Hydrology

What is an Aquifer?

An aquifer is a body of saturated rock through which water can easily move. Aquifers must be both permeable and porous and include such rock types as sandstone, conglomerate, fractured limestone and unconsolidated sand and gravel. Fractured volcanic rocks such as columnar basalts also make good aquifers. The rubble zones between volcanic flows are generally both porous and permeable and make excellent aquifers. In order for a well to be productive, it must be drilled into an aquifer. Rocks such as granite and schist are generally poor aquifers because they have a very low porosity. However, if these rocks are highly fractured, they make good aquifers. A well is a hole drilled into the ground to penetrate an aquifer. Normally such water must be pumped to the surface. If water is pumped from a well faster than it is replenished, the water table is lowered and the well may go dry. When water is pumped from a well, the water table is generally lowered into a cone of depression at the well. Groundwater normally flows down the slope of the water table towards the well.

One of Idaho's major aquifers is the Snake River Plain Aquifer.

Is an Aquifer an Underground River?
No. Almost all aquifers are not rivers. Since water moves slowly through pore spaces in an aquifer's rock or sediment, the only life-forms that could enjoy floating such a 'river' would be bacteria or viruses which are small enough to fit through the pore spaces. True underground rivers are found only in cavernous rock formations where the rock surrounding cracks or fractures has been dissolved away to leave open channels through which water can move very rapidly, like a river.

Ground water has to squeeze through pore spaces of rock and sediment to move through an aquifer (the porosity of such aquifers make them good filters for natural purification. Because it takes effort to force water through tiny pores, ground water loses energy as it flows, leading to a decrease in hydraulic head in the direction of flow. Larger pore spaces usually have higher permeability, produce less energy loss, and therefore allow water to move more rapidly. For this reason, ground water can move rapidly over large distances in aquifers whose pore spaces are large (like the lower Portneuf River aquifer) or where porosity arises from interconnected fractures. Ground water moves very rapidly in fractured rock aquifers like the basalts of the eastern Snake River Plain. In such cases, the spread of contaminants can be difficult or impossible to prevent.

What does an aquifer look like?
Every aquifer is unique, although some are more generic than others. The boundaries of an aquifer are usually gradational into other aquifers, so that an aquifer can be part of an aquifer system. The top of an unconfined aquifer is the water table. A confined aquifer has at least one aquitard at its top and, if it is stacked with others, an aquitard at its base.

The diagram represents a cut-away perspective view of this system of multiple aquifers and is greatly exaggerated in its vertical scale to show some of the details. Several different aquifers occur in this valley. In the northern valley (beneath Chubbuck and north Pocatello) multiple confined aquifers are stacked on top of one another and separated by aquitards made of clay; the aquifers tapped by Chubbuck's municipal wells are in the fractured basalts of the eastern Snake River Plain. In the southern valley (Portneuf Gap to Red Hill) the upper surface of the unconfined aquifer is the water table.

How Does an Aquifer Work?
An aquifer is filled with moving water and the amount of water in storage in the aquifer can vary from season to season and year to year. Ground water may flow through an aquifer at a rate of 50 feet per year or 50 inches per century, depending on the permeability. But no matter how fast or slow, water will eventually discharge or leave an aquifer and must be replaced by new water to replenish or recharge the aquifer. Thus, every aquifer has a recharge zone or zones and a discharge zone or zones.

 Recharge zones are typically at higher altitudes but can occur wherever water enters an aquifer, such as from rain, snowmelt, river and reservoir leakage, or from irrigation. Discharge zones can occur anywhere; in the diagram, discharge occurs not only in springs near the stream and in wetlands at low altitude, and also from wells and high-altitude springs.

The amount of water in storage in an aquifer is reflected in the elevation of its water table. If the rate of recharge is less than the natural discharge rate plus well production, the water table will decline and the aquifer's storage will decrease. A perched aquifer's water table is usually highly sensitive to the amount of seasonal recharge so a perched aquifer typically can go dry in summers or during drought years.

Why is Groundwater So Clean?
Aquifers are natural filters that trap sediment and other particles (like bacteria) and provide natural purification of the ground water flowing through them.

Like a coffee filter, the pore spaces in an aquifer's rock or sediment purify ground water of particulate matter (the 'coffee grounds') but not of dissolved substances (the 'coffee'). Also, like any filter, if the pore sizes are too large, particles like bacteria can get through. This can be a problem in aquifers in fractured rock (like the Snake River Plain, or areas outside the sediment-filled valleys of southeast Idaho).

Clay particles and other mineral surfaces in an aquifer also can trap dissolved substances or at least slow them down so they don't move as fast as water percolating through the aquifer.

Natural filtration in soils is very important in recharge areas and in irrigated areas above unconfined aquifers, where water applied at the surface can percolate through the soil to the water table. For example, in the lower Portneuf River valley, a protective layer of silt in the southern valley provides natural protection to the aquifer from septic systems, pesticide application, and accidental chemical spills.

Despite natural purification, concentrations of some elements in ground water can be high in instances where the rocks and minerals of an aquifer contribute high concentrations of certain elements. In some cases, such as iron staining, health impacts due to high concentrations of dissolved iron are not a problem as much as the aesthetic quality of the drinking water supply. In other cases, where elements such as fluoride, uranium, or arsenic occur naturally in high concentrations, human health may be affected.

How is an Aquifer Contaminated?
Contaminants reach the water table by any natural or manmade pathway along which water can flow from the surface to the aquifer.

Deliberate disposal of waste at point sources such as landfills, septic tanks, injection wells and storm drain wells can have an impact on the quality of ground water in an aquifer.

In general, any activity which creates a pathway that speeds the rate at which water can move from the surface to the water table has an impact. Waste water leaking down the casing of a poorly constructed well bypasses the natural purification afforded by soil. Excessive addition of fertilizer, agrichemicals, and road de-icing chemicals over broad areas, coupled with the enhanced recharge from crops, golf courses and other irrigated land and along road ditches, are common reasons for contamination arising from non-point sources. Removal of soil in excavations and mining reduces the purification potential and also enhances recharge; in some cases, such as the Highway Pond gravel pits south of Pocatello, the water table is exposed and becomes directly vulnerable to the entry of contaminants.

What is Groundwater?

figure 1. Click on image for larger view.

Groundwater is the water that lies below the surface of the ground and fills the pore space as well as cracks and other openings. Porosity is the percentage of a rock's volume that is taken up by openings. Most sedimentary rocks such as sandstone, shale and limestone can hold a large percentage of water. Loose sand may have a porosity of up to 40 percent; however, this may be reduced by half as a result of recrystallization and cementation. Even though a rock has high porosity, water may not be able to pass through it. Permeability is the capacity of a rock to transmit a fluid such as water. For a rock to be permeable, the openings must be interconnected. Rocks such as sandstone and conglomerate have a high porosity because they have the capacity to hold much water.

To understand porosity versus permeability, visualise that a sponge is both porus and permeable- meaning that it can both hold and transmit water. Styrofoam is an example of a material that is very porous, but lacks porosity. Thus styrofoam, though spongy, does not absorb or transmit water.

Why is Groundwater so Important?
Ground water is the second largest reservoir of water in the hydrologic cycle. But more importantly, it is the predominant source of drinking water in many western states. For example, ground water provides more than 95% of the drinking water used in Idaho.

The amount of ground water used in southeast Idaho, alone, was more than 800 million gallons per day. Of this, over 90% was used for agricultural purposes.

What is the Water Table?

In response to gravity, water seeps into the ground and moves downward until the rock is no longer permeable. The subsurface zone in which all openings of the rock are filled with water is called the zone of saturation. The upper surface of the zone of saturation is called the water table. The zone that exists between the water table and the ground surface is called the zone of aeration. In order to be successful, a well must be drilled into the zone of saturation. The velocity at which water flows underground depends on the permeability of the rock or how large and well connected the openings are.

Springs occur where water flows naturally from rock onto the surface of the land. Springs may seep from places where the water table intersects the land surface. Water may also flow out of the ground along fractures.

Why Do Some "Artesian" Wells Flow?

Wells that are drilled into confined aquifers can flow naturally under the higher pressure created by ground water trapped beneath confining layers.

The artesian well shown is a special kind of artesian well because it is a flowing artesian well. Like a pipe full of water, the confined aquifer into which this well is drilled sustains higher water pressure than in the unconfined aquifer above it, so that water is forced to rise higher in the artesian well than the local water table around it. If the water level rises above the top of the well, the well flows under natural water pressure.

Groundwater Resources

Idaho relies heavily on underground water supplies for agricultural, domestic and industrial uses. Groundwater is the largest reservoir of fresh water on the earth and is the predominant source of drinking water in many western states.

In 1995, groundwater provided more than 95% of Idaho’s drinking water from private and municipal wells. The amount of groundwater used in southeast Idaho, alone, was more than 800 million gallons per day.

Part of Idaho’s groundwater resource includes geothermal groundwater, or water naturally heated within the earth’s crust, that is available at or near the surface, either through wells or in natural springs.

Idaho has the third highest number of geothermal springs in the continental U.S.: some 258 active springs, with average water temperature of about 120° F, and individually as high as 203° F.

Idaho also has more than 600 geothermal water wells which provide heated water for recreation, aquaculture, and heating. Idaho's state capital building is heated with geothermal water, and Boise’s Warm Springs Avenue was the first geothermal heating district in The United States.

Areas of porous rock and sediment which hold water and give it up easily enough to provide water for a beneficial use are called aquifers (for drinking water and other non-thermal supplies). Where the water is heated geothermally, the groundwater resource is usually termed a geothermal reservoir.

Ground water issues forth in springs where water flows naturally from rock onto the surface of the land. Springs may seep from places where the water table intersects the land surface. Water may also flow out of the ground along fractures.

In most cases these springs contain water that has fallen upslope, been absorbed into the ground, and spent a few weeks to thousands of years traveling to the point of issue (the average amount of time spent in an aquifer by a water molecule called residence time).

Although most irrigation water today is provided from surface sources and wells, many an early homestead was located next to a spring.

Idaho has numerous aquifers which comprise an essential part of the state's overall water supply.

Unconsolidated aquifers hold water in pore spaces between the grains of sand and gravel in loose sediment, and are commonly known as valley-fill aquifers (e.g. The Rathdrum Prairie, Payette River valley, and lower Portneuf River valley).

Those which hold water in the cracks and pore spaces of solid rock are classified as consolidated aquifers. Idaho has two major types of consolidated aquifers: those in basalt (e.g. the Eastern Snake River Plain and Clearwater Plateau), and those in other volcanic and sedimentary materials that have been compacted and solidified. The amount of water available in these consolidated aquifers usually depends upon the size, number, and interconnection of cracks in the rock.

Sedimentary/volcanic aquifers in Idaho contain a mixture of unconsolidated sedimentary material, sedimentary rock (sandstone and shale), and basalt (e.g. The Treasure Valley, Salmon Falls/Rock Creek).

The most famous aquifer in Idaho is that of the Snake River Plain, which controls the economy of much of southern Idaho north and west of Pocatello (Stearns and others, 1938). Three million acres of farmland on the Snake River Plain are irrigated, with about 1/3 of this from wells and the rest from canals. This extensive irrigation system is the primary reason that Idaho has the highest per capita water consumption in the U.S.

The Snake River aquifer is a complex system, with multiple layers of high permeability. It discharges 8 million acre feet of water per year in the famous Thousand Springs area on the north wall of the Snake River canyon from Twin Falls to Hagerman. Most of the commercially produced trout in the United States are grown there.

The Snake River Plain is underlain by fractured and rubbly basalt lava flows, which form a highly permeable aquifer. Interbeds between the basalt layers are mainly sand, silt and clay, with smaller amounts of volcanic ash. Within basalts, permeable zones are mainly the tops and bottoms of lava flows, with columnar jointing in between providing slower vertical transmission of water. Rhyolite that underlies the basalt does not have high permeability, as many of the pore spaces are filled with chemical precipitates.

Water which falls mainly as snow in the mountains north and east of the eastern Snake River Plain is absorbed into the basalt in many places along the northern margin of the plain. The most obvious is the Sinks of the Big Lost River east of Howe, where waters of the Big and Little Lost Rivers, and Birch Creek sink into the lava plateau.

Dams were put on the Snake River at Milner, Minidoka, and American Falls in the early 1900s. The extensive irrigation essentially recycles the Snake River water, drawing it out of the river, and returning it to the river or the aquifer downstream. When the amount of irrigation on the Snake River Plain is reduced, output from the springs goes down also. The level of the aquifer rose dramatically after initiation of irrigation, but the level stabilized after a new equilibrium was reached. In the last 25 years, the level has begun to fall slowly.

Fundamentally, the Snake River Plain Aquifer is so large, with so much water running through it, and with residence times on the order of 100s of years, that it will be hard for man's efforts to change it much. Point sources of pollution certainly exist, but the dilution factor prevents them from becoming regional problems.

Water quality of the Snake River Plain aquifer is adversely affected by several human activities, most importantly agriculture. Runoff from fertilizer, feedlots, and potato processing plants has produced local acute pollution of the aquifer.

Another potential source of pollution is the Idaho National Engineering and Environmental Laboratory. Voluminous and expensive monitoring programs are being conducted to determine the extent of INEEL-caused pollution. The bottom line appears to be that the dry climate on the Snake River Plain combined with the huge volume of water in the Snake River Plain aquifer act to limit the amount of radionuclides that have reached the aquifer and then to dilute them below detection limits.

Idaho’s major aquifers have been prioritized based on their vulnerability to pollution by the Idaho Department of Health and Welfare, the Idaho Division of Environmental Quality, and the Idaho Department of Water Resources. Aquifers are vulnerable where groundwater is shallow or where soils are thin or very permeable. Also, the potential for contamination is greater where considerable water is applied to the land surface from precipitation or irrigation water and where population density and intensity of groundwater use are greatest.

Response Functions - What are they?

When an aquifer is pumped, ground water levels in the vicinity of the well decline, creating a cone of depression around the well.  This cone of depression is the response of the system (the aquifer) to the pumping that has been introduced (see illustration right).  Aquifer drawdown varies with distance from the well; consequently, the system response is location-dependent. The longer the well is pumped, the greater the drawdown becomes, making the system response time-dependent as well.  If we select a specific location within the cone of depression, and by field measurements or theoretical means we quantify how drawdown varies with time in response to pumping, we have developed a simple response function for that particular location and well.  In most cases, the drawdown will be proportional to the discharge of the well, so our response function, if expressed as a ratio of drawdown to well discharge, can be used to predict the system response to any pumping rate.  Cones of depression from multiple pumping wells normally can be superimposed, assuming that the system response is independent of other events occurring simultaneously.  These are the basic concepts of a response function.

Response functions are a means by which we can express cause and effect relationships for an aquifer or a river-aquifer system.  The functions may be thought of as a series of values or ratios that express the response at a specific location to aquifer recharge or discharge at another location.  Since the response changes with time, a different value is required not only for each pair of locations, but also for each time period of interest.  The following two examples illustrate the concept of response functions for a) drawdown in an aquifer, and b) for depletion of a stream.  

EXAMPLE 1: AQUIFER DRAWDOWN RESPONSE
Let's assume that we have two wells, A and B which are 1000 feet apart (see illustration above).  We measure water levels in both wells and start pumping well A at a rate of 1.0 cubic foot per second.  After 1 hour, we measure the water level in well B and note that the water level is 4 feet deeper than before we started pumping well A.  The reponse ratio expressing the response of the aquifer at point B to pumping at point A would be the ratio of the drawdown at point B (4.0 feet) to the pumping rate (1cfs) at point A.  In this example, the ratio 4 ft./1.0 cfs expresses the effects from pumping at one location on water levels in the aquifer at another location.  It is assumed that the ratio at location B holds regardless of the pumping rate at location A.  Consequently, if the pumping rate were doubled to 2 cfs, the drawdown would double to 8 feet.  It must also be noted that the drawdown increases as the pumping time increases.  For example, say that we continue pumping at 1 cfs and measure water levels in well B that were 6, 8 and 10 feet deeper at 2, 4 and 10 hours after we began pumping at well A, respectively.  There must, therefore, be a different response ratio for each time period of interest.  After one day of pumping, the ratio may have increased to 15 ft./1.0 cfs.  The term response function is used to represent the series of ratios describing responses at different times.

In addition to describing the response of water levels in an aquifer to ground water pumping, response functions may be used to describe the effect of ground water pumping (or recharge) on surface water resources.  When surface water resources are in hydraulic connection with an aquifer, ground water pumping or recharge can affect lake levels or flows in springs and streams.  An example of a response function for a stream-aquifer system follows.

EXAMPLE 2: RIVER DEPLETION RESPONSE

Let's assume that we have a stream that traverses a plain and is in hydraulic connection with an underlying aquifer (see figure at left).  That stream (a gaining stream) is being fed by the aquifer at a rate of 3 cubic feet per second (cfs)  in our reach of interest between two gaging stations.  A new well installation in the aquifer begins continuous pumping at a rate of 2 cfs.  After 100 days of pumping, the stream is now only gaining 2 cfs rather than the 3 cfs it used to gain in this reach.  The stream flow in this reach has therefore been depleted by one cfs after 100 days of pumping.  The response ratio representing this pumping location to this river reach at 100 days is calculated as the ratio of the depletion (1 cfs) to the pumping rate (2 cfs) or 0.5.  This ratio will change over time.  After 200 days, the ratio may increase to 0.6.  The series of ratios representing responses of this river reach to pumping (or recharge) at this location, at different times, comprise the response function for this well and river reach.  A different response function will exist for different river reaches and for different pumping locations.

It is assumed that the ratios determined between the pumping well and the river reach are valid for all pumping rates.  Pumping from the well for 100 days at a rate of 4 cfs rather than 2 cfs would deplete the stream by 0.5 x 4 cfs or 2 cfs.  This means the stream would be gaining 1 cfs rather than the 3 cfs gain that existed before pumping started.  If the rate of depletion were to exceed the rate of river gain (3 cfs in this example) the reach would become a losing rather than gaining reach of the stream. In this case, the ratio would hold only as long as 1) the river stays in hydraulic conection with the aquifer (the reach does not become perched) and 2) there is enough water flowing in the river to meet the loss (the river does not go dry).    

Although response functions can be developed to represent the drawdown response of an aquifer as in the first example, this description is focusing on ground water and surface water interactions and, therefore, on stream-aquifer response functions as illustrated in the second example.

The stream depletion response to continuous aquifer pumping has been illustrated for the Eastern Snake River Plain aquifer by Johnson, and others (1993) and Hubbell, and others (1997).  These descriptions portray the response of four reaches of the Snake River to ground water pumping at selected locations in the Snake River Plain aquifer.  The response varies dramatically with location.  Graphs of response in two river reaches to continuous pumping at five locations can be seen in the above figure.  Although this example shows response functions as graphs of proportioned depletion (depletion rate/pumping rate) vs. time, the response functions could also have been expressed as a matrix of response ratios (for each time, pumping location, and river reach), or as equations representing depletion as a function of time and location.

Response Functions - What Factors Affect Response Functions?

System response is controlled by the physical characteristics of the system.  The stream depletion effects resulting from pumping a given well will be controlled by:
1) the proximity of the stream and well,
2) the degree to which the stream and aquifer are interconnected,
3) the distribution of aquifer properties such as transmissivity and storativity,
4) layering of the aquifer and the depth and open interval of the well,
5) the distance to other hydraulically connected surface water bodies within the same aquifer, and
6) the distance to low-permeability aquifer boundaries. 

Obviously, the estimation of response functions can become very complicated.  Since we never fully understand the characteristics and physical properties of the aquifer, generated response functions represent only an approximation of actual system response.  The reliability of estimated response functions depends on the degree of complication of the real system and the degree to which we understand and represent the complexities in the method we choose to calculate response functions.  There are several ways, with varying levels of accuracy, to calculate response functions.  These are described in the section on "How are Response Functions Determined?".  Regardless, our understanding of the real system and our estimates of response functions are far from perfect.

Response Functions - What if Wells are not Continuously Pumping?

The examples (in the "Response Functions- What are They?") illustrated how response functions can be developed and used when wells are operating continuously.  In reality, however, this is seldom the case.  We need to be able to evaluate stream depletion from wells that are used intermittently.  Response functions can be determined for wells that are pumped for a brief period and then turned off.  The procedure is described in the section "How are Response Functions Determined?".

Wells that are pumped for a brief period may produce very minor stream depletion effects that persist long after pumping has ceased.  The accompanying graph shows that pumping at a rate of 1 cfs has greatly attenuated effects on a hydraulically connected stream reach.  Although the illustration is hypothetical, it is important to recognize that ground water pumping impacts may persist for years or even decades into the future, depending upon the scale and properties of the system.

Response Functions & Aquifer Recharge

Most of the above discussion and examples related to depletion of streams resulting from aquifer pumping.  In conditions where response functions can be used, pumping and aquifer recharge create equal but opposite effects on stream and spring discharge.  Where ground water pumping results in a depletion of surface water resources, aquifer recharge will result in an increase in flows.  The rate of increase will be proportional to the rate of recharge.

In the second example, if the well were recharging at a rate of 2 cfs, rather than pumping, then the stream gains would have increased, rather than decreased, by 1 cfs (the response ratio was 0.5) after 100 days.

Combinations of pumping and recharge can be evaluated by adding responses from individual activities on the stream reach of interest.

Response Functions - How Can Response Functions be Used?

Response functions describe the response of specific river reaches to ground water pumping or recharge at specific locations for specific times.  In physical situations where response functions are applicable, response functions may have several uses.

One of the most basic uses of response functions may be to obtain and convey a better understanding of the way in which surface water systems interact with ground water systems.  Graphs showing how response (stream depletion) changes with time are one way of gaining an understanding of the attenuation of pumping effects on surface water resources.  Superimposing these graphs on a map provides additional information on how impacts change depending on the location of pumping (see figure right).  Contouring response ratios (response functions at a single point in time) for an entire aquifer can portray how different pumping locations impact a given river reach.  In the Snake River Plain aquifer, contours of steady state response functions (response after many years of continuous pumping) can provide guidance to water managers as to the degree that pumping in any area impacts different reaches of the Snake River:  Upper Snake reaches, Blackfoot to Neeley reach, Neeley to Minidoka reach, and Kimberly to King Hill reach.

In many states, ground water and surface water supplies are being conjunctively managed.  This integrated management philosophy may result in ground water users being held partially responsible for surface water shortages.  If this is the case, then the quantities that individuals or groups of ground water users are accountable for must be determined.  This determination is an essential step in development of mitigation plans.  Mitigation in the form of managed recharge will be designed to offset injury resulting from pumping.  Just as pumping impacts may be readily determined from response functions, the counter-effect of recharge may be assessed.  Response functions may be incorporated into spreadsheet water accounting programs to determine debits, credits, and balances associated with ground water pumping and recharge.

In a simple analytical expression, or a table of numbers, response functions can describe the response of a surface water body to ground water pumping or recharge at a selected location. Subdividing an aquifer into a series of zones allows representation of cause and effect relationships by a simple series of independent equations or tables.  These simplified relationships can then be incorporated into regional surface water or multi-disciplinary models that represent the aquifer as one component of a larger system (see figure below).  This allows the inclusion of ground water systems into more holistic ecosystem models.

The additive nature of response functions also makes them applicable to optimization techniques.  Optimization methods may be used to identify schemes to accomplish goals such as minimizing pumping cost or drawdown at specific locations.  Development of response functions is a necessary part of optimization in ground water systems.

Response Functions - How are Response Functions Determined?

Response functions may be determined by several methods.  The methods may be divided into three basic categories: 1) direct measurement, 2) analytical methods, and 3) numerical methods.  These methods vary in the level of assumtions employed and accuracy of the results. The method selected should be commensurate with the purpose of the evaluation and the information available for each situation. Each method is described in the following paragraphs.

Direct measurement of stream or spring depletion by pumping is possible in relatively few cases.  Measurement of depletion resulting from pumping of a specific well is possible only when the well is relatively close to the stream or spring and well pumping is a significant proportion of the stream or spring flow.  It is also sometimes difficult to isolate the effects of a single well from other influences that may be causing changes in discharge.  When it is possible to measure the relationships between pumping and stream or spring discharge, the proportion of depletion can be determined from measurements of stream or spring flow and well discharge.  The depletion changes with time, so observations are required at different times.  The response function can be represented by the proportion of well pumping appearing as depletion of the stream or spring.  The response function will be valid within some limits of pumping rate, stream flow, and aquifer water level.  These limits are site-specific and related to the assumptions identified in the section "Assumptions Supporting Response Functions".

Analytical methods have been developed and used to estimate the effects of ground water pumping on stream depletion.  Methods such as those of Jenkins (1968) and Glover (1968) are burdened with intensive assumptions such as straight and fully penetrating streams, fully penetrating wells, and homogeneous and infinite aquifers.  These methods, however, can be employed to develop response functions when data are inadequate to use more sophisticated techniques.  In these cases, response functions involve little more than plugging the site-specific data into explicit equations.

Response functions can be developed from numerical models in situations where more data are available and numerical models have been developed. Some model codes generate response functions directly, in other situations it may be necessary to run multiple simulations, each simulating response to ground water pumping at a specific location.  MODFLOW is the most widely used code for ground water modeling.  It is accepted as the industry standard for numerical modeling of ground water systems. Simulated changes, when divided by the magnitude of the pumping rate, yield response functions.  The simulations must be based on linear equations.  This means that changes in aquifer thickness from pumping must be small relative to total thickness, and head-dependent boundary conditions must be linear functions of aquifer head.  This is perhaps the most restrictive condition relative to the use of response functions.  If springs dry up, streams transition between hydraulically connected and perched, or other non-linear conditions develop, and if these features significantly affect the operation of the system, then response functions should not be used.  Their use should be limited to the range of conditions where these sort of changes do not significantly impact the system.  This topic is also addressed in the section "Assumptions Supporting Response Functions".

Regardless of the technique used to develop the response functions, it must be recognized that the response functions are only as good as our conceptual understanding of the system and the data used in the development of the models!

Response functions describe the changes in the system (ground water levels or stream and spring discharge) resulting from ground water pumping or recharge at a specified site for a specified time duration.  The response functions become useful tools because of the ability to the add effects of multiple pumping or recharge events.  The events may be occurring at the same location sequentially, at multiple locations simultaneously, or both.  This makes it most effective to generate response functions for the shortest duration of pumping that is of interest.  The response to longer periods of pumping can then be developed by adding the effects from one pumping period to that of a second period immediately following the first.  These sorts of operations are ideally suited to spreadsheets and data bases.

Response Functions - Assumptions Supporting Response Functions

Response functions cannot be universally applied to all situations.  The validity of response functions is linked to the concept that responses, such as river depletion from pumping, are additive and proportional to the pumping or recharge rate.  This assumption is valid in many ground water environments.  Each situation should be evaluated by a qualified professional hydrologist, however, to determine if any of the following excluding conditions are likely to have a significant effect on the ground water flow system in the area of interest.  

  EXCLUDING CONDITIONS:

1) Saturated aquifer thickness changes, resulting in a significant change in aquifer properties, normally transmissivity.

2) Springs either begin or cease flowing as a result of natural or man-imposed changes in aquifer water level.

3) Streams transition between perched and hydraulically connected with the aquifer.

4) Evapotranspiration or other water consumption varies non-linearly with aquifer head.

5) Enough water is flowing in the river to meet demands in losing reaches.

These conditions need to be evaluated, not just for the development of response functions, but for their application to each specific circumstance.  If ground water elevations are changing dramatically in a given situation, then the above conditions are more likely to occur, and response functions should not be used.

Response functions generated by field measurements, analytical techniques, or numerical models will be burdened with all of the assumptions of the method used in their development.  For example, if the Jenkins (1968) analytical technique is used to generate the response functions, then one of the assumptions underlying the response functions is that the stream is straight and fully penetrating.  If a numerical model is used to generate the response functions, then the accuracy of the response functions is directly dependent on the accuracy of the numerical model's calibration and the underlying conceptual model.  In many cases, this will be the greatest source of error in application of response functions.

The Snake River Basin - Physical Description

The SR3 study area includes that portion of the Snake River Basin which is upstream of Brownlee Dam. As seen on the adjacent map, the drainage area associated with the Snake River in this study covers portions of five states: Wyoming, Idaho, Utah, Nevada, and Oregon. The Fort Hall (Shoshone-Banock) and the Duck Valley (Shoshone-Paiute) Reservations are also located in the area. The drainage basin includes over 72,000 square miles.

 The area includes rugged mountains, semi-arid desert, fertile agricultural land (primarily irrigated), and barren outcrops of lava flows.  Most of the famous "Idaho potatoes" are grown in the irrigated portions of the Snake River Plain, but range, lava flows, and timber are the dominant land covers in the basin.  Pine and spruce forests inhabit the higher elevations.  Most of the land in the basin is owned by the Federal Government (U.S. Forest Service, U.S. Bureau of Land Management, and U.S. Department of Energy).

One of the most prominent physiographic features of the basin is the Snake River Plain.  This curved topographic feature extends across southern Idaho into eastern Oregon.  The Snake River Plain is approximately 350 miles long and varies in width from 30 to 75 miles.  The Plain is discussed in more detail in "Origin of the Snake River Plain" and the "Eastern Snake River Plain".

The Snake River is the dominant hydrologic feature of the basin and is the only river discharging from the area.  The Snake extends from its source in Jackson Lake, Wyoming, to its confluence with the Columbia River in Washington.  This discussion, however, is limited to the portion above Brownlee Dam.  To travel down the Snake River from Jackson Dam to Brownlee Reservoir is a journey of over 700 miles.

Along the way, the Snake and its tributaries tumble over spectacular waterfalls, meander through deep and scenic canyons, and provide the water for irrigating millions of acres of agricultural land.

The Snake River is perhaps most well known for its recreational features such as world-class fishing, white water rafting, and the many lakes and reservoirs with excellent opportunities for boating, camping and fishing.

The Snake River has many tributary streams that are important components of the river system.  The tributaries provide a means of collecting the precipitation that accumulates in the mountains surrounding the Snake River Plain.  Water collected in the tributaries, enters the Snake River directly as surface flows, evaporates, or infiltrates into the subsurface where it later enters the river as spring flows.

Fifteen of the Nation's 65 class one springs (greater than 100 cubic feet per second discharge) are in the Snake River basin.  These springs support fish hatcheries that produce the majority of the Nation's commercial trout and produce juvenile fish for planting in lakes and streams.

The amount of natural flow in most of the streams varies throughout the year due to the annual cycle of precipitation.  Water accumulates during the winter snowfalls and is released by spring melting of the snow pack.  The normally hot dry periods of late summer and early fall are additional factors driving the cyclic nature of flow volumes.  In many locations the annual variation in stream flow volume is altered depending on the operational needs of the many reservoirs that have been constructed within the system.

The Snake River and its tributaries, including the aquifers that make up the ground water system, provide water for many uses including:  agricultural use, municipalities, industrial and domestic uses, recreation, Native American cultural needs, and habitat for fish and wildlife. The U.S. Bureau of Reclamation, along with other state and federal agencies and private groups, is attempting to manage the water resources of the basin for the many, and sometimes competing, uses.  The Snake River Resources Review (SR3) is an effort to take an integrated look at all uses and needs and provide managers with the tools and information necessary to make informed and reasonable decisions.  The water resource, and consequently the information, must cross the boundaries of five states and two Indian reservations.

Snake River Plain -Tributary Basins

Basins tributary to the Snake River in the SR3 study area cover parts of Idaho, Wyoming, Utah, Nevada, and Oregon. The Snake River from Jackson Lake, Wyoming to Brownlee Dam, on the Idaho-Oregon border, is nearly 700 miles long. The tributary basins, combined with the east and west parts of the Snake River Plain, drain more than 72,000 square miles (46,000,000 acres). Depending on the scale or detail with which the Snake River drainage system is examined, there are at least 60 separate streams or drainages that connect to the main stem of the river or at least deliver water to the Snake River Plain (Kjelstrom, 1986; Peterson, 1988).

Jackson Lake is the beginning of the Snake River. The lake is nestled at the base of the Teton Mountains within Grand Teton National Park  About 15,300 square miles of the study area is associated with the Snake River Plain with an additional 56,000 square miles within the hydrologic units that extend up the tributary basins.

Water in the Snake River begins its journey flowing south through Jackson Hole, as shown in photo to left..  The major tributaries in this region include the Gros Ventre River, Hoback River, Greys River, and the Salt River.

More than twenty tributary streams feed into the Snake River in the eastern portion of the Snake River basin. The larger tributaries in this area include: Henrys Fork, Teton River, Falls River, Big Wood River, Blackfoot River, Big Lost River, and Portneuf River. The Snake River drops in elevation from more than 5,015 feet on the eastern side of the plain, to about 2,100 feet on the western edge near Weiser, Idaho.

The most downstream reach for this study, the Middle Snake-Boise sub basin, extends from King Hill to Brownlee Dam and includes the western Snake River Plain. The western Snake River Plain is about 50 miles wide and 145 miles long (Newton, 1991). The major tributaries in this region include: Payette River, Boise River, Weiser River, Owhyee River, Bruneau River, Malheur River, Powder River, and Burnt River.

Snake River Plain -The Importance of Tributary Basins to the Snake River

figure 9. PRISM average annual precipitation map with SR3 outline (after Daly 1998). Image by Oregon State University.

While the flow of water within the Snake River receives a tremendous amount of attention, it is necessary to take a closer look at the areas where the flow originates. Precipitation is the sole source of recharge in tributary basins. The Oregon Climate Service (Daly, 1998) created an average annual precipitation map for the Western United States covering the time period 1961-1990 (see map to left). This map shows that within the Snake River Plain precipitation is less than 15 inches per year with some areas receiving less than 10 inches per year. Precipitation totals in the tributary basins can exceed 60 inches per year. These maps were created using the Parameter-Elevation Regressions on Independent Slopes Model (PRISM).

Two factors stand out as reasons to include tributary basins when discussing the flow of water within the Snake River. First, the majority of recharge occurs within the tributary basins. Second, the large areas associated with the tributary basins provide opportunities for development and use of water within the tributary basins themselves. Use of water within a tributary basin can affect the quantity and timing of water availability to the Snake River.

Snake River Basin: River-Tributary Basin Relationships

A basin tributary to the Snake River represents a geographical area with a stream or other body of water, surface or underground, that contributes water to the Snake River, even in small or intermittent quantities. With so many streams and rivers that deliver water to the Snake River, the scale or size of a basin has to be considered in allocating resources for studies or management programs.

Much of the data presented here will use the term “HUCs” (hydrologic unit code), often used synonymously with cataloging units.  Cataloging units are the smallest division set aside by the USGS as a system of nomenclature dividing the United States into several large geographic basins or regions that represent hydrologic systems.  A cataloging unit may represent a portion of a basin (example- Little Lost), or a combination of drainage basins (example, Upper Snake).  In the SR3 study area, there are 53 cataloging units;  26 in the Upper Snake sub basin and 27 in the Middle Snake Sub basin.  See illustrations "Eastern & Western" below.

Many different hydrologic relationships could exist between a river and its tributaries. Within the Snake River Basin, three main categories are readily identified:

A.  A tributary stream that is not connected to the Snake River.
B.  A tributary stream that is connected to the Snake River. Surface water and ground water are not hydraulically interconnected.
C.  A tributary stream connected to the Snake River. Surface water and ground water are at least partially interconnected.

Category A-Examples In the northeastern portion of the Snake River Plain, located within the State of Idaho, there are several streams which the Bureau of Reclamation grouped in their SR3 Blueprint (1996) under the heading “Streams that disappear into the Snake Plain Aquifer” (see "Catagory A" figure below). These streams, located on the northern portion of the Upper Snake sub basin, are not tiny ephemeral streams. The largest of the group, the Big Lost River, annually delivers more than 200,000 acre-feet of water that travels down the river to “disappear” or infiltrate into the Snake River Plain. Others in this group include Camas-Beaver Creek, Medicine Lodge Creek, Birch Creek, and Little Lost River. Combined, these basins are the source for over 9 percent (945,000 ac-ft) of the annual water contributions to the Upper Snake River Basin (data from Kjelstrom, 1986).

Category B-Examples: IDWR (Idaho Department of Water Resources, 1997) has described the Rexburg Bench- Moody Creek region as an area that is not hydraulically interconnected with the regional aquifer. In another example, Horn and Jeong (1989), have suggested a similar interpretation describing the Camas Creek basin, Idaho.

Category C-Examples: The third category represents most of the tributary basins. Most of the tributary streams are considered to have at least some degree of interconnectedness with their associated aquifers. It may be difficult in some areas to determine if the associated ground water is the regional system or a perched zone.

Snake River Basin: River-Land Use Data

Recent land use GIS data were obtained from the respective state agencies of Idaho, Wyoming, and Oregon and used to identify presently irrigated lands. Oregon is in the process of converting older data sets to useable GIS files; however, they did provide that portion of the data currently available. There are more areas of agricultural use than shown in Oregon and that data should be available to incorporate into a data set in the near future. Data from Idaho did enable acreage tabulation of the irrigated and non-irrigated lands. See the table below which provides a summary of the distribution of irrigated and non-irrigated acres for HUCs in Idaho.

Teton, Raft, Portneuf, and Blackfoot are those HUCs which contain significant non-irrigated lands with potential for conversion to irrigation. Of the eight HUCs with the largest irrigated acreage, seven are located primarily on the Snake River Plain, see figure below.

Snake River Basin: Stream Flow Data

Most tributary streams are considered to be at least somewhat hydraulically interconnected with the aquifer, changes in stream flow can affect the amount of water available for aquifer recharge. Also, significant changes in the quantity of ground water diverted or the amount of surface water consumptively used might be indicated by a reduction in stream flow relative to other nearby tributaries.   See following table for a summary of stream flows in the Snake River Basin.

Eastern Snake River Plain- Physical Description

The eastern Snake River Plain extends as a two hundred mile long arc, about 60 miles in width, across southeast Idaho.  This plain was formed by the deposition of basaltic lava extruded from numerous vents across the plain.  Wind and water deposited sediments overlie the basalt in most areas and are also found interbedded with basalt flows in the subsurface.

Precipitation ranges from about 8 inches/year in the lower elevations in the west to about 14 inches/year in the higher elevations in the northeast.  The majority of the water supply originates in mountains on the north and east sides of the basin, including the southern portion of Yellowstone National Park.  Within the boundaries of the Snake River Plain, rainfall is insufficient to support commercial levels of agriculture without irrigation that requires substantial diversions from surface and ground-water systems.  The Snake River flows along the southern margin of the plain, fed by tributaries flowing out of the mountains on the south and east side of the plain.  A few tributaries from the northern valleys flow into the Snake River, but many disappear through seepage into the permeable Snake River Plain basalts.

The Eastern Snake River Plain Aquifer

figure 1

The aquifer beneath the eastern Snake River Plain is perhaps the single-most important aquifer in Idaho. Composed of layered basalt lava flows and some sediment, it covers an area of approximately 10,800 square mile.

Although the total thickness of basalts is estimated to be more than 5,000 feet (figure 1), groundwater flows most rapidly in the upper 300 - 500 feet, which is the most productive portion of the aquifer. Interconnected pore spaces in the rubbly tops of lava flows transmit water very readily, and well yields above 3,000 gallons per minute are not uncommon.

Total ground-water storage in the upper 500 feet of the aquifer is estimated at 200 to 300 million acre-feet, roughly the equivalent of Lake Erie.

The direction of ground water flow in the upper part of the aquifer is generally from east-northeast to west-southwest.

Human activity has had a tremendous impact on the water balance of this aquifer. About sixty percent of total recharge to the aquifer is derived from irrigation with surface water (figure 2). Most groundwater still leaves the aquifer via springs and seepage losses in two major upper basin reaches, although pumping withdrawals contribute significantly to the aquifer’s total losses.

Irrigation practices have and continue to exert a major influence on water resources of the Eastern Snake River Plain. Prior to 1950, spring discharges (figure 3) and the water table between Kimberly and Bliss rose by 60-70 feet on average during the period 1907-1959, accounting for a cumulative increase of more than 5 % of the aquifer’s total storage.

figure 3

During the 1950s and 1960s more land began to be irrigated with groundwater and irrigation efficiency increased through the use of sprinkler irrigation and conservation. The result was a substantial decline in groundwater levels in parts of the Plain between 1975 and 1995, leading to a cumulative decrease in aquifer storage of about 3 %, and decreased spring flows between Kimberley and Bliss (figure 3).

In general, the declines in spring discharge and ground water levels have been due to increased groundwater pumping, more efficient irrigation methods, and reduced reliance on surface water diversions for irrigation. However, localized declines may be predominantly the result of increased pumping withdrawals in some areas.

Eastern Snake River Plain- Hydrogeology

Flow in the Snake River Plain aquifer is generally from recharge areas in the north and east, to springs in the American Falls and Thousand Springs reaches of the Snake River.

The highly productive Snake River Plain aquifer underlies the eastern Snake River Plain. It has been declared a sole source aquifer by the U.S. Environmental Protection Agency, due to the nearly complete reliance on the aquifer for drinking water supplies in the area.

The aquifer is hosted in layered basalts with sediment occasionally deposited between layers.  Highly fractured rubble zones at the contacts between layers provide the primary conduit for ground-water flow.  The aquifer is considered to be unconfined but may locally respond as a confined aquifer during short duration pumping.  This is presumably due to vertical stratification and the presence of lower permeability sediments interbedded among the basalt layers.

Aquifer recharge occurs mainly in the north and east portions of the plain, resulting in generally southwest trending flow lines.  Natural discharge from the aquifer occurs primarily along two reaches of the Snake River:  1) near American Falls Reservoir, in which spring discharges total about 2,600 cfs; and 2) in the Kimberly to King Hill reach (Thousand Springs reach), where the collective discharge is about 5,200 cfs.

During summer, the spring flows provide the majority of the flow in the Snake River below the irrigation diversions of Milner Dam.  The Snake River basin contains 15 of the Nation's 65 first magnitude springs (discharge greater than 100 cfs).

The graph to the left is a water budget for the Snake River Plain aquifer representing 1980 conditions.  Surface water irrigation is by far the largest component of aquifer recharge, with smaller contributions from tributary valley underflow and seepage from rivers.  During the past several decades, ground water storage has been depleted, causing water levels to drop.

Variations in weather patterns and changes in irrigation practices on the Snake River Plain have caused changes in aquifer water levels. Some areas of the aquifer have experienced drops in water levels where other areas have experienced slight increases in water levels. 

One of the major concerns of conjunctive management is the identification of river reaches or surface water bodies that are hydraulically interconnected with an aquifer.  The conceptual basis for this concern is described in the section on "Surface Water and Ground Water Interaction".  In some cases it is difficult to determine the degree of interconnection because of uncertainties in river bottom conditions and water table depth and because conditions vary with time.  A river reach that at one time is hydraulically connected to the aquifer may be perched at another time when aquifer water levels are lower.  The State's computer model of the Snake River Plain aquifer treats four major reaches (bounded by gaging stations) of the Snake River as interconnected with the aquifer.

1) The Kimberly to King Hill reach (Thousand Springs reach), in which the river is deeply incised in a canyon and springs discharge along the canyon wall and in the bottom of the river.  Total spring discharge in this reach is about 5,200 cfs.  The discharge in this reach varies seasonally and also has shown long term variations reflecting weather and irrigation patterns.

2) The Neeley to Minidoka reach which may alternately gain and lose water depending upon water table elevation.  The U.S. Geological Survey estimated that this reach had a net gain of 180 cfs in 1980 (Garabedian, 1992).

3) The Blackfoot to Neeley reach in which springs contribute about 2,600 cfs to the flow of the river.  Spring discharges in this reach exhibit seasonal variation, but have not shown the long-term variation like the Kimberly to King Hill reach.  The reason for the long-term stability in this reach is not known.

4) The Henrys Fork and Upper Snake River reaches which were estimated to jointly gain approximately 260 cfs in 1980 (Garabedian, 1992).

Changes in water table elevation, due to natural causes or man caused activities, result in changes in river gains and losses in these reaches.  Although the effects of ground water pumping cannot be measured or separated from effects of natural events, ground water models can provide estimates of individual and collective pumping effects.

Eastern Snake River Plain- Changes in Water Use

Extensive irrigation from the Snake River and its tributaries began in the late 1800s on the eastern Snake River Plain.  Gravity irrigation systems typically divert more than twice the amount of water necessary to meet crop requirements (Goodell, 1985).  The remainder of the water returned to the Snake River or infiltrated to the aquifer.  The incidental recharge from the approximately 900,000 acres of surface water irrigated land resulted in increased elevation of ground water levels.  The volume of water stored in the aquifer, as shown in the above graph,  increased by about 15 million acre-feet between 1915 and 1955.  On the average, 340,000 acre-feet of water were being added to aquifer storage annually during this period. Spring discharge, especially in the Thousand Springs reach, also increased dramatically during this period due to higher water levels.  Cumulative discharge in the Thousand Springs reach increased from about 4,800 cfs in 1915 to about 6,800 cfs in 1955.  An infrared image of the plain shows the approximate extent of irrigated lands in the early 1990s for areas that appear in red adjacent to the Snake River.

In the mid-1950s, irrigation technology on the eastern Snake River Plain began to change.  An increased water use efficiency resulted from completion of additional surface water storage facilities, water conservation programs, and, probably most importantly, increased use of sprinkler irrigation.  Surface water diversions for irrigation began decreasing in the early 1970s (see right graph).  The increased efficiency of the system led to decreased ground-water recharge that has contributed to the decline of ground water levels and spring discharge.  In addition, ground-water withdrawals for irrigation increased dramatically during the last half of the century.  About 800,000 acres of ground water irrigated land have been brought into production since the 1950s. At an average estimated irrigation demand of 1.8 acre-feet/acre, the total aquifer withdrawal is about 1.5 million acre-feet/year.  The combined effects of decreased recharge from surface water irrigation and increased ground-water withdrawals, along with weather variation, are apparent in the declines in ground-water storage and spring discharge since the mid-1950s.  The average rate of decline in ground-water storage between 1975 and 1995 is about 350,000 acre-feet/year.

Eastern Snake River Plain- Recent Challenges in System Management

The State of Idaho administers water rights according to the Prior Appropriation Doctrine.  Idaho fully recognized the need to implement conjunctive management of its water resources in 1984 when the Idaho Supreme Court determined that hydropower water rights of Idaho Power Company at Swan Falls Dam were not subordinated to junior upstream irrigation rights.  The case alerted water users in the basin that ground water pumping for irrigation was impacting spring discharge and flow in the Snake River, and that surface and ground water rights were to be jointly administered.  In 1992, a moratorium was imposed on new irrigation pumping on the eastern Snake River Plain (Idaho Department of Water Resources, 1996), which is still in place.  Subsequently, IDWR promulgated conjunctive management rules to provide a mechanism to stem conflicts between surface and ground water users when water supplies are limited.  IDWR has also formed water measurement districts in the Eastern Snake River Plain (see above figure) that require the measurement and reporting of ground-water pumping at rates exceeding 0.24 cfs, or irrigating areas greater than 5 acres.  

Depletion of spring flows and declining ground-water levels are a collective effect of drought, changes in surface-water irrigation acreage and practices, and ground-water pumping.  A recent model study (IDWR, 1997) indicates that the collective effects of all ground-water pumping within the boundaries of the eastern Snake River Plain depletes spring discharge and flow of the Snake River by about 900,000 acre-feet per year (1,200 cfs).  The same study projects that changes in surface water irrigation practices have depleted the spring discharge by about 500,000 acre-feet per year (700 cfs).  IDWR and the courts are placed in the position of determining the degree to which junior ground-water users have injured senior surface-water users.  Isolating cause and effect relationships on a case by case basis will be difficult and costly.

Although most water users and managers accept the concept that ground water use depletes surface water supplies, it is not necessarily accepted that depletion constitutes legal injury.  The conjunctive management rules provide for weighing the time of year in which depletion is experienced, the efficiency of use of the senior water users, and the maximum economic benefits of all uses, against the possibility of "futile call".

The State's conjunctive management rules allow junior priority water users to mitigate injury to senior surface and ground water users.  One of the mechanisms is to provide supplemental recharge to the aquifer.  Both surface and ground water users have embraced artificial or managed recharge as a means of avoiding future conflicts and litigation.

Eastern Snake River Plain- Estimates of Surface & Groundwater Interaction

Aquifer inflows in balance with outflows.

There are several reaches of the Snake River, as well as small streams, that are hydraulically connected with the Snake River Plain aquifer.  Ground water pumping from the aquifer initially causes a localized decline in the water table.  That decline, or cone of depression, propagates progressively outward until it encounters hydraulically connected surface water bodies.  The surface water bodies are subsequently depleted as a result of the pumping.  There are four primary points to recognize about the effects of pumping on surface water in the eastern Snake River Plain.  The reader should recognize that throughout this discussion the focus is on ground water pumping, but the same concepts, in reverse, apply to aquifer recharge.

1) Pumping effects propagate in all directions through the aquifer, not just down-gradient.  This means it is possible for a down-gradient water user to affect stream flow in the upper reaches of the plain.  This appears to be in contrast to the logic that "water flows downhill", but in fact it is not.  Consider the analogy of an water tank in which water is entering from two sources on one end and continuously discharging from an overflow weir on the other end, as shown in the illustration.  The water in the tank represents the Snake River Plain aquifer.  The one source of fill is a faucet that does not make direct contact with the water level in the tank, therefore it cannot siphon.  This represents recharge to the aquifer resulting from perched streams, precipitation, and irrigation sources.  If the water level in the tank (i.e. aquifer) changes, it has no effect on this recharge.  The second source of fill is a pipe connected below the water surface in the tank.  This source represents hydraulically connected stream and river channels.  If the water level in the tank drops, more water will flow out of the pipe and into the tank.  If a pump is introduced to extract water from the middle of the tank, what will happen?  Water levels in the tank will decline, causing the outflow over the weir to be reduced (similar to Thousand Springs).  In addition, the inflow from pipe connected beneath the water surface will increase or outflow will decrease (similar to river connection in the Henrys Fork and the upper Snake River).  This increase occurs despite the fact that water is flowing through the tank from the inlet to the outlet sides.  In the Snake River Plain aquifer, if water is pumped, or recharged, in the center of the plain, gains and losses of the Snake River may be affected at many locations, not just along the flow lines.  Flow lines in an aquifer have limited  meaning when evaluating the propagation of pumping or recharge effects; they are significant with respect to water quality considerations.

The radial propagation of pumping effects is evident from depletion graphs generated from a numerical model of the Snake River Plain aquifer.  It is apparent from the graphs superimposed on the map of the Snake River Plain that effects do not preferentially propagate along the flow lines in the aquifer.  Although pumping sites in the upper portion of the basin are aligned with flow lines that discharge near Thousand Springs, the majority of the impact is expected near American Falls.  The simulations did not include effects of the hydraulic connection of the Henrys and upper Snake River, although they may be significant.

2) The total volume of water pumped and consumptively used from the Snake River Plain aquifer will ultimately be depleted from surface water sources and cause a reduction in ground water storage.  It is obviously true that water pumped and consumptively used is water that would otherwise have gone somewhere else.  If we again consider the water tank above, when our pump is taking water out of the tank, the discharge of the tank is diminished and the inflow from the submerged  pipe is increased.  The pumping has not exceeded the rate of recharge to the tank, but it has impacted outflow (analogous to springs) and inflow (analogous to a hydraulically connected river reach).  In the Snake River Plain aquifer, the entire volume of water pumped and consumptively used will either be depleted from spring discharge, cause a corresponding increase in river losses, or cause a corresponding decrease in river gains.   We can neither create nor destroy water in the process of pumping.

3) Pumping and aquifer recharge effects on surface water are often greatly attenuated.
Even though the entire volume of water consumptively pumped throughout the Snake River Plain aquifer will ultimately be drawn from surface water sources and ground water storage, that depletion may be distributed over time periods ranging from days to decades.  The attenuation of the effects is related to the proximity of the pumping location and surface water body, and the hydraulic properties of the aquifer and stream.  The expected approximate attenuation of pumping or recharge effects within about 25 miles of the Snake River in the Thousand Springs area is illustrated graphically.  The effects of a 30 day pumping or recharge event are seen to become more attenuated as the site becomes progressively more distant from the river.  The illustration uses aquifer properties typical of the Thousand Springs area that may not be representative of other locations within the Snake River Plain aquifer.  At greater distances, the effects are much more attenuated.  The effects of a 30 year pumping event in the northeast portion of the plain are expected to continue for decades even after the pumping ceases.

4) Our ability to estimate ground water pumping impacts on surface water resources is limited.  Although this page has presented many illustrations that quantitatively relate consumptive ground water pumping or recharge to surface water depletion, these illustrations are approximate.  They are the result of analytical and numerical models, but those models are the current representations of our limited knowledge about the real system.  More detail can be found in the section on "Evaluation Methods".

The above points are extremely significant to water management in the Snake River and the Snake River Plain aquifer.  Some of the primary management considerations are:

  1) Negative impacts can result from consumptive ground water pumping, even though the rate of pumping does not exceed natural recharge.  This is because other users or system needs are dependent on the aquifer.

  2) There is no "no-impact" consumptive pumping.  Every gallon of water consumptively used is not available somewhere else in the system where it would otherwise have existed.

  3) Conjunctive administration of water rights under the Prior Appropriation Doctrine will be an involved process.  Complication results from the propagation of effects to changes in consumptive ground water pumping or managed recharge in all directions and the attenuation of those effects in the aquifer and to the stream, and due to our limited knowledge about the aquifer.

  4) Managed aquifer recharge can offset some of the adverse economic and environmental impacts of consumptive ground water pumping.

Eastern Snake River Plain- Evaluation Methods

Several methods may be applied to estimate the impact of ground water pumping or recharge on surface water resources.  General application of these methods is discussed in the section on "Surface Water and Ground Water Interaction".  The primary method used for the Snake River Plain aquifer has been numerical modeling.  Numerical modeling allows us to use as much information about the system physical characteristics as we have available;  however, our knowledge of the system is never complete.

Several models have been constructed of the Snake River Plain aquifer, or portions of the aquifer. The two most complete models were constructed by the University of Idaho for the Idaho Department of Water Resources (IDWR) and the U.S. Geological Survey (USGS).  These two models have similar boundaries and employ the same computer code.  They differ, however, in their purpose for construction and, consequently, their design.  The USGS model was constructed largely as an investigative tool to explore concepts of the regional ground water flow and improve our scientific understanding of the system.  The IDWR model was designed primarily as an aquifer planning and management tool.  The IDWR model presents a more simplified concept of the aquifer in that it uses a single model layer.  The single layer was used because it was felt that data were inadequate to develop the multi-layer approach used by the USGS.  Nevertheless, extremely sophisticated concepts can be simulated with each model.  Our development of models is limited by data availability and our understanding of the real system.  A comparison of predictions from these two models is currently being explored as part of the Bureau of Reclamation's SR3 project.  More information on these models can be found in Cosgrove and others (1999) and Garabedian (1992).

The model developed for the IDWR is the tool that has been, and probably will continue to be, used for evaluating ground water and surface water relationships. The model was used to perform the Upper Snake River Basin Study (IDWR, 1997) and was used to develop response functions for the river and aquifer (Johnson and Cosgrove, 1999, to be supplied).

The models of the Snake River Plain aquifer described above have been used for many years and presently are accepted to represent the effects that consumptive ground water pumping and managed recharge have on ground water storage and on interactions between the river and the aquifer.  However, it is important to recognize that these models are not precise.  Although our models will never be perfect, they can always be improved.  For example, more ground water-level measurements are needed near the Snake River to better understand and represent the interconnection between the river and the aquifer.

Western Snake River Plain- Treasure Valley General Description

The Treasure Valley, which includes the lower Boise River basin and extends south to the Snake River is located within the northwest-trending topographic depression known as the western Snake River Plain. The western Snake River Plain is a relatively flat lowland separating Cretaceous-age granitic mountains of west-central Idaho from the granitic/volcanic Owhyee mountains in southwestern Idaho. The western Snake River Plain extends from about Twin Falls, Idaho northwestward to Vale, Oregon. The Snake River Plain is about 30 miles wide in the section containing the lower Boise River. The depression is believed to have been formed by crustal extension, beginning as early as 17 million years ago (Malde, 1991).

Western Snake River Plain- Treasure Valley Water Use

Agricultural
Approximately half of the land in the Treasure Valley is irrigated agriculture, and of this, approximately 74% is irrigated with surface water. Surface irrigation water is distributed through an extensive series of canals. The largest of these, the New York Canal, diverts approximately 2,500 cfs in a typical irrigation season. The canals are operated by a variety of irrigation districts, canal companies, and other entities.

An acre-foot is an expression of water quantity. One acre-foot will cover one acre of ground one foot deep. An acre-foot contains 43,560 cubic feet, 1,233 cubic meters, or 325,829 gallons (U.S.).About 1,380,000 acre feet per year are diverted for agricultural irrigation from the Boise River. In addition, approximately 360,000 acre feet are diverted from the Payette River to the Treasure Valley.

Ground water is used to irrigate approximately 42,300 acres of farmland, primarily in the southern portion of the valley. In addition, many of the irrigators dependent on surface water supplies use supplemental irrigation wells during periods of drought. It is estimated that approximately 72,000 acre feet of ground water are withdrawn annually for agricultural irrigation. The image above shows a typical pivot irrigation system in the Treasure Valley.

Municipal
Most municipal water in the Treasure Valley comes from ground water. Municipal water is supplied by a variety of entities, including public companies, cities, and water districts. The Idaho Department of Environmental Quality has compiled a map. The largest water purveyor in the Treasure Valley is United Water Idaho (UWI). UWI provides water services to about 190,000 people in Boise and surrounding communities. The company is a subsidiary of United Water Resources, one of the nation's largest water services companies

United Water Idaho customers receive their water from both groundwater and surface water sources. Groundwater is drawn from wells drilled into deep aquifers that produce about 14 billion gallons of water per year. The groundwater quality is excellent and free from harmful bacterial contamination. As a result, treatment is limited to disinfection with chlorine. Unfortunately, the advantages of excellent bacteria-free groundwater are often accompanied by disadvantages like high iron and manganese content. This is associated with discoloration problems -- some of United Water's groundwater sources have a high iron and manganese content. We are improving these sources with geoscience techniques to screen out water high in these minerals or by adding a phosphate compound to hold these minerals in solution.

Eight percent of United Water Idaho (UWI) water is drawn from the Boise River at the Marden Street Treatment Plant; 89 wells supply , and 92% is pumped from a total of 89 wells scattered throughout the Boise area. The Marden Lane Water Treatment Plant is a conventional filtration plant that produces about 1.8 billion gallons of water per year. Treatment involves filtering to remove particulate matter, followed by disinfection with chlorine to destroy any harmful bacteria. We also adjust the pH to reduce the water's corrosiveness and decrease the possibility of dissolving metals from household plumbing. Some facts from United Water Idaho's website:

Commercial & Industrial
Industrial ground water use is difficult to quantify because many industries rely on different water sources, such as a combination of municipal supply and self-supplied water.Also, municipal suppliers usually do not distinguish between commercial and industrial use, i.e., the commercial category includes small businesses, multi-family housing, and industrial facilities.That said, the estimated self-supplied industrial ground water withdrawals in 1996 are shown in the table below (Urban and Petrich, 1998).

Notes:
1. Industry categories and 1995 employee census data from Idaho Dept. of Employment, Research and Analysis, except for Micron Technology, Inc, which supplied its own population and water use data for 1995.
3. Agriculture category refers to amount of water personally consumed by the employee; does not include irrigation water, livestock water, or other agricultural uses. Rate of 15 gpd/person obtained from Idaho Water Law Handbook, 1988, Appendix IV; value for "day camps, no lunch served."
4. Manufacturing category includes electronics industries (except Micron Technology, Inc. of Boise, which is considered separately).
5. This rate reflects the amount of water pumped from Micron wells only; an additional 123 gpd/employee was purchased from United Water Idaho.
6. Wood products category includes lumber and wood industries, such as lumber, plywood, and cabinet making. It does not include pulp and paper industries.

Western Snake River Plain- Treasure Valley: The Boise River

The lower Boise River is the 64-mile stretch that flows from Lucky Peak Dam above Boise, Idaho to the Snake River below Parma, Idaho. The river flows primarily through Ada and Canyon Counties, but also drains portions of Elmore, Gem, Payette, and Boise counties. The watershed encompasses 1290 square-miles of rangeland, forests, agricultural lands, and urban areas. The river flows in a northwesterly direction from its origin at Lucky Peak Dam to its confluence with the Snake River.

Boise River- Typical July Conditions

Boise River Diversions

Diversions and Returns
The Boise River is the primary channel bringing water to the Treasure Valley, and a primary destination of ground water discharge. Water is withdrawn for the Boise River beginning at Diversion Dam. Some of the water seeps from the Boise River into underlying shallow aquifers, primarily above Capital Street Bridge. Water returns to the Boise River as (1) return flows from irrigation (water that was diverted but not used), (2) ground water discharge to canals (that then flows into the Boise River), and (3) direct ground water discharge to the river channel.

The graphic (right) illustrates flows out of and into the Boise River under typical July conditions. Note that flows may be reduced to 250 cubic feet per second (cfs) in the vicinity of Star Bridge. Below this point return flows exceed diversions.

Flooding
Annual flooding has been reduced substantially since the construction of three major dams in the upper Boise River Basin – Anderson Ranch, Arrowrock, and Lucky Peak. Reservoirs created by these dams reduce flooding in the lower Boise River and store water for use during summer irrigation. However, flooding still occurs, from dam releases under full reservoir conditions and from surface water runoff from tributary basins in the Treasure Valley. The Federal Emergency Management Agency (FEMA) is the independent agency of the federal government responsible for protecting the public when it comes to flooding.

In September of 1999, the Idaho USGS completed a "Restudy of the Boise River Flood Plain in Ada County, Idaho". The USGS surveyed Boise River cross sections and identified existing elevation reference marks. FEMA (Federal Emergency Management Agency) will use this information to update the flood plain and floodway boundaries along a 32 mile stretch of the Boise River from Barber Dam to the Ada/Canyon county line. The Federal Emergency Management Agency -- FEMA -- is an independent agency of the federal government, reporting to the President. Since its founding in 1979, FEMA's mission has been clear:

to reduce loss of life and property and protect our nation's critical infrastructure from all types of hazards through a comprehensive, risk-based, emergency management program of mitigation, preparedness, response and recovery.

Surface Water Quality
Terms such as effluent trading, Total Maximum Daily Loads, and run-off are issues that affect the quality of the Boise River.

The Idaho Department of Environmental Quality has produced a draft document in pdf format called "Lower Boise River Nutrient Subbasin Assessment". It provides an overview of the Lower Boise River Watershed, including characterization, water-quality concerns, pollution-source inventory, and pollution-control efforts as they pertain to nutrients. (pdf 1.1 Mb, 61 pages)

The Idaho Department Of Environmental Quality report, "Summary of Participant Recommendations for an Effluent Trading Framework (Lower Boise River)" summarizes the efforts of the Lower Boise River Effluent Trading Pilot Project participants, and the recommendations that have emerged for an effluent trading program framework.

"Lower Boise River Nutrient Subbasin Assessment" is a draft document which provides an overview of the Lower Boise River Watershed, including characterization, water-quality concerns, pollution-source inventory, and pollution-control efforts as they pertain to nutrients. Public comment period closed August 17, 2001. (pdf 1.1 Mb, 61 pages).

Western Snake River Plain- Treasure Valley Ground Water

Conceptual Cross-Section (Regional Scale)

Ground Water Flow Systems
The Treasure Valley contains a complex system of shallow, intermediate, and deep aquifers. Shallow aquifers often supply water to rural domestic and some irrigation wells. Municipal, industrial, and some irrigation wells typically draw water from deeper aquifers. Intermediate aquifers, found in the transition from shallow to deep zones, supply water for domestic, irrigation, and municipal uses.

Shallow aquifers, present throughout the central portion of the Treasure Valley are often contained in the Snake River Group sediments. Depths of these aquifers are generally less than 250 feet below ground surface. Ground water in shallow aquifers generally originates at ground surface, in the form of precipitation, infiltration from irrigated areas, or infiltration from river and stream channels or canals (see “Aquifer Recharge”). Shallow aquifers can contain very localized flow systems such as from an irrigated field to the nearest drainage ditch, or extend tens of miles.

A deeper, regional aquifer system underlies shallower aquifers. The regional system extends throughout the valley, with ground water flowing in a generally westerly direction. Water enters the regional system at the basin margins or in the easternmost portions of the valley. Some of the tilted sedimentary zones underlying the geologic unconformity represent productive aquifer zones. Coarse-grained sediments overlying the unconformity may act as a manifold distributing water from the east Boise and/or peripheral areas into the underlying aquifer zones.

Estimated Recharge to Shallow Aquifers

Aquifer Water Balance

Aquifer Recharge
“Aquifer recharge” refers to the water that is entering the aquifer system. Recharge to the Treasure Valley aquifers was estimated on the basis of land use (Urban and Petrich, 1998) . Approximately 50 percent of the Treasure Valley land area is flood or sprinkler irrigated. Seepage from flood irrigation (including canal seepage) accounts for approximately 95 percent of recharge to shallow aquifers. Only a small portion of this water, however, enters deeper aquifers; most of the shallow aquifers discharge into river, canal, or ditch channels.

Infiltration from flood irrigation and canal seepage far exceeds recharge from precipitation or other sources (see “Water balance”). Ground water withdrawals for industrial, rural domestic, municipal, and irrigation uses are much less than the water that returns to ground surface as natural discharge. However, much of the withdrawals occur from deeper aquifer zones, while much of the discharge occurs from shallow aquifers.

References:
Urban, S.M. and Petrich, C.R., 1998. 1996 Water Budget for the Treasure Valley Aquifer System, Idaho Department of Water Resources Research Report.

Ground Water Levels
Ground water levels have been measured on a regular basis as a part of the Treasure Valley Hydrologic Project. Over 350 Treasure Valley wells were measured six times in mass measurements. A mass measurement is the measurement of a large number of wells in a short time (in this case, usually within a one-week period). Mass measurements were conducted in spring and fall of 1996, 1998, and 2000 by the U.S. Geological Survey (http://id.water.usgs.gov/). A mass measurement provides ground water level information at one period in time, which is used to determine a potentiometric surface (in an unconfined aquifer the potentiometric surface is the water table). The potentiometric surface is used to determine ground water flow directions.

In addition, water levels in about 70 wells have been measured on a monthly basis. Hydrographs, drawn from monthly water level data, are a graphic representation of water level data over time for one location.

Ground Water Level Changes
Seasonal changes in ground water levels can range from few to about 10 feet. These seasonal variations depend on the amount and timing of local recharge and pumping.

Ground water levels in most parts of the Treasure Valley have remained relatively constant. A water level change map for the Treasure Valley compares water levels from the period 1969-1976 with water levels in the year 2000.

Water quality constituents were analyzed in water samples from 281Treasure Valley wells. The constituents included common ions (calcium magnesium, chloride, sulftate, etc.), nutrients (nitrate, ammonia, etc.), trace elements (arsenic, copper, iron, zinc, etc.), radioactive elements, volatile organic compounds (benzene, perchloroethylene, etc), bacteria, and pesticides.

In 1997, 49 (17 percent) of 281 sampling sites (wells) had one or more constituents with concentrations greater than primary Maximum Contaminant Levels (MCLs) (Neely and Crockett, 1998) . The MCLs are established by the U.S. Environmental Protection Agency (EPA) for public dringing water supplies. Constituents exceeding these standards included arsenic, bacteria, fluoride, nitrate, and some volatile organic compounds.

Nitrate is often an indicator of aquifer vulnerability because higher concentrations are generally caused by land use activities. More recent data collected between 1997 and 2000 show that 35 percent of the Statewide Program wells in the Treasure Valley shallow system had nitrate levels equal to or greater than 5 milligrams per liter, and ten percent had concentrations over 10 mg/l (Neely, 2001) . Nitrate concentrations of two mg/l generally are considered to be above background in the Treasure Valley, and 10 mg/l nitrate is the drinking water standard. The map below shows the distribution of elevated nitrate concentrations in the Treasure Valley. More information on recent water quality measurements is available from http://www.idwr.state.id.us/planpol/techserv/gwmon/status_of_gwq_tv.pdf.

Use of MODFLOW for Development of Response Functions

ABSTRACT
Numerical models, such as MODFLOW, provide excellent tools to assist in the water resourc decision making process. A simplified representation of the system may, in some cases, be obtained by the development of response functions from numerical models. These functions express temporal relationships between cause and effect at specific points within the aquifer and are developed through simulation. The functions are valid so long as the equations governing flow in the system are approximately linear with respect to aquifer head.

. Response functions can be generated from multiple MODFLOW simulations or more simply from the MODFLOW based MODRSP program. Response functions can be developed to describe how aquifer water levels, aquifer storage, surface water depletion, or ground water flow velocities are affected by ground water pumping or recharge in any prescribed location. In areas where the use of response functions is valid, they can provide a highly useful tool for water managers.

INTRODUCTION
Numerical models such as MODFLOW can produce predictive simulations of cause and effect when properly calibrated and applied to an area. This process normally involves comparing results of a series of predictive scenarios to results of a base study, possibly projecting current conditions into the future. The process is valid and useful; however, it requires at least one simulation and comparison for each scenario of interest and has limited capability in presenting cause and effect relationships in more general terms.

Response functions are analytical expressions, graphs, or coefficients that describe the relative response of the aquifer system at a given location to a unit stress at a second location (figure 1, below). Because the response is expressed in relative terms, it may be scaled to any magnitude of stress desired. The functions may express transient or steady-state response of the system to the stress. The development and use of response functions require that response is proportional to the magnitude of the stress; consequently, the governing equations must be approximately linear. Responses may be in terms of aquifer water level change (drawdown), changes in head-dependent flux (capture), change in storage, or changes in ground-water flow velocity. Similar or identical concepts have been called discrete kernels (Morel-Seytoux and Daly, 1975), influence coefficients (Illangasekare and Morel-Seytoux, 1982), algebraic technologic functions (Maddock, 1972) and "drawdown simulations" (Anderson and Woessner, 1992). The assumption of linearity of the governing equations is the major constraint of the application of response functions and will be addressed in greater detail in the following section.

Figure 1. Concept of Stream Capture Response Functions.

There are several ways in which response functions may be applied. They may be used to 1) conceptualize and visualize the manner in which pumping or recharge effects propagate through an aquifer, 2) quantify how aquifer pumping or recharge impacts ground water levels or stream flows, or 3) provide mathematical expressions or matrices to incorporate into more comprehensive water models or optimization schemes. These applications can be accommodated without performing specific predictive modeling scenarios and are described in the following paragraphs.

Response functions can aid in visualization and conceptualization of pumping and recharge effects because the response is assumed to be proportional to the stress. This relationship allows a generic presentation of cause and effect relationships. Hubbell, et al (1997) used a similar approach to describe zones in the Snake River Plain aquifer where ground-water pumping predominantly affects one of four reaches of the Snake River. Refinement of the zones developed by Hubbell, et al (1997) may ultimately form the basis for conjunctive administration of water rights in the eastern Snake River Plain.

Quantification of impacts from individual pumping or recharge activities may be required in adjudication of water rights or development of mitigation plans. Johnson et al (1993) evaluated the depletion of springs from the Snake River Plain aquifer by generating response functions for 18 selected stress locations on the eastern Snake River Plain. The impacts of ground-water use on spring discharge and flow of the Snake River can be approximately assessed for any location on the Plain by using response functions from the nearest location. Similar information may ultimately be used to establish mitigation requirements for ground water pumpers.

The simplified linear form of the response functions permits incorporation into surface water models and optimization schemes. El-Beshri and Labadie (1994) incorporated capture response functions into the surface water model MODSIM (Labadie, 1991). Response or influence coefficients have been applied in simulation/optimization models by several researchers including Ejaz and Peralta (1995).

Response functions can be generated analytically or from calibrated numerical models. Analytically generated response functions are little more than calibration of an analytic expression, such as the Theis Equation, to conditions representing a specific aquifer. Substituting appropriate values for aquifer transmissivity and distance (representing a specific stress location and response location) graphs, response coefficients, or equations can be developed to show how drawdown or stream depletion from a unit stress is related to time. The numerous assumptions inherent in analytical techniques can be avoided by generating response functions from numerical models. The numerical model can be either 1) run under a special set of conditions to evaluate response to a unit stress, or 2) if MODFLOW is used, a special adaptation, MODRSP (Maddock and Lacher, 1991), can be used to generate the response relationships.

The purpose of this paper is to describe how response functions may be generated either directly from a MODFLOW simulation, or through application of MODRSP.

CONSTRAINTS ON USE OF RESPONSE FUNCTIONS
Response functions describe the relative response of the aquifer or stream to an applied aquifer stress. It is normally necessary to assume that the responses of multiple stresses may be superimposed in order to describe aquifer response in general terms. The use of response functions is therefore normally limited to cases where the system can be adequately described using linear equations Reilly, et al (1987) describe the use of linear equations in ground water flow systems.

Numerical models, including MODFLOW, may be based on governing equations that are either linear or non-linear. The partial differential equation representing ground-water flow is linear with respect to the independent variable representing aquifer head. This equation is the foundation from which the finite-difference expressions for saturated, confined, ground-water flow are developed. The linearity of the equation implies that superposition concepts, including response functions, are valid when this equation describes flow within a system.

MODFLOW and other numerical model codes include other head-dependent relationships representing system boundaries. Head-dependent functions exist to represent aquifer exchange with rivers, drains, evapotranspiration, and other features. Many of these are represented as piece-wise linear relationships (figure 2). The discontinuity in the linearity of these relationships cannot be accommodated in the use of response functions. The functions will be valid so long as conditions within the aquifer do not cross the discontinuity of slope. When simulating rivers using the River or Streamflow Routing Packages, this is equivalent to requiring that the aquifer heads either continuously remain above or below the elevation of the bottom of the river. The river cannot transition from head-dependent to perched conditions. When simulating drains, the aquifer head at the drain cannot transition across the elevation of the drain. The drain must either remain active or inactive.

Unconfined aquifers require a different form of the partial differential representing ground water flow. The Boussinesq equation is not linear with respect to aquifer head. Superposition and response functions cannot, therefore, be used unless the Dupuit assumption (small head change relative to aquifer thickness) can be applied. If this is not the case, then the response of the system is significantly dependent on other stresses occurring simultaneously, and the system response cannot be expressed without describing all concurrent recharge and discharge activities. Response functions cannot be used in this case.

There are many cases in which non-linearity may exist in a ground-water model. The question to be addressed by the modeler is whether these non-linearities significantly affect the results of the model for the range of stresses of interest. If the non-linearities are negligible, then response functions may be used to approximately describe the response of the system in a general sense. The developer, however, must caution subsequent users of the functions relative to the approximate nature of the functions and the range over which their use is approximately valid.

GENERATING RESPONSE FUNCTIONS USING MODFLOW
MODFLOW can be used in either of two ways to generate response functions. It may be either 1) applied to a single stress with no initial hydraulic gradient, or 2) the user may use the version MODRSP (Maddock and Lacher, 1991) to directly calculate response coefficients. Both methods require the same assumptions and produce equivalent results. Application of MODRSP is normally more convenient than performing multiple MODFLOW simulations; however, MODRSP currently does not include the Drain Package and some of the more recently added modules to MODFLOW and does not include a pre- or post-processor. If newer modules are required for an application, the most efficient procedure may be to conduct multiple MODFLOW simulations.

A calibrated MODFLOW model of an area can be used, with some modification, to directly calculate response functions. Input adaptations are required to remove all recharge and discharge and eliminate all hydraulic gradients within the system. This procedure was outlined and applied by Hubbell et al (1997) and includes the following steps.

1. Boundary conditions and stresses are evaluated to ensure they are linear functions.
2. Boundary conditions and the spatial distribution of aquifer properties and leakage coefficients are provided by a previous model calibration and/or analytical techniques.
3. An arbitrary, horizontal potentiometric surface is established as an initial condition.
4. Prescribed head (head-dependent) conditions are established at the same arbitrary datum.
5. Unconfined conditions are approximated as confined (when constant thickness can be assumed).
6. Recharge and discharge are limited to a single location for a selected point of interest.

If the Drain Package is to be used, the elevation of the drains should be set to the elevation of the starting potentiometric surface and a recharge stress (positive sign) should be applied causing the drain to be active. Altering model input data sets to the described conditions can normally be accomplished within a few hours.

The modified model is run with the single specified stress. System response can be extracted from the model output in either a steady-state or transient form. Development of transient response functions requires that the model include storage characteristics. Response, in terms of changes in aquifer water level, or changes in flux with head-dependent boundaries, can be determined for any desired location by extracting drawdown or flux for that location. In the case of Hubbell et al (1997) the river flux was summed for four reaches of the river and the collective response was described for each river reach. Response to stress at other locations requires repeating the simulation process, again with a single stress used at the point of interest. Hubbell, et al (1997) ran 18 simulations to develop responses for stress at 18 different locations.

An arbitrarily large stress may be used to evaluate the system response. In this case, the stress should be sufficiently large to maintain a reasonably accurate mass balance, minimizing the significance of numerical error. If an arbitrarily large stress is used, the response must be divided by the magnitude of the stress in order to express the results as a response to a unit stress. These results are then easily applied to stresses of any magnitude.

Alternately, a unit stress may be applied at the point of interest. In this case, the iteration closure criteria must be greatly reduced to maintain a valid mass balance and minimize effects of numerical error. The simulated response, however, is produced in a form that is already normalized.

It is also possible to determine the response function as the difference between two simulations where recharge, discharge and hydraulic gradients have not been removed. In this case, the system response at the locations of interest can be expressed as the difference between a simulation with a given stress present and one with the stress absent. The magnitude of the stress, and the closure criteria must be adjusted with consideration of the discussion in the two previous paragraphs.

The second means of obtaining response functions is through application of a MODFLOW variation, MODRSP (Maddock and Lacher, 1991). MODRSP is capable of determining drawdown, velocity, storage loss, and capture response functions. Capture may be stream depletion, change in evapotranspiration, change in head-dependent boundary flux, or leakage from adjacent aquifers. MODRSP is a revision of the 1983 version of the MODFLOW code. Because this program is based on an early version of the program, not all of the currently available packages are accommodated. The SIP, SSOR, and PCG solution packages can be used; however, more recent additions like the Stream-Flow Routing Package are not available. The Drain Package is not included in MODRSP, presumably due to the potential for non-linear effects.

MODRSP solves the finite difference equations for a unit stress for a specified location and duration. Because a unit stress is always used, head change at any location represents the drawdown response function. Capture and storage response functions are calculated from the drawdown response function in the same way as MODFLOW would calculate head-dependent flux or storage change. The velocity response is calculated from inter-cell flow and the equation relating velocity to flow and cell dimensions.

Transient simulations with MODRSP automatically apply a unit stress during the first model stress period. Response functions are provided at the end of each stress period. Response functions generated for subsequent stress periods (after the first) represent the residual effects of the stress through time. Effects of extended pumping may be determined by superimposing response functions with an appropriate time lag.

MODRSP simulates response of the aquifer to a series of stresses at prescribed locations. These stresses are applied through the WELL Package. The user specifies stress locations and MODRSP sequentially simulates individual response to a unit stress at each of the prescribed locations. No other stresses, in the Well Package, Recharge Package, or other packages are input or used. MODRSP automatically applies the previously discussed conditions of no initial hydraulic gradient and no recharge and discharge except at points from which response functions will be evaluated. A personal computer version of MODRSP has been developed in the Civil Engineering Department at Colorado State University.

Either of the two methods described will yield identical response functions. The method chosen should depend on the efficiency of either method for the given situation and the MODFLOW features needed.

ANTICIPATED APPLICATION OF RESPONSE FUNCTIONS IN THE EASTERN SNAKE RIVER PLAIN
The State of Idaho has recently committed to conjunctive management of surface and ground water through the promulgation of conjunctive management rules. These rules focus on the eastern Snake River Plain that contains most of the surface and ground water irrigation in the state. The highly productive Snake River Plain aquifer underlies the eastern Snake River Plain and discharges over 18 million cubic meters per day in the Thousand Springs and American Falls reaches of the Snake River. These spring discharges are highly appropriated for irrigation, hydropower, and other uses. Ground water pumping for irrigation generally has junior water rights priorities relative to the more senior surface water uses. Ground water users are, therefore, likely to be held accountable for depletion of spring discharges and flows of the Snake River.

Although the conjunctive management rules indicate that junior ground water users can be held accountable for depletion of surface water flows, they do not specify a) the rate of accountability, b) how accountability changes with location in the basin, or c) how accountability changes with time. These important details have not yet been determined.

Development of response functions describing cause and effect relationships for different areas of the aquifer and different river reaches may provide a means of understanding and quantifying pumping and recharge impacts on the river. Steady state response functions can be used to identify areas in which pumping most significantly impacts springs along a given reach of the river. Transient response functions will describe the temporal response of spring discharges to ground water pumping or recharge in any given area. It is expected that response functions will be used in a qualitative sense to assist water managers in understanding cause and effect relationships in the aquifer and river and in a quantitative fashion to estimate impacts and mitigation requirements. The U.S. Bureau of Reclamation will also incorporate the response functions into a surface water model of the Snake River.

CONCLUSION
In some cases, response functions can serve as a valuable qualitative tool to aid in understanding cause and effect relationships within an aquifer and as a quantitative tool to express, in simple form, quantitative and transient impacts of ground water pumping and recharge. Response functions can be generated from multiple MODFLOW simulations or more simply from the MODFLOW based MODRSP program. Response functions can be developed to describe how aquifer water levels, aquifer storage, surface water depletion, or ground water flow velocities are affected by ground water pumping or recharge in any prescribed location. The primary constraint on the development and use of response functions is that all significant components of the system must be represented by linear equations. In areas where the use of response functions is valid, they can provide a highly useful tool in a water manager’s toolbox.

ACKNOWLEDGEMENTS
This work is supported by the U.S. Bureau of Reclamation Snake River Resources Review Project (SR³). The work is conducted in collaboration with the Idaho Department of Water Resources.

REFERENCES