A recent insightful Law360 Expert Analysis by my Integral colleague R. Jeffrey Davis (“Regulators Must Get Creative To Keep Groundwater Flowing”; September 8, 2023) discussed challenges and possible solutions to the problem of overuse of groundwater resources on which so much of the western US depends. Although it is often quipped that water flows uphill towards money, a significant source of difficulties is that it often does not, or even if it does, it doesn’t pay its own way. As Jeff noted, institutional barriers are preventing reallocation of water to its best uses—my interpretation is that we increasingly need water to run uphill, downhill, or over hill towards social value. What can this mean, and how can it inform water policy and management?

It is useful to develop a (very) simplified economic model to elaborate on the issues Jeff raised.^[1] Lower case letters will denote what an individual water user does and upper case letters will denote water in the aggregate. If individual groundwater extractors pump and use an amount e in a year (net of any return flow to the aquifer), summing this up yields total extraction E. Let A be the total amount of water in storage in the aquifer, and e×c(A) be the cost of pumping, where c(A) is the unit cost of pumping and supplying groundwater (with less water in storage implying a larger pumping cost). For each groundwater user, let v^p(e) be the incremental private value (to the extractor) from using a little more water beyond some base amount of e units of water employed (with higher base water usage implying a smaller incremental value, i.e., there is diminishing incremental value of water).

Now, consider Jeff’s first point that several of the western states have had a “reasonable use” or “rule of capture” doctrine. Each groundwater user will want to employ water each year until their incremental benefit from use of that water matches the cost of additional extraction, i.e. until v^pe^o=c(A). The "o" superscript on extraction stands for “open access” to water under these management regimes. If someone is allotted less than e^o they will want to exceed that allotment and, depending on the assiduity of enforcement and size of potential penalties, may choose to do so.

If R_t is the amount of recharge in a year (which depends on precipitation and surface water supplies, among other things), the total stock of groundwater under open access evolves through time according to A_t+1=A_t+R_t-E_t^o. Next year’s stock is this year’s stock, plus recharge, minus aggregate extraction. As each of the groundwater users pumps e_t^o, the stock changes. A declining stock (extraction greater than recharge) raises everyone’s costs and depletes what may become a scarce resource, but there is no charge to each extractor for the social cost of using the stock per se. Therefore, little account is taken of either (1) the effect of more pumping on others’ costs, or (2) the individuals’ impact on total extraction and the overall depletion of the aquifer.

The problem here is not that water runs uphill towards money but that it runs towards the private value rather than the highest social value. Groundwater is an open access resource with each “straw” or extractor covering its own costs and ignoring aggregate effects, and it takes only a handful of users for the outcome to depart significantly from optimal use and approximate the open access outcome.

Let V(A) be the incremental social value of water that accounts for impacts of a little more extraction on everyone’s costs as well as for aquifer depletion over time. If these social effects are included, there is a different extraction level e^s ("s" for “social”) characterized by v^pe^s=CA+ V(A). With the larger cost of pumping, diminishing incremental value implies that e^s is generally less than e^o. Note the "p" is still there on the incremental value—the private “capitalist” value to each independent water user supports the socially-efficient use of water at the quantity e^s. Under open access, the aquifer itself is provided for free even though it is scarce.

Second, consider the concern Jeff raises regarding the transfer of water from one use (say, agriculture) to others (say, municipal use or water in rivers and lakes). This calls for a proper accounting of these in terms of relative social values. The goal is to allocate water such that the incremental social value is the same in all uses; that is, for all alternative groundwater uses i and j, we want v^pe_i=v^pe_j. For if not, and some use i has a larger incremental value than another use j, then i has too little water and j has too much (recall diminishing incremental value). A transfer from j to i has an incremetnal social benefit [v^pe_i] that is greater than its incremental social cost [v^pe_j].^[2]

The above quantities e are net of return flows (or example, irrigation above the level of plant requirements that infiltrates the aquifer). Some return flows are natural and some are constructed (effluent from waste water treatment facilities). A more robust model recognizes that quality dimension of water and that grey or recycled water can be allocated to some uses (depending on the degree of treatment).

Another use of water is to support ecological functioning. What is the value of water flowing in the Rio Grande or stored in the Great Salt Lake, or delivering sediments to coastal areas compared to irrigation, residential, or industrial consumption?

These are hard but not insurmountable questions to answer—and ones that cannot be avoided. Any allocation has an implied set of values, and the management issue is whether the current one reflects the balancing of incremental values condition descried above. The barriers to reallocations Jeff points out prevent water moving over hill to equalize incremental social values across alternative uses, thereby achieving higher overall social value from the limited overall supplies we have. Economic analysis can shed credible light on such issues.

A third approach recommended by Jeff is to move water through time towards social value. He noted the potential for aquifer storage and recovery (ASR) to smooth the time path of highly variable surface water supplies using groundwater aquifers as a reservoir—filling them up when surface water is plentiful and drawing them down when it is not. There is a cost to running such conjunctive surface/ground water management programs. What are they worth?

Consider a unit of water delivered at different times (now and the future) as different e_n and e_f. The equalization of incremental values across uses above applies with equal force across time. Thus, a key to assessing the benefits of ASR is to properly account for the movement through time of the incremental social values of water. This doesn’t alter the overall average availability of surface water and groundwater supplies but allocates them to when they are needed most, thereby getting more social value bang for each acre-foot buck. Note that this means the social value of water in the present may be greatest when it is not extracted but if rather stored and transferred to future needs.

An aquifer augments surface water supplies, but with the latter distributed randomly through time. A cogent question is: what amount of surface water does the groundwater augment? When doing water resource planning, it is common to estimate long term surface water supply as the average amount of surface supply expected to be available. But is this the best approach? Thinking this option through carefully yields some informative and perhaps surprising results.

A more elaborate model provides some insight into how to frame the conjunctive management of ground and surface waters. Suppose that in any given year t, the realized surface water supply is S_t. This varies randomly from year to year around some long-term trend. Some fraction of this, call it D_t, is diverted for use and consumed (i.e., net of return flows) for irrigation, industrial, and municipal supply. Another fraction R_t naturally recharges groundwater aquifers, and the remainder r_t goes where it goes in the broader water cycle, providing ecological services in rivers and streams. If E_t is total groundwater extraction in year t, total water supply to the economy in a year is W_t=D_t+E_t.

The ASR option is to capture some fraction of surface supplies, call this s_t, in good years and add it to the natural recharge, thereby making total (conjunctive) recharge equal to R_t^c=R_t+s_t. Of course, the additional induced recharge s_t has to come from somewhere, so either the amount delivered to users D_t and/or the surface flows r_t need to be reduced. The dismal science says no free lunches.

But in good years for surface supply, the opportunity cost of shunting an increment of water to an aquifer is lower, as is the incremental value of groundwater extraction. The transfer to recharge satisfies the “equal incremental value in all uses” rule. Suppose instead that a constant amount of groundwater was set for extraction each year based on average safe yield. Then as actual surface water fluctuates, so will incremental values, which violates the equality rule.

This increase in value from moving water through time to equate incremental values, over and above the average approach, is called the “stabilization value” (or buffer value) of groundwater. What is needed to realize it is a time-varying incremental social value of groundwater V(A). This is the “virtual price” toward which water should flow over time, that it currently does not.

How big is this stabilization value? That is, how big is the mistake from using the average recharge in water planning? In water-scarce areas it can be very large indeed. In a paper that identified the dynamic stabilization value, Yacov Tsur and I found it to be 84% (!) of the total value of groundwater used for irrigation for the water-short Negev area of Israel.^[3] Subsequent investigations in other settings found a more modest but still large stabilization value of groundwater in the range of 25% to 50%. In other words, using the expected amount of recharge when planning may miss much (or even most) of the value of groundwater when conjunctive use is being evaluated.

If managers have the data to calculate the average amount of surface supply, they can instead generate the entire distribution and make their plans based on the full range of probabilities and how these are trending with climate change. While they don’t know exactly which future years will be good or bad, they can build their water use rules and infrastructure to reflect the certainty that fluctuations will arise.

An unexpected outcome of careful thought here is that the stabilization value of groundwater makes extraction of groundwater more valuable on average. Therefore, recognizing uncertainty in surface water supplies in groundwater planning leads to a lower long-run average groundwater stock, not a bigger one. This conclusion is offset if the chances of a large negative deviation in surface supplies – an extended drought. ^[4] Which effect dominates and whether the ultimate groundwater steady state (where average extraction and average recharge are balanced) should have more or less water in the aquifer than now is an open question. But it is a question, and the path chosen will make all the difference.

The lesson of all this? While some aspects of a simple economic analysis are rather obvious, more elaborate investigations yield valuable insights into both the problem, the solutions, and practical ways to implement solutions. They also tell us that certain intuitive expectations sometimes fail us, and that simple expedients may lead us quite far astray. No one said this was going to be easy….