Table 1 Calculation formulas for four ecosystem services.

Carbon storage

Ctotal = Cabove + Cbelow + Csoil + Cdead

The carbon storage module estimates total carbon sequestration, comprising four fundamental carbon pools: aboveground biomass carbon, belowground biomass carbon, soil organic carbon, and dead organic matter carbon.

\({\text{Q}}_{{{\text{xj}}}} = {\text{H}}_{{\text{y}}} \left[ {1 - \left( {\frac{{{\text{D}}_{{{\text{xy}}}}^{{\text{Z}}} }}{{{\text{D}}_{{{\text{xy}}}}^{{\text{Z}}} {\text{ + K}}^{{\text{z}}} }}} \right)} \right]\)

Habitat quality

In the formula: Qxj represents the habitat quality of grid x in land use type j, Qxj ∈ [0, 1], with a larger value indicating better habitat quality; Hj represents the habitat suitability of land use type j; z and k are default parameters in the model.

\({\text{Yxi}} = \left[ {1 - \frac{{{\text{AETxi}}}}{{{\text{Px}}}}} \right] \times {\text{Px}}\)

Water yield

In the formula: Yxi represents the annual water yield (mm) on the grid x when the land use type is i; Px represents the annual average precipitation (mm) of the grid x; AETxi represents the actual annual average evapotranspiration (mm).

\({\text{SD}} = {\text{R}} \times {\text{K}} \times {\text{LS}} \times \left( {1 - {\text{C}} \times {\text{P}}} \right)\)

Soil conservation

In the formula, SD represents soil conservation amount; R represents rainfall erosivity factor; K represents soil erodibility factor; LS represents slope length and steepness factor; C represents vegetation cover factor; P represents soil conservation practice factor.