• 1) Using stochastic differential equations to understand catchment dynamics

- for probabilistic, risk-based analysis

[Currently working as a postdoctoral researcher at Univ. of California, Berkeley. (Dr. Laurel Larsen's group)]

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 will employ 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. (blue - model output: black - observation). Figure (below): The conventional storage-streamflow relationships.

  • 2) Reliable predictions for evolving deltas: tackling uncertainty in hydromorphological models using satellite and aerial observations

[Research proposal for the SNSF Postodctoral Fellowship approved in May 2020. I am expected to start working at Caltech from June, 2022. (Prof. Michael Lamb's group) ]

Streamflow sculpts river and delta geometries—eroding, carrying, and depositing large amounts of sediments on its way from upstream to downstream. Representing the complex intersection of river hydraulics with coastal morphology, and affecting some of the most populated areas in the world, the history and fate of river deltas are of high scientific and technological interest. Moreover, there is an urgency to gauge the influence of rising sea levels on the future of these deltas. This research proposal aims to reliably predict deltaic evolution. In this research project, I propose tailoring the spatially-distributed deterministic delta evolution 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 deltaic evolution are accounted for, resulting in a substantial gain in terms of model usability to facilitate policy. (Wax Lake Delta as the case study.)

Figure: Project schematic.


  • 3) Is flow control in a space-constrained drainage network effective? A performance assessment for combined sewer overflow reduction

[Worked on this topic and supervised an exchange PhD researcher, Ms. Wenqi Wang, from Nanjing Univ., China. In collaboration with Dr. Joao Leitao. Work recently published in Environmental Research.]

Recurring combined sewer overflows (CSOs) can have a significant impact on the ecological condition of receiving water bodies. There are several structural measures, like adding retention basins and switching to low impact development solutions, that have been proposed to reduce the number of sewage overflows. Besides, several flow control strategies have been discussed in scientific literature that take advantage of the space within urban drainage networks, which is assumed to be adequate, for temporary storage. The adequacy of such storage space, however, is not a universally valid assumption as a large fraction of drainage networks frequently operate close to their design discharge. In this paper, we investigate the efficacy of flow control for a space-constrained drainage network. We employ a low-cost, heuristic real time control strategy with the use of flow control devices (FCDs) and available in-sewer space to reduce the magnitude of CSOs. We consider the long-term performance of the proposed control strategy and discuss the effect of FCD location on CSO reduction. Our results are based on over 300 rainfall-event simulations.

Figure: Graphical abstract.

  • 4) Floodproofing a house: the diversity of the available structural solutions in South Asia

[As a supervisor, I conceptualized the project and am working with Mr. Rahul Dutta (PhD researcher, Univ. of British Columbia, CA), Mr. Solomon Vimal (PhD researcher, Univ. of California, LA), and Mr. Ishan Buxy (masters student, Indian Institute of Technology, Madras, IN). Manuscript in preparation.]

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.)


  • 5) Adequacy of urban water infrastructure in the USA under climate change

[As a cosupervisor, with Dr. Lauren Cook as the main supervisor (Eawag, CH), I am working with 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: Copulas can also be used to model the nonstationary dependence (with proper parameterization) between extreme precipitation and extreme discharge, where each of these variables marginally follows a GEV distribution.

  • 6) Navigating murky waters: optimal representations of uncertainty for risk-based decision-making in water resources management

[I and Mr. Rizwan Ghani conceptualized this proposal for his PhD. Dr. Biswa Bhattacharya has agreed to be the main supervisor (IHE Delft, NL) and we are soon going to apply for funding.]

Project abstract: Mathematical models capturing the dynamics of water quantity and water quality are important tools in designing and managing engineered water systems. These predictions are also used for informed decision-making, to choose between various policy alternatives to avoid further negative impacts. However, given the inherent complexity of water and weather-related processes, deterministic model-based forecasts for various environmental system variables are rarely accurate. In recent decades, some statistical techniques have been introduced to capture such uncertainties in models. The deterministic model estimates, for example, for heavy rainfall events, flood forecasting, groundwater depletion/contamination, etc. are supplemented with probabilities, representing how trustworthy such predictions are. This has become all the more important for highly parameterized, machine learning algorithms. However, explicit quantification of uncertainty related to models has not been readily accepted by practitioners, as it is still unclear how to incorporate it in decision making. Also, the public perception of risk and likelihood is different from that of experts, most of the time public misinterpreting such probabilities. A challenge to risk communication is the difficulty of expressing quantitative risk-related information in a readily comprehensible form. Cognitive limitations cause biases in the human ability to interpret numerical probabilities; particularly small probabilities are especially difficult to interpret. Under some conditions, people overestimate them, and under others, they round down to zero. This PhD aims to: 1) identify optimal representations of uncertainty in water-resources/water-infrastructure modeling results so that they can be conveyed in a simple and efficient manner to the policymakers and the public. 2) using such representations, bridge the gap between objective statistical risk metrics - e.g. likelihood of floods, sewer overflows, droughts, groundwater depletion - and the risk perception generated by such projections in decision-makers as well as the general population 3) make quantitative recommendations for the implementation of such optimal representations to the policymakers 4) to figure out whether the increase in the reliability of the water-resources models is achieved or not.

Figure: A specific modelling example representative of the sources of uncertainty in environmental models. ( Wani, 2018. Adapted from Kavetski, 2018.)


  • 7) Adopting Bayesian deep learning to probabilistically classify water-area using satellite imagery

[In collaboration with Dr. Candace Chow as the principal researcher (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.)