Enhancing long short-term memory (LSTM)-based streamflow prediction with a spatially distributed approach

Deep learning (DL) algorithms have previously demonstrated their effectiveness in streamflow prediction. However, in hydrological time series modelling, the performance of existing DL methods is often bound by limited spatial information, as these data-driven models are typically trained with lumped (spatially aggregated) input data. In this study, we propose a hybrid approach, namely the Spatially Recursive (SR) model, that integrates a lumped long short-term memory (LSTM) network seamlessly with a physics-based hydrological routing simulation for enhanced streamflow prediction. The lumped LSTM was trained on the basin-averaged meteorological and hydrological variables derived from 141 gauged basins located in the Great Lakes region of North America. The SR model involves applying the trained LSTM at the subbasin scale for local streamflow predictions which are then translated to the basin outlet by the hydrological routing model. We evaluated the efficacy of the SR model with respect to predicting streamflow at 224 gauged stations across the Great Lakes region and compared its performance to that of the standalone lumped LSTM model. The results indicate that the SR model achieved performance levels on par with the lumped LSTM in basins used for training the LSTM. Additionally, the SR model was able to predict streamflow more accurately on large basins (e.g., drainage area greater than 2000 km2), underscoring the substantial information loss associated with basin-wise feature aggregation. Furthermore, the SR model outperformed the lumped LSTM when applied to basins that were not part of the LSTM training (i.e., pseudo-ungauged basins). The implication of this study is that the lumped LSTM predictions, especially in large basins and ungauged basins, can be reliably improved by considering spatial heterogeneity at finer resolution via the SR model.</p

Event-based model calibration approaches for selecting representative distributed parameters in semi-urban watersheds

The final publication is available at Elsevier via http://dx.doi.org/10.1016/j.advwatres.2018.05.013 © 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/The objective of this study is to propose an event-based calibration approach for selecting representative semi-distributed hydrologic model parameters and to enhance peak flow prediction at multiple sites of a semi-urban catchment. The performance of three multi-site calibration approaches (multi-site simultaneous (MS-S), multi-site average objective function (MS-A) and multi-event multi-site (ME-MS)) and a benchmark at-catchment outlet (OU) calibration method, are compared in this study. Additional insightful contributions include assessing the nature of the spatio-temporal parameter variability among calibration events and developing an advanced event-based calibration approach to identify skillful model parameter-sets. This study used a SWMM5 hydrologic model in the Humber River Watershed located in Southern Ontario, Canada. For MS-S and OU calibration methods, the multi-objective calibration formulation is solved with the Pareto Archived Dynamically Dimensioned Search (PA-DDS) algorithm. For the MS-A and ME-MS methods, the single objective calibration formulation is solved with the Dynamically Dimensioned Search (DDS) algorithm. The results indicate that the MS-A calibration approach achieved better performance than other considered methods. Comparison between optimized model parameter sets showed that the DDS optimization in MS-A approach improved the model performance at multiple sites. The spatial and temporal variability analysis indicates a presence of uncertainty on sensitive parameters and most importantly on peak flow responses in an event-based calibration process. This finding implied the need to evaluate potential model parameters sets with a series of calibration steps as proposed herein. The proposed calibration and optimization formulation successfully identified representative model parameter set, which is more skillful than what is attainable when using simultaneous multi-site (MS-S), multi-event multi-site (MS-ME) or at basin outlet (OU) approach.Natural Sciences and Engineering Research Council of Canada [NETGP 451456

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

The pie sharing problem: Unbiased sampling of N+1 summative weights

A simple algorithm is provided for randomly sampling a set of N+1 weights such that their sum is constrained to be equal to one, analogous to randomly subdividing a pie into N+1 slices where the probability distribution of slice volumes are identically distributed. The cumulative density and probability density functions of the random weights are provided. The algorithmic implementation for the random number sampling are made available. This algorithm has potential applications in calibration, uncertainty analysis, and sensitivity analysis of environmental models. Three example applications are provided to demonstrate the efficiency and superiority of the proposed method compared to alternative sampling methods.Global Water Futures Project || Integrated Modeling Program for Canada

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

Hydrologic parameter sensitivity across a large-domain

Canada First Research Excellence FundNon-Peer ReviewedDue to the computational demands of modelling large domains, model calibration of Land Surface Models (LSMs) typically involves adjustment of only a small subset of parameters. • Majority of parameters that can potentially contribute to the model output variance remain fixed/ hard coded. • Spatial variability of the parameter sensitivity over large domains with heterogenous climatic and physiographic conditions is largely ignored during the calibration process. This work, carried out for parts of the Fraser and Columbia river basins, explored how parameter sensitivity varies spatially with the dominant physical and climatic conditions, and how dominant model parameters change depending on the simulated hydrologic process. The study found that parameter sensitivity varies both geographically and with the process being simulated

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

Efficient treatment of climate data uncertainty in ensemble Kalman filter (EnKF) based on an existing historical climate ensemble dataset

The final publication is available at Elsevier via https://doi.org/10.1016/j.jhydrol.2018.11.047. © 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/Successful data assimilation depends on the accurate estimation of forcing data uncertainty. Forcing data uncertainty is typically estimated based on statistical error models. In practice, the hyper-parameters of statistical error models are often estimated by a trial-and-error tuning process, requiring significant analyst and computational time. To improve the efficiency of forcing data uncertainty estimation, this study proposes the direct use of existing ensemble climate products to represent climate data uncertainty in the ensemble Kalman filter (EnKF) of flow forecasting. Specifically, the Newman et al. (2015) dataset (N15 for short), covering the contiguous United States, northern Mexico, and southern Canada, is used here to generate the precipitation and temperature ensemble in the EnKF application. This study for the first time compares the N15 generated climate ensemble with the carefully tuned hyper-parameters generated climate ensemble in a real flow forecasting framework. The forecast performance comparison of 20 Québec catchments shows that the N15 generated climate ensemble yields improved or similar deterministic and probabilistic flow forecasts relative to the carefully tuned hyper-parameters generated climate ensemble. Improvements are most evident for short lead times (i.e., 1–3 days) when the influence of data assimilation dominates. However, the analysis and computational time required to use N15 is much less compared to the typical trial-and-error hyper-parameter tuning process.Natural Sciences and Engineering Research Council [NETGP 451456

Great Lakes Runoff Intercomparison Project Phase 3: Lake Erie (GRIP-E)

Hydrologic model intercomparison studies help to evaluate the agility of models to simulate variables such as streamflow, evaporation, and soil moisture. This study is the third in a sequence of the Great Lakes Runoff Intercomparison Projects. The densely populated Lake Erie watershed studied here is an important international lake that has experienced recent flooding and shoreline erosion alongside excessive nutrient loads that have contributed to lake eutrophication. Understanding the sources and pathways of flows is critical to solve the complex issues facing this watershed. Seventeen hydrologic and land-surface models of different complexity are set up over this domain using the same meteorological forcings, and their simulated streamflows at 46 calibration and seven independent validation stations are compared. Results show that: (1) the good performance of Machine Learning models during calibration decreases significantly in validation due to the limited amount of training data; (2) models calibrated at individual stations perform equally well in validation; and (3) most distributed models calibrated over the entire domain have problems in simulating urban areas but outperform the other models in validation

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