The quantity and residence time of deadwood or coarse woody debris in Alpine forests are crucial in assessing the carbon cycle to ensure sustainable management of forests. Coarse woody debris (CWD) is defined as large-sized deadwood pieces, such as stems of dead trees lying on the forest floor, standing dead trees and stumps, big branches, and wood boles in all stages of decomposition. Deadwood plays an important role in maintaining biodiversity in forest ecosystems (Müller and Bütler, 2010) and storing carbon (Di Cosmo et al., 2013), as well as contributing to nutrient cycle processes (Palviainen et al., 2010). The amount of deadwood varies greatly from managed to natural forests. In managed European Alpine forests, for example, the average stock of deadwood is estimated to be about 26 m3ha-1, while in old growth Alpine coniferous forests it can be up to 150–190 m3ha-1 (Barbati et al., 2014). Residence time for deadwood (e.g. Krüger et al., 2014) – from the moment the tree reaches the forest floor until it loses 95 % of the mass – can range from decades to several hundred years, depending on intrinsic and external factors. These factors include the dimensions of the log, the wood chemistry, and the site conditions, in particular the mean annual temperature and soil moisture.

Various different sampling designs have been used in the past to determine the time since death to estimate the decay rate of deadwood. Long-term studies can provide reliable results (Müller-Using and Bartsch, 2009), but the slow decay dynamics of wood usually require a decadal observation period. Bond-Lamberty and Gower (2008) used the ratio of deadwood mass input into the pool of initial deadwood to estimate its decay rate based on a 7-year observation period. Such time sequences (chronosequence) offer ideal scenarios to study deadwood dynamics. If windthrow, fire regeneration, and harvest events are known, the starting point in the timeline of the decay process can be specified. However, the exact year of such events is often uncertain, which means precisely dating a tree's death is critical. Dendrochronology can be a helpful tool to determine the year of death, and the technique has been used in several studies to determine the time elapsed since tree death (Campbell and Laroque, 2007; Lombardi et al., 2008, 2013). Other researchers have used radiocarbon dating to date the last recognisable ring of deadwood. For example, Kueppers et al. (2004) estimated the turnover time of lodgepole pine along a subalpine elevation gradient and Krüger et al. (2014) compared tree-ring cross-dating and radiocarbon dating, demonstrating that the two techniques produce comparable results. The decay rate can be estimated by relating the time since death to the density loss or mass loss of deadwood during a given time period (e.g. Busse, 1994; Melin et al., 2009). The decay rate is commonly expressed through a decay constant k, which indicates the density loss or mass loss per year. This constant is derived from a decay model (Harmon et al., 1986), which can be most simply expressed by the equation xt=x0e-kt (single-negative-exponential model), where xt is the density or mass of deadwood at a given time and x0 is the initial density or mass (Jenny et al., 1949; Olson, 1963). Other decay models have also been developed that take wood decomposition into account (reviewed by Mackensen et al., 2003). Several authors (Minderman, 1968; Wider and Lang, 1982; Means et al., 1985) consider the different wood components, e.g. bark, sapwood, heartwood, and chemical compounds, and combine them in multiple-exponential equations. Other authors (e.g. Harmon et al., 1986) consider the time elapsed from the death of a standing tree to the moment when it falls and comes in contact with the forest floor (lag-time models). In several environments, e.g. on dry mountain slopes, the time lag between death and contact with the forest floor can last for almost the entire decay process (Kueppers et al., 2004). A few models take not only the losses due to heterotrophic respiration and leaching into account but also losses due to fragmentation (Mackensen et al., 2003).

One of the most important components of deadwood is coarse woody debris. Because the spatial distribution of CWD is highly heterogeneous, only few quantitative data about its long-term decay dynamics are available for European Alpine forests. Decay models in Europe have, therefore, rarely been parameterised using empirically derived decay constants. In the field, the different stages of CWD decomposition are often described by so-called decay classes (as defined by Hunter, 1990) through a visual assessment of the wood status (Lombardi et al., 2013). In a previous study, Petrillo et al. (2015) demonstrated that the Hunter classification is particularly suitable for describing changes in the physical–chemical characteristics of European larch (Larix decidua Mill.) and Norway spruce (Picea abies (L.) Karst.) deadwood in alpine environments. The physical–chemical properties of deadwood changed distinctly during decay and correlated well with the five decay classes. Furthermore, no substantial differences between spruce and larch decay patterns were found, although the wood chemistry of the living trees differed slightly between these two species (significant differences were found in the cellulose content, with 45.1 % for spruce and 39.4 % for larch; these differences were, however, already negligible in decay class 1; Petrillo et al., 2015). European larch and spruce are widespread in the Alps. Although C stocks in soils are substantial (e.g. Johnston et al., 2004), CWD is a non-negligible C reservoir in subalpine forests (Sandström et al., 2007). Consequently, it is thus very important to know which timescales are involved in CWD decay. Jebrane et al. (2014) showed that Scots pine is more decay resistant than European larch, which suggests that the decay rate of pine is lower. Some species of larch are, however, considered economically valuable due to their hard, heavy, and decay-resistant wood (Parker, 1993), which implies that residence time of larch CWD should be longer.

The aim of our work was to find out (i) which timescales are involved in CWD decay of P. abies and L. decidua in the Alps and (ii) how these timescales correlate with the five-decay class system. We hypothesised that the CWD decay of these coniferous trees is relatively slow (due to, for example, the nutrient availability for macro- and microorganisms being unfavourable).

Although the five-decay class system is well suited to describe changes in the physical and chemical properties of deadwood (Lombardi et al., 2008), no real differences in the age of the CWD classes 1–3 could be found. The CWD in decay class 4 and 5 was, however, clearly older. This implies that the first three decay classes are not clearly related to deadwood age. Similarly, Lombardi et al. (2013) found no relationship between the age of CWD and the chemical properties of decay classes 1–3. The main explanation for this unexpected finding is that there is probably a time lag between the death of a standing tree and its contact with the soil (Kueppers et al., 2004; Zielonka, 2006; Lombardi et al., 2013). Standing dead trees, i.e. snags, can remain upright for several years and decay much more slowly than fallen dead trees (Yatskov et al., 2003). Such an effect overshadows a clear age trend in decay. If the species-specific fall rates were known the decay rates could be better assessed. Unfortunately, the fall rates of snags of the studied tree species are unknown at the investigated sites. To our knowledge, no data about fall rates of snags of either species, i.e. Picea abies (Norway spruce) or Larix decidua Mill. (European larch), are available. In this respect, the data situation in North America is much better. A good overview is given, for example, in Hilger et al. (2012) and Dixon (2015). According to Hilger et al. (2012), Engelmann spruce (Picea engelmannii Parry ex Engelm.) and subalpine larch (Larix lyallii Parl.) have similar snag fall rates. Due to morphological, ecological, and physiological similarities, we have to assume (but cannot ultimately prove) that Norway spruce and European larch should exhibit a similar reaction to Engelmann spruce and subalpine larch. As a consequence, no particular difference in the fall rate between European larch and Norway spruce is to be expected. Therefore, differences in the decay rates between European larch and Norway spruce are hypothesised not to be due to different fall rates.

Angers et al. (2012), however, observed that the wood density in snags in boreal forests already decreases after a few years. Decay rates they calculated are comparable to those in our study. The density loss in standing dead trees could be due to the activity of cerambycid larvae, while the activity of the wood decomposers, mainly fungi, was impeded in snags due to the lack of moisture. The discrepancy between the macromorphology of deadwood (and consequently decay class) and the age of deadwood seems to be therefore related to the individual tree death history. Shortly after tree death, in fact, the wood is rapidly colonised by fungi (Zielonka, 2006). The CWD in classes 4 and 5 showed a relation to deadwood age that seems to be species-specific since larch CWD is older than spruce in both classes. With respect to the CWD ages in our study, classes 1–3 appear to be a single group, while classes 4 and 5 are different. The oldest sample (larch CWD) was about 244 years old – a surprisingly old age for wood lying on the forest floor (i.e. not buried). Spruce CWD in decay classes 4 and 5 seems to be significantly younger than larch CWD. Few empirical assessments of time since the death of a tree have been made in Europe. Krüger et al. (2014) used both dendrochronology and radiocarbon dating to assess the time since death of Norway spruce in Bavarian forests. They estimated a total residence time of 61–62 years for this species. Our values are slightly lower. One major problem in determining the age using 14C is the sometimes large age ranges obtained after calibration (due to plateaus) for samples having a pre-bomb age. We used the ranges with the highest probabilities (varying from 50 to 82.2 %; Table 4; commonly the age 1σ range, i.e. 68 % is considered) for CWD dated to the time period before the bomb peak. Consequently, this procedure introduces an uncertainty. According to Krüger et al. (2014), radiocarbon analysis and dendrochronological cross-dating revealed a similar year of tree death for samples having a post-bomb age. The results of Krüger et al. (2014) suggest that both methods are suitable for the age determination of CWD. In Atlantic Canada, Campbell and Laroque (2007) found an age of 56–84 years (depending on the investigated sites) in the latest decay stage (decay class 5; black spruce and balsam fir). Lombardi et al. (2008) estimated stumps of beech and silver fir in decay class 3 to be 55 and 59 years, which is close to our findings.

The decay rates reflect the determined ages of the CWD, and spruce therefore had a higher decay rate constant than larch. Consequently, decay rates are species specific due to, among others things, the initial differences in the physical–chemical properties of the wood of the living trees and in environmental factors. Larch has, for example, a higher density (Fig. 5) and a lower nutrient content than spruce (Petrillo et al., 2015). Shorohova and Kapitsa (2014) also found that decay rates can strongly vary among tree species. The decay rate (i.e. 0.032 y-1) they found for spruce was slightly higher than that in our study (Fig. 6). The variability in the decay rates given in the literature may also arise from using different mathematical models or different methods to determine wood density or the age of the CWD. According to Hale and Pastor (1998), the decay rates of oak and maple logs (in a temperate forest) varied between 0.00 and 0.18 y-1 (their dating of the logs, however, was based on estimates). The decay rates of tree species in a Mediterranean-climate area (Australia; Brown et al., 1996) varied in the range of 0.05 up to 0.22 y-1, while in a cool-continental climate (Alban and Pastor, 1993), decay rates were 0.042 and 0.055 for red and jack pine, respectively, and 0.07 and 0.08 y-1 for spruce and aspen. Fukusawa et al. (2014) estimated decay rates by using the annual input of CWD divided by the CWD accumulation, and obtained a value of 0.036 y-1. With the chronosequence approach, however, the rates were of the order of 0.020–0.023 y-1.

The determined decay rates for spruce and larch in our investigation seem to be very low (Table 6). As pointed out by Kruys et al. (2002), the chronosequence approach, and thus the snapshot sampling, may overestimate the CWD age and consequently residence time. Thus, the decay rate may be underestimated. It seems, however, that this error is not overwhelmingly distinct in our case or even absent. The approach according to Kruys et al. (2002) and variant (a) in Table 6 gave similar results. The regression approach (variant b in Table 6) probably slightly underestimated the decay rates.

Using mass losses instead of density losses to estimate the decay rates may result in higher values, because the losses for fragmentation are added to the mineralisation losses (Yin, 1999). This might explain why our decay rate constants were lower than those in some other studies (Rock et al., 2008; Herrmann et al., 2015). Moreover, the decay rates are sensitive, at a regional scale, to climatic conditions such as temperature and precipitation (Shorohova and Kapitsa, 2014), although the decay rates for a mean annual temperature of 0–10 ∘C are, however, quite similar, and rates below 0.04 y-1 are often reported (Mackensen et al., 2003). Soil temperature was found to be the main explanatory variable for differences in the decay rates of standard wood, such as aspen and pine (Risch et al., 2013). Although the data are too limited to draw a clear conclusion, some of the differences in the decay rates we observed are likely to be due to environmental factors. On south-facing sites, for instance, we found that the decay rates were slightly, but not significantly, higher than those on north-facing sites (Fig. 6), which is comparable to the observations of Shorohova and Kapitsa (2014).

Although our measured k values are very low, they fit reasonably well to those of the recent compilation of Russel et al. (2015). For environments having a mean annual temperature of < 10 ∘C, the decay rate constants are usually < 0.1 (median value is 0.027 for such sites). The compilation of Russel et al. (2015), however, only considers two sites having Picea abies (k values = 0.044 and 0.027; Krankina et al., 1999; Næsset, 1999) and none for larch. Together with our results, a residence time of about 20–90 years for Picea abies in subalpine (boreal) climates might be suggested.

The concentrations of cellulose and lignin in the CWD are given as a function of time in Fig. 5. Due to the faster decomposition of cellulose, lignin is relatively enriched. Lignin, however, also decomposes with time. To unravel the decay behaviour of these compounds, a multiple-exponential model was applied (Means et al., 1985; Mackensen et al., 2003), with the general form xt=x1e-k1t+x2e-k2t…+xne-knt, where xt is the density or mass of deadwood at a given time and x1…n are partitioned parameters. The portioning of cellulose and lignin is solved graphically using their mass per unit volume over time and fitting them to an exponential regression curve. From this, the half-life of cellulose or lignin in the CWD could be calculated: t1/2=ln⁡(1/2)-k, where t1/2 is the half-life and k is the decay constant (obtained from the exponential regression curve). Using the k values in Fig. 7, the following half-lives were obtained: a.

for cellulose: 21 years (spruce) and 50 years (larch);

In decay classes 4 and 5, the CWD starts to become more and more part of the soil. The further fate of CWD compounds strongly depends on their interaction with the mineral soil. The introduced organic matter into soils can be either further degraded or stabilised to a certain extent. The persistence of organic matter in soils is largely due to complex interactions between the organic matter and its environment, such as the interdependence of compound chemistry, reactive mineral surfaces, climate, water availability, soil acidity, soil redox state, and the presence of potential degraders in the immediate micro-environment (Schmidt et al., 2011). Together with physical protection, organo-mineral interactions are generally thought to be the main mechanism for SOM stabilisation (e.g. Nierop et al., 2002; Kleber et al., 2005; Marschner et al., 2008).

The first three decay classes do not seem to reflect the age of the CWD, but they are relevant for the description of its decay stage. The time lag between the death of a standing tree and its contact with the soil overshadows a clear age trend. Taking classes 1–3 as one group and relating them to the decay classes 4 and 5, a time trend with increasing decay stage can then be detected. This time trend also closely correlates with the wood density, and the cellulose and lignin content. The oldest CWD age of a larch tree reached the considerable age of 244 years. We used a chronosequence approach and applied several calculation techniques to estimate the overall decay rate constants of European larch and Norway spruce. The stage-based matrix model of Kruys et al. (2002) that corrects for sampling bias was in good agreement with the often-used single-negative-exponential model. The regression approach probably underestimated slightly the decay rates. The decay rate constant for spruce seems to be in the range of 0.018–0.022 (y-1) and for larch it is about 0.012 (y-1). The rates seemed to be slightly higher on south-facing sites (although this was not statistically significant). An effect of the altitude on the decay rates was, however, not discernible. Using the dating approach (dendrochronology and 14C dating), the behaviour of cellulose and lignin as a function of time could be assessed. Our findings demonstrate that lignin in larch may persist particularly long, with a mean residence time of > 100 years. This indicates that turnover rates of CWD organic matter are even in a comparable range to that of SOM.

More empirical data are, however, needed to ascertain our findings. A major issue is that fall rates between European larch and Norway spruce could not be compared. Furthermore, the preparation and precise dating of CWD is time-consuming, cost-intensive, and in some cases also difficult (particularly samples with a pre-bomb age in decay classes 4 and 5). Since CWD represents an important forest carbon pool, improving the informative potential of the decay classes (including the dating of the CWD) would contribute to sustainable forest management and make carbon accounting easier.