Spatial heterogeneity of multi-scale trade-off synergies in ecosystem services

Analysis of the characteristics of land use type transfer

The mutual transformation information of land use types in area and geographical location at the start and finish of the study can be reflected in the land use type transfer matrix (Chen, Mao & Morrison, 2021). The evolution trajectory of land use type area from 2000 to 2020 is obtained. The specific mathematical expression is as follows:

(1) $$S_{ij}=\left|\begin{array}{cccc}{S}_{11}& S_{12}& \dots & S_{1n}\\ S_{21}& S_{22}& \dots & S_{2n}\\ \dots & \dots & \dots & \dots \\ S_{n1}& S_{n2}& \dots & S_{nn}\end{array}\right|.$$

Among them, S_ij refers to the area of land that is transformed from Class i land at the beginning of the study to Class j land at the end of the study. n represents the number of types of land use types.

Ecosystem services assessment

The InVEST model (intergrated valuation of ecosystem services and tradeoffs), designed to simulate alterations in ecosystem service quality and value triggered by diverse land use patterns, offers a comprehensive evaluation of various ecosystem services. In Suzhou City, given the local environmental conditions and data availability, water yield, soil conservation, and carbon storage were selected for assessment. After quantifying the three services, the partitioned statistics method is used to map them to different scales.

• (1)

  Water yield (WY)

The data required for the operation of this module include land use data, precipitation data, evapotranspiration data and so on. WY can be quantitatively described as the following equation (Xue et al., 2023):

(2) $$Y_x=\left(1-{\displaystyle \frac{AETx}{P_x}}\right)\times P_x$$where Y_x is the average annual water yield depth of grid cell x on land cover type j. AET_x is the actual evapotranspiration of land cover type j on grid x. P_x is the annual precipitation on grid x.

The required biophysical coefficient table is shown in Table 2, lucode is the land use code, kc is used to calculate the potential evapotranspiration to modify the reference evapotranspiration, root_depth is the maximum root depth of land use plants, and LULC_veg is the code used to indicate whether the LULC class is vegetated for the purpose of AET.

• (2)

  Carbon storage (CS)

The total carbon storage is calculated by the formula (Zhao et al., 2023). The data required for the operation of this module include land use data, carbon pool data. It can be quantitatively described as the following equation:

(3) $$C_{total}=C_{above}+C_{below}+C_{soil}+C_{dead}$$where C_total represents the total carbon storage. C_above is the aboveground carbon storage. C_below is the underground carbon storage. C_soil is the soil carbon storage. C_dead is the dead organic carbon storage.

The required biophysical coefficient table is shown in Table 3, the other four types of data respectively represent different types of carbon storage.

• (3)

  Soil conservation (SC)

The data required for the operation of this module include land use data, precipitation erosivity data, soil erodibility data and so on. The formula for calculating the model is as follows (Li et al., 2024b):

(4) $$SEDRE{T}_x=R_x\times K_x\times L{S}_x\times (1-C_x\times P_x)+SED{R}_x$$

(5) $$SED{R}_x=S{E}_x\sum _{y=1}^{x=1}USL{E}_y\prod _{z=y+1}^{x=1}(1-S{E}_{z)}$$

(6) $$USL{E}_x=R_x\times K_x\times L{S}_x\times C_x\times P_x$$where SEDRET_x and SEDR_x are the soil conservation and sediment retention of grid x. USLE_x and USLE_y are the actual soil erosion of the grid and its upslope grid y. SE_x is the sediment retention efficiency of grid x. R_x, K_x, LS_x, C_x, and P_x represent the precipitation erosivity factor, slope length factor, vegetation and management factor, and soil and water conservation measures of grid x, respectively.

The required biophysical coefficient table is shown in Table 4, usle_c is the coverage management coefficient of USLE, and usle_p is the practice factor supporting USLE.

Identification of ecosystem services hotspots

According to the division method of Qiu & Turner (2013), the first 20% value of water yield, carbon storage and soil conservation was defined as the coldspots. The last 20% value was defined as the hotspots. The changing law of high and low values of ecosystem services can be seen by analyzing the spatial-temporal variations of cold and hot spots.

Trade-offs and synergies of multi-scale ecosystem services

In order to compare the scale effects of different grid unit sizes on ecosystem services, the grid-scale and county scale were selected as the research unit with reference to the construction of existing ecosystem services grid. By querying the statistical yearbook of Suzhou City, the average area of towns and villages was estimated to be 89.25 and 4.01 km², respectively. Therefore, 10 km is selected as the grid side length to fit more closely with the township scale. A total of 2 km is selected as the grid side length to fit more closely with the village scale. The different grid side lengths are set to fit with the social organization scale of the study area (Zhou et al., 2022) to realize the connection between ecosystem services and management decisions at different scales.

The difference comparison approach is used in this article to investigate the trade-offs and synergistic interaction of several ecosystem services (Zhang et al., 2020). If the multiplication of two ecosystem service changes is positive, it is a synergy relationship. If the multiplication of two ecosystem service changes is negative, it is a trade-offs relationship. The quantified ecosystem services data was mapped onto different scales. Then, the difference comparison method was used to derive the trade-offs and synergies of ecosystem services across these scales.

(7) $$\begin{array}{rl}& A_{T1}-A_{T2}=\mathrm{\Delta }A\\ & B_{T1}-B_{T2}=\mathrm{\Delta }B\\ & \mathrm{\Delta }A\times \mathrm{\Delta }B\ge 0\\ & \mathrm{\Delta }A\times \mathrm{\Delta }B<0.\end{array}$$

In this expression, T1 and T2 refer to two different time phases. For ecosystem service A, its value in T1 and T2 phases is labeled A_T1 and A_T2, respectively. Accordingly, the values of ecosystem service B at T1 and T2 are recorded as B_T1 and B_T2, respectively. The variables ∆A and ∆B specifically reflect the respective magnitude of changes in ecosystem services A and B from T1 to T2.

Analysis of water yield change

By using the InVEST model, the water yield, carbon storage and soil conservation were calculated from 2000 to 2020. The outcomes demonstrated that their distribution was heterogeneous. The water yield exhibited a tendency of first declining and then increasing between 2000 and 2020 (Fig. 3). The area with high water yield in 2000 was mainly distributed in the east, and the area was small. The low-value proportion reached 86.2%, mainly distributed in cultivated land and water. From 2000 to 2005, the water yield revealed a declining pattern. The area of the high-value area changed significantly. The proportion of high-value areas expanded from 1.5 to 7.3%. The low-value areas were the largest water yield types, accounting for 70.9%, which were widely distributed. Some cultivated land was also transformed into low-value areas. From 2005 to 2010, the water yield indicated a rising pattern. The area of high-value areas decreased rapidly. Some high-value areas became second-high-value. The area’s percentage dropped to 0.4%, which was distributed in the eastern urban land, and the low-value area decreased rapidly to 27.0%. From 2010 to 2015, the water yield indicated a rising pattern. The area of the high-value area continued to decrease to 0.1%, mainly transferred to the second-highest value area. The proportion of the low-value area continued to decrease to 12.6%, mainly distributed around the urban area. From 2015 to 2020, the water yield showed an increasing trend. The high-value area changed from continuous decrease to rapid expansion. The area percentage of the area rose from 0.9% to 14.6%. In addition to the urban construction land, the more scattered areas in the north, east, northeast and south changed from the second-highest value to the high-value area in a cluster distribution. The area of low-value areas continued to decrease, mainly distributed around Taihu Lake, Yangcheng Lake and the southern region.

Analysis of changes in carbon storage

The carbon storage demonstrated a tendency of first decline and then increase between 2000 and 2020. The distribution of the carbon storage was low in the southwest and high in the northeast in 2000 (Fig. 3). The high-value carbon storage areas made up 55.3% of the total area and were widely distributed. The low-value areas are widely distributed, including the Yangtze River, Taihu Lake, Yangcheng Lake, Chenghu Lake and many rivers and lakes. In 2005, the high-value carbon storage area underwent substantial alteration. The dilation of construction land contributed to the increase of the area of the low-value area and then encroached on the high-value area. The percentage of the area decreased to 48.4%. The percentage of low-value area increased from 42.6% to 49.8%. Combining with the above land use pattern, the surface water area indicated a slow growth trend from 2000 to 2005. Hence there was not a noticeable shift in the low-value water area. In 2010, the region of high-value carbon storage area continued to decrease, mainly turning into low-value area. The spatial pattern of the rest of the area changed significantly. Most of the high value was found in the northeast and north. The distribution was gradually fragmented due to the existence of various types. The spatial distribution of Low-value area has undergone significant modification. The construction land has increased in the past five years. The proportion of low-value area increases accordingly. It is mainly reflected in the increase of urban land and rural settlements in the northern, eastern and central urban areas. In 2015, the region of the northern and eastern high-value areas continued to decrease. The proportion of the area continued to decrease to 40.8%, most of which moved to the low-value areas. The spatial distribution showed a fragmented and clumpy distribution. The area of low-value area increased slightly. The low value of carbon storage mainly included construction land and water areas. From 2010 to 2015, with the acceleration of urbanization, the area of construction land continued to increase. The water body showed a slow shrinking trend at this stage. As a result, low carbon storage value indicated an upward tendency. In 2020, the high value of carbon storage raised slightly, which was mainly reflected in the islands in Taihu Lake, the southern part of Suzhou City and the northern part of Yangcheng Lake, while the change of the remaining high-value areas of carbon storage was not significant. The proportion of low-value areas of carbon storage changed slightly, but the spatial pattern changed significantly, which was mainly reflected in the increase of the area of the median area of construction land, and the decrease of the area of the median area of waters.

Analysis of soil conservation change

There were two types of soil erosion that were actual soil erosion and potential soil erosion. By deducting the actual soil erosion from the actual soil erosion, one can obtain the soil conservation. From 2000 to 2020, the actual soil erosion and soil conservation first reduced, then elevated. The real soil erosion and soil conservation followed a similar spatial trend, with the distribution pattern of high values in the islands of Taihu Lake, the western part of the city and the northern part of Shanghu Lake in a large area and low values in other areas (Fig. 3). In 2000, the proportion of the area with low value of actual soil erosion was 98.6%. The proportion of the low-value area did not change significantly until 2020. The proportion of the area was always about 98.0%, and the change value of soil erosion was not significant. The spatial pattern from 2000 to 2015 is similar. Combining with the land use map, the lowest value of soil conservation is water area, construction land. The highest value of soil conservation is forest land. The other land use types are the median value. By 2020, the spatial pattern had changed significantly, some high-value areas had been transformed into medium-low value areas. And the correlation with land use distribution is less. The large range of low value distribution is the main type. There was no discernible change in the regional distribution of soil conservation between 2000 and 2020. Forest land was the highest valuable type of soil conservation. The low value was dominated by water. The soil conservation is calculated by soil erosion, and the two are closely related, rather than opposing distribution patterns. Both natural and man-made causes have an impact on actual soil erosion. The impact of human activity and soil and water conservation measures on soil erosion is mostly reflected in soil conservation.

Ecosystem service trade-offs and synergies in the 2 km grid

The intricate relationships among ecosystem services can be separated into trade-offs and synergies based on their respective ratios. From 2000 to 2005, the interactions between water yield-carbon storage (WY-CS), carbon storage-soil conservation (CS-SC), and water yield-soil conservation (WY-SC) of ecosystem services were mainly synergistic and distributed in a large area in the study area. Among which the synergies between WY-SC were much higher than those between WY-CS and CS-SC. From 2005 to 2010, the synergistic area ratio of WY-CS and CS-SC decreased while the trade-off area ratio increased. The trade-off was the main effect, and the synergistic effect was mainly distributed in the central urban area and the eastern region. The WY-SC was still dominated by the synergistic relationship, and the trade-off relationship was slightly distributed in the southern part of Taihu Lake. From 2010 to 2015, the proportion of trade-off area between WY-CS and CS-SC decreased. But the trade-off relationship was still dominated, and the synergies were mainly distributed around Taihu Lake and in the northeast and southeast of the urban area. The synergies between WY-SC were dominated, and a small amount of trade-offs turned into synergies during this period. From 2015 to 2020, although the regional proportion of trade-off between WY-CS continues to decrease, the dominant relationship is still in the trade-off state. In contrast, the regional proportion of the slight trade-off between CS-SC did not change much, but its spatial distribution pattern showed significant signs of adjustment, which was mainly reflected in the increase of trade-off area around Taihu Lake and the cooperative transformation of trade-off in the northeast and southeast of the city. The interaction between WY-SC is mainly synergistic, and this synergistic relationship is dominant, during this period, the trade-off effect replaced the synergistic effect in the southern portion of Taihu Lake, and the northern synergistic effect was enhanced (Fig. 5).

Ecosystem service trade-offs and synergies in the 10 km grid

On the 10 km grid scale from 2000 to 2005, the interaction between WY-CS, WY-SC, CS-SC ecosystem services was mainly slightly synergies. The first two pairs of ecosystem services have similar spatial pattern. The spatial distribution pattern of both was mainly large area synergistic distribution, southwest of Taihu Lake was the distribution of the minor trade-off relationship. The relationship between WY-SC was dominated by a mild synergistic effect, and the intensity of this synergistic effect significantly exceeded the synergistic effect between water WY-CS, and between CS-SC. From 2005 to 2010, there were significant changes in the relationship between WY-CS and CS-SC. In the meantime, the characteristics of the synergistic area proportion present a significant reduction, from the predominant synergistic distribution to the predominant trade-off distribution, with a large area distributed in the study area, and a small amount of synergistic relationship distributed only in the southern and central parts of the study area. The distribution of trade-off between WY-SC decreased significantly during this period. The synergistic relationship covered almost the whole study area, but the synergistic effect was weakened overall. From 2010 to 2015, the area proportion of trade-off relationships between WY-CS and CS-SC decreased. But the trade-off relationship was still dominated by the trade-off relationship. The two ecosystem service interactions have a similar spatial structure. The southwest, southeast and north had a synergistic relationship and showed an aggregation state. While the rest had a large-scale distribution trade-off relationship. The distribution of WY-SC was still dominated by the synergistic relationship. But the area proportion of the middle-high synergistic relationship decreased, and the distribution area of the low synergistic relationship increased. From 2015 to 2020, the overall relationship between WY-CS and CS-SC is still dominated by trade-offs. The southwest of Taihu Lake and the south of Suzhou City suffered a marked shift in the trade-off between WY-SC. The overall function relationship is still dominated by the synergistic relationship (Fig. 6).

Ecosystem service trade-offs and synergies at the county level

On the county scale from 2000 to 2005, the interactions between WY-SC, CS-SC, WY-CS were mainly mildly synergistic. From 2005 to 2010, the interaction between WY-CS and CS-SC changed from a synergistic relationship to a trade-off relationship. The distribution of the lowest and highest interaction between WY-CS was the same as that between 2000 and 2005. The distribution pattern was lower in southwest and higher in northeast. The distribution of high and low values of CS-SC was the same as that of 2000–2005. The trade-off effect of the two groups was not strong, and it was a mild trade-off. The effect of WY-SC was unchanged, but the synergistic effect was weakened. From 2010 to 2015, the relationship between WY-CS, WY-SC, and CS-SC remained unchanged. From 2015 to 2020, the trade-off synergies between WY-CS, CS-SC were distributed. The trade-off synergies distribution pattern was the same. Wuzhong District, Wujiang District, Xiangcheng District and Changshu City showed a synergistic effect. The other counties showed a trade-off effect, the WY-SC relationship showed a synergistic effect. The overall distribution of synergistic effects showed a pattern of weak distribution in the south and strong distribution in the north (Fig. 7).