Cut or keep: What should a forest owner do after a windthrow?

Highlights

• Importance of modelling storm impacts from a physical and an economic standpoint.

• After storms, stand full destruction and clear-cut by default: not good assumptions.

• The cut-or-keep decision rule significantly increases the land expectation value.

• Keeping stand after a storm: often a sound economic decision.

• Some variables (age, diameter) include the relevant information for decision making.

Abstract

After a windstorm hits a forest stand the forest owner has two possibilities: clear cut and start a new rotation or let the standing trees grow until maturity. We compute the Land Expectation Value (LEV) under the risk of windthrow and introduce an endogenous rule to account for this decision. We compare the result with the default alternative of systematic clear felling and replanting (commonly assumed in existing literature). We have calibrated our model to represent maritime pine plantations in south-western France. Results show that by following this rule, payoffs may increase by up to 90% when the economic risk (i.e. probability of having a windstorm) is high. About 75% of the time it is profitable to keep the standing trees until maturity. Although payoffs are sensitive to economic risk, the optimal rotation age does not change much with significant increases in the risk probability.

Introduction

Windstorms are one of the most important risks for forest management. The impacts of catastrophic events and the risk of total destruction on the optimal rotation age have been addressed by previous works focussing on even-aged forests (e.g. Martell, 1980, Routledge, 1980, Reed, 1984). In these earlier works three major simplifying assumptions have been used to obtain analytical expressions for the model’s optimal solutions: (i) The probability of a catastrophic event is exogenous; (ii) whenever a catastrophic event hits the forest stand, it is completely destroyed as a result, hence damages are also exogenous; and (iii) the salvage value after the catastrophe is equal to zero.

While the assumption of exogeneity of a catastrophic event is rather easy to justify, the other two are harder to meet in the real world. Therefore, several studies have tried to relax these assumptions, often through numerical methods.

Valsta (1992) relaxed the assumption of total destruction of the stand by using an uniformly-distributed random variable to represent the fraction of the stand destroyed, and assumed a salvage value. Haight et al. (1995) introduced an age-dependent damage risk and a salvage proportion. Successively, Thorsen and Helles (1998) computed the optimal rotation length and thinning regime using an endogenous damage function that depends on the forest’s characteristics as well as on the forest management (i.e. thinning operations). While Thorsen and Helles (1998) and Haight et al. (1995) assumed an exogenous land value, Loisel, 2011, Loisel, 2014 computed the optimal rotation age and thinning regime that maximise the land expectation value (LEV) – hence taking into account the value of successive rotations – under the risk of destructive events while accounting for the salvage value of windthrown timber.

In an evaluation context, rather than in an optimisation one, Bright and Price (2000) proposed a simple and elegant way to compute the expected LEV under the risk of hazards whose realisation implies the end of the rotation. A similar methodology was applied by Deegen and Matolepszy (2015) to compute site-dependent optimal rotation ages and expected LEV based on historical management data in Germany.

All these studies have assumed total clearing of the stand after a windthrow, independently of the level of damage. However, following a windthrow, it might be profitable to keep the standing trees until the “prescribed” end of the rotation. The continuation of the rotation after a disturbance was firstly discussed by Xu et al., 2016a, Xu et al., 2016b, who analysed the forest management problem under the risk of two sequential disturbances. They tested three alternative strategies: (i) the systematic clearing and replanting of the stand after the first disturbance (the common assumption in previous literature); (ii) keeping the standing trees after the first disturbance and cutting and replanting after the second disturbance; (iii) keeping the standing trees also after the second disturbance² and harvest the stand at maturity. Their results showed that ignoring the continuation options could lead, under some circumstances (i.e. disturbances’ arrival rates, survival probabilities and post-disturbance tree-growth losses), to suboptimal harvest decisions and land expectation values.

In their work, Xu et al., 2016a, Xu et al., 2016b assumed and compared the outcomes of fixed continuation strategies that are kept constant along the planning horizon. However, whether keeping the standing trees is profitable or not will ultimately depend on the cost structure as well as the characteristics of the stand after the windstorm.

In this paper we relax the hypothesis of a fixed continuation strategy and introduce a condition to determine when it is profitable to continue with the remaining trees until maturity and, alternatively, when it is best to cut them immediately and replant the whole stand. We assume (i) an exogenous rate of return for windstorms as in previous works, as well as (ii) an endogenous damage function determining the fraction of windthrown trees after a storm; (iii) a positive salvage value for the windthrown trees, and (iv) explicit clearing costs.

In Section 2 of this paper we present the theoretical model and in Section 3 we introduce the cut-or-keep decision rule. In Section 4 we calibrate our model with real data for maritime pine in Landes Region in France and run a Monte Carlo simulation. Sections 5 and 6 are devoted to presenting and discussing the results.