Introduction

Ecosystem services (ESs) are all the goods and values that humans derive, directly or indirectly, from the processes, structures, and functions that operate in ecosystems1,2,3. The ecosystem service value (ESV) is to express the benefits that human beings obtain from the ecosystem in numerical values4. Scientific quantification of ESs can provide a basis and reference for governments to formulate appropriate ecological protection policies and modes of regulating economic development according to local conditions5,6. With the intensification of global climate change, the sharp decline of biodiversity and the degradation of ecological functions, ESV assessment has become a central tool for the international community to solve the sustainable development challenges. The quantification of its value is not only at the crossroads of ecology and economics, but also a scientific basis for global environmental governance and policy development7. Therefore, research on ESV is of extreme importance8,9,10. The study of ESV has become a hot research topic in the field of ecology11,12,13. Costanza et al.2 and Xie Gao Di et al.14 laid the foundation for the measurement of ESV in China15. To date, the main methods of accounting for ESV are the functional value approach and the equivalent factor approach. The functional value method usually uses an ecological model to calculate ESV. As there are more factors to consider, the calculation results are relatively reliable. However, the calculation process is more complicated and more suitable for single land use type or small-scale ESV assessment, which limits the expansion of its application16. In comparison, the equivalent factor method ignores the role of ecosystem structure and function changes on ESV in the evaluation process. However, because it is more convenient to apply, the assessment results are more intuitive and the basic data for assessment are easy to obtain, it is the most used assessment method at present17,18. This has been widely recognized by scholars and applied to related fields of research19,20,21. In recent years, a large number of scholars have carried out extensive and in-depth research on ESV based on the equivalent factor method22,23,24,25.

Studies of ESV need to consider significant differences in assessment results due to different evaluation scales26. And the study between evaluation scale and evaluation results has been reported27,28,29. For example, Yongqi Chen et al.27, Wu Yan et al.26, and Zheng Defeng et al.30 chose the scales of grids, townships, counties, and munici-palities to study the relationship between trade-offs/synergies, geodetection factors, spatial distributions, and agglomeration of ESVs and spatial scales. Changsheng Xiong et al.28 and Ma Chaoqun et al.31 selected some scales in the range of 1 km \(\times\) 1 km \(\sim\) 15 km \(\times\) 15 km scales and explored the relationship between the spatial clustering characteristics, trade-offs/synergistic relationships, and impact factors of ESVs and the grid scale. Wei Xiaojian et al.32 used geodetectors and spatial regression models to study the influencing factors of spatial heterogeneity of ESV at different scales and their scale variability. The grid scale of 3 km \(\times\) 3 km was found to be informative for the study of the Greater Nanchang Metropolitan Area. Yang Guangzong et al.33 combined the topographic features, area size and terrain elevation of Nanchang City, and found that the grid scale of 1 km \(\times\) 1 km is more advantageous in studying the land category mosaic pattern, fit and stability at the city scale. At the same time, based on this scale, the expression of spatial information imbalance and heterogeneity of ESV can provide a basis for the ecological spatial plan-ning and ecological use control programme in Nanchang. This further shows that it is very necessary to study the scale dependence of ESV and its optimal scale. The above related research focuses on analyzing the different characteristic laws of ESV aggregation, trade-off/synergy relationship, influence factors, etc. between different grid scales. According to the existing studies, it is known that although the scale dependence of ESV has attracted academic attention, these studies have not analysed the scale effect of county ESV from a multi-scale system. Therefore, this paper mainly explores the following two aspects: (1) We need to explore whether there is scale dependence in the total value and spatial differentiation of ESV. If scale dependence exists, whether it tends to stabilise after a particular scale, and whether the optimal scale for exploring ESV can be identified after stabilisation. Addressing the specific characteristics and changing patterns of these key issues is of great significance in revealing the nature and mechanisms of ecosystems. (2) We found that exploring the scale dependence of total ESV value and spatial differentiation through data from only one time point may be unconvincing. Instead, it should be studied and discussed on a long time series. Therefore, this paper chooses five time points to explore this key issue in depth.

Based on these considerations, we choose five periods of data in 2000, 2005, 2010, 2015 and 2020 for this study. We launch a detailed exploration of the scale dependence of the total value and spatial heterogeneity of ESV in a long time series of 20 years. We use the ArcGIS tool to obtain a spatial scale grid for the 100 m-300 0m interval in 100 m isochronous steps. Combined with ArcGIS and SPSS software, this paper uses the equivalent factor method and difference test. We analyze the scale variation characteristics of the total value of ESVs. Then, we use the area percentage at different rank levels and difference test to explore the scale dependence of the spatial heterogeneity of ESV. We also investigate the optimal scale of spatial heterogeneity of ESV and the spatial change pattern of ESV under the optimal scale according to the method of variation coefficient and Moran index. This study aims to (1) reveal the optimal scale for ESV research by systematically analyzing the scale dependence of total value and spatial heterogeneity of ESV. This will provide a scientific basis for the accurate assessment of ESV, the formulation of ecological conservation strategies and resource management. (2) This study is also expected to promote the in-depth development of ESV scale dependence. It provides new ideas and methods for research in related fields.

Study area and data resources

Study area

The study area is shown in Fig. 1. Gangu County belongs to the northwestern part of Tianshui City, Gansu Province, and is located in the upper reaches of the Wei River. It is located between \(104^\circ\)58\('\) - \(105^\circ\)31\('\) east longitude and \(34^\circ\)31\('\) - \(35^\circ\)03\('\) north latitude. It is connected to Tongwei County in the north, Qinzhou District and Lixian County in the south, Qin’an County and Maiji District in the east, and Wushan County in the west. The topography of the region is undulating, with altitudes ranging from 1,194 to 2,690 metres above sea level34. It has a temperate continental monsoon climate with four distinct seasons and plenty of light. Its average annual temperature is 11.8 \(^\circ C\) and its average annual precipitation is about 500 mm, with precipitation mainly concentrated in summer35. The county has a total population of 612,000 and a total area of about 1,572.6 \(\hbox {km}^2\). Its topography is high in the south and low in the north, and the central part is a faulted river valley area with deep soil layers. Due to the complex and varied topography of Gangu County, there are some differences in climatic conditions in different regions. This climatic diversity further contributes to the complexity and stability of the ecosystem. In recent years, with the in-depth promotion of ecological civilization and the popularization of the concept of sustainable development, Gangu County has paid more and more attention to the protection and enhancement of ecosystems. The flow of the study is shown in Fig. 2.

Fig. 1
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Geographical location of the study area (created by ArcGIS 10.2 software, http://desktop.arcgis.com/cn/).

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Fig. 2
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Flow chart of this study.

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Data sources

The data involved in this article includes land use data, DEM data, county boundary and township boundaries, agricultural economic data, etc (Table 1). According to the Chinese Academy of Sciences (CAS) LULC classification standards, the LULC types were reclassified by ArcGIS software and were divided into six LULC types, namely, forest land, cultivated land, grassland, construction land, watershed, and unused land.

Table 1 Study area data sources.
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Research methods

ESV assessment methodology

According to the ESV system model presented by COSTANZA2 and the modified Chinese terrestrial ESV equivalent table by Xie Gao Di14, this paper chose the mean value of sown area, mean value of yields, and mean value of grain price of three major crops, namely wheat, maize, and potato, of Gangu County in the five years from 2000 to 2020 as the basic data. By reviewing the “Gangu County Statistical Yearbook” and “China Statistical Yearbook” and other materials, combined with the actual social and economic development status of Gangu County, we revised the economic value of the farmland grain output per unit area of the research area. One ecosystem service value equivalent is 1/7 of the grain production value per unit area36. We calculated the economic value of one ecosystem service value equivalent factor in Gangu County as 1522.28 \(\hbox {CNY/hm}^2\). The formula is as follows37:

$$\begin{aligned} E_{a}=\frac{1}{7} \sum _{i=1}^{n} \frac{m_{i} p_{i} q_{i}}{M} \end{aligned}$$
(1)

Where \(E_{a}\) denotes the economic value provided by natural grain output per unit area of farmland. \(m_{i}\), \(p_{i}\), \(q_{i}\) denote the average sowing area of the i-th grain crop in Gangu County (2000, 2005, 2010, 2015 and 2020), and the average price of the i-th grain crop and the average per-amount yield per-area of the i-th grain crop. M denotes the average total area of n grain crops in Gangu County (2000, 2005, 2010, 2015 and 2020). n is the type of food crop.

Due to the vast territory of China, ecosystems in different regions have different characteristics. To reduce the error caused by directly using the “Equivalent value of ecosystem services per unit area”38, which was improved by Xie Gao Di in 2015, this paper revised the coefficients of ESV for each category with reference to the existing studies and the real situation39. Since the construction land does not address the associated eco-function, it is denoted by 0. According to the Gangu County ESV base equivalent table per unit area for each LULC type, we calculated the coefficient of ESV per unit area in Gangu County Table 2. The calculation formula for the value of ecosystem services is as follows:

$$\begin{aligned} & ESV=\sum _{k=1}^n A_i \times VC_{i} \end{aligned}$$
(2)
$$\begin{aligned} & EC_{i}=\sum _{j=1}^k EC_{j} \times E_{a} \end{aligned}$$
(3)

Where ESV denotes the value of ecosystem service in Gangu County (CNY). i denotes the land use type. j denotes the type of ecosystem service. \(A_{i}\) denotes the i-th land use type area (\(\hbox {hm}^2\)). \(VC_{i}\) denotes the ecosystem service value coefficient (\(\hbox {CNY/hm}^2\)) of land use type i. \(EC_{j}\) denotes the j th ecosystem service value equivalent of the land use type. k denotes the number of ecosystem service types. \(E_{a}\) denotes the economic value of 1 ecosystem service value equivalent factor (\(\hbox {CNY/hm}^2\)).

Dividing the ESV Grid scale

In previous studies, they only selected individual grid scales for analysis. Although the differences in ESV at different scales are revealed, the scale effects of ESV may not be fully revealed (such as scale turning points, feature scales). The impact of scale selection on ESV evaluation results is not systematically explored, but individual single scales are selected based on experience or data availability. This may lead to a lack of comparable and universality in the study results. To solve this problem, this paper selects a scale range of 100–3000 m, and divides the research area into 30 types of continuous square grids with 100 m as equal step. Then, based on land use data with a resolution of 30 meters, we extracted them to 30 different grid scales respectively. Finally, we calculate the ESV values at different grid scales and summarize the ESV values on each grid scale. This method selects multiple scales from small scale (100 m) to large scale (3000 m) while maintaining the same resolution. This not only avoids the error introduced due to different resolutions, but also comprehensively captures the scale effect of ESV.

Difference-in-difference test analysis

In this study, the one-sample t-test in SPSS 26 software was used to infer the difference between the mean of the overall data and the specified test value40. The conditions for the application of the one-sample t-test need to obey a normal distribution. \(H_0:\mu =\mu _0\), \(H_1:\mu \ne \mu _0\), and its test statistic is calculated as \(t=\frac{\bar{x}-\mu _0}{\frac{s}{\sqrt{n}}}\), \(v=n-1\) . After obtaining the t-value, the table was looked up to obtain the corresponding p-value. If p>0.05, the original hypothesis could not be rejected and the difference between the group data and the test value was considered not statistically significant. On the contrary, the difference was considered statistically significant.

Table 2 Correction coefficient of ESV per unit area in Gangu County.
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Ecological contribution rate

The ecological contribution rate expresses the percentage of change in ESV of a site category to the total ecosystem service value change over a specific period of time41. It can be used to explain the main contributing factors and sensitivities affecting the changes in the ecosystem service value of the study area. This helps us to understand the dynamics of ecosystem service values more deeply. The calculation formula is as follows:

$$\begin{aligned} C_i=\frac{\left| \Delta E S V_i\right| }{\sum _{i=1}^6\left| \Delta E S V_i\right| } \times 100 \% \end{aligned}$$
(4)

Where \(C_{i}\) represents the ecosystem service contribution rate of the ith land use type. \(\Delta E S V_i\) represents the change in ecosystem service value of the ith ecosystem service (CNY).

Analysis of spatial distribution characteristics

Analysis of the coefficient of variation

The coefficient of variation is a statistical measure of the degree of dispersion or volatility of data42. The smaller the value of the CV, the lower the dispersion of the data and the more stable the data. Conversely, the larger the value of the coefficient of variation, the higher the dispersion of the data and the more unstable of the data. This calculation expression is as follows:

$$\begin{aligned} \textrm{CV}=\sigma / \mu \end{aligned}$$
(5)

Where \(\sigma\) represents the overall standard deviation. \(\mu\) represents the overall mean.

Global spatial autocorrelation

To explore the variability and correlation of the spatial distribution of ESV at the optimal scale42,43, the global spatial autocorrelation index Moran’s I value44 is selected to reveal the pattern of the spatial distribution of ESV in Gangu County. Moran’s I can reflect the overall trend of the spatial correlation of ESV in the whole Gangu County, and its value is between -1 and +1. If Moran’s I > 0, it means that it is positively correlated. The larger the value, the more significant the positive correlation and the stronger the spatial agglomeration. If Moran’s I < 0, it means that it is negatively correlated. The smaller the value, the more significant the negative correlation. And Moran’s I = 0 indicates no correlation45. The expression is as follows:

$$\begin{aligned} \text { Moran's } I= \frac{n \sum _{i=1}^n \sum _{j=1}^n W_{i j}\left( x_i-\bar{x}\right) \left( x_j-\bar{x}\right) }{\sum _{i=1}^n\left( x_i-\bar{x}\right) \sum _{i=1}^n \sum _{j=1}^n W_{i j}} \end{aligned}$$
(6)

Where \(\text { Moran's } I\) represents the global spatial autocorrelation index. n represents the number of grids. \(x_{i}\) and \(x_{j}\) represent the attribute values of grids i and j. \(\bar{x}\) represents the mean value of the attribute. And \(W_{ij}\) denotes the spatial weighting matrix.

Local spatial autocorrelation

In this article, local spatial autocorrelation is selected to reveal whether there is spatial clustering of ESVs within a specific area. The specific distribution characteristics of ESVs in the study area are explored by drawing LISA aggregation maps17. The calculation process is shown in the following expression:

$$\begin{aligned} I_i=\frac{\left( x_i-\bar{x}\right) \sum _{j=1}^n W_{i j}\left( x_j-\bar{x}\right) }{\sum _{j=1}^n\left( x_i-\bar{x}\right) ^2 / n} \end{aligned}$$
(7)

Where \(I_{i}\) represents the local spatial autocorrelation index. \(x_{i}\) , \(x_{j}\), \(\bar{x}\) and \(W_{ij}\) represent the same meaning as the formula (6).

Ecological System Service Change Index (ESCI, Ec)

The ESCI characterizes the status of ES impairment or gain46. Positive values denote gains in ecosystem services and negative values indicate losses in ecosystem services. A value close to zero indicates that the level of ecosystem services is stable or the change is not obvious47. The formula is as follows:

$$\begin{aligned} E_c=\frac{E_2-E_1}{E_1} \end{aligned}$$
(8)

Where \(E_{2}\) denotes the end ecosystem service value. \(E_{1}\) denotes the beginning ecosystem service value.

Ecosystem service value sensitivity

In order to verify the representativeness of ecosystem types to land use types and the accuracy of the ecological value coefficient, this paper introduces the ecological sensitivity index. We take into account the effects of climate, scientific and technological progress, and anthropogenic disturbances on the biomass of various ecosystems. Therefore, this study reflects the dependence of ESV on the value coefficient by adjusting the ecological value coefficients of cultivated land, forested land, grassland, watershed and unused land upward and downward by 50 percent, respectively48,49. If CS \(\ge\) 1, it means that the ecosystem service value is elastic to VC, indicating that the corrected coefficient is unreliable. If CS \(\le\) 1, it means that the ecosystem service value is inelastic to VC, indicating that the modified coefficient is reliable. The formula is as follows:

$$\begin{aligned} C S=\frac{\left( E S V_j-E S V_i\right) / E S V_i}{\left( V C_{j k}-V C_{i k}\right) / V C_{i k}} \end{aligned}$$
(9)

Where CS denotes the sensitivity index. \(ESV_{i}\) and \(ESV_{j}\) denote the total value of ESV before and after correction, respectively. \(VC_{ik}\) and \(VC_{jk}\) denote the coefficients of ESV of land use type k before and after correction, respectively.

Results and analyses

Analysis of the total value of ESVs in Gangu County at different grid scales

Characterizing changes in the total value of ecosystem service values

The total value of ESV at different grid scales for the five periods of 2000, 2005, 2010, 2015, and 2020 are calculated. The results show Fig. 3 that the total values of ESV in Gangu County for all 5 periods show an increasing trend when the grid scale increases from 100 m to 3000 m. Among them, in 2000, 2005, and 2010, the total value of ESV in the scale range of 100–600 m has obvious scale dependence and shows a large upward trend. There is an obvious inflection point value at the scale of 600 m grid. The total value of ESV in the scale range of 600 m -3000 m basically stays stable. In 2015 and 2020, the total value of ESV significantly changed in the ranges of 100–700 m and 100–900 m, respectively, with obvious scale dependence. They show inflection points at 700 m and 900 m. The total value of ESV shows small upward and downward fluctuations in the scale ranges of 700–3000 m and 900–3000 m, and the magnitude of changes gradually decreases, which is weakened by the influence of scale changes.

Overall, the pattern of scale variation of ESVs in the 5 periods is generally consistent overall. However, there is a slight difference in the 100–400 m scale range in 2020 compared with the other four periods. This is mainly due to the \('\)jumping\('\) development of construction land expansion, with the built-up area of the city expanding by 1.8 times in 2020 compared with 2015, forming several newly developed patches. This discontinuous land use change produces a significant edge effect at scales below 400 m, which increases the fluctuation of the calculated ESV by 2 - 3 times.

Fig. 3
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Changes in the total value of ESV for 5 periods from 2000 to 2020 at different grid scales.

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Differential significant analysis of the total value of ESV

To further analyze and screen out a uniform critical scale for studying the variations in the total value of ESV, this paper selects the one-sample t-test to analyze the differences in the total value of ESV under different grid scales in the five periods. We first perform the normal distribution test and choose the S-W test for small sample data. If the test results show significance (p-value less than 0.05 or 0.01), it means that it does not meet the normal distribution. However, it is usually difficult to fulfill this test. When the absolute value of the kurtosis of the sample is less than 10 and the absolute value of the skewness is less than 3, combined with the normal distribution graph, we can consider that it basically conforms to the normal distribution. The results show Table 3 that the significance p-value of 5 periods before the 1300 m scale is less than 0.05, but the absolute values of kurtosis and skewness are less than 10 and 3. This indicates that the total value of ESV basically obeys the normal distribution at different grid scales, which satisfies the normal characterization, and a one-sample t-test can be carried out.

According to the results in Table 4, in 2000, 2005 and 2010, the P-value are less than 0.05 in the range of 100–1000 m grid scale. When the grid scale increased to 1100 m, the P value is greater than 0.05. This indicates that the variability of the total value of ESV is extremely statistically significant within 1100 m. The total value of ESV in the range of 1100–3000 m grid scale is not characterized by significant variability. We believe that the scale dependence of the total value of ESV disappears after the 1100 m grid scale. Similarly, the scale dependence of the total value of ESV in 2015 and 2020 disappears at the 1000 m grid scale. The comprehensive analysis shows that there is significant variability in the total value of ESV within the 1100 m grid scale, which will have a large impact on the results of the study, so it is excluded. Therefore, the 1100 m grid scale can be regarded as a unified critical scale for studying the variation of the total value of ESV with or without scale dependence.

Exploring the scale dependence of ESV spatial heterogeneity

Analysis of ESV spatial heterogeneity at different grid scales

When the total value of ESV tends to a stable scale, we further explore in depth the characteristics of the response of the spatial distribution pattern of ESV to scale changes. Based on the amount of ESV within different evaluation units, we analyzed the trends of the area percentage changes of the ESV spatial distribution results at five levels for five periods at different scale levels. According to the natural breakpoint method, the ESVs under each scale are divided into 5 levels. And one-way analysis of variance (ANOVA) is used to explore the significant difference of area share under different scales.

According to Fig. 4a, there are obvious similarities and discrepancies in the spatial distribution of ESV at different scales. We can intuitively assess the extent of the effect of scale variation on the spatial distribution pattern of ESV based on the trend line. The closer \(\hbox {R}^2\) is to 1, it means that the fitted trend line describes the data well. This indicates that scale variation has a strong impact on the spatial distribution of ESVs, with a stronger scale dependence. Conversely, it indicates a smaller effect and weaker scale dependence. The spatial distribution pattern of ESVs under each level is more differently affected by scale changes, with obvious scale dependence. The strength of its influence by scale is as follows: low level (0.9730)> lower level (0.8376)> high level (0.7952)> medium level (0.7884)> higher level (0.5273).

According to the area share ratio, it can clearly excavate the change rule of ESV spatial pattern distribution. Combined with Fig. 4b, the comprehensive analysis shows that the trends of the area percentage in 2000, 2005, 2010, 2015, and 2020 are basically the same. With the increase of scale, the overall trend of the area share of low and lower values is decreasing. The area percentage of the medium, higher, and high values shows an overall fluctuating upward trend. The magnitude of area proportion in the five phases of this study area is medium level> lower level> higher level> high level > low level. Among them, the area share of the medium level remains above 50%, the area share of the lower level remains around 20%, and the sum of the two reaches above 70%. It indicates that medium level and lower level dominate the spatial distribution of ESV. The area share of low level, higher level, and high level is very small, which has little influence on the change of spatial distribution of ESVs and can be ignored.

Table 3 Results of the Normality Test Analysis.
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The letter labeling method allows for distinguishing whether there is a significant difference in area share between different scales. The same letter indicates that there is no significant difference between different grid scales, and different letters denote that there are remarkable differences between different scales. The area percentage of the medium level is significantly changing in the 1100–1700 m scale range, with its value increasing from 20 to 60%, and showing different letters (a, b, c). This indicates that there is significant variability within this scale range. After the 1700 m scale, the area proportion is stable, and its value remains at about 60%, and the letters are all a. This suggests that there is no remarkable difference after the 1700 m scale. Similarly, the lower level is also not significantly different after 1700 m. Therefore, the grid scale of 1700 m is the critical scale for ESV spatial distribution with or without scale dependence. It shows that the changes and variability of spatial data after the 1700 m scale are not affected by the scale, and the analysis of spatial heterogeneity can be carried out more accurately.

Table 4 Single sample t test analysis results.
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Fig. 4
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Area share of the spatial distribution of ESVs under different levels and its significant differences.

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Fig. 5
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Descriptive statistical parameters of ESV at different scales in Gangu County.

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Exploration of optimal grid scales for ESV spatial distribution patterns

To further excavate the optimal grid scale for the spatial distribution of ESVs, this paper analyzes the descriptive statistical parameters at different scale levels using spatial data exploration analysis. Combined with the variation coefficient(CV) and Moran’s I, the spatial distribution of ESV is analyzed in a more refined way. The ESV is firstly processed without dimension, and then we use the standard deviation and mean value to calculate the coefficient of variation values of ESV at different grid scales. Meanwhile, Moran’s I values of ESV at different grid scales are derived using the spatial neighbor weight matrix of Queen’s principle in GeoDa software.

As shown in Fig. 5, with the increase of grid-scale, the overall trend of coefficient of variation value is decreasing and then increasing, which are all above 50%. Among them, the value of the CV in 2000 is the smallest at the scale of 2100 m. The values of the CV in 2005 and 2010 are the smallest at the scale of 1900 m. The values of the coefficient of variation in 2015 and 2020 are the smallest at the scale of 2000 m. The comprehensive analysis shows that the value of the coefficient of variation of 5 periods is smaller in the scale range of 1900–2100 m. It indicates that the data are less discrete in this scale range and the data are more stable. It implies that the spatial heterogeneity of the data is lower in this scale range, which helps to capture the spatial characteristics of the data in more detail. When Moran’s I > 0, the larger the value, the stronger the positive spatial correlation. As the scale increases, Moran’s I values of ESV are all greater than 0.5 and the trend of change is fluctuating up and down. The Moran’s I values all peaked at the 1900 m grid scale, indicating that the spatial autocorrelation is the strongest at this scale. That is, there are significant similarities and differences between the data values of neighboring regions. Combining the coefficient of variation values of the five periods and the change rule of Moran’s I value, we can conclude that the 1900 m grid scale is the optimal scale for exploring the spatial distribution pattern. This scale can better capture the spatial heterogeneity of the data and better maintain the spatial autocorrelation of the data.

Changing patterns of ESV in Gangu County at optimal scale

Based on the optimal scale derived above, the characteristics of ESV changes in Gangu County from 2000 to 2020 are explored. Choosing the best scale for analysis can increase the accuracy of ESV expression and make the results more informative. With the help of ArcGIS software, we explored the distribution pattern of ESV under the 1900 m \(\times\) 1900 m grid.

Analysis of the ecological contribution of each land use type

Losses and inflows are larger in each land use conversion in Gangu County during the period 2000-2020. Therefore, the contribution to the change of ESV is also larger. The specific changes are shown in Fig. 6, where the ecological contribution of grassland is the largest, with a mean value of about 50.21%. The ecological contribution of other land use types is in the order of cultivated land (24.95%), forested land (17.61%), watershed (7.17%), and unused land (0.05%). The sum of the ecological contribution of grassland, cultivated land and forest land was as high as 92.77%. This indicates that the three land use types, grassland, cropland and woodland, are the main contributing factors to the changes in ESV in the Gangu County area over the past 20 years. Grassland is the land type with the highest ecological contribution in all study periods. In most of the other study periods, woodland and cultivated land are second only to grassland in terms of ecological contribution. In summary, grassland, cultivated land and woodland are the most significant land categories in terms of ecological contribution in the Gangu County area. Among them, grassland has the largest ecological contribution and its fluctuation is also the strongest. Therefore, maintaining the stability of grassland area in Gangu County will be the key to determine the ESV of the region.

Fig. 6
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Contribution of each land use type to ESV change in Gangu County.

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Analysis of the spatial distribution pattern of ESV

As shown in Table 5, The low ESV zones in the study area are all less than 3% of the area, and their area variation is comparatively minor. The ESV in this study area is mainly concentrated in the medium ESV zone, and its proportion is above 55%. It indicates that the ES function in this study area is relatively balanced. Meanwhile, the area of the medium, higher, and high ESV zones showed a decreasing trend during 2000-2020. Whereas, the area of low and lower ESV zones increased as a whole. This may imply the existence of ecological decline or impairment of ecological function due to human interference in the region.

This paper uses ArcGIS to depict the ESV level maps and the spatial distribution maps of the ecosystem service change index in 2000, 2005, 2010, 2015, and 2020. The overall and local change characteristics of ESV in space were specifically analyzed. The results are shown in Fig. 7, the high-value zone is mostly located in the natural pastures and secondary forests in the southern part of the study region, as well as the Weihe area in the central part. This is due to the intensity of human activities and the degree of interference in this region is weak. The higher-value zones are primarily located in the south. The medium value is dominant and mainly distributed in the middle and northern regions of the study zone. The lower values are mostly found in the central and northern parts of the study area in the areas of construction land and cultivated land. The low values are distributed in the outer edges of the study area. Over time, the ESV spatial distribution mainly evolves from high value to low -value and gradually decreases from south to north. The value of the ecosystem service change index in 2000-2020 is between − 30 and 30%. The proportion of grids that realized a decrease in the total value of ecosystem services is 48%. They are mainly located in the cultivated areas of Gangu County and the densely populated and highly urbanized construction areas.

Table 5 Area statistics for different levels in Gangu County, 2000-2020.
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Fig. 7
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Spatial changes of ESV in Gangu County at the optimal scale (created by ArcGIS 10.2 software, http://desktop.arcgis.com/cn/).

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Spatial autocorrelation analysis of ESV

According to Table 6, it can be seen that the global Moran’s I values for ESV in the study region for all 5 years are more than 0, with p-values less than 0.001. It indicates that the Space distribution of ESV in the study area has a strong positive correlation and there is an obvious clustering effect. The global Moran’s I values of the five periods increased and then decreased, indicating that the spatial positive correlation of ESV in Gangu County during the 20 years was first enhanced and then weakened.

Table 6 Global Moran’s I Statistics for ESV in Gangu County, 2000-2020.
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Introducing the method of local autocorrelation analysis, we further excavate the internal spatially divergent features. A total of four spatial correlation types are categorized as high-high (HH) clustering, high-low (HL) clustering, low-high (LH) clustering, and high-low (HL) clustering. As analyzed in Fig. 8, the high-high agglomerations are mainly located in the southern mountainous areas and the Weihe River basin in the central part of the country. This is because the southern region has a large area of forest and grassland distribution and less human disturbance, and the ecological background quality is high. The distribution of high-low and low-high agglomerations is relatively small and scattered, and most of them are in the vicinity of high-high and low-low agglomerations. They are mostly distributed in the Weihe River basin. Due to the human disturbance that destroyed the ecosystem structure around the Weihe River watershed, the ESV around the watershed decreased, showing significant high-low and high-low agglomerations. Most of the low-low agglomeration is scattered along the northern edge of the study area, which is mostly constructed land and cultivated land, all with low ESVs.

Fig. 8
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LISA distribution of ESVs at optimal scales (created by ArcGIS 10.2 software, http://desktop.arcgis.com/cn/).

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Analyzed from a temporal perspective, the central region has changed significantly between 2000 and 2020. The north and south regions were largely stabilized, and the number of low-high agglomeration grids in the central region decreased significantly during the 20 years. The number of high-high agglomeration grids increased significantly, with a total increase of 15 grids, accounting for 34.2% of the number of high-high agglomeration grids in the whole study area. The above changes have occurred mainly in the central part of the country, due to the fact that in the last 20 years, the region has become more concerned about population growth, urbanization, economic development, as well as about environmental sustainability, and the protection and restoration of watersheds. At the same time, the government has implemented new environmental protection policies, resulting in corresponding improvements in ecosystem protection and restoration. This has significantly enhanced the high - high clustering effect of ESV.

Sensitivity analyses of the ecosystem services value

Using sensitivity modelling, this paper focuses on testing the response of ecosystem service values to changes in the value coefficient (VC) of land use types50. By adjusting the coefficients up and down by 50 percent for each land type, we calculate the adjusted ecosystem service value (ESV). In this way, we analyse the trend of ESV over time and its dependence on the value coefficients. The results are shown in Table 7, the sensitivity index values of the value coefficients of land use types in Gangu County for each year from 2000 - 2020 are between 0 - 0.5. The change of sensitivity index of different land use types in different periods is small, and the sensitivity index of different land use types is less than 1. This indicates that the ESV of Gangu County is inelastic and insensitive to the value co-efficient, and the results of the study are reliable. Therefore, it can be proved that the ecosystem service value coefficients from 2000 to 2020 are basically consistent with the situation in Gangu County. The dynamic change of land use has less influence on the value of ecosystem services, so the results of the study are more credible.

Table 7 Sensitivity indexes of different land types from 2000 to 2020.
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Discussion

Selection of research scale

In the study of ESV, the assessment of ESV is not an easy task. It is affected by many complex factors, one of which is scale dependence. The choice of scale is crucial, which is directly related to the accuracy and applicability of the research results. Firstly, This paper selects 30 m high-resolution land use data to provide the basis for ESV calculation. This can more accurately identify the spatial distribution characteristics and change rules of ESV in Gangu County, especially the spatial information of some complex zones in Gangu County. Based on various considerations such as data accuracy and detail capture, scale conversion and consistency, as well as practical application and operability, the choice of 30 m resolution helps to improve the efficiency and effectiveness of data processing while maintaining data accuracy. Meanwhile, in this paper, we combine the scale selection results of Changsheng Xiong et al.28 and Wei Xiaojian et al32. We choose the scale range of 100–3000 m and take 100 m as the isochronous step. The study is carried out from small scale to large scale, and this result just complements this deficiency of the previous authors.

Scale-dependent analysis of ESV total values

Zhang Xuepeng et al.51 and Ni Weiqiu et al.52 suggest that different scales affect the calculation of the total value of ESV. But how it affects and what is the specific influence pattern has not been checked. Therefore, this paper explores this issue. This pa-per concludes that there is a significant scale dependence in the total value of ESV. As the scale increases, the total value of ESV shows a clear turnaround at the 1100 m scale. And it remains flat after that scale. This indicates that the significant difference in the total value of ESV disappears at scales after 1100 m, and its influence by scale changes is small and negligible. By determining the scale threshold (e.g., 1100 m) at which the total value of ESVs stabilizes, we can more accurately explore the scale dependence of the spatial heterogeneity of ESVs.

Scale-dependent analysis of spatial heterogeneity of ESVs

When conducting studies on the scale dependence of spatial heterogeneity of ESVs, it is crucial to choose an appropriate scale range. If the scale is too large, it may hide some important detailed information. If the scale is too small, it may be affected by random factors. Therefore, we choose the scale range of 1100–3000 m where the total value of ESV remains stable, and further explore the relevant laws of spatial heterogeneity to ensure the accuracy and reliability of the results. The spatial heterogeneity tends to stabilize after the 1700 m scale. This indicates that the scale dependence of the spatial heterogeneity of ESV disappears after 1700 m scale. This finding has important implications for determining the optimal scale.

Choosing the appropriate scale is a long-standing problem32. Our study found that 1900m scale is the best scale to study ESV. Whereas Wei Xiaojian considered the results of the 3 km \(\times\) 3 km grid to be more informative, Wang Dan considered the 5 km \(\times\) 5 km grid scale to be more valuable for the study. This difference is closely related to the fineness of the research scale. Wei Xiaojian and Wang Dan et al. used 1km as the grid unit divided by equal steps, and in this paper, the grid scale is divided by 100m as the equal steps. Therefore, this study is able to capture the spatial heterogeneity of ecosystem service value (ESV) more precisely. In contrast, Wei Xiaojian (3 km \(\times\) 3 km) and Wang Dan (5 km \(\times\) 5 km) use 1 km equal steps, which have a coarser granularity. This may fail to identify a better intermediate scale due to too large a scale jump. This refinement not only improves the spatial resolution, but also allows the study to capture the subtle variations and spatial heterogeneity of the ESV more precisely. It also provides new ideas for the development of scale conversion methods. This discovery not only enriches our understanding of the dependence of ESV scales, but also provides a more accurate scale reference for future ecosystem protection and management. The following several aspects: (1) Improvement of management efficiency: At the best scale, decision makers can more effectively identify hot spots and key areas of ecosystem services, so that resource allocation and policy implementation can be more accurate. This avoids waste of resources or management failures caused by improper scale. (2) Provide information for ecosystem management: We identify areas with high ESV (such as forests, wetlands) at the optimal scale, and thus we can prioritize these areas to avoid over-exploitation. At the same time, the boundaries of ecological protection zones can be scientifically delineated to ensure that the scope of the protected zones can cover key ecosystem service provision areas. At the best scale, we can allocate ecological protection and restoration resources more reasonably, and give priority to investing in areas with higher ESVs to improve resource utilization efficiency. (3) Support ecosystem protection strategy: We use the best scale ESV evaluation results to identify areas with low ESV but with recovery potential, and give priority to ecological restoration projects. At the same time, the grid scale of 1900 m \(\times\) 1900 m is the best scale for studying ESV. This conclusion was drawn after in-depth analysis based on the ecological and socioeconomic conditions of Gangu County. However, it should be clear that this study result may have higher applicability in Gangu County and similar areas to Gangu County, while adjustments may be required in areas with greater differences. Although the research results may not be applicable to all regions, the research methods in this paper (such as: construction of ESV models, division of grid scales, etc.) still have certain reference value for other regions. Other regions can use their own ecological and socioeconomic conditions to learn from the research methods of this article and select local evaluation scales to evaluate the value of ecosystem services. Therefore, we recommend that similar studies be conducted in regions with different climate and land use patterns, verify the applicability of the 1900 m \(\times\) 1900 m scale, and explore possible adjustment methods.

In addition, the contents considered in this paper may not be comprehensive enough and need to be further strengthened and improved in future studies. As can be seen from the studies of Zhang Xuyang et al.50 and Yang Guangzong et al.33 who chose the national scale and the city scale to discuss the change rule of ESV with scale. We only chose the county scale to analyze the scale dependence of ESV. However, the issue of scale dependence on a larger scale, such as city, province and nationwide etc., has yet to be developed in depth. Therefore, we hope that our research work can cause more scholars to verify the results from a wider range. Meanwhile, in this paper, we consider the scale dependence of the total value and spatial heterogeneity of ESV at five time points during 2000 - 2020. We observe that the results vary across time points. This suggests that future work is needed to further validate this result on longer time series.

Conclusions

This article quantitatively analyzed the scale dependence of ESV with the help of SPSS 26 software, ArcGIS 10.2 software, and GeoDa 1.20.0 software. We explored the scale effects on the total value and spatial distribution pattern of ESVs in five phases as well as determined the optimal scale for the spatial distribution of ESVs. This breaks the limitation of administrative divisions and divides the study area into grid scales, which improves the precision of the resultant analysis. We also analyzed the characteristics of the spatial distribution of ESV at the optimal scale during the period 2000 - 2020, and the details are as follows:

(1) As the grid scale increases, there is a significant scale effect on the total value and spatial differentiation of ESVs in 2000, 2005, 2010, 2015, and 2020. The scale dependence of the total value of ESVs disappears after 1100 m and the scale dependence of the spatial distribution of ESVs disappears after 1700 m.

(2) At a scale that maintains the stability of the total value and spatial distribution of ESV, the coefficient of variation values for the five periods show a minimum in the 1900–2100 m scale range, and Moran’s I all peaks at the 1900 m scale. 1900m is the optimal grid scale for exploring ESV.

(3) At the best scale, the ESVs in Gangu County mainly exists in the medium-value area during the period from 2000 to 2020. The spatial distribution of ESVs evolves from high to low values and decreases from south to north, with an overall distribution pattern of \('\) high in the south and low in the north \('\). The ESVs of the five phases all have significant agglomeration effects, with high - high agglomeration as the main focus. During the 20 - year period, the central region has changed from low - high agglomeration to high - high agglomeration.