Climate elasticity assessment on groundwater recharge to the Edwards Balcones Fault Zone Aquifer, United States

This study presents a comprehensive analysis of the characteristics of precipitation, temperature, and groundwater recharge in the recharge zone of the nine basins of the San Antonio segment of the Edwards Balcones Fault Zone Aquifer, which is one of the major groundwater systems in the United States and serves as primary water sources for approximately 1.7 million people in south‐central Texas. Datasets of monthly precipitation and average temperature (1895–2019) and groundwater recharge (1934–2019) are used to examine the decadal variability in precipitation, temperature, and groundwater recharge on the annual scale with a normalized 20‐year moving average of variance. Climate elasticity (precipitation and potential evapotranspiration) of groundwater recharge is estimated to evaluate impacts of climate change on groundwater recharge. The results of this study show that precipitation and temperature variability exhibit decadal cyclic patterns. Elasticity analysis of groundwater recharge indicates that a 1% change in annual precipitation may result in 2%, with a likely range of 0.15%–2.8%, change in groundwater recharge, and a 1% change in annual potential evapotranspiration may lead to −3.3% change in groundwater recharge with a likely range of −8.9% to 4% in the study area. This study suggests that climate elasticity of groundwater recharge may provide an alternative means for evaluating climate impacts on groundwater recharge to an aquifer.

weather pattern in a region, is generally assessed based on long-term weather datasets.Climate variability and change can influence groundwater systems directly through effects on natural replenishment by recharge (Taylor et al., 2013).Groundwater recharge is the amount of water percolating into aquifers from the ground surface through vadose zones or infiltrating directly from surface waters (such as streams) through discrete features (such as dissolution channels or open fractures) and is highly dependent on prevailing climate, land cover, and underlying geology (Taylor et al., 2013).Karst aquifers may have limited storage capacity and respond rapidly to fluctuations in recharge and discharge; thus, understanding impacts of climate variability and change on groundwater recharge is paramount for groundwater management and sustainability (Atawneh et al., 2021).
Climate elasticity can be calculated with statistical methods based on the empirical, site-specific relationships between hydrological system variables and climate variables using historical datasets (Atawneh et al., 2021).The concept of climate elasticity was first introduced to assess how climate change impacts streamflow (Andréassian et al., 2016;Ma et al., 2010;Sankarasubramanian et al., 2001;Yang & Yang, 2011) and then later was extended to other hydrological variables, such as low flows (Cooper et al., 2018), baseflow (Ahiablame et al., 2017;Mo et al., 2021), and evapotranspiration (Avanzi et al., 2020).However, there are very few studies that apply climate elasticity to assessment of climate impacts on groundwater recharge.Schreiner-McGraw and Ajami (2021) estimated precipitation elasticity of groundwater recharge in the Kaweah River watershed, located in the southern Sierra Nevada Mountains in California, United States.Hartmann et al. (2017) conducted comparisons of recharge sensitivity to climate variability in the carbonate rock regions of Europe, Northern Africa, and the Middle East in terms of climate elasticity.Crosbie et al. (2013) used elastic analysis to evaluate potential climate change effects on groundwater recharge in the High Plains Aquifer, United States.Similarly, using the concept of climate elasticity, Barron et al. (2012) evaluated climatic controls on diffuse groundwater recharge across Australia.Those limited studies, however, focus on assessment of only precipitation elasticity of groundwater recharge to an aquifer.Because groundwater recharge can be affected by not only precipitation but also potential evapotranspiration, it is necessary to include both climate variables when assessing sensitivity of groundwater recharge to climate.
The Edwards Balcones Fault Zone Aquifer (BFZA) is a carbonate, karstic aquifer that plays a vital role in serving as the primary source of water to a growing region of south-central Texas and supports a unique ecosystem of aquatic life, including several threatened and endangered species (Chen et al., 2001;Ding & McCarl, 2020;Liu et al., 2017;Loáiciga et al., 2000;Mace & Wade, 2008;Martinez & Maidment, 1998;Nielsen-Gammon et al., 2020;ZARA Enviromental LLC, 2010;Zhang et al., 2020).Typically, about 70% of recharge to the Edwards BFZA is focused (stream loss) with the remainder diffuse recharge occurring in the areas between drainage channels.
The main objectives of this study are twofold: (1) to examine decadal variability in precipitation and temperature based on the historical weather datasets and (2) to evaluate sensitivity of Edwards BFZA groundwater recharge to climate variables, particularly precipitation and potential evapotranspiration (PET) using the elasticity analysis.The relationship of the elasticity of climate variables to recharge can help in understanding the climatic controls on recharge under the historical climate and may assist in the analysis of recharge projections under a future climate.To the best of our knowledge, this study is the first to report PET elasticity of groundwater recharge.We believe that the values of PET elasticity of groundwater recharge reported in our study can be considered as a reference value to future similar studies among the scientific community.This paper is organized as follows.Section 2 describes the study area, data sources, and methods used to analyze decadal variability in precipitation, temperature, and groundwater recharge and calculate climate elasticity of groundwater

Research Impact Statement
Based on the long-term historical data, climate elasticity of groundwater recharge can reveal climate impacts on groundwater recharge to an aquifer and be valuable for water resource management.recharge in terms of precipitation and PET.Section 3 presents results of the analyses of decadal variability in precipitation, temperature, and groundwater recharge and climate elasticity of groundwater recharge in the recharge basins.Section 4 provides discussion on the results.Finally, major conclusions are given in Section 5.

| Study area
Figure 1 shows the location of the study area, which includes nine basins that cover the recharge zone of the San Antonio segment of the Edwards BFZA.From east to west, the nine basins are the Blanco basin, the Guadalupe (Guad) basin, the Cibolo basin, the area between the Medina basin and the Cibolo basin (MedCib), the Medina basin, the area between the Sabinal basin and the Medina basin (SabMed), the Sabinal basin, the Frio basin including the Frio and the Dry Frio rivers, and the Nueces basin including the Nueces and West Nueces rivers.Figure 1 also shows the location of the Edwards BFZA recharge and artesian zones in relation to the contributing zones of the nine basins.The study area covers all or part of 13 Texas counties and stretches over 261 km from east to west, extending across an area of ~17,000 km 2 .variables at a 4-km resolution for the entire United States (Daly et al., 2012).Gridded monthly cumulative precipitation and monthly average temperature data (1895-2019) in the study area were averaged over the recharge zone of each individual basin.Table 1 lists the statistics of annual precipitation and annual average temperature over the period of record in the nine basins.Spatial distribution of annual average of precipitation, mean temperature, and PET in the region over the period 1960-2019 are shown in the supplementary materials (Figure S1).

| PRISM monthly precipitation and temperature and potential evapotranspiration
Generally, precipitation is highest in May, September, and October, while December and January have the least amount of precipitation (Figure 2a; Figure S2).Mean monthly average temperature ranges from 10 °C in January to 28°C in July and August (Figure 2b; Figure S3).
There is no significant difference in mean monthly average temperature in the recharge zone among the nine basins.There are various methods that can be used to estimate PET or reference evapotranspiration (Archibald & Walter, 2014;Medeiros et al., 2012;Shuttleworth et al., 1988).Because of the data availability, the Thornthwaite equation for PET calculation is used in this study (Thornthwaite, 1948).Monthly PET is calculated using the Thornthwaite equation with the PRISM mean monthly air temperature and mean daily daylight hours of each month, which can be estimated from latitude.Mean annual PET is estimated around 1050 mm with a minimum value of 900 to a maximum value of 1230 mm (Table 1).Mean monthly PET is shown in Figure 2c and Figure S4.

| Monthly groundwater recharge estimates
Estimates of groundwater recharge to the Edwards BFZA are made by the USGS in cooperation with the Edwards Aquifer Authority (Puente, 1978;Slattery, 2020).In this study, the dataset of monthly groundwater recharge  estimated by the USGS is used (Slattery, 2020).The USGS method of estimating recharge is based on a water balance equation assuming that recharge within a basin is the difference between measured streamflow above and below the infiltration area (recharge zone, Figure 1) of the aquifer plus the estimated runoff (Puente, 1978).Estimates of groundwater recharge are made for each individual basin within the study area except the Guadalupe basin.Puente (1978) speculated that although the Guadalupe River crosses the recharge zone of the Edwards BFZA, it may not contribute recharge in significant quantities.Thus, no recharge in the Guadalupe basin is estimated.
The volumetric recharge (acre-feet) in each individual basin is converted to recharge depth (mm) by dividing by the total area of the contributing and recharge zones of each individual basin.Mean monthly recharge in each individual basin is shown in Figure 2d and Figure S5.May and June have the highest recharge, followed by September and October (Figure 2d), showing a similar pattern to the monthly precipitation (Figure 2a).It should be noted that the basin boundaries defined in the Puente (1978) for recharge estimation are slightly different than the basin boundaries shown in Figure 1, particularly the SabMed basin and the Medina basin.The difference in basin boundaries is negligible because instead of volumetric recharge (acre-feet), the area-normalized recharge depth (mm) is used.

| Decadal variability
To assess decadal variations in precipitation, temperature, and groundwater recharge in each individual basin, a ratio of the subperiod variance of a target variable over the period of record variance of the variable is used in this study and is defined as, (1) TA B L E 1 Statistics of annual precipitation, annual average temperature, and annual groundwater recharge over the period of records in the nine recharge basins.where 2 s is variance of a variable (precipitation, temperature, or recharge) over a moving window of a subperiod (20 years in this study), and 2 is variance of a variable over the record period.This metric has been widely used in evaluating variability of hydroclimate variables (He & Gautam, 2016;Pagano et al., 2004;Pagano & Garen, 2005).He and Gautam (2016) calculated the ratio (Equation 1) for every 30-year subperiod within the record period to characterize variability in precipitation, temperature, and drought indices in the state of California.Pagano and Garen (2005) suggested that a 20-year window allowed a large enough sample size to develop reliable interperiod estimates of variances and create enough moving window periods to observe any decadal variability.The record period in this study is 1895-2019 for precipitation and temperature and 1934-2019 for groundwater recharge.If variability is greater (less) than 1, it suggests that the variable in the subperiod is more (less) variable than usual.High (low) variability indicates more (less) extreme events occurred (He & Gautam, 2016).

| Climate elasticity of groundwater recharge
Climate elasticity of groundwater recharge can provide a measure of the sensitivity of groundwater recharge to change in climate variables such as precipitation or temperature.Instead of using temperature, PET is used as a proxy of temperature in this study.Two approaches are generally used to estimate the climate elasticity of groundwater recharge: the nonparametric approach and the bivariate linear regression approach (Andréassian et al., 2016).This study uses the bivariate linear regression approach (GLS2).With this approach, relative change in groundwater recharge to change in precipitation and PET can be given by the following equation (Andréassian et al., 2016), where P i , PET i , and R i are annual precipitation, potential evapotranspiration, and estimated recharge, and P, PET, and R are mean values of precipitation, PET, and estimated recharge.P and PET represent precipitation and PET elasticity of groundwater recharge (equivalent to the regression slope) and ω is the residual.A generalized least-square (GLS) approach can be applied to fit the bivariate linear regression model (Equation 2).Details of the GLS approach are described by Andréassian et al. (2016).The GLS approach implemented in the python package, Statsmodel (Seabold & Perktold, 2010), is used to quantify P and PET simultaneously.As Andréassian et al. (2016) pointed out, the strength of the bivariate GLS approach (GLS2) lies in the fact that it accounts for the cross-correlation of P and PET.The datasets of precipitation and PET for the period of 1934-2019 are used to calculate climate elasticity of groundwater recharge.The unit of climate elasticity generally is expressed as %/% which represents percentage change in groundwater recharge caused by 1% change in a variable.

| Decadal variability
Decadal variability of annual precipitation, average temperature, and groundwater recharge for the recharge zone in each individual basin is evaluated.Figure 3 and Figure S5 show variability of annual precipitation, average temperature, and groundwater recharge, which is calculated using a 20-year moving window.The differences in annual precipitation variability among the nine basins are not significant before 1995 (Figure 3a).Annual precipitation variability shows an overall decadal cyclic pattern.There are two periods during which annual precipitation variability is less than one: 1937-1956 and 1975-1996, suggesting that during these two periods, annual precipitation was less variable than normal.After 2000, annual precipitation variability shows an overall increasing trend and approaches a maximum of ~2 in 2017-2019 (Figure 3a), suggesting that annual precipitation in the region has been more variable in recent years.The magnitude of precipitation variability is highest in the eastern basins of the Edwards BFZA region where the largest increases in annual average precipitation have occurred since 1975 (Nielsen-Gammon et al., 2021).Analysis of the top 10 and the bottom 10 annual precipitation values for the period from 1895 to 2019 indicates that more than half of these maxima or minima occurred after 1980, suggesting that frequency of precipitation extremity has been intensified during the recent years.This finding in the region is consistent with the Intergovernmental Panel on Climate Change (IPCC) report that the magnitude and intensity of extreme precipitation has very likely increased since the 1950s (Masson-Delmotte et al., 2021).
Annual average temperature variability also shows decadal fluctuations (Figure 3b).Interestingly, and unlike that for precipitation, annual average temperature variability is less than 1 in recent years.However, an increasing trend in annual average temperature variability is appreciable after the 1980s (Figure 3b), which correlates to significant increases in annual average temperatures in each of the basins over the same time frame (Nielsen-Gammon et al., 2021).The IPCC report also states that there is evidence of an increase in intensity and frequency of hot extremes and decrease in the intensity and frequency of cold extremes for the North America, though there are substantial spatial and seasonal variations in the trends (Masson-Delmotte et al., 2021).Note that the differences in annual average temperature variability among the basins are insignificant although the study area stretches over 261 km from east to west (Figure 3b).Annual PET variability is not shown here because PET is estimated based on temperature with the Thornthwaite equation, showing a similar behavior to the annual average temperature variability.
Because the period of groundwater recharge data is 1934-2019, with a 20-year moving window, annual groundwater recharge variability is estimated for 1953-2019, as shown in Figure 3c.Differences in groundwater recharge variability among the eight basins that contribute recharge are noticeable, especially during 1960-1978and 1990-2012. Prior to 1990, groundwater recharge variability in Nueces, MedCib, Frio, and Blanco basins is less than 1 and appears quite stable.Annual groundwater recharge variability in most of the basins shows an overall increasing trend after 1990, and the range of variability among the basins increases before a decline with narrowing of the range in variability after 2012.However, annual groundwater recharge variability in the Medina basin shows an opposite trend.Among the total 66 years of data for the Medina basin, 44 years have recharge variability less than 1, suggesting that groundwater recharge in the Medina basin is less variable.
A possible explanation is that a major contributor to groundwater recharge in the Medina basin is Medina Lake, which has relatively stable

| Climate elasticity of groundwater recharge
Relative change in groundwater recharge against relative change in precipitation and change in temperature for the eight basins that contribute recharge is shown in Figures 4 and 5. Relative change in annual groundwater recharge ( R − R R ) shows an overall positive correlation with relative change in annual precipitation ( P − P P ) (Figure 4) and weakly negative correlation with change in temperature ( PET − PET PET ) (Figure 5).These relationships appear reasonable because more precipitation will result in more groundwater recharge, while higher PET will lead to more water evaporated from the soil zones and thus less groundwater recharge to the aquifer.
Table 2 lists climate elasticity of groundwater recharge calculated with the bivariate generalized linear regression (GLS2) for the eight basins that contribute recharge.Figure 6 shows precipitation elasticity of recharge ( P ) calculated with the bivariate GLS (GLS2) approach.
Values of P range from 0.46 to 2.4%/% using the GLS2 approach.Among the eight basins, P in the Medina basin is the smallest, approximately Estimated PET with the GLS2 approach on the annual scale is shown in Figure 6 (b).Based on the results of the GLS2 approach, annual groundwater recharge in the Sabinal basin appears to be the most sensitive to change in PET with an PET of −4.9%, indicating that groundwater recharge would decrease 4.9% relative to its multi-year mean if PET is increased 1% from its multi-year mean.In this study, the multi-year mean values are calculated over the period of 1934-2019.The median value of PET over the eight basins is −3.28%/%.

| Comparisons with other studies
Table 2 also lists some reference values of precipitation elasticity of groundwater recharge found in the literature.Generally, reference values of precipitation elasticity of groundwater recharge vary from 1%/% to 4%/% with the exception that Schreiner-McGraw and Ajami (2021) reported a wider range (−1%/% to 6%/%) in their study.In this study, precipitation elasticity of groundwater recharge in the recharge basins of Edwards BFZA varies from 1.4%/% to 2.5%/% which is consistent with the values reported in literature.The reason that precipitation elasticity of groundwater recharge in the Medina basin is smaller compared to the other basins is likely because the recharge in that basin is contributed largely from Medina Lake.
There are very few values of PET elasticity of groundwater recharge reported in literature.However, some researchers reported sensitivity of groundwater recharge to change in temperature.Schreiner-McGraw and Ajami (2021) estimated temperature elasticity of groundwater recharge through four different recharge paths in the Kaweah River watershed in California, United States, and reported recharge sensitivity to temperature values ranging from −60 to 30%/°C.Hartmann et al. (2017) reported that the recharge sensitivity to annual average temperature under heterogeneous subsurface ranges −0.05 to −0.26%/°C in the carbonate rock regions of Europe, Northern Africa, and the Middle East.This study shows that the temperature elasticity of groundwater recharge estimated with the GLS2 method in the region area varies from −40.5 [−68.9, −12.2] %/°C in the Sabinal basin to 16.3 [−8.1, 40.7] %/°C in the Nueces basin (values within [] represent the 95% confidence interval).Temperature elasticity of groundwater recharge shows a wide range of values in different regions which may lead to misunderstanding of impacts of change in temperature on groundwater recharge.Thus, temperature elasticity of groundwater recharge is less useful as a general comparator.

| Limits
While the elasticity analysis has been widely used to assess climate impacts on streamflow and some other hydrological variables in a basin, the climate elasticity of groundwater recharge estimated in this study has limits.Firstly, climate elasticity of groundwater recharge is derived   from the historical datasets at the annual scale.It cannot be used to interpret response to the sub-annual (e.g.monthly to seasonal) time scale (Fu et al., 2007).Secondly, while the elasticity method allows use of past observations to predict the impact of future changes, its ability to extrapolate to the future changes is uncertain (Andréassian et al., 2016).Thirdly, change in groundwater recharge is attributed to climate in this study.However, anthropogenic activities, such as land use, may also contribute to change in groundwater recharge.Separating climate impacts from anthropogenic impacts on groundwater recharge in the study area will be a focus in future studies.
Lastly, because estimation of climate elasticity of groundwater recharge relies on data quality, any uncertainties in the datasets, particularly PET and groundwater recharge which are calculated with models, may propagate to uncertainties in the calculation of climate elasticity of groundwater recharge.To evaluate impacts of uncertainties in the datasets on estimation of climate elasticity of groundwater recharge, we conducted six case analyses by adding errors to the datasets (precipitation, PET, and groundwater recharge).The errors are assumed to have a normal distribution with a mean value = 0. Table 3 lists climate elasticity of groundwater recharge calculated for the six cases in the two basins (the Blanco basin and the Nueces basin).Uncertainty in groundwater recharge has trivial impacts on precipitation elasticity and minor impacts on PET elasticity of groundwater recharge (Cases 1 and 2 in Table 3).Uncertainty in precipitation results in minor impacts on precipitation elasticity of groundwater recharge (Cases 3 and 4 in Table 3).However, uncertainty in the PET dataset can lead to significant uncertainty in the PET elasticity of groundwater recharge.With 3% error added to the PET dataset, ε PET is 0.44 (Case 3 in Table 3) and with 6% error, ε PET is −0.7 in the Nueces basin (Case 4 in Table 3).Both values are different than the value of ε PET , 0.9, in Table 2.This suggests that uncertainty in the PET dataset may significantly impact on estimation of climate elasticity of groundwater recharge.

| SUMMARY AND CON CLUDING REMARK S
This study conducts a comprehensive analysis of the statistical characteristics of precipitation, temperature, and groundwater recharge in the recharge zone of the nine basins of the Edwards BFZA.A dataset containing 125 years of monthly precipitation and average temperature data gridded with PRISM (PRISM Climate Group, 2015) and 86 years of monthly groundwater recharge estimated using the Puente method by the USGS (Puente, 1978) is used for these analyses.The decadal variability in time series of precipitation, temperature, and groundwater recharge on both annual and seasonal scales is examined in terms of a 20-year moving average of variance divided by the variance of the period of record.
F I G U R E 6 Bar plots of (a) precipitation and (b) PET elasticity of annual groundwater recharge using bivariate GLS approach (Guadalupe basin is excluded because no groundwater recharge is estimated for that basin).Error bars represent the 95% confidence interval of elasticity estimated with the GLS2 approach.
Data for monthly precipitation and temperature in the study area are extracted from the datasets of the Parameter-Elevation Regressions on Independent Slopes Model (PRISM), developed by the PRISM Climate Group at Oregon State University.The PRISM is a hybrid statisticalgeographical approach that blends information about topography and point estimates of precipitation to derive gridded fields of climate F I G U R E 1 Location of the study area and the nine basins (inset showing location of study area in USA).

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Plots of (a) mean monthly precipitation, (b) mean monthly temperature, (c) mean monthly potential evapotranspiration (PET), and (d) mean monthly groundwater recharge of the recharge zone of the nine basins from January (1) to December (12) based on historical records of precipitation and temperature (1895-2019) and groundwater recharge (1934-2019).Range of mean monthly precipitation, temperature, PET, and groundwater recharge in each of the 12 months are shown in the Figures S2-S5.
water storage and thus may contribute more steadily to recharge over time.Groundwater recharge variability in the seven basins other than the Medina basin shows an overall increasing trend after 1980, consistent with increases in precipitation and temperature variability.The sharp decrease in annual groundwater variability for the Blanco and Sabinal basins in 2012 might be caused by decline in annual groundwater recharge during the 2011-2014 major drought period in Texas.

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I G U R E 3 Long-term variability of (a) annual precipitation, (b) annual average temperature, and (c) annual groundwater recharge in the nine recharge basins.0.46%/%.Groundwater recharge in the SabMed and the MedCib basins is most sensitive to precipitation compared to the other basins.The median value of ε P among the eight basins is about 2%/%.This suggests that, in general, a 1% change in annual precipitation may lead to likely a 2% change in annual groundwater recharge in the study area.

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I G U R E 4 Plots of relative change in annual groundwater recharge to relative change in annual precipitation in the eight basins, a) Nueces, b) Frio, c) Sabinal, d) SabMed, e) Medina, f) MedCib, g) Cibolo, and h) Blanco.Guadalupe basin is excluded because no groundwater recharge was estimated by USGS.Note the R mean and P mean are mean values of groundwater recharge and precipitation over the period of 1934-2019 in each individual basin.The red line is the trend, and the shaded area represents the 95% confidence interval.

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I G U R E 5 Plots of relative change in annual groundwater recharge to relative change in annual PET in the eight basins, a) Nueces, b) Frio, c) Sabinal, d) SabMed, e) Medina, f) MedCib, g) Cibolo, and h) Blanco.Guadalupe basin is excluded because no groundwater recharge was estimated by USGS.Note the R mean and PET mean are mean values of groundwater recharge and PET over the period of 1934-2019 in each individual basin.The red line is the trend, and the shaded area represents the 95% confidence interval.TA B L E 2 Climate elasticity of groundwater recharge calculated with the bivariate generalized linear regression in the eight basins.
Note that values within [] represent the 95% confidence interval for climate elasticity estimated with GLS2.R 2 is a measure of goodness of fit in the GLS2.The parentheses for the values reported in the literature are the range reported by the authors.
R E N C E SAhiablame, L., A.Y. Sheshukov, V. Rahmani, and D. Moriasi.2017."Annual Baseflow Variations as Influenced by Climate Variability and Agricultural Land Use Change in the Missouri River Basin."Journal of Hydrology 551: 188-202.
Climate elasticity of groundwater recharge calculated with errors in estimated groundwater recharge, precipitation, and PET.Note: Note that Case 1 assumes 3% error only in estimated groundwater recharge; Case 2 assumes 6% error only in estimated groundwater; Case 3 assumes 3% error in precipitation and PET; Case 4 assumes 6% error in precipitation and PET; Case 5 assumes 3% error in precipitation, PET, and estimated groundwater recharge; and Case 6 assumes 6% error in precipitation, PET, and estimated groundwater recharge.
TA B L E 3