domain: sde phys

text:
Rory G J Fitzpatrick
email: r.g.j.fitzpatrick@austin.utexas.edu

Douglas J Parker

John H Marsham

David P Rowell

Francoise M Guichard

Chris M Taylor

Kerry H Cook

Edward K Vizy

Lawrence S Jackson

Declan Finney

Julia Crook

Rachel Stratton

Simon Tucker

What Drives the Intensification of Mesoscale Convective Systems over the West African Sahel under Climate Change?

published or not. The documents may come

Introduction

The socio-economic risks to vulnerable people across West Africa due to climate change are manifold (USAID 2017). Of particular interest are projections of the frequency and intensity of extreme precipitation events. Mesoscale convective systems (MCSs) are responsible for the majority of annual rainfall over the Sahel [START_REF] Laurent | How important is the contribution of the mesoscale convective complexes to the Sahelian rainfall?[END_REF][START_REF] Laing | Contribution of mesoscale convective complexes to rainfall in Sahelian Africa: Estimates from geostationary infrared and passive microwave data[END_REF][START_REF] Fink | Spatiotemporal variability of the relation between African Easterly Waves and West African Squall Lines in 1998 and 1999[END_REF]; understanding future change of these events is pivotal to ascertaining future risk associated to rainfall.

The purpose of this study is to understand the processes by which climate change can affect MCS precipitation rates, particularly the 99 th percentile of surface precipitation rates from MCSs (hereafter termed the extreme precipitation rate), over the West African Sahel. We use a state-of-the-art regional climate model without any active convection parameterization scheme to understand how variability on the synoptic-to-climate timescale may affect MCS extreme precipitation rates.

The multi-decadal drought afflicting the Sahel in the 1970s and 80s has been followed by a so-called "recovery period" [START_REF] Nicholson | 0n the question of the "recovery" of the rains in the West African Sahel[END_REF][START_REF] Hagos | Ocean warming and late-twentieth-century Sahel drough and recovery[END_REF][START_REF] Lebel | Recent trends in the Central and Western Sahel rainfall regime (1990-2007)[END_REF][START_REF] Lodoun | Changes in seasonal descriptors of precipitation in Burkina Faso associated with late 20th century drought and recovery in West Africa[END_REF][START_REF] Evan | Water Vapor-Forced Greenhouse Warming over the Sahara Desert and the Recent Recovery from the Sahelian Drought[END_REF][START_REF] Sanogo | Spatio-temporal characteristics of the recent rainfall recovery in West Africa[END_REF] during which average annual rainfall has returned to near-long-term mean levels [START_REF] Lélé | Variability of the Intertropical Front (ITF) and Rainfall over the West African Sudan-Sahel Zone[END_REF]their Fig. 1). However, the nature of intra-seasonal rainfall variability has changed over the Sahel during recent decades, with an observed increase in the frequency of very rainy MCSs separated by longer periods of little to no rainfall [START_REF] Panthou | Recent trends in the regime of extreme rainfall in the Central Sahel[END_REF][START_REF] Taylor | Frequency of extreme Sahelian storms tripled since 1982 in satellite observations[END_REF]. More intense rain events carry increased risk of flooding, with observational studies suggesting that flood events over the Sahel have become more frequent over the past decades [START_REF] Panthou | Recent trends in the regime of extreme rainfall in the Central Sahel[END_REF][START_REF] Nka | Trends in floods in West Africa: analysis based on 11 catchments in the region[END_REF][START_REF] Panthou | Rainfall intensification in tropical semi-arid regions: the Sahelian case[END_REF]Tazen et al., 2018;[START_REF] Wilcox | Trends in hydrological extremes in the Senegal and Niger Rivers[END_REF].

Accepted for publication in Journal of Climate. DOI 10.1175/JCLI-D-19-0380.1.

Intense but temporarily sparse rain events can also deteriorate soil quality through nutrient run off [START_REF] Panagos | Global rainfall erosivity assessment based on high-temporal resolution rainfall records[END_REF] . [START_REF] Taylor | Frequency of extreme Sahelian storms tripled since 1982 in satellite observations[END_REF] observe a threefold increase in the frequency of earlyevening MCSs with mean cloud-top temperature < -75 °C over the Sahel since the 1980s. This increase is associated with an intensification of midday wind shear in the vertical pressure column, henceforth wind shear, calculated as the difference between low-level south-westerly/westerly winds and mid-level easterly winds, as well as a drying of the Saharan air layer. Cold pools, and organized squall lines have also been observed to intensify over the same timeframe, although the presence of drier mid-level air and stronger cold pools may be coincidental and not dynamically linked (c.f., [START_REF] James | A Numerical Investigation of the Effects of Dry Air Aloft on Deep Convection[END_REF].

On the storm timescale, [START_REF] Taylor | Frequency of extreme Sahelian storms tripled since 1982 in satellite observations[END_REF] found that ambient wind shear intensity is significantly correlated with the mean cloud-top temperature of MCSs, with subsequent observational work suggesting that ambient wind shear strength may also influence the maximum precipitation rates of storms (Supplementary Fig. S1). These findings are consistent with previous studies highlighting the role of wind shear in organizing convection [START_REF] Browning | Airflow in convective storms[END_REF][START_REF] Moncrieff | The dynamical structure of two-dimensional steady convection in constant vertical shear[END_REF]Moncrieff , 1981;;[START_REF] Thorpe | Two-dimensional convection in nonconstant shear: a model of midlatitude squall lines[END_REF][START_REF] Dudhia | The two-dimensional dynamics of west African squall lines[END_REF][START_REF] Nicholls | The sensitivity of two-dimensional simulations of tropical squall lines to environmental profiles[END_REF][START_REF] Rotunno | A theory for strong, long-lived squall lines[END_REF][START_REF] Mapes | Gregarious Tropical Convection[END_REF][START_REF] Houze | Cloud Dynamics[END_REF][START_REF] Tao | The effect of melting processes on the development of a tropical and midlatitude squall line[END_REF][START_REF] Ferrier | Factors responsible for precipitation efficiencies in midlatitude and tropical squall simulations[END_REF][START_REF] Lemone | The role of environmental shear and thermodynamic conditions in determining the structure and evolution of mesoscale convective systems during TOGA COARE[END_REF][START_REF] Mohr | Intense convective systems in West Africa and their relationship to the African easterly jet[END_REF][START_REF] Alfaro | Low-Tropospheric Shear in the Structure of Squall Lines: Impacts on Latent Heating under Layer-Lifting Ascent[END_REF].

Cloud-resolving model (CRM) studies have suggested that other ambient and storm-relative variables are more important than wind shear in controlling MCS precipitation rates. [START_REF] Takemi | A sensitivity of squall line intensity to environmental static stability under various shear and moisture conditions[END_REF]2010;2014) find that the vertical distribution of high CAPE in the lower troposphere controls mean MCS precipitation rates to a Accepted for publication in Journal of Climate. DOI 10.1175/JCLI-D-19-0380.1.

greater extent than lower/mid-tropospheric shear. However, Takemi (2010) also found an inverse relationship between lower-tropospheric temperature lapse rate and the maximum precipitation intensity of MCSs (their Fig. 14b), implying that increased CAPE could be negatively correlated with maximum precipitation rates. A similar result is found in [START_REF] Lucas | Sensitivity of Tropical West Pacific Oceanic Squall Lines to Tropospheric Wind and Moisture Profiles[END_REF], where enhanced wind shear positively impacts total precipitation from MCSs, but negatively impacts maximum precipitation rates. These results imply that storm-related drivers can be shown to positively or negatively impact MCS intensity depending on the definition of storm intensity. It is for this reason we primarily focus on extreme precipitation rates.

Finally, variability in moisture and ascent rates within MCSs have previously been identified as influential in MCS precipitation rate variability. Increased inflow of moist, buoyant air, and vertical ascent within convective updrafts increase maximum precipitation rates [START_REF] Alfaro | Low-Tropospheric Shear in the Structure of Squall Lines: Impacts on Latent Heating under Layer-Lifting Ascent[END_REF], as does enhanced lower-tropospheric relative humidity [START_REF] Lucas | Sensitivity of Tropical West Pacific Oceanic Squall Lines to Tropospheric Wind and Moisture Profiles[END_REF]. Takemi (2014) hypothesized that increased precipitable water available to a developing MCS will be positively correlated with maximum precipitation rates. This theory is not explicitly tested by the author.

Rising temperatures under global warming have the potential to intensify many of the MCS intensity drivers discussed above. Amplified warming of the Sahara [START_REF] Cook | Detection and analysis of an amplified warming of the Sahara Desert[END_REF][START_REF] Vizy | Seasonality of the observed amplified Sahara warming trend and implications for Sahel rainfall[END_REF] will increase the meridional temperature gradient across West Africa, leading to enhanced lower-to-midtropospheric wind shear over the Sahel, in part through the enhancement of the African Easterly Jet [START_REF] Cook | Generation of the African Easterly Jet and Its Role in Determining West African Precipitation[END_REF]. It is posited that a greater future meridional temperature gradient over West Africa will lead to heavier precipitating MCSs under climate change due to the strong water vapor feedback over the region [START_REF] Dong | Dominant role of greenhouse-gace forcing in the recovery of Sahel rainfall[END_REF][START_REF] Evan | Water Vapor-Forced Greenhouse Warming over the Sahara Desert and the Recent Recovery from the Sahelian Drought[END_REF]. Through the Clausius-Clapeyron relationship, it is Accepted for publication in Journal of Climate. DOI 10.1175/JCLI-D-19-0380.1.

expected that increased warming over the Sahel will lead to an increase in total column water (TCW); this relationship has been identified previously within the model used in this study [START_REF] Kendon | Enhanced future changes in wet and dry extremes over Africa at convection-permitting scale[END_REF]. Over the tropics, Takemi (2012a,b) also find an increase in lower-tropospheric CAPE under global warming. In our analysis, we examine the magnitude by which the above-identified MCS intensity drivers increase in a potential future climate, and their subsequent dynamic effect on MCS precipitation rates.

Coarse-resolution models with convection parameterization schemes, which do not account for the role of wind shear, can struggle to model Sahelian storms and their intensities accurately [START_REF] Marsham | The role of moist convection in the West African monsoon system -insights from continental scale convection-permitting simulations[END_REF]. Convection-permitting models at ~4 km horizontal resolution have been shown to realistically simulate present day monsoon flow, cold pool outflows [START_REF] Marsham | The role of moist convection in the West African monsoon system -insights from continental scale convection-permitting simulations[END_REF], convergence (Birch et al. 2014a,b), the diurnal cycle of rainfall (Vizy and Cook 2018a,b), and agricultural decision-maker relevant monsoon metrics [START_REF] Garcia-Carreras | The Impact of Parameterized Convection on the Simulation of Crop Processes[END_REF]. Future climate simulations of the West African climate at convection-permitting resolutions therefore provide an opportunity to better understand changes in MCS dynamics under global warming.

Section 2 describes the model used in this paper, with Section 3 explaining the methods employed. Sections 4-7 provide results: first, we identify climatological changes in the West African Monsoon between the current and future CP4-A climate runs, then we analyze future changes in distributions of MCS precipitation intensity relative to the current climate and the potential causes at different times of the day.

Section 8 gives conclusions and recommendations for future work.

Data

Accepted for publication in Journal of Climate. DOI 10.1175/JCLI-D-19-0380.1.

Within the Future Climate for Africa (FCFA) program, the Improving Model Processes for African Climate (IMPALA) project has produced two 10-year model simulations for the African continent at the convection-permitting horizontal grid spacing of ~4.4 km. These simulations are referred to hereafter as "Convection Permitting for Africa" (CP4-A; [START_REF] Stratton | A Pan-African Convection-Permitting Regional Climate Simulation with the Met Office Unified Model: CP4-Africa[END_REF][START_REF] Kendon | Enhanced future changes in wet and dry extremes over Africa at convection-permitting scale[END_REF]. The CP4-A simulations project the changes in African climate for the end of the 21 st Century with ~4 K sea-surface temperature (SST) warming and ~5 K mean near-surface temperature increase over the continent [START_REF] Kendon | Enhanced future changes in wet and dry extremes over Africa at convection-permitting scale[END_REF]. The model has 80 vertical levels with finer vertical resolution within the tropopause and boundary layer.

We provide a brief overview of the model and its quality below.

CP4-A is a regional model spanning longitudes 24°W -56°E, and latitudes 45°S -39°N. The model is forced by lateral boundary conditions from an atmosphere-only version the UK Met Office Global Climate Model (GCM) with ~25 km horizontal grid spacing, and with prescribed daily SSTs. Land surface properties are initialized using the most recent JULES land surface scheme [START_REF] Walters | The Met Office Unified Model Global Atmosphere 7.0/7.1 and JULES Global Land 7.0 configurations[END_REF], and allowed to evolve freely over time. CP4-A uses an applied moisture conservation scheme [START_REF] Aranami | A mass restoration scheme for limited-area models with semi-Lagrangian advection[END_REF] and a three-dimensional blended boundary layer scheme [START_REF] Boutle | Seemless Stratocumulus Simulation across the Turbulent Gray Zone[END_REF]. The large-scale cloud scheme is described in [START_REF] Smith | A scheme for predicting layer clouds and their water content in a general circulation model[END_REF], and has been used in other convection-permitting versions of the Met Office Unified Model. The cloud scheme diagnoses liquid cloud fraction and condensed water when the gridbox mean relative humidity exceeds a critical value. Ice water content is determined by the microphysics scheme, with cloud fractions then diagnosed as in [START_REF] Abel | The role of precipitation in controlling the transition from stratocumulus to cumulus cloud in a Northern Hemisphere cold-air outbreak[END_REF].

Other parameterization schemes are documented in [START_REF] Stratton | A Pan-African Convection-Permitting Regional Climate Simulation with the Met Office Unified Model: CP4-Africa[END_REF] Table 2). Both CP4-A, and the driving GCM, use the Even Newer Dynamics for General Atmospheric Modelling of the Environment (ENDGame) dynamical core (Wood et al. Accepted for publication in Journal of Climate. DOI 10.1175/JCLI-D-19-0380. 1. 2014). The ENDGame dynamical core has been shown previously to improve the representation of key processes over West Africa, particularly the seasonal progression of monsoon rains [START_REF] Vellinga | Sahel decadal rainfall variability and the role of model horizontal resolution[END_REF]Fitzpatrick et al. 2016 Appendix B).

In each climate respectively, the same SSTs are prescribed for the driving GCM, CP4-A, and the parameterized model. Current climate SSTs are provided from the Reynolds daily observational dataset [START_REF] Reynolds | Daily High-Resolution-Blended Analyses for Sea Surface Temperature[END_REF]. Greenhouse gases are taken from the RCP8.5 scenario for 2100; however the same ozone and aerosol climatology is used in both simulations. Future changes in precipitation rates across West Africa between the two simulations can be attributed to rising temperatures and increases in greenhouse gases.

CP4-A has no convection scheme of any kind, using just model dynamics to explicitly represent convective clouds. We note the caveat that a model at 4.4 km grid spacing with no convective parameterization scheme may not capture the complexity of convective development simulated in higher resolution CRM studies, as model resolution has been highlighted in the past as a key issue in correctly simulating cloud processes (e.g. [START_REF] Lin | TWP-ICE global atmospheric model intercomparison: Convection responsiveness and resolution impact[END_REF]. With that said, the decision to have no active convection scheme allows for a clearer comparison between convection permitting and parameterized models produced during IMPALA.

Accepted for publication in Journal of Climate. DOI 10.1175/JCLI-D-19-0380.1. [START_REF] Kendon | Enhanced future changes in wet and dry extremes over Africa at convection-permitting scale[END_REF] find that CP4-A better recreates observed high precipitation rates over Africa compared to the parameterized-convection counterpart model and projects a larger future increase in intense precipitation rates (their Fig. 1). [START_REF] Berthou | Improved climatological precipitation characteristics over West Africa at convection-permitting scale[END_REF] find that CP4-A accurately simulates the frequency of MCSs over the AMMA-CATCH observational sites. [START_REF] Stratton | A Pan-African Convection-Permitting Regional Climate Simulation with the Met Office Unified Model: CP4-Africa[END_REF] and [START_REF] Berthou | Improved climatological precipitation characteristics over West Africa at convection-permitting scale[END_REF] also show that the seasonal transition of monsoon rains across West Africa is better captured in CP4-A compared to its parameterized convection counterpart, as well as a reduction of the persistent dry bias within CP4-A. However, [START_REF] Crook | Assessment of the Representation of West African Storm Lifecycles in Convection-Permitting Simulations[END_REF] highlight that CP4-A fails to simulate MCSs of comparable area to the largest ones observed, or speeds comparable to the quickest systems.

Simulations at the temporal and spatial scale of CP4-A incur an extensive computational expense. As such, there has been a need for compromise with regards to model design and output. There exists only one model representation for the current and future climates respectively. The authors stress that the findings of this paper are based on a research model, with a particular set of boundary conditions from one global model, and so cannot be taken as projections with a certainty level attached, but rather as results from climate sensitivity study.

The authors also stress that the two, ten-year simulations are not considered as historical and future climatologies. Decadal and multi-decadal variability of ambient conditions across West Africa can influence our results. We explore the role of this variability further in Section 6.1.

Methods

In this paper, we analyze the climatic drivers of changes in early-evening MCS extreme precipitation rates (the 99 th percentile of MCS precipitation rate) over the Accepted for publication in Journal of Climate. DOI 10.1175/JCLI-D-19-0380.1.

Sahel. The calculation methods for extreme precipitation rate and other considered MCS-relevant metrics are presented in Table 1. We define the Sahel as 15°W-15°E, 10-18°N (displayed in Fig. 3); the suitability of this region for both climates is explored in Section 4.1. The codes employed in this paper are available at http://doi.org/10.5281/zenodo.2560371 and http://doi.org/10.5281/zenodo.2560410.

MCSs are classified as any contiguous structure with an area of cold-cloud (Outgoing Longwave Radiation [OLR] <= 167 Wm -2 ) of at least 25,000 km 2 simulated during July-September. Extreme precipitation rates are therefore calculated across a region of at least 250 km 2 (~ 16 grid cells). MCS tracking is performed from storm genesis to decay using the algorithm presented in [START_REF] Stein | The representation of the West African monsoon vertical cloud structure in the Met Office Unified Model: an evaluation with CloudSat[END_REF] by identifying contiguous regions of cold cloud that partially overlap between hourly intervals.

Tracked storms are analyzed at 1800 UTC in Sections 5 and 6 as this is the time of maximum modelled precipitation (see Section 4). Different times of MCS occurrence have been evaluated in Section 7.

Tracking MCSs using OLR instead of precipitation allows for continuous identification of large-scale organized systems even when MCS precipitation may be spatially or temporarily intermittent [START_REF] Klein | Wavelet scale analysis of mesoscale convective systems for detecting deep convection from infrared imagery[END_REF]their Fig. 4a). We have analyzed precipitation-tracked events, finding little difference in key results (not shown). The choice of a fixed temporal analysis window means that MCSs may be analyzed at times when they are not at their maximum intensity; however, we believe that this decision is fair given the availability of data as well as the complementary analysis in Sections 4 and 7.

In this paper, we set two further restrictions on MCSs identification with the following rationales:

Accepted for publication in Journal of Climate. DOI 10.1175/JCLI-D-19-0380.1.

 All MCSs have an extreme rain rate at 1800 UTC greater than 10 mm/hr. This restriction excludes non-precipitating cold cloud structures. The threshold of 10 mm/hr is arbitrary. Different thresholds (between 5 -30 mm/hr) were analyzed, with little difference in results.

 All MCSs must have mean ambient (1200 UTC -1600 UTC) precipitation rate below 1 mm/hr across the region where each MCS is located at 1800 UTC. This restriction removes MCSs where the midday atmosphere is perturbed by precipitation. Use of this restriction reduces the number of MCSs analyzed (only 26% of current climate storms and 27% of future climate storms pass this criterion). Evaluation of the vertical profile of horizontal winds, and CAPE, in the environment preceding the arrival of an MCS requires an atmosphere not disturbed by the potential effects of prior storms. Complementary analysis for all MCSs regardless of this restriction shows similar findings to those given here (not shown).

There are 1020 current climate MCSs and 553 future climate MCSs that meet both criteria. The fact that CP4-A projects fewer Sahelian MCSs in the future climate fits with prior analysis (c.f., [START_REF] Riede | What's on the 5th IPCC Report for West Africa? Adaption to Climate Change and Variability in Rural West Africa[END_REF]. Berthou et al., (revised), and Kendon et al., (2019) additionally show that CP4-A simulates fewer Sahelian rain events in the future regardless of storm size.

All metrics listed in Table 1 are calculated over the location where each MCS is present at 1800 UTC. "Ambient" conditions (e.g., MU-CAPE) are evaluated at 1200 UTC consistent with [START_REF] Taylor | Frequency of extreme Sahelian storms tripled since 1982 in satellite observations[END_REF], while "internal" storm characteristics (such as minimum omega), are evaluated at 1800 UTC. Our choice of evaluation times allow us to examine the influence of pre-storm environment and the internal storm dynamics in controlling MCS extreme precipitation rates within CP4-A. We Accepted for publication in Journal of Climate. DOI 10.1175/JCLI-D-19-0380.1. highlight that our measure of ambient wind shear does not use fixed pressure levels to evaluate the low-level south-westerly and mid-level easterly ambient wind circulations. Rather, our shear measure captures the maximum difference between these two circulations across the lower to mid-atmosphere. We consider this modification of importance given that changes in surface pressure and the potential vertical displacement of the AEJ are not variables we wish to explicitly consider as potential drivers of storm intensification changes.

In our analysis, we considered both zonal wind shear (i.e. maximum low-level westerlies minus maximum mid-level easterlies) and wind shear magnitude (using both the zonal and meridional horizontal winds) [Table 1]. We found little difference in the influence of either metric on extreme precipitation rates. As such, we do not show results for both metrics. Finally, due to an irreparable issue with CP4-A, 600 hPa model output is not available for the current climate storms in 1998 and some storms in 1999.

Climatological differences in monsoon features over the Sahel.

For our analysis, a fixed geographical region has been selected for analysis across climates. However, changes in extremes may arise from shifts of the summer rain belt or other monsoon features. In this section, we consider whether the latitudes 10-18°N offer a fair comparison of the West African Monsoon across climates. across climates with the maximum change in daily precipitation rate of 1 mm/day (Fig. 1a). There is also evidence of a northwards shift of the northernmost extent of monsoon rains. Proportionally, precipitation increases are greater farther north (~40 -50% near 18°N). The ~1° northwards shift of monsoon rainfall limit across climates, as well as the higher future precipitation rates over the Sahel, and a projected reduction of precipitation rates near the Guinea Coast (5-7°N) is consistent with previous studies (e.g., [START_REF] Vizy | Projections of a Wetter Sahel in the Twenty-First Century from Global and Regional Models[END_REF][START_REF] Cook | Detection and analysis of an amplified warming of the Sahara Desert[END_REF][START_REF] Vizy | Seasonality of the observed amplified Sahara warming trend and implications for Sahel rainfall[END_REF].

Mean midday zonal wind shear (Fig. 1b) increases predominantly due to stronger low-level south-westerly flow across all latitudes of around 1-2 m/s or up to 40% (Figs. 1d-e) and a relatively smaller intensification of AEJ-level easterlies across the northern Sahel of no more than 0.5 m/s (<5% across climates Fig. 1c).

There is a projected latitudinal broadening of the AEJ in the future, most pronounced north of 13°N (Fig. 1c). However, the latitudinal position of peak zonal wind shear and 650 hPa winds is the same in the current and future climate simulations.

Enhanced low level westerlies, indicative of the West African Westerly Jet diurnal peaks (WAWJ, [START_REF] Pu | Dynamics of the West African Westerly Jet[END_REF]2012), and southerlies imply an enhanced horizontal transport of moisture over the Sahel in the future.

Mean 850 hPa temperature (Fig. 1f) indicate a future increase in the meridional temperature gradient across West Africa, with temperatures increasing over the Sahara (6-7 K) more than over the Guinea Coast (5-6 K). This increased meridional temperature gradient is consistent with the enhanced zonal wind shear across the Sahel via their co-dependence due to the thermal wind balance (Fig. 1b; [START_REF] Cook | Generation of the African Easterly Jet and Its Role in Determining West African Precipitation[END_REF][START_REF] Parker | The diurnal cycle of the West African monsoon circulation[END_REF][START_REF] Cook | Detection and analysis of an amplified warming of the Sahara Desert[END_REF]. Specific humidity (Fig. 1g) is much greater across the entire West African region in the future climate, with the difference between the two climates maximized at ~12°N. We see little (< 3%) Accepted for publication in Journal of Climate. DOI 10.1175/JCLI-D-19-0380.1. change in lower-tropospheric relative humidity between climates across the Sahel (Fig. 1h). Increased low-level southerly winds across the Guinea Coast, coupled with higher specific humidity is associated with an increase in TCW over the Sahel (Fig. 1i). The location of maximum TCW does not change across climates (9-10°N), but the greatest absolute increase occurs within the Sahel (~12-13°N).

The latitudinal pattern of each variable considered in Fig. 1 is consistent across climates. We conclude that the region 10-18°N is a fair region over which to consider MCSs in both climates.

Figure 2 shows the diurnal cycle of CP4-A precipitation (Fig. 2a) and lower-tomid-tropospheric wind shear magnitude (Fig. 2b), averaged over our analysis region.

In both climates, the maximum precipitation rate occurs during the late afternoon and is minimized around 11 UTC. Precipitation increases at all times of day with climate change, but percentage wise, the greatest increases occur prior to 1200 UTC. CP4-A has a bias towards too much midday precipitation across the Sahel, however the model is improved over parameterized counterpart models [START_REF] Berthou | Improved climatological precipitation characteristics over West Africa at convection-permitting scale[END_REF].

Hourly rainfall rates increase by less than 20% in the future climate for all times after 1400 UTC. [START_REF] Kendon | Enhanced future changes in wet and dry extremes over Africa at convection-permitting scale[END_REF] show fewer short-lived evening storms in the future climate within CP4-A, potentially explaining the relatively small absolute/percentage increase in precipitation across the afternoon and evening period.

Observed wind shear in the lower-to-mid-troposphere is maximized overnight, since this is the time of strongest south-westerly monsoon flow [START_REF] Parker | The diurnal cycle of the West African monsoon circulation[END_REF].

The diurnal cycle of zonal wind shear is consistent across climates within our observation region (Fig. 2b). We see an increase throughout the day in the percentage change of zonal wind shear across climates with a peak increase Accepted for publication in Journal of Climate. DOI 10.1175/JCLI-D-19-0380.1.

occurring at 2100 UTC (~ 40%). The larger percentage increase at 1500 -2100 UTC is due in part to these times corresponding to the diurnal minimum in shear values.

Absolute increases in zonal wind shear range between about 3.5 m/s (at 1500 UTC) and 4.8 m/s (at 2100 UTC) [Supplementary Figure S2]. Spatial changes in zonal wind shear calculated between set levels (925 and 600 hPa) are provided in Supplementary Fig. S3 and highlight that zonal wind shear increases more, in absolute terms, within the eastern Sahel.

We decide that using 1800 UTC as our storm reference time is fair as 1800 UTC is shortly after the time of maximum area-averaged precipitation in both climates and aligns with available instantaneous data for wind speed and temperature. However, there exist regions where overnight rainfall provides the majority of local precipitation over the Sahel [START_REF] Mathon | Mesoscale convective system rainfall in the Sahel[END_REF]Vizy and Cook 2018a). Drivers of MCS extreme precipitation rates at 0000 UTC and 0600 UTC storms are discussed in Section 7.

We next consider changes in TCW and their relationship to near-surface temperature changes across climates and compared them to the expected rate of change in TCW per unit warming from the Clausius-Clapeyron relationship (i.e. 7% per K warming). We use the differential rate of TCW change per Kelvin, r, expressed as a percentage change, from O'Gorman and Muller (2010; their equation 2, our Fig.

𝑟 ∆ = 𝑇𝐶𝑊 𝑓𝑢𝑡𝑢𝑟𝑒 -𝑇𝐶𝑊 𝑐𝑢𝑟𝑟𝑒𝑛𝑡 𝑇𝐶𝑊 𝑐𝑢𝑟𝑟𝑒𝑛𝑡 (2)
Figure 3 also displays spatial maps of projected TCW, 1.5-meter temperature, and near surface circulation changes across climates (Figs. 3b and3c) and r as defined in equation 1 (Fig. 3d).

Figure 3a shows that climatological 1.5 meter temperatures increase by 4-5 K near the Guinea Coast (0-5°N), and by over 6 K across the Sahara (north of 20°N).

CP4-A simulates zonally-averaged r > 7% K -1 from 10-20°N implying super-Clausius-Clapeyron scaling of TCW occurs across our analysis region (although the scaling is zonally heterogeneous as seen in Fig. 3d).

Consistent with [START_REF] Vizy | Projections of a Wetter Sahel in the Twenty-First Century from Global and Regional Models[END_REF], we see projected enhancement of the WAWJ across Senegal and southern Mali, and increased south-westerly monsoon flow across Benin, Burkina Faso and Nigeria. Both these circulation changes would be expected to increase low-level moisture across the eastern Sahel. Accordingly, there is an apparent south-westerly gradient in the percentage TCW increase between the current and future climate (Fig. 3b). Across much of the eastern Sahel, there is >50% more moisture in the future climate. Towards Senegal, the increase is 30-40%. Changes in surface temperature across climates appear relatively more zonally homogeneous across West Africa (Fig. 3c).

CP4-A projects super-Clausius-Clapeyron increases in r projected across the eastern Sahel, as well as Guinea, Liberia and Sierra Leone (Fig. 3d). This high increase in TCW per K warming is of particular interest over the Niger/Nigeria border, as this is a location where many observed MCSs originate during the boreal summer (Vizy and Cook 2018a, b) strengthened northerlies from the increased low-level cyclonic circulation about the deepened trough providing warming and drying in over this region. The zonal contrast in simulated r presented in Fig. 3d is consistent with projected CP4-A increases in extreme precipitation across the Sahel [START_REF] Kendon | Enhanced future changes in wet and dry extremes over Africa at convection-permitting scale[END_REF], currently observed spatial heterogeneity in precipitation trends [START_REF] Panthou | Rainfall intensification in tropical semi-arid regions: the Sahelian case[END_REF], and spatial patterns of seasonal precipitation change from other future climate studies using coarser-resolution models (e.g., [START_REF] James | African Climate Change Uncertainty in Peturbed Physics Ensembles: Implications of Global Warming to 4C and Beyond[END_REF]; their Fig. 1).

In conclusion, we find an intensification of climatological precipitation across much of our study region present at all times of day. There is an increase in zonal and horizontal wind shear in the future climate, primarily associated with a strengthening of the low-level monsoon flow and the WAWJ, with a relatively smaller intensification of the AEJ apparent. Zonally-averaged low-level specific humidity, and TCW increase in the future. There is a spatial heterogeneity to the increase in available moisture for MCSs relative to localized heating, which is spatially consistent with prior studies highlighting zonal contrasts in current and future precipitation trends over the Sahel.

Changes in storm intensity and drivers within and across climates

Vertical profile of storm environment: Dependence on intensity and climate

We next investigate whether selection of fixed pressure levels for comparison of storm drivers across climates is valid, or whether considerations for vertical displacement of storm intensity drivers must be taken into account. Figure 4 displays the vertical profile of mean midday zonal wind speed (Fig. 4a), 1800 UTC minimum Accepted for publication in Journal of Climate. DOI 10.1175/JCLI-D-19-0380.1. omega (Fig. 4b), and relative humidity at 1200 UTC (Fig. 4c) and 1800 UTC (Fig. 4d) for storms with the highest and lowest extreme precipitation rates in each climate.

At 925 hPa, we see stronger composite low-level westerlies preceding storms with the lowest 25% of extreme precipitation rates in the current climate simulations (Fig. 4a, ~ 1m/s difference). Stronger composite ambient westerly winds are simulated at this level in the future climate compared to the current climate, but we do not see a difference between ambient westerlies preceding MCSs with the highest and lowest extreme precipitation rates.

More intense easterlies at 650 hPa precede MCSs with higher extreme precipitation rates in the current climate with easterlies approximately 1 m/s more intense. At higher levels, current climate ambient easterlies are weaker preceding MCSs with the highest extreme precipitation rates, We also note that composite 650 hPa easterlies preceding both subsets of current climate MCSs are actually weaker than those preceding the all-storm composite at 650 hPa (not shown). In the future climate, we see enhanced mid-and upper tropospheric easterly flow preceding both subsets of storms, with the strongest composite easterlies from 650 hPa upwards simulated prior to MCSs with the lowest extreme precipitation rates. In both climates, Fig. 4a implies that enhanced ambient zonal-wind shear may not be present prior to systems with higher extreme precipitation rates. As an aside, when storm intensity is measured using mean OLR, we do see a clear pattern towards more intense midlevel easterly winds preceding colder-topped MCSs (Supplementary Fig. S4a). For the remainder of our analysis, set pressure ranges across which to evaluate lowertropospheric westerlies (925 -800 hPa), and mid-tropospheric easterlies (700 -500 hPa) for both climates are considered fair.

Accepted for publication in Journal of Climate. DOI 10.1175/JCLI-D-19-0380.1.

In both climates, MCSs with higher extreme precipitation rates have higher composite minimum omega at the time of storm throughout the mid-and upper troposphere compared to those with lower extreme precipitation rates (Fig. 4b). For storms with the highest extreme precipitation rates in either climate, composite omega values are similar between climates below 600 hPa with stronger omega simulated higher than 600 hPa in the future implying greater in-storm ascent rates.

The opposite is true for events with the lowest extreme precipitation rates, as current climate storms are simulated to have more intense in-storm omega. Figure 4b implies relatively more extremes (both strong and weak) of in-storm ascent rates simulated for future climate MCSs. Through the rest of this article, we use minimum omega above 600 hPa for each MCS as the indicator of maximum speed of ascending air in MCS convective cores (whilst appreciating that the grid-resolution of our model reduces the precision of this measurement).

We see a clear separation between composite RH profiles for MCSs with the largest extreme precipitation rates and lowest extreme precipitation rates for a given climate (Fig. 4c for 1200 UTC, Fig. 4d for 1800 UTC). In either climate, higher 1200 UTC relative humidity values are simulated below about 550 hPa preceding storms with higher extreme precipitation rates (Fig. 4c), with higher 1800 UTC RH values simulated throughout the vertical column (Fig. 4d). Across climates, we see little change in 1200 UTC composite low-level RH for either MCS subset, but greater midto upper tropospheric humidity preceding MCSs with the highest precipitation rates in the future climate. At the time of storm, there is a consistent simulated drying of the lower-to mid-troposphere simulated for future climate storms (~800 -600 hPa) for both respective MCS populations. For the rest of this paper, we evaluate 1200 UTC RH in order to focus on the influence ambient conditions have on extreme Accepted for publication in Journal of Climate. DOI 10.1175/JCLI-D-19-0380.1.

precipitation rates, and select 700 hPa as a representative pressure level for analysis of mid-tropospheric RH.

Figure 5 shows the skew-t plot of composite profiles preceding current climate (blue lines) and future climate (red lines) storms; Table 2 provides relevant statistics from these soundings. Future storms are preceded by higher equilibrium and lifting condensation levels, and greater ambient bulk CAPE and bulk CIN, which are expected to favor more intense deep convection. The higher CIN environment seen in the future climate suggests that stronger triggers (such as cold pools) are required to initiate deep convection in this environment, consistent with the greater preponderance of nocturnal propagating systems, as compared with scattered evening cumulonimbus.

Character of extreme storms and pre-storm environment in current and future climate

Figure 6 compares populations of current climate and future climate ambient/time-of-storm metrics. Changes between climates are statistically significant beyond the 90-99 th percentile for all metrics apart from 1800 UTC minimum omega (Fig. 6h). Figure 6a shows a 28% increase of mean extreme precipitation rates under climate change. Future climate storms are on average deeper, with higher rain rates, but have warmer cloud tops (Fig. 6g) due to a warmer troposphere (Fig. 5).

We find intensifications in mean 1200 UTC wind shear (Figs. 6b), 1800 UTC mean TCW (Fig. 6c), and ambient bulk CAPE of the most unstable air parcel (Fig. 6e) as well as drier ambient mid-level air (Fig. 6f). Relative to the large increase in mean 1800 UTC TCW across climates (41%), we see a smaller, but significant Accepted for publication in Journal of Climate. DOI 10.1175/JCLI-D-19-0380.1. increase in the 1800 UTC -1200 UTC TCW anomaly across climates (21%, Fig. 6d). 1-hour total precipitation accumulation increases in the future climate (Fig. 6j), as well as the temperature deficit of cold pool outflows (Fig. 6l). The future change in 1-hour precipitation accumulation is not linked to larger storms in the future; in fact there are fewer large storms in the future climate (Fig. 6k). Figure 6 highlights a significant shift in the CP4-A future climate scenario towards conditions conducive to more intense rain events.

Storm-level dynamics and intensity drivers in the current and future CP4-A simulations

What controls extreme precipitation rates in CP4-A?

Figure 7 shows the relationships between different ambient and internal variables and modelled extreme precipitation rates for both climates. There is no statistically significant (at the 95% confidence interval) correlation between future climate ambient wind shear and extreme precipitation rates, with a weak yet significant negative correlation between the same metrics seen for the present climate (Fig. 7a). The relationship between the vertical profile of lower-to-midtropospheric ambient winds and extreme precipitation rates is complex, with observational and modelling studies highlighting different potential relationships (c.f., Takemi 2014 and[START_REF] Taylor | Frequency of extreme Sahelian storms tripled since 1982 in satellite observations[END_REF]. The correlations shown in Fig. 7a agree with prior studies performed using CRMs (e.g. [START_REF] Lucas | Sensitivity of Tropical West Pacific Oceanic Squall Lines to Tropospheric Wind and Moisture Profiles[END_REF]Takemi 2010;2014), but disagree with Supplementary Fig. these two variables, an approximation for water uplift in the most intense convective core, also significantly scaling with extreme precipitation rates (not shown).

Additionally, [START_REF] Taylor | Frequency of extreme Sahelian storms tripled since 1982 in satellite observations[END_REF] hypothesized that more intense systems supply increased moisture. Figure 7c agrees with this notion with good agreement between the correlation of extreme precipitation rate and TCW anomaly at 1800 UTC across climates. However, this model result could be coincidental, with intense storms forming in large-scale environments that generate increases of TCW between 12 and 18 UTC for unrelated reasons.

Colder-topped MCSs have higher extreme precipitation rates in both climates consistent with expectations (Fig. 7e). Lower MU-CAPE (Fig. 7f) and more humid ambient mid-levels (Fig. 7g) are significantly correlated with higher extreme rain rates. We stress that MU-CAPE as defined in Table 1 is not directly comparable to the depth of high CAPE air within the lower-troposphere analyzed in Takemi (2010;2014). It is important also to note that the processes through which increased MU-CAPE can affect precipitation may be crudely modelled at 4.4 km horizontal resolution, given the potential influence of cloud-mixing and microphysical processes. Other measures of CAPE, including for surface based parcels and the mean parcel CAPE in the lowest 100 hPa of the atmosphere, have also been evaluated, with little difference in their relationship with precipitation rates.

Storms with higher extreme precipitation rates in either climate output greater quantities of rainfall during 1 hour across the entire MCS area (Fig. 7h), implying these systems potentially have broad impacts over the regions they are present.

Finally, there is no significant correlation between cold pool intensity and extreme precipitation rate in either climate (Fig. 7i). Although intense storms can be associated with strong cold pools, ice hydrometeor melting, sublimation, and Accepted for publication in Journal of Climate. DOI 10.1175/JCLI-D-19-0380.1. evaporation help generate cold pools, which can correspond to minimal precipitation at the surface.

As discussed in Section 2, our two 10-year simulations are each affected by the models own internal natural variability. We note however that the natural variability in each run is constrained by the lower and lateral boundary conditions. In order to quantify the potential influence of long-timescale variability on ambient TCW, we have compared the change in June-September TCW from a historical period to the end of the 21 st Century (2070-2099) within a 4-member GCM ensemble using a single model (HadGEM2-ES) forced with different initial conditions following RCP8.5. HadGEM2-ES is employed as it provides the best comparison to CP4-A given similarities in model design.

Historic climatological TCW values over the Sahel range from 30.3 -30.6 kg m -2 across ensemble members; future values range from 46.3 -47.1 kg m -2 . The difference in TCW across climates (~ 16 kg m -2 ) is comparable to the difference in TCW simulated in CP4-A (Fig. 7b). Inter-ensemble variability in each climate is much lower than the change projected across climates, implying that the TCW differences projected in CP4-A are likely associated with climate change and not a product of random variability.

Modelled interactions of storm intensity drivers in CP4-A

Figure 8 shows the relationships between selected ambient and time of storm metrics. Figure 8a shows a significant negative correlation between midday wind shear and mean time-of-storm OLR in both climates. The correlation coefficients are of similar magnitude to that found in observations [START_REF] Taylor | Frequency of extreme Sahelian storms tripled since 1982 in satellite observations[END_REF]; their coefficient: -0.347), suggesting that CP4-A captures the observed influence of Accepted for publication in Journal of Climate. DOI 10.1175/JCLI-D-19-0380.1. ambient wind shear on MCS organization. The role of shear in determining the structure and organization of MCSs has also been identified in observational studies and studies using CRMs (e.g., [START_REF] Newton | Morphology of thunderstorms and hailstorms as affected by vertical wind shear[END_REF][START_REF] Browning | Airflow in convective storms[END_REF][START_REF] Rotunno | A theory for strong, long-lived squall lines[END_REF]Houze Jr 2004;[START_REF] Takemi | A sensitivity of squall line intensity to environmental static stability under various shear and moisture conditions[END_REF]. We additionally note that, for a given temperature and humidity profile, there may exist a vertical wind profile which optimizes MCS organization [START_REF] Takemi | A sensitivity of squall line intensity to environmental static stability under various shear and moisture conditions[END_REF]. Across climates, the horizontal winds, humidity and temperature significantly change in CP4-A (Fig. 1) implying that the future climate ambient environment may be more conducive to MCS organization once a storm is generated.

Within the range of simulated wind shear values, we see a weak, but significant correlation between ambient shear and in-storm minimum omega (Fig. 8b) which agrees with prior studies (e.g., [START_REF] Fovell | Effect of vertical wind shear on numerically simulated multicell storm structure[END_REF][START_REF] Lucas | Sensitivity of Tropical West Pacific Oceanic Squall Lines to Tropospheric Wind and Moisture Profiles[END_REF]. In each climate, ambient wind shear is also correlated with 1200 UTC MU-CAPE (Fig. 8c). This link may be co-fluctuation not causation, may be due to intense shear in the lower troposphere inhibiting convective initiation, or may be due to the presence of enhanced low-level convergence in high shear environments. Ambient wind shear is either significantly negatively correlated (in the current climate: -0.227 correlation coefficient), or not correlated (in the future climate: 0.003 correlation coefficient) with time-of-storm TCW (Fig. 8d).

Both climates simulate stronger wind shear preceding MCSs with more intense cold pools, however this relationship is only statistically significant in the current climate (Fig. 8e). Past studies have highlighted the importance of wind shear in controlling cold pool strength [START_REF] Thorpe | Two-dimensional convection in nonconstant shear: a model of midlatitude squall lines[END_REF]Rotunno et al., 1998), but this relationship is complex [START_REF] Parker | Cold pools in shear[END_REF]. Prior research has also highlighted ambiguity with the role of other ambient conditions such as dry mid-levels in intensifying Accepted for publication in Journal of Climate. DOI 10.1175/JCLI-D-19-0380.1. convective cold pools [START_REF] James | A Numerical Investigation of the Effects of Dry Air Aloft on Deep Convection[END_REF]. Detailed analysis of cold pool simulations for CP4-A storms is beyond the scope of this paper. However, our analysis implies that the factors required to sustain a strong cold pool are likely to be prohibitive to higher extreme precipitation rates in CP4-A.

Figure 8f implies that systems preceded by higher ambient TCW have statistically significant lower 12 to 18 UTC TCW increases in both climates. As in Fig. 7c, the correlation co-efficient between these two variables is consistent across climates suggesting that the fundamental behavior of MCSs with regards to available moisture does not change under global warming. In both climates we also note that higher time-of-storm TCW is significantly correlated with increased mid-tropospheric RH with similar correlation coefficients (~0.65) found for each climate (Fig. 8g). The maximum vertical velocity of MCSs is significantly correlated with mean OLR in both climates (Fig. 8h). Finally, the maximum buoyancy of rising air parcels simulated for each MCS is closely tied to the uplift velocity (Fig. 8i) implying a realistic relationship between buoyancy and upwards motion is simulated within CP4-A.

Figures 7 and8 suggest that current-and future-climate storms simulated within CP4-A behave similarly. Ambient wind difference exhibits control on the organization of developing systems, with higher wind difference associated with colder MCS cloud-tops, potentially through the ability of lower-to-mid-tropospheric wind shear to control the verticality of ascending air within a system and the build-up of CAPE. Higher TCW and ascent rates at the time of storm are closely associated with greater extreme precipitation rates, with the product of these two variables showing good correlation with extreme precipitation rates. Although it may be expected that time-of-storm TCW correlates with precipitation metrics (as precipitation can only fall if there is precipitable water available, and precipitation Accepted for publication in Journal of Climate. DOI 10.1175/JCLI-D-19-0380.1.

actually contributes a small fraction of the TCW), it is of interest that TCW is the strongest control of the selected potential drivers of extreme rain rates within CP4-A both in each climate, and across climates.

Stronger ambient wind shear is associated with stronger cold pools in the current climate (Fig. 8e), thus encourages gregarious development of MCSs, and stronger ascent rates in both climates, implying faster uplift of moisture. However, wind shear is also associated with lower TCW and higher MU-CAPE, and therefore may also negatively impact extreme precipitation rate. Our results imply that there is no simplistic direct relationship between ambient wind shear and extreme precipitation rates in CP4-A for either climate.

Under global warming, the atmosphere becomes more conducive to higher extreme precipitation rates for early evening MCSs, however less favorable overall to MCS genesis (Berthou et al., revised). With regards to changes in extreme precipitation rates, the key climatic difference is the 41% increase in time-of-storm TCW, which is attributable to both an increase in ambient (i.e. 12 UTC) TCW, and greater 12-to-18 UTC TCW. This increase in the afternoon increase in TCW may be generated by developing MCSs, may simply reflect the greater availability of TCW in the future climate which has a diurnal variation, or may reflect a change in that diurnal cycle (we do not investigate further here). From Fig. 3, we note that the eastern Sahel is projected to have super-Clausius-Clapeyron scaling of TCW with temperature; accordingly this region sees the largest frequency of future climate MCSs (not shown). -c). MCSs with higher mean precipitation rates have significantly stronger minimum omega (Fig. 9d) and significantly colder mean OLR (Fig. 9e), consistent with Fig. 7. Figure 9f implies that increased CAPE is significantly negatively correlated with mean precipitation rates within both climates. This result is seemingly at odds with Takemi (2014) who highlight the importance of increased depth of high CAPE in the lowertroposphere. However, the effect of latitudinal variations in CAPE cannot be discounted as a cause for this difference (as seen in Section 6), nor can differences in methodology for evaluating CAPE. A more thorough investigation of the spatial and vertical distribution of CAPE in the lower troposphere simulated in CP4-A prior to MCSs of different intensities is beyond the scope of this study, but will form the basis of future work.

Drivers of extreme precipitation rates of MCSs at 0000 UTC (Fig. 10) are similar to those found for 1800 UTC extreme precipitation rates. Note that for 0000 UTC MCSs, we consider ambient conditions at 1800 UTC, and apply criteria akin to those for 1800 UTC MCSs with adjusted time windows. The quantity of ambient TCW (Fig. 10b), the 18-to-00 UTC increase in TCW (Fig. 10c), and the minimum omega within Accepted for publication in Journal of Climate. DOI 10.1175/JCLI-D-19-0380.1.

each MCS (Fig. 10d) are the predominant controls on extreme precipitation rate variability at this time.

At 0600 UTC, there is a large decline in the number of future climate MCSs simulated that meet our pre-set areal threshold (approximately 400 MCSs) and both our pre-set precipitation criteria (29 MCSs). Figure 11 therefore shows all MCSs of at least 25,000 km 2 that are preceded by ambient mean precipitation not exceeding 1 cm/hour rather than 1 mm/hour. Using this relaxed restriction allows for 354 storms to be evaluated for the future climate, and 1307 to be evaluated for the current climate.

Although different MCS triggering mechanisms have been highlighted for early evening and nocturnal systems in observations (Vizy and Cook 2018a), the degree to which our a priori drivers affect extreme precipitation rates are reasonably consistent between 0600 UTC (Fig. 11) and 1800 UTC (Fig. 7). The one exception to this finding is the weaker link between ambient CAPE and 0600 UTC extreme precipitation rates (Fig. 11f) compared to earlier MCS analysis times. Nevertheless, we conclude from Figs. 7, 10, and 11 that CP4-A highlights the particular importance of ambient TCW, time-of-storm omega and RH for MCS extreme precipitation rate variability across the early evening and night-time.

Conclusions and Discussion

Using output from the first convection-permitting model of pan-African climate changes we have evaluated the processes through which global warming within a realistic future climate scenario can impact extreme precipitation rates of Sahelian MCSs, as well as the modelled drivers of change on the storm timescale. Our work is Accepted for publication in Journal of Climate. DOI 10.1175/JCLI-D-19-0380.1. considered a climate sensitivity experiment, and the quality of projected changes is not assessed here. We further do not provide an evaluation of modelled precipitation against present observations as this has been assessed elsewhere [START_REF] Stratton | A Pan-African Convection-Permitting Regional Climate Simulation with the Met Office Unified Model: CP4-Africa[END_REF][START_REF] Berthou | Improved climatological precipitation characteristics over West Africa at convection-permitting scale[END_REF]. Results presented primarily focus on early evening storms (1800 UTC) across the whole Sahel (15°W -15°E, 10 -18°N). Overnight precipitation systems as well as potential longitudinal and latitudinal variation in findings have been presented, with little difference in key results.

We find a 28% increase in the mean extreme precipitation rate of early evening MCSs by the end of the 21 st Century, and an increase in precipitation rates at all times of day despite fewer MCSs in the future climate. We primarily link this increase in extreme precipitation rate to increases in TCW, which scales at close to Clausius-Clapeyron scaling (although the increases have zonal heterogeneity). The greatest TCW increases are simulated across Nigeria, Niger and Lake Chad, which corresponds to the location of most early-evening storms with particularly high extreme rain rates in the future climate. We also note that there are fewer MCSs simulated in the future climate during the early evening and overnight based on our areal threshold. Prior analysis of CP4-A output has also shown that, despite a projected increase in precipitation rates at all times of day, future rainfall over the Sahel is provided by fewer, and on average smaller systems compared to current climate precipitation [START_REF] Kendon | Enhanced future changes in wet and dry extremes over Africa at convection-permitting scale[END_REF]Berthou et al., revised).  Water vapor mixing ratios increase approximately in line with the local temperature change to maintain constant RH at low levels (Clausius-Clapeyron scaling), but with regionally super or sub-Clausius-Clapeyron scaling as the monsoon shifts and monsoon circulation increases (Fig. 3).

Across climates, the associated increases in ambient and storm-driven TCW are directly linked to enhanced extreme rain rates.

 Within each climate, increased wind shear, cold-pool strength, and in-storm buoyancy lead to an increase in updraft speeds within the storm. Moister midlevels correlate with precipitation at the surface, presumably due to increased water availability for rain formation and decreased evaporation of hydrometeors. Stronger MCS updrafts give colder cloud-top temperatures as expected, which explains the link between ambient wind shear and cloud-top temperature found in [START_REF] Taylor | Frequency of extreme Sahelian storms tripled since 1982 in satellite observations[END_REF] and in our analysis (Fig. 8a). MCS extreme precipitation rates scale with the product of time-of-storm TCW and in-storm vertical velocity with deeper storms which bear more precipitation Accepted for publication in Journal of Climate. DOI 10.1175/JCLI-D-19-0380.1. modelled in the future. Note that whilst there is no significant change in vertical velocity across climates, the distribution of vertical velocities is skewed with a longer tail of strong updrafts in the future climate simulation (Fig. 6).

 Finally, colder cold pools are simulated in the future climate. In each climate, the strength of the cold pool is significantly correlated with both near surface wind speed and wind speed cubed (a proxy for dust uplift potential -Supplementary Fig. S13). However, we do not see a significant change in near surface wind speeds across climates (Supplementary Fig. S14), and also note that the link between cold pool strength and wind speed weakens in the future. It is unclear why these results occur, and this subject requires future investigation.

Within CP4-A, there is no direct significant link between zonal wind shear and extreme precipitation rates, despite observational evidence suggesting such a link may exist (presented in Supplementary Fig. S1). The role of zonal winds in organizing systems within the tropics is complex, and with a singular model simulation, it is not possible to ascertain the cause for this discrepancy between model and observations. Future work will explore in more detail how Sahelian MCSs develop within high and low shear environments.

The findings of this paper are both aided and limited by the novel climate model employed and some caveats to our findings are required. Whilst the CP4-A dataset allows for interrogation of storm dynamic changes due to climate change that was not previously possible, only one future climate realization exists, and any model biases associated cannot be assessed fairly using multi-model ensembles. In particular, there is no current way to assess the impact that different future sea-Accepted for publication in Journal of Climate. DOI 10.1175/JCLI-D-19-0380.1.

surface temperature anomalies would affect our findings. We hypothesize from Fig.

12 that any increase in land/ocean temperatures in the future could lead to increased extreme precipitation rates following the processes we discuss. However, investment into more widely available and varying future climate scenarios at convectionpermitting spatial resolution for West Africa would greatly help improve understanding of projected precipitation changes.

We further note that the horizontal resolution of our employed model is potentially too coarse also for conclusive insight into the role of sub-cloud processes (such as speed of convective updrafts) to be interpreted from our results, however do note the agreement between our findings and past observational and higher resolution modelling studies. Finally, we cannot state whether the increase in extreme precipitation rates scales linearly with increases in TCW, thus do not extrapolate our findings here to other warming scenarios or future time periods.

It is important that similar assessments to those presented here are completed for other high resolution future climate scenarios in order to more rigorously determine the balance of processes controlling enhanced precipitation rates in the future climate. From a stakeholder perspective, it is also of importance to see what changes in extreme precipitation rate could be expected for different warming scenarios in order to better advise mitigation strategies. each profile, 600 hPa data has been omitted due to errors at this level for all 1998 and some 1999 storms.

  Future climate SSTs are calculated first by quantifying the climatological change in SST values simulated between 1975-2005 and 2085-2115 from a GCM run using the Coupled Model Inter-comparison Project phase 5 Regional Climate Pathway 8.5 (RCP8.5). This climatological SST change was calculated monthly, interpolated both spatially and temporally, and added to the current climate values to produce future SSTs.

Figure 1

 1 Figure 1 displays the zonally-averaged (across 15°W-15°E) latitudinal change

  the mean 1.5 meter temperature difference across climates, and rΔ is the fractional rate of TCW change per Kelvin, calculated as: Accepted for publication in Journal of Climate. DOI 10.1175/JCLI-D-19-0380.1.

  and occur in the current climate CP4-A simulation. Sub-Clausius-Clapeyron r values over Senegal and Mauritania are due to Accepted for publication in Journal of Climate. DOI 10.1175/JCLI-D-19-0380.1.

  S1. Time of storm TCW and vertical velocity exhibit the strongest control on extreme precipitation in either climate (Figs 7b, 7d respectively), with the product of Accepted for publication in Journal of Climate. DOI 10.1175/JCLI-D-19-0380.1.

Figures 1 ,

 1 Figures 1, and 3 highlighted zonal and meridional heterogeneity in the

Figure 9

 9 Figure 9 displays analogous information to Fig. 7, except for mean precipitation

Figure 12

 12 Figure12provides a more complete overview of modelled processes by

Figure 2 -

 2 Figure 2 -Diurnal cycle of precipitation and zonal wind shear for both climates. For

Figure 3 -

 3 Figure 3 -Climatological changes in surface temperature, Total Column Water and

Figure 4 -

 4 Figure 4 -Composite vertical profile of selected potential storm intensity metrics for

Figure 5 -

 5 Figure 5 -Composite skew T diagram of ambient conditions preceding all storms

Figure 6 -

 6 Figure 6 -Probability Density Functions of extreme precipitation rates during MCSs

Figure 7 -

 7 Figure 7 -Weighted density contour relationships between extreme precipitation

Figure 8 -

 8 Figure 8 -Weighted density contour relationships between potential drivers of

Figure 9 -

 9 Figure9-As for Fig.7, but using mean precipitation rate of 1800 UTC storms as a

Figure 10 -

 10 Figure 10 -As for Fig. 7, but measuring drivers of extreme precipitation rate for

Figure 11 -

 11 Figure 11 -As for Fig. 7, but measuring drivers of extreme precipitation rate at 0600

Figure 12 -

 12 Figure 12 -Schematic diagram explaining the processes through which increases in

Figure 1 -

 1 Figure 1 -Climatological change in the West African Monsoon in the two CP4

Figure 2 -

 2 Figure 2 -Diurnal cycle of precipitation and zonal wind shear for both climates. For

Figure 4 - 57 Figure 5 -

 4575 Figure 4 -Composite vertical profile of selected potential storm intensity metrics for

Figure 6 -

 6 Figure 6 -Probability Density Functions of extreme precipitation rates during MCSs

Figure 7 -

 7 Figure 7 -Weighted density contour relationships between extreme precipitation

Figure 8 -

 8 Figure 8 -Weighted density contour relationships between potential drivers of

Figure 9 -

 9 Figure 9 -As for Fig. 7, but using mean precipitation rate of 1800 UTC storms as a

Figure 10 -

 10 Figure 10 -As for Fig. 7 but measuring drivers of extreme precipitation rate for

Figure 11 -

 11 Figure 11 -As for Fig. 7, but measuring drivers of extreme precipitation rate at 0600

Accepted for publication in Journal of Climate. DOI 10.1175/JCLI-D-19-0380.1.

Acknowledgements

Accepted for publication in Journal of Climate. DOI 10.1175/JCLI-D-19-0380.1.

Fitzpatrick, Parker, Marsham, Guichard, Taylor, Crook and Rowell were supported by the Natural Environment Research Council/Department for International Development (NERC/DFID) program AMMA-2050: African Monsoon Multidisciplinary Analysis for 2050 projectgrant numbers NE/M017176/1, NE/M20126/1 and numbers NE/M020428/1. Finney, Marsham, and Rowell were funded by the NERC/DFID funded Integrating Hydro-Climate Science into Policy Decisions for Climate-Resilient Infrastructure and Livelihoods in East Africa (HyCRISTAL). Crook was also supported by the NERC program VERA: Vegetation Effects on Rainfall in West Africagrant number NE/M003574/1. Jackson, Tucker and Stratton were supported by NERC/DFID via the FCFA funded project, Improving Model Processes for African Climate (IMPALA, NE/MO17176/1 and NE/M017214/1). Parker was also supported by a Royal Society Wolfson Research Merit Award (2014-2018). Marsham was also supported by the National Centre for Atmospheric Science via the NERC/GCRF program ACREW: Atmospheric hazard in developing Countries: Risk assessment and Early Warning. Vizy, Cook, and Fitzpatrick's contributions towards this study was also funded by the National Science Foundation Award number 1444505. The authors wish to extend their deepest gratitude to Margaret LeMone, the journal editor and two anonymous reviewers for their comments, which contributed greatly to the results presented. Accepted for publication in Journal of Climate. DOI 10.1175/JCLI-D-19-0380.1.

Data availability

Analysis presented within this article has been performed using Python scripts available at https://zenodo.org/record/2560410 (Fitzpatrick and Burns 2019).

analysis presented in Figures 7 and8 has been reproduced for the western Sahel (15 -0°W -Supplementary Figs. S5 -S6), and the eastern Sahel (0 -15°E -Supplementary Figs. S7 -S8), as well as over more constrained latitudinal bounds (11 -12°N -Supplementary Figs. S9 -S10, and 16 -17°N -Supplementary Figs. S11 -S12). We draw similar conclusions to those presented above for MCSs within either the west or east Sahel as well as those present across 11 -12N. For MCSs found over 16 -17N, we find that their behavior is very similar to the all-storm analysis (compare Figs. 8 and Supplementary Fig. S12), however, ambient CAPE and mid-level RH do not appear to be significant drivers of extreme precipitation rate variance in either climate for these events (Supplementary Fig. S11). Although the interaction of storm processes remains similar throughout the Sahel region studied, latitudinal variations in humidity and available energy can affect the relationship between these metrics and extreme precipitation rates.

Change in correlation of storm drivers for different intensity measures, and at 0000 and 0600 UTC

In Section 6, we consider drivers of extreme precipitation rates of early evening MCSs across the Sahel. Here, we extend our analysis to consider drivers of mean precipitation rate change across climates, as well as drivers of extreme precipitation rate changes for nocturnal MCSs. This analysis is necessary, as prior work has suggested that mean MCS precipitation rates are controlled by ambient/internal drivers different from those which affect extreme precipitation rates (Takemi 2010), and different storm intensity drivers are present at different times of day (Vizy and Cook 2018a).

Accepted for publication in


D Irvandy

H H Duong

G Teyssedre

L Berquez

I Sinisuka

T T N Vu

Study on Space Charge Behavior in DC Model Cable under Thermal Gradient and Polarity Reversal

Keywords: Space charge, DC, PEA method, polarity reversal, thermal gradient I

Research on space charge related to HVDC cables is mostly achieved on small scale samples, being flat specimen or reduced size cables, for questions of cost, easiness and flexibility of tests. Resorting to measurements on model cables, there exist different ways of implementing tests using the pulsed electroacoustic (PEA) method. In this communication we turn back to the different possible arrangements and show that using a dedicated cable loop for applying the voltage pulse can be a suitable way. Some results are shown in presence of a thermal gradient.

INTRODUCTION

The use of HVDC in electric power transmission systems is becoming increasingly popular because of its advantages compared to HVAC especially for long distance and submarine transmission. Research on HVDC cables especially with regard to insulation is very important because it is related to the reliability and lifetime of the cable itself. Space charge is believed to be the phenomenon responsible for the degradation of insulating material in DC systems.

Most of the studies resorting to research about materials are achieved using small scale samples as working on full size cables is extremely expensive, and does not allow flexibility of the stress to apply on cables. Among samples, flat specimen provided with semiconducting tapes (carbon black doped polymer, semicon) constitutes one way to approach a structure representative of the cable since similar interfaces are reconstituted by co-crosslinking [START_REF] Fabiani | Polymeric HVDC cable design and space charge accumulation. Part 1: insulation/semicon interface[END_REF]. A second way consists in using cables of reduced size, which brings the cylindrical geometry as well as the possibility to heat the cable through the conductor and form a thermal gradient in the cable, a situation which approaches operating conditions of cables [START_REF] Fabiani | Polymeric HVDC cable design and space charge accumulation. Part 3: Effect of temperature gradient[END_REF]. Therefore, cable samples appear as more realistic samples, even though questions remain: e.g. the amount of crosslinking by-products stored in the cable cannot be fully representative of a thick installation [START_REF] Adi | DC model cable under polarity inversion and thermal gradient: build-up of design-related space charge[END_REF].

Model cables used for testing are often either medium voltage (MV) cables, with typically 5-10 mm thick insulation [START_REF] Fabiani | Polymeric HVDC cable design and space charge accumulation. Part 3: Effect of temperature gradient[END_REF] [5], or miniature cables with 1.5 mm insulation thickness [START_REF] Fukunaga | Measurement of charge distribution in the insulation of cables using pulsed electroacoustic method[END_REF]. The pulsed electroacoustic -PEAmethod is the main method used to probe space charge on cables [6] [7] though Laser-Induced Pressure Pulse [START_REF] Cao | Space charge measurement system based on laser PWP method for the full-size long HVDC cable[END_REF] or Thermal step method [START_REF] Castellon | Electric field and space charge measurements in thick power cable insulation[END_REF] are also used, including on full size cables. Rizzo et al [START_REF] Rizzo | Review of the PEA method for space charge measurements on HVDC cables and minicables[END_REF] recently reviewed the various principles used to implement the PEA method on cables. They vary according to the degree of intrusively acceptable for cables, and to technical feasibility. In full size cables, the objective will be to minimize the machining achieved on the cable, and an ideal case would be that the full jacket of the cable be maintained.

For small or MV cables, one way to prepare cables consists in removing the semiconducting screen on part of the cable, which can be detrimental to cable withstanding.

In this communication, we discuss different ways of configuring the set-up for measuring space charges in miniature cables having crosslinked Polyethylene (XLPE) as insulation and semicon at both interfaces. We describe an acceptable solution maintaining the integrity of the cable. We illustrate the method by some results obtained under polarity reversal and thermal gradient.

II. EXPERIMENTAL SECTION

A. Cable samples

Samples from model cables, called mini-cables were considered in this research. Mini-cables are special cables that were manufactured for research purposes. With their reduced size, these cables can reduce the cost of production, transportation and testing. They were produced by tripleextrusion (semicon/XLPE/semicon), having a conductor diameter of 1.4 mm, and inner and outer diameter for the insulation of about 1.5 and 3 mm, respectively. With these dimensions, applying 10 kV to the conductor gives geometric electric fields of 10 and 5 kV/mm, respectively at the inner and outer semicon interface.

B. Test configurations

Fig. 1 depicts a very standard way used previously to probe space charges in model cables by PEA [START_REF] Vu | Transient space charge phenomena in HVDC model cables[END_REF]. The cable is installed as a loop. A current transformer is used for the purpose of heating the cable through the conductor. In order to apply the voltage pulses while stressing the cable under DC, a decoupling capacitor is necessary. It is realized by removing the semicon on a length of about 5 cm to separate the cable section at the probing point from that used as coupling capacitor. The arrangement shown in Fig. 1 provides good reliability when working with MV cables, 4.5 mm thick insulation, up to 100 kV. For miniature cables, the part of the semiconductor being removed brings fragility to the cable, and breakdown could occur at about 50 kV. A new way of making measurements was with the introduction of a second loop of cable [START_REF] Berquez | Implementation of space charge measurement using the Pulsed Electro-Acoustic method during ageing of HVDC model cable[END_REF] for applying the pulse. Then voltage as high as 90 kV could be applied with appropriate treatment of the terminations. The measurement results appeared however somewhat degraded in respect to previous achievements and our objective in the present work is to investigate in some detail the impact of the arrangement and optimize it.

Two configurations were tested to obtain an optimal signal. The first configuration uses two cables, see Fig. 2a, where the PEA module and the impulse voltage injector are on different cables. The second configuration is measurement using a single cable. PEA modules and impulse voltage injectors are placed on the cable under test (see Fig. 2.b). It is important to note that here the semicon was not removed between excitation point and detection point. It is anticipated that these arrangements deteriorate the quality of the acoustic signal. In the first case, the distance between excitation and detection and possible impedance mismatch can be the reason. In the second case, the result may depend on the high frequency impedance of the outer semicon, which could not be measured. For comparison purpose, in each configuration, a test is performed by varying the impulse voltage, the location of the PEA module and the DC voltage on the cable.

All the cables used in these tests have a length of about 3 m. Tests were realized using a pulsed generator of 30 ns duration, at a frequency of 1.5 kHz, using pulse amplitude of 0.4 kV or 1 kV. In the optimization step, we resorted to the calibration signal obtained under DC voltages of ±3 kV or ±5 kV. Then, in a second part some space charge results are shown. They were obtained at room temperature for voltages up to 35 kV, as well as under a temperature gradient of about 4°C applied by injecting a current in the cable conductor.

III. TEST RESULTS FOR DIFFERENT CONFIGURATIONS

A. Configuration with two cables

Fig. 3 shows the rough PEA signals obtained for a pulse voltage of 1 kV and for applied voltages varying from -5 kV to +5 kV. The acoustic response under 0 V dc voltage was subtracted to remove blank response and possible response from residual charges. The pulse injector was at position 0 cm in Fig. 2a. The response associated to the interface charges appears as a double peak for both the interface between insulation and outer screen (left) and with inner screen (right). The time lag between the first positive peak to the left and the first negative peak to the right (for applied voltage of 5 kV), considered as the positions of the electrode interfaces, is 655 ns. Considering a sound velocity for XLPE of 2200 m/s, this gives an insulation thickness of 1.45 mm, consistent with the mini-cable design. The response is roughly symmetrical with changing the polarity. There are oscillations of the signal (in-between the main peaks and beyond it) that appear related to the shape of the main peaks: it seems therefore to correspond to multiple reflections in the test bench and not to external noise linked for example to the pulse generator.

We now consider test realised at a fixed DC voltage of +5 kV, still with +1 kV impulse voltage, and investigate the effect of shifting the position of the PEA module. Positions to the right and to the left of the middle point of the cable used for pulse application as far as 20 cm, 60 cm and 80 cm are considered. Fig. 4 shows the amplitude of the response at inner and outer semicon as a function of the position. We do not see strong variation in the amplitudes, being about 12% to the maximum.

When the pulse injector and PEA cell are not placed symmetrically on the loops, there can be some time lag appearing between excitation and detection depending on the route considered for electric pulse propagation. Considering a relative permittivity of 2.2, the pulse velocity in the cable is of the order 0.15 m/ns. The propagation time for the voltage pulse is therefore of the order of 6 ns per meter, which is still small in respect to the propagation time of acoustic waves in the sample (x 100). Therefore, it is reasonable to detect mild effects as far the length difference remains of the order of 1 m, and the pulse absorption by the cable is small (the later was not evaluated). However, because of impedance mismatch, there can be harmonic voltages that produce delayed acoustic waves and hence some spurious peaks. The highest signal amplitudes in both the outer and inner interface response signals are obtained when the impulse injector module is located at -60 cm (counter-clockwise) from the middle of the loop.

B. Configuration with one cable

Fig. 5 shows the rough signals obtained in the configuration with one single cable, voltage conditions being the same as above. The distance between the pulse injector and the PEA module was 30 cm, see Fig. 2b. Comparatively to the previous response (Fig. 3), the peak-to-peak amplitude is substantially reduced, by a factor of more than 2. Changing the position on the same loop increased slightly the amplitude, without reaching that of the first arrangement.

Besides, the oscillations in the signal remain important and no improvement seems reached. For this reason, we conclude that the first configuration using two cable loops is much more suited. An advantage of this method is that the pulse connector is permanently maintained, providing better reproducibility of the results when changing cable sample for example.

IV. SPACE CHARGE RESULTS

A. Calibration

The calibration of the signal was achieved following the procedure described in [START_REF] Vissouvanadin | Deconvolution techniques for space charge recovery using pulsed electroacoustic method in coaxial geometry[END_REF] in which attenuation and dispersion of acoustic waves are taken into account. Fig. 6a depicts the rough calibration signal and that reconstructed taking into account the transfer function for acoustic waves through the insulation as well as the geometric factor for the cable. Results correspond to a DC field of 5 kV and a pulse voltage of 400 V. The charge profile of Fig. 6b obtained from the calibration signal provides an idea of the spatial resolution (which could be improved by lowering the smoothing of the output).

B. Space charge and field at room temperature

First tests were carried following a protocol in which voltage steps at -20 kV, +20 kV, -25 kV, +25 kV, -35 kV, +35 kV were applied successively for 1 h each. The applied pulse voltage was 0.4 kV, at a frequency of 1.5 kHz. Space charges were acquired about every 6 min along the protocol. Fig. 7.a shows the space charge distributions obtained during the all cycle. The profiles are very similar in shape, and appear symmetrical when changing the polarity. A small amount of charges is present in the middle of the cable and near the inner semicon, which changes sign with changing polarity. The response could be the consequence of some conductivity gradient along the radius.

The charge amounts are small, linked to the fact that the applied stresses are moderate, stressing time relatively short and measurements are at room temperature. In addition, the tested cables have been stored for several years in ambient conditions in such a way that crosslinking by-products that could stay as residues in the cable have been evacuated during storage.

Fig. 7b shows the distribution of electric fields in the cable. The field grossly follows a capacitive distribution vs. radius, i.e. it is about twice at the inner semicon compared to the outer semicon. A capacitive distribution is obtained under DC under the condition that conductivity is homogeneous (not dependent on the radius, therefore not dependent on the field) and that no space charge accumulates in the insulation.

C. Space charge and field under temperature gradient

In order to produce more significant amounts of charge, measurements were achieved while injecting a current in the conductor. With a current of 32 A, we have estimated that the temperature drop along the insulation of the cable was about 4°C. As the PEA cell acts a heat sink [START_REF] Berquez | Implementation of space charge measurement using the Pulsed Electro-Acoustic method during ageing of HVDC model cable[END_REF], the temperature at the measurement point was low, being about 30°C at the outer screen and 26°C at the inner screen.

The stress cycle consisted here in 3 h under -35 kV followed by one hour in volt-off. Then, the cycle was repeated for positive polarity. Fig. 8 shows the obtained results. Profiles do not appear as symmetrical as previously. There is a clear evolution in the charge pattern as a function of stressing time. The influence charge at the inner interface decreases in time while that at the outer interface increases. This corresponds to the field redistribution observed in Fig. 8b, leading to a nearly homogeneous field after 3 h charging. The evolutions found here seem to correspond mainly to a smoothing of the field by the conductivity gradient imposed by heating the cable: the field is moved to the cold part of the cable and a homocharge viewed from the hotter electrode develops in the bulk of the insulation. The residual space charge (at V=0) is somewhat larger after positive voltage application than negative one and this is reflected in the shape of residual field profile. Consistent results are therefore obtained under the moderate field applied in the present results.

CONCLUSIONS

We have shown that using a second cable loop for applying voltage pulses in PEA experiments constitutes the best way for avoiding to remove the semicon in the middle part of the cable prior to PEA measurements. This is of particular importance in the perspective of space charge measurements in miniature cables under high field in which weak point of the cable occurs after peeling the semicon. Some space charge and field distributions results were presented with polarity reversal under moderate field, at room temperature and under thermal gradient. The material behavior appears mostly governed by conductivity gradient due to non-homogenous field and/or temperature, which appears consistent with the fact that cables were practically free from crosslinking by-products after long storage in ambient conditions. More work is to be achieved regarding the higher field behavior.

Figure 2 .

 2 Figure 2. Tested configurations using (a): 2 cables; (b): 1 cable.

Figure 3 .

 3 Figure 3. Rough PEA signals at applied voltages of ±5 kV and ± 3 kV. X-axis: 1000 points correspond to 800 ns with the sampling rate of 1.25 Gs/s used. Dotted lines represent the responses from the capacitive charge peaks (left: outer semicon, right: inner semicon).

Figure 4 .Figure 1 .

 41 Figure 4. Peak to peak voltage comparison at +5 kV and varying impulse injector position.

  (a) Rough acoustic signal (b) Charge profile for 5 kV DC voltage.

Figure 6 .Figure 7 .

 67 Figure 7. Space charge (a) and field (b) distributions for applied voltages of +/-20, 25 and 35kV for 1 h at room temperature.

Figure 5 .Figure 8 .

 58 Figure 5. Response to different voltage levels when positioning impulse injector at 30 cm from the PEA module on a single cable. 0 500 1000 1500 2000