Assessing the ecosystem services provided by urban green spaces along urban center-edge gradients

Urban green spaces provide various ecosystem services, especially cultural services. Previous assessment methods depend either on hypothetic payments for ecosystems or real payments not directly related to ecosystems. In this paper, we established a method for assessing the cultural ecosystem services in any location in urban area using only two variables, green space (ecosystem) and land rent (real payment). We integrated the cultural and the regulating services into the total ecosystem services because urban green spaces provide almost no provisioning services. Results showed that the same area of green spaces near the center provided much higher cultural services than that near the urban edge; the regulating services accounted for 5% to 40% of the total ecosystem services from the center to the edge of urban area; along the center-edge gradient, there was a threshold out which the ecosystem services were lower than the maintenance cost of green spaces.

sequestration per urban land area, (ton CO 2 m -2 urban area yr -1 ) was, where C (ton CO 2 m -2 green space yr -1 ) is ×0.5, NPP (ton biomass m -2 green space yr -1 ) is the net primary productivity of green space; 0.5 is the carbon conversion coefficient.
The NPP was the annual increment of DBH measured by tree ring samples from field surveys in the three case cities (method followed by Nowak et al., 2008). CG l is the green space coverage in location l (see Eq. (1) in the main text) and divided by 100 for unit conversion.
Oxygen release The O 2 released by green spaces per urban land area in location l, (ton m -2 yr -1 ) was, where was calculated in Eq. (1).

Air filtering
We calculated the amount of air filtered by urban green spaces per land area in location l, AF l (ton m -2 urban area yr -1 ), based on the method of Jim and Chen (2008) and divided by urban area, where AF l is air filtering of green space (ton m -2 green space yr -1 ).

Runoff mitigation
We quantified rainwater runoff mitigation ( RM l , ton m -2 urban area yr -1 ) through precipitation, and the runoff coefficient to calculate the capacity (Pataki et al., 2011;Barral and Oscar, 2012) by dividing by urban area, where RM l is the runoff mitigation of green space (ton m -2 green space yr -1 ); pr is the average annual precipitation; RI im is the runoff rate on an impervious surface (0.83 based on Pataki et al. (2011)). RI g is the runoff rate in an urban green space (0.13 based on Bonan (2002)); ρ is water density.

Noise reduction
We calculated the noise reduction by urban green space per land area in location l, NR l (ton m -2 urban area yr -1 ), based on the structure characteristics of the green spaces (Fang and Ling, 2003), and divided by urban area, where NR l is the noise reduction ability (ton m -2 green space yr -1 ).

Microclimate regulation
We calculated the microclimate regulation by urban green space per land area in location l, MR l (ton m -2 urban area yr -1 ), which can be measured by the energy consumption savings from air conditioning (Wang et al., 2005;Yang et al., 2005), divided by urban area, where B f is the leaf biomass (ton m -2 ); B t is the biomass of urban trees (ton m -2 ); α is the proportion of leaf biomass in tree biomass (8. 73%, Yao et al., 2003); l p is evapotranspiration intensity (451.9 ton water per ton fresh leaf per year, here we assume that the energy will be reduced during the summer time, which is set at 3 months); sw is the soil evaporation coefficient (this article takes 0.05); h is the heat consumed by vaporization of a ton of water (2.26×10 6 kJ), e is the efficiency of energy reduction from evapotranspiration (we set 10%).

Biogenic volatile organic compound (BVOC) emissions
The BVOC emissions from green spaces per urban land area, BVOC l (ton C m -2 urban area yr -1 ) followed the method by Chang et al. (2012) and divided by urban area, where BVOC l was the emission intensity (ton m -2 green space yr -1 ).
Monetizing the regulating services The values were calculated by using the biophysical values multiplied by the prices, and then calculated the sum of them, where RES l is the regulating service (yuan m -2 urban area yr -1 ) in location l; il is the biophysical value of regulating service i in location l (ton m -2 urban area yr -1 ); n is the number of considered categories of regulating services; PR i is the price of regulating service i (yuan ton -1 ). The price of each regulating service was listed in Supplementary   Table S6, and the monetary value was listed in Supplementary Table S7.

Contingent valuation method (CVM)
We collected the data of the total cultural services of green spaces in a city assessed in the literature (Supplementary Table S5). Since the CVM has only a total value of cultural services of the green spaces in a city, we then divided the total value by the total urban area to get the average value of cultural services per land area.

Hedonic pricing method (HPM)
We collected the data of price elasticity of green spaces for house price assessed by the HPM (Supplementary Table S5). The value of cultural services of a green space in a location was calculated by multiplying the house price with the price elasticity. The datasets were not equal in size for we could only get the data of those houses that were near green spaces from existing studies.  Data source: Atack and Margo (1998). In the function, x means distance from the city center (km), y means land price ($ per m 2 ).