Windthrows are natural hazards and a significant body of literature has been published on this particular issue ( Ulanova, 2000 ; Klaus et al. , 2011 ; Nilsson et al ., 2004 ; Schliemann & Bockheim, 2011 ; Boon, 2012 ). Nowadays, windthrows are included into the large concept of natural disturbances (Popa, 2008 ), along with wildfires, droughts, and insects' attacks.

One important outcome and symptom of the climate change is the frequency and geographical distribution of endemic windthrows (EW), which are affecting larger and larger areas (Res et al. , 2006; Senf & Seidl, 2017 ). EW were defined by Lanquaye-Opoku & Mitchell, (2005) as disturbances produced by peak winds, with return intervals shorter than 5 years. The amount of wood blown down may vary from tens of cubic meters to hundreds and this wide interval of variation is caused by the 'domino effect', quite difficult to take into consideration ( Nolet, 2012 ; Nolet & Béland, 2017 ). Lohmander & Helles, (1987) summarized a series of theories on the causes of windthrows while ( Mitchell, 1998 ) came up with a methodological framework based on the so-called windthrow triangle, which makes use of data concerning the stand condition, soil, and exposure.

Due to the large variety in geographic distribution and economic loss, studying natural disturbances under climate change is very provocative in statistical terms. Yousefpour et al. , (2012) ranked the methodological approaches and found out that the most used models are geometric Brownian motion and probability distribution. The authors also produced some interesting statistics of the articles published on risk-related issues on forestry and concluded that the trend of articles published each year is exponential. Markov Chains and Bayesian models, we have used in our exercise, were among the least used approaches.

Long-term sustained yield has long been modeled as MC ( Kouba, 2002 ) and Buongiorno & Zhou, (2011) demonstrated that even the Faustmann's formula is a particular case of MC, assuming that all transitions from one phase to the next one are certain, meaning that all stands will reach the prescribed maturity age.

Holecy & Hanewinkel (2006) produced a forest insurance model based on probabilities given by Weibull functions plugged into a MC model while Strigul et al. , (2012) developed a MC model to study the dynamic mosaic of forest stands; they concluded that age-class structures of the forest are skewed to the right, which is consistent with a MC stationary distribution.

The new paradigm of adaptive forest management stems from a mixture of extensive use of recent knowledge, risk management and a series of measures able to maintain the ecosystem resilience ( Bolte et al. , 2009 ). In line with this new paradigm, the forest management planning shall come up with a more flexible approach of forest sustainability and, in particular, a deeper understanding of the sustained yield principle.

An extensive literature review on assessing the natural hazard risks in forestry has been published by Hanewinkel et al. (2010) who came up with a flowchart about the risks pertaining to different geographical scales of the decision-making process. However, the first step of the procedure, that is the framework analysis, takes into consideration just the regional climate models and the general circulation model, which are relevant for extreme events only ( Popa, 2008 ).

The sustained yield principle (SYP) has long been adopted by Romanian forest policy makers and, it has been implemented into the algorithm of calculating the AAC too. As anyone would expect, SYP was an important pillar of forest management under the command and control economy, and it made sense for many reasons. During the transition to market economy SYP has been justified by the social concern that freeing too much the forest planning will encourage the forest owners to use any legal loophole to make the most of their own forests ( Bouriand, 2005 ). Obviously, many illegal loggings reported by the media and the Court of Accounts in 2013 ( Anonymous, 2013 ) gave to politicians a convincing reason for keeping a tight control on the annual harvest, despite that, after 2008, the allowable cut adopted by the forest management planning had been rigorously checked by the public authority.

However, on a long run, pursuing only SYP could be ineffective and somehow dangerous for the forest economy and forest ecosystems, for two reasons at least: 1) SYP cannot go along with any ecological leeway simply because the planning methods based on SYP do not account for any uncertainty; and 2) pursuing SYP per se has created a positive feed-back loop because more salvage fellings in stands older than 60 years old have replaced mature stands initially included into the cutting budget and the harvesting plan.

Having salvage fellings instead of regular harvesting operations is even more convenient from a sheer economic standing point: according to the Forest Act, the regeneration fund, which is a sort of insurance deposit for having enough money to regenerate a given stand after final felling, is fed by 10% of the income provided by the main yield only. Such a 'tax relief' for salvage cuttings makes sense for catastrophic events, like the windthrow that took place in 1995, when more than 8 million m ³ have fallen in one night ( Popa, 2005 ). At that time, the broken trees were left un-hauled in remote areas for more than three years, due to extremely difficult harvesting conditions. Noteworthy, the Forest Act was adopted in 1996 when the consequences of that catastrophic event were apparent. On the contrary, when it comes to EW such a legal provision turns into a loophole, because more salvage fellings instead of regular harvest allow forest owners to avoid feeding this regeneration fund.

The aforementioned feedback loop has been imple­mented into an official regulation which states that every year the annual harvest is made of 80% of the current AAC, plus 20% of AAC of the previous year unless salvage products are to be harvested from stands older than 60 years.

If salvage fellings occur in stands older than 60 ye­­ars, due to whatever reason, their total volume is deducted from the previous year's left AACR. If the salvage volume is higher than the previous year reserve, the difference will be deducted from the next year 20% AAC, and so forth. Eventually, having salvage cuttings each year, by the end of the planning period (every ten years) at least 20% of the harvestable volume will have been left uncut. This 20% AACR has neither economic nor technical support, being based on a rough assessment of the contribution of the catastrophic windthrows to the national cutting budget since 1995.

From the standpoint of mid and long-term planning, sooner or later the mature stands, postponed from harvesting, will eventually pile up into the last age class and the AAC stops being a means to normalizing the forest age structure. This particular situation shall also be addressed, in order to find out how the process of getting the mature stands older and older can be stopped.

Often, due to logging settings, salvage cuttings brought about by the windthrow are not applied only to the broken trees but also to some healthy trees that have to be removed in order to make broken trees accessible, which makes sense from the technological point of view ( Waldron et al. , 2013 ). Therefore, the scope of any perturbation is always larger than the forest area covered by the damaged trees.

When it comes to windthrows, the gap between case-studies based on different methodologies and effective headways towards a better forest planning is still large. Therefore, this study aims to producing an algorithm that utilizes the data referring to EW occurred in the past to improve the decisions regarding the annual cutting budget every next year. We developed a cascading Bayes model ( Keith et al. , 2003 ) to assess the EW likelihoods considering all possible permutations of three EW contributing factors (proximity of a prior EW, terrain conditions and slenderness). The EW likelihoods are further plugged into a MC model that shows the tendency of having a slant age class structure, regardless the normal age pursued by the forest planning. Finally, the share of each age class produced by MC is plugged into an intuitive formula that helps the forester decide the share of each annual allowable cut (AAC) that must be put off for the coming year in order to compensate for the EW volume that might occur in the current year

The key issue discussed here is whether or not the sheer Bayes' rule is a good option for making statistical inferences. The Bayes' rule assumes interchangeable roles between hypotheses and evidences ( Nöth & Weber, 2003 ). This assumption is counterintuitive because most of the people are inclined rather to think in terms of cause and effect; once this epistemological difficulty is overcome things become clearer if we associate the hypothesis with a causal chain strengthen by more evidence, which turns into a new hypothesis, and so forth ( Wintle & Lindenmayer, 2008 ).

Based on the old concept of windthrow triangle ( Mitchell, 1995 ) we considered just three enabling factors, in all possible orders conveyed into six permutations. Having one more attribute, say the position on the slope, given that in many cases the stands located on foothills are blown down by the wind coming from the opposite direction, the number of all possible permutations (i.e. hierarchies of factors to be tested) rises to 24. From the computational point of view this is not big challenge because all calculations can be plugged into spreadsheet and the input data are produced by a simple cross-tabulation, provided that all important attributes had been included into the GIS table of attributes ( deFillipi et al. , 2004 ).

A 30 m wide buffer may indicate as adjacent two stands separated by a 59.99 m wide strip of trees which were not yet blown down, if the two stands affected by EW are separated by a stand of trees narrower than 60 m. Such situations are represented by very thin buffers, some of them being screen-captured in Figure 4 and marked with yellow circles. Hence, prior EW vicinities might have been overestimated in some cases, but such situations can instantly be spotted.

For the first age group of stands the best predictability corresponds to a seemingly unexpected permutation of factors: vicinity-terrain-slenderness. It is quite surprising because most of the young stands are not actually thinned, and slender. Even more surprisingly, slenderness plays the most important role for the EW produced in middle-aged stands ( Konopka et al. , 1987 ). For the last age group none of the permutations of factors proved to be a serious threat, considering the combinations of EW and values taken by the three enabling factors.

We tested the accuracy of predictions with the ROC-AUC procedures. The main disadvantage of gauging any prediction made by discrete-output procedures - and Bayes' rule turns discrete likelihoods - is the ROC shape ( Schindler et al. , 2009 ). All discrete values taken by EW likelihoods are shown in Table 3 but, associated to the stands, they appear in lesser combinations, depending on how numerous are the stands that fall into one of the three age groups. Yet the most complex situations are characterized by eight likelihoods, only the ones with likelihoods grated than 0.5 are being considered, as shown in Figure 8. The first one (a) was the most complex (with four discrete values) but most of other ROC look like (b), with three discrete probabilities and (c), with only two discrete values.

The fourth situation (d) typifies all ROC curves for the last age group. In Figure 8 d) we have only two true positives situations, without any false positives. Because the cumulative frequencies are plotted against the two axis, summed up from the lowest to the highest likelihood, the two pints are vertically aligned to the right, having no area below. However, the loss of information is not important because the EW likelihood of the last age class must be forced to one, because all mature stands are supposed to be harvested within the next two decades.

If the young stands had higher growths, the AACR would have been higher: an average of 3.7 m ³ /year/ha, as Table 6 shows, is a hint of having unstocked stands in the first two age classes.

By cascading the Bayes tree probabilities for each development stage, we assumed that it must be an order in which all three enabling factors weaken most of the trees, although the order is yet unknown. Hence, we had to conceive all possible orders of factors and see which ones behave better in terms of accuracy of prediction.

Our case study showed that what really matters is not the predefined set of enabling factors, but the number of cases analyzed in order to train the model. Having more cases in the first age group, four ROC, out of six, are meaningful (greater than 0.5), while the second age group has just two significant ROC (for STV, and VST respectively, see Table 4).

We have confined our study to two periods of ten years each to match the data required by the model with the data supplied at no additional cost by the Romanian forest planning system. Worth noting, for Brosteni FD, as well as for any public FDs in Romania, the last and the last but one forest management plans have been produced in GIS technology, allowing cheap data processing; consequently, we couldn't go back too much in the past. In other conditions, having a greater amount of data and more GIS maps for the same area.

This study is the first attempt in calculating AACR, which shall be put off for the next year, given a certain pattern of EW (or whatever disturbance) for Romanian forest planning. The study demonstrated that 10% AACR is enough in mountainous area, where EW are quite frequent. The 10% or 20% of the AAC left unharvested from the previous year, and the same amount of wood left uncut for the coming year is not, allegedly, a substantial improvement of forest management. However, a slimmer AACR is advantageous for logging companies who are bidding for harvesting contracts every year, because they can make more combinations with the tracts worth bidding for, simply because the share of the main yield auctioned every year by the forest managers is 10 % greater.

If the SYP fails to normalize the age-class structure of the forest due to the positive feed-back loop previously described, the model allows a better control on the total yield, and eventually can be used to improve the calculation of AAC, considering a slant age-class structure, not an even one. Having better predictions of EW, knowing their future locations (elevation, slope and aspect) and the hydrological effects of a clear-felling, the forest planners will be able to integrate this information into more complex decision-making models, able to better balance the wood production with water runoff management.

We have considered only three enabling factors, but the list is open: besides slenderness, terrain conditions and EW vicinity, other factors can be added, such as vertical structure of the stands, presence of wind-resisting species of trees, or their location (uphill or downhill). The hints for taking into consideration a new factor are the values stored into the contingency table; and the more permutation of enabling factors are at hand, the more curved ROC will be, allowing better predictions of further EW.

We are deeply grateful to the two peer reviewers for their supportive suggestions. We also acknowledge the staff of Brosteni FD who provided us the input data.