investors own 52% of the MSCI World and 77% of the MSCI USA (Medina et al., 2022, Figure 4.3, page 33). In other countries, these figures are lower: 39% of the MSCI Europe, 31% of the MSCI Japan and 16% of the MSCI Emerging Markets.

<table><caption>Table 6.3: Major holders of Exxon Mobil Corporation (percentage and cumulative)</caption><thead><tr><th>#</th><th>Institutional investor</th><th>%</th><th>Cum.</th><th>Top mutual fund holders</th><th>%</th><th>Cum.</th></tr></thead><tbody><tr><td>1</td><td>Vanguard</td><td>9.80</td><td>9.80</td><td>Vanguard Total Stock Market</td><td>3.15</td><td>3.15</td></tr><tr><td>2</td><td>Blackrock</td><td>6.88</td><td>16.68</td><td>Vanguard 500 Index Fund</td><td>2.47</td><td>5.62</td></tr><tr><td>3</td><td>State Street</td><td>5.44</td><td>22.12</td><td>SPDR Energy Select</td><td>2.05</td><td>7.67</td></tr><tr><td>4</td><td>Fidelity Investments</td><td>3.71</td><td>25.83</td><td>Fidelity 500 Index Fund</td><td>1.19</td><td>8.86</td></tr><tr><td>5</td><td>Geode Capital Management</td><td>1.93</td><td>27.76</td><td>SPDR S&P 500 ETF Trust</td><td>1.16</td><td>10.02</td></tr><tr><td>6</td><td>JP Morgan Chase</td><td>1.55</td><td>29.31</td><td>iShares Core S&P 500 ETF</td><td>1.01</td><td>11.03</td></tr><tr><td>7</td><td>Bank of America</td><td>1.48</td><td>30.79</td><td>Vanguard Value Index Fund</td><td>0.84</td><td>11.87</td></tr><tr><td>8</td><td>Morgan Stanley</td><td>1.41</td><td>32.20</td><td>Vanguard Institutional Index Fund</td><td>0.67</td><td>12.54</td></tr><tr><td>9</td><td>NBIM</td><td>1.39</td><td>33.59</td><td>Vanguard Dividend Appreciation</td><td>0.58</td><td>13.12</td></tr><tr><td>10</td><td>Northern Trust</td><td>1.08</td><td>34.67</td><td>Vanguard Energy Index Fund</td><td>0.53</td><td>13.65</td></tr></tbody></table>

Source: finance.yahoo.com/quote/XOM/holders.

<table><caption>Table 6.4: Major holders of BP p.l.c. (percentage and cumulative)</caption><thead><tr><th>#</th><th>Institutional investor</th><th>%</th><th>Cum.</th><th>Top mutual fund holders</th><th>%</th><th>Cum.</th></tr></thead><tbody><tr><td>1</td><td>State Street</td><td>0.78</td><td>0.78</td><td>DFA International Core Equity</td><td>0.13</td><td>0.13</td></tr><tr><td>2</td><td>Fisher Asset Management</td><td>0.68</td><td>1.46</td><td>Vanguard Energy Fund</td><td>0.12</td><td>0.25</td></tr><tr><td>3</td><td>Arrowstreet Capital</td><td>0.65</td><td>2.11</td><td>John Hancock Mutual Fds III</td><td>0.12</td><td>0.37</td></tr><tr><td>4</td><td>Acadian Asset Management</td><td>0.61</td><td>2.72</td><td>Vanguard Growth and Income Fund</td><td>0.09</td><td>0.46</td></tr><tr><td>5</td><td>Morgan Stanley</td><td>0.48</td><td>3.20</td><td>T. Rowe Price Real Assets Trust</td><td>0.08</td><td>0.54</td></tr><tr><td>6</td><td>Dimensional Fund Advisors</td><td>0.43</td><td>3.63</td><td>T. Rowe Price Real Assets Trust I</td><td>0.08</td><td>0.62</td></tr><tr><td>7</td><td>Blackrock</td><td>0.39</td><td>4.02</td><td>T. Rowe Price New Era Fund</td><td>0.07</td><td>0.69</td></tr><tr><td>8</td><td>Wellington Management</td><td>0.37</td><td>4.39</td><td>T. Rowe Price Real Assets Fund</td><td>0.07</td><td>0.76</td></tr><tr><td>9</td><td>Boston Partners</td><td>0.32</td><td>4.71</td><td>DFA International Value Series</td><td>0.06</td><td>0.82</td></tr><tr><td>10</td><td>Goldman Sachs</td><td>0.32</td><td>5.03</td><td>BlackRock Basic Value Fund</td><td>0.05</td><td>0.87</td></tr></tbody></table>

Source: finance.yahoo.com/quote/BP/holders.

There is also a large dispersion among companies in the same industry. In Tables 6.3 and 6.4 we report on the major shareholders of Exxon Mobil Corporation and BP p.l.c. and find that the capital structure is completely different. These two companies operate in the oil and gas sector. The top 10 institutional investors control almost 35% of Exxon, while they control only 5% of BP. On average, with the rise of passive management, ownership of listed companies tends to be concentrated among a small number of investors, particularly institutional investors. For example, the top three institutional investors own 23.50% of US listed companies. These figures are 22.60% in the United Kingdom, 21.70% in Denmark and 20.10% in the Netherlands (Medina et al., 2022, Table A.3, page 49). In the United States, the top three institutional investors are typically Vanguard, BlackRock, and State Street. These three asset managers dominate the market for passive management, giving rise to the concept of the “Big Three” (Fichtner et al., 2017). Bebchuk and Hirst (2019) showed that “the Big Three have quadrupled their collective ownership stake in S&P 500 companies over the past two decades; [...] they collectively cast an average of about 25% of the votes at S&P 500 companies.” Extrapolating from past trends, the Big Three could cast 40% of the votes at S&P 500 companies within two decades. The authors concluded that “voting in most significant public companies will come to be dominated by the future Giant Three.” Azar et al. (2021) examined the influence of the
Big Three in reducing corporate carbon emissions worldwide. By analyzing their engagement with individual companies, the study found that they focus on large companies with high CO2 emissions and significant ownership stakes. It also found a negative relationship between Big Three ownership and subsequent carbon emissions among MSCI index constituents, which strengthens over time as these institutions publicly commit to addressing ESG issues. This example shows that institutional investors have significant engagement and voting power, and they can certainly influence companies.

### 6.1.5 Performance of active ownership

Previously, we have seen that institutional investors have a lot of power to engage with companies and to vote. However, we may wonder whether active ownership has a real impact on companies. Measuring the performance and success of active ownership is not an easy task. Certainly, the most famous research on these issues is the study conducted by Dimson et al. (2015):

> "We analyze an extensive proprietary database of corporate social responsibility engagements with US public companies from 1999-2009. Engagements address environmental, social, and governance concerns. Successful (unsuccessful) engagements are followed by positive (zero) abnormal returns. Companies with inferior governance and socially conscious institutional investors are more likely to be engaged. Success in engagements is more probable if the engaged firm has reputational concerns and higher capacity to implement changes. Collaboration among activists is instrumental in increasing the success rate of environmental/social engagements. After successful engagements, particularly on environmental/social issues, companies experience improved accounting performance and governance and increased institutional ownership." (Dimson et al., 2015, page 3225).

Two measures of performance are then used: the stock market reaction to engagements (or cumulative abnormal returns around initial engagements) and the company's post-engagement ESG performance (or post-engagement ESG score/rating). This initial publication has been followed by a few studies that have at least partially confirmed these results (Grewal et al., 2016). However, we must be cautious about these academic conclusions for several reasons. First, as we saw earlier, there are different forms of engagement, and some of them, such as behind-the-scenes engagement, are not public. In this case, it is not possible to assess their performance. Second, the different forms of engagement are usually employed by different investors at the same time. How can the impact of one form be disentangled from that of another? For example, most shareholder resolutions do not receive majority support. However, Grewal et al. (2016) found that they can have an impact. We may wonder whether this is just because shareholders have proposed a resolution or whether it is due to other forms of engagement, particularly engage behind the scenes, voice or exit. A third reason is that the results of most theoretical models are very sensitive and can lead to different conclusions depending on the framework. In particular, equilibria are very fragile (Gollier and Pouget, 2022) or can be multiple (Levit et al., 2024). These models emphasize that multiple factors are at play, meaning that each engagement is unique. This is also the view of professionals who engage with companies. The success of the engagement depends not only on the investors, but also to a large extent on the management of the company, the shareholder structure and the country. Investors have the impression that it's case-by-case and that we can't generalize, especially since there's a lot of survivor bias. In fact, investors communicate a lot about their successes, but there are many unsuccessful cases that are not known and not in databases. The final reason is that different forms of engagement do not have the same impact. For example, the performance of exit is generally considered to be negative. The same conclusion applies to voting, since most shareholder resolutions never receive a majority.
## 6.2 ESG voting

According to PRI (2021b), voting is the most important pillar of an engagement policy and a powerful tool in the stewardship toolkit. Over the years, voting has become an integral part of many ESG investment policies. In this section, we introduce the voting process and how proxy voting works. We also discuss the voting principles that define a voting policy. Finally, we present the current landscape of ESG voting with statistics on asset managers and asset owners.

### 6.2.1 Voting process

Each country has its own voting process. Nevertheless, they share some common ground. According to NBIM (2020), they typically include the following steps:

* "The company sets the agenda for the annual shareholder meeting;

* The custodian confirms the identity of the shareholders and the number of shares eligible for voting — often for a specific date ahead of the meeting (record date);

* Shareholders receive the meeting materials from the company (may be before or after the record date);

* Shareholders procuring proxy advisory services receive voting recommendations;

* Shareholders instruct the custodian on how to vote, often through a proxy voting service provider, within a deadline ahead of the shareholder meeting (cut-off date);

* Voting takes place at the shareholder meeting;

* Shareholders receive confirmation from the service provider that their voting instructions have been carried out."

### 6.2.2 Proxy voting

Proxy voting is a process by which a shareholder of a company authorizes another party, known as a proxy, to attend the annual general meeting (AGM) and vote on his or her behalf. This allows shareholders who are unable or unwilling to attend the meeting to participate in the decision-making process. This may be for a variety of reasons, including that the shareholder is unable to attend the meeting in person or prefers to have someone with more expertise or aligned interests vote on his or her behalf. Proxy voting is very common in the asset management industry because asset managers generally do not have the resources to attend thousands of shareholder meetings. Therefore, they hire a proxy firm to do the job.

According to Larcker et al. (2018), the proxy voting market is dominated by two firms:

* **Institutional Shareholder Services (ISS)**
  Founded in 1985, ISS is the world's largest proxy advisory firm, providing recommendations on more than 40 000 shareholder meetings each year. They provide research, analysis, and voting recommendations on a wide range of corporate governance issues, including executive compensation, board composition, and environmental and social responsibility (ESG) proposals. The firm employs 3 000 employees across 25 global locations in 15 countries and serves approximately 3 400 clients. It is owned by Deutsche Börse Group.
* Glass Lewis

Founded in 2003, Glass Lewis is the second largest proxy advisory firm in the world, advising on more than 30 000 shareholder meetings annually in over 100 countries. Similar to ISS, they provide research, analysis and voting recommendations on various corporate governance issues to influence the decisions of institutional investors. The firm employs 380 employees and serves approximately 1 300 investors. It is owned by Peloton Capital Management, a private equity firm, and Stephen Smith, a financial services entrepreneur.

As of 2021, Shu (2024) estimates that ISS and Glass Lewis collectively control approximately 90% of the US market. The other major players in the US are Egan-Jones Proxy Services and Broad- bridge/ProxyVote. However, ISS and Glass Lewis are global players with a strong presence in Europe. They have also acquired many local players such as Proxinvest in France (Glass Lewis) or Nordic Investor Services in Sweden (ISS).

<figure><img src="image_271.png" /><figcaption>Figure 6.7: The two largest proxy advisory firms</figcaption></figure>

According to many academic studies, proxy voting has many drawbacks and controversies (Davis and Kim, 2007; Larcker et al., 2018; Malenko et al., 2021; Bernard et al., 2023). The main criticism is that proxy voting implies homogeneity of votes for two main reasons. The first is that most investors follow the recommendations of the proxy advisor, resulting in a high correlation among institutional votes (Shu, 2024). The second is that the market is highly concentrated. These two reasons mean that there is a lack of diversity in voting. As a result, we may face a situation where it is difficult to distinguish the votes of ESG and non-ESG mutual funds or the votes of two different investors. The similarity between the votes has led to the emergence of the concept of robo-voting. Strictly defined, robo-voting is the phenomenon whereby an investor or a mutual fund automatically adopts the voting recommendations of its proxy advisor. This practice has been facilitated by the emergence of online voting platforms, which allow proxy advisors to pre-fil these platforms with their recommended votes, making the process more streamlined for investors and funds. In a broader sense, robo-voting involves investors closely following the recommendations of proxy firms, with minimal adjustments made only to demonstrate a degree of independent decision- making. According to Matsusaka and Shu (2024), the phenomenon of robo-voting is underestimated, but it applies mainly to small investors and index funds.

**Remark 74** Proxy voting and proxy advisory firms are regulated by the SEC. In July 2020, the SEC adopted rule amendments regarding proxy advisory services, reaffirming that they constitute a solicitation under the federal proxy rules. They clarified that the omission of certain information could violate antifraud provisions and introduced more disclosure and procedural requirements for proxy advisors to maintain exemptions from the federal proxy rules. The goal was to provide more transparent, accurate and complete information to investors using proxy advisory services. However, in July 2022, the Securities and Exchange Commission adopted rule amendments that rescinded significant portions of the 2020 rules.
### 6.2.3 Defining a voting policy

A voting policy refers to the guidelines or principles that institutional investors, such as mutual funds, pension funds, or other entities with significant ownership stakes in publicly traded companies, use to guide their decisions when voting on corporate matters at shareholder meetings. These voting policies outline the criteria and considerations that investors use to evaluate proposals made by companies, such as the election of directors, executive compensation plans, mergers and acquisitions, corporate governance practices, environmental and social responsibility initiatives, and other matters that may affect shareholder value. The terms “voting policy”, “proxy voting guidelines” or “voting principles” are interchangeable. In Figure 6.8, we show four different voting policies from two asset managers (DWS and Vanguard) and two asset owners (Ontario Teachers’ pension plan and New York City pension funds).

<figure><img src="image_272.png" /><figcaption>Figure 6.8: Voting policy</figcaption></figure>

Source: Corporate websites.

An example of the structure of a voting policy is shown in Box 6.3. In most cases, a proxy voting policy is articulated around the same components. For instance, Vanguard identifies four pillars: (1) board composition and effectiveness, (2) board oversight of strategy and risk, (3) executive compensation, and (4) shareholder rights. BlackRock defines its proxy voting policy around the following themes: (1) boards and directors, (2) auditors and audit-related issues, (3) capital structure proposals, (4) mergers, acquisitions, transactions and other special situations, (5) executive compensation, (6) material sustainability risks and opportunities, (7) general corporate governance issues, and (8) shareholder protection. The voting policy of DWS has five components: (1) board, (2) management and board remuneration, (3) audit related agenda items, (4) financial accounts, use of profits and share capital related items, (5) say on climate and shareholder decarbonisation proposals, (6) statutes & legal structure agenda items, (7) market for control, (8) related-party transactions and (9) shareholder proposals. For the asset owner Ontario Teachers' pension plan, five issues are important: (1) board composition, (2) compensation, (3) corporate structure and capital management, (4) takeover protections and (5) shareholder rights and shareholder proposals. These examples illustrate the recurrence of certain elements, including boards, compensation, auditing, and shareholder rights, while sustainability, ESG and climate issues depend on the institutional investor. Voting guidelines are generally descriptive, but they also include some quantitative constraints. Here are two examples: (1) “CalSTRS generally supports poison pills that are applied equitably to all shareholders, have at least 20% trigger threshold and have a sunset provision of no more than three
Box 6.3: Amundi voting guidelines (structure of the voting policy)

1. Shareholders' rights: "A corporate governance regime must protect and facilitate the exercise of shareholders' rights and ensure fair treatment of all shareholders, including minority and foreign shareholders."

* General meeting organization

* Voting rights and shareholder retention

* Anti-takeover measures

* Overall balance and transparency (payment of a responsible dividend, discharge of directors, choice and remuneration of auditors, regulated agreements)

* Relocations and change of listing

2. Boards, committees and governing bodies: "While the board is accountable to the company and its shareholders, it must also take due account of other stakeholders and respect their interests, in particular those of employees, creditors, clients and suppliers."

* Quality of corporate governance information (quality of comply or explain on governance, board responsiveness)

* Composition and balance of the board (independence, audit committee, nomination committee, remuneration committee)

* A clear distribution of powers to forestall conflicts of interest

* Functioning of the board

* Attendance fees and remuneration of non-executive directors

3. Financial structure: "With regard to shareholders' rights, [...] cumulative capital increases should not represent more than 60% of share capital."

* Share issues without preferential subscription rights

* Share issuance with preferential subscription rights

* Mergers, acquisitions, demergers and other restructuring projects

* Repurchase of own shares

* Employee share ownership

4. Remuneration policy

* General principles on executive remuneration

* Balance of remuneration and value sharing

* Transparency and remuneration report

* Stock option and performance share plans

* Severance pay

* Pension plans

* Exceptional remunerations (discretionary Power)

5. Environmental and Social issues

* Natural capital preservation and the energy transition (say on climate)

* Social cohesion

* Board responsibility on environmental and social issues

* Shareholder proposals
years. CalSTRS believes that all poison pills should be approved by shareholders within 12 months or the next shareholder meeting, whichever comes first.”; (2) “Fidelity generally will support employee stock purchase plans if the minimum stock purchase price is equal to or greater than 85% (or at least 75% in the case of non-US companies where a lower minimum stock purchase price is equal to the prevailing best practices in that market) of the stock’s fair market value and the plan constitutes a reasonable effort to encourage broad based participation in the company’s stock.”

### 6.2.4 Statistics about ESG voting

In this section, we analyze the behavior of investors in voting on ESG resolutions. In the case of asset managers, we use the annual reports published by ShareAction. The most recent report covered the 2023 proxy season and was published in January 2024 (Figure 6.9). For asset owners, data is more difficult to find. We use various surveys and supplement the assessment by studying the engagement reports of some pension funds. As a result, we don't have a true picture of asset owners' ESG voting.

<figure><img src="image_273.png" /><figcaption>Figure 6.9: 2023 Voting Matters</figcaption></figure>

Source: https://shareaction.org.

#### Asset managers

ShareAction launched the Voting Matters series in 2019. At that time, the report examined how the largest asset managers voted on shareholder resolutions related to climate change (ShareAction, 2019). In 2020 and 2021, the analysis was expanded to include the (S) pillar in addition to the (E) pillar (ShareAction, 2020, 2021). The 2022 edition also analyzes shareholder-filed governance resolutions that directly relate executive compensation and political spending policies to environmental and social issues (ShareAction, 2023). Finally, the 2023 edition adds the lobbying dimension to the (E) and (S) pillars (ShareAction, 2024). To better understand the difference between the three categories, we list the sub-themes for each pillar:

* Environmental: biodiversity, climate change financing, climate change lobbying, climate change reporting, climate change strategy, climate change targets, plastics and packaging, pollution, sustainability pay metrics, water;
* Social: civil and social rights, diversity and discrimination, human rights, labour rights, public health, sustainability pay metrics;

* Lobbying: congruency of political spending, lobbying payments and policy, political contributions.

After merging the five datasets and cleaning the data<fnref n="29" />, we obtain a database with 85 unique asset managers with the following frequencies: 35 in 2019, 54 in 2020, 65 in 2021, 68 in 2022 and 69 in 2023. There is only 25 asset managers<fnref n="30" />, which are present every year. The scores calculated by ShareAction were based on 65 selected shareholder proposals in 2019, 102 in 2020, 146 in 2021, 252 in 2022 and 257 in 2023. In Table 6.5, we report some statistics of the selected shareholder resolutions. Let $s_j$ be the support rate of resolution j. The resolution has majority support if $s_j \ge 50\%$. For instance, of the 64 shareholder resolutions in 2019³¹, only three received majority support, implying a success rate of 4.7%. For the period 2019–2022, this success rate is about 15%. It drops dramatically in 2023 due to the ESG backlash in the US. We have also reported the 10%, 25%, 75% and 90% percentiles<fnref n="32" />. The interquartile range is between 12% and 43%. Finally, we notice that the average support rate is higher for environmental resolutions than for social resolutions.

<table><caption>Table 6.5: Statistics of success rate shareholder resolutions</caption><thead><tr><th>Year</th><th>2019</th><th>2020</th><th>2021</th><th>2022</th><th>2023</th></tr></thead><tbody><tr><td>Number of resolutions</td><td>64</td><td>102</td><td>144</td><td>249</td><td>261</td></tr><tr><td>Resolutions with majority support</td><td>3</td><td>15</td><td>29</td><td>37</td><td>8</td></tr><tr><td>Success rate (in %)</td><td>4.7</td><td>14.7</td><td>20.1</td><td>14.9</td><td>3.1</td></tr><tr><td>Average support rate (in %)</td><td>28.2</td><td>29.9</td><td>32.9</td><td>29.9</td><td>23.2</td></tr><tr><td></td><td>10%</td><td>6.5</td><td>9.2</td><td>7.2</td><td>9.4</td><td>8.2</td></tr><tr><td>Percentile of support rate (in %)</td><td>25% 75% 90%</td><td>17.0 37.7 41.8</td><td>13.1 42.6 55.2</td><td>12.0 42.8 81.2</td><td>13.5 40.3 57.6</td><td>13.1 31.6 37.6</td></tr><tr><td>Average support rate (in %)</td><td>28.2</td><td>35.8</td><td>41.8</td><td>31.6</td><td>22.2</td></tr><tr><td></td><td>(E) (S)</td><td>24.5</td><td>28.8</td><td>27.4</td><td>22.4</td></tr></tbody></table>

Source: ShareAction (2019, 2020, 2021, 2023, 2024) & Author's calculations.

For each asset manager, the support rate is calculated as:

$$ \text{support rate} = \frac{\# \{ \text{for} \}}{\# \{ \text{for} + \text{against} + \text{abstention} + \text{dit-not-vote} + \text{split-vote} \}} $$

In Table 6.6, we calculate the average support rate for shareholder resolutions using two methods. The arithmetic mean is the simple average across all asset managers, while the contribution of each asset manager is proportional to its assets under management for the weighted mean. We observe that the arithmetic mean of the support rates increases continuously since 2019 when we consider the overall score and the (S) pillar. This is not the case for the (E) pillar for which we observe a lower

<footnote n="29">²⁹Notably, some asset managers have merged or changed their name.</footnote>

<footnote n="30">³⁰They are APG AM, AXA IM, Abrdn, Allianz GI, Amundi AM, BNP PAM, BlackRock, Capital Group, DWS, Fidelity Investments, Generali Insurance AM, Goldman Sachs AM, HSBC Global AM, Invesco, J.P. Morgan AM, Legal & General, M&G IM, Ninety One, Northern Trust AM, SSGA, Schroders, T. Rowe Price, UBS AM, Vanguard, and Wellington Management.</footnote>

<footnote n="31">³¹Some resolutions are excluded from the analysis because we don't have all the numbers.</footnote>

<footnote n="32">³²See Figure 6.10 for the empirical histogram.</footnote>
<figure><img src="image_274.png" /><figcaption>Figure 6.10: Histogram (in %) of support rates</figcaption></figure>

Source: ShareAction (2019, 2020, 2021, 2023, 2024) & Author's calculations.

value in 2022 and 2023 compared to 2021. Moreover, the value of 65% that we found in 2022 for the total score is due to the introduction of the pay & politics topic. We also note the high support for the lobbying pillar in 2023. If we focus on the weighted average, the figures are lower. For instance, the average support in 2023 is 39.8% instead of 65.2%. This means that the largest asset managers vote less in favor of shareholder proposals than the others.

<table><caption>Table 6.6: Average support rate in % for ESG resolutions</caption><thead><tr><th>Topic</th><th>Method</th><th>2019</th><th>2020</th><th>2021</th><th>2022</th><th>2023</th></tr></thead><tbody><tr><td rowspan="2">Overall</td><td>Arithmetic</td><td>45.8</td><td>57.4</td><td>58.9</td><td>65.0</td><td>65.2</td></tr><tr><td>Weighted</td><td>32.7</td><td>42.1</td><td>47.6</td><td>46.5</td><td>39.8</td></tr><tr><td rowspan="2">Environment</td><td>Arithmetic</td><td>45.8</td><td>61.0</td><td>66.0</td><td>64.8</td><td>64.0</td></tr><tr><td>Weighted</td><td>32.7</td><td>44.7</td><td>55.8</td><td>48.8</td><td>39.8</td></tr><tr><td rowspan="2">Social</td><td>Arithmetic</td><td></td><td>53.3</td><td>55.2</td><td>62.7</td><td>64.3</td></tr><tr><td>Weighted</td><td></td><td>39.0</td><td>43.7</td><td>44.3</td><td>39.0</td></tr><tr><td rowspan="2">Pay & politics</td><td>Arithmetic</td><td></td><td></td><td></td><td>71.5</td><td></td></tr><tr><td>Weighted</td><td></td><td></td><td></td><td>47.8</td><td></td></tr><tr><td rowspan="2">Lobbying</td><td>Arithmetic</td><td></td><td></td><td></td><td></td><td>69.9</td></tr><tr><td>Weighted</td><td></td><td></td><td></td><td></td><td>42.1</td></tr></tbody></table>

Source: ShareAction (2019, 2020, 2021, 2023, 2024) & Author's calculations.
<figure><img src="image_275.png" /><figcaption>Figure 6.11: Arithmetic average support rate in % per region and year</figcaption></figure>

Source: ShareAction (2019, 2020, 2021, 2023, 2024) & Author's calculations.

<figure><img src="image_276.png" /><figcaption>Figure 6.12: Weighted average support rate in % per region and year</figcaption></figure>

Source: ShareAction (2019, 2020, 2021, 2023, 2024) & Author's calculations.
If we perform a regional analysis (Figures 6.11 and 6.12), we observe the following facts. British and European<fnref n="33" /> asset managers have similar voting patterns. Their level of support is significantly higher than in the US. Nevertheless, US asset managers improve their ESG voting policy in 2020 and 2021, which explains the increase in the overall score for the world. In 2022 and 2023, the increase in the European support is offset by the American setback.

<table><caption>Table 6.7: Best performers (2022, overall)</caption><thead><tr><th>Rank</th><th>Name</th><th>Country</th><th>AUM</th><th>Overall</th><th>E</th><th>S</th><th>Pay</th></tr></thead><tbody><tr><td>1</td><td>Achmea IM</td><td>Netherlands</td><td>251</td><td>100</td><td>100</td><td>100</td><td>100</td></tr><tr><td>1</td><td>Impax AM</td><td>UK</td><td>56</td><td>100</td><td>100</td><td>100</td><td>100</td></tr><tr><td>3</td><td>BNP PAM</td><td>France</td><td>761</td><td>99</td><td>97</td><td>100</td><td>100</td></tr><tr><td>3</td><td>MN</td><td>Netherlands</td><td>193</td><td>99</td><td>97</td><td>100</td><td>100</td></tr><tr><td>5</td><td>Candriam</td><td>Luxembourg</td><td>180</td><td>98</td><td>97</td><td>99</td><td>100</td></tr><tr><td>6</td><td>PGGM</td><td>Netherlands</td><td>331</td><td>97</td><td>93</td><td>100</td><td>97</td></tr><tr><td>7</td><td>Man</td><td>UK</td><td>149</td><td>96</td><td>98</td><td>94</td><td>98</td></tr><tr><td>8</td><td>Robeco</td><td>Netherlands</td><td>228</td><td>95</td><td>94</td><td>94</td><td>100</td></tr><tr><td>9</td><td>Aviva Investors</td><td>UK</td><td>363</td><td>93</td><td>88</td><td>96</td><td>100</td></tr><tr><td>10</td><td>Amundi AM</td><td>France</td><td>2 348</td><td>93</td><td>93</td><td>92</td><td>98</td></tr><tr><td>11</td><td>Nordea AM</td><td>Finland</td><td>333</td><td>91</td><td>93</td><td>89</td><td>90</td></tr><tr><td>12</td><td>Aegon AM</td><td>Netherlands</td><td>466</td><td>90</td><td>85</td><td>94</td><td>90</td></tr><tr><td>13</td><td>Federated Hermes</td><td>UK</td><td>672</td><td>89</td><td>88</td><td>87</td><td>90</td></tr><tr><td>14</td><td>Pictet AM</td><td>Switzerland</td><td>284</td><td>88</td><td>85</td><td>90</td><td>91</td></tr><tr><td>15</td><td>Legal & General</td><td>Switzerland</td><td>1 923</td><td>86</td><td>84</td><td>84</td><td>98</td></tr></tbody></table>

Source: ShareAction (2023) & Author's calculations.

<table><caption>Table 6.8: Worst performers (2022, overall)</caption><thead><tr><th>Rank</th><th>Name</th><th>Country</th><th>AUM</th><th>Overall</th><th>E</th><th>S</th><th>Pay</th></tr></thead><tbody><tr><td>59</td><td>Goldman Sachs AM</td><td>US</td><td>2 218</td><td>35</td><td>56</td><td>24</td><td>24</td></tr><tr><td>60</td><td>Baillie Gifford</td><td>UK</td><td>455</td><td>31</td><td>29</td><td>29</td><td>45</td></tr><tr><td>61</td><td>SSGA</td><td>US</td><td>4 140</td><td>29</td><td>30</td><td>31</td><td>22</td></tr><tr><td>62</td><td>BlackRock</td><td>US</td><td>10 014</td><td>24</td><td>28</td><td>24</td><td>15</td></tr><tr><td>63</td><td>T. Rowe Price</td><td>US</td><td>1 642</td><td>17</td><td>26</td><td>11</td><td>18</td></tr><tr><td>64</td><td>Fidelity Investments</td><td>US</td><td>4 520</td><td>17</td><td>23</td><td>19</td><td>2</td></tr><tr><td>65</td><td>Vanguard</td><td>US</td><td>8 274</td><td>10</td><td>12</td><td>9</td><td>9</td></tr><tr><td>66</td><td>Dimensional Fund Advisors</td><td>US</td><td>679</td><td>4</td><td>6</td><td>5</td><td>0</td></tr><tr><td>67</td><td>Santander AM</td><td>Spain</td><td>220</td><td>4</td><td>0</td><td>5</td><td>6</td></tr><tr><td>68</td><td>Walter Scott & Partners</td><td>UK</td><td>95</td><td>3</td><td>0</td><td>6</td><td>0</td></tr></tbody></table>

Source: ShareAction (2023) & Author's calculations.

In Tables 6.7 and 6.8, we report the ranking of the top fifteen and the bottom ten asset managers when considering the 2022 total score<fnref n="34" />. Two asset managers receive a score of 100%: Achmea IM and Impax AM Group. The top 15 rankings are dominated by asset managers based in the Netherlands, the UK and France, while seven American asset managers are in the bottom 10.

<footnote n="33">³³This includes the following countries: Finland, France, Germany, Italy, Luxembourg, the Netherlands, Spain, Sweden, and Switzerland.</footnote>

<footnote n="34">³⁴For each row, we show the rank, the name, the country, the assets under management (in $ billion), and the 2022 score expressed as a percentage.</footnote>
<table><caption>Table 6.9: Ranking of the 25 largest asset managers (2022, overall)</caption><thead><tr><th rowspan="2">Rank<br>2022</th><th rowspan="2">Name</th><th rowspan="2">Country</th><th rowspan="2">AUM<br>2022</th><th colspan="5">Overall</th><th colspan="5">Environment</th><th colspan="5">Social</th><th colspan="2">Pay<br>Lobbying</th></tr><tr><th>2019</th><th>2020</th><th>2021</th><th>2022</th><th>2023</th><th>2020</th><th>2021</th><th>2022</th><th>2023</th><th>2020</th><th>2021</th><th>2022</th><th>2023</th><th>2022</th><th>2023</th></tr></thead><tbody><tr><td>22</td><td>BlackRock</td><td>US</td><td>10 014</td><td>7</td><td>12</td><td>40</td><td>24</td><td>8</td><td>11</td><td>53</td><td>28</td><td>9</td><td>12</td><td>34</td><td>24</td><td>8</td><td>15</td><td>7</td></tr><tr><td>25</td><td>Vanguard</td><td>US</td><td>8 274</td><td>8</td><td>14</td><td>26</td><td>10</td><td>3</td><td>15</td><td>38</td><td>12</td><td>5</td><td>12</td><td>20</td><td>9</td><td>2</td><td>9</td><td>2</td></tr><tr><td>23</td><td>Fidelity Investments</td><td>US</td><td>4 520</td><td>9</td><td>31</td><td>29</td><td>17</td><td>16</td><td>20</td><td>23</td><td>23</td><td>12</td><td>44</td><td>33</td><td>19</td><td>21</td><td>2</td><td>12</td></tr><tr><td>21</td><td>SSGA</td><td>US</td><td>4 140</td><td>26</td><td>35</td><td>32</td><td>29</td><td>23</td><td>40</td><td>42</td><td>30</td><td>29</td><td>29</td><td>27</td><td>31</td><td>20</td><td>22</td><td>16</td></tr><tr><td>18</td><td>J.P. Morgan AM</td><td>US</td><td>2 742</td><td>7</td><td>43</td><td>37</td><td>37</td><td>23</td><td>51</td><td>50</td><td>43</td><td>26</td><td>34</td><td>31</td><td>25</td><td>11</td><td>53</td><td>41</td></tr><tr><td>16</td><td>Capital Group</td><td>US</td><td>2 716</td><td>5</td><td>8</td><td>28</td><td>45</td><td>8</td><td>12</td><td>26</td><td>37</td><td>8</td><td>4</td><td>31</td><td>47</td><td>11</td><td>58</td><td>0</td></tr><tr><td>2</td><td>Amundi AM</td><td>US</td><td>2 348</td><td>66</td><td>89</td><td>93</td><td>93</td><td>98</td><td>91</td><td>97</td><td>93</td><td>100</td><td>88</td><td>90</td><td>92</td><td>96</td><td>98</td><td>100</td></tr><tr><td>20</td><td>Goldman Sachs AM</td><td>US</td><td>2 218</td><td>37</td><td>45</td><td>47</td><td>35</td><td>5</td><td>48</td><td>57</td><td>56</td><td>7</td><td>43</td><td>40</td><td>24</td><td>2</td><td>24</td><td>5</td></tr><tr><td>3</td><td>Legal & General</td><td>UK</td><td>1 923</td><td>82</td><td>96</td><td>77</td><td>86</td><td>92</td><td>96</td><td>87</td><td>84</td><td>89</td><td>95</td><td>73</td><td>84</td><td>92</td><td>98</td><td>100</td></tr><tr><td>24</td><td>T. Rowe Price</td><td>US</td><td>1 642</td><td>5</td><td>22</td><td>31</td><td>17</td><td>6</td><td>27</td><td>44</td><td>26</td><td>9</td><td>17</td><td>25</td><td>11</td><td>4</td><td>18</td><td>2</td></tr><tr><td>15</td><td>Invesco</td><td>US</td><td>1 611</td><td>34</td><td>37</td><td>37</td><td>47</td><td>39</td><td>52</td><td>51</td><td>54</td><td>35</td><td>19</td><td>28</td><td>37</td><td>37</td><td>61</td><td>52</td></tr><tr><td>12</td><td>Morgan Stanley IM</td><td>US</td><td>1 566</td><td></td><td>55</td><td>64</td><td>58</td><td></td><td>59</td><td>64</td><td>51</td><td></td><td>53</td><td>65</td><td>62</td><td>63</td><td>65</td><td></td></tr><tr><td>14</td><td>Wellington Management</td><td>US</td><td>1 426</td><td>10</td><td>51</td><td>44</td><td>48</td><td>29</td><td>62</td><td>60</td><td>63</td><td>31</td><td>39</td><td>37</td><td>41</td><td>26</td><td>36</td><td>33</td></tr><tr><td>7</td><td>Northern Trust AM</td><td>US</td><td>1 348</td><td>21</td><td>70</td><td>60</td><td>83</td><td>77</td><td>79</td><td>68</td><td>83</td><td>69</td><td>59</td><td>57</td><td>78</td><td>80</td><td>96</td><td>93</td></tr><tr><td>13</td><td>Nuveen AM</td><td>US</td><td>1 271</td><td>62</td><td>63</td><td>56</td><td>59</td><td></td><td>71</td><td>76</td><td>57</td><td></td><td>56</td><td>48</td><td>52</td><td></td><td>79</td><td></td></tr><tr><td>8</td><td>UBS AM</td><td>Switzerland</td><td>1 216</td><td>90</td><td>79</td><td>75</td><td>83</td><td>82</td><td>91</td><td>72</td><td>84</td><td>82</td><td>67</td><td>75</td><td>80</td><td>82</td><td>87</td><td>82</td></tr><tr><td>4</td><td>DWS</td><td>Germany</td><td>1 055</td><td>74</td><td>66</td><td>85</td><td>86</td><td>86</td><td>66</td><td>92</td><td>86</td><td>89</td><td>65</td><td>80</td><td>80</td><td>77</td><td>100</td><td>98</td></tr><tr><td>10</td><td>AXA IM</td><td>France</td><td>1 009</td><td>79</td><td>71</td><td>55</td><td>73</td><td>75</td><td>85</td><td>72</td><td>69</td><td>76</td><td>55</td><td>45</td><td>68</td><td>65</td><td>95</td><td>95</td></tr><tr><td>6</td><td>Schroders</td><td>UK</td><td>991</td><td>56</td><td>62</td><td>73</td><td>85</td><td>83</td><td>63</td><td>78</td><td>81</td><td>84</td><td>60</td><td>70</td><td>87</td><td>81</td><td>87</td><td>83</td></tr><tr><td>17</td><td>AllianceBernstein</td><td>US</td><td>779</td><td></td><td>43</td><td>33</td><td></td><td></td><td>40</td><td>16</td><td></td><td></td><td>39</td><td>42</td><td></td><td>60</td><td>55</td><td></td></tr><tr><td>5</td><td>Allianz G1</td><td>Germany</td><td>766</td><td>89</td><td>81</td><td>77</td><td>86</td><td>85</td><td>89</td><td>81</td><td>80</td><td>83</td><td>73</td><td>76</td><td>91</td><td>86</td><td>85</td><td>93</td></tr><tr><td>1</td><td>BNP PAM</td><td>France</td><td>761</td><td>48</td><td>72</td><td>98</td><td>99</td><td>96</td><td>65</td><td>96</td><td>97</td><td>95</td><td>80</td><td>99</td><td>100</td><td>97</td><td>100</td><td>94</td></tr><tr><td>19</td><td>Columbia Threadneedle</td><td>US</td><td>754</td><td></td><td>37</td><td>55</td><td></td><td></td><td>43</td><td>50</td><td></td><td></td><td>25</td><td>54</td><td>53</td><td>67</td><td></td><td></td></tr><tr><td>9</td><td>Manulife IM</td><td>Canada</td><td>723</td><td></td><td>75</td><td>84</td><td></td><td></td><td>77</td><td>85</td><td></td><td></td><td>68</td><td>78</td><td>89</td><td>93</td><td></td><td></td></tr><tr><td>11</td><td>APG AM</td><td>Netherlands</td><td>721</td><td>72</td><td>70</td><td>59</td><td>72</td><td>87</td><td>80</td><td>65</td><td>89</td><td>96</td><td>59</td><td>56</td><td>57</td><td>76</td><td>83</td><td>94</td></tr></tbody></table>

Source: ShareAction (2019, 2020, 2021, 2023, 2024) & Author's calculations.
Focusing on the largest asset managers, we obtain the 2022 rankings shown in Table 6.9. For each row, we report the rank according to the 2022 total score, the name, the country, the assets under management (in $ billion) as of December 2022, the total score expressed as a percentage for the five reporting years (2019 to 2023). We also report the thematic scores (environmental, social, pay & politics and lobbying). In this case, the six best performers are BNP Paribas Asset Management, Amundi, Legal & General, DWS, Allianz GI and Schroders (two UK, two French and two German asset managers respectively). We also note that some asset managers have improved significantly. For example, BNP PAM's score improves from 48% in 2019 to 99% in 2022. For Northern Trust AM, we have 21% in 2019 versus 83% in 2022. If we look at the four largest US asset managers, they improve their scores between 2019 and 2021, but they support fewer resolutions in 2022 than in 2021. In 2023, their scores are even worse. This is certainly explained by political pressure and the anti-ESG movement in the US<fnref n="35" />. If we extend the analysis to the 85 managers in the database, we get the dynamics shown in Figure 6.13. Overall, the trends are upward, although we note some setbacks, especially in the US.

<figure><img src="image_277.png" /><figcaption>Figure 6.13: Evolution of the support rate in % per asset manager</figcaption></figure>

Source: ShareAction (2019, 2020, 2021, 2023, 2024) & Author's calculations.

According to ShareAction (2023), the main findings of the 2022 report are the following:

1. "49 additional resolutions would have received majority support if the largest asset managers had voted in favour of them.

2. Voting performance has been stagnant in the US and the UK compared to 2021, while European asset managers have shown a large improvement.

<footnote n="35">³⁵See footnote 65 on page 30.</footnote>
3. Asset managers across the board are hesitant to back action-oriented resolutions, which would have the most transformative impact on environmental and social issues.”

These trends are confirmed in the 2023 report with a decline in support for key environmental and social shareholder resolutions. In 2023, only 3% of the resolutions assessed were passed, down from 21% in 2021, with the four largest asset managers showing significant declines in support. However, there are pockets of progress, particularly in Europe, where legislative requirements appear to have improved voting performance. Some asset managers have consistently supported resolutions and also voted against directors on environmental and social grounds. Although many asset managers have made net-zero commitments, they often fail to back these up with action when it comes to voting. Greenwashing remains prevalent, with weak excuses such as claims that resolutions are too prescriptive. Some asset managers, including members of the Climate Action 100+, fail to adequately address climate change concerns.

<table><caption>Table 6.10: Statistics on Say on Climate resolutions</caption><thead><tr><th rowspan="2">Resolution sponsor</th><th colspan="4">2022</th><th colspan="4">2023</th></tr><tr><th>#</th><th>Avg.</th><th>Min.</th><th>Max.</th><th>#</th><th>Avg.</th><th>Min.</th><th>Max.</th></tr></thead><tbody><tr><td>Shareholder</td><td>6</td><td>21.98%</td><td>1.00%</td><td>46.50%</td><td>6</td><td>19.68%</td><td>16.60%</td><td>24.40%</td></tr><tr><td>Management</td><td>30</td><td>89.17%</td><td>51.00%</td><td>99.90%</td><td>11</td><td>90.83%</td><td>69.70%</td><td>98.60%</td></tr></tbody></table>

In addition to the previous analysis, the 2022 and 2023 ShareAction reports include statistics on say on climate resolutions (Table 6.10). These are resolutions in which shareholders express their approval or disapproval of the company's global climate strategy. In 2022, of the 36 resolutions selected, only six were submitted by shareholders asking the company to hold an annual advisory vote on the company's climate plan. The remaining thirty resolutions were sponsored by the management. The shareholder- and management-sponsored proposals received an average of 21.98% and 89.17%, respectively. The range is between 1% and 46.5% for shareholder-sponsored resolutions, while it is between 51% and 99.9% for management-sponsored resolutions. In 2023, the results are similar, but the number of say on climate filed by management has been divided by 3.

Box 6.4: Case studies: Barclays, EDF and Woodside Energy say on climate resolutions

Electricité de France or EDF (French energy company) filed a management-sponsored say on climate resolution at its AGM on 12 May. The group's climate transition plan to achieve carbon neutrality by 2050 was approved by 99.1%.

The management of Barclays (UK bank) filed a Say on Climate resolution at the 2022 AGM on 4 May. They asked for approval of Barclays' climate strategy, targets and progress. Despite the plan's shortcomings on coal, the result was 80.8% for and 19.2% against. According to some NGOs, some asset managers prefer to vote 'for' in the hope that the company will improve its plan and return next year with an upgraded climate resolution.

Woodside Energy Group Ltd. (Australian energy company) filed a say on climate resolution at its 2022 AGM on 19 May. Management asked for approval of its climate report. The support rate was 51.03%, meaning that 48.97% of the company's shareholders voted against its climate transition plan. These disappointing results may force management to submit a new resolution in 2023, with a high risk of failure, or discourage management from submitting new Say on Climate resolutions in future years.
## Asset owners

The comprehensive ShareAction report for asset managers has no equivalent for asset owners. As a result, we do not have global statistics on ESG voting by asset owners. To go further, one of the difficulties is having a clear view of the universe of asset owners. Each year, the Thinking Ahead Institute publishes a report listing the world's largest asset owners. Table 6.11 shows the top 50. According to Thinking Ahead Institute (2023), an asset owner has five qualifying characteristics:

1. "Works directly for a defined group of beneficiaries/savers/investors as the manager of their assets in a fiduciary capacity under delegated responsibility;

2. Works with a sponsoring entity (government affiliate, company or not for profit);

3. Works within explicit law and possesses an implicit societal license to operate because of its societal trust and legitimacy;

4. Delivers mission specific outcomes to beneficiaries and stakeholders in the form of various payments or benefits into the future;

5. Employs a business model that combines a governance budget (resources and processes) and a risk budget (reflecting the mix of financial assets that delivers on the mission)."

The ranking in Table 6.11 considers three types of asset owners: pension funds (PF), sovereign wealth funds (SWF) and outsourced chief investment officers (OCIO). A pension fund is a type of investment fund established by an employer, union, or government agency to provide retirement benefits for employees. The primary purpose of a pension fund is to accumulate assets over time through contributions from both the employer and the employees, and through the investment performance of the fund's investments. The goal is to generate returns that will pay future retirement benefits. A general distinction is made between public and private pension funds. A key difference between an asset manager and a pension fund is that the latter must meet liability targets. A sovereign wealth fund is a state-owned investment fund typically established by a government. These funds are created to manage and invest a country's excess reserves or revenues, often derived from commodities such as oil, natural gas, or other exports. The goal is to accumulate wealth for future generations. Unlike pension funds, SWFs do not necessarily have liabilities to meet. An outsourced chief investment officer, or OCIO, is essentially a third-party firm that an asset owner hires to manage its investment portfolio. As such, OCIOs are asset managers or advisory firms. The CIO delegation can take several forms: investment policy, strategic asset allocation, tactical asset allocation, reporting, due diligence, asset management, etc. In addition to PFs, SWFs and OCIOs, the other two categories of asset owners are foundations and endowments, and insurance companies. As a result, it is sometimes difficult to distinguish between asset owners and asset managers. In fact, many insurance companies also have an asset management business with both internal assets from the insurance business and external assets from other clients. This is typically the case with AXA IM or Allianz GI. This is also the case for public investment platforms (PIF), which are institutional investors that manage and invest a pool of capital from various depositors or funds. For example, the three leading asset owners in the Netherlands (APG, PGGM and MN Services) are considered public investment platforms because they manage the assets of several pension funds. In a sense, they are also asset managers. For this reason, they are also included in the Voting Matters series. According to Thinking Ahead Institute (2023), the three largest asset owners are the Government Pension Investment Fund (GPIF), Norges Bank Investment Management (NBIM) and China Investment Corporation (CIC).

Asset owners are at the forefront of many climate change and sustainability initiatives. For example, the PRI was created thanks to the founding asset owners. The Net Zero Asset Owner
<table><caption>Table 6.11: 50 largest asset owners in the world (Thinking Ahead Institute, 2023)</caption><thead><tr><th>#</th><th>Name</th><th>Country</th><th>Assets (in $ bn)</th><th>Fund type</th><th>Sigle</th></tr></thead><tbody><tr><td>1</td><td>Government Pension Investment Fund</td><td>Japan</td><td>1 449</td><td>PF</td><td>GPIF</td></tr><tr><td>2</td><td>Norges Bank Investment Management</td><td>Norway</td><td>1 250</td><td>SWF</td><td>NBIM</td></tr><tr><td>3</td><td>China Investment Corporation</td><td>China</td><td>1 149</td><td>SWF</td><td>CIC</td></tr><tr><td>4</td><td>SAFE Investment Company</td><td>China</td><td>1 034</td><td>SWF</td><td>SAFE</td></tr><tr><td>5</td><td>Abu Dhabi Investment Authority</td><td>United Arab Emirates</td><td>831</td><td>SWF</td><td>ADIA</td></tr><tr><td>6</td><td>Kuwait Investment Authority</td><td>Kuwait</td><td>769</td><td>SWF</td><td>KIA</td></tr><tr><td>7</td><td>National Pension Service</td><td>South Korea</td><td>706</td><td>PF</td><td>NPS</td></tr><tr><td>8</td><td>GIC Private Limited</td><td>Singapore</td><td>690</td><td>SWF</td><td>GIC</td></tr><tr><td>9</td><td>Federal Retirement Thrift</td><td>US</td><td>690</td><td>PF</td><td>TSP</td></tr><tr><td>10</td><td>Public Investment Fund</td><td>Saudi Arabia</td><td>620</td><td>SWF</td><td>PIF</td></tr><tr><td>11</td><td>Algemene Pensioen Groep</td><td>Netherlands</td><td>490</td><td>PF</td><td>APG</td></tr><tr><td>12</td><td>California Public Employees</td><td>US</td><td>432</td><td>PF</td><td>CalPERS</td></tr><tr><td>13</td><td>Qatar Investment Authority</td><td>Qatar</td><td>425</td><td>SWF</td><td>QIA</td></tr><tr><td>14</td><td>Canada Pension Plan</td><td>Canada</td><td>421</td><td>PF</td><td>CPP</td></tr><tr><td>15</td><td>Central Provident Fund</td><td>Singapore</td><td>407</td><td>PF</td><td>CPF</td></tr><tr><td>16</td><td>National Social Security Fund</td><td>China</td><td>347</td><td>PF</td><td>NSSF</td></tr><tr><td>17</td><td>Mercer</td><td>US</td><td>338</td><td>OCIO</td><td></td></tr><tr><td>18</td><td>Temasek Holdings</td><td>Singapore</td><td>298</td><td>SWF</td><td></td></tr><tr><td>19</td><td>Caisse de dépôt et placement du Québec</td><td>Canada</td><td>297</td><td>PF</td><td>CDPQ</td></tr><tr><td>20</td><td>California State Teachers</td><td>US</td><td>290</td><td>PF</td><td>CalSTRS</td></tr><tr><td>21</td><td>Mubadala Investment Company</td><td>United Arab Emirates</td><td>276</td><td>SWF</td><td>Mubadala</td></tr><tr><td>22</td><td>Goldman Sachs</td><td>US</td><td>247</td><td>OCIO</td><td>GS</td></tr><tr><td>23</td><td>Stichting Pensioenfonds Zorg en Welzijn</td><td>Netherlands</td><td>243</td><td>PF</td><td>PGGM</td></tr><tr><td>24</td><td>New York State Common</td><td>US</td><td>233</td><td>PF</td><td>NYSCRF</td></tr><tr><td>25</td><td>Investment Corporation of Dubai</td><td>United Arab Emirates</td><td>233</td><td>SWF</td><td>ICD</td></tr><tr><td>26</td><td>New York City Retirement</td><td>US</td><td>228</td><td>PF</td><td>NYCERS</td></tr><tr><td>27</td><td>Employees Provident Fund</td><td>Malaysia</td><td>228</td><td>PF</td><td>EPF</td></tr><tr><td>28</td><td>Local Government Officials</td><td>Japan</td><td>207</td><td>PF</td><td>PAL</td></tr><tr><td>29</td><td>MN Services N.V.</td><td>Netherlands</td><td>207</td><td>PF</td><td>MN</td></tr><tr><td>30</td><td>BlackRock</td><td>US</td><td>197</td><td>OCIO</td><td></td></tr><tr><td>31</td><td>Bureau of Labor Funds</td><td>Taiwan</td><td>195</td><td>PF</td><td>BLF</td></tr><tr><td>32</td><td>Public Service Pension Investment Board</td><td>Canada</td><td>185</td><td>PF</td><td>PSP</td></tr><tr><td>33</td><td>Florida State Board</td><td>US</td><td>183</td><td>PF</td><td>SBA</td></tr><tr><td>34</td><td>Ontario Teachers</td><td>Canada</td><td>182</td><td>PF</td><td>OTPP</td></tr><tr><td>35</td><td>AON</td><td>US</td><td>178</td><td>OCIO</td><td>AON</td></tr><tr><td>36</td><td>AustralianSuper</td><td>Australia</td><td>176</td><td>PF</td><td></td></tr><tr><td>37</td><td>Public Investment Corporation</td><td>South Africa</td><td>176</td><td>SWF</td><td>PIC</td></tr><tr><td>38</td><td>Texas Teachers</td><td>US</td><td>173</td><td>PF</td><td>TRS</td></tr><tr><td>39</td><td>Turkey Wealth Fund</td><td>Turkey</td><td>171</td><td>SWF</td><td>TWF</td></tr><tr><td>40</td><td>Korea Investment Corporation</td><td>South Korea</td><td>169</td><td>SWF</td><td>KIC</td></tr><tr><td>41</td><td>British Columbia Investment</td><td>Canada</td><td>169</td><td>PF</td><td>BCI</td></tr><tr><td>42</td><td>Future Fund Management Agency</td><td>Australia</td><td>165</td><td>SWF</td><td></td></tr><tr><td>43</td><td>Willis Towers Watson</td><td>US</td><td>165</td><td>OCIO</td><td>WTW</td></tr><tr><td>44</td><td>Employees' Provident</td><td>India</td><td>159</td><td>PF</td><td>EPFO</td></tr><tr><td>45</td><td>Australian Retirement Trust</td><td>Australia</td><td>158</td><td>PF</td><td>ART</td></tr><tr><td>46</td><td>Abu Dhabi Developmental Company</td><td>United Arab Emirates</td><td>157</td><td>SWF</td><td>ADQ</td></tr><tr><td>47</td><td>Washington State Investment Board</td><td>US</td><td>155</td><td>PF</td><td>WSIB</td></tr><tr><td>48</td><td>State Street Global Advisors</td><td>US</td><td>153</td><td>OCIO</td><td>SSGA</td></tr><tr><td>49</td><td>Russell Investments</td><td>US</td><td>152</td><td>OCIO</td><td></td></tr><tr><td>50</td><td>Russian National Wealth Fund</td><td>Russia</td><td>148</td><td>SWF</td><td>NWF</td></tr></tbody></table>

Source: www.thinkingaheadinstitute.org/research-papers/the-asset-owner-100-2023.
Alliance (NZAOA) is the first initiative to emerge from the various net zero groups. Asset owners also launched the One Planet Sovereign Wealth Funds<fnref n="36" /> (OPSWF) in 2017 and the Paris Aligned Asset Owners commitment<fnref n="37" /> in 2019. As leaders in the global sustainability movement, we can expect asset owners to be ahead of the curve compared to asset managers when it comes to engaging and voting with companies.

Climate Votes has published two research studies on asset owner voting practices. In the first study, they analyze the direct climate voting activities of the 46 asset owners that are part of the NZAOA, as well as the (proxy) voting practices reported in their 2019 PRI transparency reports (Cojoianu et al., 2021). To do so, they compare the climate voting behavior of NZAOA members and other PRI members that are not members of the NZAOA, and find that:

> "Our research reveals that between April 2009 to September 2021, asset owners that are now members of the NZAOA were more likely to vote in favour of climate action at Annual General Meetings (AGMs) of companies than the non-NZAOA peer group. This is an indicator that investors that joined the NZAOA in its first two years were early adopters of strong climate voting policies. However, when we analysed the voting pattern of NZAOA members and their non member peer group, we found that after becoming an NZAOA member, the NZAOA group's increase in pro-climate voting is not statistically different to the increase of the non-NZAOA peer group during the same time period. This is an indicator that joining the Alliance may be a recognition of existing voting practice, not an accelerator of that practice." (Cojoianu et al., 2021, page 5).

Furthermore, their research shows that there is a lack of transparency regarding the voting records of NZAOA members as reported in their most recent PRI reports. In fact, only a small fraction of NZAOA members have publicly available records of their climate-related voting decisions made directly by them. Climate Votes releases a second study in January 2023 using the votes of 73 NZAOA in 2022. Among the different findings, Chin et al. (2023) observed that NZAOA members tend to vote in favor of climate-related proposals more often than their counterparts outside the group. However, it was noted that NZAOA members rarely take the initiative to sponsor such proposals themselves. Additionally, during the 2022 proxy season, NZAOA members did not consistently lead the way in supporting proposals aimed at ending the financing of new fossil fuel extraction. On the positive side, Alliance members often diverged from proxy advisor recommendations on climate resolutions in 2022, voting for them twice as often as Glass Lewis recommended.

An analysis of the voting practices of the largest pension funds reveals two groups. A first group where voting is not encouraged to influence. For example, on the GPIF website, we can read that "GPIF itself does not exercise voting rights and instead entrusts its external asset managers with the exercise of voting rights in order to avoid having a direct influence on corporate management." A second group where voting is encouraged to influence. For example, on the CalPers website, we can read that "as a long-term shareowner, we view proxy voting as one of the primary tools to influence a company's operations and corporate governance practices. That's why it's important for shareowners like us to vote our proxies based on the full understanding of publicly available information." So, as with asset managers, we can find asset owners who are very transparent and where we have access to their voting records, as well as asset owners where information is not available.

<footnote n="36">³⁶The six founding members are ADIA, KIC, New Zealand Superannuation Fund (NZ Super Fund), NBIM, PIF and QIA.</footnote>

<footnote n="37">³⁷The website is www.parisalignedassetowners.org.</footnote>
<figure><img src="image_278.png" /></figure>
# Chapter 7

## Extra-financial Accounting

7.1 Historical perspectives

7.2 Single vs. double materiality

7.3 Environmental accounting

7.3.1 National environmental accounts

7.3.2 Corporate environmental accounts

7.4 Sustainability accounting

7.4.1 Social issues

7.4.2 Governance factors
<figure><img src="image_279.png" /></figure>
# Part II

## Climate Risk
<figure><img src="image_280.png" /></figure>
# Chapter 8

## The Physics and Economics of Climate Change

This second part focuses on the financial and economic implications of climate change. It is more technical than ESG because modeling climate risks is more complex than processing extra-financial data. Before presenting climate risk measures, analyzing transition and physical risks, optimizing portfolios with climate metrics, and managing risk, we need to have a minimum background on climate change. Three dimensions are important to consider: the fundamentals of climate change, the ecosystem, and the impact on the economy. It has taken a long time to understand the phenomenon of global warming and to accept the idea that humans are responsible for the increasing temperature anomaly since the industrial revolution. The fact that the global temperature at the earth's surface changes is not new and has been the case since the earth was formed. What is new, however, is that the temperature has changed so rapidly in just a century or two. In general, it has taken several thousand years to observe a change in temperature. In the first section, we explain how and why it has been possible to observe such an abrupt change. We present simple energy balance models to define three important physical concepts of climate change: the concept of radiative forcing, the estimation of equilibrium climate sensitivity, and the definition of tipping points. Awareness of the impacts of climate change has led governments to take, or attempt to take, action. The creation of the IPCC and the publication of its assessment reports have contributed greatly to the dissemination of scientific knowledge on climate change at the political and societal levels. The Earth Summit held in Rio de Janeiro in 1992 was a major step in politicizing climate change and popularizing this issue as a global problem for the world. It has been reinforced by the annual organization of the Conferences of the Parties. Today, we are in a climate change ecosystem where regulations can have a major impact on the business and strategy of companies. As we have not yet solved the problem, we can expect the regulatory environment to play an even greater role in the economy. Incorporating climate risk into economic models is not straightforward because the accepted economic models were developed before the 1980s, when climate change was not considered a problem outside a few aware people and scientific circles. Integrated assessment models are complex systems that focus on environmental or socio-economic issues and integrate information from economics, climate science, energy and agriculture. They emerged in the early 1980s and are now the main tools for evaluating climate policies and understanding the long-term impacts of climate change on the economy. They are central to defining climate scenarios and are widely used by the financial community, including central banks and regulators. The second major family of economic-climate models are extended versions of input-output models. Simpler than integrated assessment models, they are used to conduct sectoral analysis and measure consumption-based carbon footprints.
# 8.1 Awareness of climate change impacts

In this section, we review some important dates in climate science, from the discovery of the greenhouse effect in the early nineteenth century to the evidence of global warming in the late eighties. We will then examine natural and anthropogenic climate change. In particular, we will ask: Are human activities responsible for global warming? Finally, we will present some physical climate models that help to understand climate dynamics and the balance of greenhouse gas emissions.

## 8.1.1 Scientific evidence of global warming

### The greenhouse effect

The greenhouse effect is the natural warming of the Earth that occurs when gases in the atmosphere trap heat from the sun that would otherwise escape into space (Figure 8.1). Without the greenhouse effect, the average temperature on Earth would be -18 degrees Celsius instead of the +15 degrees Celsius it is today.

<figure><img src="image_281.png" /><figcaption>Figure 8.1: Diagram showing how the greenhouse effect works</figcaption></figure>

Source: US EPA (2012), https://energyeducation.ca/encyclopedia/Greenhouse_effect.

The founding text of the greenhouse effect is a French scientific publication written by Joseph Fourier in 1824: *Remarques générales sur les températures du globe terrestre et des espaces planétaires*<fnref n="1" />. Using some theoretical mathematical models he had developed earlier, Fourier (1824) calculated that the Earth should not be as warm as it is, given its distance from the sun and its size. He then defined the various sources of heat on the Earth's surface:

> "The heat of the Earth's surface derives from three sources, which must first be distinguished:

<footnote n="1">¹General Remarks on Global and Planetary Temperatures.</footnote>
1. The Earth is heated by the sun's rays, whose uneven distribution produces the diversity of climates.

2. The Earth's temperature depends on the common temperature of planetary spaces, as it is exposed to the irradiation of the innumerable stars that surround the solar system on all sides.

3. The earth has retained within its mass some of the primitive heat it contained when the planets were formed."

He showed that the third effect is not significant and that the heat on the Earth's surface comes mainly from the sun (first factor). He distinguished luminous heat<fnref n="2" /> ("chaleur lumineuse") and dark radiant heat<fnref n="3" /> ("chaleur rayonnante obscure"), and explained that the difference between the two types of heat is due to the presence of the atmosphere. Joseph Fourier also referred to the work of the Swiss physicist and geologist Horace Bénédict de Saussure. In 1774, Saussure found that exposing a dark box with a pane of glass to the sun increased the temperature inside the box by several degrees compared to the temperature outside in the shade. He named this phenomenon "l'effet de serre" (the greenhouse effect in English). For Joseph Fourier, the interposition of the atmosphere is responsible for this greenhouse effect and is the factor that keeps the planet warmer because "heat in the state of light meets with less resistance in penetrating the air than in returning to the air when it is converted into non-luminous heat."

Pouillet (1838) developed a pyrheliometer to measure the solar irradiance at the surface as a function of the atmospheric air mass. He found that the solar constant $S_0$ is equal to $1\,230\,\text{Wm}^{-2}$, while the current estimate is about $1\,368\,\text{Wm}^{-2}$. He also estimated the temperature in space to be –142°C. In fact, the temperature in space approaches absolute zero (or –273°C). According to NASA<fnref n="4" />, it can reach 120°C during the lunar day at the moon's equator and drop to –130°C at night. At the moon's poles, temperatures can drop even lower, reaching –250°C. Like Joseph Fourier, Claude Pouillet explained that the greater absorption of the sun's rays and the relatively small variations in temperature were mainly due to the atmospheric stratum.

John Tyndall's work marks a new milestone. As an experienced mountaineer with a passion for glacier formation and melting, he studied climate-induced changes in the ice caps. In 1859, Tyndall showed that water vapor has a high heat absorption capacity. He went on to show that carbon dioxide and other gases could also absorb and radiate heat. Tyndall was not only interested in theory and equations, he also carried out many experiments to calculate the heat capacity of many gases using a measuring device based on thermopile technology. He realized the implications of his findings for climate change<fnref n="5" />:

> "De Saussure, Fourier, Pouillet, and Hopkins regard this interception of the terrestrial rays as exercising the most important influence on climate. Now if, as the above experiments indicate, the chief influence be exercised by the aqueous vapour, every variation of this constituent must produce a change of climate. Similar remarks would apply to the carbonic acid diffused through the air; while an almost inappreciable admixture of any of the hydrocarbon vapours would produce great effects on the terrestrial rays and produce corresponding changes of climate. It is not therefore necessary to assume alterations in the density and height of the atmosphere, to account for different amounts of heat being preserved to the earth at different times; a slight change in its variable

<footnote n="2">²This corresponds to the ultra-violet light.</footnote>

<footnote n="3">³This corresponds to the thermal infrared radiation.</footnote>

<footnote n="4">⁴See https://science.nasa.gov/mission/lro.</footnote>

<footnote n="5">⁵Carbonic acid was the historical name given to $CO_2$ in the nineteenth century.</footnote>
constituents would suffice for this. Such changes in fact may have produced all the muta-
tions of climate which the researches of geologists reveal. However this may be, the
facts above cited remain; they constitute true causes, the extent alone of the operation
remaining doubtful.” (Tyndall, 1861, pages 28-29).

Tyndall is the first scientist to prove that greenhouse gases exist and are responsible for the green-
house effect.

In fact, Tyndall was not the first to discover the existence of greenhouse gases. Three years earlier, in 1856 and 1857, the American scientist Eunice Newton Foote had published two research papers with experiments showing that water vapor and carbon dioxide absorb heat from solar radiation. However, her work was forgotten until it was rediscovered by Raymond Sorenson in 2011. Foote's work led to debates about the paternity of greenhouse gases (Ortiz and Jackson, 2022).

<figure><img src="image_282.png" /><figcaption>Figure 8.2: The pioneers of the greenhouse effect</figcaption></figure>

Svante Arrhenius was the first scientist to calculate the effect of a change in atmospheric CO2 on ground temperature. Svante Arrhenius (1859-1927) was a renowned Swedish chemist who won the Nobel Prize<fnref n="6" /> in Chemistry in 1903 for his ionic dissociation theory. In 1896, he argued that variations in atmospheric carbon dioxide could significantly affect the Earth's heat balance. Making extensive use of the empirical works of Knut Ångström, Alexander Buchan, F. Paschen, Charles Pouillet, and especially the data collected by Samuel Pierpont Langley, he came to the following conclusion:

"We may now inquire how great the variation of the carbonic acid in the atmosphere be
to cause a given change of the temperature. [...] Thus if the quantity of carbonic acid
increases in geometric progression, the augmentation of the temperature will increase
nearly in arithmetic progression." (Arrhenius, 1896, Section IV, pages 265-267).

This rule has often been interpreted to mean that a doubling of the CO₂ concentration leads to an increase in the average global temperature of about 5°C. This is the first time that an estimate of

<footnote n="6">⁶Arrhenius was involved in the establishment of the Nobel Institute from 1901, when he was elected a member of the Royal Swedish Academy of Sciences. From that year he was a member of the Nobel Committee for Physics and also for Chemistry. When the Nobel Institute for Physical Research was established in Stockholm in 1905, he was appointed rector of the Institute, a position he held until 1927. Svante Arrhenius is credited with many stories and intrigues about the awarding or not of the Nobel Prize, including the conflicts he had with Paul Ehrlich (theory of immunology) and Dmitri Mendeleev (periodic table of elements).</footnote>
climate sensitivity has been calculated<sup>7</sup>. In the final section, devoted to the geological consequences, his calculations showed that:

> "One may now ask, How much the carbonic acid vary according to our figures, in order that the temperature should attain the same values as in the Tertiary and Ice ages respectively? A simple calculation shows that the temperature of the Arctic regions would rise about 8°C to 9°C, if the carbonic acid increased 2.5 or 3 times its present value. In order to get the temperature of the ice age between the 40th and 50th parallels, the carbonic acid in the air should sink to 0.62-0.55 of present value (lowering the temperature 4°C-5°C)." (Arrhenius, 1896, Section V, page 268).

The last part of the article is remarkable. He discussed the work of his friend and colleague Arvid Hogbom (1857-1940) on the influence of natural carbon dioxide cycles on the Earth's ice ages. In particular, he argued that these cycles were a much better explanation of climate change on a geological scale than the theory of James Croll (1821-1890), who assumed that it was due to the variations in the Earth's orbit<sup>8</sup>. He also discussed the impact of human activity on the concentration of CO₂ in the atmosphere, and in particular the impact of coal mining and production.

While Arrhenius studied only the heat absorption capacity of CO₂, Tyndall calculated the heat power of several gases: water vapor, carbon dioxide, oxygen, nitrogen, hydrogen, nitrous oxide, etc. However, Tyndall assumed that water vapor was the main contributor to the greenhouse effect and that the effect of carbon dioxide was negligible. We now know that this is not true. Since the 1970s, many scientific studies have been carried out to investigate the other greenhouse gases and their effects on the environment and global warming. Ozone has received much attention (World Meteorological Organization, 1982), followed by chlorofluorocarbons or CFCs (Ramanathan, 1975), nitrates and sulfates. The survey of Ramanathan et al. (1985) summarizes the state of scientific knowledge in the 1980s. It was at this point that a number of scientists began to reintroduce methane as a growing threat to climate change. For example, Kvenvolden (1988) analyzed the process of permafrost warming and methane release from gas hydrates and possible destabilization in the Arctic.

<table><caption>Table 8.1: List of greenhouse gases</caption><thead><tr><th>Greenhouse gas</th><th>Formula</th><th>Kyoto Protocol</th></tr></thead><tbody><tr><td>Water vapor</td><td>H<sub>2</sub>O</td><td></td></tr><tr><td>Carbon dioxide</td><td>CO<sub>2</sub></td><td>✓</td></tr><tr><td>Methane</td><td>CH<sub>4</sub></td><td>✓</td></tr><tr><td>Nitrous oxide</td><td>N<sub>2</sub>O</td><td>✓</td></tr><tr><td>Ozone</td><td>O<sub>3</sub></td><td></td></tr><tr><td colspan="3" style="border-top: 1px dashed black; padding: 0.5em 0;"></td></tr><tr><td colspan="3" style="border-bottom: 1px dashed black; padding: 0.5em 0;"></td></tr><tr><td colspan="2">Fluorinated or F-gases</td><td></td></tr><tr><td>Sulfur hexafluoride</td><td>SF<sub>6</sub></td><td>✓</td></tr><tr><td>Nitrogen trifluoride</td><td>NF<sub>3</sub></td><td>✓</td></tr><tr><td>Chlorofluorocarbons</td><td>CFCs (CFC-11, CFC-12, etc.)</td><td></td></tr><tr><td>Hydrofluorocarbons</td><td>HFCs (HFC-23, HFC-32, etc.)</td><td>✓</td></tr><tr><td>Hydrochlorofluorocarbons</td><td>HCFCs (HCFC-12, etc.)</td><td></td></tr><tr><td>Perfluorocarbons</td><td>PFCs (CF<sub>4</sub>, C<sub>2</sub>F<sub>6</sub>, etc.)</td><td>✓</td></tr></tbody></table>

<footnote n="7"><sup>7</sup>Climate sensitivity measures the global temperature increase that will occur in response to a doubling of atmospheric CO₂ concentrations compared to pre-industrial levels.</footnote>

<footnote n="8"><sup>8</sup>Today it is accepted that the two theories co-exist and explain the phenomenon of global glaciation (Hays et al., 1976; Delmas et al., 1980).</footnote>
Global warming

The discovery of the greenhouse effect implies that the temperature of the Earth depends on the
concentration of greenhouse gases in the atmosphere. It does not mean that we are observing a
global warming of the Earth, and even less that this global warming is due to human activities.
For that, we need to show that the concentration of greenhouse gases has recently increased due to
human influence. We also need to calculate the net effect of each gas. For example, the loss of ozone
that we have observed in the lower stratosphere has a cooling effect on the Earth's surface, while the
increase in ozone that has occurred in the troposphere has a warming effect on the Earth's surface.

Guy Stewart Callendar was a British steam engineer. In 1938, he linked the increased burning of fossil fuels to rising global temperatures. He compiled weather data and estimated a global temperature increase of about 0.25°C over the last fifty years. He also showed that the concentration of CO₂ in the atmosphere had increased by 10% during the same period, and he argued that this rising carbon dioxide content of the atmosphere was due to the burning of fossil fuels. Thus was born the “Callendar Effect”, which links global warming to man’s artificial production of carbon dioxide:

> "By fuel combustion man has added about 150 000 million tons of carbon dioxide to the air during the past half century. The author estimates from the best available data that approximately three quarters of this has remained in the atmosphere. The radiation absorption coefficients of carbon dioxide and water vapour are used to show the effect of carbon dioxide on sky radiation. From this the increase in mean temperature, due to the artificial production of carbon dioxide, is estimated to be at the rate of 0.003°C per year at the present time. The temperature observations at zoo meteorological stations are used to show that world temperatures have actually increased at an average rate of 0.005°C per year during the past half century." (Callendar, 1938, page 223).

Guy Stewart Callendar, however, thought that this was not a bad thing. Like Svante Arrhenius<sup>9</sup>,
he believed that higher temperatures would be beneficial to civilization:

> "In conclusion it may be said that the combustion of fossil fuel [...] is likely to prove beneficial to mankind in several ways, besides the provision of heat and power. For instance the above mentioned small increases of mean temperature would be important at the northern margin of cultivation, and the growth of favourably situated plants is directly proportional to the carbon dioxide pressure [...] In any case the return of the deadly glaciers should be delayed indefinitely." (Callendar, 1938, page 236).

According to Archer and Pierrehumbert (2011) (Table 8.1), three major research papers were
written in the fifties. First, from 1956, the Canadian physicist Gilbert Norman Plass published a
series of papers on the absorption of infrared radiation. His work confirmed that more carbon dioxide

<footnote n="9"><sup>9</sup>Thirty years earlier, in his book *Worlds in the Making: The Evolution of the Universe*, Arrhenius argued that a rise in global temperature could be beneficial to agriculture, providing more food for the world's population:</footnote>

<footnote>> "We often hear lamentations that the coal stored up in the earth is wasted by the present generation without any thought of the future, and we are terrified by the awful destruction of life and property which has followed the volcanic eruptions of our days. We may find a kind of consolation in the consideration that here, as in every other case, there is good mixed with the evil. By the influence of the increasing percentage of carbonic acid in the atmosphere, we may hope to enjoy ages with more equable and better climates, especially as regards the colder regions of the earth, ages when the earth will bring forth much more abundant crops than at present, for the benefit of rapidly propagating mankind." (Arrhenius, 1908, Chapter II, page 63).</footnote>
Box 8.1: The collected papers on global warming by David Archer and Raymond Pierrehumbert (1800–1980)

* **1824** On the Temperatures of the Terrestrial Sphere and Interplanetary Space (Fourier)

* **1861** On the Absorption and Radiation of Heat by Gases and Vapours, and on the Physical Con- nexion of Radiation, Absorption, and Conduction (Tyndall)

* **1896** On the Influence of Carbonic Acid in the Air upon the Temperature of the Ground (Arrhenius)

* **1938** The Artificial Production of Carbon Dioxide and its Influence on Temperature (Callendar)

* **1956** The Influence of the 15μ Carbon-dioxide Band on the Atmospheric Infra-red Cooling Rate (Plass)

* **1957** Carbon Dioxide Exchange Between Atmosphere and Ocean and the Question of an Increase of Atmospheric CO₂ during the Past Decades (Revelle and Suess)

* **1958** Distribution of Matter in the Sea and Atmosphere: Changes in the Carbon Dioxide Content of the Atmosphere and Sea due to Fossil Fuel Combustion (Bolin and Eriksson)

* **1960** The Concentration and Isotopic Abundances of Carbon Dioxide in the Atmosphere (Keeling)

* **1967** Thermal Equilibrium of the Atmosphere with a Given Distribution of Relative Humidity (Man- abe and Wetherald)

* **1969** The Effect of Solar Radiation Variations on the Climate of the Earth (Budyko) A Global Climatic Model Based on the Energy Balance of the Earth-Atmosphere System (Sellers)

* **1970** Is Carbon Dioxide from Fossil Fuel Changing Man's Environment? (Keeling)

* **1972** Man-Made Carbon Dioxide and the Greenhouse Effect (Sawyer)

* **1975** The Effects of Doubling the CO₂ Concentration on the Climate of a General Circulation Model (Manabe and Wetherald)

* **1977** Changes of Land Biota and Their Importance for the Carbon Cycle (Bolin) Neutralization of Fossil Fuel CO₂ by Marine Calcium Carbonate (Broecker and Takahashi)

* **1979** Carbon Dioxide and Climate: A Scientific Assessment (Charney, Arakawa, Baker et al.)

Source: Archer and Pierrehumbert (2011).
Box 8.2: The collected papers on global warming by David Archer and Raymond Pierrehumbert (1980–2005)

* 1984 Climate Sensitivity: Analysis of Feedback Mechanisms (Hansen, Lacis, Rind et al.)

* 1985 Evidence From Polar Ice Cores for the Increase in Atmospheric CO₂ in the Past Two Centuries (Neftel, Moor, Oeschger and Stauffer)

* 1986 Global Temperature Variations Between 1861 and 1984 (Jones, Wigley and Wright)

* 1987 Vostok Ice Core Provides 160,000-Year Record of Atmospheric CO₂ (Barnola, Raynaud, Kortkevich and Lorius)

* 1990 Observational Constraints on the Global Atmospheric CO₂ Budget (Tans, Fung and Takahashi)

* 1991 Abrupt Deep-Sea Warming, Palaeoceanographic Changes and Benthic Extinctions at the End of the Palaeocene (Kennett and Stott)

* 1992 Effects of Fuel and Forest Conservation on Future Levels of Atmospheric Carbon Dioxide (Walker and Kasting)

* 1995 Climate Response to Increasing Levels of Greenhouse Gases and Sulphate Aerosols (Mitchell, Johns, Gregory and Tett)

* 1999 Northern Hemisphere Temperatures During the Past Millennium: Inferences, Uncertainties, and Limitations (Mann, Bradley and Hughes)

* 2000 Acceleration of Global Warming Due to Carbon-Cycle Feedbacks in a Coupled Climate Model (Cox, Betts, Jones, Spall and Totterdell)
Reduced Calcification of Marine Plankton in Response to Increased Atmospheric CO₂ (Riebe-sell, Zondervan, Rost et al.)

* 2002 Surface Melt-Induced Acceleration of Greenland Ice-sheet Flow (Zwally, Abdalati, Herring et al.)

* 2003 Anthropogenic Carbon and Ocean pH (Caldeira and Wickett)

* 2004 Contribution of Stratospheric Cooling to Satellite-Inferred Troposphoric Temperature Trends (Fu, Johanson, Warren and Seidel)

* 2005 Earth's Energy Imbalance: Confirmation and Implications (Hansen, Nazarenko, Ruedy et al.)

Source: Archer and Pierrehumbert (2011).
would have a warming effect and showed that: (1) a doubling of CO₂ would warm the planet by 3.6°C; (2) halving the amount of CO₂ would reduce the surface temperature by 3.8°C; (3) human activities have increased the concentration of CO₂ in the atmosphere at a rate of 30% per century; (4) this increase implies a warming of 1.1°C per century (Plass, 1956, pages 152-153). Secondly, Revelle and Suess (1957) showed that the average lifetime of a CO₂ molecule in the atmosphere before it is dissolved in the ocean is of the order of 10 years. The resistance to atmospheric carbon dioxide being absorbed by the surface layer of the ocean is known as the “buffer factor” or “Revelle factor”. They concluded that most of the CO₂ released by artificial fuel combustion since the beginning of the industrial revolution must have been absorbed by the oceans. However, they felt that the exponential increase in industrial fuel combustion could pose a problem in the future and dramatically increase atmospheric CO₂. The mechanism of the ocean's buffering capacity was explored in a third research paper by Bolin and Eriksson (1958), who developed a dynamic model of atmosphere-ocean interactions with respect to CO₂. They estimated that the upper ocean must have absorbed less than 10% of fossil fuel emissions and acted as a barrier to the transport of CO₂ to the deep ocean. They concluded that if industrial production continues to rise, atmospheric CO₂ is likely to increase by 25% by the end of the century. In addition to the impact of CO₂ on ocean acidification, they highlighted the impact of land use and biosphere:

> "Because of the small buffering effect of the sea it seems likely that the biosphere on land may play a more important role for the changes actually occurring in the atmosphere due to the release of CO₂ by combustion than previously believed." (Bolin and Eriksson, 1958, page 130).

In Revelle and Suess (1957), the authors concluded that “present data on the total amount of CO₂, in the atmosphere, on the rates and mechanisms of CO₂, exchange between the sea and the air and between the air and the soils, and on possible fluctuations in marine organic carbon, are insufficient to give an accurate base line for measurement of future changes in atmospheric CO₂.” Several initiatives were launched in the 1950s, particularly in Scandinavia. However, the data collected were extremely noisy and the CO₂ measurements were not stable. Roger Revelle invited Charles David Keeling to join the Scripps Institution of Oceanography (SIO) in 1956. Keeling received his Ph.D. in chemistry from Northwestern University in 1953 and was a postdoctoral fellow in geochemistry at CalTech until 1956, where he developed a stable instrument capable of measuring carbon dioxide in atmospheric samples. He decided to install his equipment in Antarctica (Little America), California (La Jolla) and on the Mauna Loa volcano in Hawaii and started collecting carbon dioxide samples in 1958. In 1960, he published a first report and tabulated the monthly average concentrations of atmospheric CO₂ at the three stations. He concluded that there were strong seasonal variations in CO₂ levels in the northern hemisphere (La Jolla, California and Mauna Loa, Hawaii), and a small but persistent increase in concentration was found in Antarctica (Keeling, 1960, page 200). In 1961, he presented new data showing a steady increase in CO₂ levels and introduced the famous “Keeling curve”, a measurement of atmospheric carbon dioxide concentration made at Mauna Loa since 1958 (Keeling, 1978). The data was collected by Keeling until his death in 2005, and then by his son. The current version of the Keeling curve is shown in Figure 8.3. In March 1958, the CO₂ concentration was equal to 315.71 ppm<fnref n="10" /> or 611.8 mg/m³. The limit of 400 ppm was reached in February 2015. In June 2023, the measure was 423.39 ppm or 820.5 mg/m³.

In the 1960s, a small number of scientists developed simple mathematical models of the planet's climate system. After completing his PhD at the University of Tokyo in 1959, Syukuro Manabe

<footnote n="10">¹⁰One part per million (ppm) denotes one part per $10^6$ parts. It is equal to $10^{-6}$. So one milliliter of gas in 1000 liters of air would be 1 ppm.</footnote>
<figure><img src="image_283.png" /><figcaption>Figure 8.3: Keeling curve: monthly mean CO₂ concentration in Mauna Loa (1958–2023)</figcaption></figure>

Source: Keeling *et al.* (2001) and https://scrippsco2.ucsd.edu.

went to the United States to work at the National Oceanographic and Atmospheric Administration (NOAA). Together with co-authors, Manabe published several research papers in 1961, 1964 and 1965 to develop a climate model. With the help of computer simulations, Manabe and Wetherald (1967) were able to obtain a first, but basic, model for predicting temperature by incorporating the hydrologic cycle (convective adjustment, feedback effect of water vapor, distribution of humidity, cloudiness). They found that as the concentration of carbon dioxide in the atmosphere increases, the temperature at the Earth's surface and in the troposphere rises, while it falls in the stratosphere. They also estimated the climate sensitivity to be between 1.3°C and 2.3°C. Manabe continued his research in the seventies and eighties. He and Kirk Bryan developed a general circulation model (GCM) and published the results in 1969. Manabe and Wetherald later used this original model to simulate the first three-dimensional experiment to test the idea of global warming. Their results were published in 1975.

In 2021, Syukuro Manabe and Klaus Hasselmann were awarded the Nobel Prize for their work on climate models. Klaus Hasselmann is a German oceanographer. He is known for his stochastic prediction model of climate change (Hasselmann, 1976; Frankignoul and Hasselmann, 1977). In fact, weather and climate forecasting has a long history, beginning with the book of Richardson (1922). However, it was the development of digital computers that accelerated the science of weather forecasting. Using the pioneering ENIAC computer and with the help of John von Neumann, Jules Charney and his team created a two-dimensional weather simulation model (Charney *et al.*, 1950), but the first general circulation model (GCM) is generally attributed to Phillips (1956). A GCM is a mathematical representation of the interactions between the components of the climate system (atmosphere, land surface, ocean and sea ice). In addition to the works of Manabe and Hasselmann,
we can also cite the research of Mikhail Budyko (1920–2001) and William Sellers (1928–2014), who introduced energy balance models<fnref n="11" /> and warned of how positive and negative feedbacks (i.e., loops of mutually reinforcing effects) could amplify human impacts on the global climate. In particular, Budyko (1969) and Sellers (1969) developed two models of catastrophic ice-albedo feedbacks. Today, these feedback loops are fully integrated into GCMs, and dozens of teams around the world use sophisticated GCM models and supercomputers to predict weather and climate change<fnref n="12" />. Another milestone was the Charney Report, *Carbon Dioxide and Climate: A Scientific Assessment*, prepared for the American Academy of Sciences, whose conclusions were presented to President Carter in 1979. On July 23-27, 1979, Jule Charney formed a study group to “assess the scientific basis for projection of possible future climatic changes resulting from man-made releases of carbon dioxide into the atmosphere” (Charney et al., 1979, page iv). The study group had 13 members, including eminent scientists Akio Arakawa, Bert Bolin, Henry Stommel, etc. The report examined the results of five global climate models that simulate the climatic response to an increase in atmospheric CO2: three by Manabe and his colleagues at NOAA’s Geophysical Fluid Dynamics Laboratory and two by James Hansen and his colleagues at NASA’s Goddard Institute for Space Studies. The report estimated a climate sensitivity of 3°C, with an error of ±1.5°C.

<figure><img src="image_284.png" /><figcaption>Figure 8.4: The fathers of the concept of global warming</figcaption></figure>

The term “*global warming*” was popularized by Broecker (1975). Wallace Broecker was a famous American geochemist and the author of more than 500 scientific articles and many books. His works on the role of the ocean in climate change, the global ocean circulation map, radiocarbon dating, etc. are considered the foundation of carbon cycle science. While the term global warming appears less than 10 times before 1975, many research papers will use the term extensively after Broecker’s publication. Between 1975 and 1980, more than 2500 scientific articles made reference to global warming. In the 1980s, Broecker and other scientists warned politicians about the dangers of climate change. In 1984, for example, Broecker testified at the Congressional hearing on climate change, declaring that carbon dioxide was the number one long-term environmental problem. On

<footnote n="11">¹¹Scientists distinguish between Energy Balance Models (EBM), Earth System Models of Intermediate Complexity (EMIC), and General Circulation Models (GCM), from the simplest to the most complex. However, the distinction between these climate models is generally not obvious.</footnote>

<footnote n="12">¹²Nowadays, GCMs are generally classified into three types of families: (1) Atmospheric General Circulation Model (AGCM), (2) Oceanic General Circulation Model (OGCM), and (3) Atmosphere-Ocean General Circulation Model (AOGCM).</footnote>
June 23, 1988, James Hansen was invited to another Congressional hearing on climate change<fnref n="13" />, organized by Senator Al Gore, and stated<fnref n="14" />:

> "Mr. Chairman and committee members, thank you for the opportunity to present the results of my research on the greenhouse effect which has been carried out with my colleagues at the NASA Goddard Institute for Space Studies. I would like to draw three main conclusions. Number one, the earth is warmer in 1988 than at any time in the history of instrumental measurements. Number two, the global warming is now large enough that we can ascribe with a high degree of confidence a cause and effect relationship to the greenhouse effect. And number three, our computer climate simulations indicate that the greenhouse effect is already large enough to begin to affect the probability of extreme events such as summer heat waves."

So in the late eighties, climate change began to become a political issue. In 1988, the United Nations Environment Programme (UNEP) and the World Meteorological Organization (WMO) established the Intergovernmental Panel on Climate Change (IPCC) to provide policy makers with regular scientific assessments of climate change, its impacts and potential future risks, and to recommend options for adaptation and mitigation. Twenty years later, the IPCC and Al Gore were awarded the 2007 Nobel Peace Prize.

**Remark 75** The reader who wants to go further and delve into the history of climate change research will find a vast amount of material and references on the website developed by Weart (2023): https://history.aip.org/climate/index.htm. The PDF version of the contents has more than 350 pages. Among the thirty sections, the most interesting are: Introduction and Summary, The Carbon Dioxide Greenhouse Effect, Roger Revelle's Discovery, General Circulation Models of Climate, and Past Climate Cycles: Ice Age Speculations.

## 8.1.2 From the Holocene to the Anthropocene?

### Definition

The Anthropocene is a proposed geological epoch that dates from the beginning of significant human impacts on Earth's geology and ecosystems, including but not limited to human-induced climate change. The Earth was formed 4.6 billion years ago. Its history can be traced using the geologic time scale (GTS) shown in Figure 8.5. Earth's history is divided into five subdivisions: eon, era, period, epoch, and age. The first three eons (Hadean, Archean and Proterozoic) can be grouped into a supereon called the Precambrian (covering the first 4 billion years). The Phanerozoic runs from the Cambrian to the present. We are in the Cenozoic era, Quaternary period, Holocene epoch and Meghalayan age. It is on the scale of ages that the question of the transition from the Holocene to the Anthropocene is currently being asked.

According to Lewis (2015), the term Anthropocene was popularized by Paul Crutzen<fnref n="15" /> and Eugene Stoermer<fnref n="16" /> in 2000 (Crutzen and Stoermer, 2000). In 2009, the Anthropocene Working

<footnote n="13">¹³Other scientists attended this congressional hearing, notably future lead authors for chapters of IPCC reports: Syukuro Manabe, Michael Oppenheimer, Professor at Princeton University, and William Moomaw, Professor at Tufts University.</footnote>

<footnote n="14">¹⁴Source: https://babel.hathitrust.org/cgi/pt?id=uc1.b5127807, pages 39-41.</footnote>

<footnote n="15">¹⁵Paul Crutzen (1933–2021) was awarded the 1995 Nobel Prize in Chemistry for his work in atmospheric chemistry, and in particular for his efforts to study the formation and decomposition of atmospheric ozone.</footnote>

<footnote n="16">¹⁶Eugene Stoermer (1934–2012) was a professor of biology who specialized in the study of freshwater species and diatoms.</footnote>
<figure><img src="image_285.png" /><figcaption>Figure 8.5: Geologic time scale</figcaption></figure>

Source: International Commission on Stratigraphy (2023), https://stratigraphy.org/chart.

Group (AWG) was established as part of the quaternary stratigraphy subcommission<fnref n="17" />, a constituent body of the International Commission on Stratigraphy (ICS). In 2019, the AWG agreed to submit a formal proposal to the ICS to establish the Anthropocene epoch, but the Anthropocene has not yet been ratified by the ICS. Indeed, the definition of the Anthropocene as a geological epoch rather than a geological event remains controversial and difficult. For example, scientists do not agree on the starting point of this epoch, known as the Global Stratotype Section and Point or GSSP. Lewis (2015) listed nine potential start dates<fnref n="18" />: (1) Megafauna extinction, 50 000–10 000 yr BP; (2) Origin of farming, ~11 000 yr BP, (3) Extensive farming, ~8 000 yr BP to present (4) Rice production, 6 500 yr BP to present; (5) Anthropogenic soils, ~3 000–500 yr BP; (6) New-old world collision, 1 492–1 800; (7) Industrial Revolution, 1 760 to present; (8) Nuclear weapon detonation, 1 945 to present; (9) Persistent industrial chemicals, ~1 950 to present. In 2016, the AWG proposed that the Anthropocene began in the 1950s, while in 2023 it chose Crawford Lake in Ontario, Canada, to best capture the geological impact of the Anthropocene. According to Waters et al. (2016), the effects of human impact are diverse and of different types. They listed several lines of evidence: the

<footnote n="17">¹⁷The AWG website is http://quaternary.stratigraphy.org/working-groups/anthropocene.</footnote>

<footnote n="18">¹⁸In the calendar marking system, BP is “Before Present”, while BC is “Before Christ”. According to standard practice, the present is set to 1950 Anno Domini (AD).</footnote>
alteration of sedimentary processes, the altered geochemical signatures in recent sediments and ice, the radiogenic signatures and radionuclides in sediments and ice, the carbon cycle evidence from ice cores, the climate change and rates of sea level change since the end of the last ice age, and the loss of biodiversity. However, the debate about the status of the Anthropocene is reignited by the publication of Gibbard et al. (2022):

> "Over the course of the last decade the concept of the Anthropocene has become widely established within and beyond the geoscientific literature but its boundaries remain undefined. Formal definition of the Anthropocene as a chronostratigraphical series and geochronological epoch following the Holocene, at a fixed horizon and with a precise global start date, has been proposed, but fails to account for the diachronic nature of human impacts on global environmental systems during the late Quaternary. By contrast, defining the Anthropocene as an ongoing geological event more closely reflects the reality of both historical and ongoing human-environment interactions, encapsulating spatial and temporal heterogeneity, as well as diverse social and environmental processes that characterize anthropogenic global changes. Thus, an Anthropocene Event incorporates a substantially wider range of anthropogenic environmental and cultural effects, while at the same time applying more readily in different academic contexts than would be the case with a rigidly defined Anthropocene Series/Epoch." (Gibbard et al., 2022, page 395).

It is certainly too early to consider a new era explained by human activity, but it remains relevant that human activity has an impact on climate.

## Geological history of the climate

**Precambrian and the age of early life** The Earth's climate patterns change naturally on time scales ranging from decades to millions of years<fnref n="19" />. During the Hadean eon (4.6–4.0 Gyr BP), the planet was characterized by volcanism and asteroid impacts. It was very hot, with temperatures certainly averaging around 80°C. The Moon was formed during this period. The Archean eon (4.0–2.5 Gyr BP) is the period when life on Earth began and oceans probably formed. Carbon dioxide emissions were abundant, and this high concentration probably gave rise to the greenhouse effect. The surface temperature decreased and may have been between 0°C and 40°C (Catling and Zahnle, 2020). The Proterozoic eon lasted from 2.5 billion to 540 million years ago. This was a time of oxygen accumulation in the Earth's atmosphere. The temperature history of the Proterozoic is controversial. There is evidence that the first glaciations occurred during the Proterozoic. However, the average temperature during the Proterozoic is estimated to have been between 10°C and 30°C.

<table><caption>Table 8.2: Units of time</caption><thead><tr><td>Symbol</td><td>Definition</td><td>(in year)</td><td>Symbol</td><td>Name</td></tr></thead><tbody><tr><td>Kyr/kyr</td><td>Thousand/Kilo years</td><td>10<sup>3</sup></td><td>ka</td><td>Kiloannus</td></tr><tr><td>Myr/myr</td><td>Mega/Million years</td><td>10<sup>6</sup></td><td>Ma</td><td>Megaannus</td></tr><tr><td>Gyr/byr</td><td>Giga/Billion years</td><td>10<sup>9</sup></td><td>Ga</td><td>Gigaannus</td></tr></tbody></table>

To estimate temperatures during the Precambrian, scientists use indirect methods, including geochemical proxies (chemical properties of rocks and minerals), paleontological studies (type and distribution of fossils and sedimentary rocks), and general circulation models. One of the most

<footnote n="19">¹⁹in Table 8.2, report the two time units commonly used in geology (yr vs. a, e.g., Gyr vs. Ga).</footnote>
Box 8.3: Faint young Sun paradox & Snowball Earth hypothesis

The faint young Sun paradox describes the apparent contradiction between observations of liquid water early in Earth's history and the astrophysical expectation that the Sun's output during the Archean eon would be only 75% as intense as it is today. If the Sun was fainter when the Earth was young, we might expect the Earth to be completely frozen, but there is evidence for the presence of liquid water on the Earth's surface at that time (Feulner, 2012). Many explanations have been proposed: ammonia, methane, reduced albedo, tidal heating, etc. However, the most credible assumption is the high concentration of carbon dioxide during this period of weaker solar radiation:

> "[...] we argue that the faint young Sun problem for Earth has essentially been solved. Unfrozen Archean oceans were likely maintained by higher concentrations of CO₂, consistent with the latest geological proxies, potentially helped by additional warming processes. This reinforces the expected key role of the carbon cycle for maintaining the habitability of terrestrial planets." (Charnay et al., 2020, page 1).

Other curious events during the Precambrian are the Proterozoic glaciations. The Snowball Earth hypothesis proposes that the planet's surface was completely or nearly completely frozen during these icehouse climates, especially between 750 and 550 Ma (Hoffman et al., 1998; Hoffman and Schrag, 2002). The Snowball Earth hypothesis can be explained by a runaway ice-albedo feedback. Albedo is the fraction of sunlight reflected back into space by a surface. For example, ice and snow have a high albedo, which means they reflect a lot of sunlight. As more ice and snow cover the Earth's surface, more sunlight is reflected back into space, causing the Earth to cool. This cooling leads to more ice and snow formation, which further cools the Earth, and so on. This is the runaway ice-albedo feedback. This hypothesis is currently a topic of debate among scientists, with alternative explanations also presented in the academic literature, including the high-obliquity hypothesis and the volcanic ash hypothesis. The high-obliquity hypothesis suggests that during a glacial period, the Earth had a much larger axial tilt than it does todayª. The result would have been a decrease in the amount of solar radiation reaching the poles and an increase in the amount of solar radiation absorbed at the equator. As a result, glaciers would have melted at the equator and ice caps would have formed at the poles. The volcanic ash hypothesis suggests that volcanic ash filled the Earth's atmosphere, resulting in a cooling effect caused by the blocking of sunlight.

common methods is the clumped isotope thermometer, which is based on the analysis of the isotopic composition of certain molecules, such as carbonate minerals. For example, we can use the ratio of the two carbon isotopes ¹²C and ¹³C in carbonate rocks to infer the temperature at which the rocks formed. Its definition is:

$$ \delta^{13}\text{C} = 1000 \times \left( \frac{\frac{^{13}\text{C}}{^{12}\text{C}_{\text{sample}}} / \frac{^{13}\text{C}}{^{12}\text{C}_{\text{standard}}} - 1}{\frac{^{13}\text{C}}{^{12}\text{C}_{\text{standard}}} - 1} \right) \quad (8.1) $$

<footnote>ªThis explanation refers to the Milankovitch cycles, which are variations in the Earth's orbit around the Sun that affect the amount of sunlight the planet receives. The main cycles concern the shape of the Earth's ellipsoid orbit (eccentricity), the axial tilt or angle of the Earth's axis (obliquity), and the direction of the Earth's axis of rotation (precession).</footnote>
The unit of $\delta^{13}$C is parts per thousand$^{20}$ (per mil or ‰). Databases of $\delta^{13}$C can be found in the permanent repository ClumpDB$^{21}$ or scientific journals that publish research papers on geological temperatures. Below we consider the Precambrian Marine Carbonate Isotope Database (PMCID) provided by Shields and Veizer (2002), which can be downloaded from https://earthref.org/ERDA/48. The PMCID is a compilation of strontium, carbon, and oxygen isotope compositions of about 10 000 marine carbonate rocks of Archean to Ordovician age (between 3 800 Ma and 450 Ma), and includes data from 150 published articles and books. In Figure 8.6, we have reproduced the graph of the evolution of the carbon isotopes of marine carbonate obtained by Shields and Veizer (2002). We observe a high variation of $\delta^{13}$C, which indicates that the temperatures on Earth have varied a lot during the Precambrian. This also implies a large uncertainty in the estimates, and we must be careful with the figures calculated for this period.

<figure><img src="image_286.png" /><figcaption>Figure 8.6: Carbon isotopic evolution of marine carbonate</figcaption></figure>

Source: Shields and Veizer (2002, Figure 2, page 5) & https://earthref.org/ERDA/48.

Another controversy is the Snowball Earth hypothesis presented in Box 8.3. How do we explain the massive perturbations in the carbon cycle during the Proterozoic (Figure 8.7), and how do we explain the snow and glaciers on all continents between 750 Ma and 550 Ma, when they seem to have been near the equator? Again, we must be careful because there may be multiple answers and a combination of factors. Moreover, it is difficult to imagine the time when we refer to the palaeoclimate, because the magnitude of these periods is so different from what we have experienced or learned in history, even if we consider the last 3500 years, which corresponds to the first written records. To better understand that these developments are very long, we generally use a tool called the cosmic calendar (Figure 8.8). This is a scale that maps the 13.8 billion year age of the universe

<footnote>$^{20}$The standard for $\delta^{13}$C is the Pee Dee Belemnite (PDB), which has a ratio $\frac{^{13}\text{C}}{^{12}\text{C}}$ equal to 0.011238.</footnote>

<footnote>$^{21}$The web address is www.earthchem.org/communities/clumpdb.</footnote>
<figure><img src="image_287.png" /><figcaption>Figure 8.7: Neoproterozoic carbon isotope data compilation</figcaption></figure>

Source: Cox et al. (2016, Figure 2, page 90).

<figure><img src="image_288.png" /><figcaption>Figure 8.8: Cosmic calendar</figcaption></figure>

<table><thead><tr><th colspan="8">December</th></tr><tr><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th></tr></thead><tbody><tr><td>8</td><td>9</td><td>10</td><td>11</td><td>12</td><td>13</td><td>14</td></tr><tr><td>15</td><td>16</td><td>17</td><td>18</td><td>19<br>Vertebrates<br>appear.</td><td>20<br>Land plants<br>appear.</td><td>21</td></tr><tr><td>22</td><td>23</td><td>24</td><td>25<br>Dinosaurs<br>appear.</td><td>26<br>Mammals<br>appear.</td><td>27</td><td>28</td></tr><tr><td>29</td><td colspan="2">30<br>Dinosaurs<br>become extinct.</td><td colspan="2">31<br>Humans<br>appear.</td><td colspan="2"></td></tr></tbody></table>

Source: https://courses.lumenlearning.com/suny-astronomy/chapter/a-conclusion-and-a-beginning.
to a single year to make it more intuitive for educational purposes. On this scale, the Big Bang took place at midnight on January 1, and the present time is mapped to midnight on December 31. The time in days is then equal to:

$$t_{\text{days}} = \left( 1 - \frac{t_{\text{Ga}}}{13.797} \right) \times 365 \text{ days}$$

According to Sagan (1986), the Precambrian period begins on September 14 and ends on December 17. The first primates appear on December 29 and humans on December 31 at 22:30. They invent agriculture at 23:59:20. The invention of writing is at 23:59:45, and the voyage of Christopher Columbus takes place in the last second at 23:59:59. Modern human civilization then occurs in the last twenty minutes.

Box 8.4: Temperature scales

Three different scales are commonly used to measure temperature: Celsius, Kelvin, and Fahrenheit. Their symbols are °C, K, and °F, respectively. The Fahrenheit scale was developed by the German physicist Gabriel Fahrenheit in 1724. The Fahrenheit scale is defined by two fixed points: 32°F for the freezing point of water at sea level and 212°F for the boiling point of water at sea level. The interval between these two points is divided into 180 steps. The Celsius scale was developed by the Swedish astronomer Anders Celsius in 1742. This scale divides the interval between the two fixed points into 100 steps. The Celsius scale is also known as the centigrade scale. Finally, the Kelvin scale, developed by Lord Kelvin in 1848, is a modification of the Celsius scale in which 0 K is absolute zero. The relationships between the Celsius and Kelvin scales are $T_{\circ C} = T_{\circ K} - 273.15$ and $T_{\circ K} = T_{\circ C} + 273.15$. For Celsius and Fahrenheit, we have $T_{\circ C} = \frac{5}{9}(T_{\circ F} - 32)$ and $T_{\circ F} = \frac{9}{5}T_{\circ C} + 32$. Absolute zero is -273.15°C, 0 K and -459.67°F, implying that $T \ge -273.15°C$, $T \ge 0 K$, and $T \ge -459.67°F$. The melting point (at standard pressure) is obtained at temperatures of 0°C, 273.15 K and 32°F, while the boiling point of water corresponds to temperatures of 100°C, 373.15 K and 212°F.

**Palaeoclimate during the Phanerozoic** Studying the climate of the Phanerozoic era is generally easier than studying the Precambrian, because this period, which begins 541 million years ago, is characterized by a more abundant and diverse fossil record. In addition, we can use other materials, such as ice cores and ocean sediments. Figure 8.9 shows the global picture of temperature evolution during the Phanerozoic<fnref n="22" />. It was produced in 2014 by Glen Fergus, who has done a remarkable job of collecting data from a dozen published research papers<fnref n="23" />. It shows several episodes of hothouse scenarios and glacial cycles. The average temperature range compared to today is between -6°C and +15°C. The graph is divided into five panels. The first panel corresponds to the Palaeozoic (Cambrian, Ordovician, Silurian, Devonian, Mississippian, Pennsylvanian and Permian) and Mesozoic (Triassic, Jurassic and Cretaceous) eras. It covers the period from 541 Ma to 66 Ma. The second panel corresponds to a part of the Tertiary period and includes the Paleocene, Eocene, Oligocene and Miocene epochs (from 66 Ma to 5.3 Ma). The third and fourth panels show the average temperature of the Pliocene and Pleistocene. The Quaternary, which begins at 2.6 Ma BP, is characterised by many glaciations, while the Holocene is marked by an increase in temperature.

<footnote n="22">²²Scientists use the Celsius, Kelvin and Fahrenheit scales indifferently. That is why we have given their definition in Box 8.4.</footnote>

<footnote n="23">²³We have removed some data from the original figure.</footnote>
<figure><img src="image_289.png" /><figcaption>Figure 8.9: Earth temperature since 500 Myr BP (°C vs. 1960–1990 average)</figcaption></figure>

This shows estimates of global average surface air temperature over the 540 Myr of the Phanerozoic eon, since the first major proliferation of complex life forms on our planet. A major achievement of the last 30 years of climate science has been the production of a large set of actual measurements of temperature history (from physical proxies), replacing much of the earlier geological induction (i.e., informed guesses). The graph shows selected proxy temperature estimates. Because many proxy temperature reconstructions indicate local rather than global temperature – or ocean rather than air temperature – considerable approximation may be involved in deriving these global temperature estimates. As a result, the relativities of some of the estimates plotted are approximate, especially the early ones. Surface air temperature is plotted as anomalies (differences) from the average over the reference interval 1960–1990 (which is about 14°C).

Time is plotted forward to the present, taken as 2015 CE. It connects five separate linearly scaled segments, expanding by about an order of magnitude at each vertical break. The first segment groups the Cambrian (C), Ordovician (O), Silurian (S), Devonian (D), Carboniferous (C), Permian (P), Triassic (Tr), Jurassic (J), and Cretaceous (K). The first break is at the Mesozoic-Cenozoic boundary (~65 Myr ago). This is the K-T boundary (called Cretaceous-Paleogene) where the dinosaurs became extinct. The second segment groups the Paleocene, Eocene, OLigocene, and Miocene. The second break is at the Miocene-Pliocene boundary (~5.3 Myr ago). The last three segments are Pliocene, Pleistocene, and Holocene. The last two breaks are at 1 Myr BP and 20 kyr BP.

Source: Glen Fergus (2014), en.wikipedia.org/wiki/File:All_palaeotemps.png & https://gergs.net/all_palaeotemps-2.
Let us know how these temperatures are estimated. To do this, we need to go back to the scientific history of climate change presented in section 8.1.1. Paleoclimate research began in the 1950s with several advances: radiocarbon dating with carbon 14, analysis of deep-sea cores and marine sediments, drilling of ice cores in Greenland and Antarctica, etc. Whichever method we use, we need two modelling tools: an age dating model and a formula that converts the calculated metric into a temperature, because the latter is not observed.

The history of ice core science is studied in Langway (2008) (2008) and Jouzel (2013). One of the first attempts to explore the interior of an ice sheet was made by Ernst Sorge during the Alfred Wegener Expedition to Eismitte in central Greenland from July 1930 to August 1931. Using a 15-meter deep pit, he investigated the individual limits of annual snow accumulation. Between 1949 and 1952, the first ice cores were extracted separately by three international research teams at depths of between 100 and 150 meters, but the quality of the ice cores was poor. With several initiatives (Site 2, Byrd Station and Little America), the period 1957–1958 is generally considered to be the starting point of ice core research (Jouzel, 2013). A new step was achieved in 1961, when the first ice core longer than 1000 meters was taken at Camp Century. Since then, many projects have been carried out<sup>24</sup>, but the most famous remains the ice-core drilling in Vostock, Antarctica (Petit et al., 1999). Indeed, the depth record is held by the Vostock station, where scientists have drilled to a depth of 3770 meters. In fact, it is very difficult to go beyond this figure because we reach the surface of oceans or lakes. In addition, the bottom of the ice core at very deep depths is modified by the water at the ocean surface and does not contain any palaeoclimate information.

<table><caption>Table 8.3: Recovered deep and very deep ice cores</caption><thead><tr><th colspan="3">Greenland</th><th colspan="3">Antarctica</th></tr></thead><tbody><tr><td>Site 2</td><td>1956</td><td>305 m</td><td>Byrd Station</td><td>1957–1958</td><td>307 m</td></tr><tr><td>Site 2</td><td>1957</td><td>411 m</td><td>Little America</td><td>1958–1959</td><td>264 m</td></tr><tr><td>Camp Century</td><td>1961–1966</td><td>1387 m</td><td>Byrd Station</td><td>1966–1968</td><td>2164 m</td></tr><tr><td>Dye 3</td><td>1971</td><td>372 m</td><td>Vostock</td><td>1990–1998</td><td>3623 m</td></tr><tr><td>Milcent</td><td>1973</td><td>398 m</td><td>Dome Fuji</td><td>1994–1997</td><td>2503 m</td></tr><tr><td>Crete</td><td>1974</td><td>405 m</td><td>Vostock</td><td>2005–2007</td><td>3658 m</td></tr><tr><td>Dye 3</td><td>1979–1981</td><td>2037 m</td><td>Dome Fuji</td><td>2003–2007</td><td>3035 m</td></tr><tr><td>GRIP</td><td>1989–1992</td><td>3029 m</td><td>Dome C</td><td>1999–2005</td><td>3270 m</td></tr><tr><td>GISP 2</td><td>1989–1993</td><td>3057 m</td><td>Kohnen Station</td><td>2001–2006</td><td>2774 m</td></tr><tr><td>NGRIP</td><td>1996–2004</td><td>3090 m</td><td>WAIS</td><td>2006–2011</td><td>3405 m</td></tr></tbody></table>

Source: Langway (2008, Appendix A).

Analysis of trapped air bubbles in ice cores provides a direct record of the composition of the atmosphere at the time the ice formed. For example, we can measure the concentrations of greenhouse gases such as carbon dioxide and methane in the air bubbles to reconstruct past climate conditions. However, these measurements are not very robust and scientists prefer to use indirect measures. Dansgaard’s seminal paper in 1964 discussed methods based on stable isotopes (Dansgaard, 1964). He defined the relative deviation $\delta$ of the heavy isotope content as follows:

$$ \delta = 1000 \times \left( \frac{R_{\text{sample}} - R_{\text{standard}}}{R_{\text{standard}}} \right) \qquad (8.2) $$

<footnote n="24"><sup>24</sup>In Table 8.3, we have listed some of these projects and the corresponding depth of the drilling. The locations of the projects are shown in Figures 8.10 and 8.11.</footnote>
<figure><img src="image_290.png" /><figcaption>Figure 8.10: Greenland deep drilling sites</figcaption></figure>

Source: Langway (2008, Appendix A), created with paintmaps.com.

<figure><img src="image_291.png" /><figcaption>Figure 8.11: Antarctica deep drilling sites</figcaption></figure>

Source: Langway (2008, Appendix A), created with paintmaps.com.
Box 8.5: Isotopes of chemical elements

Isotopes are atoms of the same element. They have the same number of protons but differ in the number of neutrons. To write the symbol for an isotope, we use the standard AZE notation<sup>a</sup> $_{Z}^{A}E$, where E is the chemical symbol for the element, A is the atomic mass number (the total number of protons and neutrons in the nucleus of the atom) and Z is the atomic number (the number of protons in the nucleus of the atom). For example, hydrogen has seven isotopes: $_{1}^{1}$H (protium), $_{1}^{2}$H or D (deuterium), $_{1}^{3}$H or T (tritium), $_{1}^{4}$H, $_{5}^{1}$H, $_{6}^{1}$H, and $_{7}^{1}$H. We also distinguish between stable and unstable isotopes. Stable isotopes have a stable nucleus and the forces holding the protons and neutrons together are strong enough to prevent the nucleus from decaying. The most stable isotopes have a neutron to proton ratio close to one. Unstable (or radioactive) isotopes have an unstable nucleus and they can decay into other elements. The most frequent isotope of an element is called the major (or principal) isotope. In the case of hydrogen, protium and deuterium are the two stable isotopes and protium is the main isotope, accounting for about 99.98% of all occurring hydrogen atoms. In addition to these two isotopes, five other isotopes of hydrogen are unstable. The table below lists the stable and unstable isotopes of hydrogen, carbon, oxygen and uranium. The main isotope and its abundance are also given.

<table><thead><tr><th>Element</th><th>Stable isotopes</th><th>Unstable isotopes</th><th>Major isotope</th></tr></thead><tbody><tr><td>Hydrogen</td><td><sup>1</sup>H and <sup>2</sup>H</td><td><sup>3</sup>H - <sup>7</sup>H</td><td>Protium (99.98%)</td></tr><tr><td>Carbon</td><td><sup>12</sup>C and <sup>13</sup>C</td><td><sup>8</sup>C - <sup>11</sup>C and <sup>14</sup>C - <sup>22</sup>C</td><td>Carbon-12 (98.90%)</td></tr><tr><td>Oxygen</td><td><sup>16</sup>O and <sup>18</sup>O</td><td><sup>17</sup>O and <sup>19</sup>O - <sup>27</sup>O</td><td>Oxygen-16 (99.76%)</td></tr><tr><td>Uranium</td><td></td><td><sup>232</sup>U - <sup>242</sup>U</td><td>Uranium-238 (99.27%)</td></tr></tbody></table>

A heavy isotope is an isotope of an element that has more neutrons than the most abundant isotope. In general, heavy isotopes are more stable, and can have different chemical properties. The heavy isotopes of the previous elements are $_{1}^{2}$H, $_{13}^{6}$C, $_{18}^{8}$O and $_{92}^{238}$U.

where *R* is the absolute content. *δ* is measured in ‰. This is the general form of Equation (8.1) given on page 627, if we replace the ratio of the carbon isotope by *R*. As the chemical formula of water is H₂O, climate reconstruction from ice cores is based on the analysis of hydrogen and oxygen. In the case of hydrogen, the common isotope is ¹H, while the heavy isotope is ²H (also called the deuterium or D). The ratio *R* is then $\frac{^{2}\text{H}}{^{1}\text{H}}$ and the relative variation is written as $\delta\text{D}$. In the case of oxygen, the common isotope is ¹⁶O, while the heavy isotope is ¹⁸O. The ratio *R* is then $\frac{^{18}\text{O}}{^{16}\text{O}}$ and the relative variation is written as $\delta^{18}\text{O}$. To compute $\delta\text{D}$ and $\delta^{18}\text{O}$, we need the standard values of ²H/¹H and ¹⁸O/¹⁶O. Using the standard mean ocean water (SMOW), they are equal to 0.00015576 and 0.0020052. Dansgaard (1964) assumed that the isotopic fractionation of water implies that $\delta\text{D} = (8.1 \pm 0.1) \delta^{18}\text{O} + (11 \pm 1)$ at equilibrium<fnref n="25" />. More generally, Merlivat and Jouzel (1979) showed that the relationship is linear: $\delta\text{D} = s\delta^{18}\text{O} + d$ where the slope *s* and the deuterium excess *d* may depend on several factors: temperature, latitude, humidity, etc.

<footnote><sup>a</sup>We generally simplify the notation with <sup>A</sup>E because all the isotopes of the same element have the same atomic number.</footnote>

<footnote n="25">²⁵This relationship has already been established by Craig (1961), who found that $\delta\text{D} = 8.0 \delta^{18}\text{O} + 10$. It is known as the meteroic water line.</footnote>
<figure><img src="image_292.png" /><figcaption>Figure 8.12: Part of an ice core at WAIS Divide Field Camp</figcaption></figure>

Source: Eli Duke, Antarctica: WAIS Divide Field Camp (Flickr), www.flickr.com/photos/80547277@N00/9518403333.

The aim of ice core analysis is to estimate the temperature function $t \mapsto \mathcal{T}(t)$ with respect to the time age $t$. The raw analysis provides two measurements: the depth $d$ of the ice core drilling and the isotope ratio measure $\delta$, which is calculated using an instrument called an isotope ratio mass spectrometer (IRMS). We therefore observe the isotope function $d \mapsto \delta(d)$. To obtain the temperature function, we proceed in two steps:

1. First, we transform the depth $d$ of the ice core drilling into the time age $t$:

$$t = \varphi_t (d)$$

2. We then estimate the temperature $\mathcal{T}$ associated with the isotope ratio $\delta(d)$:

$$\mathcal{T} = \varphi_{\mathcal{T}}(\delta(d))$$

Combining the two previous equations gives the desired parametric function $t \mapsto \mathcal{T}(t)$. To illustrate the temperature reconstruction, we consider the research of Petit et al. (1999), who estimated the climate and atmospheric history of the past 420 000 years using the Vostok ice cores. To do this, we download the file deutnat-noaa.txt from https://www.ncei.noaa.gov/access/paleo-search/study/2453. Below we report a sample of this dataset:

# Vostok - Isotope and Gas Data and Temperature Reconstruction

#--------------------------------------------

# World Data Service for Paleoclimatology, Boulder

# and

# NOAA Paleoclimatology Program

# National Centers for Environmental Information (NCEI)

#--------------------------------------------
[...]

<table><thead><tr><th>Variables</th><th>format</th><th>Short_name</th><th>&lt;tab&gt;</th></tr></thead><tbody><tr><td>what</td><td>material</td><td>error</td><td>units</td><td>seasonality</td><td>data_type</td><td>detail</td></tr><tr><td>method</td><td>data_format</td><td>additional_information</td><td>Note:</td><td>the Short_name does not require a PaST term.</td><td></td><td></td></tr></tbody></table><table><thead><tr><th>depth_m</th><th>ice_ageBP</th><th>deltaD</th><th>deltaTS</th></tr></thead><tbody><tr><td>0</td><td>0</td><td>-438.0</td><td>0.00</td></tr><tr><td>1</td><td>17</td><td>-438.0</td><td>0.00</td></tr><tr><td>2</td><td>35</td><td>-438.0</td><td>0.00</td></tr><tr><td>3</td><td>53</td><td>-438.0</td><td>0.00</td></tr><tr><td>4</td><td>72</td><td>-438.0</td><td>0.00</td></tr><tr><td>5</td><td>91</td><td>-438.0</td><td>0.00</td></tr><tr><td>6</td><td>110</td><td>-438.0</td><td>0.00</td></tr><tr><td>7</td><td>129</td><td>-438.0</td><td>0.00</td></tr><tr><td>8</td><td>149</td><td>-442.9</td><td>-0.81</td></tr><tr><td>9</td><td>170</td><td>-437.9</td><td>0.02</td></tr><tr><td>10</td><td>190</td><td>-435.8</td><td>0.36</td></tr><tr><td>11</td><td>211</td><td>-443.7</td><td>-0.95</td></tr><tr><td>12</td><td>234</td><td>-449.1</td><td>-1.84</td></tr><tr><td>13</td><td>258</td><td>-444.6</td><td>-1.09</td></tr><tr><td>14</td><td>281</td><td>-442.5</td><td>-0.75</td></tr><tr><td>15</td><td>304</td><td>-439.3</td><td>-0.22</td></tr><tr><td>16</td><td>327</td><td>-440.9</td><td>-0.48</td></tr><tr><td>17</td><td>351</td><td>-442.5</td><td>-0.75</td></tr><tr><td>18</td><td>375</td><td>-436.6</td><td>0.23</td></tr><tr><td>19</td><td>397</td><td>-430.0</td><td>1.33</td></tr><tr><td>20</td><td>420</td><td>-435.9</td><td>0.35</td></tr></tbody></table>

[...]

<table><tr><td>3300</td><td>416872</td><td>-430.8</td><td>1.36</td></tr><tr><td>3301</td><td>417419</td><td>-430.3</td><td>1.43</td></tr><tr><td>3302</td><td>417969</td><td>-430.4</td><td>1.40</td></tr><tr><td>3303</td><td>418526</td><td>-431.1</td><td>1.27</td></tr><tr><td>3304</td><td>419095</td><td>-433.0</td><td>0.94</td></tr><tr><td>3305</td><td>419682</td><td>-435.5</td><td>0.51</td></tr><tr><td>3306</td><td>420281</td><td>-435.2</td><td>0.54</td></tr><tr><td>3307</td><td>420888</td><td>-436.4</td><td>0.32</td></tr><tr><td>3308</td><td>421507</td><td>-437.3</td><td>0.15</td></tr><tr><td>3309</td><td>422135</td><td>-437.6</td><td>0.08</td></tr><tr><td>3310</td><td>422766</td><td>-436.6</td><td>0.23</td></tr></table>
This dataset has four variables: depth *d* (meter), age *t* (yr BP), deuterium isotope ratio δD (‰) and surface temperature Δ*T* (°C). We have included the first 20 observations and the last 10 observations. Note that the measurement is made at every meter of the ice core. For example, the 11th observation corresponds to a depth of 10 meters and the authors have calculated a deuterium isotope ratio δD of -435.8‰. Using an age dating model<sup>26</sup>, this depth corresponds to an age of 190 years BP. Using a climate model<sup>27</sup>, the authors obtained a surface temperature variation Δ*T* of 0.36 degrees Celsius. In the first panel of Figure 8.13, we plot the function *d* ↦ *δD* (*d*). The maximum depth is 3310 meters while *δD* (*d*) varies between -500‰ and -400‰. Several peaks and cycles are observed. The results of the age dating model are shown in the second panel. When the depth is less than 2000 meters, we have a linear relationship between *d* and the age *t*. Beyond this threshold, the function is convex. The mapping between δD and ΔT depends on the model chosen. In our case, we use a linear function ΔT = 78.2361 + 0.1794 × δD, which is shown in the third panel. This gives the relationship between depth *d* and temperature ΔT in the fourth panel. Finally, the temperature function *t* ↦ *T* (*t*) is shown in Figure 8.14. In Petit *et al.* (1999), this corresponds to panel b (isotopic temperature of the atmosphere) of Figure 3 on page 431.

<figure><img src="image_293.png" /><figcaption>Figure 8.13: Isotopic reconstruction of Vostok ice cores</figcaption></figure>

Source: Petit *et al.* (1999), https://www.ncei.noaa.gov/access/paleo-search/study/2453 & Author's calculations.

**Remark 76** Other variables can be found in the dataset. For example, we report the gas concentration of CH₄ (in ppbv or parts per billion by volume) and CO₂ (in ppmv or parts per million by volume) and also the isotope ratio δ¹⁸O in Figure 8.15.

<footnote n="26"><sup>26</sup>See Parrenin *et al.* (2007) for a review of the construction of the time scale with a focus on the EDC3 chronology, the importance of age markers and the mapping process.</footnote>

<footnote n="27"><sup>27</sup>Described in the second section on page 431 of the article.</footnote>
<figure><img src="image_294.png" /><figcaption>Figure 8.14: Temperature reconstruction of Vostok ice cores</figcaption></figure>

Source: Petit et al. (1999) & https://www.ncei.noaa.gov/access/paleo-search/study/2453.

<figure><img src="image_295.png" /><figcaption>Figure 8.15: Gas concentration of Vostok ice cores</figcaption></figure>

Source: Petit et al. (1999) & https://www.ncei.noaa.gov/access/paleo-search/study/2453.
In addition to ice cores, the previous analysis can be applied to rocks, lake and ocean sediments, and tree rings. Let's go back to Figure 8.9 and look at the different scientific references used to calculate the Earth's temperature since 500 Myr BP:

* The works of Royer et al. (2004) are related to the works of Veizer et al. (1999) and Veizer et al. (2000). Veizer et al. (1999) collected a total of 2 128 calcitic and phosphatic shells, mainly brachiopods with some conodonts and belemnites, and measured their $^{87}$Sr/$^{86}$Sr, $\delta^{13}$C and $\delta^{18}$O values. It is a statistical study where the authors calculated correlograms, trends and performed a factor analysis to show that the $^{87}$Sr/$^{86}$Sr, $\delta^{13}$C and $\delta^{18}$O system is driven by three factors: the first two are tectonic factors while the third is a biologically mediated redox balance of carbon and sulfur cycles. In 2000, Jàn Veizer and two co-authors used the previous database to write a controversial paper entitled "*Evidence for decoupling of atmospheric CO$_2$ and global climate during the Phanerozoic eon*". In particular, they concluded:

> "[...] our data conflict with a temperature reconstruction using an energy balance model that is forced by reconstructed atmospheric carbon dioxide concentrations. The results can be reconciled if atmospheric carbon dioxide concentrations were not the principal driver of climate variability on geological timescales for at least one-third of the Phanerozoic eon, or if the reconstructed carbon dioxide concentrations are not reliable." (Veizer et al., 2000, page 698).

The research by Dana Royer and his co-authors consisted of examining the dataset and the reconstructed temperature curve, and proposing a new reconstructed curve by applying a correction based on seawater pH:

> "Recent studies have purported to show a closer correspondence between reconstructed Phanerozoic records of cosmic ray flux and temperature than between CO$_2$ and temperature. The role of the greenhouse gas CO$_2$ in controlling global temperatures has therefore been questioned.[...] We explore the possible influence of seawater pH on the $\delta^{18}$O record and find that a pH-corrected record matches the glacial record much better. Periodic fluctuations in the cosmic ray flux may be of some climatic significance, but are likely of second-order importance on a multimillion-year timescale." (Royer et al., 2004, page 4).

* In 2004, the North Greenland Ice Core Project (NGRIP) members published an article in *Nature*, with two main contributions. First, they extensively studied the late Eemian period, which is the last interglacial period which began about 130 000 years ago and ended about 115 000 years ago. They revealed a previously unrecognised warm period initiated by an abrupt climate warming about 115 000 years ago, before glacial conditions had fully developed. North Greenland Ice Core Project members (2004, pages 2-3). Second, they observed significant regional climate differences when analyzing ice cores from northern (NGRIP) and central (GRIP/GISP 2) Greenland regions, and suggested that "*the extent of ice in the Northern Hemisphere modulated the latitudinal temperature gradients in Greenland*" North Greenland Ice Core Project members (2004, page 1).

* The research carried out by Lisiecki and Raymo (2005) is remarkable. They studied the LR04 database, which contains over 38 000 individual $\delta^{18}$O measurements from 57 ocean drilling sites$^{28}$. Benthic $\delta^{18}$O records are a climate proxy used to reconstruct past ocean temperatures (and also ice volume). Benthic foraminiferal calcite is the calcium carbonate material that

<footnote>$^{28}$Most of them were in the Atlantic Ocean, a few in the Pacific Ocean and even fewer in the Asian Ocean.</footnote>
makes up the shells of benthic foraminifera, tiny organisms that live on the ocean floor. The calcium carbonate incorporates oxygen from the seawater, and the ratio $\delta^{18}$O in foraminiferal shells depends on the temperature of the seawater when the shell was formed. Cooler water has higher $\delta^{18}$O values, while warmer water has lower $\delta^{18}$O values. The authors used various alignment and stacking techniques to synchronise the 57 time series. They were then able to derive a graphical correlation and create a unique series showing the common pattern of the 38 000 individual $\delta^{18}$O measurements.

* The data labelled EPICA Dome C, Antarctica correspond to those calculated by Jouzel et al. (2007). A preliminary version of these data was published three years earlier (EPICA community members, 2004). This article focused on the comparison of the deuterium isotope ratio $\delta$D between the Vostok and Dome C ice cores. The article by Jouzel et al. (2007) went further by converting the $\delta$D data into a temperature record$^{29}$. They also found that the combined effects of the precession and obliquity Milankovitch cycles drove the dynamics of the ice ages, implying that climate variability over the past 800 000 years cannot be explained by the radiative forcing of CO$_2$ and CH$_4$ alone.

* James Zachos and his co-authors have collected several sources of data (Zachos et al., 2001, 2008). They have used similar data to those studied by Lisiecki and Raymo (2005), but they have included both the isotope ratios $\delta^{13}$C and $\delta^{18}$O. By crossing these two pieces of information, they deduced the partial pressure of carbon dioxide$^{30}$ pCO$_2$ in the ocean over the past 65 million years. Another important contribution of these papers is the consideration of feedbacks and new estimates of climate sensitivity.

* Friedrich et al. (2012) compiled a new dataset of benthic foraminifera $\delta^{13}$C and $\delta^{18}$O ratios for the middle to late Cretaceous, spanning 55 million years. They highlighted the role of ocean circulation in greenhouse Earth episodes. For example, they showed that:

1. "There was widespread formation of bottom waters with temperatures above 20°C during the Cretaceous hothouse world;

2. These bottom waters filled the North Atlantic and probably originated as thermocline or intermediate waters in the tropical oceans;

3. The interbasin $\delta^{13}$C gradient was unusually large during the Cretaceous hot greenhouse, probably because the North Atlantic sills prevented the free exchange of waters in the deep basin;

4. The hot greenhouse ended when the Equatorial Atlantic Gateway opened sufficiently to flood the deep North Atlantic with relatively cool polar waters formed in the Southern Ocean."

According to this study, plate tectonic movements are then an important factor for understanding the temperature dynamics during the Mesozoic, because they have influenced the circulation of warm and cold waters.

* Hansen et al. (2013a) proposed a simplified model to investigate the state dependence of climate sensitivity, sea level and atmospheric CO$_2$ through the Cenozoic. Their basic idea is

<footnote>$^{29}$The original data from Jouzel et al. (2007) can be accessed at www.ncei.noaa.gov/access/paleo-search/study/6080 (file edc3deuttemp2007.txt). To obtain all the EPICA Dome C published data (80 files), the reader can explore the directory ftp.ncdc.noaa.gov/pub/data/paleo/icecore/antarctica/epica_domec.</footnote>

<footnote>$^{30}$pCO$_2$ is a measure of the amount of carbon dioxide dissolved in a gas or liquid. It is measured in ppm or ppmv (parts per million by volume).</footnote>
to estimate Cenozoic sea level and temperature from empirical data, filtering the data with minimal assumptions and modelling. In fact, the paper contains only five equations. For example, the equation for the lower ocean temperature is:

$$ \mathcal{T}_{LO} = \begin{cases} 5 - 8 \left( \frac{\delta^{18}\text{O} - 1.75}{3} \right) & \text{if } \delta^{18}\text{O} < 3.25 \\ 1 - 4.4 \left( \frac{\delta^{18}\text{O} - 3.25}{3} \right) & \text{otherwise} \end{cases} $$

while the surface air temperature is equal to $\mathcal{T}_{AT} = 2\mathcal{T}_{LO} + 12.25$ during the Pleistocene. The relationship between the oxygen isotope ratio $\delta^{18}\text{O}$, the deep ocean temperature $\mathcal{T}_{LO}$ and the atmospheric temperature $\mathcal{T}_{AT}$ is shown in Figure 8.16. Their results are very impressive, especially Figures 2c and 6, which compare the raw estimates of sea level and global mean surface temperature anomalies with the fitted estimates calculated with the equations. In Figure 8.16 we can see that the atmospheric temperature varies between 9.35°C and 14.37°C. This illustrates how an impact of $\pm 3^\circ\text{C}$ can have a large effect on the Earth's climate.

<figure><img src="image_296.png" /><figcaption>Figure 8.16: Relationship between $\delta^{18}\text{O}$, $\mathcal{T}_{LO}$ and $\mathcal{T}_{AT}$ during the Pleistocene</figcaption></figure>

A comparison of Figure 8.14 with Figure 8.15 shows a high correlation between CO₂ concentration and temperature. But we also see that there is a high correlation when we look at the CH₄ concentration. If we consider a longer period, these correlations are lower. For example, we report the temporal evolution of atmospheric CO₂ reconstructed by Foster et al. (2017). Using a sample of 1500 estimated atmospheric CO₂, they have performed a Loess regression. Their results for the last 420 million years are shown in Figure 8.17. Comparison with Figure 8.9 suggests that the evolution of CO₂ and $\Delta\mathcal{T}$ may be asynchrone in some periods, because CO₂ is not the only explanatory factor.
<figure><img src="image_297.png" /><figcaption>Figure 8.17: Evolution of the atmospheric CO₂ during the last 420 million years</figcaption></figure>

Source: Foster et al. (2017, Figure 1, page 3) & Supplementary Data 2 (www.nature.com/articles/ncomms14845).

## Anthropogenic factors of climate change

The term “anthropogenic” is derived from the Greek words “anthropos” (human) and “genesis” (origin) and refers to anything caused or influenced by human activity. This includes both direct and indirect impacts, such as climate change, pollution, deforestation, and biodiversity loss. In this section, we examine the human impact on climate change since the beginning of the Industrial Revolution, which is assumed to have occurred in 1760. First, we examine the temperature anomaly, then we consider anthropogenic greenhouse gas emissions, and finally we discuss the planetary boundaries framework. Chapter 12 on page 1125, on physical risks, complements this section and extends the analysis to other climate impacts such as flooding, sea-level rise, hurricanes, wildfires, heat waves, and agricultural productivity.

**Temperature anomaly** We define the temperature anomaly at time t as the difference between the temperature at time t and the temperature for a reference period:

$$ \Delta T(t) = T(t) - T_{\text{Base}} $$

where $T_{\text{Base}}$ is the reference temperature. It is generally the average of the temperature of the reference period:

$$ T_{\text{Base}} = \frac{\sum_{j \in \text{Base}} T(j)}{n_{\text{Base}}} $$

For example, the reference temperature can be the average temperature of the 20th century (from 1901 to 2000) or the pre-industrial period. In Figure 8.18, we report the global temperature anomaly
obtained with the HadCRUT5 database<fnref n="31" />. The reference period for the calculation of $T_{\text{base}}$ is 1961–1990. The blue circle corresponds to the annual average, while the red line is the 10-year moving average. For each year, we have also provided the 95% confidence interval with a black vertical line. In 2023, the temperature anomaly was +1.04°C with a 95% confidence interval between 0.97°C and 1.10°C, while the 10-year moving average was 0.86°C. Since 1975 there has been a clear upward trend. If we estimate the linear trend between 1975 and 2023, we get the dashed black line. A simple projection gives the following forecasts: +1.43°C in 2050, +1.93°C in 2075 and +2.42°C in 2100.

<figure><img src="image_298.png" /><figcaption>Figure 8.18: Global average land-ocean temperature anomaly relative to 1961–1990 average</figcaption></figure>

Source: Morice et al. (2021) & https://www.metoffice.gov.uk/hadobs/hadcrut5.

The previous analysis is a global picture. In fact, the temperature anomaly is calculated for a given location defined by a latitude, a longitude and an altitude. Let $\Delta T_i(t)$ be the temperature anomaly for location $i$. The calculation of the temperature anomaly for a region is the weighted average of all locations belonging to the region grid:

$$ \Delta T_{\mathcal{R}_{\text{region}}}(t) = \sum_{i \in \text{Grid}(\mathcal{R}_{\text{region}})} w_i \cdot \Delta T_i(t) $$

where $w_i$ is the weight of location $i$. So we can calculate the temperature for a country, a continent and even a hemisphere. In Figure 8.19, we show the temperature anomaly for the northern and southern hemispheres, calculated by Morice et al. (2021), using a regular 5° latitude by 5° longitude grid of the Earth. In fact, the global temperature anomaly shown in Figure 8.18 is just the simple average of the northern and southern hemisphere temperature anomalies shown in Figure 8.19. We can see that the temperature in the northern hemisphere has risen faster than in the southern

<footnote n="31">³¹This database is produced and maintained by the Met Office Hadley Centre, which is also responsible for many other datasets that can be found at https://www.metoffice.gov.uk/hadobs.</footnote>
<figure><img src="image_299.png" /><figcaption>Figure 8.19: Average land-ocean temperature anomaly in the northern and southern hemispheres relative to the 1961–1990 average</figcaption></figure>

Source: Morice et al. (2021) & https://www.metoffice.gov.uk/hadobs/hadcrut5.

hemisphere. The slope of the trend since 1975 is +2.78°C per century for the northern hemisphere, which is higher than the slope of +1.18°C per century for the southern hemisphere. We therefore project a temperature anomaly of +3.35°C degrees and +1.50°C degrees respectively by 2100. All these results are summarized in Table 8.4.

<table><caption>Table 8.4: Linear projection of land-ocean temperature anomaly (in °C)</caption><thead><tr><th rowspan="2">Year</th><th colspan="3">HadCRUT5</th><th colspan="3">NOAAGlobalTemp v5.1</th></tr><tr><th>Global</th><th>Northern</th><th>Southern</th><th>Global</th><th>Northern</th><th>Southern</th></tr></thead><tbody><tr><td>2050</td><td>1.4336</td><td>1.9595</td><td>0.9078</td><td>1.4576</td><td>1.9894</td><td>0.9247</td></tr><tr><td>2075</td><td>1.9288</td><td>2.6540</td><td>1.2035</td><td>1.9185</td><td>2.6715</td><td>1.1642</td></tr><tr><td>2100</td><td>2.4239</td><td>3.3486</td><td>1.4992</td><td>2.3795</td><td>3.3536</td><td>1.4038</td></tr><tr><td>Slope</td><td>0.0198</td><td>0.0278</td><td>0.0118</td><td>0.0184</td><td>0.0273</td><td>0.0096</td></tr></tbody></table>

Source: https://www.ncei.noaa.gov/access/monitoring/global-temperature-anomalies/anomalies, https://www.metoffice.gov.uk/hadobs/hadcrut5 & Author's calculations.

The previous figures were obtained using the HadCRUT5 dataset, which is based on several historical datasets, models, and reanalyses. A reanalysis is a process that combines historical weather observations with a computer model to produce a consistent and complete record of past weather conditions. This is necessary because historical records are not available in a grid. Reanalysis then allows the creation of a homogeneous database of temperature records for a given grid and time period. However, the temperature records depend on the database. Below we list five land-ocean
gridded temperature datasets, their web addresses, and the scientific reference that explains how these temperature records were calculated:

1. Berkeley Earth, berkeleyearth.org/data (Rohde and Hausfather, 2020);

2. ERA5, cds.climate.copernicus.eu/cdsapp#!/dataset/reanalysis-era5-single-levels (Hersbach et al., 2020);

3. HadCRUT5, www.metoffice.gov.uk/hadobs/hadcrut5 (Morice et al., 2021);

4. GISTEMP v4, data.giss.nasa.gov/gistemp (Lenssen et al, 2019);

5. NOAAGlobalTemp v5.1, www.ncei.noaa.gov/products/land-based-station/noaa-global-temp (Vose et al., 2021).

A comparison of these datasets shows a high degree of consistency between the estimates, but we must be careful because it also shows that the results can be different, especially if we look at specific locations (e.g., a point on the grid or a country) rather than global locations.

<table><caption>Table 8.5: Linear projection of land and ocean temperature anomalies (in °C)</caption><thead><tr><th rowspan="2">Year</th><th colspan="2">Global</th><th colspan="2">Northern</th><th colspan="2">Southern</th></tr><tr><th>Land</th><th>Ocean</th><th>Land</th><th>Ocean</th><th>Land</th><th>Ocean</th></tr></thead><tbody><tr><td>2050</td><td>2.4212</td><td>1.0238</td><td>2.8388</td><td>1.3482</td><td>1.4719</td><td>0.7972</td></tr><tr><td>2075</td><td>3.2386</td><td>1.3243</td><td>3.8176</td><td>1.8061</td><td>1.9222</td><td>0.9875</td></tr><tr><td>2100</td><td>4.0560</td><td>1.6247</td><td>4.7964</td><td>2.2641</td><td>2.3725</td><td>1.1779</td></tr><tr><td>Slope</td><td>0.0327</td><td>0.0120</td><td>0.0392</td><td>0.0183</td><td>0.0180</td><td>0.0076</td></tr></tbody></table>

Source: NOAAGlobalTemp v5.1 & Author's calculations.

We look at NOAAGlobalTemp v5.1 and display the land-ocean temperature anomaly in Figure 8.20. Note that the time series are very close to those plotted in Figures 8.18 and 8.19. The correlation between HadCRUT and NOAAGlobalTemp is 99.04% for the global surface, 99.27% for the northern hemisphere, and 97.74% for the southern hemisphere. Figure 8.20 also shows the decomposition of the land-ocean temperature into land and ocean temperatures. It can be seen that the temperature anomalies are more important for the land surface than for the ocean surface, implying that global warming is more important for the land than for the oceans. This is especially true in the northern hemisphere. We have calculated the trend<fnref n="32" /> as before and reported the estimates in Tables 8.4 and 8.5. By the end of this century, the projected land temperature anomaly is +4.06°C for the world, 4.80°C for the northern hemisphere and 2.37°C for the southern hemisphere.

The discrepancy between the northern and southern hemispheres is even more pronounced when we look at countries. To illustrate this, we look at the temperature anomalies<fnref n="33" /> on land as calculated by the FAO. As before, we calculate the trend with the temperature anomalies between 1975 and 2022 by country and project the trend to 2100. The results are shown in Figure 8.21. The range is from 0.64°C to 7.63°C. According to these results, Greenland and Russia<fnref n="34" /> will be most affected, followed by Europe, Canada and the Middle East.

<footnote n="32">³²The base period used by the NOAA model is different and is 1901–2000. To reconcile the two datasets, we need to adjust the HadCRUT5 data to have the same reference period as the NOAA data. This is equivalent to adding 0.10°C, 0.06°C, and 0.14°C degrees to the global surface, northern hemisphere, and southern hemisphere temperature anomalies of the HadCRUT5 data, respectively.</footnote>

<footnote n="33">³³We filter the database at https://www.fao.org/faostat/en/#data/ET using the item meteorological year and the element temperature change.</footnote>

<footnote n="34">³⁴For Russia and the countries of the former Soviet Union, historical data start in 1992 and may explain an overestimation of the trend.</footnote>
<figure><img src="image_300.png" /><figcaption>Figure 8.20: Average temperature anomaly (land-ocean, land and ocean)</figcaption></figure>

Source: Vose et al. (2021) &
https://www.ncei.noaa.gov/access/monitoring/global-temperature-anomalies/anomalies.

<figure><img src="image_301.png" /><figcaption>Figure 8.21: Projection of temperature anomaly by 2100 (in °C)</figcaption></figure>

Source: https://www.fao.org/faostat/en/#data/ET & Author's calculations (created by Datawrapper).
**Anthropogenic GHG emissions** In order to study anthropogenic greenhouse gas emissions, we need to introduce some definitions and clarify some concepts of the global greenhouse gas budget. Let us first consider anthropogenic carbon dioxide emissions. According to Friedlingstein et al. (2022), the global carbon budget has five main components:

1. Fossil fuel combustion and oxidation from all energy and industrial processes, including cement production and carbonation;

2. Emissions from land-use change;

3. The growth rate of atmospheric CO₂ concentration;

4. The uptake of CO₂ by the oceans (ocean sink);

5. The uptake of CO₂ by the land (land sink).

These components are denoted $\mathcal{C}\mathcal{E}_{\text{Industry}}$, $\mathcal{C}\mathcal{E}_{\text{Land}}$, $\mathcal{C}\mathcal{E}_{\text{AT}}$, $\mathcal{C}\mathcal{S}_{\text{Ocean}}$, $\mathcal{C}\mathcal{S}_{\text{Land}}$ respectively. From a theoretical point of view, we have the following identity:

$$ \mathcal{C}\mathcal{E}_{\text{AT}} = \underbrace{(\mathcal{C}\mathcal{E}_{\text{Industry}} + \mathcal{C}\mathcal{E}_{\text{Land}})}_{\text{Positive emissions}} - \underbrace{(\mathcal{C}\mathcal{S}_{\text{Ocean}} + \mathcal{C}\mathcal{S}_{\text{Land}})}_{\text{Negative emissions}} $$

As Friedlingstein et al. (2022) explained, this equality is not verified because of imperfect spatial and temporal data coverage, estimation errors and omission of minor terms. The authors therefore defined the estimated budget imbalance, which measures the mismatch between estimated emissions and estimated changes in the atmosphere, land and oceans:

$$ \mathcal{C}\mathcal{B}_{\text{Imbalance}} = \mathcal{C}\mathcal{E}_{\text{Industry}} + \mathcal{C}\mathcal{E}_{\text{Land}} - (\mathcal{C}\mathcal{E}_{\text{AT}} + \mathcal{C}\mathcal{S}_{\text{Ocean}} + \mathcal{C}\mathcal{S}_{\text{Land}}) $$

In the database provided by the authors<fnref n="35" />, they split the carbon emissions $\mathcal{C}\mathcal{E}_{\text{Industry}}$ into gross industrial emissions excluding carbonation minus cement carbonation sink<fnref n="36" />: $\mathcal{C}\mathcal{E}_{\text{Industry}} = \mathcal{C}\mathcal{E}_{\text{Industry}}^{*} - \mathcal{C}\mathcal{S}_{\text{Cement}}$.

In 2021, the authors estimate the following figures expressed in gigatonnes of carbon: $\mathcal{C}\mathcal{E}_{\text{Industry}}^{*} = 10.13$, $\mathcal{C}\mathcal{E}_{\text{Land}} = 1.08$, $\mathcal{C}\mathcal{E}_{\text{AT}} = 5.23$, $\mathcal{C}\mathcal{S}_{\text{Ocean}} = 2.88$, $\mathcal{C}\mathcal{S}_{\text{Land}} = 3.45$, $\mathcal{C}\mathcal{S}_{\text{Cement}} = 0.23$, and $\mathcal{C}\mathcal{B}_{\text{Imbalance}} = -0.58$. Expressed in gigatonnes of CO₂ we obtain: $\mathcal{C}\mathcal{E}_{\text{Industry}}^{*} = 37.12$, $\mathcal{C}\mathcal{E}_{\text{Land}} = 3.94$, $\mathcal{C}\mathcal{E}_{\text{AT}} = 19.14$, $\mathcal{C}\mathcal{S}_{\text{Ocean}} = 10.55$, $\mathcal{C}\mathcal{S}_{\text{Land}} = 12.64$, $\mathcal{C}\mathcal{S}_{\text{Cement}} = 0.84$, and $\mathcal{C}\mathcal{B}_{\text{Imbalance}} = -2.12$. Anthropogenic CO₂ emissions are therefore 36.28 GtCO₂ for industrial processes ($\mathcal{C}\mathcal{E}_{\text{Industry}}$) and 3.94 GtCO₂ for land-use change. Since the total is 40.22 GtCO₂, 26.23% and 31.43% of the total anthropogenic CO₂ emissions have been absorbed by oceans and land, respectively, while 47.60% remain in the atmosphere. In Figure 8.22, we show the evolution of $\mathcal{C}\mathcal{E}_{\text{Industry}}$ and $\mathcal{C}\mathcal{E}_{\text{Land}}$. While carbon dioxide emissions from land-use change are relatively stable, carbon dioxide emissions from

$$ \mathrm{Ca(OH)_2} + \mathrm{CO_2} \rightarrow \mathrm{CaCO_3} + \mathrm{H_2O} $$

<footnote n="35">³⁵The full data set can be found at https://www.icos-cp.eu and https://globalcarbonbudgetdata.org. The main variables are available at https://globalcarbonbudget.org/wp-content/uploads/Global_Carbon_Budget_2022v1.0.xlsx. Carbon emissions are expressed in billion tonnes of carbon per year (GtC/yr). To convert these figures to billion tonnes of carbon dioxide (GtCO₂/yr), we multiply them by $\frac{44.011}{12.011}$ or 3.664. In fact, the atomic mass of carbon is 12.011 g/mol, and the atomic mass of oxygen is 15.999 g/mol. The molecular weight of CO₂ is therefore $12.011 + 2 \times 15.999 = 44.011$ g/mol.</footnote>

<footnote n="36">³⁶Cement carbonation sink is a natural process in which concrete absorbs carbon dioxide from the atmosphere. This process occurs when the calcium hydroxide in cement reacts with carbon dioxide in the air to form calcium carbonate:</footnote>
<figure><img src="image_302.png" /><figcaption>Figure 8.22: Annual CO₂ emissions (in GtCO₂)</figcaption></figure>

Source: Friedlingstein et al. (2022), https://globalcarbonbudget.org & Author's calculations.

<figure><img src="image_303.png" /><figcaption>Figure 8.23: Cumulative CO₂ emissions and carbon sinks (in GtCO₂)</figcaption></figure>

Source: Friedlingstein et al. (2022), https://globalcarbonbudget.org & Author's calculations.
<figure><img src="image_304.png" /><figcaption>Figure 8.24: Cumulative CO₂ budget imbalance in atmosphere (in GtCO₂)</figcaption></figure>

Source: Friedlingstein et al. (2022), https://globalcarbonbudget.org & Author's calculations.

industrial processes are growing faster since 1950. Looking at cumulative CO₂ emissions, we get Figure 8.23. We also show the negative emissions due to the two carbon sinks. From 1750, industrial processes and land-use change have emitted a total of 1717 and 742 GtCO₂, respectively, and ocean and land sinks have absorbed a total of 678 and 841 GtCO₂, respectively. We can then calculate the cumulative CO₂ emissions remaining in the atmosphere in Figure 8.24. From 1750 to 2021, the net balance is 1076 GtCO₂ of anthropogenic emissions. Friedlingstein et al. (2022) defined the airborne fraction as the ratio of the atmospheric CO₂ growth rate to total anthropogenic emissions. For the period 1750–2021, this ratio is equal to:

$$AF = \frac{\mathcal{CE}_{\text{AT}}}{\mathcal{CE}_{\text{Industry}} + \mathcal{CE}_{\text{Land}}} = \frac{1076}{1717 + 742} = 43.8\%$$

This means that 43.8% of anthropogenic emissions have not been absorbed by natural carbon sinks. The authors concluded that:

> “The observed stability of the airborne fraction over the 1960–2020 period indicates that the ocean and land CO₂ sinks have on average been removing about 55% of the anthropogenic emissions.” (Friedlingstein et al., 2022, page 4834).

Let us now look at the contribution of different energy sources. Table 8.6 shows the breakdown of anthropogenic CO₂ emissions between coal, oil, gas, cement, flaring<fnref n="37" />, and others. In 1850,

<footnote n="37">³⁷Gas flaring is the burning of the natural gas associated with oil extraction. This gas is often burned because it is not economically feasible to collect and transport it. The top five flaring countries are Russia, Iraq, Iran, the United States, and Nigeria.</footnote>
<table><caption>Table 8.6: Breakdown of anthropogenic CO₂ emission by energy source (in %)</caption><thead><tr><th></th><th>Energy</th><th>1850</th><th>1900</th><th>1950</th><th>1975</th><th>2000</th><th>2020</th></tr></thead><tbody><tr><td rowspan="6">Annual CO₂ emissions</td><td>Coal</td><td>100.00</td><td>95.85</td><td>65.10</td><td>34.74</td><td>36.18</td><td>40.11</td></tr><tr><td>Oil</td><td>0.00</td><td>3.55</td><td>26.79</td><td>47.64</td><td>40.42</td><td>33.23</td></tr><tr><td>Gas</td><td>0.00</td><td>0.60</td><td>6.09</td><td>13.17</td><td>18.61</td><td>20.38</td></tr><tr><td>Cement</td><td>0.00</td><td>0.00</td><td>1.13</td><td>1.99</td><td>2.87</td><td>4.33</td></tr><tr><td>Flaring</td><td>0.00</td><td>0.00</td><td>0.81</td><td>2.18</td><td>1.05</td><td>1.12</td></tr><tr><td>Other</td><td>0.00</td><td>0.00</td><td>0.08</td><td>0.29</td><td>0.86</td><td>0.83</td></tr><tr><td rowspan="6">Cumulative CO₂ emissions</td><td>Coal</td><td>100.00</td><td>97.58</td><td>85.24</td><td>63.49</td><td>50.00</td><td>46.29</td></tr><tr><td>Oil</td><td>0.00</td><td>2.05</td><td>12.13</td><td>27.43</td><td>35.10</td><td>35.02</td></tr><tr><td>Gas</td><td>0.00</td><td>0.37</td><td>2.15</td><td>6.88</td><td>11.72</td><td>14.52</td></tr><tr><td>Cement</td><td>0.00</td><td>0.00</td><td>0.40</td><td>1.17</td><td>1.77</td><td>2.56</td></tr><tr><td>Flaring</td><td>0.00</td><td>0.00</td><td>0.03</td><td>0.87</td><td>1.03</td><td>1.06</td></tr><tr><td>Other</td><td>0.00</td><td>0.00</td><td>0.06</td><td>0.16</td><td>0.39</td><td>0.55</td></tr></tbody></table>

Source: Friedlingstein et al. (2022), https://globalcarbonbudget.org & Author's calculations.

<figure><img src="image_305.png" /><figcaption>Figure 8.25: Energy source breakdown of anthropogenic cumulative CO₂ (in %)</figcaption></figure>

Source: Friedlingstein et al. (2022), https://globalcarbonbudget.org & Author's calculations.
100% of carbon emissions came from coal. Then we started burning oil, and later gas. Today, coal still accounts for 40% of current carbon emissions, while oil and gas account for 33% and 20%, respectively. The evolution of the distribution of cumulative CO₂ by energy source shows that the share of coal has decreased while the share of oil and gas has increased over the last century (Figure 8.25). In total, 46% of cumulative CO₂ emissions are due to coal, followed by oil and gas at 35% and 15%, respectively.

We also look at the breakdown of CO₂ emissions by region and country. The results are shown in Figures 8.26 to 8.29. Europe and North America have long been the main contributors, but Asia is now the world's largest CO₂ emitter. The country analysis shows that the top five emitters are China, India, Japan, Russia and the United States.

Box 8.6: Kaya identity

In the early seventies, the IPAT equation was proposed to describe the factors of the human impact on the environment (Chertow, 2000):

$$I = P \times A \times T$$

where *I* is the level of human impact on climate, *P* is the population, *A* is the affluence<sup>a</sup> and *T* is the technology. In the 1990s, this equation was supplanted by the Kaya identity, which states:

$$\text{Anthropogenic CO}_2 \text{ emissions} = \text{Population} \times \frac{\text{GDP}}{\text{Population}} \times \frac{\text{Energy}}{\text{GDP}} \times \frac{\text{CO}_2 \text{ emissions}}{\text{Energy}}$$

Using the notations of Kaya and Yokobori (1997), this identity is generally expressed as<sup>b</sup>:

$$F = P \times \frac{G}{P} \times \frac{E}{G} \times \frac{F}{E}$$

Therefore, the key drivers of anthropogenic CO₂ emissions include four main factors: the population (demographics), the GDP per capita (economics), the energy intensity of the GDP (engineering) and the carbon intensity (physics). Over the last century, we have observed that the first two factors have increased while the third factor has decreased. Looking into the future, we can expect these trends to continue. Decarbonizing the economy therefore means drastically reducing the carbon intensity of the energy supply. For example, if *P* ↗ 30%, *G*/*P* ↗ 20%, *E*/*G* ↘ 15%, the carbon intensity must decrease by 32.6% to not increase the level of carbon emissions and decrease by 62.3% to reduce the carbon emissions by two.

The Kaya identity was popularised by Raupach et al. (2007). It is a mathematical equation for understanding the factors that explain CO₂ emissions (Box 8.6). According to this identity, the four drivers of emissions are population growth, GDP per capita, energy intensity (quantity of energy consumed per unit of GDP) and carbon intensity (amount of CO₂ emitted per unit of energy consumed). In Figure 8.30, we plot the CO₂ per unit energy (kgCO₂ per kWh), the energy per GDP (kWh per dollar), the CO₂ per GDP (kgCO₂ per dollar of GDP) and the GDP per capita (1000

<footnote><sup>a</sup>The affluence represents the average consumption of each person in the population. A common proxy for measuring affluence is the GDP per capita or the wealth per capita.</footnote>

<footnote><sup>b</sup>See for instance Davis and Caldeira (2010).</footnote>
<figure><img src="image_306.png" /><figcaption>Figure 8.26: Share of CO₂ emissions by region (in % of total)</figcaption></figure>

Source: Friedlingstein et al. (2022), https://globalcarbonbudget.org & https://github.com/owid/co2-data.

<figure><img src="image_307.png" /><figcaption>Figure 8.27: Share of cumulative CO₂ emissions by region (in % of total)</figcaption></figure>

Source: Friedlingstein et al. (2022), https://globalcarbonbudget.org & https://github.com/owid/co2-data.
<figure><img src="image_308.png" /><figcaption>Figure 8.28: Share of CO₂ emissions by country (in % of total)</figcaption></figure>

Source: Friedlingstein et al. (2022), https://globalcarbonbudget.org & https://github.com/owid/co2-data.

<figure><img src="image_309.png" /><figcaption>Figure 8.29: Share of cumulative CO₂ emissions by country (in % of total)</figcaption></figure>

Source: Friedlingstein et al. (2022), https://globalcarbonbudget.org & https://github.com/owid/co2-data.
<figure><img src="image_310.png" /><figcaption>Figure 8.30: Key drivers of the Kaya identity</figcaption></figure>

Source: Friedlingstein et al. (2022), https://globalcarbonbudget.org & https://github.com/owid/co2-data.

<figure><img src="image_311.png" /><figcaption>Figure 8.31: CO₂ emissions per capita (in tCO₂ per person)</figcaption></figure>

Source: Friedlingstein et al. (2022), https://globalcarbonbudget.org & https://github.com/owid/co2-data.
dollars per person). The first three measures fall, but GDP per capita does not. As people get richer, they consume more goods and services and emit more CO₂. This is the main driver of CO₂ emissions. This can be summarised by the trend in CO₂ per capita in Figure 8.31. We observe five periods: a continuous increase between 1800 and 1913, a flattening out between 1914 and 1945, a new increase between 1946 and 1979, a slight decrease between 1980 and 1999, and an upward trend again since 2000. Today, we produce about 5 tonnes of CO₂ per person.

<figure><img src="image_312.png" /><figcaption>Figure 8.32: GHG emissions (in GtCO₂e)</figcaption></figure>

Source: Jones et al. (2023), https://zenodo.org/records/7636699#.ZFCy4exBweZ & Author's calculations.

The above analysis can be extended to other GHG emissions such as methane and nitrous oxide emissions. For each gas, it is important to specify the scope (e.g., including or excluding land-use change and forestry). Using the data set calculated by Jones et al. (2023), we plot the evolution of greenhouse gas emissions<fnref n="38" /> since 1850 and their decomposition into CO₂, CH₄ and N₂O in Figure 8.32. GHG emissions include both industrial and land-use change sources. For the year 2021, Jones et al. (2023) estimated the following figures: 41.12 GtCO₂ for carbon dioxide, 10.18 GtCO₂e for methane and 2.97 GtCO₂e for nitrous oxide. The repartition is then 75.8%, 18.8% and 5.5%.

<table><caption>Table 8.7: 2021 greenhouse gas emissions (in GtCO₂e)</caption><thead><tr><th colspan="3">CH<sub>4</sub></th><th colspan="3">CO<sub>2</sub></th><th colspan="3">N<sub>2</sub>O</th></tr><tr><th><i>C</i><i>E</i><sub>Industry</sub></th><th><i>C</i><i>E</i><sub>Land</sub></th><th><i>C</i><i>E</i><sub>Total</sub></th><th><i>C</i><i>E</i><sub>Industry</sub></th><th><i>C</i><i>E</i><sub>Land</sub></th><th><i>C</i><i>E</i><sub>Total</sub></th><th><i>C</i><i>E</i><sub>Industry</sub></th><th><i>C</i><i>E</i><sub>Land</sub></th><th><i>C</i><i>E</i><sub>Total</sub></th></tr></thead><tbody><tr><td>6.23<br>(61.2%)</td><td>3.95<br>(38.8%)</td><td>10.18<br>(18.8%)</td><td>37.11<br>(90.3%)</td><td>4.00<br>(9.7%)</td><td>41.12<br>(75.8%)</td><td>0.79<br>(26.7%)</td><td>2.18<br>(73.3%)</td><td>2.97<br>(5.5%)</td></tr></tbody></table>

Source: Jones et al. (2023), https://zenodo.org/records/7636699#.ZFCy4exBweZ & Author's calculations.

<footnote n="38">³⁸To calculate the CO₂ equivalent of CH₄ and N₂O, we use a global warming potential of 27.9 and 273 (see Section 9.1.1 on page 870.).</footnote>
**Planetary boundaries** In addition to climate change, the impact of human activity on the Earth system affects many other issues. They can be summarised in terms of planetary boundaries, a concept developed by Rockström et al. (2009). We can define planetary boundaries as a normative framework for setting limits to the impact of human activities on the Earth system. Beyond these boundaries, the environment may no longer be able to regulate itself and the Earth system may leave the Holocene period of stability during which human society developed. The planetary boundaries framework has been updated twice, in 2015 (Steffen et al., 2015b) and 2023 (Richardson et al., 2023). We report the details of the current framework in Table 8.8 and Box 8.7. For each critical Earth process system, Richardson et al. (2023) defined a set of control variables and associated metrics. The baseline metric $m_{1750}$ corresponds to the pre-industrial Holocene base value. The planetary boundary is defined by a threshold $m_{Boundary}$, while $m_{Upper}$ indicates the upper end of the increasing risk. Finally, $m_{2023}$ is the current value of the control variable. If we assume that the risk increases with the metric, we have $m_{1750} \le m_{Boundary} \le m_{Upper}$. If $m_{2023} \ge m_{Boundary}$, the boundary is exceeded. If $m_{2023} \ge m_{Upper}$, this indicates a high risk. According to Richardson et al. (2023), six of the nine planetary boundaries have been crossed (Figure 8.33). They are climate change, biodiversity loss, biogeochemical flows, land-use change, freshwater change, and novel entities. The ocean acidification planetary boundary can be reached in a few years, while atmospheric aerosol loading and stratospheric ozone depletion are not at risk.

<figure><img src="image_313.png" /><figcaption>Figure 8.33: Planetary boundaries</figcaption></figure>

Source: Richardson et al. (2023, Figure 1, page 4).
<table><caption>Table 8.8: Current status of planetary boundaries</caption><thead><tr><th>No</th><th>Earth process system</th><th>Control variable</th><th>m<sub>1750</sub></th><th>m<sub>Boundary</sub></th><th>m<sub>upper</sub></th><th>m<sub>2023</sub></th><th>Crossed</th></tr></thead><tbody><tr><td rowspan="3">1</td><td rowspan="3">Climate change</td><td>Atmospheric CO<sub>2</sub> concentration (ppm)</td><td>280</td><td>350</td><td>450</td><td>417</td><td>✓</td></tr><tr><td>Atmospheric radiative forcing (W/m<sup>2</sup>)</td><td>0</td><td>1.0</td><td>1.5</td><td>2.91</td><td>✓</td></tr><tr><td>Genetic diversity (E/MSY)</td><td>1</td><td>10</td><td>100</td><td>&gt; 100</td><td>✓</td></tr><tr><td rowspan="2">2</td><td rowspan="2">Biodiversity loss</td><td>Functional integrity (% HANPP)</td><td>1.9</td><td>10</td><td>20</td><td>30</td><td>✓</td></tr><tr><td>Stratospheric O<sub>3</sub> concentration (DU)</td><td>290</td><td>276</td><td>261</td><td>284.6</td><td></td></tr><tr><td rowspan="3">3</td><td rowspan="3">Stratospheric ozone depletion</td><td>Carbonate ion concentration (Q<sub>arg</sub>)</td><td>3.44</td><td>2.752</td><td>2.75</td><td>2.8</td><td></td></tr><tr><td>Phosphate flow (TgP/yr) – global</td><td>0</td><td>11</td><td>100</td><td>22.6</td><td>✓</td></tr><tr><td>Phosphate flow (TgP/yr) – regional</td><td>0</td><td>6.2</td><td>11.2</td><td>17.5</td><td>✓</td></tr><tr><td rowspan="4">4</td><td rowspan="4">Ocean acidification</td><td>Nitrogen flow (TgN/yr)</td><td>0</td><td>62</td><td>82</td><td>190</td><td>✓</td></tr><tr><td>Area of forested land (%) – global</td><td>100</td><td>75</td><td>54</td><td>60</td><td>✓</td></tr><tr><td>% area remaining – tropical</td><td>100</td><td>85</td><td>60</td><td>58.6</td><td>✓</td></tr><tr><td>% area remaining – temperate</td><td>100</td><td>50</td><td>30</td><td>41.1</td><td>✓</td></tr><tr><td rowspan="2">5</td><td rowspan="2">Biogeochemical flows</td><td>% area remaining – boreal</td><td>100</td><td>85</td><td>60</td><td>63.5</td><td>✓</td></tr><tr><td>Blue water (%)</td><td>9.4</td><td>10.2</td><td>50</td><td>18.2</td><td>✓</td></tr><tr><td rowspan="2">6</td><td rowspan="2">Land-use change</td><td>Green water (%)</td><td>9.8</td><td>11.1</td><td>50</td><td>15.8</td><td>✓</td></tr><tr><td>Inter-hemispheric difference (AOD)</td><td>0.03</td><td>0.10</td><td>0.25</td><td>0.076</td><td></td></tr><tr><td>7</td><td>Freshwater change</td><td>Synthetic chemicals (%)</td><td>0</td><td>0</td><td>N̄A</td><td>&gt; 0</td><td>✓</td></tr><tr><td>8</td><td>Atmospheric aerosol loading</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>9</td><td>Novel entities</td><td></td><td></td><td></td><td></td><td></td><td></td></tr></tbody></table>

Source: Richardson et al. (2023, Table 1, pages 4-5).
Box 8.7: Planetary boundaries defined by Richardson et al. (2023, Table 1, pages 4-5)

The planetary boundaries for climate change are defined by two control variables. First, the atmospheric CO₂ concentration CC_AT must be less than 280 ppm. Second, the total anthropogenic radiative forcing at the top of the atmosphere must be less than +1.0 W/m². For biodiversity loss, there are again two targets. The genetic diversity target implies less than 10 extinctions per million species-years (E/MSY). Functional integrity measures the amount of energy produced by photosynthesis (net primary production or NNP). The control variable is herbivore-adjusted net primary production (HANPP), which is the amount of energy available to herbivores after plants have been consumed. The variation in HANPP must be less than 10% of the pre-industrial Holocene NPP. Stratospheric ozone depletion is measured by the stratospheric O₃ concentration CCₐ₃ or the total amount of ozone in a vertical column through the atmosphere (Dobson units or DU). The limit is CCₐ₃ ≤ 276 DU, which is 5% less than the pre-industrial level. For ocean acidification, the authors use the carbonate ion concentration [CO₃²⁻], which is a measure of the amount of dissolved carbonate ions in seawater. The control variable is the average global surface ocean saturation state with respect to aragonite Ω<sub>arag</sub> = [CO₃²⁻] / κ<sub>sp</sub> where κ<sub>sp</sub> is the solubility product constant of aragonite. The limit Ω<sub>arag</sub> is set to 80% of the pre-industrial Holocene baseline (Ω<sub>arag</sub> = 3.44). Biogeochemical flows reflect anthropogenic disturbances to the phosphorus (P) and nitrogen (N) cycles. The P cycle is assessed both globally (P flow from freshwater systems to the ocean) and regionally (P flow from fertilizers to erodible soils). The global limit is set at 11 Tg phosphorus per year, while the regional limit is set at 6.2 Tg phosphorus per year. Perturbation of the N cycle is measured by industrial and intentional nitrogen fixation. Its limit is set at 62 Tg nitrogen per year. The sixth Earth system process is assessed with both global (e.g., deforestation, agriculture and urbanization) and biome-specific (e.g., transformation of forests, grasslands, savannas, and deserts) land system changes. The global figure is calculated as the area of forest as a percentage of the original forest cover, while the biome figure is the area of forest as a percentage of the potential forest (% remaining area). The limits are 75% for the global figure, 85% for the tropical biome, 50% for the temperate biome and 85% for the boreal biome. Freshwater change is divided into blue water and green water. Blue water refers to surface water available for human use, while green water refers to water stored in the soil and vegetation (i.e., water available to plants). The blue water control variable is the 95th percentile of global land area with deviations greater than the pre-industrial period, and its limit is set at 10.2%. The green water metric is the percentage of land area with deviations from pre-industrial variability. The pre-industrial Holocene baseline is 9.8%, and the limit is 11.1%. The eighth Earth system process is the atmospheric aerosol loading, the control variable is the inter-hemispheric difference in aerosol optical depth<sup>a</sup> (AOD), and the limit is 0.1 mean annual inter-hemispheric difference. The final planetary boundary concerns novel entities such as industrial chemicals, pesticides, microplastics, nanoparticles, nuclear waste and genetically modified organisms (GMO). The associated control variable is the percentage of synthetic chemicals released into the environment without adequate safety testing. This ninth planetary boundary is not well defined, because it is difficult to collect data on.

<footnote><sup>a</sup>AOD measures the amount of light absorbed by aerosols in the atmosphere. The inter-hemispheric difference in AOD is the difference between the average AOD in the Northern Hemisphere and the average AOD in the Southern Hemisphere.</footnote>
### 8.1.3 The physics of climate change

In this section, energy and forcing are two interchangeable terms, meaning that $F_{solar} := \mathcal{E}_{solar}$, $F_{thermal} := \mathcal{E}_{infrared}$, etc. Moreover, we have made extensive use of Hartmann's Handbook on Climate Physics, particularly chapters 2, 3 and 10 (Hartmann, 2016).

#### Simple energy balance models

The Earth's temperature is closely related to its energy balance, which is the balance between the energy it receives from the Sun and the energy it emits:

> "Temperature [...] is a measure of the energy contained in the movement of molecules. Therefore, to understand how the temperature is maintained, one must consider the energy balance that is formally stated in the first law of thermodynamics. The basic global energy balance of Earth is between energy coming from the Sun and energy returned to space by Earth's radiative emission. The generation of energy in the interior of Earth has a negligible influence on its energy budget." (Hartmann, 2016, page 25).

The first law of thermodynamics, also known as the law of conservation of energy, is a principle of physics which states that energy cannot be created or destroyed, it can only be transferred or converted from one form to another. This means that the total amount of energy in a closed system is conserved.

**Basics** To calculate the Earth's temperature, we need three basic tools of physics. They are the total solar irradiance, the Stefan-Boltzmann law and the emission temperature of a planet.

**Total solar irradiance** According to Hartmann (2016, page 29), the total amount of electromagnetic energy emitted by the Sun, also called the solar luminosity is $L_{\odot} = 3.828 \times 10^{26}$ watts. Using the first law of thermodynamics, the amount of energy emitted by any sphere with the Sun at its centre should be equal to the total energy flux from the Sun. Total solar irradiance (TSI) is defined as:

$$S_d = \frac{L_{\odot}}{4\pi d^2} \qquad (8.3)$$

where $d$ is the distance of the sphere from the Sun in meters. For the Earth, the distance is between 147.1 and 152.1 million kilometers because the Earth's orbit around the Sun is not a perfect circle. Using a mean value of 149.6 million kilometers, we get:

$$S_0 = \frac{3.828 \times 10^{26}}{4\pi (149.6 \times 10^9)^2} = 1372.11 \text{ W/m}^2$$

A direct measurement by astrophysicists gives 1368 W/m² and we use this number in the sequel.

**Stefan-Boltzmann law** The Stefan-Boltzmann law describes the relationship between the total amount of radiation $\mathcal{E}$ emitted by a body and its temperature $T$:

$$\mathcal{E} = \varepsilon\sigma T^4 \qquad (8.4)$$

where $\varepsilon \in [0, 1]$ is the emissivity of the body and $\sigma = 5.67 \times 10^{-8} \text{ W/m}^2\text{K}^{-4}$ is the Stefan-Boltzmann constant. For an ideal black body, we have $\varepsilon = 1$ and Equation (8.4) is related to the
Planck distribution<fnref n="39" /> $B_ν$ (or the intensity of the black body radiation):

$$ 
\begin{aligned}
\mathcal{E} &= \pi \int_{0}^{\infty} B_{\nu}(\nu, \mathcal{T}) \, d\nu \\
&= \frac{2\pi^{5}k^{4}}{15c^{2}h^{3}}\mathcal{T}^{4} \\
&= \sigma\mathcal{T}^{4}
\end{aligned}
$$

where $h$ is Planck's constant, $c$ is the speed of light in a vacuum and $k$ is Boltzmann's constant.

Box 8.8: Planck radiation law and spectral density of electromagnetic radiation

In physics, Planck's law describes the spectral distribution of electromagnetic radiation emitted by a black body in thermal equilibrium at a given temperature. The expression for the spectral density function is:

$$ B_{\nu}(\nu, \mathcal{T}) = \frac{2h\nu^{3}}{c^{2}} \frac{1}{\exp\left(\frac{h\nu}{k\mathcal{T}}\right) - 1} $$

where $h = 6.62607015 \times 10^{-34} \text{ J Hz}^{-1}$ is Planck's constant, $c = 299 792 458 \text{ m s}^{-1}$ is the speed of light in a vacuum, $k = 1.380649 \times 10^{-23} \text{ J K}^{-1}$ is Boltzmann's constant, $\mathcal{T}$ is the temperature measured in Kelvin, and $\nu$ is the frequency in hertz. Alternatively, the law can be written in terms of the wavelength $\lambda$ expressed in meters:

$$ \lambda = \frac{c}{\nu} \quad \left( \sim \frac{\text{m s}^{-1}}{\text{Hz}} = \text{m} \right) $$

We deduce that:

$$ B_{\lambda}(\lambda, \mathcal{T}) = \frac{2hc^2}{\lambda^5} \frac{1}{\exp\left(\frac{hc}{\lambda k \mathcal{T}}\right) - 1} $$

Since we have $\frac{\text{J Hz}^{-1} \text{m s}^{-1}}{\text{m J K}^{-1} \text{K}} = 1$ and $\frac{\text{J Hz}^{-1} (\text{m s}^{-1})^2}{\text{m}^5} = \text{J s}^{-1} \text{m}^{-2} \text{m}^{-1} = \text{W m}^{-2} \text{m}^{-1}$, the unit of $B_\lambda(\lambda, \mathcal{T})$ is W/m² m⁻¹. In Figure 8.34, we show the spectral density for two values of temperature. We also show the visible spectrum, which is the band of the electromagnetic spectrum that is visible to the human eye. The electromagnetic spectrum also includes ultraviolet and infrared wavelengths. We use the following classification: UV (less than 380 nm), visible (380 nm to 780 nm), and infrared (greater than 780 nm). The temperature has a high impact on emitted radiations, since the spectral density is completely different for $\mathcal{T} = 5 000 \text{ K}$ and $\mathcal{T} = 3 000 \text{ K}$. Now let us illustrate the difference between solar and terrestrial radiation. In Figure 8.35, we scale the spectral density of the Earth's surface by a factor of $2.6 \times 10^6$ so that the two peaks are at the same level. Note that the spectrum of sunlight is shortwave radiation, while the spectrum of the Earth's surface is longwave radiation. We also see that the atmosphere is mainly transparent to a large part of the visible spectrum.

<footnote n="39">³⁹The Planck distribution describes the probability of a photon being emitted with a particular energy.</footnote>
<figure><img src="image_314.png" /><figcaption>Figure 8.35: Comparison of the radiation spectra of sunlight and the Earth's surface (in $10^{12} \text{ W/m}^2 \text{ m}^{-1}$)</figcaption></figure>

<figure><img src="image_315.png" /></figure>
**Effective temperature of stars** Since the radius of the Sun $R_\odot$ is about 696 342 kilometers, the solar irradiance at the photosphere$^{40}$ is equal to:

$$S_{\odot} = \frac{L_{\odot}}{4\pi R_{\odot}^2} = \frac{3.828 \times 10^{26}}{4\pi (696 342 \times 10^3)^2} = 62 822 741 \text{ W/m}^2$$

If we assume that the sun is a perfect black body$^{41}$, then we have:

$$\sigma T_{\odot}^4 = S_{\odot} \Leftrightarrow T_{\odot} = \sqrt[4]{\frac{S_{\odot}}{\sigma}}$$

The numerical calculation gives:

$$T_{\odot} = \sqrt[4]{\frac{62 822 741}{5.67 \times 10^{-8}}} = 5 769 \text{ K}$$

This effective temperature is slightly overestimated compared to a direct physical measurement. The previous analysis can be extended to other stars. Let $R_{\text{star}}$ be the stellar radius of the star. Since we have $L_{\text{star}} = 4\pi R_{\text{star}}^2 S_{\text{star}}$ and $S_{\text{star}} = \mathcal{E} = \sigma T^4$, we get:

$$T_{\text{star}} = \sqrt[4]{\frac{L_{\text{star}}}{4\pi R_{\text{star}}^2 \sigma}} \qquad (8.5)$$

$T_{\text{star}}$ is defined as the temperature of a black body radiating the same amount of energy per unit area as the star. It may differ from the actual temperature of a star, which depends on its kinetic energy.

**Zero-order model of the atmosphere** Let us see how the effective temperature of the Earth is calculated.

**Incoming solar radiation** The incoming solar radiation is equal to:

$$F_{\text{solar}} = \frac{1}{4} (1 - \alpha_p) S_0$$

where $\alpha_p$ is the planetary albedo, which measures the amount of reflected sunlight. For example, $\alpha_p$ is equal to zero for a perfect black body, and one for a perfect white body. The ratio $\frac{1}{4}$ comes from the fact that no point on the planet receives the sun's energy continuously during a full day. This is particularly true at night, but also during the day, as the point is not necessarily at the sun's zenith. On average, we can show that a point on the planet receives $\frac{1}{4}$ of the solar energy, which is the ratio of the projected area of the sphere ($\mathcal{A}rea = \pi r^2$) divided by the surface area of the sphere ($\mathcal{A}rea = 4\pi r^2$). This incoming solar radiation is illustrated in Figure 8.36.

In the case of the Earth, we have $\alpha_p \approx 0.29$ (Stephens et al., 2015, page 141). We deduce that:

$$F_{\text{solar}} = \frac{1}{4} (1 - 0.29) \times 1368 = 242.82 \text{ W/m}^2$$

To get an idea of how much energy is involved, consider a room with a surface area of x square meters and receiving an energy $\mathcal{E}$ expressed in watts. The radiation per square meter received by

<footnote>$^{40}$This is the visible surface of the Sun.</footnote>

<footnote>$^{41}$In fact, the emissivity of the sun is $\varepsilon = 0.96$.</footnote>
<figure><img src="image_316.png" /><figcaption>Figure 8.36: Incoming solar radiation</figcaption></figure>

this room is equal to $\mathcal{E}/x$. If the room receives the same equivalent solar radiation $F_{solar}$, the energy must be equal to:

$$ \mathcal{E} = x \cdot F_{solar} $$

Using a standard 200 watt lamp, we can calculate the number of lamps required to achieve the same equivalent solar radiation. The results are shown below:

<table><thead><tr><th>x (in m²)</th><th>1</th><th>5</th><th>10</th><th>20</th><th>50</th><th>100</th></tr></thead><tbody><tr><td>ε (in watts)</td><td>242.8</td><td>1 214</td><td>2 428</td><td>4 856</td><td>12 141</td><td>24 282</td></tr><tr><td># lights</td><td>1.2</td><td>9</td><td>12</td><td>24</td><td>61</td><td>121</td></tr></tbody></table>

For a room of 20 m², we need 24 lights.

**Effective temperature of the Earth** The Earth receives the incoming solar radiation $F_{solar}$, while the black body radiation is given by the Stefan-Boltzmann law. The schematic energy flow diagram is given in Figure 8.37. We deduce that:

$$ \sigma \mathcal{T}_e^4 = \frac{1}{4} (1 - \alpha_p) S_0 \Leftrightarrow \mathcal{T}_e = \sqrt[4]{\frac{(1 - \alpha_p) S_0}{4\sigma}} $$

The numerical calculation gives:

$$ \begin{aligned} \mathcal{T}_e &= \sqrt[4]{\frac{(1 - 0.29) \times 1368}{4 \times 5.67 \times 10^{-8}}} \\ &= 255.81 \text{ K} \\ &= 255.81^{\circ}\text{C} - 273.15^{\circ}\text{C} \\ &= -17.34^{\circ}\text{C} \end{aligned} $$

The effective temperature of the Earth is then close to -17.34°C. Without greenhouse gases, the surface temperature of the Earth should be equal to the effective temperature. However, we observe

$$ \mathcal{T}_s \approx +15^{\circ}\text{C} \gg \mathcal{T}_e \approx -17^{\circ}\text{C} $$
<figure><img src="image_317.png" /><figcaption>Figure 8.37: Zero-order model</figcaption></figure>

To explain this difference of 32°C, we need to introduce the greenhouse effect.

**Impact of the greenhouse effect** To illustrate the greenhouse effect, Hartmann (2016) proposed to include an atmosphere in the global energy balance. He assumed that the atmosphere is a black body for terrestrial radiation but transparent to solar radiation:

> "Since solar radiation is mostly visible and near infrared, and Earth emits primarily thermal infrared radiation, the atmosphere may affect solar and terrestrial radiation very differently. [...] Since the atmospheric layer absorbs all of the energy emitted by the surface below it and emits like a blackbody, the only radiation emitted to space is from the atmosphere in this model." (Hartmann, 2016, pages 32-32).

From Figure 8.38, we can deduce that the energy balance for the Earth's surface is:

$$F_{\text{solar}} + \sigma \mathcal{T}_{\text{a}}^{4} = \sigma \mathcal{T}_{\text{s}}^{4}$$

while the radiation balance for the atmosphere verifies:

$$\sigma \mathcal{T}_{\text{s}}^{4} = 2\sigma \mathcal{T}_{\text{a}}^{4}$$

It follows that:

$$F_{\text{solar}} + \sigma \mathcal{T}_{\text{a}}^{4} = 2\sigma \mathcal{T}_{\text{a}}^{4}$$

or$^{42}$:

$$F_{\text{solar}} = \sigma \mathcal{T}_{\text{a}}^{4} = \sigma \mathcal{T}_{\text{e}}^{4}$$

We conclude that:

$$\left\{ \begin{array}{l} \mathcal{T}_{\text{a}} = \mathcal{T}_{\text{e}} \\ \mathcal{T}_{\text{s}} = \sqrt[4]{2\mathcal{T}_{\text{e}}} \end{array} \right.$$

<footnote>$^{42}$We use the fact that the effective temperature $T_e$ is defined by the relation $\sigma \mathcal{T}_e^4 = \frac{1}{4} (1 - \alpha_p) S_0 := F_{\text{solar}}$.</footnote>
Using the previous numerical values, we obtain:

$$ \begin{cases} \mathcal{T}_a = 255.81 \text{ K} = -17.34^{\circ}\text{C} \\ \mathcal{T}_s = 304.22 \text{ K} = 31.07^{\circ}\text{C} \end{cases} $$

We find that the surface temperature is warmer than the observed global mean surface temperature. This is because the assumption that the atmosphere absorbs all the heat radiated from the surface is not true.

<figure><img src="image_318.png" /><figcaption>Figure 8.38: Zero-order model with greenhouse effect</figcaption></figure>

Another way to illustrate the greenhouse effect is to estimate the reflection parameter $\gamma_p$, which measures the net thermal radiation of the atmosphere with respect to the black body energy (Dom-menget, 2022). We deduce that the balance $\mathcal{E}_{net}$ is:

$$ \mathcal{E}_{net} = F_{solar} - \sigma \mathcal{T}_s^4 - \gamma_p \sigma \mathcal{T}_s^4 $$

Solving the equation $\mathcal{E}_{net} = 0$ gives:

$$ \gamma_p = 1 - \frac{F_{solar}}{\sigma \mathcal{T}_s^4} = 1 - \frac{(1 - \alpha_p) S_0}{4 \sigma \mathcal{T}_s^4} $$

Using a surface temperature of 15°C, we get $\gamma_p = 0.3788$. This means that only 62% of the infrared radiation goes into space and 38% stays on the surface.

**Multi-layer model of the atmosphere** Let us now consider the energy balance when we have two layers. This extension is motivated by the simplifying assumption that an atmosphere can be represented as a single black body:

> "A layer of atmosphere that is almost opaque for longwave radiation can be crudely approximated as a blackbody that absorbs all terrestrial radiation that is incident upon it and emits like a blackbody at its temperature. For an atmosphere with a large infrared optical depth, the radiative transfer process can be represented with a series of blackbodies arranged in vertical layers. Two layers centered at 0.5 km and 2.0 km altitudes provide a simple approximation for Earth's atmosphere." (Hartmann, 2016, page 71).
<figure><img src="image_319.png" /><figcaption>Figure 8.39: Two-layer model</figcaption></figure>

If we assume that the atmospheric layers are transparent to solar radiation, we have the schematic energy flow diagram shown in Figure 8.39. We have:

$$ \left\{ \begin{array}{l} F_{\text{solar}} + \sigma \mathcal{T}_1^4 = \sigma \mathcal{T}_s^4 \\ \sigma \mathcal{T}_2^4 + \sigma \mathcal{T}_s^4 = 2\sigma \mathcal{T}_1^4 \\ \sigma \mathcal{T}_1^4 = 2\sigma \mathcal{T}_2^4 \end{array} \right. $$

By replacing $F_{\text{solar}}$ by $\sigma \mathcal{T}_e^4$ and dividing the equations by $\sigma$, we get:

$$ \left\{ \begin{array}{l} \mathcal{T}_s^4 = 3 \mathcal{T}_e^4 \\ \mathcal{T}_1^4 = 2 \mathcal{T}_e^4 \\ \mathcal{T}_2^4 = 1 \mathcal{T}_e^4 \end{array} \right. $$

The solution is then equal to:

$$ \left\{ \begin{array}{l} \mathcal{T}_s = \sqrt[4]{3} \mathcal{T}_e = 336.67 \, \text{K} = 63.52^{\circ}\text{C} \\ \mathcal{T}_1 = \sqrt[4]{2} \mathcal{T}_e = 304.22 \, \text{K} = 31.07^{\circ}\text{C} \\ \mathcal{T}_2 = \sqrt[4]{1} \mathcal{T}_e = 255.81 \, \text{K} = -17.34^{\circ}\text{C} \end{array} \right. $$

It is easy to generalize these results to the multi-layer atmosphere layer. Let $n$ be the total number of layers and $\mathcal{T}_k$ be the temperature at layer $k$. We have:

$$ \left\{ \begin{array}{l} \mathcal{T}_s = \mathcal{T}_0 = \sqrt[4]{n+1} \mathcal{T}_e \\ \mathcal{T}_k = \sqrt[4]{n+1-k} \mathcal{T}_e \quad \text{for } k = 0, 1, \dots, n \end{array} \right. \qquad (8.6) $$

The multi-layer model is important because the atmosphere cannot be considered as a homogeneous black body. If this were true, the temperature of the atmosphere would be the same regardless of altitude. In reality, we observe that the temperature is highest at the Earth's surface and decreases
<table><caption>Table 8.9: Layers of the Earth’s atmosphere</caption><thead><tr><th>Index</th><th>Layer</th><th>Altitude (in Km)</th></tr></thead><tbody><tr><td>1</td><td>Troposphere</td><td>12</td></tr><tr><td>2</td><td>Stratosphere</td><td>50</td></tr><tr><td>3</td><td>Mesosphere</td><td>80</td></tr><tr><td>4</td><td>Thermosphere</td><td>500</td></tr><tr><td>5</td><td>Exosphere</td><td>6 200</td></tr></tbody></table>

as we move towards the vacuum of space. This explains why the Earth’s atmosphere is generally divided into five layers based on temperature and composition, as shown in Table 8.9. The solution of the multi-layer model given in Equation (8.6) satisfies the property that the temperature decreases with the layer index:

$$ \frac{\partial \mathcal{T}_k}{\partial k} = -\frac{1}{4} (n + 1 - k)^{-3/4} \mathcal{T}_e \le 0 $$

Let $z$ be the altitude in km. Since $z$ is an increasing function of the layer index $k$, we deduce from the previous property that:

$$ \frac{\partial \mathcal{T}(z)}{\partial z} \le 0 $$

With this simple multi-layer model, we then showed that temperature is a decreasing function of altitude, that the Earth is warmer at the surface, and that the global temperature surface depends on the multi-layer structure of the atmosphere. So it also depends on the composition of the atmosphere, because that is the main determinant of the structure of the atmosphere. However, the previous multi-layer model is not realistic because the estimated temperatures are far from the observed mean temperatures.

**Emissivity model of the atmosphere** The previous model is too simple for several reasons. The first reason is that the real atmosphere is not opaque. This means that it is more of a gray body than a black body. In addition to radiation, energy is also transported by convection$^{43}$. Therefore, we cannot ignore the effect of emissivity.

We consider the one-layer model described in Figure 8.38, and introduce the emissivity $\varepsilon$ of the atmosphere (Figure 8.40). The energy balance equilibrium becomes:

* The balance at the top of the atmosphere is:

$$ F_{\text{solar}} - (1 - \varepsilon) \sigma \mathcal{T}_s^4 - \varepsilon \sigma \mathcal{T}_a^4 = 0 $$

* The balance of the atmosphere is:

$$ \varepsilon \sigma \mathcal{T}_s^4 - 2 \varepsilon \sigma \mathcal{T}_a^4 = 0 $$

* The balance at the surface is:

$$ F_{\text{solar}} + \varepsilon \sigma \mathcal{T}_a^4 - \sigma \mathcal{T}_s^4 = 0 $$

The first equation is equivalent to:

$$ (1 - \varepsilon) \sigma \mathcal{T}_s^4 + \varepsilon \sigma \mathcal{T}_a^4 = F_{\text{solar}} = \sigma \mathcal{T}_e^4 $$

<footnote>$^{43}$Another important missing factor is ocean transportation.</footnote>
<figure><img src="image_320.png" /><figcaption>Figure 8.40: One-layer model with atmospheric emissivity</figcaption></figure>

Using the second equation, it follows that:

$$ \sigma \mathcal{T}_e^4 = (1 - \varepsilon) \sigma \mathcal{T}_s^4 + \frac{1}{2} \varepsilon \sigma \mathcal{T}_s^4 = \left(1 - \frac{1}{2} \varepsilon\right) \mathcal{T}_s^4 $$

Finally, we conclude that$^{44}$:

$$ \mathcal{T}_s = \sqrt[4]{\frac{2}{2 - \varepsilon}} \mathcal{T}_e $$

and:

$$ \mathcal{T}_a = \sqrt[4]{\frac{1}{2 - \varepsilon}} \mathcal{T}_e $$

The relationship between atmospheric emissivity $\varepsilon$ and temperature ($\mathcal{T}_s$ and $\mathcal{T}_a$) is shown in Figure 8.41. It is an increasing function. Therefore, for a given temperature $\mathcal{T}_s^*$, we can find the unique value of the emissivity:

$$ \varepsilon^* = 2 - 2 \left( \frac{\mathcal{T}_e}{\mathcal{T}_s^*} \right)^4 $$

Since $\mathcal{T}_s^* \approx 15^{\circ}\text{C}$, the emissivity of the atmosphere is 78%. This model then predicts an atmospheric temperature of $-30.8^{\circ}\text{C}$.

**Remark 77** More generally, the Earth's energy balance is the sum of net shortwave radiation and net longwave radiation (Liang et al., 2019):

$$ \mathcal{E}_{\text{net}} = \underbrace{\mathcal{E}_{\text{down}}^{\text{short}} - \mathcal{E}_{\text{up}}^{\text{short}}}_{\text{Net shortwave}} + \underbrace{\mathcal{E}_{\text{down}}^{\text{long}} - \mathcal{E}_{\text{up}}^{\text{long}}}_{\text{Net longwave}} $$

where $\mathcal{E}_{\text{down}}^{\text{short/long}}$ is shortwave/longwave downward radiation and $\mathcal{E}_{\text{up}}^{\text{short/long}}$ is shortwave/longwave upward radiation. In the previous model, we have $\mathcal{E}_{\text{net}}^{\text{short}} = \frac{1}{4} (1 - \alpha_p) S_0$ and $\mathcal{E}_{\text{net}}^{\text{long}} = \varepsilon \sigma \mathcal{T}_a^4 - \sigma \mathcal{T}_s^4$. Using more realistic assumptions, we get the Earth's energy balance shown in Figure 8.42. This type of representation was popularized by Kiehl and Trenberth (1997) and Trenberth et al. (2009).

<footnote>$^{44}$We also check that the third equation is satisfied.</footnote>
<figure><img src="image_321.png" /><figcaption>Figure 8.42: Earth's Energy Budget</figcaption></figure>

<figure><img src="image_322.png" /></figure>

Source: NASA, https://mynasadata.larc.nasa.gov/basic-page/earths-energy-budget.