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• Published: 24 January 2024

Rapid groundwater decline and some cases of recovery in aquifers globally

• Scott Jasechko   ORCID: orcid.org/0000-0001-6470-7708 1   na1 ,
• Hansjörg Seybold 2   na1 ,
• Debra Perrone   ORCID: orcid.org/0000-0002-4268-8478 3   na1 ,
• Ying Fan   ORCID: orcid.org/0000-0002-0024-7965 4 ,
• Mohammad Shamsudduha   ORCID: orcid.org/0000-0002-9708-7223 5 ,
• Richard G. Taylor   ORCID: orcid.org/0000-0002-9867-8033 6 ,
• Othman Fallatah   ORCID: orcid.org/0000-0001-6189-9767 7 , 8 &
• James W. Kirchner 2 , 9 , 10  

Nature volume  625 ,  pages 715–721 ( 2024 ) Cite this article

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Groundwater resources are vital to ecosystems and livelihoods. Excessive groundwater withdrawals can cause groundwater levels to decline 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , resulting in seawater intrusion 11 , land subsidence 12 , 13 , streamflow depletion 14 , 15 , 16 and wells running dry 17 . However, the global pace and prevalence of local groundwater declines are poorly constrained, because in situ groundwater levels have not been synthesized at the global scale. Here we analyse in situ groundwater-level trends for 170,000 monitoring wells and 1,693 aquifer systems in countries that encompass approximately 75% of global groundwater withdrawals 18 . We show that rapid groundwater-level declines (>0.5 m year −1 ) are widespread in the twenty-first century, especially in dry regions with extensive croplands. Critically, we also show that groundwater-level declines have accelerated over the past four decades in 30% of the world’s regional aquifers. This widespread acceleration in groundwater-level deepening highlights an urgent need for more effective measures to address groundwater depletion. Our analysis also reveals specific cases in which depletion trends have reversed following policy changes, managed aquifer recharge and surface-water diversions, demonstrating the potential for depleted aquifer systems to recover.

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Groundwater is the primary water source for many homes, farms, industries and cities around the globe. Unsustainable groundwater withdrawals and changes in climate can cause groundwater levels to fall 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , making groundwater resources less accessible 17 . Global maps of groundwater storage trends are available 7 from the Gravity Recovery and Climate Experiment (GRACE) satellites, although at a resolution that is too coarse (>150,000 km 2 ; ref.  19 ) to detect local changes and inform local management. Measuring multidecadal groundwater-level declines and managing their consequences—including seawater intrusion 11 , land subsidence 12 , 13 , streamflow depletion 14 , 15 , 16 and wells running dry 17 —requires in situ groundwater-level measurements from networks of monitoring wells. Such monitoring-well networks have been used at local and regional scales to estimate groundwater recharge 20 , 21 , characterize streamflow depletion 14 , evaluate the risk of wells running dry 17 and test whether surface-water diversions 22 , 23 or market and policy interventions 24 have succeeded in slowing groundwater losses. However, in situ groundwater-level observations have rarely been analysed at the global scale because we lack a global compilation of in situ groundwater-level time series.

Here we compile and analyse in situ measurements of groundwater-level trends in about 170,000 monitoring wells. The measurements provide new constraints on the prevalence of rapid and accelerating groundwater-level declines and their correlation with land use and climatic drivers. Furthermore, the measurements highlight individual cases in which groundwater levels have recovered following policy changes 25 and inter-basin water transfers 26 .

Local hotspots of groundwater-level changes

We compiled and quality-controlled groundwater-level time series in monitoring wells from more than 40 countries (see  Methods and Supplementary Notes  1 and 2 ). We calculated twenty-first century trends in depth to groundwater level for about 170,000 monitoring wells with time series that span at least 8 years using Theil–Sen robust regression (Fig. 1 ; analyses based on alternative regression techniques and on different quality-control thresholds yield similar results; see Supplementary Notes  3 , 4 , 5 and 6 ). Positive Theil–Sen slopes indicate deepening groundwater levels (red points in Fig. 1 ). Trends in groundwater levels often differ substantially from well to well, and local hotspots of groundwater decline can be found even in regions in which nearby groundwater levels are stable or rising, and vice versa (Fig. 1 ), highlighting the importance of analysing groundwater-level trends at the scales defined by the boundaries of individual aquifer systems.

Each point represents one monitoring well, coloured to represent the Theil–Sen trend of annual median groundwater levels during the twenty-first century. Blue and red points indicate shallowing and deepening, respectively, of groundwater levels over time, with darker colours indicating faster rates. a , Spatial distributions of groundwater-level trends in globally distributed monitoring wells. b – o , Regional maps illustrating the substantial spatial variability in groundwater-level trends. Supplementary Notes  16 and 17 show monitoring wells and their groundwater-level trends at subcontinental scales (Supplementary Note  16 ) and in 207 individual aquifer systems (Supplementary Note  17 ). Background imagery shown in b – o from https://www.arcgis.com/home/item.html?id=10df2279f9684e4a9f6a7f08febac2a9 .

Source Data

To evaluate aquifer-scale groundwater-level trends, we manually delineated the boundaries of 1,693 aquifer systems—areas underlain by one or more aquifers—using maps and descriptions from 1,236 local and regional studies (see  Methods and Supplementary Note  7 ). We calculated aquifer-scale groundwater-level trends as the median of the Theil–Sen slopes of all monitoring wells located within each aquifer system (Fig. 2 ). Most aquifer-scale groundwater-level trends range from −0.1 to 0.9 m year −1 (5th to 95th percentiles), in which negative values represent shallowing groundwater levels and positive values indicate deepening groundwater levels.

Each polygon represents one aquifer system. Dark grey represents aquifer systems in which groundwater levels have been relatively stable (median Theil–Sen slope between −0.1 and 0.1 m year −1 ). Yellow, orange and red represent aquifer systems in which groundwater levels became deeper (median Theil–Sen slope >0.1 m year −1 ). Blue represents aquifer systems in which groundwater levels became shallower (median Theil–Sen slope of <−0.1 m year −1 ). Darker colours indicate faster rates. Circular points mark locations for which we lack monitoring-well data but groundwater-level trends have been documented in the literature, with colours indicating the average of the minimum and maximum literature values (Supplementary Note  15 ). Statistics describing the spatial variability of groundwater-level trends within individual aquifers are presented in Supplementary Note  23 . Median Theil–Sen slopes for all 1,693 aquifer systems are tabulated in Supplementary Note  24 .

Groundwater levels became deeper over time at rates exceeding 0.1 m year −1 in 36% of the aquifer systems (617 of 1,693) and exceeding 0.5 m year −1 in 12% (210) of them. Aquifer systems that exhibit groundwater-level deepening and are too small to be detected by GRACE satellite observations (for example, southeastern Spain) highlight the value of in situ groundwater-level measurements to complement global-scale insights 5 , 7 , 9 , 19 made possible by the GRACE (see  Methods and Supplementary Note  8 ).

Groundwater levels became shallower over time faster than −0.1 m year −1 in 6% of the aquifer systems (97 of 1,693) and faster than −0.5 m year −1 in only 1% (13) of them. Some groundwater-shallowing trends may be explained by reductions in groundwater withdrawals, land-cover changes, managed aquifer recharge projects (for example, in Arizona’s East Salt River basin 22 ) and inter-basin surface-water transfers (for example, the Wanjiazhai water diversion to China’s Taiyuan basin 26 ).

Accelerating groundwater-level declines

To place twenty-first century groundwater-level declines into context, we compared them with groundwater-level trends during the late twentieth century (1980–2000); this analysis was possible in 542 of the 1,693 delineated aquifer systems (see  Methods and Supplementary Note  9 ).

In 30% of these aquifer systems, groundwater-level declines accelerated, with early twenty-first century groundwater-level declines outpacing those of the late twentieth century (the red points in Fig. 3a ; see the red time series in Fig. 3b and Extended Data Fig. 1 for illustrative examples). These cases of accelerating groundwater-level declines are more than twice as prevalent as one would expect from random fluctuations in the absence of any systematic trends in either time period (12.5%; P -value < 0.001 by the binomial test). Furthermore, among all cases in which groundwater levels declined in both the late twentieth and early twenty-first centuries, declines in the early twenty-first century outpaced those in the late twentieth century much more often than one would expect by chance (163 red points versus 107 orange points in Fig. 3a ; P -value < 0.001 by the sign test). If we exclude cases in which groundwater-level trends changed by less than 0.1 m year −1 between these two periods (that is, considering only points lying outside the grey diagonal band in Fig. 3a ), we find that accelerating declines (red points) outnumber decelerating declines (orange points) by a ratio of 5:2 ( P -value < 0.001 by the sign test). In summary, groundwater-level declines have accelerated in a substantial share of the analysed aquifer systems.

a , Scatter plot of aquifer-scale trends (median Theil–Sen slopes) during 2000–2022 ( x -axis values) and during 1980–2000 ( y -axis values). The colour of each point indicates one of the following categories of trends: (1) groundwater levels became shallower during 1980–2000 and continued to become shallower (purple points); (2) groundwater levels became shallower during 1980–2000 but have since become deeper (yellow points); (3) groundwater levels became deeper during 1980–2000 but have since become shallower (blue points); (4) groundwater levels became deeper during 1980–2000 and continued to become deeper but at a slower rate (that is, decelerated deepening; orange points); and (5) groundwater levels became deeper during 1980–2000 and continued to become deeper at a faster rate (that is, accelerated deepening; red points). The intensity of each colour scales with the absolute value (that is, magnitude) of the difference between the late twentieth and early twenty-first century trends in groundwater level (see legend). b , Examples of groundwater-level time series illustrating each of our five categories (see legend). c – i , Maps of aquifer systems categorized by their late twentieth and early twenty-first century trends in groundwater levels (colours correspond to categories in the legend). For an expanded version of this figure, see Supplementary Note  9 .

To test for a potential statistical relationship between accelerating groundwater-level declines and climate variability, we analysed precipitation rates over the past four decades (Supplementary Note  10 ). We show that most (>80%) of the aquifer systems exhibiting accelerating groundwater-level declines also experienced a decline in precipitation over time (that is, lower average annual precipitation during the early twenty-first century than in the late twentieth century). Declines in precipitation can cause groundwater levels to fall as a result of both indirect impacts (for example, increased groundwater abstractions during droughts) and direct impacts (for example, reduced recharge rates during droughts; see ref.  27 ). Our finding—that early twenty-first century precipitation rates were lower than in the late twentieth century in most aquifer systems exhibiting accelerating groundwater-level declines—highlights a potential link between decadal-scale climate variability and accelerating groundwater-level declines. Accelerating groundwater-level declines, regardless of their potential drivers, are likely to also accelerate the consequences of those declines, including land subsidence 12 , 13 and wells running dry 17 .

Slowing and reversing groundwater-level declines

Many previous studies 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 have highlighted groundwater losses, but the potential for slowing or reversing these losses has received less attention. Our analysis of groundwater levels suggests that long-term groundwater losses are neither universal nor inevitable. Specifically, in half (49%) of the 542 aquifer systems in our analysis, groundwater-level declines have decelerated (that is, slowed; orange in Fig. 3 ; 20%) or reversed (blue in Fig. 3 ; 16%), or groundwater levels have continued to rise (purple in Fig. 3 ; 13%).

In 20% of the aquifer systems, groundwater-level deepening has decelerated, as late twentieth century groundwater declines continued in the early twenty-first century, but at a slower rate (the orange points in Fig. 3a ; see orange time series in Fig. 3b and Extended Data Fig. 2 for illustrative examples). Although these cases are outnumbered by those for which groundwater declines have accelerated, they demonstrate that it is possible to slow, and potentially even reverse, groundwater-level declines. For example, our analysis shows marked deceleration of groundwater-level deepening in the Eastern Saq aquifer of Saudi Arabia, possibly owing partly to policies designed to reduce agricultural water demands 28 (see labelled orange point in Fig. 3a , which corresponds to the orange line in Fig. 3b ).

In 16% of the aquifer systems, groundwater level declines reversed—defined as cases in which groundwater levels declined in the late twentieth century but rose in the early twenty-first century (the blue colours in Fig. 3 ; see blue time series in Fig. 3b and Extended Data Fig. 3 for examples). For example, in the Bangkok basin (Thailand), groundwater levels deepened during the late twentieth century but shallowed in the early twenty-first century (see labelled blue point in Fig. 3a ); this reversal has been attributed 25 to regulatory measures (groundwater pumping fees and licensing of wells). Another example is Iran’s Abbas-e Sharghi basin, in which twentieth century groundwater-level declines were reversed by the diversion of water to the basin from the Kharkeh Dam 29 . In other areas, groundwater deepening has been reversed following the implementation of managed aquifer recharge projects 22 (for example, west of Tucson, Arizona; Extended Data Fig. 3 ). Recharge projects are sometimes only viable where excess surface waters are available, emphasizing the importance of coordinating groundwater and surface-water management 30 . Nevertheless, these examples illustrate that interventions of sufficient scope and scale can reverse declining groundwater trends.

In a further 13% of the aquifer systems, groundwater levels rose in both the late twentieth and the early twenty-first centuries (purple colours in Fig. 3 ; see purple time series in Fig. 3b and Extended Data Fig. 4 for examples). Some of these cases indicate that aquifers that were heavily exploited before 1980 are recovering. Aquifer recovery can potentially ameliorate the consequences of groundwater pumping (for example, land subsidence 31 ). In other cases, however, rising groundwater levels can be problematic. For example, rising groundwaters can lead to flooding of coastal cities 32 , waterlogging of farmlands 33 and salinization of groundwaters and soils 34 . Rising groundwater levels may be driven by reductions in groundwater withdrawals 25 or increases in recharge rates owing to land clearing 35 , 36 , irrigation 33 or managed aquifer recharge 37 . Our aquifer-scale groundwater-level trends can help predict where rising groundwater levels may pose challenges.

Although these examples illustrate that groundwater declines can be slowed or reversed, several caveats must be kept in mind. In general, rates of groundwater-level shallowing are much slower than rates of groundwater-level decline. Of the aquifer systems in Fig. 3 with rising twenty-first century groundwater levels (blue and purple points), only 6% are rising faster than −0.2 m year −1 . By contrast, of the aquifer systems with deepening twenty-first century groundwater levels (yellow, red and orange points in Fig. 3 ), 25% are falling faster than 0.2 m year −1 . Furthermore, across these aquifer systems, the average rate of twenty-first century deepening (0.2 m year −1 ) exceeds the average rate of shallowing (−0.05 m year −1 ) by a factor of four. Thus, rapidly rising groundwater levels are rare, but they demonstrate that aquifer recovery is possible, especially following policy changes 25 , managed aquifer recharge 37 and inter-basin surface water-transfers 26 .

Groundwater declines in cultivated drylands

Many of the aquifer systems with declining twenty-first century groundwater levels (Fig. 2 ) underlie drylands, defined 38 as areas in which average precipitation divided by potential evapotranspiration is less than 0.65. Rapidly deepening groundwater levels (faster than 0.5 m year −1 ) are found in 11%, 24% and 8% of aquifers in climate zones classified 38 as hyper-arid, arid and semi-arid, respectively. Notably, aquifer systems with rapidly deepening groundwater levels are virtually absent (<1%) in humid and dry subhumid climate zones. Our 1,693 aquifer-scale groundwater-level trends exhibit a moderately strong rank correlation with precipitation divided by potential evapotranspiration 39 (Spearman ρ  = −0.40, P -value < 0.001; Supplementary Note  11 and Methods ), implying that groundwater deepening is more common in drier climates (Fig. 4 ). As well as rapid groundwater-level declines, we also find that accelerating groundwater-level declines are more common in drier climates, especially underlying cultivated lands (Supplementary Note  9 ), probably reflecting greater reliance on groundwater for irrigation.

a , The percentage of aquifer systems with rapidly deepening groundwater (median Theil–Sen slope steeper than 0.5 m year −1 ) when categorized by climate conditions and cropland prevalence. Aquifer systems with rapidly deepening groundwater are most common in hyper-arid, arid and semi-arid climate zones (see categories on the x axis) and where a larger proportion of land is under cultivation (see categories on the y axis). b , Scatter plot of aquifer-scale average annual precipitation divided by potential evapotranspiration 39 , and the percentage of land area under cultivation 40 (estimated for the year 2015). The colour of each point represents the twenty-first century aquifer-scale groundwater-level trend (median Theil–Sen slope). Blue and red points indicate shallowing and deepening, respectively, of groundwater, with darker colours indicating faster rates. Background shades represent climate zones classified by annual precipitation divided by potential evapotranspiration (that is, x -axis values). Several aquifer systems are absent from this plot because either no land is under cultivation (incompatible with the log scale of the y axis) or precipitation divided by evapotranspiration values fall outside the shown range of x -axis values. For alternative versions of this figure showing these aquifer systems, see Supplementary Note  11 .

Irrigation is estimated to account for 70% of global groundwater withdrawals 18 . A lack of high-resolution, ground-truthed data quantifying groundwater withdrawals for irrigation precludes statistical tests of their correlation with groundwater-level changes over time. However, using high-resolution global land cover data 40 , we can test for statistical relationships between land-use patterns and groundwater trends (Fig. 4 ). Aquifer systems with rapidly deepening groundwater levels (>0.5 m year −1 ) are relatively common (17%) where more than one-fifth of the land surface is cultivated, but are virtually absent (0.8%) where cultivation accounts for <1% of the land surface. Across the 1,693 aquifer systems, rates of groundwater-level deepening are significantly correlated with the proportion of land under cultivation 40 (Spearman ρ  = 0.17, P -value < 0.001; Fig. 4 ). This statistical relationship becomes stronger when we account for the correlation between cultivation and climatic aridity (partial rank correlation coefficient = 0.32, P -value < 0.001; see Supplementary Note  11 ). Our analyses demonstrate that rapid groundwater declines are most common in cultivated drylands.

Groundwater losses from dryland aquifers pose management challenges. Aquifer recharge is typically slow in drylands 41 , meaning that depleted dryland aquifers will generally take longer to recover than aquifers in wetter climates 42 , except where recharge rates are artificially increased (for example, seepage from unlined canals in the Indus basin 33 ). Moreover, groundwater is often the sole source of perennial drinking water for communities in drylands. As groundwater levels become deeper, shallower wells can run dry 17 , compromising local water access. Even where groundwater levels remain stable, groundwater withdrawals can deplete the flow of nearby streams by reducing natural seepage of groundwater to rivers, or even inducing streamwater leakage into underlying aquifers (see discussion of ‘capture’ by ref.  43 ). Indeed, leakage from surface waters may replenish pumped aquifers and stabilize groundwater levels at the expense of streamflow. The prevalence of rapid and accelerating groundwater declines in cultivated drylands suggests that, even if management strategies are in place, they have often been insufficient—either in concept or in implementation—to slow or reverse groundwater depletion.

Depleting and recovering groundwater resources

Our analysis of groundwater-level measurements demonstrates that: (1) groundwater levels are declining rapidly (>0.5 m year −1 ) in many regions (Fig. 2 ); (2) groundwater declines are accelerating in many aquifer systems around the world (Fig. 3 ); and (3) both rapid and accelerating groundwater declines are particularly evident in aquifers underlying cultivated drylands (Fig. 4 and Supplementary Notes  9 and 11 ). Our analysis also identifies cases in which late twentieth century groundwater declines have been reversed in the early twenty-first century (blue points in Fig. 3 ). However, cases of rapidly rising groundwater levels remain outnumbered by cases of rapidly deepening groundwater levels.

Our results indicate that twenty-first century realities—including climatic trends, hydrogeologic conditions, groundwater withdrawal rates, land uses and management approaches—have resulted in widespread, rapid and accelerating groundwater-level declines. Nevertheless, the compiled in situ observations also capture numerous cases in which declines in groundwater levels have slowed, stopped or reversed following intervention (for example, implementation of regulatory measures 25 ). Although our work represents the most extensive analysis of groundwater-level monitoring records so far, it does not cover the globe (see  Methods section entitled ‘Limitations’). Further, analysed monitoring wells do not represent a randomized sample of global wells and we are only able to analyse groundwater level trends where monitoring data are available. Global maps of groundwater storage changes from GRACE satellite observations 7 suggest that groundwater stores are declining in some regions in which monitoring data are not publicly available and, thus, cannot be evaluated here. GRACE data are also important for characterizing impacts of climate change and variability 9 , 19 , 44 , 45 , 46 and evaluating global hydrologic models 47 . Evaluating such models is important because they are widely used to estimate groundwater depletion (see ref.  6 and Table 3 in ref.  48 ). Our compilation of monitoring-well data could facilitate future efforts to reconcile GRACE-based, model-based and piezometric-based groundwater time series (see refs.  49 , 50 ). Combining these diverse data products—and thus exploiting both the high spatial resolution of monitoring-well networks and the global coverage of GRACE 7 , 9 , 19 and hydrologic models 2 , 3 , 6 , 16 , 48 —may yield new insights into the causes, consequences and spatial patterns of groundwater depletion.

Groundwater depletion can threaten ecosystems and economies. Specifically, groundwater depletion can damage infrastructure through land subsidence 12 , 13 , impair fluvial ecosystems through streamflow depletion 14 , 15 , 16 , jeopardize agricultural productivity 51 and compromise water supplies as wells run dry 17 . Our methodologically consistent analysis of groundwater-level trends across 1,693 globally distributed aquifer systems demonstrates widespread, rapid and accelerating twenty-first century groundwater-level declines, particularly in cultivated drylands.

Our analysis also documents cases for which groundwater declines have slowed or reversed after: (1) the implementation of groundwater policies; (2) the alleviation of groundwater demand by means of surface-water transfers; or (3) the addition of groundwater storage following managed aquifer recharge projects. To address the growing problem of global groundwater depletion, these kinds of success stories would need to be replicated in dozens of aquifer systems with declining groundwater levels. Thus, our analysis illustrates the potential for depleted aquifers to recover, while demonstrating how much work remains to be done to protect groundwater resources. By documenting global hotspots of groundwater-level decline and recovery, this analysis can inform efforts to address rapid and accelerating groundwater depletion.

Delineating global aquifer systems based on literature review of local studies

For each country in our study, we consulted published accounts of local-scale studies 52 , 53 , 54 , 55 , 56 , 57 , 58 , 59 , 60 , 61 , 62 , 63 , 64 , 65 , 66 , 67 , 68 , 69 , 70 , 71 , 72 , 73 , 74 , 75 , 76 , 77 , 78 , 79 , 80 , 81 , 82 , 83 , 84 , 85 , 86 , 87 , 88 , 89 , 90 , 91 , 92 , 93 , 94 , 95 , 96 , 97 , 98 , 99 , 100 , 101 , 102 , 103 , 104 , 105 , 106 , 107 , 108 , 109 , 110 , 111 , 112 , 113 , 114 , 115 , 116 , 117 , 118 , 119 , 120 , 121 , 122 , 123 , 124 , 125 , 126 , 127 , 128 , 129 , 130 , 131 , 132 , 133 , 134 , 135 , 136 , 137 , 138 , 139 , 140 , 141 , 142 , 143 , 144 , 145 , 146 , 147 , 148 , 149 , 150 , 151 , 152 , 153 , 154 , 155 , 156 , 157 , 158 , 159 , 160 , 161 , 162 , 163 , 164 , 165 , 166 , 167 , 168 , 169 , 170 , 171 , 172 , 173 , 174 , 175 , 176 , 177 , 178 , 179 , 180 , 181 , 182 , 183 , 184 , 185 , 186 , 187 , 188 , 189 , 190 , 191 , 192 , 193 , 194 , 195 , 196 , 197 , 198 , 199 , 200 , 201 , 202 , 203 , 204 , 205 , 206 , 207 , 208 , 209 , 210 , 211 , 212 , 213 , 214 , 215 , 216 , 217 , 218 , 219 , 220 , 221 , 222 , 223 , 224 , 225 , 226 , 227 , 228 , 229 , 230 , 231 , 232 , 233 , 234 , 235 , 236 , 237 , 238 , 239 , 240 , 241 , 242 , 243 , 244 , 245 , 246 , 247 , 248 , 249 , 250 , 251 , 252 , 253 , 254 , 255 , 256 , 257 , 258 , 259 , 260 , 261 , 262 , 263 , 264 , 265 , 266 , 267 , 268 , 269 , 270 , 271 , 272 , 273 , 274 , 275 , 276 , 277 , 278 , 279 , 280 , 281 , 282 , 283 , 284 , 285 , 286 , 287 , 288 , 289 , 290 , 291 , 292 , 293 , 294 , 295 , 296 , 297 , 298 , 299 , 300 , 301 , 302 , 303 , 304 , 305 , 306 , 307 , 308 , 309 , 310 , 311 , 312 , 313 , 314 , 315 , 316 , 317 , 318 , 319 , 320 , 321 , 322 , 323 , 324 , 325 , 326 , 327 , 328 , 329 , 330 , 331 , 332 , 333 , 334 , 335 , 336 , 337 , 338 , 339 , 340 , 341 , 342 , 343 , 344 , 345 , 346 , 347 , 348 , 349 , 350 , 351 , 352 , 353 , 354 , 355 , 356 , 357 , 358 , 359 , 360 , 361 , 362 , 363 , 364 , 365 , 366 , 367 , 368 , 369 , 370 , 371 , 372 , 373 , 374 , 375 , 376 , 377 , 378 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, 712 , 713 , 714 , 715 , 716 , 717 , 718 , 719 , 720 , 721 , 722 , 723 , 724 , 725 , 726 , 727 , 728 , 729 , 730 , 731 , 732 , 733 , 734 , 735 , 736 , 737 , 738 , 739 , 740 , 741 , 742 , 743 , 744 , 745 , 746 , 747 , 748 , 749 , 750 , 751 , 752 , 753 , 754 , 755 , 756 , 757 , 758 , 759 , 760 , 761 , 762 , 763 , 764 , 765 , 766 , 767 , 768 , 769 , 770 , 771 , 772 , 773 , 774 , 775 , 776 , 777 , 778 , 779 , 780 , 781 , 782 , 783 , 784 , 785 , 786 , 787 , 788 , 789 , 790 , 791 , 792 , 793 , 794 , 795 , 796 , 797 , 798 , 799 , 800 , 801 , 802 , 803 , 804 , 805 , 806 , 807 , 808 , 809 , 810 , 811 , 812 , 813 , 814 , 815 , 816 , 817 , 818 , 819 , 820 , 821 , 822 , 823 , 824 , 825 , 826 , 827 , 828 , 829 , 830 , 831 , 832 , 833 , 834 , 835 , 836 , 837 , 838 , 839 , 840 , 841 , 842 , 843 , 844 , 845 , 846 , 847 , 848 , 849 , 850 , 851 , 852 , 853 , 854 , 855 , 856 , 857 , 858 , 859 , 860 , 861 , 862 , 863 , 864 , 865 , 866 , 867 , 868 , 869 , 870 , 871 , 872 , 873 , 874 , 875 , 876 , 877 , 878 , 879 , 880 , 881 , 882 , 883 , 884 , 885 , 886 , 887 , 888 , 889 , 890 , 891 , 892 , 893 , 894 , 895 , 896 , 897 , 898 , 899 , 900 , 901 , 902 , 903 , 904 , 905 , 906 , 907 , 908 , 909 , 910 , 911 , 912 , 913 , 914 , 915 , 916 , 917 , 918 , 919 , 920 , 921 , 922 , 923 , 924 , 925 , 926 , 927 , 928 , 929 , 930 , 931 , 932 , 933 , 934 , 935 , 936 , 937 , 938 , 939 , 940 , 941 , 942 , 943 , 944 , 945 , 946 , 947 , 948 , 949 , 950 , 951 , 952 , 953 , 954 , 955 , 956 , 957 , 958 , 959 , 960 , 961 , 962 , 963 , 964 , 965 , 966 , 967 , 968 , 969 , 970 , 971 , 972 , 973 , 974 , 975 , 976 , 977 , 978 , 979 , 980 , 981 , 982 , 983 , 984 , 985 , 986 , 987 , 988 , 989 , 990 , 991 , 992 , 993 , 994 , 995 , 996 , 997 , 998 , 999 , 1000 , 1001 , 1002 , 1003 , 1004 , 1005 , 1006 , 1007 , 1008 , 1009 , 1010 , 1011 , 1012 , 1013 , 1014 , 1015 , 1016 , 1017 , 1018 , 1019 , 1020 , 1021 , 1022 , 1023 , 1024 , 1025 , 1026 , 1027 , 1028 , 1029 , 1030 , 1031 , 1032 , 1033 , 1034 , 1035 , 1036 , 1037 , 1038 , 1039 , 1040 , 1041 , 1042 , 1043 , 1044 , 1045 , 1046 , 1047 , 1048 , 1049 , 1050 , 1051 , 1052 , 1053 , 1054 , 1055 , 1056 , 1057 , 1058 , 1059 , 1060 , 1061 , 1062 , 1063 , 1064 , 1065 , 1066 , 1067 , 1068 , 1069 , 1070 , 1071 , 1072 , 1073 , 1074 , 1075 , 1076 , 1077 , 1078 , 1079 , 1080 , 1081 , 1082 , 1083 , 1084 , 1085 , 1086 , 1087 , 1088 , 1089 , 1090 , 1091 , 1092 , 1093 , 1094 , 1095 , 1096 , 1097 , 1098 , 1099 , 1100 , 1101 , 1102 , 1103 , 1104 , 1105 , 1106 , 1107 , 1108 , 1109 , 1110 , 1111 , 1112 , 1113 , 1114 , 1115 , 1116 , 1117 , 1118 , 1119 , 1120 , 1121 , 1122 , 1123 , 1124 , 1125 , 1126 , 1127 , 1128 , 1129 , 1130 , 1131 , 1132 , 1133 , 1134 , 1135 , 1136 , 1137 , 1138 , 1139 , 1140 , 1141 , 1142 , 1143 , 1144 , 1145 , 1146 , 1147 , 1148 , 1149 , 1150 , 1151 , 1152 , 1153 , 1154 , 1155 , 1156 , 1157 , 1158 , 1159 , 1160 , 1161 , 1162 , 1163 , 1164 , 1165 , 1166 , 1167 , 1168 , 1169 , 1170 , 1171 , 1172 , 1173 , 1174 , 1175 , 1176 , 1177 , 1178 , 1179 , 1180 , 1181 , 1182 , 1183 , 1184 , 1185 , 1186 , 1187 , 1188 , 1189 , 1190 , 1191 , 1192 , 1193 , 1194 , 1195 , 1196 , 1197 , 1198 , 1199 , 1200 , 1201 , 1202 , 1203 , 1204 , 1205 , 1206 , 1207 , 1208 , 1209 , 1210 , 1211 , 1212 , 1213 , 1214 , 1215 , 1216 , 1217 , 1218 , 1219 , 1220 , 1221 , 1222 , 1223 , 1224 , 1225 , 1226 , 1227 , 1228 , 1229 , 1230 , 1231 , 1232 , 1233 , 1234 , 1235 , 1236 , 1237 , 1238 , 1239 , 1240 , 1241 , 1242 , 1243 , 1244 , 1245 , 1246 , 1247 , 1248 , 1249 , 1250 , 1251 , 1252 , 1253 , 1254 , 1255 , 1256 , 1257 , 1258 , 1259 , 1260 , 1261 , 1262 , 1263 , 1264 , 1265 , 1266 , 1267 , 1268 , 1269 , 1270 , 1271 , 1272 , 1273 , 1274 , 1275 , 1276 , 1277 , 1278 , 1279 , 1280 , 1281 , 1282 , 1283 , 1284 , 1285 , 1286 , 1287 , 1288 (Supplementary Note  7 ) to delineate 1,693 study areas, each underlain by one or more aquifers and/or low-permeability geologic formations that are, collectively, referred to as an ‘aquifer system’. Each aquifer system was delineated by consulting maps and reading descriptions within local-scale reports. Specific steps applied to delineate the boundaries of each aquifer system are detailed in Supplementary Note  7 .

Downloading groundwater-level data

Our study focuses on more than 40 countries for which we compiled monitoring-well data. We analysed groundwater-level time series derived from numerous data repositories (dataset-specific details are available in Supplementary Note  1 ; some of these datasets are described in refs.  1289 , 1290 , 1291 , 1292 , 1293 , 1294 , 1295 , 1296 , 1297 ). The compiled groundwater-level databases span different time intervals and have different measurement frequencies (see heat map plot and global maps showing monitoring-well time series durations and measurement frequencies in Supplementary Note  12 ).

Quality controlling groundwater-level time series

We completed five pre-processing steps before analysing groundwater-level data. First, we identified replicate groundwater-level measurements, defined as cases in which an identical measurement date and an identical groundwater-level measurement were reported from the same monitoring well; in these cases, we retain only one of these replicates. Second, we identified cases in which several groundwater-level measurements from the same monitoring well reported identical measurement dates. In these cases, we calculated the median among all groundwater-level measurements sharing the same measurement date and the adjacent points in the time series (that is, the median of the group of measurements with identical dates and the measurements immediately preceding and following the same-date measurements); we then kept only the single water-level measurement whose value was closest to this calculated median (Supplementary Note  2 ). Third, we excluded extreme values of depth to groundwater (that is, >1,000 m and <−1,000 m) and implausibly high groundwater elevations (that is, >8,000 m above sea level). Fourth, we excluded groundwater-level measurements with values of ‘999’, ‘−9,999’ or ‘0’, because some databases used these values as a code for missing measurements (see figures in Supplementary Note  2 ). Fifth, we excluded outlier values detected by a machine-learning algorithm 1298 (based on an additive regression model 1299 ; for details, see Supplementary Note  2.1 ). This algorithm was applied to each monitoring well with more than 15 groundwater-level measurements, yielding a prediction for each time step and its 99% confidence interval. We defined points to be outliers and excluded them if they fell outside the range defined by the predicted groundwater level ±0.75 times this confidence interval. If a large number of measurements within a monitoring well’s time series were classified as outliers, we excluded the entire time series from our analysis (in which a ‘large number of measurements’ is defined as cases for which there were at least five outliers identified by the machine-learning algorithm and for which these outliers comprise >1% of all measurements in the time series; for visualization, see schematics in Supplementary Note  2 ). Among the approximately 170,000 monitoring wells presented in Fig. 1 , only about 12% had one or more outlier points removed by means of this machine-learning approach, highlighting that this machine-learning approach affected only a small proportion of consulted monitoring wells. Furthermore, a comparison of aquifer-scale trends in depth to groundwater with versus without the use of a machine-learning-based outlier-exclusion procedure suggests that our machine-learning approach had no substantial influence on our findings (see Supplementary Note  13 ).

Flagging groundwater-level measurements based on rapid increases or decreases

After excluding potential outliers (through the steps outlined in the previous paragraph), we calculated each monitoring well’s annual median groundwater levels for each calendar year with at least one measurement. We then visually inspected plots of annual median groundwater levels over time. On visual inspection, we noted that a small number of monitoring wells show ‘spikes’ in their annual groundwater-level time series, in which a ‘spike’ is defined as a high-magnitude (absolute value > 20 m year −1 ) groundwater-level change followed directly by another high-magnitude groundwater-level change in the opposite direction (for example, a high-magnitude groundwater-level deepening trend between two adjacent points in the time series, directly followed by a high-magnitude groundwater-level shallowing trend between two adjacent points). We flagged these data points as potentially suspect. The first or last point in each time series was also flagged if it differed by more than 20 m year −1 from the second or next-to-last point. We compared groundwater-level trends with and without these flagged points and observed only trivial differences (Supplementary Note  5 : ‘Similar aquifer-scale trends obtained with and without flagged measurements’). The results presented in the main text (for example, Fig. 1 ) derive from annual median groundwater-level time series that exclude the flagged measurements.

Statistical analyses of twenty-first century groundwater-level trends (Figs. 1 and 2 )

To evaluate groundwater-level trends since the year 2000, we excluded all previous measurements. Next, we excluded all monitoring wells for which the earliest and most recent annual medians were separated by fewer than 8 years. We calculated trends in annual median groundwater levels for all monitoring wells that met these minimum criteria for analysis (for a similar method, see ref.  1288 ).

Some data sources report groundwater levels as elevations (metres above sea level) and others report them as depth to groundwater (metres below the land surface, or below the top of the well). In cases in which both were reported, we used the depth to groundwater data. If groundwater levels were only reported as elevations, we reversed the signs of the calculated trends, to obtain trends in depth to groundwater.

Our results in the main text are based on Theil–Sen regression slopes 1300 , 1301 but we also applied several different regression techniques, including ordinary least squares, iteratively reweighted least squares 1302 , 1303 , 1304 and RANSAC (or random sample consensus) 1305 , which yielded comparable results (Supplementary Note  3 ; for non-parametric regression techniques, see Supplementary Note  4 and ref.  1306 ). We present our results as trends in depth to groundwater, meaning that positive slopes represent groundwater levels becoming deeper over time. We calculated an aquifer-scale groundwater-level trend for each aquifer system by taking the median of the Theil–Sen slopes of all monitoring wells within its boundaries (Fig. 2 ).

Comparing groundwater-level trends between the late twentieth and early twenty-first centuries (Fig. 3 )

To contextualize twenty-first century trends in depth to groundwater, we identified monitoring wells with sufficient data during two periods: the late twentieth century (1980–2000) and the early twenty-first century (2000–2022). Here well time series are ‘sufficient’ if their earliest and latest annual medians are separated by at least 8 years within a given time interval (that is, 1980–2000 or 2000–2022). There are 45,911 monitoring wells in the compiled dataset with sufficient groundwater-level data for trend analyses during both periods. For these monitoring wells, we calculated Theil–Sen trends in depth to groundwater for the late twentieth century. Next, we grouped monitoring wells located within the same aquifer system and calculated aquifer-scale trends for the late twentieth century (medians of the Theil–Sen slopes for all wells in each system; that is, y -axis values presented in Fig. 3a ). Only aquifer systems with at least five monitoring wells for both time periods (1980–2000 and 2000–2022) satisfying the aforementioned requirements were used to compare late twentieth century and early twenty-first century trends in depth to groundwater. Last, we assigned each aquifer system to one of five categories based on its late twentieth century and early twenty-first century trends in depth to groundwater: (1) groundwater levels became shallower during 1980–2000 and continued to become shallower (purple points in Fig. 3a ); (2) groundwater levels became shallower during 1980–2000 but have since become deeper (yellow points in Fig. 3a ); (3) groundwater levels became deeper during 1980–2000 but have since become shallower (blue points in Fig. 3a ); (4) groundwater levels became deeper during 1980–2000 and continued to become deeper but at a slower rate (that is, decelerated deepening; orange circles in Fig. 3a ); and (5) groundwater levels became deeper during 1980–2000 and continued to become deeper at a faster rate (that is, accelerated deepening; red circles in Fig. 3a ). Further details are available in Supplementary Note  9 .

Geospatial analysis of potential explanatory variables (Fig. 4 )

To test for statistical relationships between the spatial distributions of environmental conditions and groundwater-level trends, we downloaded two geospatial datasets: (1) long-term mean annual precipitation divided by potential evapotranspiration (the ‘CGIAR-CSI Global-Aridity and Global-PET Database’; ref.  39 ) and (2) the proportion of land area under cultivation (estimated for the year 2015; ref.  40 ). Next, we averaged each of these geospatial datasets over each of the 1,693 aquifer systems (Fig. 4 ). We calculated rank correlations between twenty-first century aquifer-scale groundwater-level trends and both of the potential explanatory variables (namely, (1) long-term mean annual precipitation divided by potential evapotranspiration and (2) the proportion of land area under cultivation). We also used multiple regression on the rank transforms of these explanatory variables to account for their covariation (Supplementary Note  11 ).

Limitations

Our analyses are based on the best available measurements but nonetheless have limitations. Here we detail some of these limitations and evaluate how some may affect our main conclusions.

Although we have used several steps, as outlined above, to detect and remove outliers, we cannot independently verify the accuracy of all groundwater-level time series. Nevertheless, our analysis is based on several layers of robust estimation (for example, Theil–Sen regression on annual medians), minimizing its sensitivity to unreliable data.

Groundwater-level data from individual monitoring wells span different time intervals and have different measurement frequencies, as detailed in Supplementary Note  12 . Furthermore, about 41% of the analysed monitoring wells have discontinuous time series of annual groundwater levels (for which ‘discontinuous’ time series are defined as those lacking a groundwater-level measurement for at least one of the calendar years that lie between the earliest and most recent twenty-first century groundwater-level measurements; for an example of a discontinuity in an annual groundwater-level time series, see Supplementary Fig. 3c ).

We could not obtain groundwater-level data for many countries around the globe and our conclusions are only directly applicable where we have data. GRACE satellite data 1307 , 1308 , 1309 , 1310 , 1311 suggest that groundwater storage has declined in some of the areas in which we lack monitoring-well data (Supplementary Note  8 ). Further, simulation results from a global model suggest that substantial groundwater depletion may have occurred in some of the countries in which we lack monitoring-well data, so groundwater-level deepening may be even more widespread than our results indicate (refs.  16 , 1312 ; Supplementary Note  14 ). We reviewed published and grey literature 20 , 427 , 802 , 1282 , 1313 , 1314 , 1315 , 1316 , 1317 , 1318 , 1319 , 1320 , 1321 , 1322 , 1323 , 1324 , 1325 , 1326 , 1327 , 1328 , 1329 , 1330 , 1331 , 1332 , 1333 , 1334 , 1335 , 1336 , 1337 , 1338 , 1339 , 1340 , 1341 , 1342 , 1343 , 1344 , 1345 , 1346 , 1347 , 1348 , 1349 , 1350 , 1351 , 1352 , 1353 , 1354 , 1355 , 1356 to obtain groundwater-level trends for some of the countries in which we lack monitoring-well data (that is, point data in Fig. 2 ; details available in Supplementary Note  15 ).

We highlight that monitoring wells are not distributed evenly across each aquifer system. Consequently, some locations within aquifer systems are not captured by compiled monitoring-well data (see discussion of Dhaka (Bangladesh) in Supplementary Note  15 ). The aquifer-scale trends that we present in the main text (Figs. 2 – 4 ) do not provide insights into the spatial patterns of groundwater-level trends within individual aquifer systems. The high variability in monitoring-well densities within aquifer systems, as well as the substantial variability in groundwater-level trends even among co-located monitoring wells, are presented in a suite of maps for individual aquifer systems in Supplementary Notes  16 and 17 . Specifically, our analysis demonstrates that groundwater-level trends can vary greatly among wells within individual aquifer systems (Fig. 1 and Supplementary Notes  16 and 17 ), implying that local-scale groundwater-level declines may be even more widespread than our Fig. 2 suggests (Supplementary Note  18 ). Some of the variability in groundwater-level trends among co-located wells may be partly explained by differences in the depths of nearby monitoring wells, as shallow and deep aquifers can have different groundwater-level trends (see Supplementary Note  19 ).

We stress that groundwater-level trends may differ between deeper and shallower wells (for example, ref.  1357 ) owing to, for example, differences in the depths of nearby wells used to extract groundwater and differences in storage coefficients between unconfined and confined aquifers (see, for example, refs.  1358 , 1359 ). Steep groundwater-level trends—both upward and downward—are more common in deeper wells than in shallower wells, possibly due in part to the greater prevalence of confined conditions at deeper depths (discussion and analyses available in Supplementary Note  19 ). 2D geologic data are available at the global scale 1360 , but an accurate high-resolution 3D hydrogeologic dataset remains unavailable for the globe, meaning that key hydrogeologic conditions (for example, whether the monitoring well captures unconfined versus confined conditions) cannot be ascribed for deep versus shallow wells at the global scale.

We highlight that our approach to delineating boundaries for individual aquifer systems—although based on local-scale studies—potentially introduces inconsistencies, because local norms for delineating aquifer-system boundaries may differ. Further, some (16%) of the 170,000 monitoring wells fall outside the boundaries of the aquifer systems delineated here and, therefore, are excluded from our aquifer-scale statistical analyses. We present groundwater-level trends for monitoring wells both within and outside aquifer-system boundaries in a series of regional-scale maps (Supplementary Note  16 ).

It is possible that some of monitoring-well-based time series may be truncated where the monitoring well itself has run dry (see ref.  1361 ), possibly excluding monitoring wells located in areas experiencing rapid groundwater depletion. We analysed monitoring-well depths and depth to groundwater data for 72,000 wells and conclude that it is possible that a small proportion of the groundwater-level time series was truncated owing to well desiccation (see Supplementary Note  20 ). Thus, rapid and accelerating twenty-first century groundwater-level deepening may be even more prevalent than our analysis indicates.

Our main-text results are based on annual median groundwater levels. However, we acknowledge that trends in depth to groundwater can differ when based on measurements made during specific seasons (for example, long-term trends in pre-monsoon depth to groundwater can differ from long-term trends in post-monsoon depth to groundwater; see ref.  1362 ). We highlight that trends in season-specific groundwater levels may differ from trends in annual median groundwater levels (as presented in Fig. 1 ), especially where intra-annual groundwater-level variability is changing over time (for example, time series from the Bengal basin in Supplementary Note  21 ; see also the time series presented in refs.  21 , 1363 , 1364 ).

The compiled groundwater-level time series do not allow us to infer trends over longer (for example, centennial-scale) time intervals. In some areas, substantial groundwater-level changes took place long before the four decades that we focus on here. For example, there is evidence 1365 , 1366 that substantial accumulation occurred during the twentieth century in parts of South Asia and that groundwater levels were much deeper at the start of the twentieth century than they are today (see, specifically, Fig. 3b in ref.  1365 ). Some aquifer systems in our dataset, for example, may have been heavily depleted during the mid-twentieth century, but have exhibited relatively stable groundwater levels (or even shallowing groundwater-level trends) during the twenty-first century. Given the potential for such cases, we make no claim that stable twenty-first century groundwater levels necessarily imply a lack of previous or continuing disturbance.

We do not make claims about aquifer-specific drivers behind rapid and accelerating groundwater declines (although we do make note of case studies in the literature that have identified important drivers; for example, ref.  25 ). We acknowledge that groundwater abstractions can perturb flow systems and, in many cases, deplete aquifers. Many of the aquifer systems exhibiting rapid groundwater-level declines are being accessed by wells, as evidenced by recorded well-completion events throughout the early twenty-first century (Supplementary Note  22 ; data described in refs.  17 , 1367 , 1368 , 1369 ) and by regional-scale research 108 , 1370 , 1371 . Further, we acknowledge that climate variability and change can have both direct impacts on groundwater levels (such as through changes in groundwater recharge owing to, for example, changes in temporal variability in precipitation) and also indirect impacts on groundwater levels (for example, through changes in groundwater demand in response to climate variability, such as increased groundwater withdrawals during drier time intervals; see ref.  27 ). Available precipitation data 1372 , 1373 suggest that most of the aquifer systems characterized as exhibiting accelerating groundwater-level declines (that is, red points in Fig. 3 ) are situated in areas in which early twenty-first century annual precipitation rates were lower than late twentieth century annual precipitation rates (Supplementary Note  10 ), highlighting that, at a minimum, we cannot rule out an influence of climate variability (direct or indirect) on groundwater-level changes over time.

Data availability

Annual groundwater-level data are available for download in all cases for which we have received permission from a database manager to post data (data are available from Zenodo ( https://doi.org/10.5281/zenodo.10003697 ) and CUAHSI HydroShare ( https://www.hydroshare.org/resource/da946dee3ada4a67860d057134916553/ )); these datasets include groundwater-level data for: Afghanistan 1289 , Austria, Belgium, Brazil, Bulgaria, Canada (Alberta, British Columbia, Manitoba, Northwest Territories, Ontario, Prince Edward Island, Saskatchewan, Yukon), China 1290 , Croatia, Czech Republic, Denmark, France 1291 , Germany, Guam, Ireland, Israel, Italy, Latvia, Lithuania, New Zealand, Norway, Paraguay, Poland, Slovenia, Sweden, Switzerland and the USA (Groundwater Ambient Monitoring and Assessment Program, U.S. Geological Survey’s (USGS) National Water Information System and the Texas Water Development Board). The databases for which we have received written permission to post annual groundwater-level data encompass 59% of annual groundwater-level data analysed here (specifically, we received permission to post 66% ( n  = 4,170,802 of n  = 6,314,793) of all annual ‘depth to groundwater’ data and 18% ( n  = 190,879 of n  = 1,049,502) of all ‘groundwater elevation’ data). These datasets are specified in Supplementary Table 1 (see column entitled ‘Written permission received to post annual groundwater-level data’). Source data for each of the main-text figures are available here. Supplementary tables associated with this work are available at https://doi.org/10.5281/zenodo.10003697 . Geospatial data for the 1,693 aquifer systems studied here are available from CUAHSI HydroShare ( https://www.hydroshare.org/resource/73834f47b8b5459a8db4c999e6e3fef6/ ) and Zenodo ( https://doi.org/10.5281/zenodo.10003697 ).  Source data are provided with this paper.

Code availability

Analyses presented here do not depend on specific code; the approach can be reproduced following the procedures described in the Methods section.

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CONAGUA. Actualización de la disponibilidad media anual de agua en el acuífero Guadalupe Garzarón (3212), estado de Zacatecas. https://sigagis.conagua.gob.mx/gas1/Edos_Acuiferos_18/zacatecas/DR_3220.pdf (2020).

CONAGUA. Actualización de la disponibilidad media anual de agua en el acuífero Hidalgo (3202), estado de Zacatecas. https://www.gob.mx/cms/uploads/attachment/file/104507/DR_3202.pdf (2015).

CONAGUA. Actualización de la disponibilidad media anual de agua en el acuífero Huatulco (2011), estado de Oaxaca. https://sigagis.conagua.gob.mx/gas1/Edos_Acuiferos_18/oaxaca/DR_2011.pdf (2020).

CONAGUA. Actualización de la disponibilidad media anual de agua en el acuífero La Blanca (3228), estado de Zacatecas. https://www.gob.mx/cms/uploads/attachment/file/104536/DR_3228.pdf (2015).

CONAGUA. Actualización de la disponibilidad media anual de agua en el acuífero Lampazos Villaldama (1901), estado de Nuevo León. https://sigagis.conagua.gob.mx/gas1/Edos_Acuiferos_18/nleon/DR_1901.pdf (2020).

CONAGUA. Actualización de la disponibilidad media anual de agua en el acuífero Libres-Oriental (2102), estado de Puebla. https://sigagis.conagua.gob.mx/gas1/Edos_Acuiferos_18/puebla/DR_2102.pdf (2020).

CONAGUA. Actualización de la disponibilidad media anual de agua en el acuífero Loreta (3229), estado de Zacatecas. https://sigagis.conagua.gob.mx/gas1/Edos_Acuiferos_18/zacatecas/DR_3229.pdf (2020).

CONAGUA. Actualización de la disponibilidad media anual de agua en el acuífero Méndez San Fernando (2802), estado de Tamaulipas. https://sigagis.conagua.gob.mx/gas1/Edos_Acuiferos_18/tamaulipas/DR_2802.pdf (2020).

CONAGUA. Actualización de la disponibilidad media anual de agua en el acuífero Navidad-Potosí-Raíces (1916), estado de Nuevo León. https://www.gob.mx/cms/uploads/attachment/file/103175/DR_1916.pdf (2015).

CONAGUA. Actualización de la disponibilidad media anual de agua en el acuífero Ojocaliente (3212), estado de Zacatecas. https://sigagis.conagua.gob.mx/gas1/Edos_Acuiferos_18/zacatecas/DR_3212.pdf (2020).

CONAGUA. Actualización de la disponibilidad media anual de agua en el acuífero Perote-Zalayeta (3004), estado de Veracruz. https://sigagis.conagua.gob.mx/gas1/Edos_Acuiferos_18/veracruz/DR_3004.pdf (2020).

CONAGUA. Actualización de la disponibilidad media anual de agua en el acuífero Pino Suárez (3233), estado de Zacatecas. https://sigagis.conagua.gob.mx/gas1/Edos_Acuiferos_18/zacatecas/DR_3233.pdf (2020).

CONAGUA. Actualización de la disponibilidad media anual de agua en el acuífero Poza Rica (3001), estado de Veracruz. https://sigagis.conagua.gob.mx/gas1/Edos_Acuiferos_18/veracruz/DR_3001.pdf (2020).

CONAGUA. Actualización de la disponibilidad media anual de agua en el acuífero Puerto Madero (3224), estado de Zacatecas. https://sigagis.conagua.gob.mx/gas1/Edos_Acuiferos_18/zacatecas/DR_3224.pdf (2020).

CONAGUA. Actualización de la disponibilidad media anual de agua en el acuífero Río Cañas (2513), estado de Sinaloa. https://sigagis.conagua.gob.mx/gas1/Edos_Acuiferos_18/sinaloa/DR_2513.pdf (2020).

CONAGUA. Actualización de la disponibilidad media anual de agua en el acuífero Río Presidio (2509), estado de Sinaloa. https://sigagis.conagua.gob.mx/gas1/Edos_Acuiferos_18/sinaloa/DR_2509.pdf (2020).

CONAGUA. Actualización de la disponibilidad media anual de agua en el acuífero Río Sinaloa (2502), estado de Sinaloa. https://sigagis.conagua.gob.mx/gas1/Edos_Acuiferos_18/sinaloa/DR_2502.pdf (2020).

CONAGUA. Actualización de la disponibilidad media anual de agua en el acuífero Sabinas (3201), estado de Zacatecas. https://sigagis.conagua.gob.mx/gas1/Edos_Acuiferos_18/zacatecas/DR_3201.pdf (2020).

CONAGUA. Actualización de la disponibilidad media anual de agua en el acuífero Sain Alto (3216), estado de Zacatecas. https://sigagis.conagua.gob.mx/gas1/Edos_Acuiferos_18/zacatecas/DR_3216.pdf (2020).

CONAGUA. Actualización de la disponibilidad media anual de agua en el acuífero Sabinas-Parás (1902), estado de Nuevo León. https://sigagis.conagua.gob.mx/gas1/Edos_Acuiferos_18/nleon/DR_1902.pdf (2020).

CONAGUA. Actualización de la disponibilidad media anual de agua en el acuífero San Felipe-Punta Estrella (0222), estado de Baja California. https://www.gob.mx/cms/uploads/attachment/file/103420/DR_0222.pdf (2015).

CONAGUA. Actualización de la disponibilidad media anual de agua en el acuífero San José de Guaymas (2636), estado de Sonora. https://sigagis.conagua.gob.mx/gas1/Edos_Acuiferos_18/sonora/DR_2636.pdf (2020).

CONAGUA. Actualización de la disponibilidad media anual de agua en el acuífero Valle de Canatlán (1002), estado de Durango. https://sigagis.conagua.gob.mx/gas1/Edos_Acuiferos_18/durango/DR_1002.pdf (2020).

CONAGUA. Actualización de la disponibilidad media anual de agua en el acuífero Valle de Escuinapa (2511), estado de Sinaloa. https://sigagis.conagua.gob.mx/gas1/Edos_Acuiferos_18/sinaloa/DR_2511.pdf (2020).

CONAGUA. Actualización de la disponibilidad media anual de agua en el acuífero Vanegas-Catorce (2401), estado de San Luis Potosi. https://sigagis.conagua.gob.mx/gas1/Edos_Acuiferos_18/sanluispotosi/DR_2401.pdf (2020).

CONAGUA. Actualización de la disponibilidad media anual de agua en el acuífero Vicente Guerrero-Poanas (1004), estado de Durango. https://sigagis.conagua.gob.mx/gas1/Edos_Acuiferos_18/durango/DR_1004.pdf (2020).

CONAGUA. Actualización de la disponibilidad media anual de agua en el acuífero Villa de Arriaga (2406), estado de San Luis Potosi. https://sigagis.conagua.gob.mx/gas1/Edos_Acuiferos_18/sanluispotosi/DR_2406.pdf (2020).

CONAGUA. Actualización de la disponibilidad media anual de agua en el acuífero Villa García (3213), estado de Zacatecas. https://sigagis.conagua.gob.mx/gas1/Edos_Acuiferos_18/zacatecas/DR_3213.pdf (2020).

CONAGUA. Actualización de la disponibilidad media anual de agua en el acuifero Orizaba-Córdoba (3007), estado de Veracruz. https://www.gob.mx/cms/uploads/attachment/file/104452/DR_3007.pdf (2015).

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Acknowledgements

We gratefully acknowledge the contributions from individuals in dozens of organizations who are responsible for the generation of the primary datasets used in this study (see Supplementary Table 1 ). This material is based on work supported by the National Science Foundation under grant nos. EAR-2048227 and EAR-2234213. This research was supported by funding from the Zegar Family Foundation. This material is based on work supported by the U.S. Geological Survey (USGS) through the California Institute for Water Resources (CIWR) under grant/cooperative agreement no. G21AP10611-00. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the opinions or policies of the USGS/CIWR. Mention of trade names or commercial products does not constitute their endorsement by the USGS/CIWR. R.G.T. acknowledges the support of a fellowship (ref. 7040464) from the Canadian Institute for Advanced Research under the Earth 4D programme. S.J. acknowledges the Jack and Laura Dangermond Preserve ( https://doi.org/10.25497/D7159W ), the Point Conception Institute and the Nature Conservancy for their support of this research.

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Bren School of Environmental Science & Management, University of California, Santa Barbara, Santa Barbara, CA, USA

Scott Jasechko

Department of Environmental Systems Sciences, ETH Zürich, Zürich, Switzerland

Hansjörg Seybold & James W. Kirchner

Environmental Studies Program, University of California, Santa Barbara, Santa Barbara, CA, USA

Debra Perrone

Department of Earth and Planetary Sciences, Rutgers University, New Brunswick, NJ, USA

Institute for Risk and Disaster Reduction, University College London, London, UK

Mohammad Shamsudduha

Department of Geography, University College London, London, UK

Richard G. Taylor

Department of Nuclear Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah, Saudi Arabia

Othman Fallatah

Center for Training and Radiation Protection, Faculty of Engineering, King Abdulaziz University, Jeddah, Saudi Arabia

Swiss Federal Research Institute WSL, Birmensdorf, Switzerland

James W. Kirchner

Department of Earth and Planetary Science, University of California, Berkeley, Berkeley, CA, USA

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S.J., D.P., M.S. and R.G.T. conceived the idea to analyse global piezometric records and S.J., H.S., D.P., Y.F., M.S., R.G.T. and J.W.K. co-developed the approach to analyse these records. S.J., H.S. and D.P. compiled groundwater-level data. M.S. compiled GRACE satellite data. O.F. accessed Saudi Arabian groundwater-level data. S.J. and H.S. completed geospatial and statistical analyses. S.J. delineated aquifer-system boundaries and wrote the first draft of the manuscript. S.J., H.S., D.P., Y.F., M.S., R.G.T. and J.W.K. contributed to writing and editing the manuscript.

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Extended data figures and tables

Extended data fig. 1 illustrative examples of individual monitoring wells that record cases for which groundwater levels declined during late twentieth century and continued to decline at a faster rate in the early twenty-first century (that is, accelerated deepening)..

a , Global map depicting the locations of the six monitoring wells (that is, each point represents one monitoring well). The aquifer system that each monitoring well lies in is labelled next to each point. b – g , Measured groundwater-level variations over time for individual monitoring wells. Each panel presents groundwater-level data for a single monitoring well.

Extended Data Fig. 2 Illustrative examples of individual monitoring wells that record cases for which groundwater levels declined during late twentieth century and continued to decline but at a slower rate in the early twenty-first century (that is, decelerated deepening).

Extended data fig. 3 illustrative examples of individual monitoring wells that record cases for which groundwater levels declined during late twentieth century but rose during the early twenty-first century (that is, cases of groundwater level recovery)., extended data fig. 4 illustrative examples of individual monitoring wells that record cases for which groundwater levels rose during late twentieth century, and continued to rise during the early twenty-first century., supplementary information, supplementary information, peer review file, source data, source data fig. 1–4, rights and permissions.

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Jasechko, S., Seybold, H., Perrone, D. et al. Rapid groundwater decline and some cases of recovery in aquifers globally. Nature 625 , 715–721 (2024). https://doi.org/10.1038/s41586-023-06879-8

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Aquifer Characterization and Groundwater Potential Evaluation in Sedimentary Rock Formation

M. A. M. Ashraf 1 , R. Yusoh 2 , M. A. Sazalil 1 and M. H. Z. Abidin 3

Published under licence by IOP Publishing Ltd Journal of Physics: Conference Series , Volume 995 , International Seminar on Mathematics and Physics in Sciences and Technology 2017 (ISMAP 2017) 28–29 October 2017, Hotel Katerina, Malaysia Citation M. A. M. Ashraf et al 2018 J. Phys.: Conf. Ser. 995 012106 DOI 10.1088/1742-6596/995/1/012106

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1 School of Civil Engineering, Engineering Campus, Universiti Sains Malaysia, 14300, Penang, Malaysia

2 School of Physics, Universiti Sains Malaysia, 11800, Penang, Malaysia

3 Faculty of Civil and Environmental Engineering, Universiti Tun Hussein Onn, Malaysia, 86400 Batu Pahat, Johor, Malaysia

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This study was conducted to characterize the aquifer and evaluate the ground water potential in the formation of sedimentary rocks. Electrical resistivity and drilling methods were used to develop subsurface soil profile for determining suitable location for tube well construction. The electrical resistivity method was used to infer the subsurface soil layer by use of three types of arrays, namely, the pole–dipole, Wenner, and Schlumberger arrays. The surveys were conducted using ABEM Terrameter LS System, and the results were analyzed using 2D resistivity inversion program (RES2DINV) software. The survey alignments were performed with maximum electrode spreads of 400 and 800 m by employing two different resistivity survey lines at the targeted zone. The images were presented in the form of 2D resistivity profiles to provide a clear view of the distribution of interbedded sandstone, siltstone, and shale as well as the potential groundwater zones. The potential groundwater zones identified from the resistivity results were confirmed using pumping, step drawdown, and recovery tests. The combination among the three arrays and the correlation between the well log and pumping test are reliable and successful in identifying potential favorable zones for obtaining groundwater in the study area.

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Groundwater potential modelling and aquifer zonation of a typical basement complex terrain: a case study

• Published: 29 April 2024

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• Ayodeji K Ogundana 1 &
• Philips Omowumi Falae   ORCID: orcid.org/0000-0001-9407-1229 1  

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Geophysical exploration utilizing Vertical Electrical Resistivity (VES) techniques was employed to analyze aquifer characteristics and their impact on groundwater potential and vulnerability in the study area. The primary objective was to investigate the nature and groundwater-yielding potential of the area under scrutiny, comprehending the roles played by various aquifer parameters and their influence on the groundwater potential and effective characterization of hydrogeological units. To achieve the defined study objective, the electrical resistivity method was applied, employing Schlumberger electrode arrays with a maximum electrode separation (AB/2) of 50 m across 30 distinct locations for data acquisition. The acquired geoelectrical sections were subsequently utilized to generate contour maps for the aquifer parameters. The comparison of the diverse contour maps, depicting variations in hydrogeological parameters in multiple ways, proved to be insightful. The findings revealed that the overall trend of groundwater potential within the selected area is low, as indicated by Aquifer resistivity (17–678 Ωm), hydraulic conductivity 0.004–0.047 m/s), transmissivity (0.003–1.130 m 2 /day), and porosity (− 9.71 to 11.73). The groundwater potential Index map produce shows that the area is predominately made up of medium to low groundwater potential. About 56% of the area under investigation falls within the medium groundwater potential, followed by low (32%), High (10%), and very low (2%). The GWPI map created for the area can be instrumental in designing appropriate groundwater exploration and management strategies within the region, serving as a roadmap for the further expansion of research efforts.

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Ogundana, A.K., Falae, P.O. Groundwater potential modelling and aquifer zonation of a typical basement complex terrain: a case study. Environ Dev Sustain (2024). https://doi.org/10.1007/s10668-024-04940-8

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ORIGINAL RESEARCH article

Reinforcement learning for watershed and aquifer management: a nationwide view in the country of mexico with emphasis in baja california sur.

• 1 Centro de Investigación Científica y de Educación Superior de Ensenada-Unidad La Paz, La Paz, Mexico
• 2 CONAHCYT-Centro de Investigacion Cientifica y de Educacion Superior de Ensenada-Unidad La Paz, La Paz, Mexico
• 3 Universidad Autónoma de Baja California Sur, Posgrado en Ciencias Marinas y Costeras, La Paz, Mexico

Reinforcement Learning (RL) is a method that teaches agents to make informed decisions in diverse environments through trial and error, aiming to maximize a reward function and discover the optimal Q-learning function for decision-making. In this study, we apply RL to a rule-based water management simulation, utilizing a deep learning approach for the Q-learning value function. The trained RL model can learn from the environment and make real-time decisions. Our approach offers an unbiased method for analyzing complex watershed scenarios, providing a reward function as an analytical metric while optimizing decision-making time. Overall, this work underscores RL’s potential in addressing complex problems, demanding exploration, sequential decision-making, and continuous learning. External variables such as policy shifts, which are not readily integrated into the model, can substantially influence outcomes. Upon establishing a model with the requisite minimal states and actions, the subsequent learning process is relatively straightforward, depending on the selection of appropriate RL model algorithms. Its application depends on the specific problem. The primary challenge in this modeling approach lies in model definition, specifically in devising agents and actions that apply to complex scenarios. Our specific example was designed to address recent decision-making challenges related to constructing dams due to water scarcity. We present two examples: one from a nationwide perspective in Mexico and the other focused on Baja California Sur, the state with the highest water stress. Our results demonstrate our capability to prioritize watersheds effectively for the most significant benefits, particularly dam construction.

1 Introduction

Water management plays a crucial role in ensuring the sustainability of cities and addressing various challenges related to water use, scarcity minimization, and sustainability performance. Water distribution networks encompass a complex web of components and activities, from aqueduct planning to leak repair and modeling, all aimed at efficiently transporting water to households, businesses, and public facilities. The management of water resources is a global concern, with implications for policy and stakeholders worldwide ( Savenije and Van Der Zaag, 2005 ; Gorelick and Zheng, 2015 ; Ingold and Tosun, 2020 ; Ramos et al., 2020 ).

Particularly critical is the management of aquifers in arid regions, given their pivotal role in maintaining water availability and quality. Effective policies are essential for sustainable aquifer use, mitigating depletion risks ( Chichilnisky and Heal, 1993 ; Mohtadi, 1996 ) and preserving ecosystems dependent on groundwater resources ( Huang and Uri, 1990 ). Aquifer management often involves navigating legal obligations, environmental regulations, socioeconomic factors, and ethical considerations, making it a complex task. Traditional static or rule-based strategies may fall short in adapting to changing conditions or capturing the intricate dynamics of aquifer systems.

In response to these challenges, new technologies such as RL have emerged as a promising avenue for optimizing public policy ( Binas et al., 2019 ; Strnad et al., 2019 ; Chen et al., 2021 ; Skirzyński et al., 2021 ; Emamjomehzadeh et al., 2023 ; Ghobadi and Kang, 2023 ; Sivamayil et al., 2023 ). RL allows computers to learn from experience, enabling intelligent decision-making in complex environments ( Lee et al., 2022 ). In this context, we focus on simulating a water management system that allows an autonomous agent the opportunity to learn through trial-and-error interactions driven by reward signals.

The primary objective of this study is to explore the application of RL techniques in groundwater management, specifically in determining the necessity of investigating an aquifer for dam construction in arid regions while addressing internal issues and striving to maintain a delicate balance between water network maintenance, the construction of dams, and the development of aqueducts, all while optimizing these efforts to ensure efficient water management. Incorporating the assessment of technical, economic, and ecological factors into dam projects aligns well with an RL approach. RL can adaptively balance these diverse considerations, optimizing dam planning, especially in arid regions where benefits often surpass ecological concerns, ensuring effective and sustainable strategies. We propose a reward structure and state-action representations that capture the dynamics and tradeoffs within aquifer systems using rule-based environments that directly validate agent decisions.

Reinforcement learning is well-suited for sequential decision-making to maximize cumulative rewards ( Santoro et al., 2016 ; Strnad et al., 2019 ; Sivamayil et al., 2023 ). It leverages the Q-learning algorithm to enable the agent to learn an optimal strategy by estimating the action value function (Q-function) through environmental interactions. For temporal problems, RL employs temporal difference learning, allowing the agent to learn from experience over time. The Q-function iteratively updates based on the difference between predicted and observed rewards, continuously refining the agent’s decision-making capabilities.

Notably, RL has found applications in various water-related domains, including water distribution, heating, water metering, and reservoir operation ( Castelletti et al., 2010 ; Ruelens et al., 2018 ; Hu et al., 2020 , 2022 ; Amasyali et al., 2021 ; Chen and Ray, 2022 ; Khampuengson and Wang, 2022 ). However, integrating rule-based environments within RL for water management simulations is new. It offers several advantages, enhancing adaptability and learning capacity, such as: (a) Incorporating Expert Knowledge: Rule-based environments encapsulate domain-specific expertise, preventing catastrophic errors and accelerating learning. (b) Safety and Compliance: Enforcing regulations and safety measures ensures ethical and environmentally responsible decision-making. (c) Providing a Baseline: Rule-based environments offer a foundational understanding for RL agents before exploring more complex strategies. (d) Rapid Prototyping and Testing: Rule-based systems enable quick prototyping and testing, as they do not rely on deploying complex city sensors, saving time and resources.

The most significant difficulty in this type of modeling is defining the model itself that is, creating agents and actions that are useful and applicable to a problem of this complexity. For example, we might be tempted to use states like lithology, permeability, and hydraulic conductivity, but these states could be encompassed in a single state called “modeling.” On the other hand, a state that cannot be included, such as changes in the city’s external policies, could have a considerable impact. The learning part is relatively straightforward once the model has been defined and the minimum number of states and actions has been determined. It simply requires choosing the appropriate algorithms to solve the RL model.

The definition of states and actions in any policy is inherently driven by its specific goal, and this goal cannot be universally applied to all management scenarios. For instance, when the aim is to construct a dam, the focus naturally shifts toward defining states and actions that optimize the construction process. However, this approach is not directly applicable to other objectives, like reducing water consumption. In this new scenario, strategies should focus on conservation measures, monitoring usage, and encouraging reduced consumption behaviors. Varying goals demand distinct plans. We must make particular strategies for each goal and understand the problem.

We used an example that was custom-made for a specific situation. This example was designed to address the challenges that emerged when the government of Mexico started building aqueducts, but we need to study aquifers to manage water resources effectively. The main idea is to demonstrate how a particular method can benefit stakeholders. So, this specific case illustrates our approach to tackling complex issues, showing its potential applicability in various situations.

First, this paper presents the mathematical formalism in the methodology section. Then, we have three main sections: “Environment,” “Deep Q-Learning” (DQN), and “ε-Greedy.” These sections focus on mathematical algorithms related to rule-based RL presented in the methodology section. We offer two examples: one showcasing a nationwide application in Mexico and the other demonstrating a more detailed focus on Baja California Sur.

2 Methodology

Reinforcement learning can be explained mathematically as Markov Decision Processes (MDPs, Bellman, 1957 ). An MDP is an extension of Markov chains that involves decision-making and actions taken by an agent to maximize cumulative rewards over time. Like Markov chains, MDPs are based on a fixed set of states, where each represents the current environment situation. With MDPs, the agent can take actions to influence state transitions and achieve specific goals. The agent’s actions determine the probability of transitioning to different states. MDPs contain rewards associated with state transitions and actions. The agent’s goal is to learn a strategy that maximizes the cumulative rewards achieved over time.

In RL, we formalize the process as a MDP with the following components:

1. A set of states, S, and a distribution of initial states, p ( s ) .

2. A series of actions, A ∈ a .

3. Dynamics of transitions, T ( s t + 1 |, s t |, a t ) , which is the probability distribution of the next state at time t + 1 taking into account the state and the action at time t .

4. An immediate reward function, R ( s t , a t , s t + 1 ) specifies the reward that is obtained when moving from state s t to s t + 1 after execution of the action a t .

5. A discount factor, γ ∈ [ 0 , 1 ] with lower values favoring immediate rewards.

The value of a state s under the policy π , abbreviated as V π ( s ) is the expected return on investment in the state s and under the policy π . The discounted model with an infinite time horizon can be expressed as follows:

Thereby γ is a discount factor and E π ⋅ is an optimal value, k stands for time steps, r t + k denotes the rewards to be gained in the transition to the state s t and the expected value is related to the policy π .

Similarly, a state action value function Q : S × A → ℝ can be defined as the expected yield starting from the state s with the action a , and then the following policy π :

where a t denotes the action to be taken in the next state s after the policy π .

A fundamental property of value functions is their recursive nature. For each policy π and each state s , the expression in Equation (2) can be defined recursively using the Bellman equation ( Bellman, 1957 ):

The Bellman equation states that the expected value of a state is defined by the immediate reward and the values of possible following states, weighted by their transition probabilities and by a discount factor. V π is the only solution to these equations. It is worth noting that several strategies can have the same value function, but for a given strategy π, V π is unique. It follows that the optimal strategy is:

This expression is known as the Bellman optimality equation , which states that the value of a state under an optimal policy must equal the expected return for the best action in that state. For organizational purposes, the terms are T ( s , π ( s ) , s ′ ) R ( s , a , s ′ ) are elaborated in a section labeled Environment , while the γ V π ( s ′ ) and the final calculation V ∗ ( s ) is performed in another section called Agent . However, R ( s , a , s ′ ) which is the reward function where the environment receives the action, is not always a deterministic function, but in the real world behaves like a stochastic function with a probability of

P r | s , a , s ′ is the probability of receiving a reward r when the agent takes action from the state s and transitions to state s′ . r is a specific reward value that can be received.

Several challenges in RL deserve attention. (1) Discovering the optimal strategy requires trial-and-error interactions with the environment, and the agent’s learning signal is the reward it receives. (2) Its actions influence the agent’s observations and can have significant temporal correlations. (3) Agents must deal with extensive temporal dependencies, where the consequences of an action may only become apparent after several environmental transitions. This is referred to as the temporal credit allocation problem .

We examine these challenges in building a dam to supply water to a city. While the end goal of aquifer investigation and dam design may be clear, the exact sequence of actions required is uncertain. Long-term processes involve challenges such as population growth and severe droughts that could affect decision-making. To find the optimal course of action, we must balance exploration with learning from the consequences of our experiments over time.

3 Environment

The environment manages rules for actions. At its core, the primary function of the environment is to receive an action from the agent, which is implemented as a neural network along with a learning algorithm. The main task of the environment is to check the validity of the action provided by the agent and then generate the corresponding new state. This process is illustrated in Figure 1 . Five state variables were deliberately chosen because they can distinguish different levels that contribute to the evaluation of the state of the aquifer and the environment, including the population center. We encapsulated the environment in a class that uses the OpenAI Gym framework ( Brockman et al., 2016 ). This class provides a structured and standardized way to interact with the environment , allowing seamless integration with other components and facilitating an organized and efficient implementation.

Figure 1 . Sequence of the reinforcement learning process. At time t , the environment receives an action, which is validated and results in a change of state “s” with reward function “r.” It is then updated as a new state reward input to the agent (DQN). The environment checks if the action is valid and sends a signal to the agent.

Starting from scratch could lead to excessive work and a higher chance of errors. Instead, using OpenAI Gym saves time by providing ready-to-use tools. This platform was chosen for its thorough testing, accessibility, universality, scalability, and ease of debugging. However, no hard-coded routines were used; only the provided framework was utilized. Other platforms, such as Sci-Kit Learn or Tensorflow ( Abadi et al., 2016 ), have the capabilities of Deep Learning, but none of them have coded agent-environment interactions. We wrote all the necessary functions so our results would be the same on any platform. The only difference is the organization of the code.

Essentially, the environment is designed to simulate a natural physical environment. This environment relies on sensors that measure changes such as temperature or pressure for smart home appliances. In the case of ruled-based, the environment is simulated with clear and well-structured relations with states and actions.

Our main goal is to build dams sustainably. Our environment is rule-based and includes four states: “ Annual Volume ,” “ Availability ,” “ Distance ,” “ Necessity ,” and “ Modeling .” These states have the following meanings: (1) Annual volume refers to the amount of water in the aquifer, measured in hectometers. This parameter remains nearly constant across all actions, except for the transition to “construction of dams,” the action that directly affects this state. Although these levels change throughout the year and even over several decades, in terms of public policy, the source used to analyze the aquifer is based on a study called “ Mean Annual Availability , ” which in turn treats this variable as a constant number that assumes that this availability does not vary. For this reason, this value is considered constant. (2) Availability represents the total amount of water withdrawn from the annual water volume of the aquifer. The resulting value represents the amount of water remaining in the aquifer and available for various purposes such as irrigation, drinking water supply and industrial use. This parameter can take either positive or negative values depending on whether there is a water deficit or surplus. This calculation is essential for managing and maintaining sustainable use of groundwater resources. When water withdrawal exceeds the natural rate, overuse and depletion of the aquifer occur, leading to serious environmental problems and water scarcity in the region. (3) Distance is the measurement in kilometers between the water source and populated areas. The distance may change after constructing an aqueduct, which is a practical value affecting policy. In other words, if there is already an aqueduct, this aquifer can be used similarly if another aquifer is nearby. (4) Necessity represents the water demand of the nearest heavily populated area, measured in liters per second (l/s). (5) Modeling is a level that quantifies the level of understanding of the aquifer and is expressed on a scale of 0–100. It reflects progress in 3D groundwater modeling, the maturity of studies conducted, and advances in geophysical, geologic, and hydrologic research. This measure is an abstract representation and is always presented as a fraction of the total knowledge required to build a dam. Various variables were explored, such as lithology, porosity, and climate, which are natural and physical factors influential in the situation. However, the aim was to go beyond and directly consider the involved society. The goal was to make a decision that not only took into account the purely physical aspects of the environment but also those directly related to the affected community. This implies understanding how the decision would impact people, their specific needs, and concerns. In summary, a more holistic approach focused on people, rather than solely relying on geological or environmental factors, was sought.

Our model differs from classic RL because the environment can sense and decide if an action is valid. This has several important reasons. First, in our mathematical framework ( Equation 4 ), there is no requirement for a separate function between the environment and the agent. Both the environment and the agent play equal roles in the MDP. Additionally, the environment plays a crucial role in validating actions and determining if they should lead to a new state and reward. In our case, the environment is represented as a rule-based physical simulation, such as a city with people, sensors, and needs. The actions correspond to policy decisions, such as those made by city councils. Consequently, the environment can either accept or reject actions. This is not unusual because, in real life, various mechanisms exist for accepting and validating actions after they have been taken. For instance, legal protections may apply to specific political actions, or environmental regulations not initially considered may affect the agent’s decisions.

The actions are divided into four categories: (a) “ Repairing leaks ,” (b) “ Building aqueducts ,” (c) “ Building dams ,” and (d) “ Conducting studies .” These actions were carefully chosen to influence states while serving as common approaches to address water scarcity in the driest regions with high water stress.

The environment not only updates the state when receiving actions from the agent but also performs essential quality control and testing of the action state. This is mathematically and physically accepted because the environment constantly interacts with the agent in real life. It also computes a reward function that plays a central role in controlling the learning process. In some cases, the environment contains stochastic elements that introduce random events, simulating the variability of the real world. These stochastic factors mimic situations where the environment might react differently than rule-based expectations. For example, dams might be built without proper studies, or due to tax policy or leakage. Another example is that repairs might be delayed even though they were needed.

However, we want to simulate the optimal solution of Q-learning to ensure an accurate representation of the optimal solution. With this approach, we can focus on finding the best possible actions and the appropriate rewards to achieve the desired Q-learning outcome.

The reward is a simple function that relates the value of the states and evaluates them in terms of cost. The reward function considers the aspects of volume, availability, distance, necessity, and modeling of the environment. It encourages the agent to prefer actions that increase the volume and availability of water while minimizing the distance and necessity. Defined as:

Where, A = 1 , B = 0.001 , C = 10 , D = 1 , E = 20 . The differences in scale are adjusted to achieve a balanced and consistent reward multifactor function in hectometer, lt/s, and percent units. This ensures that each factor contributes meaningfully to the total reward despite the inherent differences in their scales. Given the Monte Carlo and Variance-Based sensitivity analysis results, we observe a dynamic interaction between input variables and their impact on the system’s output. The Monte Carlo simulation ( Figure 2 ), showcasing a broad distribution of rewards, suggests a significant influence on our parameters, highlighting the model’s sensitivity. This wide distribution is crucial because the reward function can show significant variations when selecting an action. Concurrently, the Variance-Based analysis provides a deeper understanding of each variable’s contribution to the output variance. The first-order sensitivity indices reveal the most critical parameters, guiding us toward areas requiring precise calibration or robust data collection. These analyses offer a comprehensive view of the system’s behavior, enabling targeted adjustments to enhance model reliability and decision-making efficacy in complex scenarios.

Figure 2 . Sensitivity analysis using a Monte Carlo simulation, a broad distribution of rewards suggests a significant influence on our parameters highlighting the model’s sensitivity.

The following sections will incorporate the reward function into the learning process. By assigning rewards for different actions and states, the agent will be able to identify the most favorable choices that lead to higher rewards and, consequently, better performance.

4 Deep Q-learning

Learning an optimal strategy can be done in different ways; Bellman’s dynamic programming is the most common way. Bellman’s dynamic programming is a fundamental approach in RL that breaks down decision-making processes into simpler sub-problems. It relies on the principle of optimality, which asserts that the optimal policy can be derived by making optimal decisions based on the current and future states at each stage. This approach is advantageous for problems with a discrete and finite state space, where the entire decision process can be systematically analyzed and solved. The major strength of Bellman’s method is its comprehensiveness and precision in finding the optimal solution through recursion and backward induction. However, its primary drawback is the “curse of dimensionality”; as the state and action spaces expand, the computational resources and time required to compute the solution increase exponentially, making it impractical for complex, high-dimensional problems.

Another option besides dynamic programming is DQN, which combines RL with deep neural networks, leveraging the approximation capabilities of deep learning to estimate the value function. This approach allows handling environments with high-dimensional state spaces, making it well-suited for tasks like image-based problems where traditional methods falter. DQNs can generalize across states, reducing the need to explicitly compute the value of each state-action pair, which significantly mitigates the curse of dimensionality. However, DQNs introduce challenges, such as the need for large amounts of data to effectively train the neural network, the risk of overfitting, and the complexity of tuning network architectures and hyperparameters. Moreover, the black-box nature of neural networks makes the decision-making process less interpretable than Bellman’s dynamic programming.

In our case, a neural network model is trained using the Tensorflow Keras library ( Abadi et al., 2016 ) to learn an optimal strategy for actions that affect state variables. Figure 3 shows the neural network’s architecture that is trained to obtain an action based on states. DQNs combine Deep Learning and Q-learning elements to handle complex, high-dimensional state spaces, making them particularly effective for tasks where traditional Q-learning approaches may become impractical or inefficient.

Figure 3 . The architecture of the DQN neural network consists of three fully connected layers and a final softmax connection. During the training process, the network is controlled by a reward function while interacting with the environment.

The network consists of four layers with different numbers of neurons and activation functions. The first layer includes 16 neurons and expects input with five features. The ReLU activation function adds nonlinearity to the network and improves its ability to learn complicated relationships. The second layer consists of 32 neurons and uses ReLU activation. The third layer includes 64 neurons with ReLU activation. Finally, the output layer consists of four neurons corresponding to the four actions in the environment, respectively. Using the activation function “Softmax,” this layer converts the output values into a probability distribution for the actions. The neural network is designed to accept a state representation with five features as input and generate action probabilities from which the agent can choose. With ReLU activation when learning complex Q -value relationships and softmax activation, the architecture is best suited for RL tasks using the DQN methodology.

Figure 4 shows the outlines of a generic training loop for RL. It involves iteratively training an agent through multiple episodes in an environment. During each episode, the agent selects actions based on its current state and a learned strategy. The actions can be selected by exploration (random) or exploitation (based on the predictions of the strategy). The agent then observes the next state and immediate reward from the environment. The rewards are normalized to a consistent range. The algorithm updates its internal model or Q -values based on the observed transitions to improve the agent’s strategy. The process is repeated for a specified number of episodes, storing the cumulative rewards achieved in each episode. Ultimately, the training loop aims to optimize the agent’s strategy to maximize cumulative rewards over time.

Figure 4 . RL training loop with ε-greedy-exploration-transition.

5 ε-Greedy

ε-Greedy is an exploration and exploitation strategy agents use to make decisions in uncertain environments. ε-Greedy was chosen because it can switch to new actions when the agent exploits a particular strategy. For example, repair leaking or modeling states were often exploited without a balance in the agents’ decisions so needed to strike a balance between trying new actions (exploration) and exploiting the best-known actions (exploitation) to maximize long-term rewards. We added the ε-Greedy strategy to balance all the decisions; the ε-Greedy strategy is simple and easy to implement ( Figure 5 ). At each time step “t,” the agent selects an action according to the following rule:

1. With a probability of ε (epsilon), the agent chooses a random action from the set of available actions. This promotes exploration by allowing the agent to try different actions and learn more about the environment.

2. With probability (1 − ε), the agent exploits its current knowledge and chooses the action with the highest estimated reward based on previous experience. Exploitation aims to take advantage of the actions shown to yield higher rewards.

Figure 5 . ε-Greedy. The random part represents the exploration section where different options are searched.

By adjusting the value of ε, an agent can control the degree of exploration versus exploitation. A higher ε-value encourages more exploration, while a lower ε-value tends toward more exploitation. The main advantage of ε-Greedy is its simplicity and versatility. It is a nonparametric approach that requires no assumptions about the underlying environment. In addition, ε-Greedy is computationally efficient, making it suitable for a wide range of applications. However, ε-Greedy also has some drawbacks. A significant limitation is that it treats all actions during exploration as equally uncertain, which may not be the case in complex environments. It may be suboptimal in situations where some actions are worth exploring more than others.

To address this constraint, alternatively, different forms of ε-Greedy have been suggested, including implementing a decreasing ε schedule. The idea is to start with a high ε-value to explore more at the beginning of the learning process, gradually decreasing this value over time, focusing more on exploitation as the agent gains more experience. Although ε-Greedy and Metropolis-Hastings are different algorithms used in different contexts (RL and Markov chain Monte Carlo methods, respectively), they have some conceptual similarities when considering their connections to MDPs and Markov chains. Both the ε-Greedy and Metropolis-Hasting methods involve a tradeoff between exploration and exploitation. In ε-Greedy, the agent weighs between exploring new actions (with probability ε) and using the currently known best actions (with probability 1 − ε) during the decision process in an MDP. In Metropolis-Hastings, the algorithm weighs between exploring new states (by proposing transitions to new states with a certain probability) and using states with higher probability (by accepting or rejecting the proposed transitions based on the acceptance probability) during the sampling process in a Markov chain. In ε-Greedy, the agent randomly chooses an action (with probability ε) during exploration rather than always choosing the best-known action. This stochastic introduces exploration and ensures the agent is not stuck in a suboptimal strategy.

In ε-Greedy, the agent’s decision-making is based on the current state of the environment, which satisfies the Markov property of MDPs. The agent does not need to maintain a history of past states to make decisions. In ε-Greedy, as the agent collects more data through interactions with the environment, it is expected to converge to the optimal action—value function (Q-function) or strategy for the MDP.

The model’s performance is evaluated by testing it in the environment and selecting actions based on the highest predicted action probability. Our final code can be obtained in Ortega, (2024) .

6 Implementation

In Figure 6 , we depict the states and actions that were illustrated in our RL process. The states (1) Annual Volume , (2) Necessity , (3) Availability , (4) Distance , and (5) Modeling interact with the actions: (a) Repair leaking , (b) Construction of aqueducts , (c) Dam construction , and (d) Perform studies . Note that states and actions are intrinsically connected, for example, the action Repair leaking with Necessity and Construction of aqueducts with Distance .

Figure 6 . Illustration of states and actions of this specific example. The states and actions are intrinsically connected; for example, action “Perform studies” with “Modeling” and “Construction of aqueducts with Distance.” The agent receives states and decides an action based on a function DQN. Internally, there is a reward function that controls the efficiency of the RL process.

Unlike other machine learning methods that focus on accuracy without guiding the learning process, RL aims to teach the agent how to learn and make good decisions in its environment. During training, the agent explores the environment and refines its understanding of state transitions and action sequences. Thus, in RL, how we learn is more important rather than merely focusing on accuracy. The RL’s iterative nature and adaptive approach allow for continuous updating of strategies based on feedback from the environment, making it different from traditional supervised learning. Further research and experiments can extend this approach to more complex environments.

The Environment class simulates a water management system with five continuous state variables, each with specific ranges. The neural network model is built using Tensorflow Keras ( Abadi et al., 2016 ) and consists of three hidden layers with 16, 32, and 64 neurons, respectively, and a final output layer with four neurons corresponding to the discrete actions. The model is trained to predict the action probabilities based on the current state, learning the optimal environmental strategy. In the training loop, episodes are run to gain experience and update the model based on the observed transitions. Rewards are calculated using the coefficient-based reward function, highlighting the importance of each state variable. The model’s performance is evaluated by testing it in the environment and selecting actions based on the highest predicted action probabilities.

Model complexity is generally strongly related to training stability ( Hu et al., 2021 ). The initial state is chosen for the city of La Paz, Mexico, which is the capital city of Baja California Sur. In RL, a step is a single interaction between the agent and its environment. During each step, the agent selects an action, and the environment responds by transitioning to a new state and providing a reward signal. This action-state-reward cycle is fundamental to RL algorithms, and the agent often updates its policy or value function based on the outcomes of these steps. In Q-learning, the agent updates its Q -values after each step.

Conversely, an episode refers to a sequence of steps that begins with an initial state and concludes when a predefined terminal condition is met. Episodes are a way to structure RL tasks and define when the agent has completed a specific task or goal. The termination of an episode could be due to reaching a goal state (infinite time horizon), exceeding a maximum number of steps (finite time horizon), or encountering a particular event. Also, epochs pertain to the training process of DQN neural networks. During each epoch, the entire training dataset is passed through the neural network forward and backward. Deep learning models are typically trained over multiple epochs to enhance their performance. The number of epochs is a hyperparameter that can be adjusted based on the model’s convergence behavior.

In Figure 7 , we provide an instance of the total reward function across various episodes. Decision changes are significant just before the learning trend stabilizes, meaning decision policies compete to establish a learning trend. For this reason, episodes 1–7 show variability in the four actions. Figure 7 displays all learning episodes to demonstrate that the trend has begun to stabilize. The increase in rewards signifies that the RL agent is learning from its interactions with the environment and is finding better strategies or policies over time. As it accumulates experience, it becomes better at selecting actions that lead to higher rewards (exploitation). At the same time, the RL process may have found a good balance between exploration (trying new actions) and exploitation (choosing known good actions) to maximize rewards.

Figure 7 . The learning curve illustrates the agent’s performance based on the total reward function in each episode. After episode 10, the agent shows significant progress, indicating an increased level of learning.

Since the DQN starts without knowledge, the reward function slowly performs better until it has the optimal behavior. However, we found that the reward function does not always behave the same way because it depends on the initial random state. We can estimate the Q -value ( Figure 8 ) at each episode depending on the different actions. Decision changes are significant just before the learning trend stabilizes, meaning decision policies compete to establish a learning trend. For this reason, episodes 1–7 show variability in the four actions. Note that Figure 7 displays all learning episodes to demonstrate that the trend begins to stabilize, but Figure 8 enhances those changes.

Figure 8 . Q -values for different actions.

We note that in all cases, the learning process behaves similarly. First, performing studies is constantly growing as the most important activity until it reaches its highest value, then repair leaking starts. While performing studies is decreasing, it reaches a level where construction of aqueducts begins; this is because the studies are solid enough that modeling the aquifer has reached robust results. Then, the dam construction starts. Note in Figure 8 that dam construction has an opposite trend because it is defined in that way in the reward function construction.

The reward function in RL plays a pivotal role in governing the efficiency and optimization of a process. It essentially serves as the guide that directs an agent toward its goals. This function encapsulates the objectives and priorities of an experienced group, defining what they seek to maximize in their chosen task, thereby shaping the agent’s decision-making to reach those goals.

Designing the reward function in RL is crucial because it guides the learning process, shaping the agent’s behavior to achieve desired goals. However, crafting an effective reward function can be challenging.

Learning can be slow or stall if the agent receives infrequent feedback. Striking the right balance between rare and frequent rewards is essential, so we found that 20 steps is a good balance. We tried exponential and complex linear behavior, but we found that a simple linear combination helps to converge to solutions. Reward engineering requires deep domain knowledge and an understanding of the task. A poorly designed reward function can lead to suboptimal or undesirable agent behavior. Moreover, reconciling conflicting objectives can be tough. Different stakeholders may have different goals, so designing a reward function that balances these objectives is challenging.

A well-designed reward function should also generalize to various situations, allowing the agent to adapt to new scenarios without extensive manual adjustments.

Our example represents one of the different variants of politics that can be implemented. In our case, we have focused on the construction of dams since this corresponds to an immediate need. The phases and actions in the RL process are, therefore, presented only for the purpose of a simple exercise and test. Our computer code is published at https://github.com/rortegaru/DQNWATER .

Once we have implemented the RL process, we can use it for various purposes. The different ways to use this methodology include:

(a) Classification: Benefit serves as a measure to classify the aquifer most beneficial to society’s needs. In our case, the benefit is the reward function when compared to all the different aquifers. (b) Optimal Sequences: Another more traditional approach is to analyze each aquifer separately, attempting to understand the RL learning process. This helps us determine how to apply the relationships between actions and states for each case. (c) Complexity: We can introduce additional elements, like a complex water network system and observe the decision-making behavior. We have provided some examples of these analyses.

7 Application to the Mexican aquifers

According to the World Water Assessment Program ( Water, 2012 ), Mexico is in a region that is quickly approaching absolute physical water scarcity ( Figure 9 ). Climate change, urban growth, and farming needs drive Mexico’s water scarcity. The country’s diverse climates, ranging from arid in the north to humid in the south, make managing water problems difficult. As development increases, so does the pressure on water supplies, raising concerns about ensuring clean water for everyone. This urgent issue challenges policymakers to find ways to save and manage water to avoid a crisis.

Figure 9 . Global map of physical water scarcity. The red square shows the study region [Adapted and modified from World Water Assessment Program (WWAP), March 2012].

Suppose we want to classify the aquifers requiring immediate attention. In that case, we can utilize the entire database of the Federal Commission of Water (CONAGUA, from the Spanish acronym Comisión Nacional del Agua). In Figure 10 , we depict the 564 aquifers of Mexico with the four initial states. The Mexican aquifers comprise a combination of the United States Hydrological Unit Codes (HUC) 6 and 8 ( Seaber et al., 1987 ). Data were collected from the repositories of CONAGUA and the Mexican Census 2020 ( Instituto Nacional de Estadística, Geografía e Informática, 2020 ; Comisión Nacional del Agua, 2023 ). Figure 10 depicts four distinct states for each watershed.

Figure 10 . Maps representing the watersheds of Mexico based on four different states. (A) Availability in hectometers, (B) necessity in hectometers. (C) shortest distance to population and (D) Annual volume in hectometers.

Next, we selected only deficit watersheds ( Figure 11 ). Notably, desert and highland regions are in deficit, while the northern part of the country faces more significant availability challenges than the southern part. We refer to watersheds in deficit as critical watersheds.

Figure 11 . Deficit and available watersheds in Mexico. The watersheds in deficit are used for further analysis in the RL process.

In Figure 12 , we compare critical and non-critical watersheds. Based on availability, we display the highest and lowest values for four states in critical watersheds. Out of 653 watersheds, 56 are considered critical due to deficits. In the Electronic Supplement, we present that table. Critical watersheds, accounting for merely 8.6% of the total, span 41% of Mexico’s land area. This emphasizes the crucial importance of studying these critical watersheds. We have excluded modeling values, assuming most studies start from scratch without prior modeling.

Figure 12 . Percentage of critical watersheds: (A) based on numbers, (B) Based on area, (C) Maximum and minimum values of four different states representing critical watersheds.

Next, we evaluated critical watersheds using our RL process and illustrated the benefits in Figure 13 . Aquifers with the highest benefit scores receive the highest reward function values. This includes aquifers that are in proximity, have nearby populations, are in critical condition, and can address issues through water infrastructure repairs.

Figure 13 . Watersheds with highest benefits.

Finally, we analyzed only the watersheds of Baja California Sur. In Figure 14 , we show the watersheds in a similar way to what we presented in Mexico. According to the latest available data, Baja California Sur stands out as the state with the highest water stress levels in Mexico. This situation mirrors challenges seen in other countries across the American continent, such as Chile. Addressing the pressing issues in Baja California Sur is crucial. However, it is essential to note that while this case highlights a significant concern; our approach should not be overly generalized. Instead, we should tailor our strategies and actions to the specific circumstances of each case. By maintaining a critical perspective and focusing on localized solutions, we can effectively address water stress issues and inform targeted public policies.

Figure 14 . Maps of Baja California Sur based on four different states. (A) Availability in hectometers, (B) annual volume in hectometers, (C) shortest distance to population, and (D) necessity in hectometers.

In this case, we proceeded in the same way as we did in the entire country; however, we added a simple simulation that includes a “repair leaking” based on the distribution of the streets in the major cities of Baja California Sur. Instead of using a simple percentage of 30% ( Jornada, 2023 ), we used the number of streets and buildings and performed our steps based on that number. In Figure 15 , we show the water network that we constructed to simulate that number.

Figure 15 . Water grids of the five cities with population higher to 10,000 habitants. (A) Cd. Constitución, (B) Loreto, (C) La Paz, (D) Cabo San Lucas, and (E) San José del Cabo.

In Figure 16 and Table 1 , our results reveal a complex trade-off among the states and actions defining the final benefit value. Notably, proximity to population centers and needs plays a crucial role in hierarchical definitions. Consequently, as requested by the Mexican Consejo Nacional de Humanidades, Ciencias y Tecnologías (CONAHCYT) in the 10-year project Researchers for Mexico , we have successfully derived an unbiased value to prioritize the study of watersheds, considering social, technical, and beneficial aspects. Following our analysis, we recommend prioritizing the study of four watersheds (Todos Santos, Melitón Albañez, Cañada Honda, and Plutarco Elias Calles) due to their highest benefit scores.

Figure 16 . Benefit map of Baja California Sur. All the numbered watersheds are in a deficit state. The assessment of benefits is quantified using the reward function. Watersheds correspond to Table 1 .

Table 1 . Benefit value defined a complex trade-off among the states and actions.

8 Discussion

It is necessary to have an intrinsic connection between states and actions in the RL framework for water management Annual Volume , Necessity , Availability , Distance and Modeling are crucially linked with actions such as Repair leaking , Construction of aqueducts , Dam construction , and Perform studies , requiring a tailored approach to address specific aspects of water management. The success of water management depends more on the specific model we create than on the RL technique itself. Although RL is used for optimization, the real challenge is building a model that accurately represents water management issues through its states and actions. Essentially, how well RL works depends on how good the model is, making the model’s design crucial for addressing real-world problems.

This integrated setup underscores RL’s unique capability to guide learning processes toward making informed decisions, distinguishing it from other machine learning methods that might prioritize accuracy without steering the learning. RL’s adaptability and iterative nature, guided by continuous feedback, enable dynamic strategy updates, starkly contrasting conventional supervised learning paradigms. Our exploration further delves into the practical application within a simulated water management system, emphasizing the role of a carefully designed reward function and the challenge of balancing complex state-actions relationships to foster efficient learning and decision-making.

Our findings highlight the delicate balance between exploration and exploitation in the RL process, where the agent progressively refines its strategy to achieve greater rewards. However, this aspect of learning is not the most critical component because, ultimately, the key factor is the score of the reward function. Even if learning becomes stagnant, it is essential to continually evaluate the reward function, as its performance is the ultimate measure of success in this context. In some cases, having a robust evaluation metric, such as the score of the reward function, is more important than the specific steps taken to reach the optimal decision.

The finite-infinite time horizon problem deals with limiting the number of steps; using a high number of steps, say 10,000, is a useful practice in certain cases. However, limiting the number of steps can be problematic because we do not know if the goal will be reached. Therefore, waiting for the RL to reach its final target is better. For this reason, we have not limited the number of steps; instead, we have carefully revised the penalty rules so that it will always reach its target, no matter if it is thousands of steps. Remember that the optimization mechanism will oversee finding the best solution.

Calibrating the hyperparameters (ε, η) is a work in progress and is currently out of our reach. An example is the discount factor η ( Equation 1 ), which balances the previous rewards with the current one. A low value favors the immediate rewards, while a high value favors the long-term values; that is, it controls the “memory” of the rewards of each state. Although we have decided to use high values to give weight to all the values using a factor that allows us to remember the previous states, a detailed study is necessary to find the optimal value.

Reinforcement learning offers a multitude of advantageous facets beyond mere optimization in complex systems like water management. Its adaptability allows it to tackle unforeseen challenges and dynamic changes within an environment, making it an invaluable tool for long-term planning and decision-making. Moreover, RL’s ability to learn from interactions and feedback enables the development of strategies that improve over time, thereby enhancing efficiency and effectiveness in achieving goals. This iterative learning process, grounded in trial and error, fosters innovation by encouraging the exploration of new solutions. Furthermore, RL’s versatility extends its applicability across various domains, from robotics and automation to healthcare and finance, demonstrating its potential to provide tailored, impactful solutions in diverse settings.

Our study demonstrates how RL can effectively address key water management challenges, as shown in our analysis of Mexican aquifers and the distinction between critical and non-critical watersheds. By using RL to assess watersheds for potential benefits, we gain a deeper understanding of these complex issues. Our findings lead to recommending specific watersheds for focused study, considering their impact on society, technology, and benefits to guide future water management strategies.

Traditional water management methods, such as the Analytic Hierarchy Process (AHP) and others, have offered structured frameworks to address complex decision-making by deconstructing problems into more straightforward, hierarchical elements. These methods stress systematic analysis and prioritization grounded in expert judgment and pairwise comparisons, enabling a more deterministic approach to decision-making. While effective for static and well-defined problems, these conventional methods may lack the flexibility and adaptability to confront dynamic environmental conditions and evolving water management challenges. Their dependence on predefined criteria and expert input can also constrain their capacity to assimilate new data and adapt to unforeseen water availability or demand changes.

In contrast, RL presents a more dynamic and adaptive approach to water management, capable of continuously learning from the environment and optimizing decisions based on real-time feedback. Unlike methods such as AHP, RL algorithms can navigate complex and uncertain environments through trial and error, adjusting strategies based on outcomes and rewards. This capacity for learning and adaptation renders RL particularly suited for the complexities of water management, where conditions can swiftly change due to climatic variability, population growth, and shifting land use patterns. RL’s potential to derive optimal strategies through iterative learning and its ability to handle high-dimensional data and uncertainty positions it as a promising tool for innovative water management solutions, marking a significant advancement over traditional methods.

In addition to the AHP, traditional water management has depended on methods such as Cost–Benefit Analysis (CBA), Linear Programming (LP), and Multi-Criteria Decision Making (MCDM). CBA evaluates the financial aspects of water projects by comparing costs and benefits, focusing on economic efficiency. LP addresses water resource allocation problems through mathematical optimization, striving for the optimal outcome within specified constraints. MCDM, akin to AHP, considers various factors and stakeholder preferences to inform decision-making, providing a systematic approach to assessing intricate scenarios.

Reinforcement learning represents a departure from these traditional methods by adopting a dynamic, feedback-oriented approach. Unlike the static, often linear frameworks of CBA, LP, and MCDM, RL excels in environments characterized by incomplete information and fluctuating conditions. It learns optimal actions through trial and error, guided by a reward system aligned with water management goals. This adaptability enables RL to address real-world complexities, such as sudden water availability or demand patterns, rendering it a versatile tool for contemporary water management challenges. While traditional methods offer valuable insights through structured analysis, RL’s capacity for continuous learning and adaptation presents a forward-looking approach to managing water resources in an increasingly uncertain world.

This study marks a pioneering effort in Mexico, particularly within Baja California Sur, by concentrating on watershed management for public use. While previous research ( Mendoza et al., 1997 ) on climate change and urban studies ( Cotler et al., 2022 ) has primarily focused on ecosystems and sustainability, our work stands out by applying RL to watershed management. This innovative approach represents a growing trend globally in leveraging advanced computational techniques for environmental management. Notably, to our knowledge, this is the first work employing a rule-based RL strategy specifically tailored for watershed management, introducing a novel perspective to the field and potentially setting a precedent for future studies. We show a global tendency toward water management and machine learning, including the paradigm of RL in a more graphical way using bibliometric analysis ( Figure 17 ).

Figure 17 . Bibliometric analysis of papers on machine learning and water management from 2020 to 2024. (A) General overview and (B) RL enhancement. The RL paradigm is still in its nascent stage.

In practical terms, implementing RL in water management requires the involvement of stakeholders who can influence activities and outcomes. Boards of directors and governing bodies should take part in formulating strategies and actions, while experts design initial prototypes and establish the groundwork for the relationships between actions and states. These experts should also contribute to defining the reward function, as it will be the basis for optimization.

For instance, if we aim to optimize the design and installation of desalination plants using RL, essential factors such as: energy requirements (in MWatts), intake water quality (measured by total dissolved solids), discharge rate (in l/s), etc., should be identified as states. Discussions should then focus on determining appropriate reward functions and considering initial states. An optimization analysis can show the relationships between states and actions, leading to decisions like placing absorption wells or choosing between direct intake or well-intake methods.

9 Conclusion

We have developed an RL with the ruled-based system to generate a process that defines optimal decision values over time. This process allows us to choose the best actions based on different states within a complex aquifer system, where we have integrated physical characteristics and changes in social and human factors within an artificial intelligence framework. The most important conclusions of this work are as follows:

a. Integrating rule-based actions to achieve optimal decisions in water management needs specific goals that are not universally applicable.

b. Classifying critical watersheds is an effective process for RL.

c. RL tackles the complex connections among its constituent elements.

Our research field opens new avenues for the definition of reward functions and state-change algorithms to improve continuously. Future research should explore integrating rule-based actions alongside RL to refine decision-making for specific objectives, like identifying watersheds that significantly benefit society, especially in mountainous and arid regions that remain a priority. This entails a deeper analysis of the intricate relationships within these ecosystems and the urgent need for interventions in areas facing acute water scarcity.

In summary, this approach to water management and decision-making policies forms part of an intricate decision network that can expand over time.

Data availability statement

The datasets presented in this study can be found in online repositories. The names of the repository/repositories and accession number(s) can be found in the article/ Supplementary material .

Author contributions

RO: Writing – original draft, Writing – review & editing. DC: Writing – original draft, Writing – review & editing. AC-M: Writing – review & editing.

The author(s) declare that financial support was received for the research, authorship, and/or publication of this article. The financial support for this research was provided through the grants CF–2023-G-958 and 319664 from CONAHCYT, and the “Investigadores por México” Project 1220 and CICESE Internal projects 691-106 and 691-118.

Acknowledgments

We extend our deepest gratitude to the two reviewers whose invaluable insights and suggestions have significantly broadened and enriched the scope of our work. Their expertise has enhanced the quality of our research and inspired us to explore our topic from a more comprehensive perspective. The authors acknowledge the authorities of the State Water Commission of Baja California Sur, the National Water Commission, and the municipality of La Paz, including its operating organization, for their valuable recommendations and feedback.

Conflict of interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Publisher’s note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

Supplementary material

The Supplementary material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/frwa.2024.1384595/full#supplementary-material

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Keywords: reinforcement learning, water management simulation, deep learning, Q-learning value function, dam construction, decision-making

Citation: Ortega R, Carciumaru D and Cazares-Moreno AD (2024) Reinforcement learning for watershed and aquifer management: a nationwide view in the country of Mexico with emphasis in Baja California Sur. Front. Water . 6:1384595. doi: 10.3389/frwa.2024.1384595

Received: 09 February 2024; Accepted: 15 April 2024; Published: 09 May 2024.

Reviewed by:

Copyright © 2024 Ortega, Carciumaru and Cazares-Moreno. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY) . The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

*Correspondence: Roberto Ortega, [email protected]

Disclaimer: All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher.

New research paper says uranium mining near Grand Canyon threatens regional groundwater

Researchers at the University of New Mexico say uranium mining near the Grand Canyon could pose a greater threat to groundwater than previously shown. In a recent paper , they call for a halt in mining operations.

The scientists say aquifers and other groundwater systems near the canyon are interconnected in ways that aren’t totally understood. As a result, uranium mining and other contaminants could threaten public health and the environment, and impact the Grand Canyon’s springs along with the Havasupai Tribe’s sole water source and other tribal sacred sites.

The Pinyon Plain Mine near the South Rim began producing ore in early 2024 and the researchers warn uranium mining represents a quote “considerable risk of contamination” in parts of the regional aquifer system. The paper continues, "... the authors favor abundant caution and no mining in this sensitive region."

"This is unsurprising for anyone who has looked at the mixing of rivers, but similar processes are more hidden and incompletely understood in groundwater," said lead author Karl Karlstrom in a press release. "Water flows down gradient, and fault pathways control where groundwater ponds in sub-basins. In the Grand Canyon region, these sub-basins are each vented by major springs on tribal or Park lands."

The mine is located within the Baaj Nwaavjo I'tah Kukveni - Ancestral Footprints of the Grand Canyon National Monument declared last summer by President Joe Biden. It banned new uranium mining claims on almost a million acres but the Pinyon Plain Mine was exempt from the designation.

Curtis Moore, senior vice president for marketing and corporate development for Pinyon Plain’s owner, Energy Fuels Resources, says previous studies have shown there are no faults or fractures near the mine, and that it poses no risk to groundwater.

"The UNM report does not reveal any new science or facts," says Moore. "… Scientists know there no faults, fractures, or similar conduits near the Pinyon Plain mine. It is also known that there is no real potential for the mine to even contaminate the perched groundwater zones. The science remains crystal clear: the risk to groundwater is zero."

The Arizona Department of Environmental Quality, which issued the mine’s aquifer protection permit in 2022, says it’s reviewing the study but that the operation is among the most highly regulated uranium mines in the nation.

"Studied, scrutinized, and litigated for over 30 years, the mine has an extensive record," says ADEQ spokesperson Caroline Oppleman. "The record demonstrated, and ADEQ agreed, that adverse impacts to groundwater from the mine are extremely unlikely."

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The Ever-Resilient Pupfish Makes a Comeback in Death Valley

The spring population of the critically endangered species is at a 25-year high, a surprising rebound in a tiny desert cave.

By Alexander Nazaryan

When it comes to sheer resilience, few, if any, species can match the tiny Devils Hole pupfish.

Cyprinodon diabolis , as the species is known, has the most ruthlessly circumscribed natural habitat of any vertebrate: Devils Hole , an exceptionally deep, water-filled cave in a limestone formation in the unforgiving Nevada desert, where the fish mostly stay on a rock shelf little more than 200 square feet. Not only that, but the pupfish are believed to be one of the most inbred of all species , a lack of genetic variation that makes it difficult for the creatures to procreate and thrive.

And yet, improbably, Devils Hole pupfish are thriving. Late last month, the National Park Service announced that the spring population of the species had grown to 191 , the highest in 25 years, according to a count conducted twice a year by scuba divers. Because of seasonal fluctuations in food sources, fall counts tend to be higher, meaning that this year’s tally could be a watershed.

“If, this fall, we have over 300, I’ll be really ecstatic,” said Kevin Wilson, an aquatic ecologist at the National Park Service who has studied the Devils Hole pupfish for more than two decades. (Devils Hole is officially part of Death Valley National Park , most of which is in California.)

If the pupfish census does not seem especially impressive, consider that there were only 35 pupfish left in Devils Hole in 2013, prompting worries about extinction. For now, that danger has receded ever so slightly.

“This is a tremendous success story,” said Christopher Martin , an evolutionary biologist and pupfish expert at the University of California, Berkeley. “Ten years ago, we couldn’t have expected this level of success.”

Biologists have been feeding the pupfish frozen food to supplement their regular diet of algae since 2007. In 2019, the biologists finally arrived at the optimal formula of mysid shrimp, water fleas and blood worms. “This change in the supplemental food probably did enhance that increase in population numbers we’re seeing,” Dr. Wilson said.

Hurricane Hilary, which hit last summer, also helped. Even though the storm caused flooding and damage to the park , it benefited the pupfish living in Devils Hole by “adding nutrients that washed off the surrounding land surface in a fine layer of clay and silt,” according to the National Park Service.

The tiny pupfish, usually about an inch in size, is believed to have lived in Devils Hole for at least 10,000 years and probably much longer, Dr. Martin said. Its name alludes to a playful, puppylike disposition.

How the pupfish ended up in the Nevada desert is not known for certain. Much of Nevada was once underwater . The waters eventually receded, but somehow the pupfish found a refuge in the vast expanse of scrubland and sand.

To this day, no person is known to have completed an exploration of the lowest depths of Devils Hole, which is hundreds of feet deep. (A submersible would never fit into the narrow cavern, Dr. Wilson said.) In a notorious accident in 1965, two young men died during a dive in Devils Hole .

Not much for deepwater exploration, the pupfish stay at depths of 80 feet or less. There, the temperature is 93 degrees Fahrenheit, potentially even hotter near the surface.

Because the pupfish are effectively perched on a shallow underwater ledge, changes to the water table can harm prospects for survival. Dr. Wilson worries that the profusion of enormous solar panel farms in the surrounding desert could drastically increase water usage, damaging the delicate Amargosa River system . Mining is booming again in Nevada. Pahrump, a desert town near Ash Meadows, has seen its population explode .

“There’s increasing pressure on groundwater,” Dr. Wilson said. A well could inadvertently tap the Devils Hole aquifer, causing a drastic drop in the water level there.

Perhaps the greatest danger to the species is its lack of genetic diversity, which increases the incidence of harmful genetic mutations and thus makes it harder for the population to grow. In a classic Catch-22, the pupfish have only one way of inbreeding less: by growing their population.

To prepare for potential catastrophe, the U.S. Fish and Wildlife Service has been breeding Devils Hole pupfish in captivity since 2013. Introducing bred pupfish into Devils Hole is unfeasible for a variety of reasons, but should something happen to the wild pupfish, the species will live on.

For now, however, the wild pupfish are hanging on in Devils Hole. Christopher Norment, a vertebrate ecologist and the author of “Relicts of a Beautiful Sea,” a book about Death Valley, said that although he was “somewhat jaundiced” about the long-term prospects of the Devils Hole pupfish, he was impressed by its tenacity.

“It’s the story of survival in the face of overwhelming odds,” he said.

Explore the Animal Kingdom

A selection of quirky, intriguing and surprising discoveries about animal life..

Indigenous rangers in Australia’s Western Desert got a rare close-up with the northern marsupial mole , which is tiny, light-colored and blind, and almost never comes to the surface.

For the first time, scientists observed an orangutan, a primate, in the wild treating a wound  with a plant that has medicinal properties.

A new study resets the timing for the emergence of bioluminescence back to millions  of years earlier than previously thought.

Scientists are making computer models to better understand how cicadas  emerge collectively after more than a decade underground .

New research questions the long-held theory that reintroduction of Yellowstone’s wolves caused a trophic cascade , spawning renewal of vegetation and spurring biodiversity.

To protect Australia’s iconic animals, scientists are experimenting with vaccine implants , probiotics, tree-planting drones and solar-powered tracking tags.

2024 NGWA University Franklin Electric Scholarships application window is now open

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May 10, 2024

Franklin Electric, in partnership with NGWA and Oklahoma State University, announced that applications are now being accepted for the 2024 NGWA University Franklin Electric Scholarship program .

These scholarships are given annually to five emerging groundwater industry professionals and provide critical continuing education in NGWA University’s comprehensive Drilling Basics Course. This year’s application window runs through September 1 and winners will be announced at Groundwater Week 2024 , December 10-12 in Las Vegas, Nevada.

The Franklin Electric scholarships are open to professionals currently employed in the groundwater industry. Scholarship recipients will be given access to several foundational groundwater courses: Groundwater 101, General Workplace Safety, Drill Rig Safety, Geology and Groundwater, Hydrogeology and Fluid Mechanics, and Rig Types and Well Design. The online training program, powered by Oklahoma State University, is designed specifically to improve the safety and skills of drilling industry members, and train the next generation of drillers to address the critical shortage of professionals in the industry.

“Part of our vision as a company is to help nurture and support those who wish to pursue and advance their careers in the groundwater industry,” said Andrew Schwarze, Franklin Electric senior business unit director, groundwater distribution. “By sponsoring these scholarships, we’re assuring tomorrow’s industry professionals gain skills that help them grow and solve new challenges.”

In addition to sponsoring the scholarships, Franklin Electric is a longtime supporter of NGWA. The company is a Platinum Founding Industry Partner of NGWA University’s Drilling Basics Course and a proud sponsor of the NGWA Learning Center that houses state-approved training for contractors, on-demand courses, member-exclusive webinars, and more.

Click here to fill out the 2024 NGWA University Franklin Electric Scholarship application .

Click here to learn more about NGWA University online training .

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