Assessing the Ecological Risks Based on the Three-Dimensional Ecological Footprint Model in Gansu Province

Abstract

It has become a hot topic in sustainable development to determine how to use data series to predict the trajectory of ecological footprints (EFs), precisely map biocapacity (BC), and effectively analyze regional sustainability. The sustainability of the ecological system in Gansu province must be investigated because the province is situated in western China and serves as a significant economic and transportation hub. We used the EF model to compute the per capita EF and BC of Gansu province from 2010 to 2020. We created a three-dimensional ecological footprint ($E{F}_{3D}$) model by incorporating the ecological footprint size ($E{F}_{size}$) and ecological footprint depth ($E{F}_{depth}$) into the EF model and the $E{F}_{3D}$ of Gansu province from 2010 to 2020 was measured. The $E{F}_{3D}$ value was estimated using the gray GM (1, 1) prediction model in order to determine the sustainability condition of Gansu province during the next ten years. Finally, the risk of ecosystem loss in the province of Gansu was ultimately assessed using an ecological risk model (EVR). The results show that Gansu province’s per capita EF and BC displayed generally rising trends and the province is experiencing unsustainable development. The region’s projected future consumption of natural capital was estimated by the results, and the $E{F}_{3D}$ of Gansu province is expected to increase significantly in the future. These findings have a certain reference value for adjusting the industrial structure and utilizing resources in Gansu province. Furthermore, these findings will assist Gansu province in achieving sustainable development policy recommendations.

1. Introduction

The ecological environment is essential to human life and growth, and human behavior has a significant impact on the environment. Population growth and social and economic development have impacts on the planet’s ecosystem. Additionally, the problems (such as broad environmental deterioration, resource depletion, and the deteriorating relationship between man and nature) have increased. Consequently, sustainable development has become the consensus [1]. Researchers studied the ideas of social development and sustainable development, moving away from the idea of simple economic growth and toward the idea of integrated development of the economy, society, and the environment [2,3]. However, the scarcity of natural resources affects the quality of human activities [4]. This is a current research hotspot, i.e., how to handle the connection between natural assets, civilization, and economic growth under the constraints of ecological resources and the environment. Regional ecological sustainability is extremely significant to balance the connection between economic growth, social progress, and resource management [5]. Sustainable development goals call on all nations to take action in order to promote global prosperity through resource management, sustainable production and consumption, and environmental protection [6].

An ecological footprint (EF) was a term created by Rees et al. [7]. Biologically productive land (including land and water) is required to sustainably produce all resources needed by a population and to remove the waste generated is known as the ecological footprint [8,9,10]. The term biocapacity refers to the total amount of land and water that is genuinely available for biological production and that can be made available to people in a given amount of time, namely, the ability of natural resources to regenerate through time. The gap between the demand for natural ecosystem services from human economic systems and the carrying capacity of natural ecosystems was calculated and compared by Wackemagel et al. [11] to quantitatively assess the degree of sustainable resource use. The EF method offers a clear-cut theoretical framework for evaluating the sustainability of regional development [12]. For example, at the global level, Andreína et al. [13] analyzed and researched BC and EF, and predicted and analyzed biodiversity and the environmental footprint behaviors of five continents (up to the year 2030) through a neural network. At the national level, according to the national average output from 1989 to 2018, Sobhani et al. [14] examined the semi-arid climate zone of Iran to determine the sustainability of resource use and the pressure that human activities place on natural capital. Kovacs Zoltan et al. [15] analyzed the environmental sustainability of Hungarian urbanization and the long-term changes in environmental footprints and biological capacity. At the regional level, Zhang et al. [16] built a framework for evaluating Panzhihua City’s sustainable development from 2000 to 2020 based on EF; they developed an EF model using the provincial hectare as the unit. The city’s capacity for sustainable development was then thoroughly assessed using a collection of ecological indices, including EPI, EFG, ESI, and ECI. Sonia and Samir [17] used the bottom-up model based on component EF technology to determine the demand of Algiers fishing port for fishery resources. The classic EF calculation approach was enhanced by Xie et al. [18], who also created the port energy EF model and researched the ecological state of port logistics from 2009 to 2018. Additionally, using the EF model, Yang et al. [19] and Li et al. [20] assessed regional sustainable development.

To create the $E{F}_{3D}$ model, Niccolucci added $E{F}_{size}$ and $E{F}_{depth}$ to the EF model [21,22]. The $E{F}_{3D}$ model was introduced to China by Fang et al. [23,24], who also improved it to address the offset issue with various land-use patterns. The capital inflow utilization ratio and the capital stream’s quota were devised to assess how natural capital was used in 11 countries. While energy use and economic status significantly impact the footprint, the $E{F}_{3D}$ model better captures regional growth. Based on an optimized $E{F}_{3D}$ and the human development index at the metropolitan scale, Long et al. [25] developed a model for evaluating ecological well-being performance and the efficacy of local sustainable development. The revised $E{F}_{3D}$ model was used by Chen et al. [1] to thoroughly assess the ecological security status in Henan Province from 2007 to 2016. According to the report, Henan province’s capital flow is in an unsustainable stage of development. Deng et al. [26] assessed the ecological efficiency of Hunan Province based on the $E{F}_{3D}$ model. Their research provides a scientific basis for other provinces to establish sustainable development strategies for ecological civilization.

When revealing and predicting the economy, the EF prediction is crucial to forecast the value of urban ecological environments, assess their state of development, and offer acceptable and workable policy recommendations to regional decision-makers for sustainable development [13]. The question of how to correctly forecast the evolution of EF values has received a lot of attention, and numerous techniques have been employed to model future EF. Deep neural networks were utilized by Andreína et al. [13] to adapt data to the global footprint network and make predictions. In order to calculate and simulate the EF value of Suzhou from 1999 to 2018, Yao et al. [27] used the ARIMA model and the GM (1, 1) model. They also examined the city’s current state of ecological sustainability. The EF of Shandong province from 2018 to 2030 was predicted by Li et al. [28] using the BPNN technique, along with whether or not future economic policies would lessen or accelerate ecological degradation. Su et al. [29]’s predictions for 2020 and 2025 regarding the per capita water EF were made using the quadratic exponential smoothing technique. The Gray prediction was utilized by Peng et al. [30,31] to predict the EF.

Ecological risk assessment is a new technical means and method used to assess and manage various ecological risk probability problems in the ecological environment [32]. Numerous experts have begun to perform numerous ecological environmental studies to slow down the ecological environment’s destruction and enhance the living conditions of humans. Researchers have created and enhanced the content, breadth, methodologies, and models of ecological risk assessment after more than 20 years of development. Researchers from all over the world have even started utilizing the theories and methods of ecological risk assessment to completely evaluate the numerous hazards faced by ecological systems due to the theory’s rapid development and the rise in the popularity of ecological problems. For instance, the landscape’s ecological risk index was developed by Liu et al. [33,34,35] to direct the sustainable use of land resources. The ecotoxicity of heavy metals in sediment columns was evaluated using the following metrics by Nimmi et al. [36,37]: pollution degree, organic pollution index, contributing factors, site accumulation index, potential ecological indicator, toxicity unit, and toxicity risk index. Liu [38] employed the VAR method of financial risk analysis market portfolio to perform a risk analysis of the value of ecosystem services, and he designated the EVR (ecological value at risk) model.

The social economy of northwest China cannot grow sustainably owing to the region’s difficult environmental circumstances, precarious ecological status, frequent human activities, and numerous environmental issues [39]. A substantial commercial and transportation hub, specifically in the province of Gansu, contributes significantly to the social and economic growth of the northwest region and even the entire country. The social and economic development of Gansu province is currently being hampered by ecological issues, which have grown to be the biggest issues [40,41]. As a result, it is imperative to research the ecosystem of Gansu province to support its sustainable growth. Based on this, we focused on the province of Gansu, calculated its EF value and $E{F}_{3D}$ value from 2010 to 2020, and used the GM (1, 1) model to predict its $E{F}_{3D}$ value from 2020 to 2030 in order to assess its level of sustainable development. For the risk analysis of the value of ecosystem services, we use the VAR method of the financial risk analysis market portfolio [42]. To evaluate the ecosystem risk in Gansu Province from 2010 to 2020, an ecosystem risk model was developed. It offers a fresh concept for the ecological economy’s long-term growth in Gansu province.

2. Materials and Methods

2.1. Study Area

In the high and middle reaches of the Yellow River, the western Chinese province of Gansu is located between poles 32°11′–42°57′ N and 92°13′–108°46′ E [40] (Figure 1). The overall area of Gansu province, which makes up 4.72% of China’s total area, is 454,430 square kilometers, with an east–west length of 1659 km and a north–south breadth of 530 km. The climate diversity, biological diversity, and landform diversity are highly apparent because the east and west are long and narrow. The Yellow River, the Yangtze River, three inland river basins, and nine river systems are the principal sources of water in Gansu province. Grassland and woodland make up most of the province’s land types, followed by cultivated land. As of the end of 2018, 119 different types of minerals have been found there. The province receives 400 mm of rain on average each year, and the average annual temperature ranges from 4 to 15 °C, depending on the location [43]. There is a lot of sunshine, and the temperature swings dramatically. The province’s primary economic sectors, including farming, forestry, industrial, animal rearing, tourism, and the ecological environment, greatly impact the provincial economy.

2.2. Data Sources

This study opted to analyze the changes in the ecological environment in Gansu province from 2010 to 2020 based on the availability of the data itself in order to correctly portray the features of sustainable changes in the ecological environment of Gansu Province. The six categories of land use types in the basin are fossil energy, building land, cultivated area, grassland, forest land, and water area. These categories are based on the “Land Use Status Classification” standard established by the Ministry of Land and Resources.

Table 1. Biological productivity accounts for various land types in Gansu Province.

Resource Account	Land Type	Indicator Details	Data Sources
Biological resource account	Fossil energy	Coal, gasoline, natural gas	“Gansu Statistical Yearbook 2010–2020”
	Building land	Electricity
	Cultivated area	Wheat, grains, beans, corn, potatoes, cotton, sugar beets, Vegetables, oilseeds
	Grassland	Meat, poultry, eggs, dairy, wool
	Woodland	Fruit
	Water area	Aquatic products

displays the biological productivity accounts for the various types of land in Gansu province. Additionally, research on energy consumption primarily concentrates on coal, gasoline, natural gas, electricity, and other fuels. The two resource datasets mentioned above come from the Gansu Statistical Yearbook for 2010–2020.

The degrees of productivity of the six biologically productive lands varied in different places, thus the data were translated to areas with the same environmental value by multiplying the land areas of the six diverse productivity levels by a balance factor. This study is based on the “Equivalence factor” of China’s EF, which Wackernagel presented in the “National Footprint and Biocapacity Accounts” report in 1997; the difference in supply capacity is a critical criterion. This study corresponds to the actual condition of Gansu province. We calculate the “Production Factor” for each year by combining the annual different productivity (average annual output) of Gansu province with the global average productivity statistics on biological resources published by the United Nations Food and Agriculture Organization in 1993 (see

Table 2. Equivalence factor and production factor of biologically produced land.

Model Parameters	Fossil Energy	Building Land	Cultivated Area	Grassland	Woodland	Water Area
Equivalence Factor	1.10	2.80	2.80	0.50	1.10	0.20
Production Factor	0.00	1.66	1.66	0.19	0.91	1.00

).

Additionally, according to a report by the World Commission on Environment and Development (WCED) [44,45], about 12.0% of the land is used for biodiversity protection. Therefore, 12.0% of the land in this study’s calculation of BC was subtracted as ecological protection land for the region, leaving the remaining land to contain biological resources [19]. The boundary data of Gansu province were obtained from the Aliyun platform (https://datav.aliyun.com, accessed on 14 May 2022).

2.3. Research Methods

The EF, which includes the volume of total resource consumption in a given area and the scale of resource availability, is the total amount of land resources utilized by human activities. It also exposes the ecological threshold for sustained human life [5]. It consists of six different types of land resources: fossil energy, building land, cultivated area, grassland, woodland, and water area. The six lands produce differently on average. For the purpose of comparing the calculations, an equilibrium factor was multiplied by each land type, and EF was then computed using the weight of the biologically productive land area. This is the calculation’s formula.

$$\mathrm{ef}=\sum r_j\times (c_i/p_i)j=1,2\cdots 6,$$

(1)

$$\mathrm{EF}=N\times \mathrm{ef},$$

(2)

where ef is the per capita ecological footprint (hm²/cap); $r_j$ is the equivalence factor of Gansu province; i is the consumption of ith types; j is the land types; $c_i$ is the per capita consumption of ith commodities; $p_i$ is the global average output of the ith projects; N is the total population of the region (cap).

The total amount of productive land in an area that can supply resources and energy for consumption by locals is known as biocapacity (BC). The unit production of the six land types varies depending on each region’s resources and land productivity. The actual acreages of specific types of biological production land in various countries and regions were compared using the standards and production features of various forms of biological production land. The formula below is used to determine BC.

$$\mathrm{bc}=\sum a_j\times r_j\times y_j,$$

(3)

$$\mathrm{BC}=\mathrm{bc}\times N,$$

(4)

where bc is the per capita biocapacity (hm²/cap); $a_j$ is the per capita biological production area of the jth project; $y_j$ is the production factor.

Ecological carrying capacity (ECC) is a measure of the effective use of natural resources by a population in a study area. When EF decreases BC and the calculation result is negative, it is called ecological reserve (ER), indicating that the resource demand of the area is sustainable. When EF minus BC is positive, it is called ecological deficit (ED). An ecological deficit is a situation in which an area’s available resources exceed its ecological capacity. Therefore, this development is not sustainable. The formula is described as,

$$\mathrm{ECC}=\mathrm{EF}-\mathrm{BC}.$$

(5)

Numerous academics have researched the $E{F}_{3D}$ model. $E{F}_{size}$ and $E{F}_{depth}$ are two fundamental indicators employed in the $E{F}_{3D}$ model to represent the buildup of the ecological overdraft over time. While $E{F}_{size}$ measures the human occupancy of yearly natural capital income, $E{F}_{depth}$ measures the depletion of natural capital stock.

With the aid of $E{F}_{depth}$, we can assess the sustainability of current human activities and development trends in relation to the limitations of renewable resources and ecological services without depleting natural capital stocks. We can also identify which biological components are overloaded in the study area.

$$E{F}_{size}=\sum Min\left\{\mathrm{EF},\mathrm{BC}\right\},$$

(6)

$$E{F}_{depth}=1+\frac{\sum Max\left\{\mathrm{EF}-\mathrm{BC},0\right\}}{\sum \mathrm{BC}},$$

(7)

$$E{F}_{3D}=E{F}_{depth}\times E{F}_{size},$$

(8)

2.4. The Gray GM (1, 1) Model Introduced

The term “gray system” was first used in an academic study by Professor Deng in the 1980s, when the gray system theory was initially proposed [46]. A system with partial information, where some information is unknown, is referred to as a “gray system”. In order to achieve the quantitative prediction of the system’s future changes, GM (1, 1), the fundamental model of the gray forecasting theory, essentially fits the original data series exponentially using the least squares approach after starting with a quadratic function [5]. Less historical data and low sequence integrity and reliability are issues that the model is better able to address. It can also generate erroneous original data to produce generated sequences with high regularity, and the operation is straightforward and simple to verify.

1.

Sequence generation by accumulation;

The accumulation generation number 1-AGO serves as a placeholder for a single operation $x^{\left(0\right)}=(x^{\left(0\right)}\left(1\right),x^{\left(0\right)}\left(2\right),\cdots ,x^{\left(0\right)}\left(11\right)),$ represents the $E{F}_{3D}$ from 2010 to 2020, and creates the cumulative sequence.

2.

Model establishment and solution;

This series is used to generate the prediction model, which is based on a first-order differential equation with a single variable and is known as the GM (1, 1) model. The gray differential equation and the corresponding whitening differential equation are established. By the least square method, we find the estimate of u that minimizes $J\left(u\right)={(Y-Bu)}^T(Y-Bu)$. The GM (1, 1) model’s time-response function was obtained.

3.

Calculation of the residual error and the relative error.

$${\epsilon }^{\left(0\right)}\left(k\right)=x^{\left(0\right)}\left(k\right)-{\widehat{x}}^{\left(0\right)}\left(k\right),$$

$$\delta \left(k\right)=\frac{\left|x^{\left(0\right)}\left(k\right)-{\widehat{x}}^{\left(0\right)}\left(k\right)\right|}{x^{\left(0\right)}\left(k\right)},k=1,2,\cdots ,11,$$

where ${\widehat{x}}^{\left(0\right)}\left(1\right)=x^{\left(0\right)}\left(1\right),$${\epsilon }^{\left(0\right)}\left(k\right)$ is the residual error and $\delta \left(k\right)$ is the relative error.

2.5. Model of Ecological Value at Risk

The term “ecological risk” refers to the risk to which the ecosystem and its components are exposed [47]. It describes the potential effects of unforeseen accidents or disasters on the ecosystem and its constituents in a specific location. These outcome effects may damage the ecosystem’s structure and function, putting its safety and well-being in jeopardy.

2.5.1. Risk Calculation Method

Expectation and standard deviation are two different types of risk indicators used in ecosystem risk assessment [38,48]. Expectation primarily reflects a central tendency of risks; the higher the expectation value, the greater the overall risk. Standard deviation reveals the level of dispersion of risk or deviation from the indicator.

Expected value:

$$E\left(x\right)=\sum _{i=1}^n{x}_i{p}_i,$$

(9)

where $x_i,p_i(i=1,2,3,\cdots n)$ are the discrete risk variable and its corresponding probability.

Standard deviation:

$$\sigma =\sqrt{E{(x-E(x\left)\right)}^2}.$$

(10)

2.5.2. Ecological Value at Risk Model

The ecological value at risk (EVR) of the region was calculated as part of the regional ecosystem risk management model, which is a risk assessment model [38]. In general, we define it as the worst-case loss of a certain type of ecological index or its comprehensive index is predicted to occur at a specific point in the future, i.e., the maximum potential loss, in a normal ecological environment and at a specific confidence level. It is simple for ecosystem managers to monitor, operate, and control by determining the amount of energy exposed to risk in the regional ecosystem and comparing the numerical numbers.

We define $V_{i,n}$ as the total EF of resource i consumed in the n year in the region, $R_{i,n}$ is the growth rate of the total ecological consumption of the i resource in the n year in the region, $EV{R}_i$ is the maximum value where the growth rate of the EF of the i resource in the $n+1$ year is lower than the initial expected value under a certain confidence level $1-\alpha ,$ where $E\left(R_i\right)$ is the initial expected value and the standard deviation is $\sigma .$

The mathematical description is:

$$P(R_{i,n+1}>E\left(R_i\right)-EV{R}_i)=1-\alpha .$$

(11)

It means that the growth rate of the ecosystem EF of the i resource in the region in year $n+1$ may be $1-\alpha ,$ which will not be lower than the initial expectation $E\left(R_i\right)$ by $EV{R}_i$.

Due to

$$R_{i,n+1}=\frac{V_{i,n+1}-V_{i,n}}{V_{i,n}}.$$

(12)

Further, we obtain the following formula.

$$P(V_{i,n+1}>V_{i,n}(1+E\left(R_i\right)-EV{R}_i))=1-\alpha .$$

(13)

It means that in the future, the maximum loss of the ecosystem EF rate of the i resource in the region with $1-\alpha$ in the year $n+1$ is $V_{i,n}(EV{R}_i-E\left(R_i\right)).$

2.5.3. EVR Model Calculation Method

The footprint of the ecosystem is assumed to be approximately normally distributed. Because of the existence theorem: if a random variable $X\sim N(\mu ,{\sigma }^2),$ then $U=(X-\mu )/\sigma \sim N(0,1).$ To do this, we first normalize the distribution of the ecological footprint, namely:

$$\epsilon =\frac{R-E\left(R\right)}{\sigma }\sim N(0,1).$$

(14)

Transform (11) into

$$P(\epsilon >\frac{-EVR}{\sigma })=1-\sigma .$$

(15)

when the confidence interval is given, by looking up the standard normal distribution quantile table, the quantile $K=\frac{-EVR}{\sigma }$ can be obtained, and the $EVR$ value can be solved.

$$EVR=-K\times \sigma .$$

(16)

2.5.4. Model Evaluation

In the process described above, we researched the risk of $E{F}_{3D}$ loss and developed a risk model for $E{F}_{3D}$ to assess the risk of $E{F}_{3D}$ in Gansu province from 2010 to 2020. The relevant recommendations are provided in the conclusion to lessen the risk of losing the ecosystem’s economic value in this area.

3. Results

3.1. Evaluation of the EF and BC in Gansu Province

3.1.1. Calculation of the EF and BC in Gansu Province in 2020

Both biological resources and fossil energy resources are taken into account while calculating EF. The biological resources vary according to location. Crop, animal, and aquatic products are how we categorize the utilization of biological resources [49]. A total of 15 biological resources were chosen from the total number available, including grains, vegetables, fruits, meat, milk, and aquatic products. To obtain the appropriate per capita EF, we translate the global average production into biological resources.

Table 3. Biological resources in the per capita EF of Gansu province in 2020.

Item	Global Average Production (kg/ha)	Per Capita Consumption (GJ/a)	Per Capita EF (hm2/cap)	Type of Cultivated Land
Wheat (10 kt)	2744	98.0086	0.0357	Cultivated area
Cereals (10 kt)	2744	288.1468	0.1050	Cultivated area
Beans (10 kt)	2744	13.8478	0.0050	Cultivated area
Corn (10 kt)	2744	152.5012	0.0556	Cultivated area
Potatoes (10 kt)	2744	72.3443	0.0264	Cultivated area
Cotton (10 kt)	1000	2.9531	0.0030	Cultivated area
Beet (10 kt)	1800	8.6016	0.0048	Cultivated area
Vegetable (10 kt)	18,000	482.6053	0.0268	Cultivated area
Oil (10 kt)	1856	25.0197	0.0135	Cultivated area
Fruit (10 kt)	18,000	116.9775	0.0065	Woodland
Meat (10 kt)	33	1.0272	0.0050	Grassland
Poultry eggs (10 kt)	400	4.1797	0.0104	Grassland
Milk (10 kt)	502	17.4962	0.0349	Grassland
Hairs (10 kt)	15	11.5549	0.7703	Grassland
Aquatic products (10 kt)	29	4.8167	0.1661	Water area

present the findings.

Coal, gasoline, natural gas, and electricity were our four basic choices for fossil fuels. The world average EF conversion factor is converted to the fossil land area, other energy consumption types are converted to fossil energy, and electricity is converted to the building land area.

Table 4. Fossil energy resource accounts in the per capita EF of Gansu province in 2020.

Item	Per Capita Consumption (GJ/a)	Consumer Price Level (GJ/a)	Global Average EF Conversion Factor (GJ/ (ha.a))	Per Capita EF (hm2/cap)	Land Type
coal (kg)	130.6000	3.8299	55	0.0696	Fossil energy
gasoline (kg)	2.2400	0.1030	93	0.0011	Fossil energy
natural gas (m3)	7.4300	0.2823	71	0.0040	Fossil energy
electricity (kw/h)	209.2700	5.7778	1000	0.0058	Building land

lists the outcomes. The findings indicate that in 2020, Gansu province’s per capita fossil energy use was 0.0805 hm²/cap, while its per capita coal usage was 0.0696 hm²/cap, making up 86.46% of the total per capita fossil energy use area. These results suggest that the coal industry still accounts for the majority of energy consumption in Gansu province, despite the fact that coke significantly pollutes the air and environment and that the province’s energy consumption structure is inefficient.

In 2020, the biological production area in Gansu province was used to compute and compare per capita EF and BC. Grassland, with a per capita EF of 1.1736 hm²/cap, was the most significant EF in Gansu province in 2020, followed by the cultivated area and fossil energy (

Table 5. Per capita EF and BC of Gansu province in 2020.

Item	Area (hm2)	Equivalence Factor	Per Capita EF (hm2/cap)	Land Type	Production Factor	Biocapacity (hm2/cap)
Fossil energy	0.8598	1.10	0.9458	CO2 absorption	0.00	0.0000
Building land	0.0128	2.80	0.0359	Building land	1.66	0.0595
Cultivated area	0.3564	2.80	0.9980	Cultivated area	1.92	1.9162
Grassland	2.3471	0.50	1.1736	Grassland	0.39	0.4577
Woodland	0.0107	1.10	0.0117	Woodland	0.91	0.0107
Water area	0.1943	0.20	0.0389	Water area	1.00	0.0015
Land Total	3.7811		3.2039	Existing total area		2.4457
				Total area available	minus 12%	2.1522

). The cultivated area, with a per capita BC of 1.9162 hm²/cap, is the largest in a similar manner to the Grassland. In Gansu province, per capita EF in 2020 was 3.2039 hm²/cap, whereas per capita BC was just 2.4457 hm²/cap. The per capita available BC was 2.1522 hm²/cap, and the per capita ECC was 1.0517 hm²/cap after 12% of biodiversity protection reserves were subtracted from the per capita BC. It demonstrates that the region’s supply of land resources falls well short of the demand, and the ecological system is in an unsustainable condition.

The scarcity of fossil energy land is the most significant among the many land use types, followed by the shortage of grassland. This is strongly tied to Gansu province’s lack of development. Energy is used extensively in industrial production as the local economy grows. By using fossil fuels, the region’s water, land, and other resources will become more polluted, its economic growth rate will slow, and its ability to develop sustainably will be impacted. Building land should also be taken into consideration as it is also becoming saturated (Figure 2).

3.1.2. Dynamic Changes in the per Capita EF and BC in Gansu Province between 2010 and 2020

The per capita EF and BC of Gansu province were calculated using the same methods from 2010 to 2020. The BC was given the value of BC × 0.88 since 12% of the area should be reserved for conserving biodiversity after deduction. The variation trends of per capita EF and BC in Gansu province from 2010 to 2020 are depicted in Figure 3 and Figure 4. We discovered that the variations in per capita EF and BC trends tended to follow similar patterns: they increased from 2010 to 2015, decreased gradually from 2015 to 2019, and then significantly increased from 2019 to 2020. At the same time, we can see that the annual change trends of the six different land types are not particularly clear.

Figure 5 shows that the per capita EF in the fraction of grassland is the highest; fossil energy and cultivated area are comparable. In BC, the cultivated area is the largest, followed by grassland, while fossil energy accounted for 0. The cultivated area per capita EF is less than BC, indicating the area of Gansu province is in a surplus. Grassland per capita EF is greater than BC, illustrating that the grassland area of Gansu province is in a state of deficit. It is important to note that fossil energy is experiencing a deficit. Additionally, we discovered that there is relatively little variance in the annual land area of different forms of biological production.

3.1.3. Dynamic Evolution of the $E{F}_{3D}$ in Gansu Province from 2010 to 2020

Table 6. $E{F}_{3D}$ in Gansu province from 2010 to 2020.

Year	Per Capita EF (hm2/cap)	Total Available Area for EC (Minus 12%)	Ecological Deficit	Ecological Footprint Size ($\mathit{E}{\mathit{F}}_{\mathit{s}\mathit{i}\mathit{z}\mathit{e}}$)	Ecological Footprint Depth ($\mathit{E}{\mathit{F}}_{\mathit{d}\mathit{e}\mathit{p}\mathit{t}\mathit{h}}$)	Three-Dimensional Ecological Footprint ($\mathit{E}{\mathit{F}}_{3\mathit{D}}$)
2010	2.5721	1.6514	0.9207	1.6514	1.5575	2.5721
2011	2.6481	1.7285	0.9196	1.7285	1.5321	2.6481
2012	2.7951	1.8907	0.9044	1.8907	1.4784	2.7951
2013	2.8501	1.9205	0.9296	1.9205	1.4840	2.8501
2014	2.9553	2.0140	0.9413	2.0140	1.4674	2.9553
2015	3.0689	2.0240	1.0449	2.0240	1.5163	3.0689
2016	2.8921	1.8981	0.9940	1.8981	1.5237	2.8921
2017	2.9059	1.8955	1.0104	1.8955	1.5330	2.9059
2018	2.8851	1.9446	0.9405	1.9446	1.4837	2.8851
2019	2.9069	1.9620	0.9449	1.9620	1.4816	2.9069
2020	3.2039	2.1522	1.0517	2.1522	1.4887	3.2039

demonstrates that in Gansu province, the $E{F}_{size}$ climbed from 1.6514 hm² in 2010 to 2.0240 hm² in 2015, then fell to 1.8981 hm² in 2016 before rising to 2.1522 hm² in 2010. With variations over time, Gansu’s $E{F}_{3D}$ climbed from 2.5721 hm² in 2010 to 3.0689 hm² in 2015 and then declined to 2.8921 hm² in 2016, finally reaching 3.2039 hm², which is consistent with variations in the trends of per capita EF. The ecological and economic developments of Gansu province were in deficits from 2010 to 2020, as evidenced by the fact that the $E{F}_{depth}$ has always been larger than 1 and the EF always exceeds the BC.

According to Figure 6, the per capita ECC in Gansu province from 2010 to 2012 showed a steady decline, i.e., the unsustainable development status of Gansu province was eased. However, per capita ECC in Gansu province increased gradually between 2012 and 2015, indicating that with the change in the economy and the improvement in living standards, as the consumption of biological resources and fossil energy continues to increase, the sustainability of Gansu province will decline year by year and the contradiction between social and economic development and environmental resource management will become more obvious. The Gansu province’s per capita ECC fell between 2015 and 2018, indicating that the province’s resource utilization rate is increasing but can still be improved. Per capita ECC in Gansu province rose sharply from 2018 to 2020, and the state of unsustainable development still needs more attention.

3.2. $E{F}_{3D}$ Prediction by GM (1, 1) Model

The analysis in 3.1.3 informs us that the $E{F}_{3D}$ of Gansu province from 2010 to 2020 displayed a fluctuating rising tendency during the course of the study period. The GM (1, 1) model is capable of simulating it. The GM (1, 1) model was developed using the data series of the $E{F}_{3D}$ values. Following the execution of the software, the model precision and the fitting $E{F}_{3D}$ values could be acquired (

Table 7. The estimated $E{F}_{3D}$ in Gansu province from 2010 to 2020.

Year	Actual Data	Prediction Data	Residual Error	Relative Error (%)
2010	2.5721	2.5721	0.0000	0.0000
2011	2.6481	2.7607	−0.1126	−0.0425
2012	2.7951	2.7931	0.0020	0.0007
2013	2.8501	2.8259	0.0242	0.0085
2014	2.9553	2.8590	0.0963	0.0326
2015	3.0689	2.8926	0.1764	0.0575
2016	2.8921	2.9265	−0.0344	−0.0119
2017	2.9059	2.9609	−0.0549	−0.0189
2018	2.8851	2.9956	−0.1105	−0.0383
2019	2.9069	3.0307	−0.1239	−0.0426
2020	3.2039	3.0663	0.1376	0.0429

). Figure 7 shows a visualization of the GM (1, 1) model’s simulation performance. In the left ordinate of Figure 7, the relative error ($\delta$) is between −0.0426% and 0.0575%, while the residual error ($\epsilon$) is between −0.1239 and 0.1764.

Gray system modeling is a technique for identifying the features of complex data and creating precise simulation models [50,51]. It can forecast nonlinear data sequence events. The value of this region’s EF is dynamic, complicated, and nonlinear, and a variety of socioeconomic factors may influence it. According to the above-mentioned fitting results, the gray model is capable of understanding the nonlinear relationship between the series, and the GM (1, 1) model’s simulation performance is precise (Figure 7).

However, the approximation model invariably results in certain simulation mistakes (relative errors in Figure 7). Prior to 2012, when the relative error was minor, the $E{F}_{3D}$ value was relatively low and the model overestimated the actual $E{F}_{3D}$. From 2013 to 2015, the model somewhat underestimated the value of the $E{F}_{3D}$, with a reasonably big relative error in 2015. With a significant relative inaccuracy, the model once more overestimated this parameter from 2016 to 2019. The value of the $E{F}_{3D}$ after 2020 was marginally underestimated by the model. The relative inaccuracy fluctuates generally, and the changing trend of the $E{F}_{3D}$ value in Gansu province is strongly tied to the reality of the situation.

The forecast is a projection of Gansu province’s future use of natural resources. According to forecasts, the province’s $E{F}_{3D}$ will increase to 3.4457 by 2030, or 1.34 times what it was in 2010 (

Table 8. The prediction of $E{F}_{3D}$ in Gansu province from 2021 to 2030.

Year	2021	2022	2023	2024	2025	2026	2027	2028	2029	2030
$E{F}_{3D}$	3.1023	3.1387	3.1755	3.2128	3.2505	3.2886	3.3272	3.3662	3.4057	3.4457

). Future forecasts predict a steady rise in the $E{F}_{3D}$ of Gansu province. This implies that Gansu province’s ECC will keep growing and the region is already undergoing unsustainable regional development. Regarding sustainability, Gansu province will encounter formidable obstacles. To achieve sustainable urban growth, local governments should create relevant regional strategic plans with a focus on increasing energy efficiency, developing high-tech businesses, gradually modifying the industrial structure, and reducing the percentage of the industry. By raising the GDP share of the tertiary sector, creating more environmentally friendly products, etc., the city can reduce its use of natural resources and return to the path of sustainable growth.

3.3. Ecological Risk Assessment in Gansu Province

The $E{F}_{3D}$ of Gansu province is assessed for risk from 2010 to 2020 using an $E{F}_{3D}$ risk model. The process is broken down into four steps: organizing the data, estimating the expectation and standard deviation, estimating the EVR value, and figuring out the maximum loss.

3.3.1. Organize Data

We verify the pertinent ecological data for Gansu province from 2010 to 2020, then use the footprint model to determine the 11-year EF and $E{F}_{3D}$.

3.3.2. Calculate the Expectation and Standard Deviation

The expectation of the growth rate of the $E{F}_{3D}$ in Gansu province in 2021, as well as the standard deviation, are displayed in Table; they are based on the definition and algorithm of the EVR model (

Table 9. Growth rate of $E{F}_{3D}$ and its expectation and standard deviation.

Year	$\mathit{E}{\mathit{F}}_{3\mathit{D}}$	${\mathit{EF}}_{3\mathit{D}}$ Growth Rate (%)	Growth Rate Expectations $\mathit{E}\left({\mathit{R}}_{\mathit{i}}\right)$ (%)	Standard Deviation of Growth Rate $\mathit{\sigma }$ (%)
2010	2.5721	N/A	2.2982	4.1885
2011	2.6481	2.9548
2012	2.7951	5.5511
2013	2.8501	1.9677
2014	2.9553	3.6911
2015	3.0689	3.8439
2016	2.8921	−5.7610
2017	2.9059	0.4772
2018	2.8851	−0.7158
2019	2.9069	0.7556
2020	3.2039	10.2171

).

As shown in the above table, the expected growth rate of $E{F}_{3D}$ in Gansu province in the recent 11 years (2010–2020) is 2.2982%, and the standard deviation is 4.1885%.

3.3.3. Calculate the Value of EVR

In this paper, seven confidence levels of 50%, 80.00%, 90.00%, 95.00%, 97.50%, 99.00%, and 99.90% were selected, and the EVR values of the $E{F}_{3D}$ growth rate at different confidence levels $1-\alpha$ were calculated using the quantile table of standard normal distribution (see

Table 10. EVR values of $E{F}_{3D}$ growth rates at different confidence levels.

Confidence Level $1-\mathit{\alpha }$	Quantiles (K)	EVR
50.00%	0.000	0.000%
80.00%	−0.842	3.5267%
90.00%	−1.282	5.3697%
95.00%	−1.645	6.8901%
97.50%	−1.960	8.2095%
99.00%	−2.326	9.7425%
99.90%	−3.090	12.9425%

).

Table 10 shows that, at the 99.90% confidence level, the EVR value of the $E{F}_{3D}$ growth rate in Gansu province in the recent 11 years (2010–2020) is 12.9425%. This indicates that the growth rate of $E{F}_{3D}$ in Gansu province is 99.90%, which is likely to be 12.9425% lower than the expected growth rate of 2.2982 ha/cap.

3.3.4. Maximum Loss

By calculating the EVR value of $E{F}_{3D}$ at the 99.90% confidence level, the maximum loss table of $E{F}_{3D}$ from 2010 to 2021 was calculated according to the EVR model (See

Table 11. Maximum loss of $E{F}_{3D}$ at the 99.90% confidence level.

Year	${\mathit{EF}}_{3\mathit{D}}$	Growth Rate Expectations $\mathit{E}\left({\mathit{R}}_{\mathit{i}}\right)$ (%)	Standard Deviation of the Growth Rate $\mathit{\sigma }$ (%)	Confidence Level	Quantiles	EVR (%)	Maximum Loss ($\mathit{Sej}$)
2010	2.5721	2.2982	4.1885	0.9990	−3.0900	12.9425	0.3410
2011	2.6481
2012	2.7951
2013	2.8501
2014	2.9553
2015	3.0689
2016	2.8921
2017	2.9059
2018	2.8851
2019	2.9069
2020	3.2039

).

According to Table 11, the maximum loss value of $E{F}_{3D}$ in Gansu province in the recent 11 years (2010–2020) was 0.3410.

4. Discussion

4.1. Comparison and Discussion of Results

Based on the aforementioned calculations and analysis of EF, BC, and $E{F}_{3D}$ in the Gansu province from 2010 to 2020, it is clear that, out of all the different types of land use, the scarcity of fossil energy land is the most important. The coal industry continues to be responsible for the vast majority of energy consumption in the province. Energy use in industrial output has increased significantly with the growth of the local economy. By burning fossil fuels, the region’s water, land, and other resources will become more badly polluted, the rate of economic growth will drop, and it will be more difficult to achieve sustainable development. This conclusion is in line with the findings in [40], which calculated the rate of change and scissors difference of the per capita EF and BC time series in Gansu Province between 1991 and 2003. According to the findings, fossil fuel usage has almost doubled in recent years. In Gansu province, the carrying capacity of the ecological environment has decreased due to overuse and depletion of natural resources. We can observe consistency between the outcomes produced by various techniques. We can also draw the same conclusion from [1,41].

We discovered that the grassland area in Gansu province is deficient, and one of the potential causes of this finding may be due to overgrazing in the pastoral districts of Gansu province. The government ought to encourage herdsmen to choose the appropriate number of animals to graze based on the size of the grassland [52]. Herdsmen might receive incentives and subsidies from the government if they minimize the quantity of grazing. This will help us to address the issue of overgrazing, increase the yield and coverage of grassland vegetation, and increase the carrying capacity of grassland [53]. In addition, the footprint of building land in Gansu province is approaching its carrying capacity due to population increase, faster urbanization, and large-scale urban construction. In the medium term, changing the method of production and hastening structural adjustment remain challenging tasks. From 2010 to 2020, the ecological economy’s growth in Gansu province fell short of expectations. Future trends indicate that $E{F}_{3D}$ in Gansu province will increase steadily. This means that the ecological deficit of Gansu province will continue to grow, and the region is already in unsustainable regional development. In terms of sustainable development, Gansu province will face huge obstacles.

4.2. Policy Implication

Based on the aforementioned research findings, the following suggestions are given for the sustainable development of Gansu Province in order to improve regional sustainability. (1) Slow down EF’s rate of growth by controlling the population. Change the unreasonably high human consumption mode and lower EF on the assumption that consumption will not be reduced. (2) We will actively promote the development of low-carbon circular economy industries, enhance resource utilization effectiveness, and cut back on the use of fossil fuels. Additionally, for companies that consume a lot of energy, emphasis should be placed on industrial structural transformation, energy conservation, emissions reductions, and assisting Gansu Province’s sustainable development. (3) To build a healthy environment, we will continue to step up the implementation of ecological projects, such as converting cropland back to forests and grasslands and combining agriculture and animal husbandry. (4) Change the industrial structure and utilize various land resources in a balanced manner. It is possible to implement scientific and logical resource allocations by making the necessary adjustments to the industrial structure. (5) By advancing science and technology, we can boost productivity, raise biocapacity, close the gap between EF and BC, and finally put Gansu province back on the path to sustainable development. (6) Boost ecological awareness while cutting down on resource waste. The government ought to prioritize environmental preservation initiatives, enact stringent laws and regulations, and raise public knowledge of energy conservation.

4.3. Limitations and Prospects of the Study

This study still has limitations. Only 11 years (2010–2020) of ecological footprint and biocapacity calculations have been made to examine the state of sustainable development in Gansu province, which may cause certain issues with the consistency and reliability of the model’s calculation results. The outcomes differ when using different equivalence and production factors. The ecological footprint as a tool for measuring sustainability may have limited application due to different results. Future ecological footprint research must continue to enhance ecological footprint accounting. The short-term future can only be assessed using the GM (1, 1) prediction model, while the long-term future cannot be predicted. Therefore, it will be crucial to enhance the EF model and combine several prediction models in future studies in order to accomplish a more thorough evaluation of various regions. These initiatives may offer more practical means of enhancing the equilibrium between ecological economics and sustainable development.

5. Conclusions

The EF model was utilized in this study to examine how sustainable use has changed over time in Gansu province. First, using the EF method, we calculated the per capita EF and BC of Gansu province from 2010 to 2020. We discovered that Gansu province’s per capita EF and BC displayed a generally rising trend. Second, we determined the $E{F}_{3D}$ of Gansu province from 2010 to 2020 using the $E{F}_{3D}$ model. Our research revealed that Gansu province is experiencing unsustainable development because $E{F}_{depth}$ was always larger than 1 over the study period, indicating that EF is always greater than BC. Then, the GM (1, 1) model was presented in order to simulate and forecast the $E{F}_{3D}$ of the province of Gansu. Through a test of model correctness, it was established that the GM (1, 1) model was appropriate for accurate data series simulation and short-term $E{F}_{3D}$ value forecasting in Gansu province. Our projected future consumption of natural capital was estimated by the results. The $E{F}_{3D}$ of Gansu province is expected to increase significantly in the future and will be 1.34 times higher in 2030 than it was in 2010. As a result, Gansu province’s economy will continue expanding, and the region is currently in an unsustainable stage of regional development. Finally, the $E{F}_{3D}$ values of Gansu province were utilized as historical data to estimate the risks faced by the ecological system in Gansu province from 2010 to 2020 using the ecological risk EVR model. The findings revealed the following: using a 99.90% confidence level as an example, we found that the growth rate of $E{F}_{3D}$ in Gansu province from 2010 to 2020 had an EVR value of 12.9425%, and it was 99.90% likely to not be lower than the initial assumption of 2.2982%. Thus, the annual $E{F}_{3D}$ rate of the ecosystem in this area is 99.90% likely to undergo a maximum loss of 0.3410 in the future.

On the basis of the data shown above, pertinent suggestions are given for the sustainable ecological and economic development of Gansu Province. The occupation of flow resources is growing as a result of the province’s development, and the cumulative impact of stock resource use is becoming more obvious as shown by the increasing footprint of fossil fuels and arable land per person. Thus, the region should develop a sensible consumption pattern and advance the development of ecological civilization under the presumption of environmental protection. In addition to identifying regional goals for ecological and environmental protection and economic development, the region should promote low-carbon and environmentally friendly consumption. The region should also implement an effective, environmentally friendly development strategy for important development regions, including converting agriculture to forests. The study’s findings have significant implications for resource allocation; the industrial structure was optimized, social-economic growth was promoted, and the harmonious development between man and nature was realized.