Quantifications of single- and multiple-stage adaptations
At the early stage of planning a coastal adaptation, option holders can take either single- or multiple-stage adaptation path. This decision affects a way to incorporate flexibility in the considered adaptation option, subsequently leading to change in economy efficiency. After the coastal adaptation is designed, the economy efficiency of the adaptation depends on how to use the flexibility. The efficiency of a single-stage adaptation can be maximised by the optimal investment based on the observation of sea-level rise. On the other hand, the size of an adaptation and the number of stages for the upgrade have effects on the efficiency of the adaptation - which is represented as option value (NPVopt). Table 1 shows the option values of all the adaptation paths including single-stage and multiple-stage adaptations. The sets of option values for coastal adaptations are the maximum values that decision-makers can gain by the current and future decisions. The option evaluation process is explained in Supplement 3. In addition, the optimal investment times and option values for each adaptation are shown by different SLR scenarios and different flexibility premiums in the supplementary document.
Effect of flexibility costs on economy efficiency
For comparisons between the single-stage adaptations and the multiple-stage adaptations, the option values of each adaptation path are plotted across the flexibility premiums under each SLR scenario as shown in Fig. 5.
For the H++ SLR scenario, the adaptation pathway Uc → 4.0m shows the highest option value among all the adaptation pathways. The single-stage adaptation path of Uc → 3.5m has the second-highest option value in a range of flexibility cost from 30 to 50%. The single-stage adaptation paths are more efficient than the multiple-stage adaptation paths in the extreme SLR scenario. The risk of the coastal flooding is very high and sea level is fast-growing at the rate of 2.54cm/year in the H++ SLR scenario so that an interval between the first adaptation and the next adaptation is relatively short (e.g. 30 to 40 years later). Thus, splitting the investment is inefficient in the worst-case SLR scenario. Multiple-stage adaptations including the smallest size of adaptation component (i.e. Uc → 3.0m) are ranked low in the H++ SLR scenario.
On the contrary, the adaptation paths extendable up to 4.0 mAOD show lower performance than the adaptation paths up to 3.0mAOD or 3.5mAOD in the mild SLR scenarios. The adaptation paths including the small size of coastal defence upgrade (i.e. Uc → 3.0m) are considered to be more efficient than those including the large size of coastal defence upgrade (i.e. Uc → 3.5m or Uc → 4.0m) in these cases. As these scenarios are mild comparing to the H++ SLR scenario in the risk of coastal flooding, the high standard of the coastal defence is not yet needed for Lymington. Thus, the single large investment (Uc → 4.0m) shows much lower efficiency, as shown in Fig. 5(c), (d) and (e), than the multiple-stage adaptation paths or the single small investment (i.e. Uc → 3.0m) because the high standard-of-protection coastal defence is considered as an excessive adaptation in such mild SLR scenarios.
c → 3.0m × U3.0m → 3.5m shows the second-highest economy efficiency in managing coastal flood risk under most SLR scenarios except the H++ SLR scenario. In the H++ SLR scenario, Uc → 3.0m × U3.0m → 3.5m is ranked the fourth after Uc → 4.0m, Uc → 3.5m and Uc → 3.5m × U3.5m → 4.0m. If the mild SLR scenarios are expected to realise, only Uc → 3.0m will be made during the twenty-first century. Thus, the further investment will not be made if sea-level rise does not exceed the trigger value 55 cm—beyond which the implementation of U3.0m → 3.5m is optimal (refer to Table 3.4 in Supplement 3). In this regard, Uc → 3.0m × U3.0m → 3.5m is considered to be an efficient and robust strategy against the uncertain conditions of sea-level rise.
For further protection, a set of adaptations that can be raised up to 4.0 mAOD (e.g. Uc → 3.0m × U3.0m → 3.5m × U3.5m → 4.0m, Uc → 3.0m × U3.0m → 4.0m, Uc → 3.5m × U3.5m → 4.0m and Uc → 4.0m) could be taken as adaptation strategies for Lymington. However, these types of adaptations show lower performance than those extendable up to 3.5mAOD under these mild SLR scenarios. Increase in the overall costs for further protection under mild SLR scenarios leads to the inefficiency or redundancy of the overall adaptation. Nevertheless, these adaptations may be more proper to option holders who prefer to address all the range of sea-level rise.
As shown in Fig. 5(a), under the H++ SLR scenario, Uc → 3.5m is relatively a better strategy in the high cost of flexibility (40 to 50%) than the equivalent level of a multiple-stage adaptation (i.e. Uc → 3.0m × U3.0m → 3.5m). It is because the high cost of flexibility increases the overall investment cost of Uc → 3.0m × U3.0m → 3.5m. Thus, flexibility does not lead to an increase in economic efficiency under the high cost of flexibility. With this in mind, flexible coastal defence should be designed to lower the flexibility cost.
Compared in Fig. 5, the single-stage large investment may be the best option in the most extreme SLR scenario (i.e. the H++ SLR scenario). However, these types of options show the lowest performance in other mild SLR scenarios (e.g. high to low SLR scenarios). On the contrary, the single small investment (Uc → 3.0m) which shows the highest performance in the high to low SLR scenarios is the least adaptive to the H++ SLR scenario as it shows the lowest option value in this extreme SLR scenario. Thus, a robust decision against uncertainty is to take a multiple-stage adaptation that can perform relatively well across all the possible future scenarios.
Economy efficiency of different types of adaptations under different SLR scenarios
For an illustrative purpose, changes in option value for all the adaptation paths are visualised across the SLR scenarios in 20% and 50% flexibility premium scenarios (Fig. 6). These curves enable us to understand how to trade-off between efficiency and robustness in choosing an adaptation option under the uncertainty of sea-level rise. The process of option trade-off is detailed by the comparison of option values as below.
As Uc → 3.0m, Uc → 3.5m and Uc → 4.0m are all the single-stage adaptations, there is no flexibility premiums in these types of adaptations. When comparing Uc → 3.5m and Uc → 4.0m, Uc → 3.5m is more efficient than Uc → 4.0m in a range from the Historical SLR scenario to the H1 SLR scenario. On the contrary, in a range between the H1 SLR scenario and the H++ SLR scenario, the option value of Uc → 4.0m significantly increases to be higher than that of Uc → 3.5m. Nevertheless, Uc → 4.0m is less efficient than Uc → 3.5m if sea-level rise in 2100 is under 1.6m. As sea − level rise over 1.6m is physically possible but less likely, Uc → 3.5m would be more likely to be chosen as an efficient adaptation option when making a choice between Uc → 3.5m and Uc → 4.0m.
c → 3.5m is a more efficient option than Uc → 3.5m × U3.5m → 4.0m. Regardless of flexibility costs, Uc → 3.5m gives higher option value across all the SLR scenarios than Uc → 3.5m × U3.5m → 4.0m. Thus, Uc → 3.5m × U3.5m → 4.0m should be rejected in option choice when comparing to Uc → 3.5m.
When the flexibility cost is low (e.g. 20%), Uc → 3.0m × U3.0m → 4.0m and Uc → 3.0m × U3.0m → 3.5m × U3.5m → 4.0m may be better strategies than Uc → 3.5m in the low rates of SLR scenarios. On the contrary, when the flexibility cost is higher than 20%, the economic efficiency of Uc → 3.0m × U3.0m → 4.0m and Uc → 3.0m × U3.0m → 3.5m × U3.5m → 4.0m is less than that of Uc → 3.5m across all the SLR scenarios. The choice of multiple stages of adaptation paths is an efficient decision when the flexibility cost is low. In the opposite cases, Uc → 3.0m × U3.5m → 4.0m and Uc → 3.0m × U3.0m → 3.5m × U3.5m → 4.0m are less useful than Uc → 3.5m because a low standard-of-protection measure (i.e. Uc → 3.0m) in the first stage makes less efficient such high standard-of-protection adaptations (i.e. coastal adaptations up to 4.0mAOD). A low-level coastal defence before a high-level coastal adaptation seems to be less efficient combination in the design of a multiple-stage adaptation.
In terms of Uc → 3.5m and Uc → 3.0m × U3.0m → 3.5m, we can see that Uc → 3.0m × U3.0m → 3.5m is much more efficient than Uc → 3.5m in most of the SLR scenarios. Only in the H++ SLR scenario, Uc → 3.5m is more efficient than Uc → 3.0m × U3.0m → 3.5m because the lifespan of the first stage adaptation is relatively short in the high rate of sea-level rise. As the H++ SLR scenario is a low-probability case, it is less likely that the option value of Uc → 3.5m is higher than that of Uc → 3.0m × U3.0m → 3.5m. Thus, Uc → 3.0m × U3.0m → 3.5m is likely to be a more efficient adaptation strategy than Uc → 3.5m.
As seen in Fig. 6(a) and (b), Uc → 3.0m gives the highest option value between the historical SLR scenario and the high SLR scenario. This adaptation provides protection for Lymington at the lowest cost. However, its option value is the lowest in the worst-case SLR scenario. This also implies that the least costly adaptation is very sensitive to the uncertainty of SLR scenarios. In addition, Uc → 3.0m is a less efficient adaptation than Uc → 3.0m × U3.0m → 3.5m beyond the H1 SLR scenario. This adaptation option seems to be the most vulnerable to the extreme SLR scenario.
Lastly, the option evaluation of Uc → 3.25m × U3.25m → 4.0m is included for comparison to coastal adaptations with different increments (i.e. 0.5m, 0.75m and 1m). In the relatively mild SLR scenarios (i.e. historical trend to high SLR scenarios), single- or multiple-stage adaptations starting with Uc → 3.0m show higher option values than Uc → 3.25m × U3.25m → 4.0m because the low-level coastal defence, when it is set in the first stage, is more efficient than the high-level coastal defence. Likewise, Uc → 3.25m × U3.25m → 4.0m is estimated to be more efficient than Uc → 3.5m × U3.5m → 4.0m in the high to historical SLR scenarios. However, Uc → 3.25m × U3.25m → 4.0m becomes less efficient than Uc → 3.5m × U3.5m → 4.0m if sea-level rise in 2100 is over 0.7m. Uc → 3.25m × U3.25m → 4.0m is estimated to be more efficient than Uc → 4.0m when sea-level rise in 2100 is below 1.5m for 20% flexibility premium. As more severe coastal flooding is expected in the extreme SLR scenario, a high level coastal defence is more effective in defending the coastal areas.
Implications of option evaluations for applications
Compared by option values, in the most extreme SLR scenario, high-level coastal defence upgrade in single stage is better than low-level coastal defence upgrade in many stages, whereas, in the mild SLR scenarios, low-level coastal defence upgrade in many stages is better than high-level coastal defence upgrade in fewer stage. For the given SLR scenarios and coastal defence conditions in Lymington, Uc → 3.0m × U3.0m → 3.5m is considered as the most efficient adaptation to perform relatively well across all the SLR scenarios.
There are some important notions in applications to climate change adaptations. Firstly, the possible range of sea-level rise in the future has an effect on the option choice. If the possible range of sea-level rise was narrow, no change in the ranking of adaptation options might occur. In this case, an adaptation with the highest option value would be chosen within the given range of sea-level rise. For example, if the possible range of sea-level rise in 2100 was between 0.1m and 0.6m (Fig. 6(a)), the optimal option would be a small single-stage adaptation (i.e. Uc − 3.0m). In the other hand, if the possible range was within 0.8m to 1.4m, the two-stage adaptation of Uc − 3.0m × U3.0m − 3.5m would be an optimal choice for protection. Thus, when the option choices are considered under uncertainty, all the adaptations need to be assessed within the uncertainty range of sea-level rise in the future. This provides an important implication as the effort towards narrowing the uncertainty range may be more helpful in the option choice than considering all the possible future states.
As the flexibility premium is a cost, it also changes the option values of the flexible adaptations. Thus, the relative orders of adaptation options in option value differ depending on how the flexibility is included in the adaptation options. The higher the flexibility cost is, the lower the option value is. However, the option values of non-flexible adaptations are constant over the flexibility premiums as they do not include the flexibility. The high flexibility premium leads to narrowing a range within which flexible adaptations are preferable to non-flexible adaptations. By comparing it with the possible range of sea-level rise, an optimal(robust) and flexible adaptation can be chosen among all the adaptations.
Thirdly, this research restricts the application of real option analysis only to physical (irreversible) types of coastal adaptations. If sea-level keeps increasing beyond the certain level, the option values of coastal adaptations start to decrease (as seen in Fig. 6). This is due to the limitation of physical capacity of coastal adaptations against extreme coastal flooding caused by sea-level rise. If such extreme coastal flooding materialize, other types of adaptations should be considered to protect coastal areas. For example, retreat from a flood zone or building new types of coastal defence may be possible adaptations which can be added to the already-made adaptation options.
Fourthly, the option values of multiple-stage adaptations reflect future learning from the future generation. The designing of coastal adaptations at the cost of the flexibility enables the future generation to resolve the uncertainty with more information. Subsequently, the remaining adaptation options provide an opportunity to make a suboptimal decision with the future information, leading to the most use of flexibility in response to the future state. There was a need to explain how to reduce the uncertainty of the future sea-level rise with real option analysis in this research. This will be met by using flexibility included in adaptation options in the future.
The impact curves that represent the relations between climatic variables and flood damages in the case study area were made in experimental setting. The accuracy of the impact curves needs to be improved for the implementation level of the decision. In addition, if the lead time of 4 to 5 years was considered for option evaluations, the investment should occur earlier. The effect of the lead time on the option value is assessed to be quantitatively small and unidirectional for all the adaptation paths when compared to other factors (e.g. sea-level rise, investment costs) because the investment cost is spread over the construction time and the benefit would occur after the construction (4 to 5 years). Generally, the spread costs increase the option value of an adaptation option while the delayed benefits decrease it. The effect of the lead time is excluded in order to simplify the option evaluation. However, this is a very practical issue when we make an investment decision. Thus, a way to find an investment time for a coastal adaptation needs to be investigated in association with a lead time for future research. This study has upgraded the coastal defence height up to 4.0 mAOD in one or two stages. We could further increase the number of stages, if appropriate. Although it provides more flexibility for adaptation pathways, it does not seem to be an efficient option because the overall investment cost may significantly rise due to the flexibility premiums.