Application of the Global Uncertainty and Sensitivity Analysis to assess the importance of deadwood characteristics for forest biodiversity

Data acquisition for sustainable forest management has focused on obtaining high quality information to estimate biomass. Improving the quality of non-timber sustainability indicators, like deadwood volume, has been a minor interest. To explore how inventory approaches could be improved, we applied a Global Uncertainty and Sensitivity Analysis (GUSA) to evaluate which factors propagate more errors in deadwood modelling and how better data collection can minimize them. The impact of uncertainty on deadwood characteristics (diameter, collapse ratio, decay class, tree species, and position) was explored under stakeholders´ preferences, management actions, and climate change scenarios. GUSA showed that removing the prediction error in deadwood tree species and diameter would alter the most the total uncertainty in deadwood volume. We found that assessment of high deadwood volume was less uncertain for the scenarios where small deadwood items were left decaying on the forest floor (BAU) and for high-end climate change scenario (RCP8.5) which resulted in lower deadwood accumulation in forest stands and therefore also in lower likelihood of erroneous estimates. Reduced uncertainty in tree species and diameter class will elevate the certainty of deadwood volume to a similar level achieved in living biomass estimation. Our uncertainty and sensitivity analysis was successful in ranking factors propagating errors in estimate of deadwood and identified a strategy to minimize uncertainty in predicting deadwood characteristics. The estimation of uncertainty in deadwood levels under the scenarios developed in our study can help decision makers to evaluate risk of decreasing deadwood value for biodiversity conservation and climate change mitigation.


Introduction
In Fennoscandia, current forest management prioritizes sustainable provisioning of timber, bioenergy, and bioproducts.This is reflected in data acquisition for forest management: research has focused on improving the precision and reducing the uncertainty in structural forest indicators, like tree density, tree height, tree growth, and forest living biomass resulting from prediction errors from airborne laser scanning (Maltamo et al. 2021).In this context, we identify uncertainty as the knowledge about the environmental indicator, referring to both its accuracy and variability.The uncertainty in the future projections of these forest indicators is related both to the uncertainty in model structure and parameterization and to the uncertainty in the input data inferred via laser scanning.Model uncertainty is related with the propagation of the error in the allometric equations chosen to estimate tree biomass.Uncertainty in the input data is small, as inventory errors involved in biomass prediction derive from small inventory errors in tree basal area and tree height (for both, % Standard Error (SE) < = 20% in laser scanning according to Naesset 2004).
Instead, forest management has focused on providing a sustainable supply of timber and has given less priority to sustainably providing other values (Eyvindson et al. 2018), such as deadwood.Deadwood supplies carbon cycling, carbon storage, enhanced soil fertility, the maintenance of soil moisture, habitat creation and biodiversity conservation (Lassauce et al. 2011;Campbell et al. 2019).This is reflected in the few resources dedicated to monitoring the non-timber indicators of Sustainable Forest Management (SFM), such as the deadwood volume accumulated in the forest stand via tree death and decomposition (Woodall et al. 2009;Chirici et al. 2012).Consequently, the estimates of total deadwood volume from laser scanning are affected by large inventory errors (Root Mean-Square Error ranging between 128 and 203% in commercial forest stands, Maltamo et al. 2014).These uncertainties are far larger than those related with biomass estimation.
Quantifying the accumulation of deadwood in the forest depends on three key main drivers: the rate of tree mortality at the stand, the decomposition rate, and the frequency of deadwood removal through human intervention (Stokland et al. 2012).The uncertainties in deadwood volume estimates are impacted by assumptions of the chosen models for tree mortality and decomposition (Harmon et al. 2020).Decomposition occurs in stages, providing specific resources for the life-cycle of different species living in deadwood, and is impacted by the collapse class, decay class, and tree species of the deadwood (Kouki and Tikkanen 2007;Tikkanen et al. 2006Tikkanen et al. , 2007)).Deadwood of different tree species decays at different rates, with the fastest decay occurring for deciduous trees (birch and aspen), an intermediate rate for spruce, and the slowest decay for pine (Shorohova and Kapitsa 2014).This different decay rate is the reason for the capacity of different tree species to support a different number of species thriving in deadwood included in the Finnish Red List of threatened species (Tikkanen et al. 2007; https:// punai nenki rja.laji.fi/ en).
In the Finnish forests, coniferous deadwood hosts a higher number of red-listed species compared with deciduous deadwood, with Norway spruce deadwood hosting more species than Scots pine (Tikkanen et al. 2006).Decay classes are not equally important for hosting red-listed deadwood-dependent species.While deciduous trees host similar number of species in recent deadwood and in advanced decay stages, coniferous trees host far more species in advanced decay than in recent deadwood.Among the coniferous trees, Scots pine hosts the same number of species in the early and advanced decay stages, while Norway spruce hosts far more species in deadwood in advanced decay (Tikkanen et al. 2006).Finally, a substantial proportion of deadwood species are specialized to live in large-diameter trunks (> 30 cm) (Tikkanen et al. 2006).In the heavily managed Fennoscandian boreal forests these types of deadwood fractions (the deadwood of deciduous trees in general and deadwood of coniferous trees in advanced decay classes) are often found in very small quantities, making it rare or impossible to find species depending on these resources (Gibb et al. 2005).
Quantifying uncertainty in deadwood volume is a research gap that must be addressed, given the current pressure of the society to promote multiple values from forests (see, e.g., Mönkkönen et al. 2014;Triviño et al. 2017;Pohjanmies et al. 2017Pohjanmies et al. , 2021)).Assessing the uncertainties is of utmost importance, as assessments of environmental indicators like deadwood volume are often conducted reporting only the indicator status against target values without ascertaining any confidence interval as measure of uncertainty (Carstensen and Lindegarth 2016).The assessment of uncertainty bounds for environmental indicators helps to verify the effectiveness of management actions targeting conservation values (c.f., McCarthy et al. 2012).Failing to implement them properly can have serious ecological consequences.For example, in Northern Europe 20-25% of the forest-dwelling species are dependent on deadwood habitats (Siitonen 2001) and the availability of a deadwood volume of at least 20 m 3 ha −1 is certainly the most important requirement for the presence of threatened wood-inhabiting fungi in the Finnish forests (Junninen and Komonen 2011).Therefore, management actions releasing deadwood below this threshold may lead several species to extinction (Le Saout et al. 2013).
To address this concern, we use an uncertainty and sensitivity analysis approach to evaluate which factors propagate more errors in the estimates of deadwood volume and how these errors can be minimized.According to Campbell et al. (2019), who studied the sources of uncertainty in current field-based deadwood estimates in the northeastern United States, the uncertainty in the estimate of total deadwood volume on the forest floor is mostly determined by the uncertainties in five factors, related to the deadwood characteristics.These factors are (1) the diameter of the deadwood items, which directly relates to their volume, (2) the deadwood item´s collapse, a reliable estimate of the proportion of the deadwood volume remaining during the decay process, (3) the decay class of each deadwood item, reflecting the stage of deadwood decomposition, (4) the tree species to which each deadwood item belongs to, reflecting wood density and tree characteristics and, (5) the position of the deadwood item, whether it is standing as a snag or lying as a log on the forest floor, which affects its diameter and the decay rate.Most countries that conduct deadwood inventories measure deadwood according to the volume categorized by these five characteristics, whose assessment in sample transects or plots is error-prone (Rondeux and Sanchez 2010).
Through the quantification of the relative importance of the uncertainty, it is possible to improve the inferences of a SFM indicator like deadwood volume.This assessment identifies the elements of deadwood monitoring to prioritize so that the total uncertainty is minimized, and the inference errors are reduced.The Global Uncertainty and Sensitivity Analysis (GUSA) (Saltelli et al. 2004(Saltelli et al. , 2008) ) can be used to estimate how the uncertainties related to deadwood characteristics contribute to the overall uncertainty of the total deadwood (a similar approach was applied by Campbell et al. 2019).GUSA assesses confidence levels around the estimate of an environmental indicator and evaluates which of the errors related to the indicators´ factors has a higher impact on the overall uncertainty of the indicator.By indicating where the monitoring design can be improved, GUSA allows decision makers to better allocate monitoring resources to reduce errors in the estimate of the indicators (Campbell et al. 2019).
The aim of this study is to evaluate the potential impact of the uncertainties in the five deadwood characteristics on the overall uncertainty in the total deadwood volume predicted via laser scanning for a production forest landscape in Finland.
In addition to the uncertainty related to the deadwood characteristics, we hypothesize that the uncertainty regarding the total estimated deadwood volume depends upon three factors: (a) The forest values preferred by the forest owner, i.e., nature conservation vs. timber production, (Koskela and Karppinen 2020;Juutinen et al. 2021).Biodiversity-friendly forest owners may decide to leave all the wood to decay naturally on the forest floor after clearcut, while forest owners primarily interested in timber production may also collect a considerable proportion of trees felled by natural mortality (i.e., collection of ~ 75% naturally felled trees to be sold or used for bioenergy production), removing this resource from the forest.(b) The management actions applied on the forest, which alter the forest structure and consequently the initial levels of deadwood in the forest (McCarthy and Bailey 1994;Riffell et al. 2011).In Fennoscandia, stands managed for timber production are mostly governed with rotation forestry (Business As Usual, BAU), that uses regeneration harvest methods such as thinning from below and clearcutting producing even-aged stands (e.g., in Finland: Äijälä et al. 2014).Stands managed with Continuous Cover Forestry (CCF) are treated with selection harvest of single large trees (thinning from above) and natural regeneration instead of planting or seeding (Pukkala et al. 2013).Finally, in stands left growing unmanaged as Set-Asides (SA), timber is not extracted but totally left to grow fully stocked, allowing natural mortality to be high due to self-thinning.(c) The impact of climate change on the forest, which affects how much deadwood is accumulated (Heinonen et al. 2017;Blattert et al. 2020).Climate change has a direct impact on biomass accumulation in trees and soil (Creutzburg et al. 2017) and conversely on how much deadwood is accumulated in the forest (Blattert et al. 2020) and how fast it decays (Russell et al. 2014;Mazziotta et al. 2016).The uncertainty associated with alternative three IPCC radiative forcing scenarios (i.e., Representative Concentration Pathways (RCP) 2.6, 4.5 and 8.5, van Vuuren et al. 2011) is likely to induce a large variability on the deadwood volume, on the capacity of different tree species to thrive in the stands, and on the time window of persistence of certain deadwood decay classes (Blattert et al. 2020).
To account for these three factors, we explored separately the impact of uncertainty in the five deadwood characteristics on the overall uncertainty in total deadwood volume under alternative stakeholders´ choice of deadwood extraction, choice of management actions, and climate change scenarios.

Study area
The study area is in the Central Finland region and is primarily located in the southern boreal vegetation zone (Fig. 1).It covers 2240 ha and consists of 1475 forest stands of diverse age, productivity, and tree species composition.Among these stands, we have randomly selected 158 stands for simulation (i.e., 10.7% of the total).The area is a typical Finnish production forest landscape, consisting of a mosaic of stands with the current stand age ranging between 0 and 133 years and an average of 48 years (Table 1).The most common tree species are Scots pine (Pinus sylvestris, the dominant species in 50.1% of the stands), Norway spruce (Picea abies, 34.9%), silver birch (Betula pendula, 2.2%), downy birch (B.pubescens, 1.1%) and other deciduous trees (8.1%).While we have no specific information on the past management of the area, the relatively young age-class distribution of the stands suggests that the area has been managed extensively for production forestry, following an even-aged management that was the legally required management system until 2014 (Äijälä et al. 2014).Forests in the study area are privately owned and managed using a diverse set of silvicultural treatments (Kuuluvainen et al. 1996).

Inventory data
The stand-level inventory data derived from airborne laserscanning for our study area was extracted from openly available data managed by the Finnish Forest Centre (FFC 2021) and used as input data in the forest growth simulator.The data used in this study are owned and archived by the Finnish Forest Centre (www.metsa keskus.fi).The data are available from the authors upon reasonable request and with permission of the Finnish Forest Centre.
Key stand level variables used in our simulations are reported in Table 1.Initial deadwood characteristics for Central Finland were obtained from measurements from experimental plots from the Finnish National Forest Inventory (NFI) for the years 1980-2015 (Korhonen et al. 2020).We utilized NFI data of deadwood to simulate them wallto-wall, mimicking laser scanning data suitable for forest  planning.Using NFI data for deadwood initialization was necessary, as Forestry Centre currently does not produce deadwood data.Deadwood initialization parameters are summarized by tree species, diameter, decay class, position and years after death (Table 2).

Simulations of forest growth and decomposition
The simulation of the future states of the forest was conducted using SIMO, an open-source forest simulation and optimization software (Rasinmäki et al. 2009).Using forest growth models, SIMO produces projections of future stand development based on the stand's initial characteristics and the forestry operations to be applied to the stand.The forest simulator creates a wide range of management actions using a decision tree following the Tapio guidelines (Äijälä et al. 2014).The implementation of alternative management actions in the simulator is described in more detail by Eyvindson et al. (2018).
The formation of deadwood and its decomposition from initial deadwood values is predicted with the empirical statistical model developed for Scots pine, Norway spruce, and silver birch by Mäkinen et al. (2006).The models estimate the remaining fraction of deadwood volume based on the years´ after death with a Gompertz function.The mortality Means and uncertainties (i.e., standard deviations, SD) are estimated on the basis of deadwood inventory errors for each parameter.Density ad, volume ad, and biomass ad are the density, volume, and biomass estimated immediately after tree death (i.e., ad).The density, volumes and biomass after tree death represent means of the values taken only at year 0 after death, while other variables represent means across all the years after death of single trees in SIMO is determined by a probability model taking into account tree competition and aging, and the tree to die is selected randomly in each simulation (Hynynen et al. 2002).
The 158 stands with the initial deadwood characteristics were simulated for 100 years into the future to account for climate change effects (see the paragraph "uncertainty scenarios" for details).The simulator produced predictions of stand development at 5-year time steps.To evaluate the highest impact of climate change on forest dynamics we compared the last year of each scenario (Kellomäki et al. 2008).

Management actions
The initial deadwood values used in the simulation were based on the regional level deadwood characteristics of the Finnish NFI (Table 2).These values were used in a spin-up process to construct initial deadwood volumes based on a variation of management regimes (Table 3).We assume that historical management alternatives, as well as natural mortality, are represented in the prevailing deadwood volumes at regional level.Specifically, all the 158 stands were simulated for each combination of management regime (either BAU, CCF, or SA) and deadwood removal levels from the forest floor (either 0%, 40% or 75%) for 30 years into the future at 5-year time steps.The average volume of deadwood was estimated by the end of the simulation horizon.A conceptual model explaining the flow of the deadwood initialization is represented in Fig. 2 (see also Mazziotta et al. 2023).

Estimate of total volume from deadwood characteristics
We estimated the total volume of deadwood per hectare ( V j in m 3 ha −1 ) in each forest stand j of the total simulated stands (J = 158) at the end of the planning horizon.This is calculated as the sum of the combinations of the volumes for 9 discrete diameter classes as standard output from the simulator (set D, expressed in cm, with mean values from 2 to 42 cm with 5 cm intervals), 5 discrete collapse ratio classes (set C, calculated as ratio between volume after death and volume at each time step, split according to the following intervals: 0.01-0.2,0.21-0.4,0.41-0.6,0.61-0.8,0.81-1), 3 tree species (set S, i.e., Norway Spruce, Scots pine, and deciduous trees), 4 deadwood decay classes based on time since tree death (set L, i.e., recently dead tree = 1, medium decayed tree = 3, very decayed tree = 4, almost decomposed tree = 5, Stokland et al. 2012; decay class 2 (= weakly decayed tree) is not reported because it lasts only for three years, that is for less time than the minimum 5 year time step of our forest simulator), and 2 positions on the forest floor (set P, i.e., snag, upright, or log, lying on the forest floor): The five deadwood characteristics affecting total volume are simulated with the SIMO simulator (Rasinmäki et al. 2009) on the basis of the Finnish NFI-derived distributions.Therefore, uncertainty affecting the predictors of total (1) deadwood volume derives both from inventory errors and from assumptions in the models embedded in SIMO.Our metric of uncertainty was the 95% confidence interval (95% CI), calculated as the difference between the 2.5th and the 97.5th percentiles of the distribution of deadwood values.
To evaluate the independent impact of each source of uncertainty on the total deadwood uncertainty, the uncertainty in the total volume was calculated as the sum of the fractions of deadwood volumes for each deadwood characteristic.For example, to evaluate the impact of the volumes of each tree species (V s ) on the uncertainty in the total volume ( V j ), this was calculated for each stand in set J as: To evaluate the impact of excluding one source of uncertainty in a certain deadwood fraction from the overall uncertainty in deadwood volume, the uncertainty in the total volume was calculated, via a leave-one-out procedure, as the sum of the volumes of deadwood items with all characteristics but one.For example, to evaluate the impact of the exclusion from the variability in the total volume of the variability derived only from measuring the volumes by diameter class (V d ), total volume was calculated as:

Uncertainty scenarios
Volumes for the deadwood characteristics of the 158 stands were simulated separately under 18 uncertainty scenarios, with a potential impact on the assessment of deadwood (2) volume in the forest.The uncertainty scenarios were a combination of three initial deadwood levels delivered by three management actions (BAU,CCF, and SA), two management decisions from the forest owner (75% or 0% deadwood removal, abbreviated as DWREM), and three climate change scenarios (RCP2.6,RCP4.5, and RCP8.5), as specified below: (1) INITIAL DEADWOOD VOLUME: The initial quantity of deadwood depends on the history of the management applied in the forest.To simulate the potential deadwood volume assuming different management actions we applied two alternative growth models: both BAU and SA apply the models developed by Hynynen et al. (2002), but BAU assumes even-aged forestry and SA assumes ingrowth, while CCF, assuming uneven-aged forestry, applies the models developed by Pukkala et al. (2013) and Lappi and Pukkala (2020).These two growth models affect differently the stand development, and consequently have a different impact on the quantity of deadwood.In BAU, slash from harvesting is left in the stand, so thinning and clear-felling will increase deadwood volume of small diameter.In CCF and SA deadwood accumulates throughout the forest succession, but as CCF focuses on removing the largest logs when harvesting, this reduces the fraction of large diameter deadwood that enters the litter for decomposition.Finally, in BAU competition is reduced through thinning, inducing faster tree growth of the remaining trees respect to SA and CCF, where ingrowth reduces the diameter growth.In this way, BAU is also likely to reduce the retention time of each decay class of deadwood respect to CCF and SA.The choice of growth model has only a slight impact on deadwood production Fig. 2 Flowchart describing the procedure of deadwood initialization (Pesonen 2011) and is expected to contribute to the overall uncertainty in total deadwood volume to the same extent.
(2) VALUES OF THE FOREST OWNER: The forest owners may have different management goals oriented either towards economic or ecological values (Koskela and Karppinen 2021), which can directly affect the volume of deadwood available for forest biodiversity (Deuffic and Lyser 2012).Therefore, we simulated two regimes of deadwood removal: 0% for biodiversityfriendly forest management, and 75%, for intensive forestry.
(3) CLIMATE CHANGE: The three RCPs (i.e., 2.6, 4.5 and 8.5) chosen to simulate deadwood dynamics represent low, intermediate, and high warming respectively and differ from each other by emission levels.In Finland, the annual mean temperature is projected to increase by 1.9, 3.3 and 5.6 °C by the 2080s under the RCP2.6,RCP4.5 and RCP8.5 scenarios, respectively, compared to the period 1981-2010 (Venäläinen et al. 2020).The mean annual precipitation is expected to increase by 6%, 11% and 18% under these RCPs by the 2080s.The impact of climate variables on forest growth dynamics in SIMO was included based on climate-sensitive statistical growth and yield models (Matala et al. 2005(Matala et al. , 2006)).The three RCPs were simulated for the General Circulation Model CanESM2 (von Salzen et al. 2013).

Global Uncertainty and Sensitivity Analysis (GUSA)
We evaluated the relative impact of the uncertainty in the deadwood characteristics on the total deadwood volume with a GUSA.GUSA assesses (1) the propagation of uncertainty from input variables on model outputs and (2) the relative importance of uncertainties in model input variables and their interactions on the uncertainty in model output variables (Saltelli et al. 2004).A variance-based sensitivity analysis is the study of how uncertainty in the output of a model (numerical or otherwise) can be apportioned to different sources of uncertainty in the model input factors (Saltelli et al. 2010).GUSA evaluates the entire parameter space, ranking simultaneously the relative impacts of all the uncertainty sources at once.We performed the GUSA according to the variancebased Sobol method (Sobol 1993(Sobol , 2001) and implemented it with the sensobol R package (Puy et al. 2022).The Sobol method provides a quantitative measure of the output variance with respect to the variance associated with the input parameters.These sensitivity indices are described in terms of direct (first order), and interaction (second and higher order) effects of the input parameters (Saltelli et al. 2004).
The first-order sensitivity indices (S) are calculated as the ratio of the variance associated with the input variable to the total variance of the model output.The total-effect sensitivity (T) is calculated as the ratio of the total variance (first order plus all interactions) associated with the input variable to the total variance of the model output (details in Lagerwall et al. 2014).
To calculate the Sobol indices we first selected an integer N to represent the sample size of the forest stands.The sample size was generated using a Monte-Carlo approach looking at the entire distribution of the factor's values (Saltelli et al. 2010).Next, we generated a matrix of size (N, 2 K), the Sobol matrix, where K is the number of input parameters and N is the number of draws to be taken from the parameters' probability distribution function.This matrix is split into two matrices A and B of size (N, K).We then defined matrices Di, Ci which are respectively the same as matrix A and B, except with the ith column obtained from matrix B and matrix A. Finally, we computed the model output for all the input values in A, B, Ci, Di.The details of the method are summarized in Lagerwall et al (2014).

Contribution of sources of uncertainties
The contribution of single sources of uncertainty, i.e., errors in each deadwood characteristics, on the overall uncertainty in deadwood volume was ranked via the GUSA.When all sources of uncertainties were combined, the uncertainty (i.e., 95% CI) was 31.0 m 3 ha −1 (Fig. 3).Tree species (95% CI = 43.1 m 3 ha −1 ) and deadwood position (95% CI = 30.6m 3 ha −1 ) were the deadwood characteristics projected with the greatest source of uncertainty (being respectively 139% and 98.7% of the joint uncertainties among all the 18 scenarios).All other deadwood characteristics, i.e., collapse ratio (95% CI = 23.0 m 3 ha −1 ), decay class (95% CI = 22.8 m 3 ha −1 ) and diameter class (95% CI = 21.5 m 3 ha −1 ) were all less but similarly important for the total deadwood uncertainty (being 74.2%, 73.5%, and 69.4% of all the joint sources of uncertainties) (Fig. 3).
The relative contribution of each source of uncertainty was also evaluated for each combination of stakeholders´ preferences, forest management strategies, and climate scenarios (Fig. 4).The means and 95% CI of deadwood volume inferred by all the sources of uncertainty were four times higher in the scenarios with no deadwood removal from the forest floor (Fig. 4a) than in the 75% deadwood removal scenario (Fig. 4b) (Table 3).Additionally, the relative contributions of each source of uncertainty were similar between Fig. 4a and b.The mean deadwood volume was generally comparable between BAU and CCF and the highest volume was under SA.On the other hand, the 95% CI in the deadwood volume was generally the highest under SA, intermediate under CCF, and the lowest under BAU (Fig. 4a, b, Table 3).The mean of the predicted deadwood volume either decreased (for tree species and diameter class) or remained stable (for decay class, tree position and collapse ratio) under radiative forcing scenarios of increasing greenhouse gas (GHG) concentration, from RCP2.6 to RCP4.5 to RCP8.5, while 95% CI was generally similar under the three climate change scenarios (Table 3, Fig. 4a, b).

Impacts of sources of uncertainties
To quantify the impact each deadwood characteristic had on the total uncertainty, we conducted a leave-one-out cross validation (Fig. 5).We found that the error in diameter class and tree species affected the most the total uncertainty in deadwood volume, with error-free estimate of these deadwood characteristics increasing of 30.5% and decreasing of 15.9% the total uncertainty, respectively.On the other hand, the exclusion of the uncertainty in deadwood volume induced by errors in volumes by collapse ratio, decay class and position affected only marginally the total deadwood uncertainty, as the total uncertainty increased only by 1.7%, 1.5%, and 0.3%, respectively (Fig. 5).

Contributions and impacts of uncertainties by scenarios
The relative impact of assessing the uncertainty in total deadwood by excluding each deadwood characteristics was also evaluated for each combination of uncertainty scenarios of stakeholders´ preferences, management actions, and climate change (Table 4, Fig. 6a, b).Beside the absolute magnitude of the uncertainties, the relative contributions of the exclusion of each source of uncertainty were similar between Fig. 6a and b.For the stakeholders´ preference scenarios, excluding the uncertainty in the decay stage, collapse ratio and species decreased the 95% CI in the total uncertainty under both the scenarios of no deadwood removal (− 9.1%, − 9.1%, and − 13.6%) and 75% deadwood removal (− 14.3%, − 14.3%, and − 28.6%), while the uncertainty increased excluding the error in diameter class more under no deadwood removal (+ 72.7%) than under 75% removal (+ 42.9%) (Table 4, Fig. 6a, b).Finally, excluding the error in the position the uncertainty decreased (− 4.5%) under no deadwood removal and remained stable at 75% removal.

Relationships between uncertainties in total deadwood
We plotted the relationship between the predicted overall uncertainty in deadwood volume (in y-axes) and the uncertainty in each of the five deadwood characteristics (in x-axes) (Fig. 7).The deadwood fractions that gave more "shape" to the curves describing the relationships were the ones whose uncertainty affected more, i.e., were more correlated with, the overall uncertainty in deadwood volume.The shape of the curves did not vary substantially across the 18 scenarios, therefore we reported here the results of the relationships only for a sample uncertainty scenario (i.e., DWREM0 BAU RCP2.6) (Fig. 7), while the relationships for all the scenarios were reported in the Supplemental online material (Appendix Scatterplots).We found that the overall uncertainty in the total deadwood volume was primarily determined by the uncertainty in the volumes of deadwood fractions with large diameter classes, especially of the last three classes, with trees larger than 30 cm (see Fig. 7a), recently dead (decay class 1), (Fig. 7b) characterized by limited loss in volume due to decomposition (collapse ratio ≥ 0.61) (Fig. 7c), from either spruce or pine trees (cf., Fig. 7d) and lying as logs on the forest floor (Fig. 7e).

Sensitivity indices
Sobol indices were calculated by partitioning the uncertainty in the total deadwood volume with respect to the uncertainty in the five deadwood characteristics (Fig. 8).The ranking of the Sobol indices did not vary substantially across the Fig. 5 Impact of the exclusion of each deadwood characteristics from the uncertainty in all deadwood characteristics.The boxplots represent the predicted deadwood volumes based on the Global Uncertainty and Sensitivity Analysis accounting for the uncertainties in all the deadwood characteristics but one.Definitions of the box, interquartile range and whiskers as in Fig. 3.
18 uncertainty scenarios of stakeholders´ preferences, management actions and climate change; therefore, we reported here the plots for first order (S) and total order (T) Sobol indices for a single uncertainty scenario randomly selected (i.e., DWREM0 CCF RCP2.6), while the plots for all the scenarios are reported in the Supplemental online material (Appendix Sobol Indices).
For the diameter classes, we found that the uncertainty in total deadwood was increasingly explained (higher % of the Sobol index) by deadwood fractions of increasing diameter (Fig. 8a), with deadwood of 2 cm explaining on average among scenarios only -0.015% (Sobol index range: min.= − 0.034%, max.= 0.0042%) of the total deadwood uncertainty and deadwood of 42 cm explaining on average 17% of the uncertainty (range: 4.7%, 30.4%).However, among the diameter classes of deadwood only the items of 42 cm diameter, whose average S value was the only one above the red dotted line of the S dummy parameter, could be considered influential for the uncertainty of total deadwood (Fig. 8a).
For the decay classes, deadwood in decay class 1, i.e., recently dead tree with the longest retention time was responsible on average for 44.9% of the uncertainty in total deadwood (range: 23%, 74.7%), while the decay classes 3 (medium decayed tree), 4 (very decayed tree) and 5 (almost decomposed tree) were respectively responsible only for 10.2% (range: 5.6%, 13.8%), 8.7% (range: 4.7%, 14%) and 10.3% (range: 4.6%, 30.7%) of the uncertainty (Fig. 8b).However, only the average S value in deadwood fractions in decay class 1 was above the horizontal red dashed line, therefore their uncertainty could be considered influential for the uncertainty of total deadwood (Fig. 8b).
For collapse ratio, we found that the uncertainty in total deadwood was increasingly explained by deadwood fractions with lower loss in volume (Fig. 8c).Deadwood which had lost almost all its volume respect to the initial value (i.e., in collapse class 0.01-0.2) explained on average only 2.1% of the total deadwood uncertainty (range: 0.03%, 12.9%) while deadwood which still retained all its volume (in collapse class 0.81-1) was responsible on average for 33.7% of the uncertainty (range: 10%, 68.1%).Only the average S value of the deadwood belonging to this latter collapse class could be considered influential for the uncertainty of total deadwood (Fig. 8c).
For tree species, spruce deadwood fractions were responsible on average for 33% of the uncertainty in total deadwood (range: 15.5%, 45.4%) and pine fractions for 30% of the uncertainty (range: 13.8%, 48%) (Fig. 8d).Deciduous fractions were less influential, representing on average only the remaining 2.7% of the uncertainty (range: 0.7%, 5.9%), likely because the bulk of deadwood was from coniferous trees.Only the two coniferous deadwood fractions showed Predicted means and 95% confidence intervals (CI) of deadwood volume summarized for the exclusion of each deadwood characteristic from the total (All) uncertainty and for each stakeholder's preference (DWREM0% and DWREM75%), management action (BAU, CCF, and SA), and climate change scenario (RCP 2.6,RCP 4.5,RCP 8.5)  an average S value above the horizontal red dashed line, therefore their uncertainty was influential for the uncertainty of total deadwood (Fig. 8d).Finally, log deadwood fractions were responsible on average for 67% of the uncertainty in total deadwood (range: 46.2%, 92.6%), while snag fractions were much less influential, representing on average only 6.2% (range: 3.6%, 14%) of the uncertainty (Fig. 8e).Only the uncertainties in log deadwood fractions were influential for the uncertainty of total deadwood (Fig. 8e).
The overlap between the confidence intervals of the first order (S) and total order (T) Sobol indices in all the deadwood fractions revealed an absence of relevant interactions among uncertainties affecting the overall deadwood uncertainty (Fig. 8).

Contribution and impact of sources of uncertainties
The GUSA provides evidence that the large total deadwood uncertainty is mainly determined by the uncertainty in the initial inventory data and the uncertainty in deadwood characteristics estimated from the projections.This agrees with a recent uncertainty analysis of deadwood empirically measured in NFI plots (Campbell et al. 2019).
The decomposition model embedded in SIMO overestimates the mean residence time of deadwood in each decay class (Mäkinen et al. 2006), therefore the overall uncertainty in the total deadwood volume may be systematically overestimated.

Contribution of sources of uncertainties
The analysis on the contributions of single sources of uncertainty revealed that the five deadwood characteristics are not equally important in explaining the total variability in deadwood.In our case study, this variability is more derived from the variability in volumes of deadwood items of different tree species and position on the forest floor and less from the variability in the collapse ratio, decay class, and diameter.This finding reflects the ranking of the impact of these factors on the deadwood decomposition rate found in a global comparative analysis conducted by Harmon et al. (2020).The fact that the total variability in the five deadwood characteristics was smaller than the variability induced by deadwood items of different species is likely explained by an interaction effect between sources of uncertainties, with errors of opposite sign cancelling each other (Mäkinen et al. 2010).

Impacts of sources of uncertainties
The evaluation of the impacts of the exclusion of single sources of uncertainties in deadwood characteristics from the overall deadwood uncertainty showed that the uncertainties induced by tree species and deadwood diameter are the two most crucial in altering the estimates of the total deadwood volume, cumulatively contributing the most to the total uncertainty.In a laser-scanning based inventory, this would be possible by moving from predicting the expected deadwood volume for each pixel to identifying each dead log lying in the forest floor separately.Such approach is only possible for the largest logs (> 30 cm) which can be most efficiently located in the forest (Heinaro et al. 2021).Identifying the large logs individually would also reduce a large part of their position error.It can be assumed that the option of locating the largest individual dead trunks will become more and more realistic in the future and have strong implications for tracking resources suitable for biodiversity.For example, knowledge about the position of large logs would improve the decisions also concerning the optimal level of firewood taken from the forests and the allocation of conservation areas in the production landscape (cf., Mazziotta et al. 2023).
Our ranking of the importance of the sources of uncertainty in deadwood volume partly reflects the empirical results of the uncertainty analysis conducted by Campbell et al (2019).They also found that diameter was an important source of uncertainty in the measurement of downed coarse woody debris at plot level while collapse ratio and decay class had minor importance.In our simulations, the large uncertainty in deadwood of large diameter classes likely derived by the initial uncertainty of the large logs.Our analysis confirms that minimizing the error in the inference of certain deadwood characteristics can improve the level of confidence to assess habitat quantity and quality available for species dwelling in deadwood (Tikkanen et al.  2006, 2007;Kouki and Tikkanen 2007).In our study, the initial uncertainty in the deadwood inventory reflects that of the regional NFI, meaning that the assumed uncertainty level is an underestimate for an actual laser-scanning-based forest management inventory.However, as we consider the relative effects of different diameter classes, it does not have an effect on the conclusions.

Contributions and impacts of uncertainties by scenarios
The GUSA for the scenarios of stakeholders´ preferences, management actions, and climate change showed that in some scenarios the prediction of deadwood volumes with certain characteristics could be less certain than in others.
The impact of the exclusion of each source of uncertainty was also sensitive to the uncertainty scenario adopted.This means that in some scenarios the error-free inference of certain deadwood characteristics can be more important than in others to reduce the uncertainty in deadwood estimation.
The choice of the forest owners to remove deadwood from the forest floor decreased the variability in deadwood volume.The assessment of the tree species and diameter class was less uncertain when most of the deadwood had been removed from the forest floor, likely because of the selective removal of the less decomposed deadwood logs belonging to the largest diameter classes, all characteristics that caused most of the uncertainty.Behaviour of private forest owners may create bias in the snag/log ratio and NFI deadwood data.Based on the 9 th Finnish NFI data, it is suggested that removal of snags and hard deadwood from forests for firewood reduces the number of logs and larger diameter deadwood of advanced decay classes in southern Finland (Tikkanen et al. 2009).A similar north south bias in the snag/log ratio in forest inventory data has been reported in Sweden (Fridman and Walheim 2000).
The variability of deadwood volumes increased with management actions attempting a close to-nature silviculture, likely due to the increased representation of deadwood of large diameter classes at least in the short term (Kuuluvainen et al. 2012).The estimate of deadwood characteristics in stands under CCF was more error-prone compared with stands under other management actions.This is likely due to the presence of deadwood logs of large diameter in CCF, which were created more often by the mortality model in CCF respect to the other two regimes.Under BAU, the predicted volume of deadwood is similar or even higher than the deadwood in CCF (see the "All" case in Table 3).However, this high volume is not available as habitat for biodiversity, as site preparation after clear-cut (e.g., harrowing) and movements of forest machinery destroys coarse woody debris which has been left since the previous tree generation (Hautala et al. 2004).Furthermore, in BAU clear-cutting residues left on the ground contribute deadwood with small diameters and limited variability in decay classes which reduces the total deadwood uncertainty (Kuuluvainen et al. 2012).The amount of tree canopy remaining after timber extraction is larger in CCF than in BAU, and this can affect the quantity of deadwood and its characteristics.This is likely because gaps left following clearcutting operations in BAU management will lead to more solar radiation hitting the surface of the deadwood, leading to potential photodegradation and to warmer and drier conditions either favouring or retarding the decomposition process (Harmon et al. 2020).It must be noticed that the deadwood decomposition model adopted in our simulator has been validated on the material collected from commercial and dense unthinned single-species stands (Mäkinen et al. 2006).Therefore, its application might have some limitations when predicting deadwood volumes in mixed stands managed with CCF and old-growth SA.In our simulations we assumed that BAU, CCF and SA are equally applied in forest management.However, this is not currently the case, with BAU being the dominant management regime in Finland, CCF applied especially in peatlands and SA officially only in state-owned or voluntary nature reserves.However, it is not known how the proportion of these management regimes may change in the future to comply with sustainability goals and pressures to adapt forests to climate change and this represents a large source of uncertainty in forest planning.
Finally, climate change increased the total deadwood volume (see the "All" case in Table 3) but not the variability in its characteristics.This can be related to the increase in the decomposition rate, which reduces the deadwood residence time (Mazziotta et al. 2014;Russell et al. 2014;Ekman et al. 2024).Consequently, it might be more difficult to detect deadwood items with certain characteristics, as their presence on the forest floor is more ephemeral.However, it must be considered that the model parameters for decomposition used in our forest simulator were not dependent on an increase in temperature and process rates, therefore it may well be that the actual representation of deadwood volumes with different characteristics, and their uncertainties, could be different from our projections.Furthermore, our forest simulator did not incorporate forest disturbances (e.g., drought, windstorms, insect and disease outbreaks, wildfires), and the changes in their frequency and magnitude induced by climate change.These extreme events may further alter the inputs into the standing and downed deadwood pools (Russell et al. 2014;Venäläinen et al. 2020).

Relationships between uncertainties in total deadwood and sensitivity indices
The analysis of the relationships between uncertainties and the sensitivity indices showed that the representation from the simulator of the distribution of the deadwood items can be erroneous, i.e., with a large prediction error.The deadwood items whose distribution is erroneously estimated from the simulator predictions are: logs with large diameters, recently dead trees characterized by low collapse in their volume, coniferous rather than deciduous tree species, and logs rather than snags.On the other hand, at stand level, the large uncertainty is likely explained by the fact that buried logs, as they have already been almost totally decomposed, generally exhibit the lower decomposition rate than snags aboveground, allowing the coexistence of a larger variability in deadwood characteristics (Stokland et al. 2016), especially of large diameter classes and advanced decay stages, whilst the decomposition rate of conifer snags is lower than logs, as the snags of old pines can be very durable (Yatskov et al. 2003).Reducing the initial uncertainty in estimate of deadwood items with these characteristics may help decision makers and forest managers to drastically reduce the uncertainty in the final estimate of the deadwood volume.The higher importance of the classes of deadwood with a larger diameter in affecting deadwood volumes might be explained by the fact that larger trees have larger variability in volume than small trees; the higher importance of coniferous rather than deciduous trees by their larger occurrence in the managed stands.Finally, the larger impact of uncertainty on the early decay classes might be due to a bias in our decomposition model, caused by the low number of observations in the most advanced decomposition stages.In fact, the predictions for the most advanced decomposition phases are extrapolations and, thus, less reliable (Mäkinen et al. 2006).

Conclusions
Our study confirms that stakeholders´ decisions, management actions, and climate change can alter the distribution of the frequency classes of deadwood volumes in the forest.
The forest owners' decision to leave or remove deadwood from the forest floor respectively increased and reduced the availability of deadwood in the landscape for forest-dwelling species (Koskela and Karppinen 2020).This decision was certainly the one that affected the most the availability of deadwood on the forest floor and the certainty of its estimation.When the forest management followed a decreasing gradient of forest intensification, from mainstream evenaged forestry to single tree selection harvest, to closer-tonature development, the deadwood volume increased consistently (Pohjanmies et al. 2021).Deadwood accumulated more in forest stands under high-end (RCP8.5)climate scenarios triggered by a higher forest growth (Creutzburg et al. 2017;Blattert et al. 2020) but also the likelihood of erroneous estimates.
To summarize, a reduction of the uncertainty of selected deadwood characteristics is instrumental in reducing the uncertainty in deadwood volume estimation from projections and in aligning the level of certainty in the assessment of the deadwood volume to the elevated level of certainty already achieved in biomass estimation.Better modelling of the deadwood decomposition pathway can be achieved by reducing the sources of uncertainty in the inventory of various deadwood pools (Russell et al. 2014).In our case study, the uncertainty and sensitivity analysis were successful in ranking the factors propagating errors in the inferences of deadwood and helped to identify a strategy for minimizing uncertainty in the estimation of deadwood characteristics.Deadwood has the capacity to supply several forest ecosystem services, including regulating services, for its capacity of climate regulation by storing carbon (Stokland et al. 2016) and maintenance services, for its capacity to create habitat for forest biodiversity (CICES, Common International Classification of Ecosystem Services, Haines-Young and Potschin 2018; NCP, Nature's Contributions to People, Díaz et al. 2018).The capacity of deadwood to supply these services in the long term is continuously changing in a forest landscape modified by stakeholders´ preferences, management actions, and climate change.These scenarios are expected to have large impacts on the capacity of the forest to produce deadwood.In this context, the estimation of the uncertainty in deadwood levels under the scenarios developed in our study can help decision makers to evaluate the risk of decreasing its value for biodiversity conservation and climate change mitigation.
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Fig. 1
Fig. 1 Locations of the study area in in Central Finland and Finland in northern Europe

Fig. 4
Fig. 4 Contribution of each source of uncertainty to total deadwood volume, and all sources of uncertainty combined for 9 combinations of uncertainty scenarios of climate change (RCP 2.6, RCP 4.5, RCP 8.5) and management actions (BAU, CCF and SA), separated

Fig. 6
Fig. 6 Impact of the exclusion of each deadwood characteristics from the uncertainty in all deadwood characteristics for 9 combinations of uncertainty scenarios of climate change (RCP 2.6, RCP 4.5, RCP 8.5) and management actions (BAU, CCF and SA), separated by the two

Fig. 7
Fig. 7 Relationships between the variability in the simulated values of deadwood volumes, in x axes, of each of the five deadwood characteristics (in the panels: a = 9 diameter classes expressed in cm, b = 4 decay classes, c = 5 collapse classes, d = 3 tree species, e = 2 deadwood positions), and the predictions of total deadwood (for the Sobol´ G function, cf., Puy et al. 2022) in y axes, for one

Fig. 8
Fig. 8 First (Si) and total (Ti) order Sobol indices (derived from the Sobol´ G function, cf., Puy et al. 2022) of the total deadwood volume uncertainty partitioned by the uncertainty in each of the five deadwood characteristics (in the panels: a = 9 diameter classes, b = 4 decay classes, c = 5 collapse classes, d = 3 tree species, e = 2 dead-

Table 1
Summary statistics for key stand level variables used in the simulations (N = 158 stands)

Table 2
Summary statistics of the deadwood parameters used to initialize the simulations for NFI stands' estimates for Central Finland (N = 1475)

Table 4
Impact of the exclusion of each deadwood characteristics from the uncertainty in all deadwood characteristics