Citation:

Mallya, G., A. Gupta, Mohamed M. Hantush, AND R. Govindaraju. Uncertainty quantification in reconstruction of sparse water quality time series: Implications for watershed health and risk-based TMDL assessment. ENVIRONMENTAL MODELLING AND SOFTWARE. Elsevier Science Ltd, New York, NY, 131:104735, (2020). https://doi.org/10.1016/j.envsoft.2020.104735

Impact/Purpose:

Environmental-decision-making often relies on mathematical modeling of the system under consideration (Beven, 2007; Refsgaard et al., 2006). Any mathematical representation of open systems, such as the ones encountered in environmental modeling, has inherent uncertainties due to lack of knowledge, inadequate representation of available knowledge through mathematical equations, erroneous data used for model specification (parameter estimation) and difficult-to-represent local characteristics of the system (Beven, 2007). Probabilistic methods are popularly used for uncertainty quantification (Smith, 2014; Nearing et al., 2016). Ahamadisharaf et al. (2019) reviewed current practices for uncertainty estimation in water-quality (WQ) modeling: It may be noted that quantification of uncertainty due to model-errors is rarely attempted (see Hoque et al., 2012; Hantush and Chaudhary, 2014; Chaudhary and Hantush, 2017; for a few exceptions) despite growing awareness about the importance of uncertainty due to model-error (Gotzinger and Bardossy, 2008; Montanari and Koutsoyiannis, 2012; Brynjsdottir and O’Hagan, 2014). n this study, model-errors refer to the differences between simulated and observed responses. This observed residual sequence is an aggregate of measurement errors, structural errors, and errors in the numerical implementation of the model. Structural errors imply that model is wrong or incomplete in terms of theory, not implementation. The errors in the numerical implementation are expected to be negligible. Therefore, the observed residual sequence is the aggregate of measurement and structural errors. Decision makers frequently rely on analyses that require availability of continuous sequence of water quality (WQ) data to address impaired water bodies. Examples include (a) identification of source areas of pollution in receiving water bodies, and (b) computation of load reduction required to restore a waterbody to healthy conditions given observations of streamflow and WQ parameters. Whereas streamflows are densely (both in space and time) measured hydrologic quantities in a watershed, WQ parameters such as suspended-sediment, nitrogen, and phosphorus concentrations etc. are measured very sparsely and are not amenable for direct use in reliable decision making (Kjeldsen and Rosbjerg, 2004). Therefore, various models have been developed for temporal and spatial reconstruction of WQ data (Runkel et al., 2004); all these models incur uncertainties.

Description:

Despite the plethora of methods available for uncertainty quantification, their use has been limited in the practice of water quality (WQ) modeling. In this paper, a decision support tool (DST) that yields a continuous time series of WQ loads from sparse data using streamflows as predictor variables is presented. The DST estimates uncertainty by analyzing residual errors using a relevance vector machine. To highlight the importance of uncertainty quantification, two applications enabled within the DST are discussed. The DST computes (i) probability distributions of four measures of WQ risk analysis- reliability, resilience, vulnerability, and watershed health- as opposed to single deterministic values and (ii) concentration/load reduction required in a WQ constituent to meet total maximum daily load (TMDL) targets along with the associated risk of failure. Accounting for uncertainty reveals that a deterministic analysis may mislead about the WQ risk and the level of compliance attained with established TMDLs.

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