Ground Water: The Water Budget Myth

A while back I heard a state water official say that he would calculate a water budget to determine the number of wells that could be permitted in a particular basin. I cringed when I heard that. But it wasn't the first time, nor will it be the last time, that I heard someone who should know better utter such a statement.

It did serve one useful purpose: I decided to post on the folly of using steady-state water budgets to determine ground water development. The cutesy title is not my own, but is from a 1982 paper by USGS ground water giants John D. Bredehoeft, Steve Papadopulos, and Hilton H. Cooper. I will let that paper, plus a seminal paper by C.V. Theis that is approaching 70 years old, do the talking. Another excellent resource is the U.S. Geological Survey's Circular 1186, Sustainability of Ground-Water Resources, by W.M. Alley, T. E. Reillly, and O.L. Franke.

Download Bredehoeft Water Budget Myth

Download Theis - Source of Water

The aforementioned two papers are quite technical; the circular, less so.  Anyone involved with ground water should have a firm understanding of the concepts in all three.

So what's the problem?

What most people don't realize is that once you start the development (i.e., pumping), the water budget, usually calculated under steady-state conditions, becomes invalid. Why? Because you have imposed a new stress on the system - pumping - and that means that the water budget has changed. But most water managers don't realize this, and blithely assume a steady-state budget when transient conditions actually apply.

Theis' paper, "The source of water derived from wells: essential factors controlling the response of an aquifer to development", stated that the source of water discharging from a well comes from:

1. increase in recharge;
2. decrease in discharge (springflow, ET, baseflow to a stream); and/or
3. change in water storage in the aquifer.

As long as some water comes from storage, well water levels will continue to drop. Only when pumpage is balanced by (1), (2), or some combination of (1) + (2) will water levels cease to decline and a new equlibrium is reached. It may take many years for this to happen.

The above, from USGS Circular 1186 and another USGS publication by Ralph Heath (1983), shows a pristine situation in (A). The paragraph below is the caption.

Under natural conditions (A), recharge at the water table is equal to ground-water discharge to the stream. Assume a well is installed and is pumped continuously at a rate, Q₁, as in (B). After a new state of dynamic equilibrium is achieved, inflow to the ground-water system from recharge will equal outflow to the stream plus the withdrawal from the well. In this new equilibrium, some of the ground water that would have discharged to the stream is intercepted by the well, and a ground-water divide, which is a line separating directions of flow, is established locally between the well and the stream. If the well is pumped at a higher rate, Q₂, a different equilibrium is reached, as shown in (C). Under this condition, the ground-water divide between the well and the stream is no longer present, and withdrawals from the well induce movement of water from the stream into the aquifer. Thus, pumping reverses the hydrologic condition of the stream in this reach from ground-water discharge to ground-water recharge. Note that in the hydrologic system depicted in (A) and (B), the quality of the stream water generally will have little effect on the quality of ground water. In the case of the well pumping at the higher rate in (C), however, the quality of the stream water can affect the quality of ground water between the well and the stream, as well as the quality of the water withdrawn from the well. Although a stream is used in this example, the general concepts apply to all surface-water bodies, including lakes, reservoirs, wetlands, and estuaries.

The graph below, also from Circular 1186, shows the mix of water (as a percentage) being discharged from the well as a function of time.

The percentage of ground-water pumpage derived from ground-water storage and capture of streamflow (decrease in ground-water discharge to the stream or increase in ground-water recharge from the stream) is shown as a function of time for the hypothetical stream-aquifer system shown in the figure above. A constant pumping rate of the well is assumed. For this simple system, water derived from storage plus streamflow capture must equal 100 percent. The time scale of the curves shown depends on the hydraulic characteristics of the aquifer and the distance of the well from the stream.

The above discussion illustrates why I don't immediately fly into a tizzy when someone proclaims that "My well water levels are dropping!" Yeah, that's what they are supposed to do. But what is the rate of decline and is it increasing?

So let's get back to water budgets.

Bredehoeft et al. (1982) said it best:

Water-resource scientists are concerned that some basic principles are being overlooked by water managers. Rather than discuss the scope of groundwater hydrology, we have chosen to focus on a common misconception to illustrate the point.

Perhaps the most common misconception in groundwater hydrology is that a water budget of an area determines the magnitude of possible groundwtaer development. Several well-known hydrologists [Note: Theis in 1940, Richmond Brown in 1963, and Bredehoeft and Young in 1970; see paper for citations] have addressed the misconception and attempted to dispel it. Somehow, though, it persists and continues to color decisions by the water management community. The laws governing the development of groundwater in Nevada as well as several other states are based on the idea that pumping within a groundwater basin shall not exceed the recharge. It is the intent of this paper to re-examine the issue.

Bredehoeft et al. take Theis one step further ans use a numerical  ground water model to illustrate the issue and show that such things as wellfield placement can influence how long it takes to reach a new equilibrium. They make several important points:

1. Magnitude of development depends upon the effects you want to tolerate.

2. The magnitude of sustained ground water pumpage generally depends upon how much of the natural discharge can be captured and how much recharge can be increased.
    
3. The placement of the wells significantly affects the system's dynamic response and the rate at which natural discharge can be captured.
   
4. Steady state is reached only when pumping is balanced by capture, that is, the increase in recharge (R) + decrease in discharge (D). Since the increase in R is often small, the change in D often controls.
   
5. Some ground water must be mined before the system reestablishes a new equilibrium.

Bredehoeft actually revisited this concept in 2002: Bredehoeft, John D., 2002. "The water budget myth revisited: why hydrogeologists model", Ground Water (40)4: 340-345. This paper also cites some of the more important work in this area since the 1982 article. [Note: John emailed me to say that this is a better reference than the 1982 paper, so if you can get it, read it.]

I am partial to the Bredehoeft et al. paper. When I discovered it 26 years ago while at the Desert Research Institute, I promptly photocopied it and sent it to the Nevada State Engineer, with the notation, "Have your ground water staff read and understand this paper." What got me in trouble was the "and understand" part. I almost got fired for that little episode. I doubt they read it down in Carson City.

Lesson's over for today. But promise me one thing: if you ever hear a speaker mention that s/he will use a water budget to determine how much ground water can be pumped in a region, immediately protest and tell them to read this post.

"These concepts must be kept in mind to manage groundwater resources adequately. Unfortunately, many of our legal institutions do not adequately account for them." -- Bredehoeft et al., 1982, p 57.

Comments

[Laurel Lacher]

Thanks for the nice summary. Just wanted to make a correction to one citation: it should be USGS Circular 1186 not 1168.