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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.

Learning management systems (LMSs) are ubiquitous components of the academic technology experience for learners across a wide variety of instructional contexts. Learners' interactions within an LMS are often contingent upon how instructors architect a module, course, or program of study. Patterns related to these learner interactions, often referred to as learning analytics implementation (LAI), can be represented by combining system-level LMS data with course-level design decisions to inform more granular insights into learner behaviour. The purpose of this paper is to use the LAI framework, specifically the principles of coordination and comparison (Wise & Vytasek, 2017), to examine how learner interaction patterns associated with LMS-use variables correspond to deliberate learning design decisions and course outcomes for a group of courses in the same undergraduate writing program. Visualizations of learner activity exhibited similar patterns of learner engagement across courses, corroborating the observation that design decisions heavily influence learner behaviour. Predictive analyses demonstrated strong influence of LMS use on final grades while accounting for course instructor. That is, while page views were not related to final grade, the length of discussion entries was often predictive. These results suggest that students who practised writing more -- the main learning objective of this course -- had higher final grades, regardless of variations in instructor and semester.

As droughts have widespread social and ecological impacts, it is critical to develop long-term adaptation and mitigation strategies to reduce drought vulnerability. Climate models are important in quantifying drought changes. Here, we assess the ability of 285 CMIP6 historical simulations, from 17 models, to reproduce drought duration and severity in three observational data sets using the Standardized Precipitation Index (SPI). We used summary statistics beyond the mean and standard deviation, and devised a novel probabilistic framework, based on the Hellinger distance, to quantify the difference between observed and simulated drought characteristics. Results show that many simulations have less than ±10% error in reproducing the observed drought summary statistics. The hypothesis that simulations and observations are described by the same distribution cannot be rejected for more than 80% of the grids based on our H distance framework. No single model stood out as demonstrating consistently better performance over large regions of the globe. The variance in drought statistics among the simulations is higher in the tropics compared to other latitudinal zones. Though the models capture the characteristics of dry spells well, there is considerable bias in low precipitation values. Good model performance in terms of SPI does not imply good performance in simulating low precipitation. Our study emphasizes the need to probabilistically evaluate climate model simulations in order to both pinpoint model weaknesses and identify a subset of best-performing models that are useful for impact assessments.

The Community Land Model (CLM) is the land component of the Community Earth System Model (CESM) and is used in several global and regional modeling systems. In this paper, we introduce model developments included in CLM version 5 (CLM5), which is the default land component for CESM2. We assess an ensemble of simulations, including prescribed and prognostic vegetation state, multiple forcing data sets, and CLM4, CLM4.5, and CLM5, against a range of metrics including from the International Land Model Benchmarking (ILAMBv2) package. CLM5 includes new and updated processes and parameterizations: (1) dynamic land units, (2) updated parameterizations and structure for hydrology and snow (spatially explicit soil depth, dry surface layer, revised groundwater scheme, revised canopy interception and canopy snow processes, updated fresh snow density, simple firn model, and Model for Scale Adaptive River Transport), (3) plant hydraulics and hydraulic redistribution, (4) revised nitrogen cycling (flexible leaf stoichiometry, leaf N optimization for photosynthesis, and carbon costs for plant nitrogen uptake), (5) global crop model with six crop types and time-evolving irrigated areas and fertilization rates, (6) updated urban building energy, (7) carbon isotopes, and (8) updated stomatal physiology. New optional features include demographically structured dynamic vegetation model (Functionally Assembled Terrestrial Ecosystem Simulator), ozone damage to plants, and fire trace gas emissions coupling to the atmosphere. Conclusive establishment of improvement or degradation of individual variables or metrics is challenged by forcing uncertainty, parametric uncertainty, and model structural complexity, but the multivariate metrics presented here suggest a general broad improvement from CLM4 to CLM5.

Accurate discharge values form the foundation of effective water resource planning and management. Unfortunately, these data are often perceived as absolute and deterministic by users, modelers, and decision-makers, despite the inherent subjectivity and uncertainty in the data preparation processes. This study is undertaken to examine the discharge estimation methods used by the Water Survey of Canada (WSC) and their impacts on reported discharge values. First, we explain the hydrometric station network, essential terminologies, and fundamental concepts of rating curves. Subsequently, we examine WSC's standard operating procedures (SOPs), including shift, temporary shift, and override, in discharge estimation. Based on WSC's records of ∼ 1800 active hydrometric stations for discharge monitoring, we evaluated sample rating curves and their correlation with stage and discharge measurement. We investigate under-ice measurements, ice condition periods and frequency, and extreme values in contrast to rating curves. Employing an independent workflow, we demonstrate that 69 % of existing records align with the rating curve and temporary shift concept, while the remaining 31 % follow alternative discharge estimation methods (override). Selected example stations illustrate discharge estimation methods over time. We also demonstrate the impact of override and temporary shifts on commonly assumed uncertainty models. Given the practices of override and temporary shifts within WSC, there is a need to explore innovative methods for discharge uncertainty estimation. We hope our research helps in the critical challenge of estimating and communicating uncertainty in published discharge values. [ABSTRACT FROM AUTHOR]

The diversity in hydrologic models has historically led to great controversy on the "correct" approach to process-based hydrologic modeling, with debates centered on the adequacy of process parameterizations, data limitations and uncertainty, and computational constraints on model analysis. In this paper, we revisit key modeling challenges on requirements to (1) define suitable model equations, (2) define adequate model parameters, and (3) cope with limitations in computing power. We outline the historical modeling challenges, provide examples of modeling advances that address these challenges, and define outstanding research needs. We illustrate how modeling advances have been made by groups using models of different type and complexity, and we argue for the need to more effectively use our diversity of modeling approaches in order to advance our collective quest for physically realistic hydrologic models.

Seasonal streamflow forecasts provide key information for decision-making in fields such as water supply management, hydropower generation, and irrigation scheduling. The predictability of streamflow on seasonal timescales relies heavily on initial hydrological conditions, such as the presence of snow and the availability of soil moisture. In high-latitude and high-altitude headwater basins in North America, snowmelt serves as the primary source of runoff generation. This study presents and evaluates a data-driven workflow for probabilistic seasonal streamflow forecasting in snow-fed river basins across North America (Canada and the USA). The workflow employs snow water equivalent (SWE) measurements as predictors and streamflow observations as predictands. Gap-filling of SWE datasets is accomplished using quantile mapping from neighboring SWE and precipitation stations, and principal component analysis is used to identify independent predictor components. These components are then utilized in a regression model to generate ensemble hindcasts of streamflow volumes for 75 nival basins with limited regulation from 1979 to 2021, encompassing diverse geographies and climates. Using a hindcast evaluation approach that is user-oriented provides key insights for snow-monitoring experts, forecasters, decision-makers, and workflow developers. The analysis presented here unveils a wide spectrum of predictability and offers a glimpse into potential future changes in predictability. Late-season snowpack emerges as a key factor in predicting spring and summer volumes, while high precipitation during the target period presents challenges to forecast skill and streamflow predictability. Notably, we can predict lower-than-normal and higher-than-normal streamflows during spring to early summer with lead times of up to 5 months in some basins. Our workflow is available on GitHub as a collection of Jupyter Notebooks, facilitating broader applications in cold regions and contributing to the ongoing advancement of methodologies. [ABSTRACT FROM AUTHOR]

Recent advances in differentiable modeling, a genre of physics-informed machine learning that trains neural networks (NNs) together with process-based equations, have shown promise in enhancing hydrological models' accuracy, interpretability, and knowledge-discovery potential. Current differentiable models are efficient for NN-based parameter regionalization, but the simple explicit numerical schemes paired with sequential calculations (operator splitting) can incur numerical errors whose impacts on models' representation power and learned parameters are not clear. Implicit schemes, however, cannot rely on automatic differentiation to calculate gradients due to potential issues of gradient vanishing and memory demand. Here we propose a "discretize-then-optimize" adjoint method to enable differentiable implicit numerical schemes for the first time for large-scale hydrological modeling. The adjoint model demonstrates comprehensively improved performance, with Kling–Gupta efficiency coefficients, peak-flow and low-flow metrics, and evapotranspiration that moderately surpass the already-competitive explicit model. Therefore, the previous sequential-calculation approach had a detrimental impact on the model's ability to represent hydrological dynamics. Furthermore, with a structural update that describes capillary rise, the adjoint model can better describe baseflow in arid regions and also produce low flows that outperform even pure machine learning methods such as long short-term memory networks. The adjoint model rectified some parameter distortions but did not alter spatial parameter distributions, demonstrating the robustness of regionalized parameterization. Despite higher computational expenses and modest improvements, the adjoint model's success removes the barrier for complex implicit schemes to enrich differentiable modeling in hydrology. [ABSTRACT FROM AUTHOR]

Lakes and reservoirs are an integral part of the terrestrial water cycle. In this work, we present the implementation of different water balance models of lakes and reservoirs into mizuRoute, a vector‐based routing model, termed mizuRoute‐Lake. As the main advantage of mizuRoute‐Lake, users can choose between various parametric models implemented in mizuRoute‐Lake. So far, three parametric models of lake and reservoir water balance, namely Hanasaki, HYPE, and Döll are implemented in mizuRoute‐Lake. In general, the parametric models relate the outflow from lakes or reservoirs to the storage and various parameters including inflow, demand, volume of storage, etc. Additionally, this flexibility allows users to easily evaluate and compare the effect of various water balance models for a lake without needing to reconfigure the routing model or change the parameters of other lakes or reservoirs in the modeling domain. Users can also use existing data such as historical observations or water management models to specify the behavior of a selected number of lakes and reservoirs within the modeling domain using the data‐driven capability of mizuRoute‐Lake. We demonstrate the flexibility of mizuRoute‐Lake by presenting global, regional, and local scale applications. The development of mizuRoute‐Lake paves the way for better integration of water management models, locally measured, and remotely sensed data sets in the context of Earth system modeling. Plain Language Summary: Lakes and reservoirs impact the hydrological cycle. While there are many lake and reservoir models, a modeling framework typically encompasses a single selected lake and/or reservoir model representation. Including various lake discharge models in one model framework is useful for many applications of water resources. In this study, we present the implementation of various lake and reservoir water balance models in the mizuRoute‐Lake. mizuRoute‐Lake provides the flexibility to use and evaluate different lake and reservoir water balance models in river basins. Such flexibility can facilitate the integration with Earth system models, land surface models, water management models, and in situ or remote sensing observations. Additionally, it can help shed light on often neglected interactions and uncertainties in lake and reservoir models and their parameterizations within the hydrological cycle. Key Points: mizuRoute‐Lake offers the flexibility to select from multiple parametric models for lakes and reservoirs' water balanceUsers can leverage existing data, historical observations, water management models, and remotely sensed data, to specify lake behaviorThe versatility of mizuRoute‐Lake is demonstrated through its application at different scales, global to local [ABSTRACT FROM AUTHOR]

Editors of several journals in the field of hydrology met during the General Assembly of the European Geosciences Union-EGU in Vienna in April 2017. This event was a follow-up of similar meetings held in 2013 and 2015. These meetings enable the group of editors to review the current status of the journals and the publication process, and to share thoughts on future strategies. Journals were represented at the 2017 meeting by their editors, as shown in the list of authors. The main points on invigorating hydrological research through journal publications are communicated in this joint editorial published in the above journals.

This study assesses the impact of different flux parameterizations and model parameters on simulations of snow depth. Through a sensitivity analysis in a process-based snow model based on the SUMMA framework, various options for parametrizing snow processes and adjusting parameter values were evaluated to identify optimal modeling approaches, understand sources of uncertainty, and determine reasons for model weaknesses. The study focused on model parameterizations of precipitation partitioning, liquid water flow, snow albedo, atmospheric stability, and thermal conductivity. In this study, sensitivity analysis (SA) is performed using the one-at-a-time (OAT) SA method as well as the Morris Method to estimate Elementary Effects, aiming to further explore the magnitudes and patterns of sensitivities. The sensitivity analyses in this study are used to evaluate process parameterizations, model parameter values, and model configurations. Performance metrics such as the Nash-Sutcliffe Efficiency (NSE), the Kling-Gupta Efficiency (KGE), the root mean squared log error (RMSLE), and mean are used to assess the similarity between simulated and observed data. Bootstrapping is employed to estimate the variability of mean Elementary Effects and establish confidence bounds. The key findings of this research indicate that sensitivity analysis of snow modelling parameters plays a crucial role in understanding their impact on decision outcomes. The study identified the most sensitive parameters, such as critical temperature and thermal conductivity of snow, as well as liquid water drainage parameters. It was observed that water balance fluxes exhibited higher sensitivity than energy balance fluxes in simulating snow processes. The analysis also highlighted the importance of accurately representing water balance processes in snow models for improved accuracy and reliability. A key finding in this study is that the sensitivity of performance metrics to model parameters is contaminated by equifinality (i.e., parameter perturbations lead to similar performance metrics for quite different snow depth time series), and hence many published parameter sensitivity studies may provide misleading results. These findings have implications for snow hydrology research and water resource management, providing valuable insights for optimizing snow modelling and enhancing decision-making. [ABSTRACT FROM AUTHOR]

Global sensitivity analysis (GSA) enhances our understanding of computational models and simplifies model parameter estimation. VarIance‐based Sensitivity analysis using COpUlaS (VISCOUS) is a variance‐based GSA framework. The advantage of VISCOUS is that it can use existing model input‐output data (e.g., water model parameters‐responses) to estimate the first‐ and total‐order Sobol' sensitivity indices. This study improves VISCOUS by refining its handling of marginal densities of the Gaussian mixture copula model (GMCM). We then evaluate VISCOUS using three types of generic functions relevant to water system models. We observe that its performance depends on function dimension, input‐output data size, and non‐identifiability. Function dimension refers to the number of uncertain input factors analyzed in GSA, and non‐identifiability refers to the inability to estimate GMCM parameters. VISCOUS proves powerful in estimating first‐order sensitivity with a small amount of input‐output data (e.g., 200 in this study), regardless of function dimension. It always ranks input factors correctly in both first‐ and total‐order terms. For estimating total‐order sensitivity, it is recommended to use VISCOUS when the function dimension is not very high (e.g., less than 20) due to the challenge of producing sufficient input‐output data for accurate GMCM inferences (e.g., more than 10,000 data). In cases where all input factors are equally important (a rarity in practice), VISCOUS faces non‐identifiability issues that impact its performance. We provide a didactic example and an open‐source Python code, pyVISCOUS, for broader user adoption. Plain Language Summary: Global sensitivity analysis is a method used to better understand and estimate parameters in computational models. VarIance‐based Sensitivity analysis using COpUlaS (VISCOUS) is a framework for this purpose. It estimates the sensitivity of model outcomes to different uncertain model input factors by using the existing input and output data (e.g., water model parameters and responses). This study improved VISCOUS and tested it with various functions. We found that its performance depends on the number of input factors, the amount of input and output data available, and our ability to determine VISCOUS's parameters. VISCOUS is good at estimating the importance of individual input factors, even with limited data (e.g., 200) and numerous input factors. It always correctly ranks input factor importance, whether individually or collectively. When estimating the importance of input factors together, VISCOUS is recommended when the number of input factors is not very high (e.g., <20), as it is challenging to generate enough input and output data for estimating VISCOUS's parameters. When all input factors hold equal importance (though rare in practice), VISCOUS's performance is impacted due to the difficulty of estimating VISCOUS's parameters. To help people use VISCOUS, we provide an example and an open‐source Python code, pyVISCOUS. Key Points: We improve the VarIance‐based Sensitivity analysis using COpUlaS (VISCOUS) global sensitivity analysis framework in its handling of marginal densities of the Gaussian mixture copula modelWe evaluate VISCOUS and demonstrate how its performance is affected by function dimension, input‐output size, and non‐identifiabilityWe provide a didactic example and an open‐source Python code called pyVISCOUS to make VISCOUS easier to understand and apply [ABSTRACT FROM AUTHOR]

Sandwich placements and other integrated work and study schemes are increasingly advocated as a key means by which universities can promote students' employability. However, there is little understanding of how successful placements work in terms of facilitating learning and development. Drawing on three longitudinal case studies of students who have undertaken placements, two successfully, we use Bourdieu's conceptions of habitus and field to theorise successful placements. We establish the importance of the initial "fit" between an individual's habitus and the field they enter to undertake a sandwich placement, together with the extent of the "horizon for learning" emerging through the continuing interaction of habitus and field. Further, we argue that this relational approach can help us to recognise the importance of non-cognitive aspects of informal learning through placements and to understand how successful placements can be the catalyst for better grades on return to university study.

Recent advances in differentiable modeling, a genre of physics-informed machine learning that trains neural networks (NNs) together with process-based equations, has shown promise in enhancing hydrologic models' accuracy, interpretability, and knowledge-discovery potential. Current differentiable models are efficient for NN-based parameter regionalization, but the simple explicit numerical schemes paired with sequential calculations (operator splitting) can incur large numerical errors whose impacts on models' representation power and learned parameters are not clear. Implicit schemes, however, cannot rely on automatic differentiation to calculate gradients due to potential issues of gradient vanishing and memory demand. Here we propose a "discretize-then-optimize" adjoint method to enable differentiable implicit numerical schemes for the first time for large-scale hydrologic modeling. The adjoint model demonstrates comprehensively improved performance, with Kling-Gupta efficiency coefficients, peak-flow and low-flow metrics, and evapotranspiration that moderately surpass the already-competitive explicit model. Therefore, the previous sequential-calculation approach had a detrimental impact on the model's ability to represent hydrologic dynamics. Furthermore, with a structural update that describes capillary rise, the adjoint model can better describe baseflow in arid regions and also produce low and peak flows that outperform even pure machine learning methods such as long short-term memory networks. The adjoint model rectified some parameter distortions but did not alter spatial parameter distributions, demonstrating the robustness of regionalized parameterization. Despite higher computational expenses and modest improvements, the adjoint model's success removes the barrier for complex implicit schemes to enrich differentiable modeling in hydrology. [ABSTRACT FROM AUTHOR]

We merge classical extreme value methods to extract high (high temperatures (HT)) and low (low temperatures (LT)) temperatures and form time series having at least one extreme value per year. Observed daily maximum and minimum temperature records are used from 4,797 quality‐controlled, global, surface stations over 1970–2019. We assess changes in the magnitude and frequency of extreme temperatures by introducing and applying novel methods that exploit the definition of stationarity. Analysis shows significant increasing (40.6% of the stations) and decreasing (41.1%) trends in the frequency of high and LT, respectively, and increasing trends in both high‐ and low‐temperature values (35.6% and 49.7%). Globally, HT and LT frequencies are increasing and decreasing, respectively, by 0.9% and 1.1% per year, relative to the expected frequencies under the assumption of stationarity. The global mean annual HT and LT magnitudes are increasing by 0.004 and 0.016°C/year compared to the expected ones under stationarity. The results indicate that the assumption of stationarity fails to explain the observed changes. The proposed methods are an alternative approach to classical extreme value methods and a useful tool to reveal changes in extremes in the era of earth‐system change. Plain Language Summary: We present a method which determines the extreme temperature series by combining the advantages of classical extreme value methods. In this, the series of extremes have at least one extreme value per year. We apply the approach to 4,797 stations of high and low daily temperatures globally and estimate their trends during 1970–2019. We find that during the last 50 years, high and, especially, low temperatures (LT) have become significantly warmer. Fewer low‐temperature events occur with time, while the number of high‐temperature events is increasing. The results indicate that extreme high and LT are non‐stationary. The presented method has potential applications in the statistical modeling of extreme values. Key Points: We merge Annual Maxima (AM) and Peaks Over Threshold (POT) to extract extreme high and low‐temperature time series from a global observational data setNonstationarity is observed in the frequency and magnitude of extreme temperatures, particularly at low temperatures, which are becoming warmerWe compare trends in extreme temperatures extracted by our method and those obtained by AM and POT and examine further applications [ABSTRACT FROM AUTHOR]