Deep learning (DL), a new generation of artificial neural network research, has transformed industries, daily lives, and various scientific disciplines in recent years. DL represents significant progress in the ability of neural networks to automatically engineer problem‐relevant features and capture highly complex data distributions. I argue that DL can help address several major new and old challenges facing research in water sciences such as interdisciplinarity, data discoverability, hydrologic scaling, equifinality, and needs for parameter regionalization. This review paper is intended to provide water resources scientists and hydrologists in particular with a simple technical overview, transdisciplinary progress update, and a source of inspiration about the relevance of DL to water. The review reveals that various physical and geoscientific disciplines have utilized DL to address data challenges, improve efficiency, and gain scientific insights. DL is especially suited for information extraction from image‐like data and sequential data. Techniques and experiences presented in other disciplines are of high relevance to water research. Meanwhile, less noticed is that DL may also serve as a scientific exploratory tool. A new area termed AI neuroscience, where scientists interpret the decision process of deep networks and derive insights, has been born. This budding subdiscipline has demonstrated methods including correlation‐based analysis, inversion of network‐extracted features, reduced‐order approximations by interpretable models, and attribution of network decisions to inputs. Moreover, DL can also use data to condition neurons that mimic problem‐specific fundamental organizing units, thus revealing emergent behaviors of these units. Vast opportunities exist for DL to propel advances in water sciences.

Many of the scientific and societal challenges in understanding and preparing for global environmental change rest upon our ability to understand and predict the water cycle change at large river basin, continent, and global scales. However, current large-scale land models (as a component of Earth System Models, or ESMs) do not yet reflect the best hydrologic process understanding or utilize the large amount of hydrologic observations for model testing. This paper discusses the opportunities and key challenges to improve hydrologic process representations and benchmarking in ESM land models, suggesting that (1) land model development can benefit from recent advances in hydrology, both through incorporating key processes (e.g., groundwater-surface water interactions) and new approaches to describe multiscale spatial variability and hydrologic connectivity; (2) accelerating model advances requires comprehensive hydrologic benchmarking in order to systematically evaluate competing alternatives, understand model weaknesses, and prioritize model development needs, and (3) stronger collaboration is needed between the hydrology and ESM modeling communities, both through greater engagement of hydrologists in ESM land model development, and through rigorous evaluation of ESM hydrology performance in research watersheds or Critical Zone Observatories. Such coordinated efforts in advancing hydrology in ESMs have the potential to substantially impact energy, carbon, and nutrient cycle prediction capabilities through the fundamental role hydrologic processes play in regulating these cycles.

Earth System Models (ESMs) are essential tools for understanding and predicting global change, but they cannot explicitly resolve hillslope-scale terrain structures that fundamentally organize water, energy, and biogeochemical stores and fluxes at subgrid scales. Here we bring together hydrologists, Critical Zone scientists, and ESM developers, to explore how hillslope structures may modulate ESM grid-level water, energy, and biogeochemical fluxes. In contrast to the one-dimensional (1-D), 2-to 3-m deep, and free-draining soil hydrology in most ESM land models, we hypothesize that 3-D, lateral ridge-to-valley flow through shallow and deep paths and insolation contrasts between sunny and shady slopes are the top two globally quantifiable organizers of water and energy (and vegetation) within an ESM grid cell. We hypothesize that these two processes are likely to impact ESM predictions where (and when) water and/or energy are limiting. We further hypothesize that, if implemented in ESM land models, these processes will increase simulated continental water storage and residence time, buffering terrestrial ecosystems against seasonal and interannual droughts. We explore efficient ways to capture these mechanisms in ESMs and identify critical knowledge gaps preventing us from scaling up hillslope to global processes. One such gap is our extremely limited knowledge of the subsurface, where water is stored (supporting vegetation) and released to stream baseflow (supporting aquatic ecosystems). We conclude with a set of organizing

46Process-based hydrological models have a long history dating back to the 1960s. 47Criticized by some as over-parameterized, overly complex, and difficult to use, a more 48 nuanced view is that these tools are necessary in many situations and, in a certain class of 49 problems, they are the most appropriate type of hydrological model. This is especially the 50 case in situations where knowledge of flow paths or distributed state variables and/or 51 preservation of physical constraints is important. Examples of this include: spatiotemporal 52 variability of soil moisture, groundwater flow and runoff generation, sediment and 53 contaminant transport, or when feedbacks among various Earth's system processes or 54 understanding the impacts of climate non-stationarity are of primary concern. These are 55 situations where process-based models excel and other models are unverifiable. This article 56 presents this pragmatic view in the context of existing literature to justify the approach where 57 applicable and necessary. We review how improvements in data availability, computational 58 resources and algorithms have made detailed hydrological simulations a reality. Avenues for 59 the future of process-based hydrological models are presented suggesting their use as virtual 60 laboratories, for design purposes, and with a powerful treatment of uncertainty. 61

There are a growing number of large-scale, complex hydrologic models that are capable of simulating integrated surface and subsurface flow. Many are coupled to land-surface energy balance models, biogeochemical and ecological process models, and atmospheric models. Although they are being increasingly applied for hydrologic prediction and environmental understanding, very little formal verification and/or benchmarking of these models has been performed. Here we present the results of an intercomparison study of seven coupled surface-subsurface models based on a series of benchmark problems. All the models simultaneously solve adapted forms of the Richards and shallow water equations, based on fully 3-D or mixed (1-D vadose zone and 2-D groundwater) formulations for subsurface flow and 1-D (rill flow) or 2-D (sheet flow) conceptualizations for surface routing. A range of approaches is used for the solution of the coupled equations, including global implicit, sequential iterative, and asynchronous linking, and various strategies are used to enforce flux and pressure continuity at the surface-subsurface interface. The simulation results show good agreement for the simpler test cases, while the more complicated test cases bring out some of the differences in physical process representations and numerical solution approaches between the models. Benchmarks with more traditional runoff generating mechanisms, such as excess infiltration and saturation, demonstrate more agreement between models, while benchmarks with heterogeneity and complex water table dynamics highlight differences in model formulation. In general, all the models demonstrate the same qualitative behavior, thus building confidence in their use for hydrologic applications.