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A direct method for calculating instrument noise levels in side-by-side seismometer evaluations

The subject of determining the inherent system noise levels present in modem broadband closed loop seismic sensors has been an evolving topic ever since closed loop systems became available. Closed loop systems are unique in that the system noise can not be determined via a blocked mass test as in older conventional open loop seismic sensors. Instead, most investigators have resorted to performing measurements on two or more systems operating in close proximity to one another and to analyzing the outputs of these systems with respect to one another to ascertain their relative noise levels. The analysis of side-by-side relative performance is inherently dependent on the accuracy of the mathematical modeling of the test configuration. This report presents a direct approach to extracting the system noise levels of two linear systems with a common coherent input signal. The mathematical solution to the problem is incredibly simple; however the practical application of the method encounters some difficulties. Examples of expected accuracies are presented as derived by simulating real systems performance using computer generated random noise. In addition, examples of the performance of the method when applied to real experimental test data are shown.

Open-File Report↗

Simulating groundwater flow in karst aquifers with distributed parameter models—Comparison of porous-equivalent media and hybrid flow approaches

Understanding karst aquifers, for purposes of their management and protection, poses unique challenges. Karst aquifers are characterized by groundwater flow through conduits (tertiary porosity), and (or) layers with interconnected pores (secondary porosity) and through intergranular porosity (primary or matrix porosity). Since the late 1960s, advances have been made in the development of numerical computer codes and the use of mathematical model applications towards the understanding of dual (primary [matrix] and secondary [fractures and conduits]) porosity groundwater flow processes, as well as characterization and management of karst aquifers. The Floridan aquifer system (FAS) in Florida and parts of Alabama, Georgia, and South Carolina is composed of a thick sequence of predominantly carbonate rocks. Karst features are present over much of its area, especially in Florida where more than 30 first-magnitude springs occur, numerous sinkholes and submerged conduits have been mapped, and numerous circular lakes within sinkhole depressions are present. Different types of mathematical models have been applied for simulation of the FAS. Most of these models are distributed parameter models based on the assumption that, like a sponge, water flows through connected pores within the aquifer system and can be simulated with the same mathematical methods applied to flow through sand and gravel aquifers; these models are usually referred to as porous-equivalent media models. The partial differential equation solved for groundwater flow is the potential flow equation of fluid mechanics, which is used when flow is dominated by potential energy and has been applied for many fluid problems in which kinetic energy terms are dropped from the differential equation solved. In many groundwater model codes (basic MODFLOW), it is assumed that the water has a constant temperature and density and that flow is laminar, such that kinetic energy has minimal impact on flow. Some models have been developed that incorporate the submerged conduits as a one-dimensional pipe network within the aquifer rather than as discrete, extremely transmissive features in a porous-equivalent medium; these submerged conduit models are usually referred to as hybrid models and may include the capability to simulate both laminar and turbulent flow in the one-dimensional pipe network. Comparisons of the application of a porous-equivalent media model with and without turbulence (MODFLOW-Conduit Flow Process mode 2 and basic MODFLOW, respectively) and a hybrid (MODFLOW-Conduit Flow Process mode 1) model to the Woodville Karst Plain near Tallahassee, Florida, indicated that for annual, monthly, or seasonal average hydrologic conditions, all methods met calibration criteria (matched observed groundwater levels and average flows). Thus, the increased effort required, such as the collection of data on conduit location, to develop a hybrid model and its increased computational burden, is not necessary for simulation of average hydrologic conditions (non-laminar flow effects on simulated head and spring discharge were minimal). However, simulation of a large storm event in the Woodville Karst Plain with daily stress periods indicated that turbulence is important for matching daily springflow hydrographs. Thus, if matching streamflow hydrographs over a storm event is required, the simulation of non-laminar flow and the location of conduits are required. The main challenge in application of the methods and approaches for developing hybrid models relates to the difficulty of mapping conduit networks or having high-quality datasets to calibrate these models. Additionally, hybrid models have long simulation times, which can preclude the use of parameter estimation for calibration. Simulation of contaminant transport that does not account for preferential flow through conduits or extremely permeable zones in any approach is ill-advised. Simulation results in other karst aquifers or other parts of the FAS may differ from the comparison demonstrated herein.

Florida↗

Mathematical simulation of temperatures in deep impoundments: verification tests of the Water Resources Engineers, Inc. model - Horsetooth and Flaming Gorge Reservoirs

Successful use of predictive mathematical models requires verification of the accuracy of the models by applying them to existing situations where the prediction can be compared with reality. A Corps of Engineers' modification of a deep reservoir thermal stratification model developed by Water Resources Engineers, Inc., was applied to two existing Bureau of Reclamation reservoirs for verification. Diffusion coefficients used for the Corps' Detroit Reservoir were found to apply to Horsetooth Reservoir in Colorado, for which very food computer input data were available. The Detroit diffusion coefficients gave a reasonable simulation of Flaming Gorge Reservoir in Wyoming and Utah, which has very complex and variable physical characteristics and for which only average-quality computer input data were available.

Colorado↗

Temperature and solute-transport simulation in streamflow using a Lagrangian reference frame

A computer program for simulating one-dimensional, unsteady temperature and solute transport in a river has been developed and documented for general use. The solution approach to the convective-diffusion equation uses a moving reference frame (Lagrangian) which greatly simplifies the mathematics of the solution procedure and dramatically reduces errors caused by numerical dispersion. The solution procedure has the further advantages, relative to conventional Eulerian solution schemes, of being easy to understand in the physical sense, of being extremely stable numerically, and of providing an accounting system which is very useful for model calibration. The model documentation is presented as a series of four programs of increasing complexity. The conservative transport model can be used to route a single conservative substance, such as dye, through a reach of a river. The simplified temperature model is used to predict water temperature in rivers, either with or without thermal loading, when few meteorological data are available. Only equilibrium temperature and windspeed are required. It is suggested that air temperature can be used to approximate equilibrium temperature. The complete temperature model is highly accurate but requires rather complete meteorological data. Finally, the 10-parameter model can be used to route as many as 10 interacting constituents through a river reach. The mathematical description of the interaction between the constituents, which does not need to be linear, is generally up to the user to supply. An example problem is solved for a three-parameter system involving temperature, dissolved oxygen, and biochemical oxygen demand. For simplicity, all models are developed and presented assuming steady non-uniform flow. Generalization of the models to allow unsteady flow is extremely simple, involving the addition of no more than 18 cards to the program deck. The report is concluded by describing this generalization for any of the models. Before using the models with unsteady flow, a flow model must be used to calculate and store the necessary flow data at each cross section and time step. Such a flow model is available and documented.

Water-Resources Investigations Report↗

A vertically averaged spectral model for tidal circulation in estuaries

A frequency dependent computer model based on the two-dimensional vertically averaged shallow-water equations is described for general purpose application in tidally dominated embayments. This model simulates the response of both tides and tidal currents to user-specified geometries and boundary conditions. The mathematical formulation and practical application of the model are discussed in detail. Salient features of the model include the ability to specify: (1) stage at the open boundaries as well as within the model grid, (2) velocities on open boundaries (river inflows and so forth), (3) spatially variable wind stress, and (4) spatially variable bottom friction. Using harmonically analyzed field data as boundary conditions, this model can be used to make real time predictions of tides and tidal currents. (USGS)

Water-Resources Investigations Report↗

A three-dimensional method-of-characteristics solute-transport model (MOC3D)

This report presents a model, MOC3D, that simulates three-dimensional solute transport in flowing ground water. The model computes changes in concentration of a single dissolved chemical constituent over time that are caused by advective transport, hydrodynamic dispersion (including both mechanical dispersion and diffusion), mixing (or dilution) from fluid sources, and mathematically simple chemical reactions (including linear sorption, which is represented by a retardation factor, and decay). The transport model is integrated with MODFLOW, a three-dimensional ground-water flow model that uses implicit finite-difference methods to solve the transient flow equation. MOC3D uses the method of characteristics to solve the transport equation on the basis of the hydraulic gradients computed with MODFLOW for a given time step. This implementation of the method of characteristics uses particle tracking to represent advective transport and explicit finite-difference methods to calculate the effects of other processes. However, the explicit procedure has several stability criteria that may limit the size of time increments for solving the transport equation; these are automatically determined by the program. For improved efficiency, the user can apply MOC3D to a subgrid of the primary MODFLOW grid that is used to solve the flow equation. However, the transport subgrid must have uniform grid spacing along rows and columns. The report includes a description of the theoretical basis of the model, a detailed description of input requirements and output options, and the results of model testing and evaluation. The model was evaluated for several problems for which exact analytical solutions are available and by benchmarking against other numerical codes for selected complex problems for which no exact solutions are available. These test results indicate that the model is very accurate for a wide range of conditions and yields minimal numerical dispersion for advection-dominated problems. Mass-balance errors are generally less than 10 percent, and tend to decrease and stabilize with time.

Water-Resources Investigations Report↗

A two-phase debris-flow model that includes coupled evolution of volume fractions, granular dilatancy, and pore-fluid pressure

Pore-fluid pressure plays a crucial role in debris flows because it counteracts normal stresses at grain contacts and thereby reduces intergranular friction. Pore-pressure feedback accompanying debris deformation is particularly important during the onset of debrisflow motion, when it can dramatically influence the balance of forces governing downslope acceleration. We consider further effects of this feedback by formulating a new, depth-averaged mathematical model that simulates coupled evolution of granular dilatancy, solid and fluid volume fractions, pore-fluid pressure, and flow depth and velocity during all stages of debris-flow motion. To illustrate implications of the model, we use a finite-volume method to compute one-dimensional motion of a debris flow descending a rigid, uniformly inclined slope, and we compare model predictions with data obtained in large-scale experiments at the USGS debris-flow flume. Predictions for the first 1 s of motion show that increasing pore pressures (due to debris contraction) cause liquefaction that enhances flow acceleration. As acceleration continues, however, debris dilation causes dissipation of pore pressures, and this dissipation helps stabilize debris-flow motion. Our numerical predictions of this process match experimental data reasonably well, but predictions might be improved by accounting for the effects of grain-size segregation.

Conference Paper↗

Suspended-sediment yields and stream-channel processes on Judy's Branch watershed in the St. Louis Metro East region in Illinois

Judy's Branch watershed, a small basin (8.64 square miles) in the St. Louis Metro East region in Illinois, was selected as a pilot site to determine suspended-sediment yields and stream-channel processes in the bluffs and American Bottoms (expansive low-lying valley floor in the region). Suspended-sediment and stream-chan-nel data collected and analyzed for Judy's Branch watershed are presented in this report to establish a baseline of data for water-resource managers to evaluate future stream rehabilitation and manage-ment alternatives. The sediment yield analysis determines the amount of sediment being delivered from the watershed and two subwatersheds: an urban tributary and an undeveloped headwater (pri-marily agricultural). The analysis of the subwater-sheds is used to compare the effects of urbanization on sediment yield to the river. The stream-channel contribution to sediment yield was determined by evaluation of the stream-channel processes operat-ing on the streambed and banks of Judy's Branch watershed. Bank stability was related to hydrologic events, bank stratigraphy, and channel geometry through model development and simulation. The average suspended-sediment yield from two upland subwatersheds (drainage areas of 0.23 and 0.40 sq.mi. was 1,163 tons per square mile per year (tons/sq.mi.-year) between July 2000 and June 2004. The suspended-sediment yield at the Route 157 station was 2,523 tons/sq.mi.-year, near the outlet of Judy's Branch watershed (drainage area = 8.33 sq.mi.). This is approximately 1,360 tons/sq.mi.-year greater than the average at the upland stations for the same time period. This result is unexpected in that, generally, the suspended-sediment yield decreases as the watershed area increases because of sediment stored in the channel and flood plain. The difference indicates a possible increase in yield from a source, such as bank retreat, and supports the concept that land-use changes increase stream-flows that may in turn result in higher rates of bank retreat. Utilizing both bank-rod data and resurveyed cross-section data, it was determined that approxi-mately half of the suspended- sediment yield at Route 157 during July 2000-June 2004 came from bank retreat. Given that bank retreat can be a substantial portion of the sediment yield, understanding bank stability processes is important. Bank stability can be assessed mathematically by computing the factor of safety, which is defined by the ratio of the shear strength (resisting force) along the failure surface and the shear stress (driving gravitational force). Once the factor of safety falls below one, the bank theoretically becomes unstable. Bank-stability conditions were related to hydrologic events, bank type, and channel geometry through model develop-ment and simulation. The most common type of bank in the watershed consists of cohesive alluvial soil deposits overlying a stiff glacial till. A stabil-ity chart for different bank types was developed using a bank-stability analysis. Banks steeper than 70 degrees and higher than from 10 to 11.5 feet (depending on bank type) become at risk for mass failure in the watershed under conditions that pro-mote saturation of the bank and a sudden drop in the river level.

Scientific Investigations Report↗

Simulation of ground-water flow at Anchorage, Alaska, 1955-83

The groundwater system at Anchorage, Alaska was analyzed by using a two-layer three-dimensional mathematical model. By use of existing data, both nonpumping and pumping steady-state conditions and transient conditions were simulated. Under steady-state conditions, calculated directions of groundwater flow were similar to observed flow patterns, and calculated stream discharges generally were within 10% of observed values. However, in many parts of the modeled area computed hydraulic head values were more than 20 ft higher or lower than observed values. Hydraulic conductivity and transmissivity are the most sensitive hydraulic parameters under steady-state conditions. Under steady-state conditions, a pumping rate of 18.8 Mgal/d lowers heads in the confined aquifer by as much as 30 ft, but reduces streamflow by less than 5%. Transient conditions show that drawndowns due to withdrawals by production wells follow similar patterns of nearby observation wells. On the basis of analytical techniques, the confining layer does not appear to hold significant quantities of water. (USGS)

Water-Resources Investigations Report↗

Dimensional effects of inter-phase mass transfer on attenuation of structurally trapped gaseous carbon dioxide in shallow aquifers

Based on experimental evidence and using mathematical modeling, inter-phase mass transfer processes of CO 2 exsolving from and dissolving into water in heterogeneous porous media are investigated under two fundamentally different flow conditions: in a quasi one dimensional vertical column and in a two-dimensional tank with a lateral background water flow, both at laboratory scale. In both cases, the CO 2 dissolved in water under a given overpressure is injected for a certain period at the bottom of the tank, exsolves, and migrates upwards. A layer of fine sand is present in the tanks designed to mimic geological scenarios of accumulation and trapping of exsolved CO 2 in shallow aquifers. Then, clean water is injected and the accumulated CO 2 is dissolved back into the flowing water. The study aims to point out the differences in the mass transfer processes between the quasi-1D and 2D cases using a mathematical model of two-phase compositional flow in heterogeneous porous media calibrated to the experimental datasets, and expose strategies that should be explored in future research. Additionally, temperature variations observed during the 2D experiments allow for analysis of isothermal versus non-isothermal effects on the processes of multiphase CO 2 evolution. The mathematical model is discretized and solved using the mixed hybrid finite element method in 2D that allows for the simulation of both advection- and diffusion-dominated processes accurately.

Journal of Computational Physics↗

Simulating and mapping spatial complexity using multi-scale techniques

A central problem in spatial analysis is the mapping of data for complex spatial fields using relatively simple data structures, such as those of a conventional GIS. This complexity can be measured using such indices as multi-scale variance, which reflects spatial autocorrelation, and multi-fractal dimension, which characterizes the values of fields. These indices are computed for three spatial processes: Gaussian noise, a simple mathematical function, and data for a random walk. Fractal analysis is then used to produce a vegetation map of the central region of California based on a satellite image. This analysis suggests that real world data lie on a continuum between the simple and the random, and that a major GIS challenge is the scientific representation and understanding of rapidly changing multi-scale fields.

International Journal of Geographical Information ↗

User's Guide for Mixed-Size Sediment Transport Model for Networks of One-Dimensional Open Channels

This user's guide describes a mathematical model for predicting the transport of mixed sizes of sediment by flow in networks of one-dimensional open channels. The simulation package is useful for general sediment routing problems, prediction of erosion and deposition following dam removal, and scour in channels at road embankment crossings or other artificial structures. The model treats input hydrographs as stepwise steady-state, and the flow computation algorithm automatically switches between sub- and supercritical flow as dictated by channel geometry and discharge. A variety of boundary conditions including weirs and rating curves may be applied both external and internal to the flow network. The model may be used to compute flow around islands and through multiple openings in embankments, but the network must be 'simple' in the sense that the flow directions in all channels can be specified before simulation commences. The location and shape of channel banks are user specified, and all bedelevation changes take place between these banks and above a user-specified bedrock elevation. Computation of sediment-transport emphasizes the sand-size range (0.0625-2.0 millimeter) but the user may select any desired range of particle diameters including silt and finer (<0.0625 millimeter). As part of data input, the user may set the original bed-sediment composition of any number of layers of known thickness. The model computes the time evolution of total transport and the size composition of bed- and suspended-load sand through any cross section of interest. It also tracks bed -surface elevation and size composition. The model is written in the FORTRAN programming language for implementation on personal computers using the WINDOWS operating system and, along with certain graphical output display capability, is accessed from a graphical user interface (GUI). The GUI provides a framework for selecting input files and parameters of a number of components of the sediment-transport process. There are no restrictions in the use of the model as to numbers of channels, channel junctions, cross sections per channel, or points defining the cross sections. Following completion of the simulation computations, the GUI accommodates display of longitudinal plots of either bed elevation and size composition, or of transport rate and size composition of the various components, for individual channels and selected times during the simulation period. For individual cross sections, the GUI also allows display of time series of transport rate and size composition of the various components and of bed elevation and size composition.

Water-Resources Investigations Report↗

The application of ensemble wave forcing to quantify uncertainty of shoreline change predictions

Reliable predictions and accompanying uncertainty estimates of coastal evolution on decadal to centennial time scales are increasingly sought. So far, most coastal change projections rely on a single, deterministic realization of the unknown future wave climate, often derived from a global climate model. Yet, deterministic projections do not account for the stochastic nature of future wave conditions across a variety of temporal scales (e.g., daily, weekly, seasonally, and interannually). Here, we present an ensemble Kalman filter shoreline change model to predict coastal erosion and uncertainty due to waves at a variety of time scales. We compare shoreline change projections, simulated with and without ensemble wave forcing conditions by applying ensemble wave time series produced by a computationally efficient statistical downscaling method. We demonstrate a sizable (site-dependent) increase in model uncertainty compared with the unrealistic case of model projections based on a single, deterministic realization (e.g., a single time series) of the wave forcing. We support model-derived uncertainty estimates with a novel mathematical analysis of ensembles of idealized process models. Here, the developed ensemble modeling approach is applied to a well-monitored beach in Tairua, New Zealand. However, the model and uncertainty quantification techniques derived here are generally applicable to a variety of coastal settings around the world.

JGR Earth Surface↗

Mathematical model for simulating discharges on the Sabine River between Tatum and Ruliff, Texas

A mathematical model for simulating discharges on the Sabine River between Tatum and Ruliff, TX., was developed to evaluate the effects of release schedules on discharges from the Toledo Bend Reservoir compared to discharges under natural conditions. Using the discharge at Tatum, TX., the rainfall over the basin, and the discharge release schedule for the reservoir, discharge hydrographs for the natural and reservoir-controlled conditions can be computed.

Texas↗

FEMFLOW3D; a finite-element program for the simulation of three-dimensional aquifers; version 1.0

This document describes a computer program that simulates three-dimensional ground- water systems using the finite-element method. The program was developed to simulate regional ground-water systems, but it can be applied to small-scale problems as well. This program can be used to simulate both confined and water-table aquifers. The program simulates a linearized three-dimensional free-surface ground-water system with a fixed grid. FEMFLOW3D is applicable to the simulation of various free-surface ground-water systems for which the change in aquifer thickness is small relative to the overall aquifer thickness. The finite-element method provides flexibility in the design of a geometric grid that represents the physical dimensions of an aquifer system. For example, features that can be well represented with a finite-element grid include irregular, random geographic and geologic features; irregular boundaries; and increased detail within localized areas of particular interest within the study area. The structure of the computer program consists of a main program, which serves as a simple driver, and a set of subroutines in which the calculations are performed. The background, mathematical basis, structure, and inputs for each of the subroutines are described in the document where applicable. Each subroutine generally handles (1) a part of the mathematical calculations related to the finite-element method, (2) a specific feature of the hydrologic system, or (3) special features related to the management input or output data. Hydrologic features that can be represented with the program include stream-aquifer interactions, phreatophytic evapotranspiration, highly permeable fault zones, land subsidence, and land-aquifer interactions associated with land-use activities. The program can also represent the primary features associated with complex irrigation systems, such as irrigated agriculture, and can calculate the ground-water recharge that results from these activities. Three boundary conditions, including specified-head boundaries, specified-flux boundaries, and variable-flux boundaries, can be represented with the program. The program also provides a method for identifying aquifer and river-bed parameters that can be used in the calibration of models. This document also includes model validation, source code, and example input and output files. Model validation was performed using four test problems. For each test problem, the results of a model simulation with FEMFLOW3D were compared with either an analytic solution or the results of an independent numerical approach. The source code, written in the ANSI x3.9-1978 FORTRAN standard, and the complete input and output of an example problem are listed in the appendixes.

Open-File Report↗

Data requirements for simulation of hydrogeologic effects of liquid waste injection, Harrison and Jackson Counties, Mississippi

Available literature and data were reviewed to quantify data requirements for computer simulation of hydrogeologic effects of liquid waste injection in southeastern Mississippi. Emphasis of each review was placed on quantifying physical properties of current Class I injection zones in Harrison and Jackson Counties. Class I injection zones are zones that are used for injection of hazardous or non-hazardous liquid waste below a formation containing the lowermost underground source of drinking water located within one-quarter of a mile of the injection well. Several mathematical models have been developed to simulate injection effects. The Basic Plume Method was selected because it is commonly used in permit applications, and the Intercomp model was selected because it is generally accepted and used in injection-related research. The input data requirements of the two models were combined into a single data requirement list inclusive of physical properties of injection zones only; injected waste and well properties are not included because such information is site-specific by industry, which is beyond the scope of this report. Results of the reviews of available literature and data indicated that Class I permit applications and standard-reference chemistry and physics texts were the primary sources of information to quantify physical properties of injection zones in Harrison and Jackson Counties. With the exception of a few reports and supplementary data for one injection zone in Jackson County, very little additional information pertaining to physical properties of the injection zones was available in sources other than permit applications and standard-reference texts.

Mississippi↗

Analog experiments of lava flow emplacement

Laboratory experiments that simulate lava flows have been in use by volcanologists for many years. The behavior of flows in the lab, where “eruption” parameters, material properties, and environmental settings are tightly controlled, provides insight into the influence of various factors on flow evolution. A second benefit of laboratory lava flows is to provide a set of observations with which numerical models of flow emplacement can be tested. Models of lava flow emplacement vary in mathematical approach, physical assumptions, and computational cost. Nonetheless, all models require thorough testing and evaluation, and laboratory experiments produce an excellent test for models. This paper provides a primer on modern analog laboratory lava flow experiments. It reviews scaling con- siderations and provides quantitative information meant to guide future experimentalists in designing their experiments to be relevant to natural processes. Traditional and novel laboratory techniques are described, including a discussion of current limitations. New insights from recent experiments highlight the impact of topographic conditions and highlight the importance of considering bed roughness, major obstacles, and slope breaks. The influence of episodic or non-uniform effusion rate is demonstrated through recent experi- mental works. Lastly, the paper discusses several open questions about lava flow emplacement and the ways in which future improvements in experimental methods, such as the ability to utilize three-phase suspensions and materials with complex rheologies and to image the interior of flows could help answer these.

Annals of Geophysics↗

Ground-water appraisal of the Pineland Sands area, central Minnesota

The Pineland Sands area consists of 770 square miles of surficial glacial outwash, which is undergoing increasing ground-water development for irrigation. The aquifer material is commonly very fine sand to fine gravel, and grain size generally increases from south to north. Thickness, transmissivity, and theoretical well yields are highest in the northern part. In places, saturated thickness exceeds 100 feet, transmissivity exceeds 20,000 feet squared per day, and expected well yields exceed 2,000 gallons per minute. Water in the aquifer is chemically suitable for irrigation. It is calcium bicarbonate water generally containing dissolvedsolids concentrations of 100-300 milligrams per liter. An estimated long-term water budget for the aquifer involves inflow and outflow of 295 cubic feet per second. Over 80 percent of recharge to the aquifer is directly from snowmelt and spring rain; the remainder is from underflow across the northern boundary of the aquifer and locally from streams and lakes. Over 90 percent of discharge from the aquifer is flow to streams and lakes; the remainder is through evapotranspiration. A mathematical model of the surficial aquifer was made to facilitate analysis of the hydrologic system. The model was calibrated through simulation of the natural ground-water flow system. Subsequent applications of the model to estimate effects of future ground-water development indicate that much of the system can safely support long-term, large-scale withdrawals. Results of model analysis show that present development (withdrawals totaling 3.3 cubic feet per second) has no significant effect on the aquifer system. Simulations of hypothetical withdrawals of 60 to 120 cubic feet per second resulted in computed water-table declines as great as 12 feet in places. Most pumpage is derived from intercepted base flow to streams, thus reducing streamflow. Similarly, some lake levels can be expected to decline in response to nearby intensive development.

Minnesota↗