Dynamics of extreme risk and resilience for distributed stormwater infrastructure systems
During extreme rainfall events, floodwaters inundate many road networks - disrupting mobility, jeopardizing traffic, and impacting roads’ structural integrity. It is estimated that approximately 75% of flood-related fatalities occur when individuals drive into or attempt to walk through floodwaters. Furthermore, anticipated changes in the loading brought on by climate and land-use change may cause additional capacity deficits in stormwater infrastructure, potentially leading to enormous financial losses. Within this context, the economic impact of culvert failures is significant. For example, the average cost of replacing a culvert in the USA, according to one study, could amount to approximately $800,000, with the highest recorded cost being $4.2 million. Therefore, it is highly desirable to have a unified, uncertainty-aware framework that produces insights into the risk and resilience of the distributed culvert infrastructure - utilizing high-resolution DEM and other readily available geospatial features. Decision makers are additionally interested in knowing how the culvert failure risks change (a) with the location and size of the catchment, i.e., the dynamics of risk in space, and (b) with land use change and shifts in precipitation patterns due to climate change - i.e., dynamics in time. In this project, we aim to propose such a framework and generate corresponding insights for distributed stormwater infrastructures.
Figure: New York State land cover projection. [GIF generated by Omid Emamjomehzadeh.]
Flooding, nonlinear dynamics and Jensen’s inequality
Nonlinear relationships between river discharge and flood inundation complicate effective flood risk assessments. In this study, we characterize the behavior of these nonlinearities. We explore the nature of the expected shifts in mean and variance of inundation due to various kinds of river discharge nonstationarities. Viewing flood inundations through the lens of Jensen’s inequality, we show that the shifts in flood discharge do not result in proportionate shifts in inundation extent. We introduce a Jensen’s Inundation Factor(JIF), which is an aggregate index dependent on the river-reach nonlinearity and the parameters of the discharge distribution. We highlight the implications of Jensen’s inequality by running an operational NOAA OWP HAND flood inundation model across six catchments in the United States. Our results confirm a variety of nonlinear relationships across all basins, with critical discharge thresholds - providing insights that allow for more reliable flood risk estimation. We use these examples as a basis to highlight the need to understand river-reach level nonlinearities for evaluating climate nonstationarities - as global shifts in rainfall will not translate to proportionate shifts in inundation extent.
Figure: Conceptualization of Jensen’s inequality for different discharge-inundation nonlinearities. Preprint: https://doi.org/10.31223/X5M424
Using stochastic differential equations to understand catchment dynamics - for probabilistic, risk-based analysis
For any risk-based decision-making related to the design of water infrastructure or its robust operation, uncertain system responses within built or natural environments need to be reported with representative probabilities. With this overarching goal, in the current research project, I am exploring the benefits of using a suite of stochastic differential equations to model catchment storage (e.g. figure below). This research work aims to inform us about both the dynamics of catchment storage and the dynamics of its parametric and predictive uncertainties.
Figure: Modeling the relationship between catchment storage and rainfall using (a) an ordinary differential equation and (b) a stochastic differential equation. The ordinary differential equation encapsulates our physical understanding of the system (K and β are model parameters). But the ODE does not take into account the uncertainties associated with the storage state, which can be, for examples, modeled using a Wiener process (Wt). Notice that dWt is multiplied to St , making the perturbation dependent on the storage state. The bottom subplot shows 100 realizations from the SDE and the red line is the mean of those realizations.
Figure (above): In a stochastic dynamical system, the evolution of the system states will get represented by changing probabilities. (red - model output: black - observation). Figure (below): The conventional storage-streamflow relationships.
Reliable probabilistic predictions for evolving fluvial geomorphological systems
Streamflow sculpts river and delta geometries—eroding, carrying, and depositing large amounts of sediments on its way from upstream to downstream. The history and fate of such migrating and evolving fluvial systems are of high scientific and technological interest. Moreover, there is an urgency to gauge the influence of global warming on such evolution. This research proposal aims to reliably predict river-driven landscape evolution. In this research project, we propose tailoring the spatially-distributed deterministic river-migration and river-delta models with appropriate stochastic descriptions. This will allow for proper assimilation of observational data into the modelling process. Also, model predictions will then be an evaluation of probabilities, such that all possible future scenarios of the landscape evolution are accounted for, resulting in a substantial gain in terms of model usability to facilitate policy.
Figure: Project schematic.
Adequacy of urban water infrastructure in the USA under climate change
There is growing evidence that climate change poses a risk to urban drainage infrastructure, which is often under-sized, to withstand expected increases in frequency and intensity of extreme rainstorms. However, given the large uncertainties related to climate signals, models, and input data. it is often unclear how infrastructure should be sized to accommodate increases in stormwater runoff due to climate change. The goal of this thesis is to determine the size (volume stored) and cost of a vegetated retention basin that would be needed in 10 U.S. cities to avoid sewer surcharge under climate change. This will be compared to the size and cost of a sewer pipe that would be needed to account for excess flows. Building on existing data and models to update intensity-duration-frequency (IDF) curves under climate change, the first task of this thesis is to use Bayesian inference to predict non-stationary changes in extreme rainfall, accounting for modelling and parameter uncertainty. For the second task, this information, in the form of a “design storm”, will be used along with land use characteristics to estimate the volume of stormwater that would need to be captured over time by the storage basin. Finally, using available cost data, the cost to store this volume will be compared to the cost to upgrade the pipe to receive the equivalent flow.
Figure: GEV-based rainfall return level estimates of 1-h duration. [ Location: Phoenix, USA. RCM data from NA-CORDEX, 2014-2099, RCP 8.5]. [In collaboration with Dr. Lauren Cook (Eawag, CH). Plot by Dawar Qureshi. ]
Bayesian deep learning to probabilistically classify damages using satellite imagery
In cases where image classification/segmentation using conventional computer vision algorithms can be uncertain, we plan to analyze the utility (both pros and cons) of Bayesian schemes in generating probabilistic classification/segmentation of water-body images. (Didactic figure: Pseudocolor Landsat 8 (NASA) and Sentinal 2 (ESA) images of Wax Lake Delta. Generated on SentinelHub.) [In collaboration with German Aerospace Center, DLR).]
