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Optimal forest management in the presence of endogenous fire risk and fuel control

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Abstract

This study develops a stochastic dynamic model to optimize site value from timber and non-timber benefits for a landowner in the southeast United States who integrates wildfire risk and fuel accumulation into forest management and fire prevention decisions. The derived model determines optimal fuel treatment frequencies, timing, and level simultaneously and as a function of fire risk and fuel biomass dynamics under a range of economic and biophysical conditions. The landowner’s optimal prevention decisions are highly dependent on the type of fuel biomass growth and the association between fire arrival rate and fuel accumulation, which can vary across a broad forest landscape. Results indicate that policymakers should develop their management strategies based on their long-run objectives and fuel accumulation patterns, and these strategies should vary in timing and effort level within each rotation.

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Data availability

The data can be found in Table 1 of this study.

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Notes

  1. To facilitate the interpretation, the figures can be divided into three time intervals, \(t \le 10\),\(10 < t \le 20\), and \(t > 20\). The three time intervals can also be referred as first, second, and last third periods of the rotation, respectively.

  2. The three time intervals \(t \le 10\),\(10 < t \le 20\), and \(t > 20\) can also be referred as first, second, and last third periods of the rotation, respectively.

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Acknowledgements

The authors thank the participants of the World Congress of Environmental and Resource Economics in June 2018 for their valuable insight during earlier phases of this research.

Funding

This paper was partially supported by the USDA National Institute of Food and Agriculture [project number 2017–48791-26835], McIntire-Stennis [project number ME041825], through the Maine Agricultural & Forest Experiment Station.

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Authors and Affiliations

  1. Department of Natural Resource Economics, Sultan Qaboos University, Muscat, Oman

    Ibtisam Al Abri

  2. Department of Food and Resource Economics, University of Florida, Gainesville, FL, USA

    Kelly Grogan

  3. School of Forest Resources, University of Maine, Orono, ME, USA

    Adam Daigneault

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  1. Ibtisam Al Abri
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Conceptualization: I.A. and K.G.; Methodology: I.A., K.G. and A.D.; Formal Analysis: I.A.; Investigation: I.A. and K.G.; Resources: I.A., K.G. and A.D.; Writing—original draft: I.A.; Writing—review and editing: K.G. and A.D.

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Correspondence to Ibtisam Al Abri.

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Appendix 1

Appendix 1

Sensitivity analysis is conducted to determine the impacts of variations in several simulation parameters on total site values and optimal fuel treatment paths. The sensitivity analysis helps in checking the robustness of the simulated model to changes in some parameter values. The examined parameters are: the fixed fuel treatment cost \((c_{{{\text{fix}}}} )\); the variable cost of the fuel treatment \((c_{{\text{var}}} )\); the rate of incendiary events \((\gamma )\); and the effectiveness of fuel removal for mitigating fire occurrence \((W)\). For each parameter, the baseline value is first halved, then doubled. Table 4 reports percent deviations from baseline optimal site value as a result of changes in the parameters under consideration for all possible fuel growth functions and management interests. The results indicate that the variation on baseline optimal site value is most heavily explained by the effect of ignition risk \((\gamma )\). In the case of a relatively low risk of incendiary events (\(\gamma = 0.02\): two fires every 100 years), the obtained site value is 5.59% above that of the baseline optimal site value in the best possible outcome. This best outcome belongs to the scenario when the landowner is market-oriented and his forest follows an exponential fuel accumulation; all other scenarios have site values close to this best outcome. In contrast, when the risk of incendiary events is relatively high (\(\gamma = 0.08\) or eight fires every 100 years), the worst site value is 9.53% below that of the baseline optimal site value, and is found with the case of the market-oriented landowner under logistic fuel accumulation.

Variations on baseline optimal site value are moderate when examining changes in the variable cost of the fuel treatment \((c_{{\text{var}}} )\). When the variable cost is halved \((c_{{\text{var}}} = 1.25)\), the effect of less expensive fuel removal on site values is anywhere from 2.33% to 3.84% above that of the baseline optimal site value. On the other hand, when fuel treatment is expensive,\((c_{{\text{var}}} = 5)\), landowners obtain site values that range from 4.10% to 5.59% below that of the baseline optimal site value.

Changes in both the fixed cost of the fuel treatment \((c_{{{\text{fix}}}} )\) and the effectiveness of fuel removal \((W)\) have a very small effect on the baseline optimal site value. When both parameters are halved, landowners gain site values from 1.27 to 1.76% above that of the baseline optimal site value. In contrast, when both parameters are doubled, the attained site values under all scenarios are within the range of 1.02% to 1.53% below that of the baseline optimal site value.

In addition, Table 5 show the effect of changes in the same set of simulation parameters on the deviation from the average level of baseline optimal fuel removal for all possible fuel growth functions and management interests. Similar to the analysis of deviations from baseline optimal site value, results of the sensitivity analysis indicate that the risk of ignition, \((\gamma )\), explains most of the variations on the baseline optimal average level of fuel treatment relative to other parameters. When ignition risk is low,\(\gamma = 0.02\), the reduction in the optimal average level of fuel removal could be as much as 6.44% relative to the baseline outcome. However, when ignition risk is high,\(\gamma = 0.08\), the increase in the optimal average level of fuel management does not exceed an increase of 5.05% relative to the baseline outcome. Further, a change in the variable cost of fuel treatment, \((c_{{\text{var}}} )\), causes a small variation in the optimal average level of treatment. When fuel removal is inexpensive, the deviation in the level of fuel treatment ranges from 1.93 to 2.23% above that of the baseline optimal outcome; while, costly fuel treatment leads to deviations from 2.11 to 2.92% below the baseline optimal outcome. Additionally, changes in the fixed cost of the fuel treatment \((c_{{{\text{fix}}}} )\) and the effectiveness of fuel removal \((W)\) bring about a very little effect on the optimal level of fuel management, where the absolute deviations do not exceed 1% relative to the baseline outcome in all scenarios under consideration.

Table 4 Percentage deviation from baseline optimal site value with changes in cost of fuel removal (fixed and variable), fire arrival rate, and effectiveness of fuel treatment
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Table 5 Percentage changes in average level of fuel treatment with changes in cost of fuel removal (fixed and variable), fire arrival rate, and effectiveness of fuel treatment
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Al Abri, I., Grogan, K. & Daigneault, A. Optimal forest management in the presence of endogenous fire risk and fuel control. Eur J Forest Res 142, 395–413 (2023). https://doi.org/10.1007/s10342-023-01530-7

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