### Benefit transfer

The value transfer method in valuation of urban nature using methods from environmental economics is a rapidly expanding area of research, which is in particular suitable when conducting a primary valuation study on site is infeasible^{14,36}. Value transfer makes use of existing primary valuation estimates and applies these estimates to a policy site at a different place or in a different context.

Meta-analysis is a statistical method that explains variation in values from primary valuation studies^{37}. Aggregation of information from a variety of primary studies, and control for methodological and context-specific differences are its main advantages. This study uses a recently estimated value transfer function for urban nature^{14} (see below), and applies it to selected NBS in European policy cities. The resulting estimates capture the total economic value of a nature site, including its direct and indirect use values, as well as non-use value that exists even when individuals are unlikely to use the site. Thus, the monetised value for specific urban nature site reflects the local socio-economic context (level of income and population density in a specific city) and the specific type of intervention (type of urban nature and its size).

We apply the following global value transfer function^{14}:

$$Value,of,nature,per,year, = ,exp left( {7.718 – 0.964 times left( {ln left( {Area} right) – ln left( {1474} right)} right) + 1.527 times left( {ln left( {GDP} right) – ln left( {23026} right)} right) + 0.241 times left( {ln left( {Density} right) – ln left( {396} right)} right) + 1.900 times Dleft( {Choice,experiment} right) – 2.723 times Dleft( {Tax} right) + 1.674 times Dleft( {Park} right) + 0.059 times Dleft( {Forest} right) – 0.144 times Dleft( {Small,urban,green} right) – 0.589 times Dleft( {Green,connected,to,grey} right) + 0.221 times Dleft( {Blue} right) + 0.231 times Dleft( {Multiscape} right)} right).$$

(1)

In formula (1), *ln* stands for a natural logarithm, *D* stands for a dummy variable that takes a value of 1 if true, and 0 otherwise. All continuous explanatory variables are centered logarithms. The variables and dummies used in the model can be seen as grouped based on socio-economic, study and site characteristics. Socio-economic characteristics include area size of a project, GDP per capita, and population density on the metropolitan or regional level. Study characteristics include payment vehicle used in the primary studies eliciting resident preferences for urban nature (tax), and method of value elicitation (choice experiment). Standard, for estimations, these are set to the sample average values from the original estimated meta-function^{14}. Types of urban nature include urban park, forest, small urban green areas, green connected to grey infrastructure, blue nature. In addition, the multiscape dummy variable captures the variability in urban nature when a project was specified to include multiple nature or landscape types, such as park(scape), water(scape), soil(scape), etc.

Estimated coefficients in equation (1) reflect the contribution of each variable to the value of urban nature per hectare, and is based on a regression model of 147 values of various types of urban nature obtained from 60 original valuation studies. Theoretically, the meta-function should be preferred for applications to cases which closest approximate the similarity of contexts^{37}. Our meta-analysis used studies predominantly from Europe, North America and Asia, so the value transfer function as in equation (1) can be directly applicable to urban green areas in these regions. Application procedure and examples are described elsewhere^{14}.

### Maintenance and implementation costs

Due to the uncertainty of future money flows and human time preferences, the costs and benefits that occur in the future need to be discounted, thus attributing to those less weight relative to current costs and benefits. Although the initial costs were likely paid over a period of time, the UNA database (https://una.city/) does not provide this information on a project basis. Thus, initial investments were assumed to be lump-sum investments and were not discounted.

For estimates of the net present value of urban nature, the estimates of the yearly operational costs were obtained and projected to make up a percentage of initial costs, for each identified urban nature type (Table 2). These values were obtained through a literature review of operational and maintenance costs of urban green projects in Google Scholar. Search terms used are: (i) Method: cost–benefit analysis, cash flow analysis, net present value, internal rate of return, lifecycle costs; (ii) Location: urban, city, local, community; (iii) Type of nature: natural infrastructure, green infrastructure, blue infrastructure, blue amenities, terrestrial water, wetlands, canals, lakes, water, green, green belt, green corridor, green roof, garden, park, forest; (iv) Type of costs: initial costs, ongoing costs, maintenance, management, financial costs, monetary costs. Studies published in English and that included both the investment costs and operational costs were included resulting in 21 study with varying geographical spread (1 African, 1 Australian, 2 Asian, 5 North American and 12 European) and varying methodologies. From each study, an average ratio of operational costs to initial investment cost were obtained, as well as minimum and maximum values. Averaging per NBS type resulted in the operational costs relative to initial investment estimates shown in Table 2.

The yearly operational costs in USD per project is thus the initial investment multiplied by the estimated percentage of maintenance costs. Maintenance costs and yearly benefits were assumed to occur in the future throughout the lifetime of the project.

### Net present value (NPV)

A threshold scenario assumed a lifetime of urban nature of 40 years and a threshold discount rate of 3%. This is in line with literature surrounding the discount rate^{38} and is the same discount rate used in^{14}. A declining discount rate was not applied because the project lifetime estimate is below 50 years. The net present value (NPV) was calculated by summing the discounted benefits over time, from which the sum of the discounted operational costs and the initial investment was subtracted. Benefits of urban nature to urban residents is obtained by application of the benefit transfer method described above. The benefit-to-cost ratio (BCR) is given by the total discounted benefits divided by the sum of initial costs and total discounted maintenance costs. 65% of the projects had a positive NPV for the threshold scenario and can thus be considered ‘socially profitable’. The obtained NPV and BCR were further tested for sensitivity to the alternative discount rates of 1% and 5%. Results indicate that the NPV (net present value, positive for profitable projects) of NBS projects drops, but still remains positive, for the same amount of projects at a 5% discount rate compared to the threshold scenario of 3%. This indicates that our results remain robust for discount rates up to 5%. At 1%, the percentage of NBS projects with a positive NPV increases from 65% to 67.3%. In addition, sensitivity of our results to the height of operational costs was tested, assuming a 50% increase and decrease in operational costs compared to the threshold scenario. Results indicate that a flat 50% increase in operational costs would leave 61.67% of the selected NBS interventions with positive NPV compared to 65% at the threshold scenario. A flat 50% decrease in operational costs would make 73.33% of the selected NBS interventions end up with a positive NPV.