Forest liming in the face of climate change: the implications of restorative liming on soil organic carbon in mature German forests

Forest liming is a management tool that has and continues to be used extensively across northern 12 Europe to counteract acidification processes from anthropogenic sulfur and nitrogen (N) deposition. In this study, we quantified how liming affects soil organic carbon (SOC) stocks and attempt to 14 disentangle the mechanisms responsible for the often-contrasting processes that regulate net soil carbon (C) fluxes. Using a paired-plot experimental design we compared SOC stocks in limed plots with 16 adjacent unlimed control plots at 28 experimental sites to 60-cm soil depth in mature broadleaf and coniferous forests across Germany. Historical soil data from a subset of the paired experiment plots 18 was analyzed to assess how SOC stocks in both control and limed plots had changed between 1990 and 2019.


Introduction 42
Millions of hectares of forest have been limed in Germany and across northern Europe over the last few decades to counteract soil acidification processes derived from anthropogenic sulfur (S) and 44 nitrogen (N) deposition. Soil acidification is responsible for hindering organic matter decomposition processes and concomitantly immobilizing nutrients and carbon (Shen et al., 2021).The application of 46 lime on acidic soils, as either calcium carbonate (CaCO3) or dolomite (CaMg(CO3)2) elicits a strong biochemical response by lowering soil acidity, reducing both aluminum (Al) and manganese toxicity 48 and increasing the soil's buffering capacity. These changes subsequently drive a cascade of ecosystem responses, with implications on soil fertility, forest productivity, stand vitality and litter decomposition 50 (Derome et al., 2000, Kreutzer, 1995, which in turn correspondingly affect the ecosystem carbon (C) balance (Melvin et al., 2013;Persson et al., 2021) and soil greenhouse gas (GHG) budgets. The direction 52 and magnitude of ecosystem responses to liming depends on numerous factors, including: (1) the inherent soil characteristics of the site (soil acidity, soil texture, the chemical make-up of the forest 54 floor layer), (2) vegetation characteristics (species distributions, tree density, and stand age), (3) the application of lime (type and quantity of lime, and frequency of liming) and (4) the ongoing acidification 56 from recent N and S deposition. In this context, both above-and below-ground carbon stocks have been shown to have quite variable responses to liming (Court et al., 2018;Lundström et al., 2003;58 Melvin et al., 2013;Persson and Ahlström, 1990;Persson et al., 2021).
While it is broadly reported that liming stimulates soil microbial activity leading to accelerated soil 60 organic matter (SOM) decomposition Nilsson, 2001, Kreutzer, 1995), some studies report either no change in litter and forest floor decomposition (Smolander et al., 1996) or even forest 62 floor organic matter accumulations (Derome et al., 2000;Melvin et al., 2013). Soil organic carbon (SOC) stock gains as a result of liming can be attributed to different drivers. First, earthworm abundance is 64 known to increase after liming (Persson et al., 2021) which, by actively incorporating and binding SOM with the mineral soil improves physical properties, such as soil structure and aggregate stability 66 (Bronick and Lal, 2005). Second, physicochemical properties are also affected. Liming-induced changes in nutrient-stoichiometry may enhance cation mediated cross-linking between SOM compounds and 68 divalent calcium (Ca) or magnesium (Mg) ions (Kalbitz et al., 2000) thereby stabilizing soil carbon. It has also been shown that higher soil Ca availability increases lignin contents in leaf litter which makes 70 litter more recalcitrant and resistant to decomposition (Eklund and Eliasson, 1990;Xing et al., 2021).
Third, liming will affect microbial community structure and abundance, which has the potential to 72 create nutrient imbalances (such as phosphorus) on decomposer communities and trees (Melvin et al., 2013) which in turn may decrease microbial breakdown of SOM. Lastly, liming-induced improvements 74 in nutrient availability (Jansone et al., 2020;Long et al., 2015), may increase ecosystem productivity which correspondingly can increase SOM inputs from aboveground (e.g. leaf litter (Lin et al., 2015)) 76 and belowground sources (e.g. root detritus).
In this study, we quantified the magnitude of SOC stock changes resulting from forest liming activities, 78 with the explicit intent to better understand the implications of liming on soil organic carbon and forest soil greenhouse gas (GHG) budgets. Given the lack of a consistent direction in which SOC stocks 80 respond to liming as reported in literature, we attempted to disentangle the mechanisms responsible for the often-contrasting processes that regulate net carbon fluxes in the soil. Here, we also assessed 82 liming effects across different time scales, ranging from the immediate effects liming has on soil carbon dioxide (CO2) production, to methane (CH4) uptake, to long-term changes in soil carbon stocks 84 measured several decades after liming. The study was implemented at experimental sites in managed mature forests across Germany using both space-for-time substitution and chronosequence 86 approaches.
We hypothesized that liming-induced changes in SOC stocks will be most pronounced at the soil 88 surface. More specifically, we expect that there will be significant decreases in the forest floor layer C stock because SOM decomposition will be stimulated by reduced pH levels. However, these C losses 90 will be offset if not exceeded, by significant gains in SOC stocks in the topsoil because of improved ecosystem productivity, increased fine root biomass in the upper mineral soil horizons and increased 92 earthworm activity, which will improve soil structure thereby protecting SOM from mineralization.

Experimental study sites
Liming effects on soil organic carbon stocks were determined at 28 liming experiment sites distributed 96 across Germany ( Figure A1). All sites consisted of mature forest stands whereby all, except one (HLI 2680) were managed, meaning these sites were occasionally selectively harvested. Lime was applied 98 in different forms (dolomite (CaMg(CO3)2) and calcium carbonate (CaCO3)) and in differing quantities, ranging from a total between 2-9 tons per hectare spread over multiple application dates (Table 1). 100 The last lime application at most sites was typically 20 to 30 years prior to our sampling, and therefore findings reflect the long-term effects liming has on belowground carbon. The experiment was 102 conducted using a paired plot design, where each site consisted of a limed plot adjacent to a control plot which was not limed. In total, for this analysis, we sampled nine sites with European beech (Fagus 104 sylvatica L.), two with common oak (Quercus robur L.), 16 with Norway spruce (Picea abies L. karst.) and one European red pine (Pinus sylvestris L.) site. General site characteristics are described in Table  106 1. At two spruce sites (GOH 155, SEG 244) we only had data from the forest floor layers, and not the mineral soil as soil bulk density data were unavailable. Nitrogen deposition was ascertained from the 108 German Environment Agency (Umweltbundesamt, 2019).

Soil organic carbon stocks
We collected soil and forest floor samples from both limed and control plots from each site at four 114 locations distributed around the plot. Samples were taken from the forest floor (L/Of and Oh) as well as from the mineral soil at four predefined depths (0-5, 5-10, 10-30 and 30-60 cm). Samples of the 116 forest floor and the topsoil (0-30 cm) were taken using a root auger (diameter 8 cm) and samples of the subsoil (30-60 cm) using a gouge auger (diameter 3 cm). At each of the four sampling locations per 118 plot, three samples were taken in close proximity to another for each depth and pooled. Forest floor samples were subsequently oven dried at 60 °C, sieved (2 mm) and ground. Mineral soil samples were 120 oven dried at 40 °C, sieved (2 mm) and also ground. Both forest floor and mineral soil samples were then analyzed for carbon (C) and nitrogen (N) contents using a CN analyzer (Euro EA -CN Elemental 122 Analyzer, HEKAtech GmbH, Wegberg, Germany). Carbonates were measured in soil samples that had a pH (H2O) greater than 6.2. This however consisted of just 21 samples (<2% of the complete dataset), 124 and carbonate contents were a fraction of total soil carbon. Sieved forest floor and mineral soil samples were also analyzed for pH in a 1:2.5 H2O solution and mineral soil samples for exchangeable cations 126 (Ca, Mg, K, Na, Al, Fe, Mn) using an ICP-AES instrument (Thermo Scientific iCAP 7400 Radial, Thermo Scientific, Dreieich, Germany). Base saturation was calculated as percentage exchangeable base 128 cations of the effective cation exchange capacity (ECEC). Soil texture was determined using the pipette method at 16 experiment sites. 130 Soil bulk density and the mineral soil dry mass per unit area was determined using a modified version of the Blake and Hartge (1986) core method. Samples were taken at four soil pits per plot for the same 132 respective depths where samples were taken for chemical analysis. Depending on the size and relative abundance of stones observed in the soil profile, different approaches were employed to estimate the 134 bulk density of the soil fine-fraction. Methods and equations are described by König et al. (2014). All samples were oven dried at 105 °C for 48 hours and subsequently weighed. Volumes of coarse 136 fragments were determined using the volume displacement method. For the mineral soil, we calculated the fine earth soil mass per unit area for each respective sampling layer as follows: 138 Fine earth mass per unit area = BD * (1-stone content) * d * 10 (1) Where, fine earth soil mass per unit area is in kg m -2 , BD is the soil bulk density in g cm -3 , stone content 140 is relative volumetric coarse fragment content, d is the thickness (depth) of the sampling horizon in centimeters and 10 is a conversion factor for converting g cm -2 to kg m -2 . 142 The organic layer dry mass per unit area was determined at the same four sampling locations where the samples for the chemical analysis were collected using a root auger (diameter 8 cm). The organic 144 material from within the auger was collected and separated into the two forest floor layers (L/Of and Oh). Roots and plant debris larger than 2 cm in size were removed from the sample, whereupon 146 samples were oven dried and weighed (König et al., 2014): Organic layer dry mass per unit area = (MH *100) / SA *10 (2) 148 whereby, organic layer mass per unit area is in kg m -2 , MH is the dry mass of the organic layer in grams, and SA is the surface area that was sampled in cm 2 , and 10 is a conversion factor for converting to kg 150 m -2 . Mineral and forest floor organic carbon stocks were calculated as follows: whereby, SOC stock is in Mg C ha -1 , OC is the organic C content in g kg -1 , MuA is the mass per unit area in kg m -2 , and 100 is a conversion factor for converting to Mg C ha -1 . 154 SOC stocks in the limed plots were corrected for fixed-depth differences incurred because of liminginduced changes in soil bulk density ( Figure A2) by using the equivalent soil mass (ESM) approach 156 described by Wendt and Hauser (2013). This approach fits a cubic spline curve of cumulative organic carbon stocks with the corresponding soil mass of the reference profile. 158 Effects of liming were evaluated using two approaches. First, the difference in soil C stocks between limed and control plots were calculated to assess the relative differences. Second, a chronosequence 160 approach was used to assess temporal changes in soil C stocks using historic data, between 1990 and 2019, collected at a subset of the paired experiment sites (forest floor: n = 17, mineral soil: n = 13). 162 Table S1 shows the years when forest floor and mineral soil samples were collected. The change in SOC stocks over time was estimated by calculating the slope of a linear best fit function of the SOC stock 164 values over time. In this analysis, we assumed that soil density did not change during this time and accordingly we used bulk density estimates from the most recent measurement date. 166

Short term effects of liming on soil CO2 and CH4 fluxes
Soil carbon dioxide (CO2) and methane (CH4) fluxes were measured at three beech forest sites (Dassel 168 4227 (DAS 4227), Sellhorn 34 (SEL 34), Göhrde 157 (GOH 157)) in both control and limed plots to assess both short and long-term effects of liming. All three sites were freshly re-limed with an equivalent of 170 3 Mg CaCO3 ha -1 in August-September 2020. Accordingly, the measurements made after these liming events reflect the short-term effects of liming on soil respiration and soil methane fluxes. The soil trace 172 gas fluxes were measured using the vented static chamber method. Round chamber bases (polyvinyl chloride, covering a ground area of 0.07 m 2 ) were inserted 1-2 cm into the soil surface at four randomly 174 locations within each plot. These chamber bases were covered with polyethylene lid (∼22 L headspace volume), from which gas samples were collected at 20-minute intervals for one hour (2, 22, 42 and 62 176 minutes) and stored in pre-evacuated 12 mL Labco Exetainers® (Labco Limited, Lampeter, UK). To minimize effects from diurnal fluctuations we randomized the order the plots were measured during 178 each measurement campaign. Gas samples were analyzed using a gas chromatograph (GC, SRI 8610c, SRI Instruments, Torrance, USA), equipped with a flame ionization detector to measure CH4 and CO2. 180 The latter gas species was analyzed by converting it to CH4, using a built-in methanizer in the GC. The GC was calibrated prior to each analysis using three calibration gases (Deuste Steininger GmbH, 182 Mühlhausen, Germany), spanning the concentration range of the field samples. Soil gas fluxes were calculated using the ideal gas law, based on the linear increase of gas concentrations in the chamber 184 over time and corrected with air temperature and atmospheric pressure measured at the time of sampling. A positive flux indicates a net emission, while a negative flux indicates a net consumption. 186 In parallel to the greenhouse gas flux measurements, we also measured air pressure, soil and air temperature and chamber volume during each measurement. 188 In early September 2020, we measured soil CO2 and CH4 fluxes at one site (DAS 4227) three times in the week prior to lime application (on Sep 7, 2020) to evaluate baseline fluxes and determine whether 190 there were long-term effects of previous liming events still evident. After liming, we measured GHG fluxes weekly for two months (to Nov. 3, 2020) to evaluate immediate effects of the liming. 192 Subsequently, in the spring of 2021, we resumed gas flux measurements on a bi-weekly basis at the DAS 4227 site, and additionally also commenced soil GHG measurements at the two other sites (SEL 194 34, GOH 157). These measurements were made from Mar. 11, 2021 to Jul. 8. 2021.

Calculation of lime-derived CO2 emissions 196
The proportion of lime-derived CO2 to the overall CO2 flux, was determined using δ 13 C stable isotope approaches and a two-pool mixing model at the same three sites where soil GHG fluxes were 198 measured. Unlike the soil GHG measurements, we collected gas samples for δ 13 CO2 analysis every second measurement campaign. Samples were collected two minutes and 62 minutes after chamber 200 closure. The 13 C signature of newly formed CO2 (δn) between time point t = 1 (2 minutes; δ1) and t = 2 (62 minutes; δ2), and the newly formed CO2 fraction at t = 2 is given by the following mass balance 202 equation (Martinson et al., 2018): The fraction of lime-derived CO2 to total CO2 emissions is calculated following the two-pool mixing model under the assumption that (1) biologically-derived 13 CO2 is equal between limed and unlimed 206 plots and (2) CO2 from lime carbonates and from lime-induced respiration is in isotopic equilibrium: 208 whereby, δ is the isotopic signature of 13 CO2 from limed plots, δ0 the isotopic signatures of 13 CO2 from unlimed plots, δ1 the isotopic signature of lime. 210 The carbon isotope signature (δ 13 C) of CO2 was determined by isotope ratio mass spectrometry after gas chromatographic separation, the δ 13 C of the added lime was analyzed using an isotope ration mass 212 spectrometer coupled to an elemental analyzer, both at the Centre for Stable Isotope Research and Analysis (KOSI) at the University of Göttingen. 214

Statistical analysis 216
Liming effects on SOC stocks at each soil depth were tested using linear mixed effects (LME) models (Crawley, 2013). In these models, the C stock was the response variable, the treatment (control, limed) 218 was the fixed effect, and the site was the random effect. For the soil trace gas flux measurements, the treatment was considered a fixed effect and the measurement date were considered random effects. 220 Significance levels were tested separately for each site. Differences were considered significant if P ≤ 0.05 and marginally significant if P ≤ 0.1. The input C stock data as well as the output model 222 residuals were tested for normality using Shapiro-Wilk test. To gain an insight into the underlying factors regulating C stocks in the control (unamended plots) and the relative changes in C stocks as a 224 result of liming, we used Spearman's rank correlation analyses to assess how C stocks correlated with climatic parameters, stand parameter as well as the inherent soil properties (of the control plot) and 226 the liming induced changes in soil properties (difference between limed and control plots). The goodness of fit of the non-linear best-fit models were assessed using Pearson correlation analyses 228 between model-predicted values and measured values. All statistical analyses were carried out using R, version 4.0.02 (R Core Team, 2020). 230

SOC stocks in the control plots: magnitude and drivers
There was a large variability in SOC stocks across the experimental sites, ranging between 49 and 366 234 Mg C ha -1 (forest floor to 60 cm, in the control plots). In the soil profile, SOC content was highest in the forest floor layer and decreased with soil depth ( Figure S1a). In the control plots, 23 % of the total SOC 236 stock was found in the forest floor layer, 27 % in the topsoil (0-10 cm), and the remaining 50 % was found below 10 cm depth (10-60 cm) ( Figure S1b). Soils under coniferous forests stored approximately 238 38 % more carbon than broadleaf forests (conifer: 157 ± 17 Mg C ha -1 (mean ± standard error (SE)), broadleaf: 97 ± 9 Mg C ha -1 ), where differences were most pronounced in the forest floor L/Of horizon 240 and below 10 cm soil depth. Soil bulk density was lowest at the soil surface (0-5 cm) and increased with soil depth. SOC stocks in the mineral soil correlated significantly with soil chemical and physical 242 properties, but not with climatic variables such as temperature, precipitation, or elevation (Table S2).
In the forest floor layers, SOC stocks were correlated with both N deposition and pH. For the latter, 244 there was an exponential decrease in the SOC stocks with increasing pH (Figure 1), where, particularly in the L/Of layer, there was large decline in SOC stocks when pH increased from 3.5 to 4.5. Next, N-246 deposition exhibited a significant positive correlation with SOC stock in the L/Of horizon, whereby these effects were only evident in coniferous forests ( Figure A3a). This trend was largely driven by the 248 strong linear correlation present between C content and N deposition ( Figure A3b), and although the mass of the L/Of horizon correspondingly increased with N deposition, the most increases were only 250 consistent when N deposition was higher than 25 kg N ha -1 yr -1 (n = 4) ( Figure A3c).

258
In the mineral soil, SOC stocks correlated with soil texture fractions. This was evident in the significant negative correlations between SOC stock and sand contents at 0-5 cm and 5-10 cm, as well as the 260 positive correlation with clay content at 10-30 cm (Table S2). In the subsoil (30-60 cm), SOC stocks exhibited a similar exponential decay relationship with soil pH as the forest floor layers (data not 262 shown).

SOC stock response to liming: chronosequence approach 264
At a subset of experimental sites where historical data were available, most dating back to 1990 (Table   S1), forest floor C stocks in the control plots increased in time (0.5 ± 0.1 Mg C ha -1 yr -1 ; Figure 2a), 266 whereby the increases were largely driven by C accumulations at coniferous forest site (0.8 ± 0.3 Mg C ha -1 yr -1 ). Although forest floor SOC stocks in the limed plots also increased over time, the accumulation 268 rates in the L/Of horizon were significantly lower than the control (Figure 2b). In the mineral soil, there were no significant changes in SOC stocks at any depth during this period. Nevertheless, when C stock 270 change rates were compared between limed and control plots, liming did bolster C accumulation rates slightly at 5-10 cm depth. 272 Figure 2: Average (± 95 % T-test-confidence interval) annual changes in SOC stocks experienced over 274 the last two decades in a) both the control and limed plots and b) the difference between the limed and control plots. Statistical significance was tested using LME models for each respective soil depth 276 or layer at P ≤ 0.05 (*).
The liming quantities which are responsible for the changes in soil pH, exhibited a negative linear 292 relationship with SOC stock changes ( Figure A4), indicating that higher liming dosages result in larger SOC losses. In the forest floor layer, the proportion of C losses or C gains (at a few sites) could further 294 be explained by the initial C stock present on the site (control plot C stock), whereby the C losses were largest at sites with medium amounts of stored C (between 20 and 35 Mg C ha -1 ), and less pronounced 296 (or even positive) at sites with either little or large C stocks present in the reference state (Figure 4e). Mg C ha -1 ). LAU75 is Lauterberg 75 and RAN50 is Rantzau 50.

308
Overall, there were no significant changes in mineral SOC stock at any depth (Figure 3a), when all sites are pooled together. Unlike coniferous forests, broadleaf forest plots (n = 11) exhibited significant 310 increases in SOC stock in the topsoil (0-5 cm) (3.5 ± 1.9 Mg C ha -1 , Figure 3b). While it was not significant for SOC stock changes (Table S3), changes in soil C content hinged on the inherent (control) C content 312 ( Figure A5). In the mineral soil, the experimental sites that initially had low C contents exhibited increases in C, while sites with already high C contents exhibited decreases. Accordingly, when sites 314 were classified as having either inherently high C contents (>5.5 % at 0-5 cm, n = 9) or inherently low C contents (<5.5 % at 0-5 cm, n = 17), large differences in SOC stocks between the two categories 316 became evident in soil profile (Figure 3c). Namely, SOC stocks increased significantly at sites which inherently had low C contents in the control plots (C content <5.5 % at 0-5 cm, Figure 3c). Here, gains 318 in mineral SOC stocks (0-60 cm) were significantly higher than zero (13.1 ± 4.7 Mg C ha -1 ), although these gains were partially offset by the SOC losses in the forest floor layers (-10.6 ± 5.6 Mg C ha -1 ). 320 Conversely, the sites that inherently had high SOC contents in the control plots (C content >5.5 % at 0-5 cm), did not exhibit significant changes in SOC stock at any soil depth throughout the profile, whereby 322 there was a tendency to have SOC losses throughout the profile (forest floor: -5.6 ± 3.5 Mg C ha -1 , mineral soil 0-60 cm: -16.4 ± 3.8 Mg C ha -1 ). Next, SOC stocks significantly increased in the 0-5 cm layer 324 in sandy sites (<50 % sand, Figure 3d), while sites with higher clay and silt fractions exhibited no change in SOC stocks at any depth. In both the forest floor Oh horizon and at 0-5 cm depth, soil C:N ratios 326 decreased significantly as a result of liming ( Figure S2).

Liming effects on soil CO2 and CH4 fluxes in beech forests 330
The soil greenhouse gas flux measurements made prior to re-liming at the DAS 4227 site (indicative of the long-term effects of liming) showed that (1) there were no significant differences in soil respiration 332 rates between limed and control plots (P = 0.49, Figure 5a), but that (2) methane uptake was twice as high in the limed plots compared to the control (P < 0.01, Figure 5d-f). Immediately following the re-334 liming, soil CO2 fluxes increased and remained consistently higher than the control (P < 0.01, Figure 5a) for the duration of the measurements. Soil methane uptake on the other hand did not respond to the 336 liming application, and remained consistently lower than the control (P < 0.01 Figure 5d).  (Figure 5b). Overall, soil methane uptake was significantly higher in the limed 354 treatments (P < 0.01) and was on average two times higher than the control at all three sites ( Figure   5d-f). 356 Using a stable isotope analysis approach, the overall contribution of lime-derived CO2 was low, averaging 2.7 % of the total CO2 flux in the first two months after lime application at the DAS 4227 site. 358 At this site, there was only one short-lived lime-derived CO2 pulse immediately after a rewetting event five days after liming (Figure 5a) which accounted for 23 % of total (biotic and abiotic) CO2 emissions. 360 The lime-derived CO2 contribution remained negligible the following spring when we measured at the three sites, averaging 0.7 ± 0.5 % (n = 3) of the total CO2 flux. 362 4. Discussion 364

Liming effects on organic C stocks in the forest floor layers
Over the last three decades, forest floor C stocks have gradually been accumulating in both the limed 366 and control plots (Figure 2a), with increases most being pronounced at coniferous sites. These gains likely reflect the influence of elevated N depositions (among other factors) that can (1) enhanced tree 368 growth which accordingly increase litter inputs (Court et al., 2018, Van der Perre et al., 2012 and/or (2) constrain organic matter decomposition rates (Knorr et al., 2005). The effects of N additions were 370 particularly evident at our coniferous forest plots where sites with higher N deposition had larger forest floor carbon accumulations over time ( Figure A3). 372 Considering the biochemical environment plays an intrinsic role in many soil biological processes (Andersson and Nilsson, 2001;Persson et al., 2021;Melvin et al., 2013), changes in soil pH from liming 374 can and will cause a cascade of responses that concomitantly affect the net soil C balance. In the temporal (chronosequence) analysis, the small absolute gains in the forest floor C stocks measured in 376 the limed plots over time ( Figure 2a) were significantly lower than those measured in the unlimed control plots (Figure 2b), highlighting how lime applications have (in the majority of sites) promoted 378 organic matter mineralization and offset forest floor OM accumulations. Since overall C stock gains were comparatively minor (in relation to the control), it indicates that lime applications here helped 380 maintain stable organic matter decomposition and nutrient cycling rates.
These results are further substantiated in the paired approach analysis, where a larger number of plots 382 were included (Figure 3a). Although this analysis partly contrast the findings reported by the German National Forest Soil Inventory (which showed that liming decreased forest floor C stocks while unlimed 384 plots remained unchanged over time (Grüneberg et al., 2019)), both of these studies show the same relative trends: namely that liming stimulates organic matter mineralization. This too is corroborated 386 by most other studies (Court et al., 2018;Kreutzer, 1995;Marschner and Wilczynski, 1991;Persson et al., 2021), whereby some publications (Derome et al., 2000;Melvin et al., 2013) have reported the 388 opposite, namely that under certain conditions liming can actually increase soil C stocks.
In this study, we found a clear exponential relationship evident between forest floor C stocks and forest 390 floor layer pH (Figure 1), namely poor sites with acidic pH had high C accumulations in contrast to sites with higher pH that had lower C stocks. In conjunction with increased microbial-induced SOM 392 mineralization, it is also likely that increases in earthworm activity, which is known to increase with liming (Persson et al., 2021), will have assisted the breakup of the litter and the mixing of the organic 394 matter with soil particles and microorganisms throughout the soil layer (Kreutzer, 1995, Persson et al., 2021. Next, the improvements in forest floor composition and morphology were also visually evident 396 at six of the 28 experimental sites, where the humus-form classification improved along the moder to mull gradient. Similarly, at seven sites, the application of lime meant that the humic horizons (Oh) 398 either did not develop or perhaps were lost over time, indicative of comparatively faster organic matter mineralization rates and/or earthworm bioturbation. Next, there was also an additive effect of the 400 lime quantity on C stock, where higher lime applications translated to larger differences in C stocks with the limed plots (Siepel et al., 2019, Figure A4). 402 The proportional net change in forest floor C stocks, either C losses or C gains (which were observed at a few plots) could best be explained when put in the context of the C stock present in the control 404 plot. This is because the inherent forest floor C stock (in the control plots) is a good measure of organic matter stability showing the integral effect of different biochemical drivers (such as pH and litter 406 quality) that regulate SOM breakdown. For instance, sites with high C stocks had correspondingly acidic pHs (Figure 4a), high C:N ratios (Figure 4b), and both high C contents ( Figure 4c) and high SOM mass 408 ( Figure 4d). This contrasts those sites with inherently low forest floor C stocks which had higher pH, low C:N ratios, low C contents and thin organic matter layers. When we use the C stock of the control 410 plots as a measure of carbon bioaccumulation, we see that liming effects on forest floor C stocks are most pronounced at sites with intermediate amounts of carbon (18-35 Mg C ha -1 ), and less prominent 412 at the other ends of the index (Figure 4e). First, liming additions to sites which had inherently low forest floor C stocks (characterized by thin SOM layers and high pH) exhibited only small proportional 414 losses in overall C stocks (Figure 4e). This minor response is because these sites already had relatively high pH values and the addition of lime did not change the biogeochemical environment dramatically, 416 and accordingly there were no large changes in forest floor C stocks. Next, further along this carbon accumulation gradient, sites with intermediate amounts of carbon exhibited large C losses (up to 75 % 418 decreases). This is because the application of lime improved the biochemical environment for microbial communities thereby stimulating organic matter decomposition, which led to strong C losses 420 at these sites. Finally, sites which have inherently high forest floor C stocks, the application of lime had an increasingly muted effect on C losses, ultimately leading to negligible changes in C stocks, and 422 even gains at some sites (for example LAU75). Sites at this end of the spectrum were particular poor, having inherently low pH and thick organic horizons. Here we suspect that more lime had to be applied 424 in order to buffer soil acidification in an extent that leads to pH improvements favorable for soil microorganisms and other soil biota. Thus, microbial activity and accordingly also decomposition rates 426 remained more or less unchanged. We suspect that the inherent biochemical conditions at this end of the spectrum are likely similar to those reported by Melvin et al. (2013) in hardwood forests in the USA 428 and by Derome et al. (1990Derome et al. ( , 2000 in spruce and pine stands in Finland, who both report significant gains in SOC stocks as a result of liming. 430

Liming effects on organic carbon stocks in the mineral soil 432
In the mineral soil, liming had a variable response on SOC stocks. In the temporal analysis (Figure 2b) we measured a liming-induced increases in SOC in the topsoil (5-10 cm) over time, similar but less 434 pronounced than those reported by the German National Forest Soil Inventory (Grüneberg et al., 2019). In the paired approach analysis we found that the direction and magnitude of net SOC changes 436 in response to liming at each site hinged on the strength of different processes at each site. These are primarily influenced by the sites' biochemical conditions and forest type (Figure 3b-d). The observed 438 variable response is driven by the dynamic balance in soil carbon accumulation rates, namely organic matter inputs, its stabilization and losses as CO2 or dissolved organic carbon (Jackson et al., 2017). 440 Considering the broad biophysical spectrum of sites we sampled at, this net C balance (losses versus gains) varied considerably in response to the increases in soil pH and base saturation in the topsoil. 442 Like in the forest floor layer, SOC losses can be attributed to the stimulation of microbial decomposition of organic matter. The direction and magnitude of the liming-induced SOC stock changes in the mineral 444 soil (at all soil sampling depths) could however best be explained by the soil's SOC storage capacity and how much carbon was stored therein. Generally, we found that sites with low inherent soil carbon 446 contents (in the control plots) exhibited SOC increases, while at the other end of the spectrum those sites with inherently high carbon contents, exhibited decreases in SOC ( Figure A5). This trend was also 448 observed by van Straaten et al. (2015) after land-use change, and shows that sites with inherently high SOC stocks are more vulnerable to SOC losses than sites which initially had little to lose. When we 450 separated our dataset into "carbon rich" (SOC content > 5.5 % at 0-5 cm depth) and "carbon poor" sites (SOC content < 5.5 %) we recorded significant increases in SOC stocks in those sites which initially 452 had low carbon (Figure 3c), but no significant change for sites with initially high SOC stocks. The lack of a significant response in this case likely reflects that we did not sample many sites with inherently high 454 soil carbon. Considering the "carbon-poor" sites mostly had high sand content and low soil fertility, the corresponding SOC increases after liming likely reflect a re-equilibration of the ecosystem carbon 456 cycling dynamics (Figure 3d). We suspect, that C stocks were initially depleted at these sites because sustained acidification over decades which will likely have constrained aboveground net primary 458 productivity, which accordingly reduced C inputs into the soil. Subsequent improvements in nutrient availability and reduced Al toxicity as a result of liming likely improved tree growth (Court et al., 2018, 460 Van der Perre et al., 2012), which in turn increased C inputs into the soil. These suppositions are supported by Grüneberg et al. (2019), who similarly report that liming led to high C accumulations at 462 sites with low clay contents, and C losses at sites with high clay contents.
Next, improvements in both the biochemical environment and litter palatability will likely have 464 stimulated earthworm bioturbation (Persson et al., 2021), as is evident from the higher C-contents measured in the top 5 cm of soil in the limed plots in the broadleaf forest plots (data not shown). . And 19 while earthworm activity is known to promote organic matter mineralization (Lubbers et al., 2017), they also foster the stabilization of physico-chemically protected carbon in soil aggregates by building 468 up mineral-protected microbial necromass (Angst et al., 2019). It is also suspected that the decreases in soil bulk densities in the topsoil ( Figure A2) are attributed to this intensified earthworm activity in 470 the liming plots, which will have loosened and aerated the soil improving gas diffusion, therein also incorporating SOM from the Oh into the mineral soil. Although the net effect of earthworm activity on 472 SOC stocks may not be clear (Persson et al., 2021), it may offer an insight into why net SOC stocks significantly increased in the topsoil (0-5 cm) in the broadleaf forest sites (Figure 3a) where leaf Ca 474 increased as a result of liming, but not in the coniferous forests where needle Ca did not improve (data not shown). Another possible mechanism for the measured increases is through Ca-SOM bridging. 476 Here, the divalent Ca 2+ cations bonded on negatively charged organic matter exchange complexes which stabilize the SOM, thereby reducing the dissolution and mobility of the SOM (Kalbitz et al., 2000) 478 and correspondingly also reducing decomposition processes (Grüneberg et al., 2019;Melvin et al., 2013). 480

Liming effects on soil respiration and soil methane fluxes 482
The comparable soil respiration rates measured in the limed and control plots at the DAS 4227 site prior to a third lime application, highlight that (at least at this site) soil organic matter mineralization 484 rates had equilibrated after liming (done 27 years prior, Figure 5a-c). The third application of lime (in August 2020) consequently elicited a pronounced and prolonged increase in soil respiration rates at 486 all three sites (Rosikova et al., 2019). These increases were primarily driven by biotic sources with only a very minor contribution (<3 %) coming from lime-derived CO2 (Figure 5a-c). This is in agreement with 488 Biasi et al. (2008) who measured similarly low abiotic CO2 production in a limed peatland forest in Finland. It is most likely that the resulting improvements in the soil biochemical environment created 490 suitable conditions for microbial populations to mineralize organic complexes, which led to the increased CO2 production. However, like SOC stock responses to lime application, the size (and 492 duration) of the CO2 production increase varied for the three sites. Notably, the two sites with thick SOM horizons (SEL 34 and GOH 157) had smaller and also shorter-lived CO2 flushes than the more 494 fertile site (DAS 4227). This again supports the earlier observations that especially at poorer sites characterized with thick forest floor layers, liming only moderately improves organic matter 496 mineralization rates.
Interestingly, long-term soil CH4 uptake in the limed plots was more than twice that of the control plot 498 at the Dassel 4227 site (Figure 5b). Although, we did not take baseline measurements at the other two sites, they too had double the CH4 consumption than their respective control plots after liming. This 20 strong CH4 consumption corresponds to the findings of Borken and Brumme (1997), who attributed this to the fact that liming improves both the soil structure (Bronick andLal, 2005, Schack-Kirchner and502 Hildebrand, 1998) and reduces the forest floor layer thickness, which in turn improves CH4 diffusion into the soil. Furthermore, it has been shown that methanotroph abundance and activity is optimal at 504 pHs just below 6 (Amaral et al., 1998). Despite these soils being a relatively large CH4 sink, their CO2 equivalency (global warming potential) nevertheless is still dwarfed by CO2 emissions from organic 506 matter mineralization. 508

Conclusions
We hypothesized that liming would lead to decreases in the forest floor layer C stock and that these C 510 losses would be offset, if not exceeded, by significant gains in SOC stocks in the topsoil. Liming indeed resulted in significant decreases in forest floor SOC stocks, but these losses were only partially offset 512 by small gains made in the mineral soil under certain conditions. However, the question of whether liming enhances forest soil C sequestration is not straight forward. Although there were overall 514 decreases in C stocks in the forest floor, the size of these losses depended on the inherent pH and decomposability of the organic material (before liming). While liming stimulated decomposition at 516 most sites, some poorer quality sites which were characterized by thick organic matter accumulations exhibited either only minor C losses, and in a few plots even C gains. Although there were no significant 518 changes in SOC stocks in the mineral soil as a result of liming, the direction and magnitude of C stock changes here were likewise site-dependent. Specifically, sites with sandy soils and/or inherently low C 520 storage exhibited large increases in SOC stocks as a result of liming, while on the other hand, C rich sites were more predisposed to C losses, suggesting that the SOC stocks here were more vulnerable to 522 decomposition than at sites which had little to lose. Independent of liming, there is evidence of C accumulation in the forest floor layers over the last few 524 decades (likely a response to elevated N deposition), but liming was able to moderate the amount of C that has become immobilized in the organic matter. Liming-induced increases in mineralization rates 526 seem to last for only a limited amount of time, as seen on the respiration rates of the soil, while the doubling in methane consumption due to liming lasts for several decades. Still, CO2-emissions dwarf 528 the CH4-consumption of the soil.
We can conclude that liming has an influence on forest soil organic carbon stocks. The effect is largest 530 in the forest floor, where liming counteracts the observed temporal organic matter accumulation (due to N deposition), thereby reducing nutrient immobilization in the forest floor. In the mineral soil the 532 effect of liming on soil organic carbon stocks in less pronounced, but there are indications that liming promotes some carbon accumulation processes in the topsoil. In total, the implications of liming on 534 forest soil greenhouse gas budgets are small, but highly site-specific. and Dr. Jan Evers for valuable input in the data analysis and interpretation. We also thank Lena Wunderlich, Vanessa Dietrich and all the other field and lab technicians for their contribution to field 576 and laboratory work. . Lastly, we would like to thank the two anonymous reviewers for their constructive comments and suggestions. 578