Comparison of forest ecosystem services value evaluation methods: a case study of Sichuan Province, China

ABSTRACT: The survival of human and sustainable development of the society both closely rely on forest ecosystem services. Employing two different methods, this paper based on benefit transfer method calculated the forest ecosystem services value of Sichuan province, China. The results showed that the total forest ecosystem services value had a steady rate of increase in Sichuan province from 2008 to 2018, and meanwhile, the different evaluation methods resulted in significant deviation of estimation outcomes. This paper considered the differences of biomass and socioeconomic development which were ignored in prior studies. The Carnegie-Ames-Stanford approach was employed to estimate the net primary productivity of different forest species. Further, the S type R. Pearl growth curve was employed to estimate people’s willingness and ability to pay for forest ecosystem services. This paper provided implications to help forest managers and policy makers pay additional attention to the evaluation systems choosing on forest ecosystem services value and the differences of biomass and socioeconomic development by using benefit transfer method method.


INTRODUCTION
Forest ecosystem is one of the most vital ecosystems on the earth.Forest ecosystem services value (FESV) means the beneficial values that people can derive from the characteristics and functions of forest ecosystems directly or indirectly, including value of economic service (such as goods of timber, raw material and food), value of ecological service (such as controlling soil erosion and regulating the climates), and value of cultural service (such as landscaping, recreation and sporting) (COSTANZA et al., 1997;DALY et al., 1997;MA, 2005;DE GROOT et al., 2012;SEPUL et al., 2020).The survival of human and sustainable development of the society both intensively rely on the FESV (FARLEY & COSTANZA, 2010).Therefore, estimation of the FESV in monetary units has a critical role to play in demonstrating the importance of forest ecosystem directly and heightening environmental awareness of the public.However, different evaluation methods may result in significant deviation of estimation Ciência Rural, v.53, n.1, 2023.
Jiang & Yang outcomes, and the wide ranges of methods need to be adopted to know the estimation of the FESV better (COSTANZA et al., 2014).As such, this paper takes Sichuan province, China as an example, and employs two different evaluation methods, that is, grain equivalent coefficient method (also named GEC method) proposed by XIE et al. (2003), and the method of DE GROOT et al. (2012) (also named DEG method), to evaluate the monetary estimation outcomes of the FESV.This paper does not intend to display a judgment that the evaluation methods of the FESV are good or bad by comparing the calculation outcomes, but is meant to comb the principles of the two different methods, and provided a direction to make the choice of the FESV evaluation methods receiving further attention.
The neoclassic welfare economics is the first to put forward the theoretical analysis of the estimation of the FESV.The neoclassical welfare economics has proposed that the FESV is the total of individual willingness to pay for the services provided by forest ecosystem, and its economic value evaluation is to measure the degrees of people's preference for those forest ecosystem services (FRANCO et al., 2019).Market price can represent individual preferences for the services of natural resources (LIU et al., 2020).However, most of the services provided by forest ecosystem cannot be traded in market directly, and its market prices cannot be obtained intuitively (NAIME et al., 2020).As such, on the theoretical basis of neoclassical welfare economics, to measure the degree of people's preference for the services provided by forest ecosystem and elicit the FESV, the direct evaluation methods, such as contingent valuation method (CVM), and the indirect evaluation methods, such as benefit transfer method (BTM) appeared (ZHU et al., 2019).
In terms of the CVM, the classical direct evaluation method, it is based on the hypothetical market, employs face-to-face, telephone or mail questionnaire survey to obtain personal quotations for forest ecosystem services, and evaluates the FESV in monetary term (WOODWARD & WUI, 2001).Although, the CVM can obtain the individual preferences for forest ecosystem services directly, the implementation cost is extremely high.The survey process is time-consuming for gathering individual quotations one by one (UTSUNOMIYA, 2018).Therefore, if the acknowledged results which showed individual preferences for forest ecosystem services and were obtained by means of the CVM can be extended to other study cases, it might be highly meaningful.The BTM is such a method.The BTM can transfer the estimated FESV results of one studied area (also referred to study site) to others studied area (also referred to policy site) by means of economic technologies (ZHOU et al., 2020).Compared with employing direct evaluation methods, it is an attractive choice to quickly obtain the FESV via applying the BTM.
The indirect evaluation method of the BTM can be divided into two types, the basic BTM and the adjusted BTM (SU et al., 2020).The basic BTM regards the individual willingness to pay for forest ecosystem services and biomass in study sites and policy sites as the same, and takes the average FESV of one or more study sites as the unit FESV of policy sites (BATKER et al., 2008).Compared with the basic BTM, the adjusted BTM has considered the differences of socioeconomic development and biomass between study sites and policy sites, which has made the transfer of FESV be more accurate.To some extent, per capita GDP can represent people's ability to pay for the FESV.Therefore, the ratio of per capita GDP in study sites and policy sites is frequently used to adjust the differences of socioeconomic development (NAVRUD, 2009).Further, the ratio of forest net primary productivity (NPP) in study site and policy site is regarded as biomass adjustment factor (CAO et al., 2020).NPP is the direct manifestation of biomass.It refers after deducting the autotrophic respiration, the total amount of organic matter accumulated by green plants through photosynthesis in unit area and unit time (BARRAHMOUNE et al., 2019;CHEN et al., 2020).
Two global studies by employing the BTM are the basis of various scales the estimations of FESV.By employing the basic BTM, COSTANZA et al. (1997) transferred the ecosystem value in 100 study sites to the ecosystem services value of globe, and obtained an average value of each ecosystem in globe ($/ha/year).Considering the limited number of study sites and the interdependence among ecosystems, DE GROOT et al. (2012) screened over 665 study sites, constructed spatial statistical models, and presented a revised average value of each ecosystem in globe ($/ ha/year).The evaluation of FESV based on the result of DE GROOT et al. (2012) is called DEG method.In the two global studies, the average value of global forest ecosystem and its revised average value have formed the fundamentals for the regional and national FESV evaluations all around the world.
Based on the two studies, the prior literature conducted a FESV transfer.These studies used the average value of global forest ecosystem or its revised average value directly to specific countries or regions to acquire the FESV.However, among these studies, the socioeconomic development and biomass differences are largely ignored (LI et al., 2019).People's willingness to pay needs to be matched by the ability to pay to finalize the payments for forest ecosystem services.To facilitate the calculation, previous studies did consider people's ability to pay for FESV by using the ratio of per capita GDP, but the people's willingness to pay is neglected in the process of FESV transfer (LIU, 2018;YIRSAW et al., 2016).Further, previous study has revised the biomass difference by adopting the ratio of forest NPP of study site and policy site (CAO et al., 2020), and calculated the forest NPP by employing Miami or Thornthwaite Memorial models to simplify the calculation process.Thus, the NPP of different forest species are ignored, such as coniferous forest, broad-leaved forest, and mixed forest, which may make the results be deviated from the actual situation (SU et al., 2020).
To make the FESV estimation be closer to the facts of the policy sites, the average value of global ecosystem calculated by COSTANZA et al. (1997) was improved somewhat by expert opinion method of local condition in China (BATKER, 2008).The GEC method developed by XIE et al. (2003), is the most widely used expert opinion method in Chinese setting to evaluate the services value of ecosystems (SHENG et al., 2017).The GEC method reckons the ecosystem of cultivated land is the most vital ecosystem on the earth.To reflect the contributions of forest ecosystems to the potential capacity of the whole ecosystem services value, the GEC method evaluates the FESV based on the average value of global cultivated land ecosystem.The GEC method divides the average value of global forest ecosystem ($/ha/year) by the average value of global cultivated land ecosystem, 54 ($/ha/year) firstly.The average value of global forest ecosystem and the average value of global cultivated land ecosystem both were accessed in the study of COSTANZA et al. (1997).Accordingly, the standard global FESV equivalent factor ($/ha/year) of the GEC method is obtained.Then, the research team invited 251 experts to score the standard global FESV equivalent factor ($/ha/ year) in terms of actual situation of China.After that, combining the experts' scores and the standard global FESV equivalent factor ($/ha/year), the standard FESV equivalent factor of China (yuan/ha/year) is acquired.Lastly, the economic value of a standard FESV equivalent factor of China (yuan/ha/year) is equivalent to the 1/7 market value of annual grain yield of per unit cultivated land (yuan/ha/year) (XIE et al., 2005).It is the reason why the method called "grain equivalent method".Figure 1 displays the summary of the study of COSTANZA et al. (1997), the DEG method, and the GEC method.
In 2008, the GEC method recognized the calculation bias caused by the heterogeneity of biomass of each province in China.The biomass adjustment factors based on the biomass of cultivated land of each province were proposed.For instance, the biomass of cultivated land in Sichuan province approximately is 1.35 times that of the whole country on average.Therefore, the biomass adjustment factor of Sichuan province values 1.35 (XIE et al., 2008).On these grounds, prior study in Chinese setting used the biomass adjustment factors based on cultivated land directly when calculating the FESV (KANG et al., 2019).Although it is indeed desirable to obtain a standard FESV equivalent factor from the perspective of expert opinion method, employing biomass adjustment factors based on cultivated land to evaluate the FESV is inaccurate (LEI et al., 2019).With the advancement of GIS technologies, biomass is no longer as difficult to observe as it used to be.As aforementioned, the NPP of different forest species can be applied to adjust the biomass heterogeneity of study site and policy site.
Since the calculation of the ecosystem service value of a single ecosystem is more accurate than that of multiple ecosystems (DAI et al., 2018), this paper only focused on the forest ecosystem.This study attempts to fill some research gaps in current studies on evaluation of FESV.First, by using timesensitive official data, this paper used the DEG method based on the global perspective, and GEC method based on local expert opinion, to provide a comprehensive understanding of FESV evaluation methods.Second, the Carnegie-Ames-Stanford approach (CASA) was employed to estimate the NPP of different forest species as biomass adjustment factor to overcome the biomass differences of forest ecosystems in study site and policy site.Third, to address the socioeconomic development differences, the S type R. Pearl growth curve was employed to assess people's willingness and ability to pay for forest ecosystem services.
We organized the remainder of this study as follows, in section 2, we presented the study area, data, and the methods we employed.In section 3, the calculation results were provided.Section 4 included conclusions, and discussions on policy implications.
Jiang & Yang 34°19' N, is a big province in financial, business and technology, as well as the transportation and communication hub for the southwest of China.It is in a vital position in the layout of China's regional economic development.Sichuan province covers an area of 486,000 km 2 , and ranks as the fifth biggest province in China.Sichuan province shoulders the mission of maintaining national ecological security.It is the upper reaches of many major rivers (e.g., the Yangtze River) in China, and its ecological status is very crucial (Figure 2).
According to the Forest Resources Inventory Report of China, the forested areas of Sichuan province were with coverage of 38.8%, and Sichuan province occupied the third place out of the total 31 provinces in China in the end of 2018 (Data source: National Bureau of Statistics, http:// www.stats.gov.cn).Sichuan province is composed of mountains, hills, plains, basins, and plateaus.There are two types of major climates, the subtropical monsoon climate in Sichuan Basin (East) and the mountainous climate in Sichuan Plateau (West).As such, based on the International Geosphere Biosphere Program Scheme, we mainly focus on the four dominant forest categories, that is, coniferous forests, broad-leaved forests, mixed forests, and shrublands (ABELSON, 1986).By employing the ArcGIS software, figure 3 visualizes the land utilization of Sichuan province from 2008 to 2018 (Data source: National Forestry and Grassland Administration, http://www.forestry.gov.cn).Table 1 displays the area of the four dominant forest categories in Sichuan province (Data source: National Forestry and Grassland Administration, http://www.forestry.gov.cn).

CASA model
The CASA model is a frequently used method to calculate the NPP of vegetation (BAO et al., 2016;YE et al., 2019).It employs the remote sensing technology to obtain the NPP outcomes of vegetation through photosynthetic active radiation (APAR) absorbed by vegetation and the actual light energy utilization rate ɛ (POTTER et al., 1993).The specific CASA model can be written as follows:

NPP(x,t)=APAR(x,t)×ɛ(x,t)
where (, ) is the NPP (gC•m -2 •t -1 ) accumulated by vegetation in pixel x over the period t. (, ) indicates the photosynthetic active  The APAR (MJ•m -2 •t -1 ) absorbed by vegetation in pixel x over the period t can be written as follows: APAR(x,t)=SOL(x,t)×FPAR(x,t)×0.5 where SOL(x,t) represents the total solar radiation is received by pixel x in the period t (MJ•m -2 •t -1 ).

FPAR(x,t) is the absorption ratio of photosynthetic
active radiation by vegetation in pixel x.The constant 0.5 represents the proportion of solar radiation to total solar radiation in vegetation utilization.

GEC method
GEC method has redrawn the 17 categories of forest ecosystem services in the study of COSTANZA into four ecosystem services, that is, services of provisioning, services of regulation, services of support, and services of culture.Specifically, services of provisioning include food and raw material production; services of regulation contain gas regulation, climate regulation, water regulation, and waste treatment; services of support are composed by soil formation and conservation, and biodiversity maintenance.Further, services of culture are represented by recreation.The nine sub-categories of forest ecosystem services of GEC method and its standard FESV equivalent factor are provided in table 2.

Jiang & Yang
As proposed in the introduction section, in GEC method, the economic value of one standard equivalent factor of FESV in China is equivalent to the 1/7 market value of annual natural grain yield of per unit cultivated land.As such, the economic value of one standard equivalent factor of FESV in China can be written as follows: where E is economic value of one standard equivalent factor of FESV in China (yuan/ha).P is the average market price of grain per unit of Sichuan province in study years (yuan/kg).S is the area of cultivated land of Sichuan province in study years (ha).Q is the total grain yield of Sichuan province in study years (kg).
Referring to the GEC method and the theoretical combing of the adjusted BTM, an assessment model of FESV in Sichuan province can be constructed.The specific FESV calculation equation is written as follows: where FESV is the forest ecosystem service value (yuan).A i is area of the i th forest categories (ha).SE is the standard equivalent factor of each forest ecosystem service in table 2. B i is the biomass adjustment factor, and PI i is the socioeconomic adjustment factor.
Based on the adjusted BTM, B i and PI i can be written as follows: where NPP s is the NPP (gC•m -2 •t -1 ) of the i th forest categories in Sichuan province, and NPP c is the NPP (gC•m -2 •t -1 ) of the i th forest categories in China.In this paper, to facilitate evaluation, we adopt the NPP c results calculated by PIAO et al. (2001) andHE et al. (2005), which employed CASA model and observes the terrestrial NPP of China.
The calculation of socioeconomic adjustment factor is as follows: where W t is dictated the people's willingness to pay for the FESV.When the value of W t becomes larger, people's willingness to pay the FESV is higher.A t is the people's ability to pay for the FESV, which is calculated based on per capita GDP.The greater A t , the higher people's ability to pay for the FESV is.
With the development of social economy, people's life quality has increased, and the concern It can be seen from figure 4 that when t goes to negative infinity (-∞), l equals 0. It can be indicated that when the level of social development (t) is extremely low, people's willingness to pay

Jiang & Yang
for the FESV basically is zero.In contrast, when t towards positive infinity (+∞), l is equal to 1.That represents when the level of social development (t) is extremely high, the maximum value of people's willingness to FESV reaches 100%.It means that people's willingness to pay for the FESV is equivalent to the actual FESV.Therefore, no matter from the change trend or the range, the S type R. Pearl growth curve can represent the relationship between people's willingness to pay for the FESV and the level of social and economic development.
For the social development level, this paper defines the social development stages by obtaining the Engel coefficient (En, %) of study years.As the S type R. Pearl growth curve in figure 4 is positive, 1/ En should be used to replace the abscissa of the curve rather than En.
Considering the reality of China's rapid economic development, in this paper we slightly adjusted the En proposed by the Food and Agriculture Organization, to determine the stage of social development.Specifically, the value of En is greater than 50% or the value of 1/En is less than 0.5, which is defined as poor life.When the value of En is between 50% to 25%, it represents well-off life.Likewise, the value of 1/En is between 0.5 to 4, which is also means well-off life.If the value of En is less than 25% or the value of 1/En greater than 4, it indicates a wealthy life.The specific social development stages are presented in table 3.
1/En is a non-negative number.When the S type R. Pearl's growth curve shifts four units to the right side, the curve just covers almost all stages of social development, that is, all possible values of 1/ En.The relationship of the S type R. Pearl's growth curve and 1/En was presented in figure 5.
In figure 5, the origin in the x-axis has shifted 4 units to the right compares figure 4. The abscissa of the S type R. Pearl's growth curve is 1/ En, which means the social development stage.
The ordinate of the S type R. Pearl's growth curve represents people's willingness to pay for FESV.Once En is known, the W t can be calculated.
where GDP s and GDP c are denoted the per capita GDP of Sichuan province and the per capita GDP of China in study years, respectively.

DEG method
The DEG method is an amendment of COSTANZA calculation system, and it extended the number of case study sites and considered the symbiosis of various ecosystems.DEG method contained 11 categories forest ecosystem services according to the ecosystem services classification scheme from the Economics of Ecosystems and Biodiversity Foundation Report (DE GROOT et al., 2010).Table 4 provides the specific categories forest ecosystem services and its revised average value of global forest ecosystem.
When using the DEG method to evaluate the FESV of a provincial scale of China, the adjusted BTM must be employed to facilitate the international transfer.Therefore, this study constructed the assessment model of the FESV suitable for the DEG method.The specific calculation equation is as follows: where FESV is the forest ecosystem service value (yuan).A i is area of the i th forest categories in Sichuan province (ha).and RAV indicates the revised average value of forest ecosystem in globe in table 4 ($/ha/ year, 2007 price level).B ic and PI ic are biomass and socioeconomic factor adjustment factors respectively, which are employed to overcome the biomass and socioeconomic differences between globe and China.R ic indicates the official average exchange rate of US dollar to RMB in 2007.The definitions and calculations of B i and PI i are the same as those in the GEC method, which are used to address the biomass and socioeconomic differences between China and Sichuan province.
where B c is the biomass in China, while B g is the biomass of globe.In this paper, we have assumed the biomass of globe and China are same, therefore, B ic equals 1.The calculation principle of PI ic is the same as the GEC method, and PI ic can be written as follows: PI ic =W ic ×A ic where W ic indicates the coefficient of people's willingness to pay for the FESV in China.In this paper, we have assumed the payment preferences of China and globe are with no differences, thus, W ic equals 1.A ic is the coefficient of people's ability to pay for the FESV in China.
where GDP c is per capita GDP ($/year) of China in study year, and GDP g is global per capita GDP ($/ year) in study year which is calculated according to purchasing power parity of each country.

Data
The forest data including forest area and forest land cover types were extracted from the

Results of socioeconomic development adjustment factor
The

Ecosystem services
Revised average value

Climate regulation 152
Waste treatment 7 Erosion prevention 5

Nutrient cycling 93
Biological control 235

Esthetic information 989
Cognitive and 2018, respectively.Since this paper assumes that people's payment preferences of China and globe are with no differences, the W ic is equal to 1. Therefore, the value of A ic equivalents to PI ic .It can be seen from table 6, with advancement of the socioeconomic across the ten years, the Engle index shows a downward trend, and people's willingness and ability to pay for FESV are increased.

Results of FESV by employing GEC method
The grain yield per unit area of Sichuan province was 4854.1, 5320.7, and 5575.6 kg/ha in 2008, 2013 and 2018, respectively.Simultaneously, the average market price of grain in Sichuan province was 3, 3.2, and 3.5 yuan/kg in study years.
As such, economic value of one equivalent factor of FESV, E is calculated to be 2080.33, 243233, .34 and 278733, .82 in Sichuan province 200833, , 201333, and 2018, respectively. , respectively.On the basis of the A i , the area of the each forest categories (ha), B i , the biomass adjustment factor, Pi i , the socioeconomic development adjustment factor, and E, economic value of one equivalent factor of FESV (yuan/ha) that we have obtained, the results of FESV by employing the GEC method are presented in table 7. Further, the FESV of the four dominant forest categories in Sichuan province are displayed in figure 6.
It can be observed from table 7 that by using the GEC method, the total FESV of Sichuan province is 109.364,152.377 and 315.740 billion yuan in 2008, 2013 and 2018, respectively.Specifically, across the ten years, the forest ecosystem service of biodiversity    7).The area of Sichuan province has increased 265.18 (10 4 ha) from 2008 to 2018, thus, the going up FESV can be attributed to the rising area of the forest to a large extent.Among the nine sub-categories of forest ecosystem services, across the ten years, the value of gas regulation shows the biggest rise, while the value of food observes the smallest.
Concerning the FESV of different forest types, figure 6 illustrates that across the ten years, the coniferous forests and broad-leaved forests have the higher FESV, compared with the mixed forests and shrublands.Since the area of coniferous forests and broad-leaved forests are the two largest forests in Sichuan province, and meanwhile, its NPP are relatively high than other forests.

CONCLUSION
This paper based on the BTM, employing two different methods (the GEC method and DEG method) calculated the FESV of a provincial area, Sichuan province, China.The results showed that, by using the GEC method, the total FESV of Sichuan province increased 206.376 billion yuan (from 109.364 to 315.740) from 2008 to 2018.By adopting the DEG method, the total FESV of Sichuan province has changed 93.875 billion yuan (from 14.203 to 108.077).The results displayed the total FESV has a steady rate of increase in Sichuan province.Different from the previous studies, this paper neither directly employed the standard equivalent factor for the FESV, nor the revised average value for the global FESV.To adjust the standard equivalent factor and the revised average value, the biomass adjustment factors for different categories forest type were calculated through employing MODIS dataset.The socioeconomic adjustment factor basing on people's willingness and ability to pay for FESV was considered.This paper provided contribution to help researchers, forest managers, and policy makers pay additional attention to evaluation systems of the FESV, and regional heterogeneities of forest biomass and socioeconomic development.
For the total FESV, the results of the two methods were a long way from each other.The FESV in 2008 calculated by the GEC method was almost eight times than it calculated by the DEG method.In terms of the tremendous difference between the two different methods, the policy maker or restoration manager should propose the official and authoritative concept and estimation system of the FESV to achieve green social economic development.With the concept of green GDP put forward, the FESV will be calculated in national green GDP, and the great difference in different calculation systems should be considered circumspectly.
For the division of forest ecosystem services categories, the GEC method defined nine subcategories (food production, raw material production, gas regulation, climate regulation, water regulation, waste treatment, soil formation and conservation, biodiversity maintenance, and recreation).The DEG method contained 11 sub-categories forest ecosystem services (food, water, raw materials, climate regulation, waste treatment, erosion prevention,  Obviously, the DEG method extended the regulation and culture ecosystem services of forest, while in the GEC calculation system they were slightly weakened.Therefore, the DEG method might be more suitable for evaluating the value of forest ecosystem providing significance on the regional regulation and culture services. Regarding the average value (equivalent) of forest ecosystem, after converting revised average value for global FESV (US dollar) into RMB (yuan), the average equivalent in the GEC method was lower than it in the DEG method, while the estimated total FESV showed an opposite result.It was likely that the GEC method overestimated the average equivalent of forest ecosystem service by employing the market value of grain production.Although, the FESV of the DEG method was smaller, the DEG method studied large number of ecosystems, different types of landscapes, definitions of services, scale, area, time, and complexity (LEE & BROWN, 2021).It can be argued that the results of DEG might be closer to the actual situation.
Regarding the adjustment factors, the biomass factors and socioeconomic development adjustment factor showed increase trends, which indicated the advantage of forest biomass and socioeconomic development in Sichuan province relative to the average value of national's biomass and socioeconomic development increase continuously.This study showed that no matter what kind of calculation system was used to obtain FESV, the adjustment factor must be used to obtain a relatively accurate result.

Figure 1 -
Figure 1 -Summary of the methods.
•m -2 •t -1 ) absorbed by vegetation in pixelx over the period t. (, ) represents the actual light energy utilization rate (gC•MJ -1 ) of vegetation in pixel x in the period t.

Figure 3 -
Figure 3 -Land utilization of Sichuan province from 2008 to 2018.

Figure 4 -
Figure 4 -The S type R. Pearl growth curve.

National
Forestry and Grassland Administration (Data source: National Forestry and Grassland Administration, http://www.forestry.gov.cn),China Statistical Yearbook 2008-2018 (Data source: National Bureau of Statistics, http://www.stats.gov.cn), and Sichuan Province Statistical Yearbook 2008-2018 (Data source: Sichuan Provincial Bureau of Statistic, http://tjj.sc.gov.cn).The data sources of the related socioeconomic indices are as follows: the area of cultivated land, the per-capita GDP of Sichuan province and China, the official average exchange rate, and the Engle index of Sichuan province were obtained from the China Statistical Yearbook 2008-2018 (Data source: National Bureau of Statistics, http://www.stats.gov.cn), and Sichuan Province Statistical Yearbook 2008-2018 (Data source: Sichuan Provincial Bureau of Statistic, http://tjj.sc.gov.cn).The average market price of grain per unit of Sichuan province in study years were acquired from the Sichuan Provincial Development and Reform Commission (Data source: Sichuan Provincial Development and Reform Commission, http:// fgw.sc.gov.cn).The yearly grain yield of Sichuan province in study years were obtained from People's Government of Sichuan Province (Data source: People's Government of Sichuan Province, http:// www.sc.gov.cn).Further, the per-capita GDP of globe in study years were obtained from the World Bank (Data source: World Bank, https://www.worldbank.org/en/understanding-poverty).

Figure 5 -
Figure 5 -The shifted S type R. Pearl's growth curve.
NPP of the four forest species, MODIS data and geo-spatial meteorological data were chosen as input parameters to CASA.MODIS-derived 16-day composite vegetation indices (MOD13A1) of atmospherically corrected maximal values at 500m resolution were downloaded from EOS data gateway (Data source: http://edcimswww.cr.usgs.gov/pub/imswelcome/).Additionally, the meteorological data of Sichuan province (including monthly mean temperatures, monthly total precipitation, and monthly total solar radiation data) was obtained from China Meteorological Data Sharing Service System (Data source: China Meteorological Data Sharing Service System, http://cdc.nmic.cn/).
forests in Sichuan province are temperate forests, so the revised average value of global forest ecosystem is referred to the value of temperate forests in the study of DE GROOT et al. (2012).Ciência Rural, v.53, n.1, 2023.11 years, A ic is 0.335, 0.705 and 0.883 in 2008, 2013 regulation, water regulation are constant top three contributors to the FESV of Sichuan province, while the forest ecosystem service of food, waste treatment and recreation are the three least contributors.In terms of change trend of the FESV of Sichuan province from 2008 to 2018, the total FESV shows an upward trend, increasing from 109.364 to 315.740 billion yuan.Likewise, values of the nine sub-categories of forest ecosystem services are also increased (Table

Figure 6 -
Figure 6 -Forest ecosystem services value (FESV) of the four dominant forest categories in Sichuan province evaluated by GEC method (billion yuan).
biological control, genetic diversity, esthetic information, and cognitive development).

Table 1 -
The area of four dominant forest categories in Sichuan province (unit: 10 4 ha).

Table 2 -
Standard equivalent factor for forest ecosystem services value.

Table 3 -
Judgment on social development stages.
Note: En is the Engle index of Sichuan province.
W t , A t , PI i , A ic and PI ic are listed in table 6.Specifically, En (%) of Sichuan province in 2008, 2013 and 2018 were 52.0%, 43.5% and 35.2%, respectively.Therefore, W t are 0.11, 0.15 and 0.24 in 2008, 2013 and 2018, correspondingly.According to GDP s and GDP c in 2008, 2013 and 2018, A t equals 0.643, 0.743 and 0.741 respectively.As such, PI i is obtained.Further, R ic were 7.5215, that is, one dollar equals 7.5215 yuan in 2007.Based on the per capita GDP of globe and per capita GDP of China in study

Table 4 -
Revised average value of forest ecosystem in globe ($/ha/year, 2007 price level).

Table 5 -
Mean value NPP of four dominant forest categories in Sichuan province and China.

Table 6 -
Bi is the biomass adjustment factor of Sichuan province.NPP is net primary productivity.Socioeconomic development adjustment factor.En is the Engle index of Sichuan province; Wt is dictated the people's willingness to pay for the FESV of Sichuan province; At is the people's ability to pay for FESV of Sichuan province.PIi is the socioeconomic factor adjustment coefficient of Sichuan province; Wic indicates the coefficient of people's willingness to pay for the forest ecosystem services value (FESV) of China.

Table 7 -
The Evaluation results of forest ecosystem services value (FESV) by employing GEC method (billion yuan).

Table 8 -
The Evaluation results of forest ecosystem services value (FESV) by employing DEG method (billion yuan).