A formal likelihood function for parameter and predictive inference of hydrologic models with correlated, heteroscedastic, and non?Gaussian errors

Estimation of parameter and predictive uncertainty of hydrologic models has traditionally relied on several simplifying assumptions. Residual errors are often assumed to be independent and to be adequately described by a Gaussian probability distribution with a mean of zero and a constant variance. Here we investigate to what extent estimates of parameter and predictive uncertainty are affected when these assumptions are relaxed. A formal generalized likelihood function is presented, which extends the applicability of previously used likelihood functions to situations where residual errors are correlated, heteroscedastic, and non?Gaussian with varying degrees of kurtosis and skewness. The approach focuses on a correct statistical description of the data and the total model residuals, without separating out various error sources. Application to Bayesian uncertainty analysis of a conceptual rainfall?runoff model simultaneously identifies the hydrologic model parameters and the appropriate statistical distribution of the residual errors. When applied to daily rainfall?runoff data from a humid basin we find that (1) residual errors are much better described by a heteroscedastic, first?order, auto?correlated error model with a Laplacian distribution function characterized by heavier tails than a Gaussian distribution; and (2) compared to a standard least?squares approach, proper representation of the statistical distribution of residual errors yields tighter predictive uncertainty bands and different parameter uncertainty estimates that are less sensitive to the particular time period used for inference. Application to daily rainfall?runoff data from a semiarid basin with more significant residual errors and systematic underprediction of peak flows shows that (1) multiplicative bias factors can be used to compensate for some of the largest errors and (2) a skewed error distribution yields improved estimates of predictive uncertainty in this semiarid basin with near?zero flows. We conclude that the presented methodology provides improved estimates of parameter and total prediction uncertainty and should be useful for handling complex residual errors in other hydrologic regression models as well.Water ManagementCivil Engineering and Geoscience

Simulation–optimization modeling for sustainable conjunctive water management in irrigated agriculture: WEAP-MODFLOW application in the Miyandoab plain, Urmia basin, Iran

Water Resource

A WEAP-MODFLOW surface water-groundwater model for the irrigated Miyandoab plain, Urmia lake basin, Iran: Multi-objective calibration and quantification of historical drought impacts

This study develops and applies the first coupled surface water-groundwater (SW-GW) flow model for the irrigated Miyandoab plain located in the Urmia basin, in the northwest of Iran. The model is implemented using a dynamic coupling between MODFLOW and WEAP and consists of spatially distributed monthly water balances for the aquifer, root-zone, rivers, canals, and reservoirs. Multi-objective calibration of the model using river discharge and GW level data yields accurate simulation of historical conditions, and results in better constrained parameters compared to using either data source alone. Model simulations show that crop water demand cannot be met during droughts due to limited GW pumping capacity, and that increased GW pumping has a relatively strong impact on GW levels due to the small specific yield of the aquifer. The SW-GW model provides a unique tool for exploring management options that sustain agricultural production and downstream flow to the shrinking Urmia Lake.Accepted author manuscriptWater Resource

Population and climate pressures on global river water quality

Water ManagementCivil Engineering and Geoscience

Inference of reactive transport model parameters using a Bayesian multivariate approach

Parameter estimation of subsurface transport models from multispecies data requires the definition of an objective function that includes different types of measurements. Common approaches are weighted least squares (WLS), where weights are specified a priori for each measurement, and weighted least squares with weight estimation (WLS(we)) where weights are estimated from the data together with the parameters. In this study, we formulate the parameter estimation task as a multivariate Bayesian inference problem. The WLS and WLS(we) methods are special cases in this framework, corresponding to specific prior assumptions about the residual covariance matrix. The Bayesian perspective allows for generalizations to cases where residual correlation is important and for efficient inference by analytically integrating out the variances (weights) and selected covariances from the joint posterior. Specifically, the WLS and WLS(we) methods are compared to a multivariate (MV) approach that accounts for specific residual correlations without the need for explicit estimation of the error parameters. When applied to inference of reactive transport model parameters from column-scale data on dissolved species concentrations, the following results were obtained: (1) accounting for residual correlation between species provides more accurate parameter estimation for high residual correlation levels whereas its influence for predictive uncertainty is negligible, (2) integrating out the (co)variances leads to an efficient estimation of the full joint posterior with a reduced computational effort compared to the WLS(we) method, and (3) in the presence of model structural errors, none of the methods is able to identify the correct parameter values.Water ManagementCivil Engineering and Geoscience

Scenario-based decision making in water resource management: A case study in the Yellow River Delta; abstract

Water ManagementCivil Engineering and Geoscience

Meeting agricultural and environmental water demand in endorheic irrigated river basins: A simulation-optimization approach applied to the Urmia Lake basin in Iran

Competition for water between agriculture and the environment is a growing problem in irrigated regions across the globe, especially in endorheic basins with downstream freshwater lakes impacted by upstream irrigation withdrawals. This study presents and applies a novel simulation-optimization (SO) approach for identifying water management strategies in such settings. Our approach combines three key features for increased exploration of strategies. First, minimum environmental flow requirements are treated as a decision variable in the optimization model, yielding more flexibility than existing approaches that either treat it as a precomputed constraint or as an objective to be maximized. Second, conjunctive use is included as a management option by using dynamically coupled surface water (WEAP) and groundwater (MODFLOW) simulation models. Third, multi-objective optimization is used to yield entire Pareto sets of water management strategies that trade off between meeting environmental and agricultural water demand. The methodology is applied to the irrigated Miyandoab Plain, located upstream of endorheic Lake Urmia in Northwestern Iran. Results identify multiple strategies, i.e., combinations of minimum environmental flow requirements, deficit irrigation, and crop selection, that simultaneously increase environmental flow (up to 16 %) and agricultural profit (up to 24 %) compared to historical conditions. Results further show that significant temporary drops in agricultural profit occur during droughts when long-term profit is maximized, but that this can be avoided by increasing groundwater pumping capacity and temporarily reducing the lake's minimum environmental flow requirements. Such a strategy is feasible during moderate droughts when resulting declines in groundwater and lake water levels fully recover after each drought. Overall, these results demonstrate the usefulness and flexibility of the methodology in identifying a range of potential water management strategies in complex irrigated endorheic basins like the Lake Urmia basin.Accepted Author ManuscriptWater Resource

Global analysis of population growth and river water quality

Water ManagementCivil Engineering and Geoscience

Global impacts of the meat trade on in-stream organic river pollution: The importance of spatially distributed hydrological conditions

In many regions of the world, intensive livestock farming has become a significant source of organic river pollution. As the international meat trade is growing rapidly, the environmental impacts of meat production within one country can occur either domestically or internationally. The goal of this paper is to quantify the impacts of the international meat trade on global organic river pollution at multiple scales (national, regional and gridded). Using the biological oxygen demand (BOD) as an overall indicator of organic river pollution, we compute the spatially distributed organic pollution in global river networks with and without a meat trade, where the without-trade scenario assumes that meat imports are replaced by local production. Our analysis reveals a reduction in the livestock population and production of organic pollutants at the global scale as a result of the international meat trade. However, the actual environmental impact of trade, as quantified by in-stream BOD concentrations, is negative; i.e. we find a slight increase in polluted river segments. More importantly, our results show large spatial variability in local (grid-scale) impacts that do not correlate with local changes in BOD loading, which illustrates: (1) the significance of accounting for the spatial heterogeneity of hydrological processes along river networks, and (2) the limited value of looking at country-level or global averages when estimating the actual impacts of trade on the environment.Water Resource

Daily reservoir inflow forecasting using weather forecast downscaling and rainfall-runoff modeling: Application to Urmia Lake basin, Iran

Study region: This study develops the first daily runoff forecast system for Bukan reservoir in Urmia Lake basin (ULB), Iran, a region suffering from water shortages and competing water demands. Study focus: A weather forecast downscaling model is developed for downscaling large-scale raw weather forecasts of ECMWF and NCEP to small-scale spatial resolutions. Various downscaling methods are compared, including deterministic Artificial Intelligence (AI) techniques and a Bayesian Belief Network (BBN). Downscaled precipitation and temperature forecasts are then fed into a rainfall-runoff model that accounts for daily snow and soil moisture dynamics in the sub-basins upstream of Bukan reservoir. The multi-objective Particle Swarm Optimization (MOPSO) method is used to estimate hydrological model parameters by maximizing the simulation accuracy of observed river flow (NSEQ) and the logarithm of river flow (NSELogQ) in each sub-basin. New hydrological insights for the region: Results of the weather forecast downscaling model show that the accuracy of the BBN is greater than the various deterministic AI methods tested. Calibration results of the rainfall-runoff model indicate no significant trade-off between fitting daily high and low flows, with an average NSEQ and NSELogQ of 0.43 and 0.63 for the calibration period, and 0.54 and 0.57 for the validation period. The entire forecasting system was evaluated using inflow observations for years 2020 and 2021, resulting in an NSE of 0.66 for forecasting daily inflow into Bukan reservoir. The inflow forecasts can be used by policymakers and operators of the reservoir to optimize water allocation between agricultural and environmental demands in the ULB.Water Resource