By Jon Herman, UC Davis
Multi-sector infrastructure systems face a number of uncertainties that are difficult to characterize and quantify. These include exogenous uncertainty in climate forcing, propagated through a chain of models and downscaling procedures; endogenous uncertainty in human-environmental system dynamics across scales; and sampling uncertainty due to the finite length of historical observations and future projections. Under these conditions, it is difficult to apply traditional infrastructure planning methods such as cost-benefit analysis and expected value utility theory. Instead, we might adopt a dynamic planning approach in which adaptations are taken over time in response to new information. Yet even an adaptation policy designed in this way is subject to the uncertainty assumptions used to model its performance.
Our recent paper in Water Resources Research reviews this challenge from the standpoint of water infrastructure systems, but with broader implications for coupled multi-sector systems. The dynamic planning problem is framed as a control problem (figure below), while recognizing that the challenge of uncertainty characterization prevents the unambiguous application of control methods to the problem of long-term infrastructure planning. We then provide some perspectives on how this challenge can be approached, drawing from the latest work in the water resources field.
Approaches to characterizing uncertainty
Dynamic planning methods must identify a set of possible scenarios and models (physical or statistical) to quantify uncertainty, either as a probability distribution or an ensemble of realizations. The majority of recent studies in the water resources field have adopted a large ensemble simulation approach, where synthetic scenarios are generated to describe weather and/or streamflow. This has been done in two primary ways: (1) using historical observations to parameterize a stationary stochastic process, which is then perturbed according to projected climate trends; and (2) using climate projections to directly parameterize a nonstationary stochastic process. These synthetically generated scenarios provide an arbitrarily large number of scenarios that are similar to, but not limited by, variability in the observed record. Importantly, all stochastic generation techniques rely on a probability distribution (whether explicit or not), which often requires subjective assumptions for uncertainties that are difficult to quantify.
The three categories of uncertainty (sampling, exogenous, endogenous) are represented differently. Sampling uncertainty is addressed in part with the large ensemble approach. However, it is very difficult to ensure a sufficient sample size to capture the frequency and magnitude of extreme events, which often drive the infrastructure planning process. As we show using an example dataset, flood and drought extremes are projected with the highest uncertainty among other types of change. Studies of exogenous uncertainties benefit from decomposition into contributions from climate models, downscaling approaches and hydrologic models. From the perspective of infrastructure planning studies, we find significant potential to better integrate these process-based insights into the experimental design. Finally, endogenous uncertainty in the human-environmental system may be the most difficult to characterize, because it involves not only the parameters but also the structure of the state transition equations inside the control volume. Long-term infrastructure planning must consider changes in population, land use, and ecosystems that are partly driven by climate but also by unrelated social factors. Whether these can be reliably sampled in the same way as other uncertainties remains an open question.
Policy training, validation, and robustness
Given a characterization of uncertainty, adaptive policies can be designed using one of several control methods, such as stochastic dynamic programming or direct policy search. The adaptations could include irreversible infrastructure investments, or changes to the operating schemes of existing systems. These policies can then be tested on out-of-sample scenarios to ensure their ability to generalize. We distinguish between testing against (1) more realizations sampled from the same uncertainty characterization, versus (2) scenarios in which new uncertain variables are sampled, or the same variables are sampled from new distributions. This is a conceptual distinction between validation and robustness testing, though in practice the computational details are often similar. The choice of which uncertainties to include in the training and testing phase is highly subjective, but this process can help provide context for the training results and suggest improvements in the experimental design based on the relationship of system performance in the validation, optimization, and perfect foresight cases (figure below).
Key points and relevance to Multi-Sector Dynamics
While optimal control methods cannot solve the climate adaptation problem, or any “wicked” public policy problem for that matter, they are still a valuable component in decision support. The purpose of framing long-term infrastructure planning as a control problem is not necessarily to implement the policy directly, but rather to provide decision support by identifying near-term plans that can best prepare the system for the long-term future as new observations and projections become available. In our review we find three key points relevant to the field of water resources systems sciences, though with broader applicability to other types of infrastructure systems:
1. Uncertainty in endogenous system dynamics may equal or exceed that contributed by climate forcing on long planning horizons. Dynamic planning would therefore benefit from an improved understanding of the nonlinear dynamics linking climate, hydrology, and human behavior. This is particularly important in the multi-sector case, where infrastructure systems are coupled across regions and scales. The traditional prescriptive focus of infrastructure planning cannot be separated from the descriptive question of how systems will evolve in the presence or absence of policy interventions.
2. No uncertainty characterization can be proven correct, but can be justified according to the timescale, variable, and time horizon of the problem, potentially with links to physical processes. An optimized adaptation policy implicitly reflects the probabilities of the extreme events it was trained against, whether or not these are defined explicitly or through scenario ensembles. These assumptions can alter the choice of preferred policy alternatives (for a specific example, see Quinn et al. 2020, the subject of a forthcoming MSD blog post.
3. Given that any simulation or projection of the future will not occur exactly, model-based planning should employ sensitivity analyses to identify: (1) the sensitivity of the system to structural and parametric uncertainties throughout the modeling chain, and (2) the sensitivity of an optimized policy to different assumptions regarding the uncertainty characterization.
These points are closely connected to the research challenges currently under investigation by a number of MSD Working Groups, particularly the group on Uncertainty Characterization and Scenario Development led by Dr. Vivek Srikrishnan and Dr. Jon Lamontagne. The challenges described above become substantially more difficult in the multi-sector context, where scale mismatches, heterogeneity, and model complexity are amplified relative to a typical study of regional water infrastructure planning. The MSD Working Groups are aiming to advance our understanding of the co-evolving human and Earth systems through a community of practice; learn more here.
Herman, J. D., Quinn, J. D., Steinschneider, S., Giuliani, M., & Fletcher, S. (2020). Climate adaptation as a control problem: Review and perspectives on dynamic water resources planning under uncertainty. Water Resources Research, 56(2), e24389.
Quinn, J. D., Hadjimichael, A., Reed, P. M., & Steinschneider, S. Can exploratory modeling of water scarcity vulnerabilities and robustness be scenario neutral?. Earth’s Future, e2020EF001650.