Table 2 Description of the eight modeled landscape services and how their values were calculated for each raster cell

From: Assessing potential landscape service trade-offs driven by urbanization in Switzerland

LSS name and description

Quantification equation

Variable description

Housing: provisioning of space for humans to live in

Housing = 1 × FFH + 6 × MFH

FFH: few-family houses

MFH: multi-family houses

Jobs: places that provide jobs in the 2nd and 3rd economic sectors

Jobs = MSI

MSI: manufacturing and service infrastructure

Crop production: total production of plant-based agricultural products, proportional to the production costs

Crop production = (1 × AL + 1.04 × G&M + 10 × OVH) × LW factor

AL: arable land

G&M: grassland and meadows

OVH: Orchard, vineyard and horticulture

LWfactor: productivity factor based on agricultural zones in Switzerland (FOAG, 2017), Range: 0.4–1

Reared animals: distribution of land use types that can potentially host reared animals or provide fodder for them

Reared animals = G&M + AAL

G&M: grassland and meadows

AAL: Alpine agricultural land

Forest products: primarily provisioning of timber, but indirectly a rough indication of carbon sequestration potential

Forest products = FO × Vol

FO: Forests

Vol: standing volume per economic region (Abegg et al., 2014), Range: 225–465 m3

Hazard protection by forests: protection by forests where the risk of a local natural hazard exists and any sort of infrastructure is close by; only where forests are present

\(\begin{array}{l}{\rm{Hazard}}\,{\rm{protection}} = {\rm{Hazard}}\_{\rm{risk}}\\ \times \mathop {\sum}\nolimits_{9 \times 9\,{\rm{cells}}} {\left( {{\rm{FFH}} + {\rm{MFH}} + {\rm{MSI}} + {\rm{Transportation}}} \right)} \\ \times \mathop {\sum}\nolimits_{5 \times 5\,{\rm{cells}}} {\rm{{FO}}} \end{array}\)

FFH: few-family houses

MFH: multi-family houses

MSI: manufacturing and service infrastructure

Transportation: large transportation routes

FO: forests

Hazard_risk: presence of local hazard risk derived from the data of the SilvaProtect-CH Project of FOEN (Losey and Wehrli, 2013)

Biodiversity: general biodiversity, including special responsibilities for species with limited spatial distribution

\(\begin{array}{l}{\rm{Biodiversity}} = \\ \sum_{9 \times 9\,{\rm{cells}}} {\left[ \begin{array}{l}1 \times \left( {{\rm{MSI}} + {\rm{FFH}} + {\rm{MFH}} + {\rm{AL}}} \right)\\ + 2 \times {\rm{OVH}} + 3 \times {\rm{AAL}}\\ + 3 \times \left( {{\rm{G}}\& {\rm{M}} \cap {\rm{TWW}}} \right)\\ + 1 \times \left( {{\rm{G}}\& {\rm{M}}\backslash {\rm{TWW}} \times {\rm{Slope}} + 1} \right)\\ + {\rm{FO}} \times \left( {1 - \frac{{\sum_{9 \times 9\,{\rm{cells}}} {\rm{FO}}}}{{9 \times 9}} + 2} \right)\end{array} \right]} \end{array}\)

MSI: manufacturing and service infrastructure

FFH: few-family houses

MFH: multi-family houses

AL: arable land

OVH: Orchard, vineyard and horticulture

AAL: Alpine agricultural land

G&M: grassland and meadows

TWW: dry meadows

Slope: relative steepness of slope, Range: 0 (flat)–1 (steep)

FO: forests

Recreation: available space to perform outdoor activities close to the place of residence on a daily basis; a combination of supply and demand, both normalized to range from 0 to 1.

\(\begin{array}{l}{\rm{Demand}} = \sum_{9 \times 9\,{\rm{cells}}} {\left( {0.5 \times {\rm{FFH}} + 3 \times {\rm{MFH}}} \right)} \\ {\rm{Supply}} = \sum_{9 \times 9\,{\rm{cells}}} {\left[ \begin{array}{l}1 \times {\rm{AL}}\\ + 2 \times \left( {{\rm{OVH}} + {\rm{G}}\& {\rm{M}} + {\rm{AAL}}} \right)\\ + 3 \times \left( {{\rm{FO}} + {\rm{Lakes}} + {\rm{Rivers}}} \right)\end{array} \right]} \\ {\rm{Recreation}} = \left\{ {\begin{array}{*{20}{c}} {{\rm{Supply}} - {\rm{Demand}},\quad \quad {\rm{Demand}} \ge {\rm{Supply}}} \\ {{\rm{Demand}},\quad \quad {\rm{Demand}}\, < \,{\rm{Supply}}} \end{array}} \right.\end{array}\)

FFH: few-family houses

MFH: multi-family houses

AL: arable land

OVH: Orchard, vineyard and horticulture

G&M: grassland and meadows

AAL: Alpine agricultural land

FO: forests

Lakes: lake present

Rivers: river present

  1. Input variables always refer to rasters whose value range is either indicated or binary (1: feature present, 0: feature absent). The sum signs (Ʃ) indicate a sum neighborhood analysis, where the index below indicates the size of the considered window around the focal cell