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Technical Papers
Feb 27, 2021

Estimating Agricultural Groundwater Withdrawals with Energy Data

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Publication: Journal of Water Resources Planning and Management
Volume 147, Issue 5


Agricultural water use is the leading cause of groundwater overdraft in California. However, agencies tasked with managing groundwater resources do not have access to accurate and reliable measurements of groundwater extraction. Previous studies identified a relationship between pump energy consumption and groundwater extraction and indicated that the efficiency lift method (ELM) can produce reliable estimates of groundwater extraction if based on reliable data. Recent advances in the availability of electricity and pump operating condition data have made the ELM viable for estimating large-scale groundwater extraction. This study considered the feasibility of using the ELM to estimate groundwater extractions from both individual wells and larger areas and identified the best data sources available for such estimates. Researchers found mean error rates of 5% at the individual well level and 3.3% for collections of wells when using the most specific data sources available, such as pump test reports and spatial groundwater level datasets. This research suggests that the ELM is a reasonable approach for estimating groundwater extraction on a large scale.


Groundwater is a significant urban and agricultural water source in California, accounting for nearly 40% of the total statewide water supply (DWR 2016b). Agricultural irrigation accounts for nearly 80% of California groundwater use (Newman et al. 2018). During extensive dry periods when surface water supplies are inadequate, groundwater provides up to 100% of the irrigation water supply in some areas (Freeman et al. 2010). Given California’s dependence on groundwater, preserving groundwater is fundamental to ensuring water reliability. However, California has a history of fragmented groundwater management and is one of the only western states that lacks a groundwater rights system to manage extractions (Freeman et al. 2010).
In 2014, the California State Legislature passed the Sustainable Groundwater Management Act (SGMA) in recognition of the need to regulate and monitor groundwater supplies to ensure groundwater basin resiliency (DWR 2015). SGMA establishes a new policy framework mandating that groundwater in California be managed at the local level through the formation of a Groundwater Sustainability Agency (GSA) for each designated groundwater basin. Each GSA must develop a water budget and, thus, must estimate total groundwater extractions within its groundwater basin.
The most accurate and reliable method to track groundwater extraction is to have flow meters installed on all groundwater wells. However, pre-existing flow meters are not widespread, and growers are generally opposed to installing new flow meters that would allow GSAs to accurately track groundwater extractions from agricultural wells (Austin 2014).
In the absence of flow meters, the California Department of Water Resources (DWR) currently recommends the California Central Valley Groundwater Surface Water Simulation Model (C2VSim) to estimate groundwater extraction (DWR 2016a). C2VSim can be used to calculate agricultural groundwater extraction based on precipitation, soil moisture, specific crop water needs, and surface water availability. However, C2VSim is unlikely to produce accurate estimates on smaller spatial scales given potential variations in individual farm operations (e.g., deficit irrigation). Further, C2VSim is a highly parameterized hydrologic model designed to simulate all water flows within the Central Valley. It is not optimized for estimating groundwater extraction, in part due to a lack of reliable large-scale estimates of groundwater extraction that could be used to calibrate the model (Brush et al. 2013).
The broader literature on agricultural groundwater use further emphasizes the limitations of the two current approaches to estimating groundwater withdrawal. Recent research focused on either direct measurement of groundwater extractions using flow meters (Pfeiffer and Lin 2014; Mieno and Brozović 2017) or large-scale estimates using remote sensing and groundwater modeling (Minderhoud et al. 2017; Thatch et al. 2018). Studies that use flow meters can only be conducted in areas in which flow meters are widely used, which are currently limited. Studies that use remote sensing and groundwater models may lack precision and spatial resolution due to the lack of extraction data for calibration. In the present study, we explore the efficacy of an alternative method of quantifying agricultural groundwater extractions known as the efficiency lift method (ELM).
The ELM provides a framework to convert well pump energy use data into an estimate of groundwater extraction. Previous studies on the ELM demonstrated its accuracy but encountered problems obtaining reliable data (Ogilbee 1966; Anderson and Ogilbee 1967; Allison 1968; Cline and Collins 1992). No previous research has evaluated the ELM within the contemporary data landscape, whereas recent legislation and other advances in data availability have significantly improved the viability of the data for the ELM to estimate groundwater extraction on a large scale.
This study evaluates different approaches to using the ELM to estimate agricultural groundwater extractions in California. With each approach, herein referred to as a scenario, different sources of available data were used in the ELM. The accuracy of each scenario was quantified by comparing the estimated quantity of groundwater extracted to measured quantities from a small collection of wells. The performance of each scenario served as the basis for formulating recommendations on best practices and sources of error.


The volume of groundwater pumped is directly related to the power required to lift the water. The ELM leverages this relationship to calculate water pumped using three data inputs:
where V = volume of groundwater pumped (ha-m); E = pump energy consumption (kW·h); η = overall pumping plant efficiency (OPPE), which is the ratio of the pump’s mechanical power output over electrical power input (%); H = total dynamic head (TDH), which is the total equivalent vertical distance the pump moves water (m), 27.2285 = energy required to lift 1 ha-m of water 1 vertical meter [kW·h/(ha-m)m].
The three data inputs required to compute volume (V) are energy use (E), OPPE (η), and TDH (H). TDH is comprised of depth to groundwater, drawdown depth, pipe friction losses, and other components, as illustrated in Fig. 1. Data for each of these ELM inputs are maintained or tabulated by a range of entities across California, with various levels of accuracy, spatial resolution, temporal resolution, and accessibility. To analyze the performance of the ELM in the context of the contemporary data landscape, identifying the primary data sources for each of the required data inputs for the ELM and assessing the quality and accessibility of these data are crucial.
Fig. 1. Cross-section of groundwater well and components of total dynamic head.
Recent developments in California have significantly improved the quality of the data available for applying the ELM on a large scale. Past studies on the ELM relied on highly aggregated electricity data (Ogilbee 1966; Anderson and Ogilbee 1967; Allison 1968), which makes pump-level extraction estimates impossible, or on electricity data provided by well owners (Frenzel 1984; Dash et al. 1999), which may be unfeasible and impractical for large-scale groundwater estimations. Although obtaining electricity data for individual wells is possible with direct permission from well owners, collecting and maintaining permission from all well owners in a large geographic area would be infeasible in many cases. However, customer-level electricity data are now available through the California Energy Data Request Program (EDRP). The EDRP was established in 2014 by CPUC decision 14-05-016 and allows academic entities to obtain customer-level electricity data directly from energy utilities.
Aside from energy data, the ELM also requires accurate estimates of OPPE (η) and TDH (H). A wide variety of data sources are available to estimate these values for each well pump. Pump test reports provide the most reliable data for TDH and OPPE for individual wells. Growers regularly have their pumps tested, resulting in pump test reports with measured TDH and OPPE for individual wells, along with a variety of other measurements. However, researchers must obtain pump test reports from well owners, and reported values are only accurate for the conditions at the time that the pump test was performed.
In past studies, whereas the pump test reports have been the sole reliable source of information for TDH and OPPE, several data sources are now available to estimate these values. Measured groundwater depths are now available statewide from the California Statewide Groundwater Elevation Monitoring program (CASGEM), established in 2009, and from groundwater contour maps available on DWR’s Groundwater Information Center Interactive Map Application (GICIMA), established in 2016. In addition, the Irrigation Training and Research Center (ITRC) at Cal Poly San Luis Obispo has published summary statistics of a database maintained by Fresno State containing more than 15,000 electric irrigation pumps in California’s Central Valley. ITRC has published regional averages of pump test report results (Burt 2011) and statistics on the relationship between various pump characteristics (Pérez Urrestarazu and Burt 2012).


A study by the UC Davis Center for Water–Energy Efficiency (CWEE) assessed the accuracy of the ELM and developed best practices for its application. To do so, CWEE collaborated with the Angiola Water District in California’s San Joaquin Valley to obtain measured water extraction data for agricultural well pumps within the district. This measured data would serve as the basis for estimating the accuracy of the ELM under different scenarios.
CWEE gathered data for each input to the ELM from multiple sources and combined these data sources in different ways to generate five ELM scenarios. This section describes the data used in this study, including processing steps, and the specifics of each scenario.

Measured Groundwater Withdrawal Data

Angiola provided monthly volumetric groundwater extraction data for nine of the 30 pumps studied from 2010 to 2015 and an additional five pumps in 2016. These measurements were generated with flow meters installed on the wells. For the purposes of this study, these values were assumed to be correct and accurate. However, flow meters can be inaccurate, with error rates varying by meter type, operating conditions, and maintenance level. Angiola used McCrometer propeller flow meters on all wells, which have an accuracy of ±2% when properly installed, calibrated, and maintained (McCrometer 2020).

Energy Consumption Data

CWEE obtained electricity data from the local investor-owned utility, Pacific Gas & Electric (PG&E), for the Angiola region, including monthly billing data for 30 wells and one-hour interval data for 26 wells. These data were obtained by a data request submitted to PG&E through the EDRP. Due to potential errors in aligning monthly billing data to the same start- and end-date, hourly interval data were used instead of monthly billing data when available.

Pump Operating Parameter Data

In addition to pump energy consumption data, the ELM requires pump operating parameter data. Data sources for pump operating parameters can be divided loosely into three categories: site-specific, calculation derived, and regional averages. The three represent a spectrum of specificity that starts with the most site-specific data source—pump test reports. Contour maps and CASGEM well data can be used to effectively simulate site-specific data. Finally, regional averages can provide reasonable proxies in some cases.

Gathering and Processing Pump Test Reports

Angiola provided 56 pump test reports for 30 well pumps. Pump test reports were produced in either 2015 or 2017 and included—as measured at the time of the test—groundwater depth, drawdown, discharge flow, OPPE, measured kilowatt power input, and more. The data presented a range of values from 75 to 250 horsepower (hp) pumps, TDH from 52 to 150 m (178 to 490 ft), tested discharge flows from 1,930 to 8,215 lpm (511 to 2,170 gpm), and reported OPPE from 27% to 75%.
Pump test report data were used to develop input data for two of five scenarios. Groundwater depth—the most sensitive data point—was applied on a well-by-well basis for the first scenario and averaged for the second. The remaining components of TDH (including pressure head, drawdown, and friction losses) and OPPE were determined through a linearly weighted blending of measurements reported in pump test reports per well pump. Some pumps in the study did not have any pump test reports available. In this case, averaged pump parameters were used. Pump operations were assumed to not change significantly during the study period. Thus, minor losses, drawdown, and OPPE were treated as predictable or constant in accordance with pump test reports.

Estimating Groundwater Depth

When site-specific pump test reports were not available, other data sources were needed to establish the groundwater depth. CWEE collected publicly available CASGEM data within a 50-km radius from Angiola (Fig. 2). The selected wells had at least two measurements of groundwater depth per year during the study period. CWEE used these measurements to generate well depth estimates for each well in Angiola for each month in the study period. CASGEM wells spatially closer to an Angiola well received a higher weight for the estimated groundwater depth for that well, and CASGEM well measurements that occurred closer in time to a given month received a higher weight for the estimated groundwater depth in that month.
Fig. 2. All CASGEM wells near Angiola filtered to a 50-km radius from the district center.
CWEE also accessed groundwater depth contour maps managed by DWR and available through the web-based GICIMA tool. The benefit of these contour maps is that, within covered areas, groundwater depth estimates are already generated (i.e., do not require further processing) and can be extracted from the downloaded data source. However, these contour maps also have some limitations. There are many areas within the state with poor coverage by these maps, and most of Angiola Water District is not covered. Fortunately, the wells in the study area were mostly concentrated in the northeastern portion of the district, which is the area with the best coverage for DWR contour data (Fig. 3).
Fig. 3. DWR contour coverage and Angiola well locations.
Estimation methods using both DWR depth contour and CASGEM well data produced inaccurate measurements on a per-well basis. On average, however, the estimates from CASGEM wells significantly outperformed the DWR contour estimates. We found that the DWR contours generally appeared to significantly underestimate well depth, whereas the CASGEM method did not consistently overestimate or underestimate (Fig. 4). Because the DWR contour estimates produced such consistently poor results—underestimating groundwater depth by more than an average of 30 m (100 ft)—they were not used to produce the results in this study.
Fig. 4. Comparison of estimated versus measured groundwater depth for two estimation methods.

Calculating Drawdown

Drawdown can be calculated using the Theis equation (Theis 1935), as follows:
where S = drawdown (m); Q = discharge (m3/s); T = transmissivity (m2/day); t = time (days); s = storage coefficient (dimensionless); and r = radial observation distance from the pumped well (m).
To calculate the drawdown of a well at a particular time, values must be generated for the discharge rate of the pump (Q), the length of time the pump has been operating (t), the radius of the pipe (r), and the aquifer geological parameters for transmissivity (T) and the storage coefficient (s). The geological parameters for the Tulare Basin aquifer, the study area, were assumed to be T=8,000  m2/day and s=0.5 (Page 1983). The pipe radius, which is effectively equivalent to the radial observation difference, was assumed to be approximately 0.15  m. W(x) is a symbolic representation of an exponential integral that is further detailed in Theis (1935). This approach provides a theoretical estimation of drawdown under ideal conditions, but many additional factors can impact the rate at which water and air pass between the well assembly and the surrounding soil formation. Drilling fluid residuals, corrosion, and fouling of the screens and well casing can reduce well productivity. Maintenance and rehabilitation can reverse these effects. For the purposes of this study, these variables are taken to be unobservable. Angiola did not provide maintenance records for their wells or any other data that could be used to determine the condition of any well screen or casing. However, pump test reports provided by Angiola provide precise drawdown measurements that can be used to determine the accuracy of the Theis equation in this context.
Energy billing data were used to estimate the pump discharge rate. The month with the highest total energy use was assumed to represent nearly continuous pump usage. Flow in that month was estimated using the ELM and regional average pump operating parameters. When comparing the estimated pump flow values to the measured pump flow from the provided pump test reports, a strong correlation exists with a slight bias toward overestimation (Fig. 5).
Fig. 5. Estimated pump flow versus tested pump flow with 11 line.
The value t, or the number of days of continuous pumping, was also estimated using energy data. Months with the highest energy usage were assumed to represent 30 days of continuous pumping, whereas months with the lowest energy use were assumed to represent 0 days of pumping. For each month, the t value was estimated by summing the number of preceding months with high energy usage and multiplying by 30 days, then adding 15 days for the current month.
Given that all values are known, derived, or estimated, the drawdown for each pump and each month was then calculated. When compared with the measured data, the results indicated a general correlation and a mean absolute error of 7.7 m (25.4 ft), and a mean error of 49% (Fig. 6). Inaccuracies in our flow estimates explain some of this error, but our estimates of soil transmissivity, the storage coefficient, and the impacts of unobservable soil bore conditions are all likely to contributed to the error. Although these results produced a relatively high error on a per-pump basis, the mean estimated drawdown of 18.1 m (59.5 ft) was relatively close to the mean measured drawdown of 15.5 m (50.7 ft). This method for estimating drawdown was used in the Calculated scenario (Table 1: Summary of ELM scenarios).
Fig. 6. Estimated drawdown versus measured drawdown.
Table 1. Summary of ELM scenarios
NumberScenarioGroundwater depthDrawdownPump efficiency
1Individual TestsPump test reports by wellPump test reports by wellPump test reports by well
2Averaged TestsPump test reports averaged for all wellsPump test reports averaged for all wellsPump test reports averaged for all wells
3CalculatedWeighted CASGEM well depth data (see the “Estimating Groundwater Depth” section)Calculated using Theis equation (see the “Calculating Drawdown” section)Calculated using linear regression (see the “Calculating Pump Efficiency” section)
4CASGEMWeighted CASGEM well depth data (see the “Estimating Groundwater Depth” section)Region average (see the “Using Regional Averages” section)Region average (see the “Using Regional Averages” section)
5All RegionalRegion average (see the “Using Regional Averages” section)Region average (see the “Using Regional Averages” section)Region average (see the “Using Regional Averages” section)

Calculating Pump Efficiency

OPPE is largely a function of the quality and condition of a pump; therefore, there is no way to determine OPPE using only energy data. However, correlations between OPPE and other pump operating parameters provide an opportunity for estimation. Pérez Urrestarazu and Burt (2012) presented several such correlations in their analysis of Fresno State’s pump test report database. We extended their work using a linear model to estimate OPPE based on TDH (in m), well energy usage (in MW·h/year), and whether or not the pump was “high flow” (>100  L/s), including an interaction term on usage and flow. The resulting model explained 75% of the variation in OPPE of the summary dataset with a high significance (p<0.001) for all model parameters. Because this model was not constructed using the original survey dataset, it does not represent true correlations between OPPE and pump operating parameters. Instead, it is a predictive tool to estimate OPPE using other observable pump data.
OPPE was estimated for each pump using CASGEM-estimated TDH, annual energy usage from PG&E data, and flow estimates, as described in the previous section. The resulting mean OPPE was 56.0%, slightly higher than the measured mean OPPE of 54.2%. There was a linear correlation of measured versus estimated OPPE for each well, but it was not a 11 relationship (Fig. 7).
Fig. 7. Measured versus estimated OPPE with 11 line.

Using Regional Averages

When none of these other data sources are available, regional averages may serve as a data source of last resort. Using regional averages is also the simplest approach to estimating pump operating parameters. Burt (2011) collected data from more than 15,000 pump test reports and published averages for three major valleys in California. In the case of Angiola in the San Joaquin Valley, the corresponding TDH was listed as 79 m (260 ft) and OPPE at 57%, the first underestimating the actual site-specific TDH average of 101 m (330 ft) and the second slightly overestimating the actual average site-specific OPPE of 54.2%.

ELM Scenarios

Five ELM scenarios were developed that reflect the data landscape in California (Table 1). The first two scenarios use pump test data, the following two use data with varying levels of relationship to the particular wells (and are described here as derived sources), and the last scenario uses only regional level data. In Table 1, these scenarios are organized from most to least specific.
The Individual Tests scenario used data for each pump collected directly from specific wells. Averaged Tests used an average of all of the data from all of the pump test reports gathered for the 30 wells in this study (i.e., all pumps were assumed to have the same OPPE and TDH based on an average value from all pump test reports).
The Calculated scenario used data from CASGEM wells in the study area to estimate the groundwater depth (see the “Estimating Groundwater Depth” section), the Theis equation to estimate the drawdown (see the “Calculating Drawdown” section), and regression analysis of pump parameters to estimate OPPE (see the “Calculating Pump Efficiency” section). The “CASGEM” scenario also used CASGEM wells to estimate groundwater depth, but all other components of TDH and OPPE were assumed to equal regional averages (see the “Using Regional Averages” section). Finally, the All Regional scenario used regional averages for all pump operating parameters.

Results and Discussion

Study results are presented in two sections, one reflecting the use of the ELM to estimate groundwater extractions of individual wells, and the other reflecting the use of the ELM to estimate groundwater extractions for a collection of wells. Sources of the error and the generalizability of the ELM study findings throughout California are discussed in the third and fourth sections, respectively.

Estimating Groundwater Extractions of Individual Wells Using the ELM

If the priority is to estimate extractions accurately for individual wells, using data derived directly from those wells appears to be the most accurate approach. Using pump test reports well represented the best approach to minimizing errors on a per-well, per-month basis (Individual Tests scenario). When individual pump test reports are not available, the next best data inputs for pump operating parameters are CASGEM well data and either calculated estimates or regional averages of drawdown and OPPE (Calculated scenario).
Compared with other approaches, using individual pump test reports resulted in the lowest error rate on a per-well, per-month basis at 13.5% (Fig. 8). Averaging pump test report data resulted in a 15.8% error on average, which was slightly better than the Calculated and CASGEM approaches, and both had error rates of 17.2%. Using regional averages led to the highest error rate of 19.9%.
Fig. 8. Mean absolute percentage error for ELM scenarios on monthly well-by-well basis.
With a mean absolute error (MAE) of 1.5 ha-m (12.16  acre-ft), the Individual Tests scenario has a statistically significantly (p<0.05) lower MAE than the second-best Averaged Tests scenario at 1.78 ha-m (14.41  acre-ft). In addition, using individual tests resulted in a statistically significantly lower MAE than the calculated, CASGEM, and regional scenarios (p<0.001). Using averaged pump tests also resulted in a significantly lower MAE than any of the scenarios that do not use pump test reports (p<0.001).
Among the scenarios that do not use pump test reports, the Calculated approach resulted in the lowest MAE at 2.15 ha-m (17.43  acre-ft), although it is not statistically significantly different from the MAE of 2.16 ha-m (17.48  acre-ft) produced using CASGEM data. However, both the Calculated and CASGEM approaches produced far fewer errors than the All Regional approach (p<0.001). These results are summarized in Table 2.
Table 2. MAE for monthly estimates of individual wells for each scenario
Individual Tests1.5Lower MAE than Averaged (p<0.05). Lower MAE than Calculated, CASGEM, and All Regional (p<0.001).
Averaged Tests1.78Lower MAE than Calculated, CASGEM, and All Regional (p<0.05).
Calculated2.15Not different from CASGEM (p>0.2). Lower MAE than All Regional (p<0.001).
CASGEM2.16Lower MAE than All Regional (p<0.001).
All Regional2.87Highest MAE (p<0.001).
With an error greater than 10% in even the most accurate scenario, the ELM appears to be less accurate than flow meters when estimating monthly groundwater extractions for individual pumps. If the ELM is applied to perform this estimation, applying the most specific dataset available is vital.

Improving Individual Well Results Using Annualized ELM Input Data

ELM input data were aggregated to an annual basis in an attempt to improve the estimates of groundwater extraction from individual wells. Aggregation of the data reduced the error associated with each scenario. For example, on a well-by-well basis, the mean absolute percentage error (MAPE) for the Individual Tests approach improved to 5.0% on an annual basis (Fig. 9) from 13.5% (Fig. 8), a difference that was statistically significant (p<0.001).
Fig. 9. Mean absolute percentage error for ELM scenarios on annual well-by-well basis.
This reduction in error comes from two potential sources. The first is the reduction in the error from the variation in pump operating parameters during each year. Whereas some of this variation is random, increased overestimation occurred in July and August. When all months in a year are combined, the impact of random and seasonal variations in pump operating parameters is reduced. The second reduction in the error comes from the smoothing of errors introduced from standardizing the billing data into calendar month periods. The electricity billing data used in this study did not correspond to calendar months, whereas the measured flow data did. Standardizing the billing data to correspond to calendar months resulted in a significant error. However, standardizing the billing data to correspond to calendar years has a much lower potential for error. The scatterplot in Fig. 10 indicates a strong correlation between the estimated and actual water use when the data are annualized.
Fig. 10. Estimated versus measured water use per well per month: (a) compared to per well per year (shown on an average monthly basis for purposes of comparison); and (b) for the Individual Pump Tests scenario.
Annualizing monthly estimates of groundwater extraction for individual wells significantly improves the accuracy of the results. Annualized estimates based on data from individual pump test reports produced error rates similar to flow meters, indicating that the ELM may be a suitable alternative to flow meters in some cases.

Estimating Groundwater Extractions of a Collection of Wells Using the ELM

Summing individual well estimates into an aggregate extraction estimate for a collection of wells reduced the average error associated with some scenarios. The Averaged Tests scenario showed the largest reduction in average annual error, falling from 8.5% on an individual well basis to 3.3% on an Angiola-wide basis (Fig. 11). The Individual Tests and Calculated scenarios showed little change in the error rate, and the CASGEM and All Regional scenarios had increased errors.
Fig. 11. Mean absolute percentage error for ELM scenarios on annual, Angiola-wide basis.
The Averaged Tests scenario produced inaccurate results when estimating individual well extractions because it failed to capture the significant variation in OPPE and TDH between pumps. However, this variation is less important when estimating extractions from a collection of wells. Estimates of OPPE and TDH that most closely reflect the true average of all pumps in the collection are all that are needed to produce an accurate estimate of aggregate groundwater extraction.
Because all wells were aggregated together for this analysis, the sample sizes were reduced, leading to reduced statistical significance of the perceived differences. The MAE produced using individual pump tests was 4.35 ha-m (35.3  acre-ft) per month, which was slightly significantly higher than the MAE produced using averaged pump tests at 2.64 ha-m (21.4 acre-ft) (p<0.2). Of the scenarios that do not use the pump test report data, the Calculated approach was again the best, followed closely by the CASGEM scenario. Again, using all regional data produced the highest error of all scenarios (p<0.001). See Table 3 for a summary of these findings.
Table 3. MAE for annual estimates for Angiola water district for each scenario
Individual4.35Possibly higher MAE than Averaged Tests (p<0.2). Lower MAE than Calculated, CASGEM, and All Regional (p<0.001).
Averaged2.64Lower MAE than Calculated, CASGEM, and All Regional (p<0.001).
Calculated7.51Possibly lower MAE than CASGEM (p<0.1) and All Regional (p<0.001).
CASGEM9.58Lower MAE than All Regional (p<0.001).
All Regional15.46Highest MAE (p<0.001).
Collecting individual pump test reports and matching each report with a specific well’s energy data may not be necessary if the ELM is to be used to estimate groundwater extraction at a large spatial scale. Instead, generating an accurate estimate of the average pump operating parameters may be sufficient.
Because the Averaged scenario applies the same values for OPPE and TDH for each well, there is no additional value in using pump-level electricity data. The same estimates could be produced if all of the electricity data were aggregated into total monthly consumption and would be just as accurate. This information is particularly significant for entities such as GSAs, which may not be able to access individual-level electricity data but is permitted to request aggregated electricity data from energy utilities through the EDRP. Therefore, GSAs could perform this estimate by requesting aggregated data for all wells in their territory and collecting a representative sample of pump test reports to calculate the average values of TDH and OPPE.

Sources of Error

We carefully analyzed the results produced by each scenario to understand the factors that contribute to the inaccuracy of the ELM given the current data landscape in California.

Errors Impacting Accuracy of Individual Well Estimates

When estimating groundwater withdrawals from wells on a monthly basis, the estimates indicate a strong correlation to the actual water use (Fig. 12). These errors in the Individual Test scenario are approximately normally distributed, indicating that random variations in physical conditions are the most likely drivers of errors rather than issues in the underlying data. This assumption was further tested by comparing the measured water-energy ratio of pumps to the modeled estimates. The measured water-to-energy ratio was obtained by dividing the measured well groundwater extractions using the PG&E hourly data for the same period. The modeled ratio was calculated by dividing the estimated OPPE by 27.2285 times the TDH for a well in a given month, where 27.2285 is the energy required to lift one ha-m of water a vertical distance of one meter at 100% efficiency in kW·h. Although these values typically followed a similar trend, the measured water-to-energy ratio displayed higher variance and less consistency (Fig. 13).
Fig. 12. Distribution of errors for Individual Tests scenario (histogram) versus normal distribution (black line).
Fig. 13. Measured versus modeled water-to-energy relationship for example well.
The general overestimation trend may have been an artifact of this particular subset of wells; alternatively, it could point to a problem with the model assumptions. The overestimation of water extractions could result from a bias toward an overestimation of OPPE and/or an underestimation of TDH. If the average OPPE calculated by the pump test report is higher than the average OPPE of the pump, then a bias toward overestimation is expected. Similarly, although efforts were taken to account for seasonal changes in groundwater depth, the groundwater depth or drawdown may have increased beyond what this model expected during the summer months.
Finally, all of the pump tests in this study display a very low pressure head, meaning that during the pump test, the irrigation system beyond the well itself was either unpressurized or was pressurized by a booster pump. If the pump test reports were conducted in a situation that does not reflect the system’s normal downstream pressure demands, then this could also be a potential cause for the overestimation. In addition to potential errors with TDH and OPPE, the energy data itself could cause overestimation if there were other energy demands on the same meter as the well pump.
Overestimation disproportionately occurred in late summer and early fall months, which can be visualized by comparing measured groundwater extractions over time to modeled extractions (Fig. 14). According to a regression analysis on errors in the dataset, the months of July, August, and September had statistically significant (p<0.001) overestimation trends, with expected monthly overestimations of 1.47, 1.8, and 1.16 ha-m (11.9, 14.6, and 9.4  acre-ft) per well, respectively. A one-sample t-test was performed on the vector of all monthly errors, and the overestimation was statistically significant, with a 95% confidence interval of 0.3–0.75 ha-m (2.46.1  acre-ft) per well per month. Repeating the t-test with July through September removed resulted in no significant overestimate. May and June also had statistically significantly higher errors than average with expected overestimates of 0.79 and 0.72 ha-m (6.4 and 5.8  acre-ft) per well per month, respectively.
Fig. 14. Measured versus modeled groundwater extractions for select wells.
Given that overestimation is concentrated in July through September and, to a lesser extent, May and June, the error likely has to do with conditions unique to these months. Because these months have the hottest temperatures and lowest rainfall, the overestimations might be correlated to the total pumping. Increased pumping likely increases drawdown, which this model does not capture. In addition, increased irrigation demand may lead to pumps being operated beyond their set points, resulting in inefficiencies not captured in the model. Alternatively, the groundwater depth could drop further than the model expects during these months. Without more data on pump operating conditions, determining the cause of these discrepancies with any certainty is impossible. However, given the significance of this seasonal overestimation trend, such questions should be a priority for future investigations.

Errors Impacting Accuracy of Estimates for Collections of Wells

All of the errors that impact the accuracy of the previously described individual well estimates also impact the estimates for a collection of wells, although the errors caused by the random variations captured in the normal distribution of errors can average out when aggregating all of the results, as indicated by the overall reduction in error in Figs. 8, 9, and 11. However, the overall bias toward overestimation is not removed by aggregation.
One major source of error that differs between each scenario was the error in the TDH estimate. The similarity of the average TDH used in each scenario to the average TDH of the pump test reports was a good indicator of the overall accuracy of regional estimates (Fig. 15). The Averaged Tests scenario, which by design exactly matches the averages from the pump test reports, had the lowest MAPE, whereas scenarios 4 and 5 had the largest difference in TDH and, correspondingly, had the largest difference from the regional water extraction estimate. These results indicate that accurate results for regional estimates of groundwater extraction do not necessarily require site-specific data or models to estimate the change in the groundwater level over time but do require accurate regional average estimates of TDH and OPPE.
Fig. 15. Averaged components of TDH from pump test reports (actual) compared with scenario averages.

Measurement Errors

The measured groundwater extraction data used in the production of these results may not represent true water demand. Changes in pump operating conditions and flow meter maintenance can significantly impact the accuracy of a flow meter; therefore, some of the differences between the measured and estimated extractions could be explained by measurement error.


The Angiola Water District represents only a small portion of the California Central Valley, and this analysis does not capture the full range of conditions for well pumps throughout the state. For example, wells operating in confined and unconfined aquifers may need to be treated differently to generate accurate estimates of groundwater extraction. Although the wells in the study area likely draw from both shallow unconfined aquifers and deep confined aquifers, Angiola did not provide the necessary data to make any distinction. Further, differences in soil type, annual variations in the groundwater level, and regional variations in irrigation practices can all create additional challenges when applying the ELM.
Before this methodology is applied at the statewide level, additional studies on the generalizability of our findings should be conducted. However, observationally, there were no consistent patterns of inaccuracies in the ELM estimates across wells. Although the wells and aquifer conditions in Angiola are more homogenous than those in the state of California, the random nature of the errors provides some evidence that the unobserved differences between wells in our study do not play a significant role in the accuracy of the method. Alternatively, regulators can adopt this methodology only where it is most likely to be accurate. Regulations for the state of Colorado currently permit the use of electricity data to estimate groundwater extractions of individual wells, but only under stable water table conditions and pumping operations (2 CCR §402-16 2015). The ELM is only as accurate as its OPPE and TDH estimates and can be used most confidently when those variables are stable over time.


The current California data landscape provides adequate resources for estimating groundwater extractions from agricultural well pumps using the ELM. The variety of resources available allows for multiple approaches, the selection of which will depend on three primary factors: the spatial resolution required of the results (for example, for an individual well, a collection of wells, or regionally); the required volumetric accuracy of the results; and the desired simplicity of the calculation. Although greater requirements for spatial resolution or volumetric accuracy demand site-specific data in the form of pump test reports, applications that necessitate simplicity can use regional averages.

Individual Well Groundwater Extraction Estimates

In the most detailed findings, the study determined that the most accurate approach to estimating individual well groundwater extractions is to gather pump test reports and estimate the change in groundwater depth over time. This Individual Tests scenario resulted in an average 13.5% error on a per-month basis. Recalculating estimates on an annual basis dramatically improved the accuracy of this approach, resulting in a 5% mean error. If individual well accuracy is the priority, obtaining pump test reports for each well studied and calculating groundwater extractions on an annual, rather than monthly, basis may be necessary.
The best approach to estimating individual well extraction quantities that does not rely on pump test reports uses CASGEM well data and either calculated estimates of drawdown and pump efficiency or regional averages. These Calculated and CASGEM approaches both led to a 17.2% error on a monthly basis and a 10.1% error rate on an annual basis. Finally, the All Regional scenario presents the simplest method and produces a 19.9% error on a per-month basis and a 13.6% error when annualized. These errors are significantly higher than all other approaches but may still be an improvement over the estimates generated by C2VSim.

Groundwater Extraction Estimates for a Collection of Wells

Estimating extractions for a collection of wells does not necessarily require site-specific data for each well. The most accurate approach for estimating total groundwater extractions from all pumps is to calculate the average TDH and OPPE from pump test reports and to then apply these values to all wells, holding them constant over time as was done for the Averaged Tests scenario. This approach led to an overall error of 3.3% on an annual basis, the lowest error rate observed in this study. A large and representative sample of pump test reports, instead of pump test reports from all wells in a particular area, would likely be sufficient for generating these averages. As regulatory agencies, GSAs are able to request aggregated electricity data through the EDRP. Because the Averaged Tests scenario does not require pump-level electricity data, GSAs may be able to collect all of the necessary data to generate large-scale estimates of groundwater extraction with error rates of 3.3%.
The most accurate method that does not use pump test reports estimates groundwater depth using CASGEM wells, and the remaining pump operating parameters use calculations and relationships from the literature, as represented by the Calculated scenario. This scenario led to an overall error rate of 9.5% on an annual basis. However, this approach is still fairly complex. The CASGEM approach is simpler and could be performed quickly for any region of the state. Using CASGEM wells to estimate groundwater depth and regional estimates for the remaining pump operating parameters resulted in a 12% error on an annual basis.

Potential for Use

The methods developed in this study could be used to track estimated groundwater usage on a month-by-month basis for individual wells at a lower level of accuracy than pump flow meters. Annualizing such estimates and averaging the results for a collection of wells can result in a relatively high level of accuracy. Hence, the ELM may be beneficial to agencies tasked with developing groundwater sustainability plans (GSPs). However, further research is required to assess the accuracy of the ELM in different pumping conditions before the method is used to estimate groundwater withdrawals on a statewide basis. Using electricity data to estimate groundwater extraction may also provide new insights for researchers and policymakers who study agricultural groundwater demand. Well-specific estimates of groundwater extraction could be combined with other spatial agricultural datasets to track groundwater usage by crop type, land cover type, or other spatial parameters.

Data Availability Statement

Some or all of the data, models, or code generated or used during this study are proprietary or confidential in nature and may only be provided with restrictions. The data used in this study that were obtained under a nondisclosure agreement between the University of California Davis and the data owners may not be shared with others and must be obtained directly from the data owners. These data include all electricity data, pump test reports, and measured water consumption data. Data on groundwater depth and regional average estimates for pump operating parameters were gathered from publicly available data sources and can be made available from the corresponding author on reasonable request. The code used to perform the calculations in this study can also be shared on reasonable request but relies on data that cannot be shared; therefore, the code will not function correctly.


This project was funded by the California Department of Water Resources (DWR), Agreement No. 4600011684. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the funding agency. The authors thank Kendra Olmos, Andy Holguin, Halona Leung, and the remaining staff at CWEE that made this research possible. This study would also not have been possible without the willing collaboration of the staff at Angiola Water District, including Matthew Hurley, Christine Rutter, and Joe Ortega.


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Information & Authors


Published In

Go to Journal of Water Resources Planning and Management
Journal of Water Resources Planning and Management
Volume 147Issue 5May 2021


Received: Sep 25, 2019
Accepted: Oct 11, 2020
Published online: Feb 27, 2021
Published in print: May 1, 2021
Discussion open until: Jul 27, 2021



Ph.D. Student, Center for Water-Energy Efficiency, Univ. of California, Davis, CA 95616. ORCID: Email: [email protected]
Robert T. Good
Engineering Manager, Center for Water-Energy Efficiency, Univ. of California, Davis, CA 95616.
Frank J. Loge, Ph.D. [email protected]
Professor, Center for Water-Energy Efficiency, Univ. of California, Davis, CA 95616 (corresponding author). Email: [email protected]

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