Addressing uncertainties related to climate change
detection, natural variability, solar influences, and climate sensitivity to radiative forcing will enhance predic
tions and better inform sustainable climate strategies. Keywords: Climate change detection, attribution and hazard assessment; Climate model validation; An
thropogenic vs. natural climate drivers; Equilibrium climate sensitivity; Solar cycles and influence on climate. Cite as: Scafetta, N.: 2025. Detection, attribution, and modeling of climate change: Key open issues. Highlights:
This paper argues that climate science still faces unresolved key issues. Global Climate models struggle in reproducing natural variability at all time scales and may exaggerate warming. Global Climate models likely exgerate the ECSand significantly underestimate solar influences. Empirical models projects moderate warm ing challenging strict net-zero climate policies.
New climate models that better reflect natural climate drivers and variations are needed. 1 Introduction
Throughout human history, climate change has profoundly influenced both the natural environment and soci etal structures, leaving a lasting imprint through its wide-ranging positive and negative effects. The negative impacts encompass a range of potential threats, including diminished food production, increased transmis sion of diseases, and the disruption of ecosystems and infrastructure caused by extreme weather events such as heatwaves, floods, hurricanes, sea level rise, and droughts. Importantly, the effects of climate change are unevenly distributed across the globe, with socio-economic disparities accentuating differences in exposure and vulnerability. Marginalized communities, particularly those facing economic constraints,
are disproportionately affected by climate-related hazards. Such disparities underscore the enduring con cern humanity has had regarding climate change. Nevertheless, the science underpinning climate change, its causative factors, and the reliability of future climate projections remain subjects of significant scientific un certainty. This contrasts with prevalent public assertions claiming that climate change is “ settled science ”. The United Nations Intergovernmental Panel on Climate Change (IPCC) has published a series of Assess ment Reports (ARs) since 1990, which address the detection and attribution of climate change. These reports are regarded by many scientists, policymakers, and members of the public as providing robust evidence of a significant anthropogenic contribution to unprecedented global warming since the pre-industrial period of 1850–1900. Fossil fuel combustion — resulting in the release of greenhouse gases, particularly carbon dioxide — is identified as the primary driver of increased radia tive forcing leading to rising global surface temperatures. Global climate models (GCMs) process a number of radiative forcing inputs and simulate global temperature increases, attributed in gran part to the activation of allegedly-positive climatic feedback mechanisms. The outputs of these GCMs are subsequently employed to assess future climate scenarios based on hypothetical shared socioeconomic pathways (SSPs) and associ ated hazards. This information forms the basis for the IPCC recommendations aimed at guiding policymakers in crafting comprehensive and costly climate mitigation strategies to avert projected adverse climate change
outcomes. For instance, the European Union has adopted the “ Green Deal ”, a policy initiative targeting at least a 55%
reduction in net greenhouse gas emissions by 2030 and achieving carbon neutral ity, or “ Net-Zero ”, by 2050. This policy framework seeks to balance greenhouse gas emissions with their removal via natural absorption processes and emerging carbon sequestration technolo gies. The overarching goal of the Net-Zero policies is to keep the “ increase in the global average temperature to well below 2 °C above pre-industrial levels ” with efforts “ to limit the temperature increase to 1.5 °C above pre-industrial
levels ”. Strategies include transitioning from fossil fuels to renewable energy sources
(geothermal, hydroelectric, solar, and wind power) and replacing internal combustion vehicles with electric
alternatives. However, the implementation of the Green Deal policies entails significant economic investments, poten tially jeopardizing industrial development and economic growth. Therefore, a thorough evaluation of the feasibility of these policies and the underlying scientific justifications is imperative. Serious economic challenges render Net-Zero targets difficult, if not impossible to achieve. As of 2023, the
European Union’s 27 member states collectively contributed only 6.08% of global greenhouse gas emission,
which continues to grow globally by approximately 2% annually, despite reductions in Europe. The continued global reliance on fossil fuels — evident in the approximately 1,000 coal fired power plants across Asia currently under construction or planned, particularly in China and India — suggests that achieving Net-Zero emissions may remain impractical throughout the 21 [st] century. Also the depletion of critical metals essential for low-carbon technologies and electric vehicles (e.g., Co, Ni, Cu, Se, Ag, Cd, In, Te,
and Pt) by 2060 could hinder further technological advancements. Furthermore, economic
meta-analyses indicate that the costs associated with implementing Net-Zero policies to meet the targets of the Paris Agreement could outweigh the anticipated benefits even in the most favorable scenario. The above findings suggest the need of a meticulous evaluation of energy and climate policies by carefully weighing their potential advantages and disadvantages. To accurately assess the risks associated with projected climate changes and the effectiveness of mitigation
policies, it is essential to first evaluate the reliability of current climate science. The IPCC Assessment Reports directly address this point by explaining in great details how the Coupled Model Intercomparison Project
rigorously tests global climate models (GCMs) against historical climate records. These models un dergo thorough a number of statistical validation in an attempt to ensure that their confidence intervals align well with the observed temperature trends. Additionally, climate models are cross-checked with paleoclimate
data from ice cores and tree rings, as well as insights from oceanography, atmospheric physics, and geophysics. By integrating evidence from multiple disciplines, the IPCC attempts to maintain consistency between climate projections and real-world observations. However, unresolved major scientific questions regarding the science of climate change persist. In fact,
contrary to some popular perception, climate science remains unsettled and highly debated. Recent research highlights persistent uncertainties in the detection, attribution, and prediction of climate change, and advocate for a more cautious approach to this multifaceted complex issue. Scientific challenges in climate detection, attribution, and modeling stem from three primary issues:
1. the inherent uncertainty of what measurements really indicate complicates the detection of climate change and its causative factors;
2. the anthropogenic contribution is superimposed to natural climate variability, necessitating comprehen sive understanding and accurate modeling of the latter;
3. key physical processes, such as cloud formation and solar contributions to climate dynamics, remain poorly characterized. Anthropogenic climate change becomes meaningful only if it is significant relative to expected natural vari ability. Accurate attributions require precise modeling of external forcing mechanisms and climate responses. However, ongoing uncertainties in these areas continue to impede the accurate attribution of observed climatic changes to either natural or human influences.
Appendix A. (Top) The figure illustrates that there are the approximately 1,000 coal-fired power plants across Asia currently under construction or planned, particularly in China and India. (Bottom) The figure illustrates that as of 2023, the European Union’s 27 member states collectively contributed only 6.08% of global greenhouse gas emission, which continues to grow globally by approximately 2% annually, despite reductions in Europe. Data from the “JRC SCIENCE FOR POLICY REPORT GHG EMISSIONS OFALL WORLD COUNTRIES 2024”. Section 2 of this paper outlines the evolution of the “ Anthropogenic Global Warming Theory ” (AGWT) as pre sented in the IPCC Assessment Reports published from 1990 to 2023. Sections 3 and 4 critically examine uncertainties surrounding the reliability of global temperature records, the extent of solar influences on climate change, and climate sensitivity to radiative forcing. Evidence suggests that estimates of global surface warming since the pre-industrial period may have been exaggerated and that solar and astronomical con tributions to climate dynamics may have been underestimated. Additionally, contemporary GCMs remain insufficiently validated, and climate sensitivity parameters may be lower than previously anticipated. Empirical models incorporating natural variability are discussed in Section 5 and suggest that global warming during the 21 [st] century under realistic SSPs may be moderate and not as severe as projected by the IPCC. Consequently, it is investigated whether the risks associ ated with future climate change have been overestimated, underscoring the need to address several physical uncertainties prior to develop and implement effective climate policies. 2 The Anthropogenic Global Warming Theory (AGWT)
This section outlines the key arguments supporting the Intergovernmental Panel on Climate Change’s theory of anthropogenic global warming, and traces the evolution of the AGWT from the 1990s to the most recent assessment report. 2.1 The IPCC Assessment Reports from 1990 to 2023
The IPCC’s Sixth Assessment Report claims definitive evidence linking human activities to the observed global warming. According to the report: “ Global surface temperature was 1.09 °C higher in 2011–2020 than 1850–1900, with larger increases over land than over the ocean ”; further, “ It is unequivocal that human influence has warmed the atmosphere, ocean and land ” owing to
“ observed increases in well-mixed greenhouse gas (GHG) concentrations since around 1750 are unequivocally caused by human activities ”. The report concludes: “ The likely range of total human-caused global surface temperature increase from 1850–1900 to 2010–2019 is 0.8 °C to 1.3 °C , with a best estimate of 1.07 °C”. These statements support the conclusion that nearly 100% of the global surface warming observed from the pre-industrial period to 2011–2020 is attributable to anthropogenic drivers, which forms the basis of the Anthropogenic Global
Warming Theory (AGWT). However, the IPCC’s attribution of natural versus anthropogenic contributions to climate change has evolved significantly over time. The IPCC’s First Assessment Report acknowledged that in the 20 [th] century human activities had begun influencing global climate, but precise quantification of their contribution remained elusive due to uncertainties surrounding natural variability. FAR highlighted the paleoclimatic temperature record of the last millennium by Lamb. This was a proxy temperature reconstruction for England that could more broadly represent the European and North Atlantic climates.
This reconstruction identified a pronounced
Medieval Warm Period (MWP), which was estimated definitely warmer than the first half of the 20 [th] century, followed by the Little Ice Age (LIA). On the basis of such evidence, FAR noted that the warming observed since 1900 was “ broadly consistent with predictions of climate models, but it is also of the same magnitude as natural climate variability ”, and suggested that “ the observed increase could be largely due to this natural variability; alternatively this variability and other human factors could have offset a still larger human-induced
greenhouse warming ” (FAR Executive Summary, p. xii). The Second Assessment Report largely corroborated FAR’s findings, estimating that anthro pogenic activities could have accounted for approximately 50% of the observed global warming of the 20 [th]
century with natural variability contributing the remainder.
SAR and FAR also noted a moderate global cool ing from the 1940s to the 1970s. The IPCC’s Third Assessment Report posited that human activities likely accounted for around
70% of the observed warming since 1900, emphasizing the role of greenhouse gas emissions (e.g., carbon diox ide, methane, nitrous oxide) from industrial processes, agriculture, and deforestation. TAR introduced a novel reconstruction of the Northern Hemisphere temperatures over the past millennium, which depicted the controversial “ hockey-stick ” pattern showing a very modest ~0.2°C cooling from MWP to LIA
followed by ~1°C warming from 1900 to 2000. This graph suggested that the 20 [th] -century warming was un precedented and that the overall temperature pattern of the last millennium correlated well with historical greenhouse gas concentration records; such a correlation increased confidence in climate models and in their climate attribution assessments. However, the hockey-stick graph contradicted earlier pa leoclimate research and sparked controversy due also to methodological concerns, rapidly becoming even apolitically charged debate. The Fourth Assessment Report proposed again the hockey-stick graph and concluded that “ most of the observed increase in global average temperatures since the mid-20 [th] century is ’very likely’
due to the observed increase in anthropogenic greenhouse gas concentrations ”. Meanwhile, several novel paleoclimatic studies revealed a more pronounced MWP, sometimes comparable to the Current Warm Period (CWP) of the last of the last decades of the 20 [th] century. These records were acknowledged in the IPCC Fifth Assessment Report, where the original hockey-stick temperature graph was abandoned. However, the report maintained that “It is ’extremely likely’
that human influence was the dominant cause of global warming between 1951 and 2010 ”. Finally, AR6 attributed 0.8–1.3°C of the observed 0.95–1.20°C warming to anthropogenic emissions, and relied on the PAGES-2K Consortium proxy model,
which again attenuated the Medieval Warm Period although more moderately than in the original hockey-stick
temperature record proposed by Mann et al.. However, representing the Common Era temperature history through a single paleoclimatic reconstruction has been recently criticized as reductive, indicating that the debate remains ongoing. Accurate assessments of past climates are necessary to validate the AGWT, as discussed below. 2.2 The crucial role of the “Global Climate Models” (GCMs)
Despite significant uncertainties in paleoclimate temperature reconstructions, the IPCC’s understanding of climate change attribution from the pre-industrial period to the present largely relies on compu tational experiments conducted with sophisticated numerical climate models. The principal characteristics and findings of these models are extensively summarized in the IPCC’s Fourth, Fifth, and Sixth Assessment
Reports. Numerical climate models, commonly referred to as “ General Circulation Models ” or “ Global Climate Models ”
(GCMs), are advanced computational tools designed to simulate the dynamics of the climate system. These models capture interactions between the ocean, atmosphere, and land, predicting variations in climate pa rameters based on imposed radiative forcing functions. Radiative forcing functions include alterations driven by greenhouse gas concentrations, atmospheric aerosols (e.g., in dustrial sulphate aerosols, black carbon), land-use changes (e.g., deforestation, urbanization), solar radiation
fluctuations, and volcanic activity, which introduces aerosols and gases into the atmosphere: see Figures 1A
and 1C. Each of these factors can perturb the energy balance of the climate system, resulting in either warm ing or cooling effects. GCMs simulate the system’s integrated response to the combination of these forcing functions. The climate system’s response to variations in radiative forcing is mediated by mechanisms known as climate feedbacks. These feedbacks may amplify or diminish the initial changes induced by the forcing; they are categorized as positive (leading to enhanced warming) or negative (leading to mitigated warming). Key Figure 1: (A) Compilation of the radiative forcing functions utilized in the CMIP5 GCMs. (B) Variations in observed global surface temperature (black) alongside the CMIP3 and CMIP5 model simulations incorporating only natural forcing and combined natural-anthropogenic forcing. (C) Compilation of the radiative forcing functions utilized in the CMIP6 GCMs. (D) Observed global surface temperature variations (black) alongside the CMIP6 model simulations incorporating only natural forcing and combined naturalanthropogenic forcing.
Notably, in both (B) and (D), the observational data necessary to validate the GCM predictions that consider only natural forcings are not reported because they do not exist. feedback mechanisms include:
- Water Vapor Feedback — A positive feedback governed by the Clausius-Clapeyron law, which links ocean evaporation rates to temperature increases;
- Albedo Feedback — A positive feedback arising from changes in surface reflectivity due to ice and snow cover variations;
- Cloud Feedback — Particularly challenging to quantify, as cloud formation, type, and distribution are sen sitive to warming; certain clouds cool the surface by reflecting solar radiation, while others trap emitted
heat, making their net contribution highly uncertain;
- Lapse Rate Feedback — A negative feedback involving modifications to atmospheric temperature vertical
gradients;
- Carbon Cycle Feedback — Activated by warming-induced CO 2 release from soils and oceans (per Henry’s
law), further increasing atmospheric CO 2 concentrations; - Vegetation Feedback — Temperature and precipitation changes alter vegetation cover, which influences carbon storage and surface albedo. While all available GCMs indicate that the positive feedbacks surpass the negative ones thus amplifying the effects of radiative forcing, large uncertainties associated with crucial feedback mechanisms — particularly those related to water vapor and cloud formation — remain substantial. A doubling of atmospheric CO 2 from pre-industrial levels to 560 ppm is estimated to increase ra diative forcing by approximately ∆ F 2 × CO 2 = 3.7 W/m at the Earth’s surface. Under idealized assumptions —
neglecting feedbacks and treating Earth as a black body governed by the Stefan-Boltzmann law — this forcing would theoretically result in ∼ 1°C warming upon restoration of energy balance: ∆ T 2 × CO 2 = ∆ F 2 × CO 2 /4 σT ≈
1°C.
However, the Coupled Model Intercomparison Project Phase 6 GCMs adopted in AR6 estimate equilibrium climate sensitivity (ECS) — the projected warming at equilibrium due to a CO 2 doubling — ranging from 1.8°C to 5.6°C, reflecting substantial theoretical uncertainty in the net climate feedback amplification. The development of GCMs has been organized under the Coupled Model Intercomparison Project, a global collaborative initiative aimed at advancing climate modeling capabilities and understanding climate change processes. Initiated in 1995 by the World
Climate Research Programme’s (WCRP) Working Group on Coupled Modeling (WGCM), CMIP operates in phases:
- CMIP1 & CMIP2 — Developed during the 1990s, comprising 18 models;
- CMIP3 — Published in the mid-2000s, including 20 models used for AR4;
- CMIP5 — Conducted between 2010 and 2014, integrating 40 models from over 20 international groups for AR5;
- CMIP6 — Initiated in 2013 and ongoing, incorporating 55 models that formed the basis for AR6. Through CMIP, the scientific community continues to refine the GCMs, yet uncertainties in feedback processes and ECS highlight the need for ongoing improvements in climate modeling physical reliability and accuracy. 2.3 Summary of the GCM results supporting the AGWT
Figure 1 summarizes the findings of the GCMs developed during the Coupled Model Intercomparison Project
(CMIP) phases 3, 5 and 6. Figures 1A and 1C illustrate the effective radiative forcing functions utilized in the CMIP5 and CMIP6 GCMs, respectively, while Figures 1B and 1D present the observed global surface temperature record (black) alongside the GCM simulations generated under two scenarios: one including only natural forcings (solar + volcanic) and the other combining both natural and anthropogenic
forcings. Figures 1A and 1C show that the combined contributions of the solar and volcanic effective radiative forc ings are substantially smaller relative to the cumulative impact of anthropogenic forcings. Solar forcing ex hibits a modest 11-year cycle superimposed on an almost negligible upward trend, while volcanic forcing is characterized by sharp negative spikes resulting from major eruptions. These volcanic spikes induce short term cooling effects lasting only a few years. The GCM simulations depicted in Figures 1B and 1D strongly support the Anthropogenic Global Warm ing Theory (AGWT). When GCMs are driven solely by solar and volcanic forcing functions — the only two natural components assumed to influence Earth’s climate — the numerical simulations fail to produce any substantial warming or cooling trends throughout the 20 [th] century. This indicates that, absent anthropogenic
contributions, the models predict a relatively stable climate from the pre-industrial era to present. Figure 2: Attributions of warming associated with the radiative forcing functions utilized in the CMIP6 GCMs from 1850–1900 to 2010–2019. Notably, natural components — including solar and volcanic drivers, as well as internal variability — are estimated to have contributed an average of 0 °C each. Thus, the observed warming is attributed to anthropogenic drivers alone. However, by incorporating anthropogenic radiative forcing functions, the GCMs successfully replicate the ob served global surface warming trend. This comparison implies that, according to these GCMs, nearly 100%
of the warming recorded since the 1850–1900 period is attributable to anthropogenic factors, as explicitly con
cluded in AR6. Figure 2 explicitly illustrates the attribution results derived from the CMIP6 models, showing the average warming contribution of radiative forcing components from 1850–1900 to 2010–2019. According to these GCMs, both natural (solar + volcanic) forcings and internal climate variability con tributed approximately 0°C to the observed warming. Instead, nearly 100% of the observed 1.07°C global sur face warming is attributed to anthropogenic forcings, with well-mixed greenhouse gases contributing ∼ 1.5°C
and anthropogenic aerosols offsetting ∼ 0.4°C of the warming. The CMIP6 GCMs are also employed to simulate future climate scenarios based on hypothetical radiative
forcing functions derived from Shared Socioeconomic Pathways (SSPs). The ones mainly adopted in the IPCC
AR6 are:
- SSP1-2.6 — low greenhouse gas emissions, with robust adaptation and mitigation measures leading to
Net-Zero CO 2 emissions between 2050–2075;
- SSP2-4.5 — intermediate emissions, where CO 2 levels remain near current levels until 2050 and subse
quently decline without achieving Net-Zero by 2100;
- SSP3-7.0 — high emissions, with CO 2 concentrations doubling by 2100 under minimal policy interven Figure 3: CMIP6 GCM ensemble mean simulations spanning from 1850 to 2100, employing historical effective radiative forcing functions from 1850 to 2014 and the forcing functions based on the SSP scenarios 1-2.6, 2-4.5, 3-7.0, and 5-8.5. Curve colors are scaled according to the equilibrium climate sensitivity (ECS) of the models. The right panels depict the risks and impacts of climate change in relation to various global Reasons for Concern (RFCs).. tion;
- SSP5-8.5 — very high emissions, with CO 2 levels tripling by 2075 under a worst-case scenario devoid of mitigation measures. Figure 3 shows the ensemble mean simulations of the CMIP6 GCMs spanning 1850–2100. These simulations adopt historical radiative forcing functions from 1850–2014 and SSP-derived forc ing functions for 2015–2100. The color-coded curves correspond to the Equilibrium Climate Sensitivity (ECS)
values of the models.
Results indicate that the global surface temperature could rise significantly — potentially up to 8°C relative to the 1850–1900 reference period — if SSP5-8.5 is implemented and the ECS value is high
. The right panels of Figure 3 illustrate the projected impacts and risks of climate change associated with various global Reasons for Concern (RFCs).
These projections suggest that only SSP1-2.6, which employs aggressive mitigation and Net-Zero policies, can limit the 21 [st] -century warming to below 2°C relative to pre industrial levels, which is the threshold identified as critical under the Paris Agreement. 2.4 Conclusion
Over the span of approximately three decades, from the publication of the First Assessment Report to the Sixth Assessment Report, the Intergovernmental Panel on Climate Change
(IPCC) has significantly advanced its understanding of the role of anthropogenic emissions in driving global warming. In the 1990s the IPCC posited that both natural mechanisms and human activities could have con
∼ tributed roughly equally to the observed warming of the 20 [th] century. However, since the years
2000s the prevailing scientific opinion has shifted, and the IPCC now asserts that human activ
∼ ities are almost exclusively responsible for the global warming and climate change observed from
1850–1900 to 2011–2020. The most recent assessment reports IPCC underscore this conclusion with striking clarity. As shown in Figure 2, the average contribution of natural factors — solar and volcanic forcing and internal natural variability — to global warming during the aforementioned period is estimated to be approximately 0°C. Consequently, from the CMIP GCM perspective, concerns about future climate warming due to additional
anthropogenic greenhouse gas (GHG) emissions are well-founded. However, this conclusion depends on the reliability of global surface temperature records and the robustness of the physical science underpinning global climate models (GCMs). Under the worst-case scenario, the SSP5-8.5, which assumes very high and accelerating GHG emissions without mitigation, the GCM projections indicate alarming potential warming of 4°C to 8°C by 2080–2100. Despite these concerning projections, the IPCC expresses low confidence in attributing changes in the frequency, severity, or extent of several climate impact drivers, such as: river floods,
frost, landslides, hydrological drought, drought, agricultural and ecological drought, fire weather, mean wind
speed, severe wind storms, tropical cyclones, sand and dust storms, heavy snow and ice storms, hail, snow
avalanches, coastal erosion, coastal flooding, marine heat waves, air pollution, and surface radiation. Con versely, AR6 identifies moderate-to-high confidence in climate impact drivers more directly linked to increas ing atmospheric CO 2 concentrations and global warming. These include: increases in mean air temperature,
extreme heat events, sea level, mean ocean temperature, ocean acidity, and ocean salinity; decreases in cold
spells, snow cover, glaciers, ice sheets, permafrost, lake ice, river ice, sea ice, and dissolved oxygen; regional variability in mean precipitation (increasing in some regions and decreasing in others).
This evolution of understanding underscores the complexity of the climate system and the importance of continuously refining projections through improved climate modeling and robust observational datasets. 3 Main challenges to the AGWT
Scientific critiques of the Anthropogenic Global Warming Theory (AGWT) emerge from diverse perspectives,
reflecting significant concerns about persistent physical uncertainties and the potential validity of alternative explanations for climate change. 3.1 Erroneous or unsatisfactory critiques
First of all, it is crucial to differentiate scientifically substantiated critiques from various misguided claims often circulating online, which tend to oversimplify the physics of climate change. One such incorrect argument asserts that additional CO 2 emissions cannot affect the climate due to a supposed saturation of the infrared
(IR) absorption bands of such gas. This claim is demonstrably inaccurate, as the CO 2 IR absorption bands have not reached their maximum capacity yet. This fact is also acknowledged by van Wijngaarden and Happer
— two noted skeptics of climate change alarmism — who calculated that doubling CO 2 concentrations from 400 to 800 ppm would reduce the upward IR heat flux by approximately 3 W/m at the mesopause altitude under standard atmospheric conditions without clouds, assuming a surface temperature of 288.7 K. This result is slightly lower and does not differ significantly from what already reported in the scientific literature and in the IPCC reports, and can be easily verified using the MODTRAN Infrared
[Light in the Atmosphere model (available online at https://climatemodels.uchicago.edu/modtran/, accessed](https://climatemodels.uchicago.edu/modtran/)
on April 10, 2025), which also estimates a downward IR heat flux at the surface of about 3.6 W/m under identical physical conditions. In fact, the CO 2 infrared (IR) absorption bands are quasi-saturated, leading to a logarithmic relationship between CO 2 concentration and radiative forcing. For instance, a doubling of atmospheric CO 2 concentration from 400 to 800 ppm results in a typically-estimated increase in radiative forcing of approximately 3.7 W/m,
yielding to a theoretical radiative forcing function of the type: ∆ F CO 2 ≈ 3.7 log 2 W/m with a
10% uncertainty; here P CO 2 is the CO 2 atmospheric concentration. This evidence directly contradicts the saturation hypothesis that incorrectly infers that any increase in CO 2 levels would result in a radiative forcing increase of 0.0 W/m . As already explained in Section 2.2, the CMIP6 GCMs
predict that a radiative forcing of 3.7 W/m could induce, at equilibrium, a warming from about 1.8 to 5.7°C,
depending on the modeled net feedback strength. It is important to realize that the principal scientific challenge lies not in debating the CO 2 saturation ar gument but rather in accurately determining the climate sensitivity to radiative forcings that depends on the sign and magnitude of the climate feedback, the actual forcings of the climate system, and the quantitative de tection of climate change. Addressing these complex scientific issues requires a detailed understanding of the climate system, of its astronomical environment and of its feedback mechanisms, domains that remain highly uncertain and form a critical focus of ongoing research, as elaborated below. van Wijngaarden and Happer expressed skepticism only toward climate change alarmism by arguing that the net climate feedback should predominantly be negative. This is a legitimate physical expectation that the authors supported by citing the findings of Lindzen et al. and Lindzen and Choi ob tained by comparing high-frequency deseasonalized fluctuations in sea surface temperatures and the concur rent fluctuations in top-of-atmosphere (TOA) outgoing radiation using ERBE and CERES satellite data from
1985 to 2008. However, van Wijngaarden and Happer specifically invoked also Le Chatelier’s Princi ple — which states that when a system at equilibrium experiences a disturbance, it will adjust to counteract the disturbance and establish anew equilibrium — to suggest that the climate system should inherently re sists radiative perturbations. Citing Le Chatelier’s Principle to conclude that the net climate feedback should be strictly negative appears to oversimplify the complexity of the climate system, which incorporates both negative feedbacks (such as increased cloud cover reflecting sunlight) and positive feedbacks (like ice-albedo
effects, where melting ice reduces reflectivity and accelerates warming). It is the interplay between these posi tive and negative feedbacks that ultimately determines the thermodynamic conditions of the new equilibrium of the climate system. The new equilibrium temperature will depend on the prevailing feedback mechanisms;
whether the net feedback is negative or positive just determines whether the resulting temperature deviates downward or upward from the level expected solely due to increased atmospheric CO 2, which is ∼ 1°C for
CO 2 doubling. Thus, in this regard, van Wijngaarden and Happer appear to express only an opinion against the possibility of a catastrophic runaway greenhouse effect scenario where Le Chate lier’s Principle is not satisfied because the new equilibrium is never reached. Such a catastrophic scenario did not occur even during the Cambrian Period when the Earth’s temperature was much higher than today and atmospheric CO 2 levels were estimated to be 4,000–5,000 ppm,
that is ten times larger than current levels. In this regard, van Wijngaarden and Happer do not appear to have actually developed a solid critique of the AGWT advocated by the IPCC, which is perfectly compatible with Le Chatelier’s Principle. Indeed, none of the CMIP GCMs used in IPCC reports predicts a catastrophic runaway greenhouse effect scenario. Only critiques grounded in empirical observations could offer a solid foundation for challenging the AGWT. In the following, Section 3 provides a summary of the primary scientific critiques of the AGWT outlined in
Section 2. It further sets the stage for the exploration of alternative interpretations of climate change, discussed in Sections 4 and 5. Together, these critiques underscore the complexity of the debates surrounding the causes and consequences of climate change and highlight the range of scientific opinions in this evolving research field.
Appendix B. In relation to Section 3.1, the figure below illustrates the infrared light spectra obtained using [MODTRAN (available at the web page: https://climatemodels.uchicago.edu/modtran/) in a standard](https://climatemodels.uchicago.edu/modtran/) atmosphere under the physical conditions shown in the right-hand inset. The MODTRAN model simulates the emission and absorption of infrared radiation in the atmosphere. The curves represent theoretical emission spectra at different atmospheric CO 2 concentrations: (green) 0 ppm, (blue) 400 ppm, and (red) 800 ppm. The top-left panel displays the infrared light spectra observed at the surface of the atmosphere looking upward. The top-right panel shows the spectra at the top of the atmosphere looking downward; this figure closely aligns with the results obtained by van Wijngaarden and Happer. The total energy flux from all infrared light is labeled as Upward IR Heat Flux, F , measured in units of W / m . The quantities ∆ Fin the upper inserts indicate the variation in radiative forcing relative to the baseline value at 400 ppm. The bottom panel illustrates how radiative forcing changes as a function of CO 2 concentration relative to the pre-industrial level of 280 ppm. The blue curve represents ∆ F values obtained with MODTRAN, while the red curve corresponds to the traditionally used approximation function ∆ F = 3.7 log 2 .
in crisis ” and warning that unmitigated climate change poses the 21 [st] -century “ greatest threat to global public health ”. These appeals align with the commitments under the Paris
Agreement adopted at the United Nations Conference of the Parties in 2015. Despite claims of scientific consensus, skepticism persists among scientists and the public due to unre solved uncertainties and concerns surrounding these assertions. Studies suggesting overwhelming agreement among climate scientists — often citing figures such as 97% or even 99% —
are frequently interpreted as evidence of consensus on AGWT. However, critics challenge such conclusions, pointing to statistical flaws and misleading interpretations, which rely on selective datasets and imprecise survey methodologies. A case in point is the ambiguous nature of the statement “ humans are causing global warming ”. This statement can be interpreted to mean that nearly all observed warming is due to anthro pogenic activities, as asserted by the AGWT and explicitly claimed by the IPCC. However, the same statement could also mean that only a portion of the warming is attributable to human influence,
reflecting earlier IPCC reports such as FAR and SAR. Reliable surveys must, therefore, distin guish between these divergent attribution scenarios, as their implications for climate science and assessments of future risks differ significantly. When surveys adopt clearer attribution distinctions, the diversity of scientific opinions on climate change becomes evident. Broadly, there is general agreement among scientists on qualitative aspects such as that global warming has occurred since 1850–1900, the greenhouse effect is real, anthropogenic emissions have exacerbated it, and this has contributed to warming over the past century. However, there is no consensus on the precise quantitative attribution of natural versus anthropogenic factors to the observed warming. For example, Figure 4 summarizes a national survey by the American Meteorological Society revealing a wide range of opinions among respondents about the causes of climate change. While 96% agreed that climate change is occurring, only 29% attributed it mainly or entirely to human activities, while 38% attributed it mostly to human activities. Fourteen percent attributed climate change equally to human and natural causes, and smaller percentages leaned toward predominantly natural drivers or expressed uncertainty. This means that at least 71% of the respondents disagree with the IPCC AR6’s claim that humans are responsible for 100% of the observed global warming. Additionally, two-thirds of respondents believed that aggressive mitigation policies would only moderately or slightly reduce future warming. This diversity of opinions is not unexpected because it well aligns with the range of views documented in the IPCC assessment reports from
FAR to AR6. Inded, although the IPCC findings have evolved to assert in AR6 that anthropogenic factors are the sole cause of climate change since 1850–1900, shifts in scientific conclusions do not necessarily reflect genuine
progress, which requires reducing underlying uncertainties. In science, new findings that appear to challenge earlier results must rigorously justify the invalidation of previous conclusions, not just propose an alternative viewpoint. However, in geosciences, conflicting studies often coexist, with earlier findings persisting despite newer apparently contradictory research.
One prominent example of persistent uncertainty in climate science is the assessment of the equilibrium climate sensitivity (ECS), a crucial metric for gauging the response of the climate system to radiative forcing. From Charney et al. to AR6, the ECS uncertainty range has remained relatively unchanged
— if not broadened — as illustrated in Figure 5A. This persistent uncertainty underscores unresolved methodological and scientific challenges. Consensus-based arguments also risk logical fallacies, such as appeals to popularity or authority. In fact,
many individuals, including researchers in climate-related fields, may accept the IPCC conclusions without critically engaging with the uncertainties highlighted within the IPCC’s own reports. Consequently, reliance on such forms of “ consensus ” does little to resolve the crux of the climate debate regarding whether human activity accounts for 100% of observed warming between 1850–1900 and 2011–2020, as asserted by AR6, or whether a more moderate contribution might better align with actual scientific findings. If the latter opinion holds, the projected 21 [st] -century warming based on the CMIP5 and CMIP6 GCMs would be substantially lower, mitigating assessments of future climate change risks and hazards. The following subsections delve into key scientific open issues that question the reliability of the GCMs
and directly challenge the AGWT. These open key issues continue to be debated in the scientific literature. 3.3 The impossibility of testing the main prediction of the GCMs
The scientific method necessitates that the hypotheses, including physical models, are rigorously tested to ensure that their predictions align with empirical evidence. When evidence supports a hypothesis, the model may be retained; however, when results challenge it, the model must be discarded or revised, requiring the formulation of anew hypothesis or model. As discussed in Section 2 and illustrated in Figures 1B and 1D, the claim that human activity accounts for approximately 100% of the observed warming from 1850–1900 to 2011–2020 is derived solely from the climate simulations of the existing GCMs. These simulations rely on specific radiative forcing functions, which are assumed to be complete and accurate. However, the only tangible evidence is that there is no data fully con firming the main GCM prediction. More specifically, no data exists to demonstrate that, absent anthropogenic
forcing, the Earth’s climate would have remained stable from 1850–1900 to the present. Thus, such critical prediction of the GCMs cannot be empirically validated, as there is no “ twin Earth ” devoid of human influence from which to obtain the necessary data. Consequently, the absence of such data — as also reflected in Figures
1B and 1D — highlights the key limitation in the validation of these models. Therefore, the AGWT remains a hypothesis contingent upon the reliability of the current GCMs, which can only be “assumed” but not “proven” correct.
The fact that the primary prediction of these models has neither been experimentally validated nor is it likely to be so in the future, leaves open the possibility that the present
GCMs and their climate attribution assessments may be fundamentally flawed. While certain qualitative arguments, supported by paleoclimatic evidence suggest that the current warm period surpasses past warm peri Figure 5: [A] Historical progression of the equilibrium climate sensitivity (ECS) estimates from Charney et al. to AR6, with the addition of the recent estimates from Lewis and Scafetta. The lowest estimate — ECS = 1.1 ± 0.4 °C — assumes that the climate system is hypersensitive to solar activity variations; see Sections 4.2.3 and 4.3.2. [B] The equilibrium climate sensitivity (ECS) and [C] the transient climate response (TCR) of the CMIP6 GCMs. ods such as the Medieval Warm Period on a global scale, such evidence does not confirm the validity of the
AGWT’s climate attribution assessments proposed in the latest IPCC assessment report. Hockey stick reconstructions, as Crowley posited, may “ enhance confidence ” that anthropogenic forcings signifi
∼ cantly contributed to current warming but cannot definitively prove they are its sole cause. Crowley, for example, used hockey-stick temperature records and still estimated that “ about 25% of the 20 [th]
century temperature increase can be attributed to natural variability ”, which was primarily due to increased solar activity during the 19 [th] and 20 [th] centuries. Importantly, the GCMs themselves may be based on assumptions, mechanisms, and specific forcings that could inadequately capture the complexity of the Earth’s climate system. Such limitations can result in over estimated projections of anthropogenic warming and its impacts. For instance, natural processes like solar forcing and internal climate variability may not be accurately represented in the GCMs, a fact that could have yielded to potentially underestimate their contributions to observed climate variability. Indeed, natural pro cesses may have had a larger influence on climate variability than the 0°C warming predicted by the CMIP6
models. Additionally, many GCM mechanisms depend on parameterization, calibration, and tuning of free parame ters. These parameters are adjusted to enable the GCMs to approximate the observed climate system as closely as possible. Tuning involves iterative tests to identify parameter values that produce optimal agreement between model outputs and observational data. However, such tuning does not guarantee that the models are physically accurate. Parameter values can vary significantly when model mechanisms and forcings are altered, as demonstrated in various studies. Thus, the apparent agreement between the GCM predictions and observed warming from 1850–1900 to 2011–2020 under specific radiative forcing functions, as shown in Figure 1, may stem more from tuning methodologies rather than from intrinsic physical accuracy. 3.4 The GCMs’ failure in capturing natural climate variability
In scientific literature and in the same IPCC assessment reports there is growing evidence of physical uncer tainty that raises significant questions about the reliability of the GCMs. A key challenge lies in the inherent difficulty of rigorously validating these models as also argued above. This section explores some of the most pressing open questions currently under debate, including the pervasive issue of the GCMs’ inability to recon struct major patterns in natural climate variability. 3.4.1 The “ hot model ” problem
As shown in Figure 5, the CMIP6 GCMs predict a wide and inconsistent range of equilibrium climate sensi tivity (ECS) and transient climate response (TCR) values, spanning from 1.8°C to 5.6 °C and from 1.33°C to
2.79°C, respectively. This large uncertainty range presents significant challenges to accurately evaluating the risks and potential hazards of future climate change, as suggested in Figure 3. The ECS uncertainty is attributed to variations in the mechanisms, parameterizations, and free parameter settings employed by different GCMs. These differences significantly influence the modeling of key climate
feedbacks, such as water vapor and cloud formation. The discrepancies among GCM pro jections become especially pronounced outside the historical period, where internal free parameter tuning is not possible. For instance, under the same Shared Socioeconomic Pathways (SSPs), the GCMs display diver gent climate projections for the 21 [st] century, as illustrated in Figure 3 with curves color-coded by ECS values ranging from low [blue] to high [red] values. A major unresolved question in climate science is how to constrain the ECSand TCR values to better approximate the true sensitivity and response times of the climate system. While the GCMs estimate ECS to fall within 1.8°C to 5.6°C, broader literature reports ranges as wide as 0.5°C to 10°C. IPCC proposed a likely ECS range from 2.5°C to 4.0°C and a very likely range from
2.0°C to 5.0°C, based on the assessment by Sherwood et al., who used multiple lines of evidence by emerging constraints and paleoclimate data. However, such assessment remains contentious. For example, the reanalysis of the same line of evidences proposed by Lewis directly challenged the assessment by Sherwood et al. by highlighting a num Figure 6: [A, B, C] The CMIP6 GCM simulations separated into three macro-GCM ensembles based on their ECS values, as represented by a colored scale. The synthetic temperature records are compared with the HadCRUT v5.0 (infilled data) global surface temperatures and the UAH-MSU lt v6.1 satellite-based temperature dataset. [D, E] Temperature changes from 1980–1990 to 2012– 2022, as simulated by the 42 adopted GCMs, are evaluated against the warming observed in the HadCRUT v5.0 and UAH-MSU lt v. 6.1 records, against the ECSand TCR values of the GCMs.. ber of possible statistical errors and other shortcomings. Lewis estimated that the same evidence could suggest a significantly lower ECS range, with a median of 2.16°C. Other studies propose even lower values centered between 0.5°C to 2°C. Similar low ECS estimates have been reported by Scafetta. See Figure 5A. In general, Gervais, Knutti et al.
and Rugenstein et al. highlighted that already in the early 2010s, several authors noted that cli mate sensitivity estimates from climate models differed significantly from those based on observed warming and radiative balance studies, with the latter suggesting much lower values. Attempts to solve this conun drum — for example by assessing whether ECS may be variable under different time-scales and/or physical conditions — are under investigation. ECSand TCR values are critical for understanding the climate’s sensitivity to radiative forcing and for estimating expected future warming under different SSP scenarios. Notably, the GCM derived ECSand TCR estimates cannot be treated as repeated measurements of a single observable but rather as diverse theoretical estimates. Consequently, the true ECSand TCR values may fall either within or outside the ranges reported by the GCMs. For example, the actual ECSand TCR values could potentially be lower than those predicted by any GCM, as suggested in multiple studies. Several lines of evidence indicate that the GCMs may inadequately represent key aspects of climate change. For example, the CMIP6 GCMs — particularly those with ECS values exceeding 3°C — tend to overestimate the warming observed from 1980 to 2022. This persistent bias, which is undisputed for high-ECS GCMs, is widely referred to as the “ hot model ” problem. Furthermore,
the GCMs significantly overestimate warming trends between 1979 and 2014 across the vertical atmospheric
profile, particularly in the upper tropical troposphere (left), alongside its multi-scale acceleration analysis (MSAA) colored diagram (right). North Atlantic Oscillation (NAO) from Luterbacher et al. (left), alongside its MSAA colored diagram (right). The diagrams highlight a consistent 55–70-year oscillation since 1700, represented by alternating green and red regions within the 30–110-year scale.. Hudson, 2023). This problem is documented by the IPCC and, in the literature,
it is referred to as the “ missing hot-spot ” conundrum. In fact, while models predict a strong warming in the upper tropical troposphere, several observations suggest a weaker or absent warming in that region. Potential reasons for the missing hot-spot include data errors, natural variability, but, of course, also climate model
limitations. Figures 6A–C compare the CMIP6 GCM simulations against the HadCRUT5 global surface temperature record and
satellite-based UAH-MSU v. 6.1 record. The warm bias of the medium- and high-ECS
models is statistically significant. Figures 6D–E further highlight these biases, showing that the GCM-predicted
warming from 1980–1990 to 2012–2022 exceeds observed warming by the HadCRUT5 and
UAH-MSU v6.1. Figure 6 updates Scafetta, where this issue is discussed in more
details. The analysis shown in Figure 6 does not consider the years 2023–2024, which were marked by a sud den temperature spike possibly linked to the Hunga Tonga-Hunga Ha‘apai eruption in 2022. This submarine volcanic eruption significantly increased stratospheric water vapor by ~10%, potentially exerting a positive
radiative forcing effect. However, even accounting for this anomaly,
the warming estimates for 2014–2024 remain below most of the GCM projections. In the future, the rapid cooling that has been observing since the mid-2024 peak could further exacerbate the “ hot model ” problem rather than mitigate it. 3.4.2 The 50–70-year cycle and its implications
The CMIP3 and CMIP5 GCMs have been identified as failing to adequately reconstruct observed climate oscil lations on decadal to multidecadal timescales. Specifically, the climate system exhibits a distinct quasi-60-year oscillation that these models fail to replicate. This natural oscillation has resulted in alternating warming (w) and cooling (c) phases superimposed on a long-term secular trend: 1850–1880 (w),
1880–1910 (c), 1910–1940 (w), 1940–1970 (c), 1970–2000 (w), and possibly 2000–2030? (c). Evidence of this oscillation has also been recently observed in sunshine hours over central Europe, suggesting a direct link between surface temperatures and cloud cover. A prominent manifestation of a quasi-60-year oscillation can be seen in the Atlantic Multidecadal Os cillation (AMO) index, which tracks the variability of the North Atlantic sea surface temperatures (SSTs)
.
The AMO index is calculated by removing the linear trend from the
SSTs observed within the region, thereby isolating the oscillation from the broader secular warming trend that may still have both natural and anthropogenic origins. This oscillation has been documented in climate data since 1700, it is recognized as a defining feature of the North
Atlantic ocean-atmosphere variability over the past 8,000 years, and it is found also in the
paleoclimatic reconstruction of the Northern Hemisphere by Mann et al. during the last millennium, as well as in other long-term climate records. For instance, Figure 7 compares the global sea level record and the North Atlantic
Oscillation (NAO) record since 1700. The right panels feature their multi-scale accel eration analysis (MSAA) plot introduced by Scafetta. The analyses highlight the 50–70-year oscillation evident in both datasets. Such spectral coherence between two independent yet physically coupled indices —
AMO and NAO — underscores the assertion that this quasi-60-year oscillation is a genuine dynamical feature of the climate system, rather than an artifact. The warming observed from the 1910s to the 1940s, followed by the cooling from the 1940s to the 1970s, clearly appeared in some figures published in the IPCC FAR. Notably, this oscillatory pattern shows no correlation with the anthropogenic forcing functions, which have monotonically accelerated since 1750. Figure 8 provides further evidence by comparing observed oceanic surface temperatures in the region
, as captured by: (a) CMIP6 GCM ensemble simulations; (b) HadSST4 records and NOAA/CIRES/DOE 20 [th] Century Reanalysis V3; and (c) the AMO index from NOAA. The data reveal that the GCMs fail to replicate the amplitude of the natural oscillation observed in the historical
∼ record. For instance, while GCMs predict a monotonic warming trend from 1880 to 1960 — with oc casional interruptions from volcanic events — the data show a distinct oscillatory pattern, alternating between warming and cooling phases with amplitudes up to 0.4–0.5°C. The existence of a natural 50–70-year cycle not modeled by the CMIP6 GCMs challenges the AGWT, particularly because the observed warming from the 1970s to 2000s is strikingly similar to the warming from the 1910s to 1940s. This suggests that natural variability, such as the quasi-60-year
oscillation, may have contributed to the recent warming trends, contrary to the finding of the GCMs attributing all 1970–2000 warming solely to anthropogenic forces. Figures 8A–B estimate the warming from 1940 to 2020 as +0.8°C for the GCMs and +0.4°C for the observed data, which further demonstrates the discrepancy between the GCM simulations and the empirical records. Discrepancies between model predictions and observations spanning decadals and longer timescales are
significant. Indeed, climate models are expected to reproduce changes occurring over periods exceeding ∼ 15
years, whether driven by external forcings or internal variability. For example, Knight et al. remarked that “ simulations rule out zero trends for intervals of 15 year or more ” implying that observing such prolonged data inconsistencies with the GCM expected warming rates signals physical flaws in the models. Figure 8: [A] CMIP6 GCM ensemble temperature simulation for the North Atlantic Ocean surface. [B] Sea surface temperature records for the same North Atlantic region derived from HadSST4 and the NOAA/CIRES/DOE 20 [th] Century Reanalysis V3. The side panel shows the approximate warming from 1940 to 2020: +0.8 °C based on GCM simulations; and +0.4°C based on observational data. [C] Atlantic Multidecadal Oscillation (AMO) index, calculated as the linearly detrended North Atlantic Ocean surface temperature anomalies from 1856 to 2022. The insert in [A] depicts the approximate North Atlantic region used to define the AMO index. Similar multi-decadal discrepancies are evident in precipitation patterns and trends.
Both CMIP5 and
CMIP6 GCMs struggle to model also such climatic patterns accurately, as demonstrated by various studies
. Figure 9: Climate reconstructions derived from 1,272 scientific studies on the “Medieval Warm Period” (MWP) spanning from 1000–1200 AD. Each point represents the location of a specific study where the color represents the observed climate: warm (red), cool (blue), dry (yellow), wet (green), and no trend or
3.4.3 The Medieval Warm Period
Global climate records from the past 1500 years reveal two prominent periods of anomalous temperatures predating the 20 [th] century: the Medieval Warm Period (MWP), spanning approximately 900–1300 AD, and the Little Ice Age (LIA), occurring roughly from 1400 to 1850 AD. The magnitude and spatial patterns of the MWP have been a focal point of scientific debate, particularly following the introduction of the
hockey-stick temperature graph by Mann et al., which minimized its significance. A wealth of evidence,
however, supports the existence of a distinct MWP and LIA, with regions such as Europe, the North Atlantic and China having potentially experienced temperatures comparable to or exceeding those of the modern warm
period. While discussions continue on whether the MWP was a global or predominantly regional phenomenon Figure 10: The Medieval Warm Period (MWP) temperature conundrum. [A] Comparison of simulated versus reconstructed Northern Hemisphere temperature anomalies over the last millennium, including the Medieval Climate Anomaly (MCA), Little Ice Age (LIA), and 20 [th] century.
This failure is particularly apparent in the CMIP6 models, where simulations exhibit a climatic
near-stationarity between 850 and 1900 AD, apart from brief cooling periods triggered by volcanic eruptions. Figure 10C reinforces this point by comparing an empirical simulation of the multi-model mean (cyan curve)
with the Moberg et al. reconstruction (red curve), calibrated with the HadCRUT dataset (green curve)
since 1850, as proposed by Scafetta, who attributed this modeling failure to inadequate repre sentation of solar forcing in the CMIP5 and CMIP6 GCMs. The GCMs assume minimal secular solar variability as Section 4.2 discusses in more detail. The IPCC explicitly acknowledges “ larger disagreements between models and temperature reconstructions ” before the year 1300. Notably, AR6 emphasized the PAGES-2K Consortium temperature
reconstruction, which dampens the MWP anomaly compared to alternative reconstructions. This decision to exclusively utilize the PAGES-2K Consortium paleoclimatic proxy re construction has been recently criticized as reductive because it oversimplifies the physical complexity of the Common Era climate variability as highlighted in the scientific literature. In conclusion, the CMIP6 GCMs predict an approximately stable natural climate extending from 800 AD
to the present when only natural (solar + volcanic) radiative forcings are applied. However, this prediction conflicts with extensive paleoclimatic evidence and historical records documenting pronounced cooling from the MWP to the LIA. All recent multi-proxy reconstructions consistently capture a significant temperature decline over this inter val, although the extent of this cooling depends on the adopted paleoclimatic record. The failure of the GCMs
to replicate such natural variability underscores severe limitations in their ability to accurately reconstruct past climate dynamics.
Reconstructing the warm periods of the pre-industrial era is an essential condition in ensur ing the reliability of the GCM assessments regarding the attribution of the global surface warming reported from 1850–1900 to 2010–2019. This is because the recent global surface warming may have been par tially driven by the same natural mechanisms (e.g. solar forcing) that caused other warm periods over the past
millennia. 3.4.4 The Holocene temperature conundrum
The limitations of the GCMs in simulating natural climate change become increasingly apparent when the entirety of the Holocene epoch is analyzed. The mismatch between data and model predictions over this prolonged period, termed the “ Holocene temperature conundrum ”, raises further substantial concerns about the reliability of the existing global climate models. The core of this conundrum lies in the gradual and near-monotonic increase in atmospheric greenhouse gases — carbon dioxide and methane — likely driven by processes such as oceanic degassing and permafrost melting. Over this epoch, the climate models predict a quasi-monotonic
warming due to the rise in the greenhouse gas concentrations. However, paleoclimatic Figure 11: The Holocene temperature conundrum: (black line) global median temperature proxy from Kaufman et al.; (red line) global climate model ensemble from Liu et al.; (green dots) EPICA Dome-C CO 2 record from Bereiter et al.; (blue line) Antarctic temperature proxy from Kaufman et al.. proxies derived from natural archives — including ice cores, sediment layers, and biological indicators —
consistently suggest the occurrence of an early-to-mid Holocene Thermal Maximum (HTM), which is also known as the “ Holocene Optimum ”. The HTM contradicts the models’ predictions. Empirical evidence supports a significantly warm HTM, with summer temperatures in East Greenland during the early Holocene estimated to be at least 3°C higher than present. Similar warming trends were documented in central Europe, the eastern Mediterranean
, in Japan, and in numerous other regions. Antarctica appears to be the notable exception, showing a gradual warming rather than an HTM. Nevertheless,
even this claim is debated, with alternative studies suggesting the existence of the HTM in Antarctica as well
. On a global scale, several paleoclimatic reconstructions suggest that the HTM was warmer than present-day temperatures, although some estimates, such as those in Figure 11,
appear to mitigate its intensity. Additional support for a warm HTM comes from other studies showing that global mean sea levels were higher than today during the mid-Holocene, and showing evidence of the African Humid
Period (also known as the “ Green Sahara ”), which occurred between approximately 14,800 and 5,500 years
ago. After the HTM, the surface temperatures declined throughout the late Holocene, culminating in the minimum recorded during the Little Ice Age. This dynamics correlates strongly with the changes in mean daily insolation at 65°N on summer solstices due to variations in the orbital parameters of the Earth.](https://biocycle.atmos.colostate.edu/shiny/Milankovitch/)
Efforts to address the Holocene temperature conundrum have included investigating seasonal temperature variations since many paleoclimatic proxies actually represent summer temperatures, as suggested by Bova et
al.. However, such interpretations have been challenged by other researchers confirming the HTM also in annual temperature proxies. The Holocene temperature conundrum ultimately casts doubt on the accuracy of either paleoclimatic re constructions or the climate models, or both. However, the large body of empirical evidence supporting a Figure 12: Synchronous quasi-millennial cycles observed in: [A] a reconstruction of total solar irradiance; [B] a reconstruction of the Northern Hemisphere surface temperatures; [C] a reconstruction of the summer European temperatures. prominent HTM implies that even the latest climate models significantly overestimate the impact of green house gases relative to other factors, such as the climatic impact of variations in solar radiation input. Additionally, the Holocene epoch appears marked by pronounced quasi-millennial oscillations. Current climate models lack the capability to re construct these quasi-periodic warm and cool periods, as evidenced by their failure to accurately simulate the latest past warm and cool periods such as the cooling from the Medieval Warm Period (MWP) to the Little Ice
Age (LIA). 3.5 Conclusion: assessing the CMIP GCMs versus natural climate variability
The evidence presented above highlights critical limitations in the Global Climate Models (GCMs), casting doubts on the robustness of the Anthropogenic Global Warming Theory (AGWT). AGWT is heavily reliant on the climate attribution analyses derived from the GCMs, yet substantial empirical data challenges the validity of these models. Specifically, the GCMs have consistently failed to reproduce natural climate variability across multiple timescales throughout the Holocene, particularly during key historical warm periods. Furthermore,
their central prediction — that Earth’s climate would have remained stable from 1850–1900 to 2011–2020 in the absence of anthropogenic forcing — cannot be validated because of lack of data. The notion that the discrep ancies between models and observational data may arise solely from data uncertainties does not resolve the presented challenges, as scientific models must ultimately be validated through empirical evidence. Conse quently, the AGWT promoted by the IPCC cannot be considered supported by empirical evidence. The inability of the CMIP3, CMIP5 and CMIP6 GCMs to accurately reconstruct natural climate variability
— including the Medieval Warm Period (MWP), and other extended warm periods of the past such as the
Holocene Thermal Maximum (HTM) — raises fundamental questions. Specifically, concerns arise regarding whether these models employ appropriate natural radiative forcings and incorporate essential physical mech anisms necessary to accurately simulate past warm periods. This shortcoming suggests that the observed warming from 1850–1900 to 2011–2020 may not be exclusively attributable to anthropogenic activities because it cannot be ruled out that it was partly induced by the same mechanisms responsible for the other natural warm periods observed throughout the Holocene; mechanisms that are absent or remain insufficiently imple mented in the current GCMs because of the models’ failure in reconstructing the warm periods of the past. For example, a significant quasi-millennial oscillation has been documented in the climate system over the past ∼ 9,000 years.
This oscillation is evident in records such as the Greenland GISP2 ice core and many others. Notably, the Medieval
Warm Period (MWP) was preceded by the Roman Warm Period (RWP), which occurred roughly 900–1000
years earlier. The existence of this quasi-millennial cycle — expected to peak again in the second half of the 21 [st] century for solar and astronomical reasons — contrasts sharply with the AGWT’s assertion that the warming observed since 1850–1900 is solely
due to human emissions. Figure 12 illustrates this quasi-millennial cycle by comparing two paleoclimatic temperature reconstruc tions of the Northern Hemisphere and summer temperatures in Europe with a reconstruction of total solar irradiance based on the C record. The analysis highlights three warm periods — the Roman, the Medieval, and the contemporary
warm periods — which appear equally warm, along with two cold periods: one during the
Dark Ages (DACP) and one, even colder, during the Little Ice Age (LIA). This evidence suggests that the warming observed in the 20 [th] century was partly driven by the warm phase of a
quasi-millennial natural cycle driven by solar activity, which itself exhibits a similar cyclical variation. Further discussion on this issue is provided in Section 4.2. 4 Alternative approaches to the detection, attribution, and modeling of climate change
This section explores several critical and unresolved challenges concerning the reliability of global surface tem perature records used for detecting climate change, as well as how the solar effect on the climate is addressed in modeling frameworks. 4.1 Challenges in assessing the reliability of global surface temperature records
The Intergovernmental Panel on Climate Change (IPCC) Sixth Assessment Report states that the
“ Global surface temperature was 1.09 °C higher in 2011–2020 than 1850–1900, with larger increases over land than over the ocean ”. Despite this, determining the precise magnitude of the global warming between 1850–1900 and 2011–2020 remains contentious due to the sensi tivity of the outcomes to methodological decisions, which has led to notable discrepancies among alternative temperature datasets. Global surface temperature anomalies are constructed from observational records collected at meteorolog ical stations distributed worldwide and from sea surface temperature data obtained from buoys, ships, and ocean reference stations. The processing methodology involves calculating monthly mean temperatures at each station from daily maximum and minimum values, from which annual averages are derived. These av erages are then normalized relative to a chosen baseline period and aggregated to produce yearly global temperature anomalies. However, significant methodological issues persist throughout these
stages. A prominent concern is the uneven geographical distribution of the observational networks, such as weather stations and shipping routes. This issue is typically addressed through gridded averaging, wherein the Earth’s surface is divided into cells based on latitude and longitude, and temperature anomalies for each cell are averaged to produce global estimates. Nonetheless, historical underrepresentation of vast areas
— such as the Southern Hemisphere and sparsely inhabited regions like deserts, polar regions, forests, and expansive oceanic zones — introduces substantial uncertainties. For instance, prior to 1950, the majority of the temperature records originated from North America, Europe, and East Asia, complicating efforts to accurately reconstruct global temperature anomalies during earlier historical periods. Furthermore, gaps in station operation, changes in instrumentation, and station relocations lead to missing data and biases, undermining temperature trend analyses. Collectively, spatial and temporal in consistencies in local temperature records pose significant obstacles to accurately assessing global temperature
trends. Another fundamental issue pertains to the suitability of local temperature records for analyzing long-term
climate trends. Weather stations are primarily designed to monitor short-term meteorological variations rather than long-term climatic changes. Over extended periods, environmental transformations surrounding stations
— such as urbanization, deforestation, or afforestation — alongside station replacements and relocations, can introduce systematic non-climatic biases into the data. These biases, if predominantly aligned in one direction,
could significantly distort ensemble averages and, consequently, affect global temperature anomaly computa tions.
As a result, the integrity of the temperature records as indicators of long-term
climatic trends demands critical evaluation. 4.1.1 The urban heat island effect
Urban areas are consistently warmer than their rural counterparts due to several contributing factors. In cities,
natural soil is frequently replaced by heat-absorbing artificial materials, while high-rise buildings disrupt air flow and create heat-trapping canyon effects. Additionally, in urban landscapes rainwater drains, unlike in rural areas where water moistens the soil and facilitates cooling via evaporation. Vegetation, which is more prevalent in rural areas, utilizes sunlight for photosynthesis rather than converting it into heat. Furthermore,
anthropogenic activities, including vehicular emissions, building heating and the use of air conditioning sys tems, intensify urban heating. This cumulative phenomenon is widely recognized as the “ urban heat island ”
(UHI) effect. As urbanization progresses, the temperature recorded by proximate weather stations tends to increase,
reflecting enhanced UHI effects. This issue is particularly significant given that urban areas account for less than 4% of the Earth’s land surface, yet a substantial proportion of weather stations within the Global Historical
Climatology Network (GHCN) are situated in urban settings. Additionally, the ongoing shift of weather stations from rural to urban environments exacerbates the problem. The global marked increase in urbanization since 1900 and, in particular, after 1950 underscores the growing relevance of this issue. The IPCC Sixth Assessment Report asserts that global surface temperature records are minimally affected by UHI bias, estimating its contribution to global warming to be less than 10%, thereby suggesting it can be disregarded for first-order analyses. However, a study by Helbling and Meierrieks,
which analyzed data from 118 countries spanning from 1960 to 2016, identified a strong correlation between rising temperatures and urbanization rates.
For instance, Moberg et al. argued that tree-ring records are more effective at capturing the high-frequency components of climate signals while attenuating the secular and millennial low-frequency modulation, potentially due to biological adaptations of Had-CRU UAH 6.1 Had-CRU – UAH % STAR5 Had-CRU – STAR % region ( °C) ( °C) ( °C) % ( °C) ( °C) % Global (Land+Ocean) 0.73 ± 0.02 0.58 ± 0.02 0.15 ± 0.03 -21% ± 04% 0.53 ± 0.02 +0.20 ± 0.03 -27% ± 04% Global (Land) 1.03 ± 0.15 0.79 ± 0.02 0.24 ± 0.15 -23% ± 14% 0.68 ± 0.02 +0.35 ± 0.15 -34% ± 14% Global (Ocean) 0.58 ± 0.02 0.49 ± 0.02 0.09 ± 0.03 -16% ± 05% 0.46 ± 0.02 +0.12 ± 0.03 -21% ± 05% NH (Land+Ocean) 1.03 ± 0.03 0.69 ± 0.02 0.34 ± 0.04 -33% ± 04% 0.72 ± 0.02 +0.31 ± 0.04 -30% ± 04% NH (Land) 1.24 ± 0.15 0.83 ± 0.02 0.41 ± 0.15 -33% ± 12% NH (Ocean) 0.77 ± 0.02 0.59 ± 0.02 0.18 ± 0.03 -23% ± 04% SH (Land+Ocean) 0.42 ± 0.05 0.46 ± 0.02 -0.04 ± 0.06 +10% ± 14% 0.34 ± 0.02 +0.08 ± 0.06 -19% ± 14% SH (Land) 0.62 ± 0.31 0.70 ± 0.02 -0.08 ± 0.31 +12% ± 49% SH (Ocean) 0.40 ± 0.02 0.42 ± 0.02 -0.02 ± 0.03 +5% ± 07%
Table 1: Temperature increase from January 2014 to December 2024 relative to the baseline period of January 1981 to December 1990, as determined from surface temperature records compared to the satellite UAH-MSU v6.1 and NOAA-STAR v5.0 lower troposphere temperature record. These records are illustrated in Figure 14. Error bars represent approximately the 95% confidence interval. For UAH-MSU and NOAA-STAR v5.0, the error bars are not explicitly reported but assumed here to match the global surface temperature error across all regions. the trees to changing climatic conditions. Nevertheless, the substantial and anomalous divergence observed af ter 1980 together with the divergence observed with the record from the rural-only
stations, casts doubt on the accuracy of the adopted climatic temperature records. Figure 14 highlights critical concerns regarding the reliability of the current global surface temperature
records. It presents a comparative analysis of the HadCRUT5 (global), CRUTEM5 (land), and HadSST (ocean)
surface temperature datasets with the satellite based UAH MSU v.6.1 lower troposphere temperature records, which is available since
December 1978. Additionally, the figure delineates results by hemisphere, distinguishing the Northern Hemi sphere from the Southern Hemisphere
. The warming of the lower troposphere should approximate the expected surface warming across suffi ciently large spatial scales. However, the GCMs predict that the troposphere — particularly at its top — should exhibit greater warming than at the surface,
as illustrated in the IPCC. Contrary to these predictions, Figure 14 reveals that satellite observations report a markedly lower warming rate relative to global surface temperature records. Specifically, the surface records exhibit a excess warming of approximately 21%, which equates to a global excess warming of roughly +0.15°C from 1981–1990 to 2014–2024, a significant discrepancy. Furthermore, the figure indicates pronounced surface excess warming in the Northern Hemisphere: approximately 33% over land and 23% over ocean. In contrast, the surface and satellite temperature trends in the Southern Hemisphere
— across both land and ocean — align well within their uncertainties. Similarly, at the upper tropical troposphere the GCMs predict a “ hot-spot ” that is not observed in the data. The compatibility of surface and satellite temperature records in the Southern Hemisphere, as evidenced in Figure 14, supports the assumption that the warming trend in the two records should be comparable, im plying that the substantial warming bias observed in Northern Hemisphere land surface temperatures implies the influence of non-climatic factors, notably urban heat island (UHI) effects. Similarly, Northern Hemisphere sea surface temperatures display a slight warming bias relative to the satellite measurements, potentially at tributable to inadequate monitoring of the extensive polar regions. In such areas, missing data are recon structed using models, which may inadvertently introduce additional warming biases, as discussed by Scafetta
. The reduced land area and the lower population density in the Southern Hemisphere likely mitigate the impact of non-climatic warming biases unrelated to climate change.
If the warming trend indicated by the lower troposphere satellite temperature record offers a more reliable estimate of the actual global surface temperature trend, the above findings further question the accuracy of the CMIP6 GCMs, as they would all appear to overestimate the actual warming, as noted in Section 3.3.1 and in Figure 6. The UAH-MSU lower troposphere temperature record has been subject to debate,
particularly following adjustments to the Remote Sensing System (RSS) dataset in 2014. These revisions led to the development of an alternative satellite-based temperature record by Mears and Wentz, aligning more closely with the accepted surface-based global temperature records. The NOAA-STAR v. 4.0 dataset also reflected similar trends, seemingly in contradiction to the UAH-MSU findings. However,
the UAH-MSU-lt dataset has demonstrated consistency with global warming trends derived from the Inte grated Global Radiosonde Archive (IGRA) and reanalysis datasets. Additionally, recent updates to the NOAA-STAR records have acknowledged prior errors, culminating in the
NOAA-STAR v. 5.0 dataset. This latest dataset exhibits slightly lower warming from 1981–1990 to 2014–2024
relative to UAH-MSU. Collectively, these observations suggest that the global surface temperature records may be significantly warm-biased due to improper data processing and
non-climatic influences at the surface, particularly over land. 4.1.3 The excessive Tmin warming relative to the Tmax warming
An alternative method for identifying non-climatic warming biases in surface temperature records has been ex plored by Scafetta and Ouyang and Scafetta. Their analysis revealed substantial regions within global land surface temperature datasets that exhibit anomalously high nighttime warming (Tmin) relative to daytime temperatures (Tmax). This finding diverges from the predictions of the GCMs, which typically suggest only moderate additional nighttime warming in comparison to daytime warming. Daytime surface warming is effectively mitigated by convective vertical air movements, facilitated by a relatively elevated boundary inversion layer. In contrast, nighttime warming forces a horizontal dispersion of warm air near the surface due to the typically lower position of the boundary inversion layer. In urban environments, this meteorological behavior expands urban heat island (UHI) effects during
night, resulting in a stronger influence on nearby thermometers at night compared to during day. Conse quently, as urban areas continue to grow, urbanization amplifies the warming trend in Tmin compared to
Tmax. Figure 15 illustrates the global spatial divergence between Tmin and Tmax across the periods 1945–1955
and 2013–2023, utilizing the CRU-TS4.08 land temperature data. Prominent orange-red
regions in the Northern Hemisphere, often forming localized warm clusters, indicate intense nighttime warm ing, which are often near urban centers. Conversely, the Southern Hemisphere exhibits a lower variability. Interestingly, even small urban centers can produce significant UHI effects. The darkest wide areas may reflect anomalies in the dataset, which could be potentially linked to regions exhibiting minimal warming in Tmin or influenced by phenomena such as urban cool island (UCI)
effects as in arid areas, in deforestation zones, or in regions where permafrost may be melting. 4.1.4 Urban blending and homogenization uncertainties
The above findings appear to underscore critical failures of the adopted “ homogenization ” processes. These are designed to correct biases in meteorological records caused by environmental, instrumental, or methodological changes. Homogenization algorithms aim to enhance the accuracy of temperature datasets by identifying and rectifying such inconsistencies, thus enabling accurate assessment of true climate trends. For instance, the Global Historical Climatology Network (GHCN) provides temperature datasets in both non homogenized and homogenized formats, with the latter used for constructing global climate records. Despite their intended function, these algorithms exhibit limitations.
found that the homogenized temperature records can change each time the raw temperature records are reprocessed by such homogenization algorithms. Figure 15: [Top] Diagram illustrating boundary layer structure over a city and its surrounding areas: a high daytime boundary layer facilitates heat dispersion, while a low nocturnal boundary layer retains hot air near the surface. [Bottom] Global map of the divergence between T min and T max comparing the periods 1945–1955 and 2013–2023, based on the CRU-TS4.08 land temperature data..
Moreover, Katata et al. identified evidence of “ urban blending ” or aliasing of trend biases within homogenized records. The blending artifact occurs when homogenization algorithms inadvertently transfer portions of the warm bias from heavily affected urban stations to less affected nearby stations, thereby dis torting temperature records. As urbanization expands globally, these blending effects may have contributed to artificial warming biases in global surface temperature datasets. This phenomenon could explain the above observed discrepancies when comparing surface temperature records against rural-only datasets, satellite based records, tree-ring chronologies, or the observed excessive divergence between daytime and nighttime temperature trends. Figure 16: Comparison of global temperature records: HadCRUT3, HadCRUT4, and HadCRUT5, including both the infilled and noninfilled versions. 4.1.5 The “disappearance” of the 2000–2014 temperature “ pause ” or “ hiatus ”
Global temperature datasets used for climate change analyses are subject to continuous updates, often reflect ing substantial changes between successive versions. For example, the transition from HadCRUT3 to HadCRUT4 and subsequently to HadCRUT5 resulted in notable temperature alterations during the overlapping pe riods. In particular, Figure 16 highlights increasingly larger warming trends in these updated records after
2000, with increases up to 20% by 2014. These modifications are likely to be attributable to the incorporation of additional input data, adjustments in homogenization algorithms, and the inclusion of
model-based synthetic data to fill uncovered regions. Such changes may have been also influenced by efforts to mitigate the discrepancies observed between the GCM predictions and earlier datasets like HadCRUT3,
where the data-model divergences had become increasingly apparent. In
fact, the latest revisions of the global surface temperature records effectively removed the well documented temperature “ pause ” or “ hiatus ” observed from 2000 to 2014 in several records, whose existence was acknowl edged also by the IPCC. However, this 2000–2014 hiatus is still well visible in the latest ocean and satellite-based temperature records, raising further questions about the reliability of the latest global surface temperature records, in particular, over land. In summary, while substantial evidence supports a global surface warming between 1850–1900 and 2011–
2020, several factors — including comparisons of sea and land records with model projections
— indicate that the actual global surface temperature warming may be 15–25% lower than what reported by the IPCC.
The concerns surrounding the reliability of current temperature records merit further investigation and scrutiny. Figure 17: [A] Schematic deviations in the C cosmogenic record. [B] Interpretation of the curve [A] as representing the long-term envelope of solar activity. [C] Four estimates of historical climate: periods of Alpine glacier advance and retreat; global glacier fluctuations; (T) mean annual temperature estimates in Central England; (W) winter-severity index for the Paris-London region. The left top side shows a list of documented warm and cold periods in human history.. [D, E] Comparison of the C cosmogenic record with two climate records. [F] Correlation between reconstructed total solar irradiance and the flood layer frequency in central Europe. 4.2 Climate and the changing Sun conundrum
The correlation between solar activity and climate change throughout the Holocene has been extensively doc umented in scientific literature, particularly since the second half of the 20 [th] century. This period marked the availability of several long-term solar and climate proxy records. Figures
17A, 17B and 17C illustrate this foundational understanding by reproducing, with adaptations, a figure pub lished by Eddy, which demonstrates that the Holocene C cosmogenic record — a widely used proxy for variations in solar activity — is significantly correlated with multiple climatic indices. These include:
the timing of Alpine and global glacier advances and retreats;
an estimated mean annual temperature in England; and reconstructed winter severity indices for the
Paris-London region, dating back to the Medieval Warm Period. Notably, historical records extensively document similar alternating warm and cold periods, which are closely linked to the rise and de cline of civilizations. For instance, the Viking settlements in Greenland thrived during the Medieval Warm Period — a time of prolonged high solar activity — but were abandoned with the onset of the Little Ice Age, which was characterized by long periods of low solar activity. Recent studies have further substantiated the presence of a significant correlation between solar and climate variability throughout the Holocene, including in the last century. Figures 17D–F provide examples of this connection. However, as discussed in Section 2, the IPCC aligns with the CMIP6 GCMs’ prediction that the solar influence on climate change is negligible, particularly from 1850–1900 to the present. This raises a fundamental question: how can the IPCC’s claim be reconciled with the paleoclimate evidence that indicates a robust correlation between solar activity and climatic records throughout the Holocene? This apparent paradox has been addressed in numerous recent studies. One key finding suggests that the CMIP6 GCMs underestimate the solar contri bution to climate change by a large factor because these models rely only on a specific TSI forcing function characterized by a very low secular variability, which, however, may be fundamentally
flawed. Additionally, these models may likely exclude significant solar-climate physical mechanisms simply because they are still poorly understood. The CMIP6 GCMs primarily attribute the Sun’s influence on climate to variations in its luminosity, as re ported in the total solar irradiance (TSI) and solar spectral irradiance (SSI) forcings. While orbital changes also affect solar irradiance reaching Earth, these factors are categorized as orbital forcings and are predom inantly relevant on multi-millennial or longer timescales. The issues related to these topics warrant further
examination, as outlined below.
4.2.1 The TSI satellite composites
Decadal and long-term variations in solar activity remain largely uncertain due to the limitations in the avail able data, as solar irradiance can only be accurately measured by satellites since 1978. Satellite-based total solar irradiance (TSI) records have been the subject of considerable debate, as their composites are not unique; for a detailed discussion, see Scafetta et al. and Connolly et al.. Scien tific studies highlight that, in addition to the well-documented 11-year solar cycle, various TSI composites are possible, and they exhibit distinct multidecadal trends. Such differences depend on the specific TSI satellite records utilized, the adjustments applied to the officially published data, and the selection of the overlapping
periods. For example, while some TSI composites indicate a slight decrease or negligible trend from 1980 to
2023, others suggest a modest positive trend, and others even suggest a pronounced increase from 1980 to
2000 followed by a stabilization or slight decline from 2000 to 2023. Figure 18A illustrates examples of these
TSI satellite composites; additional details are provided in Connolly et al.. Notably, the TSI composites constructed using the 1979–2013 ACRIM TSI satellite composite depict an increase from 1980 to 2000, followed by either a slight decrease or a near-stationary
trend depending on the dataset used. The NASA-JPL ACRIM-based TSI composites show a strong correlation with the global surface temperature changes from 1980 to 2014, including a rapid warming trend from 1980 to Figure 18: [A] Compilation sample of available total solar irradiance (TSI) satellite composites. [B, C, D] Compilation of alternative TSI proxy records.
2000, and a subsequent plateau from 2000 to 2014. These observations suggest a significant solar contribution to climate change. By contrast, the CMIP6 GCMs adopted the solar forcing model proposed by Matthes et al., which averages two distinct TSI models: NRLTSI2 and SATIRE. The TSI forcing proposed by
Matthes et al. posits a slight decline in TSI from 1980 to 2020, which explains why the CMIP6 GCMs
attribute no significant warming to solar influence during this period. A critical scientific question arises regarding the accuracy of the TSI forcing proposed by Matthes et al. , as its declining trend from 1980 to the present conflicts with the ACRIM-based TSI satellite composites,
which is a composite constructed directly from the published TSI satellite data. The ACRIM-based composites contradict the NRLTSI2 and SATIRE TSI models. Among the few TSI composites compatible with NRLTSI2
are those that make use of the satellite TSI records modified by PMOD.
However, even the
PMOD-adjusted composites fail to align with the substantial downward trends in successive solar minima predicted by the SATIRE model, as highlighted also by de Wit et al.. The modifications applied by PMOD to the published TSI satellite records rely on subjective decisions by
Dr. Fröhlich, who adopted TSI proxy models and hypothetical sensor degradation corrections, which were re vised multiple times. This methodology has been criticized, as it departs from the standard scientific approach, which typically involves adjusting models to fit experimental published data rather than altering published data based on model assumptions. In general, published experimental data can be further adjusted only based on strict experimental considerations alone. For a comprehensive discussion, see Scafetta et al.
and
Connolly et al.. The PMOD adjustments of the published TSI satellite records remain contentious and were never endorsed by the TSI satellite experimental teams led by other researchers such as Drs. Richard C. Willson for ACRIM and Douglass V. Hoyt for Nimbus7. Consequently, the unresolved
ACRIM-PMOD controversy continues to carry significant implications for both solar and climate science. Despite this, the IPCC has recently chosen to disregard this debate, even though it was acknowledged in the earlier IPCC assessment reports. 4.2.2 The long-scale TSI proxy models
To investigate long-term variations in solar activity, researchers employ proxies such as sunspot numbers and
cosmogenic isotope records of C and Be. In the absence of direct Total Solar Irradiance (TSI) measurements prior to 1978 and due to uncertainties in the TSI satellite composites after 1980, modeling TSI changes over centuries and millennia remains highly challenging. While sunspot numbers and cosmogenic records can identify alternating periods of high and low solar activity, the precise magnitude of solar luminosity variations remains unknown, rendering rigorous validation of solar models unfeasible. Consequently, various TSI proxy models have been proposed in recent decades. Selected examples of these models are illustrated in Figures
18B, 18C, and 18D. Notably, the TSI model developed by Matthes et al., which underpins the TSI forcing for the CMIP6
GCMs, shows minimal secular variability, as it remains nearly constant from 1850 to 2020. For
millennial-scale simulations, the CMIP6 GCMs use the TSI forcing derived from the SATIRE-M model, which similarly shows a modest secular modulation. Consequently, it is unsurprising that the CMIP6 GCMs attribute negligible climate effects to solar forcing. In contrast, other TSI proxy models documented in the literature display significantly larger secular vari ability. These models suggest a marked increase in solar activity since the 17 [th] century and continuing during the 20 [th] century, which correlates well with the observed global warming since the Little Ice Age. An increase of solar activity during the 19 [th] and 20 [th] century is also supported by records of the solar coronal magnetic
field. This solar-climate correlation is evident over centuries and millennia and is particularly robust when specific TSI models are chosen.
However, observations of strong correlations between cosmic ray flux and cloud cover during Forbush decreases — which are sudden drops in cosmic ray flux typically caused by solar coronal mass ejections — suggest that the conclusions of the CLOUD experiment may require re-evaluation. Additional recent evidence for a pronounced 11-year solar cycle signature in cloud records has been documented by Miyahara et al.. Moreover, Svensmark showed that the correlation between the cosmic ray flux record and climatic data extend over the last 3.5 billion years, where ocean nutrient proxy data were found to covary with supernova frequency. These latest results further reinforce the hypothesis that cosmic rays can significantly drive climate changes. Another potential corpuscular forcing mechanism involves interplanetary dust falling on Earth, which remains an area requiring further investigation.
Ionized interplanetary dust may exert direct influence on cloud nucleation and contribute to climate variability. For instance, Scafetta et al. identified a 60-year
cycle in meteorite fall frequency that exhibits strong coherence with the 60-year climatic oscillation. This cycle, which has persisted for centuries, appears to be linked to the 60-year modulation of Jupiter’s orbital eccentricity, primarily governed by its gravitational interaction with Saturn. The prospect that solar activity could indirectly influence the climate through corpuscular forcings and space weather dynamics — processes which are not accounted for in the current GCMs — merits further
scrutiny. Variability in cloud cover has been proposed as a primary driver of climate change, as illustrated Figure 19: Comparison of the UAH-MSU lt v6.1 global satellite temperature record (blue) with: [A] the global cloud cover percentage data from the International Satellite Cloud Climatology Project (ISCCP); [B] the total anthropogenic effective radiative forcing employed in the CMIP6 GCMs. by Scafetta, who demonstrated a strong negative correlation between the ISCCP global monthly cloud cover and the global temperature records from 1983 to 2010. Figure 19A highlights this negative correlation by plotting the UAH MSU lt v 6.1 global satellite temper ature record (blue) against the ISCCP global cloud cover percentage record from July 1983 to December 2009
(inverted scale). Both curves exhibit a well-correlated increase from 1980 to 2000 followed by a more con stant level from 2000 to 2010. In contrast, Figure 19B juxtaposes the same temperature record with the total
anthropogenic effective radiative forcing function adopted by the CMIP6 GCMs, which exhibits a continuous linear increase from 1980 to 2010.
This comparison underscores that global temperature records align more closely with variations in cloud cover than with the anthropogenic forcing record. 5 Modeling climate change using empirical and semi-empirical models
As discussed above, several fundamental challenges complicate the detection, attribution, and modeling of climate change. Global surface temperature records may exhibit significant warming biases, while numerical climate models may contain unresolved physical uncertainties. Additionally, the actual solar forcing — recog nized as the dominant natural driver of climate change on millennial timescales — remains highly uncertain because the long-term solar activity variability is not well known and the mechanisms through which solar phenomena influence climate may include both radiative forcing and a poorly understood corpuscular forc ing. In response to these concerns, various proposals advocate for the use of empirical and semi-empirical models to enhance climate change modeling. 5.1 From reductionist to holistic approaches in climate modeling
The Intergovernmental Panel on Climate Change Assessment Reports have relied predom inantly on computer-based global climate models (GCMs). These models exemplify a reductionist scientific
approach, which seeks to simplify complex systems by focusing on individual components. While reduction ism can offer valuable insights, it also presents several limitations such as:
1. loss of context — by isolating individual components, reductionist methodologies may overlook critical
interactions, leading to an incomplete understanding of the climate system. 2. oversimplification — certain essential processes, such as cloud formation, remain poorly represented in the GCMs, affecting their accuracy in climate simulation and projections;
3. emergent properties — some systemic properties only manifest when the climate system is analyzed holis tically and cannot be discerned by examining isolated components;
4. interconnected systems — complex climate feedback mechanisms and relationships may be inadequately captured by reductionist models, leading to misleading conclusions;
5. application limits — insights derived from reductionist models may not be readily transferable to real world applications where a broader, integrative understanding is required. Given these constraints, a more comprehensive approach incorporating holistic methodologies is necessary to achieve an improved understanding of complex climate dynamics. Holistic models, particularly empirical and
semi-empirical frameworks, offer several advantages such as:
1. reliance on observational data — these models emphasize empirical data, enabling a direct modeling of
real-world climate patterns, thereby addressing limitations present in numerical climate models such as the CMIP6 GCMs;
2. simplicity and transparency — compared to complex GCMs, empirical models tend to be more accessible and interpretable;
3. robust statistical frameworks — these models apply rigorous statistical techniques to quantify the influence of both anthropogenic and natural climate drivers;
4. direct attribution of climate signals — by comparing observed trends with historical records, empirical models help to link specific climate variations to their underlying physical drivers;
5. policy and adaptation applications — empirical models provide clear evidence that can inform climate policy and adaptation strategies more effectively than complex numerical models. However, empirical models also have inherent limitations:
1. data dependence — the reliability of empirical models is contingent on the quality and completeness of the available data, which can sometimes lead to inaccuracies;
2. simplification assumptions — while useful, empirical models may overlook complex climate interactions,
leading to potential misrepresentations; 3. nonlinearity and complexity — the inherently nonlinear behavior of the climate system poses challenges for empirical modeling, sometimes resulting in oversimplifications;
4. regional specificity — findings based on one geographic region may not be universally applicable, compli cating broader climate assessments. 5. attribution uncertainty — while empirical models provide valuable insights into climate change attribu tion, they may be less robust than physically based models for quantifying the contributions of individual
factors. Thus, the study of complex natural systems necessitates the integration of both holistic and reductionist
methodologies. Since each approach has inherent strengths and limitations, comparing numerical and em piric models should allow for a more accurate representation of climate processes. Let us now discuss some of the empirical modeling of the climate system proposed in scientific literature. 5.2 Empirical and semi-empirical approaches in climate science
Several types of empirical and semi-empirical models are commonly employed in climate science such as:
1. Empirical Climate Models (ECMs) — ECMs use statistical techniques such as multiple linear regression and spectral analysis to identify relationships between climate change and external drivers. Examples include models assessing El Niño-Southern Oscillation dynamics, volcanic aerosol contributions, solar radiation,
and anthropogenic influences. These models provide preliminary attribution of observed temperature
changes. 2. Energy Balance Models (EBMs) — EBMs represent climate dynamics by balancing incoming solar radia tion with outgoing thermal emissions. They range from simple zero-dimensional models, which treat the Earth as a single thermal unit, to more complex one-dimensional and multi-dimensional
formulations that account for latitudinal and spatial variations.
3. Statistical Downscaling Models (SDMs) — SDMs refine broad-scale climate projections from the GCMs to more localized resolutions, enabling assessments of regional climate impacts. 4. Machine Learning Models (MLMs) — Machine learning methodologies have recently been introduced in climate research, offering promising capabilities for identifying nonlinear relationships and predicting climate patterns from large datasets. While MLMs have notable potential, challenges related to inter pretability and data requirements remain.
Each of these modeling approaches possesses unique strengths and limitations, and they are frequently utilized in combination to provide a more comprehensive understanding of climate change. The following subsections provide an overview of empirical models presented in the literature that at tribute climate change to both anthropogenic and natural drivers by directly analyzing the climatic records. This discussion will primarily focus on studies published after the release of the IPCC’s Sixth Assessment Re port. These models employ diverse mathematical methodologies and underscore the significant role of solar influences in climate change, though the extent of this contribution varies depending on underly ing assumptions and the specific methodologies used by model developers. For further technical details and statistical validation, readers are encouraged to consult the cited references. 5.3 A simple linear regression model
Regression models are widely regarded as the simplest and most used analytical tools in climate change at tribution studies. They rely on statistical techniques such as multi-linear regression analysis to explore re lationships between climate variables and a set of predictors. For instance, Chylek et al. utilized this approach to model the global surface temperature record by incorporating known radiative forcing functions of greenhouse gases (GHG), aerosols (AER), solar irradiance (SOL), volcanic activity (VOLC), as well as indices for the El Niño Southern Oscillation (ENSO) and the Atlantic Multidecadal Oscillation (AMO) as explanatory
variables. They proposed the following multi-linear regression model:
T ( t ) = a 0 + a 1 · F GHG ( t ) + a 2 · FAER ( t ) + a 3 · F SOL ( t ) + a 4 · F VOLC ( t ) + a 5 · I ENSO ( t ) + a 6 · I AMO ( t )
where the free parameters a 0...6 represent six regression coefficients. In their analysis, Chylek et al. adopted the climate forcin
g functions derived from the GISS ModelE, which utilizes an earlier version of the
NRLTSI TSI model based on the PMOD-modified TSI satellite composite. They concluded that
anthropogenic forcing and the positive phase of the AMO collectively accounted for approximately two-thirds
and one-third, respectively, of the global warming observed since 1975. Despite its apparent utility, the proposed model has several potential limitations. First, its reliance on a po tentially inaccurate solar forcing function likely skewed the results because as the post-1975 warming, which the model attributed to AMO, could have also be partially attributed to solar activity variations if TSI records compatible with the ACRIM TSI satellite composite were used. Second, the climate system processes the radiative forcing functions through inherently
non-linear mechanisms, and thus the assumed linear relationships between T ( t ) and its radiative forcing com ponents may oversimplify reality. Furthermore, ENSO and AMO are subsystems of the climate system and,
therefore, they cannot necessarily be considered physically independent of the forcing functions. Multi-linear regression analysis can also produce ambiguous or erroneous results when significant collinear ity exists among predictors or when non-linear effects are neglected. For example, Benestad and Schmidt applied a multilinear regression model to global surface temperatures incorporating the ten radiative forcing functions used by the GISS model. Their result suggested that solar forcing may have contributed approxi mately 0.1°C to the 0.65°C warming observed from 1900 to 2000, but they acknowledged the lack of robustness for such finding. In fact, Scafetta demonstrated that multilinear regression models using GISS forcing functions could effectively reproduce global temperature records even if the well-mixed GHG forcing function were ignored because of its collinearity with the other predictors. Additional analyses by Scafetta and West and later Scafetta indicated that the solar influences may have contributed to 50% or more of the warm ing between 1900 and 2000. These findings were derived using analytical methods such as wavelet frequency decomposition and simplified zero-dimensional energy balance models, which account for some non-linear
effects. Models such as the one proposed in Eq. 1 may underestimate solar contributions due to the cli mate system’s tendency to attenuate high-frequency signals while amplifying low-frequency components, a consequence of its thermal inertia.
In this context, Benestad and Schmidt identified a significant solar
signature, though it was attenuated relative to the finding of Scafetta and West largely due to methodological errors in wavelet analysis, as later highlighted by Scafetta. 5.4 A simple ECM based on a zero-dimensional EBM
Empirical regression models are most effective when they balance simplicity and complexity. They should incorporate the minimum number of physically relevant predictors, chosen carefully to avoid collinearity. Additionally, these models should simulate some non-linearity. For example, radiative forcing functions are not inherently linear predictors of climate behavior, as the climate system processes them by attenuating the
high-frequency components relative to the low-frequency ones due to its thermal capacity.
Taking into account the above considerations, Scafetta proposed modeling the global surface tem perature record, T ( t ), using the following equation:
T ( t ) = TA ( t ) + TV ( t ) + TS ( t ) + ξ ( t ) = TAVS ( t ) + ξ ( t ),
where T ( t ) is derived from four components: anthropogenic, TA ( t ) ; volcano, TV ( t ) ; solar, TS ( t ) ; plus a fast fluctuating component, ξ ( t ), simulating fast fluctuations such as the ENSO signal. The three main contributors can be estimated using a 0-D energy balance equation with a given time response, which can be generally modeled as:
C [dT] [(] [t] [)]
S − σε T ( t ) + G . 4
[(] [t] [)]
= [ −] [a] dt 4
On the left side, T ( t ) is the mean global temperature in Kelvin, C represents the effective heat capacity of the
Earth’s surface and atmosphere. On the right side, in the first term a denotes the albedo, Sis the incoming solar radiation adjusted for the planetary sphericity; the second term represents the outgoing longwave radiation, which depends on the temperature itself; finally, G incorporates the effect of the greenhouse gases. By redefining the constants and simplifying the formulation, the above equation can be approximated for each forcing component using differential equations based on the temperature anomalies, ∆ T ( t ) = T ( t ) − T 0,
which are relative to a given mean temperature T 0 :
∆ TA ( t ) − ∆ TA ( t − ∆ t )
= α A · FA ( t ) − β · ∆ TA ( t − ∆ t ) τ
∆ TA ( t − ∆ t ) = k A FA ( t ) − ∆ TA ( t − ∆ t )
∆ t τ
∆ TV ( t − ∆ t ) = k V F V ( t ) − ∆ TV ( t − ∆ t )
∆ t τ
∆ TV ( t ) − ∆ TV ( t − ∆ t )
= α V · F V ( t ) − β · ∆ TV ( t − ∆ t ) τ
∆ TS ( t ) − ∆ TS ( t − ∆ t )
= α S · F S ( t ) − β · ∆ TS ( t − ∆ t ) τ
∆ TS ( t − ∆ t ) = k S F S ( t ) − ∆ TS ( t − ∆ t )
∆ t τ
Here, FA ( t ), F V ( t ), and F S ( t ) represent the anthropogenic, volcanic, and solar effective forcings, respectively. The coefficients α A = k A / τ, α V = k V / τ, α S = k S / τ, and β = 1/ τ depend on the sensitivity parameters k A,
k V and k Sand the characteristic time response τ, which is directly related to the Earth’s effective heat capacity. For simplicity, τ is assumed constant for all forcings. Under equilibrium conditions, the temperature change ∆ T 2 × CO 2, with corresponds to doubling atmo spheric CO 2 concentration, is the equilibrium climate sensitivity
ECS = ∆ T 2 × CO 2 = k A ∆ F 2 × CO 2 = 3.7 k A . For the transient climate response (TCR), which is defined as the temperature average over 20 years around the time of CO 2 doubling under a linear increase scenario, the calculation gives:
TCR = 3.7 k A −
70
1 − e [−] [τ] [�] = ECS 1 − [τ] 70 [k] [A] [τ] � � 70
1 − e [−] [τ] [��] . �
By iterating, these equations can be reformulated as:
∆ T ( t ) − ∆ T ( t − ∆ t ) = α A · FA ( t ) + α V · F V ( t ) + α S · F S ( t ) − β · ∆ T ( t − ∆ t ),
∆ t where ∆ t is set to 1 year. Using multilinear regression analysis, the regression coefficients ( α A, α V, α Sand β )
can be evaluated, and can be used to reconstruct the climatic signatures of each forcing and compute ∆ TAVS ( t ),
the deterministic component of T ( t ) . Unlikely Eq. 1, the model expressed by Eq.
9 accounts for the climate system’s non-linear processing of the forcing functions due to its heat capacity, which leads to a timescale dependent amplitude and time-lag in the response of the climate system to the input forcing function. Scafetta demonstrated that if the climate sensitivity is set to be equal for all forcings ( α A = α V = α S )
— indicating that the climate is equally sensitive to all types of forcings — the solar contribution to the global Figure 20: [A] Comparison of the HadCRUT5 global surface temperature record with the CMIP6 GCM ensemble average. [A’] Both records are detrended using the function f ( t ) = a, correlation coefficient of r = 0.45 for the period 1850–1950.
[B] Comparison of the HadCRUT5 global surface temperature record with the ECM derived from Eq. 2 utilizing a medium-high variability Total Solar Irradiance (TSI) proxy model and assuming the condition α A = α V ̸ = α S . [B’] The same detrending analysis as in [A’] is applied, yielding an improved correlation coefficient of r = 0.55. Adapted from Scafetta. warming from 1850–1900 to 2011–2022 is minimal, particularly when it is adopted the low-secular-variability
TSI model used by the CMIP6 GCMs. Under this scenario, the ECS was estimated to be 2.1 ± 0.7 °C, which is consistent with the low ECS range proposed by the IPCC. In this circumstance, the result suggests that most of the observed warming could be attributable to the anthropogenic forcing, although the ECS was estimated to be lower than 3.0°C. This empirically derived ECS range optimally fits the findings of Lewis and. Alternatively, assuming α A = α V ̸ = α S, which means that the climate sensitivity to solar variations can be different from that to the other radiative forcings, Scafetta found that the climate could be also 4 to 6
times more responsive to TSI forcing than to anthropogenic or volcanic forcing. In this circumstance, the result implies an ECS that could be as low as 1.1 ± 0.4 °C, suggesting that solar activity may directly influence the Earth’s albedo by physical mechanisms currently absent in the GCMs. Under this scenario, if
high-secular-variability TSI models are adopted, solar activity changes could explain ∼ 50% or more of the observed warming from 1850–1900 to 2011–2022. Figures 20A and 20B, respectively, compare the HadCRUT5 global surface temperature record (black)
against the CMIP6 GCM ensemble mean simulation and the ECM output (red) curves. The latter was obtained using high-secular-variability TSI models under the condition α A = α V ̸ = α S . The green curves in both panels
A and B highlight the distinct multi-decadal modulation pattern evident in the red curves of the two types of models. In panel A, the red curve demonstrates a steadily increasing trend, reflecting the anthropogenic
forcing function. In contrast, the red curve in panel B exhibits a quasi 60-year oscillatory behavior that closely resembles the observed climate temperature record. This distinction becomes more evident in panels A’ and
B’, which display the detrended curves. In Figure 20A’, the correlation coefficient for the period 1850 to 1950 is r = 0.45, whereas in Figure 20B’, the correlation coefficient is notably higher at r = 0.55. More specifically, the CMIP6 GCM ensemble average simulation inadequately captures the warming observed from the 1900s to the
1940s and the subsequent cooling from the 1940s to the 1970s. In contrast, these patterns are more accurately reproduced by the ECM derived from Eq.
2 under the outlined assumptions. 5.5 Astronomically-based empirical harmonic models of natural climate variability
There is another widely utilized empirical approach to model climate change, which again considers three primary components: anthropogenic, volcanic, and other natural factors. However, the latter component is conceptualized as made of a complex harmonic signal. The modeling is based on the hypothesis that these other natural climatic components derive from astronomical, solar and lunar forcings that could exhibit ap proximate harmonic behavior. This empirical methodology involves analyzing the periodogram of the climate
records, identifying relevant frequencies, and generating constituent harmonic functions using multiple linear regression analysis. The harmonics are subsequently combined to empirically reconstruct the hypothesized harmonic natural patterns of the climate system. One notable advantage of this approach lies in its ability to extend harmonics for forecasting purposes. For example, it is well known that seasonal variations can be approximately modeled using annual and semi annual cycles. However, issues arise when the selected frequencies lack physical justification. Misinterpreta tion of artifacts in the periodogram as genuine physical frequencies may lead to harmonic models that perform well within the calibration interval, and yet they could diverge substantially from reality outside the regres sion period. Furthermore, periodograms of climatic records may only approximate true physical frequencies,
particularly in the low-frequency domain where error margins are larger. To mitigate the possibility of using non-physical frequencies, Scafetta proposed se lecting only those frequencies that can be theoretically derived from astronomical considerations, which is a methodology analogous to that employed in ocean tidal modeling since the seminal work of Sir William Thom son (Lord Kelvin) in 1879. This approach appears justified, because temperature records present periodograms spectrally coherent with planetary, solar, and lunar harmonics. Solar records themselves exhibit plan etary harmonics across annual to multi-millennial scales. These harmonics include the 11-year solar cycle, the Eddy quasi-millennial
cycle, and the Bray-Hallstatt oscillation identified in radiocarbon and climate records spanning the Holocene. In general, it appears that the natural harmonics of the solar system synchronize both solar and climate oscillations, although the mechanisms underlying such planetary synchronization phenomenon remain under investigation. Scafetta extended the model first proposed in Scafetta by hypothesizing that the climate system incorporates 13 major harmonics with periods spanning approximately 3 to 1000 years. Anthropogenic
and volcanic contributions were derived from the ensemble mean of the CMIP6 GCM simulations, utilizing half the climate sensitivity estimated by these models, which means that the ECS was estimated to be about 1.5 2.0°C, to incorporate a natural variability described by the adopted harmonic constituent model. The proposed equation is as follows
13 T ( t ) = T 0 + ∑ A i sin + 0.5 · GCM ( t ),
i = 1
where A i, f i and α i per i = 1, ..., 13 are coefficients discussed in detail by Scafetta. Figure 21A shows the output of the above model extended to 2100 using the SSP2-4.5 scenario, which is considered to be the most realistic one. Figure 21B presents burning ember plots for the top five global reasons for concern (RFCs), based on the IPCC findings under minimal adaptation assumptions. The comparison of panels A and B indicates that the projected tem peratures throughout the 21 [st] century are likely to remain within the safe adaptation threshold indicated by the Paris Agreement limiting global warming to less than 2°C relative to the 1850–1900 pre-industrial
period.
By contrast, the CMIP6 GCM projections forecast significantly higher, and potentially hazardous,
warming levels. Similar conclusions were reached by Connolly et al. using an alternative and more simple empirical model with low climate sensitivity to radiative forcing under business-as-usual
scenarios. Figure 21: [Top] Comparison of the harmonic empirical global climate model under the SSP2-4.5 scenario with the HadCRUT4.6 record alongside the burning ember diagrams representing the five primary global Reasons for Concern (RFCs) under low-to-no adaptation scenarios, as reported by the IPCC AR6. [Bottom] Summary and analysis of the projected impacts and risks of global warming for the 2080–2100 period compared to the climate “thermometer” projections from Climate Action Tracker. Adapted from Scafetta. Figure 21C compares the IPCC predictions with the outputs of alternative empirical climate modeling un der three different assumptions based on the considerations discussed in the above sections:
1. using only the CMIP6 GCMs with ECS < 3°C;
2.
rescaling the GCMs to fit the satellite low troposphere temperature record;
3. using the empirical model expressed by Eq. 11. Detailed explanations are found in Scafetta. Figure 22: [A] Extended effective anthropogenic and volcanic forcings utilized by CMIP6 GCMs, backdated from 1 to 1750 AD. [B] Synthetic model of total solar irradiance constructed using specific identified climatic harmonics. [C] Climate output generated using the ECM based on Eq. 2, incorporating the parameters obtained by processing the TSI-2 and HadSST4 records from Scafetta. [D] Same as [C], but with pink noise added to simulate the internal variability of the climate system. The empirical approaches exhibit more robust alignment with the historical data and project a moderate cli mate warming throughout the 21 [st] century under realistic development scenarios, such as the SSP2-4.5.
These projections suggest that adaptation policies may be sufficient to address future climate challenges without the necessity of adopting economically disruptive Net-Zero mitigation strategies to meet the climate targets of the
Paris Agreement. 5.6 A synthetic solar-based empirical climate model from 1 to 2017 AD
Let us finally discuss a synthetic empirical climate model spanning from 1 to 2017 AD that may provide rele vant insights into climate patterns over the past two millennia. Figure 22 illustrates an ideal application of the empirical climate model (ECM) formulated in Eq. 2, which integrates the following components:
- anthropogenic effective radiative forcing — zero anthropogenic forcing is applied from 1 to 1749
AD, while the forcing values adopted by the CMIP6 GCMs are utilized for the period from 1750 to 2017; - volcanic effective radiative forcing — the volcanic forcing values used in the CMIP6 GCMs
for the period 1750–2017 are extended back from 1 to 1749 AD using the volcanic aerosol optical depth records provided by Toohey and Sigl;
- solar effective radiative forcing — this forcing is derived from a synthetic total solar irradiance
(TSI) model that simulates the major features of the proxy solar records. The function is calculated by subtracting 1361 W/m² and dividing by 8 to align with the TSI effective forcing scale used in the CMIP6 GCMs. The synthetic TSI model serves as an idealized representation of solar activity variations by reproducing five long harmonics whose frequencies and phases are strictly based on astronomical considerations. Additionally, the model incor porates a simulated 11-year solar cycle, with amplitude variations linked to solar activity, that is it diminishes during grand solar minima such as the Maunder Minimum of the 17 [th] century. The periods of the five har monics are: P 1 = 60.95 years, P 2 = 114.78 years, P 3 = 129.95, years, P 4 = 983.40 years, and P 5 = 2318 years. The chosen secular harmonics — P 1, P 2, and P 3 — account for alternating solar maxima and minima, such as the Maunder and Dalton minima, while the longer millennial oscillations — P 4 and P 5 — correspond to the
Eddy and the Bray-Hallstatt cycles observed in both solar and climate records. The amplitude of these harmonics approximates the variability found in high-secular-variability
TSI models, as those shown in Figure 18. The ECM model used the following parameters, estimated by Scafetta using a solar vari ability model and the HadSST4 record: α A = α V = 0.083 °Cm /yW, α S = 0.427 °Cm /yW, and β = 0.303
1/y. These values imply an ECS equal to 1 ± 0.3 °C, and an enhanced sensitivity to TSI forcing by a factor of
5.1 ± 1.5.
flood frequencies and solar proxy records — Holocene flood frequency records, likely influenced by variations in cloud cover, exhibit significant correlations with solar proxies. The high equilibrium climate sensitivity (ECS) estimates of the GCMs primarily stem from assumptions about a strong water vapor positive feedback mechanism, initially hypothesized by Manabe and Wetherald. This hypothesis suggests that warming leads to increased evaporation, further amplifying warming. How ever, uncertainties surrounding water vapor and cloud feedbacks have been acknowledged since the 1960s
and are still unresolved. Recent analyses indicate that numerical climate models may overestimate evaporation rates. Additionally, top-of-atmosphere (TOA) radiative flux measurements suggest that long-wave feedbacks — such as those associated with cirrus cloud formations — may be negative rather than positive. Schildknecht also argues that a proper accounting of cloud-cover dynamics brings ECS estimates closer to or below 1°C. A number of empirical analyses suggest a moderate climate sensitivity to radiative forcing, with ECS es timates varying depending on the data and assumptions considered. Realistic ECS values could be approxi mated at least at 2.1 ± 0.7 °C by combining several lines of climate sensitivity evidence. However, significantly lower ECS estimates — even as low as 1.1 ± 0.4 °C
— are also possible if solar variability plays a dominant role through mechanisms alternative to the TSI forcing. Such low ECS estimates indicate the existence of balanced positive and negative feedback mechanisms, and have been supported by several researchers. In any case, it is also possible that feedback mechanisms could exhibit scale-dependent behavior. Over short and decadal timescales, they may tend to show slightly negative responses, primarily due to rapid cloud related adjustments. Over longer timescales, however, feedback responses may become increasingly positive as surface albedo effects linked to glacial melting and vegetation expansion gain influence. Consequently, ECS
values around 1.1 ± 0.4 °C or slightly larger may be realistic when climate change is assessed over interannual
to millennial timescales. Biases in global surface temperature records, particularly over land areas, raise concerns about the reported global and regional warming trends. The urban heat island effect, exacerbated by increasing urbanization,
likely contributes to these biases. Temperature homogenization algorithms,
designed to correct non-climatic warm biases in the meteorological records, appear to blend them into sur rounding rural and suburban stations rather than fully removing urban-induced thermal anomalies. Consequently, land surface temperature records — particularly those from the Northern Hemisphere — tend to show exaggerated warming trends compared to alternative
datasets, including the satellite-based lower troposphere temperature measurements and sea sur face temperature records. The IPCC, unequivocally attributes the observed global surface warming from 1850–1900 to 2011–
∼ 2020 almost entirely to anthropogenic drivers; such assessment supports the climate alarmist frame works that dominate European policymaking that yielded to policies such as the EU Green Deal and Net-Zero
by 2050. However, the CMIP GCM prediction that without anthropogenic drivers the climate would have re mained nearly stable from 1850–1900 to 2011–2020 cannot be validated because of missing data. Moreover, the
IPCC assessments are based on surface temperature datasets and theoretical simulations derived from GCMs
that appear flawed in many ways and that incorporate equally problematic low-variability TSI forcing func tions. These models contradict each other regarding the ECS valueand appear to conflict with a sub stantial body of empirical evidence spanning the entire Holocene. Notably, they fail to accurately reconstruct the secular-scale warm periods of the past including the MWP, RWP and HTM, which should be a prerequisite for trusting the GCM-based climate attributions for the period from 1850–1900 to 2011–2020
depicted in Figure 2, underestimate the warming from the 1900s to the 1940s and overestimate the global surface warming of the last 40 years. In contrast, semi-empirical and empirical modeling approaches, which try to account for natural variability,
emphasize a significant role of solar variability in climate change. The IPCC tends to ignore the efforts of empirical modelings of the climate system.
Climate science remains far from settled, yet trillions of dollars continue to be allocated toward policies aimed at mitigating extreme hypothetical warming scenarios based on potentially flawed GCM outputs. His torically, atmospheric CO 2 levels have been 10 to 20 times higher than current concentrations during approx imately 95% of Earth’s history since complex life emerged 600 million years ago. Notably, CO 2 concentrations often lag temperature changes across different timescales, suggesting temperature fluctuations may drive CO 2 variations rather than vice versa. Since 1900, atmospheric CO 2 concentrations have increased from 295 ppm to 425 ppm, primarily due to human emissions and, to a lesser extent, rising sea surface temperatures. While higher CO 2 levels can neg atively impact marine biodiversity by lowering the pH of the sea surface microlayer, they also contribute to planetary greening through fertilization effects, enhancing crop yields. As CO 2 is a greenhouse gas, climate hazard assessments related to its future emissions depend largely on the Equilibrium Climate Sensitivity (ECS) and Transient Climate Response (TCR) values of the climate system,
as well as on the projected emission scenarios. Notably, extreme concentration pathways — such as SSP3 7.0 and SSP5-8.5 — are increasingly regarded as “ unlikely ” and “ very unlikely ”, respectively, and emphasizing climate model simulation based on such scenarios could be misleading. This fact should be taken into account when developing climate related policies for not harming the economy with unnecessary mitigation policies, which should be based on realistic risks. In this regards, the meta economic analysis by Tol appears particularly compelling when comparing the costs and benefits of the Paris climate targets. Advancing climate science requires directly confronting uncertainties in detection, attribution, and mod eling.