# Research on Forest Carbon Sequestration Based on FSC Model and DeepAR Algorithm

Authors: Yin-di Xu
Journal: Journal of Mathematics
 (2022)

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## Abstract

Forestry resources play an irreplaceable role in solving the problem of climate change. Forest managers to find a balance between carbon sinks and forest products, decisions must therefore take into account many aspects of forest value. This paper clarifies that forest carbon sequestration is mainly influenced by three aspects: human, climate, and nonclimatic physical factors, constructs a model for estimating the carbon sequestration rate of forest ecosystems based on forest age and the logistic growth equation, and combines human behaviour and climate influencing factors to make comprehensive corrections to the carbon sequestration rate of forest ecosystems per unit area. A model for calculating the carbon sequestration rate over time in a forest system was developed, which combined with the DeepAR Algorithm to obtain carbon sequestration. Then, this paper then assesses the various values of the forest, dividing the 25 factors affecting forest value assessment into five indices to establish a model of the forest ecosystem value assessment system for application to forest value assessment under different conditions. After determining the index system, we use the EWM-CVM to integrate the indexes into the value index based on the forest ecosystem to propose a management plan. And the PSO-BP algorithm is used to determine the transition point for forest management in order to optimise the ecological value of the forest.


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## Body

## 1. Introduction

In recent years, the emission of carbon dioxide and other greenhouse gases in the process of production and living has increased dramatically [1].Forestry resources play an irreplaceable role in solving the problem of climate change. The main ecological function of forests is to absorb carbon dioxide and release oxygen [2–6].This is conducive to reducing greenhouse gases in the atmosphere. However, if climate change is to be effectively addressed, carbon sequestration is needed. Forest management strategies with appropriate logging are conducive to carbon sequestration. For forest managers to find a balance between carbon sinks and forest products, decisions must therefore take into account many aspects of forest value.In this paper, an FCS model based on classical logistic equations of forest age and biomass was developed to explore the carbon cycle between vegetation, litter and soil. In order to consider the effects of herbivores, fire and water erosion on the carbon sink, the results of a combined analysis were used, considering 58% of the ideal state as the result, assuming that the model excludes the interference of human behaviours and climate effects. Forest carbon sequestration is one of the main ways to mitigate climate change, and forests, as the mainstay of terrestrial ecosystems, are the largest carbon reservoir in the system. Forest carbon sinks are also one of the most cost-effective ways to combat climate change. Forests sequester carbon using natural processes that do not require high costs and at the same time have ecological benefits such as protecting biodiversity, conserving water and preventing wind and sand.


## 2. Literature Review

In recent decades, scientists have carried out a great deal of research on climate change and its effects. The wide range of research and the variety of research methods all indicate that the effects of climate change are very complex, affecting almost all natural and socio-economic systems. The impact of climate change has a certain transmissibility, which can be reflected in natural systems and transmitted to social and economic systems [7].In order to cope with the increasingly severe global climate change situation, the IPCC calls on countries to reduce carbon emissions and promote carbon neutrality, and strive to achieve net zero emissions of carbon dioxide. In order to achieve this goal, in addition to large-scale implementation of renewable energy substitution and tapping the potential of energy saving and carbon reduction technologies such as hydrogen production from renewable energy, it is also necessary to vigorously develop carbon capture and storage technologies [8–14].This shows the role of “carbon sequestration” in addressing the impacts of climate change. The ability of carbon management in forest management plans to effectively manage carbon emissions led to the birth of the International Carbon Management Partnership, which sets guidelines for forest managers around the world.As the composition, climate, population, interests and values of forests vary greatly around the world, different management plans need to be formulated according to different situations. Only by considering various factors can the forest management plans thus obtained be practical. Therefore, it is necessary to establish a decision-making model to determine the specific forest management plan in order to solve the impact of climate change.


## 3. Assumptions and Symbols

In response to the problems studied in this article, to better establish the model without affecting the accuracy of the model, we have made the following assumptions: (i) The development from the current state to the proposed state is stable. Sudden changes can be ignored because of their rareness; (ii) Excluding the impact of uncontrollable factors on the data, such as fires, planetary impacts on forests, etc; (iii) The climatic impact on NPP variations can be estimated by RC on a location basis in an LVSA zone; (iv) Statistics we collect from the website are actual and reliable; (v) Assuming that global climate change is consistent and that temperature and precipitation are important parameters in FCS models, however, under different global climate change scenarios, the estimates may contain a high degree of uncertainty, which may lead to uncertainty in forest carbon stock estimates. At the same time, the abbreviations and definitions mentioned in this article are shown in Table1.Table 1
Notations.
SymbolsDefinitionFVForest value, ESTSCSocio-economic conditions indexIVIndirect value indexViThe coefficient of variation of the indexiθiThe standard deviation of the indexiTiqThe desired outputs of the network under the network weights OiqFCSForest carbon sequestrationNPPNet primary productivityFVForest value, ESTSCSocio-economic conditions indexIVIndirect value indexViThe coefficient of variation of the indexi


## 4. Forests Carbon Sequestration Model Based on the Logistic

### 4.1. Forests Vegetation Year in the FCS Model

Based on the classical logistic equation of forest age and biomass, the FCS model was established [15] to explore the carbon cycle among vegetation, litter, and soil. To consider the impacts of herbivores, fire, and water erosion on carbon sinks, we used the results of the integrative analysis conducted [16] and regarded 58% in the ideal state as the result. We assume that this model excludes the interference of human behaviour and climatic influences. With forest development, forest biomass gradually reaches a relative equilibrium state [17]. The annual growth rate of vegetation biomass can be simply defined by follows:(1)dBtdt=v01−BtBmaxBt,(2)Bt=Bmax1+Bmax/Bt0−1×e−v0×t−t0,where Bt is the forest vegetation biomass (Mg ha−1); V0 is the intrinsic growth rate, representing the maximum growth rate when vegetative growth is not limited by the environment, nutrients, or disturbances; Bmax is the maximum vegetation biomass under the mature forest scenario (Mg ha−1); 1˗Bt/Bmax represents the fractional deficiency of the current biomass to its saturation level; and t is the forest age (year).Three key parameters were well defined or validated using the field data at a large scale [18].In this study, we considered 80 years as the age of a mature forest and collected vegetation biomass data of mature forests from the public databases. Vegetation biomass in mature forests was calculated by MAT and MAP using:(3)BmaxMAT,MAP=3442.914×0.05+exp0.000158×MAP1+exp−0.037×MAT−95.606+33.128.In equation (6), MAT is the mean annual temperature (°C), and MAP is the mean annual precipitation (mm).The Miami model considered MAT and MAP to be key factors for vegetation productivity.dBMiami is the annual productivity estimated by the modified Miami model (Mg ha−1 yr−1) in the following equation:(4)dBMiami=30×1−exp−0.00031×MAP1+exp0.12345−0.2606×MAT,(5)v0=dBMiamiBt=0.081×exp0.038×MAT+0.065×lnMAP−0.38.


### 4.2. Soil Carbon Cycles in the FCS Model

The soil organic carbon (SOC) level in forests is the result of the combined effects of the humification and mineralization processes [19].When the factors of forests are relatively stable, the humification and mineralization processes will tend to balance the SOC level, as shown in(6)dCtdt=It−k2Ct,where Ct is the SOC density (Mg C ha−1) and It is the annual input of SOC (Mg ha−1 a−1);(7)It=hk1Lt.Lt is the litter content (Mg ha−1); k1 is the litter decomposition coefficient; k2 is the SOC decomposition rate (a−1); and h is the decay coefficient (0.3).(8)Ct=Itk2−Itk2−Ct0exp−k2t−t0.During the development of the FCS model, we used the multi-source investigation data over the past few decades to optimise the key parameters.


### 4.3. Forest Carbon Sequestration of Human and Climatic Factors

The net carbon flows from natural and mixed forests published by UNESCO are shown in Figure1. Spatial differences in forest carbon sequestration will be entirely attributable to human influence once the differential effects of climate and non-climate on forest carbon sequestration are excluded. We use net primary productivity(NPP) to express the carbon sequestration capacity of forests in terrestrial ecosystems. Our main objective is to assess how much carbon can realistically be obtained from global terrestrial vegetation by renewing humans alone, without changing land use and land cover or forest biomes. We use publicly available time series datasets to analyse the carbon gap. The data source is from Google Earth Engine (GEE) [20]. Data pre-processing and analysis was also performed on the GEE computing platform. There are four sets of data sources involved, namely climate-related variables, (non-climate) physical environment variables, country productivity and world population. These data sets, if not at the 500m scale, were uniformly resampled to a resolution of 500m. Region segmentation of homogeneous natural environments to detach non-climate impacts on NPP variation. Region segmentation is performed by over-laying the layers of landform (L), vegetation type (V), soil type (S)and tree age(A) characteristics to derive homogeneous zones, known as homogeneous LVSA zones.Over the pixels within the same LVSA zone, the impact from the non-climate environmental factors on the internal NPP variation is uniform. Thus, any NPP variation within an LVSA zone is attributed to varied climatic and human impacts only [21].Figure 1
Net carbon flows from natural and mixed forests published by UNESCO.The NPP dataset provides a direct indicator of the carbon sequestration of forests, and reflects the spatial and temporal variability of forests carbon sequestration [22].We assume that the Miami model can be applied to measure the relative impact on NPP from climate variations in an LVSA zone. The Miami model is used to assess the climate impact on PNPP, which takes the form(9)PNPP=λ×min30001+e1.315−0.119t,3000×1−e−0.000664p,where t is the annual average temperature (°C), p is the annual precipitation (mm), and λ is a conversion coefficient (0.50 for woody ecosystems and 0.45 for herbaceous) that converts dry matter to carbon unit (gCm−2yr−1).For discriminating the varied climate impact on NPP in an LVSA zone, wherePNPP(i, g) is PNPP at i in g, PNPPmeang is the mean PNPP of all the locations in g:(10)RCi,g=PNPPi,g−PNPPmeang.The climatic and human impact determine the NPP variations across an LVSA zone characterized by the identical landform, forests cover, and soil properties. Climate-rectified NPP (NPPCR ) at location i in g can be derived using the function(11)NPPCRi,g=NPPi,g−RCi,g.NPPCR(i,g) is the rectified NPP at location i in g after the climatic impact on NPP is removed. When spatial variations of NPPCR within an LVSA zone are observed, it is attributed to human influence, i.e., the difference in land-management practices (LMPs).These best LMPs can be deemed to be the optimal BLMPs under similar environmental conditions over this LVSA zone. A window size specifies a local neighborhood surrounding given location in which theNPPCR values at all the locations with the identical LVSA in this window are taken as input to compute the NPPCRfinal. To decide the window size, a stratified random selection approach is taken to sample 5000 points in the vegetated land with the sample size weighted by the area of each of the biome types [23].As can be seen from Figure2, the horizontal axis represents the distance and the vertical axis represents the amount of carbon sequestered, which presents a relatively stable stage when the distance is over 20 km from the piecewise linear function fitting. Hence, the carbon sequestration at location i is computed as the difference between the current NPPCR and the NPPCRfinal within the 20 km window in the environmentally homogeneous zone:(12)Ci=max0,NPPCRfinal−NPPCRi.Figure 2
Samples with peak NPPCRfinal present in each distance bin.The candidate of BLMPs for a location is decided by referring to the LMPs within the distance-constrained local window that boast identical environmental contexts but exhibit a higher level of carbon sequestration (i.e., whereNPPCRNPPCRfinal).


## 4.1. Forests Vegetation Year in the FCS Model

Based on the classical logistic equation of forest age and biomass, the FCS model was established [15] to explore the carbon cycle among vegetation, litter, and soil. To consider the impacts of herbivores, fire, and water erosion on carbon sinks, we used the results of the integrative analysis conducted [16] and regarded 58% in the ideal state as the result. We assume that this model excludes the interference of human behaviour and climatic influences. With forest development, forest biomass gradually reaches a relative equilibrium state [17]. The annual growth rate of vegetation biomass can be simply defined by follows:(1)dBtdt=v01−BtBmaxBt,(2)Bt=Bmax1+Bmax/Bt0−1×e−v0×t−t0,where Bt is the forest vegetation biomass (Mg ha−1); V0 is the intrinsic growth rate, representing the maximum growth rate when vegetative growth is not limited by the environment, nutrients, or disturbances; Bmax is the maximum vegetation biomass under the mature forest scenario (Mg ha−1); 1˗Bt/Bmax represents the fractional deficiency of the current biomass to its saturation level; and t is the forest age (year).Three key parameters were well defined or validated using the field data at a large scale [18].In this study, we considered 80 years as the age of a mature forest and collected vegetation biomass data of mature forests from the public databases. Vegetation biomass in mature forests was calculated by MAT and MAP using:(3)BmaxMAT,MAP=3442.914×0.05+exp0.000158×MAP1+exp−0.037×MAT−95.606+33.128.In equation (6), MAT is the mean annual temperature (°C), and MAP is the mean annual precipitation (mm).The Miami model considered MAT and MAP to be key factors for vegetation productivity.dBMiami is the annual productivity estimated by the modified Miami model (Mg ha−1 yr−1) in the following equation:(4)dBMiami=30×1−exp−0.00031×MAP1+exp0.12345−0.2606×MAT,(5)v0=dBMiamiBt=0.081×exp0.038×MAT+0.065×lnMAP−0.38.


## 4.2. Soil Carbon Cycles in the FCS Model

The soil organic carbon (SOC) level in forests is the result of the combined effects of the humification and mineralization processes [19].When the factors of forests are relatively stable, the humification and mineralization processes will tend to balance the SOC level, as shown in(6)dCtdt=It−k2Ct,where Ct is the SOC density (Mg C ha−1) and It is the annual input of SOC (Mg ha−1 a−1);(7)It=hk1Lt.Lt is the litter content (Mg ha−1); k1 is the litter decomposition coefficient; k2 is the SOC decomposition rate (a−1); and h is the decay coefficient (0.3).(8)Ct=Itk2−Itk2−Ct0exp−k2t−t0.During the development of the FCS model, we used the multi-source investigation data over the past few decades to optimise the key parameters.


## 4.3. Forest Carbon Sequestration of Human and Climatic Factors

The net carbon flows from natural and mixed forests published by UNESCO are shown in Figure1. Spatial differences in forest carbon sequestration will be entirely attributable to human influence once the differential effects of climate and non-climate on forest carbon sequestration are excluded. We use net primary productivity(NPP) to express the carbon sequestration capacity of forests in terrestrial ecosystems. Our main objective is to assess how much carbon can realistically be obtained from global terrestrial vegetation by renewing humans alone, without changing land use and land cover or forest biomes. We use publicly available time series datasets to analyse the carbon gap. The data source is from Google Earth Engine (GEE) [20]. Data pre-processing and analysis was also performed on the GEE computing platform. There are four sets of data sources involved, namely climate-related variables, (non-climate) physical environment variables, country productivity and world population. These data sets, if not at the 500m scale, were uniformly resampled to a resolution of 500m. Region segmentation of homogeneous natural environments to detach non-climate impacts on NPP variation. Region segmentation is performed by over-laying the layers of landform (L), vegetation type (V), soil type (S)and tree age(A) characteristics to derive homogeneous zones, known as homogeneous LVSA zones.Over the pixels within the same LVSA zone, the impact from the non-climate environmental factors on the internal NPP variation is uniform. Thus, any NPP variation within an LVSA zone is attributed to varied climatic and human impacts only [21].Figure 1
Net carbon flows from natural and mixed forests published by UNESCO.The NPP dataset provides a direct indicator of the carbon sequestration of forests, and reflects the spatial and temporal variability of forests carbon sequestration [22].We assume that the Miami model can be applied to measure the relative impact on NPP from climate variations in an LVSA zone. The Miami model is used to assess the climate impact on PNPP, which takes the form(9)PNPP=λ×min30001+e1.315−0.119t,3000×1−e−0.000664p,where t is the annual average temperature (°C), p is the annual precipitation (mm), and λ is a conversion coefficient (0.50 for woody ecosystems and 0.45 for herbaceous) that converts dry matter to carbon unit (gCm−2yr−1).For discriminating the varied climate impact on NPP in an LVSA zone, wherePNPP(i, g) is PNPP at i in g, PNPPmeang is the mean PNPP of all the locations in g:(10)RCi,g=PNPPi,g−PNPPmeang.The climatic and human impact determine the NPP variations across an LVSA zone characterized by the identical landform, forests cover, and soil properties. Climate-rectified NPP (NPPCR ) at location i in g can be derived using the function(11)NPPCRi,g=NPPi,g−RCi,g.NPPCR(i,g) is the rectified NPP at location i in g after the climatic impact on NPP is removed. When spatial variations of NPPCR within an LVSA zone are observed, it is attributed to human influence, i.e., the difference in land-management practices (LMPs).These best LMPs can be deemed to be the optimal BLMPs under similar environmental conditions over this LVSA zone. A window size specifies a local neighborhood surrounding given location in which theNPPCR values at all the locations with the identical LVSA in this window are taken as input to compute the NPPCRfinal. To decide the window size, a stratified random selection approach is taken to sample 5000 points in the vegetated land with the sample size weighted by the area of each of the biome types [23].As can be seen from Figure2, the horizontal axis represents the distance and the vertical axis represents the amount of carbon sequestered, which presents a relatively stable stage when the distance is over 20 km from the piecewise linear function fitting. Hence, the carbon sequestration at location i is computed as the difference between the current NPPCR and the NPPCRfinal within the 20 km window in the environmentally homogeneous zone:(12)Ci=max0,NPPCRfinal−NPPCRi.Figure 2
Samples with peak NPPCRfinal present in each distance bin.The candidate of BLMPs for a location is decided by referring to the LMPs within the distance-constrained local window that boast identical environmental contexts but exhibit a higher level of carbon sequestration (i.e., whereNPPCRNPPCRfinal).


## 5. Optimal Assessment of Forest Value Benefits

### 5.1. Index Selection

#### 5.1.1. Ecosystem Service Types

They can be divided into eight categories: (X1,X2,X3,X4,X5, X6,X7,X8), forest fruit products, water harvesting, carbon sequestration and oxygen release, air purification, forest recreation, biodiversity conservation, soil conservation, and nutrient accumulation. The eight types of ecosystem services can be classified as follows: there are significant differences in value assessment results depending on the type of ecosystem service.


#### 5.1.2. Vegetation Zones

There are eight types of vegetation zones: (X9,X10,X11,X12,X13,X14,X15,X16), cold temperate coniferous forests, temperate mixed coniferous forests, warm temperate deciduous broadleaved forests, subtropical evergreen broadleaved forests, tropical (seasonal) rainforests, temperate grasslands, temperate deserts, and alpine vegetation zones. The vegetation zones determine the natural environmental conditions for forest growth and influence the supply of ecosystem services [24].


#### 5.1.3. Area Characteristics

Fundamental to the enhancement of forest eco-efficiency is the continuous growth of forest resources. The total value of ecosystem services in a certain region is the sum of the value of all service functions provided by ecosystems in the region, which varies with the quality, area, and type of ecosystems in the region.(1)
Forest Area (X17). As forest area increases, the value of forest ecosystem services increases with the increase in forest cover. At the same time, the value of ecosystem services may have a marginal effect as forest area increases.(2)
Forest Abundance (X18). It has the area of other forests within a 50 km radius from the centre of the study area. When the surrounding forests provide the same type of ecosystem services as the study area, i.e., they are substitutes, the value of ecosystem services in the study area may decrease as the area of other forests increases; conversely, if they are complements, there may be a positive relationship between the value of ecosystem services in the study area and the area of other forests.(3)
Railway Length (X19). It has the length of the railway within a 50 km radius from the centre of the study area. The construction of railways causes fragmentation of the landscape. Therefore, there may be a negative relationship between the value of ecosystem services and railway length. There may be a negative relationship between the value of ecosystem services and the length of the railway [25].


#### 5.1.4. Socio-Economic Conditions

(1)
Population (X20). It means the number of people in an area with a radius of 50 km from the centre of the study area. On the one hand, an increase in population means an increase in market and demand, which promotes the development and use of forest ecosystems; on the other hand, the concentration of population and the irrational use of resources increases the risk of environmental damage and causes the decline of ecosystems. Therefore, there is no definite a priori relationship between the value of ecosystem services and the number of people.(2)
GDP Per Capita (X21). GDP per capita is a reflection of the local economy and the standard of living of the people. Similar to the impact of population size, economic development can promote the use and conservation of forest ecosystems on the one hand, but can also lead to overexploitation of resources and ecological degradation on the other. There is therefore no definitive a priori relationship between the value of ecosystem services and GDP per capita.(3)
Employment Benefits (X22). Exploring the impact on the value of employment through the growth model of employment benefits from forest resources to enhance the sustainable use of forest resources, maintain ecological balance and sustainable socio-economic development.


#### 5.1.5. Indirect Value

The social benefits of forests at the regional level are evaluated in three main areas: historical benefits, scientific and educational benefits, and cultural benefits(X23, X24, X25).The scientific and educational benefits are considered in terms of education and research, the historical benefits are considered in terms of the value of famous and ancient trees, and the cultural benefits are mainly evaluated in terms of forest cultural products and forest practices.


### 5.2. Data Normalization

In our research, all index data firstly go through dimensionless treatment. According to the indicator data, we adopt the threshold method in linear dimensionless methods to make all the indicator data dimensionless [26].These 25 indicators can be classified into three types, cost-type index, benefit-type index, and moderate-type index. Among the three classes of indexes, the smaller the cost-type index is, the better the competitiveness degree of Ecosystems is. The benefit-type index is the opposite. The moderate-type index is better when it closer to a specific value. Due to the different contributions of the indexes, the three types of data are normalized in different ways [27].(1)Qjϵ cost-type index. Let xij denote the j−th index of the i−th , and it can be expressed as(13)xij=xjmax−xijxjmax−xjmin,where xjmax is the most considerable value of Qj, xjmin is the smallest value of Qj.(2)Qjϵ benefit-type index.(14)xij=xij−xjminxjmax−xjmin.(3) Qjϵ moderate-type index.(15)xij=1−s1−dijmaxs1−djmin,djmax−s2,dij<s1,1,dij=s1,1−dij−s2maxs2−djmin,djmin−s2,dij>s1,where s1 is the best value of the indicator. Q.


### 5.3. Weight of Indicators

#### 5.3.1. Entropy Weight Method

With the indicators defined above, we further determine the weights of these indicators, resulting in the combination of primary indicators. Recalling the entropy weight method (EWM) [28], we carry out the standardized treatment, making each variable optimal and worst value after alternation is 1 and 0, respectively. The evaluation indexes are X1,X2,X3,…,Xk, where Xi=xi1,xi2,…,xin.After standardization, we introduce(16)pij=yij∑i=1nyij,According to the concepts of self-information and entropy in the information theory, we can calculate the information entropyEi of each evaluation indicator; hence we can obtain(17)Ei=−lnn−1∑j=1npijlnpij.Based on the information entropy, we will further compute the weight of each evaluation indicator we defined before:(18)wi=1−Eik−∑iEi,i=1,2,…,k,


#### 5.3.2. Coefficient of Variation Method

Furthermore, we apply the coefficient of variation method to weight these six indices and merge them into a comprehensive metric. Therefore, we will introduce the application of the coefficient of variation method briefly.The coefficient of variation method (CVM) [29] utilizes the information from various indexes and achieves each Indicator weight through calculating, which shows an objective approach to give weight:(19)V=θizii=1,2,3,4,5,where Vi is the coefficient of variation of the index i, which can also be called as standard deviation coefficient, and θi means the standard deviation of the index i.And the Z1-5 separately means EST, VZ, AC, SC, and IV.Then the weight of each index comes to us:(20)Wi=Vi∑i=1nVi.In this way, we are able to achieve the weight of each index without any subjective impression in Table2.(21)FV=W1×EST+W2×VZ+W3×AC+W4×SC+W5×IV.Table 2
Index weights for forest value benefits.
Index (I)WeightIndex (II)WeightIndex (II)WeightIndex (II)WeightX10.1340X40.0474X70.1476Ecosystem service types0.2657X20.1712X50.0276X80.2059X30.1689X60.0974EST0.2657X90.2046X120.1529X150.1535Vegetation zones0.2014X100.0418X130.0473X160.0601X110.0945X140.2453VZ0.2014Area characteristics0.1416X170.4883X180.0993X190.4124Socio-economic conditions0.1884X200.1883X210.6137X220.1980Indirect value0.2029X230.0752X240.5782X250.3466


## 5.1. Index Selection

### 5.1.1. Ecosystem Service Types

They can be divided into eight categories: (X1,X2,X3,X4,X5, X6,X7,X8), forest fruit products, water harvesting, carbon sequestration and oxygen release, air purification, forest recreation, biodiversity conservation, soil conservation, and nutrient accumulation. The eight types of ecosystem services can be classified as follows: there are significant differences in value assessment results depending on the type of ecosystem service.


### 5.1.2. Vegetation Zones

There are eight types of vegetation zones: (X9,X10,X11,X12,X13,X14,X15,X16), cold temperate coniferous forests, temperate mixed coniferous forests, warm temperate deciduous broadleaved forests, subtropical evergreen broadleaved forests, tropical (seasonal) rainforests, temperate grasslands, temperate deserts, and alpine vegetation zones. The vegetation zones determine the natural environmental conditions for forest growth and influence the supply of ecosystem services [24].


### 5.1.3. Area Characteristics

Fundamental to the enhancement of forest eco-efficiency is the continuous growth of forest resources. The total value of ecosystem services in a certain region is the sum of the value of all service functions provided by ecosystems in the region, which varies with the quality, area, and type of ecosystems in the region.(1)
Forest Area (X17). As forest area increases, the value of forest ecosystem services increases with the increase in forest cover. At the same time, the value of ecosystem services may have a marginal effect as forest area increases.(2)
Forest Abundance (X18). It has the area of other forests within a 50 km radius from the centre of the study area. When the surrounding forests provide the same type of ecosystem services as the study area, i.e., they are substitutes, the value of ecosystem services in the study area may decrease as the area of other forests increases; conversely, if they are complements, there may be a positive relationship between the value of ecosystem services in the study area and the area of other forests.(3)
Railway Length (X19). It has the length of the railway within a 50 km radius from the centre of the study area. The construction of railways causes fragmentation of the landscape. Therefore, there may be a negative relationship between the value of ecosystem services and railway length. There may be a negative relationship between the value of ecosystem services and the length of the railway [25].


### 5.1.4. Socio-Economic Conditions

(1)
Population (X20). It means the number of people in an area with a radius of 50 km from the centre of the study area. On the one hand, an increase in population means an increase in market and demand, which promotes the development and use of forest ecosystems; on the other hand, the concentration of population and the irrational use of resources increases the risk of environmental damage and causes the decline of ecosystems. Therefore, there is no definite a priori relationship between the value of ecosystem services and the number of people.(2)
GDP Per Capita (X21). GDP per capita is a reflection of the local economy and the standard of living of the people. Similar to the impact of population size, economic development can promote the use and conservation of forest ecosystems on the one hand, but can also lead to overexploitation of resources and ecological degradation on the other. There is therefore no definitive a priori relationship between the value of ecosystem services and GDP per capita.(3)
Employment Benefits (X22). Exploring the impact on the value of employment through the growth model of employment benefits from forest resources to enhance the sustainable use of forest resources, maintain ecological balance and sustainable socio-economic development.


### 5.1.5. Indirect Value

The social benefits of forests at the regional level are evaluated in three main areas: historical benefits, scientific and educational benefits, and cultural benefits(X23, X24, X25).The scientific and educational benefits are considered in terms of education and research, the historical benefits are considered in terms of the value of famous and ancient trees, and the cultural benefits are mainly evaluated in terms of forest cultural products and forest practices.


## 5.1.1. Ecosystem Service Types

They can be divided into eight categories: (X1,X2,X3,X4,X5, X6,X7,X8), forest fruit products, water harvesting, carbon sequestration and oxygen release, air purification, forest recreation, biodiversity conservation, soil conservation, and nutrient accumulation. The eight types of ecosystem services can be classified as follows: there are significant differences in value assessment results depending on the type of ecosystem service.


## 5.1.2. Vegetation Zones

There are eight types of vegetation zones: (X9,X10,X11,X12,X13,X14,X15,X16), cold temperate coniferous forests, temperate mixed coniferous forests, warm temperate deciduous broadleaved forests, subtropical evergreen broadleaved forests, tropical (seasonal) rainforests, temperate grasslands, temperate deserts, and alpine vegetation zones. The vegetation zones determine the natural environmental conditions for forest growth and influence the supply of ecosystem services [24].


## 5.1.3. Area Characteristics

Fundamental to the enhancement of forest eco-efficiency is the continuous growth of forest resources. The total value of ecosystem services in a certain region is the sum of the value of all service functions provided by ecosystems in the region, which varies with the quality, area, and type of ecosystems in the region.(1)
Forest Area (X17). As forest area increases, the value of forest ecosystem services increases with the increase in forest cover. At the same time, the value of ecosystem services may have a marginal effect as forest area increases.(2)
Forest Abundance (X18). It has the area of other forests within a 50 km radius from the centre of the study area. When the surrounding forests provide the same type of ecosystem services as the study area, i.e., they are substitutes, the value of ecosystem services in the study area may decrease as the area of other forests increases; conversely, if they are complements, there may be a positive relationship between the value of ecosystem services in the study area and the area of other forests.(3)
Railway Length (X19). It has the length of the railway within a 50 km radius from the centre of the study area. The construction of railways causes fragmentation of the landscape. Therefore, there may be a negative relationship between the value of ecosystem services and railway length. There may be a negative relationship between the value of ecosystem services and the length of the railway [25].


## 5.1.4. Socio-Economic Conditions

(1)
Population (X20). It means the number of people in an area with a radius of 50 km from the centre of the study area. On the one hand, an increase in population means an increase in market and demand, which promotes the development and use of forest ecosystems; on the other hand, the concentration of population and the irrational use of resources increases the risk of environmental damage and causes the decline of ecosystems. Therefore, there is no definite a priori relationship between the value of ecosystem services and the number of people.(2)
GDP Per Capita (X21). GDP per capita is a reflection of the local economy and the standard of living of the people. Similar to the impact of population size, economic development can promote the use and conservation of forest ecosystems on the one hand, but can also lead to overexploitation of resources and ecological degradation on the other. There is therefore no definitive a priori relationship between the value of ecosystem services and GDP per capita.(3)
Employment Benefits (X22). Exploring the impact on the value of employment through the growth model of employment benefits from forest resources to enhance the sustainable use of forest resources, maintain ecological balance and sustainable socio-economic development.


## 5.1.5. Indirect Value

The social benefits of forests at the regional level are evaluated in three main areas: historical benefits, scientific and educational benefits, and cultural benefits(X23, X24, X25).The scientific and educational benefits are considered in terms of education and research, the historical benefits are considered in terms of the value of famous and ancient trees, and the cultural benefits are mainly evaluated in terms of forest cultural products and forest practices.


## 5.2. Data Normalization

In our research, all index data firstly go through dimensionless treatment. According to the indicator data, we adopt the threshold method in linear dimensionless methods to make all the indicator data dimensionless [26].These 25 indicators can be classified into three types, cost-type index, benefit-type index, and moderate-type index. Among the three classes of indexes, the smaller the cost-type index is, the better the competitiveness degree of Ecosystems is. The benefit-type index is the opposite. The moderate-type index is better when it closer to a specific value. Due to the different contributions of the indexes, the three types of data are normalized in different ways [27].(1)Qjϵ cost-type index. Let xij denote the j−th index of the i−th , and it can be expressed as(13)xij=xjmax−xijxjmax−xjmin,where xjmax is the most considerable value of Qj, xjmin is the smallest value of Qj.(2)Qjϵ benefit-type index.(14)xij=xij−xjminxjmax−xjmin.(3) Qjϵ moderate-type index.(15)xij=1−s1−dijmaxs1−djmin,djmax−s2,dij<s1,1,dij=s1,1−dij−s2maxs2−djmin,djmin−s2,dij>s1,where s1 is the best value of the indicator. Q.


## 5.3. Weight of Indicators

### 5.3.1. Entropy Weight Method

With the indicators defined above, we further determine the weights of these indicators, resulting in the combination of primary indicators. Recalling the entropy weight method (EWM) [28], we carry out the standardized treatment, making each variable optimal and worst value after alternation is 1 and 0, respectively. The evaluation indexes are X1,X2,X3,…,Xk, where Xi=xi1,xi2,…,xin.After standardization, we introduce(16)pij=yij∑i=1nyij,According to the concepts of self-information and entropy in the information theory, we can calculate the information entropyEi of each evaluation indicator; hence we can obtain(17)Ei=−lnn−1∑j=1npijlnpij.Based on the information entropy, we will further compute the weight of each evaluation indicator we defined before:(18)wi=1−Eik−∑iEi,i=1,2,…,k,


### 5.3.2. Coefficient of Variation Method

Furthermore, we apply the coefficient of variation method to weight these six indices and merge them into a comprehensive metric. Therefore, we will introduce the application of the coefficient of variation method briefly.The coefficient of variation method (CVM) [29] utilizes the information from various indexes and achieves each Indicator weight through calculating, which shows an objective approach to give weight:(19)V=θizii=1,2,3,4,5,where Vi is the coefficient of variation of the index i, which can also be called as standard deviation coefficient, and θi means the standard deviation of the index i.And the Z1-5 separately means EST, VZ, AC, SC, and IV.Then the weight of each index comes to us:(20)Wi=Vi∑i=1nVi.In this way, we are able to achieve the weight of each index without any subjective impression in Table2.(21)FV=W1×EST+W2×VZ+W3×AC+W4×SC+W5×IV.Table 2
Index weights for forest value benefits.
Index (I)WeightIndex (II)WeightIndex (II)WeightIndex (II)WeightX10.1340X40.0474X70.1476Ecosystem service types0.2657X20.1712X50.0276X80.2059X30.1689X60.0974EST0.2657X90.2046X120.1529X150.1535Vegetation zones0.2014X100.0418X130.0473X160.0601X110.0945X140.2453VZ0.2014Area characteristics0.1416X170.4883X180.0993X190.4124Socio-economic conditions0.1884X200.1883X210.6137X220.1980Indirect value0.2029X230.0752X240.5782X250.3466


## 5.3.1. Entropy Weight Method

With the indicators defined above, we further determine the weights of these indicators, resulting in the combination of primary indicators. Recalling the entropy weight method (EWM) [28], we carry out the standardized treatment, making each variable optimal and worst value after alternation is 1 and 0, respectively. The evaluation indexes are X1,X2,X3,…,Xk, where Xi=xi1,xi2,…,xin.After standardization, we introduce(16)pij=yij∑i=1nyij,According to the concepts of self-information and entropy in the information theory, we can calculate the information entropyEi of each evaluation indicator; hence we can obtain(17)Ei=−lnn−1∑j=1npijlnpij.Based on the information entropy, we will further compute the weight of each evaluation indicator we defined before:(18)wi=1−Eik−∑iEi,i=1,2,…,k,


## 5.3.2. Coefficient of Variation Method

Furthermore, we apply the coefficient of variation method to weight these six indices and merge them into a comprehensive metric. Therefore, we will introduce the application of the coefficient of variation method briefly.The coefficient of variation method (CVM) [29] utilizes the information from various indexes and achieves each Indicator weight through calculating, which shows an objective approach to give weight:(19)V=θizii=1,2,3,4,5,where Vi is the coefficient of variation of the index i, which can also be called as standard deviation coefficient, and θi means the standard deviation of the index i.And the Z1-5 separately means EST, VZ, AC, SC, and IV.Then the weight of each index comes to us:(20)Wi=Vi∑i=1nVi.In this way, we are able to achieve the weight of each index without any subjective impression in Table2.(21)FV=W1×EST+W2×VZ+W3×AC+W4×SC+W5×IV.Table 2
Index weights for forest value benefits.
Index (I)WeightIndex (II)WeightIndex (II)WeightIndex (II)WeightX10.1340X40.0474X70.1476Ecosystem service types0.2657X20.1712X50.0276X80.2059X30.1689X60.0974EST0.2657X90.2046X120.1529X150.1535Vegetation zones0.2014X100.0418X130.0473X160.0601X110.0945X140.2453VZ0.2014Area characteristics0.1416X170.4883X180.0993X190.4124Socio-economic conditions0.1884X200.1883X210.6137X220.1980Indirect value0.2029X230.0752X240.5782X250.3466


## 6. Model Validation

### 6.1. CSRs in the Forests from 2010 to 2080

As can be seen from Figure3, without considering extreme events and human interference, as expected, higher CSRs were observed in the young forests from 2010 to 2050,irrespective of the forests and soils, existing forests, and forestation level. However, 2050 to 2080 show a clear downward trend. The transition period lies between 2045 and 2055. The practical value (2010∼2021) and predicted value(2021∼2080) of CSRs in the forests from 2010 to 2080. The blue line is made by the method of FCS model, and the red dotted line is a fitting curve with a confidence interval of 0.95 [30].Figure 3
Fitting curve of available benefit data over time.The model was constructed using long-term datasets, which can suitably fit the relationship between forests biomass and forest age, but more long-term forest succession datasets are required to reduce the errors, considering the complexity of forest types and their wide distribution. At the establishment of the FCS model used here, some key parameters of the model were calibrated according to the investigated data of forest plots. Therefore, these representative local parameters made it better simulate the spatial C storage in forests to a large extent [31].


### 6.2. PSO-BP Algorithm Seeks Transition Points

The particle swarm algorithm can perform a rough search in the global scope to get an initial solution for BP relay, while the BP neural network algorithm can be used for gradient search with a strong refinement capability to perform a more careful search of the data. Here the transition point can be determined by using the algorithm for iterative search in the transition interval to get the final result. If the traditional gradient descent method is followed to find the optimum, this method often converges slowly and tends to fall into a local optimum [32]. In this paper, a combination of the PSO optimisation method and BP neural network is adopted to improve it. The connection weights and thresholds of the BP neural network are treated as elements of the position vector X of the particles in the particle swarm, and then the gradient descent method of the BP network is used instead of the particle swarm optimisation method to optimise the connection weights and thresholds of the network. The error in the output of this method comes mainly from the weights between the individual transmission channels.The activation function chosen for this model is the Sigmoid function, which is given by(22)fx=11+e−x.Net activation expression is given by(23)neti=∑j=1nwijxj−θi.The input and output of each layer of neurons is calculated as follows:(24)hihk=∑i=1nwih−θh,h=1,2,…,p,(25)hohk=fhihk,h=1,2,…,p,(26)yiok=∑h=1nwohhohk,h=1,2,…,p,(27)dik=fyiok,h=1,2,…,p.The velocity of each particle is updated continuously during the training process and it is judged whether the updated velocity is greater than the maximum velocity, if it is greater than the maximum velocity, the updated velocity takes the value of the maximum velocity, otherwise, it remains unchanged. Similarly, the position of each particle is updated.After the previous calculation the actual output can be obtained, using the actual output and the expected value can be calculated:(28)δok=∂e∂yio=∂1/2∑i=1qdik−yoik2∂yoi=−dik−yoikyoik,(29)∂e∂who=∂e∂yiokΔ∂yiok∂who,∂yiok∂who=∂∑h=1pwhohohk−θo∂who.Calculate the fitness value for each particle:(30)fi=1nt∑q=1ntOiq−Tiq2,where nt is the number of training samples;Oiq and Tiq are the actual and desired outputs of the network under the network weights and thresholds determined by the positions of the training samples at the ith particle, respectively.Calculate the global minimum adaptation value of the particle swarm; if the current number of iterations reaches the maximum number of iterations, then the iteration stops; otherwise, calculate the individual extreme value and global extreme value position of each particle, and continue to update the velocity and position of the particles. Finally, the network weights and thresholds determined by the global pole position are output [33].Now the trained BP neural network model can only output the normalized data, in order to get the real data, you can use the function mapminmax, the formula is as follows:(31)y=ymax−yminx−xminxmax−xmin.The PSO-BP algorithm in this paper has been debugged several times to achieve the best fit for the modelling approach and to reduce errors. The final training results were obtained in Figure4.Figure 4
PSO-BP algorithm-based comparison of true and predicted values.After several iterations, the minimum mean square error was reached with MSE = 5.0839e-08, and the best performance validation plot was obtained, as shown in Figure5.Figure 5
PSO-BP algorithm-based the best performance validation.


### 6.3. A Simple Case: Salonga National Forest Park

The Salonga National Park [34], located in the Zaire Nature Reserve, is situated in the central plains of Africa and covers an extensive area of 36,000 square kilometres. It is located at an altitude of 200–500 metres above sea level. Established in 1970 to protect the equatorial forest environment, it is one of the largest forest parks in the world. It is divided into two main areas, the northern and southern, and the management office is located in Montecito. The park has a wide variety of flora and fauna, and most of the Salunga National Park is covered with equatorial forest, the forests composition of which varies according to the terrain. The forest grows mainly on swamps, riversides and dry land. The land between the rivers is almost exclusively covered with semi-deciduous forest, while the riverbanks are covered with early or short-growing plants. The northern area is dense grassland (rather than savannah), which covers 0.5% of the entire area of the park.Criterion (1): the Salonga National Park very rarely preserves the very complete ecological communities of central Africa. It also includes extensive swampy areas and forest corridor.Criterion (2): the plants and animals in Salonga National Park are an example of biological evolution and of the adaptation of life forms to the complex equatorial rainforest environment. The sheer size of the park ensures the possibility of continued evolution of species and biomes in a relatively undisturbed forest.


#### 6.3.1. Establishment of the Transition Points

As a result of the above feature changes in the particular forest included its location, and we make the inclusion of harvesting in its management plan, and each neuron in the hidden layer is as follows:(32)δok=∂e∂hihk=∂1/2∑h=1qdik−yoik2∂hihk=∂hohk∂hihk=−∑o=1qδokwho∂hohk∂hihk,(33)∂e∂wih=∂e∂hihkΔ∂hihk∂wih,∂hihk∂wih=∂∑h=1nwihxik−θh∂wih=xik.As can be seen from Figure6, in 2049.22, when the carbon sequestration in the Salonga National Forest Park reached the peak of the CSRs, the project that does not consider foresty ecosystem services is not implemented in an appropriate environment due to the damage to the foresty ecological environment beyond its capacity.Figure 6
Determination of transition points for carbon sequestration system of the case.As a result, efficiency decreases gradually and benefit decreases rapidly with time. In 2050.87, the two curves intersect, indicating whether the benefit-cost of the foresty ecological cost service is equivalent at this time. After that, the benefits brought about by the foresty ecological service should be greater than the benefits brought from that on. When reaching 2054.18, do not consider the cost services will lead to the destruction of the ecological environment seriously affecting the project operation, so that the cost-effectiveness about the forest reach to 0.


#### 6.3.2. DeepAR Model-Based Prediction of Carbon Sequestration

The DeepAR method based on deep learning can easily take into account features additional to the one-dimensional time series itself, and its prediction target is the probability distribution of the values taken by the series at each time step. In the particular scenario of this question, probabilistic prediction makes more sense than single-point prediction. The DeepAR algorithm may suffer from memory loss for longer time series, failing to capture information about long periods and seasons. This paper therefore incorporates a concern mechanism in the input section, using contemporaneous data as a feature:(34)vi=1+1t0∑t=1t0zi,t,wherev is a parameter of the model and its value determines the accuracy of the model. Learn the correlation properties within different time series through deep recurrent neural networks, using multiple or multiple target numbers to improve overall prediction accuracy.As can be seen from Figure7, the upper and lower limits of carbon sequestration over 100 years of the forest, as predicted by the DeepAR method, are 8.67 PgC and 6.85 PgC, respectively, after incorporating a modest rotation plan into the Salonga National Forest Park management system.Figure 7
Projections of carbon sequestration from different forest management plans.


#### 6.3.3. Result Validation

After several iterations of training, validation, and testing of the algorithm, the neural network model based on the particle swarm algorithm finally converged to the best performance validation state, and the correlation coefficient plots for the training, validation, testing, and final total training results of the neural network are shown below, respectively.Figure8 indicates that the training, validation, testing, and final total correlation coefficient plots for the neural network are all around 0.9999, indicating that the model fits ideally well. For the FCS model, the transition points can be determined using this particle swarm algorithm-based neural network for the final prediction [35, 36].Figure 8
The training, validation, testing, and final total correlation coefficient plots.


## 6.1. CSRs in the Forests from 2010 to 2080

As can be seen from Figure3, without considering extreme events and human interference, as expected, higher CSRs were observed in the young forests from 2010 to 2050,irrespective of the forests and soils, existing forests, and forestation level. However, 2050 to 2080 show a clear downward trend. The transition period lies between 2045 and 2055. The practical value (2010∼2021) and predicted value(2021∼2080) of CSRs in the forests from 2010 to 2080. The blue line is made by the method of FCS model, and the red dotted line is a fitting curve with a confidence interval of 0.95 [30].Figure 3
Fitting curve of available benefit data over time.The model was constructed using long-term datasets, which can suitably fit the relationship between forests biomass and forest age, but more long-term forest succession datasets are required to reduce the errors, considering the complexity of forest types and their wide distribution. At the establishment of the FCS model used here, some key parameters of the model were calibrated according to the investigated data of forest plots. Therefore, these representative local parameters made it better simulate the spatial C storage in forests to a large extent [31].


## 6.2. PSO-BP Algorithm Seeks Transition Points

The particle swarm algorithm can perform a rough search in the global scope to get an initial solution for BP relay, while the BP neural network algorithm can be used for gradient search with a strong refinement capability to perform a more careful search of the data. Here the transition point can be determined by using the algorithm for iterative search in the transition interval to get the final result. If the traditional gradient descent method is followed to find the optimum, this method often converges slowly and tends to fall into a local optimum [32]. In this paper, a combination of the PSO optimisation method and BP neural network is adopted to improve it. The connection weights and thresholds of the BP neural network are treated as elements of the position vector X of the particles in the particle swarm, and then the gradient descent method of the BP network is used instead of the particle swarm optimisation method to optimise the connection weights and thresholds of the network. The error in the output of this method comes mainly from the weights between the individual transmission channels.The activation function chosen for this model is the Sigmoid function, which is given by(22)fx=11+e−x.Net activation expression is given by(23)neti=∑j=1nwijxj−θi.The input and output of each layer of neurons is calculated as follows:(24)hihk=∑i=1nwih−θh,h=1,2,…,p,(25)hohk=fhihk,h=1,2,…,p,(26)yiok=∑h=1nwohhohk,h=1,2,…,p,(27)dik=fyiok,h=1,2,…,p.The velocity of each particle is updated continuously during the training process and it is judged whether the updated velocity is greater than the maximum velocity, if it is greater than the maximum velocity, the updated velocity takes the value of the maximum velocity, otherwise, it remains unchanged. Similarly, the position of each particle is updated.After the previous calculation the actual output can be obtained, using the actual output and the expected value can be calculated:(28)δok=∂e∂yio=∂1/2∑i=1qdik−yoik2∂yoi=−dik−yoikyoik,(29)∂e∂who=∂e∂yiokΔ∂yiok∂who,∂yiok∂who=∂∑h=1pwhohohk−θo∂who.Calculate the fitness value for each particle:(30)fi=1nt∑q=1ntOiq−Tiq2,where nt is the number of training samples;Oiq and Tiq are the actual and desired outputs of the network under the network weights and thresholds determined by the positions of the training samples at the ith particle, respectively.Calculate the global minimum adaptation value of the particle swarm; if the current number of iterations reaches the maximum number of iterations, then the iteration stops; otherwise, calculate the individual extreme value and global extreme value position of each particle, and continue to update the velocity and position of the particles. Finally, the network weights and thresholds determined by the global pole position are output [33].Now the trained BP neural network model can only output the normalized data, in order to get the real data, you can use the function mapminmax, the formula is as follows:(31)y=ymax−yminx−xminxmax−xmin.The PSO-BP algorithm in this paper has been debugged several times to achieve the best fit for the modelling approach and to reduce errors. The final training results were obtained in Figure4.Figure 4
PSO-BP algorithm-based comparison of true and predicted values.After several iterations, the minimum mean square error was reached with MSE = 5.0839e-08, and the best performance validation plot was obtained, as shown in Figure5.Figure 5
PSO-BP algorithm-based the best performance validation.


## 6.3. A Simple Case: Salonga National Forest Park

The Salonga National Park [34], located in the Zaire Nature Reserve, is situated in the central plains of Africa and covers an extensive area of 36,000 square kilometres. It is located at an altitude of 200–500 metres above sea level. Established in 1970 to protect the equatorial forest environment, it is one of the largest forest parks in the world. It is divided into two main areas, the northern and southern, and the management office is located in Montecito. The park has a wide variety of flora and fauna, and most of the Salunga National Park is covered with equatorial forest, the forests composition of which varies according to the terrain. The forest grows mainly on swamps, riversides and dry land. The land between the rivers is almost exclusively covered with semi-deciduous forest, while the riverbanks are covered with early or short-growing plants. The northern area is dense grassland (rather than savannah), which covers 0.5% of the entire area of the park.Criterion (1): the Salonga National Park very rarely preserves the very complete ecological communities of central Africa. It also includes extensive swampy areas and forest corridor.Criterion (2): the plants and animals in Salonga National Park are an example of biological evolution and of the adaptation of life forms to the complex equatorial rainforest environment. The sheer size of the park ensures the possibility of continued evolution of species and biomes in a relatively undisturbed forest.


### 6.3.1. Establishment of the Transition Points

As a result of the above feature changes in the particular forest included its location, and we make the inclusion of harvesting in its management plan, and each neuron in the hidden layer is as follows:(32)δok=∂e∂hihk=∂1/2∑h=1qdik−yoik2∂hihk=∂hohk∂hihk=−∑o=1qδokwho∂hohk∂hihk,(33)∂e∂wih=∂e∂hihkΔ∂hihk∂wih,∂hihk∂wih=∂∑h=1nwihxik−θh∂wih=xik.As can be seen from Figure6, in 2049.22, when the carbon sequestration in the Salonga National Forest Park reached the peak of the CSRs, the project that does not consider foresty ecosystem services is not implemented in an appropriate environment due to the damage to the foresty ecological environment beyond its capacity.Figure 6
Determination of transition points for carbon sequestration system of the case.As a result, efficiency decreases gradually and benefit decreases rapidly with time. In 2050.87, the two curves intersect, indicating whether the benefit-cost of the foresty ecological cost service is equivalent at this time. After that, the benefits brought about by the foresty ecological service should be greater than the benefits brought from that on. When reaching 2054.18, do not consider the cost services will lead to the destruction of the ecological environment seriously affecting the project operation, so that the cost-effectiveness about the forest reach to 0.


### 6.3.2. DeepAR Model-Based Prediction of Carbon Sequestration

The DeepAR method based on deep learning can easily take into account features additional to the one-dimensional time series itself, and its prediction target is the probability distribution of the values taken by the series at each time step. In the particular scenario of this question, probabilistic prediction makes more sense than single-point prediction. The DeepAR algorithm may suffer from memory loss for longer time series, failing to capture information about long periods and seasons. This paper therefore incorporates a concern mechanism in the input section, using contemporaneous data as a feature:(34)vi=1+1t0∑t=1t0zi,t,wherev is a parameter of the model and its value determines the accuracy of the model. Learn the correlation properties within different time series through deep recurrent neural networks, using multiple or multiple target numbers to improve overall prediction accuracy.As can be seen from Figure7, the upper and lower limits of carbon sequestration over 100 years of the forest, as predicted by the DeepAR method, are 8.67 PgC and 6.85 PgC, respectively, after incorporating a modest rotation plan into the Salonga National Forest Park management system.Figure 7
Projections of carbon sequestration from different forest management plans.


### 6.3.3. Result Validation

After several iterations of training, validation, and testing of the algorithm, the neural network model based on the particle swarm algorithm finally converged to the best performance validation state, and the correlation coefficient plots for the training, validation, testing, and final total training results of the neural network are shown below, respectively.Figure8 indicates that the training, validation, testing, and final total correlation coefficient plots for the neural network are all around 0.9999, indicating that the model fits ideally well. For the FCS model, the transition points can be determined using this particle swarm algorithm-based neural network for the final prediction [35, 36].Figure 8
The training, validation, testing, and final total correlation coefficient plots.


## 6.3.1. Establishment of the Transition Points

As a result of the above feature changes in the particular forest included its location, and we make the inclusion of harvesting in its management plan, and each neuron in the hidden layer is as follows:(32)δok=∂e∂hihk=∂1/2∑h=1qdik−yoik2∂hihk=∂hohk∂hihk=−∑o=1qδokwho∂hohk∂hihk,(33)∂e∂wih=∂e∂hihkΔ∂hihk∂wih,∂hihk∂wih=∂∑h=1nwihxik−θh∂wih=xik.As can be seen from Figure6, in 2049.22, when the carbon sequestration in the Salonga National Forest Park reached the peak of the CSRs, the project that does not consider foresty ecosystem services is not implemented in an appropriate environment due to the damage to the foresty ecological environment beyond its capacity.Figure 6
Determination of transition points for carbon sequestration system of the case.As a result, efficiency decreases gradually and benefit decreases rapidly with time. In 2050.87, the two curves intersect, indicating whether the benefit-cost of the foresty ecological cost service is equivalent at this time. After that, the benefits brought about by the foresty ecological service should be greater than the benefits brought from that on. When reaching 2054.18, do not consider the cost services will lead to the destruction of the ecological environment seriously affecting the project operation, so that the cost-effectiveness about the forest reach to 0.


## 6.3.2. DeepAR Model-Based Prediction of Carbon Sequestration

The DeepAR method based on deep learning can easily take into account features additional to the one-dimensional time series itself, and its prediction target is the probability distribution of the values taken by the series at each time step. In the particular scenario of this question, probabilistic prediction makes more sense than single-point prediction. The DeepAR algorithm may suffer from memory loss for longer time series, failing to capture information about long periods and seasons. This paper therefore incorporates a concern mechanism in the input section, using contemporaneous data as a feature:(34)vi=1+1t0∑t=1t0zi,t,wherev is a parameter of the model and its value determines the accuracy of the model. Learn the correlation properties within different time series through deep recurrent neural networks, using multiple or multiple target numbers to improve overall prediction accuracy.As can be seen from Figure7, the upper and lower limits of carbon sequestration over 100 years of the forest, as predicted by the DeepAR method, are 8.67 PgC and 6.85 PgC, respectively, after incorporating a modest rotation plan into the Salonga National Forest Park management system.Figure 7
Projections of carbon sequestration from different forest management plans.


## 6.3.3. Result Validation

After several iterations of training, validation, and testing of the algorithm, the neural network model based on the particle swarm algorithm finally converged to the best performance validation state, and the correlation coefficient plots for the training, validation, testing, and final total training results of the neural network are shown below, respectively.Figure8 indicates that the training, validation, testing, and final total correlation coefficient plots for the neural network are all around 0.9999, indicating that the model fits ideally well. For the FCS model, the transition points can be determined using this particle swarm algorithm-based neural network for the final prediction [35, 36].Figure 8
The training, validation, testing, and final total correlation coefficient plots.


## 7. Conclusion

This paper clarifies that forest carbon sequestration is mainly influenced by three aspects: human, climate, and nonclimatic physical factors, constructs a model for estimating the carbon sequestration rate of forest ecosystems based on forest age and the logistic growth equation, and combines human behaviour and climate influencing factors to make comprehensive corrections to the carbon sequestration rate of forest ecosystems per unit area. A model for calculating the carbon sequestration rate over time in a forest system was developed, which combined with the DeepAR algorithm to obtain the model of forest carbon sequestration. Then, this paper then assesses the various values of the forest, dividing the 25 factors affecting forest value assessment into five indices to establish a model of the forest ecosystem value assessment system for application to forest value assessment under different conditions. After determining the index system, we use the EWM-CVM to integrate the indexes into the value index based on the forest ecosystem. Whereas the cost of a forest ecosystem depends to a large extent on the actual size of the area , the model’s evaluation index is highest when the benefit ratio of the system is at its highest, and this is used as the effective area of the forest to propose a management plan [37, 38]. The transition point is the moment when the forest management cost and forest carbon sequestration value reach balance. This paper uses the PSO-BP algorithm to determine the transition point of forest management plan.



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*Source: 2281202-2022-05-19.xml*