Rapid groundwater decline and some cases of recovery in aquifers globally.

Groundwater resources are vital to ecosystems and livelihoods. Excessive groundwater withdrawals can cause groundwater levels to decline1-10, resulting in seawater intrusion11, land subsidence12,13, streamflow depletion14-16 and wells running dry17. 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 withdrawals18. 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.

Through history to growth dynamics: deciphering the evolution of spatial networks.

Many ramified, network-like patterns in nature, such as river networks or blood vessels, form as a result of unstable growth of moving boundaries in an external diffusive field. Here, we pose the inverse problem for the network growth-can the growth dynamics be inferred from the analysis of the final pattern? We show that by evolving the network backward in time one can not only reconstruct the growth rules but also get an insight into the conditions under which branch splitting occurs. Determining the growth rules from a single snapshot in time is particularly important for growth processes so slow that they cannot be directly observed, such as growth of river networks and deltas or cave passages. We apply this approach to analyze the growth of a real river network in Vermont, USA. We determine its growth rule and argue that branch splitting events are triggered by an increase in the tip growth velocity.

Widespread potential loss of streamflow into underlying aquifers across the USA.

Most rivers exchange water with surrounding aquifers1,2. Where groundwater levels lie below nearby streams, streamwater can infiltrate through the streambed, reducing streamflow and recharging the aquifer3. These 'losing' streams have important implications for water availability, riparian ecosystems and environmental flows4-10, but the prevalence of losing streams remains poorly constrained by continent-wide in situ observations. Here we analyse water levels in 4.2 million wells across the contiguous USA and show that nearly two-thirds (64 per cent) of them lie below nearby stream surfaces, implying that these streamwaters will seep into the subsurface if it is sufficiently permeable. A lack of adequate permeability data prevents us from quantifying the magnitudes of these subsurface flows, but our analysis nonetheless demonstrates widespread potential for streamwater losses into underlying aquifers. These potentially losing rivers are more common in drier climates, flatter landscapes and regions with extensive groundwater pumping. Our results thus imply that climatic factors, geological conditions and historic groundwater pumping jointly contribute to the widespread risk of streams losing flow into surrounding aquifers instead of gaining flow from them. Recent modelling studies10 have suggested that losing streams could become common in future decades, but our direct observations show that many rivers across the USA are already potentially losing flow, highlighting the importance of coordinating groundwater and surface water policy.

Groundwater level observations in 250,000 coastal US wells reveal scope of potential seawater intrusion.

Seawater intrusion into coastal aquifers can increase groundwater salinity beyond potable levels, endangering access to freshwater for millions of people. Seawater intrusion is particularly likely where water tables lie below sea level, but can also arise from groundwater pumping in some coastal aquifers with water tables above sea level. Nevertheless, no nation-wide, observation-based assessment of the scope of potential seawater intrusion exists. Here we compile and analyze ~250,000 coastal groundwater-level observations made since the year 2000 in the contiguous United States. We show that the majority of observed groundwater levels lie below sea level along more than 15% of the contiguous coastline. We conclude that landward hydraulic gradients characterize a substantial fraction of the East Coast (>18%) and Gulf Coast (>17%), and also parts of the West Coast where groundwater pumping is high. Sea level rise, coastal land subsidence, and increasing water demands will exacerbate the threat of seawater intrusion.

Wetting controls of droplet formation in step emulsification.

The formation of droplets is ubiquitous in many natural and industrial processes and has reached an unprecedented level of control with the emergence of milli- and microfluidics. Although important insight into the mechanisms of droplet formation has been gained over the past decades, a sound understanding of the physics underlying this phenomenon and the effect of the fluid's flow and wetting properties on the droplet size and production rate is still missing, especially for the widely applied method of step emulsification. In this work, we elucidate the physical controls of microdroplet formation in step emulsification by using the wetting of fluidic channels as a tunable parameter to explore a broad set of emulsification conditions. With the help of high-speed measurements, we unequivocally show that the final droplet pinch-off is triggered by a Rayleigh-Plateau-type instability. The droplet size, however, is not determined by the Rayleigh-Plateau breakup, but by the initial wetting regime, where the fluid's contact angle plays a crucial role. We develop a physical theory for the wetting process, which closely describes our experimental measurements without invoking any free fit parameter. Our theory predicts the initiation of the Rayleigh-Plateau breakup and the transition from dripping to jetting as a function of the fluid's contact angle. Additionally, the theory solves the conundrum why there is a minimal contact angle of α = 2π/3 = 120° for which droplets can form.

Symmetric rearrangement of groundwater-fed streams.

Streams shape landscapes through headward growth and lateral migration. When these streams are primarily fed by groundwater, recent work suggests that their tips advance to maximize the symmetry of the local Laplacian field associated with groundwater flow. We explore the extent to which such forcing is responsible for the lateral migration of streams by studying two features of groundwater-fed streams in Bristol, Florida: their confluence angle near junctions and their curvature. First, we find that, while streams asymptotically form a 72° angle near their tips, they simultaneously exhibit a wide 120° confluence angle within approximately 10 m of their junctions. We show that this wide angle maximizes the symmetry of the groundwater field near the junction. Second, we argue that streams migrate laterally within valleys and present a new spectral analysis method to relate planform curvature to the surrounding groundwater field. Our results suggest that streams migrate laterally in response to fluxes from the surrounding groundwater table, providing evidence of a new mechanism that complements Laplacian growth at their tips.

A free-boundary model of diffusive valley growth: theory and observation.

Valleys that form around a stream head often develop characteristic finger-like elevation contours. We study the processes involved in the formation of these valleys and introduce a theoretical model that indicates how shape may inform the underlying processes. We consider valley growth as the advance of a moving boundary travelling forward purely through linearly diffusive erosion, and we obtain a solution for the valley shape in three dimensions. Our solution compares well to the shape of slowly growing groundwater-fed valleys found in Bristol, Florida. Our results identify a new feature in the formation of groundwater-fed valleys: a spatially variable diffusivity that can be modelled by a fixed-height moving boundary.

Path selection in the growth of rivers.

River networks exhibit a complex ramified structure that has inspired decades of studies. However, an understanding of the propagation of a single stream remains elusive. Here we invoke a criterion for path selection from fracture mechanics and apply it to the growth of streams in a diffusion field. We show that, as it cuts through the landscape, a stream maintains a symmetric groundwater flow around its tip. The local flow conditions therefore determine the growth of the drainage network. We use this principle to reconstruct the history of a network and to find a growth law associated with it. Our results show that the deterministic growth of a single channel based on its local environment can be used to characterize the structure of river networks.

Bifurcation dynamics of natural drainage networks.

As water erodes a landscape, streams form and channellize the surficial flow. In time, streams become highly ramified networks that can extend over a continent. Here, we combine physical reasoning, mathematical analysis and field observations to understand a basic feature of network growth: the bifurcation of a growing stream. We suggest a deterministic bifurcation rule arising from a relationship between the position of the tip in the network and the local shape of the water table. Next, we show that, when a stream bifurcates, competition between the stream and branches selects a special bifurcation angle α=2π/5. We confirm this prediction by measuring several thousand bifurcation angles in a kilometre-scale network fed by groundwater. In addition to providing insight into the growth of river networks, this result presents river networks as a physical manifestation of a classical mathematical problem: interface growth in a harmonic field. In the final sections, we combine these results to develop and explore a one-parameter model of network growth. The model predicts the development of logarithmic spirals. We find similar features in the kilometre-scale network.

Bifurcation dynamics of natural drainage networks.

As water erodes a landscape, streams form and channellize the surficial flow. In time, streams become highly ramified networks that can extend over a continent. Here, we combine physical reasoning, mathematical analysis and field observations to understand a basic feature of network growth: the bifurcation of a growing stream. We suggest a deterministic bifurcation rule arising from a relationship between the position of the tip in the network and the local shape of the water table. Next, we show that, when a stream bifurcates, competition between the stream and branches selects a special bifurcation angle alpha = 2pi/5. We confirm this prediction by measuring several thousand bifurcation angles in a kilometre-scale network fed by groundwater. In addition to providing insight into the growth of river networks, this result presents river networks as a physical manifestation of a classical mathematical problem: interface growth in a harmonic field. In the final sections, we combine these results to develop and explore a one-parameter model of network growth. The model predicts the development of logarithmic spirals. We find similar features in the kilometre-scale network.

Ramification of stream networks.

The geometric complexity of stream networks has been a source of fascination for centuries. However, a comprehensive understanding of ramification--the mechanism of branching by which such networks grow--remains elusive. Here we show that streams incised by groundwater seepage branch at a characteristic angle of 2π/5 = 72°. Our theory represents streams as a collection of paths growing and bifurcating in a diffusing field. Our observations of nearly 5,000 bifurcated streams growing in a 100 km(2) groundwater field on the Florida Panhandle yield a mean bifurcation angle of 71.9° ± 0.8°. This good accord between theory and observation suggests that the network geometry is determined by the external flow field but not, as classical theories imply, by the flow within the streams themselves.

Modeling river delta formation.

A model to simulate the time evolution of river delta formation process is presented. It is based on the continuity equation for water and sediment flow and a phenomenological sedimentation/erosion law. Different delta types are reproduced by using different parameters and erosion rules. The structures of the calculated patterns are analyzed in space and time and compared with real data patterns. Furthermore, our model is capable of simulating the rich dynamics related to the switching of the mouth of the river delta. The simulation results are then compared with geological records for the Mississippi River.