Xin Mengmeng Wang

Xin Sun

Baichuan Cao

Nona R Chiariello

Kathryn M Docherty

Christopher B Field

Qun Gao

Jessica L M Gutknecht

Xue Guo

Genhe He

Bruce A Hungate

Jiesi Lei

Audrey Niboyet

Xavier Le Roux

Zhou Shi

Wensheng Shu

Mengting Yuan

Jizhong Zhou
email: jzhou@ou.edu

Yunfeng Yang
email: yangyf@tsinghua.edu.cn

Long-term elevated precipitation induces grassland soil carbon loss via microbe-plant-soil interplay

Keywords: elevated precipitation, soil carbon loss, microbial functional trait, viral shunt, resource acquisition, water-limited ecosystems

Global climate models predict that the frequency and intensity of precipitation events will increase in many regions across the world. However, the biosphere-climate feedback to elevated precipitation (eP) remains elusive. Here, we report a study on one of the longest field experiments assessing the effects of eP, alone or in combination with other climate change drivers such as elevated CO 2 (eCO 2 ), warming, and nitrogen deposition. Soil total carbon (C) decreased after a decade of eP treatment, while plant root production decreased after two years. To explain this asynchrony, we found that the relative abundances of fungal genes associated with chitin and protein degradation increased and were positively correlated with bacteriophage genes, suggesting a potential viral shunt in C degradation. In addition, eP increased the relative abundances of microbial stress tolerance genes, which are essential for coping with environmental stressors.

Microbial responses to eP were phylogenetically conserved. The effects of eP on soil total C, root production, and microbes were interactively affected by eCO 2 .

Collectively, we demonstrate that long-term eP induces soil C loss, owing to changes in microbial community composition, functional traits, root production, and soil moisture. Our study unveils an important, previously unknown biosphere-climate feedback in Mediterranean-type water-limited ecosystems, namely how eP induces soil C loss via microbe-plant-soil interplay.

Introduction

The Anthropocene era has brought significant changes in Earth's precipitation patterns [START_REF] Shaw | Grassland responses to global environmental changes suppressed by elevated CO 2[END_REF]. The global hydrologic cycle has intensified along with climate warming [START_REF] Huntington | Evidence for intensification of the global water cycle: Review and synthesis[END_REF], leading to an increase in annual precipitation in many regions during 1980-2019 [START_REF] Gulev | Changing State of the Climate System[END_REF]. Extreme precipitation events are anticipated to become more frequent in the 21 st century [START_REF] Corringham | Atmospheric rivers drive flood damages in the western United States[END_REF][START_REF] Stevenson | Twenty-first century hydroclimate: A continually changing baseline, with more frequent extremes[END_REF]. As water availability serves as a limiting factor for most terrestrial ecosystems, the precipitation regime is a critical regulator of ecosystem functioning in soils, which comprise the Earth's largest terrestrial C reservoir [START_REF] Reichstein | Climate extremes and the carbon cycle[END_REF]. However, how precipitation regime shifts will affect soil C storage remains highly uncertain. To date, biogeochemical models have failed to reproduce precipitation-related patterns of soil C dynamics [START_REF] Falloon | Direct soil moisture controls of future global soil carbon changes: An important source of uncertainty[END_REF], hampering our ability to predict how future scenarios of altered precipitation will influence soil C source or sink capacity.

The central west coast of North America, mainly in California, has a Mediterranean-type climate regime characterized by hot, dry summers, and cool, wet winters. The Jasper Ridge Global Change Experiment (JRGCE), which was conducted in a California annual grassland, demonstrated that net primary productivity (NPP) responded unimodally to variations in precipitation [START_REF] Zhu | Nonlinear, interacting responses to climate limit grassland production under global change[END_REF]. A short-term (3-year) elevated precipitation (eP) treatment increased NPP, primarily due to an increase in shoot production [START_REF] Shaw | Grassland responses to global environmental changes suppressed by elevated CO 2[END_REF]. However, the positive shoot responses were largely offset by negative root responses, resulting in an insignificant increasing trend in total NPP over a 5-year eP treatment [START_REF] Dukes | Responses of grassland production to single and multiple global environmental changes[END_REF]. In addition, a study conducted in another California grassland revealed that long-term trajectories of plant species richness and abundances of invertebrate herbivores and predators differed from short-term responses to the eP treatment [START_REF] Sullivan | Grassland responses to increased rainfall depend on the timescale of forcing[END_REF], suggesting that long-term eP treatment could restructure ecological relationships that ultimately affect soils and soil biota.

Soil microorganisms respond more rapidly to changes in soil water content than plants due to their faster intrinsic growth rates [START_REF] Prosser | The role of ecological theory in microbial ecology[END_REF]. In a study of California grassland, soil active bacterial community examined by meta-transcriptomic analysis was rapidly affected by a wet-up event within 1-72 hours, showing a consistent pattern conserved at the sub-phylum level [START_REF] Placella | Rainfall-induced carbon dioxide pulses result from sequential resuscitation of phylogenetically clustered microbial groups[END_REF]. At the DNA level, wetting decreased the relative abundance of Actinobacteria but increased that of Acidobacteria [START_REF] Barnard | Responses of soil bacterial and fungal communities to extreme desiccation and rewetting[END_REF]. However, these responses to short-term wetting were transient, displaying marked resilience. In contrast, fungal communities were largely unaffected, suggesting that fungi might be more resistant to changes in water availability. Furthermore, viral abundance in soils can be strongly influenced by water availability [START_REF] Williamson | Viruses in Soil Ecosystems: An Unknown Quantity Within an Unexplored Territory[END_REF].

Although numerous field experiments have explored the effect of short-or mid-term eP treatment on the taxonomic composition of microbial communities, the results have been inconsistent: microbial community composition was affected by eP (3 years) [START_REF] Ochoa-Hueso | Links between soil microbial communities, functioning, and plant nutrition under altered rainfall in Australian grassland[END_REF], or not (2-8 years) [START_REF] Docherty | Soil microbial responses to fire and interacting global change factors in a California annual grassland[END_REF][START_REF] Gutknecht | Microbial communities and their responses to simulated global change fluctuate greatly over multiple years[END_REF][START_REF] Qi | Microbial functional responses explain alpine soil carbon fluxes under future climate scenarios[END_REF]. In addition, the functional potentials of soil microbial communities, which underlie ecological processes, can be altered by eP. For instance, precipitation-mediated changes in microbial communities were strongly associated with increased soil respiration [START_REF] Chou | The sensitivity of annual grassland carbon cycling to the quantity and timing of rainfall[END_REF]. Soil nitrifying and denitrifying enzyme activities, as well as the abundances of ammonia-oxidizing bacteria and nitrite-oxidizing bacteria, were also altered by the eP treatment in the JRGCE over 2-8 years since the experiment began [START_REF] Barnard | Several components of global change alter nitrifying and denitrifying activities in an annual grassland[END_REF][START_REF] Horz | Ammonia-oxidizing bacteria respond to multifactorial global change[END_REF][START_REF] Roux | Predicting the responses of soil nitrite-oxidizers to multi-factorial global change: a trait-based approach[END_REF], Niboyet et al., 2011b). Increased soil N 2 O emissions were reported under eP, which were associated with increased denitrification rates [START_REF] Brown | Effects of multiple global change treatments on soil N 2 O fluxes[END_REF]. Similarly, changes in the abundances and enzyme activities of soil denitrifiers were detected for a semi-arid grassland in response to precipitation-mediated changes [START_REF] Shi | Responses of soil N 2 O emissions and their abiotic and biotic drivers to altered rainfall regimes and co-occurring wet N deposition in a semi-arid grassland[END_REF].

Most studies examining soil microbial responses have focused on short-term eP treatments. It remains unclear whether microbial communities adapt to long-term altered soil moisture regimes as they do to elevated temperature [START_REF] Melillo | Long-term pattern and magnitude of soil carbon feedback to the climate system in a warming world[END_REF], or whether they continue to shift in the long-term trajectories to differ from short-term responses, as macrofauna and macroflora do [START_REF] Sullivan | Grassland responses to increased rainfall depend on the timescale of forcing[END_REF]. To address it, we examined plant and microbial responses (e.g., bacteria, fungi, and viruses) to a 14-year eP treatment (+50%) alone or combined with elevated CO 2 (eCO 2 , +275 μmol•mol -1 ), warming (+1.0 o C in topsoils ) and nitrogen (N) deposition (+7g•m -2 •y -1 ) in the JRGCE, one of the longest manipulations of precipitation in a natural ecosystem. We hypothesized that long-term eP may lead to shifts in soil microbial community composition and functional traits, contradicting the short-term responses where eP affected microbial gene expression and physiology with no or transient changes in microbial community composition [START_REF] Barnard | Responses of soil bacterial and fungal communities to extreme desiccation and rewetting[END_REF][START_REF] Gutknecht | Microbial communities and their responses to simulated global change fluctuate greatly over multiple years[END_REF]. We also hypothesized that the microbial responses to eP might be interactively affected by other climate change factors such as eCO 2 , warming, and N deposition, as previously reported for plant production [START_REF] Zhu | Nonlinear, interacting responses to climate limit grassland production under global change[END_REF].

Materials and Methods

Experimental design and soil sampling. The JRGCE is located in an annual grassland within a 481-ha protected area along the eastern foothills of the Santa Cruz Mountains in northern California (37°40' N, 122°22' W). The mean annual precipitation at the study site over 45 years was 604 mm, with more than 80% of precipitation occurring as rain between November and March. The average annual air temperature over 45 years was 13.4°C. The soil is a fine-loamy, mixed, thermic Typic Haploxeralf, with a pH of 6.5-7.0 and a water-holding capacity of 21% [START_REF] Brown | Effects of multiple global change treatments on soil N 2 O fluxes[END_REF].

The JRGCE was established in October 1998 to evaluate grassland ecosystem responses to global change treatments. The experiment consisted of eight blocks as replicates, each with four circular plots of 3.14 m 2 area. Each plot was equally divided into four quadrants, resulting in a total of 128 quadrants. To simulate the projected future precipitation regime in the California grassland, half of the quadrants received an additional 50% precipitation with sprinklers after each natural rainfall event, and two additional watering events in the spring at the end of the rainy season to simulate an extension of the rainy season by three weeks, while ambient precipitation (aP) quadrants received no water addition, serving as controls. During the 14 years of treatments preceding our study, ambient precipitation averaged 610 mm per year, and precipitation in the eP treatment averaged 870 mm (i.e. +42.6%, Fig. S1A). In addition to elevated precipitation, the experiment included elevated carbon dioxide (ambient vs. +275 μmol•mol -1 CO 2 ), warming (ambient vs. elevated temperature by ~1.0 o C in topsoils), and N deposition (ambient vs. +7 g N m -2 •y -1 as Ca(NO 3 ) 2 ), all conducted in a full factorial design [START_REF] Shaw | Grassland responses to global environmental changes suppressed by elevated CO 2[END_REF]. The treatments were arranged in a randomized block split-plot design, with warming and CO 2 elevation at the plot level and N deposition and eP assigned randomly at the subplot level [START_REF] Dahlin | Environmental and community controls on plant canopy chemistry in a Mediterranean-type ecosystem[END_REF][START_REF] Gutknecht | Microbial communities and their responses to simulated global change fluctuate greatly over multiple years[END_REF]. In 2003, an accidental wildfire burned two of the eight blocks. In 2011, a controlled burn was carried out in half of the blocks, including the two blocks burned in 2003, to provide a fire treatment.

Since previous studies found that fire significantly affected microbial communities and ecosystem functioning across four global change treatments (Niboyet et al., 2011a[START_REF] Strong | Experimental fire increases soil carbon dioxide efflux in a grassland long-term multifactor global change experiment[END_REF][START_REF] Yang | Fire affects the taxonomic and functional composition of soil microbial communities, with cascading effects on grassland ecosystem functioning[END_REF], the burned blocks were excluded from the present analysis.

A total of 64 soil samples were collected on April 26 th and 27 th , 2012, 14 years after the initial treatments were implemented. Soil samples were obtained by collecting one 7 cm deep × 5 cm diameter core from each quadrant and thoroughly homogenizing the soil. These soil samples were then sieved through a 2 mm mesh and stored at -20 o C for geochemical analyses or at -80 o C for microbial analyses.

Environmental variables. We determined soil total C and total N by combustion analysis on a Carlo Erba Model 1500 CNS Analyzer (Carlo Erba Strumentazione, Milan, Italy). Soil C: N ratios were then calculated as mass ratios of total C to total N. We also collected soil total C and N data in 1998 (Year 0) and from 2000 (Year 2) to 2012 (Year 14) on a yearly basis. To measure soil temperature, we buried thermo-couples at a depth of 2 cm in each quadrant and recorded hourly data, which we then averaged over April 1 st -27 th , 2012 (Niboyet et al., 2011b). We determined soil moisture by comparing the mass of a 10-g soil sub-sample before and after drying at 105°C for one week. We measured soil pH by suspending 5 g of soil in 10 mL of distilled water. We determined soil ammonium (NH 4 -N) and nitrate (NO 3 -N) concentrations by suspending 5 g of soil in 50 mL of 2 M KCl solution, followed by measuring filtered extracts using an Automated Segmented Flow Analyzer (SEAL Analytical, Mequon, WI, USA). We collected soil CO 2 efflux data as previously described [START_REF] Strong | Experimental fire increases soil carbon dioxide efflux in a grassland long-term multifactor global change experiment[END_REF], which were measured from April 27 th -29 th to June 20 th -25 th , 2012.

The ecosystem NPP and its components, i.e., aboveground NPP (ANPP) and belowground NPP (BNPP) were measured as previously described [START_REF] Zhu | Nonlinear, interacting responses to climate limit grassland production under global change[END_REF]. Specifically, we collected aboveground plant materials from a 141 cm 2 area of each quadrant twice at the peak of standing biomass, once in mid-April to early May and again in early to late May. The biomass was analyzed using a maximum of two harvests to reduce phenological variation bias under different treatments. We measured the total aboveground biomass by clipping all aboveground biomass, separating individual plant species into functional groups: annual grass, perennial grass, annual forb, and perennial forb [START_REF] Gao | Long-term warming in a Mediterranean-type grassland affects soil bacterial functional potential but not bacterial taxonomic composition[END_REF]. We determined litter biomass by collecting all senesced plant material from the ground within the same area. After the first aboveground harvest, we determined belowground biomass by taking four soil cores (2.5 cm diameter) in the same area, with two cores for shallow roots (0-15 cm) and two for deep roots (15-30 cm). Fine roots in a depth of 0-15 cm were separated from tap roots. All plant materials were oven-dried at 70 o C and weighed. NPP, ANPP, and BNPP data in 1998and from 2000to 2011(BNPP and NPP in 1999and 2007 not available) were also collected as previously described [START_REF] Zhu | Nonlinear, interacting responses to climate limit grassland production under global change[END_REF].

DNA extraction, purification, and quantification. We extracted soil DNA by freeze-grinding mechanical lysis, as previously described [START_REF] Zhou | DNA recovery from soils of diverse composition[END_REF]. We purified DNA with a 0.5% low-melting-point agarose gel electrophoresis followed by phenol-chloroform-butanol extraction. We assessed DNA quality using absorbance ratios of 260/280 nm and 260/230 nm (260/280 > 1.8 and 260/230 > 1.7) with a NanoDrop ND-1000 Spectrophotometer (NanoDrop Technologies, Wilmington, DE, USA). We then quantified the final DNA concentration with a PicoGreen method, using an FLUO star Optima (BMG Labtech, Jena, Germany) as previously described [START_REF] Yang | The microbial gene diversity along an elevation gradient of the Tibetan grassland[END_REF].

MiSeq sequencing and raw data preprocessing. We constructed the 16S rRNA gene library and processed sequencing data as previously described [START_REF] Guo | Climate warming accelerates temporal scaling of grassland soil microbial biodiversity[END_REF]. We targeted the V4 region of the 16S rRNA gene with primers 515F (GTGCCAGCMGCCGCGGTAA) and 806R (GGACTACHVGGGTWTCTAAT) and ITS2 region between 5.8S and 28S rRNA genes with primers gITS7 (GTGARTCATCGARTCTTTG) and ITS4 (TCCTCCGCTTATTGATATGC) in PCR amplification. We then sequenced PCR products by 2 × 250 bp paired-end sequencing with a MiSeq instrument (Illumina, San Diego, CA, USA). We identified paired-end raw sequences by paired barcodes and combined them using FLASH [START_REF] Magoč | FLASH: fast length adjustment of short reads to improve genome assemblies[END_REF]. We further trimmed sequences to the length of > 245 bp for the 16S rRNA gene or >220 bp for the ITS. We generated amplicon sequence variants (ASVs), also known as zero-radius operational taxonomic units or unique sequence variants, by UNOISE3 [START_REF] Edgar | Updating the 97% identity threshold for 16S ribosomal RNA OTUs[END_REF]. We annotated the representative sequence taxonomy using the QIIME2 Naive Bayes classifier trained for the V4 region of the 16S rRNA gene (version Silva-132-99-515-806) and ITS based on UNITE QIIME release (version ver8_97_10.05.2021) [START_REF] Abarenkov | UNITE QIIME release for Fungi, UNITE Community[END_REF][START_REF] Quast | The SILVA ribosomal RNA gene database project: improved data processing and web-based tools[END_REF]. We removed the singlet ASVs and those classified as mitochondria and chloroplasts to improve data reliability. We retrieved 3,391,680 high-quality sequences for the 16S rRNA gene and 661,632 high-quality sequences for ITS. Then, we resampled 16S rRNA gene sequences at a depth of 31,441 reads and ITS sequences at a depth of 17,397 reads for each of the 64 samples (Fig. S2). The representative 16S rRNA gene sequences were aligned using MAFFT and used for constructing phylogenetic trees by FastTree on QIIME2 [START_REF] Bolyen | Reproducible, interactive, scalable and extensible microbiome data science using QIIME 2[END_REF]. Although the ITS2 region has a high resolution for identifying evolutionarily close taxa, the high rate of insertion and deletion makes the evolutionarily distant taxa vary greatly and difficult to be aligned. Therefore, we constructed the fungal phylogenetic tree by specifying constraint alignment in FastTree v2. 1.10 (Price et al., 2010). The constraint alignment was converted from a guide tree constructed using ghost-tree [START_REF] Fouquier | Ghost-tree: creating hybrid-gene phylogenetic trees for diversity analyses[END_REF], which grafted the taxonomically assigned ITS sequences to a reference foundation tree (Silva Ver. SSU 138) by mapping genus names.

GeoChip experiments and raw data preprocessing. We carried out DNA labeling with Cy3 and hybridization with the functional array GeoChip 4.6, as previously described [START_REF] Wang | Microbial responses to inorganic nutrient amendment overridden by warming: Consequences on soil carbon stability[END_REF]. We scanned the fluorescent intensities of each probe on GeoChip, using a NimbleGen MS 200 Microarray Scanner with 100% laser power and 100% photomultiplier tube (Roche, Basel, Switzerland). We discarded spots with a signal-to-noise ratio of less than 2.0. Probe signals that were detected only once among four biological replicates were also excluded. As a result, a total of 60,619 probes, including 53,748 probes derived from bacteria, 4,661 probes from eukaryotes, 1,821 probes from archaea, and 389 from viruses, were detected. We performed a natural logarithmic transformation of each detected probe ( ) (probe , sample

) to get (we added 1 to because the natural logarithm of zero is not defined). We normalized by dividing the average signal intensity of all probes in the sample i to get (m is the total number of probes, i.e. 60,619).

Statistical analyses.

All statistical analyses were performed in R version 3.5.2

(http://www.r-project.org) unless otherwise specified. P-values < 0.050 are considered to be statistically significant. P-values between 0.050 and 0.100 are considered to be marginally significant, given the large variations among blocks.

P-values > 0.100 are not considered to be statistically significant.

Diversity analyses. We calculated the α-diversity of the Shannon index for taxonomic diversity (based on rarefied ASV tables) and functional gene diversity (based on functional genes of GeoChip), and Faith's phylogenetic diversity. We utilized the vegan and picante packages for these analyses.

Treatment effect analyses. To assess the treatment effect, we calculated the effect size of precipitation as follows: % effect = 100% × (eP -aP)/aP (n = 64 under eP and aP for data in 1998 and 2000-2003 before the 2003 fire, n = 48 for data in 2004-2011 before the 2011 fire, and n = 32 for data in 2012). The statistical significance of the treatment effect was tested by split-plot ANOVA using aov function in R. We applied log or square root transformations to improve normality when necessary. To analyze the treatment effect on functional and taxonomic compositions of microbial communities, we performed split-plot PERMANOVA with PRIMER 6 + PERMANOVA software [START_REF] Marti | PERMANOVA+ for PRIMER: Guide to Software and Statistical Methods[END_REF]. We used negative binomial models in the DESeq2 package to identify significantly changed ASVs with eP (baseMean > 10, log2 fold change > 0.5, and FDR adjusted P value < 0.050), and examined the significance with Wald tests [START_REF] Love | Moderated estimation of fold change and dispersion for RNA-seq data with DESeq2[END_REF]. Using DESeq2 and split-plot ANOVA, we also examined the effects of the eP treatment across different taxonomic levels to determine whether the alterations in taxonomic lineages were phylogenetically clustered. We adjusted P-values using the FDR method when conducting multiple comparisons, such as assessing the eP effect on multiple functional genes and taxonomic lineages.

ConsenTRAIT analysis. We performed consenTRAIT analysis to determine whether the responses of bacteria and fungi to eP were phylogenetically conserved, using the castor package [START_REF] Louca | Efficient comparative phylogenetics on large trees[END_REF][START_REF] Martiny | Phylogenetic conservatism of functional traits in microorganisms[END_REF]. Since FastTree only estimates branch lengths by inferring approximately-maximum-likelihood phylogenetic trees, we constructed a maximum likelihood (ML) tree of the 16S rRNA gene sequences to obtain accurate branch lengths for the consenTRAIT analysis. For ITS sequences, it is difficult to align the sequences and construct an ML tree because of high variations, we constructed the phylogenetic tree using constrained FastTree's topology search instead.

Ecological process analyses. Microbial community assemblies are shaped by ecological processes, including both stochastic processes (e.g., dispersal, birth-death events, and ecology drift) and deterministic processes (e.g., environmental filtering) [START_REF] Hubbell | The unified neutral theory of biodiversity and biogeography (MPB-32)[END_REF][START_REF] Ning | A general framework for quantitatively assessing ecological stochasticity[END_REF]. We estimated the stochastic ratio using a modified method based on null-model algorithms with taxonomic metrics (Sorensen) as previously described [START_REF] Guo | Climate warming leads to divergent succession of grassland microbial communities[END_REF][START_REF] Ning | A general framework for quantitatively assessing ecological stochasticity[END_REF]. The effect of the eP treatment on the estimated stochastic ratio was evaluated by split-plot permutational multivariate analysis of variance (PERMANOVA).

Structural equation modeling and aggregated boosted tree analyses. Structural equation modeling (SEM) was employed to reveal how biotic and abiotic variables affect soil total C across aP and eP quadrants. Since soil total C was altered by both eP and N deposition (Table S1), only samples under the ambient N condition (a total of 32 samples) were used for SEM analysis to exclude the effect of N deposition. The community compositions were represented by PC1 from the principal coordinate analysis based on the Bray-Curtis dissimilarity of the ASV matrix, which captured 9.3% -15.5% variations of microbial community composition. We first established a full model with all reasonable pathways (Fig. S3), and then we used a stepwise approach to remove non-significant pathways with the highest P-value at each step until the final model was obtained. The SEM analysis was performed using the lavaan R package [START_REF] Rosseel | lavaan: an R package for structural equation modeling[END_REF].

We performed the aggregated boosted tree (ABT) analysis, a machine learning algorithm, to investigate the relative influences of biotic and abiotic variables in regulating soil total C [START_REF] De | Boosted trees for ecological modeling and prediction[END_REF]. We first established a hyper grid of parameters, including learning rate (shrinkage), interaction depth, the minimum number of observations in the terminal nodes of trees (n.minobsinnode), and subsampling fraction (bag.fraction), for tree training and tuning (Data S1). However, when shrinkage was set to 0.001, the optimal trees became too large, which might lead to overfitting of the ABT models. Therefore, we opted for the optimal combination of parameters, which included shrinkage = 0.01, interaction depth = 1, n.minobsinnode = 3, and bag.fraction = 0.8. Finally, we evaluated the model by 10-fold cross-validation. ABT models were built by gbm function in gbm R package, and model evaluation was performed by train function in caret R package.

Results

Edaphic and plant variables

The eP treatment did not change soil total C in the early phase of the 2 nd -9 th year since the experiment began (Fig. 1A & Table S2). In the late phase of the 10 th -14 th year, eP decreased soil total C by 4.2% (P < 0.001, Fig. 1A & Table S2), with significant eP effects on soil total C in the 10 th , 13 th , and 14 th year (P < 0.021, Fig. S1B). Soil total N was not altered by eP alone (Fig. 1B & Table S2). As a result, the C: N ratio was significantly decreased by eP (P = 0.002, Fig. 1C & Table S2). Treatment effects on other soil variables were described in Supplementary Text A.

Aboveground net primary production (ANPP) was increased from 591 g•m -2 •y -1 in ambient precipitation (aP) quadrants to 632 g•m -2 •y -1 in eP quadrants throughout the 2 nd -14 th year (P = 0.018, Fig. 1D & Table S2). In contrast, belowground NPP (BNPP)

was decreased from 463 g•m -2 •y -1 in aP quadrants to 401 g•m -2 •y -1 in eP quadrants (P < 0.001, Fig. 1D & Table S2). The decline in BNPP counterbalanced the increase in ANPP, resulting in an unchanged NPP by the eP treatment (Fig. 1D). However, eP effects on ANPP and BNPP varied considerably by year (Fig. S1C & S1D). ANPP was significantly increased in only two years of the 14-year observations (Fig. S1C), while BNPP was significantly decreased by 14.9%-25.2% during the first 2 nd -5 th years (P < 0.021, Fig. S1D). However, the decline in BNPP was only observed in three years during the late 6 th -14 th years (Fig. S1D).

There was an interactive effect of precipitation × warming on soil total C (P = 0.048, Table S2), which was decreased by eP when the temperature was ambient but was unaltered by eP when the temperature was elevated (Fig. 1E). In the early phase of the 2 nd -9 th year, soil total C was not altered by eP alone or combined with other global change factors (Table S2). In contrast, soil total C was interactively affected by precipitation × CO 2 × warming in the late phase of the 10 th -14 th year (P = 0.008, Table S2), leading to a decline in soil total C under eP when CO 2 or temperature was elevated (Fig. 1F). Soil CO 2 efflux was measured in the 14 th year of the experiment.

Soil CO 2 efflux was interactively affected by precipitation × CO 2 × N deposition (P = 0.022, Table S3), with eP increasing CO 2 efflux when CO 2 was elevated and N was ambient (Fig. 1G). Soil total N was interactively affected by precipitation × N deposition × warming (P = 0.047, Table S2), with eP decreasing soil total N only under N deposition and ambient temperature (Fig. 1B). BNPP and NPP were interactively affected by precipitation × CO 2 × warming (P < 0.037, Table S2), with eP decreasing BNPP when CO 2 and temperature were elevated (Fig. 1H) and decreasing NPP when CO 2 was elevated and the temperature was ambient (Fig. 1I).

Microbial functional genes

To examine the shifts in microbial communities by long-term eP, we analyzed microbial functional potentials with functional gene array (GeoChip 4.6) and prokaryotic and fungal community compositions with targeted amplicon sequencing, using soil samples collected in the 14 th year of the experiment. Microbial functional gene composition differed between the aP and eP quadrants (P = 0.050, Table S4), though functional gene α-diversity remained similar (Table S5). There were interactive effects of precipitation × CO 2 on functional gene composition and α-diversity (Table S4 &S5). Functional gene α-diversity increased with eP when CO 2 was elevated, while it was not affected by eP when CO 2 was ambient (Fig. S4).

The relative abundances of genes associated with the degradation of pectin (pme) and cellulose (the gene encoding endoglucanase derived from bacteria) were decreased in the eP quadrants (P < 0.025, Fig. 2A). In contrast, the relative abundances of fungal genes encoding enzymes related to the degradation of N-rich compounds, such as chitin (endochitinase) and protein (aspartate protease and serine protease), were increased by 4.4%-18.1% with eP (P < 0.025, Fig. 2A). In addition, the relative abundance of the marker gene for methanogenesis (mcrA) increased (P = 0.017) under eP, while those of methane oxidation genes mmoX and pmoA were unaltered (Fig. S5A). There were interactive effects of precipitation × CO 2 on C degradation genes, but not methane cycling genes (Data S2). Notably, the increase in relative abundances of genes associated with degrading N-rich compounds was greater when CO 2 was elevated (Fig. S6A). Taken together, these results suggest that eP substantially altered soil microbial C cycling potentials, especially when CO 2 was elevated.

Since bacteriophages play an important role in regulating microbial C dynamics, we investigated 221 bacteriophage genes detected in our samples. The relative abundances of bacteriophage genes associated with viral structure and replication increased by 4.7%-9.5% in eP quadrants (P < 0.040, Fig. 2B), suggesting that eP may stimulate bacteriophage growth. . In contrast, the total abundances of 101 eukaryotic viral genes detected in our samples remained unaltered (Fig. 2B). There were interactive effects of precipitation × CO 2 on bacteriophage genes (Data S2),

whose gene abundances increased with eP when CO 2 was elevated (Fig. S6B).

Since long-term eP decreased soil total C, we investigated whether microbial stress responses were stimulated. The relative abundances of eight stress response genes were significantly increased with eP (Fig. 2C), including those associated with glucose limitation, oxygen limitation, phosphate limitation, oxidative stress, and sigma factors (see Supplementary Text B for details). There were interactive effects of precipitation × CO 2 on phosphate limitation and sigma factor genes (Data S2), whose gene abundances increased with eP when CO 2 was elevated and the temperature was ambient (Fig. S6C &S4D).

Microbial taxonomic composition

We identified 4,649 to 14,940 prokaryotic amplicon sequence variants (ASVs) and 719 to 1,757 fungal ASVs per sample (Fig. S2). Their taxonomic compositions were different between the eP and aP quadrants (P = 0.001), but were barely affected by the interaction of precipitation and other climate change treatments (Table S4). The taxonomic and phylogenetic α-diversities remained unaltered between the eP and aP quadrants (Table S5).

Positive eP responders of bacteria, i.e., bacterial ASVs increased by eP, were clustered within Bacteroidetes, Gammaproteobacteria, the order Sphingomonadales of Alphaproteobacteria, and the order Blastocatellales of Acidobacteria (Fig. 3 & Data S3, see Supplementary Text C for details). Negative eP responders of bacteria, i.e., bacterial ASVs decreased by eP, were clustered within Actinobacteria, Verrucomicrobia, Chloroflexi, subgroup6 of Acidobacteria, and the family Beijerinckiaceae of Alphaproteobacteria (Fig. 3 & Data S3). The positive and negative eP responders were phylogenetically clustered in these clades at a greater depth than expected in a null model of consenTRAIT analysis (P < 0.001, Table 1), suggesting that the bacterial community's response to long-term eP was phylogenetically conserved.

Positive eP responders of fungi were clustered within the class Sordariomycetes and the order Eurotiales of Ascomycota (Fig. 4 & Data S4). Negative eP responders of fungi were clustered in the class Archaeorhizomycetes, the order Onygenales, Helotiales, and Orbiliales, the family Periconiaceae and Herpotrichiellaceae of Ascomycota, and the order Agaricales of Basidiomycota (Fig. 4 & Data S4). The negative eP responders of fungi were phylogenetically conserved in deep-rooting clades (P = 0.003), however, the positive eP responders were not, as indicated by the absence of significant phylogenetic conservation (Table 1).

Ecological processes in shaping microbial community assembly

The phylogenetically conserved response of microbial communities to eP implies that environmental filtering, a deterministic process, may be important under eP. To test this, we estimated the relative importance of stochastic and deterministic processes using a null model analysis. There were interactive effects of precipitation × CO 2 on the stochastic ratios of bacterial communities (P = 0.004), which decreased with eP when CO 2 was elevated (P = 0.031) but remained unaltered with eP when CO 2 was ambient (Fig. 5A). In contrast, stochastic ratios of fungal community decreased with eP regardless of CO 2 conditions (Fig. 5B), showing higher environmental selection.

To identify the deterministic factors that affect microbial community composition, we conducted Mantel tests to examine the linkages between environmental variables and microbial eP responders. The positive eP responders of fungi and negative eP responders of bacteria were both correlated with soil moisture and soil CO 2 efflux (Mantel's r = 0.149-0.203, P < 0.015, Fig. 5C). In contrast, the negative eP responders of fungi and positive eP responders of bacteria were correlated with environmental variables to a lesser degree (see Supplementary Text D for details). We also examined the linkages between environmental variables and stress response genes and found that stress response genes were correlated with soil total C, soil total N, and litter biomass (Mantel's r = 0.101-0.267, P < 0.050, Fig. 5C).

Biotic and abiotic variables linking to soil total C

Since soil total C decreased with long-term eP, we identified biotic and abiotic variables that could be major drivers of soil total C. Structural equation modeling (SEM) analyses were performed with the presumed relationships (Fig. S3) among the selected subsets of edaphic and plant variables that were least correlated (see Methods for details of model selection). Soil total C was negatively affected by soil moisture but positively affected by fine root biomass (Fig. 6A). Soil total C was significantly correlated with fungal community composition, which was, in turn, correlated with relative abundances of genes associated with the degradation of N-rich chitin and protein. The relative abundances of bacteriophage genes had a strong correlation with those of C degradation genes, likely revealing an important role of viral shunt on soil C cycling. Overall, these variables explain 54% of the variations in soil total C (Fig. 6A). Among all the tested independent variables, soil moisture, fine root biomass, and fungal community composition played essential roles in mediating soil total C, as revealed by both SEM and aggregated boosted tree (ABT) analysis (Fig. 6A &6B). Soil pH and enriched microbial C degradation genes influenced soil total C to lesser extents. These results indicate that soil, plant, and microbial variables explain a similar proportion of soil total C dynamics.

Discussion

Understanding how long-term climate changes affect soil microbial communities and underlying ecosystem processes is essential for better predicting the terrestrial responses to climate change [START_REF] Tiedje | Microbes and Climate Change: a Research Prospectus for the Future[END_REF]. By examining the effects of 14-years eP on edaphic variables, plants, bacteria, fungi, and viruses, our study provides explicit evidence that long-term eP, either alone or in combination with other climate change drivers, can alter ecosystem compositions and functional traits linked to soil C loss.

The long-term eP treatment shifts microbial community compositions and functional traits

Although the short-or mid-term (3-8 years) eP treatment in the JRGCE did not alter microbial community composition [START_REF] Docherty | Soil microbial responses to fire and interacting global change factors in a California annual grassland[END_REF][START_REF] Gutknecht | Microbial communities and their responses to simulated global change fluctuate greatly over multiple years[END_REF], we found that bacterial and fungal community compositions were significantly changed after 14-year eP treatment (Table S4). This result supports our hypothesis that microbial communities continue to shift in the long-term trajectories, differing from short-term responses [START_REF] Sullivan | Grassland responses to increased rainfall depend on the timescale of forcing[END_REF]. However, this discrepancy could also be attributed to technical differences. Previous studies, which relied on low-resolution microbial community fingerprinting based on lipid biomarker analysis, may not unveil variations in microbial community composition [START_REF] Docherty | Soil microbial responses to fire and interacting global change factors in a California annual grassland[END_REF][START_REF] Gutknecht | Microbial communities and their responses to simulated global change fluctuate greatly over multiple years[END_REF]. Our analysis offers supporting evidence that microbial responses to water availability are phylogenetically clustered (Table 1) [START_REF] Placella | Rainfall-induced carbon dioxide pulses result from sequential resuscitation of phylogenetically clustered microbial groups[END_REF][START_REF] Xu | Drought delays development of the sorghum root microbiome and enriches for monoderm bacteria[END_REF], which could reflect the fundamental differences in microbial life strategies, i.e., traits driving survival, growth, and reproduction responses to environmental conditions [START_REF] Barnard | Responses of soil bacterial and fungal communities to extreme desiccation and rewetting[END_REF].

The phylogenetic conservation of microbial communities could be attributed to stress tolerance and competition-related traits [START_REF] Goberna | Abiotic stress tolerance and competition-related traits underlie phylogenetic clustering in soil bacterial communities[END_REF]. In support of stronger stresses, the stochastic ratios of prokaryotic and fungal communities were decreased by the eP treatment (Fig. 5A &5B). In addition, stress tolerance genes increased in relative abundances with long-term eP (Fig. 2C), reflecting higher environmental stress. For example, increases in oxygen limitation gene abundances might result from less oxygen in soil pore space or diffusing in the water film under eP [START_REF] Eag | Net primary productivity and nutrient cycling across a mesic to wet precipitation gradient in Hawaiian montane forest[END_REF], while oxidative stress levels could be increased when microbes are under stress [START_REF] Ernst | Methane formation driven by reactive oxygen species across all living organisms[END_REF].

The functional traits related to C degradation were shifted towards the degradation of N-rich compounds (such as chitin and protein), but not chemically C-rich compounds (such as starch, pectin, and hemicellulose, Fig. 2A). These results

were consistent with previous results in the JRGCE showing that 6-year eP treatment decreased hydrolase activity in degrading starch, xylan, and cellulose, but was inconsistent with a previous result of decreased chitin hydrolase activity [START_REF] Henry | Interactive effects of elevated CO 2 , N deposition and climate change on extracellular enzyme activity and soil density fractionation in a California annual grassland[END_REF]. The discrepancies in chitin degradation might be due to variations in C degradation trait over different time scales or technical differences since our results reflect the genetic potentials for these processes, while enzyme activities reflect the maximum potential under ideal conditions. Degradation of N-rich molecules, including chitin and proteins, also increased along a precipitation gradient from arid to semi-arid grasslands [START_REF] Feng | Divergent composition and turnover of soil organic nitrogen along a climate gradient in arid and semiarid grasslands[END_REF], which could reflect a microbial need for acquiring N nutrients.

Viral shunt, which releases organic matter from microbial cells, plays an important role in regulating C and N cycling across different ecosystems such as marine and anaerobic digesters [START_REF] Coutinho | Marine viruses discovered via metagenomics shed light on viral strategies throughout the oceans[END_REF][START_REF] Zhang | Bacteriophage-prokaryote dynamics and interaction within anaerobic digestion processes across time and space[END_REF].

Consistently, the relative abundance of bacteriophage genes was increased with eP (Fig. 2B & Fig. S5B), and were positively correlated with genes associated with the degradation of chitin and protein and consequently affected soil total C (Fig. 6A).

Those results suggest that bacteriophages might play an important role in C cycling of our annual grassland ecosystem. However, we cannot yet identify the host of the bacteriophages, hindering closer examinations of interactions among bacteria and bacteriophages.

The long-term eP treatment effects are interactively affected by elevated CO 2 and warming Elevated CO 2 enhanced eP effects on microbial functional traits and bacterial community assemblies in this study (Fig. S6 & Fig. 5A). One possible explanation is that CO 2 fertilization could induce higher shortages for other resources such as N and phosphorus, according to the ecological framework of (co)limitation by multiple resources [START_REF] Ma | How do soil micro-organisms respond to N, P and NP additions? Application of the ecological framework of (co-)limitation by multiple resources[END_REF]. Also, both eCO 2 and eP could decrease root biomass [START_REF] Iwasa | Shoot/root balance of plants: Optimal growth of a system with many vegetative organs[END_REF][START_REF] Shaw | Grassland responses to global environmental changes suppressed by elevated CO 2[END_REF], consequently reducing root input to -mainly root materials-being observed after the 6-year eP treatment [START_REF] Henry | Interactive effects of elevated CO 2 , N deposition and climate change on extracellular enzyme activity and soil density fractionation in a California annual grassland[END_REF], indicating that long-term eP exacerbated soil C loss. Since soil inorganic C content is stable in areas where mean annual precipitation is greater than 600 mm, and an increase in water availability has little effect on soil inorganic C in acidic or neutral soils [START_REF] Dang | Soil inorganic carbon dynamic change mediated by anthropogenic activities: An integrated study using meta-analysis and random forest model[END_REF], the decrease in soil total C in this study might be mainly attributed to the decrease in soil organic C. This result contradicts the increase in soil organic C pools with higher precipitation on the North American Great Plains [START_REF] Derner | Carbon sequestration and rangelands: A synthesis of land management and precipitation effects[END_REF][START_REF] Morrow | Climate change predicted to negatively influence surface soil organic matter of dryland cropping systems in the inland Pacific Northwest, USA[END_REF]. A possible explanation is that the eP effect on soil C is mediated by primary production. Increased precipitation on the Great Plains led to soil C gain by supporting plant photosynthesis [START_REF] Flanagan | Seasonal and interannual variation in carbon dioxide exchange and carbon balance in a northern temperate grassland[END_REF], but the NPP in the JRGCE was not altered by the eP treatment due to decreases in root production, offsetting increases in shoot production (Fig. 1D) [START_REF] Dukes | Responses of grassland production to single and multiple global environmental changes[END_REF]. Root production may decline due to reduced allocation to roots as soil resources become more available according to the optimal shoot-root C allocation theory [START_REF] Iwasa | Shoot/root balance of plants: Optimal growth of a system with many vegetative organs[END_REF]. Alternatively, it might be due to the suppressed root respiration as soils occasionally become waterlogged in the eP treatment [START_REF] Dukes | Responses of grassland production to single and multiple global environmental changes[END_REF]. Since root exudates and decomposing root residues are large contributors to soil C pool, the decrease in root production likely explained the observed decrease in soil total C in our study (Fig. 6). Notably, the decrease in root production was consistent only during the first few years (2 nd -5 th years) of eP treatment but not over longer terms (6 th -14 th years, Fig. S1D). The decoupled decreases in root production and soil C (Fig. S1) may indicate a legacy effect of root biomass on soil total C via C-aggregate and C-mineral associations [START_REF] Sokol | Life and death in the soil microbiome: how ecological processes influence biogeochemistry[END_REF].

Microbial traits, such as resource acquisition and stress tolerance, can mediate soil C cycling [START_REF] Malik | Defining trait-based microbial strategies with consequences for soil carbon cycling under climate change[END_REF]. In resource-limited and abiotic-stressed environments, microbes tend to prioritize costly resource acquisition or stress tolerance over high growth yield, resulting in polymer decomposition and soil C loss observed in this study (Fig. 5C & 6) and elsewhere [START_REF] Malik | Defining trait-based microbial strategies with consequences for soil carbon cycling under climate change[END_REF][START_REF] Malik | Land use driven change in soil pH affects microbial carbon cycling processes[END_REF]. In addition, the enhanced microbial decomposition of soil C under eP may be responsible for soil C loss [START_REF] Nielsen | Impacts of altered precipitation regimes on soil communities and biogeochemistry in arid and semi-arid ecosystems[END_REF]. Heterotrophic respiration could be positively affected by eP, especially under eCO 2 and ambient N deposition (Fig. 1F).

Increased water availability can stimulate microbial activity, growth, and respiration, leading to a lasting effect on soil C loss [START_REF] Nielsen | Impacts of altered precipitation regimes on soil communities and biogeochemistry in arid and semi-arid ecosystems[END_REF][START_REF] Wang | Responses of enzymatic activities within soil aggregates to 9-year nitrogen and water addition in a semi-arid grassland[END_REF].

Moreover, the eP treatment altered microbial community composition, consistent with changes in microbial community preference for different C substrates [START_REF] Zhou | Microbial mediation of carbon-cycle feedbacks to climate warming[END_REF]. Higher abundances of fungal taxa (Fig. 4 & Data S4) and C-degrading genes (Fig. 2A & Fig. S8) suggest that fungi become increasingly important for degrading C under the long-term eP treatment, as supported by the SEM and ABT analyses (Fig. 6). Consistently, the abundances of Eurotiales and Sordaiales, the positive eP responders of fungi observed in this study (Fig. 4 & Data S4), were positively correlated with the soil organic C mineralization rate, while those of Agaricales and Helotiales, the negative eP responders of fungi, were negatively correlated (Wang et al., 2021, Zhang et al., 2021). Our results coincided with the finding that potential activities of fungi-mediated C degradation enzymes, such as those degrading chitin, phosphodiester, lignin, cellulose, and xylan, were positively correlated with soil moisture [START_REF] Ad | Interactive effects of temperature and soil moisture on fungal-mediated wood decomposition and extracellular enzyme activity[END_REF]. Intriguingly, the role of fungal community composition in regulating soil C was linked to the C degradation genes enriched under eP and bacteriophage genes (Fig. 6A), implying possible complex interplay among bacteriophages, bacteria, and fungi in mediating the response of soil C turnover to long-term eP.

Alternatively, nutrient leaching, occurring through soil erosion or soil C migration from terrestrial to riverine ecosystems, can also contribute to soil C loss [START_REF] Frank | Effects of climate extremes on the terrestrial carbon cycle: concepts, processes and potential future impacts[END_REF], though we do not suspect this to be the main cause of decreased soil C in this experiment. Although we did not measure the magnitude of C leaching directly, we could estimate it by analyzing soil N data because soil C and N leaching often happen simultaneously [START_REF] He | Drainage and leaching losses of nitrogen and dissolved organic carbon after introducing maize into a continuous paddy-rice crop rotation[END_REF]. The eP treatment itself did not alter N inputs either, since the supplemental water was from the domestic water supply and was added through drip irrigation and overhead sprinklers without flushing atmospheric N. Soil total N was not decreased by eP unless N deposition was elevated and the temperature was ambient (Fig. 1B), suggesting that N leaching might be only evident when more N was added to soil. Therefore, change in leaching, if any, might have played a minor role in soil C loss under eP as compared to aP.

Implications and future directions

Our findings have important implications for predicting the ecological consequences of climate change. Long-term eP altered both microbial compositions and functional traits, which differed from short-term effects [START_REF] Docherty | Soil microbial responses to fire and interacting global change factors in a California annual grassland[END_REF][START_REF] Gutknecht | Microbial communities and their responses to simulated global change fluctuate greatly over multiple years[END_REF]. Therefore, the effects of long-term climate change on ecosystems are crucial for future studies [START_REF] Melillo | Long-term pattern and magnitude of soil carbon feedback to the climate system in a warming world[END_REF]

Figure legends Figure 1 .

 legends1 Figure legends

Figure 2 .

 2 Figure 2. The effects of the long-term eP treatment on C degradation genes, viral

Figure 3 .

 3 Figure 3. The phylogenetic tree of bacterial ASVs significantly changed by eP. The

Figure 4 .

 4 Figure 4. The phylogenetic tree of fungal ASVs significantly changed by eP. The inner

Figure 5 .

 5 Figure 5. Stochastic and deterministic factors influencing microbial communities. (a),

Figure 6 .

 6 Figure 6. Biotic and abiotic drivers in regulating soil total C content. (a), The

Table 1 . The consenTRAIT analysis showing phylogenetic conservation of microbial responses to eP.

 1 . In addition, we revealed a potential role of the viral shunt in regulating soil C cycling, underscoring the importance of including soil viruses in microbial analysis. Although numerous studies have reported that eP increases soil C storage, our results demonstrate that long-term eP combined with eCO 2 induced soil C loss in this type of water-limited annual grassland via microbe-plant-soil interplay. Therefore, a long-term increase in precipitation and CO 2

	Kingdom	Response	τ D *	P-value †
		Increase	0.116	< 0.001
	Bacteria
		Decrease	0.063	< 0.001
		Increase	0.190	0.211
	Fungi
		Decrease	0.267	0.004

induced by climate change in some regions could generate a previously unexpected loss of soil C. This could represent an important positive feedback to climate change that has been overlooked so far. However, further research is necessary to determine whether soil C loss and associated regulating mechanisms will persist for longer time scales or in other ecosystems. *τ D is the mean phylogenetic depth at which the response is conserved across clades. †Significance values were estimated using 999 randomizations (P values < 0.050 in bold). A significant value indicates a greater mean depth than randomization, indicating deeper-rooting conservation across clades.

Acknowledgments

The authors wish to thank the staff of the Jasper Ridge Global Change Experiment for site preservation and sampling assistance. This study was supported National Natural Science Foundation of China grant (41825016/32161123002/42007297), Office of the Vice President for Research at the University of Oklahoma, Office of Science and Office of Biological and Environmental Research (DOE-BER) of the U.S. Department of Energy Genomic Science Program grant DE-SC0004601 and DE-SC0010715, the US National Science Foundation grant DEB-0092642/0445324, the Packard Foundation, the Morgan Family Foundation, the Second Tibetan Plateau Scientific Expedition and Research (STEP) Program grant 2019QZKK0503, Guangdong Basis and Applied Basic Research Foundation grant (2019A1515110345/2021A1515011497), Science & Technology Fundamental Resources Investigation Program grant 2019FY100700, the Key Technology R&D Program of Jiangxi Province grant 20223BBG74S02, G. Evelyn Hutchinson postdoctoral fellowship from Yale Institute for Biospheric Studies at Yale University, the Simons Foundation postdoctoral fellowship in Marine Microbial Ecology, the French Institute of Agriculture, Food and Environment Research (INRAE, ECODIV Department), and the French CNRS/INSU -EC2CO Program (project INTERACT).

Data availability statement

The data that support the findings of this study are open available in Zenodo at https://doi.org/10.5281/zenodo.7964426. GeoChip data are available in the NCBI database at https://www.ncbi.nlm.nih.gov/sra, accession number PRJNA419455. Scripts are available at https://github.com/MengmengWang223/Microbial-functional-trait-longterm-precipi tation-JRGCE.

the soil and causing soil nutrient limitation [START_REF] Mason | Evidence, causes, and consequences of declining nitrogen availability in terrestrial ecosystems[END_REF][START_REF] Shaw | Grassland responses to global environmental changes suppressed by elevated CO 2[END_REF].

Consistently, we found that eP in combination with eCO 2 decreased BNPP and even NPP (Fig. 1H &1I). Nitrogen and phosphorus limitation was supported because we revealed enhanced degradation of N-rich compounds (Fig. S6A) and decreased N cycling under eP when CO 2 was elevated (Fig. S7), as well as increased phosphate limitation genes (Fig. S6C). Alternatively, it is possible that eCO 2 decreases evapotranspiration, prolongs the period of water conserved in the soil, and increased soil moisture, as already observed in JRGCE and semi-arid shortgrass steppe of Colorado [START_REF] Nelson | Elevated CO 2 increases soil moisture and enhances plant water relations in a long-term field study in semi-arid shortgrass steppe of Colorado[END_REF][START_REF] Zavaleta | Additive effects of simulated climate changes, elevated CO 2 , and nitrogen deposition on grassland diversity[END_REF], hence enhancing the eP effect on microbial communities and ecosystem functioning.

Warming mitigated eP effects on soil total C and precipitation × CO 2 effects on plant root production and phosphate limitation genes (Fig. 1E, 1I & S4C). This could happen because increased evapotranspiration under warming could reduce water availability and the duration of water conserved in soil. Meanwhile, warming could enhance organic phosphorus and N mineralization to ameliorate nutrient limitation [START_REF] Liu | A global synthesis of the rate and temperature sensitivity of soil nitrogen mineralization: latitudinal patterns and mechanisms[END_REF][START_REF] Shaw | The effects of temperature on soil phosphorus availability and phosphatase enzyme activities: a cross-ecosystem study from the tropics to the Arctic[END_REF], although the increase in N mineralization rate in response to warming has not yet been observed at our study site [START_REF] Gao | Long-term warming in a Mediterranean-type grassland affects soil bacterial functional potential but not bacterial taxonomic composition[END_REF], Niboyet et al., 2011b).

Microbe-plant-soil interplay is essential for mediating eP-induced soil C loss

The eP treatment reduced soil total C in the JRGCE from the 10 th year of the experiment, with only a reduction in the free light fraction of soil organic matter GEO database at https://www.ncbi.nlm.nih.gov/geo/, accession number GSE107168.

MiSeq

data are available in the NCBI SRA

Competing interests

The authors declare no competing interests.


Experimental implementation of acoustic impedance control by a 2D network of distributed smart cells P David, M Collet and J-M Cote

DMA, FEMTO-ST, 24 rue de l' ´Epitaphe, 25000 Besanc ¸on, France

New miniaturization and integration capabilities available from emerging microelectromechanical system (MEMS) technology will allow silicon-based artificial skins involving thousands of elementary actuators to be developed in the near future. Smart structures combining large arrays of elementary motion pixels are thus being studied so that fundamental properties could be dynamically adjusted. This paper investigates the acoustical capabilities of a network of distributed transducers connected with a suitable controlling strategy. The research aims at designing an integrated active interface for sound attenuation by using suitable changes of acoustical impedance. The control strategy is based on partial differential equations (PDE) and the multiscaled physics of electromechanical elements. Specific techniques based on PDE control theory have provided a simple boundary control equation able to annihilate the reflections of acoustic waves. To experimentally implement the method, the control strategy is discretized as a first order time-space operator. The obtained quasi-collocated architecture, composed of a large number of sensors and actuators, provides high robustness and stability. The experimental results demonstrate how a well controlled active skin can substantially modify sound reflectivity of the acoustical interface and reduce the propagation of acoustic waves. source [START_REF] Nelson | Active Control of Sound[END_REF]. Both previous strategies act directly on the acoustical medium by using secondary sources, while the impedance control methodology tends to adjust the acoustical properties of boundary interfaces to induce suitable sound diffusion. However, the implementation of impedance control appears to be very complex due to the necessity of knowing not only the pressure, but also the corresponding velocity at the controlled point.

The classical approaches [START_REF] Furstoss | Surface impedance control for sound absorption: direct and hybrid passive/active strategies[END_REF][START_REF] Guicking | Active impedance control for one-dimensional sound[END_REF] used by many authors studying the implementation of active acoustic impedance, such as Galland et al [START_REF] Galland | Hybrid passive/active absorbers for flow ducts[END_REF][START_REF] Sellen | Passive layer optimization for active absorbers in flow duct applications Ninth[END_REF] for example, are based on the knowledge of the so-called optimal complex impedance, which they tend to implement experimentally using hybrid parietal ANC systems. Their purpose is to locally control a boundary interface to follow the pre-established frequency-dependent complex impedance. Indeed, the total absorption of normal incident waves is described by the simple impedance value Z = ρ 0 c 0 ,w h e r eρ 0 is the density of air and c 0 is the speed

Introduction

In contrast to passive systems [START_REF] Atalla | Acoustic absorption of macro-perforated porous materials[END_REF][START_REF] Ramakrishnan | Design curves for rectangular splitter silencers[END_REF][START_REF] Zheng | Minimizing vibration response of cylindrical shells through layout optimization of passive constrained layer damping treatments[END_REF], an ANC (active noise control) system may be much smaller and lighter, even for low frequency applications, but it loses its efficiency and stability at higher frequencies. A suitable combination of active and passive methods allows us to achieve an interesting compromise between dimensions, weight, and efficiency, and the resulting system proposes better performance over a wide frequency range [START_REF] Kostek | Hybrid noise control in ducts[END_REF].

Common ANC strategies, comprising local and global approaches, generally using some kind of adaptive feedback or feedforward algorithm, have been enriched in recent years by active acoustical impedance control [START_REF] Furstoss | Surface impedance control for sound absorption: direct and hybrid passive/active strategies[END_REF][START_REF] Mazeaud | Developing of an intelligent sound coating for a duct in the presence of flow PhD Thesis Laboratory of Fluid Mechanics and Acoustics[END_REF]. While local control methods consist basically in pressure suppression at particular locations predefined by the placement of error microphones, global methods deal with the reduction of the overall acoustic energy or radiated power of the primary of sound in air. However, since the acoustic waves are not always normally incident, this simple absorption condition has to be modified. The proposed solutions for impedance optimization [START_REF] Galland | Hybrid passive/active absorbers for flow ducts[END_REF][START_REF] Sellen | Passive layer optimization for active absorbers in flow duct applications Ninth[END_REF] lead to theoretical frequency-dependent impedances Z (jω) guaranteeing efficient sound absorption and depending on disturbances, boundary conditions, speed of sound, frequency band, structural interfaces, and geometry. These dependencies prohibit applications in the broadband frequency range and good efficiency is restricted to a specific configuration.

The optimally designed impedance [START_REF] Galland | Hybrid passive/active absorbers for flow ducts[END_REF][START_REF] Sellen | Passive layer optimization for active absorbers in flow duct applications Ninth[END_REF] is a frequencydependent function Z (jω), linking acoustic pressure and velocity. While its experimental implementation allows the control of these parietal quantities by using only the corresponding time operator, it also appears very interesting to introduce a wavenumber dependency so that Z = Z (jω, jk), in order to improve efficiency and versatility [START_REF] Matignon | Smart energy decay for wave equations with damping of fractional order Fourth Int[END_REF][START_REF] Montseny | Diffusive representation of pseudo-differential time-operator[END_REF]. The real-time implementation of such an optimal boundary control involves a complex partial differential operator, with not only time but also space derivatives [START_REF] Triggiani | Exact controllability of the wave equation with neumann boundary control[END_REF]. This approach requires a large amount of system resources (memory and processing speed) and therefore the use of a classical centralized controller (figure 1) is not suitable for practical applications.

To overcome the disadvantages of a centralized system, let us consider the system given in figure 2.I t r e p r e s e n t s a fluid-structure interface covered by a network of sensors and actuators that are connected by an ad hoc electronic circuit. The scheme describes a first order system where signals from two neighbouring sensors are used to control one actuator. This co-localized configuration allows implementation of a complete generalized acoustical impedance Z (jω, jk) involving a first order space operator.

The optimization problem here is to confer acoustic absorption properties on this active surface so that all incident waves, intercepted by the interface under any angle, are reflected the least possible. If the wave is normally incident a simple wall impedance ρ 0 c 0 is obtained. In other cases the impedance is much more complex and known only in the mathematical form of a pseudo-differential operator [START_REF] Montseny | Diffusive representation of pseudo-differential time-operator[END_REF]. The quasi-co-localization between sensors and actuators (figure 2) avoids a robustness problem inherent in closed-loop systems so that the performance and efficiency can be focused. The effectiveness of the system depends mainly on the transducers used but also on the control law connecting them. This law must be distributed in order to avoid the signal dephasing induced by the time delay when a large number of acquisition/control channels is used in the centralized system.

This paper is divided in three parts. The introduction presents a brief summary of active noise control (ANC) methods in the context of acoustical impedance modifications. Section 2 introduces generic methodology for computing a generalized acoustical impedance operator for total absorption of acoustic waves along a straight interface. The obtained complex operator contains space and time differential terms that are discretized in order to implement the control strategy experimentally. The great potential of the method is demonstrated on a simple example with a plane-wave tube, and the numerical modelling is compared with the experimentally obtained results. Finally, section 3 presents the development of a network with a large number of individual smart cells interconnected with the proposed control law. Some experimental results are presented to demonstrate the attenuation capabilities of such an integrated system.

Active impedance boundary control

Derivation of the control law is presented in this article only in a short form, more detailed investigation can be found in [START_REF] Collet | Active acoustical impedance using distributed electrodynamical transducers[END_REF]. Instead of presenting the formal definition of a absorbing boundary operator (generalized impedance operator), we consider the total absorption of acoustic energy contained in a half-plane by optimizing the boundary impedance. This allows us to present a new methodology for designing an interface control strategy on a simple example, nevertheless, the proposed method can be extrapolated to complex systems.

Control problem

First of all let us consider the problem in two dimensions described by the following equations representing the vibroacoustic system in figure 3,w h e r eu(x, t) is the control parameter and m(x, t) is the measured variable:

1 c 0 2 ∂ 2 p ∂t 2 -p = 0o n R x × R - * y × R * + t , (1a)
∂ p(x, 0, t) ∂y = u(x, t), (1b) m(x, t) = p(x, 0, t). ( 1c
)
The system is described by the wave equation (1a)and the measured parameter m(x, t) is the parietal acoustic pressure (i.e. p(x, 0, t)). The control variable u(x, t) is a normal derivative of the acoustic pressure on the control boundary (i.e. ∂ p(x,0,t)

∂ y

). This can be interpreted as a velocity of the active surface interacting with the air. As indicated in figure 3,u(x,t) is proportional to the normal acceleration d(x, t) of the active surface.

We could seek to define a relation u(x, 0, t) = G[m(x, t)] such that the acoustic waves on the boundary y = 0a r e totally absorbed by the active interface. This type of control is asymptotically stable because the energy inside the acoustic domain can only decrease. In general case, the control function for total absorption is given by the following equation [START_REF] Collet | Active acoustical impedance using distributed electrodynamical transducers[END_REF]:

u = G(k x ,ω)m =-2π k x 2 - ω 2 c 0 2 m. ( 2
)
The pseudo-differential operator corresponding to the control

equation (2)i s-∂ 2 y -∂ 2 t .
The interface impedance relationship implies a total wave absorption. This operator is pseudo-differential, non-local in time and space, and also appears difficult to implement on a realistic system. Different mathematical techniques have been introduced for the numerical realization of such pseudo-differential operators as the diffusive representations, presented in the work of Matignon et al [START_REF] Matignon | Smart energy decay for wave equations with damping of fractional order Fourth Int[END_REF].

A concrete realization of such a generalized impedance in real-time through a suitable distributed active system is today unrealistic because of the number and the complexity of necessary calculations. A large part of the research in this domain deals with the implementation of diffusive representations and simplifications that could be carried out [START_REF] Galucio | A fractional derivative viscoelastic model for hybrid u active-passive damping treatments in time domain-application to sandwich beams[END_REF].

Control strategy

The objective of the strategy used is to induce a reflection of the waves intercepted by the active surface so that the reflected wavenumbers k r x are negative. The incidental acoustic energy is thus sent back towards the negative x and the acoustic power flow in the domain is reduced. This condition can be directly extended to control acoustic waves in a tube. The adopted control operator defined in equation ( 2) is represented by the following transport formulation (advection equation) directed to the negative x:

u(x, t) =- 1 c a ∂m(x, t) ∂t - ∂m(x, t) ∂ x , (3)
where c a represents the transportation velocity, which stands for the control parameter and its optimal value is c a = c 0 [START_REF] Collet | Active acoustical impedance using distributed electrodynamical transducers[END_REF].

We seek to impose a solid-state transport with only one direction of propagation. This direction is obviously contrary to that for which we want to minimize the transmittance. This coupling induces only evanescent waves propagating toward the positive x direction, thereby avoiding the existence of any concordance frequency.

By combining equations (1)a n d( 3) and by symmetrization of the system, the controlled behaviour is described by the following equations:

1 c 0 2 ∂ 2 p ∂t 2 -p = 2δ(y) 1 c a ∂m(x, t) ∂t - ∂m(x, t) ∂ x on R x × R y × R * + t , (4a)
m(x, t) = p(x, 0, t), (4b)

+ initial conditions. ( 4c
)
Using the Fourier transforms in time and space, the solution of the system (4) implies that the Fourier transform of the parietal pressure along the active boundary

m(k x ,ω) =m(k x ,ω) j ω c a -k x k x 2 -ω 2 c 0 2 . ( 5
)
So, a non-zero solution exists if and only if

j ω c a -k x = k x 2 - ω 2 c 0 2 (6)
so we get the sufficient condition

2k x 2 - 2k x ω c a + 1 c a 2 - 1 c 0 2 ω 2 = 0. (7)
Thus, if we choose the control parameter c a such that c a 2 c 0 2 /2, we obtain waves with k x > 0 whatever the frequency ω and the incidence angle [START_REF] Collet | Active acoustical impedance using distributed electrodynamical transducers[END_REF]. The obtained active skin behavior also yields a very promising generalized impedance that could be used for acoustic power flow control. The design interface behavior is created by using a standard first order differential operator in time and space (3) that can be discretized and implemented through a distributed set of unit cells. In the next section, the proposed control strategy is implemented on a simple plane-wave tube.

Implementation in a tube

The acoustic system shown in figure 4 represents a simple implementation of the control law in a plane-wave tube. The active zone is composed alternately of seven circumferences of actuators and eight circumferences of sensors. These transducer channels are, in fact, implemented by a parallel distribution of four loudspeakers and four microphones.

Each row of circumferential loudspeakers is controlled by a uniquely applied signal computed by using two measurements picked up by the two adjacent rows of microphones (see figure 2). This distribution allows us to implement a discrete version of the control law given by equation [START_REF] Zheng | Minimizing vibration response of cylindrical shells through layout optimization of passive constrained layer damping treatments[END_REF]. The problem is firstly investigated numerically and the results are then compared with experiments. Only a brief view on the problem is given in this paper with some numerical and experimental results. A more detailed study of the system can be found in [START_REF] Collet | Active acoustical impedance using distributed electrodynamical transducers[END_REF].

Modelling of fluid-structure interaction.

Modelling of fluid-structure interaction is introduced as an influence of the controlled boundary on the surrounding air. The electromechanical coupling effects and the internal dynamics of corresponding internal modes of the loudspeaker's membranes are modelled by the following equation [START_REF] Collet | Active acoustical impedance using distributed electrodynamical transducers[END_REF]:

ρsp di + c sp ḋi + k sp d i + T sp d i = p•l sp + g e v i , (8)
where ρsp is the linear mass distribution of the membrane under a tension of T sp , k sp is the linear distribution of stiffness and c sp is the damping coefficient of the membrane. These mechanical characteristics have been determined from measurements of the micro-loudspeakers used. The external forces are induced by the pressure p exerted over the actuator's length l sp and by the electrodynamic control efforts g e v i (g e represents the static gain of the corresponding electromechanical coupling and v i is the injected voltage).

The global system of PDEs driving the whole coupled axisymmetric problem (fluid, structure, and loudspeaker) is given by the following equations:

y c 0 2 ∂ 2 p ∂t 2 - ∂ ∂y y ∂ p ∂y + ∂ ∂ x y ∂ p ∂ x = 0 on × R * + t , (9a)
∂ p(0, y, t) ∂ x = ω c 0 p c on Ŵ in × R * + t , (9b)
∂ p(x, R, t) ∂y =-ρ 0 di (x, t) on Ŵ i × R * + t , (9c)
∂ p(x, R, t) ∂y = 0o n Ŵ R × R * + t , (9d)
∂ p(L, y, t) ∂ x =- 1 c 0 ∂ p ∂t on Ŵ out × R * + t , (9e)
∂ p(x, 0, t) ∂y = 0o n Ŵ sym × R * + t , ( 9
f ) ρsp di + c sp ḋi + k sp d i + T sp d i = pl sp + g e v i on Ŵ i × R * + t . (9g
) p c = 20 Pa is the acoustic pressure on the input boundary Ŵ in on the left side, R is the radius and L is the length of the tube, Ŵ i is the membrane boundary corresponding to the i th loudspeaker, Ŵ R is a rigid wall, Ŵ out is the Sommerfeld radiation boundary on the right side of the tube, and Ŵ sym is the symmetry boundary. 3) theoretically developed for a 2D semiinfinite domain can be directly applied to control the acoustical flow in the tube. However, to implement the equations onto the distributed set of acoustic transducers, the control law has to be discretized. The spatial discretization of the measured pressure in equation ( 3) is introduced so that p(i dx, t) = p i and the time discretization is given by ∂ p(i dx, t)/∂t =ṗ i . The spatial discretization depends on the distance between each row of microphones, in our case dx = 0.05 m and the actuator length is l sp = 0.04 m. A simple first order Euler approximation scheme of the involved space operator is applied to obtain the control law in the discrete form:

Discrete form of the control equation. The continuous control equation (

∂ p(x, R, t) ∂y =- 1 c a ṗi+1 +ṗ i 2 - p i+1 -p i dx for x ∈[idx,(i + 1)dx]. ( 10
)
The discretization step dx = 5 cm introduces a numerical limitation at a frequency around 3400 Hz, but the time delay of the control loop is even more important parameter which considerably reduces the frequency ceiling. By assuming a monomodal response of loudspeakers, one can directly compute the imposed control voltage v i (t) so that relation [START_REF] Sellen | Passive layer optimization for active absorbers in flow duct applications Ninth[END_REF] is satisfied, hence;

v i (t) =- l sp g e p i+1 + p i 2 + M sp ρ 0 g e l sp 1 c a D p i+1 + p i 2 - p i+1 -p i dx , (11)
D denotes a simple derivative filter to introduce the time derivative operator by the following transfer function:

H D (s) = ω D 3 s (s + ω D ) 3 , (12)
where ω D is a suitably chosen optimization parameter.

Numerical results.

The system of equations (9)h a s been modelled with COMSOL Multiphysics™ software and the postprocessing has been treated in MATLAB ® to obtain the frequency response of the controlled system. The used finite element mesh is discretized so that the element size does not exceed λ lim /4, where λ lim = c 0 / f lim , f lim = 3k H z . I t is important to note that the obtained system is numerically stable. The harmonic calculations have been carried out in the frequency range 0-2000 Hz with a 10 Hz step. Figure 5 shows the pressure field corresponding to the frequency of 1000 Hz, where the control is the most efficient. The Bode diagram in figure 6 represents the acoustic transfer function between the pressure gradient at the source loudspeaker and the acoustic pressure at the output microphone. We note that the system effectiveness is very good in the range of 700-2000 Hz, with significant loss of attenuation even above the frequency limit of plane waves in the f p ≈ 1700 Hz. The attenuation of sound levels rises up to 40 dB at 950 Hz. The considerable damping rate of transducers at the first suspension mode (800 Hz) allows the loudspeaker's membranes to passively absorb energy contained in the frequency band around that of resonance.

It is necessary to underline here that the internal stiffness of the control loudspeakers is a very important dimensioning parameter that makes it possible to qualify the frequency band the system. It affects the control effectiveness, in particular, compared to spillover problems and must be as large as possible.

Experimental results.

The breadboard construction carried out in our laboratory, shown in figure 7, implements exactly the control equations that have been tested numerically. In practice, the real properties of the employed loudspeakers reduced the frequency band with great effectiveness between 700 and 1200 Hz. The limitations are due to the mechanical characteristics of the transducers, especially their first internal eigenmode at 800 Hz. The upper frequency limit at 1200 Hz is caused by the phase lag introduced by time delay of the used signal processor. Our hardware resources (dSPACE ® DS1104 R&D Controller Board) provided seven channels of control loudspeakers and eight channels of microphones to implement the control strategy. Figure 8 compares the numerical results with the measured transfer function between the signal of disturbance applied to the input loudspeaker and the acoustic pressure measured at the output of the tube. Although there is not a perfect correlation between the experimental and numerical results, one qualitatively observes the correct operation of the system compared to the numerical results. The reduction in the acoustic transfer is broadband and the form of the system response is comparable to that obtained theoretically. The amplitude peaks on the experimental curves are caused by a non-ideal anechoic termination, and their frequencies correspond to the stationary wave modes in the tube.

The main aim of this study was not to realize a precise model of the plane-wave tube with our 'handmade' anechoic termination but to qualify the control strategy. It is possible to update the passive behaviour of the numerical model by using experimental data but this work has not been carried out at this stage. Moreover, the simplified model we used allowed us to illustrate the main physical characteristic of the controlled system and to identify the most important design variables: suspension eigenfrequency, time delay of the control loop, transducer's discretization, internal dynamics of the control speakers, etc, which are the basic constraints limiting the efficient frequency band of this adaptive acoustical skin.

The transmission loss is defined as the difference in decibels between the levels of incoming acoustic power upstream and outgoing power downstream when the acoustic treatment is turned on. If reflections of acoustic waves are neglected and only plane waves are assumed, the sound transmission loss can be written as [START_REF] Hilbrunner | Developing and optimization of an active control system for hybrid acoustic absorbers[END_REF] TL = 20 log

p in p out , (13)
where p in and p out are the acoustic pressures upstream and downstream respectively. The sound transmission loss given by equation ( 13) is presented in figure 9 in third-octave bands. The plane waves frequency limit for the this experimental device is 1715 Hz. Relatively high attenuations at low frequencies are caused by the standing waves, which appear even when the control system is turned off. The applied experimental tests confirm the expected functionality in the efficient frequency band without any instability problems. The use of low quality transducers and other electronic components underlines the high robustness of this distributed strategy, which appears as a fundamental property.

Moreover, it has been revealed that the efficient frequency band, here from 700 to 1200 Hz, depends mainly on the time delay of the control loop and on the experimental space discretization of the transducers. Section 3 is dedicated to refine the test bench in order to show up experimentally the influence of the space distribution on the effectiveness of the system.

Active antinoise skin

Completely decentralized implementation of the control strategy with microcomponent technologies is studied in this section. In fact, for the control of audible frequencies, there is no necessity of very high discretization of the transducers network involving microelectromechanical system technology. We need, however, the capability of designing highly integrated electroacoustical devices comprising not only transducers (microphones and loudspeakers) but also a distributed numerical control, enabling an improvement in the architecture and properties, compared to the centralized system. The microelectronic or MEMS technology in this study is not important for developing the transducers but for integrating the control electronics in each separate cell.

The proposed decentralized system is represented by 2D network of individual active cells. Each of these cells integrates its own microcontroller, sensor and actuator, amplifiers and signal conditioning. Implementation of the used control strategy requires that each cell uses its own sensor and the signals from sensors of neighbouring cells. A schematic representation of the network is presented in figure 10. Each actuator is located in the centre between four surrounding sensors. By simple modification of the program introduced to the microcontroller of each cell, it is possible to define the direction of acoustic waves to be controlled (horizontal, vertical and even diagonal orientation). The design includes one master microcontroller to program the whole set of active cells and access the input and output signals of any cell, however, this part has not been yet implemented because of its great complexity and processing speed requirements.

Choice of electronic components

The principal condition for choosing the used components was their dimensions, because of the relatively small space discretization of 30 mm with a theoretical frequency limit of 6.5 kHz. After measuring the frequency responses of several electrodynamic and piezoelectric speakers, a microloudspeaker 0.3W /8 used generally in telecommunication devices was chosen for its best performance/size ratio, however its resonant frequency at 750 Hz cannot offer a significant attenuation at low frequencies. Figure 11 shows the frequency response of the speaker's membrane measured by a laser vibrometer. The speaker has been demounted to access its membrane with a vibrometer when excited by white noise. The choice of the employed miniature microphone 2.2 k /2 V was based simply on its size and linearity requirements in the considered frequency band. The transfer function measured in the plane-wave tube using the used miniature microphone is compared in figure 12 to that obtained by a precision capacitive reference microphone. The differences in frequency response are due to the loss of sensitivity of the miniature microphone at higher frequencies, but the change is linear across the frequency band.

Several parameters of different microcontrollers have been identified before choosing the computing unit for each of active cells. An analysis of principal constraints such as speed, dimensions and resolution of numerical conversion has led to the final choice of an ADuC7026. This 16-bit microchip offers 40 × 10 6 instructions per second, 12-bit A/D and D/A converters, fast programming in C and very small dimensions. Figure 13 shows the measured A/D and D/A conversion linearity of the microcontroller. The output signal is limited by the programming procedure used to avoid amplitude saturation.

Network development

The small space discretization given by 30 mm distance between sensors offers a theoretical frequency limit at 6.5 kHz. This small spacing results in a high degree of miniaturization to allow the fabrication of a network with a large number of cells. Two identical control devices have been built, each composed of 4 × 12 cells, giving (9 × 36) cm of active surface. Each cell can be deactivated separately and all input and output signals and the microphone's calibrating potentiometers can be accessed. Both devices are composed of three layers: (1) a supporting layer with power supply, mechanical support and fixation system; (2) a computing layer with the microcontroller and (3) an active layer with transducers and their supporting circuits (amplifiers and signal conditioning). In figures 14-16 are close-ups of one cell and a general view of the assembled active device.

The experimental set-up is composed of a chipboard tube with rectangular cross-section, an audio amplifier with source loudspeaker on the input, two devices with active surfaces and non-reflecting acoustic termination on the output. The general view of the measurement device is presented in figure 17. The wooden material offers sufficient rigidity and robustness while offering simplicity to work with. The inner dimensions of the tube are (90 × 135 × 1500) mm. It consists of three separable segments that facilitate the demounting or replacement of the active surface. The primary excitation is made by a quality loudspeaker with 8 cm diameter. The acoustically transparent termination at the output of the tube reduces the effect of eigenmodes caused by internal steady waves. As the first transversal mode eigenfrequency is at 1270 Hz, the measurement device is theoretically prepared for controlling even non-plane waves.

Validation of the cells

Firstly, all cells have been demounted and each microphone has been calibrated with a pistonphone to the level of 76 dB. Then, the control law has been sent into one of the cells and the output on the control speaker has been tested. Sinusoidal signals of the same frequency but with different phase shift on the microphones have permitted the validation of the output signal. After several program adjustments, the correct form and phase of the output signal have been found. The time delay of the control loop, caused mainly by four successive A/D conversions of the input signals from the microphones, has been identified as 90 µs. This period corresponds approximately to 11 kHz and consequently, the output signal from the controller is entirely in opposition of phase for frequencies around 5.5 kHz. However, the signal de-phasing is already large enough at 2.5 kHz and the efficiency loss of the control algorithm is expected even below this limit.

In the next step, the network has been assembled and inserted in the tube. With a sinusoidal excitation of several frequencies on the input loudspeaker, all microphone signals have been displayed on the oscilloscope. Each cell has then been programmed to identify the global behaviour of the system. Figure 18 presents a progressive amplitude reduction and phase change as the primary 1 kHz sinusoidal perturbation propagates along the microphone channels from the input to the output.

Experimental results

Only the acoustic transfer functions of the system were studied at this first stage of experimental investigation. Precision acoustic microphones in the input and output segment have enabled the measurement of the frequency response function of the system with and without control. Input excitation on the primary loudspeaker is a white noise in the frequency band between 0 and 5 kHz.

Firstly, we have tested the passive attenuation of the system when the control algorithm is turned off. In figure 19 is shown a comparison of the attenuation when rigid walls are inserted in the tube instead of the active surfaces. It can be seen that the simple replacement of rigid walls by the active system, even without control, brings a significant reduction of the acoustic level. The attenuation effect up to 8 dB is important, especially at low frequencies, where the control speakers cannot offer significant results because of their electromechanical properties (first suspension mode). The almost linear phase evolution confirms correct propagation of the sound wave along the tube.

Figure 20 presents the results when the control system is activated. In addition to passive attenuation at low frequencies, the effect of the control law appears at intermediate frequencies with the maximum of 30 dB in amplitude reduction. The efficient frequency band of the active system is situated between 800 Hz and 1.5 kHz. The lower limit is caused by the first eigenmode of the control speaker and the higher limit by the time delay of calculation process, which becomes more important and leads to the control algorithm losing its efficiency. Nevertheless, there is a significant attenuation even for non-plane waves above 1200 Hz. It is important to note that the total power consumption of the whole system under control does not exceed 30 W, which is negligible compared to other types of fully distributed acoustic control devices.

In figure 21 is shown the sound transmission loss of the control device. The plane waves in this system occur for frequencies below 1270 Hz. In comparison with the previous control device (figure 9), the levels of acoustic power attenuation are more uniform through all the considered frequency band.

Conclusion

This paper shows the development and certain numerical and experimental results obtained by a new distributed control system, completely different compared to other methods used up to now.

A new methodology for designing control strategies based on a distributed transducer network is presented. With the objective of controlling the acoustic energy transfer through a tube, it has been demonstrated on a simple example the type of results that can be obtained. The numerical modelling has been validated by experimental results. Although these results show clearly the potential benefits, they also present the difficulties of setting up the experimental realization, especially the time and space discretization and electromechanical properties of the actuators used. The obtained results are nevertheless very encouraging, and the robustness, stability and simple implementation of the control law show the potential of such a method.

The presented system has the great merit of being very effective and allows an important attenuation of the acoustic transfer without the necessity of very strong displacements of the membrane interfaces [START_REF] Collet | Active acoustical impedance using distributed electrodynamical transducers[END_REF]. It is thus possible to use this technique with transducers produced on a silicon base with thin deposits of PZT layers as actuator elements, so the proposed method appears to be suitable for use with distributed MEMS transducers to reduce noise over a large frequency band.

We have presented the development of individual cells with an integrated microcontroller, sensor and actuator, power supply, signal amplification and conditioning, and especially the possibility of interconnection of many such cells in the area network, a so-called active antinoise skin. The distributed control algorithm of every cell uses as input signal its own sensor and several sensors from neighbouring cells, which is necessary for the implementation of spatial operators. The cells, as well as the entire network, have been validated before testing the global behaviour of the entire system. It has been revealed that the critical parameters for experimental implementation are particularly the first suspension mode of the control speakers and the time delay introduced by the calculation loop. The experimental results clearly show the great potential of this approach, further experimental investigation is however necessary to determine all the system properties and limitations.

Figure 1 .

 1 Figure 1. Centralized control system.

Figure 2 .

 2 Figure 2. Distributed quasi-collocated system of the 1st order.

Figure 3 .

 3 Figure 3. Acoustic waves interacting with the active surface.

Figure 4 .

 4 Figure 4. Modelled vibroacoustic system.

Figure 5 .

 5 Figure 5. Controlled and uncontrolled pressure distribution, frequency 1000 Hz.

Figure 6 .

 6 Figure 6. Transfer function between the input and output acoustic pressure, numerical results.

Figure 7 .

 7 Figure 7. Experimental set-up.

Figure 8 .

 8 Figure 8. Comparison of transfer functions obtained numerically and experimentally.

Figure 9 .

 9 Figure 9. Sound transmission loss in 1/3 octave bands, experimental results.

Figure 10 .

 10 Figure 10. Schematic view of the network design.

Figure 11 .

 11 Figure 11. Frequency response of the control speaker's membrane.

Figure 12 .

 12 Figure 12. Comparison of the used miniature microphone with a precision reference microphone.

Figure 13 .

 13 Figure 13. Linearity of the microcontroller's converters.

Figure 14 .

 14 Figure 14. Face side of the cell.

Figure 15 .

 15 Figure 15. Underside of the cell.

Figure 16 .

 16 Figure 16. General view of 4 × 12 cells.

Figure 17 .

 17 Figure 17. Experimental set-up.

Figure 18 .

 18 Figure 18. Amplitude and phase on different channels of microphones.

Figure 19 .

 19 Figure 19. Transfer function between the input and output microphone, -active surfaces without control; •••chipboard rigid walls.

Figure 20 .

 20 Figure 20. Transfer function between the input and output microphone, -active surfaces with control; •••without control.

Figure 21 .

 21 Figure 21. Sound transmission loss in 1/3 octave bands, experimental results.