Method for measuring and calculating carbon ecological compensation standard of water receiving area of water transfer project

Abstract

The invention discloses a method for measuring and calculating a carbon ecological compensation standard of a water receiving area of a water transfer project. The method comprises the following steps: 1) data collection: collecting data of a research area; 2) carbon storage value evaluation based on an energy value theory; 3) measuring and calculating the carbon density; 4) predicting land utilization in a natural growth scene; 5) carbon reserve calculation based on an InVEST model: based on the corrected carbon density of the research area and partitioned land utilization raster data, performing partitioned calculation on the carbon reserve of the research area by adopting the InVEST model; 6) carbon storage value calculation based on an InVEST model; and 7) formulating a carbon ecological compensation standard of the water receiving area of the water transfer project. The method is based on the energy value and the InVEST model, research on the carbon ecological compensation of the water receiving area of the water transfer project is carried out from the perspective of benefit of the carbon storage function, the change condition of the carbon storage value of the water receiving area of the water transfer project after water is introduced into the water transfer project is revealed, and the accounting mode of diversified ecological compensation standards is promoted.

Description

Technical Field

[0001] The present invention relates to the field of calculating carbon ecological compensation standards, and particularly relates to a method for calculating the carbon ecological compensation standard for the water-receiving area of a water diversion project. Background Art

[0002] The InVEST model is an integrated assessment model of ecosystem services and trade-offs (Integrated Valuation of Ecosystem Services and Trade-offs), jointly developed by Stanford University, The Nature Conservancy (TNC), and the World Wide Fund for Nature (WWF) in the United States. It aims to provide a scientific basis for decision-makers to weigh the benefits and impacts of human activities by simulating the changes in the physical and value quantities of ecosystem services under different land cover scenarios. The InVEST model system for ecosystem service function assessment fills the gap in this field and realizes the spatialization of the quantitative assessment of the value of ecosystem service functions. The biggest advantage of this model compared with previous ecosystem service function assessment methods is the visual expression of the assessment results, which solves the problem that the previous ecosystem service function assessments were abstractly described in words and not intuitive enough.

[0003] The research on carbon ecological compensation for inter-basin water transfer not only helps to make up for the loss of carbon storage function in the ecological environment of the water source area due to the cross-basin allocation of water resources, but also can effectively promote the realization of the value of water resource ecosystem services and promote the coordinated and sustainable development of the ecological economy in the water source area and the water-receiving area.

[0004] However, at present, the research on carbon ecological compensation for inter-basin water transfer is still lacking, and the research on carbon ecological compensation accounting methods is insufficient. Existing research mostly follows the water quality and water quantity indicators of traditional ecological compensation and does not establish a special carbon footprint accounting system, resulting in the difficulty of quantifying the carbon sink protection benefits in the water source area. Existing methods have their respective limitations and are difficult to comprehensively and accurately reflect the actual effect of carbon ecological compensation. Summary of the Invention

[0005] The purpose of the present invention is to overcome the defects of the prior art and provide a method for calculating the carbon ecological compensation standard for the water-receiving area of a water diversion project. The research on carbon ecological compensation for the water-receiving area of a water diversion project is carried out from the perspective of benefiting from the carbon storage function, revealing the change situation of the carbon storage value in the water-receiving area of a water diversion project after the water diversion project is put into operation, and filling the gap in this field.

[0006] The purpose of the present invention is achieved as follows: A method for calculating the carbon ecological compensation standard for the water-receiving area of a water diversion project, comprising the following steps:

[0007] Step 1) Data collection: Collect data on the study area, including energy value data, gross national product data, remote sensing data, carbon density data, carbon sequestration value data, market discount rate data, and inflation rate data of the study area;

[0008] Step 2) Carbon storage value assessment based on energy value theory: Using solar energy as the benchmark for measuring the energy values ​​of various energies, the fixed CO2 increased by water diversion projects 2 The quantity is converted into carbon energy storage value, and then the carbon energy storage value is converted into carbon energy storage value through the energy value / currency ratio;

[0009] Step 3) Carbon density calculation: Select the carbon density of the same or similar area as the study area through field monitoring or literature review to obtain the carbon density of different land use types in the study area at different time periods; if the carbon density area selected from the literature review is different from the study area, carbon density correction is required;

[0010] Step 4) Land use prediction for natural growth scenario: predict the land use in the target year under natural growth conditions based on the land use situation in the study area before the water diversion project was put into operation;

[0011] Step 5) Carbon storage calculation based on the InVEST model: Based on the calibrated carbon density and regional land use grid data of the study area, the InVEST model is used to calculate the carbon storage of the study area by region;

[0012] Step 6) Calculation of carbon storage value based on the InVEST model: Combine the results of step 5), carbon sequestration value, inflation rate and market discount rate to calculate the carbon storage value of the study area under natural growth conditions and under actual conditions after the water diversion project is put into operation, and compare and analyze to obtain the carbon storage value of the water diversion project;

[0013] Step 7) Formulate carbon ecological compensation standards for the receiving areas of water diversion projects: Combine the two carbon storage value results obtained in steps 2) and 6) to give a recommended carbon ecological compensation standard range.

[0014] As a further limitation of the present invention, the fixed CO2 increased by the water diversion project in step 2) 2 The amount is calculated by the following formula:

[0015] Aquatic ecosystems can largely suppress CO 2 Concentration, plants metabolize and produce organic matter through photosynthesis. The photosynthesis equation is as follows:

[0016] 6CO 2 +6H 2 O=6O 2 +C 6 H 12 O 6

[0017] According to the photosynthesis equation of plants, plants can fix 1.47gCO for every gram of dry matter produced. 2 Combined with the average net primary productivity of lakes and rivers, biomass, and the increased water surface area in the receiving area after the water diversion project was put into operation, the fixed CO 2 The amount.

[0018] As a further limitation of the present invention, in step 3), if the carbon density area selected by consulting the literature is different from the study area, carbon density correction is required; the calculation process of the correction coefficient is:

[0019] C SP =3.3968×P+3996.1

[0020] C BP =6.7981e 0.00541P

[0021] C BT =28×T+398

[0022] Where: C SP is the soil carbon density obtained based on annual precipitation, kg·m -2 ; C BP , C BT are the biomass carbon density obtained based on annual precipitation and annual average temperature, kg·m -2 ; P is the average annual precipitation, mm; T is the average annual temperature, ℃;

[0023] Substitute the annual average temperature and annual precipitation of the study area and the area where the carbon density selected in the literature is located into the above formula to obtain the soil carbon density data C' obtained based on the annual precipitation in the study area and the area where the carbon density selected in the literature is located SP and C" SP , the carbon density data of the research area and the literature are selected based on the annual precipitation in the area where the carbon density is located. BP and C" BP , and the biomass carbon density data C' obtained based on the annual average temperature in the study area and the area where the carbon density is selected in the literature BT and C" BT ; Continue with the following calculations:

[0024]

[0025] Where: K BP , K BT are the precipitation factor and temperature factor correction coefficients of biomass carbon density, K S , K B are soil carbon density correction factor and biomass carbon density correction factor respectively;

[0026] Multiply K B and K S by the biomass carbon density and soil carbon density at different time periods selected from the literature respectively to obtain the corrected carbon density C above (k, t), C below (k, t), C soil (k, t) and C dead (k, t), where k represents four land use types and t is the time period number; C above is the carbon density of aboveground plant biomass, Mg·hm -2 ; C below is the carbon density of underground plant biomass, Mg·hm -2 ; C soil refers to the soil organic carbon density in the soil layer, Mg·hm -2 ; C dead refers to the organic matter carbon density in the litter, Mg·hm -2 .

[0027] As a further limitation of the present invention, the calculation method for predicting the land use situation in the target year under natural growth conditions according to the land use situation before the water diversion project is put into operation in step 4) is specifically as follows:

[0028] S t+1 = f(S t , N)

[0029] And

[0030] In the formula: S is a finite and discrete set of cells; t and t + 1 are two different moments respectively; N is the neighborhood of the cell; f is the cell transformation rule function of the local space; P ij is the transition probability matrix; n is the land use type.

[0031] As a further limitation of the present invention, in step 5), the InVEST model is used to calculate the carbon storage in the study area by zoning. The InVEST model is specifically as follows:

[0032] C(k, t) = C above (k, t) + C below (k, t) + C soil (k, t) + C dead (k, t)

[0033]

[0034] In the formula: C(k, t) is the total carbon density of a certain land use type at a certain time period, Mg·hm -2; S(i,t,q) is the total carbon storage of the i-th sub-area with water transfer volume q in period t, Mg; n is the total number of land use types; t is the period number; i is the sub-area number; A(i,k) is the total area covered by the k-th land type in the i-th sub-area, hm 2 .

[0035] The present invention adopts the above technical scheme, and compared with the prior art, the beneficial effects are as follows: the method of the present invention is based on energy value and InVEST model, and studies the carbon ecological compensation in the receiving area of ​​the water diversion project from the perspective of carbon storage function benefits, and reveals the changes in the carbon storage value in the receiving area of ​​the water diversion project after the water is released from the water diversion project, which helps to promote the calculation method of diversified ecological compensation standards. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 Flowchart of the present invention. DETAILED DESCRIPTION

[0037] like Figure 1 A method for calculating the carbon ecological compensation standard for the water receiving area of ​​a water diversion project shown in the figure includes the following steps:

[0038] Step 1) Data collection: the collected data include energy value data, gross national product data, remote sensing data, carbon density data, carbon sequestration value data, market discount rate data and inflation rate data of the study area;

[0039] Step 2) Carbon storage value assessment based on energy value theory: Using solar energy as the benchmark for measuring the energy values ​​of various energies, the fixed CO2 increased by water diversion projects 2 The amount is converted into carbon energy storage value, and then the carbon energy storage value is converted into carbon energy storage value through the energy value / currency ratio. The energy value / currency ratio can be obtained by combining the total energy value and gross national product of the study area in that year.

[0040] The following is the fixed CO2 added by the water diversion project: 2 Calculation method of quantity:

[0041] Aquatic ecosystems can largely suppress CO 2 Concentration, plants metabolize and produce organic matter through photosynthesis. The photosynthesis equation is as follows:

[0042] 6CO 2 +6H 2 O=6O 2 +C 6 H 12 O 6

[0043] According to the photosynthesis equation of plants, plants can fix 1.47gCO for every gram of dry matter produced. 2; Combine the average net primary productivity, biomass of lakes and rivers, and the increased water surface area in the water-receiving area after the water diversion project is put into operation to obtain the amount of fixed CO 2 amount.

[0044] Step 3) Carbon density measurement: For the collection of carbon density data at different time periods, on-site monitoring is preferred first, and secondly, referring to the literature to select the carbon density of areas that are the same as or similar to the research area, so as to obtain the carbon density of the four land use types of forest, cultivated land, grassland, and wetland water area in the research area at each time period; among them, if the area where the carbon density is selected from the literature is different from the research area, carbon density correction is required, and the calculation process of the correction coefficient is as follows:

[0045] C SP = 3.3968×P + 3996.1

[0046] C BP = 6.7981e 0.00541P

[0047] C BT = 28×T + 398

[0048] In the formula: C SP is the soil carbon density obtained according to the annual precipitation, kg·m -2 ; C BP , C BT are the biomass carbon densities obtained according to the annual precipitation and the average annual temperature respectively, kg·m -2 ; P is the average annual precipitation, mm; T is the average annual temperature, °C.

[0049] Substitute the average annual temperature and annual precipitation of the research area and the area where the carbon density is selected from the literature into the above formula respectively to obtain the soil carbon density data C' SP and C” SP of the research area and the area where the carbon density is selected from the literature obtained according to the annual precipitation, as well as the biomass carbon density data C' BP and C” BP of the research area and the area where the carbon density is selected from the literature obtained according to the annual precipitation, as well as the biomass carbon density data C' BT and C” BT of the research area and the area where the carbon density is selected from the literature obtained according to the average annual temperature; then continue the following calculations:

[0050]

[0051] In the formula: K BP , K BT are the precipitation factor and temperature factor correction coefficients of the biomass carbon density respectively, K S , K BThey are soil carbon density correction factor and biomass carbon density correction factor, respectively.

[0052] K B , K S The corrected carbon density C of the study area was obtained by multiplying the biomass carbon density and soil carbon density at different time periods selected in the literature. above (k,t),C below (k,t),C soil (k,t) and C dead (k, t), k represents four land use types, t is the time period number; C above is the carbon density of plant aboveground biomass, Mg·hm -2 ; C below is the carbon density of plant underground biomass, Mg·hm -2 ; C soil Refers to the soil organic carbon density in the soil layer, Mg·hm -2 ; C dead Refers to the organic carbon density in litter, Mg·hm -2 .

[0053] Step 4) Forecasting land use in the natural growth scenario, based on the land use situation before the water diversion project was put into operation, predicting the land use situation in the target year under the natural growth condition;

[0054] The following is the calculation method for land use prediction:

[0055] The CA-Markov model is a computer model used to simulate and study random processes in space and time. The model combines the CA model and the Markov property, allowing the simulation of complex events that occur in discrete space and time. The CA model calculation formula is:

[0056] S t+1 =f(S t ,N)

[0057] Where: S is a finite and discrete set of cells; t and t+1 are two different moments; N is the neighborhood of the cell; f is the cell transformation rule function in the local space;

[0058] Markov chain is a random process. In land use planning, Markov chain can be used to model the spatiotemporal changes of land use. By defining the state space and transition probability matrix, the distribution of different types of land use in the future can be predicted. The transfer matrix expression of Markov chain is:

[0059] and

[0060] Where: P ijis the transition probability matrix; n is the land use type.

[0061] Step 5) Carbon storage calculation based on the InVEST model: Based on the calibrated carbon density and regional land use grid data of the study area, the InVEST (Integrated Valuation of Ecosystem Services and Trade-offs) model was used to calculate the carbon storage of the study area by region;

[0062] The following is the calculation method for zoning carbon storage in the study area using the InVEST model:

[0063] The calculation formula of the model is:

[0064] C(k,t)=C above (k,t)+C below (k,t)+C soil (k,t)+C dead (k,t)

[0065]

[0066] Where: C(k,t) is the total carbon density of a certain land use type in a certain period of time, Mg·hm -2 ; S(i,t,q) is the total carbon storage of the i-th sub-area with water transfer volume q in period t, Mg; n is the total number of land use types; t is the period number; i is the sub-area number; A(i,k) is the total area covered by the k-th land type in the i-th sub-area, hm 2 .

[0067] Step 6) Based on the carbon storage value calculation of the InVEST model, combined with the results of step 5), carbon sequestration value, inflation rate and market discount rate, the carbon storage value of the study area under natural growth conditions and under actual conditions after the water diversion project is put into operation is calculated, and the carbon storage value of the water diversion project is obtained by comparative analysis.

[0068] Step 7) Formulate carbon ecological compensation standards for the water receiving areas of the water diversion project, comprehensively consider the two carbon storage value results obtained in steps 2) and 6), and give a recommended carbon ecological compensation standard range.

[0069] In order to further verify the method of the present invention, taking Jinan City as an example, the carbon ecological compensation of water resources of a water diversion project in Jinan City was calculated:

[0070] The total energy value of Jinan in 2020 is 1.26×10 23sej. As shown in Table 1, the gross national product in 2020 was 1014.091 billion yuan. Using the exchange rate of US dollars to RMB in 2020, which is 6.8996, the emergy / currency ratio of Jinan City in 2020 was obtained as 8.57×10 11 sej / $.

[0071] Table 1 Total emergy consumption in Jinan City in 2020

[0072]

[0073] The photosynthesis equation is as follows:

[0074] 6CO 2 +6H 2 O = 6O 2 +C 6 H 12 O 6

[0075] According to the photosynthesis equation of plants, it can be known that plants can fix 1.47 g of CO 2 . The average net primary productivity of lakes and rivers is 500 g / m 2 / a, and the biomass is 10 3 g / m 2 . It can be known from relevant data that the increased water surface area of a water diversion project in Jinan City is 77.8 km 2 (Two national land surveys in Jinan City). Thus, the net primary productivity is 3.89×10 10 g, and the amount of fixed CO 2 is 5.72×10 10 g. The conversion rate of carbon storage emergy is 3.78×10 10 sej / kg, so the solar emergy of carbon storage can be obtained as 2.16×10 18 sej. From 3.1.1, the emergy / currency ratio of Jinan City in 2020 was 8.57×10 11 sej / $, and the calculated value of carbon storage emergy is 2.52×10 6 $. The exchange rate of US dollars to RMB in 2020 was 6.8996, that is, the value of carbon storage emergy of a water diversion project in Jinan City was 1.74×10 7 yuan.

[0076] InVEST model method: In this embodiment, referring to the "Carbon Density Dataset of Chinese Terrestrial Ecosystems" in the 2010s and the carbon density data of the study area and adjacent areas in relevant literature, the soil carbon density and aboveground vegetation density data of Jinan City were determined, and the root-shoot ratio of 0.2 was used to calculate the vegetation carbon density. The data was corrected to carbon density data that conforms to the actual situation of the study area through the carbon density correction formula (Table 2), and its calculation formula is

[0077] C SP = 3.3968×P + 3996.1(R 2 = 0.11)

[0078] C BP = 6.7981e 0.00541P (R 2 = 0.70)

[0079] C BT = 28×T + 398(R 2 = 0.47, Pearson < 0.01)

[0080] Where: C SP is the soil carbon density obtained from the annual precipitation, t / hm 2 ; C BP , C BT are the biocarbon densities obtained from the annual precipitation and the annual average temperature respectively, t / hm 2 ; P is the annual average precipitation, mm; T is the annual average temperature, °C.

[0081] Table 2 Carbon densities of various land use types in the study area after correction Unit: t / hm 2

[0082]

[0083]

[0084] The Carbon module of the InVEST model was used to calculate the carbon storage in Jinan City in 2000, 2005, 2015, 2020, and the carbon storage under the natural growth scenario in 2020 respectively. In 2005, 2010, 2015, 2020, and the natural growth scenario (S1) in 2020, the total carbon storage in Jinan City was 95.4069 million t, 93.9952 million t, 93.7739 million t, 93.7210 million t, and 92.0375 million t respectively. Compared with 2015, the carbon storage value in the natural growth scenario (S1) in 2020 decreased by 16.17×10 6 US dollars, and this value is the economic value of the carbon storage loss in the natural growth scenario from 2015 to 2020; after water diversion, compared with 2015 in 2020, the carbon storage value decreased by 1.06×10 6 US dollars, and this value is the economic value of the carbon storage loss from 2015 to 2020. Therefore, the carbon storage value in Jinan City in 2020 after water diversion increased by 15.11×10 6 US dollars compared with the natural growth scenario. The exchange rate of US dollars to RMB in 2020 was 6.8996, and it was calculated that the carbon storage value that Jinan City benefited from a certain water diversion project was 104 million yuan.

[0085] In summary, based on emergy and the InVEST model, the carbon ecological compensation accounting results for a water diversion project in Jinan are 0.174 billion yuan and 1.04 billion yuan respectively. Therefore, it is recommended that the water-carbon ecological compensation standard for a water diversion project in Jinan be between 0.174 billion yuan and 1.04 billion yuan.

[0086] The present invention provides a method for calculating the carbon ecological compensation standard for the water receiving area of a water diversion project. Based on the emergy and InVEST models, the research on the carbon ecological compensation for the water receiving area of the water diversion project is carried out from the perspective of the benefits of carbon storage function, revealing the changes in the carbon storage value of the water receiving area of the water diversion project after the water diversion project is put into operation, which helps to promote the calculation methods of diversified ecological compensation standards.

[0087] The present invention is not limited to the above embodiments. Based on the technical solutions disclosed in the present invention, those skilled in the art can make some substitutions and deformations to some technical features without creative labor according to the disclosed technical content, and these substitutions and deformations are within the protection scope of the present invention.

Claims

1. A method for calculating the carbon ecological compensation standard for water diversion projects in water receiving areas, characterized in that: The following steps are involved: Step 1) Data collection: Collect data on the study area, including energy value data, gross national product data, remote sensing data, carbon density data, carbon sequestration value data, market discount rate data, and inflation rate data of the study area; Step 2) Carbon storage value assessment based on energy value theory: Using solar energy as the measurement benchmark for various energy values, the amount of fixed CO2 increased by the water diversion project is converted into carbon storage value, and then the carbon storage value is converted into carbon storage value through the energy value / currency ratio; Step 3) Carbon density calculation: Select the carbon density of the same or similar area as the study area through field monitoring or literature review to obtain the carbon density of different land use types in the study area at different time periods; if the carbon density area selected from the literature review is different from the study area, carbon density correction is required; Step 4) Land use prediction for natural growth scenario: predict the land use in the target year under natural growth conditions based on the land use situation in the study area before the water diversion project was put into operation; Step 5) Carbon storage calculation based on the InVEST model: Based on the calibrated carbon density and regional land use grid data of the study area, the InVEST model is used to calculate the carbon storage of the study area by region; Step 6) Calculation of carbon storage value based on the InVEST model: Combine the results of step 5), carbon sequestration value, inflation rate and market discount rate to calculate the carbon storage value of the study area under natural growth conditions and under actual conditions after the water diversion project is put into operation, and compare and analyze to obtain the carbon storage value of the water diversion project; Step 7) Formulate carbon ecological compensation standards for the receiving areas of water diversion projects: Combine the two carbon storage value results obtained in steps 2) and 6) to give a recommended carbon ecological compensation standard range.

2. According to claim 1, a method for calculating carbon ecological compensation standards for water diversion projects in receiving areas is characterized in that: The amount of fixed CO2 increased by the water diversion project in step 2) is calculated by the following formula: Aquatic ecosystems can suppress CO2 concentration to a great extent. Plants metabolize and produce organic matter through photosynthesis. The photosynthesis equation is as follows: 6CO2+6H2O=6O2+C6H 12 O6 According to the photosynthesis equation of plants, it is found that every gram of dry matter produced by plants can fix 1.47g of CO2; combined with the average net primary productivity of lakes and rivers, biomass, and the increase in water surface area in the receiving area after the water diversion project is released, the amount of CO2 fixed is obtained.

3. According to claim 1, a method for calculating carbon ecological compensation standards for water diversion projects in receiving areas is characterized in that: In step 3), if the carbon density area selected from the literature is different from the study area, carbon density correction is required; the calculation process of the correction coefficient is: C SP =3.3968×P+3996.1 C BP =6.7981e 0.00541P C BT =28×T+398 Where: C SP is the soil carbon density obtained based on annual precipitation, kg·m -2 ; C BP , C BT are the biomass carbon density obtained based on annual precipitation and annual average temperature, kg·m -2 ; P is the average annual precipitation, mm; T is the average annual temperature, ℃; Substitute the annual average temperature and annual precipitation of the study area and the area where the carbon density selected in the literature is located into the above formula to obtain the soil carbon density data C' obtained based on the annual precipitation in the study area and the area where the carbon density selected in the literature is located SP and C" SP , the carbon density data of the research area and the literature are selected based on the annual precipitation in the area where the carbon density is located. BP and C" BP , and the biomass carbon density data C' obtained based on the annual average temperature in the study area and the area where the carbon density is selected in the literature BT and C" BT ; Continue with the following calculations: Where: K BP , K BT are the precipitation factor and temperature factor correction coefficients of biomass carbon density, K S , K B are soil carbon density correction factor and biomass carbon density correction factor respectively; K B , K S The corrected carbon density C of the study area was obtained by multiplying the biomass carbon density and soil carbon density at different time periods selected in the literature. above (k,t),C below (k,t),C soil (k,t) and C dead (k, t), k represents four land use types, t is the time period number; C above is the carbon density of plant aboveground biomass, Mg·hm -2 ; C below is the carbon density of plant underground biomass, Mg·hm -2 ; C soil Refers to the soil organic carbon density in the soil layer, Mg·hm -2 ; C dead Refers to the organic carbon density in litter, Mg·hm -2 .

4. According to claim 1, a method for calculating carbon ecological compensation standards for water diversion projects in receiving areas is characterized in that: The specific calculation method of predicting the land use situation in the target year under the natural growth condition based on the land use situation before the water diversion project is as follows: S t+1 =f(S t ,N) and Where: S is a finite and discrete set of cells; t and t+1 are two different moments; N is the neighborhood of the cell; f is the cell transformation rule function in the local space; P ij is the transition probability matrix; n is the land use type.

5. According to claim 1, a method for calculating carbon ecological compensation standards for water diversion projects in receiving areas is characterized in that: In step 5), the InVEST model is used to calculate the carbon storage in the study area by region. The InVEST model is specifically: C(k,t)=C above (k,t)+C below (k,t)+C soil (k,t)+C dead (k,t) Where: C(k,t) is the total carbon density of a certain land use type in a certain period of time, Mg·hm -2 ; S(i,t,q) is the total carbon storage of the i-th sub-area with water transfer volume q in period t, Mg; n is the total number of land use types; t is the period number; i is the sub-area number; A(i,k) is the total area covered by the k-th land type in the i-th sub-area, hm 2 .

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