- 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). To test the performance of these equations, I am employing a recently-compiled multivariate hydrologic time series dataset by our lab, of various input and response variables, taken from 30 different watersheds spread across the Contiguous US. This research work is aimed 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.

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, I 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.


[With Mr. Rahul Dutta, Mr. Solomon Vimal, & Mr. Ishan Buxy.]

This manuscript documents and reviews the most critical factors—technological, commercial and economic—affecting the feasibility and choice of flood proofing solutions adoptable by individual households in the flood-prone South Asia. With the changing climate and rapid urbanization, extreme weather events and the associated losses are going to increase in the already vulnerable South Asia.  To this end, we are reviewing the available academic literature and commercial documents on flood mitigation and compile the most frequently employed structural solutions for flood-proofing residential houses, small businesses, and similar privately-owned infrastructure. Preparation, procurement and territorial equipment required for the adoption of a floodproofing technique is being discussed. Also, we are formulating a critical commentary on the durability, resilience and maintenance of commercially available options. This paper reviews and compiles the state-of-the-art in terms of structural flood mitigation at household level, and the presented comparative analysis will facilitate their appropriate adoption.

Figure: Schematic representing household flood risk. (With some typical structural flood barriers  on the left.)

[I and Dr. Lauren Cook (Eawag, CH) are supervising Mr. Dawar Qureshi on this research project. ]

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 Victor Herl, Dr. Candace Chow, Dr. Marc Wieland, & Dr. Sandro Martinis. 

(German Aerospace Center, DLR).]

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 Lansat 8 (NASA) and Sentinal 2 (ESA) images of Wax Lake Delta. Generated on SentinelHub.)