integral has experienced substantial change over the recorded period. Prediction of future sunspot numbers more than a decade or so into the future has not yet been confidently done although assessments using planetary synodic periods appear to be relevant 7,8.

As displayed in Figure 2, the time-integral of sunspot numbers alone appears to show the estimated true average global temperature trend (the net average global energy trend) during the planet warm up from the depths of the Little Ice Age.

The net effect of ocean oscillations is to cause the surface temperature trend to oscillate above and below the trend calculated using only the sunspot number time-integral. Equation (2) accounts for both and also, because it matches measurements so well, shows that rational change to the level of atmospheric carbon dioxide can have no significant influence.

Long term prediction of average global temperatures depends primarily on long term prediction of sunspot numbers.


References:
11. Graphical sunspot number prediction for the remainder of solar cycle 24http://solarscience.msfc.nasa.gov/predict.shtml
12. http://www.econ.ohio-state.edu/jhm/AGW/Loehle/Loehle_McC_E&E_2008.pdf
13.   Svensmark paper, Phys. Rev. Lett. 85, 5004–5007 (2000)  http://prl.aps.org/abstract/PRL/v85/i23/p5004_1
14.  Marsden & Lingenfelter 2003, Journal of the Atmospheric Sciences 60: 626-636  http://www.co2science.org/articles/V6/N16/C1.php
15. CLOUD experiment at CERNhttp://indico.cern.ch/event/197799/session/9/contribution/42/material/slides/0.pdf
        16. PDO index http://jisao.washington.edu/pdo/PDO.latest
        (Linked from http://www.cgd.ucar.edu/cas/catalog/climind/TNI_N34/ )