Homo sapiens now rivals the great forces of nature. Humanity is a prime driver of change of the Earth system. Industrialised societies alter the planet on a scale equivalent to an asteroid impact. This is how the Anthropocene – the proposed new geological period in which human activity profoundly shapes the environment – is often described in soundbites.
But is it possible to formalise such statements mathematically? I think so, and believe doing this creates an unequivocal statement of the risks industrialised societies are taking at a time when action is vital.
Following the maxim of keeping everything as simple as possible, but not simpler, Will Steffen from the Australian National University and I drew up an Anthropocene equation by homing in on the rate of change of Earth’s life support system: the atmosphere, oceans, forests and wetlands, waterways and ice sheets and fabulous diversity of life.
For four billion years, the rate of change of the Earth system (E) has been a complex function of astronomical (A) and geophysical (G) forces plus internal dynamics (I): Earth’s orbit around the sun, gravitational interactions with other planets, the sun’s heat output, colliding continents, volcanoes and evolution, among others.
That rate of change has been anything but steady of late. If we take a baseline of the last 7000 years, until recently, global temperature decreased at a rate of 0.01 °C per century. The current rate (last 45 years) is a rise of 1.7 °C per century – 170 times the baseline and in the opposite direction. The warmest 12 years since records began have all occurred since 1998.
The rate of carbon emissions to the atmosphere is arguably the highest in 66 million years, when the (non-avian) dinosaurs slipped off this mortal coil. The staggering loss of biodiversity in recent decades prompted researchers in 2015 to argue that the Anthropocene marks the third stage in the evolution of Earth’s biosphere, following on from the microbial stage 3.5 billion years ago and the Cambrian explosion 650 million years ago.
Pulling this together, we conclude that the rate of change of the Earth system over the last 40 to 50 years is a purely a function of industrialised societies (H).
In the equation, astronomical and geophysical forces tend to zero because of their slow nature or rarity, as do internal dynamics, for now. All these forces still exert pressure, but currently on orders of magnitude less than human impact.
This is a bold statement. But viewed this way, arguments about humans versus natural causes disappear. In 2016, Earth experienced a massive El Niño event affecting the global climate. But this is balanced by the cooler La Niña – taken together, the net rate of change of the Earth system resulting from these is zero over a decade or so.
False sense of security
We should be concerned. For the last 2.5 million years, Earth settled into a rather unusual period of potential instability as we rocked back and forth between ice ages and intervening warm periods, or interglacials. Far from living on a deeply resilient planet, we live on a planet with hair triggers. Industrialised societies are fumbling around with the controls, lulled into a false sense of security by the deceptive stability of the Holocene, the last 11,700 years. Remarkably and accidentally, we have ejected the Earth system from the interglacial envelope and are heading in to unchartered waters.
While the rate of change of the Earth system needs to drop to zero as soon as possible, the next few years may determine the trajectory for millennia. Yet the dominant neoliberal economic systems still assume Holocene-like boundary conditions – endless resources on an infinite planet. Instead, we need “biosphere positive” Anthropocene economics, where economic development stores carbon not releases it, enhances biodiversity not destroys it and purifies waters and soils not pollutes them.
While it would seem imprudent to ignore the huge body of evidence pointing to profound risks, it comes at a challenging time geopolitically, when both fact-based world views and even international cooperation are questioned. Nowhere has this been clearer than in the US in recent weeks.
It is perhaps surprising that in the 1990s, Stephen Bannon, White House strategist and ideologue, was CEO of Biosphere 2, a project in Arizona to create an artificial habitat for humans, partly to inform potential space colonisation missions. The delicate balance between humans and nature in Biosphere 2 collapsed into chaos and the experiment folded in 1994.
While Biosphere 1 – Earth – is in no such short-term danger, societies are. The stakes could not be higher, yet critical knowledge and action needed for stability is in danger of becoming collateral damage in today’s war on facts. Ignorance and uncertainty are no longer rational excuses for inaction.
Journal reference: The Anthropocene Review, doi: 10.1177/2053019616688022
What was measured:
Original Journal Entry:
The Anthropocene equation
First Published February 10, 2017
Human activities now rival the great forces of nature in driving changes to the Earth System (Steffen et al., 2007). This has led to the proposal that Earth has entered a new geological epoch – the Anthropocene (Crutzen, 2002; Crutzen and Stoermer, 2000). While substantial data have been gathered in support of the Anthropocene proposal (Waters et al., 2016), what has been missing is a high-order conceptual framework of the Earth System’s evolution within which the Anthropocene can be compared with other changes in Earth history. We propose that in terms of the rate of change of the Earth System, the current regime can be represented by an ‘Anthropocene equation’.
Earth is approximately 4.54 billion years old (Dalrymple, 2001). The Earth System is a single, planetary-level complex system composed of the biosphere, defined here as the sum of all biota living at any one time and their interactions, including interactions and feedbacks with the geosphere defined here as the atmosphere, hydrosphere, cryosphere and upper part of the lithosphere (Steffen et al, 2016). The age of Earth’s biosphere has been estimated at 3.7–4.1 billion years old (Bell et al., 2015; Nutman et al., 2016). Astronomical and geophysical forces have been the dominant external drivers of Earth System change during this period (McGregor et al., 2015; Petit et al., 1999). Astronomical forces that affect insolation and relate to solar irradiance include orbital eccentricity, obliquity and precession driven by gravitational effects of the sun and other planets (Milanković, 1941), and impact events. Geophysical forces include volcanic activity, weathering and tectonic movement.
where A is astronomical forcing, G is geophysical forcing.
While astronomical and geophysical forcings have been dominant drivers pulling the Earth System into new states (i.e. ‘basins of attraction’), internal dynamics, including biospheric evolutionary processes, interacting with these drivers, can also drive major Earth System change, for example, the Great Oxygenation Event 2.4 billion years BP that took place over hundreds of millions of years (Konhauser et al., 2009). Throughout Earth’s past, strong negative feedbacks arising from the internal dynamics of the Earth System, often involving the biosphere, have assured long periods – hundreds of millions of years at times – of relative stability (Lenton and Williams, 2013). Internal dynamics are particularly important because of their influence on the atmospheric concentration of greenhouse gases such as carbon dioxide, which in turn significantly influence the climate (Lenton, 2016).
Therefore, for completeness, an equation for the rate of change of the Earth System can be given as:
where I is internal dynamics of the Earth System.
In the recent past, subdivisions of the Quaternary (2.588 Myr to present) have been defined by climate forcing related to cyclical variation in Earth’s orbit coupled with other astronomical forcings, changes in solar irradiance, and irregular events such as volcanic eruptions (Berger et al., 2006). At present, the Earth System of the Quaternary is typified by saw-tooth oscillations of glacial–interglacial cycling initially with 40,000-year periodicity until ~1.2 Myr BP, then switching to 100,000-year periodicity. Homo sapiens evolved during a rather unusual state of potential instability in Earth’s history (Lenton and Williams, 2013). While astronomical forcing (A) has been the overriding external trigger of change in the Quaternary, relatively small astronomical forcings have resulted in distinctly different states of the Earth System because of the strong influence of internal dynamics (I), with bifurcation points influenced by small changes in atmospheric concentrations of carbon dioxide (Berger et al., 2006; Ganopolski et al., 2016). Under current astronomical forcing and atmospheric levels of carbon dioxide of about 280 ppm, Holocene-like conditions could have been expected for probably another 50,000 years (Ganopolski et al., 2016).
However, an entirely new forcing is now driving change in the Earth System: human activity (H). Although H is a subset of I (internal dynamics), here we argue that the magnitude, the unique nature of the forcing in the history of the planet, and the rate have now become so profound that H deserves to be considered in its own right in the context of Earth System dynamics. After Schellnhuber (1999), we write:
How significant is H as a driver of the rate of change of the Earth System? Steffen et al. (2004, 2011, 2015b) identified trends in socio-economic activities representative of H over the past 2.5 centuries and found a broad correlation with Earth System changes, as measured by the rates of change of biodiversity, atmospheric chemistry, marine biogeochemistry and land-use change amongst others. The authors noted a very sharp increase in the rate of change of both H and E since 1950 and a strong coupling between the two, a phenomenon now known as the Great Acceleration (Hibbard et al., 2006; Steffen et al., 2007).
Examination of individual Earth System processes show the remarkable domination of H over the other three factors in equation (3). For example, in one century, the Haber-Bosch process has doubled the amount of reactive nitrogen in the Earth System relative to the pre-industrial baseline, arguably the largest and most rapid impact on the nitrogen cycle for some ~2.5 Ga (Canfield et al., 2010). The rate of change of ocean carbonate chemistry – ocean acidification – is potentially unparalleled in at least the last ~300 Ma (Hönisch et al., 2012). The rate of carbon emissions to the atmosphere (~10 Pg/yr) are probably the highest they have been in ~66 Ma, since the start of the Cenozoic (Cui et al., 2011; Zeebe et al., 2016) (Table 1).
Notes: Current rates of change of key Earth System processes (climate, biosphere and biogeochemical cycles) relative to various time intervals in the geological and historical past. Ranges are included where significant uncertainty exists, for example, extinction rates.
For biodiversity, typical rates of background extinction are estimated to be around 0.1 extinctions/million species years (De Vos et al., 2015). Current extinction rates are estimated to be tens to hundreds of times higher than natural background rates of extinction (Barnosky et al., 2012; Ceballos et al., 2015). Humans have now modified the structure and functioning of the biosphere to such an extent that the Anthropocene may mark the beginning of a third stage in the evolution of Earth’s biosphere, following the microbial stage from ~3.5 Ga BP and the metazoan from ~650 Ma (Williams et al., 2015).
In the last 7000 years, ice volumes on Earth stabilised and carbon dioxide (CO2) levels have changed only slowly over that period. This provides a Holocene baseline for assessment of the Anthropocene rate of change of the climate system (Waters et al., 2016). Atmospheric CO2, now above 400 parts per million (ppm) is 120 ppm higher than the Holocene baseline, and has increased ~100 times as fast as the most rapid rise during the last glacial termination (Loulergue et al., 2008). Atmospheric CH4 concentration has risen rapidly to 1810 ppb in 2012, a level 2.5 times the level in 1750 (722 ppb) (Saunois et al., 2016). The rate of change appears extraordinary compared with natural changes and is more than double any observed value in the past 800,000 years (Loulergue et al., 2008; Wolff, 2011).
From 9500 to 5500 years BP global average temperature plateaued, followed by a very slight cooling trend (Marcott et al., 2013). Over the last 7000 years the rate of change of temperature was approximately −0.01°C/century. Over the last hundred years, the rate of change is about 0.7°C/century (Intergovernmental Panel on Climate Change (IPCC), 2013), 70 times the baseline – and in the opposite direction. Over the past 45 years (i.e. since 1970, when human influence on the climate has been most evident), the rate of the temperature rise is about 1.7°C/century (NOAA, 2016), 170 times the Holocene baseline rate.
We deduce, therefore, that astronomical and geophysical forcings in the Holocene, and perhaps even through the entire Quaternary, approximate to zero compared with the impact of current human pressures on the rate of change of the Earth System (Ganopolski et al., 2016; McGregor et al., 2015; Steffen et al., 2004, 2015a; Waters et al., 2016; Williams et al., 2015). We also note from the rates of change described above that I now is also significantly less than H. Therefore, following from Schellnhuber (1999), but more directly based on Steffen et al. (2004, 2011, 2015b), the current rate of change of the Earth System at the highest level of abstraction can be represented as:
which might be termed the ‘Anthropocene equation’.
When did H come to dominate the astronomical and geophysical forcings and the internal dynamics of the Earth System? Although there have been several proposed start dates for the Anthropocene, including the Neolithic revolution (Ruddiman, 2013), the rise of European empires and subsequent colonialisation (Lewis and Maslin, 2015), and the Industrial Revolution (Crutzen, 2002), none can match the mid-20th-century, global-level, synchronous step change in human enterprise and the simultaneous human-driven change in many features of Earth System structure and functioning. That is, anthropogenic impact crossed a critical threshold around 1950 with the beginning of the Great Acceleration, when H moved from being a force of similar or smaller magnitude to A and G, to usurping them entirely (Steffen, 2004, 2007, 2011; Waters, 2016).
An obvious, and critical, next step is to represent H as a sub-system of the Earth System because it is now the prime forcing driving the rate of change of the Earth System. Although a full analysis of H is beyond the scope of this paper (see McNeill and Engelke, 2016, for an analysis of the Great Acceleration), we note one attempt at describing the system dynamics of H that is particularly relevant here because it attempted to describe the dynamics of the Great Acceleration (Figure 1; adapted after Hibbard et al., 2006).
Based on Figure 1, we can represent H as:
where P is population (more specifically the global ‘consumers’: the upper and middle classes as defined by income on a national basis), C is consumption (and by definition production), and T is the Technosphere (Haff, 2014), a concept particularly well-suited to Earth System analysis (Zalasiewicz et al., 2014a). Note that equation (5) has similarities to the IPAT identity of Holdren and Ehrlich (1974).
The Technosphere can be further broken down as follows:
where En is the energy system, K is knowledge and Pe is political economy, which relates to economic systems bound by political decisions, now overwhelmingly dominated by globalisation (it is worth noting that not all individuals or groups of people are equally responsible for the impacts of H on dE/dt (Malm and Hornborg, 2015)), as shown in Figure 1. However the term H is characterised in detail, the Anthropocene equation shows the domination of natural forcings by human forcings, particularly since the mid-20th century (Hamilton and Grinevald, 2015).
Figure 2 shows a potential future trajectory of the Earth System in the Anthropocene, with the system in 2016 poised at a critical position. Remaining within the interglacial conditions of the late Quaternary will require the exceptionally rapid rate of change of the Earth System to return to close to zero, with human forcings reduced to levels less than, or at least comparable to, astronomical and geophysical forcings and the internal dynamics of the Earth System. Sustained human pressures risk abrupt exiting of the glacial–interglacial limit cycle of the late Quaternary (Clark et al., 2016; Ganopolski et al., 2016), and ushering in Earth’s sixth great extinction event (Barnosky et al., 2012).
While the next few decades are crucial in setting the trajectory of H, and hence of the Earth System, over the next tens of thousands of years (Clark et al., 2016; Ganopolski et al., 2016), in the longer term the domination of H over A, G and I is very likely to be a transient condition, perhaps similar to the Paleocene-Eocene Thermal Maximum (PETM) 56 million years ago (Hönisch, et al. 2012). In that event, a massive release of carbon (between 3000 and 7000 PgC), possibly from methane hydrates in the sea floor, drove a temperature spike of 4–8°C over a few thousand years (Steffen et al., 2016; Zeebe et al., 2016). During the PETM, a sharp perturbation in G over a few thousand years drove the instability in the Earth System, but it was short-lived with the system returning to its long-term trajectory 100,000–200,000 years after the carbon release as A, G and I restored their long-term control of the system.
In the case of the Anthropocene, efforts to achieve the long-term viability of a global civilisation – global sustainability – implies that Homo sapiens will deliberately and rapidly reduce its impacts on the Earth System so that they are more comparable in magnitude and more synergistic with A, G and particularly I. Alternatively, continued increases in H could well lead to abrupt changes in the Earth System that could trigger societal collapse, forcibly reducing H dramatically and returning control of the system to A, G and I. The legacy of the impacts of H on I through changes in the biosphere could, however, be discernible in the internal dynamics of the Earth System for millions of years (Williams et al., 2015).
The authors thank Hans Joachim Schellnhuber for helpful comments on an early version of the manuscript. This paper is a contribution to the Future Earth research agenda.
Funding This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.
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