In this study, a coupled PLUS and Markov model was used to execute dynamic simulations and make a prediction for land use. Afterwards, the change in carbon storage and the corresponding change in economic value were calculated based on the InVEST model. The advantage of the coupled PLUS-Markov model lies in integrating CA's ability to deal with the spatial changes of complex systems and Markov's ability to predict the amount of land, thus realising the full mining of the dynamic evolution of land use information in both space and quantity.
2.2.1 Future urban expansion simulation
Herein, the coupled Markov and PLUS models were applied to emulate land use changes, in which the PLUS model was used to map land use under future scenarios and obtain the driving factor of land use change, and the Markov model was utilised to obtain the amount of land use under various future scenarios.
The Markov chain is characterised by its stability and as being “after effectless”, where “after effectless” refers to the state of a thing at a certain moment in the future which is not related to any previous state but only to the current state in the random development process; stability means that its change process tends to be stable. It can generate a land use transfer matrix through different periods of land use data and calculate the transfer probability matrix of land use change in the study area. Based on this, it can be used to predict the future amount of land use types in the study area.
Combined with Wuhan City Land Use Overall Plan (2006–2020), Wuhan Central City Lake Protection Plan (2004–2020), Wuhan City Urban Planning Guiding Opinions in 2030, Wuhan City Master Plan (2017–2035), National Land Use Overall Plan Outline (2006–2020), this study refers to previous research (Chen et al., 2020; Li et al., 2020; Lu et al., 2009; Wang et al., 2020) and recommendations from relevant experts to conduct appropriate adjustments to the transition probability matrix from 2005 to 2010. This study obtained the future land use amount of Wuhan under three different scenarios, which was used for the land use spatial simulation of the PLUS model. Finally, the following three future scenarios were set.
Baseline scenario (BS): Based on the development trend of land use from 2005 to 2010 and the Markov chain, the demand for land use under the historical development trend in 2035 was obtained.
Cropland protection scenario (CP): On the basis of BS, with reference to the National Land Use Overall Plan Outline (2006–2020) and Wuhan City Land Use Overall Plan (2006–2020), cropland is protected, and the total amount of built-up land was strictly controlled to improve intensive utilisation of land. Therefore, the transfer probability of cropland to built-up land was reduced by 30%, and this was added to cropland.
Ecological protection scenario (EP): The aim of the EP scenario is to strengthen the protection of ecological lands such as grassland and forest land. Based on CP, the conversion of cropland, grassland, forest land, and wetland with ecological functions to built-up land was strictly controlled by referring to Wuhan City Land Use Overall Plan (2006–2020). Under the EP scenario, the transfer probability of crop land to built-up land was reduced by 30%, and the reduction was added to the conversion of cropland to forest land; the transfer probability of grassland and forest land to built-up land was reduced by 40%, and this was added to grassland and forest land respectively. The transfer probability of wetland to built-up land was reduced by 30%, and this was added to forest land.
Finally, the Markov model was used to calculate the land use demand in three different scenarios; the specific quantities are shown in Table 1.
Table 1 The number of demand pixels of each land use type under different scenarios in Wuhan in 2035 (units: pixel).
Various
scenarios
|
Cropland
|
Forest land
|
Grassland
|
River
|
Wetland
|
Urban built-up land
|
Rural built-up land
|
Unused land
|
2035 BS
|
3,785,307
|
790,306
|
105,455
|
304,321
|
2,088,207
|
1,870,250
|
262,183
|
3,624
|
2035 CP
|
4,079,644
|
790,381
|
106,971
|
304,992
|
2,086,895
|
1,575,721
|
261,506
|
3,525
|
2035 EP
|
3,789,281
|
1,227,642
|
118,443
|
304,097
|
2,057,836
|
1,449,455
|
259,359
|
3,522
|
The PLUS model can emulate the future land use map and excavate the drivers of land use change. In addition, compared to other widely used urban expansion simulation models (Liu et al., 2017), PLUS is easy to operate.
The land use change is the result of the combined effects of various types of land's own physical and chemical conditions and natural, social, economic, and other internal and external factors. This study selected 15 driving factors (details can be found in Appendix B) such as population, GDP, soil type, elevation, the proximity to cities and towns, and so on.
To imitate the patch evolution of land use, the PLUS model adopts a multi-type random patch seeding mechanism based on decreasing threshold, which is realised through the calculation process of overall probability. Based on the Monte Carlo method, the growth probability surface (\({P}_{i,k}^{d=1}\)) for land use and overall probability (\({OP}_{i,k}^{d=1,t}\)) can be obtained when \({\varOmega }_{i,k}^{t}\) is 0.
![](data:image/png;base64,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)
(1)
Here, r takes values from 0 to 1; \({u}_{k}\), is selected by the user, and represents the threshold for generating new land use patches for land use type k;\({\varOmega }_{i,k}^{t}\) refers to the proportions that land use k account for the neighborhood of cell i; \({D}_{k}^{t}\) denotes the gap between the present land use amount and future land use demand at iteration t. If land use c wins the competition against land use k, the decreasing threshold τ is used to evaluate the nominee land use c selected by the roulette wheel, as shown below:
$$If \sum _{k=1}^{N}\left|{G}_{c}^{t-1}\right|-\sum _{k=1}^{N}\left|{G}_{c}^{t}\right|$$
2
$$\left\{\begin{array}{c}{Change P}_{i,c}^{d=1}>\tau and {TM}_{k,c}=1\\ No change{ P}_{i,c}^{d=1}\le \tau or {TM}_{k,c}=0\end{array}\right.\tau ={\delta }^{l}\times r1$$
3
where "Step" is used to approach the future land use demand; δ is the attenuation factor; r1 takes value between 0 to 2; l is the amount of attenuation steps; and \({TM}_{k,c}\) is the transfer matrix of land use k to c, which is used to determine if the conversion of land use k to land use c is permitted. Many parameters of the model in the practice come from the tutorial of the PLUS software.
In this study, a Kappa index and a Figure of Merit (FoM) index were applied to verify the analogue accuracy of the model. A Kappa index is a test method proposed by Cohen and J. (1960) to detect whether the classification results of remote sensing images are consistent by establishing an error matrix for land use data and image classification results. It was used in this study to test the consistency between the analogue results and the current situation. The Kappa coefficient is calculated as follows:
$$Kappa=\frac{{OA}_{O}-{OA}_{E}}{(1-{OA}_{E})},{OA}_{O}=\left(\sum _{k=1}^{n}{OA}_{kk}\right)/N \left(4\right)$$
where \({OA}_{O}\) is the overall accuracy (OA) of the classification, representing the probability that the simulation result is consistent with the land use data for each random sample; \({OA}_{E}\) indicates the probability that the simulation result caused by chance coincides with the current land use data; n is the total types of land use, N is the total number of samples; \({OA}_{kk}\) is the number of samples correctly classified for the k-th land use type. The Kappa coefficient takes values from -1 to 1, where a higher value reflects a more accurate model.
FoM is used to better describe the accuracy of land use simulation than the Kappa coefficient (Pontius et al., 2008; Pontius and Millones, 2011). Its calculation equation is as follows:
$$FoM=\frac{1}{max\left\{{N}_{e},{N}_{d}\right\}}\sum _{k=1}^{{N}_{d}}\frac{1}{\left(1+\beta d{\left(k\right)}^{2}\right)} \left(5\right)$$
where \({N}_{e}\) represents the pixel amount of the simulated land use, \({N}_{d}\) represents the pixel amount of the actual land use; β is a scale factor greater than 0, usually 1/9; d(k) is the distance between the k-th detected actual land use current pixel and the nearest simulation pixel. Generally speaking, the FoM values are within 0.3. In practice, FoM usually takes values between 0.1 and 0.2 (Chen et al., 2014), which indicates that it is of relatively high accuracy.
The accuracy of the PLUS model determines the result of the experiment. Based on the land use data of Wuhan in 2005 and 2010, and the 15 driving factors, we employed PLUS to emulate the land use of Wuhan in 2010. After comparing the simulated land use with the actual in 2010, using PLUS, we found that when sampling rate was 5%, the Kappa coefficient was 0.87, the OA index was 0.917, and the FoM was 0.205, indicating that the model was of high accuracy and can be applied to the requirements of this study for the following simulation.
2.2.2 Carbon storage assessment
The InVEST model is suitable for calculating the carbon storage of the terrestrial ecosystem in the study area. Composed of land, freshwater and ocean modules, this model is used to evaluate the service functions of ecosystems and their economic value and support ecosystem management and decision-making. The carbon storage assessment model derives from the land module. According to this model, most of the existing carbon storage in the environment relies on four basic carbon pools: above-ground biomass, underground biomass, soil, and dead organic matter. The calculation equation is as follows:
$${C}_{i}={C}_{i\_above}+{C}_{i\_below}+{C}_{i\_soil}+{C}_{i\_dead} \left(6\right)$$
$${ C}_{total}=\sum _{i=1}^{n}\left({A}_{i}\times {C}_{i}\right) \left(7\right)$$
where \({C}_{i}\) is the carbon density of the i-th type of land use; \({C}_{i\_above}\), \({C}_{i\_below}\), \({C}_{i\_soil}\), and \({C}_{i\_dead}\) are the carbon densities of aboveground biomass, underground biomass, soil, and dead organic matter in the i-th type of land use, respectively; \({C}_{total}\) is the total carbon storage in the study area; \({C}_{i}\) is the carbon density of the i-th type of land use; \({A}_{i}\) is the area of the i-th type of land use; and n is the number of land use types in the study area.
The carbon density data of each land use type needed for carbon storage calculation were mainly derived from the literature related to carbon density. Carbon density data is regionally specific. Based on the existing literature on carbon density of different regions, this study obtained the carbon density data of Hubei Province (seen in Appendix C) from Ke and Tang (2019), which had a smaller application scope and a higher accuracy in the study of specific regions compared with the carbon density data in other literature. As such, less error is generated in the calculation of Wuhan’s carbon storage.
The calculation of the economic value of carbon storage requires three important parameters: (1) The value of carbon sequestration per ton (V in equation 8), where the social cost of carbon is recommended by the InVEST model; (2) the market discount rate (r in equation 8) reflects the phenomenon that current immediate benefits are preferred to future benefits in society; and (3) the inter-annual change rate of the carbon price (c in equation 8), which aims to adjust the value of carbon sequestration under the influence of changes in related losses under expected climate change. For plot x, the value of carbon storage change over a period of time is estimated by equation 8:
$$valu{e}_{{seq}_{x}}=V\frac{{sequest}_{x}}{{yr}_{fut}-y{r}_{cur}}\sum _{t=0}^{y{r}_{fut}-y{r}_{cur}-1}\frac{1}{{\left(1+\frac{r}{100}\right)}^{t}{\left(1+\frac{c}{100}\right)}^{t}} \left(8\right)$$
where \(valu{e}_{{seq}_{x}}\) denotes the economic value of carbon sequestration under current and future land use change scenarios; x represents the carbon sequestration grid; V represents the value of carbon sequestration (t/USD); r represents the market discount rate (%); t represents the annual change rate (%) of the value of carbon sequestration per ton; \(y{r}_{cur}\) represents the terrestrial ecosystem carbon storage under the current land use scenario; \(y{r}_{fut}\) represents the carbon storage of terrestrial ecosystem under the future land use scenario; and \({sequest}_{x}\) represents the amount of carbon sink or carbon loss in each grid under current and future land use scenarios. Tian et al. (2019) indicated that the current social cost of carbon emissions in China should be 9.20 $/(t C), and according to the user instruction manual of the InVEST model, the Asian Development Bank uses a discount rate of 10–12% when evaluating projects (Sharp et al., 2015). In this study, the market discount rate of the economic value of carbon sinks between 2015-2035 is determined to be 10%. The interannual change rate of the social cost of carbon is set as unchanged, 0, by referring to relevant studies (Deng et al., 2020).