Modelling sediment transport processes in macro-tidal estuary

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ANDENERG FUEL ENERGY & FUELS0887-0624工程技术2N。

新加坡国立大学水利工程与水资源管理授课型研究生申请要求新加坡国立大学简介学校名称新加坡国立大学学校英文名称National University of Singapore学校位置新加坡2020 QS 世界排名11新加坡国立大学概述新加坡国立大学（National University ofSingapore），简称国大（NUS），是新加坡首屈一指的世界级顶尖大学。

该校是环太平洋大学联盟、亚洲大学联盟、亚太国际教育协会、国际研究型大学联盟、Universitas21等著名高校联盟的成员，也通过AACSB和EQUIS认证。

其在工程、生命科学及生物医学、社会科学及自然科学等领域的研究享有世界盛名。

新加坡国立大学前身为1905年成立的海峡殖民地与马来亚联邦政府医学院。

1912年，该校改名为爱德华七世医科学校。

1928年，莱佛士学院成立。

1949年，爱德华七世医学院与莱佛士学院合并为马来亚大学。

1955年，新加坡华人社团组织创立了南洋大学。

1962年，马来亚大学位于新加坡的校区独立为新加坡大学。

1980年，新加坡大学和南洋大学合并，校名定为新加坡国立大学。

水利工程与水资源管理专业简介理学硕士(水利工程与水资源管理)项目，简称HEWRM，由土木与环境工程系主办。

该项目招收全日制和非全日制学生。

获得理学士学位的资格:考生必须成功完成至少40学分的学习计划。

土木与环境工程学院所开设的相关学科中，至少有30名硕士研究生。

对于其他模块，必须事先获得土木与环境工程部负责人或其指定人员的批准。

核心要求共28个MCs，其中8个MCs以M.Sc.(HEWRM)项目的形式存在，学生将在HEWRM领域从事创新研究，这需要得到土木与环境工程系主任或其提名者的批准。

剩下的12个MCs将从选修模块中获得。

此外，学生必须获得最低累积平均分(上限)3.00分(相当于B-的平均分数)，最好的模块相当于40微秒(包括核心模块，如有需要)。

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Modelling long-term contaminant migration in a catchment at ®ne spatial and temporal scales using the UP systemW.T.Sloan*and J.EwenWater Resource Systems Research Laboratory,Department of Civil Engineering,University of Newcastle upon Tyne,Newcastle upon Tyne,NE17RU,UKAbstract:A method has been developed to simulate the long-term migration of radionuclides in the near-surface of a river catchment,following their release from a deep underground repository for radioactive waste.Previous (30-year)simulations,conducted using the SHETRAN physically based modelling system,showed that long-term (many decades)simulations are required to allow the system to reach steady state.Physically based,distributed models,such as SHETRAN,tend to be too computationally expensive for this task.Traditional lumped catchment-scale models,on the other hand,do not give su ciently detailed spatially distributed results.An intermediate approach to modelling has therefore been developed which allows ¯ow and transport processes to be simulated with the spatial resolution normally associated with distributed models,whilst being computa-tionally e cient.The approach involves constructing a lumped model in which the catchment is represented by a number of conceptual water storage compartments.The ¯ow rates to and from these compartments are prescribed by functions that summarize the results from physically based distributed models run for a range of characteristic ¯ow regimes.The physically based models used were,SHETRAN for the subsurface compartments,a particle tracking model for overland ¯ow and an analytical model for channel routing.One important advantage of the method used in constructing the lumped model is that it makes down scaling possible,in the sense that ®ne-scale information on the distributed hydrological regime,as simulated by the physically based distributed models,can be inferred from the variables in the lumped model that describe the hydrology at the catchment scale.A 250-year ¯ow simulation has been run and the down scaling process used to infer a 250-year time-series of three-dimensional velocity ®elds for the subsurface of the catchment.This series was then used to drive a particle tracking simulation of contaminant migration.The concentration and spatial distribution of con-taminants simulated by this model for the ®rst 30years were in close agreement with SHETRAN results.The remaining 220years highlighted the fact that some of the most important transport pathways to the surface carry contaminants only very slowly so both the magnitude and spatial distribution of concentration in surface soils are not apparent over the shorter SHETRAN simulations.Copyright #1999John Wiley &Sons,Ltd.KEY WORDS catchment modelling;contaminant transport;up scaling;down scaling;environmental impact assessment;radionuclidesHYDROLOGICAL PROCESSES Hydrol.Process .13,823±846(1999)*Correspondence to Dr W.T.Sloan,Department of Civil Engineering,Cassie Building,University of Newcastle,Newcastle upon Tyne,NE17RU,UK.Contract grant sponsor:UK Nirex Ltd;NERC.824W.T.SLOAN AND J.EWENINTRODUCTIONHydrologists are increasingly being called upon to develop models of hydrology and solute transport for river basins that can be used to assess the e ects of environmental change over very long time periods.This has been prompted by two main concerns:®rst,the e ect on water resources of a probable impending change in the earth's climate(Houghton et al.,1996);secondly,the e ect of more immediate anthropogenically induced change in land use and pollution levels.In the past,river basin models aimed at addressing these concerns have often been developed at the behest of policy makers,under the in¯uence of advice from scientists regarding current technical capabilities.As a consequence,the demands made of the models and their ability to meet these demands have usually been well matched.Recently,however,policy makers have taken a much more active role in setting the underlying fundamental research agendas for environmental scientists,as an increased awareness of environmental issues within the public at large has forced governments to investigate openly the long-term environmental e ects of their policies.As a result,the detailed technical questions being posed by policy makers often go beyond the capabilities of the currently available modelling tools to produce answers(Harvey and White, 1995),and environmental modellers are,therefore,having to conduct research into new approaches to predicting the long-term e ects of environmental change.One example of such research stems from issues arising in relation to the disposal of low and intermediate level radioactive wastes.Within the UK,it is proposed to bury the waste in a repository deep below the earth's surface,and United Kingdom Nirex Limited(Nirex)has been given responsibility for developing a deep geological repository(Nirex,1995).While most radionuclides would decay in situ within a repository,on the time-scale of thousands to tens of thousands of years,some radionuclides could escape and be transported in groundwater to the earth's surface.A key component of assessing the post-closure safety of a repository is the evaluation of the radiological risks to individuals who might be exposed to released radionuclides(Environ-ment Agency et al.,1997).An important part of assessing this risk is to quantify the e ects of competing dilution and accumulation processes in the near-surface(the top few tens of metres)on the concentrations and spatial distribution of radionuclides in surface soils and surface waters(Nirex,1995).The complex nature of the interactions between these processes makes their e ects impractical to assess without the use of numerical models.Furthermore,the spatial distribution of contaminants may take many years to become fully developed and,therefore,the models used must be capable of simulating long time periods. Lumped,catchment-scale models have been developed to simulate the e ects of environmental change over very long time periods(e.g.Cosby et al.,1985);large catchments are often represented by an array of such models(e.g.Whitehead et al.,1998).However,these do not give®ne-scale,spatially distributed information on,say,the distribution of contaminants over the surface of a catchment.Conversely,the physically based distributed modelling systems currently available,such as SHETRAN(Ewen,1995),do supply spatially distributed information,but tend to be very computationally expensive;a fact that has precluded their use in very long-term simulations for the assessment of environmental change.Therefore, what is needed for long-term simulation is an intermediate approach to modelling,which gives some of the detail of physically based models yet is as practical as lumped catchment models for simulating behaviour over hundreds of years.This paper demonstrates the theory and application of the UP system(the name derives from upscaled physically-based)which uses such an intermediate approach.The UP system is computationally e cient and has been developed to simulate hydrology and solute and sediment transport at a®ne temporal resolution and a variety of spatial scales,ranging from the catchment scale(tens of square kilometres)to the continental scale.It is currently being used in a variety of research applications including environmental impact assessment,and is being coupled with a general circulation model(GCM)(as part of the TIGER project funded by the Natural Environmental Research Council,UK). The system is described in Ewen(1997)and has been developed further for the long-term modelling of water ¯ow and solute transport in a catchment.The ability of the UP system to produce some of the detail normally associated with physically based distributed models whilst remaining computationally e cient isdemonstrated here by showing that the results it gives for the ®rst 30years of a 250-year simulation are comparable with those from a 30-year SHETRAN simulation.The simulation described here is for a catchment with unchanging physical properties.However,the UP approach is very ¯exible,and similar simulations can readily be run for catchments undergoing prescribed changes in physical properties or climate.THE UP MODELLING APPROACHAt the core of the UP system is a computationally e cient catchment-scale model for water ¯ow,described as an UP element (Figure 1;adapted from Ewen,1997),which represents a catchment by a number of (conceptual)water storage compartments.Typically,the area of land represented by an UP element is less than 100km 2.For applications to a large river basin,the basin is represented by a mosaic of UP elements,the boundaries of which can lie on natural watersheds or a regular grid.The runo predicted from each UP element is routed by a model that describes the storage and ¯ow behaviour of the entire river basin channel network.The methodology for linking UP elements to represent large river basins is described elsewhere (Kilsby et al .,1996;Sloan et al .,1997).The UP elementIn traditional lumped catchment hydrological models,a catchment is represented by a number of conceptual water storage compartments.The standard approach involves using simple functions to relate the ¯ows into and out of each compartment to variables that describe the state of that compartment (e.g.volume of water stored).In some such models,the forms of the relationships between the ¯ows and variables relyonFigure 1.A schematic diagram of an UP elementMODELLING LONG-TERM CONTAMINANT MIGRATION 825826W.T.SLOAN AND J.EWENthe use of`e ective parameters'to describe the physical properties of the compartment.For example,in a compartment representing groundwater,the function may use a spatially averaged value of saturated hydraulic conductivity.The most appropriate functional forms and the best way of estimating e ective parameters is a topic that is vigorously debated in the hydrological literature under the headings of`e ective parameters',`upscaling'and`the scale problem'(e.g.Beven,1995;Bloschl and Sivapalan,1995).The UP system employs an altogether more pragmatic approach to characterizing the¯ows to and from the various compartments of an UP element,which to a large extent bypasses the debate mentioned above.The approach di ers from others in that it starts from the premise that physically based distributed models parameterized using spatially distributed data at the®nest scale available(ing high resolution digital elevation maps,DEMs)are currently the best available tools.Consequently,the¯ows between the compart-ments of an UP element should,as far as is practical,be characterized using simulation results from such models.To achieve this,an appropriate physically based distributed model is applied to each of the compartments for a range of characteristic physical conditions,and the results from this are used to create a summary data set for the state of the compartment(e.g.amount of water stored)and for the¯ows to and from the compartment.This summary data set is used to derive functions for the¯ows that depend upon the variables that describe the compartment's internal state(e.g.groundwater discharge as a function of ground-water storage),and it is these summary functions that control the behaviour of the compartment in an UP element.For convenience,the process of creating the functions from the detailed physically based model results is called upscaling.Where possible,the functions take the form of simple algebraic equations,but,where it is di cult to®nd an appropriate simple continuous functional form to describe a summary data set,a discrete transfer function or look-up table is used.The use of transfer functions to describe hydrological processes in a lumped manner is well documented(Chow et al.,1988).Look-up tables are less widely used.These store values of the function at a number of discrete values of the independent variables and the function is then evaluated at any arbitrary value of the independent variables by interpolating between the tabulated values. The UP element in Figure1can,therefore,be thought of as a framework for combining a set of simple models,which take the form of simple algebraic equations,look-up tables and transfer functions,derived from detailed physically based model results.One advantage of the UP approach to upscaling is that it makes downscaling possible,in the sense that it allows some details of the®ne-scale distributed hydrological response within each compartment to be inferred from the variables that describe the state of that compartment at the(large)scale of an UP element. For example,suppose the rate of discharge from the groundwater compartment of an UP element is governed by a single-valued function of its storage,which is derived by running a®nite di erence model of groundwater¯ow,on a®ne mesh,for a number of characteristic¯ow conditions.Then,for each character-istic condition,the distributed groundwater behaviour(e.g.¯ow pathways or distribution of water) simulated by the®nite di erence model can be mapped to a particular range of values of storage.In an UP simulation,the storage in the groundwater compartment varies continuously in response to recharge and discharge,and the distributed groundwater behaviour at any time can be taken to be the characteristic¯ow condition that corresponds to the range of storage in which the current value of storage lies.The practice of inferring the®ne-scale hydrological behaviour from the compartment state variables relies on there being a one-to-one mapping between them.Often,however,it is di cult to®nd a single state variable that fully meets this requirement.For example,it is possible that at two di erent times of the year the same total volume of water is stored in an aquifer but that its distribution in space is di erent.In such a case a second state variable is needed,and for the example presented here a suitable choice was found to be the time of year.The successful application of the UP system hinges on appropriate choices of distributed physically based models and of the functions used in the upscaling process;these can vary between applications depending on the ultimate goal.Hence,prior to giving details of the upscaling and downscaling processes,it is helpful to put them into context by®rst describing the issue that is being addressed.LONG-TERM SIMULATION OF RADIONUCLIDE MIGRATIONThe SHETRAN physically based distributed catchment modelling system (Ewen,1995)is being used to simulate the near-surface migration of contaminants in a range of hypothetical catchments representing a site that has been investigated by Nirex for the UK's deep underground radioactive waste repository.This work has included a series of simulations conducted on hypothetical catchments intended to represent an area of land into which,at some time in the far future,radionuclides from a deep repository could be released.The overall aim is to give a general representation of the steady-state migration of 36Cl and 129I for a range of di erent climate conditions.In the Nirex (1995)assessment the hypothetical catchment was one broadly based on the present-day lower catchments of the rivers Ehen and Calder,in West Cumbria,UK.Here,the sea level was deemed to have fallen and the modelled catchment included a former sea bed (Nirex,1997):a low relief landscape overlain by perforated clay sediments.SHETRAN simulates contaminant migration in these catchments with ®ne temporal and spatial resolution.It is,however,computationally expensive and,as a consequence,it is impractical to conduct simulations over very long time periods.Some experimental simulations of periods over 100years have been run,but a typical practical simulation length is 30years.Some of the subsurface pathways for radionuclide migration do not develop fully within 30years,so the UP system is used to run 250-year simulations,by which time all the pathways have developed fully.Notwithstanding that the application is for boreal climate conditions (Nirex,1997),ground and surface water freezing are not represented in the simulations presented here.The catchmentA single hypothetical catchment from the SHETRAN simulation series was selected to demonstrate the UP system.Some details of the modelled catchment,including the land use,vegetation and surface soils are given in Nirex (1995).The catchment is 17km long by 3km wide,covering an area of 46km 2(Figure 2).Its length was based on the width of the present-day coastal plain,plus an estimate of the width of the present-day o shore region that would be exposed by a 40m sea-level fall.The catchment geology consists of Quaternary drift deposits overlying sandstone of the Sherwood Sandstone Group (SSG).A simple `layer-cake'representation of the Quaternary drift deposits was used,which for the majority of thecatchmentFigure 2.Ground surface elevations and channel networkMODELLING LONG-TERM CONTAMINANT MIGRATION 827comprises:surface soils (0±1.5m depth);upper sand (1.5±10m depth);silty clay (10±14m depth);lower sand (14±20m depth);sandstone (below 20m).There are two breaks in the clay layer,where the lower sand extends upwards to 10m below ground.One break lies directly beneath the tributary channel,and the other a short distance from the main channel (Figure 3).The clay acts as a partially con®ning layer,it has a saturated hydraulic conductivity of 10À4m day À1,so the breaks in it have a signi®cant e ect on the hydraulic coupling between the sandstone and the ground surface.A deep,substantial sandstone aquifer lies below the catchment,and the contributing regional ground-water ¯ows from the deeper aquifer are represented by a constant up¯ow at the base of the catchment at a rate,averaged over the catchment,equivalent to 94.6mm year À1.The spatial distribution of this up¯ow is shown in Figure 4.The rainfall and other meteorological data for the catchment are based on data for the Kotioja catchment,located inland near the northern coast of the Gulf of Bothnia,Finland.These data were obtained from the Finland National Board of Waters and the Environment.They consist of six years of hourly precipitation,potential evaporation and temperature records.In the application,the data are repeated cyclically,as a six-year block,throughout the 250-year simulation period.For SHETRAN,the catchment was discretized into 184grid elements of 1km by 0.25km,and a no-¯ow condition was speci®ed at all lateral boundaries,except at the channel outlet.UPSCALINGThe catchment is treated as a single UP element and three di erent physically based models are used in the upscaling process to produce summary functions for the compartments of the UP element:an analytical model for channel routing,a particle tracking model for overland ¯ow and SHETRAN for subsurface ¯ow.Evaporation time-series from SHETRAN were used directly in the UP simulation,so the canopy compartment of the UP element was not used.A split sample approach was used to validate the UP model of the catchment.The ®rst three years of meteorological data were used to construct the summary functionsin Figure 3.Location of the breaks in the clay layer828W.T.SLOAN AND J.EWENthe form of look-up tables.These three years will be called the calibration period.The second three years of the data were then used to validate the functions by comparing the UP results with the ¯ows simulated by SHETRAN for that period.Subsurface watersThere are three subsurface compartments in an UP element:groundwater,inter¯ow and the unsaturated zone [in Ewen (1997)the unsaturated zone is further split into the root zone and percolation zone,but this splitting is not used here].The state of the subsurface is described by the state variables for these three compartments and the rates of ¯ow into and out of the compartments are described by functions of these state variables.The functions take the form of look-up tables and are derived from data sets that summarize SHETRAN results for the three-year calibration period.Fully three-dimensional ¯ow through variably saturated heterogeneous porous media is represented in SHETRAN (Parkin,1996),and the entire subsurface of the catchment is partitioned by a ®ne three-dimensional ®nite-di erence irregular grid,so the state of the system at any time is fully described by the quantity of water in the ®nite-di erence cells and the rates of ¯ow across the cell boundaries.Partitioning the subsurface.Before creating the summary data sets,it was ®rst necessary to identify the regions in the subsurface of the catchment that exhibit the characteristics of groundwater,inter¯ow and unsaturated zones,so that they could be associated with the appropriate compartments of an UP element.This was achieved by analysing the time-series of cell soil moisture contents and boundary ¯ow rates.The set of boundary ¯ows for all the cells in the SHETRAN grid at one instant in time corresponds to a three-dimensional velocity ®eld and the time-series of such sets corresponds to a time-series of velocity ®elds.Inter¯ow .Common to most de®nitions of inter¯ow is that it is associated with water emanating from the subsurface of a catchment,giving a hydrograph storm response that is more rapid than that associated with groundwater discharge.Bonell (1995)catalogues the physical processes that are thought to give rise to inter¯ow and outlines attempts at modelling them.SHETRAN is capable of simulating some ofthe Figure 4.Regional aquifer up¯ow (ms À1)MODELLING LONG-TERM CONTAMINANT MIGRATION 829processes that are thought to contribute to inter¯ow,such as the creation of perched water tables and lateral ¯ow in the unsaturated zone.Two techniques were used to identify regions of the subsurface that experience inter¯ow:one based on ®nding the most likely pathways for fast shallow ¯ow,and the other based on ®nding regions where the velocities change in sympathy with the discharge at the ground surface during a storm event.In preparation for the use of these two techniques,a time-series of the total rate of discharge from the subsurface was calculated from the time-series of SHETRAN velocity ®elds for the three-year calibration period.For the ®rst technique,the mean velocity ®eld associated with peak discharge rates from the subsurface was calculated.The ¯ow pathways associated with this mean velocity ®eld were then determined by tracking a pulse of water incident on the catchment.This was achieved by representing the pulse by a set of uniformly distributed particles and following these as they moved through the mean velocity ®eld.The catchment boundary is impermeable and,therefore,all the particles eventually emerged at the catchment surface or in the channel.The inter¯ow region is assumed to be associated with rapid subsurface ¯ow,so the total travel time of each particle was recorded and those particles with travel times less than a predetermined `cut-o 'value were designated as rapid.The inter¯ow region was then assumed to be associated with those SHETRAN cells through which rapid particles had travelled.The choice of cut-o value for travel time is subjective;12hours was selected after inspecting several discharge hydrographs.In the second technique,the aim is to identify the SHETRAN cells that are unsaturated prior to a storm,but that saturate quickly during the storm and contribute to discharges from the subsurface.This was achieved using the time-series of the vertical component of water velocity for each cell.For cells deep in the subsurface,or in areas of the catchment that are continuously unsaturated,the magnitude of the vertical velocity changes,but its direction rarely changes.However,in cells thath saturate quickly during a storm event there is downward ¯ow initially,but when the cell becomes saturated there is usually upward ¯ow.An example of this type of response is shown in Figure 5.It is assumed that before a cell responding in this manner can contribute to discharge from the subsurface,all the cells between it and the surface must also exhibit upward ¯ow.For this technique,cells are labelled as inter¯ow cells if they meet three criteria:®rst,the average duration of continuous upward ¯ow,post-storm,is less than a particular value,in this case 12hours;secondly,the number of times that there is a period of continuous upward ¯ow corresponds to the number of storms;and thirdly,all cells between it and the surface meet the ®rst two criteria.The two techniques are considered to be complementary and a cell was assumed to be an inter¯ow cell if it was identi®ed as such by either technique.The inter¯ow regions identi®ed in this manner are shown in Figure 6.Unsaturated zone .Cells in the subsurface are classi®ed as being unsaturated if they are not classed as inter¯ow cells and remain unsaturated at all times.Regions identi®ed in this manner are shown in Figure6.Figure 5.Typical rainfall response of the vertical component of velocity in cells in the inter¯ow region830W.T.SLOAN AND J.EWENGroundwater .When superimposed,the inter¯ow,unsaturated zone and the groundwater regions should cover the subsurface without overlapping or leaving gaps.Therefore,the groundwater regions comprise all parts of the subsurface not covered by either the inter¯ow or unsaturated regions (Figure 6).Functions for the subsurface compartments.Having identi®ed the inter¯ow,unsaturated and groundwater regions,the ¯ows to and from them (numbered 4,5,7and 8in Figure 1)have to be characterized by a set of functions.A function is also required to describe the fraction of the catchment's total surface area saturated by discharging subsurface water,since this controls the rate of saturation excess runo .All the functions depend upon state variables for the subsurface compartments,and all take the form of look-up tables.Table I describes the look-up tables used for the subsurface ¯ows and saturated area in the UP element.Two state variables were required for each compartment.The ®rst state variable is depth of water stored in the compartment.The relationship between groundwater discharge (¯ow 5)and storage in thegroundwaterFigure 6.Subsurface regions for UP modelling identi®ed using characteristic velocity ®elds from SHETRANMODELLING LONG-TERM CONTAMINANT MIGRATION 831compartment,for example,exhibited annual hysteresis (Ewen,1997),and Table I shows that the second state variable,which controls the hysteresis,is time of year.Values of the groundwater discharge were stored in a look-up table at 5Â12co-ordinates of these two variables;5ordinates for depth of water and 12for time of year.During an UP simulation,the groundwater discharge rate corresponding to the current value of storage and time of year is evaluated by linearly interpolating between the discharge values stored in the table at the co-ordinates closest to the current values.Figures 7to 11show the quality of the functions by comparing UP and SHETRAN results for the three-year calibration period.Surface waterThe ¯ow of surface water across the catchment is modelled using separate transfer functions for overland and channel ¯ow.Transfer functions are based on the assumption that the system is linear so that the response at the output to the system,O (t ),to a continuous input,I (t ),is given byO t t 0I t u t Àt d t 1 where,u (t ),the impulse transfer function,is the response of the system at time t to a unit impulse at time 0.The heterogeneity in the properties of the catchment surface,the non-linearity of the St Venant equations (which describe overland ¯ow)and the variation in storm antecedent conditions (such as the area of the catchment saturated at the surface)all ensure that the overland ¯ow response is non-linear.Therefore,it is not possible without great approximation to derive a single transfer function that is applicable across the full range of antecedent conditions and ¯ow regimes.However,it is practical to assume linearity within small ranges in the antecedent conditions and ¯ow regimes and derive a transfer function for each of these.The method used in the UP system exploits this,and uses multiple transfer functions,each of which apply over a small range of antecedent conditions and ¯ow rates.Table I.Summary of the look-up tables used in the subsurface compartments of the UP element (the ¯ow numbers are shown on Figure 1)FlowDependent variable State variables Number of ordinates Figure number 4Discharge from inter¯ow regions (a)Depth of water stored (b)Mean in®ltration rate to the inter¯ow region during the previous 12hours(a)5(b)1075Discharge from groundwater regions (a)Depth of water stored (b)Time of year(a)5(b)1287Percolation from the unsaturated zone (a)Depth of water stored (b)Instantaneous in®ltration rate(a)5(b)1098Discharge from the groundwater to the inter¯ow regions (a)Depth of water stored in the inter¯ow regions (b)Mean in®ltration rate to the inter¯ow regions during the previous 12hours(a)5(b)1010Not represented on the diagram Fraction of the total catchment area saturated by discharging subsurface waters (a)Depth of water stored in the inter¯ow regions Mean depth of water stored in the groundwater regions (b)Mean in®ltration rate to the inter¯ow regions during the previous 12hours (a)5(b)1011832W.T.SLOAN AND J.EWEN。