Friday, June 26, 2026

Uncertainties surrounding CO2 and Global temperatures.


Implications of a Hypothetical Cooling Trend

Authors: David I Birch- Gareth P Nugent-                             William A Marsh.

Date: March 29, 2025

Affiliation: Independent Oceanic and Atmospheric research studies.

Abstract

This paper examines the complexities and uncertainties inherent in the relationship between atmospheric carbon dioxide (CO2) and global temperature. While the greenhouse gas theory posits a direct correlation between increased CO2 and warming, historical climate records and the influence of other climate forcings reveal a more nuanced picture, particularly over shorter timescales. In this paper we analyses a hypothetical scenario where the Earth experiences a cooling trend over the next 30 years despite a continued increase in CO2 levels. This scenario, while seemingly contradictory to the established theory, is explored in the context of natural climate variability, including solar activity, volcanic eruptions, and ocean oscillations, as well as the role of aerosols and limitations in current climate modelling for short-term projections. The implications of such a cooling trend for the greenhouse gas theory are discussed, concluding that it would likely lead to a refinement rather than a rejection of the fundamental understanding of CO2's role in the climate system. The paper also explores alternative scientific explanations for such a decoupling of CO2 and temperature trends, emphasizing the multifaceted nature of Earth's climate system.

1. Introduction

The Earth's climate system is a complex interplay of various factors, with the greenhouse effect playing a pivotal role in maintaining a habitable temperature. This natural phenomenon involves certain atmospheric gases trapping heat radiated from the Earth's surface, preventing it from escaping into space. Key greenhouse gases responsible for this effect include water vapour, carbon dioxide (CO2), methane (CH4), nitrous oxide (N2O), and ozone (O3). Among these, carbon dioxide is recognized as a crucial component in regulating Earth's temperature; its removal would lead to a significant drop in the planet's average surface temperature. 

Since the onset of the Industrial Revolution in the mid-18th century, human activities, primarily the combustion of fossil fuels for energy, have led to a substantial increase in the concentration of atmospheric CO2.This anthropogenic increase in CO2 has enhanced the natural greenhouse effect, resulting in a discernible warming trend across the globe. Current data indicates that atmospheric CO2 levels have reached unprecedented heights, exceeding 430 parts per million (ppm) in recent years, with the rate of increase being significantly faster than natural fluctuations observed in the past. Concurrently, global average surface temperatures have shown a marked rise since the late 19th century, with the decade spanning 2011 to 2024 being the warmest on record. While long-term trends suggest a correlation between rising CO2 and temperature, the relationship is not always linear on shorter timescales due to the influence of other factors. This paper aims to investigate the inherent uncertainties in the relationship between atmospheric CO2 and global temperature. Specifically, it will analyse the implications of a hypothetical scenario where the Earth experiences a cooling trend over the next 30 years despite a continued increase in CO2 levels for the qestablished greenhouse gas theory.

2. The Foundational Understanding of the Greenhouse Gas theory.

The greenhouse effect is initiated by solar radiation entering the Earth's atmosphere, with a portion being absorbed by the planet's surface. The Earth then radiates energy back into the atmosphere in the form of infrared radiation, also known as heat. Greenhouse gases present in the atmosphere possess the property of absorbing and re-emitting this infrared radiation in all directions, effectively trapping some of the heat within the atmosphere. Different greenhouse gases exhibit varying capacities to absorb energy, referred to as radiative efficiency, and have different durations they persist in the atmosphere, known as atmospheric lifetimes. To facilitate comparisons of the warming impacts of different gases, the concept of Global Warming Potential (GWP) is utilized, which measures how much energy the emission of one ton of a gas will absorb over a given period relative to the emission of one ton of carbon dioxide.While CO2 serves as the reference gas for GWP with a value of 1, other greenhouse gases like methane and nitrous oxide possess significantly higher warming potentials per molecule, although their atmospheric concentrations are considerably lower than that of CO2. Water vapour, the most abundant greenhouse gas, plays a crucial role as a feedback mechanism, amplifying the warming initiated by other greenhouse gases. The amount of heat these gases can absorb and re-radiate determines their contribution to the greenhouse effect. Carbon dioxide specifically absorbs infrared energy at particular wavelengths, and an increase in its atmospheric concentration leads to greater absorption of outgoing infrared radiation, resulting in a net warming effect. Furthermore, CO2 plays a regulatory role in the amount of water vapour in the atmosphere, which in turn influences the planet's temperature. Even in a scenario where the absorption of radiation in the lower atmosphere reaches saturation, the addition of more CO2 in the upper atmospheric layers would still alter the planet's energy balance. This highlights that the influence of CO2 extends beyond direct heat trapping, impacting other critical components of the climate system and establishing it as a key driver of long-term temperature changes.The understanding of the greenhouse gas theory has evolved over centuries, with initial recognition of the effect dating back to the 19th century through the work of scientists like Joseph Fourier, John Tyndall, and Svante Arrhenius. Tyndall's experiments demonstrated that gases such as CO2 and water vapour absorb and radiate heat, laying the physical basis for the greenhouse effect. Arrhenius was among the pioneers who calculated the potential for human-induced emissions to cause a rise in global temperatures. Early on, some scientists held skeptical views, suggesting that the oceans would readily absorb any excess CO2 released into the atmosphere. However, in 1938, Guy Stewart Calendar presented arguments linking the observed warming to the increasing concentrations of CO2. The 1960s saw a significant advancement with Charles David Keeling's precise measurements confirming the rapid increase in atmospheric CO2 levels. Since then, the Intergovernmental Panel on Climate Change (IPCC) has provided comprehensive and periodic assessments of the scientific understanding of climate change, including the role of greenhouse gases . This historical progression underscores that the greenhouse gas theory is not a nascent concept but has been developed and refined over a considerable period, supported by a growing body of evidence and rigorous scientific inquiry .

3. Complexities and Uncertainties in the CO2-Temperature Nexus

The relationship between atmospheric CO2 and global temperature is not a simple linear one, but rather a complex interaction influenced by various factors, including climate feedback mechanisms and natural climate variability. Climate feedbacks are natural processes that respond to an initial warming or cooling by either amplifying (positive feedback) or diminishing (negative feedback) the change in the climate system Positive feedback mechanisms tend to enhance the initial temperature change. For instance, the water vapour feedback is a significant positive feedback, where warmer temperatures lead to increased evaporation, resulting in a higher concentration of water vapour in the atmosphere. Since water vapour is a potent greenhouse gas, this increase further warms the planet. Another crucial positive feedback is the ice-albedo feedback. As global temperatures rise, ice and snow melt, reducing the Earth's reflectivity (albedo). The darker surfaces of land and water then absorb more solar radiation, leading to further warming and more ice melt. The thawing of permafrost in polar regions also represents a positive feedback, as it releases significant amounts of methane and CO2, both potent greenhouse gases, into the atmosphere, thereby enhancing warming. Cloud feedback is a more complex area, as changes in cloud cover can have both positive and negative effects on temperature depending on the type, altitude, and reflectivity of the clouds.Conversely, negative feedback mechanisms tend to counteract the initial temperature change. The Planck response is a fundamental negative feedback where, as the Earth warms, it emits more infrared radiation into space, acting as a natural thermostat. The lapse rate feedback, which involves changes in the rate of temperature decrease with height in the atmosphere, is generally a negative feedback that weakens the greenhouse effect, although it can be positive in polar regions . Increased atmospheric CO2 can also lead to a limited negative feedback through enhanced photosynthesis by plants, which absorb CO2 from the atmosphere. The interplay of these positive and negative feedbacks ultimately determines the climate sensitivity, which is the estimated temperature increase resulting from a doubling of atmospheric CO2 concentrations. The wide range of estimates for climate sensitivity reflects the uncertainties associated with these complex feedback mechanisms, particularly cloud feedback, which remains a significant challenge for accurate climate modelling.

 While CO2 is a primary focus in discussions about climate change, other greenhouse gases also significantly influence the global energy balance. Methane (CH4) and nitrous oxide (N2O) are also potent greenhouse gases, exhibiting higher GWPs than CO2 over shorter timeframes. Methane, although having a shorter atmospheric lifetime compared to CO2, absorbs considerably more energy . Nitrous oxide is a long-lived greenhouse gas with a high GWP. Fluorinated gases (F-gases), while present in much smaller quantities, possess exceptionally high GWPs . Increases in the atmospheric concentrations of these gases also contribute to global warming. In 2021, carbon dioxide constituted the largest proportion of greenhouse gas emissions in the European Union, followed by methane. Therefore, a comprehensive understanding of global warming necessitates considering the contributions of these other greenhouse gases alongside CO2 in climate models and mitigation strategies.

Natural climate variability also plays a crucial role in modulating global temperatures, sometimes masking or amplifying the long-term warming trend driven by greenhouse gases. These natural factors include solar activity cycles, volcanic eruptions (and their aerosol effects), and oscillations in ocean currents. The Sun's energy output fluctuates over an approximately 11-year cycle and potentially on longer timescales . While variations in solar activity can lead to some climate variability, they are not considered the primary driver of the significant warming observed in recent decades . Mechanisms through which solar activity might influence climate include changes in total solar irradiance, variations in ultraviolet radiation, and potentially effects on cosmic rays that could influence cloud formation. Volcanic eruptions, particularly large explosive ones, can inject substantial amounts of aerosols, such as sulfur dioxide, into the stratosphere. These sulfur dioxide molecules convert to sulfuric acid aerosols, forming a haze that reflects incoming sunlight back into space, leading to a temporary global cooling that can last for a few years. While volcanoes also release greenhouse gases like carbon dioxide, the quantities emitted in contemporary eruptions are considerably smaller than those from human activities, this is however debatable.

Ocean currents play a vital role in redistributing heat across the globe, thereby influencing both regional and global climate patterns . Significant changes in ocean circulation, such as a slowdown of the Atlantic Meridional Overturning Circulation (AMOC), could potentially lead to regional cooling in areas like Western Europe despite overall global warming. Ocean-atmosphere oscillations, such as the El Niño-Southern Oscillation (ENSO), contribute to interannual variability in global temperatures. Furthermore, the ocean's immense capacity to absorb heat results in a delay in the full manifestation of greenhouse gas warming at the Earth's surface . Understanding these natural cycles and their impacts is essential for accurately interpreting temperature data,especially over shorter timeframes.

4. Limitations of Current Climate Modelling in Short-Term Projections.

Climate models serve as essential tools for understanding and projecting future climate change. These models are sophisticated computer simulations of the Earth's climate system, incorporating our knowledge of the physical, chemical, and biological processes that govern the climate. Despite their complexity, these models have inherent challenges and limitations, particularly when it comes to accurately predicting temperature trends over shorter time scales, such as 30 years. 

One significant limitation stems from computational power. The finite resolution of climate models can prevent the accurate representation of small-scale but important phenomena like clouds. While downscaling techniques are used to achieve higher resolution in specific regions, these can introduce boundary interactions that may contaminate the modelling area and propagate errors . Furthermore, our understanding of certain climate processes remains incomplete, leading to uncertainties in how these processes are represented within the models. Examples include the formation and behavior of clouds, the complex interactions involving aerosols, and the dynamics of deep ocean circulation. The chaotic nature of the climate system also makes it difficult to perfectlypredict the timing and magnitude of natural climate variability events, such as solar cycles, volcanic eruptions, and ocean oscillations, over short timescales. Accurately modelling the interactions and strengths of the various climate feedback mechanisms, both positive and negative, continues to be a challenge. In addition to these inherent complexities, climate models can also have biases, and measurement errors in input data contribute to the overall uncertainty in their projections. Short-term predictions are also more sensitive to the initial state of the climate system, which may not be known with perfect accuracy. It is important to note that the confidence in climate model predictions is generally higher for long-term climate change projections, which are driven by sustained forcings like increasing greenhouse gas concentrations, compared to short-term weather-like forecasts.Factors such as model resolution significantly impact the ability to simulate climate processes. Low-resolution models often fail to capture regional climate details and important phenomena such as clouds . Clouds themselves present a major challenge for climate models due to their multifaceted role in the climate system. They can reflect incoming sunlight, leading to a cooling effect, but they can also trap outgoing heat, contributing to warming. The net effect of clouds is sensitive to their type, altitude, and optical properties, which are difficult to model precisely. Deep ocean circulation is another critical component of the climate system, playing a significant role in the distribution of heat globally However, the slow and complex nature of these deep currents makes them challenging to represent accurately in climate models.

Unpredictable natural events, such as volcanic eruptions, can inject cooling aerosols into the stratosphere, temporarily offsetting the warming trend caused by greenhouse gases. Similarly, variations in solar activity, which can influence the amount of solar radiation reaching Earth, are also difficult to predict with high precision over the next 30 years . The inherent unpredictability of these natural climate drivers, coupled with the ongoing limitations in accurately representing complex processes within climate models, implies a higher degree of uncertainty in shortterm temperature projections.

5. Historical Insights: Decoupling of CO2 and Temperature Records.

Analysing historical climate records reveals periods where the correlation between CO2 concentrations and global temperatures has not been direct or immediate . Over very long geological timescales, such as during the ice age cycles of the past million years, CO2 and temperature have generally exhibited similar patterns, with both increasing and decreasing in tandem. However, during the transitions into and out of glacial periods, evidence suggests that temperature changes sometimes preceded changes in CO2 concentrations.On shorter timescales, within the last century and a half, there have also been instances where temperature trends did not perfectly align with the continuous rise in CO2 levels . For example, a period of cooling was observed globally from approximately 1942 to 1975, despite a concurrent increase in atmospheric CO2 concentrations. Similarly, the early part of the 20th century experienced a warming trend with a relatively slow increase in CO2 emissions, while the post-World War II era saw a rapid acceleration of CO2 emissions coinciding with a period of cooling. The eruption of Mount Pinatubo in 1991 led to a temporary global cooling that lasted for a few years, despite the ongoing increase in CO2 levels . Furthermore, the rates of increase in both CO2 and global temperature were slower during the late 19th and early 20th centuries compared to the latter half of the 20th century and the beginning of the 21st century . These historical observations indicate that while CO2 is a significant long-term driver of Earth's climate, other factors can exert a dominant influence on temperature trends over shorter periods, leading to a temporary decoupling of the otherwise expected direct correlation .

Several scientific explanations account for these historical discrepancies. The high heat capacity of the Earth's oceans plays a crucial role, causing a delay in the full impact of increased CO2 on surface temperatures as the oceans absorb a significant portion of the excess heat . Natural climate variability, particularly in the form of ocean oscillations like the El Niño-Southern Oscillation (ENSO), can cause substantial interannual fluctuations in global temperatures that can temporarily mask or amplify the underlying warming trend driven by CO2. Major volcanic eruptions that inject cooling aerosols into the stratosphere can also temporarily offset the warming effect of increasing greenhouse gases. Changes in solar activity, although not the primary cause of recent warming, can also contribute to short-term temperature variations . Additionally, anthropogenic aerosols, such as sulfate particles released from industrial pollution, have a net cooling effect on the climate by reflecting sunlight. Changes in the emissions of these aerosols, for instance due to air quality regulations, can therefore influence temperature trends. It is also important to note that the relationship between CO2 and temperature is not always unidirectional; over very long geological timescales, changes in temperature can drive changes in CO2 concentrations, such as through the outgassing of CO2 from warming oceans. These historical instances of decoupled CO2 and temperature records underscore the complexity of the climate system and highlight that the effect of increasing CO2 can be modulated or temporarily overshadowed by other significant climate forcings and natural variability.

6. Analysing the Hypothetical Cooling Scenario (Next 30 Years)

The hypothetical scenario of Earth experiencing a cooling trend over the next three decades despite a continued increase in atmospheric CO2 levels presents an apparent contradiction to the established understanding that rising CO2 leads to global warming . Such a phenomenon would likely be met with increased skepticism regarding the role of CO2 in driving climate change, despite the overwhelming scientific consensus supporting this link . Therefore, any observed cooling trend under conditions of rising CO2 would necessitate careful and thorough scientific analysis to ascertain the underlying causes . A 30-year cooling trend would indeed be a significant climatic event that would demand intensive investigation and would likely spark considerable discussion within both the scientific community and the broader public and political spheres. Such a scenario would not necessarily invalidate the fundamental principle of the greenhouse gas theory, which posits that CO2 is a greenhouse gas capable of trapping heat in the Earth's atmosphere. However, it would strongly suggest that other factors are exerting a dominant influence on global temperatures during this specific 30-year period, potentially masking or even offsetting the expected warming effect of the increasing CO2 . Furthermore, it might indicate that the climate system's sensitivity to CO2 over shorter timescales is more complex and nuanced than currently understood, or that the timing of the warming response is being significantly modulated by other processes, such as the uptake of heat by the deep ocean, Therefore, this hypothetical cooling trend would likely prompt a re-evaluation of the relative importance of different climate forcings and the role of internal climate variability when considering temperature changes over decadal timescales.

7. Implications for the Greenhouse Gas Theory: Invalidation or Refinement?

A 30-year cooling trend occurring alongside increasing atmospheric CO2 levels would not be of sufficient duration to invalidate the fundamental principles of the greenhouse gas theory. Climate trends are typically evaluated over longer periods, such as three decades, to effectively account for the inherent natural variability within the climate system. The greenhouse gas theory is underpinned by a robust foundation of evidence derived from laboratory experiments demonstrating the heattrapping properties of CO2, extensive atmospheric measurements confirming the increasing concentrations of greenhouse gases, and paleoclimate studies that reveal the long-term relationship between greenhouse gas levels and global temperatures. A temporary cooling trend of three decades would more likely signify the influence of other powerful climate forcings or modes of natural variability that are operating on shorter timescales. The core understanding of the greenhouse effect and the capacity of CO2 to absorb and re-emit infrared radiation, thus trapping heat, would likely remain valid.However, such a scenario would necessitate a careful consideration of whether other climate forcings or internal variability could indeed be strong enough to temporarily mask or counteract the warming effect expected from rising CO2. For instance, a prolonged period of unusually low solar activity could potentially contribute to a temporary cooling trend. Some research suggests that a future extended solar minimum could lead to a slight reduction in global average temperatures. Similarly, a series of major volcanic eruptions occurring within a relatively short period could inject substantial amounts of cooling aerosols into the stratosphere, potentially offsetting global warming for a decade or two. A significant and persistent shift in major ocean current systems, such as a substantial slowdown or even a temporary reversal of the Atlantic Meridional Overturning Circulation (AMOC), could also redistribute heat in a manner that leads to a global cooling trend over three decades, even if the overall heat content of the Earth system continues to increase. Furthermore, changes in anthropogenic aerosol emissions could play a role. While current trends are towards cleaner air and reduced aerosol emissions, a hypothetical scenario involving a large and sustained increase in sulfate aerosol emissions (although less likely given current environmental regulations) could enhance global cooling.

A 30-year cooling trend amidst rising CO2 would likely prompt scientists to re-examine and potentially refine the quantitative aspects of the greenhouse gas theory. This could include a closer look at climate sensitivity estimates and the relative strengths of different feedback mechanisms, particularly those that operate on shorter timescales. Such an event might also spur improvements in climate models to better represent the complex interactions between long-term forcings like greenhouse gas increases and shorter-term natural variability. 

Additionally, it could highlight areas where our understanding of specific climate processes, such as cloud feedback mechanisms or the rate of ocean heat uptake, requires further refinement and investigation. Thus, while not invalidating the core theoretical framework, a cooling trend under these conditions would likely stimulate further research and potentially lead to a more nuanced and precise quantitative understanding of the climate system's dynamics.

8. Exploring Alternative Explanations for a Cooling Trend with Rising CO2.

Several potential scientific explanations could account for a global cooling trend occurring over the next 30 years despite a continued increase in atmospheric CO2 concentrations . One possibility involves a prolonged period of exceptionally low solar activity . While the long-term warming effect of increased CO2 is substantial, a deep and extended solar minimum could potentially exert a cooling influence that partially offsets this warming, possibly leading to a net cooling trend over three decades. Historical records suggest that periods of reduced solar activity have, in some instances, coincided with cooler global temperatures.

Another plausible explanation could be a series of major volcanic eruptions occurring within a relatively short timeframe. If several large, explosive volcanic eruptions were to happen in succession, the cumulative effect of the sulfur dioxide injected into the stratosphere could lead to a sustained increase in the reflection of solar radiation back into space, causing a global cooling effect that might last for a couple of decades. A substantial and persistent shift in major ocean current systems represents another potential mechanism for a cooling trend . A significant weakening or a change in the path of key ocean currents, such as the Gulf Stream or other components of the Global Conveyor Belt, could lead to a redistribution of heat across the globe. This could result in a cooling trend in some regions and potentially a net global cooling over a 30-year period, even if the overall heat content of the Earth system continues to rise due to greenhouse gas forcing .

While current global trends are towards reducing air pollution, it is worth considering the role of anthropogenic aerosols. Sulfate aerosols, released primarily from the burning of fossil fuels, have a cooling effect on the planet by reflecting sunlight. A hypothetical scenario involving a large and sustained increase in sulfate aerosol emissions, perhaps due to a resurgence in the use of coal without stringent pollution controls, could potentially lead to an enhanced global cooling effect that might temporarily overwhelm the warming from rising CO2. However, this scenario is less probable given the increasing global awareness of air quality issues and the push for cleaner energy sources.

Anthropogenic aerosols, particularly sulfate aerosols originating from industrial pollution and the burning of fossil fuels, are known to reflect incoming solar radiation, thereby exerting a cooling influence on the Earth's climate. This cooling effect has been estimated to have partially offset the warming caused by the increase in greenhouse gases over the industrial era. Consequently, changes in the emissions of these aerosols can have a significant impact on global temperature trends. For example, reductions in aerosol emissions, driven by efforts to improve air quality, could lead to a decrease in this cooling effect, potentially resulting in a period of accelerated warming as the masking effect of aerosols diminishes.Conversely, a substantial and sustained increase in sulfate aerosol emissions, while less likely under current global trends, could theoretically contribute to a cooling trend. However, achieving a 30-year global cooling trend solely due to changes in aerosols while CO2 continues its upward trajectory appears improbable, given the magnitude of the warming forcing associated with increasing greenhouse gas concentrations.

9. Discussion

The hypothetical scenario of a 30-year global cooling trend despite increasing atmospheric CO2 concentrations presents a complex challenge to our understanding of the climate system. While the fundamental physics of the greenhouse effect, where CO2 traps outgoing infrared radiation, is well-established , the climate system's response to this forcing is modulated by a multitude of interacting factors. A sustained cooling over three decades would strongly suggest that other powerful natural or anthropogenic forcings are temporarily overriding the expected warming signal from rising CO2.

One prominent factor to consider is natural climate variability. The Sun's activity follows an approximately 11-year cycle, and prolonged periods of lower solar output have been linked to cooler temperatures in the past . While current scientific consensus indicates that solar variations are not the primary driver of the long-term warming trend , an exceptionally deep and extended solar minimum could potentially exert a significant cooling influence over a 30-year period.

Volcanic eruptions represent another significant source of natural climate variability. Major explosive eruptions inject sulfur dioxide into the stratosphere, (most recently Hunga Tunga) which converts to sulfate aerosols that reflect sunlight back into space, causing a temporary global cooling. A cluster of large eruptions occurring within a few decades could potentially lead to a sustained cooling trend that lasts for the better part of 30 years.

Ocean currents play a crucial role in redistributing heat around the globe. Shifts in major ocean circulation patterns, such as a significant weakening of the Atlantic Meridional Overturning Circulation (AMOC), could lead to regional cooling in some areas and potentially contribute to a global cooling trend over several decades. The slow timescales associated with deep ocean processes mean that their impact on surface temperatures can unfold over extended periods.

Anthropogenic aerosols, particularly sulfate aerosols from the burning of fossil fuels, have a net cooling effect on the climate by reflecting sunlight. While efforts to improve air quality are leading to reductions in these aerosols in many parts of the world, a hypothetical scenario involving a substantial and sustained increase in their emissions could enhance global cooling, potentially masking the warming effect of rising CO2 for a few decades.

It is important to note that a 30-year cooling trend would not necessarily invalidate the greenhouse gas theory. Climate scientists emphasize that long-term trends, typically assessed over periods of 30 years or more, are needed to discern the impact of sustained forcings like greenhouse gas increases from shorter-term natural variability. A temporary cooling period would more likely highlight the complex interplay of various factors that influence Earth's climate and the potential for other forcings to dominate on decadal timescales.

Such a scenario would undoubtedly spur further scientific investigation into the relative contributions of different climate forcings and the mechanisms through which they interact. It might also lead to refinements in climate models to better capture the nuances of shortterm climate variability and improve their predictive capabilities over decadal timescales. Ultimately, while a 30-year cooling trend alongside rising CO2 would be an intriguing phenomenon, it would likely serve as a catalyst for deeper understanding rather than a refutation of the fundamental role of CO2 in Earth's long-term climate.

I hope you have enjoyed reading this paper.

David-Gareth and Bill.


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