Environmental variables (env) which can be chosen for the probabilistic risk assessment are monthly values of the Standardized Precipitation Evapotranspiration Index, SPEI (-), but also monthly values of precipitation, temperature, or consecutive dry days with precipitation below 1 mm. The SPEI is a recent extension of the Standardized Precipitation Index by the influence of temperature on the potential evapotranspiration and was calculated with function spei of R package SPEI with a 3-monthly averaging interval. SPEI values have an average of 0 and are regarded as an indicator of drought below -1.0 or water surplus above 1.0.

In our case, we choose S as monthly SPEI values and give results for other env in appendix . We use env values from 1981 to 2010 (see Sect. ).

To derive the system variable sys, we use results of the global, dynamic process-based vegetation model LPJmL (see Sect. ). For the analysis, daily meteorological data described in Sect.  are used as forcing data for the simulations with LPJmL. A detailed protocol of the model set up is given in Sect. . All processes, including fire, are simulated at a daily resolution in this study, so that extreme conditions contained in the climate input data set will have an impact on the simulated ecosystem variables. To derive sys, we select monthly values of net primary production (NPP), heterotrophic respiration (Rh) and burned biomass (BB) (all given in gC m-2 month-1) from which net biome production (NBP) is calculated (Eq. ). NBP=NPP-Rh-BB In order to detect hazardous conditions outside their average seasonal dynamics and to include lagged effects of the ecosystem in the months following after the extreme weather event, a moving time window of 12 months is defined, during which NBP values were considered. The system variable sys for month i in the period of m years is chosen as the sum of NBP over the 12-month moving window including month i and the following 11 months (Eq. ). sysi=∑k=ii+11NBPkfori∈(1,…,m×12). With this definition, sysi integrates over a 12-month period but does not refer to the calendar year. It eliminates the effect of seasonal dynamics within NBP, independent of differences in growing seasons between biomes and regions. The choice of the moving time-window aims at the consideration of long-term impacts of weather extremes and the exclusion of seasonal effects, for example by plants in seasonally dry ecosystems that are adapted to dry summer months. Moving the one-year window month by month further accounts for droughts of varying duration. The env variable SPEI with an averaging interval of 3 months represents a medium-term situation on the subseasonal scale . The combination with the ecosystem condition over a cycle of 12 months allows for the identification of responses which exceed seasonal variations.

We define a hazard as a month i for which the system variable sysi is negative (sysi<0), i.e. the ecosystem is a net source of carbon for the following 12-month period. Hence, the performance of the vegetation model is decisive for the classification as hazardous or not, but only the sign of the carbon balance and not the extent of the reaction. Since the magnitude of the vulnerability and risk values determined by Eqs. () and () result from the average deviation of the meteorological variables, it does play a role whether the processes in the model include or react to feedbacks important in drought situations, but the exact representation of the magnitude of the response does not play a role in our approach.

We use WATCH-ERA-Interim daily climate data at 0.25∘ × 0.25∘ grid cell resolution to the European spatial domain (29.125 to 71.375∘ N and -23.875 to 45.375∘ E). This data set is based on downscaled WATCH climate data for the years 1901–1978 and extended to 2010 using downscaled ERA-Interim climate data see details in. The variables in the daily climate data set include temperature (minimum and maximum daily values), precipitation, wind speed, and long-wave and short-wave downward radiation flux. Annual atmospheric CO2 concentrations for 1901–2010 are based on data from ice-core records and NOAA atmospheric observations .

LPJmL simulates carbon and water cycles as well as vegetation growth dynamics depending on daily climatic conditions and soil texture. Natural vegetation is represented in LPJmL at the biome level by nine plant functional types (PFTs) . The model calculates closed balances of carbon fluxes (gross primary production, auto- and heterotrophic respiration) and pools (in leaves, sapwood, heartwood, storage organs, roots, litter and soil), as well as water fluxes (interception, evaporation, transpiration, snowmelt, run-off, discharge) . Photosynthesis is simulated following the Farquhar model approach . Processes of carbon assimilation and water consumption are parameterized on the leaf level and scaled to the ecosystem level. Carbon and water dynamics are closely linked so that the effects of changing temperatures, declining water availability and rising CO2 concentrations are accounted for and their net effect can be evaluated . Physiological and structural plant responses determine water requirements and consumption.

LPJmL has been used in various studies where the hydrological cycle and the plants reaction to water shortage were a major factor. In these studies, different affected processes were investigated including run-off , and local carbon fluxes and water flux dynamics see comparison with eddy-flux tower measurements for the northern latitudes in Figs. S2 and S3 in the Supplement,. Furthermore, system response to drought stress of the LPJmL model has been compared to observational data for the European summer 2003 climate anomaly . On the European scale, coincidence pattern of NPP reductions were compared to tree ring data which revealed a strong sensitivity of the model to extremely low precipitation.

Thus, when the climate forcing includes prolonged periods of drought and/or high temperatures, these have direct effects on carbon assimilation and water stress in the model. LPJmL simulates physiological processes depending on the current climate conditions and their history which is reflected in the composition of the plant community and their carbon stocks accumulated so far. Hence, the response of the model to a certain extreme event is not always the same. Biological mechanisms responding to extreme events include net primary productivity driven by climate conditions and by atmospheric CO2 concentration which changes the amount of leaf biomass simulated for each PFT. Under rising atmospheric CO2 concentrations, stomatal conductance decreases, leading to higher water-use efficiency which can buffer increasing drought impacts. Another example of physiological adaptation is carbon allocation to new roots, which is an adaptive response to increasing soil water limitations. Unproductive individuals with a low growth rate are likely to die. The resulting model response is a combination of the climate conditions and of the characteristics of the present PFTs. Competition between PFTs due to differences in their performance under given climate conditions, can lead to changes in vegetation composition as less adapted PFTs can be out-competed and replaced. Subsequently to changes in vegetation composition, i.e. changes in the PFT distribution, changes in the productivity and the respective carbon fluxes can also be quantified. This applies to long-term climate trends as well as interannual climate variability, including the impact of extreme events. Therefore, the LPJmL model is indeed capable of capturing dynamic responses to, for example, single or consecutive drought events.

Fire is simulated within the process-based submodule SPITFIRE . emphasize the importance of using daily maximum temperature in fire risk calculation to better capture extreme risk situations. The Nesterov Index , used to calculate fire risk in SPITFIRE, considers daily maximum temperature. Given the daily resolution of the input data set, the model should respond to prolonged drought and heat. Vegetation re-growth on burnt areas, simulated by SPITFIRE, depends on respective tree seedling performance and grass establishment under given climate conditions and follows the algorithms as described in the LPJmL model. Biomass burnt (BB) result from dead and live fuel consumption in surface fires and from crown scorching and is included in the carbon balance NBP (Eq. ).

The suitability of the LPJmL framework for vegetation and water studies has been demonstrated by validating simulated phenology , river discharge , soil moisture , evapotranspiration and carbon stored in litter biomass on the ground for temperate and boreal European ecosystems .

For deriving the system variable sys, LPJmL simulations were performed with natural vegetation. In order to derive equilibrium fluxes between soil and vegetation, 1000-year spinup were simulated by using the climatic forcing from 1901 to 1930 in repetitive loops. The transient run from 1901 to 2010 was started by a further spinup period of 30 years. Climate forcing consisted of the WATCH-ERA-Interim climate data described in Sect. . Data for the soil properties and for lightning, human population density and human ignition were regridded from a spatial resolution of 0.5∘ × 0.5∘ to 0.25∘ × 0.25∘.

For the detailed calculation of ecosystem vulnerability, we chose two sites in Europe with different climatic conditions. In site 1 in northern Germany (Fig. a) the probability for a hazardous ecosystem condition (i.e. sys<0) for the period 1981 to 2010 is 0.25, i.e. 80 of 360 data points are in the hazard group. The expectation value of the chosen env, the drought index SPEI, is 0.34 for data points with sys<0 (hazard case) and -0.09 for those with sys≥0 (non-hazard case). The difference between both sets of SPEI values is significant (p value for statistical significance <0.01) and results in negative VE and RE (Fig. c). Thus, site 1 is not vulnerable to drought but to wet conditions. Due to the infrequent hazard occurrence, the corresponding risk is low.

In the second site in Spain, the probability for sys<0 in the period 1981 to 2010 is much higher (50 %, Fig. b). The expectation value for SPEI values in the hazard group is -0.19 and 0.22 in the non-hazard group. The two sets of SPEI values are significantly different (p<0.001). Here, VE and RE are positive (Fig. c). Site 2 is vulnerable to drought, meaning that carbon losses from the ecosystem occur when SPEI is 0.4 units lower than in situations when the ecosystem is accumulating carbon. The corresponding risk value of 0.2 is in this case lower than the vulnerability of 0.41 (Fig. b) and expresses the not fully utilized vulnerability potential because such extremes occur less often. Therefore, calculated risk values cannot be related directly to the severity of drought conditions, but relates ecosystem vulnerability to the hazard occurrence.

Multiple processes can be responsible for hazardous NBP. Disentangling the carbon balance components NPP, Rh and BB under hazardous and non-hazardous conditions is one way to provide this insight. For site 1 in Germany, the distribution of NBP (Fig. a, left) is centred around 70 gC m-2 a-1 with negative values mostly above -50 gC m-2 a-1. These data points are characterized by low net primary productivity (NPP, Fig. b, left) and high heterotrophic respiration (Rh) above 480 gC m-2 a-1 (Fig. c, left). Biomass burnt (BB) is low (Fig. b, left) and does not differ between hazard and non-hazard groups. The defined hazard (negative NBP) is here occurring when SPEI values are rather high (Fig. e, left). In these situations, precipitation (and therefore, soil moisture) is above average, and radiation is below average (see area 1 in Fig. f, h).

At site 2 in Spain, mostly grasses grow with a low coverage of temperate evergreen trees. Negative NBP (Fig. a, right) is associated with low NPP (Fig. b, right), slightly lower Rh (Fig. c, right) and high BB (Fig. d, right). In the hazard case, precipitation is reduced substantially (see area 2 in Fig. f) so that NPP is water-limited and fire is often occurring. The positive VE value for site 2 reflects the impact of drought on the NBP.

When applying the ecosystem vulnerability concept to the pan-European scale under current climate (1981–2010, Fig. a), we find vulnerable ecosystems predominantly in southern Europe (VE>0.6). The border region of Ukraine, Belarus and Russia is most pronounced with positive VE values of more than 0.4. Reduced precipitation and slightly enhanced temperatures decrease photosynthesis and increase heterotrophic respiration in this forest area (area 3 in Appendix ). VE above 0.4 is also determined in the mountainous regions of Macedonia and Albania. Weather conditions are extremely variable and lead to an open forest ecosystem. Reoccurring drought conditions do not allow for an accumulation of carbon in the biosphere and soil respiration enhances the loss of carbon during hazard occurrence (area 4 in Appendix ). In the boreal zone, VE is negative meaning that those ecosystems are not vulnerable to drought. Comparing the expectation values of the hazard conditions, allows to reflect on the realized vulnerability, i.e. the risk RE for carbon loss (Eq. ). The corresponding RE (Fig. b) shows highest values in northern Africa (0.4) followed by 0.2 in the Mediterranean, the Balkan Peninsula and Ukraine.

Having described regions and conditions being vulnerable (positive VE), large regions in Europe show vulnerability values around zero or are even negative. Extensive areas in the temperate region have VE values close to zero which are not significant (areas not marked by dots in Fig. a) while in northern regions even negative values are widespread. We determine the spatial extent of vulnerable areas (positive VE) in Europe. For 24 % of the European area, positive VE values and significant differences between hazard and non-hazard groups of data are determined. In the southern region, this holds for 53 % of the grid cells, whereas this percentage is smaller for the temperate and the northern regions (Table ). Near or below zero VE values are calculated for 58 % of the European area (89 % for NEU, 49 % for CEU and 13 % for MED, SREX regions according to Table ). Here, the ecosystem hazard occurs but can not be ascribed to drought.

Reasons for negative VE could be (1) the ecosystem hazard is not explained by the selected env variable and a further env has to be identified, or (2) the range of the expected value chosen for the analysed env is not appropriate, e.g. high SPEI values are more damaging for the ecosystem than low values (see ). Negative VE values hardly occur in southern Europe (1 % of the area), but frequently in the temperate (11 %) and northern (32 %) zones.

When comparing zonal averages of VE according to the SREX regions (Table ), ecosystem vulnerability to drought is high in the Mediterranean region (MED) with 53 % of the region affected and showing the highest risk compared to other SREX regions (Table ). Positive VE values for most of central Europe (CEU, 20 % affected) indicate widespread vulnerability to water shortage. Northern Europe (NEU) is characterized by mostly negative VE affecting a negligible part of the region. Here, risk values are also relatively high because of more frequent hazard occurrence.

The proposed method allows for the quantification of the vulnerability and the associated risk of ecosystems to environmental drivers. This is also possible with other methods , but our approach differs in that hazards are defined ecologically rather than meteorologically. From our ecosystem perspective, it is not necessary to assume thresholds for a weather extreme situation such as extreme temperature or precipitation. Instead the ecosystem vulnerability concept proposed in this paper subsumes combined or single, immediate or lagged, direct or indirect effects of weather extremes on ecosystem condition into one metric (following the concept of ).

For the perception of the ecosystem hazard it is important to choose a system variable sys that represents vulnerability of an ecosystem (e.g. high respiration or low net primary productivity). But also the associated threshold for the definition of the hazard has to be selected with care (e.g. NPP <0). One option is to choose a variable for the hazard definition that is widely accepted and easy to interpret for the ecosystem under consideration. Both choices, sys and the threshold, should be made with respect to the goal of the study. Here, we selected carbon release to the atmosphere as the hazard, i.e. negative net biome production (NBP). This variable is commonly used to interpret carbon fluxes of an ecosystem as net emitter through respiration and disturbances or net accumulator through photosynthesis .

With an ecosystem in equilibrium, emissions equal gains more or less so that short-term carbon releases do not represent a hazard to the ecosystem. For ecosystems in transition, only longer lasting net losses may pose a problem and are thus suitable for defining hazard. In order to eliminate the seasonal cycle and thus short-term fluctuations, we take NBP sums over 12 months (Eq. ). This identifies situations where on an annual timescale net carbon losses of an ecosystem to the atmosphere have been larger than net gains. And it avoids the unwanted detection of vulnerability in regions of regular seasonal drought where ecosystems are adapted and usually compensate carbon losses during the vegetation period or rainy season. Thus, the chosen time window of 12 months is not related to the life expectancy of the vegetation or the expected duration of droughts.

An extension of the approach would be the application to measured data. Nevertheless, scarce data availability for larger areas (regional to continental scale) is a drawback. Eddy covariance data for single sites seem to be suitable but are seldom available for more than 20 years to provide sufficient data points for probability distributions. Data products on the continental scale would be beneficial and attractive but not yet existing . So far, the application of our concept reveals the reaction of the model LPJmL to climatic conditions which represent our condensed knowledge about plant processes. Specifically LPJmL is validated thoroughly for each of its components, the calculation of vulnerability measures from model results on the European scale provides an important and informative but nevertheless first step in this context.

With the proposed concept, ecosystem vulnerability can be integrated into the framework proposed by . For them, three main functions have to be fulfilled. First, there has to be an entity that is vulnerable, which in our case is the property of an ecosystem to be a source or a sink for carbon. Secondly, a stimulus has to exist to which the entity is vulnerable, which here is exerted by the climatic variables. Thirdly, the interaction of entity and stimulus has to have a notion of worse or better which is given by assigning a hazard to an ecosystem when it is a carbon source. The perception of of the risk also matches well to formula Eq. (), since they define risk as vulnerability weighted by the occurrence of the hazard. We go one step further in that we cannot only distinguish between vulnerable and non-vulnerable conditions, but quantify it along a continuum. This opens new ways to interpret ecosystem vulnerability in the context of gradual ecological changes and system behaviour with respect to biogeochemical cycles.

Our concept quantifies the long-term and combined impact of extreme weather events, and does not evaluate the effects of single events. By assigning each monthly value of sys to either the hazard or the non-hazard group, each individual ecosystem behaviour contributes to the assessment of our long-term ecosystem vulnerability and risk.

It links to by directly addressing the behaviour of ecosystems and relating it to the meteorological conditions under which it occurs. Exploring the connection between hazards and extremes sensu, both concepts define thresholds for hazardous or extreme conditions and both examine the physical and biological spheres independently. In contrast to , we apply not a distributional threshold (referring to extremeness) but a qualitative threshold (i.e. ecosystem as a source or sink of carbon). Applying the same logic to the environmental driver env e.g. like, a meaningful threshold can be set for the environmental variable SPEI of -1 as defined for drought in. This allows probabilities to be derived also for the transition of non-hazardous env events into hazardous and non-hazardous sys conditions. Following , it is then possible to quantify the probability of occurrence of all four combinations of the ecosystem variable sys, in our case NBP, and the environmental variable env, here SPEI (Fig. ).

We quantified all four combinations for two sites (see Fig. ) using the simulated 30-year time series (as described in Sect. ). At both sites, hazardous env conditions occur in 16% of the months but the responses of the ecosystems differ. At site 1, for which VE is negative, about 22 % of the env data belong to the hazard group and less than 3 % of the data link hazardous sys conditions with hazardous env conditions (Fig.  left). At site 2 with positive VE, about 50 % of the env time series belong to the hazard group and in about 11 % of the months, hazardous env conditions coincide with hazardous sys conditions (Fig.  right). Under current climate conditions, the Mediterranean site experiences more hazardous (extreme) environmental condition that lead to carbon release.

This shows how the proposed PRA takes up the concern of to include the ecosystem perspective into data driven probabilistic risk assessment. This way, we are able to back-up the theoretical concept of with data at the continental scale.

The quantification of ecosystem vulnerability and risk requires some careful interpretation of the obtained values. First of all, their units are defined by the chosen env and, secondly, the interpretation of their sign and magnitude depend on our interpretation of the damaging effect of env. Therefore, we give both some consideration.

High values of ecosystem vulnerability indicate high vulnerability to lose carbon due to drier conditions than usual, i.e. the SPEI difference during ecosystem hazards is decisive for the vulnerability and not the absolute values of the drought indicator. This difference reflects the distance between two average conditions: (a) advantageous climatic conditions under which the ecosystem accumulates carbon and, (b) unfavourable climatic conditions under which the defined hazard is occurring and the ecosystem emits carbon to the atmosphere. Thus, the higher the difference and therefore VE, the higher the distance between favourable meteorological conditions (non-hazard) and those leading to the ecosystem hazard. Hence, high VE values express the difference between environmental conditions to which the ecosystem is adapted and those conditions under which the ecosystem emits carbon. An increase in VE in the future can have two reasons: conditions are dry more often (low SPEI values) or become more extreme (extremely low SPEI values). The latter also means that weather extremes, in our case droughts, are causing hazardous conditions more often which result in lower mean values in the hazard group. Hence, the difference between the hazard and non-hazard groups increases.

The approach does not specifically allow the impact of single events to be identified but the long-term and general occurrence of hazardous events, either being more severe, frequent or lasting longer and more importantly impact these changes have on ecosystem status, which is interesting from an ecological and management point of view. Extremes events, such as droughts causing negative NBP, have been identified for past weather extremes . Such events, which occur during the investigated 30-year period and lead to vulnerable conditions for the ecosystem's carbon balance, fall into the hazard subset of data points. It is possible to identify the position of these hazard samples in the scatterplot (Fig. ) and estimate the severity of the corresponding extreme event. However, the presented ecosystem vulnerability approach evaluates long-term effects that these weather extremes have on the affected ecosystem. It looks not only at short-term impacts, which occur immediately after the event, but captures long-term effects determining the capacity of the ecosystem to recover and stabilize. This is an important point as it refers to the ecosystem's resilience.

Areas with ecosystem vulnerability values close to zero are those with similar mean env values in the hazard and non-hazard group. Thus, ecosystems are not or only marginally vulnerable to env, in our case drought. The proximity between both average values suggests that within the considered period any potential causal relationship between sys and env (in our case droughts causing negative NBP) did not materialize. The marginality of the impact of env was additionally evaluated by considering the statistical significance of the difference between hazard and non-hazard group.

Negative ecosystem vulnerability indicates that the ecosystem is vulnerable (carbon losses do occur) but either not to the anticipated data range of env (low or high values) or not to the specified env. In the first situation, drought is not responsible for the ecosystem's carbon loss. Here, the expected value of SPEI for negative NBP (i.e. a hazard) is higher than that for positive NBP, i.e. under non-hazard conditions. In the second situation, other environmental variables, e.g. P or T, should be considered and evaluated for their potential impact on the ecosystem. Since VE is based on a probabilistic approach, its values only indicate potential causalities which have to be evaluated subsequently.

There are two possibilities of failing VE determination: when the hazard does not occur at all in the study period, i.e. there is no vulnerability, or when there is no data point in the non-hazard group. The latter case can arise when due to changing environmental conditions each data point falls into the hazard group. In order not to misinterpret missing VE values, the reason for the calculation failure should be reported. However, the ecological interpretation for the latter case is simple: the ecosystem has converted into a continuous carbon source and might undergo rapid and profound transitions to a new ecosystem state.

An interpretation of RE values may reflect on the sign of the calculated value, i.e. whether a damaging effect of the regarded env can be stated, and on the likelihood of the quantified vulnerability. The ecosystem vulnerability approach quantifies weather conditions that caused ecosystems to become a source of carbon to the atmosphere. The risk can be lower than the vulnerability when hazardous events occur less often, i.e. the full vulnerability potential was not utilized. Similar to other metric or model concepts, the presented approach reflects the impacts of currently known ecosystem hazards. For hazards emerging in the future, the ecosystem vulnerability approach can be adjusted accordingly.

Under current climatic conditions, VE and RE values can be calculated at the European scale because hazard occurrence in the LPJmL results is sufficiently frequent. Ecosystems in southern Europe, i.e. in the Mediterranean basin, and even more so on the Balkan peninsula, in Turkey and the Ukraine, are known to experience severe drought stress . The highest VE values, though, were calculated for eastern Europe for current conditions. Already today, ecosystems in these regions lack sufficient water to compensate for drought stress in order to avoid carbon loss and fire ignition. Here, increasing attention is directed to the evaluation of carbon emissions to the atmosphere by fires . found most carbon losses in recent observational data on gross primary production (GPP) to be caused by drought and fire. It is noteworthy as they could attribute the majority of carbon loss to few and extreme situations.

Temperate regions in central and eastern Europe as well as boreal regions in northern Europe show vulnerability values against drought close to zero, most of which are not significant. In these ecosystems, the hazard occurrence is rare and the difference between hazardous and non-hazardous conditions is small. Here, the few periods during which carbon is emitted to the atmosphere are balanced by periods of carbon uptake so that the affected ecosystems are not vulnerable to drought under current climate.

For northern Europe, negative vulnerability values were calculated for boreal forests as well as tundra ecosystems. Belgium, the Netherlands, northern Germany and large areas in Scandinavia fall into this category (Fig. a, Fig. a and appendix ). In these regions, moisture supply is higher than needed. When carbon loss is observed here, vegetation growth is limited by factors other than drought. These could be caused either by unfavourable temperature or radiation conditions or an excess supply of water (see examples in appendix ). Using phyloclimatic plasticity functions, conclude that forests in Scandinavia will benefit from decreasing precipitation and increasing temperature.

We found the corresponding risk to be negligible under current conditions. Even for the Mediterranean, water scarcity as expressed with RE values for SPEI (Fig. b) and precipitation (Fig. b) occurs rarely so that the significant VE values are reduced.

Although the analysis is undertaken with model results solely, especially the responses of LPJmL to weather extremes are well validated. For the European heatwave of 2003, compared model results for GPP to remote sensing products and found a standard deviation between model results and data of less than 25 gC m-2 month-1 for the majority of the grid cells. investigated extremes in GPP at the global scale and found LPJmL to be well able to reproduce the extent and impact of extreme events. Considering the role of fire for VE values in southern Europe, an in-depth evaluation of the fire model is in progress using data from the GFED database and the EFFIS database for a joint analysis of vegetation-fire models.