For our analyses, we used the following litterbag data: Sphagnum capillifolium (capitulum and first 5 cm of the stem; 20 samples) and Typha latifolia (leaves; 20 samples) samples incubated in bog peat and pools (oxic and anoxic conditions) in Canada for 808 d , and Phragmites australis (leaves and rhizomes; 36 samples) grown under different nutrient availability and incubated under anoxic conditions in peat with different nutrient availability for 75 d . In both cases, MIRS were measured for the undecomposed litter and at the end of the incubation period. In addition, we used undecomposed litter samples (some collected under natural conditions, some grown in laboratory experiments with different nutrient availability) of Astelia pumila, Aulacomnium palustre, Betula populifolia, Calluna vulgaris, Chamedaphne calyculata, Donatia fascicularis, Empetrum nigrum, Empetrum rubrum, Eriophorum sp., Eriophorum angustifolium, Eriophorum vaginatum, Gaultheria antarctica, Isolepis setacea, Juncus effusus, Kalmia angustifolia, Larix laricina, Lepidothamnus fonkii, Polytrichum strictum, Rhododendron groenlandicum, Sphagnum sp., Sphagnum capillifolium, Sphagnum fallax, Sphagnum magellanicum, Sphagnum rubellum, Tracheophyta, Vaccinium myrtilloides, Vaccinium myrtillus, Vaccinium oxycoccos, Vaccinium uliginosum, and Vaccinium vitis-idaea (; R. Anzenhofer, unpublished; A. Hömberg, unpublished; S. Wagner, unpublished) from the Peatland Mid-Infrared Database . For undecomposed litter samples, we assumed a degree of decomposition of 0 %. In total, 169 litter samples were available for model training. All MIRS used in this study are measured in transmission mode on Fourier-transform infrared spectrometers (FTIR) as milled samples mixed with potassium bromide into transparent pellets. MIRS were measured on different devices (Cary 660 FTIR spectrometer (Agilent, Santa Clara, CA, USA), Bruker Vector 22 FTIR spectrometer (Bruker Optik, Ettlingen, Germany), Cary 600 FTIR spectrometer (Agilent, Santa Clara, CA, USA), Varian 660 FTIR spectrometer (Agilent, Palo Alto, USA), Cary 670 FTIR spectrometer (Agilent, Santa Clara, CA, USA), and Shimadzu IRTracer-100 spectrophotometer, equipped with a DLaTGS (deuterated L-alaninedoped triglycine sulfate) detector). Different devices may lead to differences in spectra not related to γ which may lead to larger prediction errors than when all MIRS were measured with the same device.

To evaluate the models and to illustrate the application of γMIRS, we used bog peat core measurements derived from the Peatland Mid-Infrared Database: a core from the peatland Odersprungmoor (OD2) , a core from the peatland Martinskapelle (MK1) , and a core from the peatland Mohoş (MH1) . Macrofossil volume fractions from these cores were used to estimate the mass fractions of individual litter components in the peat samples and average water table depth reconstructed from testate amoebae (TA-WTD) were used to relate estimated γ and NPP to changes in WTD. Age-depth models were estimated with 14C dates using rbacon (supporting Sect. S1 in the Supplement). In addition, we also used data from three ombrotrophic Patagonian peat cores from and two bog peat cores with highly degraded drainage layers from the Venner Moor to evaluate prediction domains of the models (see Sect. ).

We used beta regression models to predict γ from intensities in preprocessed MIRS. To harmonize the spectra, we interpolated them to unit wavenumber resolution and clipped them to the range 600–4000 cm-1. Depending on the variable and properties of the MIRS, different preprocessing steps may maximize predictive performance. Therefore, we computed models with different preprocessing steps in addition to the harmonization: (1) Baseline correction, signal normal variate (SNV) (model 1), (2) First derivative spectra, SNV (model 2), (3) Second derivative spectra, SNV (model 3). After that, spectra were binned (bin width 10 cm-1) to reduce the number of predictors and reduce correlation between predictors, and all predictors were z-transformed across all spectra. All preprocessing steps were performed with the ir package . Baseline correction was done with an automated convex hull procedure . Spectra of some undecomposed litter samples have artefacts from CO2, as indicated by peaks around 2360 cm-1 . To avoid that these peaks have an effect on the normalization or models, we linearly interpolated intensities between 2300–2380 cm-1 and excluded variables from this range from the models. CO2 also produces peaks around 670 and 3580–3780 cm-1, but we did not correct these because they overlap with peaks from organic matter and are smaller than the peaks between 2300–2380 cm-1 .

Beta regression models were computed with brms , using a logit link function, assuming a constant shape parameter, using a normal prior for the intercept, and regularized horseshoe priors for the slopes (for each predictor variable). The regularized horseshoe prior shrinks coefficients to zero except where they are strongly related to the response variable, conditional on other predictors. To reduce overfitting, we defined a large amount of shrinkage, by assuming that 5 of the 321 predictor variables have non-zero coefficients . Bayesian inference was done using Markov Chain Monte Carlo (MCMC) sampling with Stan , using 2000 warmup iterations and 2000 sampling iterations. Across all models, the maximum Monte Carlo standard error for the degree of decomposition predicted for the training data and all analyzed peat samples was 1.1 % for the mean, 0.5 % (for standard deviations), and 4 % (for lower and upper 95 % prediction interval boundaries). No model had divergent transitions and the largest rank-normalized R^ for model parameters was 1.01, indicating convergence of the chains .

We developed a simple Bayesian mixing model based on Eq. () that estimates γk(t) for all components in a peat sample from bulk measurements of γMIRS(t) (predicted by any of the three models) and the mass fractions of the components: γMIRS∼beta(μγMIRSϕγMIRS,(1-μγMIRS)ϕγMIRS)μγMIRS∼beta(μϕ,(1-μ)ϕ)μ=logit-1β0+∑kK(logit(γk)-β0)mkmϕ∼gamma(αϕ,βϕ)γk∼beta(αγk,βγk)3β0∼normal(β0μ,β0σ) where the third line is the same as Eq. (), the first line is a measurement error model to consider prediction errors in γMIRS (here, we approximate errors of the prediction model with a beta distribution with scale parameter ϕγMIRS computed from the average prediction error of the respective model), μ is the estimated true value of γMIRS (without measurement errors), ϕ is the scale parameter of the beta distribution (with a gamma prior with shape and rate parameters αϕ,βϕ), and γk of component k is modeled with a beta distribution with shape and rate parameters αγk and βγk. As outlined in the Introduction, linking this model to peat core data can be done with bulk measurements for γMIRS and by assuming that mk/m equals the macrofossil volume fractions of the litter components (workflow (1) in Fig. ). For individual litter types, the mixing model will only yield correct estimates for γk when they have a relatively large mass fraction because γMIRS is not sensitive to γk if component k has only a small mass fraction. To consider this error source, we used a beta(1,1) prior for γk, which gives uniform weights to all possible values. Unless the sample consists of many components, the inability to correctly estimate γk for components with small mass fraction in the sample has only a small effect on γ and an even smaller effect on the reconstructed NPP. We expect large errors not accounted for by the mixing model only when some initially dominant component is completely or nearly completely decomposed and therefore not detectable.

We applied this model to the three cores, OD2, MK1, and MH1 described in Sect.  to estimate γk of all K litter components and γ of the peat samples. With these estimates for γk, bulk densities estimated from MIRS , and age-depth models for each core, we could then estimate the initial mass of each layer, which divided by the time range of aboveground litter formation in each layer without roots equals the aboveground NPP. Reconstruction of belowground NPP is only possible with peatland models. If there is a large fraction of roots in a sample, a large fraction of the initial mass may have been added to the layer after its initial formation by aboveground litter. In presence of roots, we therefore call our estimate the initial mass accumulation rate. We developed an R package that allows to estimate the mixing model for own data .

Our analysis considers errors in estimates for γMIRS, bulk density, peat ages, and β0. Errors from γ, bulk density predicted from MIRS and peat ages are propagated to NPP estimates by computing NPP with individual draws from the posterior distributions of the respective Bayesian models. Errors for γMIRS and β0 are considered by using prior distributions within the mixing model with parameters chosen based on the prediction models for γMIRS.

Clearly, prediction of bulk density and saturated hydraulic conductivity from MIRS introduces larger errors in our analysis than necessary. We used predictions because we do not have access to peat samples with estimates for peat ages, macrofossils, bulk density, and saturated hydraulic conductivity. We present these analyses as illustrations for the suggested approach but severe tests may require more accurate estimates and measurements than are currently available. Errors can also be reduced further by measuring mass fractions of macrofossils and by measuring MIRS on individual macrofossils than on bulk samples (workflow (2) in Fig. ).

Using the estimated γ for the peat samples and saturated hydraulic conductivity (Ksat) estimated from MIRS , we tested whether Ksat–γ relations hypothesized in previous studies agree with Ksat and γ for our peat cores. The hypothesized relations are:

An assumed sigmoidal relation as used in the Holocene Peatland Model (corrected versions of Eqs. 10 and 15 in ; corrected versions are available from the supporting info to , Ksat in cmmin-1, according to ):Ksat=15070-370(ρmin4+Δρ1-0.51-erf(1-γ)-c32c4),where ρmin, Δρ, c3, and c4 are parameters defined in and erf is the error function.

All models have a similar fit to the training data (Fig. ) and similar predictive performance as measured by their ELPD during CV (Table ). Model 2 had the best average predictive accuracy (= maximum average ELPD) for the stratified CV and model 1 for the grouped CV. Using a normal approximation for ΔELPD and a two-sided significance level of 5 %, only model 3 in the stratified CV has a detectably worse predictive accuracy than the model with best average ELPD (Table ). Large errors of ΔELPD in the grouped CV indicate a large variability in predictive performance of the model for the different folds, as expected when testing the model with litter samples from species not included in the training data.

For all models, the fit to the training data is better on average (smaller average RMSE) than for predictions in the two CV scenarios (Fig. ), indicating that all models overfit. The two models using derivative spectra had, on average, the best fit to the training data, but worse or not much better predictive accuracy in the CV scenarios, indicating an, on average, larger overfitting risk than for model 1, which does not use derivative spectra.

Predictive accuracy of all models was worse for the grouped CV than for the stratified CV (Fig. ), as expected, because in the stratified CV models were tested with samples from similar studies and species as the data they were trained with, whereas in the grouped CV some folds contained samples from species the model was not trained with. In the grouped CV, γ is underestimated by all models for decomposed T. latifolia and S. capillifolium samples from . Conversely, γ is overestimated for undecomposed litter samples, with prediction errors larger than 10 % for model 1 for C. vulgaris, and for the other two models for L. fonkii, C. vulgaris, P. australis, A. pumila, L. laricina, and C. calyculata. Model 3 has, both in the grouped and stratified CV, the largest average prediction errors for undecomposed litter (Fig. ).

A comparison of the prediction domains of the models to the spectral range covered by the analyzed peat samples indicates that many of the peat samples have MIRS different to the training data. HI1630/1090 as alternative decomposition indicator, C or CMIRS, and photographs of the peat samples, suggest that samples outside prediction domains are either more decomposed or have large mineral contents (Figs. S4 and S5), which is not surprising since there are comparatively few decomposed samples and no mineral-rich samples in the training data. Data coverage by prediction domains differs between the models: 64.4 % of the peat samples are within the prediction domain for model 1 and 2.8 % and 0 % for the other two models, which indicates that derivative spectra differ more between the peat and the training data data than underived spectra. Thus, the models extrapolate for more decomposed and mineral-rich peat and the prediction domain of model 1 covers most of the peat samples.

A plot of residuals vs. N for different levels of γ suggests that model 1 underestimates γ for samples in the training data with a γ between ca. 20 % and 40 % and N content smaller than ca. 0.02 gg-1 (Fig. ). For the models computed with derivative spectra, this bias is smaller (Fig. ). This may indicate that model 1 makes less accurate predictions for the peat samples analyzed here (99 % have a N content smaller than 0.02 gg-1) and in general .

For silicates, prediction errors of all models increase the more silicates are mixed into the samples such that 95 % prediction intervals cover nearly the whole range of possible values for γMIRS (Figs. S7–S9). The behavior of predicted medians differs between the models. For model 1, predictions overall increase for undecomposed samples and decrease for more decomposed samples, but the differences are never larger than ca. 30 %. Model 3 behaves similar, but predictions always increase with more silicate influence and differences to the true value may exceed 50 %. For model 2, predictions decrease with more silicate influence for all but the undecomposed samples and compared to the other models more posterior probability is placed on smaller degrees of decomposition.

For decomposed peat, the median predicted γMIRS increases for all samples and models, as expected when adding a highly decomposed peat sample to less decomposed litter samples (Figs. S10–S12). Median predictions for the maximum addition of the decomposed peat are smallest for model 1 and largest for model 3. As for the silicate experiment, also prediction errors of all models increase the more of the decomposed sample is mixed into the samples, but prediction intervals are narrower than for the silicate experiment and, especially for already decomposed litters, their width also differs between models: Model 1 estimates the largest prediction errors and prediction errors increase the more of the decomposed peat is added to a sample, even for decomposed litter. Model 2 and in particular model 3 have narrower prediction intervals for already decomposed litter, but in most of the cases predictions do not differ significantly from those of model 1. Thus, model 1 estimates a smaller median γMIRS with larger prediction errors than the models using derivative spectra, but all models make extrapolations that are qualitatively reasonable.

Predictions of all models for samples consisting of two litter types with different degree of decomposition underestimate γ. As shown in Fig. , the bias is well described by our theoretical expectation (Eq. ). Thus, the magnitude of the bias is related to the difference in γ of the mixed litter types and their relative mass fractions in the mixture. This relation is non-linear; when one of the two litter types is clearly dominant (mass ratio of 1:1000), the bias vanishes, such that for mass ratios in-between these extremes, the bias reaches a maximum. This maximum value is larger the larger the difference in γ between the two litter types is. The difference in γ also controls the position of the maximum. The more decomposed one of the components is compared to the other component, the more is the maximum shifted towards a smaller mass fraction of the more decomposed component.

There is some deviation from this pattern due to prediction errors in γMIRS for individual litter samples. Discrepancies not related to model prediction errors for individual litter types only occur when undecomposed litter of one species is mixed with strongly decomposed litter of some different species, where the mass ratio of the more decomposed litter type is between one third and two thirds (upper right and lower left panels in Fig. , where diverse litter types are mixed with P. australis and where S. capillifolium litter is mixed with P. australis litter). If only undecomposed litter from different species and organs is mixed, γMIRS correctly estimates a small γ (values range between 0–0.02 gg-1 across all mixtures and models), which is also in line with our expectation. Overall the bias is similar across all models and for mixtures of different species and organs, and can be well described by Eq. (), with smaller deviations caused by prediction errors for γMIRS and variation between litter types. The bias estimated with model 2 matches the expected relation best.

Figure  shows γ and NPP of individual litter types estimated with γMIRS and the average γ and total aboveground NPP for the three peat cores vs. time. For MH1, γ was smaller than 50 % throughout the last 500 years; larger values were only estimated for two short phases around 1700 and in the last decades, where S. cuspidatum and E. vaginatum dominated and TA-WTD indicate drier conditions. The reconstructed median NPP at MH1 is larger than at the two other sites, the median was stable during the last 500 years and larger than 0.1 kgm-2yr-1. Recent and past drying events coincide with a decrease in NPP. For MK1, the core with the oldest layers, the median γ is ca. 75 % for the fen phase and peat formed during 500–1800 CE, but similarly small as for MH1 for the intermediate layers dominated by hummock Sphagnum species (model 3 predicts a larger γ here than the other two models). The NPP was similarly large as in MH1 only in the fen phase and much smaller (median smaller than 0.15 kgm-2yr-1) afterwards. No fen phase is covered by OD2 and γ was small and more stable than in the other cores, with only a small peak roughly during the period of the Little Ice Age. The NPP was similar to MK1. In contrast to all other cores the NPP strongly increased during the last decades in OD2. In many cases, the apparent mass accumulation rate (AMAR) is nearly identical to the reconstructed NPP, but AMAR underestimates the median NPP and decomposition mass losses for more decomposed layers. Many decomposition peaks appear to be related to peaks in reconstructed WTD (drying events) (for example MH1: ca. 1700 CE and in recent decades, MK1: ca. 1700, 1500, 1000 BCE, OD2: ca. 2700, 1700, 700, 400 BCE), but there are also WTD peaks that do not coincide with an increase in γ (also not when possible time lags between WTD and γ are considered, for example: MK1: ca. 3000 BCE, OD2: ca. 700 CE).

Common patterns between all models and cores are that dominance of Eriophorum sp. in peat often coincides with a large γ, that a small γ is estimated for the topmost layers (as expected), and that a rather small γ (<50 %) is estimated for many S. fuscum, S.rubellum, and S. magellanicum layers even though they are several thousands of years old (and similarly, the overall γ for these layers). The dominance in Eriophorum is often preceded by an increase in γ of Sphagnum peat (e.g. MK1: ca. 1300 BCE, OD2: ca. 700 and 0 BCE) and γ often only decreases after Eriophorum volume fractions are smaller again. This pattern is compatible with secondary decomposition and colonization by Eriophorum caused by drier conditions.

While the models indicate overall similar trends in γ and NPP, values of γ and NPP vary comparatively much between the three models: model 1 estimates the smallest γ and NPP, model 3 the largest values, and model 2 estimates intermediate values. Model 3 does, for example, not estimate a decrease in γ for MK1 during ca. 5000–4500 BCE. However, the estimated maximum values of γ per core are similar. Overall, model 3 suggests a smaller average difference in γ between phases with more decomposition losses and phases with less decomposition losses than the other two models. Large errors in γ are mainly due to extrapolation for more decomposed samples. Large errors in NPP are mainly due to dating errors (unlike many studies, we considered these errors here).

Our estimates for S. fuscum NPP cover the range of NPP from different studies compiled by (0.12±0.09 kg-1yr-1, average ± standard deviation) , and are contained in the wider NPP range measured in monospecific S. fuscum patches in (0.21±0.14 kg-1yr-1) or other studies . While it is not surprising that our estimates are within these broad ranges, it is reassuring to see that median estimates produced with the suggested approach do not obviously contradict expected ranges for NPP.

The estimated relation between MIRS-estimated saturated hydraulic conductivity (Ksat) and γ for the three peat cores and with γ estimated from γMIRS predicted by the three models is shown in Fig. , together with Ksat–γ relations suggested in earlier studies. At least for the cores analyzed here, default parameterizations differ from estimated averages (albeit one has to consider that both Ksat and γ estimates have relatively large errors): In contrast to the relation implemented in the Holocene Peatland Model (Eq. ), the data suggest that Ksat decreases continuously with γ and our data do not cover ranges of γ large enough to test the suggested step-like decrease for strongly decomposed peat. The relation suggested in and used in the DigiBog model overestimates Ksat and estimates a too strong decrease of Ksat with γ. The relation suggested in fits our estimates well, but the estimated depth dependence is too strong. For example, if a depth of 50 cm is assumed for all samples, Ksat would be underestimated, as shown in Fig. ; in contrast our estimates suggest a less strong control of depth (≈ total stress) on Ksat for our cores.

As outlined in the Introduction, γMIRS is biased when litter types with different γ are mixed. Our results suggests that Eq. () reasonably well fits γMIRS for mixtures of litter types; larger deviations only occur for litter mixtures that are probably rare under natural conditions (mixtures of one to two thirds of an undecomposed litter with a two to one thirds of a strongly decomposed litter). Moreover, at least for models 2, these deviations are small compared to prediction errors. Thus, since Eq. () reasonably well fits γMIRS for mixtures of litter types and since γMIRS fits γ of individual litter types well, the bias can be avoided or corrected.

There are three possible approaches to avoid or correct this bias: The first approach is to use bulk γMIRS measurements and information on the relative mass fractions of each litter type in the sample (for example from macrofossil analysis) to estimate γ from γMIRS with the mixing model (Eq. ) developed here (workflow (1) in Fig. ); this corrects the bias. The second approach is to measure MIRS for the separate litter types and weigh the litter types (component-specific analysis; workflow (2) in Fig. ). In these cases, γMIRS can be estimated for each litter type and, with reasonable prediction errors, equals γ. This can be used to estimate the initial mass of the litter types, mi(t0), from γMIRS with: mi(t0)=m(t0)/(1-γMIRS). Then, Eq. () can be used to compute γ of the entire sample; this approach avoids the bias. The third option is a combination of the first and second approach, where a component-specific analysis is conducted only for some litter types.

The second approach can be used to estimate γ more accurately, both for the sample and individual litter types, than is possible with the first approach This is particularly relevant for litter types that have only a small mass fraction because the mixing model cannot estimate γ very accurately for these litter types (for this reason, we only evaluated mixing model results for litter types with a macrofossil abundance of at least 40 % in the peat samples). Even though the sample γ is less sensitive to the values of litter types with small mass fraction than γ of these litter types, also estimates for the sample γ will have smaller errors. The third option shares this advantage and may be an option when it is difficult to separate all litter types (for example when litter types are strongly decomposed).

This points to a possible practical difficulty: it is not yet clear how to exactly define litter types and mass fractions such as to avoid biases. The mixing model and the component-specific analysis require litter types to be separated, but future studies will need to test which plant organs need to be separated to avoid biases. For example, it is quite clear that tree branches will decompose at a different rate than leaves and therefore both need to be treated as separate litter types to avoid biases. But does the same apply, for example, also to Sphagnum branches vs. stems? Here, we assumed that macrofossil volume fractions are directly proportional to mass fractions, as is done in process models, but this assumption is not well tested. Peat layers may also consist of peat formed over a long time range that is strongly compressed and may therefore consist of not much decomposed parts and strongly decomposed parts. In such cases, it may not be sufficient to define litter types only via taxonomic information because litter from the same species may have a large range of γ values in such layers. On the other hand, component-specific analysis can be used to determine whether γ of two litter types is sufficiently similar throughout the decomposition process such that the bias in γMIRS is only small and both may therefore be treated as same litter type.

Overall, it is exciting to see that the possibility to estimate γ raises these issues and offers opportunities to test them and therefore to better understand peat chemistry and degree of decomposition.

The main question we want to address here is to what extent the prediction models for γMIRS fulfill the properties of an ideal decomposition indicator suggested in the Introduction and compared to previous studies:

Linear relation to γ. Our model evaluation suggests that all three models fit γ of individual litter types with reasonable errors and no overall bias (Fig. ). For litter similar to the training data, prediction errors are comparable to or slightly larger than errors between litterbag replicates e.g. and therefore currently acceptable for many applications. Predictions for novel litter types should be treated with caution since there might be biases (Fig. ), however the dataset here already covers quite many different litter types and therefore we expect that this risk is small, except for woody plant organs which are currently underrepresented in the training data. Overall, γMIRS is linearly related to γ of individual litter types.

The carbon to nitrogen ratio (C/N) and a humification index (HI1630/1090) often used as decomposition indicators e.g. have more variable relations to the measured γ for the same litter types (compare supporting Figs. S13 to ).

Predicting γ is a complex task and as any complex method, γMIRS has limitations, many of which can be addressed in future studies:

Variability between models. Currently, it is difficult to recommend a best model because the models have trade-offs that need to be evaluated with additional data. Our recommendation is to consider the variability of model predictions while taking into account known biases (see the next point) until further tests have been performed. While confidence intervals of γ estimated by the models overlap even for samples outside of the prediction domain, the large variability indicates that at least some of these predictions are biased. Overall, we assume that predictions of model 2 are most accurate because model 1 underestimates γ for litter with small N content and model 3 probably overestimates γ for more decomposed samples.

While not considered here, an additional limitation of the current litterbag data may be that they do not consider how litter preprocessing may bias mass losses from decomposition compared to decomposition under more natural conditions e.g.. This may confound relations between MIRS and γ under more natural conditions when making predictions with models trained on litterbag data. However, the extent of this problem remains unclear at present.

Overall, this evaluation suggests that γMIRS fulfills many properties of an ideal decomposition indicator, even if not applicable to all peat samples. Despite many opportunities for improvements, we are not aware of a decomposition indicator that has the potential to predict γ as well as does γMIRS and that can be as easily measured, even with small sample amounts, as is the case for γMIRS.

Here, we discuss some problems in peatland research and restoration that may be addressed with γMIRS and illustrate some of these points with our analysis of the three mountain bog cores.

Estimation of long-term decomposition rates and improvement of process models. Our analysis of the peat cores suggests a quite large variation in γ for hummock Sphagnum species, with several peaks across the entire depth, even if the peat is several thousands of years old. These differences were probably caused by differences in aerobic decomposition losses since catotelm decomposition rates are assumed to vary less with depth and over time and since at least some layers with larger hummock Sphagnum γ coincide with or precede WTD peaks (Fig. ) . Preservation of such variations in peat may allow to better estimate long-term decomposition rates of plant functional types and reconstruct past environmental conditions with process models.

It is interesting that a small γ (smaller than 50 %, median values smaller than 25 %) is suggested by all three models (even model 3 that may overestimate γ, Fig. ) for hummock Sphagnum litter in some of the peat samples several hundreds or even thousands of years old and from all three peat cores. Some studies suggest much larger figures for γ , whereas other studies suggest values for γ similar to those found here . A litterbag synthesis suggests that under aerobic conditions, S. fuscum may lose 50 % of its initial mass after 20–50 years . Assuming a catotelm decomposition rate of 0.0004 yr-1, this would lead to an additional mass loss of ca. 15 % over 1000 years and thus a mass loss ca. 20 % larger than the upper 90 % confidence interval of γ predicted for these samples. This may suggest either that litterbag experiments overestimate decomposition rates (at least under these conditions), that the time until incorporation into the catotelm was even shorter than 20–50 years, or that other factors than moisture limited decomposition during these periods (e.g. thermodynamic constraints in the catotelm e.g., colder temperatures, etc.). When linked to process models, γMIRS may help to address these questions and therefore to better understand long-term decomposition losses.

Other open problems that may be addressed with γMIRS are: (1) A more precise quantification of differences in decomposition rates between litter types. If (aboveground) litter from the same layer decomposed under the same environmental conditions, current decomposition models e.g. assume that differences in γ rates are only controlled by differences in the maximum possible decomposition rates of these litter types. This allows to estimate differences or ratios of litter type-specific decomposition rates from γMIRS of individual litter types (supporting information Sect. S5). (2) It is commonly assumed that decomposition rates slow down the more of the initial mass has already been decomposed and this is an important control of long-term peat accumulation rates e.g.. However, this slow-down is difficult to quantify because the effect only manifests over long time periods not covered by litterbag experiments and because of difficulties to accurately estimate decomposition parameters from peat cores; measurements of γMIRS from many peat cores and samples across large time gradients may help to address this problem (supporting information Sect. S5). (3) Similarly to the slow-down due to decreasing litter quality, it is assumed that anaerobic decomposition rates decrease with depth due to thermodynamic limitations e.g., which can have large effects on long-term peat accumulation . Measurements of γMIRS may complement targeted litterbag experiments to better estimate this decrease in anaerobic decomposition rates .

In summary, this suggests that γMIRS may be useful to better understand peat accumulation, improve process models, define baselines for peatland restoration, and monitor long-term restoration trajectories.