Soil moisture statistical fractal is an important tool for downscaling remotely-sensed observations and has the potential to play a key role in multi-scale hydrologic modeling. The fractal was first introduced two decades ago, but relatively little is known regarding how its scaling exponents evolve in time in response to climatic forcings. Previous studies have neglected the process of moisture re-distribution due to regional groundwater flow. In this study we used a physically-based surface-subsurface processes model and numerical experiments to elucidate the patterns and controls of fractal temporal evolution in two U.S. Midwest basins. Groundwater flow was found to introduce large-scale spatial structure, thereby reducing the scaling exponents (τ), which has implications for the transferability of calibrated parameters to predict τ. However, the groundwater effects depend on complex interactions with other physical controls such as soil texture and land use. The fractal scaling exponents, while in general showing a seasonal mode that correlates with mean moisture content, display hysteresis after storm events that can be divided into three phases, consistent with literature findings: (a) wetting, (b) re-organizing, and (c) dry-down. Modeling experiments clearly show that the hysteresis is attributed to soil texture, whose "patchiness" is the primary contributing factor. We generalized phenomenological rules for the impacts of rainfall, soil texture, groundwater flow, and land use on τ evolution. Grid resolution has a mild influence on the results and there is a strong correlation between predictions of τ from different resolutions. Overall, our results suggest that groundwater flow should be given more consideration in studies of the soil moisture statistical fractal, especially in regions with a shallow water table.

Large-scale land models assume unidirectional land-to-river hydrological interactions, without considering feedbacks between channels and land. Using a tested, physically based model with explicit multiway interactions between overland, channel, wetland, and groundwater flows, we assessed how the representation and properties of channels influence simulated land surface hydrologic, biogeochemical, and ecosystem dynamics. A zone near the channels where various fluxes and states are significantly influenced by the channels, referred to as the fan of influence (FoI) of channels, has been identified. We elucidated two mechanisms inducing the model-derived FoI: the base flow mechanism, in which incised, gaining streams lower the water table and induce more base flow, and the relatively more efficient conveyance of the channel network compared to overland flow. We systematically varied drainage density and grid resolution to quantify the size of the FoI, which is found to span a large fraction of the watershed (25-50%) for hydrologic variables including depth to water table and recharge, etc. The FoI is more pronounced with low-resolution simulations but remains noticeable in hyperresolution (25 m) subbasin simulations. The FoI and the channel influence on basin-average fluxes are also similar in simulations with alternative parameter sets. We found that high-order, entrenched streams cause larger FoI. In addition, removing the simulated channels has disproportionally large influence on modeled wetland areas and inundation duration, which has implications for coupled biogeochemical or ecological modeling. Our results suggest that explicit channel representation provides important feedbacks to land surface dynamics which should be considered in meso or large-scale simulations. Since grid refinement incurs prohibitive computational cost, subgrid channel parameterization has advantages in efficiency over grid-based representations that do not distinguish between overland flow and channel flow.

The central Amazon forest is projected to experience larger interannual precipitation variability, with uncertain impacts on terrestrial hydrologic fluxes. How surface runoff, groundwater, and evapotranspiration (ET) change as a function of annual precipitation (AP) has large climate and biogeochemical implications. A process-based hydrological model is used to examine the sensitivity of hydrologic budgets and stream discharge Qs generation to AP in an upland Amazon catchment. The authors find that AP strongly controls infiltration, base flow, and surface runoff, but not ET. Hence, AP alone can predict interannual changes in these fluxes except ET. Experiments with perturbed rainfall show the strong control derives from the predominant groundwater component that varies linearly with AP but is insensitive to seasonal rainfall fluctuations. Most rainfall from large storms infiltrates and becomes base flow rather than runoff or ET. Annual baseflow index (BFI; the fraction of stream discharge from base flow) is nearly constant (~0.8) when AP is below ~2500 mmyr-1 and decreases with AP above this value, which represents an inflection point for increased storage-dependent saturation excess. These results indicate that the system is energy limited and groundwater dominated in dry seasons, which implies some resilience of ET to moderate droughts. The results suggest AP is a good predictor for interannual changes in infiltration. Both the seasonal near-surface soil moisture and surface runoff are correlated more strongly to the subsurface fluxes than to precipitation over monthly and annual time scales. Finally, the results confirm the importance of central Amazon groundwater flow and its buffering effect on storms and droughts, implying needed model development in regional to global models.

Floodplain lakes represent important aquatic ecosystems, and field-based estimates of their water budgets are difficult to obtain, especially over multiple years. We examine the hydrological fluxes for an Amazon floodplain lake connected to the Solimões River using a process-based hydrologic model. Water exchanges between the river and lake agree well with field estimates, including the timing of different hydrological phases. However, beyond available field data, modeling results show that the seven simulated years all differed from each other. These interannual differences were caused by the interplay between phases when water levels were rising with river-water flowing into the lake (RWRI), versus rising with lake-water flowing out to the river (RWLO). This exchange determines the river-water content in the lake (CL). Maximum CL occurred before river levels peaked because local catchment contributions can be sufficient to push lake-water out to the river, even as river levels rise. Numerical experiments show that the seasonal distribution of local rainfall, local catchment size, and interannual variability in both climate and river stage can contribute to differing dynamics of CL in a floodplain lake. Their impacts vary among phases: river-rise dominates the RWRI, whereas local hydrological processes dominate the RWLO and receding-water phases. Intermediate-to-long-term rainfall accumulation controls CL during the RWLO phase, whereas annual precipitation accumulation is important for CL during low water. Our model generalizes beyond limited available field studies and offers potential to better understand floodplain lakes in other areas and how regional versus local changes in climate may affect their hydrological dynamics.

The topography, and the biotic and abiotic parameters are typically upscaled to make watershed-scale hydrologic-biogeochemical models computationally tractable. However, upscaling procedure can produce biases when nonlinear interactions between different processes are not fully captured at coarse resolutions. Here we applied the Proper Orthogonal Decomposition Mapping Method (PODMM) to downscale the field solutions from a coarse (7 km) resolution grid to a fine (220 m) resolution grid. PODMM trains a reduced-order model (ROM) with coarse-resolution and fine-resolution solutions, here obtained using PAWS+CLM, a quasi-3-D watershed processes model that has been validated for many temperate watersheds. Subsequent fine-resolution solutions were approximated based only on coarse-resolution solutions and the ROM. The approximation errors were efficiently quantified using an error estimator. By jointly estimating correlated variables and temporally varying the ROM parameters, we further reduced the approximation errors by up to 20%. We also improved the method's robustness by constructing multiple ROMs using different set of variables, and selecting the best approximation based on the error estimator. The ROMs produced accurate downscaling of soil moisture, latent heat flux, and net primary production with O(1000) reduction in computational cost. The subgrid distributions were also nearly indistinguishable from the ones obtained using the fine-resolution model. Compared to coarse-resolution solutions, biases in upscaled ROM solutions were reduced by up to 80%. This method has the potential to help address the long-standing spatial scaling problem in hydrology and enable long-time integration, parameter estimation, and stochastic uncertainty analysis while accurately representing the heterogeneities.

The quantification of recharge and trans-valley underflow is needed in arid regions to estimate the impacts of new water withdrawals on the water table. However, for mountainous desert areas, such estimates are highly challenging, due to data scarcity, heterogeneous soils, and long residence times. Conventional assessment employs isolated groundwater models configured with simplified uniform estimates of recharge. Here, we employed a data-constrained surface-subsurface process model to provide an ensemble of spatially distributed recharge and underflow estimates using perturbed parameters. Then, the Model-Independent Parameter Estimation and Uncertainty Quantification (PEST) package was used to calibrate the aquifer hydraulic conductivity field in MODFLOW for this ensemble and reject implausible recharge values. This novel dual-model approach, broadly applicable to mountainous arid regions, was designed to maximally exploit available data sources. It can assimilate groundwater head observations, reject unrealistic parameters, and narrow the range of estimated drawdowns due to pumping. We applied this approach to the Chuckwalla basin in California, USA to determine natural recharge. Simulated recharge concentrates along alluvial fans at the mountain fronts and ephemeral washes where run-off water infiltrates. If an evenly distributed recharge was employed as in conventional studies, it would result in regional biases in estimated drawdown and larger uncertainty bounds. We also note that the speed of groundwater recovery does not guarantee sustainability: heavy pumping induces large hydraulic gradients that initially recover quickly when pumping is halted, but the system may not ultimately recover to pre-pumping levels.

Accurate prediction of snow water equivalent (SWE) can be valuable for water resource managers. Re-cently, deep learning methods such as long short-term memory (LSTM) have exhibited high accuracy in simulating hydrologic variables and can integrate lagged observations to improve prediction, but their benefits were not clear for SWE simulations. Here we tested an LSTM network with data integration (DI) for SWE in the western United States to integrate 30-day-lagged or 7-day-lagged observations of either SWE or satellite-observed snow cover fraction (SCF) to improve future predictions. SCF proved beneficial only for shallow-snow sites during snowmelt, while lagged SWE integration significantly improved prediction accuracy for both shallow-and deep-snow sites. The median Nash–Sutcliffe model efficiency coefficient (NSE) in temporal testing improved from 0.92 to 0.97 with 30-day-lagged SWE integration, and root-mean-square error (RMSE) and the difference between estimated and observed peak SWE values dmax were reduced by 41% and 57%, respectively. DI effectively mitigated accumulated model and forcing errors that would otherwise be persistent. Moreover, by applying DI to different observations (30-day-lagged, 7-day-lagged), we revealed the spatial distribution of errors with different persistent lengths. For example, integrating 30-day-lagged SWE was ineffective for ephemeral snow sites in the southwestern United States, but significantly reduced monthly-scale biases for regions with sta-ble seasonal snowpack such as high-elevation sites in California. These biases are likely attributable to large interannual variability in snowfall or site-specific snow redistribution patterns that can accumulate to impactful levels over time for nonephemeral sites. These results set up benchmark levels and provide guidance for future model improvement strategies.

The electric power grid is a critical societal resource connecting multiple infrastructural domains such as agriculture, transportation, and manufacturing. The electrical grid as an infrastructure is shaped by human activity and public policy in terms of demand and supply requirements. Further, the grid is subject to changes and stresses due to diverse factors including solar weather, climate, hydrology, and ecology. The emerging interconnected and complex network dependencies make such interactions increasingly dynamic, posing novel risks, and presenting new challenges to manage the coupled human-natural system. This paper provides a survey of models and methods that seek to explore the significant interconnected impact of the electric power grid and interdependent domains. We also provide relevant critical risk indicators (CRIs) across diverse domains that may be used to assess risks to electric grid reliability, including climate, ecology, hydrology, finance, space weather, and agriculture. We discuss the convergence of indicators from individual domains to explore possible systemic risk, i.e., holistic risk arising from cross-domain interconnections. Further, we propose a compositional approach to risk assessment that incorporates diverse domain expertise and information, data science, and computer science to identify domain-specific CRIs and their union in systemic risk indicators. Our study provides an important first step towards data-driven analysis and predictive modeling of risks in interconnected human-natural systems.

Recently, deep learning (DL) has emerged as a revolutionary and versatile tool transforming industry applications and generating new and improved capabilities for scientific discovery and model building. The adoption of DL in hydrology has so far been gradual, but the field is now ripe for breakthroughs. This paper suggests that DL-based methods can open up a complementary avenue toward knowledge discovery in hydrologic sciences. In the new avenue, machine-learning algorithms present competing hypotheses that are consistent with data. Interrogative methods are then invoked to interpret DL models for scientists to further evaluate. However, hydrology presents many challenges for DL methods, such as data limitations, heterogeneity and co-evolution, and the general inexperience of the hydrologic field with DL. The roadmap toward DL-powered scientific advances will require the coordinated effort from a large community involving scientists and citizens. Integrating process-based models with DL models will help alleviate data limitations. The sharing of data and baseline models will improve the efficiency of the community as a whole. Open competitions could serve as the organizing events to greatly propel growth and nurture data science education in hydrology, which demands a grassroots collaboration. The area of hydrologic DL presents numerous research opportunities that could, in turn, stimulate advances in machine learning as well.

Process-based modelling offers interpretability and physical consistency in many domains of geosciences but struggles to leverage large datasets efficiently. Machine-learning methods, especially deep networks, have strong predictive skills yet are unable to answer specific scientific questions. In this Perspective, we explore differentiable modelling as a pathway to dissolve the perceived barrier between process-based modelling and machine learning in the geosciences and demonstrate its potential with examples from hydrological modelling. ‘Differentiable’ refers to accurately and efficiently calculating gradients with respect to model variables or parameters, enabling the discovery of high-dimensional unknown relationships. Differentiable modelling involves connecting (flexible amounts of) prior physical knowledge to neural networks, pushing the boundary of physics-informed machine learning. It offers better interpretability, generalizability, and extrapolation capabilities than purely data-driven machine learning, achieving a similar level of accuracy while requiring less training data. Additionally, the performance and efficiency of differentiable models scale well with increasing data volumes. Under data-scarce scenarios, differentiable models have outperformed machine-learning models in producing short-term dynamics and decadal-scale trends owing to the imposed physical constraints. Differentiable modelling approaches are primed to enable geoscientists to ask questions, test hypotheses, and discover unrecognized physical relationships. Future work should address computational challenges, reduce uncertainty, and verify the physical significance of outputs.