Susanne Baur
email: susanne.baur@cerfacs.fr

Benjamin M Sanderson

Roland Séférian

Laurent Terray

Change in Wind Renewable Energy Potential under Stratospheric Aerosol Injections

niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Wind renewable energy (WRE) is a key component of the transition to a low-carbon energy system (IPCC, 2018;[START_REF] Clarke | Energy Systems[END_REF][START_REF] Riahi | Mitigation pathways compatible with long-term goals[END_REF]. Modeling assessments estimate that in Paris Agreement compatible scenarios, such as the C1 and C2 scenarios from the recent IPCC Assessment Report [START_REF] Riahi | Mitigation pathways compatible with long-term goals[END_REF], a significant portion of energy would come from wind with projected production ranging from 4,760 to 50,960 TWh/yr by 2050 depending on the scenario and model (Byers et al., 2022). However, present policies are taking us closer to a global mean surface temperature increase of 2.5-2.9°C than the Paris compatible 1.5°C (CAT, 2023), whilst current warming already leads to numerous climate change related damages [START_REF] Ripple | The 2023 state of the climate report: Entering uncharted territory[END_REF]. Hence, a growing number of people are investigating a group of technologies, termed Solar Radiation Modification (SRM), as a potential addition to conventional mitigation, to rapidly manage climate change risks. SRM does not resolve the global warming problem as it does not eliminate greenhouse gases (GHGs), but is proposed to temporarily mask some of the impacts with manuscript submitted to AGU Earth's Future the logic of providing more time to sufficiently roll out mitigation measures and halt or reverse the rise of atmospheric GHG concentration [START_REF] Horton | The emergency framing of solar geoengineering: Time for a different approach[END_REF][START_REF] Maccracken | On the possible use of geoengineering to moderate specific climate change impacts[END_REF]Royal Society, 2011;[START_REF] Schäfer | Earth's future in the Anthropocene: Technological interventions between piecemeal and utopian social engineering[END_REF]. It works by modifying the balance of incoming and outgoing radiation in the Earth system, which, if done on a significant scale, can exert a global cooling effect to counteract warming due to greenhouse gases. SRM is perceived controversially by experts and laypeople alike [START_REF] Müller-Hansen | Attention, sentiments and emotions towards emerging climate technologies on Twitter[END_REF] due, in part, to the large social and ecological risks and unknowns involved in intentionally manipulating the complex Earth system.

Various proposals have been put forward to alter the radiative equilibrium, with the injection of aerosols into the stratosphere (SAI) receiving the most attention thus far. An SAI intervention aiming at global impact entails the continuous placement of aerosols at low latitudes in the lower stratosphere [START_REF] Dai | Tailoring Meridional and Seasonal Radiative Forcing by Sulfate Aerosol Solar Geoengineering[END_REF]Kravitz et al., 2019a;[START_REF] Tilmes | Sensitivity of aerosol distribution and climate response to stratospheric SO2 injection locations[END_REF][START_REF] Tilmes | Effects of Different Stratospheric SO 2 Injection Altitudes on Stratospheric Chemistry and Dynamics[END_REF], where the Brewer-Dobson circulation slowly transports them towards the poles. The aerosols reflect the incoming short-wave radiation allowing less radiative energy to reach the surface. While this process leads to cooling at the surface, evidenced by large volcanic eruptions, not all radiation is reflected by the aerosols. Instead, some of the radiative energy is absorbed by the particles, leading to localized heating of the stratosphere, which can affect global circulation patterns [START_REF] Baldwin | Stratospheric Harbingers of Anomalous Weather Regimes[END_REF][START_REF] Dallasanta | The Circulation Response to Volcanic Eruptions: The Key Roles of Stratospheric Warming and Eddy Interactions[END_REF][START_REF] Stenchikov | Arctic Oscillation response to the 1991 Mount Pinatubo eruption: Effects of volcanic aerosols and ozone depletion[END_REF][START_REF] Graft | Pinatubo eruption winter climate effects: model versus observations[END_REF]. For example, several studies on the impact of stratospheric aerosols from volcanic eruptions have found a poleward jet shift [START_REF] Barnes | Robust Wind and Precipitation Responses to the Mount Pinatubo Eruption, as Simulated in the CMIP5 Models[END_REF][START_REF] Polvani | Tropospheric response to stratospheric perturbations in a relatively simple general circulation model[END_REF][START_REF] Simpson | The Role of Eddies in Driving the Tropospheric Response to Stratospheric Heating Perturbations[END_REF]. This has been attributed to two general mechanisms, surface cooling and stratospheric warming [START_REF] Dallasanta | The Circulation Response to Volcanic Eruptions: The Key Roles of Stratospheric Warming and Eddy Interactions[END_REF]. The surface cooling from the stratospheric aerosols decreases the tropospheric meridional temperature gradient [START_REF] Stenchikov | Arctic Oscillation response to the 1991 Mount Pinatubo eruption: Effects of volcanic aerosols and ozone depletion[END_REF][START_REF] Graf | Arctic radiation deficit and climate variability[END_REF], which reduces midlatitude baroclinity, driving a strengthening of the stratospheric vortex, which leads to a poleward shift of the jet [START_REF] Baldwin | Stratospheric Harbingers of Anomalous Weather Regimes[END_REF]. The second and primary mechanism, however, is the observed warming of the stratosphere in the tropics due to the aerosol's absorption of the radiative energy. This enhances the stratospheric meridional temperature gradient leading to a strengthened stratospheric vortex that shifts the jet poleward [START_REF] Dallasanta | The Circulation Response to Volcanic Eruptions: The Key Roles of Stratospheric Warming and Eddy Interactions[END_REF].

Modeling studies on SAI impacts have also found large-scale circulation changes. [START_REF] Liu | Impact of Stratospheric Aerosol Injection on the East Asian Winter Monsoon[END_REF] studied the East Asian Winter Monsoon under SAI and found that aerosol injections reverse the weakening of the monsoon that occurs in SSP585. In Africa, however, SAI can lead to weaker monsoon winds [START_REF] Da-Allada | Changes in West African Summer Monsoon Precipitation Under Stratospheric Aerosol Geoengineering[END_REF][START_REF] Robock | Regional climate responses to geoengineering with tropical and Arctic SO2 injections[END_REF] and a slight southward shift of the manuscript submitted to AGU Earth's Future ITCZ [START_REF] Cheng | Soil Moisture and Other Hydrological Changes in a Stratospheric Aerosol Geoengineering Large Ensemble[END_REF]. It should be emphasized that the outcomes of these studies are likely strongly reliant on the selected injection design and the underlying model [START_REF] Kravitz | Geoengineering as a design problem[END_REF](Kravitz et al., , 2019b;;[START_REF] Lee | The response of terrestrial ecosystem carbon cycling under different aerosol-based radiation management geoengineering[END_REF]MacMartin & Kravitz, 2019).

Wind power generation relies significantly on local and regional wind patterns and even minor fluctuations in wind velocity can have a meaningful impact on the energy output [START_REF] Veers | Grand challenges in the science of wind energy[END_REF]. This is because the energy in the wind follows the cube of the wind speed. While to our knowledge no research has been conducted on WRE potential under SRM, several studies have looked at the impact of climate change on wind potential. They found significant alterations in wind velocity and its temporal distribution as a result of global warming [START_REF] Solaun | Climate change impacts on renewable energy generation. A review of quantitative projections[END_REF].

One of the main mechanisms behind large-scale circulation changes from anthropogenic warming is the reduced equator-to-pole temperature gradient at the surface as a result from polar amplification, which is expected to alter tropical circulation [START_REF] Ma | Mechanisms for Tropical Tropospheric Circulation Change in Response to Global Warming*[END_REF], such as the Hadley cell, monsoon circulations and tropical cyclone frequency, as well as the behavior of midlatitude jet streams and storm tracks [START_REF] Martinez | Global wind energy resources decline under climate change[END_REF][START_REF] Pryor | Climate change impacts on wind power generation[END_REF][START_REF] Shaw | Storm track processes and the opposing influences of climate change[END_REF].

However, wind resources can be further impacted by ocean circulation and surface roughness changes from land cover modifications [START_REF] Jung | A review of recent studies on wind resource projections under climate change[END_REF][START_REF] Vautard | Northern Hemisphere atmospheric stilling partly attributed to an increase in surface roughness[END_REF][START_REF] Zeng | A reversal in global terrestrial stilling and its implications for wind energy production[END_REF]. Additionally, local wind resources exhibit high variability on sub-hourly and multi-decadal scales [START_REF] Jung | National and global wind resource assessment under six wind turbine installation scenarios[END_REF]. Due to the difficulty to accurately represent all drivers and the resulting temporal and spatial variations of wind patterns in Global Circulation Models, it is not entirely certain whether climate change will result in a decrease or increase in wind speeds at the global scale [START_REF] Pryor | Climate change impacts on wind power generation[END_REF]. Most studies find highly diverse regional trends with large increases and decreases in wind speed and wind energy potential all over the globe [START_REF] Gernaat | Climate change impacts on renewable energy supply[END_REF][START_REF] Jung | A review of recent studies on wind resource projections under climate change[END_REF][START_REF] Pryor | Climate change impacts on wind power generation[END_REF][START_REF] Solaun | Climate change impacts on renewable energy generation. A review of quantitative projections[END_REF]. As a result, on a global scale, changes in total wind energy density [START_REF] Martinez | Global wind energy resources decline under climate change[END_REF] and wind energy potential [START_REF] Gernaat | Climate change impacts on renewable energy supply[END_REF] are small and may be slightly negative.

Given that WRE already plays an important role in the prevailing mitigation strategy, and that mitigation is an important aspect of ensuring the temporary use of SRM, it is important to understand whether SRM complements or conflicts with this existing method of energy generation and mitigation. Only through an understanding of the full spectrum of consequences from SAI can responsible decision-making be enabled. Here, we analyze the interplay between WRE and SAI manuscript submitted to AGU Earth's Future by calculating and comparing on-and offshore wind potential when SAI is used versus when mitigation has brought the climate to approximately the same GMST (SSP245). Additionally, we compare the SAI-modified climate with the fossil-fuel heavy emission baseline of the scenario without SAI (SSP585).

Model Experiments and Methods

Data and Simulations

This study is based on three experiments: a fossil-fuel intensive, high-emission scenario called SSP585 [START_REF] O'neill | The Scenario Model Intercomparison Project (ScenarioMIP) for CMIP6[END_REF], a moderately ambitiously mitigated scenario, SSP245 [START_REF] O'neill | The Scenario Model Intercomparison Project (ScenarioMIP) for CMIP6[END_REF], and a stratospheric aerosol injection (SAI) simulation that cools down from an SSP585 baseline to SSP245. The SAI experiment originates from the GeoMIP6 protocol [START_REF] Kravitz | The Geoengineering Model Intercomparison Project Phase 6 (GeoMIP6): Simulation design and preliminary results[END_REF] and is referred to therein as G6sulfur. We run these experiments from 2015 to 2100 in a 6-member ensemble with perturbed initial conditions on the CNRM-ESM-2.1 Earth system model [START_REF] Séférian | Evaluation of CNRM Earth System Model, CNRM-ESM2-1: Role of Earth System Processes in Present-Day and Future Climate[END_REF]. Ensemble means are displayed except if defined otherwise.

As a proxy for SAI we use prescribed aerosol optical depth derived from the GeoMIP G4SSA experiment [START_REF] Tilmes | A new Geoengineering Model Intercomparison Project (GeoMIP) experiment designed for climate and chemistry models[END_REF] which scales up to 0.35 in the last decade of the simulation. The variables related to the directional winds u and v at 150m altitude are produced at hourly resolution on a 1°x1° grid. During the postprocessing we bilinearly regrid the climate model output to match the land use and land cover data (described in 2.2.3 Politico-economic dimension) which is on a 0.1°x0.1° grid. For the zonal winds we create two altitudinal categories: upper and surface. Upper refers to a pressure level of 200-400hPa, roughly corresponding to the upper troposphere, and surface, referring to a pressure level of 850-1050hPa, representing the air close to the Earth's surface.

Wind Potential Calculation

In the same manner as [START_REF] Baur | Solar Radiation Modification challenges decarbonization with renewable solar energy[END_REF], we use the term "potential" to refer to an enhanced version of the traditional definition of the "technical potential". The technical potential is the theoretical potential, here the surface wind resource, constrained by geographical and technical restrictions. In this study, we distinguish between three dimensions that are involved in the wind energy potential calculation: the technical dimension that establishes the technical restrictions to manuscript submitted to AGU Earth's Future the theoretical potential, the physical dimension, which is related to the energy extractable from surface wind speed, and the politico-economic one, which is related to the suitability of the grid cell 𝑖 for wind turbine placement. We calculate the wind potential in a similar fashion to [START_REF] Gernaat | Climate change impacts on renewable energy supply[END_REF] as:

𝑇𝑃 !,#$% = 𝑃𝑜𝑙𝑖𝑡𝑖𝑐𝑜𝑒𝑐𝑜𝑛𝑜𝑚𝑖𝑐 ! × 𝑇𝑒𝑐ℎ𝑛𝑖𝑐𝑎𝑙 #$% × 𝑃ℎ𝑦𝑠𝑖𝑐𝑎𝑙 !,#$% × 𝑔𝑟𝑖𝑑𝑐𝑒𝑙𝑙 ! 5 &'( )* 6 (1)
All parameters, their values, units and sources are given in Table S1. The subscript 𝑙𝑜𝑐 indicates whether it is an on-or offshore wind farm. The resulting electricity generation potential is expressed in various time slices, such as 10-year seasonal mean changes, weekly sums and yearly sums, calculated from the hourly wind speed input. Seasons refer to the four periods December, January, February (DJF), March, April, May (MAM), June, July, August (JJA) and September, October, November (SON). We calculate the Low Energy Week (LEW) metric as introduced by [START_REF] Baur | Solar Radiation Modification challenges decarbonization with renewable solar energy[END_REF].

Technical Dimension

This part of the calculation reduces the physical potential by accounting for the unavailability of the turbines due to maintenance, the wind farm array inefficiencies and the density of wind turbine placement. We use technical indicators from on-and offshore exemplary real-world wind turbines. To avoid projecting technological developments into the future we choose turbines which are either already or about to be in serial production but are at the forefront of current wind turbine development. We justify this choice with the argument that the average wind turbines of the future will be the most powerful wind turbines of today. Table 1 lists their characteristics:

D 234 = @ A=B54:;C × F "#$#%,'#( G ! 5 7869:;<= >? ! 6 (3)
We assume that turbine spacing is equal in prevailing and perpendicular wind direction.

For the turbines set out in Table 1, this gives a D 3;=H36< of 1.56 turbines/km2 and a D 3II=H36< of 0.51 turbines/km2. Translated into the more commonly used metric power density, this implies 9.68 MW/km2 onshore and 7.65 MW/km2 offshore.

Physical Dimension

The physical dimension represents the power produced by a wind turbine p(v), which is described by the wind turbine power curve [START_REF] Carrillo | Review of power curve modelling for wind turbines[END_REF][START_REF] Saint-Drenan | A parametric model for wind turbine power curves incorporating environmental conditions[END_REF]Fig S1) and calculated as:

𝑝(𝑣 ! ) ! = i 0 𝑣 < 𝑣 %! 𝑜𝑟 𝑣 > 𝑣 %$ 𝑞(𝑣 ! ) 𝑣 %! ≤ 𝑣 < 𝑣 * 𝑃 * 𝑣 * ≤ 𝑣 ≤ 𝑣 %$ n (4)
The power curve depends on the instantaneous wind speed 𝑣 and the characteristics of the wind turbine (Table 1) and distinguishes between four different operation regimes (Fig S1 ): I, the area of wind speeds (𝑣) that are smaller than the cut-in wind speed (𝑣 %! ), and therefore too low to produce any energy, II, the area of non-linear relationship between wind speed and power output (𝑞(𝑣)), III, the area of maximum power output, i.e. rated power (𝑃 * ), and IV, the area after the cut-manuscript submitted to AGU Earth's Future out threshold, where wind speed is too high (𝑣 > 𝑣 %$ ) and turbines shut down to protect themselves from damage [START_REF] Saint-Drenan | A parametric model for wind turbine power curves incorporating environmental conditions[END_REF][START_REF] Wood | Power Generation Operation and Control. 2nd Edition[END_REF].

Power production in area II follows the parametric wind turbine power curve described in Saint-Drenan et al. ( 2020) and is calculated as:

q(v : ) = 0.5 × ρ × ε 234 × v J × pc 5 KLH 7869:;< 6 (5)
With 𝜌 being the air density, which is kept constant, 𝜀 the area swept by the rotor blades calculated from the rotor blade diameters (Table 1), 𝑣 instantaneous wind speed and 𝑝𝑐 the power coefficient, a measure for aerodynamic-mechanical-electrical performance of the turbines [START_REF] Veers | Grand challenges in the science of wind energy[END_REF].

For simplicity, in our study, the power coefficient is held constant, however, as demonstrated in Saint-Drenan et al. ( 2020), it is ultimately dependent on and varies with the wind's velocity. The power coefficient parameterization leads to a slight overestimation in power output from higher wind speeds and underestimation of output from lower wind speeds in the 𝑞(𝑣 ! )-part of our calculation.

Due to the high variability of wind, a temporal resolution of 1 hour and a spatial resolution of 1°x1° may not adequately represent all prevailing wind speeds in the area during the specified time period. To account for the requirement of instantaneous wind velocity in the wind power curve calculation and the low spatial resolution of the input data, we represent wind speed through a probability density function. Weibull distributions have frequently been used to represent the spread in wind speed over a time period at a given location (e.g. [START_REF] Aukitino | Wind energy resource assessment for Kiribati with a comparison of different methods of determining Weibull parameters[END_REF][START_REF] Mohammadi | Assessing different parameters estimation methods of Weibull distribution to compute wind power density[END_REF][START_REF] Shi | Wind Speed Distributions Used in Wind Energy Assessment: A Review[END_REF][START_REF] Shu | Investigation of offshore wind energy potential in Hong Kong based on Weibull distribution function[END_REF] and as a means of downscaling to represent the spread of wind over a larger area [START_REF] Alizadeh | A distributed wind downscaling technique for wave climate modeling under future scenarios[END_REF][START_REF] Chang | Evaluation of the climate change impact on wind resources in Taiwan Strait[END_REF][START_REF] Tye | A Weibull Approach for Improving Climate Model Projections of Tropical Cyclone Wind-Speed Distributions[END_REF][START_REF] Zhou | Spatial and temporal patterns of global onshore wind speed distribution[END_REF]. The temporal resolution of the underlying wind data can range from 10 min [START_REF] Eskin | Wind energy potential of Gökçeada Island in Turkey[END_REF], to hourly [START_REF] Chang | Evaluation of the climate change impact on wind resources in Taiwan Strait[END_REF][START_REF] Li | Comparative study of onshore and offshore wind characteristics and wind energy potentials: A case study for southeast coastal region of China[END_REF][START_REF] Mohammadi | Assessing different parameters estimation methods of Weibull distribution to compute wind power density[END_REF][START_REF] Burton | Wind energy handbook[END_REF], 6-hourly [START_REF] Elsner | Continental-scale assessment of the African offshore wind energy potential: Spatial analysis of an under-appreciated renewable energy resource[END_REF], to daily [START_REF] Shu | Estimation of Weibull parameters for wind energy analysis across the UK[END_REF] and longer. [START_REF] Cradden | Consideration of Wind Speed Variability in Creating a Regional Aggregate Wind Power Time Series[END_REF] and [START_REF] Pryor | Climate change impacts on wind power generation[END_REF] have highlighted the importance of a high temporal resolution of at least 1 hour for WRE analyses. Although hourly and daily average wind speeds have been shown to lead to similar power output results from a turbine over a long time period, hourly input data is much better at representing the peaks and lows during the day and can give a more precise result for shorter time periods [START_REF] Shin | A Novel Statistical Method to Temporally Downscale Wind Speed Weibull Distribution Using Scaling Property[END_REF][START_REF] Veronesi | Comparison of hourly and daily wind speed observations for the computation of Weibull parameters and power output[END_REF][START_REF] Justus | Methods for estimating wind speed frequency distributions[END_REF]. In this study, manuscript submitted to AGU Earth's Future the Weibull distribution is used to represent sub-grid spatial and temporal variation in wind. We use a constant shape-parameter for all regions across the globe. This is a frequently applied simplification [START_REF] Dvorak | California offshore wind energy potential[END_REF][START_REF] Elsner | Continental-scale assessment of the African offshore wind energy potential: Spatial analysis of an under-appreciated renewable energy resource[END_REF][START_REF] Eurek | An improved global wind resource estimate for integrated assessment models[END_REF][START_REF] Shu | Investigation of offshore wind energy potential in Hong Kong based on Weibull distribution function[END_REF][START_REF] Sohoni | A Critical Review on Wind Turbine Power Curve Modelling Techniques and Their Applications in Wind Based Energy Systems[END_REF][START_REF] Valencia Ochoa | Data set on wind speed, wind direction and wind probability distributions in Puerto Bolivar -Colombia[END_REF]Arendt et al., 2013) related to the width of the distribution and therefore the gustiness of the wind regimes [START_REF] Eurek | An improved global wind resource estimate for integrated assessment models[END_REF] that is most commonly used in larger scale analyses. Studies have demonstrated variation of the shape parameter across regions [START_REF] Zhou | Spatial and temporal patterns of global onshore wind speed distribution[END_REF], especially for oceanic winds [START_REF] Shi | Wind Speed Distributions Used in Wind Energy Assessment: A Review[END_REF][START_REF] Perrin | A Discussion of Statistical Methods Used to Estimate Extreme Wind Speeds[END_REF]. However, apart from coastal areas, oceanic regions are excluded from this analysis and using the Rayleighform of the Weibull distribution, which sets the shape parameter 𝛽 to 2 and implies moderately gusty winds across all areas [START_REF] Eurek | An improved global wind resource estimate for integrated assessment models[END_REF], drastically reduces the computational effort. The scale parameter, 𝛼, is calculated according to [START_REF] Lysen | Introduction to Wind Energy[END_REF] as follows:

𝛼 = 𝑤𝑠 ! × (0.568 + 0.433 × 0.5) ) * (6)
with 𝑤𝑠 ! being the hourly wind speed from our model output calculated as the square root of the sum of the squares of the east-and northward wind components u and v. We calculate 𝑝(𝑣) for all 1000 samples in the Weibull distribution for each 1 m/s wind speed bin from 0-50 m/s.

The 2-parameter Weibull distribution representing the range of wind speeds prevalent in the 1hour mean 1° grid cell model output is calculated as:

f(T) = M N × x O N y MP@ × e PQ + , R - (7)
For computational feasibility we fit a curve between the 1-hour mean wind speed and the power output, i.e., 𝑝(𝑣), that takes into account the Weibull spread of wind speed and the turbine power curve:

𝑃ℎ𝑦𝑠𝑖𝑐𝑎𝑙 !,#$% = 𝑝(𝑤𝑠 ! ) #$% = 𝑎 #$% × z1 -𝑒 ./0 1 ! 2 345 | × z1 -𝑒 ./0 1 ! 5 345 | × 𝑒 ./0 1 6 345 5 &'( ST*U!VW 6 (8)
Please consult Table S1 in the SI for the values of the parameters 𝑎 #$% , 𝑏 #$% , 𝑐 #$% and 𝑑 #$% . To assess how much energy is lost due to a change in the distribution of hourly wind speeds we additionally calculate the wind potential without the cut-out wind speed limit (no-cut-out). Instead, power output at 𝑣 > 𝑣 %$ is kept at 𝑃 * . By subtracting the yearly cumulative "standard"-turbine-manuscript submitted to AGU Earth's Future power-curve power output with the output from these no-cut-out calculations, we can estimate the amount of TWh that is gained or lost in a year due to a change in fast winds. Figure S2 shows the fitted power curve of an onshore and offshore grid cell in the normal setting and in the no-cut-outsetting.

Politico-Economic Dimension

The incorporation of a politico-economic dimension is a long-standing approach for wind potential calculations (e.g. Eliott & Schwartz, 1993;[START_REF] Archer | Evaluation of global wind power[END_REF][START_REF] Bosch | Temporally-explicit and spatially-resolved global onshore wind energy potentials[END_REF][START_REF] Hoogwijk | On the global and regional potential of renewable energy sources = Over het mondiale en regionale potentieel van hernieuwbare energiebronnen[END_REF][START_REF] Zhou | Evaluation of Global Onshore Wind Energy Potential and Generation Costs[END_REF] and is related to the suitability of each grid cell to harbor wind turbines. Various parameters have been taken into account in the past. Here, we consider surface properties and land use competition for our onshore wind farms as done in [START_REF] Baur | Solar Radiation Modification challenges decarbonization with renewable solar energy[END_REF]. differentiates between 20 different land use and land cover categories. We weigh each type according to the fraction of a grid cell that could be covered by wind farms, in line with [START_REF] Baur | Solar Radiation Modification challenges decarbonization with renewable solar energy[END_REF], but with different fractions assigned (see Table S2 for land use categories and assigned suitability fractions). The rationale behind the suitability fraction is that only part of a grid cell is available for wind farms as they could potentially conflict with other land uses such as cities, agricultural production or ecosystem services from forests. A suitability fraction of 15% denotes that 15% of the grid cell is able to accommodate a wind farm. The spacing between the turbines of several hundred meters enables a certain level of coexistence between wind farms and predominant land uses. This explains the assignment of higher fractions for, for example, agricultural areas in this study than in [START_REF] Baur | Solar Radiation Modification challenges decarbonization with renewable solar energy[END_REF], which looked at solar farms.

We use the same approach as [START_REF] Baur | Solar Radiation Modification challenges decarbonization with renewable solar energy[END_REF] to weigh the proximity to highly populated areas.

The population data from the IMAGE3.0 LPJ model consists of 5-year intervals and is aggregated to 10-year means for our analysis [START_REF] Doelman | Exploring SSP land-use dynamics using the IMAGE model: Regional and gridded scenarios of land-use change and land-based climate change mitigation[END_REF][START_REF] Stehfest | Integrated Assessment of Global Environmental Change with IMAGE 3[END_REF]. Using a sigmoidal function, we impose that the weight diminishes proportionally as the distance to densely populated cells grows, ultimately tapering to zero at approximately 500 km. Unlike Baur et al. ( 2023), we exclude highly populated areas, which we define as cells where population density is larger than 1000 inhabitants/km2.

We present results that are calculated using equal weights across all scenarios and time intervals.

Therefore, the data underlying population, sea ice and land use are related to the 2090-2099 time frame of SSP245 but are used as a basis for all three scenarios. Variation in large-scale circulation has been attributed to temperature changes in the stratosphere and resulting increases or decreases in the temperature gradients at the surface and/or the upper troposphere [START_REF] Baldwin | Stratospheric Harbingers of Anomalous Weather Regimes[END_REF][START_REF] Charlesworth | Stratospheric water vapor affecting atmospheric circulation[END_REF][START_REF] Dallasanta | The Circulation Response to Volcanic Eruptions: The Key Roles of Stratospheric Warming and Eddy Interactions[END_REF][START_REF] Simpson | The Regional Hydroclimate Response to Stratospheric Sulfate Geoengineering and the Role of Stratospheric Heating[END_REF][START_REF] Stenchikov | Arctic Oscillation response to the 1991 Mount Pinatubo eruption: Effects of volcanic aerosols and ozone depletion[END_REF][START_REF] Graf | Arctic radiation deficit and climate variability[END_REF]. In our simulations we see a large temperature shift of up to 14K under SAI compared to the SSP-scenarios in the tropical stratosphere (Figure S8). The largest increase is at around 80hPa. As expected, temperatures at the surface are lower under SAI than SSP585, especially in the tropics, which is a common phenomenon observed in SRM simulations. Due to the augmented CO2 concentration, which increases the rate that the stratosphere radiates heat to space, the stratosphere is colder under SSP585 than SSP245 (Figure S8c). . While the regional differences are diverse and large, globally, relative differences are small. SAI potential is only 2.2 % lower onshore and 1.3 % lower offshore than for SSP245 and 3.0 % lower onshore and 0.9 % lower offshore than for SSP585. Between the SSP-scenarios the total global relative difference ends up being 0 % since onshore potential is increased under SSP585 compared to SSP245 by 0.6 % but onshore potential decreased by 0.6 %. manuscript submitted to AGU Earth's Future

Results

Large-scale Circulation

To evaluate how much of the changes in wind potential are caused by changes in fast wind speed, we measure the annual power loss resulting from winds exceeding the cut-out threshold. Figure 7 shows which areas are mostly affected by energy losses due to fast winds in GWh per year per grid cell. Unsurprisingly, offshore areas are mostly affected by losses due to fast winds since wind is generally significantly slower over land areas (Fig 7a-c) and we applied lower suitability restrictions on offshore than onshore grid cells. Nevertheless, there are several onshore areas that see substantial reductions, such as the Great Plains in the US, the Southern parts of the Sahara,

Central Asia and Russia. The differences between the scenarios are displayed in Figure 7d-f.

Offshore northern Europe, the tip of Argentina and eastern Canada are the only regions that have substantially higher losses due to fast winds under SAI than the SSP-scenarios. SAI makes winds offshore of China, eastern USA, New Zealand and south-east South America and, onshore, the Sahara more accessible to energy generation. The total global energy loss due to fast winds is lowest for SAI with 8.5 PWh/yr (2.6 %) and identical for SSP245 and SSP585 with 8.9 PWh/yr

(2.7 %).

Discussion

In this study, we examined the interplay between Stratospheric Aerosol Injections (SAI)

and renewable wind energy potential. We found large changes in wind potential under SAI compared to a medium emission (SSP245) or high emission (SSP585) climate state depending on manuscript submitted to AGU Earth's Future the season and region (Fig 5,6). The change in potential under SAI is especially regionally highly diverse with magnitudes frequently reaching 16 %. These large regional differences average out to a total global potential that is slightly smaller than for SSP245 or SSP585.

Wind energy potential is highly dependent on wind resources and long-term changes therein are mainly due to large-scale atmospheric circulation [START_REF] Jung | A review of recent studies on wind resource projections under climate change[END_REF]. Previous analyses on stratospheric aerosols and atmospheric circulation have found impacts on global and regional circulation patterns, in particular a poleward shift of the jet [START_REF] Barnes | Robust Wind and Precipitation Responses to the Mount Pinatubo Eruption, as Simulated in the CMIP5 Models[END_REF][START_REF] Mccusker | Rapid and extensive warming following cessation of solar radiation management[END_REF][START_REF] Polvani | Tropospheric response to stratospheric perturbations in a relatively simple general circulation model[END_REF][START_REF] Simpson | The Role of Eddies in Driving the Tropospheric Response to Stratospheric Heating Perturbations[END_REF][START_REF] Simpson | The Regional Hydroclimate Response to Stratospheric Sulfate Geoengineering and the Role of Stratospheric Heating[END_REF]. In our analysis, we also found significant differences in zonal wind between SAI and the SSP-scenarios, as well as under the stratosphere, an effect likewise observed in our experiments (Figure S8). Studies on stratospheric aerosols from volcanic eruptions and circulation anomalies have made the same observation [START_REF] Barnes | Robust Wind and Precipitation Responses to the Mount Pinatubo Eruption, as Simulated in the CMIP5 Models[END_REF][START_REF] Dallasanta | The Circulation Response to Volcanic Eruptions: The Key Roles of Stratospheric Warming and Eddy Interactions[END_REF][START_REF] Karpechko | Southern Hemisphere atmospheric circulation response to the El Chichón and Pinatubo eruptions in coupled climate models: Southern Hemisphere Response to El Chichón and Pinatubo[END_REF][START_REF] Mcgraw | Reconciling the observed and modeled Southern Hemisphere circulation response to volcanic eruptions[END_REF][START_REF] Graft | Pinatubo eruption winter climate effects: model versus observations[END_REF][START_REF] Kirchner | Climate model simulation of winter warming and summer cooling following the 1991 Mount Pinatubo volcanic eruption[END_REF] and attribution to stratospheric heating [START_REF] Barnes | Robust Wind and Precipitation Responses to the Mount Pinatubo Eruption, as Simulated in the CMIP5 Models[END_REF][START_REF] Dallasanta | The Circulation Response to Volcanic Eruptions: The Key Roles of Stratospheric Warming and Eddy Interactions[END_REF][START_REF] Polvani | Tropospheric response to stratospheric perturbations in a relatively simple general circulation model[END_REF][START_REF] Simpson | The Role of Eddies in Driving the Tropospheric Response to Stratospheric Heating Perturbations[END_REF]. However, not all volcanic modeling results lead to the same conclusion: In the Northern Hemisphere (NH), [START_REF] Ramachandran | Radiative impact of the Mount Pinatubo volcanic eruption: Lower stratospheric response[END_REF] and [START_REF] Marshall | Enhanced Seasonal Prediction of European Winter Warming following Volcanic Eruptions[END_REF] find an equatorward shift in response to the volcanic forcing instead and in the SH [START_REF] Robock | Southern Hemisphere atmospheric circulation effects of the 1991 Mount Pinatubo eruption[END_REF] and [START_REF] Roscoe | Influences of ozone depletion, the solar cycle and the QBO on the Southern Annular Mode: INFLUENCES ON THE SOUTHERN ANNULAR MODE[END_REF] found no or a slight equatorward shift. [START_REF] Simpson | The Regional Hydroclimate Response to Stratospheric Sulfate Geoengineering and the Role of Stratospheric Heating[END_REF][START_REF] Mccusker | Inability of stratospheric sulfate aerosol injections to preserve the West Antarctic Ice Sheet[END_REF] observe, and our study confirms, that the SH shows a much stronger signal, and that not all the changes in the NH are attributable to the stratospheric heating, such as, for example, in the North Pacific or the Atlantic during JJA [START_REF] Simpson | The Regional Hydroclimate Response to Stratospheric Sulfate Geoengineering and the Role of Stratospheric Heating[END_REF]. of SAI that are different from ours. The divergence in results may be partially explained by the difference in scenario comparisons but it nevertheless suggests that the impacts of SAI on wind are not well understood to date. The scenario-comparisons in Figure 4 and 5 suggest that SAI does not compensate for changes from global warming but modifies wind resources in a novel way.

While no studies exist to date that evaluate wind energy potential changes under SRM, studies looking at changes in WRE potential due to climate change have found regionally highly diverse trends (e.g. [START_REF] Gernaat | Climate change impacts on renewable energy supply[END_REF][START_REF] Solaun | Climate change impacts on renewable energy generation. A review of quantitative projections[END_REF][START_REF] Tobin | Assessing climate change impacts on European wind energy from ENSEMBLES highresolution climate projections[END_REF]. We generally see similar developments for the SSP245 and SSP585 comparison as other studies that look at wind potential under climate change. Remarkable similarities exist on the South American [START_REF] De | Estimating the impact of climate change on wind and solar energy in Brazil using a South American regional climate model[END_REF][START_REF] Gernaat | Climate change impacts on renewable energy supply[END_REF][START_REF] Pereira De Lucena | The vulnerability of wind power to climate change in Brazil[END_REF][START_REF] Pereira | The impacts of global climate changes on the wind power density in Brazil[END_REF] and African continent [START_REF] Gernaat | Climate change impacts on renewable energy supply[END_REF][START_REF] Sawadogo | Current and future potential of solar and wind energy over Africa using the RegCM4 CORDEX-CORE ensemble[END_REF] and Europe [START_REF] Carvalho | Potential impacts of climate change on European wind energy resource under the CMIP5 future climate projections[END_REF][START_REF] Davy | Climate change impacts on wind energy potential in the European domain with a focus on the Black Sea[END_REF][START_REF] Gernaat | Climate change impacts on renewable energy supply[END_REF][START_REF] Tobin | Assessing climate change impacts on European wind energy from ENSEMBLES highresolution climate projections[END_REF][START_REF] Tobin | Vulnerabilities and resilience of European power generation to 1.5 °c, 2 °c and 3 °c warming[END_REF].

Gernaat et al. ( 2021) note a relative global reduction in offshore wind potential of 2.1 % from historical values to the end of the century under an RCP6.0 pathway and a reduction in onshore potential by 4.1 %. This is much higher than what we see for SSP245 versus SSP585, which has a global mean reduction in onshore wind potential of 0.6 % and an increase in offshore potential of 0.6 %. Our analyses are not directly comparable due to differences in underlying data and methodology and because our pathways result in a greater level of warming at the point of comparison. However, the absolute temperature difference between SSP245 and SSP585 and other studies that provide wind technical potential in energy units (Table 2; [START_REF] Archer | Evaluation of global wind power[END_REF][START_REF] Bosch | Temporally-explicit and spatially-resolved global onshore wind energy potentials[END_REF][START_REF] Chu | A geographic information system-based global variable renewable potential assessment using spatially resolved simulation[END_REF][START_REF] Eurek | An improved global wind resource estimate for integrated assessment models[END_REF][START_REF] Gernaat | Climate change impacts on renewable energy supply[END_REF]Hoogwijk, manuscript submitted to AGU Earth's Future 2004;[START_REF] De Vries | Renewable energy sources: Their global potential for the first-half of the 21st century at a global level: An integrated approach[END_REF][START_REF] Lu | Global potential for wind-generated electricity[END_REF][START_REF] Krewitt | Role and Potential of Renewable Energy and Energy Efficiency for Global Energy Supply[END_REF]. Discrepancies are possible due to differences in the underlying models, unalike methodological approaches in calculating the potential, such as dissimilar assumptions regarding land suitability and the characteristics of the wind turbines, as well as the temporal resolution of the wind data. Contrary to those studies, our offshore potential is much greater than onshore, and energy losses offshore are also much higher than onshore (Figure 7). This is due to the stronger suitability constraints we apply on land grid cells and, as demonstrated by [START_REF] Martinez | Global wind energy resources decline under climate change[END_REF] and [START_REF] Tian | Observed and global climate model based changes in wind power potential over the Northern Hemisphere during 1979-2016[END_REF], the generally higher energy density offshore. The LEW metric assesses whether an area encounters notably low weekly energy production variations, tackling the intermittency apprehension of RE. Extended durations of considerably low production, as measured by the LEW metric, may be more significant than a minor decline from high production days to medium production days, as indicated by long-term average data. Several areas all over the globe see up to 6 additional or 6 fewer LEWs per year on average under SAI than the SSP-scenarios (Figure 6). The regional sign and magnitude of change mostly overlaps with that from the 10-year average changes (Figure S10). [START_REF] Baur | Solar Radiation Modification challenges decarbonization with renewable solar energy[END_REF] computed the LEW metric for Photovoltaic potential under SAI and found much larger increases in the order of up to magnitude of change between long-term average and LEW difference. While their change in LEWs is much higher than what we see for wind, their relative decrease in long-term averages is much lower. This means that in those weeks where energy production is low for wind RE, it is particularly low, pulling the long-term average to higher numbers. Whereas for Photovoltaic potential, the LEWs are frequent but not as unproductive. Since long periods of calm winds or cloudy conditions can be problematic for energy systems that rely on wind or solar RE, it is relevant to look at whether regions with high general wind potential and high LEW increase correlate with regions of high solar potential and high solar LEW increase or trends in other types of intermittent renewable energies.

Wind turbine energy output does not scale linearly with wind speed. Rather, they have a delicate range of wind speeds in which they can produce electricity, described by the wind turbine power curve. Hence, lower (higher) wind speeds do not necessarily imply lower (higher) wind potential. Nevertheless, in our analysis, with the same time periods considered, the maps of differences in wind potential (Figure S9) correlate well (correlation coefficient 0.68 for SAI; 0.70 for the SSP-scenarios) with the maps of differences in wind speed (Figure 4). However, while total global potential is smaller under SAI than in the SSP-scenarios, SAI reduces the amount of energy that is lost due to fast winds that are not harvested by wind turbines (Fig 7). The observed decrease in WRE potential under SAI can therefore not be attributed to alterations in fast wind patterns and the current quest for wind turbines with ever-higher cut-out thresholds might take up a lower priority in an SAI-modified world. The total amount of energy lost due to fast winds for all three scenarios in our results is likely to be smaller than real-world applications would suggest, partly due to the Weibull distribution we apply to power output to represent variations in wind speed over time and space. This distribution results in power outputs for 1-hour average wind speeds that are above the cut-out wind speed (Fig S2), because even if the average wind speed is above the cut-out threshold, some samples of the Weibull distribution of that average wind speed may be below the cut-out and therefore produce electricity. In reality, however, the wind turbines are not instantly turned on and off for wind gusts above or below the cut-out threshold. This means that we could be overestimating the energy gained and underestimating the energy lost from fast winds.

However, the wind turbine power curve represents the power output of a single turbine, and our positively-skewed normal distribution of power output may a better representation of the output manuscript submitted to AGU Earth's Future from an entire grid cell, as other studies have shown [START_REF] Bosch | Temporally-explicit and spatially-resolved global onshore wind energy potentials[END_REF][START_REF] Pryor | Climate change impacts on wind energy: A review[END_REF].

Wind varies greatly in space and time [START_REF] Cradden | Consideration of Wind Speed Variability in Creating a Regional Aggregate Wind Power Time Series[END_REF][START_REF] Lee | Assessing variability of wind speed: comparison and validation of 27 methodologies[END_REF][START_REF] Yan | Characterising the fractal dimension of wind speed time series under different terrain conditions[END_REF] and our hourly input data, which represents entire 1° grid cells, is not able to fully reflect that. We regridded our wind data using a bilinear method to match the spatial resolution of the land use data rather than conducting a costly statistical downscaling. As an approximation of the different wind speeds in space and time we applied a Weibull distribution. A constant Weibull shape parameter was used across the globe to ensure computational practicality. However, this approach may lead to under-or overestimation of wind power output in certain regions [START_REF] Zhou | Spatial and temporal patterns of global onshore wind speed distribution[END_REF].

Selecting a constant shape parameter in the Weibull distribution is a simplification because it ultimately relies on the regional wind system and terrain. Nevertheless, any errors that may be produced from this simplification will affect all three scenarios equally and will be largely negated when comparing the scenarios. Our study focuses on the impact of SAI on wind renewable energy potential, specifically differences in predicted future states rather than precise and accurate regional representations of wind potential.

The study's findings are specific to a single SAI experimental set-up (continuous injection of sulfate aerosols) and model that may have a larger SAI signal than is currently considered in a hypothetical deployment scenario but allows us a larger signal-to-noise ratio. Since no other modeling groups have performed SAI experiments with hourly wind output, the study's robustness is constrained by these limitations. However, several studies looking at surface wind speed changes under SAI have found similar patterns to us [START_REF] Da-Allada | Changes in West African Summer Monsoon Precipitation Under Stratospheric Aerosol Geoengineering[END_REF][START_REF] Mousavi | Future dust concentration over the Middle East and North Africa region under global warming and stratospheric aerosol intervention scenarios[END_REF][START_REF] Tang | Impact of solar geoengineering on wildfires in the 21st century in CESM2/WACCM6[END_REF]. To increase the robustness of the results, more model intercomparison studies such as Models with observations and their ability to simulate long-term trends [START_REF] Pryor | Climate change impacts on wind energy: A review[END_REF][START_REF] Pryor | Climate change impacts on wind power generation[END_REF][START_REF] Tian | Observed and global climate model based changes in wind power potential over the Northern Hemisphere during 1979-2016[END_REF]Sheperd, 2014), particularly in coastal areas [START_REF] Soares | Western Iberian offshore wind resources: More or less in a global warming climate?[END_REF][START_REF] Solaun | Climate change impacts on renewable energy generation. A review of quantitative projections[END_REF], they are presently the most reliable source for global wind projections with SAI.

manuscript submitted to AGU Earth's Future

Our offshore energy assessment may further incur inaccuracies as a result of overestimating suitable areas by ignoring common shipping lanes and their unsuitability for wind farms. It is likely that for energy generation purposes unsuitable areas such as ports and frequently used transportation routes are located in proximity to areas that we consider particularly suitable, that is, areas close to population centers.

This study looks at the large-scale changes in the dynamics of the circulation system. While these have an important influence on local wind conditions, wind speeds in the lower levels of the atmospheric boundary layer, i.e., those accessible to wind turbines, are highly susceptible to turbulence from small-scale features such as buildings, trees and valleys [START_REF] Veers | Grand challenges in the science of wind energy[END_REF]. These microscale processes are not resolved in our global analysis. An SSP245-world would likely have substantial differences in terms of land cover and population distribution compared to an SSP585or an SAI-world. As these things are hard to predict and would complicate the comparison between scenarios, we chose equal area weighting for all scenarios.

Future research should not only consider other types of renewable energy sources such as biofuels and hydropower but look at the effects of SAI on renewable energy sources in conjunction.

This would allow to identify regions where not just one RE technology, but potentially several, may experience a change in their productivity with SAI. Additionally, it is relevant to consider not only resource changes due to SRM but also demand changes. One could imagine a modified demand for heating and cooling under SRM, for example. Studies looking at other types of SRM, such as Marine Cloud Brightening, would offer a more complete picture on SRM and renewable energy. At the same time, improvements in the representation of SRM and the response of atmospheric circulation to a change in forcing in the Earth System Models would substantially increase accuracy of the results. Since stratospheric heating has been found to play an important role in changing large-scale circulation [START_REF] Simpson | The Regional Hydroclimate Response to Stratospheric Sulfate Geoengineering and the Role of Stratospheric Heating[END_REF][START_REF] Charlesworth | Stratospheric water vapor affecting atmospheric circulation[END_REF][START_REF] Baldwin | Stratospheric Harbingers of Anomalous Weather Regimes[END_REF][START_REF] Graft | Pinatubo eruption winter climate effects: model versus observations[END_REF][START_REF] Stenchikov | Arctic Oscillation response to the 1991 Mount Pinatubo eruption: Effects of volcanic aerosols and ozone depletion[END_REF][START_REF] Dallasanta | The Circulation Response to Volcanic Eruptions: The Key Roles of Stratospheric Warming and Eddy Interactions[END_REF], narrowing down the uncertainty related to the radiative properties of stratospheric aerosols could improve the understanding of the impacts of SAI on wind RE. And lastly, since SAI seems to significantly affect the spatial distribution of wind resources, regional scale analyses are an essential addition in better understanding wind potential under SAI.

Wind renewable energy is considered a critical component in the efforts to reduce greenhouse gas emissions and transition to a more sustainable energy system. Studying the interplay between SAI and wind energy is important to understand whether mitigation and SAI could work together to address climate change. Here, we examined the alterations in wind patterns and RE resources under SAI using the CNRM-ESM2-1.

We find that SAI, while counterbalancing the temperature increase of climate change, does not [START_REF] Baur | Solar Radiation Modification challenges decarbonization with renewable solar energy[END_REF]. We note that the reduction in long-term potential and the increase in low energy weeks is not due to an increase of wind speed under SAI (Fig 7).

This paper contributes to the ongoing discourse on climate intervention strategies and their implications for mitigation. While this study entails a high temporal resolution and a fairly high number of ensemble members, future studies could rely on higher spatial resolution models and a larger range of emission scenarios with SAI to test and improve accuracy of the current assumptions. Climate projections are still faced with the challenge of understanding the effect of global warming on atmospheric circulation change and pattern formation [START_REF] Shepherd | Atmospheric circulation as a source of uncertainty in climate change projections[END_REF].

Improvements in these fundamental understandings might help in attributing the changes from the combined effects of global warming and SAI on wind allowing for a better investigation of the impacts of SAI on WRE potential. We suggest that further research is necessary to assess the wider impacts of SAI on renewable energies to enable more responsible and informed decision-making on climate intervention.

Figure 1

 1 Figure 1 displays the convolutions of the single area restrictions for on-and offshore wind farms which are used in the wind potential calculation (𝑃𝑜𝑙𝑖𝑡𝑖𝑐𝑜𝑒𝑐𝑜𝑛𝑜𝑚𝑖𝑐 ! ). The single area restrictions and their weights are displayed in Figure S3 and S4. We exclude all areas marked as protected with any status as characterized by the United Nations Environment Programme (IUCN, 2023) as possible wind power installation sites and weigh areas according to the prevalent land-use and distance to highly populated centers as an indicator for the future existence of transmission lines and demand. Highly populated areas are excluded since wind turbines are rarely situated in close proximity to, or on top of, buildings. For offshore we add additional constraints, such as the bathymetry over 1000m, exclusion of grid cells outside the Exclusive Economic Zone (EEZ) (Flanders Marine Institute, 2019) and consideration of only those grid cells that are at least 95% sea-ice free in every season of the year.

Figure 1 .

 1 Figure 1. Convolution of area restrictions for a) onshore and b) offshore.

  Response to SAI Our simulations indicate substantial alterations in 10-year mean zonal wind from the present (2015-2024) to the end of the century (2090-2099) (Fig S5). While the patterns of change show some similarities for SAI, SSP585 and SSP245, the magnitude of the circulation differences from present to future varies considerably and is especially pronounced for SAI and SSP585 (Fig S5). When comparing the future conditions of the scenarios with each other, substantial differences become apparent (Fig 2). Regardless of altitude or scenario-comparison, the largest differences are registered in the Southern Hemisphere (SH): Here, the westerlies' shift towards the pole is more manuscript submitted to AGU Earth's Future pronounced under SAI compared to the SSP-scenarios and, comparing the SSP-scenarios, there is a more intense strengthening of the westerlies and poleward shift of the SH jet for SSP585 compared to SSP245 at the end of the century. The signal is strongest in the upper troposphere for all scenario-comparisons with differences in zonal wind speed of up to 4 m/s (Figure 2 a-c). While the sign of difference between SAI and the SSPs stays consistent across most seasons, the intensity varies (Fig S6, S7).

Figure 2 .

 2 Figure 2. Difference in 2090-99 mean zonal winds between a,d) SAI and SSP245, b,e) SAI and SSP585 and c,f) SSP245 and SSP585 at a-c) the upper troposphere and d-f) the surface. In the NH, the changes are less latitudinally and, over the Atlantic Ocean, altitudinally consistent. While both upper tropospheric and surface winds show a pronounced equatorward shift of the midlatitude westerlies over the Pacific under SAI compared to the SSPs, the upper troposphere over the Atlantic entails a strengthened equatorward shift of the subtropical jet that does not propagate as much to the surface as for the SH (Fig 2, 3, S5). The decrease in midlatitude wind speed under SAI moves towards the equator as it propagates to the surface when comparing to SSP245, while shifting slightly poleward when comparing to SSP585 (Fig 3 a,b). The largest circulation changes occur in the upper troposphere and stratosphere (Fig 2, 3).

Figure 3 .

 3 Figure 3. Difference in 2090-99 average zonal mean winds between a) SAI and SSP45, b) SAI and SSP585 and c) SSP245 and SSP585.

  Long-term average wind speed is substantially lower in the NH under SAI compared to the present (Fig 4a) and compared to the SSPs (Fig 4d,e). A trend fairly consistent throughout the scenarios but most noticeable in SSP585 is the increase in wind speed in tropical land regions compared to the present, especially in Brazil and on the African continent. Most other land regions experience reductions in wind speed (Fig 4a-c).

Figure 4 .

 4 Figure 4. 150m wind speed comparing present (2015-2024) and future (2090-2099) states under a) SAI, b) SSP585 and c) SSP245 and comparing future states of scenarios d) SAI and SSP245, e) SAI and SSP585 and f) SSP585 and SSP245.

Figure 5

 5 Figure 5 displays the relative difference in 2090-99 seasonal wind potential between the SSPscenarios and SAI (see Figure S9 for 10-year mean present to future comparisons for each scenario). The sign of change is relatively consistent, although varying in strength, through the different seasons for SSP245 -> SAI, except for the South East Asian and Northern European region, where DJF and MAM show a large increase in wind potential, while JJA and SON show a decrease (Fig 5a,d,g,j). The same seasonal pattern is visible for SSP585 -> SAI in South East Asia, but not in Europe. In general, the seasons appear to agree less on the sign of the relative change between SSP585 and SAI than for SSP245 and SAI. For example, apart from Europe and South East Asia, also Central Africa and Central Asia show different trends depending on the season when comparing SSP585 with SAI (Fig 5b,e,h,k). While there is not one single region that stands out with especially large differences compared to others, the most pronounced differences in SSP585 to SAI of around 16% are the large decrease in JJA in the southern Sahara (Fig 5h), the decrease in northern China in DJF (Fig 5b), the decrease in South America through all seasons but especially in Brazil in SON (Fig 5k) and Argentina, Bolivia and Paraguay in DJF (Fig 5b) and the

Figure 5 .

 5 Figure 5. Relative differences in seasonal 2090-2099 wind potential for a,d,g,j) SSP245 to SAI, b,e,h,k) for SSP585 to SAI and c,f,i,l for SSP245 to SSP585 in the seasons a-c) December, January, February (DJF), d-f) March, April, Mai (MAM), g-i) June, July, August (JJA) and j-l) September, October, November (SON). Colored areas are statistically significant p<0.05, gray areas are considered suitable for wind production but show no significant change. x -> y denotes (y -x)/x.

Figure 6 .

 6 Figure 6. Low Energy Week (LEW) metric for a) SAI, b) SSP585 and c) SSP245. The LEW is calculated between the present (2015-2019) and the future (2095-2099). See Baur et al. (2023) for the LEW equation. d-f) are the differences between a-c).

Figure 7 .

 7 Figure 7. Difference between normal power curve setting and "no-cut-out" power curve setting for a) SAI, b) SSP245 and c) SSP585. Differences in energy lost due to fast winds between a) SAI and SSP245, b) SAI and SSP585 and c) SSP585 and SSP245.

  SSP-scenarios themselves(Fig 2, 3). The largest disparities exist within the Southern Hemisphere (SH) westerlies, which show a poleward shift under SAI compared to the SSP-scenarios, leading to both an increase and a decrease in the zonal mean wind of up to 4 m/s (Figure2, 3). Our results are in agreement with those of[START_REF] Simpson | The Regional Hydroclimate Response to Stratospheric Sulfate Geoengineering and the Role of Stratospheric Heating[END_REF], who studied alterations in large-scale circulation patterns using an SAI-setup known as GLENS. GLENS uses SAI to stay at 2020 conditions under an SSP585 baseline(Tilmes et al., 2018a). Simpson et al. (2019) conducted separate isolated forcing experiments to analyze how shifts in zonal wind patterns are driven by the stratospheric temperature change from SAI in GLENS. The authors note westerly stratospheric anomalies in the extra-tropics of similar magnitude and pattern as those identified in our study, and attribute the dominant role driving this change in the SH to the heating of the tropical lower

  manuscript submitted to AGU Earth's Future[START_REF] Tang | Impact of solar geoengineering on wildfires in the 21st century in CESM2/WACCM6[END_REF] noted a total global reduction in onshore wind speed as a side effect of SAI using the same underlying scenarios as this study, but a different model and a lower temporal resolution. They see similar spatial patterns and magnitudes of change in surface wind speed as we do(Fig 5l-k in Tang et al., 2023), especially over land(Fig 4e), and results from regional analyses also broadly overlap with our findings[START_REF] Da-Allada | Changes in West African Summer Monsoon Precipitation Under Stratospheric Aerosol Geoengineering[END_REF][START_REF] Mousavi | Future dust concentration over the Middle East and North Africa region under global warming and stratospheric aerosol intervention scenarios[END_REF]. However,[START_REF] Xie | Impacts of three types of solar geoengineering on the Atlantic Meridional Overturning Circulation[END_REF] used a 6-model ensemble to identify the impacts of SAI on the Atlantic Meridional Overturning Circulation and report changes in global wind speed patterns as a result

  Gernaat et al.'s historical and end-of-century value is of similar range. Despite the much smaller relative global change in potential with climate change compared to Gernaat et al.'s study, we calculate a total global potential that is broadly comparable with the results from Gernaat et al. and

  Xie et al.'s 2022 study will need to be performed, as well as different SAI experiment designs. Not all regions have signal-to-noise ratios that are above 1 (Fig S9) or show statistically significant differences between scenarios (Fig 5, S10), which is a common occurrence for sensitive variables such as wind. Despite the ongoing debate surrounding the consistency of Global Circulation

  seem to counterbalance the effects of climate change on wind RE. Instead, our model simulations suggest that SAI may create new atmospheric circulation features (Fig 2-4). The overall long-term impact on WRE resources appears to be highly location-specific, with large increases and reductions in potential under SAI compared to SSP245 or SSP585 of 16 % (Fig 5, S10). However, the long-term total global change in potential is negligible. Furthermore, we find that SAI increases the number of weeks of considerably low production per year in most places around the world (Fig 6) compared to the SSP-scenarios and to the present, although to a much lesser degree than for solar RE

Table 1 .

 1 Exemplary on-and offshore wind turbine specifications. Data from Vestas (2023a),

	(2023b).
		Vestas V162-6.2 (onshore)	Vestas V236-15 (offshore)
	Rated power (𝑷 𝒓 )	6.2 MW	15 MW
	Cut-in windspeed (𝒗 𝒄𝒊 )	3.0 m/s	3.0 m/s
	Cut-out windspeed (𝒗 𝒄𝒐 )	25 m/s	30 m/s

Table 2 .

 2 Comparison of total global on-and offshore wind potential with previous studies. Our results: SSP245 in 2090-2099 based on yearly sums of hourly output. NA means not available.

		Onshore	Offshore	Area	Year
		[PWh/yr]	[PWh/yr]
	Our results	217	399	global	2090-2099
	Hoogwijk, 2004	96	NA	global	2000
	de Vries et al., 2007	34	NA	global	2000 / 2050
	Krewitt et al., 2009	105	16	global	2050
	Eurek et al., 2017	560	315	global	NA
	Chu & Hawkes, 2020	211	216	global	NA
	Bosch et al., 2017	587	330	global	NA
	Lu et al., 2009	690	157	global	2000
	Archer & Jacobson, 2005	630	NA	global	2000
	Gernaat et al., 2021	149	114	global	2070-2100

Acknowledgments

Susanne Baur is supported by CERFACS through the project MIRAGE. BS and RS acknowledges funding by the European Union's Horizon 2020 (H2020) research and innovation manuscript submitted to AGU Earth's Future program under Grant Agreement No. 101003536 (ESM2025 -Earth System Models for the Future), 821003 (4C, Climate-Carbon Interactions in the Coming Century) and 101003687 (PROVIDE).

Availability Statement

The code is available at https://github.com/susannebaur/SRM_wind_RE.git. Upon final publication the code will be made publicly available with a DOI under zenodo.

Underlying data is output from the CNRM-ESM2-1 Earth System Model. Due to the large size of the raw data (>1.5TB) it is available upon request from the authors until a sufficiently large storage repository has been found. The post-processed model output will be made available upon final publication with a DOI on zenodo. Land use and land cover as well as population density projections are from the IMAGE3.0-LPJ model [START_REF] Doelman | Exploring SSP land-use dynamics using the IMAGE model: Regional and gridded scenarios of land-use change and land-based climate change mitigation[END_REF][START_REF] Stehfest | Integrated Assessment of Global Environmental Change with IMAGE 3[END_REF]. Land and ocean protected areas are from the International Union for Conservation of Nature (IUCN, 2023). The Exclusive Economic Zone (EEZ) is from the Flanders Marine Institute (2019), bathymetry and sea-ice information is output from the CNRM-ESM2-1 simulations. Figures were created using the matplotlib library and the matplotlib wrapper proplot.

Conflict of Interest

The authors declare no conflict of interest.

Open Research


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Do (colored) backgrounds matter? An experiment on artificially augmented ground truth for handwritten text recognition applied to historical manuscripts

Keywords: Recognition, Data augmentation, Low tech strategy, Historical documents, Kraken

We present an experiment conducted on the augmentation of older grayscale datasets designed for automatic text recognition on contemporary handwriting (IAM-Database). The augmentation method relies on the addition of colored backgrounds taken from real-world historical blank pages and allows us to create an enhanced version of IAM-Database. We train various transcription models playing on the composition of trainset and validationset using the original and enhanced IAM-Database. We test the resulting models against the original and enhanced testsets, as well as a testset composed from real-world historical documents. We find that though the transcription engine proves robust to color changes, this technique could be used to bring up to speed older grayscale datasets to create transcription models efficient on historical handwriting. Additionally, we consider the environmental costs of using enhanced data as opposed to the original dataset, and find that the impact is minor.

Introduction

Handwritten Text Recognition (HTR) is a supervised machine learning task presenting exceptional potential for research in the humanities thanks to its capacity to open access to large amounts of primary sources. However, HTR relies on annotated data that are costly to produce and represent a challenge for the development of the technology. While more and more datasets are created to increase the performances of transcription models on historical documents, we examine the possibility to 1) bring up to speed older datasets by artificially enhancing them and 2) test their usefulness to train transcription models capable of handling historical documents.

Related works

Initiatives exist to ease access to a greater diversity of annotated data ready to be used to train HTR models efficient on historical documents (across languages and scripts) [START_REF] Chagué | I'm here to fight for ground truth": HTR-United, a solution towards a common for HTR training data[END_REF][START_REF] Pinche | CATMuS-Medieval: Consistent Approaches to Transcribing ManuScripts[END_REF]. Other datasets are specialized on a single handwriting or source [START_REF] Serrano | The RODRIGO Database[END_REF][START_REF] Sánchez | [END_REF][START_REF] Scius-Bertrand | The Bullinger Dataset: A Writer Adaptation Challenge[END_REF]. Additionally, recent experiments offered to artificially create synthetic data resembling historical documents [START_REF] Vögtlin | Generating Synthetic Handwritten Historical Documents with OCR Constrained GANs[END_REF][START_REF] Vidal-Gorène | They're veGAN but they almost taste the same: Generating similimanuscripts with artificial intelligence[END_REF] or automatically aligned transcriptions [START_REF] Tarride | Handwritten Text Recognition from Crowdsourced Annotations[END_REF].

Some datasets created before the introduction of CNNs1 are distributed with binarized/grayscale images: for example, IAM-Database [START_REF] Marti | The IAM-database: An English sentence database for offline handwriting recognition[END_REF]. 2 While this dataset is often used to benchmark HTR systems [START_REF] Alkendi | Advancements and Challenges in Handwritten Text Recognition: A Comprehensive Survey[END_REF], it is an older dataset not designed for historical documents.

An attempt to restore colors in digital copies of microfilms of medieval manuscripts did not significantly improve text recognition [START_REF] Clérice | Artificial colorization of digitized microfilms and its impact on other tasks[END_REF] as the HTR engine [START_REF] Kiessling | Important New Developments in Arabographic Optical Character Recognition (OCR), Al-Us[END_REF] proved robust to color changes. alix.chague@inria.fr (A. Chagué); hugo.scheithauer@inria.fr (H. Scheithauer) 0000-0002-0136-4434 (A. Chagué); 0000-0002-5659-4675 (H. Scheithauer)

Contribution

We propose to investigate a technique to enhance IAM-Database by adding realistic colored historical backgrounds and assess the impact when applying the resulting models to real historical manuscripts.

Our contributions are:

• a new method to artificially combine colorless text line images, taken from HTR datasets, with colored real blank pages; • an open dataset of real blank pages extracted from historical manuscripts, reusable for other tasks such as page layout detection; • the confirmation through another approach that HTR models are robust to color changes (see [START_REF] Clérice | Artificial colorization of digitized microfilms and its impact on other tasks[END_REF]); • considerations on the environmental costs of using enhanced training data.

Method

Our approach consists in utilizing two versions of IAM-Database (Fig. 1):

1. the original grayscale text lines 2. the enhanced text line images, in RGBA mode. 3The enhancement of images consists in combining a clip taken from the image of a real blank page 4 with the image of a text line (Fig. 2).

A real historical testset is built by combining samples from two English datasets (1850-1950) containing various hands [START_REF] Pham | University of Denver Collections as Data -HTR Train and Validation Set JCRS_2020[END_REF][START_REF] Schaefer | [END_REF] (Fig. 4).

Transcription models are trained with Kraken5 , using different combinations of original/modified train and validation sets before being tested on each testset (Table 1).

Results

We find that a model trained exclusively on the original IAM-Database does not perform well on colored images. If we inject enhanced images during training, the model's accuracy increases slightly on the artificially colored testset, but decreases on the original testset. As can be expected in the case of a zero-shot prediction, none of the models perform well on the historical testset. However, the model trained only on the original dataset yields the worst accuracy, suggesting that the colored samples may have positively impacted the models.

Considerations on environmental costs

Following [START_REF] Bouza Heguerte | How to estimate carbon footprint when training deep learning models? A guide and review[END_REF]'s recommendations, we used Green Algorithms' Calculator [START_REF] Lannelongue | Green Algorithms: Quantifying the Carbon Footprint of Computation[END_REF] 6 to evaluate the environmental impact of using the enhanced dataset against the original IAM-Database. While the size of the enhanced dataset is considerably increased (Table 2), we find that the computation time for the enhanced dataset is lower, with a positive impact on the environmental cost of training (Fig. 5).

Discussions

Our method opens the possibility to aggregate the enhanced IAM-Database with other real-world ground truth datasets, thus contributing to augmenting the quantity of data available to train generic transcription models.

Further investigations could be conducted on the usefulness of our method to enhance synthetically generated ground truth 7 .

  CSDH/SCHN Congress 2024: Sustaining Shared Futures, 16-19 June 2024, McGill University, Montreal, Canada * Corresponding author. † These authors contributed equally.

Figure 1 :

 1 Figure 1: Samples of text line images taken from the original dataset and their equivalent in the enhanced dataset.

Figure 2 :

 2 Figure 2: Modeling the workflow applied to blend real backgrounds into the text line images of the IAM-Dataset

Figure 3 :

 3 Figure 3: Examples of blank pages collected in Gallicalbum.

Trainset Validationset Original* IAM testset Enhanced** IAM testset Historical testset

	Original	Original	80.76	37.18	4.10
	Original	Enhanced	76.76	67.57	17.21
	Enhanced	Original	78.88	70.72	12.11
	Enhanced	Enhanced	61.75	72.99	11.74
	Manu McFrench Model V1	65.99	52.44	59.58

Table 1

 1 Character accuracy measured on each testset depending on the combination of trainset and validationset. We always test the model after 100 epochs of training. Manu McFrench Model V1[21], trained on real-world data, is used for comparison. *Original=Original Grayscale mode **Enhanced=RGBA mode with blended background.

	Split	Original IAM-Database Enhanced IAM-Database
	Trainset	325 Mb	1960 Mb
	Validationset	52 Mb	287 Mb
	Testset	107 Mb	611 Mb
	Total	484 Mb	2858 Mb

Table 2

 2 Artificially enhancing the original grayscale dataset increased its size by almost a factor of 6.

	Step	Original IAM-Database Enhanced IAM-Database
	Compiling	87s.	134s.
	Training	6113s.	5160s.
	Total	6200s.	5294s.
	Equiv.	1h43m20s.	1h28m14s.

Table 3

 3 Estimated computation times, including compiling arrow files and training transcription models on the corresponding arrow files.

Convolutional Neural Network, successfully introduced in HTR tasks at the beginning of the

2010s[9, p. 13], progressively removed the need for image binarization. Binarization is a preprocessing step wherein each pixel is classified between two classes: text (usually in black), or background (usually in white).[START_REF] Pinche | CATMuS-Medieval: Consistent Approaches to Transcribing ManuScripts[END_REF] It contains a total of 13,353 annotated text lines written by 657 writers between 1999 and 2002.

In grayscale mode, the image contains only one layer of information (there is only one color channel) whereas in RGBA mode, the image contains

layers of information: three for the primary colors (Red, Green, Blue) and one for transparency (Alpha). Converting the images to RGB is necessary to obtain colored images, and the Alpha channel is necessary for our blending technique.[START_REF] Sánchez | [END_REF] We created a dataset of blank pages taken from random real manuscripts available in Gallica, the French national library's online library. The dataset is called Gallicalbum[START_REF] Chagué | Gallicalbum[END_REF] and consists of 111 images.

We use Kraken 4.3.0. with its default training architecture and a learning rate of 1𝑒 -4 .

Accessible at http://calculator.green-algorithms.org/

Using techniques such as those presented in[START_REF] Graves | Generating Sequences With Recurrent Neural Networks[END_REF] or[START_REF] Luhman | Diffusion models for Handwriting Generation[END_REF], which usually generate black texts on white backgrounds.

Acknowledgements

The authors are grateful to the CLEPS infrastructure from the Inria Paris Center for providing resources and support.

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