Storage-discharge Relationship Research Articles

Internal structure modification of a simple monthly water balance model via incorporation of a machine learning-based nonlinear routing

ABSTRACT Among various monthly water balance models, one of the models that has the simplest structure and offers a well-behaved conceptual platform is the GR2M. Despite the widespread use of the model with two-free parameters, the fact that it tends to produce relatively large errors in peak flow months necessitates some modifications to the model. The reason for the mentioned simulation deficiencies could be that the relationship between the routing reservoir and the external environment of the basin is controlled by a single parameter, making the storage–discharge relationship linear. Therefore, in this study, least squares support vector regression, one of the nonlinear data-driven models, has replaced the routing part of the GR2M to enhance the monthly runoff simulation. The performance of the three-parameter hybrid model (GR3M), which was developed by considering the parameter parsimony point of view and including a machine learning (ML)-based nonlinear routing scheme, was examined in some locations in the Gediz River Basin in western Turkey. Statistical performance measures have shown that GR3M, which both leverages the capabilities of an ML model and blends conceptual outputs within a nested scheme, clearly outperforms the original GR2M. The proposed modification has brought significant improvements, especially to high-flow simulations.

Application and Evaluation of Stage–Storage–Discharge Methodology in Hydrological Study of the Southern Phosphate Mining Model Domain in Southwest Florida

This hydrological study investigated a combined rating methodology tested on a 14,090 km2 area in Southwest Florida. The approach applied the Hydrological Simulation Program-Fortran (HSPF) over a 23-year period and was validated by 28 stream gauging stations. The regional hydrological complexity includes natural and agricultural areas, as well as extensive phosphate mining and urbanizing areas. This application is a novel and efficient methodology for generating stage–storage–discharge relationships using a geographic information system (GIS), empirical equations, and spreadsheets for 148,000 isolated and connected alluvial wetlands within the model domain. The validation metrics used to evaluate the applied methodology for populating the stage–storage–discharge relationship demonstrated the model effectiveness in simulating a range of hydrological events across various regions. For discharge prediction, the Nash–Sutcliffe efficiency values surpassed 0.7 at most stations, with an average of 0.67, and the average R squared was 0.74. This methodology, when applied, achieved a root-mean-square error of 4 m3/s for discharge prediction and 0.47 m for stage prediction. However, limitations emerged in simulating baseflow (low flows), highlighting the need for integrated modeling approaches to accurately capture groundwater–surface water interactions. The research provides an improved means for modeling regional water resources and lays the groundwork for enhanced hydrological modeling in watersheds with complex alluvial and isolated wetland systems.

Elastic deformation as a tool to investigate watershed storage connectivity

Storage-discharge relationships and dynamic changes in storage connectivity remain key unknowns in understanding and predicting watershed behavior. In this study, we use Global Positioning System measurements of load-induced Earth surface displacement as a proxy for total water storage change in four climatologically diverse mountain watersheds in the western United States. Comparing total water storage estimates with stream-connected storage derived from hydrograph analysis, we find that each of the investigated watersheds exhibits a characteristic seasonal pattern of connection and disconnection between total and stream-connected storage. We investigate how the degree and timing of watershed-scale connectivity is related to the timing of precipitation and seasonal changes in dominant hydrologic processes. Our results show that elastic deformation of the Earth due to water loading is a powerful new tool for elucidating dynamic storage connectivity and watershed discharge response across scales in space and time.

Calibrating Complexity: A Comprehensive Approach to Developing Stage–Storage–Discharge Relationships for Geographically Isolated Wetlands (GIWs) in W-C Florida

Geographically isolated wetlands (GIWs) play a critical role in regional hydrology, streamflow, groundwater recharge, evapotranspiration, and water quality. Despite their importance, research on quantifying discharges from these wetlands remains scarce. This study focuses on the hydrological characterization of GIWs in W-C Florida, a region where they cover a significant proportion of the land surface. The paper introduces a new procedure for developing Stage–Storage–Discharge (rating) characteristics essential for deterministic hydrological modeling in larger geographic areas. The approach synthesizes and extends previous research methodologies and offers simplified key modeling coefficients (m and n), which act as intelligent calibration knobs. These coefficients, when coupled with easily derivable physical attributes such as areas, slopes, and elevations, allow for the accurate simulation of downstream discharge timings and magnitudes, including flood behavior. The proposed method was tested using observational data from well-calibrated models. The results indicated a relative error of −7.2% for stage–storage and 15% for stage–discharge. GIS-based techniques were evaluated against surveyed data, and the results showed an accuracy of 0.16 m (0.52 ft) in estimating both the invert elevation and the maximum depth of GIWs. This effort will ultimately contribute to a better understanding and management of these critical ecosystems.

Hillslope groundwater and river channel precipitation recharge to rivers in a continuous permafrost catchment of northeastern Tibetan Plateau

Climate-change driven degradation of permafrost and changes in precipitation have resulted in significant changes to hydrological processes in permafrost areas. Previous studies on hillslope-stream connectivity and associated runoff-recharge to rivers have mainly focused on the threshold conditions and processes. In contrast, there has been limited study on the capacity of the permafrost active layer to recharge rivers and the relationships between river channel precipitation and river runoff, needed to predict flood events. This study aimed to characterize river runoff generation processes in the Yakou Catchment, northeastern Tibetan Plateau. Continuous monitoring of meteorological variables (precipitation and air temperature) and hillslope hydrological elements (thaw depths, supra-permafrost groundwater, and the thickness of the saturated zone) was conducted between June–August 2021–2022. The results showed using the thickness of the saturated zone (TSZ) to determine wet and dry conditions yielded significantly higher low flow (average of 0.153 m3 s−1) and lower low flow (average of 0.049 m3 s−1) with average TSZ depths of 0.40 m and 0.12 m under wet and dry conditions, respectively. However, no significant difference was noted in quick flow. Precipitation during typical rainfall events determined the generation of quick flow, with low flow constituting the main component of river runoff. The application of a partial least squares path model showed that TSZ on the permafrost determined the generation of river low flow which mainly originated from hillslope lateral subsurface flow. Conversely, river channel precipitation determined the generation of quick flow, which can contribute up to 80 % of the peak runoff during extreme rainfall events. Specifically, this study enhances the understanding of the connectivity between hillslopes and rivers and the storage-discharge relationship in permafrost catchments. This study provides a new theoretical reference for simulations of hydrological processes in the permafrost region.

Universal recession constants and their potential to predict recession flow

Streamflow prediction during dry or recession periods is crucial for water resources management. The storage-discharge (S-Q) relationship is generally used to model recession flow in the basin. Since storage is practically unobservable, the S-Q relationship is often quantified by analyzing the relationship between -dQ/dt and Q, which Brutsaert and Nieber (1977) observed to be of a power-law type: -dQ/dt=kQα, for natural basins. Integration of the above equation yields an expression for the streamflow at any time, t, during the recession period. However, this approach relies on the availability of the streamflow data and, therefore, cannot be applied directly to ungauged or data-scarce basins. Thus, there exists a necessity for an alternative approach to predict streamflow in the ungauged basins during the recession period. In this study, we investigated recession curves from 413 basins in the United States and determined the existence of a universal relationship (k=kuQN-λu) between the storage coefficient (k) and the average past discharge (QN) that can serve as a proxy for basin storage. We tested the potential of universal recession constants (ku and λu) in predicting the recession flow in both gauged and ungauged basins. It is observed that the median NSEBC, i.e., NSE calculated using the Box-Cox transformation of discharge, was 0.78 for the gauged basins and 0.55 for the ungauged basins. Our findings provide a model-independent method for predicting the recession discharge, which can pave new avenues towards improving the predictions in ungauged basins.

Upland Hillslope Groundwater Subsidy Affects Low‐Flow Storage–Discharge Relationship

AbstractLarge‐scale cross‐site scientific synthesis on low‐flow storage–discharge relation can promote developing transferable hypotheses on the interactions among critical zone attributes and on how such interactions affect catchments’ water vulnerabilities. This study leverages cross‐site empirical and theoretical analyses and develops a similarity index, based on the interactions among critical zone attributes, to help determine the less‐explored influence of upland hillslope groundwater subsidy on storage–discharge relation. We show that an increase in the relative extent of upland hillslope groundwater subsidy to low‐flow discharge, occurring through deep slow low‐moving (e.g., bedrock) storage unit, leads to (a) an increase in the nonlinearity of low‐flow discharge sensitivity to storage (β1) and (b) an increase in the convexity of low‐flow storage–discharge relation. Our findings also raise new hypotheses on the applicability of Boussinesq‐based hydraulic groundwater theory at low‐flow condition. Empirical results show that in a portion of our study catchments, particularly in those with a relatively small extent of upland hillslope groundwater subsidy, the theory’s proposed range of nonlinearity sufficiently explains the nonlinearity of low‐flow storage–discharge relation. However, in catchments with a strong influence of upland hillslope groundwater subsidy through deep slow‐moving storage unit, the current state of hydraulic groundwater theory, using one single (non)linear representative storage unit, may not be sufficient to explain the large nonlinearity and convexity of low‐flow storage–discharge relation (or the long tail of hydrograph late recession). Considering β1 informs the low‐flow vulnerability of catchments, the findings of this study deepen and generalize our understanding of where low‐flow discharge is vulnerable to storage’s change.

Effects of mass balance, energy balance, and storage-discharge constraints on LSTM for streamflow prediction

We investigate the effects of physics-based constraints, added to the loss function of a Long Short-Term Memory (LSTM) network, on its performance in daily streamflow prediction. Three types of constraints (mass balance, energy balance, and storage-discharge relationship), along with their combinations, are tested across 34 river basins in Nebraska. We found that the addition of constraints improves the model performance in several basins, but there are also cases where the performance drops or does not differ significantly. Mass and energy balance constraints improve the performance in 38% and 32% of catchments, respectively, while storage-discharge constraints improve the performance in 12% of catchments. The combination of mass and energy balance constraints has a positive effect on 41% of catchments, while the combination of mass balance and storage-discharge constraints improves the performance in 26% of catchments. We recommend the use of constraints in cases where they boost the LSTM performance.

A probabilistic framework for robust master recession curve parameterization

Master recession curve (MRC) representing the long-term catchment streamflow recession is widely used to estimate catchment storage-discharge relationship and predict low flows. Recession analysis of the streamflow functional form (-dQ/dt∼Q) is an effective way to construct MRC. However, the great variability of recession processes among events makes it difficult to parameterize the recession processes by deterministic methods and indicates the recession rate could be thought of as a random variable. In this study, a probabilistic approach (Parameterized Binning-percentile Method, or PBM) is proposed to construct MRCs based on -dQ/dt∼Q analysis. The probabilistic PBM is introduced by describing the distribution of recession rate at partitioned -dQ/dt intervals by a Gamma distribution. MRCs at any percentile can be obtained by fitting regenerated data points of -dQ/dt∼Q in each interval. The PBM is validated by both numerically generated and observed hydrographs. It shows that the PBM is robust in capturing the distribution of recession rate and can adapt to various observed hydrographs with different recession characteristics. It is more accurate to generate probabilistic MRCs compared to the individual recession method in Q∼t form and quantile regression in -dQ/dt∼Q form. Further, MRCs from traditional deterministic methods can viewed as special cases of the probabilistic framework. Our newly proposed probabilistic framework can be used to quantify the statistical distributions of low flows, which can be helpful in regional water resources management during dry seasons.

A hybrid Budyko-type regression framework for estimating baseflow from climate and catchment attributes

Researchers seek improved models for estimating baseflow in ungauged catchments as the statistical and process-based methods traditionally used are not easily transferable and do not give robust predictions, respectively. In this study, a process-based statistical hybrid model for estimating baseflow, known here as the Budyko-type baseflow regression (BBR) model, was developed by combining the linear storage-discharge relationship with the Budyko function, and applying multiple regression. The performance of the hybrid model was then evaluated using data from 671 near-natural catchments acquired from four large-sample hydrometeorological datasets. The results showed that the BBR model performed well in estimating baseflow on both national and regional scales; the coefficient of determination between the observed and predicted mean annual baseflow varied from 0.85 to 0.94 for the calibration catchments and from 0.71 to 0.96 for the validation catchments. The BBR model has more of a physical basis, is more transferable, and is less likely to produce unrealistic (negative) mean annual baseflows than traditional multiple regression models. It is also less complex than process-based models. The calibrated BBR models were used to estimate the mean annual baseflow and the elasticity of the baseflow to climate and catchment attributes at the national scale for the United States, United Kingdom, Brazil, and Australia. The results showed that climate (precipitation and potential evapotranspiration) had the most control on the baseflow, and that the soil sand content and the Normalized Difference Vegetation Index were also important catchment attributes. The BBR model developed in this study offers scientists a new and improved method for estimating baseflow. The results generated by the model in this study will improve our understanding of how climate and landscape control the baseflow.

An Analytical Treatment of the Hysteretic Storage–Discharge Relation

An Analytical Treatment of the Hysteretic Storage–Discharge Relation

Mathematical treatment of looped storage-discharge relation

ABSTRACT In hydraulic and hydrologic modeling, the storage (S)-discharge (Q) relation is often represented by a straight line or a curve, although when plotted using field or experimental data it is found to be hysteretic or looped. The characteristics of this looped relation depend on geometric, hydrologic, and hydraulic conditions. Despite the widespread use of the storage-discharge relation, there does not appear to have been a mathematical treatment discussing what causes the relation to be looped or double-valued. The objective of this study, therefore, is to analyze the S-Q relation analytically for a catchment represented by a rectangular plane, considering rainfall excess (rainfall minus infiltration) and surface runoff or overland flow modeled by kinematic wave approximation. Depending on the duration of rainfall excess, two cases - equilibrium and partial equilibrium - are distinguished and for each case the looped relation is analyzed. It is shown that the loop is different for the two cases.

Using a mechanistic model to explain the rising non-linearity in storage discharge relationships as the extent of permafrost decreases in Arctic catchments

• There is a progression in the value of hydraulic parameters as permafrost thaws. • The hydrologic response transforms as permafrost goes from continuous to absent. • The hillslope gradient can be the controlling influence of the catchment response. • The response is the result of the interaction of multiple interdependent processes. The relationship between groundwater and discharge in Arctic and sub-Arctic regions is strongly controlled by permafrost. Previous work has shown that catchments with thawing frozen soils due to the warming climate are expected to show changes in their storage-discharge relationship. In this study, we use a mechanistic modelling approach to demonstrate that a thawing catchment underlain with continuous permafrost undergoes a dramatic change in storage-discharge relationship. We demonstrate that the effect of permafrost thaw, conceptualized as a reduction of an impermeable layer in the subsurface, will likely only be clearly observable as a change in slope of the recession curve of catchments with hillslope gradients>5 %. For flat catchments (<1% hillslope gradient), we find no relation with permafrost extent and change in recession curve slope will likely be dominated by changes in active layer parameters, such as in shallow surface permeability (Hydraulic Conductivity, above permafrost) and shallow surface and subsurface water retention (Specific Yield of Groundwater & Specific Yield of Surface). For mildly sloped Arctic catchments (5 % hillslope gradient), change in recession curve slope is controlled both by changes in permafrost extent and the subsurface flow length and subsurface hydraulic properties for the shallow flow, with minimal impact from overland flow properties and changes in meteorological factors. For moderately sloped Arctic catchments (10 % hillslope gradient), change in recession curve slope change is dominated by changes in permafrost extent, and secondly by changes in the subsurface flow length and subsurface hydraulic properties, with no impact from meteorological factors or changes in overland flow properties. Several of the parameters found to be driving shifts in recession curve slopes in our modeling, such as changes in active layer thickness and the formation of taliks, are more likely than others to evolve with the ongoing Arctic climate change in hillslopes, helping us understand what drives the real-world increases in non-linearity of storage-discharge relationships.

Climate Controls on River Chemistry

AbstractHow does climate control river chemistry? Existing literature has examined extensively the response of river chemistry to short‐term weather conditions from event to seasonal scales. Patterns and drivers of long‐term, baseline river chemistry have remained poorly understood. Here we compile and analyze chemistry data from 506 minimally impacted rivers (412,801 data points) in the contiguous United States (CAMELS‐Chem) to identify patterns and drivers of river chemistry. Despite distinct sources and diverse reaction characteristics, a universal pattern emerges for 16 major solutes at the continental scale. Their long‐term mean concentrations (Cm) decrease with mean discharge (Qm), with elevated concentrations in arid climates and lower concentrations in humid climates, indicating overwhelming regulation by climate compared to local Critical Zone characteristics such as lithology and topography. To understand the CmQm pattern, a parsimonious watershed reactor model was solved by bringing together hydrology (storage–discharge relationship) and biogeochemical reaction theories from traditionally separate disciplines. The derivation of long‐term, steady state solutions lead to a power law form of CmQm relationships. The model illuminates two competing processes that determine mean solute concentrations: solute production by subsurface biogeochemical and chemical weathering reactions, and solute export (or removal) by mean discharge, the water flushing capacity dictated by climate and vegetation. In other words, watersheds function primarily as reactors that produce and accumulate solutes in arid climates, and as transporters that export solutes in humid climates. With space‐for‐time substitution, these results indicate that in places where river discharge dwindles in a warming climate, solute concentrations will elevate even without human perturbation, threatening water quality and aquatic ecosystems. Water quality deterioration therefore should be considered in the global calculation of future climate risks.

Characterizing the groundwater storage–discharge relationship of small catchments in China

Abstract Baseflow recession is an essential part of the hydrological cycle, as it transfers unconfined aquifer storage to runoff. This study derived the parameterization of the baseflow recession from recession curves extracted from 382 catchments in China. The recession parameters of recession curves in power-law form, which control the shape of the curves and reflect the net effects of hillslope on the runoff decline process, are estimated by the baseflow recession analysis. The results show that the ranges of recession coefficient α and recession exponent β across China are 0–0.70 and 0.57–3, respectively. Most of the α values range between 0 and 0.20, and most of the β values range between 1 and 2. Generally, the α values of relatively dry catchments are higher than that of the wet catchments, and the distribution pattern of β values is opposite to that of α values. Statistical analysis is used to construct parametric equations for the recession parameters, indicating that catchment area, field capacity, etc., are essential for predicting α and β. In addition, the transplantation results of parametric equations show that equations can be applied to the estimation of α and β in other catchments. The results provide data support for storage estimation of data-scarce catchments.

An improved method to estimate the rate of change of streamflow recession and basin synthetic recession parameters from hydrographs

Recession analysis of -dQ/dt ∼ Q is popularly used for determining catchment storage-discharge relationship, estimating the aquifer hydraulic properties, and predicting low flow processes. However, there are uncertainties arising from the numerical approximation of -dQ⁄dt by the finite difference (ΔQ/Δt) for individual recession and the fitting cloud-like data of -dQ⁄dt ∼ Q for many recession events in a catchment. In this study, we proposed an improved variable time step increment method (IVTS) to minimize the effects of the noisy observations on estimating -dQ⁄dt, and a fitting method in terms of the binning-average of -dQ⁄dt ∼ Q data points to determine the basin synthetic recession parameters. The proposed methods are validated by using numerical generation of recessions with different noises and recession behaviors and the observed hydrographs from twenty catchments in Huai River Basin in China. The results from our proposed method are compared with those from the other popularly used methods. The IVTS method is proven to be robust for approximation of -dQ⁄dt, which can significantly reduce errors of the estimated -dQ⁄dt and the recession slope (b). Combining with the IVTS method, the fitting method in terms of the binning average by splitting range of -dQ⁄dt, instead of Q, could overcome the shortage of traditional recession analysis methods that underestimate the recession slope. Our study indicates that the more accurate and reliable calculation of -dQ⁄dt ∼ Q data and estimation of basin synthetic recession parameters could increase the objectivity in interpretation of recession behaviors and accuracy in perdition of low flow processes.

Storage-Discharge Relationships under Forest Cover Change in Ethiopian Highlands

Detecting the impacts of forest cover changes on hydrology is challenging given uncertainties in how changes will manifest in observed streamflow. Considering changes in the rate of change of observed streamflow (e.g., recession characteristics) may offer insights to hydrological shifts driven by forest cover change that are not seen when considering absolute changes of streamflow itself. This study assesses the impacts of forest cover changes on the storage–discharge relationships in three meso-scale watersheds in the highlands of Ethiopia based on a 30-year hydro-climatic and land cover change dataset. We analyze streamflow recessions and fitted parameters of a linear reservoir model to depict fundamental shifts in the storage–discharge relation for these watersheds. Our analysis shows that recession slopes and the total storages increase as natural forest covers decrease in the 273 km2 Woshi-Dimbira and 1980 km2 Upper-Didesa watersheds. The linear reservoir model storage coefficient parameter shows an increasing trend with time for the 41 km2 Sokoru watershed which is afforested, indicating faster drainage and reduction in storage. Our work highlights that considering storage–discharge relationships may be useful for assessing the impacts of forest cover change on water resources in regions where land use change is active and rapid.

Tracer-aided assessment of catchment groundwater dynamics and residence time

Sustainable groundwater management is becoming increasingly important due to intensifying water deficits around the world, which highlights the necessities and challenges to explore the dynamics of groundwater at the catchment-scale. In this paper, a tracer-aided approach has been developed and applied to quantify the relationships between groundwater storage and discharge, upon which the dynamics of groundwater storage and its residence time are assessed. Robust nonlinear storage-discharge relationships are found for the eight studied catchments located in a headwater region of the Murray-Darling Basin, Australia. The dynamics of groundwater storage for all the studied catchments largely show synchronization with regional climate. The estimated highest and active groundwater storages in a year are more responsive to precipitation than the lowest storages. For all the studied catchments, during dry seasons without recharge, the depletion rate of groundwater is found to decrease with the decline in groundwater storage, which can be ascribed to the vertical heterogeneity of their unconfined aquifers. The mean residence time of groundwater represented by MRT75 (i.e. time taken for groundwater storage to diminish from its mean level to the 75th percentile) varies between 57 and 111 days across the studied catchments, suggesting considerable hydrogeological differences among the studied catchments. The groundwater dynamics observed in this research could contribute to improving hydrogeological model performance in simulating the connection between groundwater and surface water at the catchment-scale. Moreover, the findings could serve to develop guidelines for groundwater extraction when considering the constraints of environmental flow requirements.

Simple Catchments and Where to Find Them: The Storage-Discharge Relationship as a Proxy for Catchment Complexity

Hydrological theory often assumes an exponential relationship between storage and discharge, but how often do we find such a behavior in real catchments? We analyze catchment attributes, discharge and weather conditions from 1992 to 2018 for 88 catchments in Hesse, Germany. All catchments have similar weather conditions, but a wide range of catchment characteristics. We find that only a fraction of catchments follow a roughly exponential behavior in their storage-discharge relationship. Far more catchments are complex and depict irregular patterns with even extreme variation from 1 year to another. This large set of catchments with similar weather conditions reveals that physical attributes that drive catchment complexity are diverse and include soil permeability, hydraulic conductivity, geology, and soil type. We link the examined simple and complex behavior to the fill and spill hypotheses and the interconnectedness of the catchments. Simpler catchments have more preferential flow and more connected hillslopes and thus lower runoff generation thresholds. This creates a more straightforward relationship between storage and discharge.

Characterization of Basin-Scale Dynamic Storage–Discharge Relationship Using Daily GRACE Based Storage Anomaly Data

Despite the fact that streamflow occurs mainly due to depletion of storage, our knowledge on how a drainage basin stores and releases water is very limited due to measurement limitations. A window of opportunity, however, is provided to us by GRACE (Gravity Recovery and Climate Experiment) satellite mission that provides storage anomaly (San) data. Many studies have explored a range of potential applications of San data such as flood forecasting. Here we argue that the capability of GRACE satellite mission has not been fully explored as most of the studies in the past have performed analysis using monthly San data for large river basins. In this study, we use daily San data for several mid-sized catchments to perform storage–discharge analysis. Our results support the earlier notion that storage–discharge relationship is highly dynamic. Furthermore, we demonstrate that San data can be exploited for prediction of k of the Brutsaet–Nieber equation −dQ/dt=kQα (Q is discharge at time t). For comparison we also use storage information provided by Catchment Land Surface Model (CLSM) as well as past discharge information to predict k. Our results suggest that GRACE based storage information can be used to predict k reasonably well in gauged as well as ungauged basins.