Transient Storage Model Research Articles

A Review on Storage Process Models for Improving Water Quality Modeling in Rivers

Water quality is intricately linked to the global water crisis since the availability of safe, clean water is essential for sustaining life and ensuring the well-being of communities worldwide. Pollutants such as industrial chemicals, agricultural runoff, and untreated sewage frequently enter rivers via surface runoff or direct discharges. This study provides an overview of the key mechanisms governing contaminant transport in rivers, with special attention to storage and hyporheic processes. The storage process conceptualizes a ubiquitous reactive boundary between the main channel (mobile zone) and its surrounding slower-flow areas (immobile zone). Research from the last five decades demonstrates the crucial role of storage and hyporheic zones in influencing solute residence time, nutrient cycling, and pollutant degradation. A review of solute transport models highlights significant advancements, including models like the transient storage model (TSM) and multirate mass transport (MRMT) model, which effectively capture complex storage zone dynamics and residence time distributions. However, more widely used models like the classical advection–dispersion equation (ADE) cannot hyporheic exchange, limiting their application in environments with significant storage contributions. Despite these advancements, challenges remain in accurately quantifying the relative contributions of storage zones to solute transport and degradation, especially in smaller streams dominated by hyporheic exchange. Future research should integrate detailed field observations with advanced numerical models to address these gaps and improve water quality predictions across diverse river systems.

Mechanistic definition and prediction of the mass exchange coefficient between rivers and hyporheic zones: The [formula omitted] of two [formula omitted]s

Solute transport in interconnected rivers and hyporheic zones is typically modeled through dual-domain models where first-order solute mass transfer between the two domains, ΩR and ΩHZ, is represented by a coefficient α. The transient storage model (TSM) is an example of such an approach. In practice, α is determined by fitting the tails of solute tracer breakthrough curves using a TSM. This approach has led to ambiguity regarding α’s physical meaning and transferability. Here, we investigated the physical basis for α and tested it with virtual experiments through the fully coupled multiphysics model hyporheicFoam for the ΩR−ΩHZ system. hyporheicFoam explicitly simulated coupled flow and solute transport over a kilometer with centimeter-scale resolution. Model results were analyzed to calculate α following its theoretical definition directly. Using the determined α within a TSM enables accurate reproduction of solute transport, underscoring α’s physical relevance and precision.

Experimental and numerical assessments of thermal transport in phase change material embedding additively manufactured triply periodic minimal surfaces: A comparative evaluation

Phase change materials (PCMs), due to their inherent low conductivity, are presently restricted in their potential applications for thermal energy storage (TES) systems. Extensive effort has been made over the past few years to investigate the potential of porous materials, such as metal foams, as effective thermal conductivity enhancers (TCEs) for PCMs. Porous materials have superior specific surface area over conventional honeycomb structures and fins, providing great potential in thermal storage systems. In this study, taking advantage of the implicit function of triply periodic minimal surface (TPMS), new varieties of lattices with continuous surface structures were developed and then manufactured by using AlSi10Mg powder via selective laser melting (SLM). A three-dimensional transient phase-change heat storage model of TPMS (Primitive and I-WP) structure-paraffin composite PCMs was adopted to study both the phase-change heat transfer performance and heat storage capability of TPMS-PCMs during the phase transition. Meanwhile, the evolution of the solid–liquid interface and temperature–time history were investigated by utilizing the visualized thermal storage experiments. The findings revealed that embedding TPMS lattice decreased the natural convection effect, resulting in a maximum flow velocity of liquid paraffin wax (PX) within TPMS-PCMs that was only 0.1 times that of pure PX. The melting onset time of TPMS-PCMs was advanced by 82.2 %-91.1 %, and the duration of phase change was shortened by 68.3 %-75.9 %, respectively. In addition, the total heat storage of TPMS-PCMs fell from 4464.0 J to 4217.2 J compared to pure PX, but their average heat storage rate rose from 1.04 to 4.58 J/s. Primitive rod (PS)-type TPMS-PCM was the most potential among the three types of TPMS lattices as the TCE for PCM because it achieved the highest heat storage rate with the most negligible overall heat storage loss.

A comprehensive assessment and comparison of the impacts of storage parameters on solute transport in streams using a novel framework

Researchers must determine the storage parameter values to understand the storage processes and compare them across streams. These parameters are highly variable in time and space, making them challenging to measure. Individual studies of a single stream cannot characterize the interrelations among the processes involved in solute transport, hydraulic variables, and physical stream characteristics. Despite decades of research, a comprehensive framework is lacking. This study uses a simple and effective Monte Carlo approach to propose a general framework within which most solute transport models can undergo sensitivity analysis. This framework provides a comprehensive depiction of model performance under various scenarios, such as flow properties, stream geomorphology, and solute status. The relative and absolute sensitivities of three solute transport models, namely, the modified advection–dispersion equation (MADE), transient storage model (TSM), and variable residence time (VART), were evaluated and compared within the proposed framework. The main findings can be summarized as follows. In most conditions, storage models are more sensitive to the ratio of the storage zone cross-section to the stream cross-section than other parameters. Increasing the exchange rate between the stream and storage zones reduces the sensitivity to its indicative parameter and, consequently, its impact on the concentration time series. MADE's capability to identify modification parameters is higher for streams where dispersion dominates over advection, and their estimates have lower uncertainty. On the other hand, as advection becomes more dominant over dispersion in TSM and VART, estimated storage parameters have lower uncertainty.“

Identifying transient storage model parameters in karst conduits using the normal-score ensemble smoother with multiple data assimilation

Transient storage model (TSM) is widely used to describe solute transport processes in karst areas. Accurately identifying model parameters is essential for predicting and mitigating groundwater contamination. This paper employs the normal-score ensemble smoother with multiple data assimilation (NS-ES-MDA) algorithm to automatically identify model parameters (cross-sectional area of main channel A, dispersion coefficient D, cross-sectional area of storage zone As, and exchange coefficient α), while evaluating their uncertainty across four cases: identification of only model parameters (case 1), model parameters alongside tracer parameters (case 2), model parameters with conduit length (case 3), and all three –model parameters, tracer parameters, and conduit length (case 4). We examine the variations in uncertainty of model parameters when tracer parameters and/or conduit length are known or unknown. We further investigate the effects of concentration observation limits and observation error variance on the identification performance. The results demonstrate that the proposed method can successfully identify model parameters, even in cases where tracer parameters and/or conduit length are unknown, although with a certain level of uncertainty. However, the calibration of tracer parameters leads to an increase in uncertainty for A and D, and a slight rise in uncertainty for α. The calibration of conduit length significantly elevates the uncertainties of A and As and causes an increase in uncertainty for D. Compared with tracer parameters, conduit length causes larger uncertainty in A and As. The identification performance significantly deteriorates when the tail of observed breakthrough curve (BTC) is truncated, and reaches its peak at an observation error variance of 1 × 10-4. This implies that it is crucial to monitor the tail in BTC and to assign a reasonable observation error when using this method to identify model parameters. Although these findings are derived from a synthetic karst conduit, they offer valuable insights for identifying model parameters as tracer data and/or conduit length are uncertain in field conditions.

Importance of Dense Aquatic Vegetation in Seasonal Phosphate and Particle Transport in an Agricultural Headwater Stream

AbstractAgricultural headwater streams and ditches commonly host dense stands of aquatic vegetation that grow and decay over seasons and exert physical and biological controls on the transport of nutrients from cropland to larger rivers. This study examined changes in the transport of phosphorus (P) in an agricultural drainage ditch in the Maumee River Basin (Ohio, USA) by conducting constant rate injections of a novel tracer mixture (conservative salt [Cl as NaCl], dissolved P [KH2PO4], and a fluorescent fine particle) in spring, summer, and fall. We quantified transport behavior for solutes and particles using a traditional transient storage modeling framework consisting of mobile and immobile storage zones connected by a first‐order exchange rate constant. Transient storage was greatest during the spring, when thicker vegetation caused more pooling and flow stagnation, and decreased through fall, as vegetation thinned. Soluble P uptake lengths were 8.7 times longer in fall than spring, likely due to declines in biological uptake rates with colder temperatures and immobile zone storage with thinning vegetation. Particle capture lengths also decreased by a factor of 4.3 from fall to spring. With the increasing eutrophication of Lake Erie and waterbodies around the world that lie downstream from agricultural landscapes, it is beneficial to understand nutrient transport across watersheds, including small agricultural streams. This study highlights the physical and biological roles that aquatic vegetation plays in small agricultural streams by creating seasonally variable immobile zones that slow the flow of nutrients, providing surface area for biofilms, and capturing particles that bind nutrients.

Discharge, Groundwater Gradients, and Streambed Micro-Topography Control the Temporal Dynamics of Transient Storage in a Headwater Reach.

Contradictory interpretations of transient storage modeling (TSM) results of past studies hamper the understanding of how hydrologic conditions control solute transport in streams. To address this issue, we conduct 30 instantaneous tracer experiments in the Weierbach stream, Luxembourg. Using an iterative modeling approach, we calibrate TSM parameters and assess their identifiability across various hydrologic conditions. Near-stream groundwater monitoring wells and LIDAR scans of the streambed are used to evaluate the area of the hyporheic zone and of the submerged sediments for each experiment. Our findings show that increasing discharge enhances parameters interaction requiring more samples of TSM parameters to obtain identifiable results. Our results also indicate that transient storage at the study site is influenced by in-stream and hyporheic exchange processes during low discharge, likely due to the hyporheic zone's large extent and the relatively low water level compared to the size of slate fragments on the streambed. However, as discharge increases, in-stream storage zones become part of the advective channel and the lower localized stream water losses to the adjacent groundwater suggests a decrease of the hyporheic exchange on transient storage. The results obtained were utilized to generate a hydrograph for the study site illustrating the dynamic evolution of in-stream and hyporheic storage with varying discharge, providing insights into the expected influence of different transient storage processes prior to tracer experiments. Overall, our study enhances the understanding of the role of the hyporheic area and in-stream storage zones in transient storage and helps estimate TSM parameters more accurately.

Estimating Net Retention Time of Solute in Storage Zones of a Stream

AbstractBecause of the influence of various storage zones, solute transport in a stream channel cannot be interpreted by advection and dispersion processes alone. Thus, in recent decades, various models that incorporate storage‐zone effects have been proposed to characterize anomalous storage mechanisms. The validity of these models has been predominantly demonstrated using tracer breakthrough curves measured in surface flow. However, the storage effect is usually less influential on the breakthrough curve behavior than in‐stream flow dynamics. Thus, for model validation, the tracer behavior within the storage zone should be investigated separately. The present study aims to quantify the time‐dependent storage effect, herein termed the net retention time distribution (NRTD), from tracer measurements in the flow zone using a deconvolution technique with manipulation in the Fourier domain. The results demonstrated that the deconvolved NRTDs successfully represented the temporal behavior of the tracer in the storage zones without significant distortion in the primary information of the observed breakthrough curves. Using estimates of NRTD, we evaluated the simulations of the transient storage model, and found that the storage effects were underestimated as much as an average 18.5% in this study. The deconvolved NRTDs were also utilized to predict the biodegradation losses of organic chemicals flowing along a stream at confidence intervals.

A Method for Calibrating the Transient Storage Model from the Early and Late-Time Behavior of Breakthrough Curves

Solute transport in rivers is controlled by mixing processes that occur over a wide spectrum of spatial and temporal scales. Deviations from the classic advection–dispersion model observed in tracer test studies are known to be generated by the temporary trapping of solutes in storage zones where velocities and mixing rates are relatively small. In this work, the relation between the early and late-time behavior of solute breakthrough curves (BTCs) and the key parameters of the Transient Storage Model (TSM) is analyzed using non-asymptotic approximations of the model equations. Two main slopes are identified corresponding to the rising and decreasing limbs of the BTCs which are linked by specific relationships to transport and storage parameters. The validity of the proposed approximations is demonstrated with both synthetic and experimental data. Consistent with the TSM assumptions, the range of validity of the proposed approximations represents the limit of separability between surface dispersion and transient storage and can be expressed as a function of a nondimensional parameter. The results of this work can help environmental scientists identify solute transport and transient storage parameters and support the design of enhanced field tracer experiments.

Temporal moments of one-dimensional advective-dispersive transport with exchange represented via memory function models: Application to river corridor transport

Practical simulation of solute transport in river corridors often relies on one-dimensional transport models with solute flux between river and hyporheic zone governed by a mass exchange term, perhaps most generally expressed using the ‘memory function’ formalism. While expressions for temporal moments of solute breakthrough curves (BTCs) are available for a number of such models, those for memory function forms are not, to our knowledge. Here we report closed-form BTC temporal moment expressions for memory function forms, found by exploiting the connection to phase exposure-dependent exchange (PhEDEx) formulations. We use these results to investigate the general capability of the memory function form to accommodate specific scaling of river tracer temporal moments reported in the literature, and we apply the method to identification of parameters in application to two recent tracer tests. The applications involve a simple numerical solution to the memory function river corridor transport model calibrated using measured temporal moments of the tracer test BTCs. The numerical model is validated only for the classical case of the transient storage model without lateral inflow, the analytical solution for which we adapt from the Lassey solution for mobile-immobile exchange in porous media. It should be noted that the temporal moments results obtained here in the context of river corridor transport also apply to one-dimensional transport in two-domain (mobile-immobile) porous media, when governed by a two-domain memory function model.

Exploring tracer information in a small stream to improve parameter identifiability and enhance the process interpretation in transient storage models

Abstract. The transport of solutes in river networks is controlled by the interplay of processes such as in-stream solute transport and the exchange of water between the stream channel and dead zones, in-stream sediments, and adjacent groundwater bodies. Transient storage models (TSMs) are a powerful tool for testing hypotheses related to solute transport in streams. However, model parameters often do not show a univocal increase in model performances in a certain parameter range (i.e. they are non-identifiable), leading to an unclear understanding of the processes controlling solute transport in streams. In this study, we increased parameter identifiability in a set of tracer breakthrough experiments by combining global identifiability analysis and dynamic identifiability analysis in an iterative approach. We compared our results to inverse modelling approaches (OTIS-P) and the commonly used random sampling approach for TSMs (OTIS-MCAT). Compared to OTIS-P, our results informed about the identifiability of model parameters in the entire feasible parameter range. Our approach clearly improved parameter identifiability compared to the standard OTIS-MCAT application, due to the progressive reduction of the investigated parameter range with model iteration. Non-identifiable results led to solute retention times in the storage zone and the exchange flow with the storage zone with differences of up to 4 and 2 orders of magnitude compared to results with identifiable model parameters respectively. The clear differences in the transport metrics between results obtained from our proposed approach and results from the classic random sampling approach also resulted in contrasting interpretations of the hydrologic processes controlling solute transport in a headwater stream in western Luxembourg. Thus, our outcomes point to the risks of interpreting TSM results when even one of the model parameters is non-identifiable. Our results showed that coupling global identifiability analysis with dynamic identifiability analysis in an iterative approach clearly increased parameter identifiability in random sampling approaches for TSMs. Compared to the commonly used random sampling approach and inverse modelling results, our analysis was effective at obtaining higher accuracy of the evaluated solute transport metrics, which is advancing our understanding of hydrological processes that control in-stream solute transport.

Transient Storage Model Parameter Optimization Using the Simulated Annealing Method

AbstractHyporheic exchange in streams is critical to ecosystem functions such as nutrient cycling along river corridors, especially for slowly moving or small stream systems. The transient storage model (TSM) has been widely used for modeling of hyporheic exchange. TSM calibration, for hyporheic exchange, is typically used to estimate four parameters, including the mass exchange rate coefficient, the dispersion coefficient, stream cross‐sectional area, and hyporheic zone cross‐sectional area. Prior studies have raised concerns regarding the non‐uniqueness of the inverse problem for the TSM, that is, the occurrence of different parameter vectors resulting in TSM solution that reproduces the observed in‐stream tracer break through curve (BTC) with the same error. This leads to practical non‐identifiability in determining the unknown parameter vector values even when global‐optimal values exist, and the parameter optimization becomes practically non‐unique. To address this problem, we applied the simulated annealing method to calibrate the TSM to BTCs, because it is less susceptible to local minima‐induced non‐identifiability. A hypothetical (or synthetic) tracer test data set with known parameters was developed to demonstrate the capability of the simulated annealing method to find the global minimum parameter vector, and it identified the “hypothetically‐true” global minimum parameter vector even with input data that were modified with up to 10% noise without increasing the number of iterations required for convergence. The simulated annealing TSM was then calibrated using two in‐stream tracer tests conducted in East Fork Poplar Creek, Tennessee. Simulated annealing was determined to be appropriate for quantifying the TSM parameter vector because of its search capability for the global minimum parameter vector.

Surrogate prediction of the breakthrough curve of solute transport in rivers using its reach length dependence

Techniques for predicting the contaminant cloud propagation along a stream are necessary for swift action against contaminant spill accidents in fluvial systems. Due to their low computational cost, one-dimensional solute transport models have conventionally been employed, in which the complex channel characteristics are considered using model parameters. However, the determination of such parameters relies predominantly on optimization techniques based on pre-measured tracer data, which are usually unavailable for unexpected accidents. The present paper suggests an alternative method for predicting a breakthrough curve (BTC) variation along an unmeasured stream reach where no flow information is provided. In this study, we investigated the relationship between directly-measured flow properties and BTC characteristics based on field tracer experiments. Using statistical features of the tracer BTCs, we devised a regressive prediction method for estimating the BTC features as a function of travel distance, and validated the method by comparison with simulations using both a one-dimensional advection–dispersion equation (ADE) and transient storage model (TSM), whose parameters were calibrated at upstream reaches. The proposed regressive predictions were relatively accurate than those from parameter-calibrated models, and this advantage was more apparent for long-distance predictions for the unmeasured river reach.

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.

An efficient fractional-in-time transient storage model for simulating the multi-peaked breakthrough curves

The multi-peaking phenomenon in a breakthrough curve (BTC) is a typical character of solute transport in complex flow fields such as a karst aquifer. Previous understanding and modeling techniques for the single-peaked BTCs would no longer be adequate for the multi-peaked one. In a traditional non-Fickian model, the overall non-Fickian effect is simply the summation of contributions from each immobile zone or heterogeneous flow path. Therefore, a resultant BTC is not sensitive to the exact location of the immobile zones on the pathway of solute, and the local peaks cannot be reproduced effectively. In this study, we introduce a fractional-in-time transient storage (TS) model (FTTS), in which, the TS zones are arranged in series (e.g., triggered at specific times) to simulate different locations of each TS zone or immobile zone along the river channel. The simulation power of the FTTS was tested by simulating observations from a tracer experiment conducted in a subterranean river and data generated from two synthetic cases. Meanwhile, the simulation results of the FTTS were compared with those from the fractional mobile/immobile model (FMIM) and the multi-rate transient storage model (MRTS). Results show that both FTTS and MRTS models could well simulate the multi-peaking phenomenon in BTC and perform better than FMIM. Further to that, compared to MRTS, the FTTS is a more efficient model because (1) when containing the same number of TS zones, the FTTS performs significantly better, and (2) when achieving similar accuracy, the FTTS uses fewer TS terms (corresponding to a smaller number of parameters) than MRTS. Moreover, all TS terms in the FTTS can form a one-to-one correspondence with the local peaks of BTC, which may be helpful for better characterizing the internal morphology of a flow field.

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.

Groundwater–Stream Connectivity Mediates Metal(loid) Geochemistry in the Hyporheic Zone of Streams Impacted by Historic Mining and Acid Rock Drainage

High concentrations of trace metal(loid)s exported from abandoned mine wastes and acid rock drainage pose a risk to the health of aquatic ecosystems. To determine if and when the hyporheic zone mediates metal(loid) export, we investigated the relationship between streamflow, groundwater–stream connectivity, and subsurface metal(loid) concentrations in two ~1-km stream reaches within the Bonita Peak Mining District, a US Environmental Protection Agency Superfund site located near Silverton, Colorado, USA. The hyporheic zones of reaches in two streams—Mineral Creek and Cement Creek—were characterized using a combination of salt-tracer injection tests, transient-storage modeling, and geochemical sampling of the shallow streambed (<0.7 m). Based on these data, we present two conceptual models for subsurface metal(loid) behavior in the hyporheic zones, including (1) well-connected systems characterized by strong hyporheic mixing of infiltrating stream water and upwelling groundwater and (2) poorly connected systems delineated by physical barriers that limit hyporheic mixing. The comparatively large hyporheic zone and high hydraulic conductivities of Mineral Creek created a connected stream–groundwater system, where mixing of oxygen-rich stream water and metal-rich groundwater facilitated the precipitation of metal colloids in the shallow subsurface. In Cement Creek, the precipitation of iron oxides at depth (~0.4 m) created a low-hydraulic-conductivity barrier between surface water and groundwater. Cemented iron oxides were an important regulator of metal(loid) concentrations in this poorly connected stream–groundwater system due to the formation of strong redox gradients induced by a relatively small hyporheic zone and high fluid residence times. A comparison of conceptual models to stream concentration–discharge relationships exhibited a clear link between geochemical processes occurring within the hyporheic zone of the well-connected system and export of particulate Al, Cu, Fe, and Mn, while the poorly connected system did not have a notable influence on metal concentration–discharge trends. Mineral Creek is an example of a hyporheic system that serves as a natural dissolved metal(loid) sink, whereas poorly connected systems such as Cement Creek may require a combination of subsurface remediation of sediments and mitigation of upstream, iron-rich mine drainages to reduce metal export.

Investigating the relationships between parameters in the transient storage model and the pool volume in karst conduits through tracer experiments

The tailing of breakthrough curves (BTCs) commonly observed in the field is often associated with the existence of pools in karst conduits. The transient storage model was always used to simulate the BTC tailing caused by the storage zone, i.e. pool, however, the relationship between parameters in this model and pool volume is not clear, which is very useful for the understanding of the internal geometry of the conduit using this model or prediction of the contaminant transport. In this paper, we performed a series of indoor tracer experiments in a pool-pipe system involving two different pool structures, symmetrical pool (SP) and asymmetrical pool (ASP) with different positions, sizes, and numbers, to explore the relationship between model parameters and the pool volume. Several experiments were conducted in the ASP of 20 cm with different discharges so as to investigate the effect of turbulent flow condition on model parameters. The experimental results indicate that the duration time of the BTC, and the mean residence time of the solute increase linearly with the pool volume (pool size or pool number). For the model parameters, the cross-sectional area of the storage zone (As) or the calculated volume (Vs) of the storage zone using As shows a good linear relationship with the pool volume (Vp) (As = 0.0078Vp + 3E−06; Vs = 0.8195Vp + 0.0003, R2 = 0.95) indicating a potential to use this parameter, which is almost constant with the discharge, to roughly estimate the pool volume. The cross-sectional area (A) of the main channel does not change with the pool volume and changes little with the discharge; it has a close value to the actual cross-sectional area. The remaining parameters, dispersion coefficient (D) and exchange coefficient (α), have strong connections with the pool type, pool distribution or flow condition, which can hardly be used to deduce the internal conduit structure directly. The relationships between model parameters and the pool volume are helpful to use the model parameters to identify the conduit geometry roughly.

High-Performance Simulation of Dynamic Hydrologic Exchange and Implications for Surrogate Flow and Reactive Transport Modeling in a Large River Corridor

Hydrologic exchange flows (HEFs) have environmental significance in riverine ecosystems. Key river channel factors that influence the spatial and temporal variations of HEFs include river stage, riverbed morphology, and riverbed hydraulic conductivity. However, their impacts on HEFs were often evaluated independently or on small scales. In this study, we numerically evaluated the combined interactions of these factors on HEFs using a high-performance simulator, PFLOTRAN, for subsurface flow and transport. The model covers 51 square kilometers of a selected river corridor with large sinuosity along the Hanford Reach of the Columbia River in Washington, US. Three years of spatially distributed hourly river stages were applied to the riverbed. Compared to the simulation when riverbed heterogeneity is not ignored, the simulation using homogeneous riverbed conductivity underestimated HEFs, especially upwelling from lateral features, and overestimated the mean residence times derived from particle tracking. To derive a surrogate model for the river corridor, we amended the widely used transient storage model (TSM) for riverine solute study at reach scale with reactions. By treating the whole river corridor as a batch reactor, the temporal changes in the exchange rate coefficient for the TSM were derived from the dynamic residence time estimated from the hourly PFLOTRAN results. The TSM results were evaluated against the effective concentrations in the hyporheic zone calculated from the PFLOTRAN simulations. Our results show that there is potential to parameterize surrogate models such as TSM amended with biogeochemical reactions while incorporating small-scale process understandings and the signature of time-varying streamflow to advance the mechanistic understanding of river corridor processes at reach to watershed scales. However, the assumption of a well-mixed storage zone for TSM should be revisited when redox-sensitive reactions in the storage zones play important roles in river corridor functioning.

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.