Janna M Barel
email: janna.barel@gmail.com

Vincent Moulia

Samuel Hamard

Anna Sytiuk

Vincent E J Jassey

Come Rain, Come Shine: Peatland Carbon Dynamics Shift Under Extreme Precipitation

Keywords: resistance, resilience, dissolved organic carbon, decomposition, water table fluctuation, rewetting, carbon dioxide, methane

Precipitation patterns are becoming increasingly extreme, particularly at northern latitudes. Current climate models predict that this trend will continue in the future. While droughts have been repeatedly studied in many ecosystems over the last decades, the consequences of increasingly intense, but less frequent rainfall events, on carbon (C) cycling are not well understood. At northern latitudes, peatlands store one third of the terrestrial carbon and their functioning is highly dependent on water. Shifts in rainfall regimes could disrupt peatland C dynamics and speed-up the rates of C loss. How will these immense stocks of C be able to withstand and recover from extreme rainfall? We tested the resistance and resilience effects of extreme precipitation regimes on peatland carbon dioxide (CO 2 ) and methane (CH 4 ) fluxes, pore water dissolved organic carbon (DOC) and litter decomposition rates by exposing intact peat cores to extreme, spring-time rainfall patterns in a controlled mesocosm experiment. We find that more intense but less frequent rainfall destabilized water table dynamics, with cascading effects on peatland C fluxes. Decomposition and respiration rates increased with a deeper mean water table depth (WTD) and larger WTD fluctuations. We observed similar patterns for CO 2 uptake, which were likely mediated by improved vascular plant performance. After a three-week recovery period, CO 2 fluxes still displayed responses to the earlier WTD dynamics, suggesting lagged effects of precipitation regime shifts. Furthermore, we found that CH 4 emissions decreased with deeper mean WTD, but this showed a high resilience once WTD dynamics stabilised. Not only do our results illustrate that shifting rainfall patterns translate in altered WTD dynamics and, consequentially, influence C fluxes, they also demonstrate that exposure to altered rainfall early in the growing season can have lasting effects on CO 2 exchange. Even though the increased CO 2 assimilation under extreme precipitation patterns signals peatland resistance under changing climatic conditions, it may instead mark the onset of vascular plant encroachment and the associated C loss.

INTRODUCTION

Climatic change includes shifting precipitation patterns along with increases in temperature and drought [START_REF] Dai | Increasing Drought under Global Warming in Observations and Models[END_REF]. Moreover, current observations of increased heavy precipitation confirm earlier predictions [START_REF] Fischer | Observed Heavy Precipitation Increase Confirms Theory and Early Models[END_REF]. In the past three decades, extreme precipitation events have become more common [START_REF] Lehmann | Increased Record-Breaking Precipitation Events under Global Warming[END_REF], particularly in North America and Europe [START_REF] Ummenhofer | Extreme Weather and Climate Events with Ecological Relevance: A Review[END_REF]. As a consequence of more intense but less frequent rainfall events in northern temperate to arctic regions, local carbon (C) dynamics are expected to change [START_REF] Blodau | Experimental Response of Peatland Carbon Dynamics to a Water Table Fluctuation[END_REF][START_REF] Gerten | Modelled Effects of Precipitation on Ecosystem Carbon and Water Dynamics in Different Climatic Zones[END_REF][START_REF] Knapp | Consequences of More Extreme Precipitation Regimes for Terrestrial Ecosystems[END_REF][START_REF] Frank | Effects of Climate Extremes on the Terrestrial Carbon Cycle: Concepts, Processes and Potential Future Impacts[END_REF][START_REF] Dai | Climate Change and Drought: A Precipitation and Evaporation Perspective[END_REF]. Heavy rain might temporarily invoke waterlogged and anoxic soil conditions and thus limit processes that require oxygen such as respiration (by plants and soil biota) and decomposition [START_REF] Knapp | Consequences of More Extreme Precipitation Regimes for Terrestrial Ecosystems[END_REF][START_REF] Reichstein | Climate Extremes and the Carbon Cycle[END_REF] and promote methanogenesis. Conversely, increasingly long intervals between heavy rain events could lead to drought stress, affecting both plant and soil microbial physiology [START_REF] Zeppel | Impacts of Extreme Precipitation and Seasonal Changes in Precipitation on Plants[END_REF][START_REF] Schimel | Life in Dry Soils: Effects of Drought on Soil Microbial Communities and Processes[END_REF], as well as related ecosystem functions, including photosynthesis, respiration, and methanogenesis [START_REF] Knapp | Rainfall Variability, Carbon Cycling, and Plant Species Diversity in a Mesic Grassland[END_REF][START_REF] Reichstein | Climate Extremes and the Carbon Cycle[END_REF][START_REF] Zeppel | Impacts of Extreme Precipitation and Seasonal Changes in Precipitation on Plants[END_REF][START_REF] Helfter | Drivers of Long-Term Variability in CO2 Net Ecosystem Exchange in a Temperate Peatland[END_REF]. While the effects of drought and flooding are reasonably well understood, the combined impact of more intense rain and increased duration of dry intervals on ecosystem C dynamics is little researched.

At northern latitudes, peatlands are one of the dominant ecosystems [START_REF] Leifeld | The Underappreciated Potential of Peatlands in Global Climate Change Mitigation Strategies[END_REF] and their C dynamics heavily depend on their hydrology [START_REF] Limpens | Peatlands and the Carbon Cycle: from Local Processes to Global Implications -a Synthesis[END_REF]. Predominant shallow water tables lead to C sequestration because of an imbalance of C entering the system through photosynthesis, while little assimilated C is lost because of repressed decomposition and respiration [START_REF] Dise | Peatland Response to Global Change[END_REF][START_REF] Turetsky | The Resilience and Functional Role of Moss in Boreal and Arctic Ecosystems[END_REF]. As a result peatlands store the equivalent of 25-50% of the global soil organic C stock (i.e., 500-1000 GtC) [START_REF] Yu | Northern Peatland Carbon Stocks and Dynamics: A Review[END_REF][START_REF] Wieder | Global Soil Carbon Projections Are Improved by Modelling Microbial Processes[END_REF][START_REF] Jackson | The Ecology of Soil Carbon: Pools, Vulnerabilities, and Biotic and Abiotic Controls[END_REF][START_REF] Nichols | Rapid Expansion of Northern Peatlands and Doubled Estimate of Carbon Storage[END_REF]. Peatland C stocks are vulnerable to ongoing climatic change [START_REF] Dise | Peatland Response to Global Change[END_REF]) and especially to hydrological shifts [START_REF] Sundh | Potential Aerobic Methane Oxidation in a Sphagnum-Dominated Peatland-Controlling Factors and Relation to Methane Emission[END_REF]. Hydrological shifts such as caused by extreme rainfall patterns or drought threaten peatland C dynamics [START_REF] Radu | Precipitation Frequency Alters Peatland Ecosystem Structure and CO2 Exchange: Contrasting Effects on Moss, Sedge, and Shrub Communities[END_REF][START_REF] Evans | Overriding Water Table Control on Managed Peatland Greenhouse Gas Emissions[END_REF], pushing peatlands toward becoming a C source by increasing decomposition rates [START_REF] Belyea | Separating the Effects of Litter Quality and Microenvironment on Decomposition Rates in a Patterned Peatland[END_REF][START_REF] Moore | Litter Decomposition in Temperate Peatland Ecosystems: The Effect of Substrate and Site[END_REF] and CO 2 respiration [START_REF] Lund | Effects of Drought Conditions on the Carbon Dioxide Dynamics in a Temperate Peatland[END_REF][START_REF] Helfter | Drivers of Long-Term Variability in CO2 Net Ecosystem Exchange in a Temperate Peatland[END_REF] and reducing CO 2 uptake [START_REF] Kuiper | Plant Functional Types Define Magnitude of Drought Response in Peatland CO2exchange[END_REF][START_REF] Helfter | Drivers of Long-Term Variability in CO2 Net Ecosystem Exchange in a Temperate Peatland[END_REF]. As a consequence of extreme drought, methanogenesis may decrease while methanotrophy increases, thus reducing CH 4 emissions (Bubier and Moore, 1994;[START_REF] Turetsky | A Synthesis of Methane Emissions from 71 Northern, Temperate, and Subtropical Wetlands[END_REF][START_REF] Evans | Overriding Water Table Control on Managed Peatland Greenhouse Gas Emissions[END_REF].

Hydrological shifts do not always translate into peatland C loss [START_REF] Robroek | Interactive Effects of Water Table and Precipitation on Net CO2assimilation of Three Co-occurringSphagnummosses Differing in Distribution above the Water Table[END_REF][START_REF] Muhr | Manipulative Lowering of the Water Table during Summer Does Not Affect CO2emissions and Uptake in a Fen in Germany[END_REF][START_REF] Nijp | Can Frequent Precipitation Moderate the Impact of Drought on Peatmoss Carbon Uptake in Northern Peatlands?[END_REF][START_REF] Wang | Dual Controls on Carbon Loss during Drought in Peatlands[END_REF]. Small but frequent rain events can be readily exploited by the crucial peat-forming Sphagnum mosses, maintaining the moisture level at the peat surface sufficiently for CO 2 uptake [START_REF] Robroek | Interactive Effects of Water Table and Precipitation on Net CO2assimilation of Three Co-occurringSphagnummosses Differing in Distribution above the Water Table[END_REF][START_REF] Strack | Moisture Controls on Carbon Dioxide Dynamics of Peat-Sphagnummonoliths[END_REF][START_REF] Adkinson | The Response of Carbon Dioxide Exchange to Manipulations of Sphagnum Water Content in an Ombrotrophic Bog[END_REF][START_REF] Nijp | Can Frequent Precipitation Moderate the Impact of Drought on Peatmoss Carbon Uptake in Northern Peatlands?[END_REF]. The influence of rain is particularly relevant when water tables are low [START_REF] Strack | Moisture Controls on Carbon Dioxide Dynamics of Peat-Sphagnummonoliths[END_REF]. Sphagnum mosses are prone to drying because they lack vascular tissue and roots to cope with dry conditions. Then again, Sphagnum photosynthesis can recover within 1 h when rewetted after a long period of drought [START_REF] Jassey | Effects of Climate Warming on Sphagnum Photosynthesis in Peatlands Depend on Peat Moisture and Species-specific Anatomical Traits[END_REF]). Yet, this quick recovery of Sphagnum C assimilation might not be sufficient to off-set autotrophic respiration costs of restarting photosynthesis [START_REF] Mcneil | Moisture Controls on Sphagnum Growth and CO2 Exchange on a Cutover Bog[END_REF][START_REF] Nijp | Can Frequent Precipitation Moderate the Impact of Drought on Peatmoss Carbon Uptake in Northern Peatlands?[END_REF]. At the same time, under dry conditions vascular plants may take-over the C sink function from Sphagnum [START_REF] Huth | The Climate Warming Effect of a Fen Peat Meadow with Fluctuating Water Table Is Reduced by Young Alder[END_REF][START_REF] Schwieger | Wetter Is Better: Rewetting of Minerotrophic Peatlands Increases Plant Production and Moves Them towards Carbon Sinks in a Dry Year[END_REF][START_REF] Radu | Precipitation Frequency Alters Peatland Ecosystem Structure and CO2 Exchange: Contrasting Effects on Moss, Sedge, and Shrub Communities[END_REF], making the effects of shifting rainfall regimes on net ecosystem exchange harder to predict. Influence of precipitation shifts on peatland C dynamics may also act through dissolved organic carbon (DOC). Flooding and heavy rains can result in a temporary increase in DOC concentration [START_REF] Moore | Some Controls on the Release of Dissolved Organic Carbon by Plant Tissues and Soils[END_REF][START_REF] Blodau | Experimental Response of Peatland Carbon Dynamics to a Water Table Fluctuation[END_REF] and DOC loss by run-off [START_REF] Pastor | Global Warming and the Export of Dissolved Organic Carbon from Boreal Peatlands[END_REF][START_REF] Leach | Twelve Year Interannual and Seasonal Variability of Stream Carbon Export from a Boreal Peatland Catchment[END_REF][START_REF] Rosset | Peatland Contribution to Stream Organic Carbon Exports from a Montane Watershed[END_REF]. Furthermore, recent evidence showed that prolonged drought has little effect on the concentration of DOC, although lowering of the water table decreased DOC aromaticity and/or lower its molecular weight [START_REF] Jassey | Tipping point in Plant-Fungal Interactions under Severe Drought Causes Abrupt Rise in Peatland Ecosystem Respiration[END_REF]. These observations highlight the uncertainty and the need for a better understanding of peatland C dynamics responses to more extreme precipitation patterns.

Besides its hydrological state, seasonal timing also controls an ecosystem's response to precipitation shifts. Indeed, disturbances to vegetation phenology can have cascading effects on peatland C uptake [START_REF] Helfter | Drivers of Long-Term Variability in CO2 Net Ecosystem Exchange in a Temperate Peatland[END_REF][START_REF] Koebsch | Refining the Role of Phenology in Regulating Gross Ecosystem Productivity across European Peatlands[END_REF]. While repeated drought stress early in the growing season may lead to a loss of resilience regarding CO 2 uptake, its effect on other C fluxes, such as decomposition, DOC, respiration, and CH 4 efflux, is little studied. This underlines the need to investigate the influence of redistribution of rainfall early in the growing season on peatland C dynamics, which may be substantial given the hydrological control on C uptake, turn-over and loss. Moreover, effects of extreme rainfall patterns on peatland C dynamics in spring could have immediate as well as longer term consequences when the response mechanisms include lasting physiological and community changes among plants and microorganisms [START_REF] Frank | Effects of Climate Extremes on the Terrestrial Carbon Cycle: Concepts, Processes and Potential Future Impacts[END_REF][START_REF] Schimel | Life in Dry Soils: Effects of Drought on Soil Microbial Communities and Processes[END_REF].

Here, we evaluated the capacity of peatland C dynamics to tolerate severe spring rainfall redistribution. We studied how peatland C dynamics continue to function during (i.e., resistance) and "bounce back" from (i.e., resilience) increasingly extreme precipitation regimes during spring (sensu [START_REF] Nimmo | Vive la résistance: reviving resistance for 21st century conservation[END_REF][START_REF] Ingrisch | Towards a Comparable Quantification of Resilience[END_REF], in order to understand how C storage in peatlands may be affected by prospective climatic change early in the growing season. For wet systems, such as peatlands, [START_REF] Knapp | Consequences of More Extreme Precipitation Regimes for Terrestrial Ecosystems[END_REF] postulated that low frequent but intense rainfall events will reduce the number of days during which the system experiences anoxic conditions. That is why we expected that 1) under more intense but less frequent rainfall C cycling rates speed up with increased assimilation, decomposition, and respiration but reduced CH 4 emissions as caused by larger fluctuations of the water table over time. Moreover, 2) peatland C dynamics are expected to be resilient and C dynamics recover after rewetting without lasting effects. We tested our hypotheses in a mesocosm experiment in which intact peat cores were exposed to increasingly intense, but less frequent rainfall for nearly 3 months, followed by rewetting and a three-week recovery period.

MATERIALS AND METHODS

Study Site

To construct the experimental mesocosms, peat monoliths with homogeneous vegetation cover were extracted from a poor fen near Counozouls in the French Pyrenees (42 o 41′16 N; 2 o 14′18E, altitude 1,350 m, 7.9 °C mean annual temperature, 1,027 mm mean annual precipitation). The site is situated within the Special Area of Conservation Natura 2,000 site "Massif du Madres Coronat." The vegetation has a moss layer dominated by Sphagnum warnstorfii Russow and S. palustre L., the vascular vegetation was characterized by Molinia caerulea (L.) Moench, Eriophorum angustifolium L., Calluna vulgaris (L.) Hull, Potentilla anglica Laich. and Drosera rotundifolia L. Intact peat monoliths (14 cm h, 27 cm l, 17 cm d) were extracted in November 2019 and climatized for 3 months in a greenhouse in watertight containers, during which time the water table was kept at approximately-4 cm below the peat surface by watering regularly (for timeline see Table 1).

Meteorological field observations at the Counozouls site served as a baseline for the precipitation regimes (Supplementary Figure S1). In spring 2019 (March-May) 248 mm of rain fell at the site, varying from 0 to 31 mm a day, while in summer (June-Aug) 177 mm of rain fell, varying from 0 to 33 mm a day. The longest consecutive period without rain was 12 days during spring and 11 days during the summer months. We further calculated the rain frequency (% of days with rain), rain intensity (average mm of rain on a rainy day), and drought intensity (average length of dry spell in days) to characterize the rainfall regime at the field site during spring and summer (Figure 1).

Experimental Design

A week before the start of the experiment, intact cores were taken from the acclimated peat monoliths to construct 30 mesocosms in watertight plant pots (13 cm d, 9.5 cm h). The depth of the mesocosms covered the actively growing Sphagnum capitula, recently senesced Sphagnum stems and approximately 5 cm bulk peat including vascular plant roots. For 11 weeks the mesocosms were exposed to experimental precipitation regimes. Each pot was randomly assigned to one of six regimes. The precipitation regimes entailed the same amount of precipitation over the 11 weeks, but administered in increasingly extreme patterns sensu [START_REF] Knapp | Consequences of More Extreme Precipitation Regimes for Terrestrial Ecosystems[END_REF], namely 133-187 mm except for the most extreme regime (regime 6) which received 106-160 mm (Supplementary Figure S2). Every regime included 8-14 drought intervals (6-7 for regime 6) that intermitted the rain events. The regimes became increasingly extreme in three aspects: increase in rainfall intensity, reduction in rainfall frequency and consequentially lengthening of dry intervals between rain events (Figure 1). Dry intervals in the least extreme regime lasted maximum 5 days and increased to maximum 29 days in the most extreme regime. In all this, regime 2 most closely resembled precipitation patterns observed at the field site during spring. In order to mimic natural variation, the five replicates within a regime varied slightly in the amount of precipitation per rain event and the exact length of a drought spell, but the order of the drought spells was synchronized to prevent pseudo-replication. The mesocosms were watered according to the precipitation treatments with artificial rain water based on the protocol by [START_REF] Garrels | Minerals, Solutions, and Equilibria[END_REF], with addition of micronutrients, see Supplementary Table S1.

The resistance and resilience responses to the experimental precipitation regimes were observed during two experimental phases (Table 1). The precipitation regimes were applied during the resistance phase (I) which lasted 11 weeks. The resilience phase (II) immediately followed the resistance phase. This lasted 20 days during which the water table was restored to pre-experimental conditions in all pots (-4 cm) by watering the pots with approximately 50 ml every 2 days. We considered this duration to be sufficient to measure recovery as photosynthetic activity in Sphagnum mosses resumes within an hour after rewetting [START_REF] Jassey | Effects of Climate Warming on Sphagnum Photosynthesis in Peatlands Depend on Peat Moisture and Species-specific Anatomical Traits[END_REF], and net CO 2 assimilation of intact peat cores was previously shown to recover in about 2 weeks [START_REF] Robroek | Interactive Effects of Water Table and Precipitation on Net CO2assimilation of Three Co-occurringSphagnummosses Differing in Distribution above the Water Table[END_REF], while photosynthetic potential of vascular plants is not or much less affected by reduced rainfall [START_REF] Rastogi | Impact of Warming and Reduced Precipitation on Photosynthetic and Remote Sensing Properties of Peatland Vegetation[END_REF].

Peat C dynamics were measured as litter decomposition rates (during phase I), CO 2 and CH 4 gas fluxes on a weekly basis, during phase I, and biweekly basis during phase II, and as dissolved organic carbon (DOC) concentrations and quality in the pore water at five time points to cover the start, middle and end of phase I, and start and end of phase II (Table 1). Mid-way the resistance phase (week 7), we counted the number of graminoid and ericoid shoots and their average length to verify whether the abundance of vascular plants was similar across the six precipitation regimes.

The 30 mesocosms (5 reps, 6 regimes) were first placed in the greenhouse in a randomized design. Unfortunately, we were forced to move the experiment to a new location in week 5, because the greenhouse facilities closed due to the outbreak of the COVID-19 pandemic. The mesocosms were moved to a sheltered location with natural, albeit reduced light at ambient outdoor temperature. The precipitation regimes were maintained and continuous monitoring of the experimental conditions and inclusion of location in our statistical analysis (both see below) safeguarded the continuation and interpretation of our measurements.

Experimental Conditions

Throughout the experiment, peat temperature (at-5 cm), volumetric moisture content and light intensity were registered every 30 min. Soil temperature and moisture loggers (5TM sensor, Decagon devices Inc., United States) were placed in three pots from precipitation regimes 1, 3, and 6, randomly chosen from among the 5 replicates per regime. We monitored the light intensity by placing a photosynthetic active radiation (PAR) light sensor (QSO-S, Decagon Devices Inc., United States of America) in the middle between the mesocosms. Water table depth (WTD), as the distance (cm) from the top of the Sphagnum layer, was measured once every 2 days during the resistance phase, and twice a week during the resilience phase.

Measurements Peatland C Dynamics

Decomposition Rates

Decomposition rates were measured during the resistance phase by incubating graminoid litter in litter bags [START_REF] Cornelissen | An Experimental Comparison of Leaf Decomposition Rates in a Wide Range of Temperate Plant Species and Types[END_REF]. The graminoid litter was collected at the field site in January 2020, dried at 60 °C for 72 h, cut to fragments (1 cm) and put in nylon bags (5 × 6 cm, mesh size <1 mm), approx. 0.75 g per litterbag. The litterbags were inserted vertically into the peat at-5 cm at the start of the resistance phase and retrieved after 75 days, at the end of the resistance phase. The collected litterbags were cleaned with tap water and dried (60 °C) before weighting. Decomposition rates were measured as constant k, following the exponential decay model by Olson (1963):

X t X 0 e -kt
where decomposition rate constant k is calculated based on the remaining mass (X t ) after t days of incubation as a fraction of the initial mass (X 0 ).

Dissolved Organic Carbon

We monitored the DOC concentration and quality by sampling 10 ml porewater from each mesocosm, and replacing the sampled amount by equal amounts of artificial rainwater to compensate for the water removal. Porewater was filtered at 1 µm to remove particles and micro-organisms (Whatman GmbH, Dassel, Germany) and stored at -20 °C before determining DOC concentration (mg C L -1 ) by combustion on a TOC analyser (TOC-L, Shimadzu Europe GmbH, Duisburg, Germany) [START_REF] Pastor | Global Warming and the Export of Dissolved Organic Carbon from Boreal Peatlands[END_REF][START_REF] Hamard | Effects of Sphagnum Leachate on Competitive Sphagnum Microbiome Depend on Species and Time[END_REF]. For DOC quality we measured the spectral absorbance along 15 wavelengths between 250-465 nm of 200 µl sample aliquots in 96-well quartz microplates using a BioTek SynergyMX plate reader (BioTek Instruments Inc., Vermont, United States) spectrofluorometer [START_REF] Jaffrain | Assessing the Quality of Dissolved Organic Matter in Forest Soils Using Ultraviolet Absorption Spectrophotometry[END_REF]. Spectral slope [S 250-465 (nm -1 )], calculated using linear regression with Ln-transformed absorptions along the 250-465 nm range, as indication of DOC quality: high S 250-465 values indicate low molecular weight compounds and or decreasing aromaticity [START_REF] Hansen | Optical Properties of Dissolved Organic Matter (DOM): Effects of Biological and Photolytic Degradation[END_REF].

Gas Fluxes (CO 2 , CH 4 ) Gas flux rates were measured using the chamber method [START_REF] Riutta | Spatial Variation in Plant Community Functions Regulates Carbon Gas Dynamics in a Boreal Fen Ecosystem[END_REF]. Mesocosms were placed in airtight flux chambers (17.4 cm × 25.7 cm x 17.4 cm) to simultaneously measure CO 2 and CH 4 fluxes using a trace gas analyser (LI-COR 7810, Li-Cor Environmental-GmbH, Bad Homburg, Germany) set to record the CO 2 and CH 4 concentration every second during 5 min. Net ecosystem exchange of CO 2 (NEE) was measured using a transparent chamber while ecosystem CO 2 respiration (R eco ) was measured using a darkened chamber. Gross primary productivity (GPP), CO 2 uptake as a result of photosynthesis, was calculated as the difference between NEE and R eco . All gas fluxes were measured at ambient temperature and light conditions in the greenhouse (week 1-4) or outdoors (week 5-14). After visually confirming that for all measurements CO 2 and CH 4 concentrations in the chamber headspace changed linearly when plotted against time, gas flux rates were calculated with linear regression models using the R package gasfluxes [START_REF] Fuss | Gasfluxes: Greenhouse Gas Flux Calculation from Chamber Measurements[END_REF]. Gas fluxes were corrected for the container volume, mesocosm surface area, light intensity and soil temperature following the package guidelines. Positive values for the CO 2 and CH 4 fluxes indicate C release from and negative values C uptake by the mesocosm.

Cumulative CO 2 and CH 4 fluxes

To assess the resistance and resilience responses of the C balance to extreme precipitation, we reconstructed the C fluxes on an hourly basis for each mesocosm. Often process-based models based on the physical processes that regulate energy, carbon and water fluxes are used to predict C fluxes (f.e. [START_REF] Lai | Modelling the Effects of Climate Change on Methane Emission from a Northern Ombrotrophic Bog in Canada[END_REF]. However, application of these models has some limitations due to the inherent complexity of the model structure and related parameters [START_REF] Tramontana | Uncertainty Analysis of Gross Primary Production Upscaling Using Random Forests, Remote Sensing and Eddy Covariance Data[END_REF]. Empirical models, and especially machine learning algorithms such as random forests, are increasingly employed to develop quantitative predictive models of C fluxes while giving more accurate predictions [START_REF] Cutler | Random Forests for Classification in Ecology[END_REF]. Therefore, we used random forests models trained with all the environmental variables and flux data recorded.

Random forests (RF) algorithm for regression trees creates successive and independent regression trees using bootstrap samples of the data (i.e., a random forest) to classify data and make predictions [START_REF] Liaw | Classification and Regression by RandomForest[END_REF][START_REF] Breiman | Random Forests[END_REF][START_REF] Cutler | Random Forests for Classification in Ecology[END_REF]. We trained a RF model with different combinations of environmental variables (soil temperature, PAR, water table depth, and volumetric water content) for each flux data type (i.e., NEE, R eco and CH 4 ; Supplementary Table S2). To get the best performing models, we iteratively tuned RF parameters in R using the randomForest package [START_REF] Liaw | Classification and Regression by RandomForest[END_REF]: number of trees to grow ("ntree") and the number of predictor variables randomly sampled as candidate at each split ("mtry") to determine the best predictor to split the response variable at each node. We further performed a 10-fold bootstrap resampling to test the performance and overfitting of the final model. For each fold, we created a bootstrap data set by randomly collecting observations from the original dataset with replacement. In other words, we repeatedly sampled data with replacement from the original training set in order to produce separate training sets. These sets were then used to allow the RF algorithm to reduce the variance of its prediction, thus greatly improving its predictive performance. We repeated this procedure 10 times and evaluated model performance using the root mean squared error (RMSE) and R 2 values calculated from the results of the bootstrapping. RMSE measures the ability of the model to predict new data, and the result are easily interpretable as they are on the same scale as the original data. The R 2 value describes the fit of the model to the data. The final RMSE and R 2 values for the ensembled C fluxes are given in Supplementary Figure S3.

The final RF models tended to underestimate NEE, R eco , and CH 4 fluxes at high flux rates (Supplementary Figure S4). Nevertheless, all models performed well in cross-validation and gave high predictive strengths (R 2 > 0.9 for all fluxes). The final RF models were used to predict NEE, R eco , and CH 4 fluxes per hour, during the resistance and resilience phases. Hourly flux rates for GPP were calculated as the difference between NEE and R eco , for day time hours, see Supplementary Figure S10 for daily averages. Finally, all hourly flux rates were summed to obtain cumulative fluxes for the resistance and resilience phases.

Data Analyses

Calculation Resilience Response

We quantified the resilience responses to rewetting during the resilience phase for DOC concentration, S 250-465 , CO 2 and CH 4 flux rates. It is recommended to express resilience responses relatively to a baseline or a control [START_REF] Ingrisch | Towards a Comparable Quantification of Resilience[END_REF]. Since regime 2 most closely resembled the rainfall regime we observed at our field site (Figure 1), we took the regime 2 as a reference treatment to control for seasonal change. We calculated the resilience response per treatment (T) as the difference in observed values for measurements in week 11 (W11, end resistance phase) and 14 (W14, end resilience phase) proportional to the median of the change in the reference treatments (R):

resilience response (T W14 -T W11 ) (median R W14 -median R W11 )
Resulting response values that are > 1 express a larger increase (a greater capacity to "bounce back") in the treatment compared to the reference regime, and vice versa.

Statistical Analyses

All numerical analyses were performed using R 3.6.1 (R Core Team 2019).

Differences in rainfall characteristics and vascular plant abundance between precipitation regimes were checked with separate generalized least squares (gls) models with regime as a fixed factor, using the nlme package [START_REF] Pinheiro | Nlme: Linear and Nonlinear Mixed Effects Models[END_REF]. Effects of the precipitation regimes on the WTD dynamics were tested with in separate linear-mixed effects (lme) models for the resistance and resilience phase, also using the nlme package. We used the square-root transformed WTD observations as a response variable, precipitation regime and sampling date and their interaction term as fixed factors, with mesocosm identity as a random factor to account for repeated measurements. Heterogeneity of variance between regimes was controlled by applying a varIdent variance structure [START_REF] Zuur | Mixed Effects Models and Extensions in Ecology with R[END_REF]. We used the standard deviation (SD) of the WTD as an index for the WTD fluctuation and tested for differences between precipitation regimes with a gls model. Per mesocosm we calculated the mean and SD WTD during the resistance phase and used both as explanatory variables in subsequent analyses.

Prior to testing the responses, we verified whether the DOC concentration and quality (S 254-465 ) and C gas fluxes were equal upon the start of the experiment, by running a linear model on the measurements of week 0 with precipitation regime as an explanatory variable (see Supplementary Tables S3,S4, Supplementary Figure S9). Since R eco values differed between regimes (F 5,24 2.80, p 0.0398) and GPP values differed marginally (F 5,24 2.60, p 0.052), we normalized the data for DOC concentration, S 254-465 , NEE, R eco , GPP, and CH 4 . For each pot, the difference between the observation (X 0 ) and the overall mean (µ 0 ) at week 0 was subtracted from all observations (X n ).

X norm X n -X 0 -μ 0

The normalized data, excluding data from week 0, were used for subsequent analysis described below. Decomposition rates were analyzed for effects of precipitation regimes with a gls model as above. We also used separate gls models to test the relationship between decomposition rates and the mean and SD WTD. For all normalized DOC concentration and S 254-465 observations we ran lme models with precipitation regime and sampling date and their interaction term as fixed factors, with mesocosm identity as a random factor. For both DOC concentration and S 254-645 the models included a varIdent on regime to account for heteroscedasticity.

The normalized gas flux rates were likewise tested for effects of precipitation regime and sampling date with lme models. Data for the resistance and resilience phase were tested separately. First, we tested whether experiment location was a significant random factor in addition to mesocosm identity for the resistance phase observations, which was the case for R eco , and GPP (Supplementary Table S5). We used the CH 4 flux rate observations from both the transparent and darkened chamber measurements and added date as an additional random factor to correct for repeated measurements. CH 4 flux rates were ln transformed before analysis. A varIdent variance structure on sampling date was applied to all gas flux rate models on the resistance phase data and for the R eco model on the resilience phase data.

Cumulative fluxes (NEE, R eco , GPP, and CH 4 ) were analyzed for effects of precipitation regime, mean, and SD WTD in separate gls models, for both the resistance and the resilience phase. Likewise, the resilience responses for all fluxes, DOC concentration and S 254-465 were tested for effects of precipitation regime, mean and SD WTD with gls models. Models testing the resilience responses of CH 4 and S 254-465 were fitted including varIdent on precipitation regimes.

Parameters of all gls and lme models were estimated with restricted maximum likelihood (REML). Normality and 2 ) and full mixed effects models (R c 2 ) were calculated according to Johnson (2014) using the MuMIn package [START_REF] Barton | MuMIn: Multi-Model Inference[END_REF]. All graphs were made using the ggplot2 [START_REF] Wickham | Ggplot2: Elegant Graphics for Data Analysis[END_REF], RColorBrewer [START_REF] Neuwirth | RColorBrewer: ColorBrewer Palettes, R Package Version 1.1-2[END_REF] and cowplot (Wilke, 2019) packages.

RESULTS

Experimental Conditions

Throughout the resistance phase the mesocosms received approximately the same amount of rainfall (145-159 mm), except for the most extreme regime, regime 6 (125 mm). Although this was part of the design to avoid overflowing of the pots, the difference was significant (Supplementary Figure S2; F 5,30 4.24, p 0.007). As planned the regimes differed significantly in rain frequency (F 5,24 98.49, p < 0.0001), rain intensity (F 5,24 56.01, p < 0.0001) and drought intensity (F 5,24 62.36, p < 0.0001) (Figure 1). The vascular plant abundance that had developed during the resistance phase did not differ between regimes (Supplementary Table S6).

The experimental rainfall patterns during the resistance phase lead to a temporal differences in WTD (Time: F 1,1370 75.49, p < 0.0001). While the WTD differed between regimes over time (Regime*Time: F 5,1370 8.80, p < 0.0001), the overall differences between regimes were not significant (Regime: F 5,1370 0.92, p 0.48). We further inspected the WTD dynamics and found that the standard deviation (SD) of WTD per mesocosm (on average 2.2 cm), differed significantly between precipitation regimes (F 5,24 4.975, p 0.0029), indicating that the mesocosms underwent WTD fluctuations with different intensities. Therein, regimes 3 and 6 had highest SD WTD values (Figure 2C).

During the resilience phase WTD was kept more or less constant, although a temporal trend was still significant (Time: F 1,114 8.65, p 0.004) and differed between regimes (Regime*Time: F 5,114 6.37, p < 0.0001). No overall differences between precipitation regimes were found (Regime: F 5,114 1.00, p 0.44, Supplementary Figure S5A). Notably, the WTD fluctuation during the resilience phase was small compared to the resistance phase (SD on average 0.94 cm), and the SD WTD did not differ between regimes (Supplementary Figure S5B).

Carbon Dynamics

Decomposition Rate

Graminoid litter lost between 2-22% of its mass during the 11 weeks of incubation in the mesocosms. This equated to values for the decomposition rate constant k varying between 0.00026-0.00328 days -1 (Figure 3, Supplementary Figure S6). Although the decomposition rates did not significantly differ between precipitation regimes (F 5,24 1.14; p 0.366), it significantly decreased along with the mean WTD (F 1,28 7.01, p 0.0132, R adj 2 0.17), and increased with the SD WTD (F 1,28 12.05, p 0.0017, R adj 2 0.28), respectively. In other words, decomposition was faster in mesocosms with a deeper mean WTD and a high SD WTD (Figure 3).

Dissolved Organic Carbon

The concentration of DOC in the porewater of the mesocosms increased over time (F 1,53 38.34 p < 0.0001). The normalized DOC concentration initially increased, then leveled off during the resistance phase, and increased again during the resilience phase (Figure 4A), with normalized values ranging from 32.78 ± 0 mg C L -1 at the start of the experiment, to a mean of 49.94 ± 2.78 mg C L -1 at the final sampling date. There were no overall differences in DOC concentration between precipitation regimes (F 5,53 1.02, p 0.426), nor did the temporal increase vary between precipitation regimes (Time * Regime: F 5,53 1.43, p 0.228). Values for S 254-465 became more negative as time progressed (F 1,54 13.03, p 0.0007, Figure 4B), ranging from -0.012 ± 0 to -0.014 ± 0.0004 nm -1 from the start to end of the experiment. We did not find significant differences between precipitation regimes (F 5,54 1.65, p 0.186) nor was the interaction term significant (F 5,54 0.81, p 0.547 S8E) and related negatively to the SD WTD (F 1,23 10.16, p 0.0041, Supplementary Figure S8F).

CO 2 and CH 4 flux Rates

During the resistance phase, gas flux rates varied over time with (near) significant influence of precipitation regimes (Table 2). Normalized NEE rates became more negative as time progressed, except for precipitation regimes 1 and 4 as indicated by the significant interaction term. R eco values displayed a significant temporal effect and overall differences between regimes (Figure 5B, Supplementary Figure S11C). Specifically, R eco gradually increased over time, with higher respiration rates as precipitation regimes got more intense and displayed a significant increase of 55.5% between regimes 1 (mean R eco 198.94 mg CO 2 m -2 h -1 ) and 5 (mean R eco 309.45 mg CO 2 m -2 h -1 ). Because R eco peaked mid-march (week 4, Figure 5B), we ran the same analysis without the week 4 measurements. After removing the peak, the results were similar with an overall effect of time (F 1,201 25.33, p < 0.0001) and differences between precipitation regimes (F 5,201 2.42, p 0.0475) but no interaction between regime and time (F 5,201 0.87, p 0.504). GPP rates decreased with time with marginal significant differences between precipitation regimes, but the interaction term (Time * Regimes) was not significant. CO 2 uptake rates tended to be stronger the more extreme the precipitation regime became, with largest differences between regime 1 and 5 (Supplementary Figure S11E). CH 4 flux rates showed a significant interaction between time and precipitation regimes, along with a significant overall effect of time. CH 4 fluxes increased gradually during the resistance phase in most precipitation regimes except in regime 6, where the flux rates decreased by 49.7% from 144.40 to 72.61 µg CH 4 m -2 h -1 (Table 2; Figure 5D).

Gas flux rates measured during the resilience phase all increased over time (Table 2; Figure 5). Yet, none of the fluxes showed significant differences between regimes, neither as main effect nor in interaction with time. The resilience response of the CO 2 fluxes did not differ between precipitation regimes. The resilience response of CH 4 , however, tended to differ between regimes (F 4,43 2.24, p 0.080) with a smaller increase in CH 4 flux rates for regime 5 compared to regime 2 (e.g. resilience < 1, Supplementary Figure S12D). Moreover, the resilience responses for NEE, R eco , and CH 4 did TABLE 2 | Outcome of linear mixed effects models testing the influence of precipitation regime (Regime, R) and sampling date (Time, T) on rates of net ecosystem exchange (NEE), ecosystem respiration (R eco ), gross primary productivity GPP), and methane (CH 4 ), during the resistance phase (I, week 1-10), and resilience phase (II, week 10-14).

Flux

Factor not relate to the earlier WTD dynamics during the resistance phase, whereas the resilience response of GPP tended to relate negatively to the mean WTD of the mesocosms during the resistance phase (F 1,23 3.25, p 0.085, Supplementary Figure S12).

I II df F P R m 2 (R c 2 ) d f F P R m 2 (

Cumulative CO 2 and CH 4 fluxes

The total uptake and release of CO 2 and CH 4 during the resistance phase related to the experimental WTD dynamics but did not differ significantly between precipitation regimes (Figure 6; Table 3). Most mesocosms released more CO 2 than they took up, as shown by the positive NEE values (Figure 6A). Particularly, mesocosm which underwent little change in WTD (measured as SD WTD) emitted most CO 2 . The underlying fluxes, namely R eco and GPP, related to mean WTD (Table 3). Mesocosms with a deep mean WTD respired more CO 2 than mesocosms with a shallow mean WTD, yet CO 2 uptake was also 6C,E). Likewise, CH 4 emissions were positively related to mean WTD, with highest emissions at shallow mean WTD (Figure 6G).

For the resilience phase, comparable relationships between CO 2 exchange and WTD dynamics were found. In other words, the WTD dynamics of mesocosms under the experimental precipitation regimes were predictive of the CO 2 dynamics when WTD dynamics were restored to pre-experimental conditions. Thus, mesocosms which underwent little variation in WTD (SD WTD) had a more positive overall CO 2 balance during resilience phase compared to mesocosms for which a high SD WTD was measured in the resistance phase. However, the relationship between mean WTD and CH 4 emission was not significant for the resilience phase; all mesocosm emitted 100-150 mg CH 4 during this three-week period. A,C,E,G) and resilience (II, panels B, D, F, H) phases, and the WTD dynamics of the resistance phase. Panels (A), (B): net ecosystem exchange (NEE) is explained by the standard deviation water table depth (SD WTD). In (C), (D) ecosystem respiration (R eco ) is plotted against WTD mean, as are gross primary production (GPP, in E and F) and methane (CH 4 , in G and H). Drawn relationships are significant at p < 0.05, based on linear regressions given in Table 3. For details on precipitation regimes, please see

DISCUSSION

Precipitation regimes are becoming more extreme, as is currently observed [START_REF] Knapp | Consequences of More Extreme Precipitation Regimes for Terrestrial Ecosystems[END_REF][START_REF] Lehmann | Increased Record-Breaking Precipitation Events under Global Warming[END_REF] and predicted by climate models [START_REF] Dai | Increasing Drought under Global Warming in Observations and Models[END_REF][START_REF] Fischer | Observed Heavy Precipitation Increase Confirms Theory and Early Models[END_REF]. While the consequences of deeper water levels on peatland C dynamics are relatively well known [START_REF] Dise | Peatland Response to Global Change[END_REF][START_REF] Page | Peatlands and Global Change: Response and Resilience[END_REF], the relationship between peatland water table dynamics and carbon cycling under shifting rainfall patterns is not. We aimed to explore how changes in water table depth (WTD) dynamics (overall mean and fluctuations) in response to more extreme precipitation regimes affects peatland C dynamics. By exposing intact peat cores to approximately the same amount of rain but according to increasingly extreme patterns, we found that C uptake (GPP), decomposition rate of graminoid litter and C loss (DOC, R eco , and CH 4 ) all relate to the altered WTD dynamics induced by the altered rainfall patterns. Most importantly, we showed that extreme rainfall early in the growing season had lasting effects on CO 2 exchange in our mesocosms, while the effects on CH 4 emission diminished quickly after restoration of the WTD dynamics. The limited depth of the mesocosms meant that hydrological conditions during the experiment could have been more extreme than under field conditions and the results represent amplified responses. Under natural conditions hydraulic lift and biological activity from deeper layers would contribute to the overall response. Nevertheless, WTD changes in the top 10 cm are considered relevant for peatland C dynamics [START_REF] Evans | Overriding Water Table Control on Managed Peatland Greenhouse Gas Emissions[END_REF]. Our findings highlight the importance of WTD fluctuations under shifting rainfall patterns in addition to mean WTD in driving peatland C dynamics, and that short-term changes in conditions may have lasting effects.

Carbon Uptake Under Extreme Precipitation

Besides a general increase in C uptake as the growing season progressed (Figure 5), we found a near significant difference between precipitation regimes with higher uptake rates under the more extreme precipitation regime 5 than 1. In addition, cumulative C uptake (GPP) was found to be increased with deeper mean WTD (Figure 6), and tended to be higher with larger WTD fluctuations. Our findings contrast with those of [START_REF] Nijp | Can Frequent Precipitation Moderate the Impact of Drought on Peatmoss Carbon Uptake in Northern Peatlands?[END_REF] who showed that photosynthesis efficiency and CO 2 uptake in Sphagnum is most efficient at high moisture content and can decline steeply as the volumetric moisture content decreases [START_REF] Nijp | Can Frequent Precipitation Moderate the Impact of Drought on Peatmoss Carbon Uptake in Northern Peatlands?[END_REF]. While high volumetric moisture content benefits Sphagnum photosynthesis, vascular plants benefit from increased aeration of the peat profile [START_REF] Breeuwer | Decreased Summer Water Table Depth Affects Peatland Vegetation[END_REF][START_REF] Jassey | Tipping point in Plant-Fungal Interactions under Severe Drought Causes Abrupt Rise in Peatland Ecosystem Respiration[END_REF]. A decrease of rainfall frequency in a field experiment resulted in reduced C uptake by Sphagnum dominated peat, while C uptake in vascular plant dominated peat increased [START_REF] Radu | Precipitation Frequency Alters Peatland Ecosystem Structure and CO2 Exchange: Contrasting Effects on Moss, Sedge, and Shrub Communities[END_REF]. Therefore, the observed negative relationship between GPP and mean WTD is most likely caused by increased performance of vascular plants. This could be experimentally verified by monitoring the plant photosynthetic activity and biomass more closely in future studies.

Upon rewetting, C uptake rates slowed down as GPP became less negative during the resilience phase. This resilience response was similar for all precipitation regimes. As a consequence, the cumulative C uptake during the resilience phase could still be predicted by the mean WTD of the peat cores during the resistance phase. These observations fit with our supposition that vascular plants grew better under extreme precipitation. Indeed, altered vascular plant growth during spring affected carbon uptake later in the growing season under field conditions [START_REF] Lund | Effects of Drought Conditions on the Carbon Dioxide Dynamics in a Temperate Peatland[END_REF][START_REF] Helfter | Drivers of Long-Term Variability in CO2 Net Ecosystem Exchange in a Temperate Peatland[END_REF].

Moreover, the reduction in C uptake rates upon rewetting could have been dampened by the capacity of Sphagnum to recover quickly from drying. [START_REF] Jassey | Effects of Climate Warming on Sphagnum Photosynthesis in Peatlands Depend on Peat Moisture and Species-specific Anatomical Traits[END_REF] found that Sphagnum photosynthetic activity can recover from droughts within an hour after rewetting. Although this shows that peatland functioning can bounce back from extreme meteorological conditions, repeated restarting of the photosynthetic pathway after droughts when rainfall frequency is low could come at the cost of increased autotrophic respiration [START_REF] Mcneil | Moisture Controls on Sphagnum Growth and CO2 Exchange on a Cutover Bog[END_REF][START_REF] Nijp | Can Frequent Precipitation Moderate the Impact of Drought on Peatmoss Carbon Uptake in Northern Peatlands?[END_REF][START_REF] Nijp | Rain Events Decrease Boreal Peatland Net CO2uptake through Reduced Light Availability[END_REF]. We further note that under natural circumstances rain coincides with cloud cover and temporally limit photosynthesis. This could act as a secondary mechanism by which reduced rainfall frequency translates to reduced cloud cover and increased evapotranspiration thereby influencing peatland carbon dynamics [START_REF] Nijp | Rain Events Decrease Boreal Peatland Net CO2uptake through Reduced Light Availability[END_REF][START_REF] Dai | Climate Change and Drought: A Precipitation and Evaporation Perspective[END_REF].

Carbon Loss Under Extreme Precipitation

Litter Decomposition

We found that graminoid litter mass loss varied between 2-22% during the resistance phase, and most importantly, that both the mean and fluctuation of the WTD explained this variation (Figure 3). These results suggest that intense rain interspersed with long dry intervals promote decomposition in peatlands. We inserted our litterbags just below the overall WTD (-4.49 cm). This finding agrees with previous studies which showed that decomposition in peatlands is optimal in [START_REF] Belyea | Separating the Effects of Litter Quality and Microenvironment on Decomposition Rates in a Patterned Peatland[END_REF][START_REF] Belyea | Feedback Control of the Rate of Peat Formation[END_REF]. The graminoid litter we utilized represents recently senesced plant material entering the pool of organic matter. In general, the young organic C deposited in the acrotelm (surface layer of peat) has a higher potential to be lost by decomposition than older organic C in the deeper catotelm [START_REF] Belyea | Separating the Effects of Litter Quality and Microenvironment on Decomposition Rates in a Patterned Peatland[END_REF][START_REF] Ise | High Sensitivity of Peat Decomposition to Climate Change through Water-Table Feedback[END_REF]. Taken together, WTD fluctuations at the level of the acrotelm are likely to have more profound consequences than further draw down of the water table into the catotelm [START_REF] Ise | High Sensitivity of Peat Decomposition to Climate Change through Water-Table Feedback[END_REF]. Our results signify the sensitivity of C stored in the acrotelm to potential loss as a consequence of shift in rainfall patterns [START_REF] Knapp | Consequences of More Extreme Precipitation Regimes for Terrestrial Ecosystems[END_REF][START_REF] Leifeld | The Underappreciated Potential of Peatlands in Global Climate Change Mitigation Strategies[END_REF].

Altered WTD dynamics could also have influenced decomposition indirectly. Increasing decomposition rates was concomitant with increasing photosynthetic C uptake (GPP). As photosynthesis and root exudation are strongly linked [START_REF] Kuzyakov | Photosynthesis Controls of Rhizosphere Respiration and Organic Matter Decomposition[END_REF], plant exudates may have influenced decomposition of organic matter by catalyzing degradation of organic molecules, triggering nutrient competition or even preferential substrate utilization by decomposers [START_REF] Kuzyakov | Priming Effects: Interactions between Living and Dead Organic Matter[END_REF][START_REF] Dijkstra | Rhizosphere Priming: A Nutrient Perspective[END_REF][START_REF] Saar | Legume Presence Reduces the Decomposition Rate of Non-legume Roots[END_REF][START_REF] Barel | Plant Presence Reduces Root and Shoot Litter Decomposition Rates of Crops and Wild Relatives[END_REF]. Indeed, vascular plants have been shown to promote C loss through increase heterotrophic respiration and enhance decomposition of peat carbon due to rhizosphere priming [START_REF] Gavazov | Vascular Plant-Mediated Controls on Atmospheric Carbon Assimilation and Peat Carbon Decomposition under Climate Change[END_REF]. Further studies are however necessary to establish whether these indirect drivers play a role in decomposition on relatively short time-frames of 3 months in peatlands.

Dissolved Organic Carbon

C lost from peatlands as DOC can reach 1-50 g m -2 y -1 and represent up to 64% of organic C in streams [START_REF] Blodau | Carbon Cycling in Peatlands -A Review of Processes and Controls[END_REF][START_REF] Rosset | Peatland Contribution to Stream Organic Carbon Exports from a Montane Watershed[END_REF]. DOC concentrations observed in our mesocosms (19.47-88.23 mg C L -1 ) approximated earlier observations at the same field site in June 2018 (22.91-65.20 mg C L -1 ) and fall within in the range (20-60 mg C L -1 ) of concentrations reported for northern peatlands [START_REF] Blodau | Carbon Cycling in Peatlands -A Review of Processes and Controls[END_REF]. We observed a seasonal increase in DOC concentration. DOC concentrations are often found to increase with temperature as a consequence of increased microbial and vegetation activity [START_REF] Blodau | Carbon Cycling in Peatlands -A Review of Processes and Controls[END_REF][START_REF] Pastor | Global Warming and the Export of Dissolved Organic Carbon from Boreal Peatlands[END_REF][START_REF] Rosset | Peatland Contribution to Stream Organic Carbon Exports from a Montane Watershed[END_REF]. Moreover, C loss by stream export varies seasonally which has been attributed to seasonal variation in hydrological and biological processes in addition to streamflow and run-off after heavy rain [START_REF] Leach | Twelve Year Interannual and Seasonal Variability of Stream Carbon Export from a Boreal Peatland Catchment[END_REF]. However, we found no indication that shifts in precipitation patterns affected the DOC concentration. Yet, the limited size of our mesocosms could have excluded mechanisms from occurring that play a role in natural DOC flows, such as the release of DOC from deeper peat layers.

Additionally, we observed a seasonal decrease in S 254-645, indicating a decrease in low molecular weight compounds and/or increase in aromaticity [START_REF] Hansen | Optical Properties of Dissolved Organic Matter (DOM): Effects of Biological and Photolytic Degradation[END_REF]. Which is in line with long-term field observations that demonstrated an increase in DOC aromaticity during spring [START_REF] Leach | Twelve Year Interannual and Seasonal Variability of Stream Carbon Export from a Boreal Peatland Catchment[END_REF]. The resilience response of S 254-645 values continued to decrease in the reference precipitation regime (regime 2), whereas mesocosms exposed to more extreme rainfall patterns did not display a decrease in S 254-465 values or to a lesser extent. As high molecular weight and aromatic compounds are presumably hard to break-down by microbial decomposers [START_REF] Kalbitz | Biodegradation of Soil-Derived Dissolved Organic Matter as Related to its Properties[END_REF][START_REF] Cotrufo | The Microbial Efficiency-Matrix Stabilization (MEMS) Framework Integrates Plant Litter Decomposition with Soil Organic Matter Stabilization: Do Labile Plant Inputs Form Stable Soil Organic Matter?[END_REF], these results could reflect the preferential break-down of low molecular weight/non-aromatic compounds under a normal compared to extreme precipitation regimes, regardless of differences in DOC concentration.

Ecosystem Respiration and Net Ecosystem Exchange

Besides a seasonal increase, CO 2 respiration rates differed significantly between precipitation regimes, with lowest R eco values for the least extreme regime (regime 1) and highest respiration under extreme precipitation (regime 5). Based on this observation we would have expected a relationship between cumulative R eco and WTD fluctuation, but there was not. Field observations demonstrated that R eco flux rates are less responsive to WTD dynamics than GPP and NEE rates, because R eco is the combined result of autotrophic and heterotrophic respiration [START_REF] Olefeldt | A Decade of Boreal Rich Fen Greenhouse Gas Fluxes in Response to Natural and Experimental Water Table Variability[END_REF]. However, we did find a significant relationship of increased cumulative R eco at deeper mean WTD during the resistance phase. This relationship follows the earlier relationships of increased heterotrophic (decomposition) and autotrophic (GPP) activity with deeper WTD.

Responses of overall CO 2 exchange (NEE) to the precipitation treatments reflected the observations in GPP and R eco . The seasonal increase in the CO 2 sink function (negative NEE rates) was stronger under extreme precipitation than the least extreme regimes. This significant interaction between time and precipitation regime echoes the differences between precipitation treatments observed in R eco and GPP flux rates. When inspecting the cumulative NEE responses, mesocosms with increasing WTD fluctuations became a weaker source of CO 2, even becoming a sink when WTD had a standard deviation of more than 3 cm, which represents the tendency for cumulative GPP to be controlled by SD WTD in a similar manner. Increased CO 2 uptake, as we found under extreme precipitation, could signal a long-term change in peatland ecology. Notably, repeated exposure of peatlands to extreme rainfall and drought is likely to trigger vascular plant encroachment [START_REF] Buttler | Experimental Warming Interacts with Soil Moisture to Discriminate Plant Responses in an Ombrotrophic Peatland[END_REF][START_REF] Dieleman | Climate Change Drives a Shift in Peatland Ecosystem Plant Community: Implications for Ecosystem Function and Stability[END_REF][START_REF] Jassey | Tipping point in Plant-Fungal Interactions under Severe Drought Causes Abrupt Rise in Peatland Ecosystem Respiration[END_REF][START_REF] Lamentowicz | Unveiling Tipping Points in Long-Term Ecological Records from Sphagnum -Dominated Peatlands[END_REF] with cascading effects on overall ecosystem functioning [START_REF] Bardgett | Hierarchical Responses of Plant-Soil Interactions to Climate Change: Consequences for the Global Carbon Cycle[END_REF][START_REF] Dieleman | Climate Change Drives a Shift in Peatland Ecosystem Plant Community: Implications for Ecosystem Function and Stability[END_REF][START_REF] Jassey | Tipping point in Plant-Fungal Interactions under Severe Drought Causes Abrupt Rise in Peatland Ecosystem Respiration[END_REF]. The fact that we found no significant relationship between cumulative NEE and mean WTD stresses the importance to include a measure of WTD fluctuation as a potential controlling factor in peatland studies researching hydrological effects on peatland carbon dynamics, in addition to the average WTD.

During the resilience phase, CO 2 uptake rates lessened while respiration rates rose slightly and resulted in a rise in NEE rates. Moreover, the relationship between NEE and the WTD fluctuation observed during the resistance phase was still measurable during the resilience phase, as were the relationships between cumulative R eco and GPP values and the mean WTD. These lagged effects indicate that exposure to extreme precipitation early in the growing season may have prolonged effects on ecosystem functioning, even if meteorological conditions return to normal [START_REF] Frank | Effects of Climate Extremes on the Terrestrial Carbon Cycle: Concepts, Processes and Potential Future Impacts[END_REF].

Methane Emissions

The evolution of CH 4 flux over time differed between precipitation regimes (Table 2). In particular, CH 4 emissions were low in mesocosms exposed to the most extreme precipitation regime (regime 6). The limited CH 4 emission of these mesocosms in the second half of the resistance phase (April) coincided with an extended period without rainfall resulting in deeper WTD (Figures 2,5). This link between WTD dynamics and CH 4 emission is further evidenced by the positive relationship between cumulative CH 4 flux and the mean WTD during the resistance phase (Figure 6).

However, these results should be interpreted with some caution. Our overall measured average CH 4 flux rate of 162.2 μg m -2 hr -1 during the resistance phase, and 482.1 μg m -2 hr -1 during the resilience phase fall in the low end of the reported range (5-80 mg m -2 d -1 ) of rates in peatlands under field conditions [START_REF] Blodau | Carbon Cycling in Peatlands -A Review of Processes and Controls[END_REF], probably because of the limited depth of our mesocosms. Under field conditions, CH 4 production in deeper peat layers would contribute to overall emissions, while hydraulic lift could maintain moisture content in the peat surface layer under dry conditions. Interestingly, our findings contrast those from Radu and Duval (2018a). They found that more extreme regimes increased CH 4 emission overall and stipulated that rainfall oscillations stimulated the build-up of labile substrate as result of aerobe respiration, which upon repeated rewetting boost CH 4 production. Our S 254-465 values for DOC indicate no such buildup, while the near-significant relationship of lower cumulative CH 4 emission with increased WTD fluctuation imply a reduction of CH 4 emission at more extreme precipitation. Instead, our findings are similar to patterns observed in other studies. WTD is a wellrecognized driver of CH 4 emissions (Bubier et al., 1994;[START_REF] Updegraff | Response of CO 2 and CH 4 Emissions from Peatlands to Warming and Water Table Manipulation[END_REF][START_REF] Blodau | Carbon Turnover in Peatland Mesocosms Exposed to Different Water Table Levels[END_REF][START_REF] Turetsky | A Synthesis of Methane Emissions from 71 Northern, Temperate, and Subtropical Wetlands[END_REF][START_REF] Riutta | Interacting Effects of Vegetation Components and Water Level on Methane Dynamics in a Boreal Fen[END_REF]. Shallow WTD promote CH 4 emissions because methanogenesis requires anaerobic conditions, while deep WTD increases the portion of aerated surface peat accommodating consumption of CH 4 by methanotrophs as it diffuses toward the atmosphere (Bubier et al., 1994;[START_REF] Sundh | Potential Aerobic Methane Oxidation in a Sphagnum-Dominated Peatland-Controlling Factors and Relation to Methane Emission[END_REF].

Drying and rewetting of peat may lead to pulses of substrate and nutrients stimulating CH 4 emissions [START_REF] Turetsky | A Synthesis of Methane Emissions from 71 Northern, Temperate, and Subtropical Wetlands[END_REF]. Recently, [START_REF] Huth | The Climate Warming Effect of a Fen Peat Meadow with Fluctuating Water Table Is Reduced by Young Alder[END_REF] observed a strong CH 4 increase after heavy precipitation in a German fen. We observed that rewetting during the resilience phase led to a steep increase in CH 4 flux rates compared to the resistance phase which tended to be restricted in the more extreme precipitation treatments. Although these results indicate that more extreme rainfall reduces the CH 4 emissions from peatlands, the contrasting results from Radu and Duval (2018a) and the variable rewetting responses between peatland types [START_REF] Turetsky | A Synthesis of Methane Emissions from 71 Northern, Temperate, and Subtropical Wetlands[END_REF] make further investigation of gas flux responses to shifting rainfall across peatland types under field conditions advisable.

Synthesis

In summary, our results imply that shifts in precipitation patterns early in the growing season are likely to influence peatland C dynamics. In our mesocosm study, increased water table fluctuations induced by shifting rainfall patterns reduced overall C emission from peatlands, whereby a deeper overall water table improved CO 2 uptake more than it increased ecosystem respiration, and reduced CH 4 emissions. Despite the limitations of our mesocosm study, our findings are in line with observations under field conditions [START_REF] Radu | Precipitation Frequency Alters Peatland Ecosystem Structure and CO2 Exchange: Contrasting Effects on Moss, Sedge, and Shrub Communities[END_REF]. Although it may seem promising that precipitation shifts increase carbon uptake, this conclusion should be treated with caution as this may signal an increased dominance of vascular plants that could off-set peatland carbon dynamics on the long-term. Our findings further showed that extreme precipitation early in the growing season can invoke changes in CO 2 fluxes that last beyond the period of altered precipitation. Therefore, in order to fully understand the consequences of shifting precipitation patterns for the capacity of peatlands to sequester carbon, the fluctuations in the water table have to be considered as a driving factor and both the immediate and lagged effects on peatland carbon dynamics should be taken into account.

FIGURE 1 |

 1 FIGURE 1 | Characteristics of rainfall patterns to which the mesocosms (circles) were exposed during the resistance phase, along with those observed at the reference site Counozouls (triangles) during spring and summer 2019. Experimental rainfall treatments fell into one of six precipitation regimes of reducing rainfall frequency but increasing intensity. Size of the bubbles is scaled to drought intensity, given as the average number of days between rainfall events.

FIGURE 2 |

 2 FIGURE 2 | Water table depth (WTD) dynamics during the experiment. WTD over time (A) during the resilience phase (I) and resistance phase (II). For the resilience phase boxplots are given for mean WTD (B) and standard deviation of the WTD (C) per precipitation regime. Values in A are means ± SE, n 1,560. In B: n 1,410, in C: n 30. Letters in C indicate significant differences (p < 0.05) based on Tukey post-hoc test. For details on precipitation regimes, please see Figure 1.

FIGURE 3 |

 3 FIGURE 3 | Decomposition rate constant k of graminoid litter plotted against the mean WTD (A) and standard deviation (SD) of the WTD (B) per mesocosm, during one of six precipitation regimes. Shown regression lines are significant at p < 0.05. In A: R 2 adj 0.17, in B: R 2 adj 0.28. For details on precipitation regimes, please see Figure 1.

FIGURE 4 |

 4 FIGURE 4 | Normalized dissolved organic carbon (DOC) concentration (A) and S 254-465 (B) measured at the start and middle of the resistance phase (I), the transition to and the end of the resilience phase (II). Values are means ± SE. A: n 118, B: n 114. For details on precipitation regimes, please see Figure 1. NOTE: data depicted have been normalized, see Supplementary Figure S7 for uncorrected data.

FIGURE 5 |

 5 FIGURE 5 | Normalized carbon flux dynamics during the resistance phase (I) and resilience phase (II): (A) net ecosystem exchange (NEE) of CO 2 , (B) ecosystem respiration (R eco ), (C) gross primary production (GPP), and (D) methane (CH 4 ), grouped by precipitation regimes as indicated by symbols and colours. Values are means ± SE. In panels (A-C), n 420; in (D) n 780. For details on precipitation regimes, please see Figure 1. NOTE: data depicted have been normalized, see Supplementary Figure S9 for uncorrected data.

FIGURE 6 |

 6 FIGURE 6 | Relationships between cumulative gas fluxes during the resistance (I, panels A, C, E, G) and resilience (II, panels B, D, F, H) phases, and the WTD dynamics of the resistance phase. Panels (A), (B): net ecosystem exchange (NEE) is explained by the standard deviation water table depth (SD WTD). In (C), (D) ecosystem respiration (R eco ) is plotted against WTD mean, as are gross primary production (GPP, in E and F) and methane (CH 4 , in G and H). Drawn relationships are significant at p < 0.05, based on linear regressions given in Table3. For details on precipitation regimes, please see Figure1.

Figure 1 .

 1 FIGURE 6 | Relationships between cumulative gas fluxes during the resistance (I, panels A, C, E, G) and resilience (II, panels B, D, F, H) phases, and the WTD dynamics of the resistance phase. Panels (A), (B): net ecosystem exchange (NEE) is explained by the standard deviation water table depth (SD WTD). In (C), (D) ecosystem respiration (R eco ) is plotted against WTD mean, as are gross primary production (GPP, in E and F) and methane (CH 4 , in G and H). Drawn relationships are significant at p < 0.05, based on linear regressions given in Table3. For details on precipitation regimes, please see Figure1.

TABLE 1 |

 1 Time line of the mesocosm experiment.

	Week	Phase	Task	WTD	Fluxes	DOC	k
	-12	Prep.	Field sampling
	-1		Mesocosms construction
	0			x	x	x	I N
	1			x	x		|
	2			x	x		|
	3			x	x		|
	4			x	x		|
	5	I		x	x	x	|
	6			x	x		|
	7		V P	x	x		|
	8			x	x		|
	9			x	x		|
	10			x	x		|
	11			x		x	OUT
	12			x	x
	13	II		x
	14			x	x	x
	Peat mesocosms were exposed to increasingly extreme precipitation regimes (see
	Figure 1) during the 11-week resistance phase (I) and allowed to recover during the
	3-week resilience phase (II) in which water table was maintained at-4 cm below the
	Sphagnum capitulum. Water table depth (WTD) was measured every 2 days during
	phase I and twice a week during phase II, CO 2 and CH 4 fluxes were measured on a
	weekly basis, and vascular plant abundance (VP), DOC, and decomposition rate
	constant (k) were. measured as indicated.

TABLE 3 |

 3 Outcome of separate linear regression models testing the influence of precipitation regime (Regime), WTD mean or SD (measured during phase I) on cumulative net ecosystem exchange (NEE), ecosystem respiration (R eco ), gross primary productivity (GPP), and methane (CH 4 ) during the resistance phase (I, week 0-10), and resilience phase (II, week 10-14).

	Flux	Model		I			II
			df	F	P	df	F	P
	NEE	Regime	5, 24	0.80	0.56	5, 24	0.44	0.81
		Mean WTD	1, 28	0.59	0.45	1, 28	0.01	0.92
		SD WTD	1, 28	4.40	0.045	1, 28	5.46	0.027
	R eco	Regime	5, 24	0.57	0.72	5, 24	0.70	0.63
		Mean WTD	1, 28	5.48	0.027	1, 28	5.31	0.029
		SD WTD	1, 28	0	0.993	1, 28	1.12	0.30
	GPP	Regime	5, 24	0.73	0.61	5, 24	0.80	0.56
		Mean WTD	1, 28	32.22	< 0.0001	1, 28	15.4	0.0005
		SD WTD	1, 28	4.01	0.055	1, 28	0.004	0.95
	CH 4	Regime	5, 24	1.933	0.13	5, 24	1.143	0.37
		Mean WTD	1, 28	9.77	0.0041	1, 28	1.43	0.24
		SD WTD	1, 28	3.97	0.056	1, 28	0.11	0.74
	See Figure 6 for supporting visualization. Bold and italic text indicate significant (p < 0.05)
	and marginally significant (p < 0.1) p values, respectively.

Frontiers in Environmental Science | www.frontiersin.org June 2021 | Volume 9 | Article 659953

ACKNOWLEDGMENTS

We thank the Plateforme Analyses Physico-Chimiques from the Laboratoire Ecologie Fonctionnelle et Environnement (Toulouse) for their analyses of dissolved organic carbon. We further thank Laure Gandois for insightful discussions, and the reviewers for their constructive feedback.

FUNDING

This work was funded by the French National Research Agency (MIXOPEAT project, grant no. ANR-17-CE01-0007 to VJ) and Fondation pour la Recherche sur la Biodiversité which acted in cooperation with the French Agency for Biodiversity (AFB), and its partners (FRB-www. fondationbiodiversite.fr).

DATA AVAILABILITY STATEMENT

The data supporting the conclusions of this article are available at 10.6084/m9.figshare.c.5468205.

AUTHOR CONTRIBUTIONS

JB and VJ conceived the experiment. SH collected the intact peat cores in the field. VM and VJ executed the experiment with support of JB, AS, and SH. JB, VM, and VJ analyzed the data. JB wrote the manuscript together with VJ to which all other authors contributed.

SUPPLEMENTARY MATERIAL

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fenvs.2021.659953/ full#supplementary-material Conflict of Interest: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


Mark Ainslie
email: mark.ainslie@eng.cam.ac.uk

Fernando Perez

Enric Pardo
email: enric.pardo@savba.skasef.ghabeli@savba.sk

Asef Ghabeli

Roberto Brambilla
email: rlbrambilla@gmail.com

Ratu Mataira
email: ratu.matairacole@vuw.ac.nz

Chris Bumby
email: chris.bumby@vuw.ac.nz

Loïc Quéval
email: loic.queval@gmail.com

Francesco Grilli
email: francesco.grilli@kit.edu

Antonio Morandi
email: antonio.morandi@unibo.it

A New Benchmark Numerical Model: The High-T c Superconducting Dynamo

Keywords: HTS dynamo, flux pump, coated conductor, numerical modelling, HTS modelling, benchmarking

The high-Tc superconducting (HTS) dynamo is a promising device that can inject large DC supercurrents into a closed superconducting circuit. It could be used, for example, to energise rotor windings in superconducting rotating machines without the need for connection to a power supply via current leads. A number of different numerical models have now been developed as useful and cost-efficient tools to further examine and explain experimental results, as well as optimise and improve flux pump design. To adequately compare the different modelling tools available, we propose a new benchmark numerical model for the HTS modelling community: the HTS dynamo. In this work, this benchmark problem is implemented using several different methods: (1) coupled H-A formulation, (2) H-formulation + shell current, (3) segregated H-formulation, (4) Minimum Electromagnetic Entropy Production (MEMEP), (5) coupled T-A formulation, (6) integral equation and (7) volume integral equation-based equivalent circuit. These different techniques are used to solve the benchmark problem and compared in terms of computational requirements, ease of use and the solutions obtained with reference to each other, as well as experimental measurements.

I. INTRODUCTION

The high-Tc superconducting (HTS) dynamo is a promising device to inject large DC supercurrents into a closed superconducting circuit. It could be used, for example, to energise rotor windings in superconducting rotating machines without the need for connection to a power supply via current leads [START_REF] Bumby | Development of a brushless HTS exciter for a 10 kW HTS synchronous generator[END_REF]. Despite the extensive experimental work carried out to date, comprehensively understanding the underlying physical mechanism of such dynamo-type flux pumps has proved challenging. A number of different explanations have been proposed to explain this mechanism, but quantitatively-accurate, predictive calculations have been difficult. It was shown recently in Mataira et al. [START_REF] Mataira | Origin of the DC output voltage from a high-Tc superconducting dynamo[END_REF] that the open-circuit voltage can be explained wellmost importantly, with good quantitative agreementusing classical electromagnetic theory. The gap dependence of the open-circuit voltage computed by Ghabeli and Pardo [START_REF] Vysotsky | The possibility of using high-Tc superconducting films as elements of a rectifier[END_REF] also agrees with experiments. In [START_REF] Vysotsky | The possibility of using high-Tc superconducting films as elements of a rectifier[END_REF], it is also shown that this voltage is independent of the critical current density, Jc, when the superconductor is fully saturated. The timeaveraged DC output voltage obtained from an HTS dynamo arises naturally from a local rectification effect caused by overcritical eddy currents flowing within the HTS stator tape: a classical effect that has been observed in HTS materials as far back as Vysotsky et al. [START_REF] Ghabeli | Modeling of Airgap Influence on DC Voltage Generation in a Dynamo-Type Flux Pump[END_REF]. A number of different numerical models have now been developed as useful and cost-efficient tools to further examine and explain the experimental results, as well as optimise and improve flux pump design. To adequately compare the different modelling tools available, we propose a new benchmark numerical model for the HTS modelling community [START_REF]HTS Modelling Workgroup: Benchmarks[END_REF]: the HTS dynamo. In the following section, the geometry of this benchmark problem is described, as well as the relevant assumptions made to simplify the problem, including implementing the model in 2D and assuming a constant Jc for the superconducting wire.

In this work, this benchmark problem is implemented using several different methods: [START_REF] Zhang | An efficient 3D finite element method model based on the T-A formulation for superconducting coated conductors[END_REF][START_REF] Benkel | T-A Formulation to Model Electrical Machines with HTS Coated Conductor Coils[END_REF]; • Integral equation [START_REF] Brambilla | Integral equations for the current density in thin conductors and their solution by the finite-element method[END_REF]; and • Volume integral equation-based equivalent circuit [START_REF] Morandi | A unified approach to the power law and critical state modeling of superconductors in 2D[END_REF].

• Coupled H-A formulation [6]; • H-formulation + shell current [2]; • Segregated H-formulation [7]; • Coupled T-A formulation [8, 9]; • Minimum Electromagnetic Entropy Production (MEMEP)
These models are compared in terms of computational requirements, ease of use and the solutions obtained with reference to each other, as well as experimental measurements.

II. BENCHMARK PROBLEM

The geometry of the HTS dynamo benchmark problem is shown in Figure 1, assuming for simplicity the 2D (infinitely long) case. A permanent magnet (PM), of width a and height b, rotates anticlockwise past the stationary HTS stator wire at the top, and the face of the PM is located at a radius, Rrotor. The initial position of the PM is such that the centre of its face is at (0, -Rrotor). The HTS wire has a width e and thickness f and is positioned such that its inner face is located at (0, Rrotor + airgap). Table I lists the assumed parameters for the model, which are based on the model presented in [START_REF] Mataira | Origin of the DC output voltage from a high-Tc superconducting dynamo[END_REF] and correspond to the experimental setup in [START_REF] Badcock | Impact of Magnet Geometry on Output of a Dynamo-Type HTS Flux Pump[END_REF]. For simplicity, Jc is assumed to be constant, since it was shown in [START_REF] Mataira | Origin of the DC output voltage from a high-Tc superconducting dynamo[END_REF] that this assumption does not impact the essential dynamics to deliver a DC voltage, i.e., a non-linear resistivity. The open-circuit and cumulative time-average voltage waveforms shown in Fig. 2 for the constant Jc case should be obtained by implementing the benchmark model.

Fig. 1 .

 1 Fig. 1. Geometry of the HTS dynamo benchmark problem. A permanent magnet rotates anticlockwise past an HTS wire.

Fig. 2 .

 2 Fig. 2. (a) Open-circuit voltage waveforms for the HTS dynamo presented in [2] for the H-formulation + shell current model using measured in-field Jc(B, θ) data for the HTS wire or a constant Jc assumption, which are compared with experimental results. (b) Cumulative time-average for each waveform, which converge to VDC in each case at t → ∞.

TABLE I

 I

	.	HTS DYNAMO BENCHMARK ASSUMED PARAMETERS
			Width, a	6 mm
	Permanent magnet	Height, b	12 mm
	(PM)		Active length/depth, L	12.7 mm
			Remanent flux density, Br	1.25 T
			Width, e	12 mm
			Thickness, f	1 μm
	HTS stator wire	Critical current, Ic [self-field, 77 K]	283 A
			n value	20
		Rotor radius, Rrotor	35 mm
	Distance between PM face & HTS surface, airgap	3.7 mm
		Frequency of rotation	4.25 Hz
		Number of cycles	10


Anvar Valiyaparambil Abdulsalam

Md Keyang Wang

Shahriar Hossain

Jeremy Weiss

Danko C Van Der Laan

Arend Nijhuis

Axial

V A Anvar

M S A Hossain

Axial and transverse load FEM analysis of CORC cables and wires

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

Abstract-Multilayered CORC ® wires can carry very high currents in background magnetic fields up to 20 T. Mechanical stresses during operation can result in irreversible degradation in the CORC ® wires/cables' performance. Different mechanical loads acting on CORC ® cable during production, winding, assembly, and electromagnetic operation are bending, axial and transverse loads. The tape's helical shape around the central core allows tapes to experience only a fraction of the total axial strain applied to the entire cable in the case of tensile loads. The winding angle is the main cabling parameter that influences the tensile strain limit of the CORC ® cable. The radial contraction of the tape depends on Poisson's ratio of the central core and winding angle. An analytical model is proposed to estimate the tensile strain in CORC ® wires and cables. With optimized cabling parameters, the irreversible strain limit of CORC ® cables and wires can be as high as 7%, which is 10 to 12 times higher than the irreversible strain limit of single REBCO tapes. The major mechanical stress in fusion and detector magnets in operation is transverse compressive stress. The transverse stress tolerance of the CORC ® cables and wires depends mainly on the gap spacing between layers, uniformity, and thickness of the copper layer in REBCO tape, core material, and surrounding material's hardness. A detailed finite element model is developed to study the effect of both tensile and transverse load in CORC ® cables and then compared against experimental data.

Keywords-CORC ® , Finite Element Modeling, REBCO tape, HTS cables, tensile load, transverse load

I. FINITE ELEMENT MODEL FOR MECHANICAL LOADS ON CORC ® CABLE

A detailed finite element model is created in ABAQUS software and validated with multilayer CORC ® cable experiments. Before applying mechanical loads, two steps are the tape production process and tape winding around the core. The tape's production process involves the MOCVD process in which a thin REBCO layer is deposited on the Hastelloy substrate at 1020 K, then cooled to 350 K to deposit copper layers on top and bottom of the tape. After this, the tape is cooled to room temperature. The tape is modeled with multilayered shell elements due to the thin layer nature. The tape layers experience thermal strain due to the difference in coefficient of thermal expansion between matrix materials.

The final shape of the tape is spherical. The tape is then wound over a cylindrical core, usually copper or steel. Then the whole CORC ® cable or wire is cooled down to liquid nitrogen temperature.

A. Axial load

Figure 1 shows the boundary condition for the axial load on the CORC ® cable. The cable's total length is 60 mm, and the grip length is 5 mm on both ends of the cable. The tensile load is applied to the grips on both ends of the cable. Figure 2 shows the strain contour in the REBCO layer when the applied tensile strain exceeds the cable's critical strain limit. The grey area in Figure 2 indicates the damaged zones where the local strain exceeds the intrinsic critical strain limit of 0.45%. The main two factors that influence CORC ® cables/wire's axial load performance are winding angle and poisons ratio. The influence of these parameters can be visualized by analytical equations, as shown in Figure 3. The z-axis corresponds to the axial strain factor. The axial strain factor is defined as the ratio of tape strain to cable strain. An optimized cable should have an axial strain factor close to zero. This can be achieved using winding angles near 30 0 and selecting a core material with a higher poisons ratio. For tapes with smaller widths, it might be required to maintain a suitable gap between twist pitches. The irreversible damage for cables with zero axial strain factor can only occur near the cable terminations.

B. Transverse loads

The CORC ® cable is pressed between two rigid plates to apply transverse load. One plate is fixed, and the other one is moved towards the cable. Since the tape is modeled as multilayer shell elements, the effect of 'dog boning' or variation in copper layer thickness is not considered. The rotational degree of freedom for the CORC ® cable axis is constrained. Figure 4 shows the used boundary conditions for applying transverse load. Figure 5 shows the strain contour in a REBCO layer of the CORC ® cable subjected to a transverse load. The grey areas indicate that the strain exceeds the intrinsic critical strain limit of 0.45% in certain areas of the tape above a critical transverse pressure.

Figure 5 -Axial strain contour in the REBCO layer of the CORC ® cable subjected to a transverse load.

Figure 6 shows the boundary condition for CORC ® CICC with 8 CORC ® cables around a central core. The transverse load in CORC ® CICC can be analyzed similarly to the case in Figure 4 but by pressing the CORC ® cable between two inclined plates. The inclination angle depends upon the number of CORC ® cables around the central core of the CICC.

Figure 1 .

 1 Figure 1. The boundary condition for the axial load applied to the CORC ® cable.

Figure 2 -

 2 Figure 2 -Strain profile on the REBCO layer when the axial load is applied to the CORC ® cable.

Figure 3 -

 3 Figure 3 -Axial strain factor for various combinations of Poisson's ratio and winding angle. The results of the F.E. model are compared with experiments conducted by Advanced Conductor Technologies on two multilayered cables. The cables have 12 tapes in 6 layers in various winding angles. The result comparison indicates that the FEM model can successfully predict the axial load behavior of CORC ® cables.

Figure 4 -

 4 Figure 4 -Boundary conditions as used for transverse load on CORC ® cables.

Figure 6 -

 6 Figure 6 -The boundary condition for CORC ® CICC with 8 CORC ® cables around a central core.


V A Anvar

J Weiss

K Wang

D C Van Der Laan

M S A Hossain

A Nijhuis

Flexibility and contact resistance of CORC ® cables and wires: Experiments and modeling

Keywords: CORC ®, Finite Element Modeling, Contact resistance, Electrical network model, REBCO tape, HTS cables I

HTS Conductor on Round Core (CORC ® ) cabling concept allows cables to be manufactured with round formers as small as two to five millimeters in diameter. CORC ® consist of several layers of helical tapes wound around a central metallic core in an alternating fashion. Various parameters like winding angle, tape width, substrate thickness, number of layers, and lubrication, significantly influence the CORC ® cables and wires' performance. A set of bending experiments is conducted on single-layer CORC ® cables and wires with different cabling parameters to check the flexibility and determine the critical bending radius. The current conduction through the CORC ® 's core is also studied by insulating the core. Results are analyzed and compared with the help of a detailed finite element (FE) model. The FE modeling consists of three stepstape production process, tape winding, and bending of CORC ® cables or wires. The local potential distributions on a scale smaller than the width of the superconductor tape are tested experimentally. An electrical network model is created to study the effects of degraded spots in the tape and visualize the strained tape's current flow. The experiment consists of measurements at local spots on the REBCO tape with a specially designed multipoint probe, which are then compared with the full length CORC ® performance. The inter-tape contact resistance of simplified CORC ® wires is also investigated at 77 K. The influence of lubrication, multiple cooldown cycles, and the bending diameter were investigated. In addition, an electrical resistance network model is also build to predict the contact resistance distribution along the wire when the bending load is applied.

INTRODUCTION

The work on CORC ® cable and wires is categorized into three sections.

A. Bending of CORC ® cables and wires

A detailed finite element model is created in ABAQUS software and validated with multilayer CORC ® cable experiments. The CORC ® FE model consists of the production process, tape winding, and cable bending. The tape's production process involves the MOCVD process in which a thin REBCO layer is deposited on a Hastelloy substrate at 1020 K, then cooled to 350 K for depositing copper layers on top and bottom of the tape. After that, the tape is cooled to room temperature. The tape is modeled with multilayered shell elements due to the thin layer nature. The tape layers experience thermal strain due to the difference in coefficient of thermal expansion between matrix materials. The final shape of the tape is spherical. The tape is then wound over a cylindrical core, usually copper or steel. Then the whole CORC ® cable or wire is cooled down to liquid nitrogen temperature. At 77 K, the cable/wire is bent to 30 mm diameter in steps. The strain in the REBCO layer is monitored during the bending process. The permanent damage or the irreversibility point is reached when the intrinsic strain in the REBCO layer exceeds locally a critical strain value of 0.45%, significantly decreasing the performance of the CORC ® cable. Locally and globally, it will affect the REBCO tape's performance, i.e., the critical current Ic and n-value will drop drastically. Figure 1 shows the strain profile in the REBCO layer on a bent CORC ® cable. An open cryostat is used to create a liquid nitrogen bath at 77 K. A bent CORC ® cable is then inserted into the cryostat with a series of voltage taps placed on the helical tape of the CORC ® cable. Bending formers of different diameters ranging from 400 to 30 mm are used to bend the cable to a suitable radius manually. At first, a straight cable is measured for the critical current and then warmed up to room temperature. The cable is then bent to 400 mm diameter, and the cycle is repeated in sequence up to 30 mm diameter. The voltage readings are recorded for each bending diameter. Different cables are selected to study the influence of core diameter, winding angle, winding tension, tape width, Hastelloy thickness, and lubrication. Due to the large fraction of core in cable and single layer nature of tested cable, the current conduction through the copper core can influence the damage analysis of the tape. A series of CORC ® wires with insulated core is also studied experimentally and compared with modeling results.

The experimental results for some CORC ® wires and cables showed some irregularity in critical current degradation with the decrease in bending curvature. The irregularities disappeared for cables with insulated former, pointing to the observation that the current conduction through the copper cope influences the result of these typical single layer CORC ® cables, especially at small bending diameters. The finite element model showed good agreement with experimental results, and thus the FE model can qualitatively predict the flexibility of CORC ® cable/wire.

B. Local potential distribution in REBCO tapes

For a CORC ® cable in bending configuration, there are areas on the tape where the critical strain is exceeded. These zones will permanently degrade the CORC ® cable performance. It should be expected that it matters where the voltage taps are placed within one revolution and the tape's width. The mechanical strain-data from the Abaqus  model is translated to the critical current of the REBCO tape using Ekin's strain formula. Since Abaqus is modeling software for the mechanical domain, the electrical domain modeling is done in a discrete simulation program in Multisim  using SPICE commands. This model showed potential distribution variation in both longitudinal and transverse directions in cases where the critical strain of the REBCO tape is exceeded. To validate the electrical network model, an experimental setup is designed to scan the variation in voltage distribution. Spring probes are assembled as voltage taps in a holder to place accurately on the tape of a bent CORC ® cable. The entire assembly was manufactured using a composite material Nylon PA 2200. The manufacturing is done with a 3D-printer; the material showed no significant shrinkage in LN2. Figure 3 shows the assembled system after manufacturing.

The network model was experimentally verified for the variation in the longitudinal direction of the REBCO tape in CORC ® configuration. Consequently, it has been proven that the placement of voltage taps along the longitudinal direction of a CORC ® cable in bending configuration matters for bending diameters where the critical strain of the REBCO tape is exceeded. An increase of approximately 10% in Ic can be measured if the voltage taps are placed approximately 50 cm away from the local damage. The transverse direction experiments remained inconclusive since only noise was measured. This is because of the limitation of the used nanovoltmeters, which introduce large errors in the transverse electric field due to very small values of measured voltage from voltage taps placed at small distances. The lubrication increases the contact resistance of the sample. For instance, some lubrication type increases the contact resistance twice the magnitude compared to certain other types. The influence of the cooldown cycle in contact resistance is not observed. The contact resistance of all samples decreased when the samples were bent around the formers. The reduction in contact resistance saturated around 80 mm bending diameter for all measured samples. The magnitude of reduction in contact resistance was different for different lubrication types. A simple electrical network model is made to predict the change in local contact resistance when the sample is bent. The network model consists of two parallel circuits of series resistance connected by a set of contact resistances and both ends of the parallel circuits connected to the terminal resistance.

Fig 1 :

 1 Fig 1: Strain on one twist pitch length of the REBCO layer after bending.

Fig 2 :

 2 Fig 2: Electrical behavior of a REBCO tape on a bent CORC ® cable -50 mm bend diameter.

Fig 3 :

 3 Fig 3: A total overview of the multipoint voltage tap probe mounted on the CORC ® cable bending setup.C. Contact resistanceTwo different experiments were carried out on four CORC ® samples with different types of lubrication. The first experiment's goal is to measure the contact resistance of the four samples and find the influence of multiple cooldown cycles on the contact resistance. The second experiment's goal is to measure the influence of the bending load on the contact resistance. An electrical network model is made to predict the local contact resistance along the sample's length.

Figure 4 :

 4 Figure 4: Voltage tap placement on the samples for the bending load experiment.