Optimal spatial harvest planning under risk of windthrow

Abstract

This study solves the problem of optimal spatial harvest planning when forest stands are faced by risk of windthrow and the risk depends explicitly on the features of the stand and its neighbours as well as on the geographical structure and orientation of the forest. First, we estimate the optimal rotation age and expected net present value for a range of discount rates and windthrow hazards for an unprotected stand. Next, the influence of shelter is evaluated for a ‘forest’ with two stands. Two different windthrow probability models are analysed. Relative to the one-stand case, the optimal rotation age and the corresponding net present value change significantly when an extra stand is included. This is due to the shelter effect reducing the risk of windthrow. Shelter also increases the optimal rotation age from the lower limit, being the optimal rotation age of a single stand, towards the upper limit being the case without risk. The optimal rotation age is shown to depend on geographic orientation as well as the age difference between the two stands of the ‘forest’. For forests with a higher number of stands, the optimal rotation ages may increase considerably due to the shelter effect. To illustrate this, we investigate the optimal harvest policy for a ‘forest’ with four stands where one of the stands is surrounded by the three others. The sensitivity towards geographic orientation is again analysed. Finally, a ‘forest’ with 16 stands is investigated to exemplify how an optimal short-term policy can be identified for an even higher number of stands, though the optimal harvest ages cannot be calculated within reasonable time.