Transient Storage Model Parameters Research Articles

Estimating the transient storage parameters for pollution modeling in small streams: a comparison of newly developed hybrid optimization algorithms.

The transient storage model (TSM) is a common approach to assess solute transport and pollution modeling in rivers. Several formulas have been developed to estimate TSM parameters. This study develops a new hybrid optimization algorithm consisting of the dragonfly algorithm and simulated annealing (DA-SA) algorithms. This robust method provides accurate formulas for estimating TSM parameters (e.g., kf, T, [Formula: see text]). A dataset gathered by previous scholars from several rivers in the USA was used to assess the proposed formulas based on several error metrics ([Formula: see text] and [Formula: see text]) and visual indicators. According to the results, DA-SA-based formulas adequately estimated the [Formula: see text] ([Formula: see text], [Formula: see text]), [Formula: see text] ([Formula: see text] [Formula: see text]), and [Formula: see text] ([Formula: see text] [Formula: see text]) parameters. Moreover, the DA-SA-1 showed higher accuracy by improving the RMSE and MAE by 98% compared to the DA and DA-SA-1 as alternatives. The formulas developed in this study significantly outperformed the results of previously proposed models by enhancing the NSE up to 70%. The hybrid DA-SA algorithm method proved highly reliable models to estimate the TSM parameters in the water pollution routing problem, which is vital for reactive solute uptake in advective and transient storage zones of stream ecosystems.

Multi-Gene Genetic Programming Regression Model for Prediction of Transient Storage Model Parameters in Natural Rivers

A Transient Storage Model (TSM), which considers the storage exchange process that induces an abnormal mixing phenomenon, has been widely used to analyze solute transport in natural rivers. The primary step in applying TSM is a calibration of four key parameters: flow zone dispersion coefficient (Kf), main flow zone area (Af), storage zone area (As), and storage exchange rate (α); by fitting the measured Breakthrough Curves (BTCs). In this study, to overcome the costly tracer tests necessary for parameter calibration, two dimensionless empirical models were derived to estimate TSM parameters, using multi-gene genetic programming (MGGP) and principal components regression (PCR). A total of 128 datasets with complete variables from 14 published papers were chosen from an extensive meta-analysis and were applied to derivations. The performance comparison revealed that the MGGP-based equations yielded superior prediction results. According to TSM analysis of field experiment data from Cheongmi Creek, South Korea, although all assessed empirical equations produced acceptable BTCs, the MGGP model was superior to the other models in parameter values. The predicted BTCs obtained by the empirical models in some highly complicated reaches were biased due to misprediction of Af. Sensitivity analyses of MGGP models showed that the sinuosity is the most influential factor in Kf, while Af, As, and α, are more sensitive to U/U*. This study proves that the MGGP-based model can be used for economic TSM analysis, thus providing an alternative option to direct calibration and the inverse modeling initial parameters.

Derivation of new analytical solution for pollution transport through large porous media

This paper investigates the application of the transient storage (TS) model for free surface flow-through rockfill media by some modification in the principles of it. For this purpose, firstly, a new analytical solution is derived by using the concepts of the VART model. In the following, a series of experiments have been operated in a box flume with two inflow rates and five injection masses. EC probes have been employed to catch breakthrough curves. Furthermore, analytical temporal moment’s equations have been derived for the numerical calculation of the TS model parameters. Also, they have been calculated for the new proposed model using the least square curve fitting method. Finally, the findings showed that the TS model, with its new analytical solution, is entirely applicable to rockfill media. Finally, the statistical analyses indicated that the model performance is excellent.

Improved Moth-Swarm Algorithm to predict transient storage model parameters in natural streams

Transient storage model (TSM) is the most popular model for simulating solutes transport in natural streams. Accurate estimate of TSM parameters is essential in many hydraulic and environmental problems. In this study, an improved version of high-level Moth-Swarm Algorithm (IMSA) was used to predict the TSM parameters. First, the performance of the improved model was successfully assessed through several benchmark functions. Next, a series of 58 measured hydraulic and geometric datasets was used to validate the model. The data were divided into two series randomly, 38 datasets were selected for derivation and the remaining 20 datasets were used to verification. Then the results of IMSA were compared with other algorithms proposed by previous researchers. Two statistical indices of root mean square error (RMSE) and coefficient of correlation (CC) were employed to evaluate the performance of the model. The results showed that despite the high complexity and uncertainty associated with the dispersion processes, the IMSA algorithm could accurately predict the TSM parameters.

Performance Evaluation of Improved Symbiotic Organism Search Algorithm for Estimation of Solute Transport in Rivers

Accurate estimation of solute transport has significant importance in water resources and environmental engineering. Among the various types of mathematical formulation for modeling of solute transport, the transient storage model has been widely applied by different researchers as an appropriate model. In this study, an improved version of symbiotic organism search (SOS) algorithm was used to estimate the parameters of transient storage model. A large set of data from natural rivers of USA was collected from the literature and used for derivation and validation of the algorithm. The performance of the algorithm was evaluated by standard statistical indices. Accordingly, the values of R and RMSE for transient storage model parameters (Kf, T and e) were obtained 0.922 and 30.62 (for Kf), 0.596 and 5645 (for T) and, 0.643 and 0.019 (for e) for whole dataset. In addition, the results of this study were compared with those obtained by different reserachers via other models. The results indicate the higher capability of improved SOS algorithim compared to the others in estimating the transient storage model parameters.

Parameter uncertainty with flow variation of the one-dimensional solute transport model for small streams using Markov chain Monte Carlo

The transient storage model (TSM) is a popular solute transport model among hydrologists and ecologists for characterizing solute retention potential of small headwater streams. TSM parameters are most commonly estimated in an inverse modeling framework using tracer breakthrough data. A key challenge in interpreting TSM parameters is the inherent difficulty in the estimation process and relating these parameters with the physical characteristics of streams. While often recognized that multiple sources of uncertainty impact transient storage modeling, rigorous evaluation of TSM parameter uncertainty is rare. Stream flow magnitude has been identified as a key variable in characterizing stream solute transport dynamics, yet no study has shown the impact of flow magnitude on TSM parameter uncertainty. In this paper we study the impact of flow magnitude on TSM parameter uncertainty by using tracer data from repeated tracer studies with changing stream flow magnitudes, and introduce a software tool to perform Markov chain Monte Carlo based parameter estimation and uncertainty evaluation. The software tool developed is capable of performing thousands of model runs within a few hours, which is necessary for Monte Carlo based parameter estimation, and provides a potentially attractive framework for model testing and improvement. TSM parameters were found to be relatively less important during higher flows with large uncertainty bounds and clear evidence of parameter correlations. The importance of TSM parameters on solute transport seemed to increase as flow decreased with seasonal baseflow recession. Our findings highlight the need for improved field methodologies to reduce parameter uncertainty and the need for further improvement in the model structure for successful stream characterization.

Identifiability of transient storage model parameters along a mountain stream

[1] Transient storage models are widely used in combination with tracer experiments to characterize stream reaches via calibrated parameter estimates. These parameters quantify the main transport and storage processes. However, it is implicitly assumed that calibrated parameters are uniquely identifiable and hence provide a unique characterization of the stream. We investigate parameter identifiability along with the stream conditions that control identifiability for 10 breakthrough curves (BTC) for 100 m pulse injections along Stringer Creek, Montana, USA. Identifiability is assessed through global, variance-based sensitivity analysis of the one-dimensional transport with inflow and storage model (OTIS). Results indicate that the main channel area parameter A and the dispersion coefficient D were the most sensitive parameters and, therefore, likely to be identifiable across all timescales and reaches. Identifiability of transient storage zone size As fell into two categories along Stringer Creek. As was identifiable for lower elevation regions, corresponding to a constrained valley, higher stream slopes, and in-channel roughness, but not for upper stream regions, corresponding to a wider valley floor, flatter stream slopes, and low roughness. The storage zone exchange parameter α was nonidentifiable across all study reaches. Our results suggest that only some of the processes represented in the model will be relevant and, therefore, identifiable for pulse injection data. As such, calibrated parameter estimates should be accompanied by an assessment of parameter sensitivity or uncertainty. We also show that parameter identifiability varies with stream setting along Stringer Creek, suggesting that physical characteristics directly influence the identification of dominant stream processes.

Variations in surface water-ground water interactions along a headwater mountain stream: Comparisons between transient storage and water balance analyses

[1] The accumulation of discharge along a stream valley is frequently assumed to be the primary control on solute transport processes. Relationships of both increasing and decreasing transient storage, and decreased gross losses of stream water have been reported with increasing discharge; however, we have yet to validate these relationships with extensive field study. We conducted transient storage and mass recovery analyses of artificial tracer studies completed for 28 contiguous 100 m reaches along a stream valley, repeated under four base-flow conditions. We calculated net and gross gains and losses, temporal moments of tracer breakthrough curves, and best fit transient storage model parameters (with uncertainty estimates) for 106 individual tracer injections. Results supported predictions that gross loss of channel water would decrease with increased discharge. However, results showed no clear relationship between discharge and transient storage, and further analysis of solute tracer methods demonstrated that the lack of this relation may be explained by uncertainty and equifinality in the transient storage model framework. Furthermore, comparison of water balance and transient storage approaches reveals complications in clear interpretation of either method due to changes in advective transport time, which sets a the temporal boundary separating transient storage and channel water balance. We have little ability to parse this limitation of solute tracer methods from the physical processes we seek to study. We suggest the combined analysis of both transient storage and channel water balance more completely characterizes transport of solutes in stream networks than can be inferred from either method alone.

Physical controls and predictability of stream hyporheic flow evaluated with a multiscale model

Improved predictions of hyporheic exchange based on easily measured physical variables are needed to improve assessment of solute transport and reaction processes in watersheds. Here we compare physically based model predictions for an Indiana stream with stream tracer results interpreted using the Transient Storage Model (TSM). We parameterized the physically based, Multiscale Model (MSM) of stream‐groundwater interactions with measured stream planform and discharge, stream velocity, streambed hydraulic conductivity and porosity, and topography of the streambed at distinct spatial scales (i.e., ripple, bar, and reach scales). We predicted hyporheic exchange fluxes and hyporheic residence times using the MSM. A Continuous Time Random Walk (CTRW) model was used to convert the MSM output into predictions of in stream solute transport, which we compared with field observations and TSM parameters obtained by fitting solute transport data. MSM simulations indicated that surface‐subsurface exchange through smaller topographic features such as ripples was much faster than exchange through larger topographic features such as bars. However, hyporheic exchange varies nonlinearly with groundwater discharge owing to interactions between flows induced at different topographic scales. MSM simulations showed that groundwater discharge significantly decreased both the volume of water entering the subsurface and the time it spent in the subsurface. The MSM also characterized longer timescales of exchange than were observed by the tracer‐injection approach. The tracer data, and corresponding TSM fits, were limited by tracer measurement sensitivity and uncertainty in estimates of background tracer concentrations. Our results indicate that rates and patterns of hyporheic exchange are strongly influenced by a continuum of surface‐subsurface hydrologic interactions over a wide range of spatial and temporal scales rather than discrete processes.

Erratum to: Predicting Transient Storage Model Parameters of Rivers by Genetic Algorithm

Erratum to: Predicting Transient Storage Model Parameters of Rivers by Genetic Algorithm

Predicting Transient Storage Model Parameters of Rivers by Genetic Algorithm

The presence of transient storage zone modifies the riverine pollutant transport. In the present work, new empirical expressions for three key parameters of transient storage model (TSM), an important method for predicting concentration variation of pollutants in rivers, have been derived employing genetic algorithm on published hydraulic data on river reaches and TSM parameters. The proposed expressions use few hydraulic and geometric characteristics of rivers that are usually available. Based on various performance indices, it can be concluded that the proposed expressions predict TSM parameters more reliably in comparison to the other empirical expressions for predicting TSM parameters.

Comparing Three Models for Treatment of Stagnant Zones in Riverine Transport

The modified advection dispersion equation (MADE) model is compared to the transient storage model (TSM) and fractional advection dispersion equation (FRADE) model for modeling riverine transport. The comparisons are illustrated using field examples. The parameter F of the FRADE model is found to be inconsistent to its physical meaning and is unrelated to dead zone fraction. Also, the estimated parameters of TSM are found to be inconsistent to their physical meaning. On the contrary, the parameters of MADE are consistent and related to the dead zone fraction. It is observed that the MADE model is easy to use and yields reliable and consistent results.

Evaluating Bacteriophage P22 as a Tracer in a Complex Surface Water System: The Grand River, Michigan

Viruses are important pathogens in both marine and fresh water environments. There is a strong interest in using bacteriophages as tracers because of their role as model viruses, since dissolved chemical tracers may not adequately describe the behavior of viruses that are suspended colloids. Despite a large number of studies that examined the transport of bacteriophages in the subsurface environment, few studies examined phage transport in large and complex surface water systems. In this paper we report the results of a dual tracer study on a 40 km reach of the Grand River, the longest river in Michigan, and we examine the performance of bacteriophage P22 relative to a chemical tracer (Rhodamine WT). Our analysis based on the transient storage (TS) model indicated that P22 can be successfully used as a tracer in complex surface water environments. Estimated P22 inactivation rates were found to be in the range 0.27-0.57 per day (0.12-0.25 log10 per day). The highest inactivation rate was found in a reach with high suspended solids concentration, relatively low dissolved organic carbon content, and sediment with high clay content. Estimated TS model parameters for both tracers were found to be consistent with surficial geology and land use patterns. Maximum storage zone sizes for the two tracers were found in different river reaches, indicating that different processes contributed to TS within the same reach for the two tracers. This model can be used to examine the arrival times and concentrations of human viral pathogens released from untreated sewage at recreational areas.

Transient storage as a function of geomorphology, discharge, and permafrost active layer conditions in Arctic tundra streams

Transient storage of solutes in hyporheic zones or other slow‐moving stream waters plays an important role in the biogeochemical processes of streams. While numerous studies have reported a wide range of parameter values from simulations of transient storage, little field work has been done to investigate the correlations between these parameters and shifts in surface and subsurface flow conditions. In this investigation we use the stream properties of the Arctic (namely, highly varied discharges, channel morphologies, and subchannel permafrost conditions) to isolate the effects of discharge, channel morphology, and potential size of the hyporheic zone on transient storage. We repeated stream tracer experiments in five morphologically diverse tundra streams in Arctic Alaska during the thaw season (May–August) of 2004 to assess transient storage and hydrologic characteristics. We compared transient storage model parameters to discharge (Q), the Darcy‐Weisbach friction factor (f), and unit stream power (ω). Across all studied streams, permafrost active layer depths (i.e., the potential extent of the hyporheic zone) increased throughout the thaw season, and discharges and velocities varied dramatically with minimum ranges of eight‐fold and four‐fold, respectively. In all reaches the mean storage residence time (tstor) decreased exponentially with increasing Q, but did not clearly relate to permafrost active layer depths. Furthermore, we found that modeled transient storage metrics (i.e., tstor, storage zone exchange rate (αOTIS), and hydraulic retention (Rh)) correlated better with channel hydraulic descriptors such as f and ω than they did with Q or channel slope. Our results indicate that Q is the first‐order control on transient storage dynamics of these streams, and that f and ω are two relatively simple measures of channel hydraulics that may be important metrics for predicting the response of transient storage to perturbations in discharge and morphology in a given stream.

Applicability of the Transient Storage Model to the hyporheic exchange of metals

Stream–subsurface exchange results from a complex ensemble of transport mechanisms that require different modeling approaches. Field and laboratory experiments show that advective exchange through the underlying sediments is an important mechanism of solutes transport and storage in riverine systems. Here, Transient Storage Model parameters are obtained for reactive solute exchange driven by bedform-induced advection. Consideration of exchange induced by this single mechanism allows specific relationships between model parameters and system properties like solute reactivity to be identified. This work shows that when a simplified model like the Transient Storage Model is applied to analyze metal storage in river sediments, particular attention must be devoted to the choice of modeling parameters.

Solute transport in multiple-reach experiments: Evaluation of parameters and reliability of prediction

We used two stream tracer studies to address issues related to using the transient storage model (TSM) in simulating solute transport in streams containing riffle-pools and step-pools. The injection durations were short such that one may consider the storage zones to consist mainly of surface water storage zones. We found that the TSM was not able to reproduce the high portion (near the peak) of the breakthrough curve in the first subreach (85 m) regardless of the functional form of the objective function. We attributed this to the presence of a large pool 35 m downstream of the injection location that caused segregation of solute flow that was completely mixed across the stream upstream of the pool. The model was able to closely fit the breakthrough curves at x=185 and 323 m, most likely because the signature of the pool diminished downstream. The fitting method did not always ensure that the parameter values represented physical reality, and we believe that physical measurements should be made and incorporated into the parameter estimation procedure utilizing Bayesian estimation. Our findings indicate that the representative values of TSM parameters in a reach do not generally fall between the representative values of its subreaches. Hence, the expression ‘reach-averaged’ should be used cautiously. The results indicated that it is more reliable to extrapolate (going downstream) than to interpolate. We believe this is due to local physical controls that could not be accounted for with parameters estimated far downstream from the controls.

Effect of morphology and discharge on hyporheic exchange flows in two small streams in the Cascade Mountains of Oregon, USA

AbstractStream‐tracer injections were used to examine the effect of channel morphology and changing stream discharge on hyporheic exchange flows. Direct observations were made from well networks to follow tracer movement through the hyporheic zone. The reach‐integrated influence of hyporheic exchange was evaluated using the transient storage model (TSM) OTIS‐P. Transient storage modelling results were compared with direct observations to evaluate the reliability of the TSM. Results from the tracer injection in the bedrock reach supported the assumption that most transient storage in headwater mountain streams results from hyporheic exchange. Direct observations from the well networks in colluvial reaches showed that subsurface flow paths tended to parallel the valley axis. Cross‐valley gradients were weak except near steps, where vertical and cross‐valley hydraulic gradients indicated a strong potential for stream water to downwell into the hyporheic zone. The TSM parameters showed that both size and residence time of transient storage were greater in reaches with a few large log‐jam‐formed steps than in reaches with more frequent, but smaller steps. Direct observations showed that residence times in the unconstrained stream were longer than in the constrained stream and that little change occurred in the location and extent of the hyporheic zone between low‐ and high‐baseflow discharges in any of the colluvial reaches. The transient storage modelling results did not agree with these observations, suggesting that the TSM was insensitive to long residence‐time exchange flows and was very sensitive to changes in discharge. Disagreements between direct observations and the transient storage modelling results highlight fundamental problems with the TSM that confound comparisons between the transient storage modelling results for tracer injections conducted under differing flow conditions. Overall, the results showed that hyporheic exchange was little affected by stream discharge (at least over the range of baseflow discharges examined in this study). The results did show that channel morphology controlled development of the hyporheic zone in these steep mountain stream channels. Copyright © 2005 John Wiley & Sons, Ltd.

Parameter Estimation of the Transient Storage Model for Stream–Subsurface Exchange

The transient storage model ~TSM! is the most commonly used model for stream-subsurface exchange of solutes. The TSM provides a convenient, simplified representation of hyporheic exchange, but its lack of a true physical basis causes its parameters to be difficult to predict. However, the simple formulation makes the model a useful practical tool for many applications. This work compares the TSM with a physically based pumping model. This comparison is advantageous for two reasons: Advective pumping is known to be an important hyporheic exchange process in many streams, and the pumping model can be used to derive dimensionless transient storage parameters that are properly scaled with important physical stream parameters. Transient storage model parameters are shown to be dependent on both the timescale of observation and the shape of the breakthrough curve, i.e., on the temporal evolution of the solute concentration in the surface water. This indicates that the transient storage model can, in practice, lead to incorrect predictions when model parameters are obtained without consideration of the stream flow dynamics, the properties of the stream bed, or the process timescale. This work emphasizes the limitations of simplified models for hyporheic transport, and indicates that such models need to be carefully applied.

Parameter estimation of the transient storage model by a routing method for river mixing processes

This paper reports on a routing method to estimate values of four parameters of a transient storage (TS) model that represent solute transport in natural streams with transient storage zones. In this approach a functional relationship between the TS model parameters and an analytical solution of the TS model equation is constructed. Results from a robust constrained nonlinear equation solver are used to obtain an explicit relationship between the mixing data and the terms in the functional relationship. The new method and several existing methods are compared with independently observed values of the TS model parameters. Laboratory flume experiments show that the parameters estimated by the new method are in better agreement with observations than are earlier methods. TS model parameters of 58 mixing data sets obtained from 33 natural streams are estimated. Dispersion data show that the concentration curves from analytical solutions using parameters estimated by the new method provide a good match to the observed concentration curves.

On the relationship of transient storage and aggregated dead zone models of longitudinal solute transport in streams

The relationship between the distributed transient storage (TS) and lumped aggregate dead zone (ADZ) models of longitudinal solute transport in rivers and streams is examined by a parallel application to tracer data and through an investigation of parameter relationships. Both models accurately describe observed solute transport in a stream where the effects of storage or dead zones significantly affect longitudinal dispersion. A moment matching technique, based on theoretical temporal moments, is used to develop parameter relationships. Tests using the previously calibrated parameters, in addition to simulation experiments, show that the moment matching procedure allows ADZ model parameters to be reliably derived from TS model parameters and vice versa. An investigation of these parameter relationships reveals an important difference between the effective solute transport velocity and the average reach flow velocity in streams subject to transient storage or dead zone processes. A number of practical uses for the derived relationships are suggested, including the ability to utilize powerful methods of system identification in the estimation of TS model parameters.