## 3 Results
### Hitelmoor 1980-2040: Complementary Assessments  
Potentially, the matrix approach by [PERSON] et al. [33] is able to reflect changes in the ecosystem service provision that result from land use changes. The Hitelmoor scenarios (Figure 2) host four land uses/land cover types: sea and ocean, beaches, dunes and sand plains, and moors and heathlands. The relative shares of the land uses/land cover types change over time in the scenarios, while the total area remains constant (570 ha) (Figure 7). It is assumed that between 1980 and 2040, coastal retreat increases the area covered by sea and ocean from 11 ha to 39 ha, while erosion reduces the area covered by dunes and sand plains from 29 ha to 17 ha. Especially after 2000, we assume an increase in moors and heathlands (from 305 ha to 318 ha) and a reduction in mixed forest coverage (form 221 ha to 196 ha) resulting from higher water levels in the moor.  
The averaged results per ecosystem service for the four scenarios Hutelmoor 1980-2040 only show minor changes between the scenarios. The effects of coastal retreat and moor restoration on ecosystem service potentials are hardly visible. The averaged ecosystem service potentials multiplied with the area indicate some changes, but these remain below 2%. We can conclude that the matrix approach does not reflect ecosystem changes sufficiently and does not provide additional insights. Since the quantitative changes between land uses/land cover types in the Ahrenshoop scenario are comparable to Hutelmoor, this approach was not applied to Ahrenshoop.  
The InVEST models are meant to reflect how changes in ecosystems cause changes in ecosystem service flows [34]. This meets the objectives of our study well and we explored whether the results are beneficial and can complement our comparative expert-based ecosystem service. InVEST Coastal Blue Carbon quantifies the value of carbon storage and sequestration services provided by coastal ecosystems. Other models, such as InVEST recreation, were tested but turned out to be not suitable for our study.  
Figure 8 shows the benefits of the Hutelmoor restoration, from an agricultural area in 1980 to a wet and partially inundated system in 2040, for carbon sequestration (InVEST Coastal Blue Carbon). While in 1980, the Hutelmoor emitted 7990 tons of CO\({}_{2}\) equivalents per year to the atmosphere; the partial rewetting (scenario 2000) reduced the emissions to 2790 tons of carbon dioxide equivalents (CO\({}_{2}\)e) per year. The largely finished rewetting (scenario 2020) further reduced the annual losses to 1896 tons CO\({}_{2}\)e. Until 2040, assuming a slight salinity increase and a dominance of reeds (_Phragmatis australis_), the area shifts towards a net sink for carbon, with a total annual sequestration of 118 t CO\({}_{2}\)e.  
Figure 7: Hutelmoor: Scores for 31 ecosystem services in the four land cover/land use types that are present in the Hutelmoor scenario, adapted after [33]. Shown are scores for ecosystem services potentials (0 = no potential; 5 = very high potential). For each scenario (1980, 2000, 2020 and 2040) the average ecosystem potentials are presented, as well as the sum (average multiplied with the area of 570 ha).  
Figure 8: Carbon stock and sequestration potentials of the four Hütelmoor scenarios based on InVEST Coastal Blue Carbon. The land use/land cover (LULC) maps represent the four scenarios. Carbon stock maps show the sum of vegetation and soil carbon storage based on general literature values for each land use/land cover type. Negative values indicate emissions to the atmosphere and positive values a net carbon sequestration over 20 years. CO2e are carbon dioxide equivalents used to compare the emissions from various greenhouse gases on the basis of their global warming potential.