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| Fig. 1: Estimated depth to water table in Central Valley in 2000. [2] (Courtesy of the USGS) |
The purpose of this note is to work out a rough estimate of the energy required to pump groundwater in the Central Valley region of California. The primary demand for water in this region is irrigation water for agriculture, and because this demand cannot be met with surface water via the Central Valley Project (CVP) and State Water Project (SWP), farmers pump groundwater in vast quantities to fill the gap. For more details about the Central Valley and California's surface water conveyance systems, see my previous report for this course.
Although a huge amount of energy is consumed by the surface water conveyance systems, a California Measurement Advisory Council (CALMAC) study found that, in the summer months, the amount of energy consumed to pump groundwater exceeded the largest three water conveyance systems in California combined. [1] There are a few reports that calculate the amount of energy used to pump groundwater with various complicated models. However, the physics involved in this calculation is quite simple if the model can be simplified. As such, it would be of interest to estimate roughly how much energy is used to pump groundwater in the Central Valley each year and compare with the results from these more complicated models to see if we can gain a basic understanding of the energy considerations.
The only physics concept that is really needed to make a rough estimate of the energy to pump groundwater is gravitational potential energy, or the energy associated with Earth's gravitational pull in this case. Essentially, when an object is a certain distance from Earth's gravitational center, it has potential energy of the amount
where E is the gravitational potential energy, g = 9.8 m/sec2 is the gravitational acceleration constant associated with Earth, and m is the mass of the object. Then, the energy required to raise groundwater from a certain distance below the surface to the surface can be calculated with this equation, substituting h as the height to the surface.
To get the total mass of groundwater pumped each year, we take the estimated volume of groundwater each year and multiply by the mass density of water, which is 1000 kg/m3. Between 1962-2003, a U.S. Geological Survey report estimates that the average withdrawals from irrigation wells in the Central Valley was 8.7 million acre-feet per year (× 1233.46 m3/ac-ft = 1.078 × 1010 m3/y). [2] This gives a total mass per year of
| Mass of groundwater | = | volume × mass density |
| = | 1.07 × 1010 m3 × 1000 kg/m3 | |
| = | 1.07 × 1013 kg |
To get the accurate height, we would have to take into account each irrigation well's depth (Fig. 1) and account for friction and pressure losses. [2] For a rough estimate, we can gather from the map that the average depth is about 70 to 100 feet. Assuming it is 100 feet or 30.48 meters, we can plug this into our estimate for the total energy each year as the height, h.
| Energy | = | mgh |
| = | 1.07 × 1013 kg × 9.8 m/s2 × 30.48 m | |
| = | 3.2 × 1015 Joules |
Thus, we get an estimate of the total yearly energy to pump groundwater to be on the order of 1015 Joules.
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| Fig. 2: California hydrologic regions. [1] (Source: Wikimedia Commons) |
Despite getting rid of many details, compared to two other estimates of the total energy spent pumping groundwater, our simple calculation matches the right order of magnitude. The CALMAC report estimates a little less than 6 TWh/year on groundwater pumping for the whole state in 2010. [1] A 2019 California Energy Commission (CEC) report states that between 2005-2015, 58.8 TWh was consumed for groundwater pumping, which averages out to 5.88 TWh/year, consistent with the CALMAC report. [3] To compare with our number, which is only for the Central Valley, the CEC report estimates that 78.8% of this energy is used in the Sacramento River, San Joaquin River, and Tulare Lake regions of California, which can be identified in Fig. 2.
Note that these three regions account for a much larger area than the Central Valley boundaries in Fig. 1 for which we computed our estimate. Let's say that the Central Valley region we are considering uses approximately 1/3 to 1/2 of the energy of the three regions the CEC number accounts for. Then, 78.8% of 5.88 TWh a year is 4.6 TWh. One third of this number is 1.53 TWh, which converts to 5.52 × 1015 Joules. Half of this number is 2.3 TWh/year, which converts to 7.2 × 1015 Joules. This range nicely matches the order of magnitude of our rough estimate.
To compare to the flow through the California Aqueduct, we refer to a CALMAC report which claims that the SWP moved 4,931 thousand-acre-feet of water (= 6.08 × 109 m3) in the year 2000, a normal water year. [4] In comparison, the estimated amount of groundwater being pumped in the Central Valley each year, 1.07 × 1010 m3, is nearly twice the amount of water coming from the SWP. This highlights the gap between surface water and the amount of water needed in the Central Valley.
Groundwater pumping in the Central Valley is a growing problem far beyond its energy consumption. We can see from comparison to the SWP water flow that this problem is not going away; there is simply not enough surface water for the amount of agricultural production that is currently being sustained in the Central Valley. Unfortunately, the problems don't stop there. In fact, the excessive pumping of groundwater in the Central Valley has led to significant sinking of the land, which is called subsidence. Not only does subsidence indicate that the groundwater is not being replenished fast enough for the rate at which it is being pumped, but subsidence also signals issues for the surface water conveyance system. With changes in elevation underneath the canals that bring water through California, the water delivery capability of the SWP California Aqueduct and other systems is projected to diminish significantly. [5] Thus we conclude that water is far more important than energy at this moment for California.
© Jessica Pan. The author warrants that the work is the author's own and that Stanford University provided no input other than typesetting and referencing guidelines. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.
[1] "Embedded Energy in Water Studies. Study 2: Water Agency and Function Component Study and Embedded Energy-Water Load Profiles," California Public Utilities Commission, August 2010.
[2] C. C. Faunt, ed., "Groundwater Availability of the Central Valley Aquifer, Californi," U.S. Geological Survey, Professional Paper 1766, 2009.
[3] H. Blum and J. Ke, "Estimates of Groundwater Pumping Electricity Use and Costs in California," California Energy Commission, CEC-500-2023-041, June 2023.
[4] "Embedded Energy in Water Studies. Study 1: Statewide and Regional Water-Energy Relationship," California Public Utilities Commission, August 2010.
[5] "Impacts of Subsidence," California Department of Water Resources, May 2025.
