2.3.3. Net Benefits

The net present value (NPV) is calculated using Equation (1)).

$$NPV = \sum\_{t=1}^{T} \frac{B\_t - C\_t}{\left(1 + i\right)^t} \tag{1}$$

where *Bt* and *Ct* are the benefits and costs at each year *t*, *i* is the discount rate, *T* is the project evaluation period.

#### **3. Results**

## *3.1. Costs*

Table 1 summarizes CAPEX and OPEX of the green infrastructure proposed in Badalona and Barcelona. The table shows that in the case of Badalona the total costs are approximately an order of magnitude lower compared to Barcelona. Barcelona has a bigger area and a much more ambitious implementation plan compared to Badalona. Further, the total GI costs of Badalona are dominated by green roofs. This is because green roofs are assumed to be retrofitted onto 5% of the total roof area of Badalona, whereas infiltration trenches are placed only on 7 different parks and infiltration pavements on 5 different parks and public squares.

**Table 1.** CAPEX and OPEX of the analyzed green infrastructure.


#### *3.2. Benefits*

The first step in order to estimate benefits derived from flood damage reduction obtained by GI implementation is the estimation of EAD for both the BAU and the GI scenarios. Table 2 shows the EAD results. Generally, the EAD of these two BAU scenarios are considered to be overestimated, particularly in the case of Barcelona (see the Discussion section). Figure 3 shows the flood damage costs simulated as a function of different exceedance probabilities for the two case studies. The EAD that is the area below the curve of Figure 3 was calculated using simple trapezoidal contributions adopting the linear interpolation between the discrete points represented Figure 3.

**Table 2.** Flood Expected Annual Damage including both direct and indirect damages.


**Figure 3.** Flood damage as a function of the exceedance probability for Barcelona (**a**) and Badalona (**b**).

Table 3 shows the details of the monetized annual (not discounted) benefits for each of the three categories proposed and their percentage contribution to the total benefits in Barcelona and Badalona. The table shows that the benefits derived from reduced combined sewage treatment costs; from reduced indirect damages to coastal economies; from air quality improvement and from reduction of the urban heat island effect and energetic consumption are in the range of 0–1%.


**Table 3.** Annual value of benefits (not discounted).

Figure 4 provides a graphical representation of the contribution of each of the three benefit categories proposed to the total benefits. Overall, significant differences are shown in the percentages of Barcelona and Badalona. In the case of Barcelona, the benefits derived from flood damage reduction are 56% of the total and in Badalona 6%. Additionally, water quality benefits have a larger share in Barcelona compared to Badalona. This is probably because of the widespread GI implementation of Barcelona compared to Badalona where a significantly less ambitious GI implementation plan was considered. A different GI location in Badalona could result in higher water related benefits. Cooper et al. [9] also looked into the contribution of multiple benefits associated to green infrastructure (considered as a coastal flood adaptation measure) showing that benefits from reduced residential damages were 69% of the total, recreational and health benefits 12% and avoided commercial damages 12%.

**Figure 4.** Contribution of each of the three different benefit categories to the total green infrastructure benefits. (**a**) Barcelona and (**b**) Badalona.

Figure 5 shows the discounted benefits during the study evaluation period (80 years, from 2020 to 2100 for the considered scenarios). The results show that the benefits reach their maximum when all GI are implemented: after 20 years in Barcelona and 5 years in Badalona.

**Figure 5.** Contributions of the different benefit categories to the total green infrastructure benefits (Discount rate = 1.23%). (**a**) Barcelona and (**b**) Badalona.

#### *3.3. Net benefits*

Figure 6 shows the discounted (rate of 1.23%) costs and benefits. Note that the y-axes of Barcelona is approximately an order of magnitude higher than the Badalona one. This figure helps visualizing that the ratio between benefits and costs is generally higher in Barcelona compared to Badalona.

**Figure 6.** Discounted (*i* = 1.23%) costs and benefits of green infrastructure. (**a**) Barcelona and (**b**) Badalona.

The evaluation period *T* in this study was selected to be 80 years in both cases. Similar studies performing CBA for climate change adaptation measures in the context of urban drainage planning used 90 years [23]; 50 years [7] and 35 years [4].

Figure 7 shows the discounted marginal benefits during the project evaluation period. Both Barcelona and Badalona and two different discount rates (1.23% and 4%) were applied. Additionally, three different combinations of benefits are included and shown. First, only benefits derived from flood damage reduction are included, then flood together with water quality benefits and finally all benefits from the three categories proposed: flood, water quality and additional benefits. These three different combinations show that including multiple GI benefits significantly affects the results and this is relevant for decision making of urban drainage planning. In the case of Barcelona, the NPV obtained considering only benefits derived from flood damage reduction and a discount rate of 1.23% (Figure 7a) increases by a factor of 1.74 when including flood and water quality benefits and by 2.37 when including all the three benefits categories. Instead, with a discount rate of 4.00% (Figure 7b), the NPV obtained considering only benefits derived from flood damage reduction increases by a factor of 1.95 when including flood and water quality benefits and by 2.76 when including all the three benefits categories. In the case of Badalona, the NPV also increases significantly by including multiple benefits. In this case, factors of increase of NPV are considered misleading because the NPV is mostly negative. The NPV in Badalona becomes positive only at the last five years of the study evaluation period (Figure 7c).

In the two cases analyzed in this study two different discount rates were considered: the 1.23% that was recommended for climate change adaptation projects in the region of Catalonia [37] where the two considered cities are located and the 4% that was used in another CBA of climate change adaptation measures of Barcelona [4]. The discount rate is a controversial topic in economic valuation of policies, in particular in the context of climate change as it involves intergenerational and social valuation issues (Atkinson et al., 2018). In addition CBA results are very sensitive to the discount rate, particularly for projects with a long time horizon, where small changes of discount rate can influence the suggested decisions [38]. High discount rates imply that future economic impacts would have a lower weight compared to today's value, and could lead to an underestimation of future benefits derived from damage reduction measures [39,40]. A CBA of GI for the case study of Melbourne used 1.4% [7] and the range of 1 to 4% for GI Danish case studies of [3,5]. Some literature also proposed a 1% discount rate (Aaheim, 2010; Lopez, 2008; Stern, 2007). Different public institutions propose different discount rates. For instance, in Denmark, the Danish Environmental Protection Agency (EPA) recommended a 3% for environmental projects while the Department of Finance suggested 5% [5]. The US EPA recommended 2–3% while the American office of management and budget proposed 7% [5]. For developing countries the World Bank recommend 10% because of the significant GDP growth [38,41]. The UK Government proposed 3.5% for project evaluation periods of 1–30 years, 3%

for 31–75 years, 2.5% for 76–125 years, 2% for 125–200 years, 1.5% for 201–300 years and 1% for larger periods [42]. Generally, it is recommendable to consider different discount rates in order to quantify favorable and unfavorable scenarios.

**Figure 7.** Accumulated marginal benefits of the proposed green infrastructure including different benefit categories and two different discount rates. (**a**) Barcelona with *i* = 1.23%; (**b**) Barcelona with *i* = 4.00%; (**c**) Badalona with *i* = 1.23%; (**d**) Badalona with *i* = 4.00%.

The cumulative NPV including all benefits in Barcelona becomes positive after 10 years with a discount rate of 1.23% (Figure 7a) and after 11 years with a discount rate of 4.0% (Figure 7b). In Badalona it becomes positive after 75 years with a discount rate of 1.23% (Figure 7c) and it remains negative with a discount rate of 4.0% (Figure 7d). Overall, the GI planning scenario of Barcelona seems to be a better socio-economical option compared to inaction. Instead, the GI planning scenario in Badalona seems to be a worse socio-economical option compared to inaction. Similarly, Zhou et al. [5] presented several stormwater infiltration scenarios that can be considered as GI scenarios showing positive NPV at discount rates of 1% and both positive and negative NPV at discount rates of both 3 and 5%. Zhou et al. [23] presented a negative 50th percentile of the NPV of their stormwater infiltration adaptation scenario. Alves et al. [6] obtained negative NPV for both a green roof and a permeable pavements adaptation scenario and a positive NPV for rainwater harvesting. Zhou et al. [3] reported a positive NPV for their stormwater infiltration scenario.

#### **4. Discussion**

This study presented a CBA to evaluate the socio-economic viability of selected GI applied to two different case studies: Barcelona and Badalona. The results are significantly different among the two cases: Barcelona has higher NPV compared to Badalona. Additionally, the accumulated marginal benefits (Figure 7) of Barcelona are mostly positive and become positive after tens of years compared to Badalona where they are mostly negative during the 80 years project evaluation period. The dominating GI benefits (Figure 4) in Barcelona are from flood damage reduction while in Badalona from additional benefits (mostly aesthetic and habitat provision). Direct comparison between the two case studies is difficult for several reasons: the scale difference (Barcelona is much bigger than Badalona), the current situation (Barcelona has much higher flood damage costs than Badalona), the different approaches used to derive CF and the differences of GI planning (Barcelona has an intensive GI implementation plan while Badalona has a sparse one). The fact of having a sparse implementation plan that was not devised to solve particular urban water problems might result in the lower socio-economic performance of the case of Badalona compared to Barcelona. Further comparison between the results obtained in Badalona and Barcelona is considered out of the scope of this study.

Generally, CBA are sensitive to parameter uncertainty and model assumptions. Therefore, quantifying uncertainty of NPV estimations of climate change adaptation options is relevant and in this study only uncertainty related to discount rate was addressed as also done in other studies [9]. Uncertainty is often quantified by analyzing different present and future climate scenarios [4,5,7] and by analyzing different investment options [3]. Zhou et al. [23], instead of using a scenario approach where variables are changed individually, quantified the NPV uncertainties using a Monte Carlo approach to fully explore the propagation of uncertainty from different models and variables choices to the final NPV. A significant source of uncertainty also comes from the hydrological performance of GI [43–45].

Additionally, in this study the EAD is considered to be overestimated, particularly for the case of Barcelona (Table 2) where EAD seems to be high when compared to flood damage compensations data. From 1996 to 2018, pluvial floods, only in the city of Barcelona, have caused more than EUR 34 million in compensations, for industries, offices, dwellings, vehicles and civil works, according to the classification adopted by the Spanish Insurance Compensation Consortium (CCS). In 2018, damages caused by four heavy rainfalls amounted to around EUR 5.5 million. It was the third most damaging year in terms of insurance indemnifications within the last 22 years. The first two years were 1999 and 2002, which compensations amounted to EUR 7.3 million and EUR 6.5 million respectively. Such values only include compensations that the CCS paid. Therefore, total damages (including also indirect damages) are usually higher. Three main contributions were identified to produce the EAD overestimation:


for the calculation of the area below the curve that corresponds to the EAD. The figure shows that the selected simulated points might not be enough to properly describe the non-linear relation between flood damages and exceedance probability, particularly for the case of Barcelona (Figure 3a) for the range of exceedance probability between 0.1 (10 year return period) and 1 (1 year return period). By introducing new simulation points (for instance at 0.2 exceedance probability) the EAD (the area below the curve) might significantly reduce [4,47].

Even though the EAD is considered overestimated and two main different causes were identified, the EADs for Barcelona were not re-calculated as these values were included in the latest drainage master plan of Barcelona.
