Table 2 Methods for calculating ESSD.

WY

\(Swyx = \left( {1 - \frac{{AET(x)}}{{P(x)}}} \right) \times P(x)\)

Where S_wyx denotes the annual water yield of grid x (m³), AET(x) is the actual annual evapotranspiration of pixel x, P(x) is the annual precipitation of pixel x⁵⁸.

\(Dwyx = Po{p_x} \times Do{m_a} + {G_x} \times In{d_a} + {A_x} \times Ag{r_a}\)

Where D_wyx denotes the annual water demand at pixel x (m³), Pop_x denotes the population density at pixel x, Dom_a denotes the per capita domestic water use, Ind_a denotes the industrial water use per 10,000 yuan of GDP, A_x denotes the area of cropland at pixel x, and Agr_a denotes the amount of water used per unit area of cropland for irrigation.

SR

\({S_{srx}} = Rx \times Kx \times Lx \times Sx \times (1 - Cx \times Px)\)

where Ssrx denotes the amount of soil retention at grid x (t), Rx is the rainfall erosion index at pixel x (MJ∙mm∙hm⁻²∙h⁻¹∙a⁻¹), Kx is the soil erosion factor at pixel x (t∙hm²∙h∙hm⁻²∙MJ⁻¹∙mm⁻¹), Lx is the slope length-gradient factor at pixel x, Cx is the crop/vegetation and management factor at pixel x, Px is the support practice factor at pixel x⁵⁹.

\({D_{srx}} = R \times K \times L \times S \times C \times P\)

Where D_srx is the amount of soil erosion at pixel x (t), R_x is the rainfall erosion index at pixel x (MJ∙mm∙hm⁻²∙h⁻¹∙a⁻¹), K_x is the soil erosion factor at pixel x (t∙hm²∙h∙hm⁻²∙MJ⁻¹∙mm⁻¹), L_x is the slope length-gradient factor at pixel x, C_x is the crop/vegetation and management factor at pixel x, P_x is the support practice factor at pixel x 。

CS

\(\:{S}_{csx}=1.63\times\:NPP\times\:\frac{12}{44}\)

\(\:NPP=APAR\times\:\epsilon\:\)

Where S_csx is the total carbon storage at pixel x (t), NPP stands for Net Primary Productivity of Vegetation. APAR indicates the amount of photosynthetically active radiation that can be absorbed by the vegetation; ɛ indicates the actual photochemical energy conversion rate.

\(\:{D}_{csx}={C}_{a}\times\:{Pop}_{x}\)

Where D_csx denotes carbon emissions at pixel x (t), C_a denotes carbon emissions per capita, and Pop_xdenotes population density at pixel x⁶⁰.

FP

\({S_{fpx}} = \frac{{NDV{I_x}}}{{NDV{I_{{\text{sum}}}}}} \times {P_{{\text{sum}}}}\)

Where S_fpx represents the grain yield at pixel x (t), 𝑁𝐷𝑉𝐼_𝑥 represents the normalized vegetation coefficient of pixel x, 𝑁𝐷𝑉𝐼_𝑠𝑢𝑚 represents the sum of the normalized vegetation coefficients of the cultivated land in the study area; and 𝑃_𝑠𝑢𝑚 is the year’s of the total grain production in the study area (t).

⁶¹

\({D_{fpx}} = Cro{p_a} \times Po{p_x}\)

Where D_fpx represents the food demand at pixel x (t). Pop_𝑥 represents the population size in pixel x; and Crop_𝑎 represents the per capita food demand (t).