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Recent work has shown that Transformers trained from scratch can successfully solve various arithmetic and algorithmic tasks, such as adding numbers and computing parity. While these Transformers generalize well on unseen inputs of the same length, they struggle with length generalization, i.e., handling inputs of unseen lengths. In this work, we demonstrate that looped Transformers with an adaptive number of steps significantly improve length generalization. We focus on tasks with a known iterative solution, involving multiple iterations of a RASP-L operation—a length-generalizable operation that can be expressed by a finite-sized Transformer. We train looped Transformers using our proposed learning algorithm and observe that they learn highly length-generalizable solutions for various tasks. 

Abstract. Plant roots act as critical pathways of moisture from the subsurface to the atmosphere. Deep moisture uptake by plant roots can provide a seasonal buffer mechanism in regions with a well-defined dry season, such as the southern Amazon. Here, mature forests maintain transpiration (a critical source of atmospheric moisture in this part of the world) during drier months. Most existing state-of-the-art Earth system models do not have the necessary features to simulate subsurface-to-atmosphere moisture variations during dry-downs. These features include groundwater dynamics, a sufficiently deep soil column, dynamic root water uptake (RWU), and a fine model spatial resolution (<5 km). To address this, we present DynaRoot, a dynamic root water uptake scheme implemented in the Noah-Multiparameterization (Noah-MP) land surface model, a widely used model for studying kilometer-scale regional land surface processes. Our modifications include the implementation of DynaRoot, eight additional resolved soil layers reaching a depth of 20 mm, and soil properties that vary with depth. DynaRoot is computationally efficient and ideal for regional- or continental-scale climate simulations. We perform four 20-year uncoupled Noah-MP experiments for a region in the southern Amazon basin. Each experiment incrementally adds physical complexity. The experiments include the default Noah-MP with free drainage (FD), a case with an activated groundwater scheme that resolves water table variations (GW), a case with eight added soil layers and soil properties that vary with depth (SOIL), and a case with DynaRoot activated (ROOT). Our results show that DynaRoot allows mature forests in upland regions to avoid water stress during dry periods by taking up moisture from the deep vadose zone (where antecedent precipitation still drains downward). Conversely, RWU in valleys can access moisture from groundwater (while remaining constrained by the water table). Temporally, we capture a seasonal shift in RWU from shallower layers in wetter months to deeper soil layers in drier months, particularly over regions with dominant evergreen broadleaf (forest) vegetation. Compared to the control case, there is a domain-averaged increase in transpiration of about 29 % during dry months in the ROOT experiment. Critically, the ROOT experiment performs best in simulating the temporal evolution of dry-season transpiration using an observation-based ET (evapotranspiration) product as the reference. Future work will explore the effect of the DynaRoot uptake scheme on atmospheric variables in a coupled modeling framework. 

Abstract Groundwater resources are vital to ecosystems and livelihoods. Excessive groundwater withdrawals can cause groundwater levels to decline^1–10, resulting in seawater intrusion¹¹, land subsidence^12,13, streamflow depletion^14–16and 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. 

Forest–savanna boundaries are ecotones that support complex ecosystem functions and are sensitive to biotic/abiotic perturbations. What drives their distribution today and how it may shift in the future are open questions. Feedbacks among climate, fire, herbivory, and land use are known drivers. Here, we show that alternating seasonal drought and waterlogging stress favors the dominance of savanna-like ecosystems over forests. We track the seasonal water-table depth as an indicator of water stress when too deep and oxygen stress when too shallow and map forest/savanna occurrence within this double-stress space in the neotropics. We find that under a given annual precipitation, savannas are favored in landscape positions experiencing double stress, which is more common as the dry season strengthens (climate driver) but only found in waterlogged lowlands (terrain driver). We further show that hydrological changes at the end of the century may expose some flooded forests to savanna expansion, affecting biodiversity and soil carbon storage. Our results highlight the importance of land hydrology in understanding/predicting forest–savanna transitions in a changing world. 

After 4.5 billion years as an evolving and dynamic planet, the Earth continues to evolve but with human‐altered dynamics. Earth scientists have special opportunities and responsibilities to accelerate our understanding of Earth's changes that are transforming our most remarkable home. 

Abstract Increasing evidence suggests that tree growth is sink-limited by environmental and internal controls rather than by carbon availability. However, the mechanisms underlying sink-limitations are not fully understood and thus not represented in large-scale vegetation models. We develop a simple, analytically solved, mechanistic, turgor-driven growth model (TDGM) and a phloem transport model (PTM) to explore the mechanics of phloem transport and evaluate three hypotheses. First, phloem transport must be explicitly considered to accurately predict turgor distributions and thus growth. Second, turgor-limitations can explain growth-scaling with size (metabolic scaling). Third, turgor can explain realistic growth rates and increments. We show that mechanistic, sink-limited growth schemes based on plant turgor limitations are feasible for large-scale model implementations with minimal computational demands. Our PTM predicted nearly uniform sugar concentrations along the phloem transport path regardless of phloem conductance, stem water potential gradients and the strength of sink-demands contrary to our first hypothesis, suggesting that phloem transport is not limited generally by phloem transport capacity per se but rather by carbon demand for growth and respiration. These results enabled TDGM implementation without explicit coupling to the PTM, further simplifying computation. We test the TDGM by comparing predictions of whole-tree growth rate to well-established observations (site indices) and allometric theory. Our simple TDGM predicts realistic tree heights, growth rates and metabolic scaling over decadal to centurial timescales, suggesting that tree growth is generally sink and turgor limited. Like observed trees, our TDGM captures tree-size- and resource-based deviations from the classical ¾ power-law metabolic scaling for which turgor is responsible. 

The photophysical properties of naturally occurring chlorophylls depend on the regioisomeric nature of the β-pyrrolic substituents. Such systems are the “gold standard” by which such effects are judged. However, simple extrapolations from what has been learned with chlorophylls may not be appropriate for other partially reduced porphyrinoids. Here we report the synthesis of a series of cis / trans -porphodilactones ( cis / trans -1) and related derivatives ( cis / trans 2–5) designed to probe the effect of regioisomeric substitution in porphyrinoids that incorporate degrees of unsaturation through the β-pyrrolic periphery that exceed those of chlorophyll. These test systems were obtained through β-pyrrolic modifications of the tetrapyrrolic core, which included reduction of β-diazalone to the corresponding dilactol moieties and 1,3-dipolar cycloadditions. In the case of cis - vs. trans -3 bearing two pyrrolidine-fused β-rings we found an unprecedented Δ Q L up to ca. 71 nm (2086 cm −1 ), where Δ Q L ( Q L means the lowest energy transfer band, also the S 0 → S 1 transition band, which is often assigned as Q y (0,0) band) refers to the transition energy difference between the corresponding cis / trans -isomers. The Δ Q L values for these and other systems reported here were found to depend on the differences in the HOMO–LUMO energy gap and to be tied to the degeneracy and energy level splitting of the FMOs, as inferred from a combination of MCD spectral studies and DFT calculations. The aromaticity, estimated from the chemical shifts of the N–H protons and supported by theoretical calculations ( e.g. , AICD plots and NICS(1) values), was found to correlate with the extent of porphyrin periphery saturation resulting from the specific β-modifications. The aromaticity proved inversely proportional to the degree to which the regioisomerism affected the photophysical properties as noted from plots of Δ Q L s in cm −1 vs. the average NICS(1) values for 1–5. Such a finding is not something that can be easily interpolated from prior work and thus reveals how aromaticity may be used to fine-tune photophysical effects in reduced porphyrinoids.