Hydrologic signatures are quantitative metrics that describe streamflow statistics and dynamics. Signatures have many applications, including assessing habitat suitability and hydrologic alteration, calibrating and evaluating hydrologic models, defining similarity between watersheds and investigating watershed processes. Increasingly, signatures are being used in large sample studies to guide flow management and modelling at continental scales. Using signatures in studies involving 1000s of watersheds brings new challenges as it becomes impractical to examine signature parameters and behaviour in each watershed. For example, we might wish to check that signatures describing flood event characteristics have correctly identified event periods, that signature values have not been biassed by data errors, or that human and natural influences on signature values have been correctly interpreted. In this commentary, we draw from our collective experience to present case studies where naïve application of signatures fails to correctly identify streamflow dynamics. These include unusual precipitation or flow regimes, data quality issues, and signature use in human-influenced watersheds. We conclude by providing guidance and recommendations on applying signatures in large sample studies

Hydrologic signatures are quantitative metrics that describe a streamflow time series. Examples include annual maximum flow, baseflow index and recession shape descriptors. In this paper, we use machine learning (ML) to learn encodings that are optimal ML equivalents of hydrologic signatures, and that are derived directly from the data. We compare the learned signatures to classical signatures, interpret their meaning, and use them to build rainfall-runoff models in otherwise ungauged watersheds. Our model has an encoder–decoder structure. The encoder is a convolutional neural net mapping historical flow and climate data to a low-dimensional vector encoding, analogous to hydrological signatures. The decoder structure includes stores and fluxes similar to a classical hydrologic model. For each timestep, the decoder uses current climate data, watershed attributes and the encoding to predict coefficients that distribute precipitation between stores and store outflow coefficients. The model is trained end-to-end on the U.S. CAMELS watershed data set to minimize streamflow error. We show that learned signatures can extract new information from streamflow series, because using learned signatures as input to the process-informed model improves prediction accuracy over benchmark configurations that use classical signatures or no signatures. We interpret learned signatures by correlation with classical signatures, and by using sensitivity analysis to assess their impact on modeled store dynamics. Learned signatures are spatially correlated and relate to streamflow dynamics including seasonality, high and low extremes, baseflow and recessions. We conclude that process-informed ML models and other applications using hydrologic signatures may benefit from replacing expert-selected signatures with learned signatures.

To describe process knowledge at the watershed scale, hydrologists commonly refer to a ‘perceptual model’, an expert summary of the watershed and its runoff processes often supported by field observations. Perceptual models are often presented as a schematic figure, although such a figure will necessarily simplify the hydrologist’s complex mental model. In this paper, our aim was to understand what constitutes a visual expert summary of watershed process knowledge, and to evaluate how perceptual models could be used to share hydrological process information at larger scales. To do so, we conducted a systematic review of the literature and found 63 perceptual model figures. We counted and categorized the stores and fluxes in each figure using a taxonomic classification and quantified a variety of figure attributes including spatial or temporal zonation, inclusion of vegetation, soils, topographical and geological data and consideration of uncertainty. Our analysis showed that a typical figure has 1 surface flux, 4 subsurface fluxes, 3–4 subsurface stores and 0–1 channel stores; 28 out of 63 figures use sub-figures to show temporal dynamics (e.g., wet/dry conditions), and 12 out of 63 show spatial zones. Perceptual model figures, therefore, provide a concise summary of watershed processes with a complexity comparable to that of many conceptual hydrological models. However, only four figures showed any information on uncertainty or knowledge gaps. We recommend that perceptual figure value could be easily increased by consistent captioning of figures to assist automated search, and wider use of standard figure annotations such as legends and scale markings to ensure that information is fully conveyed to the user. If perceptual figures are proposed as a primary method for sharing process information, the hydrological community should consider how to link more detailed text descriptions to figures, and how to represent process uncertainty.

We evaluated the Global Land Data Assimilation System surface soil moisture product (GLDAS v. 2.1) against in situ soil moisture networks in arid climates in Australia and the United States, using common statistical metrics and seasonality metrics. Our results showed that GLDAS performed well (root mean square error (RMSE) = 0.100 m³/m³; unbiased RMSE (ubRMSE) = 0.060 m³/m³; correlation coefficient (R) = 0.555 on average) but systematically overestimated the soil moisture values (Bias = 0.067 m³/m³). The performance was better in Australian Oznet and the U.S. Climate Reference Network (USCRN), compared to the US Soil Climate Analysis Network (SCAN) network. In terms of seasonality, GLDAS soil moisture seasons were biased to start earlier; on average, drying and wetting transitions started 28 and 16 days earlier than in situ data, respectively. The end dates of GLDAS seasonal transitions showed good agreement with in situ data; the errors in transition timings were limited to within a week. This tendency is stronger in the US networks compared to the Australian network.

Dominant processes in a watershed are those that most strongly control hydrologic function and response. Estimating dominant processes enables hydrologists to design physically realistic streamflow generation models, design management interventions, and understand how climate and landscape features control hydrologic function. A recent approach to estimating dominant processes is through their link to hydrologic signatures, which are metrics that characterize the streamflow timeseries. Previous authors have used results from experimental watersheds to link signature values to underlying processes, but these links have not been tested on large scales. This paper fills that gap by testing signatures in large sample data sets from the U.S., Great Britain, Australia, and Brazil, and in Critical Zone Observatory (CZO) watersheds. We found that most inter-signature correlations are consistent with process interpretations, that is, signatures that are supposed to represent the same process are correlated, and most signature values are consistent with process knowledge in CZO watersheds. Some exceptions occurred, such as infiltration and saturation excess processes that were often misidentified by signatures. Signature distributions vary by country, emphasizing the importance of regional context in understanding signature-process links and in classifying signature values as “high” or “low.” Not all signatures were easily transferable from single, small watersheds to large sample studies, showing that visual or process-based assessment of signatures is important before large-scale use. We provide a summary table with information on the reliability of each signature for process identification. Overall, our results provide a reference for future studies that seek to use signatures to identify hydrological processes.

Observational data is the foundation for most of hydrological science. However, observational data uncertainty can often have high magnitudes (e.g., ±50%–100% typical low flow uncertainty, McMillan et al., 2012) and be of complex character (e.g., Viney & Bates, 2004), which means that in some cases our data may be of limited use or even misleading in our quest to understand hydrological processes (e.g., Kauffeldt et al., 2013). Discussion of the impacts of data uncertainty on process understanding reaches from very early hydrological observations (Heberden, 1769), through early uncertainty estimation techniques (Horton, 1923) and continuing to the plea from Sevruk (1987) that data errors must not be ignored. The impacts of intrinsic data limitations and uncertainties on modelling of hydrological processes have also been long discussed by for example Klemes (1986), Beven (2002), Sivapalan et al. (2003) and Kirchner (2006). Understanding, quantifying and documenting observational uncertainty and their impacts on hydrological analysis and modelling in any study is therefore essential to draw robust conclusions about hydrological processes.

This paper presents a taxonomy (hierarchical organization) of hydrological processes; specifically, runoff generation processes in natural watersheds. Over 130 process names were extracted from a literature review of papers describing experimental watersheds, perceptual models, and runoff processes in a range of hydro-climatic environments. Processes were arranged into a hierarchical structure, and presented as a spreadsheet and interactive diagram. For each process, additional information was provided: a list of alternative names for the same process, a classification into hydrological function (e.g., flux, storage, release) and a unique identifier similar to a hashtag. We hope that the proposed hierarchy will prompt collaboration and debate in the hydrologic community into naming and organizing processes, towards a comprehensive taxonomy. The taxonomy provides a method to label and search hydrological knowledge, thereby facilitating synthesis and comparison of processes across watersheds.

Soil moisture signatures provide a promising solution to overcome the difficulty of evaluating soil moisture dynamics in hydrologic models. Soil moisture signatures are metrics that quantify the dynamic aspects of soil moisture timeseries and enable process-based model evaluations. To date, soil moisture signatures have been tested only under limited land-use types. In this study, we explore soil moisture signatures’ ability to discriminate different dynamics among contrasting land-uses. We applied a set of nine soil moisture signatures to datasets from six in-situ soil moisture networks worldwide. The dataset covered a range of land-use types, including forested and deforested areas, shallow groundwater areas, wetlands, urban areas, grazed areas, and cropland areas. Our set of signatures characterized soil moisture dynamics at three temporal scales: event, season, and a complete timeseries. Statistical assessment of extracted signatures showed that (1) event-based signatures can distinguish different dynamics for all the land-uses, (2) season-based signatures can distinguish different dynamics for some types of land-uses (deforested vs. forested, urban vs. greenspace, and cropped vs. grazed vs. grassland contrasts), (3) timeseries-based signatures can distinguish different dynamics for some types of land-uses (deforested vs. forested, urban vs. greenspace, shallow vs. deep groundwater, wetland vs. non-wetland, and cropped vs. grazed vs. grassland contrasts). Further, we compared signature-based process interpretations against literature knowledge; event-based and timeseries-based signatures generally matched well with previous process understandings from literature, but season-based signatures did not. This study will be a useful guideline for understanding how catchment-scale soil moisture dynamics in various land-uses can be described using a standardized set of hydrologically relevant metrics.

Study region
In this study, we use stable isotopes of water to quantify the flow pathways delivering water to the tributaries, mainstem river and groundwater basin underlying urban San Diego. Information about sources of stormflow and recharge are necessary to maintain the health of waterways and aquifers, but studies of these processes are scarce in urban, semi-arid regions.

Study focus
Isotopic methods have been used in experimental or natural watersheds, but also have potential to quantify urban water cycling behaviour and water sources. We sampled baseflow, precipitation, and hourly stormflow from eight events with a range of antecedent conditions, and used end member mixing analysis to determine stormflow and groundwater sources.

New hydrological insights for the region
Our results show that hydrologic connectivity controls stormflow sources. After a dry summer, and early in storm events, connectivity of pre-event water with the channel is low, so only new precipitation reaches the river. In wetter conditions, connectivity is higher and pre-event surface water mixes with infiltration-origin groundwater. Deeper groundwater composition mimics stormflow, a mix of stagnated river water and infiltration-origin water. The close connection between streamflow and groundwater implies that improving groundwater quality requires improvements to surface water quality. Average uncertainty in source fractions was ±8.0 %, suggesting that despite complex water pathways in urban, semi-arid environments, isotopic sampling is valuable for quantifying water sources.

We present a Matlab toolbox to calculate hydrologic signatures, which are metrics that quantify streamflow dynamics. Signatures are widely used for catchment characterisation, hydrologic model evaluation, and assessment of instream habitat, but standardisation across applications and advice on signature selection is lacking. The toolbox provides accessible, standardised signature calculations, with clear information on methodological decisions and recommended parameter values. The toolbox implements three categories of signatures: basic signatures that describe the five components of a natural streamflow regime, signatures from benchmark papers, and an extended set of process-based signatures. The toolbox is designed for ease of use, including documentation, workflow scripts and example data to demonstrate implementation procedures, and visualisation options. We demonstrate the accuracy and robustness of the signature calculations by applying reproducible workflows to large streamflow datasets. The modular design of the toolbox allows for flexibility and easy future expansion. The toolbox is available from https://github.com/TOSSHtoolbox/TOSSH (https://doi.org/10.5281/zenodo.4451846).

The study had two objectives; (1) Substitute National Water Model’s (NWM) runoff calculation with a conceptual hydrologic model (TOPography-based hydrological MODEL [TOPMODEL]) to simplify the model structure and resolve potential drawbacks of applying NWM in headwater catchments. (2) Investigate how varying the coupling interface (location of coupling, type of fluxes used, modification of sub-models) affects model behavior of when one-way coupling the NWM’s land surface model (LSM; Noah-Multi Parameterization) with TOPMODEL using six different scenarios. The one-way coupled model outperformed NWM and noncoupled TOPMODEL. The coupling option limiting reliance on LSM’s surface and subsurface water fluxes by constraining them within the TOPMODEL structure was the most successful. Performance declined when coupling configurations relied more on LSM calculated fluxes to override TOPMODEL internal processes. Varying the coupling interface brought unexpected changes in TOPMODEL’s parameter sensitivity and water budget even while the statistical score remained similar. The coupling interface represents a source of structural uncertainty that could be identified through conventional evaluation of performance, uncertainty, and sensitivity due to the simple structure of our one-way coupling design. The study shows that the benefits of combining the strengths of land surface and conceptual hydrological models, while recognizing that structural uncertainty from coupling design needs to be acknowledged.

Hydrologic signatures are metrics that quantify aspects of streamflow response. Linking signatures to underlying processes enables multiple applications, such as selecting hydrologic model structure, analysing hydrologic change, making predictions in ungauged basins, and classifying watershed function. However, many lists of hydrologic signatures are not process‐based, and knowledge about signature‐process links has been scattered among studies from experimental watersheds and model selection experiments. This review brings together those studies to catalogue more than 50 signatures representing evapotranspiration, snow storage and melt, permafrost, infiltration excess, saturation excess, groundwater, baseflow, connectivity, channel processes, partitioning, and human alteration. The review shows substantial variability in the number, type, and timescale of signatures available to represent each process. Many signatures provide information about groundwater storage, partitioning, and connectivity, whereas snow processes and human alteration are underrepresented. More signatures are related to the seasonal scale than the event timescale, and land surface processes (ET, snow, and overland flow) have no signatures at the event scale. There are limitations in some signatures that test for occurrence but cannot quantify processes, or are related to multiple processes, making automated analysis more difficult. This review will be valuable as a reference for hydrologists seeking to use streamflow records to investigate a particular hydrologic process or to conduct large‐sample analyses of patterns in hydrologic processes.

Hydrological signatures that represent snow processes are valuable to gain insights into snow accumulation and snow melt dynamics. We investigated 5 snow signatures. Considering inter-annual average of each calendar day, two slopes derived from the relation between streamflow and air temperature for different periods and streamflow peak maxima are used as signatures. In addition, two different approaches are used to compute inter-annual average and yearly snow storage estimates. We evaluated the ability of these signatures to characterize average (1) snow melt dynamics and (2) snow storage. They were applied in 10 Critical Zone Observatory catchments of the Southern Sierra mountains (USA) characterized by a Mediterranean climate. The relevance and information content of the signatures are evaluated using snow depth and snow water equivalent measurements as well as inter-catchment differences in elevation. The slopes quantifying the relations between streamflow and air temperature and the date of streamflow peak were found to characterize snow melt dynamics in terms of snow melt rates and snow melt affected areas. Streamflow peak dates were linked to the period of highest snow melt rates. Snow storage could be estimated both on average, considering all years, and for each year. Snow accumulation dynamics could not be characterized due to the lack of streamflow response during the snow accumulation period. The signatures were found potentially valuable to gain insights into catchment scale snow processes. In particular, when comparing catchments or observed and simulated data, they could provide insights into differences in terms of (1) snow melt rate and/or snow melt affected area over the snow melt season and (2) average or yearly snow storage. Requiring only widely available data, these hydrological signatures can be valuable for snow processes characterization, catchment comparison/classification or model development, calibration or evaluation.

A catchment’s hydrological response is controlled by climatic forcing and by the landscape through which water moves. Yet when we compare large samples of catchments, we often find climate to be the only good predictor of the hydrological response and a lot of variability is left unexplained. This contradicts extensive evidence from field and regional studies which shows the importance of catchment form (e.g. geology) on catchment hydrological processes, particularly on baseflow processes. We hypothesize that this is due to limitations in (a) the catchment attributes we use to inform our analyses and (b) the hydrological signatures we use to describe the hydrological response. To test these hypotheses we use a large sample of catchment data across the contiguous United States. By reviewing literature from several U.S. regions, we show that region‐specific knowledge is underutilized in large sample studies. To organize the findings from these regions we propose and apply a framework based on standardized perceptual models. Informed by these perceptual models, we use both available and newly calculated catchment attributes to show that baseflow signature predictions can be improved regionally. Multiple baseflow signatures are needed to better distinguish between different baseflow sources, such as the subsurface, surface water bodies, and snow. We conclude with pointing at potential future directions and argue that we should aim at a more systematic and hydrologically motivated selection of catchment attributes and hydrological signatures.

Soil moisture is a key modifier of runoff generation from rainfall excess, including during extreme precipitation events associated with Atmospheric Rivers (ARs). This paper presents a new, publicly available dataset from a soil moisture monitoring network in Northern California’s Russian River Basin, designed to assess soil moisture controls on runoff generation under AR conditions. The observations consist of 2‐min volumetric soil moisture at 19 sites and 6 depths (5, 10, 15, 20, 50, and 100 cm), starting in summer 2017. The goals of this monitoring network are to aid the development of research applications and situational awareness tools for Forecast‐Informed Reservoir Operations at Lake Mendocino. We present short analyses of these data to demonstrate their capability to characterize soil moisture responses to precipitation across sites and depths, including time series analysis, correlation analysis, and identification of soil saturation thresholds that induce runoff. Our results show strong inter‐site Pearson’s correlations (>0.8) at the seasonal timescale. Correlations are strong (>0.8) during events with high antecedent soil moisture and during drydown periods, and weak (<0.5) otherwise. High event runoff ratios are observed when antecedent soil moisture thresholds are exceeded, and when antecedent runoff is high. Although local heterogeneity in soil moisture can limit the utility of point source data in some hydrologic model applications, our analyses indicate three ways in which soil moisture data are valuable for model design: (1) sensors installed at 6 depths per location enable us to identify the soil depth below which evapotranspiration and saturation dynamics change, and therefore choose model soil layer depths, (2) time series analysis indicates the role of soil moisture processes in controlling runoff ratio during precipitation, which hydrologic models should replicate, and (3) spatial correlation analysis of the soil moisture fluctuations helps identify when and where distributed hydrologic modelling may be beneficial.

Hydrologic signatures are quantitative metrics or indices that describe statistical or dynamical properties of hydrologic data series, primarily streamflow. Hydrologic signatures were first used in eco‐hydrology to assess alterations in flow regime, and have since seen wide uptake across a variety of hydrological fields. Their applications include extracting biologically relevant attributes of streamflow data, monitoring hydrologic change, analyzing runoff generation processes, defining similarity between watersheds, and calibrating and evaluating hydrologic models. Hydrologic signatures allow us to extract meaningful information about watershed processes from streamflow series, and are therefore seeing increasing use in emerging information‐rich areas such as global‐scale hydrologic modeling, machine learning, and large‐sample hydrology. This overview paper describes the background and development of hydrologic signature theory, reviews hydrologic signature use across a variety of applications, and discusses ongoing hydrologic signature research including current challenges.

Soil moisture is an important variable in hydrological studies, but has been little used for model evaluation due to its high sensitivity to local conditions. We explore the possibility to derive hydrological signatures from soil moisture data that could overcome this limitation and be helpful for model evaluation. A set of eight hydrological signatures was built, encompassing long‐term to short‐term time scales. These signatures were tested according to robustness, representativeness and discriminatory power, using in situ data sets from New Zealand, including national network and experimental watershed data. Field capacity, type of soil moisture distribution, and starting dates of seasonal transitions typically meet the criteria, subject to uniform sensor depths and homogeneous land uses. Durations of seasonal transitions and event‐based signatures showed higher variability and lower discriminatory power. In general, long‐term signatures are more robust, more representative of large areas, and have a high discriminatory power, thus showing a good potential for use in diagnostic evaluation of regional models.

Increased climate variability is driving changes in water storage across the contiguous United States (CONUS). Observational estimates of these storage changes are important for validation of hydrological models and predicting future water availability. We estimate CONUS terrestrial water storage anomalies (TWSA) from 2007–2017 using Global Positioning System (GPS) displacements, constrained by lower‐resolution TWSA observations from Gravity Recovery and Climate Experiment (GRACE) satellite gravity—a combination that provides higher spatiotemporal resolution than previous estimates. The relative contribution of seasonal, interannual, and subseasonal TWSA varies widely across CONUS watersheds, with implications for regional water security. Separately, we find positive correlation between TWSA and the El Niño/Southern Oscillation in the southeastern Texas‐Gulf and South Atlantic‐Gulf watersheds and an unexpected negative correlation in the southwest. In the western United States, atmospheric rivers (ARs) drive a large fraction of subseasonal TWSA, with the top 5% of ARs contributing 73% of total AR‐related TWSA increases.