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  <front>
    <journal-meta><journal-id journal-id-type="publisher">ACP</journal-id><journal-title-group>
    <journal-title>Atmospheric Chemistry and Physics</journal-title>
    <abbrev-journal-title abbrev-type="publisher">ACP</abbrev-journal-title><abbrev-journal-title abbrev-type="nlm-ta">Atmos. Chem. Phys.</abbrev-journal-title>
  </journal-title-group><issn pub-type="epub">1680-7324</issn><publisher>
    <publisher-name>Copernicus Publications</publisher-name>
    <publisher-loc>Göttingen, Germany</publisher-loc>
  </publisher></journal-meta>
    <article-meta>
      <article-id pub-id-type="doi">10.5194/acp-22-9349-2022</article-id><title-group><article-title>Climate consequences of hydrogen emissions</article-title><alt-title>Climate consequences of hydrogen emissions</alt-title>
      </title-group><?xmltex \runningtitle{Climate consequences of hydrogen emissions}?><?xmltex \runningauthor{I. B. Ocko and S. P. Hamburg}?>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes">
          <name><surname>Ocko</surname><given-names>Ilissa B.</given-names></name>
          <email>iocko@edf.org</email>
        <ext-link>https://orcid.org/0000-0001-8617-2249</ext-link></contrib>
        <contrib contrib-type="author" corresp="no">
          <name><surname>Hamburg</surname><given-names>Steven P.</given-names></name>
          
        </contrib>
        <aff id="aff1"><institution>Environmental Defense Fund, New York, NY, USA</institution>
        </aff>
      </contrib-group>
      <author-notes><corresp id="corr1">Ilissa B. Ocko (iocko@edf.org)</corresp></author-notes><pub-date><day>20</day><month>July</month><year>2022</year></pub-date>
      
      <volume>22</volume>
      <issue>14</issue>
      <fpage>9349</fpage><lpage>9368</lpage>
      <history>
        <date date-type="received"><day>3</day><month>February</month><year>2022</year></date>
           <date date-type="rev-request"><day>18</day><month>February</month><year>2022</year></date>
           <date date-type="rev-recd"><day>20</day><month>May</month><year>2022</year></date>
           <date date-type="accepted"><day>13</day><month>June</month><year>2022</year></date>
      </history>
      <permissions>
        <copyright-statement>Copyright: © 2022 Ilissa B. Ocko</copyright-statement>
        <copyright-year>2022</copyright-year>
      <license license-type="open-access"><license-p>This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this licence, visit <ext-link ext-link-type="uri" xlink:href="https://creativecommons.org/licenses/by/4.0/">https://creativecommons.org/licenses/by/4.0/</ext-link></license-p></license></permissions><self-uri xlink:href="https://acp.copernicus.org/articles/22/9349/2022/acp-22-9349-2022.html">This article is available from https://acp.copernicus.org/articles/22/9349/2022/acp-22-9349-2022.html</self-uri><self-uri xlink:href="https://acp.copernicus.org/articles/22/9349/2022/acp-22-9349-2022.pdf">The full text article is available as a PDF file from https://acp.copernicus.org/articles/22/9349/2022/acp-22-9349-2022.pdf</self-uri>
      <abstract><title>Abstract</title>

      <p id="d1e88">Given the urgency to decarbonize global energy systems,
governments and industry are moving ahead with efforts to increase
deployment of hydrogen technologies, infrastructure, and applications at an
unprecedented pace, including USD billions in national incentives and direct
investments. While zero- and low-carbon hydrogen hold great promise to help
solve some of the world's most pressing energy challenges, hydrogen is also
an indirect greenhouse gas whose warming impact is both widely overlooked
and underestimated. This is largely because hydrogen's atmospheric warming
effects are short-lived – lasting only a couple decades – but standard
methods for characterizing climate impacts of gases consider only the
long-term effect from a one-time pulse of emissions. For gases whose impacts
are short-lived, like hydrogen, this long-term framing masks a much stronger
warming potency in the near to medium term. This is of concern because
hydrogen is a small molecule known to easily leak into the atmosphere, and
the total amount of emissions (e.g., leakage, venting, and purging) from existing
hydrogen systems is unknown. Therefore, the effectiveness of hydrogen as a
decarbonization strategy, especially over timescales of several decades,
remains unclear. This paper evaluates the climate consequences of hydrogen
emissions over all timescales by employing already published data to assess
its potency as a climate forcer, evaluate the net warming impacts from
replacing fossil fuel technologies with their clean hydrogen alternatives,
and estimate temperature responses to projected levels of hydrogen demand.
We use the standard global warming potential metric, given its acceptance to
stakeholders, and incorporate newly published equations that more fully
capture hydrogen's several indirect effects, but we consider the effects of
constant rather than pulse emissions over multiple time horizons. We account
for a plausible range of hydrogen emission rates and include methane
emissions when hydrogen is produced via natural gas with carbon capture, usage, and storage (CCUS) (“blue”
hydrogen) as opposed to renewables and water (“green” hydrogen). For the
first time, we show the strong timescale dependence when evaluating the
climate change mitigation potential of clean hydrogen alternatives, with the
emission rate determining the scale of climate benefits or disbenefits. For
example, green hydrogen applications with higher-end emission rates (10 %)
may only cut climate impacts from fossil fuel technologies in half over the
first 2 decades, which is far from the common perception that green
hydrogen energy systems are climate neutral. However, over a 100-year
period, climate impacts could be reduced by around 80 %. On the other
hand, lower-end emissions (1 %) could yield limited impacts on the climate
over all timescales. For blue hydrogen, associated methane emissions can
make hydrogen applications worse for the climate than fossil fuel
technologies for several decades if emissions are high for both gases; however, blue hydrogen yields climate benefits over a 100-year period. While more work is needed to
evaluate the warming impact of hydrogen emissions for specific end-use cases
and value-chain pathways, it is clear that hydrogen emissions matter for the
climate and warrant further attention from scientists, industry, and
governments. This is critical to informing where and how to deploy hydrogen
effectively in the emerging decarbonized global economy.</p>
  </abstract>
    </article-meta>
  </front>
<body>
      

<sec id="Ch1.S1" sec-type="intro">
  <label>1</label><title>Introduction</title>
      <p id="d1e100">Hydrogen is now considered an essential component in transitioning to a
low-carbon global economy and achieving net-zero greenhouse gas emission
targets. This is due to its potential to be a zero or near-zero carbon
energy carrier to replace fossil fuel use, including in hard-to-abate
sectors and for storage of renewable electricity (International Energy
Agency, 2021). Dozens of countries have recently released plans to scale up
clean hydrogen production and consumption, and USD 500 billion could be spent
across the globe on hydrogen developments by 2030 (Hydrogen Council, 2021a).
However, one climate concern has been largely absent in recent conversations
and assessments of the role of hydrogen (International Energy Agency, 2019, 2021; BloombergNEF, 2020a; Bartlett and
Krupnick, 2020; van Renssen, 2020; World Energy Council, 2021; Hydrogen
Council, 2021a; Ueckerdt et al., 2021; International Renewable Energy
Agency, 2022): the warming effects from hydrogen emitted into the
atmosphere.</p>
      <p id="d1e103">Scientists have long known and cautioned that hydrogen has indirect warming
impacts (Ehhalt et al., 2001; Derwent et al., 2001, 2006, 2020; Prather,
2003; Schultz et al., 2003; Warwick et al., 2004, 2022; Colella et al.,
2005; Wuebbles et al., 2010; Derwent, 2018; Paulot et al., 2021; Field and
Derwent, 2021). When it escapes into the atmosphere, hydrogen has two main
fates: around 70 %–80 % is estimated to be removed by soils via diffusion
and bacterial uptake, and the remaining 20 %–30 % is oxidized by reacting
with the naturally occurring hydroxyl radical (OH), yielding an atmospheric
lifetime of around a few years (Rahn et al., 2003; Derwent, 2018; Paulot et
al., 2021; Warwick et al., 2022). The oxidation of hydrogen in the
atmosphere leads to increasing concentrations of greenhouse gases in both
the troposphere and stratosphere, as described in Fig. 1 (Derwent, 2018;
Derwent et al., 2020; Paulot et al., 2021; Field and Derwent, 2021; Warwick
et al., 2022).</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F1" specific-use="star"><?xmltex \currentcnt{1}?><?xmltex \def\figurename{Figure}?><label>Figure 1</label><caption><p id="d1e108">Effects of hydrogen oxidation on atmospheric greenhouse
gas concentrations and warming.</p></caption>
        <?xmltex \igopts{width=384.112205pt}?><graphic xlink:href="https://acp.copernicus.org/articles/22/9349/2022/acp-22-9349-2022-f01.png"/>

      </fig>

      <p id="d1e118">In the troposphere, less OH is available to react with methane; given
that methane's reaction with OH is its primary sink, this leads to a longer
atmospheric lifetime for methane which accounts for around half of
hydrogen's total indirect warming effect (Paulot et al., 2021). Moreover, the production of atomic hydrogen from hydrogen oxidation in the troposphere leads
to a series of reactions that ultimately form tropospheric ozone, a
greenhouse gas that accounts for about 20 % of hydrogen's radiative
impacts (Paulot et al., 2021). In the stratosphere, the oxidation of
hydrogen increases water vapor, which, in turn, increases the infrared
radiative capacity of the stratosphere, leading to stratospheric cooling and
an overall warming effect on the climate because energy emitted out to space
is now from a cooler temperature; this stratospheric effect accounts for
about 30 % of hydrogen's climate impacts (Paulot et al., 2021). Stratospheric cooling can also lead to an increase in stratospheric polar
clouds that enable more ozone-destroying reactions to occur; however, to date,
these effects have been deemed as minor (Tromp et al., 2003; Warwick et al.,
2004, 2022; Jacobson, 2008; van Ruijven et al., 2011; Vogel et al., 2011,
2012; Wang et al., 2013; Wuebbles et al., 2010; Derwent, 2018; Paulot et
al., 2021).</p>
      <p id="d1e121">A growing body of research has affirmed that the warming effects from
hydrogen emissions are consequential, with new work showing that hydrogen's
indirect warming effects are twice as high as previously recognized (Paulot
et al., 2021; Warwick et al., 2022); this is due to the inclusion of
stratospheric effects that were not considered until recently (Derwent, 2018;
Derwent et al., 2020). Studies that take both tropospheric and
stratospheric effects from hydrogen emissions into account report an indirect radiative
efficiency of 0.13 and 0.18 mW m<inline-formula><mml:math id="M1" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> ppbv<inline-formula><mml:math id="M2" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>, respectively (Paulot et al., 2021; Warwick et al., 2022), whereas
studies that only consider tropospheric effects suggest an indirect
radiative efficiency of around 0.08 mW m<inline-formula><mml:math id="M3" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> ppbv<inline-formula><mml:math id="M4" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> (Derwent, 2018;
Derwent et al., 2020). Converting
hydrogen's full atmospheric radiative efficiencies to per unit mass
(3.64 and 5.04 <inline-formula><mml:math id="M5" display="inline"><mml:mrow><mml:mo>×</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">13</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> W m<inline-formula><mml:math id="M6" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> kg<inline-formula><mml:math id="M7" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>) and comparing them to the radiative efficiencies of carbon dioxide
(CO<inline-formula><mml:math id="M8" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula>) and methane (1.7 <inline-formula><mml:math id="M9" display="inline"><mml:mrow><mml:mo>×</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">15</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> W m<inline-formula><mml:math id="M10" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> kg<inline-formula><mml:math id="M11" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> and 2.0 <inline-formula><mml:math id="M12" display="inline"><mml:mrow><mml:mo>×</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">13</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> W m<inline-formula><mml:math id="M13" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> kg<inline-formula><mml:math id="M14" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>, respectively) shows that
hydrogen's indirect warming potency per unit mass is around 200 times that
of carbon dioxide and larger than that of methane (Forster et al., 2021).
However, like methane, hydrogen's warming effects are potent but
short-lived. Some of hydrogen's effects are shorter-lived than methane's –
occurring within a decade after emission – but its impacts on methane can
affect the climate for roughly an additional decade (Warwick et al., 2022).</p>
      <p id="d1e303">Hydrogen's warming effects have major implications for an emerging hydrogen
economy because hydrogen is a tiny molecule that is hard to contain. It can
leak across the entire value chain, including from electrolyzers,
compressors, liquefiers, storage tanks, geologic storage, pipelines, trucks,
trains, ships, and fueling stations (Bond et al., 2011; van Ruijven et al.,
2011; Melaina et al., 2013; Cooper et al., 2022; Frazer-Nash Consultancy,
2022). Furthermore, some hydrogen is deliberately vented and purged into the
atmosphere from these systems (Frazer-Nash Consultancy, 2022).</p>
      <p id="d1e306">While it is clear that hydrogen leakage poses a risk to decarbonization
goals, given its potency as an indirect greenhouse gas, there are several
challenges associated with determining the overall magnitude and, thus,
importance of its warming impacts on the effectiveness of hydrogen as a
decarbonization strategy. First, there is the uncertainty involved with how much hydrogen will
ultimately be emitted from hydrogen systems. The total amount of emissions
(e.g. leakage, venting, and purging) in current hydrogen systems remains unknown as
empirical data on leakage rates from specific infrastructure (such as
electrolyzers, pipelines, vehicles, and storage) are completely lacking. This is
because measurement efforts to date have been concentrated on safety concerns,
regulations, and risk assessment, which are focused on larger leaks.
Commercially available sensing technologies able to detect smaller leaks –
that would impact the climate but not safety – are unavailable (Mejia et
al., 2020). Furthermore, most of the hydrogen infrastructure needed to achieve
decarbonization goals has yet to be built, with plans underway to develop
more pipelines and even to pump hydrogen into individual homes (United Kingdom.
Secretary of State for Business, 2021).</p>
      <p id="d1e309">Second, there is the uncertainty involved with how much hydrogen will be deployed in the
future, how it will be produced, and what fossil fuel technologies it will
replace. Currently, hydrogen is produced mostly from natural gas, and it
accounts for only a small fraction of the global economy, with uses confined
mainly to fertilizer production and refineries (International Energy Agency,
2021). However, projections suggest that demand could increase up to 10-fold
by mid-century, with applications ranging from industrial processes,
building heating, and a diversity of transportation systems to providing clean
firm power to complement long-term renewable energy intermittency (Hydrogen
Council, 2017; BloombergNEF, 2020, 2021; International Energy Agency, 2021;
Energy Transitions Commission, 2021). While hydrogen leakage across the value
chain is a concern regardless of production method and, therefore, applies to
all hydrogen – including “green” hydrogen produced from water using
renewable energy (considered “zero-carbon” or “climate neutral”) and
“blue” hydrogen produced from natural gas using carbon capture, usage, and storage (CCUS) technologies
(considered “low-carbon”) – blue hydrogen is subject to additional
impacts on the energy balance due to residual emissions of CO<inline-formula><mml:math id="M15" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> as well
as emissions of methane from the natural gas supply value chain (see Fig. 2). The specific fossil fuel technologies that are replaced with hydrogen
alternatives will also determine the net climate benefit from deploying
clean hydrogen via how much carbon dioxide and methane emissions can be
reduced (Fig. 2).</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F2"><?xmltex \currentcnt{2}?><?xmltex \def\figurename{Figure}?><label>Figure 2</label><caption><p id="d1e324">Primary climate forcers emitted from fossil fuel technologies and
their clean hydrogen alternatives.</p></caption>
        <?xmltex \igopts{width=142.26378pt}?><graphic xlink:href="https://acp.copernicus.org/articles/22/9349/2022/acp-22-9349-2022-f02.png"/>

      </fig>

      <p id="d1e333">The third challenge is how hydrogen's warming impacts are calculated and
reported. Beyond the general uncertainties associated with estimating the
direct and indirect radiative effects of any atmospheric constituent, the
way in which scientists typically report the radiative potency of a climate
forcer (such as via radiative efficiency or radiative forcing) can be
inaccessible to and lack context for climate policy and business decision
makers. Therefore, decades ago, scientists began developing simplified
metrics for comparing the warming impacts among different greenhouse gases,
with the potency of CO<inline-formula><mml:math id="M16" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> typically being used as the baseline for the comparison given
its status as the most concerning human-emitted climate forcer. The most
well-known and widely used metric has consistently been the global warming
potential (GWP) with a 100-year time horizon, and this metric is even baked into
policies, international agreements, and greenhouse gas reporting
requirements. The GWP metric calculates the relative warming effect over a specified
time interval from a pulse of emissions of a climate forcer compared to an
equal pulse in mass of CO<inline-formula><mml:math id="M17" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula>.</p>
      <p id="d1e354"><?xmltex \hack{\newpage}?>However, mostly because of its pulse approach, using this method to compare
the climate effects between a climate forcer whose impacts are short-lived
(such as hydrogen and, most notably, methane) and a climate forcer whose
impacts are long-lived (such as CO<inline-formula><mml:math id="M18" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula>) is complicated. For example, if a
100-year time horizon is used, it masks the true impact of hydrogen during
the decades in which it is influencing the climate, providing the inaccurate
perception that hydrogen's warming effects are much smaller than they are.
On the other hand, it also provides the inaccurate perception that a pulse
of hydrogen can influence the climate 100 years later. If a 20-year time
horizon is used, it is more representative of hydrogen's impacts while it is
affecting the atmosphere, but it disregards CO<inline-formula><mml:math id="M19" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula>'s impacts after 20 years, when it is still affecting the atmosphere.</p>
      <p id="d1e376">This temporal issue of comparing warming impacts of short- and long-lived
climate forcers has been extensively discussed in the literature for decades
and has been a major source of confusion in the climate policy community; it
has also led to the development of numerous alternative metrics designed to
improve the comparisons (Shine et al., 2007; Alvarez et al., 2012; Allen et
al., 2016; Cherubini and Tanaka, 2016; Ocko et al., 2017; Fesenfeld et al.,
2018; Balcombe et al., 2018; Ocko and Hamburg, 2019; Cain et al., 2019;
Collins et al., 2020; Severinsky and Sessoms, 2021; Lynch et al., 2020).
However, stakeholders continue to rely on GWP to understand the
potency of any non-CO<inline-formula><mml:math id="M20" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> climate forcer – specifically, GWP with a
100-year time horizon (GWP-100).</p>
      <p id="d1e388">The implications of this challenge for hydrogen are that the majority of
studies to date have assessed its climate effects either using technical
indicators (such as radiative forcing) or GWP-100, which did not
convey hydrogen's near-term impacts (Derwent et al., 2001, 2006, 2020;
Prather, 2003; Schultz et al., 2003; Wuebbles et al., 2010; Derwent, 2018;
Field and Derwent, 2021; Paulot et al., 2021). Furthermore, until recently, the
only published estimates of hydrogen's warming effects were focused on
tropospheric responses. These two factors have had the result of
undervaluing hydrogen's warming potency and overlooking its near-term
effects. For example, new estimates of hydrogen's GWP that include
stratospheric effects show that hydrogen's GWP-100 is twice as high as the
previous central estimate of GWP-100 <inline-formula><mml:math id="M21" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 5 <inline-formula><mml:math id="M22" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 1 (Derwent et al., 2020;
Warwick et al., 2022). In terms of its near-term potency, the first
estimates of hydrogen's GWP for a 20-year time horizon (GWP-20) yield a
potency that is 3 times higher than its 100-year impact (GWP-20 <inline-formula><mml:math id="M23" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 33 [20–40]; Warwick et al., 2022). In other words, hydrogen's potency can be
6 times higher than commonly thought when looking at the critical next
couple of decades.</p>
      <p id="d1e412">Finally, accounting for methane emissions in climate assessments of clean
hydrogen applications also suffers the same analytical challenges as
hydrogen, given that it is also a short-lived gas commonly assessed through a
long-term lens. The climate effects of methane emissions are often further
underestimated, as natural gas leak rates are consistently
underestimated in national emission inventories (Alvarez et al., 2018; Shen
et al., 2021). Studies have shown that accounting for high methane emissions
from upstream supply chains associated with blue hydrogen production when
considered on shorter time horizons reveals near-term harm to the climate
that is not conveyed with standard GWP-100 assessments (Howarth and
Jacobson, 2021).</p>
      <p id="d1e416">Overall, the question remains: how will hydrogen's full atmospheric warming
impacts diminish its effectiveness as a decarbonization strategy across all
timescales? While more sophisticated modeling will be needed to fully
incorporate all complexities, interactions, and uncertainties described
above, a first-order analysis is possible using already published data with
minor improvements to the standard GWP metric to assess impacts over time
and account for constant emissions. A constant emission rate, as opposed to
a one-time pulse of emissions, is important because continuous emissions
more realistically represent hydrogen emissions in a hydrogen economy. In
this work, we examine the net climate impacts over time for a generic case
of replacing fossil fuel technologies with clean hydrogen alternatives using
a plausible range of future hydrogen emission rates. We also include
emissions of methane associated with blue hydrogen production for a range of
plausible leak rates. We use newly published GWP equations for hydrogen's
indirect effects (Warwick et al., 2022) and report the outcomes of constant
emissions for time horizons of 10 to 100 years.</p>
      <p id="d1e419">The approach utilized is known as the technology warming potential (Alvarez
et al., 2012), and it is similar to that of a life cycle assessment in that it
compares climate impacts from two alternative technologies to help inform
decision makers of the net benefits of switching from one to another. This
method retains the familiar GWP formulation but conveys the climate
implications over time from a sustained switch to hydrogen alternatives from
fossil fuel technologies. Furthermore, we use a simple approach to estimate
temperature responses to projected hydrogen demand levels, providing an
indication of the absolute climate consequences of hydrogen emissions.</p>
</sec>
<sec id="Ch1.S2">
  <label>2</label><title>Methodology</title>
      <p id="d1e430">Our analysis is comprised of three components. First, to provide context on
hydrogen's warming potency as an agent of climate change, we compare
hydrogen's warming effects to that of carbon dioxide for equal mass using
the traditional GWP methodology. Second, to provide context on the
implications of this warming potency for a hydrogen economy relative to a
fossil fuel one, we compare the warming impacts from deploying clean
hydrogen across a range of hydrogen and methane emission rates to that from
greenhouse gas emissions (CO<inline-formula><mml:math id="M24" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> and methane) from fossil fuel
utilization. Third, to provide context on the magnitude of this warming
impact, we estimate temperature responses to future hydrogen emissions based
on different hydrogen demand levels and leak rates.</p>
<sec id="Ch1.S2.SS1">
  <label>2.1</label><title>Climate impact calculations</title>
      <p id="d1e449">To calculate the warming effects of hydrogen, methane, and carbon dioxide
emissions, we use the traditional GWP metric but account for constant
emissions rather than a pulse of emissions. We first use the absolute global
warming potential (AGWP) components, which compute the cumulative radiative
forcing of a climate forcer over a specified time horizon in watts per square meter per kilogram per year ((W m<inline-formula><mml:math id="M25" display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M26" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula> (kg yr<inline-formula><mml:math id="M27" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>)). For carbon dioxide and methane, we
use the Intergovernmental Panel on Climate Change (IPCC) formulations of
AGWP, as shown in Eqs. (1) and (2), respectively (Myhre at al., 2013; Forster et al.,
2021). Input parameters and their sources can be found in Table 1.
            <disp-formula id="Ch1.E1" content-type="numbered"><label>1</label><mml:math id="M28" display="block"><mml:mrow><?xmltex \hack{\hbox\bgroup\fontsize{8.5}{8.5}\selectfont$\displaystyle}?><mml:msub><mml:mi mathvariant="normal">AGWP</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:msub><mml:mo>(</mml:mo><mml:mi>H</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:msub><mml:mfenced open="{" close="}"><mml:mrow><mml:msub><mml:mi>a</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:mi>H</mml:mi><mml:mo>+</mml:mo><mml:msubsup><mml:mo>∑</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow><mml:mn mathvariant="normal">3</mml:mn></mml:msubsup><mml:msub><mml:mi>a</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mfenced open="(" close=")"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:mi>exp⁡</mml:mi><mml:mfenced open="(" close=")"><mml:mrow><mml:mo>-</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mi>H</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle></mml:mrow></mml:mfenced></mml:mrow></mml:mfenced></mml:mrow></mml:mfenced><?xmltex \hack{$\egroup}?></mml:mrow></mml:math></disp-formula>

            <disp-formula id="Ch1.E2" content-type="numbered"><label>2</label><mml:math id="M29" display="block"><mml:mtable class="split" rowspacing="0.2ex" displaystyle="true" columnalign="right left"><mml:mtr><mml:mtd><mml:mrow><mml:msub><mml:mi mathvariant="normal">AGWP</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="normal">CH</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:msub><mml:mfenced close=")" open="("><mml:mi>H</mml:mi></mml:mfenced></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mo>=</mml:mo><mml:mfenced close=")" open="("><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>+</mml:mo><mml:msub><mml:mi>f</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>f</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:mfenced></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mo>×</mml:mo><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="normal">CH</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mfenced open="(" close=")"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:mi>exp⁡</mml:mi><mml:mfenced open="(" close=")"><mml:mrow><mml:mo>-</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mi>H</mml:mi><mml:mi mathvariant="italic">τ</mml:mi></mml:mfrac></mml:mstyle></mml:mrow></mml:mfenced></mml:mrow></mml:mfenced></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>
          While these equations are appropriate for climate forcers with primarily
direct radiative effects, hydrogen's radiative effects are entirely
indirect. Therefore, we use the AGWP equations recently derived specifically
for hydrogen based on sophisticated chemistry–climate modeling experiments,
which explicitly account for its three main indirect effects and their
varying temporal dynamics (methane, tropospheric ozone, and stratospheric
water vapor) (Warwick et al., 2022). The equations are shown in the following (Eqs. 3–8) and provide the same output information of cumulative radiative
forcing per time horizon ((W m<inline-formula><mml:math id="M30" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>) <inline-formula><mml:math id="M31" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula> (kg yr<inline-formula><mml:math id="M32" display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>) as in
Eqs. (1) and (2). More details on their derivation are available in Warwick
et al. (2022). Input parameters and their sources can be found in Table 1.
            <disp-formula id="Ch1.E3" content-type="numbered"><label>3</label><mml:math id="M33" display="block"><mml:mrow><?xmltex \hack{\hbox\bgroup\fontsize{9.5}{9.5}\selectfont$\displaystyle}?><mml:mtable rowspacing="0.2ex" class="split" displaystyle="true" columnalign="right left"><mml:mtr><mml:mtd><mml:mrow><mml:mi mathvariant="normal">AGWP</mml:mi><mml:msub><mml:mn mathvariant="normal">1</mml:mn><mml:mrow><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>(</mml:mo><mml:mi>H</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mi>A</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msub><mml:mi>a</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:msub><mml:mi>C</mml:mi><mml:mfenced close="" open="("><mml:mrow><mml:mi mathvariant="normal">tp</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mo>-</mml:mo><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mfenced open="(" close=")"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:mi>exp⁡</mml:mi><mml:mfenced open="(" close=")"><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mo>-</mml:mo><mml:mi mathvariant="normal">tp</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle></mml:mfenced></mml:mrow></mml:mfenced></mml:mrow></mml:mfenced></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mfenced open="" close=""><mml:mrow><mml:mo>-</mml:mo><mml:mfenced open="(" close=")"><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mfenced close=")" open="("><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:msub><mml:mo>-</mml:mo><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:mfenced></mml:mrow></mml:mfrac></mml:mstyle></mml:mfenced><mml:mfenced close="" open="("><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:msub><mml:mfenced open="(" close=")"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi>exp⁡</mml:mi><mml:mfenced close=")" open="("><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mo>-</mml:mo><mml:mi mathvariant="normal">tp</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mstyle></mml:mfenced></mml:mrow></mml:mfenced></mml:mrow></mml:mfenced></mml:mrow></mml:mfenced></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mfenced open="" close=")"><mml:mfenced open="" close=")"><mml:mrow><mml:mo>-</mml:mo><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mfenced open="(" close=")"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi>exp⁡</mml:mi><mml:mfenced open="(" close=")"><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mo>-</mml:mo><mml:mi mathvariant="normal">tp</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle></mml:mfenced></mml:mrow></mml:mfenced></mml:mrow></mml:mfenced></mml:mfenced></mml:mrow></mml:mtd></mml:mtr></mml:mtable><?xmltex \hack{$\egroup}?></mml:mrow></mml:math></disp-formula>

            <disp-formula id="Ch1.E4" content-type="numbered"><label>4</label><mml:math id="M34" display="block"><mml:mrow><?xmltex \hack{\hbox\bgroup\fontsize{9.5}{9.5}\selectfont$\displaystyle}?><mml:mtable class="split" rowspacing="0.2ex" displaystyle="true" columnalign="right left"><mml:mtr><mml:mtd><mml:mrow><mml:mi mathvariant="normal">AGWP</mml:mi><mml:msub><mml:mn mathvariant="normal">2</mml:mn><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mo>,</mml:mo><mml:mi mathvariant="normal">i</mml:mi></mml:mrow></mml:msub><mml:mo>(</mml:mo><mml:mi>H</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mo>=</mml:mo><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mfenced open="(" close=")"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msub><mml:mi>a</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:msub><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mi>C</mml:mi><mml:mfenced open="(" close=")"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi>exp⁡</mml:mi><mml:mfenced close=")" open="("><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mrow><mml:mo>-</mml:mo><mml:mi mathvariant="normal">tp</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mstyle></mml:mfenced></mml:mrow></mml:mfenced></mml:mrow></mml:mfenced></mml:mrow><mml:mrow><mml:mfenced open="(" close=")"><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:msub><mml:mo>-</mml:mo><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:mfenced></mml:mrow></mml:mfrac></mml:mstyle></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mo>×</mml:mo><mml:mfenced open="(" close=""><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:msub><mml:mfenced close=")" open="("><mml:mrow><mml:mi>exp⁡</mml:mi><mml:mfenced open="(" close=")"><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mo>-</mml:mo><mml:mi mathvariant="normal">tp</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mstyle></mml:mfenced><mml:mo>-</mml:mo><mml:mi>exp⁡</mml:mi><mml:mfenced close=")" open="("><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mo>-</mml:mo><mml:mi>H</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mstyle></mml:mfenced></mml:mrow></mml:mfenced></mml:mrow></mml:mfenced></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mfenced close=")" open=""><mml:mrow><mml:mo>-</mml:mo><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mfenced open="(" close=")"><mml:mrow><mml:mi>exp⁡</mml:mi><mml:mfenced open="(" close=")"><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mo>-</mml:mo><mml:mi mathvariant="normal">tp</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle></mml:mfenced><mml:mo>-</mml:mo><mml:mi>exp⁡</mml:mi><mml:mfenced open="(" close=")"><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mo>-</mml:mo><mml:mi>H</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle></mml:mfenced></mml:mrow></mml:mfenced></mml:mrow></mml:mfenced></mml:mrow></mml:mtd></mml:mtr></mml:mtable><?xmltex \hack{$\egroup}?></mml:mrow></mml:math></disp-formula>

            <disp-formula id="Ch1.E5" content-type="numbered"><label>5</label><mml:math id="M35" display="block"><mml:mrow><?xmltex \hack{\hbox\bgroup\fontsize{9.5}{9.5}\selectfont$\displaystyle}?><mml:mtable class="split" rowspacing="0.2ex" displaystyle="true" columnalign="right left"><mml:mtr><mml:mtd><mml:mrow><mml:mi mathvariant="normal">AGWP</mml:mi><mml:msub><mml:mn mathvariant="normal">3</mml:mn><mml:mrow><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>(</mml:mo><mml:mi>H</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mi>A</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msub><mml:mi>a</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>i</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msubsup><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:msub><mml:mi>C</mml:mi><mml:mfenced close="" open="("><mml:mfenced open="(" close=")"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:mi>exp⁡</mml:mi><mml:mfenced open="(" close=")"><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mo>-</mml:mo><mml:mi mathvariant="normal">tp</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle></mml:mfenced></mml:mrow></mml:mfenced></mml:mfenced></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mfenced open="" close=""><mml:mrow><mml:mo>-</mml:mo><mml:mfenced open="(" close=")"><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mfenced open="(" close=")"><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:msub><mml:mo>-</mml:mo><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:mfenced></mml:mrow></mml:mfrac></mml:mstyle></mml:mfenced><mml:mfenced open="(" close=""><mml:mrow><mml:mi>exp⁡</mml:mi><mml:mfenced open="(" close=")"><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mo>-</mml:mo><mml:mi mathvariant="normal">tp</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mstyle></mml:mfenced></mml:mrow></mml:mfenced></mml:mrow></mml:mfenced></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mfenced open="" close=")"><mml:mfenced close=")" open=""><mml:mrow><mml:mo>-</mml:mo><mml:mi>exp⁡</mml:mi><mml:mfenced open="(" close=")"><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mo>-</mml:mo><mml:mi mathvariant="normal">tp</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle></mml:mfenced></mml:mrow></mml:mfenced></mml:mfenced><mml:mfenced close="" open="("><mml:mrow><mml:mi>exp⁡</mml:mi><mml:mfenced open="(" close=")"><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mo>-</mml:mo><mml:mi mathvariant="normal">tp</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle></mml:mfenced></mml:mrow></mml:mfenced></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mfenced close=")" open=""><mml:mrow><mml:mo>-</mml:mo><mml:mi>exp⁡</mml:mi><mml:mfenced close=")" open="("><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mo>-</mml:mo><mml:mi>H</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle></mml:mfenced></mml:mrow></mml:mfenced></mml:mrow></mml:mtd></mml:mtr></mml:mtable><?xmltex \hack{$\egroup}?></mml:mrow></mml:math></disp-formula>

            <disp-formula id="Ch1.E6" content-type="numbered"><label>6</label><mml:math id="M36" display="block"><mml:mrow><?xmltex \hack{\hbox\bgroup\fontsize{9.5}{9.5}\selectfont$\displaystyle}?><mml:mtable class="split" rowspacing="0.2ex" displaystyle="true" columnalign="right left"><mml:mtr><mml:mtd><mml:mrow><mml:msub><mml:mi mathvariant="normal">AGWP</mml:mi><mml:mrow><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mfenced open="(" close=")"><mml:mi>H</mml:mi></mml:mfenced></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mo>=</mml:mo><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="normal">AGWP</mml:mi><mml:msub><mml:mn mathvariant="normal">1</mml:mn><mml:mrow><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mfenced open="(" close=")"><mml:mi>H</mml:mi></mml:mfenced><mml:mo>+</mml:mo><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="normal">AGWP</mml:mi><mml:msub><mml:mn mathvariant="normal">2</mml:mn><mml:mrow><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mfenced open="(" close=")"><mml:mi>H</mml:mi></mml:mfenced></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mo>+</mml:mo><mml:mi mathvariant="normal">AGWP</mml:mi><mml:msub><mml:mn mathvariant="normal">3</mml:mn><mml:mrow><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mfenced open="(" close=")"><mml:mi>H</mml:mi></mml:mfenced></mml:mrow></mml:mtd></mml:mtr></mml:mtable><?xmltex \hack{$\egroup}?></mml:mrow></mml:math></disp-formula>

            <disp-formula id="Ch1.E7" content-type="numbered"><label>7</label><mml:math id="M37" display="block"><mml:mrow><?xmltex \hack{\hbox\bgroup\fontsize{9.5}{9.5}\selectfont$\displaystyle}?><mml:msub><mml:mi mathvariant="normal">AGWP</mml:mi><mml:mrow><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CH</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:mrow></mml:msub><mml:mfenced open="(" close=")"><mml:mi>H</mml:mi></mml:mfenced><mml:mo>=</mml:mo><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mfenced close=")" open="("><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>+</mml:mo><mml:msub><mml:mi>f</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>f</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:mfenced><mml:msub><mml:mi mathvariant="normal">AGWP</mml:mi><mml:mrow><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CH</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:mrow></mml:msub><mml:mfenced close=")" open="("><mml:mi>H</mml:mi></mml:mfenced><?xmltex \hack{$\egroup}?></mml:mrow></mml:math></disp-formula>

            <disp-formula id="Ch1.E8" content-type="numbered"><label>8</label><mml:math id="M38" display="block"><mml:mrow><?xmltex \hack{\hbox\bgroup\fontsize{9.5}{9.5}\selectfont$\displaystyle}?><mml:mtable class="split" rowspacing="0.2ex" displaystyle="true" columnalign="right left"><mml:mtr><mml:mtd><mml:mrow><mml:msub><mml:mi mathvariant="normal">AGWP</mml:mi><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:msub><mml:mfenced close=")" open="("><mml:mi>H</mml:mi></mml:mfenced></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mo>=</mml:mo><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msub><mml:mi mathvariant="normal">AGWP</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi mathvariant="normal">CH</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:msub><mml:mfenced close=")" open="("><mml:mi>H</mml:mi></mml:mfenced></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mo>+</mml:mo><mml:msub><mml:mi mathvariant="normal">AGWP</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mo>,</mml:mo><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:mrow></mml:msub><mml:mfenced open="(" close=")"><mml:mi>H</mml:mi></mml:mfenced><mml:mo>+</mml:mo><mml:msub><mml:mi mathvariant="normal">AGWP</mml:mi><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mi mathvariant="normal">O</mml:mi></mml:mrow></mml:msub><mml:mfenced close=")" open="("><mml:mi>H</mml:mi></mml:mfenced></mml:mrow></mml:mtd></mml:mtr></mml:mtable><?xmltex \hack{$\egroup}?></mml:mrow></mml:math></disp-formula></p>
      <p id="d1e1630">To account for a constant emission rate of each forcer, as opposed to just a
pulse of emissions, we consider a new pulse of emissions every year.
Assuming linearity, the summation of the cumulative radiative forcing
(AGWP<inline-formula><mml:math id="M39" display="inline"><mml:msub><mml:mi/><mml:mi>i</mml:mi></mml:msub></mml:math></inline-formula>) from past and current pulses for each year is equal to the
cumulative radiative forcing from a constant emission rate (AGWP<inline-formula><mml:math id="M40" display="inline"><mml:mrow><mml:msub><mml:mi>c</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>). To
account for multiple forcers emitted from each technology, we add up the
individual AGWP<inline-formula><mml:math id="M41" display="inline"><mml:mrow><mml:msub><mml:mi>c</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>s for each time horizon. Finally, to compare the climate
impacts from hydrogen technologies to their fossil fuel technology
counterparts, we simply divide their AGWP<inline-formula><mml:math id="M42" display="inline"><mml:mi>c</mml:mi></mml:math></inline-formula> values (comparable to how GWP is
calculated). The results are then presented as a ratio of climate impacts
(using cumulative radiative forcing as a proxy) as a function of time
between two different technologies (i.e., hydrogen alternatives vs. fossil
fuel technologies). A value greater than one indicates that the alternative
technology (in this case hydrogen) has larger climate warming impacts at
time horizon <inline-formula><mml:math id="M43" display="inline"><mml:mi>H</mml:mi></mml:math></inline-formula> than the original technology (and vice versa for less than one).
In our analysis, we present the results as a percent change in climate
impacts (cumulative radiative forcing) from the original technology, such
that 1 <inline-formula><mml:math id="M44" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 0 % change (or equal), 0.5 <inline-formula><mml:math id="M45" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 50 % decrease, 2 <inline-formula><mml:math id="M46" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 100 %
increase, etc.</p>

<?xmltex \floatpos{p}?><table-wrap id="Ch1.T1" specific-use="star" orientation="landscape"><?xmltex \currentcnt{1}?><label>Table 1</label><caption><p id="d1e1703">Input parameters and sources used for the absolute global
warming potential (AGWP) calculations shown in Eqs. (1)–(8). For hydrogen
AGWPs, we replaced the IPCC Fifth Assessment Report (2013) (Myhre et al., 2013)
values that were used in Warwick et al. (2022) with those from the IPCC Sixth
Assessment Report (2021) (Forster et al., 2021).</p></caption><oasis:table frame="topbot"><?xmltex \begin{scaleboxenv}{.80}[.80]?><oasis:tgroup cols="7">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="left"/>
     <oasis:colspec colnum="3" colname="col3" align="left"/>
     <oasis:colspec colnum="4" colname="col4" align="left"/>
     <oasis:colspec colnum="5" colname="col5" align="left"/>
     <oasis:colspec colnum="6" colname="col6" align="right"/>
     <oasis:colspec colnum="7" colname="col7" align="left"/>
     <oasis:thead>
       <oasis:row rowsep="1">

         <oasis:entry namest="col1" nameend="col2">Variable </oasis:entry>

         <oasis:entry colname="col3">Definition</oasis:entry>

         <oasis:entry colname="col4">Unit</oasis:entry>

         <oasis:entry colname="col5">Value</oasis:entry>

         <oasis:entry colname="col6">Source</oasis:entry>

         <oasis:entry colname="col7"/>

       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row rowsep="1">

         <oasis:entry namest="col1" nameend="col2"><inline-formula><mml:math id="M47" display="inline"><mml:mi>H</mml:mi></mml:math></inline-formula></oasis:entry>

         <oasis:entry colname="col3">Time horizon</oasis:entry>

         <oasis:entry colname="col4">Years</oasis:entry>

         <oasis:entry colname="col5">1–100</oasis:entry>

         <oasis:entry colname="col6">n/a</oasis:entry>

         <oasis:entry colname="col7"/>

       </oasis:row>
       <oasis:row rowsep="1">

         <oasis:entry namest="col1" nameend="col2">AGWP<inline-formula><mml:math id="M48" display="inline"><mml:msub><mml:mi/><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:msub></mml:math></inline-formula></oasis:entry>

         <oasis:entry colname="col3"/>

         <oasis:entry colname="col4"/>

         <oasis:entry colname="col5"/>

         <oasis:entry colname="col6"/>

         <oasis:entry colname="col7"/>

       </oasis:row>
       <oasis:row>

         <oasis:entry namest="col1" nameend="col2"><inline-formula><mml:math id="M49" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>

         <oasis:entry colname="col3">Radiative forcing scaling factor</oasis:entry>

         <oasis:entry colname="col4">W m<inline-formula><mml:math id="M50" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> ppb<inline-formula><mml:math id="M51" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>

         <oasis:entry colname="col5"><inline-formula><mml:math id="M52" display="inline"><mml:mrow><mml:mn mathvariant="normal">1.33</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">5</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula></oasis:entry>

         <oasis:entry colname="col6">Forster et al. (2021)</oasis:entry>

         <oasis:entry colname="col7"/>

       </oasis:row>
       <oasis:row>

         <oasis:entry namest="col1" nameend="col2"><inline-formula><mml:math id="M53" display="inline"><mml:mrow><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mn mathvariant="normal">0</mml:mn><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>

         <oasis:entry colname="col3">Coefficient for fraction of CO<inline-formula><mml:math id="M54" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> remaining in atmosphere</oasis:entry>

         <oasis:entry colname="col4">Unitless</oasis:entry>

         <oasis:entry colname="col5"><inline-formula><mml:math id="M55" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.2173</mml:mn><mml:mo>;</mml:mo><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.224</mml:mn><mml:mo>;</mml:mo><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.2824</mml:mn><mml:mo>;</mml:mo><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.2763</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>

         <oasis:entry colname="col6">Myhre et al. (2013)</oasis:entry>

         <oasis:entry colname="col7"/>

       </oasis:row>
       <oasis:row rowsep="1">

         <oasis:entry namest="col1" nameend="col2"><inline-formula><mml:math id="M56" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>

         <oasis:entry colname="col3">Timescale for fraction of CO<inline-formula><mml:math id="M57" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> remaining in atmosphere</oasis:entry>

         <oasis:entry colname="col4">Years</oasis:entry>

         <oasis:entry colname="col5"><inline-formula><mml:math id="M58" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">394.4</mml:mn><mml:mo>;</mml:mo><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">36.54</mml:mn><mml:mo>;</mml:mo><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">4.304</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>

         <oasis:entry colname="col6">Myhre et al. (2013)</oasis:entry>

         <oasis:entry colname="col7"/>

       </oasis:row>
       <oasis:row rowsep="1">

         <oasis:entry namest="col1" nameend="col2">AGWP<inline-formula><mml:math id="M59" display="inline"><mml:msub><mml:mi/><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CH</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:msub></mml:math></inline-formula></oasis:entry>

         <oasis:entry colname="col3"/>

         <oasis:entry colname="col4"/>

         <oasis:entry colname="col5"/>

         <oasis:entry colname="col6"/>

         <oasis:entry colname="col7"/>

       </oasis:row>
       <oasis:row>

         <oasis:entry namest="col1" nameend="col2">A<inline-formula><mml:math id="M60" display="inline"><mml:msub><mml:mi/><mml:mrow><mml:msub><mml:mrow class="chem"><mml:mi mathvariant="normal">CH</mml:mi></mml:mrow><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:msub></mml:math></inline-formula></oasis:entry>

         <oasis:entry colname="col3">Radiative forcing scaling factor</oasis:entry>

         <oasis:entry colname="col4">W m<inline-formula><mml:math id="M61" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> ppb<inline-formula><mml:math id="M62" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>

         <oasis:entry colname="col5"><inline-formula><mml:math id="M63" display="inline"><mml:mrow><mml:mn mathvariant="normal">3.88</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">4</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula></oasis:entry>

         <oasis:entry colname="col6">Forster et al. (2021)</oasis:entry>

         <oasis:entry colname="col7"/>

       </oasis:row>
       <oasis:row>

         <oasis:entry namest="col1" nameend="col2"><inline-formula><mml:math id="M64" display="inline"><mml:mi mathvariant="italic">τ</mml:mi></mml:math></inline-formula></oasis:entry>

         <oasis:entry colname="col3">Perturbation lifetime</oasis:entry>

         <oasis:entry colname="col4">Years</oasis:entry>

         <oasis:entry colname="col5">11.8</oasis:entry>

         <oasis:entry colname="col6">Forster et al. (2021)</oasis:entry>

         <oasis:entry colname="col7"/>

       </oasis:row>
       <oasis:row>

         <oasis:entry namest="col1" nameend="col2"><inline-formula><mml:math id="M65" display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>

         <oasis:entry colname="col3">Tropospheric ozone indirect effect scaling</oasis:entry>

         <oasis:entry colname="col4">Unitless</oasis:entry>

         <oasis:entry colname="col5">0.37</oasis:entry>

         <oasis:entry colname="col6">Forster et al. (2021)</oasis:entry>

         <oasis:entry colname="col7"/>

       </oasis:row>
       <oasis:row rowsep="1">

         <oasis:entry namest="col1" nameend="col2"><inline-formula><mml:math id="M66" display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>

         <oasis:entry colname="col3">Stratospheric water vapor indirect effect scaling</oasis:entry>

         <oasis:entry colname="col4">Unitless</oasis:entry>

         <oasis:entry colname="col5">0.106</oasis:entry>

         <oasis:entry colname="col6">Forster et al. (2021)</oasis:entry>

         <oasis:entry colname="col7"/>

       </oasis:row>
       <oasis:row rowsep="1">

         <oasis:entry namest="col1" nameend="col2">AGWP<inline-formula><mml:math id="M67" display="inline"><mml:msub><mml:mi/><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:msub></mml:math></inline-formula></oasis:entry>

         <oasis:entry colname="col3"/>

         <oasis:entry colname="col4"/>

         <oasis:entry colname="col5"/>

         <oasis:entry colname="col6"/>

         <oasis:entry colname="col7"/>

       </oasis:row>
       <oasis:row>

         <oasis:entry namest="col1" nameend="col2"><inline-formula><mml:math id="M68" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>

         <oasis:entry colname="col3">H<inline-formula><mml:math id="M69" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> lifetime (combined chemical and deposition lifetime)</oasis:entry>

         <oasis:entry colname="col4">Years</oasis:entry>

         <oasis:entry colname="col5">1.9 [1.4, 2.5]</oasis:entry>

         <oasis:entry colname="col6">Warwick et al. (2022); Paulot et al. (2021)</oasis:entry>

         <oasis:entry colname="col7"/>

       </oasis:row>
       <oasis:row>

         <oasis:entry namest="col1" nameend="col2"><inline-formula><mml:math id="M70" display="inline"><mml:mi>C</mml:mi></mml:math></inline-formula></oasis:entry>

         <oasis:entry colname="col3">Conversion factor for converting H<inline-formula><mml:math id="M71" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> mixing ratio (ppb) into H<inline-formula><mml:math id="M72" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> mass (kg)</oasis:entry>

         <oasis:entry colname="col4">ppb kg<inline-formula><mml:math id="M73" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>

         <oasis:entry colname="col5"><inline-formula><mml:math id="M74" display="inline"><mml:mrow><mml:mn mathvariant="normal">3.5</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">9</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula></oasis:entry>

         <oasis:entry colname="col6">Warwick et al. (2022)</oasis:entry>

         <oasis:entry colname="col7"/>

       </oasis:row>
       <oasis:row rowsep="1">

         <oasis:entry namest="col1" nameend="col2">tp </oasis:entry>

         <oasis:entry colname="col3">Length of step emission</oasis:entry>

         <oasis:entry colname="col4">Years</oasis:entry>

         <oasis:entry colname="col5">1</oasis:entry>

         <oasis:entry colname="col6">n/a</oasis:entry>

         <oasis:entry colname="col7"/>

       </oasis:row>
       <oasis:row>

         <oasis:entry rowsep="1" colname="col1" morerows="2"><inline-formula><mml:math id="M75" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>

         <oasis:entry colname="col2">CH<inline-formula><mml:math id="M76" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:math></inline-formula></oasis:entry>

         <oasis:entry colname="col3">Radiative forcing scaling factor</oasis:entry>

         <oasis:entry colname="col4">W m<inline-formula><mml:math id="M77" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> ppb<inline-formula><mml:math id="M78" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>

         <oasis:entry colname="col5"><inline-formula><mml:math id="M79" display="inline"><mml:mrow><mml:mn mathvariant="normal">3.88</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">4</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula></oasis:entry>

         <oasis:entry colname="col6">Forster et al. (2021)</oasis:entry>

         <oasis:entry colname="col7"/>

       </oasis:row>
       <oasis:row>

         <oasis:entry colname="col2">O<inline-formula><mml:math id="M80" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula></oasis:entry>

         <oasis:entry colname="col3"/>

         <oasis:entry colname="col4">W m<inline-formula><mml:math id="M81" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> DU<inline-formula><mml:math id="M82" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>

         <oasis:entry colname="col5">0.042</oasis:entry>

         <oasis:entry colname="col6">Warwick et al. (2022)</oasis:entry>

         <oasis:entry colname="col7"/>

       </oasis:row>
       <oasis:row rowsep="1">

         <oasis:entry colname="col2">H<inline-formula><mml:math id="M83" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula>O</oasis:entry>

         <oasis:entry colname="col3"/>

         <oasis:entry colname="col4">W m<inline-formula><mml:math id="M84" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> ppb<inline-formula><mml:math id="M85" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>

         <oasis:entry colname="col5"><inline-formula><mml:math id="M86" display="inline"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">4</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula></oasis:entry>

         <oasis:entry colname="col6">Warwick et al. (2022)</oasis:entry>

         <oasis:entry colname="col7"/>

       </oasis:row>
       <oasis:row>

         <oasis:entry rowsep="1" colname="col1" morerows="2"><inline-formula><mml:math id="M87" display="inline"><mml:mrow><mml:msub><mml:mi>a</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>

         <oasis:entry colname="col2">CH<inline-formula><mml:math id="M88" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:math></inline-formula></oasis:entry>

         <oasis:entry colname="col3">Production rate of species resulting in the</oasis:entry>

         <oasis:entry colname="col4">ppb(CH<inline-formula><mml:math id="M89" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:math></inline-formula>) ppb(H<inline-formula><mml:math id="M90" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula>)<inline-formula><mml:math id="M91" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> yr<inline-formula><mml:math id="M92" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>

         <oasis:entry colname="col5"><inline-formula><mml:math id="M93" display="inline"><mml:mrow><mml:mn mathvariant="normal">1.46</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula></oasis:entry>

         <oasis:entry colname="col6">Warwick et al. (2022)</oasis:entry>

         <oasis:entry colname="col7"/>

       </oasis:row>
       <oasis:row>

         <oasis:entry colname="col2">O<inline-formula><mml:math id="M94" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula></oasis:entry>

         <oasis:entry colname="col3">indirect forcing (mixing ratio per year) per ppb H<inline-formula><mml:math id="M95" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula></oasis:entry>

         <oasis:entry colname="col4">DU ppb(H<inline-formula><mml:math id="M96" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula>)<inline-formula><mml:math id="M97" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> yr<inline-formula><mml:math id="M98" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>

         <oasis:entry colname="col5">0.0056</oasis:entry>

         <oasis:entry colname="col6">Warwick et al. (2022)</oasis:entry>

         <oasis:entry colname="col7"/>

       </oasis:row>
       <oasis:row rowsep="1">

         <oasis:entry colname="col2">H<inline-formula><mml:math id="M99" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula>O</oasis:entry>

         <oasis:entry colname="col3">change at steady state</oasis:entry>

         <oasis:entry colname="col4">ppb(H<inline-formula><mml:math id="M100" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula>O) ppb(H<inline-formula><mml:math id="M101" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula>)<inline-formula><mml:math id="M102" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> yr<inline-formula><mml:math id="M103" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>

         <oasis:entry colname="col5">0.042</oasis:entry>

         <oasis:entry colname="col6">Warwick et al. (2022)</oasis:entry>

         <oasis:entry colname="col7"/>

       </oasis:row>
       <oasis:row>

         <oasis:entry colname="col1" morerows="2"><inline-formula><mml:math id="M104" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>

         <oasis:entry colname="col2">CH<inline-formula><mml:math id="M105" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:math></inline-formula></oasis:entry>

         <oasis:entry colname="col3">Perturbation lifetime</oasis:entry>

         <oasis:entry colname="col4" morerows="2">Years</oasis:entry>

         <oasis:entry colname="col5">11.8</oasis:entry>

         <oasis:entry colname="col6">Forster et al. (2021)</oasis:entry>

         <oasis:entry colname="col7"/>

       </oasis:row>
       <oasis:row>

         <oasis:entry colname="col2">O<inline-formula><mml:math id="M106" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula></oasis:entry>

         <oasis:entry colname="col3">of species causing the</oasis:entry>

         <oasis:entry colname="col5">0.07</oasis:entry>

         <oasis:entry colname="col6">Warwick et al. (2022 )</oasis:entry>

         <oasis:entry colname="col7"/>

       </oasis:row>
       <oasis:row>

         <oasis:entry colname="col2">H<inline-formula><mml:math id="M107" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula>O</oasis:entry>

         <oasis:entry colname="col3">radiative forcing</oasis:entry>

         <oasis:entry colname="col5">8</oasis:entry>

         <oasis:entry colname="col6">Warwick et al. (2022)</oasis:entry>

         <oasis:entry colname="col7"/>

       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup><?xmltex \end{scaleboxenv}?></oasis:table><table-wrap-foot><p id="d1e1706">n/a: not applicable. DU: Dobson units.</p></table-wrap-foot></table-wrap>

      <p id="d1e2939"><?xmltex \hack{\newpage}?>This concept – an extension of AGWP and GWP that considers a constant
emission rate (as opposed to a one-time pulse) and calculates the relative
climate effects over time (as opposed to one specified time horizon, such as
over 100 years) – is further documented and discussed in Alvarez et al. (2012), where it is called the technology warming potential. Several studies
have used this metric to assess the climate impacts of different
technologies that emit multiple greenhouse gases with varying atmospheric
lifetimes, to show how the climate impacts of specific technologies change
over time relative to one another (Alvarez et al., 2012; Camuzeaux et al.,
2015; Ocko and Hamburg, 2019). However, given hydrogen's unique AGWP
equations resulting from its varying indirect effects, we do not use the
specific formulas derived in Alvarez et al. (2012) but rather follow the
calculation chain described above.</p>
      <p id="d1e2943">To account for uncertainties in our analysis, we follow the approach of
Warwick et al. (2022). First, we consider uncertainties in hydrogen's
atmospheric lifetime, which (given the uncertainty in the strength of
hydrogen's soil sink) are arguably the greatest source of uncertainty in
hydrogen's atmospheric impacts overall (Paulot et al., 2021; Warwick et al.,
2022). Compared with a central estimate of hydrogen's atmospheric lifetime of
1.9 years (Warwick et al., 2022), we use a lower-end estimate of 1.4 years
(Warwick et al., 2022) and a higher-end estimate of 2.5 years (Paulot et al.,
2021). Second, we apply a <inline-formula><mml:math id="M108" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 20 % uncertainty to hydrogen's GWP
(AGWP<inline-formula><mml:math id="M109" display="inline"><mml:msub><mml:mi/><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:msub></mml:math></inline-formula>(<inline-formula><mml:math id="M110" display="inline"><mml:mi>H</mml:mi></mml:math></inline-formula>) <inline-formula><mml:math id="M111" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula> AGWP<inline-formula><mml:math id="M112" display="inline"><mml:msub><mml:mi/><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:msub></mml:math></inline-formula> (<inline-formula><mml:math id="M113" display="inline"><mml:mi>H</mml:mi></mml:math></inline-formula>)) due to uncertainties in radiative forcing scaling factors
and CO<inline-formula><mml:math id="M114" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula>'s radiative effects (Warwick et al., 2022).</p>
      <p id="d1e3010">In order to assess the absolute warming impact from future hydrogen demand
levels based on varying hydrogen emission rates, we apply the simple
approach used by Paulot et al. (2021) to approximate long-term temperature
responses to hydrogen emissions. This method uses the best estimates of the
long-term increase in global surface temperature (equilibrium climate
sensitivity; ECS) and radiative forcing from a doubling of CO<inline-formula><mml:math id="M115" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula>
concentrations and assumes that hydrogen would have a similar efficacy. The
Coupled Model Intercomparison Project Phase 6 (CMIP6) models suggest a best estimate of 3.78 <inline-formula><mml:math id="M116" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 1.08 <inline-formula><mml:math id="M117" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C for
the ECS and a 3.93 W m<inline-formula><mml:math id="M118" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> effective radiative forcing for a doubling of
CO<inline-formula><mml:math id="M119" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> (Forster et al., 2021). This suggests a climate efficacy of 0.96 <inline-formula><mml:math id="M120" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C (W m<inline-formula><mml:math id="M121" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:math></inline-formula>)<inline-formula><mml:math id="M122" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>. To estimate temperature responses to
hydrogen emissions, we multiply this efficacy by the hydrogen effective
radiative efficiency estimated in Paulot et al. (2021) per unit of emission
per year (0.84 mW m<inline-formula><mml:math id="M123" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> (Tg yr<inline-formula><mml:math id="M124" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>)<inline-formula><mml:math id="M125" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>) and the hydrogen emissions
per year (emission inputs discussed in Sect. 2.2). To account for
uncertainties, we use a <inline-formula><mml:math id="M126" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 40 % uncertainty in the hydrogen effective
radiative efficiency, which is comparable to the uncertainty arising from
both soil sink impacts on hydrogen's atmospheric lifetime and the
uncertainty in radiative forcing scaling factors and carbon dioxide's
radiative effects (discussed above). Note that for the temperature analysis,
we do not consider additional temperature impacts from methane emissions
associated with the natural gas supply chain utilized in the production of
blue hydrogen, as we want to focus on the absolute impacts from hydrogen
emissions in particular.</p>
</sec>
<sec id="Ch1.S2.SS2">
  <label>2.2</label><title>Emissions from hydrogen technologies</title>
      <p id="d1e3142">The emissions from hydrogen applications that we consider in our analysis are
hydrogen emissions (e.g., leakage, venting, and purging) from green hydrogen
production and consumption as well as both hydrogen and methane emissions
(e.g., leakage, venting, purging, and flaring) from blue hydrogen production and
consumption. We do not consider CO<inline-formula><mml:math id="M127" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> emissions from incomplete CCUS
technologies to retain simplicity and be conservative, but this would
increase the climate impacts of blue hydrogen consumption depending on the
efficiency and the permanence of storage. We also do not consider greenhouse
gas emissions from hydrogen infrastructure build-out.</p>
      <p id="d1e3154">For hydrogen emissions, there is a paucity of quantitative data addressing
in situ hydrogen leakage along the value chain, with empirical measurements to date
focused on safety concerns (i.e., large leaks), primarily in confined spaces
(Kobayashi et al., 2018). While there are many methods of hydrogen gas
sensing (e.g., optical, acoustic, thermal, and electrochemical) and several types
of sensors exist (Najjar, 2019), there are currently no commercially
available sensors that can detect hydrogen emissions at levels well below
the threshold for hydrogen gas flammability which is required to
characterize emissions in the open.</p>
      <p id="d1e3157">It is, however, very likely that hydrogen is emitted throughout the value
chain, but it is unclear – given lack of data – which components contribute most
and least to emissions. Research suggests that loss rates from electrolyzers
could be high, and (based on the first principles of moving a small gas molecule)
it is likely that transport of hydrogen is a major source (van Rujiven et
al., 2011; Cooper et al., 2022; Frazer-Nash Consultancy, 2022). Fluid dynamics theory
suggests that hydrogen can leak 1.3 to 3 times faster than methane (the main
component of natural gas) (Swain and Swain, 1992), although a recent study
focused on low-pressure distribution pipes suggested that small leaks of
methane and hydrogen may occur at similar rates if the path to leakage is
convoluted (Mejia et al., 2020). Previous work also suggests that liquified
hydrogen could have high emission rates from boil-off (Sherif et al., 1997).</p>
      <p id="d1e3160">Total value-chain emissions will ultimately depend on the configuration of
the pathway from production through to end use, and there can be very little confidence in any published estimates of
hydrogen emissions from a future hydrogen economy in the absence of empirical
data. Of the previous studies
that have made assumptions regarding the total hydrogen emissions for the purpose of
assessing environmental impacts from a potential hydrogen economy, estimates
range from 0.3 % to 20 % for minimum to maximum emissions (Schultz et
al., 2003; Tromp et al., 2003; Colella et al., 2005; Wuebbles et al., 2010;
van Ruijven et al., 2011; Bond et al., 2011; Cooper et al., 2022;
Frazer-Nash Consultancy, 2022). All studies acknowledge major uncertainty in
the estimates due to a lack of data, and several do not include all
components of the value chain (e.g., production, compression, storage, and
end-use applications). Some studies have made assumptions on total value-chain emissions citing these previous studies, typically using a range of 1 %
to 10 % (Prather, 2003; Derwent et al., 2001, 2020; Paulot et al., 2021;
Warwick et al., 2022). Therefore, we follow the published literature and
incorporate a hydrogen emission rate of 1 % (best case) to 10 %
(worst case) per amount of hydrogen consumed.</p>
      <p id="d1e3164">For blue hydrogen production, methane is needed as both a feedstock and a
heat source, and it can be emitted along the supply chain (upstream and
midstream) before it is used for producing hydrogen. The amount of methane
needed to produce a unit mass of hydrogen will depend on the composition of
the natural gas, the efficiency of the reformer, and how much is needed as
feedstock and fuel combined. The amount needed is not well documented in the
published literature and, based on public documents and private
communications, can range anywhere from 2.5 to 4.5 times the mass of hydrogen
(Budsberg et al., 2015; Thibault et al., 2020). In this
analysis, we use a central estimate that 3 times the mass of hydrogen is
needed in the form of methane. This value is on the lower end of all
estimates but in the middle with respect to published values; this makes methane
emission assumptions from blue hydrogen applications potentially
conservative.</p>
      <p id="d1e3167">For methane emission estimates (including venting, purging, and flaring)
upstream of hydrogen production, we use a range of 1 % (best case) to
3 % (worst case) per unit methane consumed. This is based on the latest
understanding of upstream natural gas leakage from oil and gas production as
well as the distribution of natural gas (Alvarez et al., 2018).</p>
      <p id="d1e3170">Table 2 shows the hydrogen and methane emissions used in this study for
best- and worst-case leak rates based on 1 kg of either green or blue
hydrogen deployed.</p>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T2"><?xmltex \currentcnt{2}?><label>Table 2</label><caption><p id="d1e3176">Hydrogen and methane emissions (in kg) for deploying 1 kg of
either green or blue hydrogen based on best- and worst-case leak rates. We
assume that 3 times the mass of hydrogen is needed in the form of methane for
using methane as a feedstock for hydrogen production (Budsberg et al., 2015;
Thibault et al., 2020).</p></caption><oasis:table frame="topbot"><?xmltex \begin{scaleboxenv}{.90}[.90]?><oasis:tgroup cols="4">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="left"/>
     <oasis:colspec colnum="3" colname="col3" align="right"/>
     <oasis:colspec colnum="4" colname="col4" align="right"/>
     <oasis:thead>
       <oasis:row>
         <oasis:entry namest="col1" nameend="col2"/>
         <oasis:entry colname="col3">Best-case leaks,</oasis:entry>
         <oasis:entry colname="col4">Worst-case leaks,</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3">H<inline-formula><mml:math id="M128" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> and CH<inline-formula><mml:math id="M129" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:math></inline-formula>: 1 %</oasis:entry>
         <oasis:entry colname="col4">H<inline-formula><mml:math id="M130" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula>: 10 %; CH<inline-formula><mml:math id="M131" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:math></inline-formula>: 3 %</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>
         <oasis:entry colname="col1">Hydrogen</oasis:entry>
         <oasis:entry colname="col2">Produced</oasis:entry>
         <oasis:entry colname="col3">1.01</oasis:entry>
         <oasis:entry colname="col4">1.11</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">(green and</oasis:entry>
         <oasis:entry colname="col2">Consumed</oasis:entry>
         <oasis:entry colname="col3">1</oasis:entry>
         <oasis:entry colname="col4">1</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">blue)</oasis:entry>
         <oasis:entry colname="col2">Emitted</oasis:entry>
         <oasis:entry colname="col3">0.01</oasis:entry>
         <oasis:entry colname="col4">0.11</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Methane</oasis:entry>
         <oasis:entry colname="col2">Produced</oasis:entry>
         <oasis:entry colname="col3">3.06</oasis:entry>
         <oasis:entry colname="col4">3.44</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">(blue only)</oasis:entry>
         <oasis:entry colname="col2">Consumed</oasis:entry>
         <oasis:entry colname="col3">3.03</oasis:entry>
         <oasis:entry colname="col4">3.33</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">Emitted</oasis:entry>
         <oasis:entry colname="col3">0.031</oasis:entry>
         <oasis:entry colname="col4">0.103</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup><?xmltex \end{scaleboxenv}?></oasis:table></table-wrap>

      <p id="d1e3349">For estimating absolute temperature responses to future hydrogen leakage, we
consider three levels of leakage (1 %, 5 %, and 10 %) and several levels of
hydrogen demand from the present-day level (around 100 Tg yr<inline-formula><mml:math id="M132" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>) to a
theoretical maximum projected for mid-century (around 3000 Tg yr<inline-formula><mml:math id="M133" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>).
Depending on the scenario and source, projections for future hydrogen demand
range from 100 to 210 Tg by 2030 and from 130 to 1370 by 2050 (Table 3). Of 21 published estimates for hydrogen demand in 2050, the average is 590 Tg
(median is 570 Tg). The theoretical maximum of using hydrogen to supply the
entire final energy demand in 2050 is determined based on the estimates of
hydrogen demand as a percent of the final energy demand provided by Hydrogen
Council (2017) and BloombergNEF (2020a), 3055 and 2900 Mt, respectively,
that are each for scenarios of a decarbonized world.</p>

<?xmltex \floatpos{p}?><table-wrap id="Ch1.T3" specific-use="star"><?xmltex \currentcnt{3}?><label>Table 3</label><caption><p id="d1e3380">Published estimates of hydrogen demand for various
scenarios.</p></caption><oasis:table frame="topbot"><?xmltex \begin{scaleboxenv}{.95}[.95]?><oasis:tgroup cols="4">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="right"/>
     <oasis:colspec colnum="3" colname="col3" align="left"/>
     <oasis:colspec colnum="4" colname="col4" align="left"/>
     <oasis:thead>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Year</oasis:entry>
         <oasis:entry colname="col2">Estimate (Tg)</oasis:entry>
         <oasis:entry colname="col3">Source</oasis:entry>
         <oasis:entry colname="col4">Scenario description</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">2018</oasis:entry>
         <oasis:entry colname="col2">115</oasis:entry>
         <oasis:entry colname="col3">Energy Transition Commission (2021)</oasis:entry>
         <oasis:entry colname="col4">Hydrogen demand</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">2018</oasis:entry>
         <oasis:entry colname="col2">115</oasis:entry>
         <oasis:entry colname="col3">International Energy Agency (2019)</oasis:entry>
         <oasis:entry colname="col4">Hydrogen demand</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">2019</oasis:entry>
         <oasis:entry colname="col2">120</oasis:entry>
         <oasis:entry colname="col3">International Renewable Energy Agency (2020)</oasis:entry>
         <oasis:entry colname="col4">Hydrogen production</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">2020</oasis:entry>
         <oasis:entry colname="col2">89</oasis:entry>
         <oasis:entry colname="col3">International Energy Agency (2022)</oasis:entry>
         <oasis:entry colname="col4">Hydrogen demand</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">2020</oasis:entry>
         <oasis:entry colname="col2">90</oasis:entry>
         <oasis:entry colname="col3">Hydrogen Council (2021b)</oasis:entry>
         <oasis:entry colname="col4">Hydrogen demand</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">2021</oasis:entry>
         <oasis:entry colname="col2">73</oasis:entry>
         <oasis:entry colname="col3">Yusaf et al. (2022)</oasis:entry>
         <oasis:entry colname="col4">Hydrogen production</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">2030</oasis:entry>
         <oasis:entry colname="col2">102</oasis:entry>
         <oasis:entry colname="col3">International Energy Agency (2021)</oasis:entry>
         <oasis:entry colname="col4">Hydrogen projects currently under development</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">2030</oasis:entry>
         <oasis:entry colname="col2">110</oasis:entry>
         <oasis:entry colname="col3">International Energy Agency (2021)</oasis:entry>
         <oasis:entry colname="col4">Announced Pledges Scenario</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">2030</oasis:entry>
         <oasis:entry colname="col2">140</oasis:entry>
         <oasis:entry colname="col3">Hydrogen Council (2021b)</oasis:entry>
         <oasis:entry colname="col4">Net-zero 1.5 <inline-formula><mml:math id="M134" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C compatible scenario</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">2030</oasis:entry>
         <oasis:entry colname="col2">205</oasis:entry>
         <oasis:entry colname="col3">International Energy Agency (2021)</oasis:entry>
         <oasis:entry colname="col4">Net-zero 1.5 <inline-formula><mml:math id="M135" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C compatible scenario; net-zero emissions by 2050</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">2030</oasis:entry>
         <oasis:entry colname="col2">211</oasis:entry>
         <oasis:entry colname="col3">International Energy Agency (2022)</oasis:entry>
         <oasis:entry colname="col4">Net-zero emissions by 2050 scenario</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">2040</oasis:entry>
         <oasis:entry colname="col2">385</oasis:entry>
         <oasis:entry colname="col3">Hydrogen Council (2021b)</oasis:entry>
         <oasis:entry colname="col4">Net-zero 1.5 <inline-formula><mml:math id="M136" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C compatible scenario</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">2050</oasis:entry>
         <oasis:entry colname="col2">130</oasis:entry>
         <oasis:entry colname="col3">Yusaf et al. (2022)</oasis:entry>
         <oasis:entry colname="col4">Current growth trend of 1.8 %</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">2050</oasis:entry>
         <oasis:entry colname="col2">162</oasis:entry>
         <oasis:entry colname="col3">Yusaf et al. (2022)</oasis:entry>
         <oasis:entry colname="col4">Average actual growth of 2.5 %</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">2050</oasis:entry>
         <oasis:entry colname="col2">187</oasis:entry>
         <oasis:entry colname="col3">BloombergNEF (2020a)</oasis:entry>
         <oasis:entry colname="col4">Weak hydrogen policy</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">2050</oasis:entry>
         <oasis:entry colname="col2">190</oasis:entry>
         <oasis:entry colname="col3">BloombergNEF (2021)</oasis:entry>
         <oasis:entry colname="col4">Blue hydrogen with little incentive to use hydrogen</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">2050</oasis:entry>
         <oasis:entry colname="col2">240</oasis:entry>
         <oasis:entry colname="col3">International Renewable Energy Agency (2020)</oasis:entry>
         <oasis:entry colname="col4">Transforming energy scenario</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">2050</oasis:entry>
         <oasis:entry colname="col2">255</oasis:entry>
         <oasis:entry colname="col3">International Energy Agency (2021)</oasis:entry>
         <oasis:entry colname="col4">Announced Pledges Scenario</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">2050</oasis:entry>
         <oasis:entry colname="col2">287</oasis:entry>
         <oasis:entry colname="col3">International Energy Agency (2019)</oasis:entry>
         <oasis:entry colname="col4">Sustainable Development Scenario</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">2050</oasis:entry>
         <oasis:entry colname="col2">520</oasis:entry>
         <oasis:entry colname="col3">International Energy Agency (2021)</oasis:entry>
         <oasis:entry colname="col4">Net-zero emissions by 2050</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">2050</oasis:entry>
         <oasis:entry colname="col2">539</oasis:entry>
         <oasis:entry colname="col3">Hydrogen Council (2017)</oasis:entry>
         <oasis:entry colname="col4">A 2 <inline-formula><mml:math id="M137" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C compatible scenario</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">2050</oasis:entry>
         <oasis:entry colname="col2">540</oasis:entry>
         <oasis:entry colname="col3">Energy Transition Commission (2021)</oasis:entry>
         <oasis:entry colname="col4">Supply-side decarbonization only, which</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3"/>
         <oasis:entry colname="col4">includes energy productivity improvements</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">2050</oasis:entry>
         <oasis:entry colname="col2">568</oasis:entry>
         <oasis:entry colname="col3">Yusaf et al. (2022)</oasis:entry>
         <oasis:entry colname="col4">Annual growth rate of 6.5%</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">2050</oasis:entry>
         <oasis:entry colname="col2">590</oasis:entry>
         <oasis:entry colname="col3">International Renewable Energy Agency (2020)</oasis:entry>
         <oasis:entry colname="col4">A 1.5 <inline-formula><mml:math id="M138" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C compatible scenario</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">2050</oasis:entry>
         <oasis:entry colname="col2">660</oasis:entry>
         <oasis:entry colname="col3">Hydrogen Council (2021b)</oasis:entry>
         <oasis:entry colname="col4">Net-zero 1.5 <inline-formula><mml:math id="M139" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C compatible scenario</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">2050</oasis:entry>
         <oasis:entry colname="col2">696</oasis:entry>
         <oasis:entry colname="col3">BloombergNEF (2020a)</oasis:entry>
         <oasis:entry colname="col4">Strong hydrogen policy</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">2050</oasis:entry>
         <oasis:entry colname="col2">728</oasis:entry>
         <oasis:entry colname="col3">Energy Transition Commission (2021)</oasis:entry>
         <oasis:entry colname="col4">All use cases materialize combined with</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3"/>
         <oasis:entry colname="col4">energy productivity improvements</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">2050</oasis:entry>
         <oasis:entry colname="col2">770</oasis:entry>
         <oasis:entry colname="col3">BloombergNEF (2021)</oasis:entry>
         <oasis:entry colname="col4">Net-zero emissions by 2050 with widespread use of</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3"/>
         <oasis:entry colname="col4">hydrogen, mostly from nuclear</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">2050</oasis:entry>
         <oasis:entry colname="col2">801</oasis:entry>
         <oasis:entry colname="col3">BloombergNEF (2020b)</oasis:entry>
         <oasis:entry colname="col4">A well below 2 <inline-formula><mml:math id="M140" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C scenario</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">2050</oasis:entry>
         <oasis:entry colname="col2">813</oasis:entry>
         <oasis:entry colname="col3">Energy Transition Commission (2021)</oasis:entry>
         <oasis:entry colname="col4">Supply-side decarbonization only</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">2050</oasis:entry>
         <oasis:entry colname="col2">1000</oasis:entry>
         <oasis:entry colname="col3">Energy Transition Commission (2021)</oasis:entry>
         <oasis:entry colname="col4">Maximum for hydrogen use by mid-century if all use cases</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3"/>
         <oasis:entry colname="col4">materialize for net-zero emissions</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">2050</oasis:entry>
         <oasis:entry colname="col2">1318</oasis:entry>
         <oasis:entry colname="col3">BloombergNEF (2021)</oasis:entry>
         <oasis:entry colname="col4">Net-zero emissions by 2050 and widespread use of hydrogen</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3"/>
         <oasis:entry colname="col4">produced from renewables</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">2050</oasis:entry>
         <oasis:entry colname="col2">1370</oasis:entry>
         <oasis:entry colname="col3">BloombergNEF (2020a)</oasis:entry>
         <oasis:entry colname="col4">All unlikely-to-electrify sectors in economy use hydrogen</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup><?xmltex \end{scaleboxenv}?></oasis:table></table-wrap>

</sec>
<sec id="Ch1.S2.SS3">
  <label>2.3</label><title>Emissions from fossil fuel technologies</title>
      <p id="d1e4050">To estimate the potential climate concern with respect to hydrogen technologies, we
compare the net climate impacts over time from green and blue hydrogen
relative to their fossil fuel counterparts based on the anticipated avoided
greenhouse gas emissions from the consumption of 1 kg of hydrogen
continuously each year. We consider emissions of both carbon dioxide and
methane. We do not include hydrogen emissions that would be avoided from the
cessation of the combustion of fossil fuels nor other co-emitted
climate pollutants such as particulates, sulfur dioxide, and nitrogen
oxides that contain a mix of warming and cooling forcers.</p>
      <p id="d1e4053">While the carbon dioxide and methane emissions avoided from the deployment of 1 kg of hydrogen will ultimately depend on the specific technology, as a first-order approximation we explore the impacts from a generic case in which a
variety of fossil fuel technologies are replaced. We use estimates from the
Hydrogen Council (2017) that quantify avoided carbon dioxide emissions from
a scenario of supplying 18 % of the final energy demand in 2050 with hydrogen
applications. They estimate that a consumption of 550 Mt
of hydrogen (roughly the same amount as the average of the 21 projections
published in the literature for year 2050; Table 3) can avoid 6 Gt
of carbon dioxide emissions annually. In their analysis, fossil-fuel-powered
end-use applications that are decarbonized by hydrogen alternatives include
segments of transport, industry energy use, building power and heating, and
as an industry feedstock. For transport, their vision includes hydrogen-powering hundreds of millions of cars, trucks, buses, passenger ships, and
locomotives, with hydrogen-based fuels powering a share of airplanes and
freight ships. For heat and power for buildings and industry, hydrogen could
provide around 10 % of the heat and power required for global households
and industry sectors. Of the avoided 6 Gt of CO<inline-formula><mml:math id="M141" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> annually from
this level of hydrogen deployment, around half is from hydrogen applications
in the transport sector, and one-third is from industry energy and
feedstocks. Using the scenario and calculations from Hydrogen Council (2017)
provides a central estimate of 11 kg CO<inline-formula><mml:math id="M142" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> avoided per 1 kg H<inline-formula><mml:math id="M143" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula>
consumed. While this estimate is for the year 2050, in the absence of better
estimates, we assume that it can generally apply to earlier decades as well.
However, to test the sensitivity of our results to different levels of
avoided CO<inline-formula><mml:math id="M144" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> (which arguably is of further importance for specific
technologies as opposed to different years), we consider three different
levels of avoided carbon dioxide emissions (5, 10, and 15 kg).</p>
      <p id="d1e4092">Furthermore, given that the Hydrogen Council (2017) analysis does not provide
avoided methane emissions associated with their hydrogen economy vision,
additional assumptions need to be made to include their impact on the net
radiative effect of fossil fuel applications vs. their hydrogen
alternatives. First, the methane avoided will depend on the specific fossil
fuel (e.g., coal, oil, or gas) used in the displaced fossil fuel technologies. For
example, a natural-gas-driven technology will likely emit more methane than
a coal-driven
technology due to emissions associated with natural gas
production and distribution. However, a natural-gas-driven technology will
also likely emit less CO<inline-formula><mml:math id="M145" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> than a coal-driven one because burning
natural gas emits less CO<inline-formula><mml:math id="M146" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> than coal. Therefore, for each level of
avoided carbon dioxide emissions in our sensitivity analysis, we also
calculate the resulting radiative impact from these emissions if the
CO<inline-formula><mml:math id="M147" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> is generated from burning natural gas (i.e., considerable methane
emissions). Burning 1 kg of natural gas emits 2.75 kg of CO<inline-formula><mml:math id="M148" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> if the
natural gas is almost entirely methane, and we consider methane leakage
rates from 1 % to 3 %, as discussed earlier. The resulting emissions of methane
are shown in Table 4.</p>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T4"><?xmltex \currentcnt{4}?><label>Table 4</label><caption><p id="d1e4135">Methane emissions (in kg) associated with different levels of
carbon dioxide emissions (in kg) from fossil fuel technologies and for best-
and worst-case leak rates. (Note: the values presented in the table have been rounded.)</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="5">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="left"/>
     <oasis:colspec colnum="3" colname="col3" align="left"/>
     <oasis:colspec colnum="4" colname="col4" align="right"/>
     <oasis:colspec colnum="5" colname="col5" align="right"/>
     <oasis:thead>
       <oasis:row>

         <oasis:entry namest="col1" nameend="col3">Methane emissions </oasis:entry>

         <oasis:entry colname="col4">Best-case</oasis:entry>

         <oasis:entry colname="col5">Worst-case</oasis:entry>

       </oasis:row>
       <oasis:row rowsep="1">

         <oasis:entry colname="col1"/>

         <oasis:entry colname="col2"/>

         <oasis:entry colname="col3"/>

         <oasis:entry colname="col4">leaks: 1 %</oasis:entry>

         <oasis:entry colname="col5">leaks: 3 %</oasis:entry>

       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>

         <oasis:entry colname="col1"/>

         <oasis:entry rowsep="1" colname="col2" morerows="2" align="right">5</oasis:entry>

         <oasis:entry colname="col3">Produced</oasis:entry>

         <oasis:entry colname="col4">1.84</oasis:entry>

         <oasis:entry colname="col5">1.87</oasis:entry>

       </oasis:row>
       <oasis:row>

         <oasis:entry colname="col1"/>

         <oasis:entry colname="col3">Consumed</oasis:entry>

         <oasis:entry colname="col4">1.8</oasis:entry>

         <oasis:entry colname="col5">1.8</oasis:entry>

       </oasis:row>
       <oasis:row>

         <oasis:entry colname="col1"/>

         <oasis:entry rowsep="1" colname="col3">Emitted</oasis:entry>

         <oasis:entry rowsep="1" colname="col4">0.02</oasis:entry>

         <oasis:entry rowsep="1" colname="col5">0.06</oasis:entry>

       </oasis:row>
       <oasis:row>

         <oasis:entry colname="col1">Carbon dioxide</oasis:entry>

         <oasis:entry rowsep="1" colname="col2" morerows="2" align="right">10</oasis:entry>

         <oasis:entry colname="col3">Produced</oasis:entry>

         <oasis:entry colname="col4">3.67</oasis:entry>

         <oasis:entry colname="col5">3.75</oasis:entry>

       </oasis:row>
       <oasis:row>

         <oasis:entry colname="col1">emissions</oasis:entry>

         <oasis:entry colname="col3">Consumed</oasis:entry>

         <oasis:entry colname="col4">3.6</oasis:entry>

         <oasis:entry colname="col5">3.6</oasis:entry>

       </oasis:row>
       <oasis:row>

         <oasis:entry colname="col1"/>

         <oasis:entry rowsep="1" colname="col3">Emitted</oasis:entry>

         <oasis:entry rowsep="1" colname="col4">0.04</oasis:entry>

         <oasis:entry rowsep="1" colname="col5">0.11</oasis:entry>

       </oasis:row>
       <oasis:row>

         <oasis:entry colname="col1"/>

         <oasis:entry colname="col2" morerows="2" align="right">15</oasis:entry>

         <oasis:entry colname="col3">Produced</oasis:entry>

         <oasis:entry colname="col4">5.51</oasis:entry>

         <oasis:entry colname="col5">5.62</oasis:entry>

       </oasis:row>
       <oasis:row>

         <oasis:entry colname="col1"/>

         <oasis:entry colname="col3">Consumed</oasis:entry>

         <oasis:entry colname="col4">5.5</oasis:entry>

         <oasis:entry colname="col5">5.5</oasis:entry>

       </oasis:row>
       <oasis:row>

         <oasis:entry colname="col1"/>

         <oasis:entry colname="col3">Emitted</oasis:entry>

         <oasis:entry colname="col4">0.06</oasis:entry>

         <oasis:entry colname="col5">0.17</oasis:entry>

       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

<?xmltex \hack{\newpage}?>
</sec>
</sec>
<sec id="Ch1.S3">
  <label>3</label><title>Results</title>
<sec id="Ch1.S3.SS1">
  <label>3.1</label><title>Hydrogen's warming potency</title>
      <p id="d1e4343">Global warming potential has become the most familiar metric for grasping
the importance of a climate forcer as an agent of climate change. Hydrogen's
GWP has been reported for decades, although only with respect to its tropospheric effects
and for a 100-year time horizon (thereby including numerous decades when
hydrogen is not influencing the atmosphere) (Derwent et al., 2001, 2006,
2020; Derwent, 2018). This has led to an undervaluing of its impact. Recent
research has reported hydrogen's GWP for both tropospheric and stratospheric
effects and for both 20- and 100-year timeframes, revealing that hydrogen's
100-year GWP is twice as high as previously thought, and its 20-year GWP is
3 times higher than its 100-year GWP (Warwick et al., 2022). Fig. 3a
extends this work to calculate hydrogen's GWP over time.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F3" specific-use="star"><?xmltex \currentcnt{3}?><?xmltex \def\figurename{Figure}?><label>Figure 3</label><caption><p id="d1e4348">Warming potency of hydrogen relative to carbon dioxide
using cumulative radiative forcing as a proxy for <bold>(a)</bold> a one-time pulse of
equal emissions in mass (equals hydrogen's global warming potential) and <bold>(b)</bold>
a constant emission rate of both hydrogen and carbon dioxide for equal
emissions in mass. The solid lines represent the mean hydrogen lifetime and radiative
effects, the dark shaded areas correspond to a minimum and maximum hydrogen
lifetime based on soil sink uncertainty, and the light shaded areas
represent 20 % uncertainty in the radiative effects of hydrogen from its
indirect effects and uncertainties in carbon dioxide's radiative
properties. See Table 1 for all parameters used.</p></caption>
          <?xmltex \igopts{width=426.791339pt}?><graphic xlink:href="https://acp.copernicus.org/articles/22/9349/2022/acp-22-9349-2022-f03.png"/>

        </fig>

      <p id="d1e4363">Hydrogen's maximum GWP occurs around 7 years after the initial pulse of
emissions, with a range of 25 to 60 based on uncertainties, and a central
estimate of 40. This is around 8 times higher than the most well-known
GWP for hydrogen (Derwent et al., 2020). Hydrogen's GWP initially increases
before it declines again, as it takes several years for methane's
atmospheric lifetime to increase in response to less OH being available from the
reaction with hydrogen. For time horizons of 10 to 100 years, GWP
decreases, which is expected when the warming effects of a pulse of emissions
from a short-term forcer are compared to those of a long-term forcer; the
CO<inline-formula><mml:math id="M149" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> is still in the atmosphere 100 years later, whereas the short-term
forcer's impacts are long gone – meaning that the relative potency of the
short-term forcer declines. In fact, the factor of 3 difference between
hydrogen's GWP-20 (central estimate of 33) and GWP-100 (central estimate of 11) is
similar in ratio to that from methane (80 and 30, respectively; Forster et al., 2021).</p>
      <p id="d1e4376">In Fig. 3b, we use an identical GWP calculation except that a constant
emission rate is considered, rather than pulse emissions. The constant-emission-rate
approach is a more realistic representation of hydrogen leakage in a
hydrogen economy, as opposed to a one-time pulse of emissions, and is also more
sensible in that one is calculating hydrogen's warming effects compared with
carbon dioxide for cases where they are both impacting the atmosphere in
each time horizon.</p>
      <p id="d1e4379">When continuous equal emissions of both hydrogen and carbon dioxide are
considered, as opposed to just one pulse at time <inline-formula><mml:math id="M150" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 0, the potency of
hydrogen relative to carbon dioxide can be 50 % higher than that of the
pulse approach. However, this is not uniform across all timescales. In fact,
before 10 years, the pulse approach (GWP) yields higher potency values than
the constant-emission-rate approach. This is because the carbon dioxide
impact builds up more quickly in the near term for constant emissions
compared with the hydrogen impact, as the hydrogen impact takes several
years to reach its full impact. However, as time goes on, the replenishing
effect of constant hydrogen emissions (as opposed to decaying impacts)
dominates and leads to a greater relative potency compared with the pulse
approach. For hydrogen's GWP-20, constant emissions lead to around a 15 %
increase in hydrogen's potency; this increases to 50 % by a time horizon
of around 70 years and to almost 60 % by a time horizon of 100 years.</p>
</sec>
<sec id="Ch1.S3.SS2">
  <label>3.2</label><title>Warming impacts from replacing fossil fuel technologies with hydrogen
alternatives</title>
      <p id="d1e4397">The results of our analysis of the climate impacts of hydrogen and methane
emissions are shown in Fig. 4. If there were zero climate forcer emissions
from the hydrogen applications, the result would be a <inline-formula><mml:math id="M151" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">100</mml:mn></mml:mrow></mml:math></inline-formula> % change in
cumulative radiative forcing; moreover, if there was no replacement, the result
would be 0 %. If the climate forcer emissions from hydrogen alternatives
yield more (less) warming than their fossil fuel counterparts over a
particular time period, it would amount to a positive (negative) percent
change in cumulative radiative forcing.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F4" specific-use="star"><?xmltex \currentcnt{4}?><?xmltex \def\figurename{Figure}?><label>Figure 4</label><caption><p id="d1e4412">Relative warming impact over time from replacing fossil
fuel technologies with green or blue hydrogen alternatives for a generic
case. A cumulative radiative forcing ratio for annually deploying 1 kg of H<inline-formula><mml:math id="M152" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> vs. annually avoided fossil fuel emissions is used as a proxy for relative warming impacts. Emissions from hydrogen alternatives are hydrogen for green
hydrogen and hydrogen and methane for blue hydrogen. Emissions from fossil
fuel technologies are carbon dioxide, estimated at 11 kg CO<inline-formula><mml:math id="M153" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> avoided
per 1 kg H<inline-formula><mml:math id="M154" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> deployed, based on estimates from Hydrogen Council (2017).
Emissions of hydrogen and methane include a range of plausible leak rates
from 1 % (best case) to 10 % (worst case) per unit H<inline-formula><mml:math id="M155" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> deployed for
hydrogen and from 1 % (best case) to 3 % (worst case) for methane. The
height of each bar corresponds to the range of leakage. See Table 2 for the
emission inputs for hydrogen and methane; Eqs. (1)–(8) and Table 1
for equations used in the calculation and input parameters, respectively; and Sects. 2.2 and 2.3 for more details on
emission assumptions. Error bars represent uncertainties in both hydrogen's soil
sink and lifetime (solid lines) as well as uncertainties in the radiative effects of
hydrogen and carbon dioxide (<inline-formula><mml:math id="M156" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mo>±</mml:mo></mml:mrow></mml:math></inline-formula> 20 %; dashed lines). The corresponding GWP results (only difference is pulse
emissions rather than constant emission rate) are shown using the “x” and
“o” markers.</p></caption>
          <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://acp.copernicus.org/articles/22/9349/2022/acp-22-9349-2022-f04.jpg"/>

        </fig>

      <p id="d1e4469">Overall, any amount of hydrogen leakage will diminish the climate benefits
of avoided carbon dioxide emissions to some degree, but there are vastly
different outcomes – favorable and unfavorable – depending on the
production method, total emissions, and time horizon. For example, the
worst case for blue hydrogen (10 % hydrogen leakage and 3 % methane
leakage) could initially be worse for the climate than the CO<inline-formula><mml:math id="M157" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula>
emissions from the corresponding fossil fuel technologies, yielding up to
60 % more warming over the first 10 years and taking around 50 years
before the benefits of the technology switch are realized. On the other hand,
the best case for green hydrogen (1 % hydrogen leaks) could yield a near
elimination of the climate impact compared with fossil fuel's CO<inline-formula><mml:math id="M158" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula>
emissions. Recall, however, that we do not include greenhouse gas emissions
associated with installing the infrastructure that will be needed to support
the growing demand for hydrogen and its applications.</p>
      <p id="d1e4491">The importance of the clean hydrogen production method – i.e., green
(renewable electricity with water) or blue (steam methane reforming with
CCUS) – in determining the magnitude of climate benefits is clear (Fig. 4).
While hydrogen emissions can yield climate impacts for green hydrogen that
are far from climate neutral over all timescales, the cumulative radiative
impact is still less than that from fossil fuels; this signifies a decrease in
warming from using green hydrogen alternatives. On the other hand, blue
hydrogen can be better or worse for the climate depending on the leakage
rate and time horizon. For example, over a 10-year time period, worst-case
blue hydrogen emissions could increase the warming impact from fossil fuels
by 40 % [25, 60], whereas worst-case green hydrogen emissions could
decrease warming by 60 % [43, 76]. For best-case leak rates for both, blue
hydrogen could still only reduce the warming impact from fossil fuels by
65 % over the first 10 years, whereas green hydrogen could reduce the
impact by more than 95 %. For a 100-year time horizon, the story is
similar, with worst-case leak rates yielding a doubling of the climate
impact of blue hydrogen compared with green hydrogen. In fact, the worst-case
green hydrogen benefits are roughly the same as the best-case blue hydrogen
benefits across all timescales (such as a <inline-formula><mml:math id="M159" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 65 % decrease in the
warming impact from fossil fuel CO<inline-formula><mml:math id="M160" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> emissions over a 10-year period and
an 85 % decrease over a 100-year period). Given that the hydrogen
emissions are the same in both the blue and green cases, the difference is
due entirely to the warming effects of methane emissions from the natural
gas supply chain.</p>
      <p id="d1e4510">While the production method matters greatly, so does the level of emissions. For
example, how beneficial green hydrogen is to the climate in both the near
and long term will depend strongly on the level of leakage, with benefits
ranging from more than a 95 % reduction in climate impacts from fossil
fuel technologies to only 65 % over the first 10 years for total leakage
rates of 1 % and 10 %, respectively. Even in the long term (100-year time
horizon), green hydrogen may only reduce climate impacts by 85 % if there
is high leakage. The impact of leakage levels is also apparent for blue
hydrogen, where high leak rates for both hydrogen and methane could lead to
an increase in warming relative to their fossil fuel counterparts for decades,
but the low leak rates for both could cut climate impacts by more than half
within 10 years. In the longer term (over 100 years), both the worst- and
best-case leak rates for blue hydrogen would likely yield reductions in the
climate impacts; however, the magnitude of the benefits ranges from a 45 % to a
85 % reduction, respectively. These results show the importance of the
emission rate in determining the climate benefits (and potential
disbenefits) of replacing fossil fuel technologies with hydrogen
alternatives.</p>
      <p id="d1e4513">Whereas most assessments of the climate benefits of alternative technologies
inherently focus on the long-term impacts due to use of the GWP-100 metric,
our analysis shows how different the picture looks when considering time
horizons from 10 to 100 years. This is because, unlike carbon dioxide,
the warming effects of hydrogen (and methane) are short-lived and do not
accumulate over time. Therefore, the benefits of hydrogen applications grow
larger over time due to the prevention of the build-up of carbon dioxide in
the atmosphere. If only a long-term perspective is pursued when evaluating
hydrogen applications, the results will not convey the much larger relative
climate impacts over shorter time horizons. For example, for the first few
decades, the worst-case green hydrogen scenario may only halve the warming impacts
of the fossil fuel applications that it is replacing, but the
warming impacts could be reduced by three-quarters over 100 years. For blue hydrogen, the
temporal significance is even more stark due to the combination of emissions
of two short-term forcers. For example, the worst-case blue hydrogen
alternatives could increase warming relative to fossil fuel technologies for
the first several decades, but they would cut the warming impact
by nearly half over 100 years. Therefore, depending on the time horizon that is considered
in the analysis, one could receive very different insights into the climate
benefits of the decarbonization potential of hydrogen.</p>
      <p id="d1e4516">This is even more acute if the GWP metric with a pulse approach is used, as
opposed to a constant emission rate. While we consider
constant emissions in our analysis, Fig. 4 shows the corresponding result if a pulse
approach is used (see the “x” and “o” markers). While the pulse approach reasonably
captures the near-term impacts of hydrogen applications relative to those of
fossil fuels, it diverges over time and ultimately undervalues the
cumulative radiative forcing. For example, the worst-case blue hydrogen alternative could
yield a decrease in warming of only 45 % even after 100 years of replacing
fossil fuel technologies, but GWP-100 suggests a decrease in warming of
65 %. Moreover, if GWP-100 is used exclusively and taken to represent hydrogen's
impacts over any timescale (as it often is), the near- and middle-term
impacts of hydrogen (and methane) leakage will be overlooked entirely –
which, in some cases, means assuming a benefit to the climate when it is
actually a disbenefit for decades.</p>
      <p id="d1e4519">In the above, we considered a generic case for avoiding carbon dioxide
emissions from fossil fuel technologies. However, the perceived climate
benefits of hydrogen alternatives will depend on the amount of CO<inline-formula><mml:math id="M161" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula>
avoided, which will vary depending on the technology that is replaced.
Therefore, to test the sensitivity of our results to the amount of CO<inline-formula><mml:math id="M162" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula>
avoided, we consider avoided emissions of 5, 10, and 15 kg per 1 kg of
hydrogen deployed (compared with our central estimate of 11 kg) and compare
the relative climate impacts of the hydrogen applications over a 20-year
time horizon (solid bars in Fig. 5). We find that blue hydrogen could yield more than a 150 % increase in warming over the first 20 years if avoided emissions of CO<inline-formula><mml:math id="M163" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> are on the lower end and if leak rates from hydrogen and methane are at the upper end, whereas green hydrogen may only reduce warming by 20 %. However, if
avoided emissions of CO<inline-formula><mml:math id="M164" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> are on the higher end, both the worst-case blue
and green hydrogen alternatives would yield climate benefits, reducing warming by 10 % and
75 %, respectively.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F5" specific-use="star"><?xmltex \currentcnt{5}?><?xmltex \def\figurename{Figure}?><label>Figure 5</label><caption><p id="d1e4561">Relative warming impact over time from replacing fossil
fuel technologies with green or blue hydrogen alternatives for different
levels of avoided carbon dioxide and methane emissions. A cumulative radiative forcing ratio for annually deploying 1 kg of
H<inline-formula><mml:math id="M165" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> vs. annually avoided fossil fuel emissions is used as a proxy for relative warming impacts.
Emissions from hydrogen alternatives are hydrogen for green hydrogen and
hydrogen and methane for blue hydrogen. Emissions from fossil fuel
technologies are carbon dioxide and methane. Emissions of hydrogen and
methane include a range of plausible leak rates from 1 % (best case) to
10 % (worst case) per unit H<inline-formula><mml:math id="M166" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> deployed for hydrogen and from 1 %
(best case) to 3 % (worst case) for methane. The height of each bar
corresponds to the range of leakage. See Table 2 for emission inputs for
hydrogen and methane from hydrogen applications, Table 4 for emissions of
methane from fossil fuel technologies, and Eqs. (1)–(8) and Table 1 for
the equations used in the calculation and the input parameters, respectively.</p></caption>
          <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://acp.copernicus.org/articles/22/9349/2022/acp-22-9349-2022-f05.png"/>

        </fig>

      <p id="d1e4588">Given that methane emissions may also be avoided by replacing fossil fuel
technologies, we extend the analysis to consider a case where the
fossil fuel that was burned to produce the CO<inline-formula><mml:math id="M167" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> was natural gas
(hatched bars in Fig. 5), using the same best- and worst-case methane leak rates
as in the hydrogen applications. We find that the avoided methane emissions
may play a significant role in increasing the near-term benefits of hydrogen
applications, but there is a strong dependence on the corresponding CO<inline-formula><mml:math id="M168" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula>
emissions that are avoided. For example, while the worst-case blue hydrogen alternative with
the lower-end avoided CO<inline-formula><mml:math id="M169" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> values would still be worse for the climate over the
first 20 years, even when including avoided methane, the central estimate of
avoided CO<inline-formula><mml:math id="M170" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> would switch from worse for the climate to better for
the climate. For the worst-case green hydrogen alternative, climate benefits would double
for all levels of avoided CO<inline-formula><mml:math id="M171" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> when including avoided methane emissions.
However, given that natural gas emits less CO<inline-formula><mml:math id="M172" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> when burned than coal,
it is likely that CO<inline-formula><mml:math id="M173" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> emissions would be
lower if methane emissions were higher, as opposed to both being on the higher end. Therefore, a case-by-case
study with reported data on both carbon dioxide and methane emissions from
fossil fuel technologies is warranted to fully understand the impact of
avoided methane emissions.</p>
</sec>
<sec id="Ch1.S3.SS3">
  <label>3.3</label><title>Absolute warming impacts due to hydrogen emissions</title>
      <p id="d1e4663">We find that the present-day hydrogen demand
(around 100 Tg) may cause at most 0.01 <inline-formula><mml:math id="M174" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C warming for all levels of hydrogen emissions. For 2030
projections, five estimates based on different scenarios and sources suggest
an average hydrogen demand of 150 Tg (see Table 3), which could double the
100 Tg impact for upper-end leak rates (10 %) and uncertainties (0.02 <inline-formula><mml:math id="M175" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C). For 2050 projections, 21 different estimates suggest a
range in demand from 130 to 1370 Tg (Table 3), with an average of 590 Tg.
For the worst-case hydrogen leak rates (10 %), these levels of demand could
yield anywhere from 0.01 <inline-formula><mml:math id="M176" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C to 0.1 <inline-formula><mml:math id="M177" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.05 <inline-formula><mml:math id="M178" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C warming. On the other hand, if total hydrogen emissions are kept
minimal (1 %), temperature responses could be less than 0.02 <inline-formula><mml:math id="M179" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C including uncertainties. For context, a 590 Tg hydrogen
demand could supply around 20 % of the final global energy demand in 2050
under a 2 <inline-formula><mml:math id="M180" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C scenario (Hydrogen Council, 2017;
BloombergNEF, 2020a).</p>
      <p id="d1e4728">Figure 6 shows the long-term temperature responses to various hydrogen demand
levels, up to a theoretical maximum of 3000 Tg estimated for 2050 (which
would correspond to using hydrogen for the total final energy demand in a 2 <inline-formula><mml:math id="M181" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C decarbonization scenario). Using hydrogen for the total final
energy demand in 2050 could lead to greater than 0.1 <inline-formula><mml:math id="M182" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C
warming with a 5 % leak rate and up to 0.4 <inline-formula><mml:math id="M183" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C warming
with 10 % leak rates and uncertainties in hydrogen's radiative effects.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F6"><?xmltex \currentcnt{6}?><?xmltex \def\figurename{Figure}?><label>Figure 6</label><caption><p id="d1e4760">Long-term temperature responses (in <inline-formula><mml:math id="M184" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C) to different
levels of hydrogen leakage based on sustained hydrogen demand levels (in Tg).
The red, orange, and yellow markers and shading represent leakage levels of
10 %, 5 %, and 1 %, respectively. Uncertainty is based on uncertainties in both hydrogen's soil
sink and, therefore, lifetime (<inline-formula><mml:math id="M185" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mo>±</mml:mo></mml:mrow></mml:math></inline-formula> 20 %) as well as
uncertainties in hydrogen's radiative effects (<inline-formula><mml:math id="M186" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mo>±</mml:mo></mml:mrow></mml:math></inline-formula> 20 %). Markers indicate calculations, and shaded regions represent
interpolation. The histogram and shaded gray area characterize projections of
hydrogen demand for the year 2050 in the published literature (see Table 3).
The theoretical max is an estimate based on using hydrogen to supply the total
final energy demand globally in 2050 based on decarbonization scenarios.</p></caption>
          <?xmltex \igopts{width=236.157874pt}?><graphic xlink:href="https://acp.copernicus.org/articles/22/9349/2022/acp-22-9349-2022-f06.png"/>

        </fig>

      <p id="d1e4803">However, this level of hydrogen demand is not realistic. Of the available
projections in the literature for hydrogen demand in 2050, 4 suggest
values between 100 and 199 Tg, 3 suggest values between 200 and 499 Tg, 11 suggest values between 500 and 999 Tg, and 3 suggest values
between 1000 and 1999 Tg (Table 3). None project hydrogen demands below 100
or above 2000. Sustained hydrogen demands around 800 Tg or greater (which could
account for around a quarter of the final energy demand in 2050) could
contribute at least 0.1 <inline-formula><mml:math id="M187" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C of warming if leak rates and
uncertainties are at the upper end. For context, this amount of warming
could offset the avoided warming in 2050 from deploying all cost-effective
options to mitigate methane emissions globally over the next decade, which
otherwise could have slowed down global-mean warming rates by up to 15 %
(Ocko et al., 2021), or the avoided warming anticipated from the phasing out
of hydrofluorocarbons (Xu et al., 2013). This amount of warming
(<inline-formula><mml:math id="M188" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">0.1</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M189" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C) is also equal to the amount of warming
projected in 2100 from carbon dioxide emissions from international shipping
and aviation combined in the absence of climate action (Ivanovich et al.,
2019). However, if leakage does not exceed 1 %, the temperature response
could be an order of magnitude smaller.</p>
</sec>
</sec>
<sec id="Ch1.S4">
  <label>4</label><title>Discussion</title>
      <p id="d1e4843">The purpose of our study is to improve understanding of the role of hydrogen
leakage in undermining the climate benefits of the deployment of clean
hydrogen alternatives to replace fossil fuel technologies. We evaluated
hydrogen's climate consequences in three ways: its warming potency relative
to carbon dioxide, the warming impact of its leakage compared with that from
the avoided emissions of fossil fuel technologies, and the absolute
warming impacts from future levels of demand and leakage.</p>
      <p id="d1e4846">We found that hydrogen's warming potency strongly depends on the time horizon
and (similar to methane) can be at least 3 times more potent in the
near term than in the long term relative to carbon dioxide when using the
traditional GWP framework with pulses of equal emissions. If a constant
emission rate is used in the calculations instead, hydrogen's warming
potency may be 50 % higher for time horizons of several decades or
longer. When assessing the relative climate impacts of replacing fossil
fuel technologies with their hydrogen alternatives (based on a unit of clean
H<inline-formula><mml:math id="M190" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> deployed relative to the avoided CO<inline-formula><mml:math id="M191" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> emissions for a generic
case), we found that there are vastly different climate outcomes depending
on emission rates, time horizons, and production method. For example, blue
hydrogen with high hydrogen and methane emissions (a 10 % and 3 % emission
rate, respectively) can be worse for the climate for decades compared with fossil fuel
technologies, but green hydrogen with low hydrogen emissions
(1 %) can nearly eliminate climate impacts from its fossil fuel counterparts
over all timescales. On the other hand, the best-case blue hydrogen alternative (1 % for
both hydrogen and methane) can show roughly the same climate benefits as the
worst-case green hydrogen alternative (10 % emissions) – far from climate neutral but
still halving the impacts of its fossil fuel counterparts within a decade.
However, the perceived benefits of clean hydrogen alternatives compared with fossil
fuel technologies will depend on how much carbon dioxide and methane are
avoided, which needs to be assessed on a case-by-case basis with reliable
emission data. Finally, we found that a level of hydrogen demand around 800
Tg or above (which could account for around a quarter of the final energy demand
in 2050) could contribute at least 0.1 <inline-formula><mml:math id="M192" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C of warming with
high hydrogen leakage (10 %) and upper-bound uncertainties in hydrogen's
radiative properties.</p>
      <p id="d1e4876">Our findings add to recent research that has revealed that the warming
impacts of hydrogen emissions are higher than previously recognized (Paulot
et al., 2021; Warwick et al., 2022) and has explored the implications that this has
for the potential of hydrogen as a decarbonization strategy in the near and
long term. For example, for the first time,
when evaluating the climate change mitigation potential of clean
hydrogen alternatives, we show a strong dependence of the climate change mitigation potential on timescale. This is because hydrogen's warming effects are most
powerful in the 1–2 decades after hydrogen is released. While short-term
climate warming impacts – followed by long-term climate change mitigation
impacts – may lead to an eventual beneficial outcome, short-term
warming may lead to climate impacts that cause more socioeconomic and
environmental damage in the near term and that are not necessarily reversible
(Fischer et al., 2021). This could strongly affect the choice of whether or
not to deploy hydrogen in applications that have multiple “clean” options.
Moreover, if GWP-100 is exclusively relied upon, the near- and medium-term warming
power of hydrogen is masked; therefore, the anticipated climate benefits
of deploying hydrogen are perceived to be much higher over the next few
decades than in reality. However, we find that the dual approach of using both
GWP-20 and GWP-100 adequately captures the climate impacts of hydrogen over
all timescales and, therefore, is a straightforward way to effectively
understand temporal trade-offs across hydrogen deployment opportunities.</p>
      <p id="d1e4879">Taken together, our findings and the findings of previous studies make it
clear that hydrogen emissions (e.g., leakage, venting, and purging) matter for the
climate. Moreover, given that hydrogen is a very small molecule that is hard to
contain, it can easily escape from infrastructure. A new network of
production facilities, pipes, storage tanks, and hydrogen-powered homes and
vehicles could create a vast potential for hydrogen to leak. Furthermore, moving
hydrogen through existing natural gas systems that are already shown to leak
significant amounts of methane is even more problematic. However, the total
amount of leakage in current hydrogen systems remains unknown, with the
analytical capacity to accurately measure small levels of leakage in situ being largely
unavailable. The lessons learned from extensive measurements of natural gas
value-chain leaks over the last decade (similar infrastructure but larger
molecule) have shown that leakage rates are far higher than expected
(Alvarez et al., 2018). While hydrogen is arguably a more valuable product
than natural gas, given the current cost of producing it, the lack of
empirical measurements cannot confirm any assumptions regarding the
influence of the cost of lost product on leakage rates, especially if there
is no regulatory enforcement. Without measurements of hydrogen leakage and,
in turn, knowledge of strategies to mitigate leakage and deploy best
practices, we risk developing leaky systems that could significantly
contribute to climate change in the near to medium term. Thus, more attention is needed to measure and minimize hydrogen leakage as hydrogen
efforts are ramped up.</p>
      <p id="d1e4883">Beyond needing accurate measurements of hydrogen emissions, more work is
needed to improve understanding of hydrogen's atmospheric impacts. This is
because far less work has gone into refining hydrogen's radiative effects
compared with gases such as methane and carbon dioxide. There is a need for
more integrated chemistry–climate modeling to build confidence in and
refine the tropospheric and stratospheric radiative effects of hydrogen
emissions. This is especially true with respect to gaining a better understanding
of the climate impacts in the first couple of decades after hydrogen is
emitted to the atmosphere, given the complex temporal dynamics of hydrogen's
indirect effects; to date, there is only one study that explores these
near-term effects (Warwick et al., 2022). Chemistry–climate modeling is
further required to (1) understand the net effects when including
co-emissions from hydrogen and fossil fuel technologies (such as sulfur
dioxide, black and organic carbon, nitrogen oxides, and carbon monoxide),
(2) estimate climate responses to hydrogen emissions beyond forcings (such
as global surface air temperature), and (3) assess how changing
concentrations of other atmospheric constituents may affect hydrogen's
potency (such as changing concentrations of methane resulting from reduced
emissions in response to aggressive policies to address climate goals). For
example, all else equal, hydrogen emissions will lead to an increase in
other greenhouse gases. However, a new study has shown that reductions in
the emissions of carbon monoxide, nitrogen oxides, and volatile organic carbon
can lead to a smaller increase in methane's lifetime from hydrogen, as
more OH is available, and a net decrease in tropospheric ozone (Warwick et
al., 2022). These complexities and interactions will need to be explored in
assessing the climate effects of decarbonization strategies.</p>
      <p id="d1e4886">Climate benefits of clean hydrogen alternatives to fossil fuel technologies
also need to be assessed on a case-by-case basis, given (1) the dependency
of the leak rate on the production method, value-chain pathway (i.e.,
compression, storage, and distribution), and end-use application, and (2) the
dependency of the benefits on the avoided greenhouse gas emissions which, in
turn, depends on the pathway, application, fuel, and location. While
analysis of a generic hydrogen deployment case is valuable for first-order
insights, decisions will ultimately need to be made based on implications
for specific technological shifts. For example, if the hydrogen is burned in
the stratosphere (e.g., from aircraft), the direct combustion of
hydrogen could also increase stratospheric water vapor.</p>
      <p id="d1e4889">Furthermore, there are additional climate and other environmental concerns
associated with the deployment of hydrogen that need to be better understood
quantitatively. These include the diversion of renewably produced
electricity to produce green hydrogen when a potentially more effective
decarbonization pathway would be to use the renewable electricity directly
to offset fossil fuel use (Ueckerdt et al., 2021); emissions of nitrogen
oxides from combusting hydrogen, which is a health concern for local
communities (Lewis, 2021); local water availability for green hydrogen
production (Beswick et al., 2021; Simoes et al., 2021); and CCUS efficiency
and permanence for blue hydrogen (Saadat and Gersen, 2021).</p>
</sec>
<sec id="Ch1.S5" sec-type="conclusions">
  <label>5</label><title>Conclusions</title>
      <p id="d1e4901">Around the world, industry and policymakers are enthusiastic about clean
hydrogen's potential as an alternative to conventional fossil fuels, as it can conceivably
greatly reduce greenhouse gas emissions. Billions (USD) in new investments and
financial subsidies are being proposed to speed its adoption. Nevertheless, hydrogen
itself has significant climate impacts that are both widely overlooked and
underestimated, and it is a very small molecule that can easily leak into
the atmosphere from infrastructure.</p>
      <p id="d1e4904">In this study, we evaluate the climate consequences, across all timescales, of
deploying clean hydrogen given a range of plausible leak rates. Our results
indicate that hydrogen emissions can considerably undermine the climate
benefits of decarbonization strategies that involve clean hydrogen –
especially in the decades immediately following deployment. Therefore, this issue deserves more attention, both with respect to advancing the science of
hydrogen's indirect climate effects and regarding the improvement of estimates of hydrogen
emissions throughout the value chain. Minimizing leakage will be essential
to the effectiveness of hydrogen as a climate change mitigation strategy.
Furthermore, given that it may be possible to prevent leakage in some
applications and it is easier to address and minimize hydrogen leakage when
designing a system vs. retrofitting one, we have the rare opportunity to
get ahead of this issue before the infrastructure and systems are widely
deployed.</p>
      <p id="d1e4907">Our results suggest that five key actions can help minimize hydrogen's
warming effects and, therefore, maximize climate benefits in a future hydrogen
economy:
<list list-type="order"><list-item>
      <p id="d1e4912">advance research of hydrogen's indirect radiative effects and temperature
responses to hydrogen emissions by incorporating interactive emissions,
chemistry, and radiation parametrizations in further coupled
chemistry–climate models as well as reduced-complexity climate models;</p></list-item><list-item>
      <p id="d1e4916">employ climate metrics and/or models that effectively reflect the role that
hydrogen could play in meeting net-zero goals in the desired time frames –
this means not exclusively relying on GWP-100 and potentially adopting a
dual GWP-20/GWP-100 approach (Ocko et al., 2017);</p></list-item><list-item>
      <p id="d1e4920">improve quantification of hydrogen leakage rates by developing technologies
that can be taken into the field to accurately measure hydrogen emissions at
low detection thresholds (i.e., ppb level);</p></list-item><list-item>
      <p id="d1e4924">include the likelihood of hydrogen leakage and its impacts in
decision-making about where and how to effectively deploy hydrogen – such
as co-located production and end-use applications; and</p></list-item><list-item>
      <p id="d1e4928">identify leakage mitigation measures and best practices before building out
infrastructure.</p></list-item></list>
If we are to meet the climate challenge before us, it is imperative that we
carefully examine each alternative decarbonization pathway using robust and
appropriate metrics and data. The near- and medium-term warming impacts of
hydrogen emissions are higher than widely perceived. These impacts should be
explicitly and quantitatively accounted for in order to maximize the climate
benefits of replacing fossil fuel systems with hydrogen. Taking a proactive
and scientific approach to understand the implications of and address
hydrogen leakage can help ensure that the global rush to hydrogen delivers
on its promise to benefit the climate over all timescales.</p><?xmltex \hack{\newpage}?>
</sec>

      
      </body>
    <back><notes notes-type="codedataavailability"><title>Code and data availability</title>

      <p id="d1e4937">All code and data are available from the corresponding author upon reasonable request.</p>
  </notes><notes notes-type="authorcontribution"><title>Author contributions</title>

      <p id="d1e4943">IBO and SPH conceptualized the study. IBO conducted the analysis and data
visualization. IBO and SPH wrote and edited the manuscript.</p>
  </notes><notes notes-type="competinginterests"><title>Competing interests</title>

      <p id="d1e4949">The contact author has declared that neither of the authors has any competing interests.</p>
  </notes><notes notes-type="disclaimer"><title>Disclaimer</title>

      <p id="d1e4955">Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.</p>
  </notes><ack><title>Acknowledgements</title><p id="d1e4961">The authors would like to thank Tianyi Sun, Eriko Shrestha, and Naomi Cohen-Shields
for project support; Fabian Paulot and Stephen Pacala for helpful
discussions on the methodology; and Joan Ogden, Michael Oppenheimer, Roland
Kupers, Beth Trask, Hanling Yang, Aoife O'Leary, Morgan Rote, Jane Long,
Mark Brownstein, Laura Catalano, and Natasha Vidangos for thoughtful
feedback on prior versions of the paper.</p></ack><notes notes-type="financialsupport"><title>Financial support</title>

      <p id="d1e4966">This research has been supported by Robertson Foundation, the Heising-Simons Foundation, and ClimateWorks Foundation.</p>
  </notes><notes notes-type="reviewstatement"><title>Review statement</title>

      <p id="d1e4972">This paper was edited by Farahnaz Khosrawi and reviewed by two anonymous referees.</p>
  </notes><ref-list>
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