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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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Simulation and Modeling of Hypersonic Turbulent Boundary Layers Subject to Favorable Pressure Gradients due to Streamline Curvature

Direct numerical simulations (DNS) of favorable-pressure-gradient turbulent boundary layers are presented for a nominal freestream Mach number of 5, with the objective of assessing the limitations of the currently available Reynolds-averaged Navier-Stokes (RANS) models. The favorable pressure gradient is induced by the streamwise curvature of the two-dimensional, planar, convex measurement surface used during experiments at the Texas A&M University. The DNS data shows good comparison with the measured velocity profiles, strain rates, and some, but not all, of the Reynolds-stress components. The discrepancies between the predicted and the measured wall-normal as well as shear stress components are primarily attributed to the lower than actual values inferred from typical PIV measurements of turbulent boundary layers. The DNS data shows a zero or slightly negative Reynolds shear stress in the outer part of the boundary-layer, which is indicative of the decaying turbulent motion under a strong favorable pressure gradient. The DNS data is also compared with the results of RANS computations based on commonly used zero, one, and two equation eddy-viscosity models. The RANS models yield reasonable comparisons with the DNS-based skin friction under zero and weak pressure gradients, but significant discrepancies under a strong pressure gradient. The k-w SST model provided the best overall predictions of skin friction, except in the region where the flow transitions from a favorable to an adverse pressure gradient. While the RANS models examined herein also give good predictions of the Reynolds shear stress under a sufficiently weak pressure gradient, none of those models are able to appropriately capture the reduction in the Reynolds stresses when the flow was subjected to a strong pressure gradient. An a priori assessment of the turbulent heat-flux prediction based on the assumption of a constant turbulent Prandtl number with the DNS data shows that while the constant turbulent Prandtl number model is effective in predicting the wall-normal component of turbulent heat flux, it does not capture the turbulent heat transfer in the streamwise direction for all the pressure gradient cases. The failure of the constant turbulent Prandtl number model highlights a requirement for more advanced models of the turbulent heat flux.

turbulent boundary layers↗
DOE OSTI2020

Efficient Ensemble-Based Stochastic Gradient Methods for Optimization Under Geological Uncertainty

Ensemble-based stochastic gradient methods, such as the ensemble optimization (EnOpt) method, the simplex gradient (SG) method, and the stochastic simplex approximate gradient (StoSAG) method, approximate the gradient of an objective function using an ensemble of perturbed control vectors. These methods are increasingly used in solving reservoir optimization problems because they are not only easy to parallelize and couple with any simulator but also computationally more efficient than the conventional finite-difference method for gradient calculations. In this work, we show that EnOpt may fail to achieve sufficient improvement of the objective function when the differences between the objective function values of perturbed control variables and their ensemble mean are large. On the basis of the comparison of EnOpt and SG, we propose a hybrid gradient of EnOpt and SG to save on the computational cost of SG. We also suggest practical ways to reduce the computational cost of EnOpt and StoSAG by approximating the objective function values of unperturbed control variables using the values of perturbed ones. We first demonstrate the performance of our improved ensemble schemes using a benchmark problem. Results show that the proposed gradients saved about 30–50% of the computational cost of the same optimization by using EnOpt, SG, and StoSAG. As a real application, we consider pressure management in carbon storage reservoirs, for which brine extraction wells need to be optimally placed to reduce reservoir pressure buildup while maximizing the net present value. Results show that our improved schemes reduce the computational cost significantly.

58 GEOSCIENCES↗
DOE OSTI2025

Impact of Different Thermal Gradients on the Dynamics of Cylindrical Lithium-ion Cells Subject to Accelerated Aging and on Module Performance

This study investigates the impacts of applying different thermal gradient patterns to cylindrical lithium-ion cells in a module on cell dynamics (temperatures, current flows, state of charge), module performance (evolution of resistance, capacity, and energy versus cycle number), and module lifetime. The thermal gradients were generated using cooling plates (CPs) with three different flow-field designs, namely, straight, perpendicular, and U-turn. The study uses computational fluid dynamics (CFD), the pseudo-two-dimensional (P2D) battery model, capacity loss and increased impedance due to the growth of a solid-electrolyte-interphase, and the electric current distribution from module terminals to cells that depends on the series-parallel electrical connections among the cells. The impact of the thermal gradient (resulting from the CP designs) on the variability in resistance, current, state of charge, and voltage among the cells was analyzed and linked to differences in the module's performance. Applying a thermal gradient to parallel-connected strings of series-connected cells led to variation in the current through each parallel string and an imbalance in the voltage of series-connected cells. Module performance is poorer when the thermal gradient causes a voltage imbalance than when it causes a current imbalance. Module performance becomes the worst when both current variation and voltage imbalance happen together. For instance, the module's lifetime (estimated as reaching 80% of its initial capacity) varied by 5% to 17.5%, depending on the magnitude and pattern of the imposed thermal gradient. As the relative orientation between thermal gradients and cells' electrical connectivity influences the module's performance, appropriate consideration should be given to the choice of the CP, especially if large thermal gradients are allowed.

Battery thermal management↗
DOE OSTI2021

Single Molecule Spectroscopy Studies of Acid–Base Chemical Gradients Using Nile Red as a Probe of Local Surface Acidity

Single molecule spectroscopy studies of local acidity along bifunctional acid-base gradients are reported. Gradients are prepared by directional vapor phase diffusion and subsequent reaction of 3-aminopropyl-trimethoxysilane with a uniform silica film. Gradient formation is confirmed by spectroscopic ellipsometry and by static water contact angle measurements. X-ray photoelectron spectroscopy is used to characterize the nitrogen content and degree of nitrogen protonation along the gradient. Nile Red is employed as the probe dye in single molecule spectroscopy studies of these gradients. While Nile Red is well-known for its solvent sensitivity, it is used here, for the first time, to sense the acid/base properties of the film in two-color wide-field fluorescence imaging experiments. The data reveal broad bimodal distributions of Nile Red emission spectra that vary along the gradient direction. The single-molecule results are consistent with solution-phase ensemble acid/base studies of the dye. The former reveal a gradual transition from a surface dominated by basic aminosilane sites at the high-amine end of the gradient to one dominated by acidic silanol sites at the low-amine end. The sub-diffraction-limited spatial resolution afforded by superlocalization of the single molecules reveals spatial correlations in the acid/base properties of the gradient over ~ 200 nm distances. Furthermore, these studies provide data relevant to the use of aminosilane-modified silica in bifunctional, cooperative chemical catalysis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Ground and excited state gradients with end-to-end differentiable semiempirical quantum chemistry

Accurate and efficient gradients of molecular energy with respect to nuclear degrees of freedom are essential for geometry optimization and molecular dynamics, including simulations that go beyond the Born–Oppenheimer regime. A common approach involves deriving analytical formulas for new electronic structure methods, which is often conceptually difficult and requires tedious coding. Here, we implement analytical, semi-numerical, and automatic differentiation (AD)-based gradient pathways for semiempirical Hamiltonian models in the PYSEQM software package, leveraging both graphics processing unit (GPU) and central processing unit (CPU) architectures. We further extend these capabilities to excited states calculated using the configuration interaction singles and time-dependent Hartree–Fock ansätze. We benchmark wall time, peak memory usage, and accuracy across three molecular families of varying chemical complexity, including systems of up to a thousand atoms. For ground-state simulations, analytical and AD gradients achieve near-identical GPU runtimes, while semi-numerical gradients are slower on GPU but remain competitive on CPU. For excited states, both analytical and custom AD approaches using implicit differentiation show similar performance and low memory requirements, whereas gradients with full AD are memory-limited. AD gradients match analytical ones in accuracy across all tested systems, aided by a quaternion-based diatomic frame rotation for two-center quantities that ensures smooth energy surfaces. Overall, automatic differentiation emerges as a practical alternative to analytical gradients in semiempirical quantum chemistry, offering high accuracy while allowing seamless integration in AI-driven workflows and popular packages, such as PyTorch and JAX. Our results provide actionable guidance for selecting optimal gradient strategies in large-scale ground- and excited-state molecular dynamics simulations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Monsoon Depression Amplification by Horizontal Shear and Humidity Gradients: A Shallow Water Perspective

Transient, synoptic-scale vortices produce a large fraction of total rainfall in most monsoon regions and are often associated with extreme precipitation. However, the mechanism of their amplification remains a topic of active research. For monsoon depressions, which are the most prominent synoptic-scale vortex in the Asian–Australian monsoon, recent work has suggested that meridional gradients in zonal wind in the vortex environment may produce growth through barotropic instability, while meridional gradients in environmental humidity have also been proposed to cause amplification through coupling with precipitating convection. Here, a two-dimensional shallow water model on a sphere with parameterized precipitation is used to examine the relative role played by these two environmental gradients. By systematically varying the meridional moisture gradient and meridional wind shear for both weak, quasi-linear waves and finite-amplitude isolated vortices, we show that rotational winds in the initial vortex are amplified most strongly by meridional shear of the environmental zonal wind, while vortex precipitation rates are most sensitive to environmental moisture gradients. The growth rate in the presence of both gradients is less than the sum of growth rates in the presence of isolated gradients, as the phase relation between moisture and vorticity anomalies becomes distorted with increasing shear. In conclusion, these results suggest that background meridional gradients in both zonal wind and environmental humidity can contribute to the amplification of vortices to monsoon depression strength, but with some degree of decoupling of the dry rotational flow and the moist convection.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Effect of barren plateaus on gradient-free optimization

Barren plateau landscapes correspond to gradients that vanish exponentially in the number of qubits. Such landscapes have been demonstrated for variational quantum algorithms and quantum neural networks with either deep circuits or global cost functions. For obvious reasons, it is expected that gradient-based optimizers will be significantly affected by barren plateaus. However, whether or not gradient-free optimizers are impacted is a topic of debate, with some arguing that gradient-free approaches are unaffected by barren plateaus. Here we show that, indeed, gradient-free optimizers do not solve the barren plateau problem. Our main result proves that cost function differences, which are the basis for making decisions in a gradient-free optimization, are exponentially suppressed in a barren plateau. Hence, without exponential precision, gradient-free optimizers will not make progress in the optimization. We numerically confirm this by training in a barren plateau with several gradient-free optimizers (Nelder-Mead, Powell, and COBYLA algorithms), and show that the numbers of shots required in the optimization grows exponentially with the number of qubits.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1990

Experimental feasibility of investigating acoustic waves in Couette flow with entropy and pressure gradients

The feasibility is discussed for an experimental program for studying the behavior of acoustic wave propagation in the presence of strong gradients of pressure, temperature, and flow. Theory suggests that gradients effects can be experimentally observed as resonant frequency shifts and mode shape changes in a waveguide. A convenient experimental geometry for such experiments is the annular region between two co-rotating cylinders. Radial temperature gradients in a spinning annulus can be generated by differentially heating the two cylinders via electromagnetic induction. Radial pressure gradients can be controlled by varying the cylinder spin rates. Present technology appears adequate to construct an apparatus to allow independent control of temperature and pressure gradients. A complicating feature of a more advanced experiment, involving flow gradients, is the requirement for independently controlled cylinder spin rates. Also, the boundary condition at annulus terminations must be such that flow gradients are minimally disturbed. The design and construction of an advanced apparatus to include flow gradients will require additional technology development.

Parrott, Tony L.↗
DOE OSTI2019

On the exceptional damage-tolerance of gradient metallic materials

An experimental study is described on the fracture toughness and micro-mechanisms associated with the initiation and propagation of cracks in metallic nickel containing marked gradients in grain size, ranging from ~30 nm to ~4 μm. Specifically, cracks are grown in a gradient structured (GS) nickel with grain-size gradient ranging from the coarse macro-scale to nano-scale (CG → NG) and vice versa (NG → CG), with the measured crack-resistance R-curves compared to the corresponding behavior in uniform nano-grained (NG) and coarse-grained (CG) materials. It is found that the gradient structures display a much-improved combination of high strength and toughness compared to uniform grain-sized materials. However, based on J-integral measurements in the gradient materials, the crack-initiation toughness is far higher for cracks grown in the direction of the coarse-to-nano grained gradient than vice versa, a result which we ascribe primarily to excessive crack-tip blunting in the coarse-grained microstructure. Both gradient structures, however, display marked rising R-curve behavior with exceptional crack-growth toughnesses exceeding 200 MPa.m ½ .

36 MATERIALS SCIENCE↗
DOE OSTI2022

Extracting energy from ocean thermal and salinity gradients to power unmanned underwater vehicles: State of the art, current limitations, and future outlook

Thermal gradient energy-generation technologies for powering unmanned underwater vehicles (UUVs) or autonomous sensing systems in the ocean are mainly in the research development phase or commercially available at a limited scale, and salinity-gradient energy-generation technologies have not been adequately researched yet. The demand for self-powered UUVs suitable for long-term deployments has been growing, and further research related to small-scale ocean gradient energy systems is needed. In this study, we conducted a comprehensive review about harvesting energy from ocean thermal or salinity gradients for powering UUVs, focusing on gliders and profiling floats. Thermal gradient energy systems for UUVs based on phase change materials (PCM) cannot provide the energy required for powering autonomous sensing systems because of the systems' low energy conversion efficiency. Besides reducing energy consumption by developing more efficient electrical-mechanical systems, enhancing the thermal conductivity of the PCMs may help address this challenge by increasing the power generation rate of the UUVs. Several other emerging technologies, such as thermoelectric generators, shape memory alloys, and small-scale thermodynamic cycle systems, have shown potential for powering UUVs, but they are still only at the laboratory testing or conceptual design phase. The most advanced power generation technologies based on salinity gradients, reverse electrodialysis and pressure-retarded osmosis, are still not economically viable for large-scale deployment, mainly because of the high cost of the components required to operate in harsh saline environments. Our feasibility evaluation showed that existing salinity gradient power generation technologies are not directly feasible for powering UUVs in the open ocean.

16 TIDAL AND WAVE POWER↗
DOE OSTI2025

Operando Neutron Imaging of Lithium Flux and Gradient Cathode Design for Enhanced Kinetics in High‐Loading All‐Solid‐State Li─S Batteries

All-solid-state Li–sulfur batteries (ASSLSBs) are considered promising candidates for next-generation energy storage owing to their inherent safety, high energy density, and abundant sulfur resources. However, slow redox kinetics greatly limit sulfur utilization during solid-solid sulfur reactions, leading to significant challenges to achieve efficient performance in high-mass-loading ASSLSBs. Here, operando neutron image is employed to directly visualize, for the first time, that sluggish Li + transport kinetics and the uneven distribution of Li + during cathodic reactions are critical factors limiting sulfur conversion. To address this issue, gradient cathode architectures comprising three and five layers are designed, in which catholyte concentrations are strategically varied to optimize Li-ion flux and enhance ionic conductivity of the whole composite cathode electrode. Operando neutron imaging distinctly visualizes and confirms that three-layer gradient approach significantly enhances Li-ion mobility, resulting in more uniform redox reactions and greatly improved sulfur utilization compared to traditional non-gradient structures. Consequently, the three-layer gradient cathode achieves superior rate performance and reduced electrode polarization at high sulfur mass loadings of 4.5 and 6.0 mg cm −2 . Furthermore, the applicability and scalability of this design are demonstrated in a five-layer gradient cathode architecture, achieving an impressive discharge specific capacity increase from 656 mAh g −1 (three-layer gradient) to 1232 mAh g −1 at 1/20 C for ultra-high sulfur loading of 7.5 mg cm −2 . In conclusion, this innovative gradient cathode design offers substantial advancements in understanding and overcoming Li-ion transport limitations, paving the way toward practical, high-energy-density ASSLSBs.

25 ENERGY STORAGE↗
DOE OSTI2024

What is the gradient of a scalar function defined on a subspace of square matrices?

We illustrate a technique to calculate the gradient of scalar functions that are defined on any arbitrary matrix subspace. It generalizes our earlier work titled “What is the gradient of a scalar function of a symmetric matrix ?”(Indian Journal of Pure and Applied Mathematics (2022), https://doi.org/10.1007/s13226-022-00313-x), in which we considered the special case of the subspace of symmetric matrices. Extant methods to calculate the gradient in such cases have an inherent flaw which leads to spurious results that populate several publications, as well as respected textbooks and handbooks on matrix calculus. Here, we examine these sources and results in a rigorous and concrete mathematical setting of a finite-dimensional inner-product space and discover the inherent flaw and also a remedy. We demonstrate two ways to calculate the derivative/gradient and second derivative for scalar functions of matrices defined over an arbitrary matrix subspace; the first method is by considering any (differentiable) extension to the space of square matrices and projection of its gradient onto the given subspace. The second method utilizes an ordered basis and computes each component of the gradient through evaluation of the directional derivative. All the ideas presented are illustrated by non-trivial examples, namely, considering the subspace of 3 x 3 circulant and Toeplitz matrices and presenting the results of gradient-descent with both the spurious and correct gradients. Moreover, our bibliography makes it clear that a rigorous approach to matrix calculus is not common in practice, and our presentation of matrix calculus in the language of inner-product spaces will be significant and meaningful for applied mathematicians, engineers and researchers working in inter-disciplinary fields to avoid the conceptual pitfalls that exist.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Modeling the effect of temperature gradient on moisture and ionic transport in concrete

Most reinforced concrete structures are under the influence of environmental conditions, such as temperature fluctuations, moisture and chloride variations simultaneously. Thus, the moisture transfer in concrete is driven by the moisture gradient as well as the temperature gradient. Similarly, the ionic transfer in concrete is driven by the concentration gradient of the ion as well as the temperature gradient. This paper developed an analytical solution that can be used for the moisture or the chloride transport in concrete considering the effect of temperature gradient. The effect of mass transfer on the thermal conduction was not considered, so the problem is simplified as a one-way coupled problem. The analytical model was validated by using two CASE studies, in which realistic material parameters of concrete were used, the parameters were obtained from experiments in the literature. The comparisons between analytical results and experimental results showed good agreement. It indicated that the present model can successfully characterize the effect of temperature gradient on moisture transfer and the effect of temperature gradient on chloride transport in concrete.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Fast model-based scenario optimization in NSTX-U enabled by analytic gradient computation

Model-based optimization offers a systematic approach to advanced scenario planning. In this case, the feedforward-control inputs (actuator trajectories) that are needed to attain and sustain a desired scenario are obtained by solving a nonlinear constrained optimization problem. This class of problems generally minimize a cost function that measures the difference between desired and actual plasma states. Several numerical optimization algorithms, such as sequential quadratic programming, require repeated calculation of the cost function gradients with respect to the input trajectories. Calculating these gradients numerically can be computationally intensive, increasing the time needed to solve the feedforward-control optimization problem. Here, this work introduces a method to analytically calculate these cost function gradients from the current profile evolution model. This can significantly reduce the computational time and allow for fast feedforward-control optimization, which would eventually enable optimal scenario planning between discharges. The performance of the feedforward optimizer with analytical gradients is compared to a traditional optimization algorithm based on numerical gradients for different NSTX-U scenarios. The plasma dynamics in the optimization algorithm are simulated using the Control Oriented Transport SIMulator (COTSIM). Results of the work show that analytical gradients consistently reduce the computation time while achieving trajectories that are comparable to those obtained by traditional optimization algorithms based on numerical gradients.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Gradient microstructure induced shear band constraint, delocalization, and delayed failure in CuZr nanoglasses

The mechanical properties of metallic glasses (MGs) can be significantly tuned by introducing a nanoscale glass-glass interface microstructure. Here, we design three types of Cu 64 Zr 36 MG seamless gradient microstructures by combining glassy grain sizes from 3 to 15 nm. We perform tensile loading molecular dynamics simulations on the named gradient nanoglasses to characterize their mechanical behavior. In all cases, results indicate the generation of gradient plasticity following the gradient in grain size, i.e. local plasticity increases from large to small grain size regions. Loading parallel to the gradient direction results in initial broad necking followed by catastrophic failure. In contrast, loading perpendicular to the gradient direction results in diffused shear band propagation from large to small grain size regions, delaying the generation of a dominant shear band and further delocalizing plastic deformation. In conclusion, the results demonstrate the synergistic effects generated by heterogeneous gradient designs in the mechanical behavior of metallic glasses.

36 MATERIALS SCIENCE↗
DOE OSTI2023

The effect of the vertical gradients of photosynthetic parameters on the CO 2 assimilation and transpiration of a Panamanian tropical forest

Terrestrial biosphere models (TBMs) include the representation of vertical gradients in leaf traits associated with modeling photosynthesis, respiration, and stomatal conductance. However, model assumptions associated with these gradients have not been tested in complex tropical forest canopies. Here we compared TBM representation of the vertical gradients of key leaf traits with measurements made in a tropical forest in Panama, and then quantified the impact of the observed gradients on simulated canopy scale CO 2 and water fluxes. Comparison between observed and TBM trait gradients showed divergence that impacted canopy scale simulations of water vapor and CO 2 exchange. Notably, the ratio between the dark respiration rate and the maximum carboxylation rate was lower near the ground than at the top-of-canopy, leaf-level water-use efficiency was markedly higher at the top-of-canopy, and the decrease in maximum carboxylation rate from the top-of-canopy to the ground was less than TBM assumptions. The representation of the gradients of leaf traits in TBMs is typically derived from measurements made within-individual plants, or, for some traits, assumed constant due to a lack of experimental data. Our work shows that these assumptions are not representative of the trait gradients observed in species-rich, complex tropical forests.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

What is the gradient of a scalar function defined on a subspace of square matrices?

We illustrate a technique to calculate the gradient of scalar functions that are defined on any arbitrary matrix subspace. It generalizes our earlier work titled “What is the gradient of a scalar function of a symmetric matrix ?”(Indian Journal of Pure and Applied Mathematics (2022), doi:10.1007/s13226-022-00313-x), in which we considered the special case of the subspace of symmetric matrices. Extant methods to calculate the gradient in such cases have an inherent flaw which leads to spurious results that populate several publications, as well as respected textbooks and handbooks on matrix calculus. We examine these sources and results in a rigorous and concrete mathematical setting of a finite-dimensional inner-product space and discover the inherent flaw and also a remedy. We demonstrate two ways to calculate the derivative/gradient and second derivative for scalar functions of matrices defined over an arbitrary matrix subspace; the first method is by considering any (differentiable) extension to the space of square matrices and projection of its gradient onto the given subspace. The second method utilizes an ordered basis and computes each component of the gradient through evaluation of the directional derivative. All the ideas presented are illustrated by non-trivial examples, namely, considering the subspace of 3 × 3 circulant and Toeplitz matrices and presenting the results of gradient-descent with both the spurious and correct gradients. Moreover, our bibliography makes it clear that a rigorous approach to matrix calculus is not common in practice, and our presentation of matrix calculus in the language of inner-product spaces will be significant and meaningful for applied mathematicians, engineers and researchers working in inter-disciplinary fields to avoid the conceptual pitfalls that exist.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2021

Placing the East-West North American Aridity Gradient in a Multi-Century Context

Instrumental records indicate a century-long trend towards drying over western North America and wetting over eastern North America. A continuation of these trends into the future would have significant hydroclimatic and socioeconomic consequences in both the semi-arid Southwest and humid East. Using tree-ring reconstructions and hydrologic simulations of summer soil moisture, we evaluate and contextualize the modern summer aridity gradient within its natural range of variability established over the past 600 years and evaluate the effects of observed and anthropogenic precipitation, temperature, and humidity trends. The 2001–2020 positive (wet east-dry west) aridity gradient was larger than any 20-year period since 1400 CE, preceded by the most negative (wet west-dry east) aridity gradient during 1976-1995, leading to a strong multi-decade reversal in aridity gradient anomalies that was rivaled only by a similar event in the late-16th century. The 2001-2020 aridity gradient was dominated by long-term summer precipitation increases in the Midwest and Northeast, with smaller contributions from more warming in the West than the East and spring precipitation decreases in the Southwest. Multi-model mean climate simulations from CMIP6 experiments suggest anthropogenic climate trends should not have strongly affected the aridity gradient thus far. However, there is high uncertainty due to inter-model disagreement on anthropogenic precipitation trends. The recent strengthening of the observed aridity gradient, its increasing dependence on precipitation variability, and disagreement in modeled anthropogenic precipitation trends reveal significant uncertainties in how water resource availability will change across North America in the coming decades.

drought↗