Developments in Informal Multi-Criteria Calibration and Uncertainty Estimation in Hydrological Modelling

Hydrologic modelling has benefited from significant developments over the past two decades, which has led to the development of distributed hydrologic models. Parameter adjustment, or model calibration, is extremely important in the application of these hydrologic models. Multi-criteria calibration schemes and several formal and informal predictive uncertainty estimation methodologies are among the approaches to improve the results of model calibration. Moreover, literature indicates a general agreement between formal and informal approaches with respect to the predictive uncertainty estimation in single-criterion calibration cases. This research extends the comparison between these techniques to multi-criteria calibration cases, and furthermore, proposes new ideas to improve informal multi-criteria calibration and uncertainty estimation in hydrological modelling. GLUE is selected as a candidate informal methodology due to its extreme popularity among hydrological modellers, i.e., based on the number of applications in the past two decades. However, it is hypothesized that improvements can be applied to other certain types of informal uncertainty estimation as well. The first contribution of this research is an in-depth comparison between GLUE and Bayesian inference in the multi-criteria context. Such a comparison is novel because past literature has focused on comparisons for only single criterion calibration studies. Unlike the previous research, the results show that there can be considerable differences in hydrograph prediction intervals generated by traditional GLUE and Bayesian inference in multi-criteria cases. Bayesian inference performs more satisfactorily than GLUE along most of the comparative measures. However, results also reveal that a standard Bayesian formulation (i.e., aggregating all uncertainties into a single additive error term) may not demonstrate perfect reliability in the prediction mode. Furthermore, in cases with a limited computational budget, non-converged MCMC sampling proves to be an appropriate alternative to GLUE since it is reasonably consistent with a fully-converged Bayesian approach, even though the fully-converged MCMC requires a substantially larger number of model evaluations. Another contribution of this research is to improve the uncertainty bounds of the traditional GLUE approach by the exploration of alternative behavioural solution identification strategies. Multiple behavioural solution identification strategies from the literature are evaluated, new objective strategies are developed, and multi-criteria decision-making concepts are utilized to select the best strategy. The results indicate that the subjectivity involved in behavioural solution identification strategies impacts the uncertainty of model outcome. More importantly, a robust implementation of GLUE proves to require comparing multiple behavioural solution identification strategies and choosing the best one based on the modeller’s priorities. Moreover, it appears that the proposed objective strategies are among the best options in most of the case studies investigated in this research. Thus, it is recommended that these new strategies be considered among the set of behavioural solution identification strategies in future GLUE applications. Lastly, this research also develops a full optimization-based calibration framework that is capable of utilizing both standard goodness-of-fit measures and many hydrological signatures simultaneously. These signatures can improve the calibration results by constraining the model outcome hydrologically. However, the literature shows that to simultaneously apply a large number of hydrological signatures in model calibration is challenging. Therefore, the proposed research adopts optimization concepts to accommodate many criteria (including 13 hydrologic signature-based objectives and two standard statistical goodness-of-fit measures). In the proposed framework, hydrological consistency is quantified (based on a set of signature-based measures and their desired level of acceptability) and utilized as a criterion in multiple calibration formulations. The results show that these formulations perform better than the traditional approaches to locate hydrologically consistent parameter sets in the search space. Different hydrologic models, most of which are conceptual rainfall-runoff models, are used throughout the thesis to evaluate the performance of the developed strategies. However, the developments explored in this research are typically simulation-model-independent and can be applied to calibration and uncertainty estimation of any environmental model. However, further testing of these methods is warranted for more computationally intensive simulation models, such as fully distributed hydrologic models

Improving the efficiency of Monte Carlo Bayesian calibration of hydrologic models via model pre-emption

Final published version available at: Shafii, M., Tolson, B., & Shawn Matott, L. (2015). Improving the efficiency of Monte Carlo Bayesian calibration of hydrologic models via model pre-emption. Journal of Hydroinformatics, 17(5), 763–770. https://doi.org/10.2166/hydro.2015.043Bayesian inference via Markov Chain Monte Carlo (MCMC) sampling and sequential Monte Carlo (SMC) sampling are popular methods for uncertainty analysis in hydrological modelling. However, application of these methodologies can incur significant computational costs. This study investigated using model pre-emption for improving the computational efficiency of MCMC and SMC samplers in the context of hydrological modelling. The proposed pre-emption strategy facilitates early termination of low-likelihood simulations and results in reduction of unnecessary simulation time steps. The proposed approach is incorporated into two samplers and applied to the calibration of three rainfall-runoff models. Results show that overall pre-emption savings range from 5 to 21%. Furthermore, results indicate that pre-emption savings are greatest during the pre-convergence 'burn-in' period (i.e., between 8 and 39%) and decrease as the algorithms converge towards high likelihood regions of parameter space. The observed savings are achieved with absolutely no change in the posterior set of parameters.Bryan Tolson's NSERC Discovery Gran

Uncertainty-based multi-criteria calibration of rainfall-runoff models: a comparative study

The final publication is available at Springer via http://dx.doi.org/10.1007/s00477-014-0855-xThis study compares formal Bayesian inference to the informal generalized likelihood uncertainty estimation (GLUE) approach for uncertainty-based calibration of rainfall-runoff models in a multi-criteria context. Bayesian inference is accomplished through Markov Chain Monte Carlo (MCMC) sampling based on an auto-regressive multi-criteria likelihood formulation. Non-converged MCMC sampling is also considered as an alternative method. These methods are compared along multiple comparative measures calculated over the calibration and validation periods of two case studies. Results demonstrate that there can be considerable differences in hydrograph prediction intervals generated by formal and informal strategies for uncertainty-based multi-criteria calibration. Also, the formal approach generates definitely preferable validation period results compared to GLUE (i.e., tighter prediction intervals that show higher reliability) considering identical computational budgets. Moreover, non-converged MCMC (based on the standard Gelman-Rubin metric) performance is reasonably consistent with those given by a formal and fully-converged Bayesian approach even though fully-converged results requires significantly larger number of samples (model evaluations) for the two case studies. Therefore, research to define alternative and more practical convergence criteria for MCMC applications to computationally intensive hydrologic models may be warranted.NSERC Discovery Gran

A priori discretization error metrics for distributed hydrologic modeling applications

The final publication is available at Elsevier via http://dx.doi.org/10.1016/j.jhydrol.2016.11.008 © 2016. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/Watershed spatial discretization is an important step in developing a distributed hydrologic model. A key difficulty in the spatial discretization process is maintaining a balance between the aggregation-induced information loss and the increase in computational burden caused by the inclusion of additional computational units. Objective identification of an appropriate discretization scheme still remains a challenge, in part because of the lack of quantitative measures for assessing discretization quality, particularly prior to simulation. This study proposes a priori discretization error metrics to quantify the information loss of any candidate discretization scheme without having to run and calibrate a hydrologic model. These error metrics are applicable to multi-variable and multi-site discretization evaluation and provide directly interpretable information to the hydrologic modeler about discretization quality. The first metric, a sub basin error metric, quantifies the routing information loss from discretization, and the second, a hydrological response unit (HRU) error metric, improves upon existing a priori metrics by quantifying the information loss due to changes in land cover or soil type property aggregation. The metrics are straightforward to understand and easy to recode. Informed by the error metrics, a two-step discretization decision-making approach is proposed with the advantage of reducing extreme errors and meeting the user-specified discretization error targets. The metrics and decision-making approach are applied to the discretization of the Grand River watershed in Ontario, Canada. Results show that information loss increases as discretization gets coarser. Moreover, results help to explain the modeling difficulties associated with smaller upstream subbasins since the worst discretization errors and highest error variability appear in smaller upstream areas instead of larger downstream drainage areas. Hydrologic modeling experiments under candidate discretization schemes validate the strong correlation between the proposed discretization error metrics and hydrologic simulation responses. Discretization decision-making results show that the common and convenient approach of making uniform discretization decisions across the watershed performs worse than the proposed non-uniform discretization approach in terms of preserving spatial heterogeneity under the same computational cost.NSERC Canadian FloodNet gran

A diagnostic approach to constraining flow partitioning in hydrologic models using a multiobjective optimization framework

© American Geophysical Union: Shafii, M., Basu, N., Craig, J. R., Schiff, S. L., & Van Cappellen, P. (2017). A diagnostic approach to constraining flow partitioning in hydrologic models using a multiobjective optimization framework. Water Resources Research, 53(4), 3279–3301. https://doi.org/10.1002/2016WR019736Hydrologic models are often tasked with replicating historical hydrographs but may do so without accurately reproducing the internal hydrological functioning of the watershed, including the flow partitioning, which is critical for predicting solute movement through the catchment. Here we propose a novel partitioning-focused calibration technique that utilizes flow-partitioning coefficients developed based on the pioneering work of L'vovich (1979). Our hypothesis is that inclusion of the L'vovich partitioning relations in calibration increases model consistency and parameter identifiability and leads to superior model performance with respect to flow partitioning than using traditional hydrological signatures (e.g., flow duration curve indices) alone. The L'vovich approach partitions the annual precipitation into four components (quick flow, soil wetting, slow flow, and evapotranspiration) and has been shown to work across a range of climatic and landscape settings. A new diagnostic multicriteria model calibration methodology is proposed that first quantifies four calibration measures for watershed functions based on the L'vovich theory, and then utilizes them as calibration criteria. The proposed approach is compared with a traditional hydrologic signature-based calibration for two conceptual bucket models. Results reveal that the proposed approach not only improves flow partitioning in the model compared to signature-based calibration but is also capable of diagnosing flow-partitioning inaccuracy and suggesting relevant model improvements. Furthermore, the proposed partitioning-based calibration approach is shown to increase parameter identifiability. This model calibration approach can be readily applied to other models. Plain Language Summary Hydrologic models are often tasked with replicating historical hydrographs but may do so without accurately reproducing the internal hydrological functioning of the watershed, including the flow partitioning between low and high flows, which is critical for predicting solute movement through the catchment. Here we propose a novel model calibration framework that utilizes an empirical understanding about flow partitioning developed by L'vovich (1979) to constrain the outcomes of watershed models. Our hypothesis is that this approach increases model consistency leads to superior model performance. This method is also capable of diagnosing model structural errors (in flow partitioning) and suggesting relevant model improvements. Overall, this work is a step toward getting the right answer from hydrologic model for the right reasons.NSERC Strategic Partnership grant [STPGP-447692-2013]Canada Excellence Research Chair in Ecohydrology in the Department of Earth and Environmental Sciences at University of Waterlo

Salinization enhances eutrophication symptoms in a cold temperate urban lake

We thank the City of Richmond Hill for providing the data. Nina Sattolo helped with the PCA analysis; other undergraduate student assistants in the Ecohydrology Research Group helped with assembling the data set. We thank Bhaleka Persaud for help with publishing and managing data. The constructive comments of two journal reviewers improved the clarity of our manuscript.Salinization of inland freshwaters is observed around the world, but particularly in cold temperate regions due to the runoff of salt applied on roads as de-icing agents during the winter. This is the case for Lake Wilcox, a shallow kettle lake located within the greater Toronto metropolitan area in Ontario, Canada. Since the early 1900s, the lake’s watershed has experienced major land use change, including urban growth. Expanding urban imperviousness has been accompanied by noticeable water quality deterioration, including water column dissolved oxygen (DO) depletion and increases in seasonal chlorophyll concentrations and algal blooms. We analyzed 23 years (1996–2018) of water chemistry, land use, and climate data using principal component analysis (PCA) and multiple linear regression (MLR). Dimensionality reduction of the entire water quality dataset yielded four principal components (PCs) that could explain 76% of the data variability of the concentrations of DO, and phosphorus (P) and nitrogen (N) species. The MLR results revealed that the intensity of stratification, quantified by the Brunt-Väisälä frequency, as well as watershed imperviousness and lake chloride concentrations were the most important predictors of the water quality changes represented by the four PCs. We conclude that the observed in-lake water quality trends over the past two decades are linked to urbanization via increased salinization associated with expanding impervious land cover, rather than increasing external P loading to the lake. The rising salinity strengthens water column stratification, hence, reducing the oxygenation of the hypolimnion that, in turn enhances the recycling of P from the bottom sediments to the water column (i.e., internal P loading). Thus, stricter controls on the application and runoff of de-icing salts should be considered as part of managing lake eutrophication in cold climate regions.This work was supported in part by the Managing Urban Eutrophication Risks under Climate Change project under the Global Water Futures (GWF) program funded by the Canada First Research Excellence Fund (CFREF), and also by funding from the Natural Sciences and Engineering Research Council of Canada (NSERC) Strategic Partnership Grant (STPGP 521515-18)

Quantitative insights into phosphorus loadings and speciation in urban catchments

Phosphorus (P) loadings in stormwater runoff drained from urban landscapes causes eutrophication in aquatic ecosystems downstream of urban areas. Many recent research have addressed urban P dynamics to improve understanding about magnitudes and speciation of P in urban watersheds. We quantified P export and forms in four research sites including three urban sewersheds and a stormwater pond, all located within the drainage basin of Lake Ontario. P speciation laboratory analyses were conducted on water and sediment samples taken from our sites to measure a suite of P species, including total P (TP), total dissolved P (TDP), dissolved reactive P (DRP), dissolved unreactive P (DUP), particulate P (PP), and particulate reactive P (PRP). Using multiple linear regression (MLR) models, we quantified annual loadings of these P species, which appeared to be close to the lower limit of ranges reported in the literature. Average loadings among urban catchments were 0.54 kg ha-1 yr-1 for TP, 0.064 kg ha-1 yr-1 for TDP, 0.007 and 0.045 kg ha-1 yr-1 for DRP and DUP, 0.46 kg ha-1 yr-1 for PP, and 0.16 kg ha-1 yr-1 for PRP. Results indicated that larger catchment-scale loadings of reactive P species (DRP and PRP) were exported as residential development increased. We also found that the pond retained all P species significantly (77-94%), which, according to mass balance and sequential P extraction analyses, was attributed to both sedimentation and chemical precipitation of P with calcium mineral phases. Findings in our study imply that, due to loadings’ variability imposed by land-use characteristics, urban P management options need to vary from a catchment to another. Furthermore, enhancing the formation of calcium phosphate and other redox-stable mineral phases could be explored as a best management practice in existing and new ponds for improving P retention.This research was undertaken thanks, in part, with support from the Global Water Futures Program funded by the Canada First Research Excellence Fund (CFREF)

URBAN PHOSPHORUS SPECIATION AND EXPORT LOADS: A PAIRED SEWERSHED FIELD AND MODELING STUDY

In this study, annual and seasonal loads of phosphorus (P) exported from two neighbouring urban sewersheds (AJE and AJW) discharging into Lake Ontario were estimated. The following different chemical pools of P were considered: total P (TP), particulate P (PP), and dissolved P (DP), that in turn were divided in their respective reactive (R) and unreactive (U) fractions. The AJW sewershed is more residential while AJE is dominated by commercial and industrial land cover. A load-flow regression model coupled to the Stormwater Management Model (PCSWMM) was calibrated against measured flow and P speciation data and used to derive seasonal export concentrations (ECs) for the two sewersheds. The annual P loads from the sewersheds were significantly different (AJE: 0.61±0.05 kg/ha/year; AJW: 0.39±0.07 kg/ha/year). Relative to AJE, the TP loads from the more vegetated AJW were enriched in both total DP (TDP) and reactive DP (DRP). Overall, the TP loads were dominated by PP (83-91% of TP), with slightly higher PP contributions for AJE. Our chemical extraction results further simplied that close to half (38-47%) of the PP loads were comprised of reactive P forms. The large contribution of PRP to the TP loads indicates that DRP alone may not provide a reliable measure of the potentially bioavailable P exported from urban areas to downstream aquatic environments.This research was undertaken thanks, in part, with support from the Global Water Futures Program funded by the Canada First Research Excellence Fund (CFREF)

Optimizing hydrological consistency by incorporating hydrological signatures into model calibration objectives

© American Geophysical Union: Shafii, M., & Tolson, B. A. (2015). Optimizing hydrological consistency by incorporating hydrological signatures into model calibration objectives. Water Resources Research, 51(5), 3796–3814. https://doi.org/10.1002/2014WR016520The simulated outcome of a calibrated hydrologic model should be hydrologically consistent with the measured response data. Hydrologic modelers typically calibrate models to optimize residual-based goodness-of-fit measures, e.g., the Nash-Sutcliffe efficiency measure, and then evaluate the obtained results with respect to hydrological signatures, e.g., the flow duration curve indices. The literature indicates that the consideration of a large number of hydrologic signatures has not been addressed in a full multiobjective optimization context. This research develops a model calibration methodology to achieve hydrological consistency using goodness-of-fit measures, many hydrological signatures, as well as a level of acceptability for each signature. The proposed framework relies on a scoring method that transforms any hydrological signature to a calibration objective. These scores are used to develop the hydrological consistency metric, which is maximized to obtain hydrologically consistent parameter sets during calibration. This consistency metric is implemented in different signature-based calibration formulations that adapt the sampling according to hydrologic signature values. These formulations are compared with the traditional formulations found in the literature for seven case studies. The results reveal that Pareto dominance-based multiobjective optimization yields the highest level of consistency among all formulations. Furthermore, it is found that the choice of optimization algorithms does not affect the findings of this research.NSERCDepartment of Civil and Environmental Engineering at University of Waterlo

Salinization increases eutrophication symptoms in freshwater urban lakes of North America

The acceleration of global urbanization continues to fuel concerns surrounding water quality impairments in urban lakes, particularly their eutrophication. Eutrophication of freshwater environments is generally assumed to be driven by the anthropogenic augmentation of phosphorus (P) supplies which can alleviate limitations on primary production. Salinization is also recognized as a stressor on urban freshwater quality, particularly in cold climate regions in which salts are applied to road surfaces as de-icing agents. While the ecological damages caused by P enrichment and salinization to freshwaters are both well established, thus far, their impacts on water quality have only been considered independently. Although improvements to the management of urban stormwater and wastewater have decreased P inputs to freshwater systems in recent decades, many lakes worldwide remain eutrophic, as indicated by declining dissolved oxygen (DO) concentrations and rising dissolved inorganic P (DIP) concentrations in their hypolimnions. Here we present an analysis of multiple decades of water chemistry data for several urban lakes in North America (Ontario, Wisconsin, and Minnesota) to demonstrate that salinization associated with impervious land cover expansion is driving increases to anoxia and the prevalence of internal P loading, exacerbating eutrophication. Our trend analysis shows progressive salinization (observed through significant increases in chloride or electrical conductivity) of all the lakes investigated, which strengthens their thermal stratification (calculated using the Brunt-Väisälä frequency). The increasing salinity trends are accompanied by increasing hypolimnion hypoxia and increasing DIP:TP in all lakes, thereby demonstrating the mechanistic link between salinization and eutrophication. Rising salinity intensifies water column stratification, in turn, reducing the oxygenation of the hypolimnion and enhancing internal P loading from the sediments. These results highlight that stricter management of de-icing salt application rates should be considered to control lake eutrophication symptoms in cold climate regions.Financial support was provided by a Natural Science and Engineering Research Council of Canada (NSERC) Strategic Partnerships Grant (STPGP 521515-18), and the Lake Futures project and Managing Urban Eutrophication Risks under Climate Change project within the Global Water Futures (GWF) program funded by the Canada First Research Excellence Fund (CFREF)