Departmental talk (2020): Bayesian statistics for water engineers: Benefits and limitations
An overview of the historical and axiomatic basis of Bayesian probability, its applications in environmental and hydro sciences, followed by a suitable didactic excercise.
PhD defense (2018): Statistical methods for better hydrologic predictions—Improving parameter and uncertainty estimation
Introduction to hydrometeorological uncertainty, followed by a summary of three research papers related to a) proper treatment of uncertainty, b) reduction of parametric uncertainty using binary observations and c) a more flexible stochastic representation of hydrologic time series.

Blog posts

Water resources management under uncertainty (Feb - 2021)

The big picture: We have time and again come across economic metrics – ballpark estimates – for the enterprise of water management, trying to capture the scale of human engagement with water. For example, the infrastructure, operation, and maintenance costs of water systems around the world are in the range of hundreds of billions of dollars annually. Flooding—be it pluvial, fluvial or coastal—is additionally costing tens of billions of dollars annually in economic damage. Now, with the increasing urban population (projected to be twice the rural population by 2050), shifts in precipitation patterns, and rising sea levels, there is mounting pressure on the current water infrastructure and mounting apprehensions on the adequacy of the conventional water management practices. These problems, in several parts of the world, are exacerbated by under-designed urban-drainage and flood-defense systems, which were built on the premise of a stationary climate. (Here is a link to a figure (2.2) from IPCC’s Fifth Assessment Report showing the projected changes in temperature, precipitation and sea level under two different atmospheric concentrations of the greenhouse gases.) For a resource as important as water, the prospect of entirely re-imagining the design and management paradigm is very tantalizing. But more immediately, there are big technological and policy-based incentives for research that seeks improvements in the efficiency of the current water infrastructure and also enables more adaptive planning for an uncertain future. Over the past few decades, there has been a growing interest in and acknowledgment of the cascading chain of uncertainties, at all different levels, during design and operation-related decision-making. We now hear adjectives like risk-based, robust, adaptive, and even antifragile being proposed as the yardsticks for good decisions. There is an underlying prerequisite to enable such a shift in decision-making paradigms – that is the evaluation of probabilities. Leaving aside the finer details, basically, these new approaches are attempts to hedge the bets in various possible futures when we are making important decisions around our water resources.

Decision making under uncertainty: Mathematical models for water and water infrastructure are used, among other things, as insightful decision support tools for water resources management, water-related risk management, water infrastructure design and operation. You can, for example, be trying to find the design discharge for a river or drainage network with a 25-year return period, the number of combined sewer overflows if precipitation patterns intensify, or simply flood water levels for the issuance of flood warnings. However, hydrometeorological systems are complex— made up of many spatially distributed and temporally variable properties and sub-processes— and, therefore, their models are only approximate. We essentially end up with two broad classes of uncertainty. Inaccurate models/data and deeper forms of uncertainty, for example from population growth, the eventual GHG concentration pathways, the consequent effects on precipitation regimes etc. While scientists have been improving model accuracy, decision-makers can’t wait until the models are perfected to our heart’s content before decisions are made. Models, even the inaccurate ones, then play the role of well-formulated arguments. You have a model that presents the physics of a system, with plausible assumptions - you can then make a convincing case for one design over the other. However, under such circumstances, we would also like to know what happens if your assumptions don’t hold. For such robust decisions, probabilities need to be assigned to the model outputs. Evaluating and dealing with such probabilities can help in optimizing decision-making. Given the risk aversion of a community and the costs we are willing to incur to avoid a certain risk, design and operation choices can be made accordingly. Besides, safety factors in design, which are hard to justify in terms of their adequacy and economy, get replaced by the quantified likelihood of failure. For water-related phenomena that have a frequentist characteristic, e.g. annual flood extremes, the evaluation of correct probabilities will lead to predictable aggregate effects. For the subset of phenomena where probabilities are purely representative of degrees of belief, decisions can be made under consideration of risk tolerance and aversion. For example, building an irrigation or drainage network with a failure probability of p%. as opposed to 2p%. But the decisions will need to be made while keeping in mind all probable eventualities (at least the known unkowns). And as new information comes in, we are also able to update these assigned odds. This language of probabilities makes the bulwark of risk-based decision-making. While, for individual cases, there will be some winners and some losers, nonetheless, for entire communities, cities, and countries, the law of large numbers will hold sway. Having a large number of cases, the hope is that better decisions will be made on average. In other words, the house will always win.

Figures: A linear relationship between annual rainfall and annual discharge in a hypothetical stream or drainage network. The blue dots are observations and the red line is the linear model. The intercept and slope of the line fits the data to a varying degree. In order to account for uncertainty, and avoid big surprises, we use the whole range of possible parameter values to fit the model and make a projection. For example for a question like “what will be the annual discharge be for an annual rainfall of 50 units?” these uncertainties will be important. (a) Model fit with various values of intercept. (b) Model fit with various values of slope. (c) Model fit with 95% confidence intervals (blue shaded) and 95% prediction intervals (dashed lines). (The figure is only intended to serve as a demonstration for confidence and prediction intervals. In reality, error structures are much more complex and harder to formulate than the didactical example.)