Integrating natural risks into silvicultural decision models: A survival function approach

In the context of climate change, the frequency and intensity of natural disturbances of silvicultural production, such as storms and insects, are expected to increase. Hence, now more than ever before such factors must be considered in forest management. As a contribution to this topic, this article presents a calculation model implemented in Excel frames, which supports decisions in forest production under changing conditions. Risk is integrated into the model by the Weibull function, which serves as an age-dependent survival function. In order to facilitate an intuitive interpretation of its coefficients, it was used in a reparametrised form. Furthermore, salvage price reductions and cost additions caused by calamities are considered. The target variable is the ‘annuity under risk’.We demonstrate exemplarily how different parameters of the survival function influence the probability distribution and thus the expected value of the annuity of a spruce stand. The differences between the annuities with and without a consideration of risk are interpreted as current, annual risk costs. It can be shown that risk lowers the annuity, whereas scenarios with high risks in the young stand stages have a higher impact than those with high risks in mature stands. In the latter case, adaptation is possible by shortening the rotation period. This does not hold in the case of early risks, which cannot be avoided. For this case, an extension of the rotation length is recommended.By changing the parameters of the survival function, this scheme allows forest managers to incorporate changing risks into their management planning.

Research highlights
► In order to model natural risks, we used the reparametrised Weibull function.
► The advantage is that it has intuitively interpretable coefficients.
► In the decision model we used the annuity as economic target variable.
► Using the survival function the distribution and the expected value of the annuity can be calculated.
► We interpret the deviation between the annuities for the risk-free and the risky cases as annual risk costs.