# Usgs prediction ground water models-Usgs groundwater watch

This report is written for the scientifically literate reader but is not limited to those who are involved in ground-water science. The report is intended to encourage U. Geological Survey scientists to develop a sense of excitement about ground-water science in the agency, to inform scientists about existing and potential ground-water science opportunities, and to engage scientists and managers in interdisciplinary discussions and collaboration. The report is intended for use by U. Geological Survey and Department of the Interior management to formulate long-term ground-water science programs and to continue sustained support of ground-water monitoring and research, some of which may not have an immediate impact.

Figure 5. Ground-water waer models need to expand beyond applications of managing water-level declines to contaminant-plume containment, conjunctive ground-water and surface-water use, and saltwater-intrusion abatement. Integrating the Usgs prediction ground water models specializations and synthesizing the results of research to support decisionmaking for important societal issues pose important challenges to biologists, geographers, geologists, and hydrologists in the USGS. Modesl Kansas Geological Survey KGSa research and service division of the University of Kansas, is charged by statute with studying and providing information on the geologic resources of Kansas. Figure 4.

## Vintage ebony tits. Using Maps and Models to Predict Groundwater Quality

Marie, J. These models work well for rivers with very flat slopes and in estuaries where flow reversals occur. Searcy, J. Geological Survey Professional Paper A, 27 p. By: Richard L. Pollution Chemical and Biological. As can be seen on figure 16, in order for a plateau to be reached Never give up in latin any particular location, a constant injection must be maintained for a length of time equal to the duration of the tracer-response curve, T d. Google profile. R ratio: The recovery ratio for the measurement cross Usgs prediction ground water models as determined by equation 3. If discharge is constant during the passage of a tracer cloud, it Usgs prediction ground water models also be factored out of the integral. The velocity of the peak concentration and associated hydraulic data are compiled in Appendix A for more than subreaches for about 90 different rivers in the United States representing a wide range of river sizes, slopes, and geomorphic types. The USGS provides science about natural hazards that threaten lives and livelihoods; the water, energy, minerals, and other natural resources we rely on; the health of our ecosystems and environment; and the impacts of climate and land-use change. The response function characteristics at Eglisau and Birsfelden are first estimated without the aid of traveltime information. As part of the calibration process, the response to a slug injection near river km 59 was measured at Eglisau km

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- A hydrologic model is a simplified conceptual and computer model used to simulate and predict the movement and use of water.
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The NWM simulates the water cycle with mathematical representations of the different processes and how they fit together. This complex representation of physical processes such as snowmelt and infiltration and movement of water through the soil layers varies significantly with changing elevations, soils, vegetation types and a host of other variables.

Additionally, extreme variability in precipitation over short distances and times can cause the response on rivers and streams to change very quickly.

Overall, the process is so complex that to simulate it with a mathematical model means that it needs a very high powered computer or super computer in order to run in the time frame needed to support decision makers when flooding is threatened. The NWM produces hydrologic guidance at a very fine spatial and temporal scale.

It complements official NWS river forecasts at approximately locations across the CONUS and produces guidance at millions of other locations that do not have a traditional river forecast. The NWM runs four uncoupled analyses simulations of current conditions with look-back periods ranging from 28 hours to 3 hours. Additionally, the CONUS features medium-range and long-range forecasts which are each produced four times per day.

All model configurations provide streamflow for 2. The NWM provides complementary hydrologic guidance at current National Weather Service NWS river forecast locations and significantly expands guidance coverage and type in underserved locations. Separate water routing modules perform diffusive wave surface routing and saturated subsurface flow routing on a m grid, and Muskingum-Cunge channel routing down National Hydrography Dataset NHDPlusV2 stream reaches.

River analyses and forecasts are provided across a domain encompassing the CONUS, Hawaii and additional hydrologically-contributing areas. United States Geological Survey USGS streamflow observations are assimilated into each of the four analysis and assimilation configuration and all analysis and forecast configurations benefit from the inclusion of over 5, reservoirs.

The Standard Analysis and Assimilation configuration cycles hourly and produces a real-time analysis of the current streamflow and other surface and near-surface hydrologic states across the contiguous United States CONUS. The exception is the 19Z Standard Analysis cycle which ingests initial conditions from the Extended Analysis below.

The Standard Analysis also produces restart files each hour which are used to initialize the short-, medium-, and long-range forecast simulations. The Extended Analysis and Assimilation configuration cycles once per day and produces an analysis of the current streamflow and other surface and near-surface hydrologic states across the contiguous United States CONUS.

This configuration also produces restart files which are used to initialize the 19Z Standard Analysis simulation. The Long-Range Analysis and Assimilation configuration cycles hourly and produces a real-time analysis of the current streamflow and other surface and near-surface hydrologic states across the contiguous United States CONUS , using higher quality precipitation data than is available to the Standard Analysis and Assimilation. The Long-Range Analysis also produces restart files which are used to initialize the long-range forecast simulations.

Like the Long-Range configuration, it uses a simplified set of physics in comparison to the Standard and Extended Analyses. The Hawaii Analysis and Assimilation configuration cycles hourly and produces a real-time analysis of the current streamflow and other surface and near-surface hydrologic states across the Hawaii domain.

The Hawaii Analysis also produces restart files each hour which are used to initialize the Hawaii Short-Range forecast simulation. Forced with meteorological data from the HRRR and RAP models, the Short Range Forecast configuration cycles hourly and produces hourly deterministic forecasts of streamflow and hydrologic states out to 18 hours.

The model is initialized with a restart file from the Analysis and Assimilation configuration and does not cycle on its own states. Member 1 extends out to 10 days while members extend out to 8. This configuration produces 3-hourly deterministic output and is initialized with the restart file from the Analysis and Assimilation configuration. The Long Range Forecast cycles four times per day i.

There are 4 ensemble members in each cycle of this forecast configuration, each forced with a different CFS forecast member. It produces 6-hourly streamflow and daily land surface output, and, as with the other forecast configurations, is initialized with a common restart file from the Analysis and Assimilation configuration. Forced with meteorological data from the NAM-NEST model, the Hawaii Short Range Forecast configuration cycles four times per day and produces hourly deterministic forecasts of streamflow and hydrologic states out to 60 hours.

The model is initialized with a restart file from the Hawaii Analysis and Assimilation configuration and does not cycle on its own states. A full breakdown of output file contents can be found here. Output from the National Water Model is currently visualized on this website using the experimental interactive map , and the experimental image viewer. The exception are the channel output files containing streamflow and other variables representing processes along river reach segments.

To support visualization of these variables, the latitude and longitude coordinates of the centroid of each reach are made available in a separate ESRI file geo-database gdb , outside of the NWM outputs.

The file gdb can be used in many common GIS software utilities to attach coordinates to the data. The file gdb is available here. NCEP encourages all users to ensure their decoders are flexible and are able to adequately handle changes in content order and also any volume changes which may be forthcoming. These elements may change with future NCEP model implementations. NCEP will make every attempt to alert users to these changes prior to any implementations.

To download the National Water Model product description document, click here. A subset of the model parameter files used by the operational implementation of the NWM is available.

For a description of the files available, click here. To download a tar file of the available parameter files, click here. NWM Operational Configuration: The NWM runs four uncoupled analyses simulations of current conditions with look-back periods ranging from 28 hours to 3 hours. Extended Analysis and Assimilation The Extended Analysis and Assimilation configuration cycles once per day and produces an analysis of the current streamflow and other surface and near-surface hydrologic states across the contiguous United States CONUS.

Long-Range Analysis and Assimilation The Long-Range Analysis and Assimilation configuration cycles hourly and produces a real-time analysis of the current streamflow and other surface and near-surface hydrologic states across the contiguous United States CONUS , using higher quality precipitation data than is available to the Standard Analysis and Assimilation. Hawaii Analysis and Assimilation The Hawaii Analysis and Assimilation configuration cycles hourly and produces a real-time analysis of the current streamflow and other surface and near-surface hydrologic states across the Hawaii domain.

Output File Contents: A full breakdown of output file contents can be found here. Parameter Information A subset of the model parameter files used by the operational implementation of the NWM is available. Expected Impact. Affected Parameter s. Affected Region s. Model implementation questions Brian Cosgrove. Email: brian. Data flow questions Carissa Klemmer. Email: ncep.

This report compiles information from a large number of time-of-travel and dispersion studies and presents empirical relations that appear to have general applicability. Figure 10 presents a plot of the observed velocities as a function of the variables on the right side of equation Toggle navigation Sustainable Groundwater Management Menu. The regression equations that follow, however, have a constant term that has specific units, meters per second. Although many excellent models are available to make the types of calculations needed, none can be used with confidence before calibration and verification to the particular river reach in question.

### Usgs prediction ground water models. Water Resources

The site is secure. An official website of the United States government Here's how you know. Water Resources Bulletin. By: Richard L. A method is derived to efficiently compute nonlinear confidence and prediction intervals on any function of parameters derived as output from a mathematical model of a physical system.

The method is applied to the problem of obtaining confidence and prediction intervals for manually-calibrated ground-water flow models. The availability of reliable input information is, therefore, almost always the weakest link in the chain of events needed to predict the rate of movement, dilution, and mixing of pollutants in rivers and streams.

Soluble tracers can be used to simulate the transport and dispersion of solutes in surface waters because they have virtually the same physical characteristics as water Feurstein and Selleck, ; Smart and Laidlaw, This is the case in either a steady flowing river or in the unsteady oscillatory stage and flow of a tidal estuary.

Measured tracer-response curves produced from the injection of a known quantity of soluble tracer provides an efficient method of obtaining the data necessary to calibrate and verify pollutant transport models.

These data can also be used, in conjunction with the superposition principle, to simulate potential pollution buildup in streams, lakes, and estuaries without the need to use numerical models.

Extensive use of fluorescent dyes as water tracers to quantify the transport and dispersion in streams and rivers began in the United States in the early to mid's.

Kilpatrick , using the concept of unit-peak concentration and the superposition principle, illustrated how these data, obtained in the time-of-travel studies, could be generalized to a wide range of flow conditions and even to other sites.

In this report, the concepts presented by Kilpatrick , along with extensive data collected by the U. Geological Survey on time of travel and dispersion, are used to provide guidance to water-resources managers and planners in responding to spills. This will be done by providing methods to estimate 1 the rate of movement of a solute through a river reach, 2 the rate of attenuation of the peak concentration of a conservative solute with time, and 3 the length of time required for the solute plume to pass a point in the river.

It will be shown how these estimates can be used alone to make the required predictions. In addition, they are precisely the data required to calibrate or verify pollutant transport models.

The accuracy of these predictions will be greatly increased by performing time-of-travel studies on the river reach in question; but the emphasis of this report is on providing methods for making estimates in rivers where few data are available. Large fluctuations in the flow rates of the rivers during the downstream movement of a solute would cause significant differences between actual and predicted traveltimes.

These cases can best be interpreted by use of numerical models. Traveltime and concentration attenuation of pollutants not dissolved in the water are beyond the scope of this report. The report begins with a short discussion of the theory of movement and dispersion of dissolved pollutants and introduces the unit-peak concentration concept.

A brief summary of the methods used to collect time-of-travel information is then given along with a summary of the data used in the report. Methods are recommended for estimating the rate of movement and attenuation of conservative pollutants based on an analysis of the data.

The application of these results is then illustrated by use of three examples. The report concludes by introducing the superposition principle and illustrates its purpose by use of an example. Time-of-travel studies are often conducted to help understand these processes and to quantify traveltime and dispersion for a given reach of river.

The general procedure for conducting a time-of-travel study is to instantaneously inject a known quantity of water-soluble tracer into a stream, usually at the center of flow, and to observe the variation in concentration of the tracer as it moves downstream. The general distribution of a tracer concentration resulting from a slug injection is shown in figure 1. The tracer-response curves in figure 1 are shown as a function of longitudinal distance and not as a function of time.

Later in the report the response curves will generally be shown as a function of time. The dispersion and mixing of a tracer in a receiving stream take place in all three dimensions of the channel fig. In this report, vertical and lateral diffusion will be referred to in a general way as mixing. The elongation of the tracer-response cloud longitudinally will be referred to as longitudinal dispersion. Vertical mixing is normally completed rather rapidly, within a distance of a few river depths.

Lateral mixing is much slower but is usually complete within a few kilometers downstream. Longitudinal dispersion, having no boundaries, continues indefinitely. In other words, vertical mixing is likely to be complete at section I in figure 1, which is a very short distance downstream of the injection. At section II lateral mixing is still taking place rapidly, so mixing and dispersion are both significant processes between the injection and section III on figure 1.

Downstream of section III the dominant mixing process is longitudinal dispersion, so the tracer concentration can generally be assumed to be uniform in the cross section.

For a midpoint injection, the tracer cloud moves faster than the mean stream velocity upstream of section III because the bulk of the tracer is in the high velocity part of the cross section. Preferably, all measurement cross sections for a time-of-travel study are at least as far downstream as the optimum distance section III in fig.

The conventional manner of displaying the response of a stream to a slug injection of tracer is to plot the variation of concentration with time the tracer-response curve as observed at two or more cross sections downstream of the injection, as illustrated on figure 2.

The tracer-response curve, defined by the analysis of water samples taken at selected time intervals during the tracer-cloud passage is the basis for determining time-of-travel and dispersion characteristics of streams. A detailed explanation of the analysis and presentation of time-of-travel data are covered in the report by Kilpatrick and Wilson The characteristics of the tracer-response curves shown in figure 2 are described in terms of elapsed time after an instantaneous tracer injection: C p , peak concentration of the tracer cloud; T l , elapsed time to the arrival of the leading edge of a tracer cloud at a sampling location; T p , elapsed time to the peak concentration of the tracer cloud; T t , elapsed time to the trailing edge of the tracer cloud; T d , duration of the tracer cloud T t -T l ; T 10d , duration from leading edge until tracer concentration has reduced to within 10 percent of the peak concentration; and n, number of sampling site downstream of injection.

The mass of tracer to pass a cross section, M r , is computed as: eqn 1 where W is the total width of the river, C v is the vertically averaged tracer concentration, and q is the unit discharge discharge per unit width. Both C v and q are given at time t and distance w from one bank. After mixing is complete in the cross section, the equation simplifies to: eqn 2 where C is assumed to be uniform in the cross section and Q is the total discharge in the cross section at time t.

If mixing is not complete, equation 2 can still be used as long as the concentration C is the discharge-weighted, cross-sectional-average concentration. If discharge is constant during the passage of a tracer cloud, it can also be factored out of the integral. The shape and magnitude of the observed tracer-response curves shown in figures 1 and 2 are determined by four factors: the quantity of tracer injected; the degree to which the tracer is conservative; the magnitude of the stream discharge; and longitudinal dispersion.

All of these factors must be taken into consideration to predict the concentration of solutes from tracer-concentration data. It is obvious that the magnitude of the tracer concentration in a stream is in direct proportion to the mass of tracer injected, M i. Doubling the amount of injected tracer will double the observed concentrations, but the shape and duration of the tracer-response curve will remain constant.

Thus, most investigators have normalized their data by dividing all observed tracer concentrations by the mass of tracer injected, M i Bailey and others, ; Martens and others, It has also been found that various tracers are lost in transit due to adhesion on sediments and photochemical decay.

Scott and others found fluorescent dyes to be absorbed on fine sediments such as clay. Rhodamine WT dye has been shown both in the field and laboratory to decay photochemically about 2 to 4 percent per day Hetling and O'Connell, ; Tai and Rathbun, Kilpatrick noted decay rates tended to be higher in rivers, about 5 percent per day, compared to about 3 percent per day in estuaries.

To compare data and to have it simulate a conservative substance, it is desirable to eliminate the effects of tracer loss. If the stream discharge, Q, is measured at the same time and location as the tracer concentration, it is possible to evaluate the mass of tracer recovered, M r , from equations 1 or 2. When the mass of the tracer injected, M i , is known, the tracer recovery ratio R r can be expressed as: eqn 3 A factor that inversely affects the magnitude of the tracer-response curves is the stream discharge.

The diluting effect of tributary inflows, as well as that of natural ground-water accretion, differs from stream to stream and with location. To counter the variable diluting effects of differing discharges, it is desirable to adjust observed concentration data by multiplying by the stream discharge.

Observed concentrations can be adjusted for 1 the amount of tracer injected, 2 tracer loss, and 3 stream discharge three of the four factors affecting the concentration by use of what is called a "unit concentration. The 1,, simply makes the numbers closer to unity. The discharge must be expressed in units that are consistent with the denominator of the concentration, and the injected mass must be in the same units as the numerator of the concentration.

For example, if the concentration is expressed in milligrams per liter, the injected mass must be expressed in milligrams and the discharge must be expressed in liters per unit time. If the entire tracer cloud is sampled, the value of M r can be computed and the mass of injected tracer need not be known.

Equation 4 can be used to convert any measured tracer-response curve to a unit-response UR curve. This UR curve can be used as the building block for simulating the concentrations to be expected from various pollutant loadings at different stream discharges. Normalizing the tracer-response curves, in effect, fits one unit of mass of tracer into one unit of flow.

As such, when the flow is constant and mixing is complete, the area under UR curves is constant 1x10 6 for any cross section on a stream. The Modeling Approach, Its Strengths and Weaknesses A numerical model is one way to formally account for factors that influence the timing and shape of the tracer-response curves. Numerical models also tend to be complex and difficult to apply by someone without formal training.

Although the use of numerical models is encouraged, it should be remembered that the accuracy of the model is critically dependent on the accuracy of the data used as input. Indeed, unless rather detailed and accurate field data are available, the modeling approach may add little to the reliability and accuracy of the predictions over what can be obtained by the much simpler and more straightforward approach outlined in this report.

All models solve three basic equations-the continuity of the mass of water, the conservation of momentum, and the conservation of the mass of the pollutant. Generally the first two equations are solved by use of a flow model to provide the water velocity, depth, and cross-sectional area as a function of time and position along the river. Three basic types of flow models are in common use. The simplest type, called the kinematic wave flow model, solves only the simplest form of the momentum equation by assuming the boundary friction force is always in balance with the weight component along the channel.

Kinematic wave models generally provide satisfactory results for shallow flows over steep terrain, such as occurs in overland flow. Kinematic wave models generally are not recommended for routing flows in rivers. The most complex flow models, called the dynamic wave models, solve the complete form of the momentum equation.

These models work well for rivers with very flat slopes and in estuaries where flow reversals occur. They generally require at least two input boundary conditions often the upstream discharge and the downstream stage and detailed input information about the channel geometry and flow resistance. Dynamic wave models tend to become unstable as the river slope increases, particularly for rivers with shallow depths, slopes exceeding 0.

Diffusive wave models ignore the inertia of the water and equate the sum of the pressure and friction forces to the weight component of the water. These models assume there is a unique relation between a steady-state flow and stage at each point in the river, so they generally do not require the specification of a downstream stage. They also generally operate satisfactorily with less detailed channel geometry information than required by the dynamic wave models and are much more stable and easy to use.

Accuracy of diffusive wave models increase with increasing slope, and they cannot be used in situations where flow reversals occur.

By using empirical geomorphological relations to represent channel geometry, the DAFLOW model Jobson, has been shown to provide excellent accuracy using very limited data for slopes as small as 0. The DAFLOW model also allows wave speeds and transport speeds to be independently specified, which greatly facilitates the calibration of a transport model.

Transport models simulate four basic processes-advection, dilution, longitudinal mixing, and decay. Many excellent one-dimensional numerical models are available for simulating dissolved pollutant transport in rivers. Army Corps of Engineers Environmental Laboratory, All one-dimensional models solve the continuity of mass equation along the river thalweg, and so the differences between the models is generally less important than the quality of the data used to drive them.

Advection is simply the translation of the response function downstream with time. The water and the dissolved pollutant must move downstream at the cross-sectional mean water velocity that is supplied by the flow model. The accuracy of the timing, therefore, is dependent on the accuracy of the flow model, not the accuracy of the transport model.

No matter which flow model is used, the channel geometry information will generally have to be adjusted calibrated to force the timing of the simulated and observed response functions in figure 2 to agree.

Dilution by tributary inflow is a simple process that all models simulate very well. All models assume the spreading of the response function with time fig.

A Fickian process is one that assumes the flux of material along the channel is proportional to the concentration gradient. The proportionality constant is called the dispersion coefficient. Transport models can be grouped into two basic types called Eulerian models and Lagrangian models.

Eulerial models solve the continuity of mass equation at fixed locations along the channel, and Lagrangian models solve the continuity equation for a series of specific water parcels that move along the channel with the mean flow velocity. Eulerian models generally exhibit more numerical dispersion than Lagrangian models.

In estuaries where reversing flow is predominant, numerical dispersion becomes much more troublesome. Paul Conrads Geological Survey, personal commun. If Fickian dispersion correctly represented the total longitudinal mixing in rivers, the unit-peak concentration would decrease in proportion to the square root of time. Nordin and Sabol have reported that unit-peak concentration in natural rivers generally decreases more rapidly with time than predicted by the Fickian law.

It is often assumed that other processes, presumably the movement of pollutant mass into and out of dead zone storage areas Spreafico and van Mazijk, , significantly contribute to the spreading of the response function in natural rivers.

This process would tend to make the leading edge rise more steeply and the trailing edge fall more slowly than predicted by Fickian dispersion. Few models account for this process, so most models underpredict the tails on the concentration response function.

Use of the empirical approach outlined herein, however, automatically accounts for all physical processes that contribute to the longitudinal spreading of the pollutant mass. Transport models typically simulate a very limited number of chemical reactions. Prediction of the rates of chemical reactions is beyond the scope of this report. Field Measurements Time-of-travel studies may be conducted to improve the estimates of traveltimes and dispersion rates for specific river reaches and flow conditions.

The Geological Survey has published a series of reports detailing the procedures to be used Kilpatrick and Wilson, ; Kilpatrick and Cobb, ; Wilson and others, , but the following will briefly outline the data collection needs to produce a full suite of traveltime and dispersion information. The following information should be obtained at each of two or more stream discharges that bracket the flows of interest. Select the river reach and flow conditions of interest. Then establish two or more sampling cross sections where tracer concentration will be measured.

Attempt to conduct studies during times of reasonably steady flow. Measure carefully the amount of tracer to be injected. Retain a sample of the injected tracer for laboratory use in preparing standards. Inject the tracer at a sufficient distance upstream so that lateral mixing is essentially complete by the first measurement section section III on fig.

The distance required for essentially complete lateral mixing can be reduced by injecting the tracer at multiple points across the river if the amount of tracer injected at each point is proportional to the discharge in that subsection. Measure for each sampling section the concentration at several points across the river during the passage of the entire tracer cloud or at least until a concentration of less than 10 percent of the peak concentration is reached.

Measurement at several points across each sampling section allows one to better account for the entire mass of tracer recovered and to quantify the completeness of lateral dispersion. Measure independently or evaluate stream discharges at every sampling cross section during the passage of the tracer cloud. These data will provide information sufficient to allow nearly every kind of applicable analysis in the literature and provide the best practical information on predicting the effects of spills.

It is often not practical to obtain the complete information as outlined above. Probably the most valuable information for improving forecasts is to measure the traveltimes of the peak concentrations at the center of the channel for various discharges.

If only the peak traveltime is needed, the entire tracer cloud need not be sampled and it is not necessary to know the amount of tracer injected. It is important, however, that lateral mixing be nearly complete in the measurement reach and that the discharges be reasonably steady.

Rather than measuring the discharge at each measurement cross section, the local discharge is sometimes assumed to be directly related to the flow measured at a remote index site. The second most valuable information that can be gained from time-of-travel studies is the traveltimes for the leading edge of the tracer cloud. To obtain this information, sampling must begin before the arrival of the tracer and continue long enough to be sure the true peak concentration has passed.

If data are available for only one discharge, they can be extrapolated to other flows using equation 8 or other extrapolation techniques discussed later in the report. Available Data Starting in the 's, the Geological Survey conducted extensive time-of-travel studies to quantify the transport and dispersion in streams and rivers of the country.

The results of some of these studies have been generalized by Godfrey and Frederick , Boning , Nordin and Sabol , Eikenberry and Davis , and Graf Some of the studies produced a full suite of time-of-travel and dispersion information, but many concentrated only on the traveltime of the tracer peak and did not obtain enough information to determine unit-peak concentration. As many of the available data as time permitted were compiled for use in this report.

All of the compiled data are listed in Appendix A. The appendix contains two tables and a list of references to the original studies. Table A-1 contains all the data for studies in which the unit-peak concentrations could be determined. Table A-2 contains all the data for studies in which the unit-peak concentrations could not be determined. Appendix B contains a bibliography of other reports containing time-of-travel data that were not compiled because of time constraints.

The peak concentration is a very important point on a tracer-response curve, and the variation in dispersion becomes most apparent if the unit-peak concentration is considered as a function of lapsed time since injection. According to Fischer's dispersion model, the peak concentration should attenuate with time as: eqn 5 in which C up is the unit-peak concentration, t is time since injection, and b is a coefficient.

The value of b should be approximately 1. Nordin and Sabol argue that a Fickian type equation cannot adequately describe longitudinal dispersion in rivers because the value of b never decreases to a value of 0.

They conclude that a typical value of b is 0. Larger values of b indicate more rapid longitudinal mixing.

The presence of pools and riffles, bends, and other channel and reach characteristics will increase the rate of longitudinal mixing and almost always yield a value of b greater than the Fickian value of 0. Unit-peak concentrations were compiled for cross sections obtained from more than 60 different rivers in the United States. These data represent mixing conditions in rivers with a wide range of size, slope, and geomorphic type.

For example, the slope in the study reach of the Mississippi River is 0. Figure 3 is a plot of the unit-peak concentrations C up as a function of traveltime T p of the peak concentration of all the data for which the mean annual flow was available.

A tight correlation is shown by the data, indicating that a reasonable estimate of the unit-peak concentration can be determined from an expression of the form of equation 5. The regression equation based only on traveltime that best fit all of the data was: eqn 6 This equation predicted the available data points with a root mean square RMS error of 0.

The coefficient of variation was 0. The standard error of estimate of the coefficient is 4. Other river characteristics that were available to help define the relation included the drainage area D a , the reach slope S , the mean annual river discharge Q a , and the discharge at the time of the measurement Q. The most significant other variable in the correlation was the ratio of the river discharge to mean annual discharge giving a prediction equation: eqn 7 in which Q is the river flow at the section at the time of the measurement and Q a is the mean annual flow at the section.

This equation predicted the available data points with an RMS error of 0. The solid lines for high flow and low flow are plotted assuming constant values of relative discharge of 1. Slope was not significant as an explanatory variable. Various regression models based on different combinations of discharge, mean annual discharge, and drainage area were tried. None of the equations produced a smaller RMS error or a larger R 2 2 value than equation 7.

Results for individual rivers generally define a much closer relation. For example, figure 4 presents measured concentrations of dye for the Shenandoah River as published by Taylor and others Notice that the data for the Shenandoah River show almost no correlation with relative discharge.

Equations 6 and 7 are also plotted on the figure for reference. In this case the equations fit the data very closely. The Sangamon River shows strong correlations with relative discharge fig.

It should be noted, however, that one set of measurements was made at extremely low flow. At any rate, the scatter among points for a single river is typically much less than the scatter among all rivers fig. A flow-duration curve is often used to provide a common base for comparison of streams of different sizes Graf, A flow-duration curve for a site is developed by plotting the discharge as a function of the percentage of time the flow is exceeded.

Several years of continuous discharge data are required but once the flow-duration curve is established for a site, flow-duration frequencies can be determined from the curve. Flows with low flow-duration frequencies are high discharges that occur during floods, whereas flows that occur with high flow-duration frequencies are low discharges that approach base-flow conditions. The mean annual flow Q a can be easily estimated from drainage area and runoff relations for the region. An analysis of the data for the ten streams analyzed by Graf indicated that the relative discharge is equally as efficient as flow-duration frequency for predicting the unit-peak concentrations.

Figure 8 is a plot of the relation between relative discharge and flow-duration frequency for Illinois streams as determined from the data of Graf As can be seen from the figure, the average flow in Illinois streams is one that is exceeded about 30 percent of the time. The more efficient the mixing in a river, the steeper will be the relation between unit-peak concentration and traveltime.

At high flow, river channels generally tend to be relatively uniform in shape, and they tend to increasingly exhibit a pool and riffle structure as the flow decreases. A pool and riffle structure offers great opportunities for tracer trapping; therefore, a pool and riffle structure tends to be efficient in mixing and attenuating the peak concentration. Equation 7 accounts for this process by decreasing the slope of UR curve for lower relative discharges.

Time of Travel of Peak Concentration As shown in the preceding section, the time required for a tracer cloud to reach a specific point in a river is the dominant factor in determining the concentration that will occur. The traveltime itself is also of interest to local planners, who may be more interested in the minimum probable traveltime than the expected traveltime. The water velocity depends on many factors including the general morphology of the river and particularly the amount of ponding caused by dams or other manmade works.

The prediction of the traveltime is, therefore, very important and it is often more difficult than the prediction of unit-peak concentration. Stream velocity and, consequently, traveltime commonly vary with discharge. The relation of mean stream velocity, V, to discharge is generally assumed to take the form: eqn 8 which is a straight line when the logarithm of discharge, Q, is plotted against the logarithm of velocity. For accurate estimates the constant, K, and exponent, a, must be defined for each river reach of interest, and two or more time-of-travel measurements are required to define the transport characteristics of the river reach.

Geomorphic analyses by many investigators, however, suggest that the exponent in equation 8 typically has a value of about 0. The velocity of the peak concentration and associated hydraulic data are compiled in Appendix A for more than subreaches for about 90 different rivers in the United States representing a wide range of river sizes, slopes, and geomorphic types.

Four variables were available in sufficient quantities for regression analysis. These included the drainage area D a , the reach slope S , the mean annual river discharge Q a , and the discharge at the section at time of the measurement Q. It was reasoned that these variables should be combined into the following dimensionless groups. The dimensionless peak velocity is defined as: eqn 9 The dimensionless drainage area is defined as: eqn 10 in which g is the acceleration of gravity.

The dimensionless relative discharge is defined as: eqn 11 These equations are homogeneous, so any consistent system of units can be used in the dimensionless groups. The regression equations that follow, however, have a constant term that has specific units, meters per second. The most accurate prediction equation, based on data points, for the peak velocity in meters per second was: eqn 12 The standard error of estimates of the constant and slope are 0.

This prediction equation has an R 2 of 0. Figure 9 contains a plot of the observed velocities as a function of the variables on the right side of equation For responses to accidental spills, the highest probable velocity, which will result in the highest concentration, is usually a concern.

On figure 9 an envelope line for which more than 99 percent of the observed velocities are smaller is also shown. The equation for this line, the maximum probable velocity, in meters per second V mp is: eqn 13 The best equation for the velocity of the peak concentration, in meters per second, that did not include slope as a variable was: eqn 14 The standard error of estimates of the constant and slope are 0.

The root-mean-square error of the prediction equation, based on points, is 0. Figure 10 presents a plot of the observed velocities as a function of the variables on the right side of equation Also shown on the figure is a line for which 99 percent of the data points indicate a smaller velocity. The equation for this line, for the probable maximum velocity, in meters per second, is: eqn 15 The best equation for the velocity of the peak concentration, in meters per second, using only drainage area was: eqn 16 The term D a is defined by equation 10 except that the local discharge Q is used in place of the mean annual discharge Q a.

The standard error of estimates, based on points, of the constant and slope are 0. The root-mean-square error of the prediction equation is 0. Figure 11 presents a plot of the observed data as a function of the variables on the right side of equation The equation for this line is: eqn 17 Time of Travel of Leading Edge In addition to knowing when the peak concentration will arrive at a site, it is of great interest to know when the first pollutant will arrive.

The time of arrival of the leading edge of the pollutant indicates when a local problem will first exist and defines the overall shape of the concentration response function. Fewer data are available for the time-of-arrival of the leading edge sites than are available for the velocity of the peak concentration.

Eight variables were available in sufficient quantities for regression analysis. These included the drainage area D a , the reach slope S , the mean annual river discharge Q a , the discharge at the section at time of the measurement Q , the velocity of the peak concentration V p , the width of the river, the depth of the river, and the time from the injection to the passage of the peak concentration traveltime of the peak concentration, T p.

No significant correlation could be found between any of the variables and the time from injection to the arrival of the leading edge T l except for the traveltime to the peak concentration. Figure 12 contains a plot of the traveltime of the leading edge as a function of the traveltime of the peak concentration. As can be seen from the figure, the correlation between these two variables is very good with an R 2 of 0.

These data indicate that the traveltime of the leading edge can be estimated from: eqn 18 Time of Passage of Pollutant Methods have been developed for estimating the traveltime of the leading edge, T l , the traveltime of the peak concentration, T p , and the magnitude of the unit-peak concentration, C up. This information defines two points on the tracer-response curve, shown as two of the large dots on figure 2.

Kilpatrick and Taylor show that the area of a normal slug-produced tracer-response curve is very nearly equal to the area of a scalene triangle three unequal sides with a height equal to the peak concentration and the base extending from the leading edge to a point where the trailing edge concentration is equal to 0.

Because the area under the unit-response curve is 1x10 6 , this information can be used to estimate a third point on the curve. The time of passage from the leading edge to a point where the concentration has been reduced to 10 percent of the peak concentration, T d10 , can be estimated from the equation: eqn 19 Furthermore, the area under the tail of the tracer-response curve should approximately balance the area between the falling limb portion of the tracer-response curve and the falling limb of the scalene triangle fig.

This allows a complete tracer-response curve to be sketched in with reasonable accuracy based on the peak concentration and the times to the leading edge and peak. Nonconservative Constituents The unit concentration approach gives estimates of the solute concentration assuming no loss of mass during the transit from the injection to the point of observation conservative transport.

This will generally be a worst case estimate because losses normally occur with time. Losses may result from chemical transformations, photochemical decay, volatilization, trapping on sediments, or a number of other processes. Losses are often found to follow a first order decay law, which implies that the mass of material in the river decreases exponentially with time.

One way to approximate this loss is to reduce the injected mass using the equation: eqn 20 in which M ia is the apparent mass of pollutant spilled after a time of T p , M i is the actual mass of pollutant spilled, and k is the decay coefficient with units of time The apparent mass of pollutant is then used in the unit concentration relation to determine the actual concentration from the unit concentration.

The first example will assume that very few hydrologic data are available, and the second example will assume that time-of-travel measurements have been made at a relatively high and relatively low discharge.

The third example will apply the method to a river for which some data are available that was not used in the development of the equations. Example 1, Very Limited Data Assume that a truck runs off the road and instantaneously spills 6, kg of a corrosive chemical into an ungaged stream.

Estimate the most probable and the expected worst case effects of the spill on the water intake for a town that is located 15 km downstream. The worst case should occur for the shortest probable traveltime. No data exist for the stream receiving the spill, but topographic maps show that the drainage area is km 2 at the spill site and km 2 at the intake for the town. A review of available data also indicates that a gaging station exists for a nearby stream with a drainage area of km 2 and a mean-annual flow of 5.

At the time of the spill the flow at the gaging station was 3. The hydrology and weather are assumed to be fairly uniform within the area so it will be assumed that the stream carrying the spill is flowing at about 3. Likewise, the mean-annual flow of the ungaged stream is estimated to be about 5.

The first step is to estimate traveltime of the peak concentration. Because the river slope is not available, equations 14 and 15 will be used to estimate the expected and fastest probable traveltimes in the stream. With the traveltimes known, the most probable unit-peak concentration at the town intake can be estimated from equation 7 as: Rearranging equation 4, to give the peak concentration: and using the injected mass, M i , of 6x10 9 mg, the flow rate at the intake, Q, of 3.

When will the pollutant first arrive at the intake? As can be seen from equation 18, the time of arrival of the leading edge of the pollutant cloud should occur 0. It is highly unlikely that the pollutant will arrive at the intake sooner than 0. How long will the intake be affected? All of the above computations were carried out assuming no loss of pollutant between the spill and the intake.

Losses could occur by chemical reactions, volatilization, absorption on the streambed, or other processes. Equation 20 can be used to account for these losses. Example 2, Traveltime Data Available The second example assumes that 50 kg of a pollutant is spilled in the Apple River Compute the probable impact, assuming no losses, of this spill on a water intake at Hanover, which is Two time-of-travel studies have been completed on this reach of the Apple River and the data are contained in table A-1 of Appendix A as injection numbers 83 and One of these studies was conducted at relatively low flow, when the river discharge was about 0.

The first step is to estimate the times of travel of the leading edge and peak of the pollutant cloud. The traveltimes of the peak concentrations as found in table A-1 are plotted in figure From table A-1 it is seen that the traveltime of the peak concentration to Elizabeth is Also it is seen that the distance from Elizabeth to Hanover is By linear interpolation, it is easily seen that the traveltime from the injection site to Hanover would be about Likewise, the traveltime from the town of Apple River to the spill site would be 1.

In a similar manner, the traveltime from Apple River to the spill site would be Assuming a mean annual flow at the spill site of 1. Then by linear interpolation between the relative discharges, it is seen that the traveltime from Apple River to the spill site would be 5. Likewise the traveltime from Apple River to Hanover would be The traveltime from the spill site to Hanover should, therefore, be With the relatively small amount of data contained in Appendix A for the Apple River, it is possible to estimate the timing of a spill on the river with much better accuracy than would have been possible by use of equations 12 to Figure 14 is a plot of the unit-peak concentrations measured on the Apple River during the two tests.

As can be seen from the figure, the unit-peak concentration should be about 40 s -1 for a traveltime of 55 hours. The traveltime of the leading edge of the tracer cloud from the spill site to Hanover can then be estimated using the same procedure as for the peak concentration, as After In conclusion, the pollutant should first arrive at Hanover 51 hours after the spill. The peak concentration should pass the site 55 hours after the spill; and if there are no losses, it should arrive with a concentration of 0.

By 65 hours after the spill, the concentration should have fallen back to 0. If there are losses or chemical reactions between the spill and the intake, the concentrations will be smaller and either equation 20 or a numerical model could be used for predictions. Because of the high population density and heavy use, there is always the potential that the river will be accidently polluted.

The International Rhine Commission has been set up to help reduce the danger of accidents and to help respond to them if they occur. The Commission developed, calibrated, and verified the Alarm model to be used in responding to accidental spills.

As part of the calibration process, the response to a slug injection near river km 59 was measured at Eglisau km In this example, the measured response curves will first be predicted based on the river discharge and drainage area.

### Office of Water Prediction

This report is written for the scientifically literate reader but is not limited to those who are involved in ground-water science. The report is intended to encourage U. Geological Survey scientists to develop a sense of excitement about ground-water science in the agency, to inform scientists about existing and potential ground-water science opportunities, and to engage scientists and managers in interdisciplinary discussions and collaboration. The report is intended for use by U. Geological Survey and Department of the Interior management to formulate long-term ground-water science programs and to continue sustained support of ground-water monitoring and research, some of which may not have an immediate impact.

Finally, the report can be used to communicate the U. Geological Survey ground-water science. Barlow, William C. Burton, Kevin F. Dennehy, Norman G. Grannemann, Tien Grauch, Mary C. Hill, Randall J. Hunt, Kenneth J. Lanfear, Randall C. Orndorff, David L. Parkhurst, Herbert A. Pierce, Allen M. Shapiro, Edwin P. Weeks, Thomas C. Winter, and Chester Zenone of the U. Geological Survey. Ground-Water Research Opportunities. Mapping in Three Dimensions—Geology and Geophysics.

Research Opportunities. Characterizing Aquifer Heterogeneity. Developing More Effective Computer Models. Sanford, J. Caine, D. Wilcox, H. McWreath, and J. The U. Geological Survey USGS has a long-standing reputation for providing unbiased scientific leadership and excellence in the field of ground-water hydrology and geological research. This report provides a framework for continuing this scientific leadership by describing six interdisciplinary topics for research opportunities in ground-water science in the USGS.

Understanding the relations between ground water and the geological characteristics of aquifers within which ground water resides, and the relation of ground water to surface-water resources and terrestrial and aquatic biota is increasingly important and presents a considerable opportunity to draw on expertise throughout the USGS, including the science disciplines of biology, geography, geology, and hydrology.

The National Research Council also emphasizes that USGS regional and national assessments of ground-water resources should focus on aspects that foster the sustainability of the resource. The need for a comprehensive program addressing the sustainability of ground-water resources can be stated very concisely—we need enough ground water of good quality to sustain our lives, our economy, and our aquatic ecosystems.

Although societal needs for high-quality, objective ground-water science are increasing, current funding for USGS regional ground-water programs is about 40 percent of the funding available 20—25 years ago. Given the current challenges of budgetary constraints, however, this report provides a flexible set of interrelated research topics that enhance the ability of the USGS to focus limited fiscal resources on developing ground-water science tools and methods that provide high-quality, objective scientific information.

The questions that traditional earth scientists generally ask are different from those typically asked by the society we serve. Scientists ask. Scientists tend to focus on the present, the past, and the processes. Society generally wants to know about the future—the present, the past, and the processes are of interest primarily as they relate to the future. The USGS must rely on its knowledge of the present, the past, and the processes to provide science-based forecasts based on the effects of stressors yesterday, today, and tomorrow.

Ground-water resources in many parts of the United States are severely stressed by human activity. For example, in the southwestern part of the Nation, large withdrawals result in land subsidence and water shortages. In coastal areas and some inland areas, withdrawals cause saline water to intrude aquifers that formerly contained freshwater. Throughout the Nation, even in water-rich areas, ground water is subject to competing uses where water is insufficient to meet the needs of everyone. Septic tanks, landfills, applications of agricultural chemicals, disposal of chemical and radioactive wastes, and other land uses and activities introduce chemicals to ground water, potentially restrict the use of ground water for drinking, and contaminate aquatic ecosystems in streams, lakes, and wetlands.

Furthermore, responses to natural stresses, such as droughts when surface-water supplies often are supplemented with ground water, reduce the availability of ground water for future uses. Advances in the six interdisciplinary topics for research opportunities in ground-water science described in this report could greatly improve our ability to forecast ground-water availability to sustain human use and support aquatic eco-systems.

Briefly, these topics are as follows:. Improved understanding of the geologic framework of ground-water systems through the development of three-dimensional 3—D mapping and visualization tools and new applications of geophysical methods;. Improved characterization of aquifer heterogeneity in unconsolidated aquifers, fractured aquifers, and karst aquifers;.

Improved estimations of recharge, with emphasis on estimates that bridge local and regional scales;. Improved abilities to measure ground-water and surfae-water interactions, which include both inflows to and outflows from ground-water systems;. Improved computer models of ground-water flow and transport, with emphasis on developing and applying new inverse methods and uncertainty analysis. The first two topics build on the integration of water-resources, mapping, geological, and geophysical characterization research.

The next three topics emphasize the importance of quantifying the interactions of ground water with the biosphere and integrating biological and water-resources research. The sixth topic provides a vital link between process-based understandings developed through the other topics and the goal of improved forecasting. The six ground-water research topics discussed in this report are not intended to be comprehensive, nor do they cover all aspects of ground-water science that will be emphasized by the USGS.

The USGS has a central role in ground-water research among Federal agencies and is the sole Federal agency with the mission to conduct nationwide assessments of the status and trends of the surface and subsurface components of the hydrologic cycle. The Federal role is to provide scientific information for states and local agencies to use in managing water resources. Likewise, a Federal role is needed to support the management of large portions of land by the Bureau of Land Management, U.

Forest Service, and Department of Defense, and of the land contained within Indian Reservations administered by the Department of the Interior. Several of the topics identified in this report for example, those addressing karst resources and the effects of ground water on biological resources are of special concern to other Department of the Interior agencies. The research opportunities emphasized in this report are of interest to university scientists, other agencies, and private organizations.

Thus, we see many potential partners in advancing knowledge in these topics. This publication is intended primarily for persons with a scientific or technical background in the natural sciences, although we attempted to make the report of interest and accessible to a wide audience.

The research opportunities contained in this report build on an enormous amount of previous work by scientists within and outside the USGS. For the sake of brevity, we did not attempt to review the literature in the fields discussed, and literature citations are used only to support particular statements. The distributions of lithology and geologic structures in three dimensions are major controls on ground-water flow and solute transport.

These physical features, however, usually are complex, difficult to characterize, and even more difficult to visualize. These features also are linked closely to the overall aquifer heterogeneity, the second research topic presented in this report. Consequently, to understand a ground-water flow system fully, the geologic framework must be well understood and incorporated into hydrogeologic analyses and ground-water flow models.

As the demand increases for more accurate forecasts of the quantity and quality of ground-water resources, it will be necessary to more accurately characterize the geologic framework. Geologic mapping constitutes the basic foundation for modern 3—D geologic models. These models are excellent technological tools for representing the natural system by assembling and integrating diverse geologic, geophysical, geochemical, and hydrogeologic information.

A critical feature of modern 3—D geologic models developed for process modeling is the representation of uncertainties associated with the geometries and physical properties throughout the model domain and the ability to generate multiple scenarios or realizations. Geologic mapping and field-based characterization; permeability of host-rock and fault-related materials; in-situ borehole and regional geophysical data acquisition; mapping of mineralized and hydrothermally altered rock; cross-section construction; and fracture-network data collection, analyses, and modeling are all used to develop 3—D geologic framework models.

The effects of lithologic and structural features on aquifers and the uncertainties involved are investigated in a variety of geologic settings and at a variety of scales ranging from local concerns about a community ground-water supply to regional concerns, such as understanding natural as opposed to mining-related acid and metal loads to surface water, ground water, and aquatic ecosystems.

Geochemical, environmental tracer, and ground-water age data also are used in combination with the above information to develop the numerical and predictive models and modeling strategies for ground-water studies. Much of these data also are integrated effectively and explored in sophisticated geographic information systems GIS that allow a wide range of users to query multidisciplinary data and generate new and theme-specific earth-science maps.

Geophysical methods are critical for improving knowledge of subsurface geologic structure and lithologic heterogeneities at both local and regional scales. The methods provide information in both horizontal and vertical dimensions and information directly related to hydrogeology and water quality, which can be used to improve knowledge about conditions between wells, extrapolate information to areas away from wells, or provide a mapped view of a large region, such as a watershed or ground-water basin.

Developing new applications of ground-based and airborne methods and a better understanding of the relations between physical and hydraulic properties are keys to extrapolating knowledge of the third dimension over wide areas and directly importing this information into ground-water models.

Figure 1. Three-dimensional 3—D geologic framework model of Yucca Mountain, Nevada from Potter and others, Data used for 3—D framework modeling include geologic maps and cross sections, regional structural and lithostratigraphic facies analyses, geophysical investigations, and lithologic data from boreholes.

This block diagram illustrates the geometry of principal structural elements of Yucca Mountain, Nevada. Cross sections, fence diagrams, and block diagrams are traditional tools that geologists use to portray 3—D relations of geologic units and develop a conceptual understanding of the system to be modeled. Developing a useful 3—D geologic model depends on the use of powerful computer hardware, sophisticated software, and the geoscience tools required to integrate diverse data into a coherent 3—D spatial framework.

Modern computer systems handle many complex modeling applications and are evolving rapidly in both speed and storage capacity. Sophisticated software programs are available for assembling, manipulating, and visualizing 3—D geologic maps and models. Driven largely by the needs of petroleum and GIS industries, these programs continue to evolve and stay ahead of the needs of water-resource investigations.

Methods and tools for developing 3—D geologic models currently are in the early stages of development, despite the useful knowledge gained from the petroleum industry, but developers of 3—D hydrogeologic models face somewhat different challenges and much additional work.

One of the challenges of 3—D modeling involves improving the scope and utility of geophysical methods that can be applied to hydrogeologic investigations. A variety of geophysical methods are available that can be designed for specific applications, particular scales of investigation, and wide cost ranges. The types of information these geophysical methods provide include characterizing lithology such as rock type and grain size , determining the boundaries between hydrogeologic units, locating faults that partition units or control ground-water flow, estimating fracture density, mapping hydrothermal alteration or thermal waters, and detecting variations in salinity.

Some geophysical methods, such as certain borehole and shallow-looking surface and marine geophysical methods, have become well accepted in ground-water applications.

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