1 Methodology for optimization of continuous cover forestry with consideration of recreation and the forest and energy industries Методология оптимизации непрерывного неистощительного лесопользования, как для обеспечения рекреационных услуг, так и для переработки в лесной и энергетической промышленности Peter Lohmander & Zazykina Liubov FORESTS OF EURASIA - PODMOSKOVNY VECHERA Moscow State Forest University September , 2010

2 Профессор Петер Ломандер Шведский университет сельского хозяйства (SLU), Умео, Швеция Электронная почта: Аспирантка Зазыкина Любовь Московский государственный университет леса (МГУЛ) 1-ая институтская ул., Мытищи, Московская обл., Россия Электронная почта:

3 Professor Peter Lohmander Department of Forest Economics, Faculty of Forest Science, Swedish University of Agricultural Sciences (SLU), SE – Umea, Sweden Web: Профессор Петер Ломандер Шведский университет сельского хозяйства (SLU), Умео, Швеция Web:

4 Forests are used for many different purposes. It is important to consider these simultaneously. A new methodological approach to optimization of forest management with consideration of recreation and the forest and energy industries has been developed. It maximizes the total present value of continuous cover forest management and takes all relevant costs and revenues into account, including set up costs. Леса используются и могут использоваться в разных целях. Важно учесть все эти цели одновременно, разработан новый методологический подход к оптимизации лесопользовании с учетом обеспечения рекреационных услуг, переработки в лесной и энергетической промышленности. Он максимизирует общую текущую дисконтированную стоимость непрерывного неистощительного лесопользования и учитывает все затраты будущего периода и доходы, включая начальные затраты.

5 In several regions, in particular close to large cities, such as Paris and Moscow, the economic importance of recreation forestry is very high in relation to the economic results obtained from traditional production oriented forest management. This does however not automatically imply that production of timber, pulpwood and energy assortments can not be combined with rational recreation forestry. В некоторых районах, в особенности вблизи больших городов, таких как Париж или Москва, экономическая важность рекреационного лесопользования очень высока, по сравнению с экономическими результатами полученными при традиционным лесопользовании. Однако, это не означает автоматически, что рациональное рекреационное лесопользование не может быть скомбинировано с производством пиломатериалов, целлюлозы и энергии.

6 The optimization model includes one section where the utility of recreation, which may be transformed to the present value of net revenues from recreation, is added to the traditional objective function of the present value of the production of timber, pulpwood and energy assortments. In typical cases, individuals interested in recreation prefer forests with low density. Использование рекреационных услуг, которое может быть преобразовано в величину чистых доходов, от этих услуг и обавлено к традиционным целевым доходам от производства пиломатериалов, целлюлозы и энергии. В типичных случаях, предпочитаются леса под рекреацию с низкой плотностью насаждений, это означает, что лесопользование является оптимальным, когда учитываются все цели при осуществлении более частых рубок ухода в отличие от лесопользования, которое направлено только на производство пиломатериалов целлюлозы и энергии.

7 This means that forest management that is optimal when all objectives are considered, typically is characterized by larger thinning harvests than forest management that only focuses on the production of timber, pulpwood and energy assortments. же влияние на оптимизацию лесопользования, как увеличивающаяся важность рекреационных услуг в зонах близких, к большим городам.

8 The results also show that large set up costs have the same type of effect on optimal forest management as an increasing importance of recreation, close to large cities. Both of these factors imply that the harvest volumes per occation increase and that the time interval between harvests increases. Even rather small set up costs imply that the continuous cover forest management schedule gives a rather large variation in the optimal stock level over time. Оба этих фактора подразумевают, что объем вырубок на ед. времени увеличиваются, а так же увеличивается сам временной интервал между вырубками. Сравнительные малые начальные затраты означают что апланированное непрерывное неистощительное лесопользование дает относительно много вариаций оптимального уровня запаса древесины во времени.

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10 Growth Compare: Verhulst, Pierre-François (1838). "Notice sur la loi que la population poursuit dans son accroissement"."Notice sur la loi que la population poursuit dans son accroissement" Correspondance mathématique et physique 10: pp. 113–121.

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13 A separable differential equation

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24 Stock (m3/ha) Time (Years)

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26 The Present Value Function Profit from the first harvest Present value of an infinite series of profits from the later harvest

27 Initial stock level Rate of interest Harvest interval

28 * * *

29 y=250 y=200 y=150 Present Value Harvest Interval (Years) y = First Harvest Volume (m3/ha) (SEK/ha)

30 First Harvest Volume (m3/ha) Harvest Interval (Years) C = 500 Vertical Scale = Present Value (SEK/ha)

31 First Harvest Volume (m3/ha) Harvest Interval (Years) C = 500 Vertical Scale = Present Value (SEK/ha)

32 Harvest Interval (Years) First Harvest Volume (m3/ha) C = 500 Vertical Scale = Present Value (SEK/ha)

33 First Harvest Volume (m3/ha) Harvest Interval (Years) C = 500 Vertical Scale = Present Value (SEK/ha)

34 First Harvest Volume (m3/ha) Stock Level Directly After Harvest (m3/ha) C = 100

35 Stock Level Directly After Harvest (m3/ha) Harvest Interval (Years) C = 100 Vertical Scale = Present Value (SEK/ha)

36 C = 100 C = 500

37 Stock Level Directly After Harvest (m3/ha) Harvest Interval (Years) C = 100 C = 500 Vertical Scale = Present Value (SEK/ha)

38 C = 2000

39 Stock Level Directly After Harvest (m3/ha) Harvest Interval (Years) C = 2000 Vertical Scale = Present Value (SEK/ha)

40 Stock Level Directly After Harvest (m3/ha) Harvest Interval (Years) C = 100 C = 2000 Vertical Scale = Present Value (SEK/ha)

41 Stock Level Directly After Harvest (m3/ha) Harvest Interval (Years) C = 100 C = 500 Vertical Scale = Present Value (SEK/ha)

42 REM REM CCF0403 REM Peter Lohmander REM OPEN "outCCF.dat" FOR OUTPUT AS #1 PRINT #1, " x1 t h1 PV" FOR x1 = 10 TO 150 STEP 20 FOR t = 1 TO 31 STEP 5 c = 500 p = 200 r =.03 s =.05 x0 = 300 h0 = x0 - x1 x2 = 1 / (1 / (1 / x1 - 1 / 400) * EXP(-.05 * t)) h1 = x2 - x1 multip = 1 / (EXP(r * t) - 1) pv0 = -c + p * h0 pv1 = -c + p * h1 PV = pv0 + pv1 * multip PRINT #1, USING "####"; x1; PRINT #1, USING "####"; t; PRINT #1, USING "####"; h1; PRINT #1, USING "#######"; PV NEXT t NEXT x1 CLOSE #1 END

43 x1 t h1 PV

44 REM REM OCC0403 REM Peter Lohmander REM OPEN "outOCC.dat" FOR OUTPUT AS #1 PRINT #1, " C X1opt topt PVopt h1opt x2opt" FOR c = 0 TO 3000 STEP 100 FOPT = x1opt = 0 topt = 0 pvopt = 0 h1opt = 0 x2opt = 0

45 FOR x1 = 10 TO 150 STEP 5 FOR t = 1 TO 61 STEP 1 p = 200 r =.03 s =.05 x0 = 300 h0 = x0 - x1 x2 = 1 / (1 / (1 / x1 - 1 / 400) * EXP(-.05 * t)) h1 = x2 - x1 multip = 1 / (EXP(r * t) - 1) pv0 = -c + p * h0 pv1 = -c + p * h1 PV = pv0 + pv1 * multip IF PV > pvopt THEN x1opt = x1 IF PV > pvopt THEN topt = t IF PV > pvopt THEN h1opt = h1 IF PV > pvopt THEN x2opt = x2 IF PV > pvopt THEN pvopt = PV NEXT t NEXT x1 PRINT #1, USING "######"; c; x1opt; topt; pvopt; h1opt; x2opt NEXT c CLOSE #1 END

46 Optimal Stock Level Directly After Harvest (m3/ha) Set up Cost (SEK/ha)

47 Optimal Stock Level Directly Before Thinning Harvest (m3/ha) Set up Cost (SEK/ha)

48 Optimal Thinning Harvest Volumes per occation (m3/ha) Set up Cost (SEK/ha)

49 Optimal Harvest Interval (Years) Set up Cost (SEK/ha)

50 Optimal Present Value (SEK/ha) Set up Cost (SEK/ha)

51 What happens to the optimal forest management schedule if we also consider the value of recreation?

52 Source: Zazykina, L., Lohmander, P., The utility of recreation as a function, of site characteristics: Methodological suggestions and a preliminary analysis, Proceedings of the II international workshop on Ecological tourism, rends and perspectives on development in the global world, Saint Petersburg Forest Technical Academy, April 15-16, 2010, Alekseevskiy forest

53 Source: Zazykina, L., Lohmander, P., The utility of recreation as a function, of site characteristics: Methodological suggestions and a preliminary analysis, Proceedings of the II international workshop on Ecological tourism, rends and perspectives on development in the global world, Saint Petersburg Forest Technical Academy, April 15-16, 2010,

54 Interpretations and observations: #1: Several alternative interpretations are possible! #2: Furthermore, the results are most likely sensitive to local conditions, weather conditions etc..

55 Assumptions: The ideal average forest density, from a recreational point of view, is 0.5. Directly before thinning, the density is 0.8. As a result of a thinning, the density in a stand is reduced in proportion to the harvest volume. The density of a stand is a linear function of time between thinnings. The value of recreation is a quadratic function of average stand density in the forest area. The recreation value is zero if the density is 0 or 1. Under optimal density conditions, the value of recreation, per individual, hectare and year, is 30 EURO. (The value 30 has no empirical background.)

56 Approximation in the software: D =.8 * ((x1 + x2) / (2 * x2)) IF D < 0 THEN D = 0 IF D > 1 THEN D = 1 U = 120 * D * D * D PVtotU = n / r * U

57 N(Y) = Number of persons per 100 m2 a function of Y = Basal Area (m2/ha), Moscow DURING THE VERY HOT SUMMER OF 2010 Forest visitors seem to prefer forests with rather high basal area levels during hot periods.

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61 What was the most popular basal area during the hot summer of 2010 from a recreational point of view?

62 Scenic Beauty, SB, as a function of basal area, BA. The graph has been constructed using equation SB = – BA/t ln (BA), which is found in Hull & Buhyoff (1986).

63 Optimization of present value of roundwood production and recreation

64 REM OP REM Peter and Luba REM OPEN "outOP.txt" FOR OUTPUT AS #1 PRINT #1, " n x1opt topt h1opt x2opt pvopt optPV opttotU" FOR n = 0 TO 550 STEP 55 pvopt = optpv = x1opt = 0 topt = 0 h1opt = 0 x2opt = 0 c = 50 p = 40 r =.03

65 FOR x1 = 10 TO 150 STEP 5 FOR t = 1 TO 100 STEP 1 x0 = 158 h0 = x0 - x1 x2 = 1 / (1 / (1 / x1 - 1 / 316) * EXP( * t)) h1 = x2 - x1 multip = 1 / (EXP(r * t) - 1) pv0 = -c + p * h0 pv1 = -c + p * h1 PV = pv0 + pv1 * multip

66 D =.8 * ((x1 + x2) / (2 * x2)) IF D < 0 THEN D = 0 IF D > 1 THEN D = 1 U = 120 * D * D * D PVtotU = n / r * U TPV = PV + PVtotU IF TPV > pvopt THEN x1opt = x1 IF TPV > pvopt THEN topt = t IF TPV > pvopt THEN h1opt = h1 IF TPV > pvopt THEN x2opt = x2 IF TPV > pvopt THEN optpv = PV IF TPV > pvopt THEN opttotU = PVtotU IF TPV > pvopt THEN pvopt = TPV NEXT t NEXT x1

67 Approximation in the software: D =.8 * ((x1 + x2) / (2 * x2)) IF D < 0 THEN D = 0 IF D > 1 THEN D = 1 U = 120 * D * D * D PVtotU = n / r * U

68 PRINT #1, USING "######"; n; x1opt; topt; PRINT #1, USING "######"; h1opt; x2opt; PRINT #1, USING "########.##"; pvopt; optpv; opttotU NEXT n CLOSE #1 END

69 Optimal results: ( outOP.txt)

70 Optimal stock level directly after harvest

71 Optimal stock level directly before harvest

72 Optimal thinning volume per occation

73 Optimal time interval between thinnings

74 In forest areas with many visitors, close to large cities, the present value of recreation may be much higher than the present value of timber production.

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76 The case with no visitors

77 The case with many visitors that prefer low density forests

78 Conclusions: A new methodological approach to optimization of forest management with consideration of recreation and the forest and energy industries has been developed. It maximizes the total present value of continuous cover forest management and takes all relevant costs and revenues into account, including set up costs. Optimal solutions to empirically investigated cases have been analysed and reported.

79 Thank you for listening! Questions?