Spatial multi-scale relationships of ecosystem services: A case study using a geostatistical methodology

Adequately understanding the spatial multi-scale relationships of ecosystem services (ES) is an important step for environmental management decision-making. Here, we used spatially explicit methods to estimate five critical ES (nitrogen and phosphorous purifications, crop production, water supply and soil retention) related to non-point source (NPS) pollution in the Taihu Basin region of eastern China. Then a factorial kriging analysis and stepwise multiple regression were performed to identify the spatial multi-scale relationships of ES and their dominant factors at each scale. The spatial variations in ES were characterized at the 12 km and 83 km scales and the result indicated that the relationships of these services were scale dependent. It was inferred that at the 12 km scale, ES were controlled by anthropogenic activities and their relationships were dependent on socio-economic factors. At the 83 km scale, we suggested that ES were primarily dominated by the physical environment. Moreover, the policy implications of ES relationships and their dominant factors were discussed for the multi-level governance of NPS pollution. Overall, this study presents an optimized approach to identifying ES relationships at multiple spatial scales and illustrates how appropriate information can help guide water management.

Geographic Science and Natural Resources Research, Chinese Academy of Sciences. Hydrologic, water quality, used as proxies for water quality services, and lower loading values correspond to higher water quality services.

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We used the Nutrient Purification Model of Integrated Valuation of Ecosystem Services and Trade-offs (InVEST) 53 to quantify the NL and PL 5, 6 , and the major data inputs and parameters are listed in

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Water supply service 71 Water supply service (WS) is the surficial water yield generated by the hydrologic cycle, and it provides 72 water for human consumption or hydropower production. The WS is influenced by meteorological factors as 73 well as soil properties and land cover. Considering the combined impact of multiple factors, we used the Water 74 Yield Model of InVEST to quantify the annual WS 14 , and the major data inputs and parameters are listed in Table   75 S2. The equation for WS at each pixel x of landscape is expressed as follows in equation (4).

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where ω x represents a non-physical parameter and is calculated by equation (6)

Soil retention service 104
Ecosystems play an important role in preventing soil erosion inputs to streams and are associated with the 105 soil's capacity to filter pollutants, which can regulate water quality. We quantified the annual potential reduction 106 of soil loss as the indicator for soil retention service (SR) by referring to the Revised Universal Soil Loss 107 Equation (RUSLE) 25, 26 , and the major data inputs and parameters are listed in Table S3. However, RUSLE was 108 developed to model soil erosion in the Midwestern U.S. and may generate deviations from the actual conditions of the Taihu Basin region. Therefore, we adjusted the model using parameters based on experimental data from 110 the sub-watersheds. The equation for the SR in this study can be expressed as equation (8).
This model indicates that current land uses that implement vegetation cover and protection measures will 113 generate reductions in soil loss compared with land uses that lead to bare soil. R is the rainfall erosivity index  125

Crop production service 126
The annual crop yield per unit area was used as an indicator for the crop production service (CP). The crop 127 types in the study area include rice, wheat, corn, soybean, sorghum, millet, and potato, and they grow in different 128 seasons. We converted the production of different crop types into the standard yield and estimated the total yield 129 in a year using a climatic potential productivity model and cultivated land quality data of the study area, and the 130 major data inputs and parameters are listed in Table S4

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We assessed the accuracy of the estimated results at an aggregated level because actual data could be 141 acquired for each administrative unit 6 . Compared with the actual yield for 2010 at the town level, our estimate 142 showed good performance because the deviation was within 10.7% for the region. Furthermore, town-based 143 actual data and an area-weighted method based on arable area were used to adjust the regional data if errors were 144 greater than 5%.

Physical environmental factors 147
Six groups of physical environmental factors were quantified (Table S5)