3.1. Deterministic Evaluation
The results displayed in
Table 4 show that the vast majority of the paths result in a negative Net Present Value. Under a changing climate, the ability for a drainage adaptation to deliver benefits expires before it has had sufficient time to offset its costs.
Climatic stationarity allowed for extended periods during which the benefits provided by a flood alleviation scheme could accumulate and deliver a return on the capital investment. However, due to climate change, the design life of infrastructure is shortened. Over these shortened life times, it is difficult for sufficient benefits to be accrued for the capital expenditure to be offset. It may therefore be necessary to rethink infrastructure design in order to maintain historic levels of return on investment. Alternatively, the new reality of climate change may be that flood defence assets will deliver a lower return on investment than in the past. The lack of return on investment is further reflected in the poor benefit to cost ratios. In recent years, a BCR of 8:1 has been applied to flood defense related decision-making in England [
29]. The maximum BCR for the paths considered within this work is equal to only 2.33. This raises questions surrounding how high the expected returns from environmental infrastructure should be under conditions of climate change.
The order in which options are implemented can have a profound impact on the Net Present Value of a path. There were four paths leading to the implementation of the strategy with the highest ATP, these were D, H, L and Q. The BCRs for these paths were 0.53, 0.64,1.18, and 0.48 respectively. The NPVs for these paths were −£2,660,000, −£2,300,000, £1,130,000, and −£2,770,000 respectively. This strategy consists of 50% green roof coverage, deepening the lake by one-meter, and a conversion of 40% of road areas to porous pavements. Even though all four pathways were found to be technically sound, the order in which adaptation options were implemented resulted in radically different NPVs. Of these four paths, only path L consisted of the combination of solutions that resulted in the maximum ATP being reached while also resulting in a favorable BCR and NPV. This path consisted of converting 25% of roofs to green roofs, followed by a 0.5 m deepening of the lake, followed by another 0.5m deepening of the lake, converting 25% of roofs to green roofs, and finally, converting 40% of roads to porous pavements.
Even though all the paths used the same adaptations, there were very large variations in financial performance. This highlights the need to keep path dependence in mind when making decisions under conditions of deep uncertainty. The presented analysis suggests that the choice of paths through a set of Adaptation Pathways could be highly constrained once the financial viability of different strategies is considered.
3.2. Evaluation Under Uncertainty
The financial performance of the potential paths across the 200 futures are displayed in
Table 5.
The Expected Net Present Value and Expected Benefit Cost Ratio are the average financial performance across the 200 futures explored. The respective standard deviations of these performance metrics are also displayed.
Table 6 shows the results from
Table 5 compared to the deterministic assessment developed earlier. The difference columns present the absolute difference between the financial metric derived by deterministic methods and the same metric calculated under uncertainty. Negative values indicate that the metric calculated by deterministic methods over-estimated the metric when compared to the financial metric calculated under uncertainty. To provide further context, the difference between the calculated metrics were normalized by dividing by the standard deviation of the NPV or BCR of that path, giving an indication of the relative distance between the two values.
With regards to the ENPV, 10 out of 18 paths were over-predicted. Once the over and under predictions of NPVs were normalized in relation to their absolute values, it was found that the over and under predictions were of similar magnitudes to one another. The average under prediction was equal to 3.11% of the ENPV, in comparison to 3.12% for over-predictions.
The EBCR resulted in a lower BCR than the one estimated via deterministic methods for nine out of the 18 paths considered. The normalized average over prediction was 2.47%, while the average under prediction was 3.21%.
The standard deviations of both financial performance metrics were small relative to their mean values. As such, for all of the pathways considered, there were no ‘borderline’ cases that could experience failure or success depending upon which scenario was experienced. The relatively small standard deviations of performance would also indicate that the financial performances of the paths are fairly insensitive to the effects of potential futures.
As in the deterministic analysis, the order in which options are implemented can have a profound impact on the Net Present Value of a pathway. There were four pathways that lead to the implementation of the strategy with the highest ATP, these were D, H, L and Q. Even though all four paths were found to be technically sound, the order in which adaptation options were implemented resulted in radically different NPVs.
Figure 5 and
Figure 6 show the empirical cumulative distribution functions for the financial performance of these four paths under uncertainty.
All four of these paths resulted in financial performances that were clearly positive or negative. This would suggest that the effects of uncertainty could not counteract the effect of path dependence, indicating that, for this case study, the order in which adaptations are implemented is paramount, and the effect of precipitation uncertainty is a secondary consideration.
Two hundred simulations of the future were generated and used to assess the financial performance of the pathways. These simulations were developed by sampling from a probability density function estimated by the UK Environment Agency [
13] using a Monte Carlo method. While these 200 storms captured the majority of potential behaviors, several extreme cases exist which were not explored in this analysis. While further exploration of potential futures would allow for better characterization of tail events and a more robust exploration of a project’s ENPV, it is unlikely that these tail risks will impact decision-making. Furthermore, from the low standard deviation of financial performances, it can be observed that the financial performances of the paths exist in a narrow range. This would suggest that the further exploration of potential futures would not notably shift the distribution of the financial performances.
The process of evaluating projects under uncertainty requires the use of probability density functions. However, deep uncertainty denotes an inability to accurately assess the probability of future events occurring. To address this, a broad exploration of futures was utilised. The most extreme increases in storm depth explored are unlikely to occur without large stepwise changes in precipitation patterns occurring. Furthermore, the low standard deviation of the financial metrics calculated would indicate that performance is insensitive to future conditions. While this method does not fully address the issue of quantifying deep uncertainties, the resulting analysis is sufficiently robust to be of value for such conditions
The use of evaluation under uncertainty techniques resulted in more robust economic analysis than the use of deterministic methods. It was shown that the financial performance of paths determined by the deterministic method is not equal to the financial performance of the paths assessed under uncertainty. The average deviation of the deterministic method from the ENPV was equal to 0.96 standard deviations. For the BCR, the average deviation from the EBCR was equal to a distance of 0.8 standard deviations. This implies that Jensen’s inequality is in effect for the problem of urban drainage adaptation. Due to this, it can be assumed that the Expected Net Present Value and Expected Benefit-Cost Ratios estimated from the ensemble of futures deliver a more reliable assessment of financial performance than the assessment of pathways developed with the use of the deterministic projections.