## Main

Green hydrogen, defined as hydrogen produced from renewable electricity via electrolysis, and derived e-fuels1 are critical components of the energy transition2, enabling emissions reductions in sectors where direct electrification is infeasible3,4 and avoiding sustainability concerns associated with biofuels5. These features, plus its versatility, have spurred a recent surge of enthusiasm6, policy targets7,8 and investments3. Furthermore, in response to the current energy crisis, an accelerated market introduction of hydrogen is considered a key option to decrease Europe’s reliance on fossil fuel imports8. Hydrogen therefore plays a central role in facilitating many net zero emissions scenarios9,10 and government plans7. Of all ways to produce hydrogen, green hydrogen offers the lowest life-cycle emissions11 and likely lowest long-term mitigation costs12, making it most suitable for climate neutrality.

While much of the debate and research around hydrogen has revolved around demand-related questions of suitable applications, markets and sectors1, the question of supply availability is equally critical. Hydrogen is very valuable for achieving increasingly pressing and legally binding emissions reduction targets13,14 as it can provide diverse energy services, ranging from energy storage and long-distance transportation to industry feedstocks3. Due to the substantial size of these hard-to-abate sectors and because virtually all hydrogen production today is fossil3,4, ramping up green hydrogen supply is urgent15. Growing awareness that scalability is a critical success factor for climate mitigation technologies has stimulated recent research to apply insights about the pattern16,17 and pace18,19,20 of energy technology diffusion to specific feasibility analyses21,22,23 of ramping up renewable24,25,26,27,28,29 and phasing-out fossil technologies22,30,31 fast enough. However, so far no study has analysed possible expansion pathways of green hydrogen from electrolysis, a technology in its infancy that needs to experience rapid innovation and deployment to unleash its potential for climate change mitigation15.

Electrolysers are a centrepiece of future green hydrogen supply chains, and their deployment is thus an indicator of the systemic challenges of concurrently ramping up additional renewable energy capacity, transport infrastructure and hydrogen end-use applications. In addition, the ramp up of electrolysers is a key bottleneck in itself. Starting at an estimated 600 MW globally in 2021 (Fig. 1) (ref. 32) in mostly small and individually manufactured plants (<10 MW), global capacity needs to grow 6,000–8,000-fold from 2021 to 2050 to meet climate neutrality scenarios compatible with the Paris Agreement9,10. This dwarfs the simultaneously required tenfold increase of renewable power9,10, which is readily available and cost competitive33,34. While electrolysis project announcements indicate an exponential build-up of momentum in the upcoming years with triple-digit annual growth rates, 80% of additional capacity announced to come online by 2023 is not yet backed by a final investment decision (FID) (Fig. 1c,d). It thus remains unclear how many electrolysis projects will materialize in the short term and whether overall capacity can expand fast enough to meet mid- to long-term hydrogen demands.

Here we analyse the potential deployment of electrolysis capacity for green hydrogen production by combining an S-shaped logistic technology diffusion model17 with a probabilistic parameterization based on data from established successful energy technologies: wind and solar power35,36,37. Despite such high growth rates, we find strong evidence of short-term scarcity and long-term uncertainty of green hydrogen supply. This bears a high risk of a substantial gap between likely supply and potential demand, threatening the outlook of green hydrogen for urgent climate change mitigation. In contrast, if electrolysis capacity were to grow at unconventional growth rates, which some non-energy technologies have experienced under special circumstances in the past, it could quickly overcome supply scarcity and secure future green hydrogen availability.

## Three uncertain parameters that define the feasibility space

In a finite market, technology adoption starts exponentially but gradually flattens out to follow an S-shaped curve as it approaches saturation (Fig. 2). The theory behind this logistic functional form originates from Roger’s (1962) conception of technology adoption, initiating with a small group of early adopters comfortable with an unfamiliar technology and then proceeding with a much larger group of adopters with lower willingness to pay who wait for lower costs and reliable performance17. This notion has been developed by transition theory scholars, for whom the defining characteristic of early adopters is the role of niche markets where unproven technology finds initial markets38,39,40.

The resulting technology diffusion pathway follows three distinct phases. In the formative phase, policy-backed demonstration projects face technical uncertainty and high costs during the proverbial valley of death41, leading to slow and unsteady growth42. In the growth phase, increasing returns to scale43 and cost-decreasing learning effects44 accelerate market adoption. After reaching the maximum rate of expansion, growth starts to slow down as a result of technological, economic and social constraints17. This marks the beginning of the saturation phase when the final market level is approached. This trajectory characterizes all stages of the technology adoption process and is mathematically described by the three-parameter logistic function (Methods). Considering the electrolysis market ramp up, the three parameters—initial capacity (timing), emergence growth rate (steepness) and saturation (asymptote)—relating to these three stages are all uncertain and independent.

First, the initial capacity is an uncertain parameter as it depends on the possibly strong yet uncertain momentum in the upcoming years, which could propel electrolysis capacity from the formative phase to the beginning of the growth phase and therefore must be included in the analysis. Beyond the evidently speculative nature of projects pending an FID, there are further mutually opposing uncertainties. On the one hand, even projects that have secured an FID may fall behind schedule. On the other hand, data gaps due to additional future projects or missing projects might introduce downward biases. Striking a balance between including near-term momentum and excluding uncertain long-term announcements, we focus on the year 2023 as the ‘initial year’, as we do not expect any potential new projects to proceed from announcement to operation in less than two years. Figure 3a,b shows the probability distributions of the initial capacity in 2023, which spans the full range of project announcements, centred around an expected value of realizing 30% of projects in the feasibility study category45 and assuming that all projects under construction are built in time (Methods).

Second, the growth rate is an inherently uncertain function of policy support46, technological characteristics47 and possible cost reductions44, of which the latter are notoriously difficult to predict48. As the annual growth rate gradually decreases due to market saturation, we parameterize the emergence growth rate26, which is the maximum annual growth rate that is realized after the formative phase, related to the steepness parameter in the logistic function (Methods). Unlike previous research, which constructed feasibility spaces by looking at historical precedents of the same technology in different regions28,31, we instead turn to historical precedents of different technologies in the same region. This comparison is necessary because, as long as green hydrogen is uncompetitive44, historical growth rates are primarily proxies of past policy support and not necessarily indicative of future potential. In this way, we also abstract from a more granular analysis of factors that influence the pace of technology diffusion to construct different scenarios. In the conventional growth scenario, we compare electrolysis with wind and solar power, the historically fastest-growing energy technologies, which now comprise nearly 10% of global electricity generation49, during their periods of fastest relative growth, 1995–2010 (Extended Data Fig. 1). Figure 3c,d shows the corresponding distributions, revealing that solar power grew faster than wind during all seven-year intervals, both in the European Union and globally. The distributions are robust to the interval length (Extended Data Fig. 2). Extended Data Table 1 compiles drivers and challenges for higher and for lower hydrogen growth rates compared with wind and solar power, such that we carefully conclude that wind and solar PV are a valid initial proxy to derive rough estimates of green hydrogen ramp up and availability. Later, in the unconventional growth scenario, we compare these growth rates to a broader set of predominantly non-energy technologies.

Third, the final market volume is uncertain as the outcome of the competition among different climate change mitigation technologies remains undecided in many end-use applications50. In these applications, hydrogen constitutes a new energy carrier, which implies that not just its supply, but also its demand and infrastructure have to be ramped up in parallel. In contrast, wind and solar power produced an economic good with existing demand and pre-installed infrastructure, namely electricity. We capture the just-emerging hydrogen market by a steadily increasing demand pull and distinguish between its magnitude and anticipation (Fig. 2). We opt for a simple piecewise linear demand pull function, parameterized on policy targets and announcements in the short- to mid-term and on demand from climate neutrality scenarios in the long term (Methods). The demand pull therefore comprises all factors that increase market opportunities through policies, regulation and improved competitiveness51,52.

The propagation of the uncertain initial capacity and emergence growth rate (Fig. 3) defines a probabilistic feasibility space under the condition of an increasing policy-backed demand pull that spurs investment and mitigates financial risks. Table 1 summarizes the key model parameters for the electrolysis market ramp up in the European Union and globally.

## Reconciling different approaches to long-term projections

Our model steers a middle course between two approaches in the recent literature that have analysed growth trajectories of wind and solar power but arrived at different conclusions regarding their outlook. The first approach relies on fitting growth models with the asymptote as a free parameter that is estimated from historical data if possible24,28. Studies differ in their interpretation of the asymptote as the final market volume24 or as a non-indicative parameter that may be surpassed again later in the diffusion28. While including the asymptote as a free parameter often yields a good fit to data, it comes at the expense of high sensitivity to random fluctuations in the last few data points53 and to the type of growth model used28. A slowdown, which might in hindsight turn out to be just a temporary artefact, for example due to discontinuous policy54 or economic crises55 (for example, Extended Data Fig. 1a), could be misinterpreted as terminal saturation if the asymptote is taken at face value. In that case, this approach risks constraining future conditions to policy-driven historical deployment, which can negatively bias the long-term outlook.

In contrast, the second approach in the literature applies an ex ante target towards which wind and solar power diffuse from their historical trajectory26,27. While this enables an inter-decadal feasibility analysis under the presupposition that a stated market volume will be attained, it implicitly assumes an existing market with sufficient demand that technologies can penetrate. This may not be the case for hydrogen because demand-side transformations and infrastructure requirements mean it cannot immediately tap into new markets that are just emerging. In our approach, these coordination challenges are summarized by the steadily increasing demand pull that contributes to reconciling the debate on long-term projections of energy technologies, especially for hydrogen, but potentially also for wind and solar power.

Modelling green hydrogen growth using a logistic model that is driven, but also constrained, by an increasing demand pull leads to an asymmetric S-shaped adoption curve, which approaches the asymptote more gradually than the standard symmetric logistic function. While a similar shape may also be described by the Gompertz model (used in ref. 28) as another special case of the generalized logistic function (comparison in Extended Data Fig. 3 and Methods), our model allows for a more precise control of the increasing market volumes, which can be informed by additional information about policy targets, improving cost competitiveness and scenario results.

## Electrolysis capacity using growth rates from wind and solar

Figure 4 shows the probabilistic feasibility space of electrolysis capacity in the European Union and globally using a distribution of growth rates assembled from the historical growth of wind and solar power and applying demand pull anticipation of five years (sensitivity analysis in Extended Data Fig. 4). Three key insights emerge.

First, in the upcoming one to two decades, in the first half of the growth phase, electrolysis capacity is likely to remain relatively small compared with both intermediate and final targets and to total energy demand. Green hydrogen will thus remain scarce, leading to a large gap between likely supply and potential demand. Another gap exists between likely supply and project announcements (Extended Data Fig. 5). In the European Union, neither the 2024 target of 6 GW nor the 2030 target of 100 GW are within reach under conventional growth rates as both fall outside the distribution. The global target of 254 GW by 2030, which ensues from ambitious project announcements32 (Fig. 1d) plus planned EU imports8, also lies far beyond the 95th percentile, illustrating the short-term challenges of ramping up green hydrogen production within the European Union and globally.

Second, a breakthrough to high capacities is possible, but both timing and magnitude are subject to large uncertainties. The results reveal a threshold above which the probability distribution flips towards larger values and then follows the linear demand pull with a few years of delay. For the European Union, this occurs around 2038 and globally around 2045, which approximately coincides with the years of largest annual electrolysis capacity additions in the midst of the growth phase. This tipping behaviour is a property of the probability space, which combines the information of the pathway ensemble and is thus more relevant to decisionmakers than individual pathways, which are more continuous and span a larger range. The interquartile range (IQR) of probabilistic electrolysis capacity in 2040 is 94–330 GW in the European Union (246–1121 GW globally) and 412–497 GW in the European Union (1,873–3,434 GW globally) in 2050, marking the saturation phase. Substantial uncertainty thus prevails for several decades, especially globally.

Third, the propagation of uncertainties not only leads to a tipping point but also to a pronounced bimodal distribution near the tipping point, which has adverse consequences for risk management. This pattern is a direct outcome of the superposition of many S-shaped diffusion curves and occurs despite input parameters that follow a well-defined normal distribution with a clear maximum (Fig. 3). This is because, for most of the period, the logistic curve produces low and later high capacities (small annual additions); because of high growth rates, the transition phase occurs quickly (large annual additions), and thus the probability of being at an intermediate capacity is low. Using the Gompertz model (Extended Data Fig. 3), the distribution does not turn visibly bimodal until 2050 but is instead very wide and flat, implying a similarly large risk of the supply–demand gap.

Both short-term scarcity and mid- to long-term uncertainty are robust to the type of growth model used and create challenges for policymakers, system planners, industry and consumers. Relying on the large-scale availability of green hydrogen could lead to expensive path dependencies or even fossil lock-ins56 if supply expansion falls short of expectations. Accounting for these risks probably discourages investments in hydrogen supply, infrastructure and end-use technologies, thus exacerbating short-term scarcity and mid- to long-term uncertainty. In addition, scarce and uncertain supply complicates and delays required end-use transformation and infrastructure investments. As a consequence, green hydrogen could fail to realize its potential.

There are good arguments both in favour and against the hypothesis that electrolysis could grow even faster than wind and solar power did (Extended Data Table 1).

## Emergency deployment with growth beyond wind and solar

To explore what might be possible with special dedication, coordination and funding, we now parameterize our electrolysis diffusion model with unconventionally high growth rates that have been achieved under specific circumstances in the past (Fig. 5). These include mostly non-energy products in situations of wartime mobilization (for example, US aircraft or liberty ships in World War II), of massive public investments and central coordination (for example, nuclear power in France or high-speed rail in China) or of market-driven deployment of highly modular information technology innovations with low coordination requirements (for example, internet hosts or smartphones).

Figure 5a shows the normalized historical trajectories of these technologies. To cover the full spectrum of associated growth rates, we fit logistic curves and extract the respective annual emergence growth rates. The resulting distribution of unconventional growth rates has a mean value of 126% per year, substantially larger than in the conventional growth case (Table 1) and stretches beyond 300% per year (Fig. 5b). Within the analysed data, only US production during World War II achieved growth rates above 100% per year—except for the number of COVID-19 vaccinations, which far surpass all other technologies such that we exclude it as an outlier with very different circumstances and product characteristics.

For green hydrogen, reaching such unconventionally high growth rates requires policies and regulation to urgently secure business cases by creating, or even guaranteeing, revenue streams through public co-financing or direct investments. If policymakers decide for subsidies, such as co-financing of capital expenditures (CAPEX) or operating expenditures (OPEX), the funding of these programmes would need to reflect the envisaged scale of the hydrogen market ramp up. There are plans for such instruments, for example, in the European Union, which are yet to be specified and implemented. These comprise carbon contracts for differences, which subsidize additional OPEX of operating industrial processes with green hydrogen (for example, primary steel via direct reduction) or CAPEX subsidies as part of the European Union’s ‘Important Projects of Common European Interest’8. In addition, emergency policies should provide security and coordination along the whole value chain. As hydrogen requires new infrastructure, and as most hydrogen applications are not yet competitive and no hydrogen market exists, policymakers and regulatory agencies should support the coordinated ramp up of demand, supply and infrastructure together with relevant industry stakeholders. Because hydrogen infrastructure and trade will partly be international, this involves international cooperation.

The resulting probabilistic feasibility spaces show that unconventional growth rates substantially mitigate the issues of short-term scarcity and mid- to long-term uncertainty (Fig. 5c,d, sensitivity analysis in Extended Data Fig. 6). In both regions, European Union and global, green hydrogen immediately enters the growth phase, leading to a probability distribution that already tips around 2030 after which the demand pull acts as the main constraint. In 2030 an even more pronounced bimodal distribution emerges from the simulations, which however also subsides more quickly thereafter. After 2035, the demand pull, median and 95th percentile are separated only by a very small margin, effectively closing the gap between supply and demand with a high probability. While smaller than before, the 90% confidence interval still indicates a substantial spread as small growth rates cannot be ruled out. However, towards 2050, the spread swiftly decreases for the 80% confidence interval, indicating a high probability of mid- to long-term availability.

The differences between conventional growth (such as wind and solar power) and unconventional growth (emergency-like deployment) become even more apparent in the direct comparison of Fig. 6. In the conventional growth case, the breakthrough year, defined as the year of largest annual capacity additions, in the median occurs around 2040 in the European Union and 2045 globally. However, this is again subject to substantial uncertainty with an IQR of 2036–2045 in the European Union and 2043–2049 globally. In contrast, unconventional growth hastens the median breakthrough to before 2035 in both regions, even though uncertainty remains with an IQR of 2029–2036 in the European Union and 2030–2037 globally.

These marked differences in the breakthrough year are also reflected in the electrolysis capacity distributions (Fig. 6c–f and Extended Data Fig. 7). In the conventional growth case, it is likely (≥75%) that in 2030 less than 1% of final energy in the European Union (less than 0.2% globally) can be supplied with domestic green hydrogen. Under unconventional growth, supply in 2030 spans a wide IQR of 0.8–4.5% in the European Union (0.3–2.1% globally). This also increases the probability of achieving the EU 2030 target of 100 GW to 49%, as opposed to 0.2% under conventional growth. However, even under unconventional growth rates, ramping up global electrolysis capacity to 850 GW by 2030 as required by the International Energy Agency (IEA) Net-Zero Emissions by 2050 Scenario (NZE)9 is unlikely (18% probability), which is also a result of the limited demand pull at that time (compared with Extended Data Fig. 6f).

In the long run, by 2040, large uncertainties dominate in the conventional growth case, illustrated by an IQR of 3.2–11.2% in the European Union (0.7–3.3% globally), which stands in stark contrast to the narrow 11.7–12.9% in the European Union (6.6–7.8% globally) under unconventional growth. The global probability distribution under conventional growth in 2040 is skewed to low capacities, while it is wide and slightly bimodal in the European Union. Under unconventional growth, by 2040 the probability distribution is focused at the upper end of the range in both regions and primarily determined by the demand pull.

## Discussion

Despite strong momentum and enthusiasm around green hydrogen, the market ramp up of electrolysis is a decisive bottleneck on the pathway to climate neutrality. There is also substantial uncertainty about the role and potential of green hydrogen for achieving climate goals: while 1.5 °C-compatible pathways presented by the IEA and the International Renewable Energy Agency (IRENA) foresee a rapid scale up of green hydrogen, it only plays a limited role in most integrated assessment model (IAM) scenarios surveyed by the Intergovernmental Panel on Climate Change (IPCC) (Extended Data Fig. 8). We show that despite exponentially increasing project announcements for the upcoming years, green hydrogen probably (≥75%) remains scarce (<1% of final energy demand) until 2030 in the European Union and until 2035 globally if electrolysis capacity grows similarly to wind and solar power, which have been the biggest success stories of the energy transition so far. This can be explained by the nature of exponential expansion, which includes a flat beginning such that even high annual growth rates take time to translate into noteworthy market shares. However, once the breakthrough occurs, it may happen quickly—as was the case for solar power.

For the electrolysis market ramp up, however, the timing of this breakthrough in terms of largest annual capacity additions is uncertain but unlikely (≤25%) to occur before 2036 in the European Union and 2043 globally. We show that the propagation of inevitable uncertainties associated with both near-term deployment and feasible growth rates leads to uncertain availability of green hydrogen in the mid- to long-term, which implies a substantial risk of a long-term gap between likely supply and potential demand. It is important to note that the probability distributions presented here are conditional on continuous policy support assumed as part of the demand pull. Even under such policies, uncertainties prevail for decades.

In addition, future short-term scarcity and long-term uncertainty of electrolysis capacity might create additional barriers to electrolysis deployment already today. First, short-term scarcity creates problems due to the threefold coordination challenge of ramping up hydrogen supply, demand and infrastructure simultaneously, which has been described as a ‘three-sided chicken-and-egg problem’57. The lack of sufficient hydrogen volumes delays both the end-use transformation and required infrastructure developments such as the repurposing of existing gas pipelines. Second, long-term uncertainty might deter investors, who could choose to wait for the market to consolidate and for costs to drop (second-mover advantage)58. From a policy perspective, relying on the large-scale availability of green hydrogen is therefore a risky bet that, if hydrogen abundance and affordability fail to materialize, may lead to a fossil lock-in due to remaining fossil fuel infrastructure and end-use equipment. As a consequence, under conventional growth such as wind and solar power, uncertainties may translate into risks that discourage policymakers and investors such that green hydrogen might fall short of its potential and thus endanger climate targets.

By contrast, policymakers and industry could minimize these risks by fostering rapid investments into green hydrogen supply chains that enable unconventionally high growth rates of electrolysis. In this way, the feasibility space would broaden beyond what has been experienced for energy analogues such as wind and solar. This could break the vicious cycle of uncertain supply, insufficient demand and incomplete infrastructure and turn it into a positive feedback mechanism. Short-term scarcity and long-term uncertainty are two sides of the same coin and could be resolved together. Policies that kick start a rapid deployment of gigawatt-scale electrolysers in the upcoming few years could help to unlock substantial innovation and scaling effects, prompting industries to switch from manual to automated production and thus driving down costs, which would secure expectations and further accelerate growth.

Such unconventional growth could not only allow green hydrogen to meet demand in sectors inaccessible to direct electrification, but in conjunction with expanding renewable electricity, it could keep the window open to reaching a broader and more prominent role of hydrogen in a climate-neutral energy system. However, policymakers should be aware that there remains a risk of overestimating green hydrogen’s potential. While it will be possible to expand the use cases of hydrogen if supply surpasses expectations, in the opposite case, if supply falls short of expectations, it might simply be too late to switch to alternatives. Under these asymmetrically distributed risks, policymakers face a twofold problem. On the one hand, they need to accelerate the development of green hydrogen throughout the entire supply chain to foster unconventional growth; on the other hand, they need to safeguard against the inevitable risk of limited availability. Policymakers, therefore, need to strike a sensible balance between providing regulatory certainty to spur green hydrogen investment while maintaining a realistic judgement on its long-term prospects and fostering available and more efficient alternatives such as direct electrification and energy efficiency. Future research should further develop probabilistic decision frameworks59 that help enable urgent technological deployment, while navigating the uncertain feasibility space and associated risks.

## Methods

### Approach and key input data

We conduct an uncertainty analysis of the market ramp up and further expansion of electrolysis capacity in the European Union and globally, using a stochastic adaptation of the logistic technology diffusion model. The model accounts for inevitable uncertainties of two main parameters: the initial electrolysis capacity in 2023 and the annual growth rate, which we parameterize using up-to-date electrolyser capacity data from built, planned and announced projects and from empirical data on the growth of successful technologies from the past. We capture the nonlinear propagation of these uncertainties within the logistic diffusion model by a Monte Carlo simulation approach. We further assume a steadily increasing electrolysis demand pull driven by continuous policy support and expanding competitiveness of hydrogen applications (Fig. 2). This approach enables us to derive probability distributions of electrolysis capacity deployment over time, which we then interpret as a probabilistic feasibility space of scaling up green hydrogen supply. By design and by necessity, the results do not represent absolute probabilities but conditional probabilities that are contingent on the assumed demand pull from policies and markets.

Our analysis relies on global electrolysis projects from the IEA Hydrogen Projects Database32, complemented by our own market research, which we use to parameterize the initial capacity distribution, depending on the project status as explained below.

To parameterize the growth rate distribution, we draw on data of historical analogues and distinguish two cases. In the conventional growth case, we assume that electrolysis grows as fast as wind and solar power have during their period of fastest relative growth from 1995–2010 (Fig. 3). In the unconventional growth case, we explore the electrolysis market ramp up under historical growth rates of a wide set of primarily non-energy technologies that grew even faster than wind and solar power (Fig. 5).

For the demand pull (from policies, regulation and markets) that drives the technology diffusion, we parameterize its magnitude in time and its anticipation by investors. For the European Union, in the short term, the magnitude is parameterized to the political 2024 target of 6 GW, while the 2030 target of 100 GW follows from the REPowerEU Plan8, which foresees the domestic production of 10 Mt of renewable hydrogen, approximately equivalent to 100 GW electrolysis capacity. The long-term demand pull is set to 500 GW by 2050 as mentioned in the EU Hydrogen Strategy7. Globally, the short-term demand pull magnitude of 254 GW follows from cumulative project announcements of 154 GW by 2030 plus an additional 10 Mt of renewable hydrogen the European Union recently announced it plans to import8, equivalent to 100 GW of electrolysis capacity. In the long run, we use scenario data of the IEA NZE scenario, which is 3,600 GW globally by 20509. The demand pull anticipation states by how many years these targets, associated policies and hydrogen competitiveness are anticipated by potential investors, which thus constitutes a measure of both regulatory certainty and investor foresight. Our default assumption is five years, while we conduct sensitivity analyses for zero years, ten years and a hypothetical case of full anticipation of the long-term market size (Extended Data Fig. 4 and Extended Data Fig. 6).

### Data handling

We use the IEA Hydrogen Projects Database, which lists 984 global hydrogen projects, of which 886 are based on electrolysis. The database includes the project’s development status, technology characteristics, designated end-use applications and, most importantly, size as electrical capacity in MW for electrolysis projects. In addition, to ensure the model’s initial capacity in 2023 is accurately parameterized, we review all projects with an announced starting year in 2022 or 2023 and an announced size of at least 50 MW. This applies to 49 projects, which we track and include in the GitHub repository (below). Electrolysis projects with a ‘DEMO’ development status are allocated to the ‘Operational’ and ‘Decommissioned’ status, depending on whether they are still in operation. The IEA Hydrogen Projects Database also contains several entries for confidential projects between 2000–2020. We distribute these projects to all regions in proportion to the share of total capacity from other non-confidential projects within that time window and equally over time.

For the conventional growth case, we use data of installed wind and solar capacity from the BP Statistical Review of World Energy 202160. Solar capacity is available from 1997 onwards in the European Union and from 1996 globally. Wind capacity is available from 1997 in the European Union and from 1995 globally. We fit exponential models to this data in sliding seven-year intervals until 2010, which we use to parameterize the emergence growth rate distribution. This corresponds to the period in which both technologies grew the fastest (Extended Data Fig. 1). The distribution is robust to the choice of the slice length (Extended Data Fig. 2). The emergence growth rate is related to the steepness parameter in the logistic function (below) and describes the growth rate that is approximately attained in the emergence phase of the technology diffusion when the asymptote is not yet constraining.

### Truncated normal distributions

The stochastic uncertainty analysis rests on a Monte Carlo-based simulation approach to randomly sample from probability distributions that reflect the underlying parametric uncertainty. We use normal distributions with lower truncation for both the initial capacity in 2023 and the emergence growth rate.

For the initial capacity distribution, we define the lower truncation a by the capacity of all projects that are already operational or under construction and due to start production in 2023. Given the truncation interval $$\left[ {a,\infty } \right]$$, we thus need to determine the pre-truncation parameters μ (mean) and σ (standard deviation). This leaves two degrees of freedom for which we impose two conditions. First, we set the post-truncation expected value to the capacity that is equivalent to realizing 30% of feasibility study projects, $$C_{0.3\mathrm{FS}}$$. Given ϕ as the probability density function and Φ as the cumulative density function of the normal distribution, the first condition is related to the expected value and reads:

$$\begin{array}{*{20}{c}} {E(X) = \mu + \sigma \frac{{\phi \left( {\frac{{a - \mu }}{\sigma }} \right)}}{{1 - {{\Phi }}\left( {\frac{{a - \mu }}{\sigma }} \right)}} = C_{0.3\mathrm{F}S}} \end{array}$$
(1)

Second, we assign a 15% probability to the option that only those projects that are already backed by an FID, with capacity $$C_\mathrm{FID}$$, are built. Following the truncated cumulative distribution function, the second condition is:

$$\begin{array}{*{20}{c}} {F\left( {C_\mathrm{FID}} \right) = P\left( {X \le C_\mathrm{FID}} \right) = \frac{{{{\Phi }}\left( {\frac{{C_\mathrm{FID} - {\sigma}}}{{\mu }}} \right) - {{\Phi }}\left( {\frac{{a - {\sigma}}}{{\mu }}} \right)}}{{1 - {{\Phi }}\left( {\frac{{a - {\sigma}}}{{\mu }}} \right)}} = 0.15} \end{array}$$
(2)

The two equations (1) and (2) form a system of nonlinear equations that we solve numerically to obtain μ and σ. Jointly with the lower truncation value a, this defines the truncated distribution (Fig. 3a,b).

For the emergence growth rate distribution, we first calculate the mean and standard deviation of the seven-year growth rates of wind and solar power in the European Union and globally. Subsequently, we apply a lower truncation of 15% per year, which thus constitutes the lower boundary of the electrolysis market ramp up (Fig. 3c,d).

### Adapted logistic technology diffusion model

To account for the threefold coordination challenge of concurrently ramping up green hydrogen supply, demand and infrastructure, we propose an adaptation of the standard logistic technology diffusion model by including a steadily increasing demand pull that replaces the fixed final market volume. This accounts for the observation that the market for green hydrogen is just emerging, which stands in contrast to energy technologies such as wind and solar power that were able to tap into the existing electricity market (main text). We deliberately do not model market shares but instead directly describe the growing market volume because the emerging green hydrogen market is not well described by a substitution of technology shares.

The standard logistic function for the electrolysis capacity $$C\left( t \right)$$ reads

$$\begin{array}{*{20}{c}} {C\left( t \right) = \frac{{C_\mathrm{max}}}{{1 + \mathrm{e}^{ - k\left( {t - t_0} \right)}}}} \end{array}$$
(3)

where $$C_\mathrm{max}$$ is the asymptote, k is the growth constant, t0 is the inflection point and e is Euler’s number of approximately 2.718. This is the solution of the logistic differential equation

$$\begin{array}{*{20}{c}} {\frac{{\mathrm{d}C}}{{\mathrm{d}t}} = kC\left( {1 - \frac{C}{{C_\mathrm{max}}}} \right)} \end{array}$$
(4)

under the condition that $$C\left( {t_0} \right) = C_\mathrm{max}/2$$. Our model idea rests on an adaptation of this differential equation. We turn $$C_\mathrm{max}$$ into a time-dependent demand pull $$C_\mathrm{max}(t)$$ and discretize the differential equation, which yields

$$\begin{array}{*{20}{c}} {C_{t + 1} = C_t + bC_t\left( {1 - \frac{{C_t}}{{C_{t,\mathrm{max}}}}} \right)} \end{array}$$
(5)

where t denotes time in yearly units and $$b = \mathrm{e}^k - 1$$ is the annual growth rate. In the Monte Carlo simulation, we independently draw a sample (N = 10,000) for both the initial capacity $$C_{2023}$$ and the annual growth rate b and subsequently feed both into the diffusion equation (5). To improve numerical accuracy, we use a quarterly time resolution in the model with a quarterly growth rate of $$b_q = \left( {1 + b} \right)^{1/4} - 1$$. Further increasing the temporal resolution did not noticeably affect results.

### Comparison with Gompertz model

The default logistic function is a special symmetric case of the generalized logistic function

$$\begin{array}{*{20}{c}} {C\left( t \right) = \frac{{C_\mathrm{max}}}{{\left( {1 + \nu\mathrm{e}^{ - k\left( {t - t_0} \right)}} \right)^{1/\nu }}}} \end{array}$$
(6)

with v as an additional parameter, where the logistic function follows for $$\nu = 1$$. Another prominent special case of the generalized logistic function is the so-called Gompertz model, which follows as the limiting case for $$\nu \to 0$$ and may be written as

$$\begin{array}{*{20}{c}} {C\left( t \right) = C_\mathrm{max}\mathrm{e}^{ - \mathrm{e}^{ - k\left( {t - t_0} \right)}}} \end{array}$$
(7)

or in differential form as

$$\begin{array}{*{20}{c}} {\frac{{\mathrm{d}C}}{{\mathrm{d}t}} = kC\ln\left( {\frac{{C_\mathrm{max}}}{C}} \right)} \end{array}$$
(8)

where ln is the natural logarithm and which discretized translates into

$$\begin{array}{*{20}{c}} {C_{t + 1} = C_t + bC_t\ln\left( {\frac{{C_\mathrm{max}}}{{C_t}}} \right)} \end{array}$$
(9)

Compared with the default logistic function, the Gompertz function is asymmetric and approaches the asymptote much more gradually. Our adaptation of the logistic model with a steadily increasing demand pull results in a similar shape, yet one that can be controlled and parameterized more directly using additional information on policy targets and scenario results. Thus, the Gompertz model already includes an asymmetric damping term, so that we use it only with a constant asymptote, $$C_\mathrm{max} = \mathrm{const}$$. Calculating the Gompertz model together with a non-constant demand pull would introduce an undesirable superposition of different damping effects.

In contrast to the logistic model in equation (5), the Gompertz model in equation (9) does not simplify for $$C_t \ll C_{t,\mathrm{max}}$$ so that b cannot be interpreted as the emergence growth rate. Instead, we parameterize the Gompertz model such that the initial seven-year growth from 2023–2030 matches the emergence growth rate (Extended Data Fig. 3). This is in line with our definition of the emergence growth rate for which we fitted exponential models in moving seven-year windows.

### Emergency deployment

To extend the probabilistic feasibility space of electrolysis capacity to emergency deployment, we use a wide dataset of primarily non-energy technologies to parameterize a distribution of unconventional growth rates. This encompasses technologies on both the regional and global level, measured in different units, which we normalize by the respective maximum value. All technologies represent stock variables; apart from nuclear power in France and dry shale gas in the United States, which are yearly flow variables. In contrast to the conventional growth case, where we used exponential growth rates of wind and solar power to parameterize the emergence growth rate distribution, for the unconventional growth case we fit logistic models (equation (3)), because many technologies have already passed through the entire S-curve (Fig. 5a). After converting the growth constant k to the annual growth rate b, via $$b = \mathrm{e}^k - 1$$, we re-parameterize the distribution of emergence growth rates (Fig. 5b), draw another sample (N = 10,000) and run the Monte Carlo simulation again to obtain the probabilistic feasibility space of Fig. 5c,d.

### Final energy shares

We translate electrolysis capacity into corresponding shares of final energy demand that can be supplied under this capacity. This requires assumptions on the electrolysis efficiency and further processing steps, its full-load hours and final energy demand.

We assume an overall efficiency of 60%, which results from a 60–81% efficiency of electrolyser systems61 and additional losses due to further processing of some hydrogen into e-fuels1 and losses incurred during transportation, storage and conversion3. Please note that we report shares of hydrogen on the level of final energy, not useful energy. This excludes the efficiency of the end-use application (for example a fuel cell), which would further reduce the overall efficiency. Final energy is easier to measure and hence regularly reported by energy system models and frequently taken up by policymakers.

Additionally, we assume that electrolysis runs at 5,000 full-load hours, equivalent to a capacity factor of 57%. Such full-load hours could be realized, for example, by hybrid solar–wind power plants in several world regions62. Furthermore, this assumption is in harmony with the range of 3,000–6,000 full-load hours regarded as cost-minimizing using grid electricity61. In reality, higher full-load hours would reduce the demand pull for electrolysis capacity as the same hydrogen volume could be produced by fewer electrolysers. While this could slow down the growth of electrolysers, it would not impact the final energy share of hydrogen. On the other hand, higher full-load hours would reduce costs and therefore increase the competitiveness of green hydrogen, spurring investment and growth.

Final energy demand over time is obtained from scenarios that reach climate neutrality by 2050. For the European Union, due to the lack of published official modelling results beyond 2030, we use scenarios results of the INNOPATHS project, a recent European Union-specific model intercomparison study63. Specifically, we calculate the median of a total of nine scenarios, which originate from three different models (ETM-UCL, PRIMES, REMIND-EU) under three different transformation narratives (New Players 1.5, Incumbents 1.5, Efficiency 1.5). As the results are only available for the EU28, not EU27, and all British Isles (the United Kingdom and the Republic of Ireland) are aggregated into one region (UKI), we approximate the EU27 final energy demand by subtracting the UKI values from the EU28 values. This leads to a slight underestimation of the EU27 value because only the United Kingdom has left the European Union. However, as Ireland’s final energy demand accounts for only around 1% of that of the EU27, the error is negligible compared with the modelling uncertainty. Global final energy demand is given by the IEA NZE scenario9 (variable ‘total final consumption’) and linearly interpolated if necessary (for 2025, 2035, 2045 in Extended Data Fig. 7).

### Comparison with other energy modelling scenarios

In Extended Data Fig. 8, we also provide a comparison of our technology diffusion model results with integrated assessment model scenarios and single data points of policy targets, project announcements and further studies. If hydrogen volumes instead of electrolysis capacities are reported, we calculate the corresponding electrolysis capacity using an efficiency of 70% (assuming no additional losses due to transport and further processing) and 5,000 full-load hours.

For the European Union, we include climate mitigation scenarios from the recently published IPCC AR6 Scenario Explorer and Database, version 1.0 (categories C1, C2 and C3, equivalent to limiting warming to 2 °C with a probability of >67%) (ref. 64), approximating the European Union with the ‘Europe’ region from the R10 regions dataset and from the INNOPATHS project (scenarios New Players 1.5, Incumbents 1.5, Efficiency 1.5) (ref. 63), again approximating EU27 values by subtracting UKI from EU28 (above). Data from the IPCC SR1.5 is not available for Europe. As an additional point of comparison, we include 2030 and 2050 data points from a roadmap of the industry association Hydrogen Europe65, using the ‘ambitious’ scenario under the assumption that all hydrogen is produced via electrolysis.

Globally, we include climate mitigation scenarios from the IPCC SR1.5 Scenario Explorer, version 2.0 (categories Below 1.5 C, 1.5 C low overshoot, 1.5 C high overshoot and Lower 2 C) and the IPCC AR6, version 1.0 (categories C1, C2 and C3, equivalent to limiting warming to 2 °C with a probability of >67%) (refs. 64,66). In addition, we show the IEA NZE scenario9, the IRENA 1.5 °C scenario10 and the ‘green only’ scenario of the Hydrogen Council67, a global hydrogen industry association.

### Limitations

We focus on the upscaling of electrolysis capacity. However, there are other elements in the supply chain of green hydrogen that could also constitute critical bottlenecks. Of particular concern is the upscaling of technologies to capture atmospheric carbon68, especially direct air capture29, for the synthesis of climate-neutral e-fuels, which was out the scope of this article.

The capacity data of wind and solar power does not include very early upscaling before 1995. To parameterize the growth rate distribution, we are therefore limited to the interval 1995–2010, after which growth starts to slow down again. The power of prediction could possibly be improved by including a longer dataset. However, we view 1995–2010 as a valid interval to explore the feasibility space of green hydrogen under the assumption that the growth rates observed for wind and solar power in this 15-year time period can be sustained at least as long for electrolysis.

The calculation of final energy shares in the European Union leaves out imports from other world regions, which could become substantial in the longer term. An analysis of hydrogen trade was outside the scope of this article, and final energy shares must be interpreted accordingly.

All stated probability distributions are contingent on the demand pull, which assumes continuous policy support, in particular in the next decade, and an expanding competitiveness of hydrogen due to cost reductions and direct and indirect carbon pricing. While we regard this as a necessary assumption because green hydrogen is still at the very beginning of the market diffusion, future research could examine appropriate policy instruments that are capable of realizing this demand. This limitation is related to the observation that limited competitiveness of green hydrogen could also reduce the demand pull, which was however outside the scope of this analysis. Another inevitable caveat of our approach is that we need to provide an exogenous long-term demand pull as an input parameter, thereby enforcing and simultaneously constraining the market ramp up. Further energy system research is required to improve the estimates of the long-term demand for electrolysis capacity.

Finally, we deliberately do not include an analysis of fossil hydrogen, which can be available earlier than green hydrogen as steam reforming of natural gas is an established technology (grey hydrogen). Combining steam reforming with carbon capture gives ‘blue’ hydrogen with reduced emissions. Fossil hydrogen could play at least a bridging role, which would enable an early ramp up of hydrogen infrastructure and end-use transformation towards hydrogen. However, there are concerns about the life-cycle emissions of blue hydrogen11 and new fossil lock-ins69,70, which could, in turn, slow down the expansion of lower-emission green hydrogen. In addition, blue and grey hydrogen face competitiveness challenges aggravated by high current natural gas prices12, which are anticipated to persist at least for a couple of years in the European Union, such that grey and blue hydrogen would also require policy support. Further research is required to analyse the balance between taking transitionary steps and fostering the mid- to long-term availability of green hydrogen.