The flank margin model for dissolution cave development in carbonate platforms

The Bahama Islands contain many abandoned dissolution caves at elevations between two and seven metres above current sea level. The development of dissolution caves in tropical carbonate islands is dependent on the position and nature of the freshwater lens. Lens position is controlled by sea level, which in stable carbonate platforms like the Bahamas is a function of glacioeustatic sea level still stands. Caves in the Bahamas that are currently subaerial must have developed during past higher sea levels. During the Late Quaternary, sea levels higher than present have been relatively short-lived, and that limits the amount of time that a freshwater lens could be situated at the elevation required for the cave formation. The Bahama Islands are low-lying landforms where only aeolian ridges extend to elevations higher than six metres above current sea level. Past high sea level events greatly reduced the exposed land area of the Bahama Islands, thus also limiting both the catchment for and size of freshwater lenses. Caves must be younger than the rock in which they are developed; most subaerial Bahamian caves are found in limestones that are less than 150000 years old. Development of large dissolution caves under these limitations of time and lens size requires a powerful dissolutional mechanism. The mixing of discharging freshwater with tide-pulsed incoming marine water under the flanks of emergent dune ridges may have produced the conditions necessary. Bahamian caves formed by this process are phreatic chambers with complex interconnections and blind tubes. Their presence demonstrates that significant dissolution can occur rapidly as a result of the mixing of fresh and marine waters beneath small carbonate islands.     

The use of sulfur hexafluoride (SF6) as a tracer of septic tank effluent in the Florida Keys

To determine the fate and movement of sewage derived contaminants and their possible interaction with surface waters in the Florida (USA) Keys, two types of experiments were conducted using SF₆ as an artificial tracer. The first type of experiment examined fluid flow from septic tanks placed in Miami Oolite on Big Pine Key, where there is a shallow freshwater lens overlying saline groundwaters. Here groundwater transport rates were constrained to be between 0.11 and 1.87 m/h, travelling in an easterly direction. The second type of experiment took place on Key Largo where there is no freshwater aquifer and the matrix of the aquifer is solely the more porous Key Largo limestone. Here we injected the tracer into a shallow well which was screened from 0.6 to 10 m. This allowed us to evaluate groundwater movement in the shallow upper portion of the aquifer, the area to which inputs by septic tanks occur. Groundwater transport rates in the Upper Keys were as great as 3.7 m/h and were controlled by the Atlantic tide. SF₆ laden groundwater plumes moved back and forth due to tidal pumping and reached nearby surface waters within 8 h.     

Application of a mixing-ratios based formulation to model mixing-driven dissolution experiments

We address the question of how one can combine theoretical and numerical modeling approaches with limited measurements from laboratory flow cell experiments to realistically quantify salient features of complex mixing-driven multicomponent reactive transport problems in porous media. Flow cells are commonly used to examine processes affecting reactive transport through porous media, under controlled conditions. An advantage of flow cells is their suitability for relatively fast and reliable experiments, although measuring spatial distributions of a state variable within the cell is often difficult. In general, fluid is sampled only at the flow cell outlet, and concentration measurements are usually interpreted in terms of integrated reaction rates. In reactive transport problems, however, the spatial distribution of the reaction rates within the cell might be more important than the bulk integrated value. Recent advances in theoretical and numerical modeling of complex reactive transport problems [De Simoni M, Carrera J, Sanchez-Vila X, Guadagnini A. A procedure for the solution of multicomponent reactive transport problems. Water Resour Res 2005;41:W11410. doi: 10.1029/2005WR004056, De Simoni M, Sanchez-Vila X, Carrera J, Saaltink MW. A mixing ratios-based formulation for multicomponent reactive transport. Water Resour Res 2007;43:W07419. doi: 10.1029/2006WR005256] result in a methodology conducive to a simple exact expression for the space–time distribution of reaction rates in the presence of homogeneous or heterogeneous reactions in chemical equilibrium. The key points of the methodology are that a general reactive transport problem, involving a relatively high number of chemical species, can be formulated in terms of a set of decoupled partial differential equations, and the amount of reactants evolving into products depends on the rate at which solutions mix. The main objective of the current study is to show how this methodology can be used in conjunction with laboratory experiments to properly describe the key processes that occur in a complex, geochemically-active system under chemical equilibrium conditions. We model three CaCO₃ dissolution experiments reported in Singurindy et al. [Singurindy O, Berkowitz B, Lowell RP. Carbonate dissolution and precipitation in coastal environments: Laboratory analysis and theoretical consideration. Water Resour Res 2004;40:W04401. doi: 10.1029/2003WR002651, Singurindy O, Berkowitz B, Lowell RP. Correction to Carbonate dissolution and precipitation in coastal environments: laboratory analysis and theoretical consideration. Water Resour Res 2005;41:W11701. doi: 10.1029/2005WR004433], in which saltwater and freshwater were mixed in different proportions. The integrated reaction rate within the cell estimated from the experiments are modeled independently by means of (a) a state-of-the-art reactive transport code, and (b) the uncoupled methodology of [12, 13], both of which use dispersivity as a single, adjustable parameter. The good agreement between the results from both methodologies demonstrates the feasibility of using simple solutions to design and analyze laboratory experiments involving complex geochemical problems.     

Diagenetic transformations and silcrete–calcrete intergrade duricrust formation in palaeo‐estuary sediments

The Boteti palaeo‐estuary in northern Botswana is located where the endoreic Boteti river, an overflow from the regional Okavango river system, enters the Makgadikgadi pans. The present work considers diagenetic silica and calcium carbonate dominated transformations. The aims are to help identify precursor conditions for the origin of microcrystalline silcrete–calcrete intergrade deposits while developing insight into pene‐contemporaneous silica and calcite matrix formation. General precursor conditions require the presence of cyclical endoreic freshwater inflow into a saline pan. The pan should be deep enough to sustain a permanent watertable under climatic conditions sufficient to cause carbonate fractionation within the groundwater. Freshwater inflow into a saline pan drives the geochemistry of the system (from freshwater to saline, from neutral to high pH). The geochemistry is controlled by the periodicity of inflow relative to salinity levels of phreatic groundwater in the receptor saline pan. The source of most silica and localized CaCO₃ is derived from the dissolution and precipitation of micro‐fossils, while more general CaCO₃ enrichment stems from saline pan based carbonate fractionation. Diagenetic change leads to colloidal then more consolidated bSiO₂/CaO aggregate formation (amorphous silica) followed by transformations into opaline silica over time. Irregular zones of siliceous sediment forming in otherwise calcareous deposits may relate to the irregular occurrence of biogenic silica in the source sediments, inferring a source for local silica mobilization in intergrade deposits. The distribution of calcareous micro‐fossils may have a similar converse effect. Diagenetic evidence from an intergrade deposit with a low SiO₂/CaO ratio suggests that transformation occurred more into the pan, while an intergrade deposit with a high SiO₂/CaO ratio more likely formed closer to a land margin and was frequently inundated by freshwater. Pene‐contemporaneous silcrete–calcrete intergrade formation under the above conditions may take place where dissolved silica crystallizes out in the vicinity of calcite crystals due to local decreases in pH. The continuing consolidation of bSiO₂/CaO aggregates may be facilitated by the presence of increasing amounts of calcite. It appears that CaCO₃ may act as a catalyst leading to pene‐contemporaneous bSiO₂/CaO aggregate formation. However the processes involved require further work. Copyright © 2013 John Wiley & Sons, Ltd.     

Transport and Biological Fate of Toluene in Low-Permeability Soils

The effect of simultaneous sorption, diffusion, and biodegradation on the fate and transport of toluene in low-permeability soil formations was examined. A transport model accounting for vapor and liquid sorption, vapor diffusions, and first-order biodegradation was developed to describe the movement of volatile solute in unsaturated soils. Modeling studies were followed with laboratory batch and column studies on fine-grained soil samples obtained from a gasoline-contaminated site. Batch experiments yielded the sorption and diffusion coefficients for generating theoretical solute transport profiles. Column studies were conducted to examine toluene sorption, diffusion, and biodegradation under aerobic and denitrifying conditions. Results from the column studies indicated that vapor sorption onto the soil was minimal due to the high moisture content of the soil. Comparison of model predictions with experimental results indicated that the SASK model, which is based on the resistivity theory, provided a more accurate prediction of the vapor phase tortuosity than the frequently used Millington-Quirk equation. Laboratory results of toluene concentration profiles matched well with the model predictions and yielded degradation rates comparable to those obtained in the field. Column studies, examining toluene biodegradation under aerobic and denitrifying conditions in low-permeability soils, indicated that the presence of excess nitrate in aerobic environments yielded higher solute degradation rates than those observed under exclusively aerobic systems.     

Crude Oil at the Bemidji Site: 25 Years of Monitoring,Modeling, and Understanding

The fate of hydrocarbons in the subsurface near Bemidji, Minnesota, has been investigated by a multidisciplinary group of scientists for over a quarter century. Research at Bemidji has involved extensive investigations of multiphase flow and transport, volatilization, dissolution, geochemical interactions, microbial populations, and biodegradation with the goal of providing an improved understanding of the natural processes limiting the extent of hydrocarbon contamination. A considerable volume of oil remains in the subsurface today despite 30 years of natural attenuation and 5 years of pump‐and‐skim remediation. Studies at Bemidji were among the first to document the importance of anaerobic biodegradation processes for hydrocarbon removal and remediation by natural attenuation. Spatial variability of hydraulic properties was observed to influence subsurface oil and water flow, vapor diffusion, and the progression of biodegradation. Pore‐scale capillary pressure‐saturation hysteresis and the presence of fine‐grained sediments impeded oil flow, causing entrapment and relatively large residual oil saturations. Hydrocarbon attenuation and plume extent was a function of groundwater flow, compound‐specific volatilization, dissolution and biodegradation rates, and availability of electron acceptors. Simulation of hydrocarbon fate and transport affirmed concepts developed from field observations, and provided estimates of field‐scale reaction rates and hydrocarbon mass balance. Long‐term field studies at Bemidji have illustrated that the fate of hydrocarbons evolves with time, and a snap‐shot study of a hydrocarbon plume may not provide information that is of relevance to the long‐term behavior of the plume during natural attenuation.     

Relative change in stream discharge from a tropical watershed improves predictions of fecal bacteria in near-shore environments

Statistical models poorly predict bacteria in near-shore environments of tropical islands due to inaccuracies in runoff and discharge characterization of storm events. Intense, short duration storms on small, steeply sloped watersheds produce high rates of runoff, resulting in rapid pulses of discharge that influence the physical and physiological conditions of the fate and transport of pathogens. As such, increasing rates of discharge are expected to have a different influence on sediment transport and pathogen load compared to decreasing rates of discharge. Regression modeling was used to examine the affect of antecedent streamflow on the interaction between environmental parameters and two fecal indicator bacteria, enterococci and Clostridium perfringens. Including the relative change in discharge incorporates a proximate representation of the energy available to transport particulates, improving predictions of near-shore water quality. Understanding factors that influence pathogen loads improves management of watersheds and protects public health.     

Patterns of damage in igneous and sedimentary rocks under conditions simulating sea‐salt weathering

A saline‐spray artificial ageing test was used to simulate the effects produced in granites and sedimentary rocks (calcarenites, micrites and breccia) under conditions in coastal environments. Three main points were addressed in this study: the durability of the different kinds of rock to salt decay, the resulting weathering forms and the rock properties involved in the weathering processes. For this, mineralogical and textural characterization of each of the different rocks was carried out before and after the test. The soluble salt content at different depths from the exposed surfaces was also determined. Two different weathering mechanisms were observed in the granite and calcareous rocks. Physical processes were involved in the weathering of granite samples, whereas dissolution of calcite was also involved in the deterioration of the calcareous rocks. We also showed that microstructural characteristics (e.g. pore size distribution), play a key role in salt damage, because of their influence on saline solution transport and on the pressures developed within rocks during crystallization. Copyright © 2003 John Wiley & Sons, Ltd.     

Modeling microbial transport in porous media: Traditional approaches and recent developments

A substantial research effort has been aimed at elucidating the role of various physical, chemical and biological factors on microbial transport and removal in natural subsurface environments. The major motivation of such studies is an enhanced mechanistic understanding of these processes for development of improved mathematical models of microbial transport and fate. In this review, traditional modeling approaches used to predict the migration and removal of microorganisms (e.g., viruses, bacteria, and protozoa) in saturated porous media are systematically evaluated. A number of these methods have inherent weaknesses or inconsistencies which are often overlooked or misunderstood in actual application. Some limitations of modeling methods reviewed here include the inappropriate use of the equilibrium adsorption approach, the observed breakdown of classical filtration theory, the inability of existing theories to predict microbial attachment rates, and omission of physical straining and microbe detachment. These and other issues are considered with an emphasis on current research developments. Finally, recently proposed improvements to the most commonly used filtration model are discussed, with particular consideration of straining and microbe motility.     

Modelling the growth of cyanobacteria (GrowSCUM)

Toxic cyanobacteria have become a common nuisance in freshwater lakes and reservoirs throughout the world, sometimes resulting in the closure of sites with high amenity value. Cyanobacteria are able to regulate their buoyancy state in response to changing photosynthetic rates. Additionally, the cyanobacteria are liable to become entrained within wind-induced near-surface turbulent currents, resulting in mixing and mass transport. These movement processes have been modelled. A mathematical function is presented which describes light- and nutrient-limited cyanobacterial growth. The growth model is integrated with a previous movement model (SCUM: simulation of cyanobacterial underwater movement) as movement patterns and wind-induced lake mixing strongly affect the intensity and duration of light received by the cyanobacteria and thereby determine the photosynthetic potential. Results of the model suggest that cyanobacteria are resistant to periods of lake mixing and continue to increase their biomass, but at a depressed rate. Growth is most rapid under calm conditions. The results agree well with field-based findings, confirming the validity of the growth function.     

Livestock wastewater treatment by a mangrove pot-cultivation system and the effect of salinity on the nutrient removal efficiency

The present investigation compared the capacity of greenhouse pot-cultivation systems under two salinity conditions (freshwater and saline water) with two mangrove species (Bruguiera gymnorrhiza and Kandelia candel) to remove nutrients from livestock wastewater. During the whole treatment period there were relatively stable leachate TOC concentrations for wastewater-treated pots. Leachate NH4(+)-N concentration of B. gymnorrhiza pots was generally lower than that of K. candel pots. Leachate PO4(3-)-P concentration of pots receiving wastewater under freshwater condition was higher than that under saline water condition. Soil inorganic N content was more than two times higher for the wastewater treatments than that for the controls under low salinity condition and slower rate of increase under saline water condition. Soil P nutrients of both total and extractable inorganic forms significantly increased for both systems due to the discharges of livestock wastewater under both salinity conditions. The rate of increase in P contents for plants receiving livestock wastewater was 1-4 times that of the controls, much more than that in N contents (0.04-1.30 times). N nutrient removal efficiencies were 84.3% (65.6% by soil and 18.7% by plant) and 95.5% (32.2% by soil and 63.4% by plant), respectively by Kandelia candel and B. gymnorrhiza pot-cultivation systems under freshwater condition. Under saline water condition, N nutrient removal efficiencies by K. candel and B. gymnorrhiza pot-cultivation systems were 92.7% (80.7% by soil and 12.0% by plant) and 98.0% (67.6% by soil and 30.3% by plant), respectively. P nutrient removal efficiencies by K. candel and B. gymnorrhiza systems under freshwater condition were 79.2% (76.6% by soil and 2.6% by plant) and 91.8% (88.2% by soil and 3.6% by plant), respectively. The corresponding values were 88.0% (84.2% by soil and 3.8% by plant) and 97.8% (95.9% by soil and 1.9% by plant) under saline water condition.     

A reappraisal of the Engelund bed load equation

Abstract

Many bed load transport equations have been developed from differing standpoints. The Engelund equation has been selected for scrutiny since, although it accords well with experimental data in general, it has limitations under conditions of high bed load transport rates. The application of two phase flow theory has been used to derive an alternative “Engelund” equation which may be applied to both high and low transport rates.     

Mass Flux Analysis of Abiotic Tetrachloroethene Dense Nonaqueous Phase Liquid Pool Dissolution in a Heterogeneous Flow Environment

Porous aquifer materials are often characterized by layered heterogeneities that influence groundwater flow and present complexities in contaminant transport modeling. Such flow variations also have the potential to impact the dissolution flux from dense nonaqueous phase liquid (DNAPL) pools. This study examined how these heterogeneous flow conditions affected the dissolution of a tetrachloroethene (PCE) pool in a two-dimensional intermediate-scale flow cell containing coarse sand. A steady-state mass-balance approach was used to calculate the PCE dissolution rate at three different flow rates. As expected, aqueous PCE concentrations increased along the length of the PCE pool and higher flow rates decreased the aqueous PCE concentration in the effluent. Nonreactive tracer studies at two flow rates confirmed the presence of a vertical flow gradient, with the most rapid velocity located at the bottom of the tank. These results suggest that flow focusing occurred near the DNAPL pool. Effluent PCE concentrations and pool dissolution flux rates were compared to model predictions assuming local equilibrium (LE) conditions at the DNAPL pool/aqueous phase interface and a uniform distribution of flow. The LE model did not describe the data well, even over a wide range of PCE solubility and macroscopic transverse dispersivity values. Model predictions assuming nonequilibrium mass-transfer-limited conditions and accounting for vertical flow gradients, however, resulted in a better fit to the data. These results have important implications for evaluating DNAPL pool dissolution in the field where subsurface heterogeneities are likely to be present.     

Urban environments as habitats for rare aquatic species: The case of leeches (Euhirudinea, Clitellata) in Warsaw freshwaters

Reduced biological diversity in freshwater habitats situated in urban areas has been discussed in numerous studies. Certain municipal areas, however, can help save animal diversity of freshwater invertebrates. In the present study animals were collected or observed alive in 13 freshwater environments localized in Warsaw - the second largest city of Central Europe - in a densely populated, urban building complex close to the city, and also in suburban areas. Leech assemblages in all the environments under observation were numerically dominated by a few common species, but on the whole 19 species were collected or observed. The populations of six rare leech species inhabit both flowing and standing waters in Warsaw. Five of these species are on the Polish Red List of Species and one is strictly protected. The shallow Lake Powsinkowskie is the richest freshwater environment in the studied area in terms of species richness and rarity and also one of the richest lakes in Poland. Taxonomic diversity in the environments under study seems not to be directly related to the size of the water body or the level of degradation but rather to the habitat complexity, especially the diversity of the bottom in littoral zone. Certain freshwater habitats located inside this great urban complex still create good conditions for rare, highly specialized species.     

An integrated approach for modeling solute transport in streams and canals with applications

A new modeling approach for solute transport in streams and canals was developed to simulate solute dissolution, transport, and decay with continuously migrating sources. The new approach can efficiently handle complicated solute source feeding schemes and initial conditions. Incorporating the finite volume method (FVM) and the ULTIMATE QUICKEST numerical scheme, the new approach is capable of predicting fate and transport of solute that is added to small streams or canals, typically in a continuous fashion. The approach was tested successfully using a hypothetical case, and then applied to an actual field experiment, where linear anionic polyacrylamide (LA-PAM) was applied to an earthen canal. The field experiment was simulated first as a fixed boundary problem using measured concentration data as the boundary condition to test model parameters and sensitivities. The approach was then applied to a moving boundary problem, which included subsequent LA-PAM dissolution, settling to the canal bottom and transport with the flowing canal water. Simulation results showed that the modeling approach developed in this study performed satisfactorily and can be used to simulate a variety of transport problems in streams and canals.     

Applying Quantitative Molecular Tools for Virus Transport Studies: Opportunities and Challenges

Bacteriophages have been used in soil column studies for the last several decades as surrogates to study the fate and transport behavior of enteric viruses in groundwater. However, recent studies have shown that the transport behavior of bacteriophages and enteric viruses in porous media can be very different. The next generation of virus transport science must therefore provide more data on mobility of enteric viruses and the relationship between transport behaviors of enteric viruses and bacteriophages. To achieve this new paradigm, labor intensity devoted to enteric virus quantification method must be reduced. Recent studies applied quantitative polymerase chain reaction (qPCR) to column filtration experiments to study the transport behavior of human adenovirus (HAdV) in porous media under a variety of conditions. A similar approach can be used to study the transport of other enteric viruses such as norovirus. Analyzing the column samples with both qPCR and culture assays and applying multiplex qPCR to study cotransport behavior of more than one virus will provide information to under‐explored areas in virus transport science. Both nucleic acid extraction kits and one‐step lysis protocols have been used in these column studies to extract viral nucleic acid for qPCR quantification. The pros and cons of both methods are compared herein and solutions for overcoming problems are suggested. As better understanding of the transport behavior of enteric viruses is clearly needed, we strongly advocate for application of rapid molecular tools in future studies as well as optimization of protocols to overcome their current limitations.     

Estimating the Impact of Vadose Zone Sources on Groundwater to Support Performance Assessment of Soil Vapor Extraction

Soil vapor extraction (SVE) is a prevalent remediation remedy for volatile organic compound (VOC) contaminants in the vadose zone. To support selection of an appropriate condition at which SVE may be terminated for site closure or for transition to another remedy, an evaluation is needed to determine whether vadose zone VOC contamination has been diminished sufficiently to keep groundwater concentrations below threshold values. A conceptual model for this evaluation was developed for VOC fate and transport from a vadose zone source to groundwater when vapor‐phase diffusive transport is the dominant transport process. A numerical analysis showed that, for these conditions, the groundwater concentration is controlled by a limited set of parameters, including site‐specific dimensions, vadose zone properties, and source characteristics. On the basis of these findings, a procedure was then developed for estimating groundwater concentrations using results from the three‐dimensional multiphase transport simulations for a matrix of parameter value combinations and covering a range of potential site conditions. Interpolation and scaling processes are applied to estimate groundwater concentrations at compliance (monitoring) wells for specific site conditions of interest using the data from the simulation results. The interpolation and scaling methodology using these simulation results provides a far less computationally intensive alternative to site‐specific three‐dimensional multiphase site modeling, while still allowing for parameter sensitivity and uncertainty analyses. With iterative application, the approach can be used to consider the effect of a diminishing vadose zone source over time on future groundwater concentrations. This novel approach and related simulation results have been incorporated into a user‐friendly Microsoft® Excel®‐based spreadsheet tool entitled SVEET (Soil Vapor Extraction Endstate Tool), which has been made available to the public.     

Continuum-scale convective mixing in geological CO2 sequestration in anisotropic and heterogeneous saline aquifers

Deep saline aquifers are important geological formations for CO₂ sequestration. It has been known that dissolution of CO₂ increases brine density, which results in downward density-driven convection and consequently greatly enhances CO₂ sequestration. In this study, a continuum-scale lattice Boltzmann model is used to investigate convective mixing of CO₂ in saline aquifers. It is found that increasing permeability in either the vertical or horizontal direction accelerates the development of convective mixing. In a heterogeneous aquifer, increasing heterogeneity hampers the onset of convective mixing, because the heterogeneous permeability field results in a large portion of low-velocity region which reduces the instability of the system. The critical time for the onset of instability depends mainly on the coefficient of variation (COV) of the permeability field, and is insensitive to the correlation length. This implies that within the scale of critical time, mass transport is dominated by diffusion, and thus depends mainly on fine-scale heterogeneity controlled by COV. We derived an empirical formula for estimating the critical time, which leads to good estimates for all combinations of COV and correlation length. Fingering, channeling, and dispersion are the three mechanisms for mass transport. In dispersion, dissolved mass is approximately proportional to the square root of time, while in fingering and channeling it is approximately proportional to time. Mass transport by channeling depends significantly on permeability structure, while by fingering it is controlled by gravitational instability. It is also found that larger volumes of CO₂ can be stored in heterogeneous aquifers because of higher mass dissolution rates.     

Modeling interaction of fluid and salt in an aquifer/lagoon system

To simulate the dynamic interaction between a saline lagoon and a ground water system, a numerical model for two-dimensional, variable-density, saturated-unsaturated, and coupled flow and solute transport (saltwater intrusion by finite elements and characteristics [SIFEC]) was modified to allow the volume of water and mass of salt in the lagoon to vary with each time step. The modified SIFEC allows the stage of a lagoon to vary in accordance with a functional relation between the stage and water volume of the lagoon, and also allows the salt concentration of the lagoon to vary in accordance with the salt budget of the lagoon including chemical precipitation and dissolution of salt. The updated stage and salt concentration of the lagoon are in turn used as transient boundary conditions for the coupled flow and solute transport model. The utility of the modified model was demonstrated by applying it to the eastern Mediterranean coastal region of Turkey for assessing impacts of climate change on the subsurface environment under scenarios of sea level rise, increased evaporation, and decreased precipitation.     

A simple approach to estimating freshwater discharge in branched estuarine systems

In tidal estuaries, quantifying freshwater discharge is still a difficult problem that has not yet been overcome due to the inherent difficulty in measuring and analysing the tidal discharge, especially during periods of low river flow. Because observations are often made in the stations further upstream, where the ratio of river to tidal discharge is large, it remains difficult to determine the discharge rate in the saline region. Freshwater discharge estimation is even more difficult in a branched estuary system having multiple diversion channels that connect with each other at a junction. To date, several methods have been developed for estimating freshwater discharge in estuaries. The most widely used are analytical and conceptual models that employ salinity as the principal trace and numerical simulations. However, these methods are very time consuming and costly as they require large sets of observations before the computations can take place. This paper presents a simple approach to investigating the discharge distribution over branched channels by considering the energy loss due to friction. We develop an analytical model that can obtain the discharge rate quantitatively at a junction where the main flow bifurcates into two branches. The model uses the bed roughness, tidal water level, and cross‐sectional profile under tidally averaged conditions as input data. Two selected estuarine systems in the Hiroshima delta in Japan and the Mekong delta in Vietnam have been investigated. Computations of the newly developed model show good agreement with earlier published results computed by sophisticated analytical and numerical models.