Application of stochastic parameter optimization to the Sacramento Soil Moisture Accounting model

Conceptual rainfall‐runoff models are difficult to calibrate by means of automatic methods; one major reason for this is the inability of conventional procedures to locate the globally optimal set of parameters. This paper investigates the consistency with which two global optimization methods, the shuffled complex evolution (SCE‐UA) method (developed by the authors) and the multistart simplex (MSX) method, are able to find the optimal parameter set during calibration of the Sacramento soil moisture accounting model (SAC‐SMA) of the National Weather Service River Forecast System (NWSRFS). In the first phase of this study, error‐free synthetic data are used to conduct a comparative evaluation of the algorithms under “ideal” conditions. In 10 independent trials of each algorithm in which 13 parameters of the SAC‐SMA model were optimized simultaneously, the SCE‐UA method achieved a 100% success rate in locating the precise global optimum (i.e., the “true” parameter values) while the MSX method failed in all trials even with more than twice the number of function evaluations. In the second phase, historical data from the Leaf River watershed are used to conduct a comparative evaluation of the algorithms under “real” conditions, using two different estimation criteria, DRMS and HMLE; the SCE‐UA algorithm obtained consistently lower function values and more closely grouped parameter estimates, while using one‐third fewer function evaluations than the MSX algorithm.

Multiple batch extraction test to estimate contaminant release parameters using a Bayesian approach

An accurate forecast of runoff is very significant so that there is ample time for the pertinent authority to issue a forewarning of the impending flood. Due to the highly dimension and nonlinear, the calibration of hydrological model become very complex, so the unique “best” parameter set can not be obtained easily. In this study, an MCMC sampler entitled the Shuffled Complex Evolution Metropolis algorithm(SCEM-UA) is presented, which is well suited to infer the posterior distribution of hydrologic model parameters. This algorithm operates by merging the strengths of the Metropolis algorithm, controlled random search, competitive evolution, and complex shuffling in order to continuously update the proposal distribution and evolve the sampler to the posterior target distribution. Therefore, SCEM-UA is applied in this study to calibrate a lumped Xinanjiang hydrological model having 16 parameters. Three types of data were used for Xinanjiang model: rainfall, evaporation and discharge. One years’ data were used for calibration and one years’ data were used for testing. The criterion used to measure the fitness of the calculated against the observed discharges was the Deterministic Coefficient (DC) and Root Mean Square Error(RMSE). The calibration processes included first of all defining the feasible domains of the model parameters, and initialize the parameters in the feasible domains, then the model parameters were iteratively evaluated and updated, until the terminal condition was satisfied. In order to test the efficiency of the SCEM-UA, Genetic algorithm (GA) is also employed for comparison. The results showed that both calibration and testing results are satisfactory: the DC values of SCEM-UA for the calibration period is 0.79, which is much higher than that of GA, 0.73, and the DC for the testing period is 0.81, which is also better than GA, the same as the RMSE. Visual examinations shows in the high peak flood event, the simulated runoff by SCEM-UA is much better than that by GA.

Comparative evaluation of maximum likelihood ensemble filter and ensemble Kalman filter for real-time assimilation of streamflow data into operational hydrologic models

Markov Chain Monte Carlo (MCMC) methods have become increasingly popular for estimating the posterior probability distribution of parameters in hydrologic models. However, MCMC methods require the a priori definition of a proposal or sampling distribution, which determines the explorative capabilities and efficiency of the sampler and therefore the statistical properties of the Markov Chain and its rate of convergence. In this paper we present an MCMC sampler entitled the Shuffled Complex Evolution Metropolis algorithm (SCEM‐UA), which is well suited to infer the posterior distribution of hydrologic model parameters. The SCEM‐UA algorithm is a modified version of the original SCE‐UA global optimization algorithm developed by Duan et al. [1992]. The SCEM‐UA algorithm operates by merging the strengths of the Metropolis algorithm, controlled random search, competitive evolution, and complex shuffling in order to continuously update the proposal distribution and evolve the sampler to the posterior target distribution. Three case studies demonstrate that the adaptive capability of the SCEM‐UA algorithm significantly reduces the number of model simulations needed to infer the posterior distribution of the parameters when compared with the traditional Metropolis‐Hastings samplers.

RNA exosomes are large multi-subunit protein complexes involved in controlled and processive 3' to 5' RNA degradation. Exosomes form large molecular chambers and harbor multiple nuclease sites as well as RNA binding regions. This makes a quantitative kinetic analysis of RNA degradation with reliable parameter and error estimates challenging. For instance, recent quantitative biochemical assays revealed that degradation speed and efficiency depend on various factors, such as the type of RNA binding caps and the RNA length. We propose the combination of a differential equation model with Bayesian Markov Chain Monte Carlo (MCMC) sampling for a more robust and reliable analysis of such complex kinetic systems. Using the exosome as a paradigm, it is shown that conventional “best fit” approaches to parameter estimation are outperformed by the MCMC method. The parameter distribution returned by MCMC sampling allows for a reliable and meaningful comparison of the data from different time series. In the case of the exosome, we find that the cap structures of the exosome have a direct effect on the recruitment and degradation of RNA, and that these effects are RNA length-dependent. The described approach can be widely applied to any processive reaction with a similar kinetics like the XRN1-dependent RNA degradation, RNA/DNA synthesis by polymerases, and protein synthesis by the ribosome.

This paper presents a parameter estimation approach based on hydrograph descriptors that capture dominant streamflow characteristics at three timescales (monthly, yearly, and record extent). The scheme, entitled hydrograph descriptors multitemporal sensitivity analyses (HYDMUS), yields an ensemble of model simulations generated from a reduced parameter space, based on a set of streamflow descriptors that emphasize the timescale dynamics of streamflow record. In this procedure the posterior distributions of model parameters derived at coarser timescales are used to sample model parameters for the next finer timescale. The procedure was used to estimate the parameters of the Sacramento soil moisture accounting model (SAC‐SMA) for the Leaf River, Mississippi. The results indicated that in addition to a significant reduction in the range of parameter uncertainty, HYDMUS improved parameter identifiability for all 13 of the model parameters. The performance of the procedure was compared to four previous calibration studies on the same watershed. Although our application of HYDMUS did not explicitly consider the error at each simulation time step during the calibration process, the model performance was, in some important respects, found to be better than in previous deterministic studies.

Subglacial drainage models sensitively depend on the values of numerous uncertain parameters. However, the computation time associated with running these models makes it difficult to quantify the associated uncertainty in model outputs and to use field data to calibrate parameter values. To overcome these computational limitations, we construct a Gaussian Process (GP) emulator that accelerates subglacial drainage modelling by ~1000x. The GP predicts spatiotemporally resolved water pressure as a function of eight model parameters and is trained using ensembles of up to 512 simulations with the Glacier Drainage System (GlaDS) model applied to the Kangerlussuaq sector of the western Greenland Ice Sheet. The GP reproduces the spatial patterns and daily temporal variations simulated by GlaDS within ~4%, with locally higher errors near moulins and during the early melt season. As an application of the GP, we compute the sensitivity of basal water pressure to each of the eight parameters and find that three parameters (ice-flow coefficient, bed bump aspect ratio and the subglacial cavity system conductivity) explain 90% of the variance in model outputs. Next, we explore using a borehole water-pressure timeseries to calibrate the eight uncertain parameters. We take a Bayesian perspective to quantify the uncertainty in parameter estimates and use the GP in place of the physics-based model to make Markov Chain Monte Carlo sampling computationally feasible. We find meaningful constraints relative to the prior assumptions on most parameters and a factor-of-three reduction in uncertainty of the calibrated model predictions. However, significant differences between the calibrated model and the borehole data suggest that structural limitations of the model, rather than poorly constrained parameters or computational cost, remain the most important constraint on subglacial drainage modelling.

Generalized likelihood uncertainty estimation (GLUE) using adaptive Markov Chain Monte Carlo sampling

Abstract. In hydrological modeling, model structures are developed in an iterative cycle as more and different types of measurements become available and our understanding of the hillslope or watershed improves. However, with increasing complexity of the model, it becomes more and more difficult to detect which parts of the model are deficient, or which processes should also be incorporated into the model during the next development step. In this study, we first compare two methods (the Shuffled Complex Evolution Metropolis algorithm (SCEM-UA) and the Simultaneous parameter Optimization and Data Assimilation algorithm (SODA)) to calibrate a purposely deficient 3-D hillslope-scale model to error-free, artificially generated measurements. We use a multi-objective approach based on distributed pressure head at the soil–bedrock interface and hillslope-scale discharge and water balance. For these idealized circumstances, SODA's usefulness as a diagnostic methodology is demonstrated by its ability to identify the timing and location of processes that are missing in the model. We show that SODA's state updates provide information that could readily be incorporated into an improved model structure, and that this type of information cannot be gained from parameter estimation methods such as SCEM-UA. We then expand on the SODA result by performing yet another calibration, in which we investigate whether SODA's state updating patterns are still capable of providing insight into model structure deficiencies when there are fewer measurements, which are moreover subject to measurement noise. We conclude that SODA can help guide the discussion between experimentalists and modelers by providing accurate and detailed information on how to improve spatially distributed hydrologic models.

Colloids have the potential to enhance the mobility of strongly sorbing radionuclide contaminants in groundwater at underground nuclear test sites. This study presents an experimental and numerical investigation of colloid-facilitated plutonium transport in fractured porous media to identify plutonium reactive transport processes. The transport parameters for dispersion, diffusion, sorption, and filtration are estimated with inverse modeling by minimizing the least-squares objective function of multicomponent concentration data from multiple transport experiments with the shuffled complex evolution metropolis algorithm. Capitalizing on an unplanned experimental artifact that led to colloid formation, we adopt a stepwise strategy to first interpret the data from each experiment separately and then to incorporate multiple experiments simultaneously to identify a suite of plutonium-colloid transport processes. Nonequilibrium or kinetic attachment and detachment of plutonium-colloid in fractures were clearly demonstrated and captured in the inverted modeling parameters along with estimates of the source plutonium fraction that formed plutonium-colloids. The results from this study provide valuable insights for understanding the transport mechanisms and environmental impacts of plutonium in groundwater aquifers.

Water resources management and planning requires accurate and reliable spring flood forecasts. In cold and snowy countries, particularly in snow-dominated watersheds, enhanced flood prediction requires adequate snowmelt estimation techniques. Whereas the majority of the studies on snow modeling have focused on comparing the performance of empirical techniques and physically based methods, very few studies have investigated empirical models and conceptual models for improving spring peak flow prediction. The objective of this study is to investigate the potential of empirical degree-day method (DDM) to effectively and accurately predict peak flows compared to sophisticated and conceptual SNOW-17 model at two watersheds in Canada: the La-Grande River Basin (LGRB) and the Upper Assiniboine river at Shellmouth Reservoir (UASR). Additional insightful contributions include the evaluation of a seasonal model calibration approach, an annual model calibration method, and two hydrological models: McMaster University Hydrologiska Byrans Vattenbalansavdelning (MAC-HBV) and Sacramento Soil Moisture Accounting model (SAC-SMA). A total of eight model scenarios were considered for each watershed. Results indicate that DDM was very competitive with SNOW-17 at both the study sites, whereas it showed significant improvement in prediction accuracy at UASR. Moreover, the seasonally calibrated model appears to be an effective alternative to an annual model calibration approach, while the SAC-SMA model outperformed the MAC-HBV model, no matter which snowmelt computation method, calibration approach, or study basin is used. Conclusively, the DDM and seasonal model calibration approach coupled with the SAC-SMA hydrologic model appears to be a robust model combination for spring peak flow estimation.

This research investigated the applicability of a probabilistic physics-informed Deep Learning (DL) algorithm, i.e.,deep autoregressive network (DeepAR), for rainfall-runoff modeling across the continental United States (CONUS). Various catchment physical parameters were incorporated into the probabilistic DeepAR algorithm with various spatiotemporal variabilities to simulate rainfall-runoff processes across Hydrologic Unit Code 8 (HUC8). We benchmarked our proposed model against several physics-based hydrologic approaches such as Sacramento Soil Moisture Accounting Model (SAC-SMA), Variable Infiltration Capacity (VIC), Framework for Understanding Structural Errors (FUSE), Hydrologiska Byråns Vattenbalansavdelning (HBV), and the mesoscale hydrologic model (mHM). These approaches were implemented using Catchment Attributes and Meteorology for Large-sample Studies (CAMELS), Maurer datasets. Analysis suggested that catchment physical attributes such as drainage area have significant impacts on rainfall-runoff generation mechanisms while catchment fraction of carbonate sedimentary rocks parameter’s contribution were insignificant. The results of the proposed physics-informed DeepAR simulation were comparable and somewhat superior to the well-known conceptual hydrologic models across CONUS.  

Stochastic parameter estimation and inversion have become increasingly popular in recent years. Nowadays, it is computationally reasonable and regular to solve complex inverse problems within the Bayesian framework. Applications of Bayesian inferences for inverse problems require investigation of the posterior distribution, which usually has a complex landscape and is highly dimensional. In these cases, Markov chain Monte Carlo methods (MCMC) are often used. This paper discusses a Bayesian approach for identifying adsorption and desorption rates in combination with a pore-scale reactive flow. Markov chain Monte Carlo sampling is used to estimate adsorption and desorption rates. The reactive transport in porous media is governed by incompressible Stokes equations, coupled with convection–diffusion equation for species’ transport. Adsorption and desorption are accounted via Robin boundary conditions. The Henry isotherm is considered for describing the reaction terms. The measured concentration at the outlet boundary is provided as additional information for the identification procedure. Metropolis–Hastings and Adaptive Metropolis algorithms are implemented. Credible intervals have been plotted from sampled posterior distributions for both algorithms. The impact of the noise in the measurements and influence of several measurements for Bayesian identification procedure is studied. Sample analysis using the autocorrelation function and acceptance rate is performed to estimate mixing of the Markov chain. As result, we conclude that MCMC sampling algorithm within the Bayesian framework is good enough to determine an admissible set of parameters via credible intervals.

This paper illustrates a complete Bayesian decision analysis for evaluating multistock harvest goals in the fishery on Fraser River sockeye salmon (Oncorhynchus nerka). We identify four key steps necessary to assess a resource production system. Each step entails choices that can alter the perceived consequences of management decisions. A Markov chain Monte Carlo sample captures uncertainty in the population dynamics. The Bayesian formalism then translates this uncertainty into uncertain policy outcomes. We examine a relatively simple control law, designed to protect stocks at low abundance. We restrict our attention to retrospective policy analysis by investigating what might have happened to sockeye stocks if management had proceeded differently during years for which historical data are available. A formal objective function quantifies societal values associated with a range of policy options. To confine the paper to manageable scope, we consider only relatively simple assumptions. Our analytical framework offers an iterative route to policy design, where managers play an active role in formulating policy options and evaluating their consequences.